[ { "title": "QQ", "content": "Write a program which prints multiplication tables in the following format:\n\n1x1=1\n1x2=2\n.\n.\n9x8=72\n9x9=81\n template for c:\n#include\n\nint main(){\n\n return 0;\n}\n template for c++:\n#include\nusing namespace std;\n\nint main(){\n\n return 0;\n}\n template for java:\nclass Main{\n public static void main(String[] a){\n\n }\n}", "constraint": "", "input": "No input.", "output": "1x1=1\n1x2=2\n.\n.\n9x8=72\n9x9=81", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p00000", "ProblemText": "Task Description: Write a program which prints multiplication tables in the following format:\n\n1x1=1\n1x2=2\n.\n.\n9x8=72\n9x9=81\n template for c:\n#include\n\nint main(){\n\n return 0;\n}\n template for c++:\n#include\nusing namespace std;\n\nint main(){\n\n return 0;\n}\n template for java:\nclass Main{\n public static void main(String[] a){\n\n }\n}\nTask Input: No input.\nTask Output: 1x1=1\n1x2=2\n.\n.\n9x8=72\n9x9=81\n\n" }, { "title": "List of Top 3 Hills", "content": "There is a data which provides heights (in meter) of mountains. The data is only for ten mountains.\n\nWrite a program which prints heights of the top three mountains in descending order.", "constraint": "0 <= height of mountain (integer) <= 10,000", "input": "Height of mountain 1\nHeight of mountain 2\nHeight of mountain 3\n .\n .\nHeight of mountain 10", "output": "Height of the 1st mountain\nHeight of the 2nd mountain\nHeight of the 3rd mountain", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1819\n2003\n876\n2840\n1723\n1673\n3776\n2848\n1592\n922\n output: 3776\n2848\n2840", "input: 100\n200\n300\n400\n500\n600\n700\n800\n900\n900\n output: 900\n900\n800"], "Pid": "p00001", "ProblemText": "Task Description: There is a data which provides heights (in meter) of mountains. The data is only for ten mountains.\n\nWrite a program which prints heights of the top three mountains in descending order.\nTask Constraint: 0 <= height of mountain (integer) <= 10,000\nTask Input: Height of mountain 1\nHeight of mountain 2\nHeight of mountain 3\n .\n .\nHeight of mountain 10\nTask Output: Height of the 1st mountain\nHeight of the 2nd mountain\nHeight of the 3rd mountain\nTask Samples: input: 1819\n2003\n876\n2840\n1723\n1673\n3776\n2848\n1592\n922\n output: 3776\n2848\n2840\ninput: 100\n200\n300\n400\n500\n600\n700\n800\n900\n900\n output: 900\n900\n800\n\n" }, { "title": "Digit Number", "content": "Write a program which computes the digit number of sum of two integers a and b.", "constraint": "0 <= a, b <= 1,000,000\n\nThe number of datasets <= 200", "input": "There are several test cases. Each test case consists of two non-negative integers a and b which are separeted by a space in a line. The input terminates with EOF.", "output": "Print the number of digits of a + b for each data set.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 7\n1 99\n1000 999\n output: 2\n3\n4"], "Pid": "p00002", "ProblemText": "Task Description: Write a program which computes the digit number of sum of two integers a and b.\nTask Constraint: 0 <= a, b <= 1,000,000\n\nThe number of datasets <= 200\nTask Input: There are several test cases. Each test case consists of two non-negative integers a and b which are separeted by a space in a line. The input terminates with EOF.\nTask Output: Print the number of digits of a + b for each data set.\nTask Samples: input: 5 7\n1 99\n1000 999\n output: 2\n3\n4\n\n" }, { "title": "Is it a Right Triangle?", "content": "Write a program which judges wheather given length of three side form a right triangle. Print \"YES\" if the given sides (integers) form a right triangle, \"NO\" if not so.", "constraint": "1 <= length of the side <= 1,000\n\n N <= 1,000", "input": "Input consists of several data sets. In the first line, the number of data set, N is given. Then, N lines follow, each line corresponds to a data set. A data set consists of three integers separated by a single space.", "output": "For each data set, print \"YES\" or \"NO\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n4 3 5\n4 3 6\n8 8 8\n output: YES\nNO\nNO"], "Pid": "p00003", "ProblemText": "Task Description: Write a program which judges wheather given length of three side form a right triangle. Print \"YES\" if the given sides (integers) form a right triangle, \"NO\" if not so.\nTask Constraint: 1 <= length of the side <= 1,000\n\n N <= 1,000\nTask Input: Input consists of several data sets. In the first line, the number of data set, N is given. Then, N lines follow, each line corresponds to a data set. A data set consists of three integers separated by a single space.\nTask Output: For each data set, print \"YES\" or \"NO\".\nTask Samples: input: 3\n4 3 5\n4 3 6\n8 8 8\n output: YES\nNO\nNO\n\n" }, { "title": "Simultaneous Equation", "content": "Write a program which solve a simultaneous equation: \n\n ax + by = c\n dx + ey = f\nThe program should print x and y for given a, b, c, d, e and f (-1,000 <= a, b, c, d, e, f <= 1,000). You can suppose that given equation has a unique solution.", "constraint": "", "input": "The input consists of several data sets, 1 line for each data set. In a data set, there will be a, b, c, d, e, f separated by a single space. The input terminates with EOF.", "output": "For each data set, print x and y separated by a single space. Print the solution to three places of decimals. Round off the solution to three decimal places.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 3 4 5 6\n2 -1 -2 -1 -1 -5\n output: -1.000 2.000\n1.000 4.000", "input: 2 -1 -3 1 -1 -3\n2 -1 -3 -9 9 27\n output: 0.000 3.000\n0.000 3.000"], "Pid": "p00004", "ProblemText": "Task Description: Write a program which solve a simultaneous equation: \n\n ax + by = c\n dx + ey = f\nThe program should print x and y for given a, b, c, d, e and f (-1,000 <= a, b, c, d, e, f <= 1,000). You can suppose that given equation has a unique solution.\nTask Input: The input consists of several data sets, 1 line for each data set. In a data set, there will be a, b, c, d, e, f separated by a single space. The input terminates with EOF.\nTask Output: For each data set, print x and y separated by a single space. Print the solution to three places of decimals. Round off the solution to three decimal places.\nTask Samples: input: 1 2 3 4 5 6\n2 -1 -2 -1 -1 -5\n output: -1.000 2.000\n1.000 4.000\ninput: 2 -1 -3 1 -1 -3\n2 -1 -3 -9 9 27\n output: 0.000 3.000\n0.000 3.000\n\n" }, { "title": "GCD and LCM", "content": "Write a program which computes the greatest common divisor (GCD) and the least common multiple (LCM) of given a and b.", "constraint": "0 < a, b <= 2,000,000,000\n\n LCM(a, b) <= 2,000,000,000\n\n The number of data sets <= 50", "input": "Input consists of several data sets. Each data set contains a and b separated by a single space in a line. The input terminates with EOF.", "output": "For each data set, print GCD and LCM separated by a single space in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 6\n50000000 30000000\n output: 2 24\n10000000 150000000"], "Pid": "p00005", "ProblemText": "Task Description: Write a program which computes the greatest common divisor (GCD) and the least common multiple (LCM) of given a and b.\nTask Constraint: 0 < a, b <= 2,000,000,000\n\n LCM(a, b) <= 2,000,000,000\n\n The number of data sets <= 50\nTask Input: Input consists of several data sets. Each data set contains a and b separated by a single space in a line. The input terminates with EOF.\nTask Output: For each data set, print GCD and LCM separated by a single space in a line.\nTask Samples: input: 8 6\n50000000 30000000\n output: 2 24\n10000000 150000000\n\n" }, { "title": "Reverse Sequence", "content": "Write a program which reverses a given string str.", "constraint": "", "input": "str (the size of str <= 20) is given in a line.", "output": "Print the reversed str in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: w32nimda\n output: admin23w"], "Pid": "p00006", "ProblemText": "Task Description: Write a program which reverses a given string str.\nTask Input: str (the size of str <= 20) is given in a line.\nTask Output: Print the reversed str in a line.\nTask Samples: input: w32nimda\n output: admin23w\n\n" }, { "title": "Debt Hell", "content": "Your friend who lives in undisclosed country is involved in debt. He is borrowing 100,000-yen from a loan shark. The loan shark adds 5% interest of the debt and rounds it to the nearest 1,000 above week by week.\n\nWrite a program which computes the amount of the debt in n weeks.", "constraint": "", "input": "An integer n (0 <= n <= 100) is given in a line.", "output": "Print the amout of the debt in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n output: 130000"], "Pid": "p00007", "ProblemText": "Task Description: Your friend who lives in undisclosed country is involved in debt. He is borrowing 100,000-yen from a loan shark. The loan shark adds 5% interest of the debt and rounds it to the nearest 1,000 above week by week.\n\nWrite a program which computes the amount of the debt in n weeks.\nTask Input: An integer n (0 <= n <= 100) is given in a line.\nTask Output: Print the amout of the debt in a line.\nTask Samples: input: 5\n output: 130000\n\n" }, { "title": "Sum of 4 Integers", "content": "Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 <= a, b, c, d <= 9) which meet the following equality: \n\na + b + c + d = n\nFor example, for n = 35, we have 4 different combinations of (a, b, c, d): (8,9,9,9), (9,8,9,9), (9,9,8,9), and (9,9,9,8).", "constraint": "", "input": "The input consists of several datasets. Each dataset consists of n (1 <= n <= 50) in a line. The number of datasets is less than or equal to 50.", "output": "Print the number of combination in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 35\n1\n output: 4\n4"], "Pid": "p00008", "ProblemText": "Task Description: Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 <= a, b, c, d <= 9) which meet the following equality: \n\na + b + c + d = n\nFor example, for n = 35, we have 4 different combinations of (a, b, c, d): (8,9,9,9), (9,8,9,9), (9,9,8,9), and (9,9,9,8).\nTask Input: The input consists of several datasets. Each dataset consists of n (1 <= n <= 50) in a line. The number of datasets is less than or equal to 50.\nTask Output: Print the number of combination in a line.\nTask Samples: input: 35\n1\n output: 4\n4\n\n" }, { "title": "Prime Number", "content": "Write a program which reads an integer n and prints the number of prime numbers which are less than or equal to n. A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2,3,5 and 7.", "constraint": "", "input": "Input consists of several datasets. Each dataset has an integer n (1 <= n <= 999,999) in a line.\n\nThe number of datasets is less than or equal to 30.", "output": "For each dataset, prints the number of prime numbers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\n3\n11\n output: 4\n2\n5"], "Pid": "p00009", "ProblemText": "Task Description: Write a program which reads an integer n and prints the number of prime numbers which are less than or equal to n. A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2,3,5 and 7.\nTask Input: Input consists of several datasets. Each dataset has an integer n (1 <= n <= 999,999) in a line.\n\nThe number of datasets is less than or equal to 30.\nTask Output: For each dataset, prints the number of prime numbers.\nTask Samples: input: 10\n3\n11\n output: 4\n2\n5\n\n" }, { "title": "Circumscribed Circle of A Triangle.", "content": "Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.", "constraint": "$-100 <= x_1, y_1, x_2, y_2, x_3, y_3 <= 100$\n\n$ n <= 20$", "input": "Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of: \n\n$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$\nin a line. All the input are real numbers.", "output": "For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n0.0 0.0 2.0 0.0 2.0 2.0\n output: 1.000 1.000 1.414"], "Pid": "p00010", "ProblemText": "Task Description: Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.\nTask Constraint: $-100 <= x_1, y_1, x_2, y_2, x_3, y_3 <= 100$\n\n$ n <= 20$\nTask Input: Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of: \n\n$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$\nin a line. All the input are real numbers.\nTask Output: For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.\nTask Samples: input: 1\n0.0 0.0 2.0 0.0 2.0 2.0\n output: 1.000 1.000 1.414\n\n" }, { "title": "Drawing Lots", "content": "Let's play Amidakuji. \n\nIn the following example, there are five vertical lines and four horizontal lines. The horizontal lines can intersect (jump across) the vertical lines.\n\nIn the starting points (top of the figure), numbers are assigned to vertical lines in ascending order from left to right. At the first step, 2 and 4 are swaped by the first horizontal line which connects second and fourth vertical lines (we call this operation (2,4)). Likewise, we perform (3,5), (1,2) and (3,4), then obtain \"4 1 2 5 3\" in the bottom.\n\nYour task is to write a program which reads the number of vertical lines w and configurations of horizontal lines and prints the final state of the Amidakuji. In the starting pints, numbers 1,2,3, . . . , w are assigne to the vertical lines from left to right.", "constraint": "", "input": "w\nn\na_1, b_1\na_2, b_2\n.\n.\na_n, b_n\n\nw (w <= 30) is the number of vertical lines. n (n <= 30) is the number of horizontal lines. A pair of two integers a_i and b_i delimited by a comma represents the i-th horizontal line.", "output": "The number which should be under the 1st (leftmost) vertical line\nThe number which should be under the 2nd vertical line\n: \nThe number which should be under the w-th vertical line", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n4\n2,4\n3,5\n1,2\n3,4\n output: 4\n1\n2\n5\n3"], "Pid": "p00011", "ProblemText": "Task Description: Let's play Amidakuji. \n\nIn the following example, there are five vertical lines and four horizontal lines. The horizontal lines can intersect (jump across) the vertical lines.\n\nIn the starting points (top of the figure), numbers are assigned to vertical lines in ascending order from left to right. At the first step, 2 and 4 are swaped by the first horizontal line which connects second and fourth vertical lines (we call this operation (2,4)). Likewise, we perform (3,5), (1,2) and (3,4), then obtain \"4 1 2 5 3\" in the bottom.\n\nYour task is to write a program which reads the number of vertical lines w and configurations of horizontal lines and prints the final state of the Amidakuji. In the starting pints, numbers 1,2,3, . . . , w are assigne to the vertical lines from left to right.\nTask Input: w\nn\na_1, b_1\na_2, b_2\n.\n.\na_n, b_n\n\nw (w <= 30) is the number of vertical lines. n (n <= 30) is the number of horizontal lines. A pair of two integers a_i and b_i delimited by a comma represents the i-th horizontal line.\nTask Output: The number which should be under the 1st (leftmost) vertical line\nThe number which should be under the 2nd vertical line\n: \nThe number which should be under the w-th vertical line\nTask Samples: input: 5\n4\n2,4\n3,5\n1,2\n3,4\n output: 4\n1\n2\n5\n3\n\n" }, { "title": "A Point in a Triangle", "content": "There is a triangle formed by three points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ on a plain.\n\nWrite a program which prints \"YES\" if a point $P$ $(x_p, y_p)$ is in the triangle and \"NO\" if not.", "constraint": "You can assume that:\n\n$ -100 <= x_1, y_1, x_2, y_2, x_3, y_3, x_p, y_p <= 100$\n\n1.0 $<=$ Length of each side of a tringle\n\n0.001 $<=$ Distance between $P$ and each side of a triangle", "input": "Input consists of several datasets. Each dataset consists of: \n\n$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_p$ $y_p$\n\nAll the input are real numbers. Input ends with EOF. The number of datasets is less than or equal to 100.", "output": "For each dataset, print \"YES\" or \"NO\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0.0 0.0 2.0 0.0 2.0 2.0 1.5 0.5\n0.0 0.0 1.0 4.0 5.0 3.0 -1.0 3.0\n output: YES\nNO"], "Pid": "p00012", "ProblemText": "Task Description: There is a triangle formed by three points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ on a plain.\n\nWrite a program which prints \"YES\" if a point $P$ $(x_p, y_p)$ is in the triangle and \"NO\" if not.\nTask Constraint: You can assume that:\n\n$ -100 <= x_1, y_1, x_2, y_2, x_3, y_3, x_p, y_p <= 100$\n\n1.0 $<=$ Length of each side of a tringle\n\n0.001 $<=$ Distance between $P$ and each side of a triangle\nTask Input: Input consists of several datasets. Each dataset consists of: \n\n$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_p$ $y_p$\n\nAll the input are real numbers. Input ends with EOF. The number of datasets is less than or equal to 100.\nTask Output: For each dataset, print \"YES\" or \"NO\" in a line.\nTask Samples: input: 0.0 0.0 2.0 0.0 2.0 2.0 1.5 0.5\n0.0 0.0 1.0 4.0 5.0 3.0 -1.0 3.0\n output: YES\nNO\n\n" }, { "title": "Switching Railroad Cars", "content": "This figure shows railway tracks for reshuffling cars. The rail tracks end in the bottom and the top-left rail track is used for the entrace and the top-right rail track is used for the exit. Ten cars, which have numbers from 1 to 10 respectively, use the rail tracks.\n\nWe can simulate the movement (comings and goings) of the cars as follow: \n\nAn entry of a car is represented by its number.\n\nAn exit of a car is represented by 0\nFor example, a sequence\n\n1\n6\n0\n8\n10\n\ndemonstrates that car 1 and car 6 enter to the rail tracks in this order, car 6 exits from the rail tracks, and then car 8 and car 10 enter.\n\nWrite a program which simulates comings and goings of the cars which are represented by the sequence of car numbers. The program should read the sequence of car numbers and 0, and print numbers of cars which exit from the rail tracks in order. At the first, there are no cars on the rail tracks. You can assume that 0 will not be given when there is no car on the rail tracks.", "constraint": "", "input": "car number\ncar number or 0\ncar number or 0\n .\n .\n .\ncar number or 0\n\nThe number of input lines is less than or equal to 100.", "output": "For each 0, print the car number.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n6\n0\n8\n10\n0\n0\n0\n output: 6\n10\n8\n1"], "Pid": "p00013", "ProblemText": "Task Description: This figure shows railway tracks for reshuffling cars. The rail tracks end in the bottom and the top-left rail track is used for the entrace and the top-right rail track is used for the exit. Ten cars, which have numbers from 1 to 10 respectively, use the rail tracks.\n\nWe can simulate the movement (comings and goings) of the cars as follow: \n\nAn entry of a car is represented by its number.\n\nAn exit of a car is represented by 0\nFor example, a sequence\n\n1\n6\n0\n8\n10\n\ndemonstrates that car 1 and car 6 enter to the rail tracks in this order, car 6 exits from the rail tracks, and then car 8 and car 10 enter.\n\nWrite a program which simulates comings and goings of the cars which are represented by the sequence of car numbers. The program should read the sequence of car numbers and 0, and print numbers of cars which exit from the rail tracks in order. At the first, there are no cars on the rail tracks. You can assume that 0 will not be given when there is no car on the rail tracks.\nTask Input: car number\ncar number or 0\ncar number or 0\n .\n .\n .\ncar number or 0\n\nThe number of input lines is less than or equal to 100.\nTask Output: For each 0, print the car number.\nTask Samples: input: 1\n6\n0\n8\n10\n0\n0\n0\n output: 6\n10\n8\n1\n\n" }, { "title": "Integral", "content": "Write a program which computes the area of a shape represented by the following three lines: \n\n$y = x^2$\n$y = 0$\n$x = 600$\n\n\n\nIt is clear that the area is $72000000$, if you use an integral you learn in high school. On the other hand, we can obtain an approximative area of the shape by adding up areas of many rectangles in the shape as shown in the following figure:\n\n$f(x) = x^2$\nThe approximative area $s$ where the width of the rectangles is $d$ is: \n\narea of rectangle where its width is $d$ and height is $f(d)$ $+$ \narea of rectangle where its width is $d$ and height is $f(2d)$ $+$ \narea of rectangle where its width is $d$ and height is $f(3d)$ $+$ \n. . . \narea of rectangle where its width is $d$ and height is $f(600 - d)$ \n\nThe more we decrease $d$, the higer-precision value which is close to $72000000$ we could obtain. Your program should read the integer $d$ which is a divisor of $600$, and print the area $s$.", "constraint": "", "input": "The input consists of several datasets. Each dataset consists of an integer $d$ in a line. The number of datasets is less than or equal to 20.", "output": "For each dataset, print the area $s$ in a liEnglish_Program_Question_new_fix_space.jsonne.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 20\n10\n output: 68440000\n70210000"], "Pid": "p00014", "ProblemText": "Task Description: Write a program which computes the area of a shape represented by the following three lines: \n\n$y = x^2$\n$y = 0$\n$x = 600$\n\n\n\nIt is clear that the area is $72000000$, if you use an integral you learn in high school. On the other hand, we can obtain an approximative area of the shape by adding up areas of many rectangles in the shape as shown in the following figure:\n\n$f(x) = x^2$\nThe approximative area $s$ where the width of the rectangles is $d$ is: \n\narea of rectangle where its width is $d$ and height is $f(d)$ $+$ \narea of rectangle where its width is $d$ and height is $f(2d)$ $+$ \narea of rectangle where its width is $d$ and height is $f(3d)$ $+$ \n. . . \narea of rectangle where its width is $d$ and height is $f(600 - d)$ \n\nThe more we decrease $d$, the higer-precision value which is close to $72000000$ we could obtain. Your program should read the integer $d$ which is a divisor of $600$, and print the area $s$.\nTask Input: The input consists of several datasets. Each dataset consists of an integer $d$ in a line. The number of datasets is less than or equal to 20.\nTask Output: For each dataset, print the area $s$ in a liEnglish_Program_Question_new_fix_space.jsonne.\nTask Samples: input: 20\n10\n output: 68440000\n70210000\n\n" }, { "title": "National Budget", "content": "A country has a budget of more than 81 trillion yen. We want to process such data, but conventional integer type which uses signed 32 bit can represent up to 2,147,483,647.\n\nYour task is to write a program which reads two integers (more than or equal to zero), and prints a sum of these integers.\n\nIf given integers or the sum have more than 80 digits, print \"overflow\".", "constraint": "", "input": "Input consists of several datasets. In the first line, the number of datasets N (1 <= N <= 50) is given. Each dataset consists of 2 lines:\n\nThe first integer\nThe second integer\n\nThe integer has at most 100 digits.", "output": "For each dataset, print the sum of given integers in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1000\n800\n9999999999999999999999999999999999999999\n1\n99999999999999999999999999999999999999999999999999999999999999999999999999999999\n1\n99999999999999999999999999999999999999999999999999999999999999999999999999999999\n0\n100000000000000000000000000000000000000000000000000000000000000000000000000000000\n1\n100000000000000000000000000000000000000000000000000000000000000000000000000000000\n100000000000000000000000000000000000000000000000000000000000000000000000000000000\n output: 1800\n10000000000000000000000000000000000000000\noverflow\n99999999999999999999999999999999999999999999999999999999999999999999999999999999\noverflow\noverflow"], "Pid": "p00015", "ProblemText": "Task Description: A country has a budget of more than 81 trillion yen. We want to process such data, but conventional integer type which uses signed 32 bit can represent up to 2,147,483,647.\n\nYour task is to write a program which reads two integers (more than or equal to zero), and prints a sum of these integers.\n\nIf given integers or the sum have more than 80 digits, print \"overflow\".\nTask Input: Input consists of several datasets. In the first line, the number of datasets N (1 <= N <= 50) is given. Each dataset consists of 2 lines:\n\nThe first integer\nThe second integer\n\nThe integer has at most 100 digits.\nTask Output: For each dataset, print the sum of given integers in a line.\nTask Samples: input: 6\n1000\n800\n9999999999999999999999999999999999999999\n1\n99999999999999999999999999999999999999999999999999999999999999999999999999999999\n1\n99999999999999999999999999999999999999999999999999999999999999999999999999999999\n0\n100000000000000000000000000000000000000000000000000000000000000000000000000000000\n1\n100000000000000000000000000000000000000000000000000000000000000000000000000000000\n100000000000000000000000000000000000000000000000000000000000000000000000000000000\n output: 1800\n10000000000000000000000000000000000000000\noverflow\n99999999999999999999999999999999999999999999999999999999999999999999999999999999\noverflow\noverflow\n\n" }, { "title": "", "content": "When a boy was cleaning up after his grand father passing, he found an old paper: In addition, other side of the paper says that \"go ahead a number of steps equivalent to the first integer, and turn clockwise by degrees equivalent to the second integer\". His grand mother says that Sanbonmatsu was standing at the center of town. However, now buildings are crammed side by side and people can not walk along exactly what the paper says in. Your task is to write a program which hunts for the treature on the paper. For simplicity, 1 step is equivalent to 1 meter. Input consists of several pairs of two integers (the first integer) and (the second integer) separated by a comma. Input ends with \"0,0\". Your program should print the coordinate (x, y) of the end point. There is the treature where x meters to the east and y meters to the north from the center of town. You can assume that d <= 100 and -180 <= t<=180.", "constraint": "", "input": "A sequence of pairs of integers d and t which end with \"0,0\".", "output": "Print the integer portion of x and y in a line respectively.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 56,65\n97,54\n64,-4\n55,76\n42,-27\n43,80\n87,-86\n55,-6\n89,34\n95,5\n0,0\n output: 171\n-302"], "Pid": "p00016", "ProblemText": "Task Description: When a boy was cleaning up after his grand father passing, he found an old paper: In addition, other side of the paper says that \"go ahead a number of steps equivalent to the first integer, and turn clockwise by degrees equivalent to the second integer\". His grand mother says that Sanbonmatsu was standing at the center of town. However, now buildings are crammed side by side and people can not walk along exactly what the paper says in. Your task is to write a program which hunts for the treature on the paper. For simplicity, 1 step is equivalent to 1 meter. Input consists of several pairs of two integers (the first integer) and (the second integer) separated by a comma. Input ends with \"0,0\". Your program should print the coordinate (x, y) of the end point. There is the treature where x meters to the east and y meters to the north from the center of town. You can assume that d <= 100 and -180 <= t<=180.\nTask Input: A sequence of pairs of integers d and t which end with \"0,0\".\nTask Output: Print the integer portion of x and y in a line respectively.\nTask Samples: input: 56,65\n97,54\n64,-4\n55,76\n42,-27\n43,80\n87,-86\n55,-6\n89,34\n95,5\n0,0\n output: 171\n-302\n\n" }, { "title": "Caesar Cipher", "content": "In cryptography, Caesar cipher is one of the simplest and most widely known encryption method. Caesar cipher is a type of substitution cipher in which each letter in the text is replaced by a letter some fixed number of positions down the alphabet. For example, with a shift of 1, 'a' would be replaced by 'b', 'b' would become 'c', 'y' would become 'z', 'z' would become 'a', and so on. In that case, a text: this is a pen is would become: uijt jt b qfo Write a program which reads a text encrypted by Caesar Chipher and prints the corresponding decoded text. The number of shift is secret and it depends on datasets, but you can assume that the decoded text includes any of the following words: \"the\", \"this\", or \"that\"", "constraint": "", "input": "Input consists of several datasets. Each dataset consists of texts in a line. Input ends with EOF. The text consists of lower-case letters, periods, space, and end-of-lines. Only the letters have been encrypted. A line consists of at most 80 characters.\n\nYou may assume that you can create one decoded text which includes any of \"the\", \"this\", or \"that\" from the given input text.\n\nThe number of datasets is less than or equal to 20.", "output": "Print decoded texts in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: xlmw mw xli tmgxyvi xlex m xsso mr xli xvmt.\n output: this is the picture that i took in the trip."], "Pid": "p00017", "ProblemText": "Task Description: In cryptography, Caesar cipher is one of the simplest and most widely known encryption method. Caesar cipher is a type of substitution cipher in which each letter in the text is replaced by a letter some fixed number of positions down the alphabet. For example, with a shift of 1, 'a' would be replaced by 'b', 'b' would become 'c', 'y' would become 'z', 'z' would become 'a', and so on. In that case, a text: this is a pen is would become: uijt jt b qfo Write a program which reads a text encrypted by Caesar Chipher and prints the corresponding decoded text. The number of shift is secret and it depends on datasets, but you can assume that the decoded text includes any of the following words: \"the\", \"this\", or \"that\"\nTask Input: Input consists of several datasets. Each dataset consists of texts in a line. Input ends with EOF. The text consists of lower-case letters, periods, space, and end-of-lines. Only the letters have been encrypted. A line consists of at most 80 characters.\n\nYou may assume that you can create one decoded text which includes any of \"the\", \"this\", or \"that\" from the given input text.\n\nThe number of datasets is less than or equal to 20.\nTask Output: Print decoded texts in a line.\nTask Samples: input: xlmw mw xli tmgxyvi xlex m xsso mr xli xvmt.\n output: this is the picture that i took in the trip.\n\n" }, { "title": "Sorting Five Numbers", "content": "Write a program which reads five numbers and sorts them in descending order.", "constraint": "", "input": "Input consists of five numbers a, b, c, d and e (-100000 <= a, b, c, d, e <= 100000). The five numbers are separeted by a space.", "output": "Print the ordered numbers in a line. Adjacent numbers should be separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 6 9 7 5\n output: 9 7 6 5 3"], "Pid": "p00018", "ProblemText": "Task Description: Write a program which reads five numbers and sorts them in descending order.\nTask Input: Input consists of five numbers a, b, c, d and e (-100000 <= a, b, c, d, e <= 100000). The five numbers are separeted by a space.\nTask Output: Print the ordered numbers in a line. Adjacent numbers should be separated by a space.\nTask Samples: input: 3 6 9 7 5\n output: 9 7 6 5 3\n\n" }, { "title": "Factorial", "content": "Write a program which reads an integer n and prints the factorial of n. You can assume that n <= 20.", "constraint": "", "input": "An integer n (1 <= n <= 20) in a line.", "output": "Print the factorial of n in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n output: 120"], "Pid": "p00019", "ProblemText": "Task Description: Write a program which reads an integer n and prints the factorial of n. You can assume that n <= 20.\nTask Input: An integer n (1 <= n <= 20) in a line.\nTask Output: Print the factorial of n in a line.\nTask Samples: input: 5\n output: 120\n\n" }, { "title": "Capitalize", "content": "Write a program which replace all the lower-case letters of a given text with the corresponding captital letters.", "constraint": "", "input": "A text including lower-case letters, periods, and space is given in a line. The number of characters in the text is less than or equal to 200.", "output": "Print the converted text.", "content_img": false, "lang": "en", "error": false, "samples": ["input: this is a pen.\n output: THIS IS A PEN."], "Pid": "p00020", "ProblemText": "Task Description: Write a program which replace all the lower-case letters of a given text with the corresponding captital letters.\nTask Input: A text including lower-case letters, periods, and space is given in a line. The number of characters in the text is less than or equal to 200.\nTask Output: Print the converted text.\nTask Samples: input: this is a pen.\n output: THIS IS A PEN.\n\n" }, { "title": "Parallelism", "content": "There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints \"YES\" and if not prints \"NO\".", "constraint": "", "input": "Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n <= 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers: \n\n$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$\n\nYou can assume that $-100 <= x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 <= 100$.\nEach value is a real number with at most 5 digits after the decimal point.", "output": "For each dataset, print \"YES\" or \"NO\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0\n3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0\n output: YES\nNO"], "Pid": "p00021", "ProblemText": "Task Description: There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints \"YES\" and if not prints \"NO\".\nTask Input: Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n <= 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers: \n\n$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$\n\nYou can assume that $-100 <= x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 <= 100$.\nEach value is a real number with at most 5 digits after the decimal point.\nTask Output: For each dataset, print \"YES\" or \"NO\" in a line.\nTask Samples: input: 2\n0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0\n3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0\n output: YES\nNO\n\n" }, { "title": "Maximum Sum Sequence", "content": "Given a sequence of numbers a_1, a_2, a_3, . . . , a_n, find the maximum sum of a contiguous subsequence of those numbers. Note that, a subsequence of one element is also a contiquous subsequence.", "constraint": "", "input": "The input consists of multiple datasets. Each data set consists of:\nn\na_1\na_2\n.\n.\na_n\n\n

\nYou can assume that 1 <= n <= 5000 and -100000 <= a_i <= 100000.\nThe input end with a line consisting of a single 0.", "output": "For each dataset, print the maximum sum in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n-5\n-1\n6\n4\n9\n-6\n-7\n13\n1\n2\n3\n2\n-2\n-1\n1\n2\n3\n2\n1\n-2\n1\n3\n1000\n-200\n201\n0\n output: 19\n14\n1001"], "Pid": "p00022", "ProblemText": "Task Description: Given a sequence of numbers a_1, a_2, a_3, . . . , a_n, find the maximum sum of a contiguous subsequence of those numbers. Note that, a subsequence of one element is also a contiquous subsequence.\nTask Input: The input consists of multiple datasets. Each data set consists of:\nn\na_1\na_2\n.\n.\na_n\n\n

\nYou can assume that 1 <= n <= 5000 and -100000 <= a_i <= 100000.\nThe input end with a line consisting of a single 0.\nTask Output: For each dataset, print the maximum sum in a line.\nTask Samples: input: 7\n-5\n-1\n6\n4\n9\n-6\n-7\n13\n1\n2\n3\n2\n-2\n-1\n1\n2\n3\n2\n1\n-2\n1\n3\n1000\n-200\n201\n0\n output: 19\n14\n1001\n\n" }, { "title": "Circles Intersection", "content": "You are given circle $A$ with radius $r_a$ and with central coordinate $(x_a, y_a)$ and circle $B$ with radius $r_b$ and with central coordinate $(x_b, y_b)$.\n\nWrite a program which prints:\n\n\"2\" if $B$ is in $A$,\n\n\"-2\" if $A$ is in $B$, \n\n\"1\" if circumference of $A$ and $B$ intersect, and\n\n\"0\" if $A$ and $B$ do not overlap.\nYou may assume that $A$ and $B$ are not identical.", "constraint": "", "input": "The input consists of multiple datasets. The first line consists of an integer $N$ ($N <= 50$), the number of datasets. There will be $N$ lines where each line represents each dataset. Each data set consists of real numbers: \n\n$x_a$ $y_a$ $r_a$ $x_b$ $y_b$ $r_b$", "output": "For each dataset, print 2, -2,1, or 0 in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0.0 0.0 5.0 0.0 0.0 4.0\n0.0 0.0 2.0 4.1 0.0 2.0\n output: 2\n0"], "Pid": "p00023", "ProblemText": "Task Description: You are given circle $A$ with radius $r_a$ and with central coordinate $(x_a, y_a)$ and circle $B$ with radius $r_b$ and with central coordinate $(x_b, y_b)$.\n\nWrite a program which prints:\n\n\"2\" if $B$ is in $A$,\n\n\"-2\" if $A$ is in $B$, \n\n\"1\" if circumference of $A$ and $B$ intersect, and\n\n\"0\" if $A$ and $B$ do not overlap.\nYou may assume that $A$ and $B$ are not identical.\nTask Input: The input consists of multiple datasets. The first line consists of an integer $N$ ($N <= 50$), the number of datasets. There will be $N$ lines where each line represents each dataset. Each data set consists of real numbers: \n\n$x_a$ $y_a$ $r_a$ $x_b$ $y_b$ $r_b$\nTask Output: For each dataset, print 2, -2,1, or 0 in a line.\nTask Samples: input: 2\n0.0 0.0 5.0 0.0 0.0 4.0\n0.0 0.0 2.0 4.1 0.0 2.0\n output: 2\n0\n\n" }, { "title": "Physical Experiments", "content": "Ignoring the air resistance, velocity of a freely falling object $v$ after $t$ seconds and its drop $y$ in $t$ seconds are represented by the following formulas: \n\n$ v = 9.8 t $\n$ y = 4.9 t^2 $\n\nA person is trying to drop down a glass ball and check whether it will crack. Your task is to write a program to help this experiment.\n\nYou are given the minimum velocity to crack the ball. Your program should print the lowest possible floor of a building to crack the ball. The height of the $N$ floor of the building is defined by $5 * N - 5$.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset, a line, consists of the minimum velocity v (0 < v < 200) to crack the ball. The value is given by a decimal fraction, with at most 4 digits after the decimal point. The input ends with EOF. The number of datasets is less than or equal to 50.", "output": "For each dataset, print the lowest possible floor where the ball cracks.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 25.4\n25.4\n output: 8\n8"], "Pid": "p00024", "ProblemText": "Task Description: Ignoring the air resistance, velocity of a freely falling object $v$ after $t$ seconds and its drop $y$ in $t$ seconds are represented by the following formulas: \n\n$ v = 9.8 t $\n$ y = 4.9 t^2 $\n\nA person is trying to drop down a glass ball and check whether it will crack. Your task is to write a program to help this experiment.\n\nYou are given the minimum velocity to crack the ball. Your program should print the lowest possible floor of a building to crack the ball. The height of the $N$ floor of the building is defined by $5 * N - 5$.\nTask Input: The input consists of multiple datasets. Each dataset, a line, consists of the minimum velocity v (0 < v < 200) to crack the ball. The value is given by a decimal fraction, with at most 4 digits after the decimal point. The input ends with EOF. The number of datasets is less than or equal to 50.\nTask Output: For each dataset, print the lowest possible floor where the ball cracks.\nTask Samples: input: 25.4\n25.4\n output: 8\n8\n\n" }, { "title": "Hit and Blow", "content": "Let's play Hit and Blow game. A imagines four numbers and B guesses the numbers. After B picks out four numbers, A answers:\n\n The number of numbers which have the same place with numbers A imagined (Hit) \n\n The number of numbers included (but different place) in the numbers A imagined (Blow)\nFor example, if A imagined numbers:\n\n9 1 8 2\n\nand B chose:\n\n4 1 5 9\n\nA should say 1 Hit and 1 Blow.\n\nWrite a program which reads four numbers A imagined and four numbers B chose and prints the number of Hit and Blow respectively. You may assume that the four numbers are all different and within from 0 to 9.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset set consists of:\n\na_1 a_2 a_3 a_4\nb_1 b_2 b_3 b_4\n\n, where a_i (0 <= a_i <= 9) is i-th number A imagined and b_i (0 <= b_i <= 9) is i-th number B chose.\n\nThe input ends with EOF. The number of datasets is less than or equal to 50.", "output": "For each dataset, print the number of Hit and Blow in a line. These two numbers should be separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 1 8 2\n4 1 5 9\n4 6 8 2\n4 6 3 2\n output: 1 1\n3 0"], "Pid": "p00025", "ProblemText": "Task Description: Let's play Hit and Blow game. A imagines four numbers and B guesses the numbers. After B picks out four numbers, A answers:\n\n The number of numbers which have the same place with numbers A imagined (Hit) \n\n The number of numbers included (but different place) in the numbers A imagined (Blow)\nFor example, if A imagined numbers:\n\n9 1 8 2\n\nand B chose:\n\n4 1 5 9\n\nA should say 1 Hit and 1 Blow.\n\nWrite a program which reads four numbers A imagined and four numbers B chose and prints the number of Hit and Blow respectively. You may assume that the four numbers are all different and within from 0 to 9.\nTask Input: The input consists of multiple datasets. Each dataset set consists of:\n\na_1 a_2 a_3 a_4\nb_1 b_2 b_3 b_4\n\n, where a_i (0 <= a_i <= 9) is i-th number A imagined and b_i (0 <= b_i <= 9) is i-th number B chose.\n\nThe input ends with EOF. The number of datasets is less than or equal to 50.\nTask Output: For each dataset, print the number of Hit and Blow in a line. These two numbers should be separated by a space.\nTask Samples: input: 9 1 8 2\n4 1 5 9\n4 6 8 2\n4 6 3 2\n output: 1 1\n3 0\n\n" }, { "title": "Dropping Ink", "content": "As shown in the following figure, there is a paper consisting of a grid structure where each cell is indicated by (x, y) coordinate system.\n\nWe are going to put drops of ink on the paper. A drop comes in three different sizes: Large, Medium, and Small. From the point of fall, the ink sinks into surrounding cells as shown in the figure depending on its size. In the figure, a star denotes the point of fall and a circle denotes the surrounding cells.\n\nOriginally, the paper is white that means for each cell the value of density is 0. The value of density is increased by 1 when the ink sinks into the corresponding cells.\n\nFor example, if we put a drop of Small ink at (1,2) and a drop of Medium ink at (3,2), the ink will sink as shown in the following figure (left side):\n\nIn the figure, density values of empty cells are 0. The ink sinking into out of the paper should be ignored as shown in the figure (top side). We can put several drops of ink at the same point.\n\nYour task is to write a program which reads a sequence of points of fall (x, y) with its size (Small = 1, Medium = 2, Large = 3), and prints the number of cells whose density value is 0. The program must also print the maximum value of density.\n\nYou may assume that the paper always consists of 10 * 10, and 0 <= x < 10,0 <= y < 10.", "constraint": "", "input": "x_1, y_1, s_1\nx_2, y_2, s_2\n :\n :\n\n(x_i, y_i) represents the position of the i-th drop and s_i denotes its size. The number of drops is less than or equal to 50.", "output": "Print the number of cells whose density value is 0 in first line. \nPrint the maximum value of density in the second line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2,5,3\n3,6,1\n3,4,2\n4,5,2\n3,6,3\n2,4,1\n output: 77\n5"], "Pid": "p00026", "ProblemText": "Task Description: As shown in the following figure, there is a paper consisting of a grid structure where each cell is indicated by (x, y) coordinate system.\n\nWe are going to put drops of ink on the paper. A drop comes in three different sizes: Large, Medium, and Small. From the point of fall, the ink sinks into surrounding cells as shown in the figure depending on its size. In the figure, a star denotes the point of fall and a circle denotes the surrounding cells.\n\nOriginally, the paper is white that means for each cell the value of density is 0. The value of density is increased by 1 when the ink sinks into the corresponding cells.\n\nFor example, if we put a drop of Small ink at (1,2) and a drop of Medium ink at (3,2), the ink will sink as shown in the following figure (left side):\n\nIn the figure, density values of empty cells are 0. The ink sinking into out of the paper should be ignored as shown in the figure (top side). We can put several drops of ink at the same point.\n\nYour task is to write a program which reads a sequence of points of fall (x, y) with its size (Small = 1, Medium = 2, Large = 3), and prints the number of cells whose density value is 0. The program must also print the maximum value of density.\n\nYou may assume that the paper always consists of 10 * 10, and 0 <= x < 10,0 <= y < 10.\nTask Input: x_1, y_1, s_1\nx_2, y_2, s_2\n :\n :\n\n(x_i, y_i) represents the position of the i-th drop and s_i denotes its size. The number of drops is less than or equal to 50.\nTask Output: Print the number of cells whose density value is 0 in first line. \nPrint the maximum value of density in the second line.\nTask Samples: input: 2,5,3\n3,6,1\n3,4,2\n4,5,2\n3,6,3\n2,4,1\n output: 77\n5\n\n" }, { "title": "What day is today?", "content": "Your task is to write a program which reads a date (from 2004/1/1 to 2004/12/31) and prints the day of the date. Jan. 1,2004, is Thursday. Note that 2004 is a leap year and we have Feb. 29.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset consists of two integers m and d separated by a single space in a line. These integers respectively represent the month and the day. \n\nThe number of datasets is less than or equal to 50.", "output": "For each dataset, print the day (please see the following words) in a line.\n\nMonday\nTuesday\nWednesday\nThursday\nFriday\nSaturday\nSunday", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1\n2 29\n0 0\n output: Thursday\nSunday"], "Pid": "p00027", "ProblemText": "Task Description: Your task is to write a program which reads a date (from 2004/1/1 to 2004/12/31) and prints the day of the date. Jan. 1,2004, is Thursday. Note that 2004 is a leap year and we have Feb. 29.\nTask Input: The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset consists of two integers m and d separated by a single space in a line. These integers respectively represent the month and the day. \n\nThe number of datasets is less than or equal to 50.\nTask Output: For each dataset, print the day (please see the following words) in a line.\n\nMonday\nTuesday\nWednesday\nThursday\nFriday\nSaturday\nSunday\nTask Samples: input: 1 1\n2 29\n0 0\n output: Thursday\nSunday\n\n" }, { "title": "Mode Value", "content": "Your task is to write a program which reads a sequence of integers and prints mode values of the sequence.\nThe mode value is the element which occurs most frequently.", "constraint": "", "input": "A sequence of integers a_i (1 <= a_i <= 100). The number of integers is less than or equals to 100.", "output": "Print the mode values. If there are several mode values, print them in ascending order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n6\n3\n5\n8\n7\n5\n3\n9\n7\n3\n4\n output: 3\n5\nFor example, 3 and 5 respectively occur three times, 7 occurs two times, and others occur only one. So, the mode values are 3 and 5."], "Pid": "p00028", "ProblemText": "Task Description: Your task is to write a program which reads a sequence of integers and prints mode values of the sequence.\nThe mode value is the element which occurs most frequently.\nTask Input: A sequence of integers a_i (1 <= a_i <= 100). The number of integers is less than or equals to 100.\nTask Output: Print the mode values. If there are several mode values, print them in ascending order.\nTask Samples: input: 5\n6\n3\n5\n8\n7\n5\n3\n9\n7\n3\n4\n output: 3\n5\nFor example, 3 and 5 respectively occur three times, 7 occurs two times, and others occur only one. So, the mode values are 3 and 5.\n\n" }, { "title": "English Sentence", "content": "Your task is to write a program which reads a text and prints two words. The first one is the word which is arise most frequently in the text. The second one is the word which has the maximum number of letters.\n\nThe text includes only alphabetical characters and spaces. A word is a sequence of letters which is separated by the spaces.", "constraint": "", "input": "A text is given in a line. You can assume the following conditions:\n\nThe number of letters in the text is less than or equal to 1000.\n\n The number of letters in a word is less than or equal to 32.\n\n There is only one word which is arise most frequently in given text.\n\n There is only one word which has the maximum number of letters in given text.", "output": "The two words separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: Thank you for your mail and your lectures\n output: your lectures"], "Pid": "p00029", "ProblemText": "Task Description: Your task is to write a program which reads a text and prints two words. The first one is the word which is arise most frequently in the text. The second one is the word which has the maximum number of letters.\n\nThe text includes only alphabetical characters and spaces. A word is a sequence of letters which is separated by the spaces.\nTask Input: A text is given in a line. You can assume the following conditions:\n\nThe number of letters in the text is less than or equal to 1000.\n\n The number of letters in a word is less than or equal to 32.\n\n There is only one word which is arise most frequently in given text.\n\n There is only one word which has the maximum number of letters in given text.\nTask Output: The two words separated by a space.\nTask Samples: input: Thank you for your mail and your lectures\n output: your lectures\n\n" }, { "title": "Sale Result", "content": "There is data on sales of your company. Your task is to write a program which identifies good workers.\n\nThe program should read a list of data where each item includes the employee ID i, the amount of sales q and the corresponding unit price p. Then, the program should print IDs of employees whose total sales proceeds (i. e. sum of p * q) is greater than or equal to 1,000,000 in the order of inputting. If there is no such employees, the program should print \"NA\". You can suppose that n < 4000, and each employee has an unique ID. The unit price p is less than or equal to 1,000,000 and the amount of sales q is less than or equal to 100,000.", "constraint": "", "input": "The input consists of several datasets. The input ends with a line including a single 0. Each dataset consists of:\n\nn (the number of data in the list)\ni p q\ni p q\n :\n :\ni p q", "output": "For each dataset, print a list of employee IDs or a text \"NA\"", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1001 2000 520\n1002 1800 450\n1003 1600 625\n1001 200 1220\n2\n1001 100 3\n1005 1000 100\n2\n2013 5000 100\n2013 5000 100\n0\n output: 1001\n1003\nNA\n2013"], "Pid": "p00100", "ProblemText": "Task Description: There is data on sales of your company. Your task is to write a program which identifies good workers.\n\nThe program should read a list of data where each item includes the employee ID i, the amount of sales q and the corresponding unit price p. Then, the program should print IDs of employees whose total sales proceeds (i. e. sum of p * q) is greater than or equal to 1,000,000 in the order of inputting. If there is no such employees, the program should print \"NA\". You can suppose that n < 4000, and each employee has an unique ID. The unit price p is less than or equal to 1,000,000 and the amount of sales q is less than or equal to 100,000.\nTask Input: The input consists of several datasets. The input ends with a line including a single 0. Each dataset consists of:\n\nn (the number of data in the list)\ni p q\ni p q\n :\n :\ni p q\nTask Output: For each dataset, print a list of employee IDs or a text \"NA\"\nTask Samples: input: 4\n1001 2000 520\n1002 1800 450\n1003 1600 625\n1001 200 1220\n2\n1001 100 3\n1005 1000 100\n2\n2013 5000 100\n2013 5000 100\n0\n output: 1001\n1003\nNA\n2013\n\n" }, { "title": "Aizu PR", "content": "An English booklet has been created for publicizing Aizu to the world.\nWhen you read it carefully, you found a misnomer (an error in writing) on the last name of Masayuki Hoshina, the lord of the Aizu domain. The booklet says \"Hoshino\" not \"Hoshina\".\n\nYour task is to write a program which replace all the words \"Hoshino\" with \"Hoshina\". You can assume that the number of characters in a text is less than or equal to 1000.", "constraint": "", "input": "The input consists of several datasets. There will be the number of datasets n in the first line. There will be n lines. A line consisting of english texts will be given for each dataset.", "output": "For each dataset, print the converted texts in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nHoshino\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\n output: Hoshina\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa."], "Pid": "p00101", "ProblemText": "Task Description: An English booklet has been created for publicizing Aizu to the world.\nWhen you read it carefully, you found a misnomer (an error in writing) on the last name of Masayuki Hoshina, the lord of the Aizu domain. The booklet says \"Hoshino\" not \"Hoshina\".\n\nYour task is to write a program which replace all the words \"Hoshino\" with \"Hoshina\". You can assume that the number of characters in a text is less than or equal to 1000.\nTask Input: The input consists of several datasets. There will be the number of datasets n in the first line. There will be n lines. A line consisting of english texts will be given for each dataset.\nTask Output: For each dataset, print the converted texts in a line.\nTask Samples: input: 3\nHoshino\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\n output: Hoshina\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.\n\n" }, { "title": "Matrix-like Computation", "content": "Your task is to develop a tiny little part of spreadsheet software.\n\nWrite a program which adds up columns and rows of given table as shown in the following figure:", "constraint": "", "input": "The input consists of several datasets. Each dataset consists of:\n\nn (the size of row and column of the given table)\n1st row of the table\n2nd row of the table\n :\n :\nnth row of the table\n\nThe input ends with a line consisting of a single 0.", "output": "For each dataset, print the table with sums of rows and columns. Each item of the table should be aligned to the right with a margin for five digits. Please see the sample output for details.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n52 96 15 20\n86 22 35 45\n45 78 54 36\n16 86 74 55\n4\n52 96 15 20\n86 22 35 45\n45 78 54 36\n16 86 74 55\n0\n output: 52 96 15 20 183\n 86 22 35 45 188\n 45 78 54 36 213\n 16 86 74 55 231\n 199 282 178 156 815\n 52 96 15 20 183\n 86 22 35 45 188\n 45 78 54 36 213\n 16 86 74 55 231\n 199 282 178 156 815"], "Pid": "p00102", "ProblemText": "Task Description: Your task is to develop a tiny little part of spreadsheet software.\n\nWrite a program which adds up columns and rows of given table as shown in the following figure:\nTask Input: The input consists of several datasets. Each dataset consists of:\n\nn (the size of row and column of the given table)\n1st row of the table\n2nd row of the table\n :\n :\nnth row of the table\n\nThe input ends with a line consisting of a single 0.\nTask Output: For each dataset, print the table with sums of rows and columns. Each item of the table should be aligned to the right with a margin for five digits. Please see the sample output for details.\nTask Samples: input: 4\n52 96 15 20\n86 22 35 45\n45 78 54 36\n16 86 74 55\n4\n52 96 15 20\n86 22 35 45\n45 78 54 36\n16 86 74 55\n0\n output: 52 96 15 20 183\n 86 22 35 45 188\n 45 78 54 36 213\n 16 86 74 55 231\n 199 282 178 156 815\n 52 96 15 20 183\n 86 22 35 45 188\n 45 78 54 36 213\n 16 86 74 55 231\n 199 282 178 156 815\n\n" }, { "title": "Baseball Simulation", "content": "Ichiro likes baseball and has decided to write a program which simulates baseball.\nThe program reads events in an inning and prints score in that inning. There are only three events as follows:\nSingle hit\nput a runner on the first base.\n\nthe runner in the first base advances to the second base and the runner in the second base advances to the third base.\n\nthe runner in the third base advances to the home base (and go out of base) and a point is added to the score.\n\nHome run\nall the runners on base advance to the home base.\n\npoints are added to the score by an amount equal to the number of the runners plus one.\n\nOut\nThe number of outs is increased by 1.\n\nThe runners and the score remain stationary.\n\nThe inning ends with three-out.\nIchiro decided to represent these events using \"HIT\", \"HOMERUN\" and \"OUT\", respectively.\nWrite a program which reads events in an inning and prints score in that inning. You can assume that the number of events is less than or equal to 100.", "constraint": "", "input": "The input consists of several datasets. In the first line, the number of datasets n is given. Each dataset consists of a list of events (strings) in an inning.", "output": "For each dataset, prints the score in the corresponding inning.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\nHIT\nOUT\nHOMERUN\nHIT\nHIT\nHOMERUN\nHIT\nOUT\nHIT\nHIT\nHIT\nHIT\nOUT\nHIT\nHIT\nOUT\nHIT\nOUT\nOUT\n output: 7\n0"], "Pid": "p00103", "ProblemText": "Task Description: Ichiro likes baseball and has decided to write a program which simulates baseball.\nThe program reads events in an inning and prints score in that inning. There are only three events as follows:\nSingle hit\nput a runner on the first base.\n\nthe runner in the first base advances to the second base and the runner in the second base advances to the third base.\n\nthe runner in the third base advances to the home base (and go out of base) and a point is added to the score.\n\nHome run\nall the runners on base advance to the home base.\n\npoints are added to the score by an amount equal to the number of the runners plus one.\n\nOut\nThe number of outs is increased by 1.\n\nThe runners and the score remain stationary.\n\nThe inning ends with three-out.\nIchiro decided to represent these events using \"HIT\", \"HOMERUN\" and \"OUT\", respectively.\nWrite a program which reads events in an inning and prints score in that inning. You can assume that the number of events is less than or equal to 100.\nTask Input: The input consists of several datasets. In the first line, the number of datasets n is given. Each dataset consists of a list of events (strings) in an inning.\nTask Output: For each dataset, prints the score in the corresponding inning.\nTask Samples: input: 2\nHIT\nOUT\nHOMERUN\nHIT\nHIT\nHOMERUN\nHIT\nOUT\nHIT\nHIT\nHIT\nHIT\nOUT\nHIT\nHIT\nOUT\nHIT\nOUT\nOUT\n output: 7\n0\n\n" }, { "title": "Magic Tile", "content": "There is a magic room in a homestead. The room is paved with H * W tiles. There are five different tiles:\n\nTile with a east-pointing arrow\n\nTile with a west-pointing arrow\n\nTile with a south-pointing arrow\n\nTile with a north-pointing arrow\n\nTile with nothing\nOnce a person steps onto a tile which has an arrow, the mystic force makes the person go to the next tile pointed by the arrow. If the next tile has an arrow, the person moves to the next, ans so on. The person moves on until he/she steps onto a tile which does not have the arrow (the tile with nothing). The entrance of the room is at the northwest corner.\n\nYour task is to write a program which simulates the movement of the person in the room. The program should read strings which represent the room and print the last position of the person.\n\nThe input represents the room as seen from directly above, and up, down, left and right side of the input correspond to north, south, west and east side of the room respectively. The horizontal axis represents x-axis (from 0 to W-1, inclusive) and the vertical axis represents y-axis (from 0 to H-1, inclusive). The upper left tile corresponds to (0,0).\n\nThe following figure shows an example of the input:\n\n10 10\n>>>v. . >>>v\n. . . v. . ^. . v\n. . . >>>^. . v\n. . . . . . . . . v\n. v<<<<. . . v\n. v. . . ^. . . v\n. v. . . ^<<<<\n. v. . . . . . . .\n. v. . . ^. . . .\n. >>>>^. . . .\n\nCharacters represent tiles as follows:\n\n'>': Tile with a east-pointing arrow\n'<': Tile with a west-pointing arrow \n'^': Tile with a north-pointing arrow \n'v': Tile with a south-pointing arrow \n'. ': Tile with nothing\n\nIf the person goes in cycles forever, your program should print \"LOOP\". You may assume that the person never goes outside of the room.", "constraint": "", "input": "The input consists of multiple datasets. The input ends with a line which contains two 0. Each dataset consists of:\n\nH W\nH lines where each line contains W characters\n\nYou can assume that 0 < W, H < 101.", "output": "For each dataset, print the coordinate (X, Y) of the person or \"LOOP\" in a line. X and Y should be separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 10\n>>>v..>>>v\n...v..^..v\n>>>>>>^..v\n.........v\n.v<<<<...v\n.v.v.^...v\n.v.v.^<<<<\n.v.v.....v\n.v...^...v\n.>>>>^....\n6 10\n>>>>>>>>>v\n.........v\n.........v\n>>>>v....v\n^...v....v\n^<<<<<<<<<\n0 0\n output: 5 7\nLOOP"], "Pid": "p00104", "ProblemText": "Task Description: There is a magic room in a homestead. The room is paved with H * W tiles. There are five different tiles:\n\nTile with a east-pointing arrow\n\nTile with a west-pointing arrow\n\nTile with a south-pointing arrow\n\nTile with a north-pointing arrow\n\nTile with nothing\nOnce a person steps onto a tile which has an arrow, the mystic force makes the person go to the next tile pointed by the arrow. If the next tile has an arrow, the person moves to the next, ans so on. The person moves on until he/she steps onto a tile which does not have the arrow (the tile with nothing). The entrance of the room is at the northwest corner.\n\nYour task is to write a program which simulates the movement of the person in the room. The program should read strings which represent the room and print the last position of the person.\n\nThe input represents the room as seen from directly above, and up, down, left and right side of the input correspond to north, south, west and east side of the room respectively. The horizontal axis represents x-axis (from 0 to W-1, inclusive) and the vertical axis represents y-axis (from 0 to H-1, inclusive). The upper left tile corresponds to (0,0).\n\nThe following figure shows an example of the input:\n\n10 10\n>>>v. . >>>v\n. . . v. . ^. . v\n. . . >>>^. . v\n. . . . . . . . . v\n. v<<<<. . . v\n. v. . . ^. . . v\n. v. . . ^<<<<\n. v. . . . . . . .\n. v. . . ^. . . .\n. >>>>^. . . .\n\nCharacters represent tiles as follows:\n\n'>': Tile with a east-pointing arrow\n'<': Tile with a west-pointing arrow \n'^': Tile with a north-pointing arrow \n'v': Tile with a south-pointing arrow \n'. ': Tile with nothing\n\nIf the person goes in cycles forever, your program should print \"LOOP\". You may assume that the person never goes outside of the room.\nTask Input: The input consists of multiple datasets. The input ends with a line which contains two 0. Each dataset consists of:\n\nH W\nH lines where each line contains W characters\n\nYou can assume that 0 < W, H < 101.\nTask Output: For each dataset, print the coordinate (X, Y) of the person or \"LOOP\" in a line. X and Y should be separated by a space.\nTask Samples: input: 10 10\n>>>v..>>>v\n...v..^..v\n>>>>>>^..v\n.........v\n.v<<<<...v\n.v.v.^...v\n.v.v.^<<<<\n.v.v.....v\n.v...^...v\n.>>>>^....\n6 10\n>>>>>>>>>v\n.........v\n.........v\n>>>>v....v\n^...v....v\n^<<<<<<<<<\n0 0\n output: 5 7\nLOOP\n\n" }, { "title": "Book Index", "content": "Books are indexed. Write a program which reads a list of pairs of a word and a page number, and prints the word and a list of the corresponding page numbers.\n\nYou can assume that a word consists of at most 30 characters, and the page number is less than or equal to 1000. The number of pairs of a word and a page number is less than or equal to 100. A word never appear in a page more than once.\n\nThe words should be printed in alphabetical order and the page numbers should be printed in ascending order.", "constraint": "", "input": "word page_number\n :\n :", "output": "word\na_list_of_the_page_number\nword\na_list_of_the_Page_number\n :\n :", "content_img": false, "lang": "en", "error": false, "samples": ["input: style 12\neven 25\nintroduction 3\neasy 9\nstyle 7\ndocument 13\nstyle 21\neven 18\n output: document\n13\neasy\n9\neven\n18 25\nintroduction\n3\nstyle\n7 12 21"], "Pid": "p00105", "ProblemText": "Task Description: Books are indexed. Write a program which reads a list of pairs of a word and a page number, and prints the word and a list of the corresponding page numbers.\n\nYou can assume that a word consists of at most 30 characters, and the page number is less than or equal to 1000. The number of pairs of a word and a page number is less than or equal to 100. A word never appear in a page more than once.\n\nThe words should be printed in alphabetical order and the page numbers should be printed in ascending order.\nTask Input: word page_number\n :\n :\nTask Output: word\na_list_of_the_page_number\nword\na_list_of_the_Page_number\n :\n :\nTask Samples: input: style 12\neven 25\nintroduction 3\neasy 9\nstyle 7\ndocument 13\nstyle 21\neven 18\n output: document\n13\neasy\n9\neven\n18 25\nintroduction\n3\nstyle\n7 12 21\n\n" }, { "title": "Discounts of Buckwheat", "content": "Aizu is famous for its buckwheat. There are many people who make buckwheat noodles by themselves.\n\n One day, you went shopping to buy buckwheat flour. You can visit three shops, A, B and C. The amount in a bag and its unit price for each shop is determined by the follows table. Note that it is discounted when you buy buckwheat flour in several bags.\n\n\n Shop A Shop B Shop C \n\n Amount in a bag 200g 300g 500g \n\n Unit price for a bag (nominal cost) 380 yen 550 yen 850 yen \n\n Discounted units per 5 bags per 4 bags per 3 bags \n\n Discount rate reduced by 20 % reduced by 15 % reduced by 12 % \n\n \n\n For example, when you buy 12 bags of flour at shop A, the price is reduced by 20 % for 10 bags, but not for other 2 bags. So, the total amount shall be (380 * 10) * 0.8 + 380 * 2 = 3,800 yen.\n\n Write a program which reads the amount of flour, and prints the lowest cost to buy them. Note that you should buy the flour of exactly the same amount as the given input.", "constraint": "", "input": "The input consists of multiple datasets. For each dataset, an integer a (500 <= a <= 5000, a is divisible by 100) which represents the amount of flour is given in a line.\n\n The input ends with a line including a zero. Your program should not process for the terminal symbol. The number of datasets does not exceed 50.", "output": "For each dataset, print an integer which represents the lowest cost.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 500\n2200\n0\n output: 850\n3390"], "Pid": "p00106", "ProblemText": "Task Description: Aizu is famous for its buckwheat. There are many people who make buckwheat noodles by themselves.\n\n One day, you went shopping to buy buckwheat flour. You can visit three shops, A, B and C. The amount in a bag and its unit price for each shop is determined by the follows table. Note that it is discounted when you buy buckwheat flour in several bags.\n\n
\n Shop A Shop B Shop C \n\n Amount in a bag 200g 300g 500g \n\n Unit price for a bag (nominal cost) 380 yen 550 yen 850 yen \n\n Discounted units per 5 bags per 4 bags per 3 bags \n\n Discount rate reduced by 20 % reduced by 15 % reduced by 12 % \n\n \n\n For example, when you buy 12 bags of flour at shop A, the price is reduced by 20 % for 10 bags, but not for other 2 bags. So, the total amount shall be (380 * 10) * 0.8 + 380 * 2 = 3,800 yen.\n\n Write a program which reads the amount of flour, and prints the lowest cost to buy them. Note that you should buy the flour of exactly the same amount as the given input.\nTask Input: The input consists of multiple datasets. For each dataset, an integer a (500 <= a <= 5000, a is divisible by 100) which represents the amount of flour is given in a line.\n\n The input ends with a line including a zero. Your program should not process for the terminal symbol. The number of datasets does not exceed 50.\nTask Output: For each dataset, print an integer which represents the lowest cost.\nTask Samples: input: 500\n2200\n0\n output: 850\n3390\n\n" }, { "title": "Carry a Cheese", "content": "Jerry is a little mouse. He is trying to survive from the cat Tom. Jerry is carrying a parallelepiped-like piece of cheese of size A * B * C. It is necessary to trail this cheese to the Jerry's house. There are several entrances in the Jerry's house. Each entrance is a rounded hole having its own radius R. Could you help Jerry to find suitable holes to be survive?\nYour task is to create a program which estimates whether Jerry can trail the cheese via each hole.\nThe program should print \"OK\" if Jerry can trail the cheese via the corresponding hole (without touching it). Otherwise the program should print \"NA\".\n\nYou may assume that the number of holes is less than 10000.", "constraint": "", "input": "The input is a sequence of datasets. The end of input is indicated by a line containing three zeros. Each dataset is formatted as follows:\n\nA B C\nn\nR_1\nR_2\n\n .\n .\nR_n\n\nn indicates the number of holes (entrances) and R_i indicates the radius of i-th hole.", "output": "For each datasets, the output should have n lines. Each line points the result of estimation of the corresponding hole.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 6 8\n5\n4\n8\n6\n2\n5\n0 0 0\n output: NA\nOK\nOK\nNA\nNA"], "Pid": "p00107", "ProblemText": "Task Description: Jerry is a little mouse. He is trying to survive from the cat Tom. Jerry is carrying a parallelepiped-like piece of cheese of size A * B * C. It is necessary to trail this cheese to the Jerry's house. There are several entrances in the Jerry's house. Each entrance is a rounded hole having its own radius R. Could you help Jerry to find suitable holes to be survive?\nYour task is to create a program which estimates whether Jerry can trail the cheese via each hole.\nThe program should print \"OK\" if Jerry can trail the cheese via the corresponding hole (without touching it). Otherwise the program should print \"NA\".\n\nYou may assume that the number of holes is less than 10000.\nTask Input: The input is a sequence of datasets. The end of input is indicated by a line containing three zeros. Each dataset is formatted as follows:\n\nA B C\nn\nR_1\nR_2\n\n .\n .\nR_n\n\nn indicates the number of holes (entrances) and R_i indicates the radius of i-th hole.\nTask Output: For each datasets, the output should have n lines. Each line points the result of estimation of the corresponding hole.\nTask Samples: input: 10 6 8\n5\n4\n8\n6\n2\n5\n0 0 0\n output: NA\nOK\nOK\nNA\nNA\n\n" }, { "title": "Smart Calculator", "content": "Your task is to write a program which reads an expression and evaluates it.\n\nThe expression consists of numerical values, operators and parentheses, and the ends with '='.\n\nThe operators includes +, - , *, / where respectively represents, addition, subtraction, multiplication and division.\n\n Precedence of the operators is based on usual laws. That is one should perform all multiplication and division first, then addition and subtraction. When two operators have the same precedence, they are applied from left to right.\nYou may assume that there is no division by zero.\n\nAll calculation is performed as integers, and after the decimal point should be truncated\n\nLength of the expression will not exceed 100.\n\n-1 * 10^9 <= intermediate results of computation <= 10^9", "constraint": "", "input": "The input is a sequence of datasets. The first line contains an integer n which represents the number of datasets. There will be n lines where each line contains an expression.", "output": "For each datasets, prints the result of calculation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4-2*3=\n4*(8+4+3)=\n output: -2\n60"], "Pid": "p00109", "ProblemText": "Task Description: Your task is to write a program which reads an expression and evaluates it.\n\nThe expression consists of numerical values, operators and parentheses, and the ends with '='.\n\nThe operators includes +, - , *, / where respectively represents, addition, subtraction, multiplication and division.\n\n Precedence of the operators is based on usual laws. That is one should perform all multiplication and division first, then addition and subtraction. When two operators have the same precedence, they are applied from left to right.\nYou may assume that there is no division by zero.\n\nAll calculation is performed as integers, and after the decimal point should be truncated\n\nLength of the expression will not exceed 100.\n\n-1 * 10^9 <= intermediate results of computation <= 10^9\nTask Input: The input is a sequence of datasets. The first line contains an integer n which represents the number of datasets. There will be n lines where each line contains an expression.\nTask Output: For each datasets, prints the result of calculation.\nTask Samples: input: 2\n4-2*3=\n4*(8+4+3)=\n output: -2\n60\n\n" }, { "title": "Twin Prime", "content": "Prime numbers are widely applied for cryptographic and communication technology.\nA twin prime is a prime number that differs from another prime number by 2.\nFor example, (5,7) and (11,13) are twin prime pairs.\n\nIn this problem, we call the greater number of a twin prime \"size of the twin prime. \"\n\nYour task is to create a program which reads an integer n and prints a twin prime which has the maximum size among twin primes less than or equals to n\n\nYou may assume that 5 <= n <= 10000.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset is formatted as follows:\n\nn (integer)", "output": "For each dataset, print the twin prime p and q (p < q). p and q should be separated by a single space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12\n100\n200\n300\n0\n output: 5 7\n71 73\n197 199\n281 283"], "Pid": "p00150", "ProblemText": "Task Description: Prime numbers are widely applied for cryptographic and communication technology.\nA twin prime is a prime number that differs from another prime number by 2.\nFor example, (5,7) and (11,13) are twin prime pairs.\n\nIn this problem, we call the greater number of a twin prime \"size of the twin prime. \"\n\nYour task is to create a program which reads an integer n and prints a twin prime which has the maximum size among twin primes less than or equals to n\n\nYou may assume that 5 <= n <= 10000.\nTask Input: The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset is formatted as follows:\n\nn (integer)\nTask Output: For each dataset, print the twin prime p and q (p < q). p and q should be separated by a single space.\nTask Samples: input: 12\n100\n200\n300\n0\n output: 5 7\n71 73\n197 199\n281 283\n\n" }, { "title": "Grid", "content": "There is a n * n grid D where each cell contains either 1 or 0.\n\nYour task is to create a program that takes the gird data as input and computes the greatest number of consecutive 1s in either vertical, horizontal, or diagonal direction.\n\nFor example, the consecutive 1s with greatest number in the figure below is circled by the dashed-line.\n\nThe size of the grid n is an integer where 2 <= n <= 255.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset is formatted as follows:\n\nn\nD_11 D_12 . . . D_1n\nD_21 D_22 . . . D_2n\n .\n .\nD_n1 D_n2 . . . D_nn", "output": "For each dataset, print the greatest number of consecutive 1s.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n00011\n00101\n01000\n10101\n00010\n8\n11000001\n10110111\n01100111\n01111010\n11111111\n01011010\n10100010\n10000001\n2\n01\n00\n3\n000\n000\n000\n0\n output: 4\n8\n1\n0"], "Pid": "p00151", "ProblemText": "Task Description: There is a n * n grid D where each cell contains either 1 or 0.\n\nYour task is to create a program that takes the gird data as input and computes the greatest number of consecutive 1s in either vertical, horizontal, or diagonal direction.\n\nFor example, the consecutive 1s with greatest number in the figure below is circled by the dashed-line.\n\nThe size of the grid n is an integer where 2 <= n <= 255.\nTask Input: The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset is formatted as follows:\n\nn\nD_11 D_12 . . . D_1n\nD_21 D_22 . . . D_2n\n .\n .\nD_n1 D_n2 . . . D_nn\nTask Output: For each dataset, print the greatest number of consecutive 1s.\nTask Samples: input: 5\n00011\n00101\n01000\n10101\n00010\n8\n11000001\n10110111\n01100111\n01111010\n11111111\n01011010\n10100010\n10000001\n2\n01\n00\n3\n000\n000\n000\n0\n output: 4\n8\n1\n0\n\n" }, { "title": "Handsel", "content": "Alice and Brown are brothers in a family and each receives pocket money in celebration of the coming year. They are very close and share the total amount of the money fifty-fifty. The pocket money each receives is a multiple of 1,000 yen. \n\n Write a program to calculate each one 's share given the amount of money Alice and Brown received.", "constraint": "", "input": "The input is given in the following format.\n\na b\n\nA line of data is given that contains two values of money: a (1000 <= a <= 50000) for Alice and b (1000 <= b <= 50000) for Brown.\n", "output": "Output the amount of money each of Alice and Brown receive in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1000 3000\n output: 2000", "input: 5000 5000\n output: 5000", "input: 1000 2000\n output: 1500"], "Pid": "p00352", "ProblemText": "Task Description: Alice and Brown are brothers in a family and each receives pocket money in celebration of the coming year. They are very close and share the total amount of the money fifty-fifty. The pocket money each receives is a multiple of 1,000 yen. \n\n Write a program to calculate each one 's share given the amount of money Alice and Brown received.\nTask Input: The input is given in the following format.\n\na b\n\nA line of data is given that contains two values of money: a (1000 <= a <= 50000) for Alice and b (1000 <= b <= 50000) for Brown.\n\nTask Output: Output the amount of money each of Alice and Brown receive in a line.\nTask Samples: input: 1000 3000\n output: 2000\ninput: 5000 5000\n output: 5000\ninput: 1000 2000\n output: 1500\n\n" }, { "title": "Shopping", "content": "You are now in a bookshop with your friend Alice to buy a book, \"The Winning Strategy for the Programming Koshien Contest, ” just released today. As you definitely want to buy it, you are planning to borrow some money from Alice in case the amount you have falls short of the price. If the amount you receive from Alice still fails to meet the price, you have to abandon buying the book this time.\n\n Write a program to calculate the minimum amount of money you need to borrow from Alice given the following three items of data: the money you and Alice have now and the price of the book.", "constraint": "", "input": "The input is given in the following format.\n\nm f b\n\nA line containing the three amounts of money is given: the amount you have with you now m (0 <= m <= 10000), the money Alice has now f (0 <= f <= 10000) and the price of the book b (100 <= b <= 20000).", "output": "Output a line suggesting the minimum amount of money you need to borrow from Alice. Output \"NA\" if all the money Alice has with him now is not a sufficient amount for you to buy the book.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1000 3000 3000\n output: 2000", "input: 5000 3000 4500\n output: 0", "input: 500 1000 2000\n output: NA"], "Pid": "p00353", "ProblemText": "Task Description: You are now in a bookshop with your friend Alice to buy a book, \"The Winning Strategy for the Programming Koshien Contest, ” just released today. As you definitely want to buy it, you are planning to borrow some money from Alice in case the amount you have falls short of the price. If the amount you receive from Alice still fails to meet the price, you have to abandon buying the book this time.\n\n Write a program to calculate the minimum amount of money you need to borrow from Alice given the following three items of data: the money you and Alice have now and the price of the book.\nTask Input: The input is given in the following format.\n\nm f b\n\nA line containing the three amounts of money is given: the amount you have with you now m (0 <= m <= 10000), the money Alice has now f (0 <= f <= 10000) and the price of the book b (100 <= b <= 20000).\nTask Output: Output a line suggesting the minimum amount of money you need to borrow from Alice. Output \"NA\" if all the money Alice has with him now is not a sufficient amount for you to buy the book.\nTask Samples: input: 1000 3000 3000\n output: 2000\ninput: 5000 3000 4500\n output: 0\ninput: 500 1000 2000\n output: NA\n\n" }, { "title": "Day of Week", "content": "The 9th day of September 2017 is Saturday. Then, what day of the week is the X-th of September 2017? \n\n Given a day in September 2017, write a program to report what day of the week it is.", "constraint": "", "input": "The input is given in the following format.\n\nX\n\n The input line specifies a day X (1 <= X <= 30) in September 2017.", "output": "Output what day of the week it is in a line. Use the following conventions in your output: \"mon\" for Monday, \"tue\" for Tuesday, \"wed\" for Wednesday, \"thu\" for Thursday, \"fri\" for Friday, \"sat\" for Saturday, and \"sun\" for Sunday.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n output: fri", "input: 9\n output: sat", "input: 30\n output: sat"], "Pid": "p00354", "ProblemText": "Task Description: The 9th day of September 2017 is Saturday. Then, what day of the week is the X-th of September 2017? \n\n Given a day in September 2017, write a program to report what day of the week it is.\nTask Input: The input is given in the following format.\n\nX\n\n The input line specifies a day X (1 <= X <= 30) in September 2017.\nTask Output: Output what day of the week it is in a line. Use the following conventions in your output: \"mon\" for Monday, \"tue\" for Tuesday, \"wed\" for Wednesday, \"thu\" for Thursday, \"fri\" for Friday, \"sat\" for Saturday, and \"sun\" for Sunday.\nTask Samples: input: 1\n output: fri\ninput: 9\n output: sat\ninput: 30\n output: sat\n\n" }, { "title": "Reservation System", "content": "The supercomputer system L in the PCK Research Institute performs a variety of calculations upon request from external institutes, companies, universities and other entities. To use the L system, you have to reserve operation time by specifying the start and end time. No two reservation periods are allowed to overlap each other.\n\n Write a program to report if a new reservation overlaps with any of the existing reservations. Note that the coincidence of start and end times is not considered to constitute an overlap. All the temporal data is given as the elapsed time from the moment at which the L system starts operation.", "constraint": "", "input": "The input is given in the following format.\n\na b\nN\ns_1 f_1\ns_2 f_2\n:\ns_N f_N\n\nThe first line provides new reservation information, i. e. , the start time a and end time b (0 <= a < b <= 1000) in integers. The second line specifies the number of existing reservations N (0 <= N <= 100). Subsequent N lines provide temporal information for the i-th reservation: start time s_i and end time f_i (0 <= s_i < f_i <= 1000) in integers. No two existing reservations overlap.", "output": "Output \"1\" if the new reservation temporally overlaps with any of the existing ones, or \"0\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 7\n3\n1 4\n4 5\n7 10\n output: 0", "input: 3 7\n3\n7 10\n1 4\n4 5\n output: 1"], "Pid": "p00355", "ProblemText": "Task Description: The supercomputer system L in the PCK Research Institute performs a variety of calculations upon request from external institutes, companies, universities and other entities. To use the L system, you have to reserve operation time by specifying the start and end time. No two reservation periods are allowed to overlap each other.\n\n Write a program to report if a new reservation overlaps with any of the existing reservations. Note that the coincidence of start and end times is not considered to constitute an overlap. All the temporal data is given as the elapsed time from the moment at which the L system starts operation.\nTask Input: The input is given in the following format.\n\na b\nN\ns_1 f_1\ns_2 f_2\n:\ns_N f_N\n\nThe first line provides new reservation information, i. e. , the start time a and end time b (0 <= a < b <= 1000) in integers. The second line specifies the number of existing reservations N (0 <= N <= 100). Subsequent N lines provide temporal information for the i-th reservation: start time s_i and end time f_i (0 <= s_i < f_i <= 1000) in integers. No two existing reservations overlap.\nTask Output: Output \"1\" if the new reservation temporally overlaps with any of the existing ones, or \"0\" otherwise.\nTask Samples: input: 5 7\n3\n1 4\n4 5\n7 10\n output: 0\ninput: 3 7\n3\n7 10\n1 4\n4 5\n output: 1\n\n" }, { "title": "Wire", "content": "I am a craftsman specialized in interior works. A customer asked me to perform wiring work on a wall whose entire rectangular surface is tightly pasted with pieces of panels. The panels are all of the same size (2 m in width, 1 m in height) and the wall is filled with an x (horizontal) by y (vertical) array of the panels. The customer asked me to stretch a wire from the left top corner of the wall to the right bottom corner whereby the wire is tied up at the crossing points with the panel boundaries (edges and vertexes) as shown in the figure. There are nine tied-up points in the illustrative figure shown below.\n\n Fig: The wire is tied up at the edges and vertexes of the panels (X: 4 panels, Y: 6 panels)\n Write a program to provide the number of points where the wire intersects with the panel boundaries.\nAssume that the wire and boundary lines have no thickness.", "constraint": "", "input": "The input is given in the following format.\n\nx y\n\nA line of data is given that contains the integer number of panels in the horizontal direction x (1 <= x <= 1000) and those in the vertical direction y (1 <= y <= 1000).", "output": "Output the number of points where the wire intersects with the panel boundaries.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 4\n output: 5", "input: 4 6\n output: 9"], "Pid": "p00356", "ProblemText": "Task Description: I am a craftsman specialized in interior works. A customer asked me to perform wiring work on a wall whose entire rectangular surface is tightly pasted with pieces of panels. The panels are all of the same size (2 m in width, 1 m in height) and the wall is filled with an x (horizontal) by y (vertical) array of the panels. The customer asked me to stretch a wire from the left top corner of the wall to the right bottom corner whereby the wire is tied up at the crossing points with the panel boundaries (edges and vertexes) as shown in the figure. There are nine tied-up points in the illustrative figure shown below.\n\n Fig: The wire is tied up at the edges and vertexes of the panels (X: 4 panels, Y: 6 panels)\n Write a program to provide the number of points where the wire intersects with the panel boundaries.\nAssume that the wire and boundary lines have no thickness.\nTask Input: The input is given in the following format.\n\nx y\n\nA line of data is given that contains the integer number of panels in the horizontal direction x (1 <= x <= 1000) and those in the vertical direction y (1 <= y <= 1000).\nTask Output: Output the number of points where the wire intersects with the panel boundaries.\nTask Samples: input: 4 4\n output: 5\ninput: 4 6\n output: 9\n\n" }, { "title": "Trampoline", "content": "A plurality of trampolines are arranged in a line at 10 m intervals. Each trampoline has its own maximum horizontal distance within which the jumper can jump safely. Starting from the left-most trampoline, the jumper jumps to another trampoline within the allowed jumping range. The jumper wants to repeat jumping until he/she reaches the right-most trampoline, and then tries to return to the left-most trampoline only through jumping. Can the jumper complete the roundtrip without a single stepping-down from a trampoline?\n\n Write a program to report if the jumper can complete the journey using the list of maximum horizontal reaches of these trampolines. Assume that the trampolines are points without spatial extent.", "constraint": "", "input": "The input is given in the following format.\n\nN\nd_1\nd_2\n:\nd_N\n\nThe first line provides the number of trampolines N (2 <= N <= 3 * 10^5). Each of the subsequent N lines gives the maximum allowable jumping distance in integer meters for the i-th trampoline d_i (1 <= d_i <= 10^6).", "output": "Output \"yes\" if the jumper can complete the roundtrip, or \"no\" if he/she cannot.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n20\n5\n10\n1\n output: no", "input: 3\n10\n5\n10\n output: no", "input: 4\n20\n30\n1\n20\n output: yes"], "Pid": "p00357", "ProblemText": "Task Description: A plurality of trampolines are arranged in a line at 10 m intervals. Each trampoline has its own maximum horizontal distance within which the jumper can jump safely. Starting from the left-most trampoline, the jumper jumps to another trampoline within the allowed jumping range. The jumper wants to repeat jumping until he/she reaches the right-most trampoline, and then tries to return to the left-most trampoline only through jumping. Can the jumper complete the roundtrip without a single stepping-down from a trampoline?\n\n Write a program to report if the jumper can complete the journey using the list of maximum horizontal reaches of these trampolines. Assume that the trampolines are points without spatial extent.\nTask Input: The input is given in the following format.\n\nN\nd_1\nd_2\n:\nd_N\n\nThe first line provides the number of trampolines N (2 <= N <= 3 * 10^5). Each of the subsequent N lines gives the maximum allowable jumping distance in integer meters for the i-th trampoline d_i (1 <= d_i <= 10^6).\nTask Output: Output \"yes\" if the jumper can complete the roundtrip, or \"no\" if he/she cannot.\nTask Samples: input: 4\n20\n5\n10\n1\n output: no\ninput: 3\n10\n5\n10\n output: no\ninput: 4\n20\n30\n1\n20\n output: yes\n\n" }, { "title": "Loading", "content": "Aizu Ocean Transport Company (AOTC) accepted a new shipping order. The pieces of the cargo included in this order all have the same square footprint (2m x 2m). The cargo room has a rectangular storage space of 4m width with various longitudinal extents. Each pieces of cargo must be placed in alignment with partition boundaries which form a 1m x 1m square grid. A straddling arrangement with a neighboring partition (for example, protrusion by 50 cm) is not allowed. Neither an angled layout nor stacked placement are allowed. Note also that there may be some partitions on which any cargo loading is prohibited.\n\n AOTC wishes to use the currently available ship for this consignment and needs to know how many pieces of cargo it can accommodate.\n\n Make a program to report the maximum cargo capacity of the cargo space given the following information: the depth (m) of the cargo space and the loading-inhibited partitions.", "constraint": "", "input": "The input is given in the following format.\n\nH N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\n The first line provides the longitudinal depth H (2 <= H <= 10^4) of the cargo space in meters and the number of load-inhibited partitions N (0 <= N <= 4 * 10^4). Each of the subsequent N lines defines the position of the i-th load-inhibited partition x_i (0 <= x_i <= 3) and y_i (0 <= y_i <= H-1) in integers, where x = 0 and y = 0 indicate the bottom-left corner partition. A load-inhibited partition appears only once in the list.", "output": "Output the maximum number of cargo pieces loaded into the cargo space.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 3\n0 1\n1 2\n3 3\n output: 2\n Input example 1 corresponds to the cargo layout shown in the left-most figure.", "input: 6 4\n0 2\n1 3\n3 4\n0 5\n output: 4"], "Pid": "p00358", "ProblemText": "Task Description: Aizu Ocean Transport Company (AOTC) accepted a new shipping order. The pieces of the cargo included in this order all have the same square footprint (2m x 2m). The cargo room has a rectangular storage space of 4m width with various longitudinal extents. Each pieces of cargo must be placed in alignment with partition boundaries which form a 1m x 1m square grid. A straddling arrangement with a neighboring partition (for example, protrusion by 50 cm) is not allowed. Neither an angled layout nor stacked placement are allowed. Note also that there may be some partitions on which any cargo loading is prohibited.\n\n AOTC wishes to use the currently available ship for this consignment and needs to know how many pieces of cargo it can accommodate.\n\n Make a program to report the maximum cargo capacity of the cargo space given the following information: the depth (m) of the cargo space and the loading-inhibited partitions.\nTask Input: The input is given in the following format.\n\nH N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\n The first line provides the longitudinal depth H (2 <= H <= 10^4) of the cargo space in meters and the number of load-inhibited partitions N (0 <= N <= 4 * 10^4). Each of the subsequent N lines defines the position of the i-th load-inhibited partition x_i (0 <= x_i <= 3) and y_i (0 <= y_i <= H-1) in integers, where x = 0 and y = 0 indicate the bottom-left corner partition. A load-inhibited partition appears only once in the list.\nTask Output: Output the maximum number of cargo pieces loaded into the cargo space.\nTask Samples: input: 5 3\n0 1\n1 2\n3 3\n output: 2\n Input example 1 corresponds to the cargo layout shown in the left-most figure.\ninput: 6 4\n0 2\n1 3\n3 4\n0 5\n output: 4\n\n" }, { "title": "Dungeon", "content": "Bob is playing a popular game called \"Dungeon\". The game is played on a rectangular board consisting of W * H squares. Each square is identified with its column and row number, thus the square located in the x-th column and the y-th row is represented as (x, y). The left-most square in the top row is (0,0) and the right-most square in the bottom row is (W-1, H-1).\n\n Bob moves a character \"Bom Bom\" to clear the game. Bom Bom is initially located at (0,0). The game is won if Bob successfully destroys all the enemy characters on the board by manipulating Bom Bom cleverly. The enemy characters are fixed on specific squares, and Bob can manipulate Bom Bom using the following two operations any number of times.\n\n One-square movement in the up, down, left, or right direction within the board\n\n Using a bomb, eliminate all the enemy characters that are located in the same column and row as that of Bom Bom\nBom Bom consumes a Cost when it moves from one square to another. Bom Bom can use a bomb any number of times without consuming a Cost. Use of a bomb has no effect on Bom Bom 's behavior and it can move even to a square where an enemy character is located.\n\nGiven the board size and enemy information, make a program to evaluate the minimum Cost Bom Bom consumes before it destroys all enemy characters.", "constraint": "", "input": "The input is given in the following format.\n\nW H N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\nThe first line provides the number of squares in the horizontal direction W (1 <= W <= 10^5), in the vertical direction H (1 <= H <= 10^5), and the number of enemy characters N (1 <= N <= 10^5). Each of the subsequent N lines provides location information of the i-th enemy, column x_i (0 <= x_i <= W-1) and row y_i (0 <= y_i <= H-1). The number of enemy characters in a specific square can be either one or zero.", "output": "Output the minimum Cost in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 4\n0 3\n1 1\n2 2\n2 3\n output: 2", "input: 6 6 5\n2 1\n5 2\n3 3\n1 4\n1 5\n output: 4", "input: 8 8 4\n6 0\n7 0\n0 6\n0 7\n output: 0"], "Pid": "p00359", "ProblemText": "Task Description: Bob is playing a popular game called \"Dungeon\". The game is played on a rectangular board consisting of W * H squares. Each square is identified with its column and row number, thus the square located in the x-th column and the y-th row is represented as (x, y). The left-most square in the top row is (0,0) and the right-most square in the bottom row is (W-1, H-1).\n\n Bob moves a character \"Bom Bom\" to clear the game. Bom Bom is initially located at (0,0). The game is won if Bob successfully destroys all the enemy characters on the board by manipulating Bom Bom cleverly. The enemy characters are fixed on specific squares, and Bob can manipulate Bom Bom using the following two operations any number of times.\n\n One-square movement in the up, down, left, or right direction within the board\n\n Using a bomb, eliminate all the enemy characters that are located in the same column and row as that of Bom Bom\nBom Bom consumes a Cost when it moves from one square to another. Bom Bom can use a bomb any number of times without consuming a Cost. Use of a bomb has no effect on Bom Bom 's behavior and it can move even to a square where an enemy character is located.\n\nGiven the board size and enemy information, make a program to evaluate the minimum Cost Bom Bom consumes before it destroys all enemy characters.\nTask Input: The input is given in the following format.\n\nW H N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\nThe first line provides the number of squares in the horizontal direction W (1 <= W <= 10^5), in the vertical direction H (1 <= H <= 10^5), and the number of enemy characters N (1 <= N <= 10^5). Each of the subsequent N lines provides location information of the i-th enemy, column x_i (0 <= x_i <= W-1) and row y_i (0 <= y_i <= H-1). The number of enemy characters in a specific square can be either one or zero.\nTask Output: Output the minimum Cost in a line.\nTask Samples: input: 5 4 4\n0 3\n1 1\n2 2\n2 3\n output: 2\ninput: 6 6 5\n2 1\n5 2\n3 3\n1 4\n1 5\n output: 4\ninput: 8 8 4\n6 0\n7 0\n0 6\n0 7\n output: 0\n\n" }, { "title": "Swapping Characters", "content": "You are given a string and a number k. You are suggested to generate new strings by swapping any adjacent pair of characters in the string up to k times. Write a program to report the lexicographically smallest string among them.", "constraint": "", "input": "The input is given in the following format.\n\ns\nk\n\nThe first line provides a string s. The second line provides the maximum number of swapping operations k (0 <= k <= 10^9). The string consists solely of lower-case alphabetical letters and has a length between 1 and 2 * 10^5.", "output": "Output the lexicographically smallest string.", "content_img": false, "lang": "en", "error": false, "samples": ["input: pckoshien\n3\n output: ckopshien", "input: pckoshien\n10\n output: cekophsin"], "Pid": "p00360", "ProblemText": "Task Description: You are given a string and a number k. You are suggested to generate new strings by swapping any adjacent pair of characters in the string up to k times. Write a program to report the lexicographically smallest string among them.\nTask Input: The input is given in the following format.\n\ns\nk\n\nThe first line provides a string s. The second line provides the maximum number of swapping operations k (0 <= k <= 10^9). The string consists solely of lower-case alphabetical letters and has a length between 1 and 2 * 10^5.\nTask Output: Output the lexicographically smallest string.\nTask Samples: input: pckoshien\n3\n output: ckopshien\ninput: pckoshien\n10\n output: cekophsin\n\n" }, { "title": "Road Improvement", "content": "Aizu is a country famous for its rich tourism resources and has N cities, each of which is uniquely identified with a number (0 to N-1). It has a road network consisting of M one-way roads connecting a city to another.\n\n All the roads connecting the cities in Aizu have a row of cherry trees along their routes. For enhancing the cherry-viewing experience, a proposal was made to modify the road network so that a tourist can travel around all the roads. To achieve this target, it was decided to construct several one-way roads, each connecting two cities and abiding by the following rules.\n\nThe newly constructed road is for one-way traffic\n\nStarting from any city, a tourist is able to make a roundtrip and return to the city, whereby he/she drives all the roads exhaustively, including the newly constructed ones. Multiple passages of some of the roads are allowed.\n You, as a tourism promotion officer, are assigned with the task of writing a program for the road construction project.\n\n Write a program to determine the minimum number of roads to be constructed given the road network information in Aizu.", "constraint": "", "input": "The input is given in the following format.\n\nN M\ns_1 t_1\ns_2 t_2\n:\ns_M t_M\n\nThe first line provides the number of cities N (1 <= N <= 10^4) and roads M (0 <= M <= 10^5). Each of the subsequent M lines provides the numbers assigned to start and destination cities for the i-th road: s_i, t_i (0 <= s_i, t_i <= N-1) , where s_i ! = t_i. (no duplicate appearance of a road)", "output": "Output the minimum number of roads to be newly constructed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 7\n0 2\n2 1\n1 0\n2 3\n4 3\n4 5\n5 4\n output: 2", "input: 6 9\n0 2\n2 1\n1 0\n2 3\n4 3\n4 5\n5 4\n5 2\n3 4\n output: 0"], "Pid": "p00361", "ProblemText": "Task Description: Aizu is a country famous for its rich tourism resources and has N cities, each of which is uniquely identified with a number (0 to N-1). It has a road network consisting of M one-way roads connecting a city to another.\n\n All the roads connecting the cities in Aizu have a row of cherry trees along their routes. For enhancing the cherry-viewing experience, a proposal was made to modify the road network so that a tourist can travel around all the roads. To achieve this target, it was decided to construct several one-way roads, each connecting two cities and abiding by the following rules.\n\nThe newly constructed road is for one-way traffic\n\nStarting from any city, a tourist is able to make a roundtrip and return to the city, whereby he/she drives all the roads exhaustively, including the newly constructed ones. Multiple passages of some of the roads are allowed.\n You, as a tourism promotion officer, are assigned with the task of writing a program for the road construction project.\n\n Write a program to determine the minimum number of roads to be constructed given the road network information in Aizu.\nTask Input: The input is given in the following format.\n\nN M\ns_1 t_1\ns_2 t_2\n:\ns_M t_M\n\nThe first line provides the number of cities N (1 <= N <= 10^4) and roads M (0 <= M <= 10^5). Each of the subsequent M lines provides the numbers assigned to start and destination cities for the i-th road: s_i, t_i (0 <= s_i, t_i <= N-1) , where s_i ! = t_i. (no duplicate appearance of a road)\nTask Output: Output the minimum number of roads to be newly constructed.\nTask Samples: input: 6 7\n0 2\n2 1\n1 0\n2 3\n4 3\n4 5\n5 4\n output: 2\ninput: 6 9\n0 2\n2 1\n1 0\n2 3\n4 3\n4 5\n5 4\n5 2\n3 4\n output: 0\n\n" }, { "title": "Charging System for Network", "content": "There is a network consisting of N machines (sequentially numbered from 0 to N-1) interconnected through N-1 bidirectional communication cables. Any two machines can perform bidirectional communication through one or more cables. From time to time, machines in the network are renewed. When a new machine is introduced, the cables directly connected to it are also replaced with thicker ones to cope with the increased volume of communication traffic.\n\n The communication fee arising from communication traffic between any two machines is calculated by summing the charges assigned to all the cables routing via the two. A unique charging scheme is employed in this system: if the size of a cable is a multiple of K, then the cable is not charged (free of charge). Other cables are charged according to their sizes.\n\n Based on the given information on the network topology and Q instructions, write a program to execute each instruction.\n\nIncrease the sizes of all cables directly connected to the machine x by d.\n\nReport the communication charge between the machines s and t.", "constraint": "", "input": "The input is given in the following format.\n\nN K\na_1 b_1 c_1\na_2 b_2 c_2\n:\na_{N-1} b_{N-1} c_{N-1}\nQ\nquery_1\nquery_2\n:\nquery_Q\n\nThe first line provides the number of machines N (2 <= N <= 10^5) and the cable size K (1 <= K <= 10^5) (the reference value for determining free of charge cables). Each of subsequent N-1 lines provides the i-th cable information that directly connects two machines a_i and b_i (0 <= a_i < b_i <= N-1), followed by the cable 's initial size c_i (1 <= c_i <= 10^5). For any pair of machines, the number of cables directly connecting them is either one or zero. The next line following them provides the number of instructions Q (1 <= Q <= 10^5). Each of the Q lines following it provides the i-th instruction query_i, which is either one of the following two:\n\nadd x d\n\nor\n\nsend s t\n\n The instruction add x d increase the size of all cables directly connected to machine x (0 <= x <= N-1) by d (1 <= d <= 10^5).\n\nThe instruction send s t reports the charge imposed to the communication between the two machines s (0 <= s <= N-1) and t (0 <= t <= N-1), where s ! = t.\n \n\n At least one send instruction is included in the input information.", "output": "For each send command, output the communication charge between s and t.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3\n0 1 1\n0 2 1\n0 3 1\n2 4 1\n2 5 1\n3\nsend 1 4\nadd 2 2\nsend 1 4\n output: 3\n1"], "Pid": "p00362", "ProblemText": "Task Description: There is a network consisting of N machines (sequentially numbered from 0 to N-1) interconnected through N-1 bidirectional communication cables. Any two machines can perform bidirectional communication through one or more cables. From time to time, machines in the network are renewed. When a new machine is introduced, the cables directly connected to it are also replaced with thicker ones to cope with the increased volume of communication traffic.\n\n The communication fee arising from communication traffic between any two machines is calculated by summing the charges assigned to all the cables routing via the two. A unique charging scheme is employed in this system: if the size of a cable is a multiple of K, then the cable is not charged (free of charge). Other cables are charged according to their sizes.\n\n Based on the given information on the network topology and Q instructions, write a program to execute each instruction.\n\nIncrease the sizes of all cables directly connected to the machine x by d.\n\nReport the communication charge between the machines s and t.\nTask Input: The input is given in the following format.\n\nN K\na_1 b_1 c_1\na_2 b_2 c_2\n:\na_{N-1} b_{N-1} c_{N-1}\nQ\nquery_1\nquery_2\n:\nquery_Q\n\nThe first line provides the number of machines N (2 <= N <= 10^5) and the cable size K (1 <= K <= 10^5) (the reference value for determining free of charge cables). Each of subsequent N-1 lines provides the i-th cable information that directly connects two machines a_i and b_i (0 <= a_i < b_i <= N-1), followed by the cable 's initial size c_i (1 <= c_i <= 10^5). For any pair of machines, the number of cables directly connecting them is either one or zero. The next line following them provides the number of instructions Q (1 <= Q <= 10^5). Each of the Q lines following it provides the i-th instruction query_i, which is either one of the following two:\n\nadd x d\n\nor\n\nsend s t\n\n The instruction add x d increase the size of all cables directly connected to machine x (0 <= x <= N-1) by d (1 <= d <= 10^5).\n\nThe instruction send s t reports the charge imposed to the communication between the two machines s (0 <= s <= N-1) and t (0 <= t <= N-1), where s ! = t.\n \n\n At least one send instruction is included in the input information.\nTask Output: For each send command, output the communication charge between s and t.\nTask Samples: input: 6 3\n0 1 1\n0 2 1\n0 3 1\n2 4 1\n2 5 1\n3\nsend 1 4\nadd 2 2\nsend 1 4\n output: 3\n1\n\n" }, { "title": "Flag", "content": "AHK Education, the educational program section of Aizu Broadcasting Cooperation, broadcasts a children 's workshop program called \"Let's Play and Make. \" Today 's theme is \"Make your own flag. \" A child writes his first initial in the center of their rectangular flag.\n\nGiven the flag size and the initial letter to be placed in the center of it, write a program to draw the flag as shown in the figure below.\n\n+-------+\n|. . . . . . . |\n|. . . A. . . |\n|. . . . . . . |\n+-------+\n\n The figure has \"A\" in the center of a flag with size 9 (horizontal) * 5 (vertical).", "constraint": "", "input": "The input is given in the following format.\n\nW H c\n\nThe input line provides the flag dimensions W (width) and H (height) (3 <= W, H <= 21), and the initial letter c. Both W and H are odd numbers, and c is a capital letter.", "output": "Draw the flag of specified size with the initial in its center using the following characters: \"+\" for the four corners of the flag, \"-\" for horizontal lines, \"|\" for vertical lines, and \". \" for the background (except for the initial in the center).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 B\n output: +-+\n|B|\n+-+", "input: 11 7 Z\n output: +---------+\n|.........|\n|.........|\n|....Z....|\n|.........|\n|.........|\n+---------+"], "Pid": "p00363", "ProblemText": "Task Description: AHK Education, the educational program section of Aizu Broadcasting Cooperation, broadcasts a children 's workshop program called \"Let's Play and Make. \" Today 's theme is \"Make your own flag. \" A child writes his first initial in the center of their rectangular flag.\n\nGiven the flag size and the initial letter to be placed in the center of it, write a program to draw the flag as shown in the figure below.\n\n+-------+\n|. . . . . . . |\n|. . . A. . . |\n|. . . . . . . |\n+-------+\n\n The figure has \"A\" in the center of a flag with size 9 (horizontal) * 5 (vertical).\nTask Input: The input is given in the following format.\n\nW H c\n\nThe input line provides the flag dimensions W (width) and H (height) (3 <= W, H <= 21), and the initial letter c. Both W and H are odd numbers, and c is a capital letter.\nTask Output: Draw the flag of specified size with the initial in its center using the following characters: \"+\" for the four corners of the flag, \"-\" for horizontal lines, \"|\" for vertical lines, and \". \" for the background (except for the initial in the center).\nTask Samples: input: 3 3 B\n output: +-+\n|B|\n+-+\ninput: 11 7 Z\n output: +---------+\n|.........|\n|.........|\n|....Z....|\n|.........|\n|.........|\n+---------+\n\n" }, { "title": "Bange Hills Tower", "content": "A project is underway to build a new viewing tower in Bange town called “Bange Hills Tower” whose selling point will be the gorgeous view of the entire main keep of Wakamatsu Castle from top to bottom. Therefore, the view line from the top of the tower must reach the bottom of the keep without being hindered by any of the buildings in the town.\nWrite a program to calculate the minimum tower height required to view the keep in its entirety based on the following information: the planned location of the tower and the heights and locations of existing buildings. Assume all the buildings, including the keep, are vertical lines without horizontal stretch. “view of the entire keep” means that the view line from the tower top can cover the keep from the bottom to the top without intersecting (contacts at the top are exempted) any of the other vertical lines (i. e. , buildings).", "constraint": "", "input": "The input is given in the following format.\n\nN t\nx_1 h_1\nx_2 h_2\n:\nx_N h_N\n\nThe first line provides the number of existing buildings N (1<=N<=1000) and the planned location of the tower t (2<=t<=10^5) in integers. Each of the subsequent N lines provides the information of the i-th building: location x_i (1 <= x_i < t) and height from the ground h_i (1 <= h_i <= 100). All position information is one-dimensional along the ground line whose origin coincides with the Keep location. No more than one building is located in the same location (i. e. if i ! = j, then x_i ! = x_j).", "output": "Output the required height as a real number. No limits on the number of decimal places as long as the error does not exceed ± 10^-3.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 10\n6 4\n4 2\n3 2\n output: 6.666667"], "Pid": "p00364", "ProblemText": "Task Description: A project is underway to build a new viewing tower in Bange town called “Bange Hills Tower” whose selling point will be the gorgeous view of the entire main keep of Wakamatsu Castle from top to bottom. Therefore, the view line from the top of the tower must reach the bottom of the keep without being hindered by any of the buildings in the town.\nWrite a program to calculate the minimum tower height required to view the keep in its entirety based on the following information: the planned location of the tower and the heights and locations of existing buildings. Assume all the buildings, including the keep, are vertical lines without horizontal stretch. “view of the entire keep” means that the view line from the tower top can cover the keep from the bottom to the top without intersecting (contacts at the top are exempted) any of the other vertical lines (i. e. , buildings).\nTask Input: The input is given in the following format.\n\nN t\nx_1 h_1\nx_2 h_2\n:\nx_N h_N\n\nThe first line provides the number of existing buildings N (1<=N<=1000) and the planned location of the tower t (2<=t<=10^5) in integers. Each of the subsequent N lines provides the information of the i-th building: location x_i (1 <= x_i < t) and height from the ground h_i (1 <= h_i <= 100). All position information is one-dimensional along the ground line whose origin coincides with the Keep location. No more than one building is located in the same location (i. e. if i ! = j, then x_i ! = x_j).\nTask Output: Output the required height as a real number. No limits on the number of decimal places as long as the error does not exceed ± 10^-3.\nTask Samples: input: 3 10\n6 4\n4 2\n3 2\n output: 6.666667\n\n" }, { "title": "Age Difference", "content": "A trick of fate caused Hatsumi and Taku to come to know each other. To keep the encounter in memory, they decided to calculate the difference between their ages. But the difference in ages varies depending on the day it is calculated. While trying again and again, they came to notice that the difference of their ages will hit a maximum value even though the months move on forever.\n\n Given the birthdays for the two, make a program to report the maximum difference between their ages. The age increases by one at the moment the birthday begins. If the birthday coincides with the 29^th of February in a leap year, the age increases at the moment the 1^st of March arrives in non-leap years.", "constraint": "", "input": "The input is given in the following format.\n\ny_1 m_1 d_1\ny_2 m_2 d_2\n\nThe first and second lines provide Hatsumi 's and Taku 's birthdays respectively in year y_i (1 <= y_i <= 3000), month m_i (1 <= m_i <= 12), and day d_i (1 <= d_i <= D_max) format. Where D_max is given as follows:\n\n \n\n 28 when February in a non-leap year\n\n 29 when February in a leap-year\n\n 30 in April, June, September, and November\n\n 31 otherwise.\n It is a leap year if the year represented as a four-digit number is divisible by 4. Note, however, that it is a non-leap year if divisible by 100, and a leap year if divisible by 400.", "output": "Output the maximum difference between their ages.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1999 9 9\n2001 11 3\n output: 3\n\n In this example, the difference of ages between them in 2002 and subsequent years is 3 on the 1^st of October, but 2 on the 1^st of December.", "input: 2008 2 29\n2015 3 1\n output: 8\nIn this example, the difference of ages will become 8 on the 29^th of February in and later years than 2016."], "Pid": "p00365", "ProblemText": "Task Description: A trick of fate caused Hatsumi and Taku to come to know each other. To keep the encounter in memory, they decided to calculate the difference between their ages. But the difference in ages varies depending on the day it is calculated. While trying again and again, they came to notice that the difference of their ages will hit a maximum value even though the months move on forever.\n\n Given the birthdays for the two, make a program to report the maximum difference between their ages. The age increases by one at the moment the birthday begins. If the birthday coincides with the 29^th of February in a leap year, the age increases at the moment the 1^st of March arrives in non-leap years.\nTask Input: The input is given in the following format.\n\ny_1 m_1 d_1\ny_2 m_2 d_2\n\nThe first and second lines provide Hatsumi 's and Taku 's birthdays respectively in year y_i (1 <= y_i <= 3000), month m_i (1 <= m_i <= 12), and day d_i (1 <= d_i <= D_max) format. Where D_max is given as follows:\n\n \n\n 28 when February in a non-leap year\n\n 29 when February in a leap-year\n\n 30 in April, June, September, and November\n\n 31 otherwise.\n It is a leap year if the year represented as a four-digit number is divisible by 4. Note, however, that it is a non-leap year if divisible by 100, and a leap year if divisible by 400.\nTask Output: Output the maximum difference between their ages.\nTask Samples: input: 1999 9 9\n2001 11 3\n output: 3\n\n In this example, the difference of ages between them in 2002 and subsequent years is 3 on the 1^st of October, but 2 on the 1^st of December.\ninput: 2008 2 29\n2015 3 1\n output: 8\nIn this example, the difference of ages will become 8 on the 29^th of February in and later years than 2016.\n\n" }, { "title": "Electric Metronome", "content": "A boy PCK is playing with N electric metronomes. The i-th metronome is set to tick every t_i seconds. He started all of them simultaneously.\n\nHe noticed that, even though each metronome has its own ticking interval, all of them tick simultaneously from time to time in certain intervals. To explore this interesting phenomenon more fully, he is now trying to shorten the interval of ticking in unison by adjusting some of the metronomes ' interval settings. Note, however, that the metronomes do not allow any shortening of the intervals.\n \n\n Given the number of metronomes and their preset intervals t_i (sec), write a program to make the tick-in-unison interval shortest by adding a non-negative integer d_i to the current interval setting of the i-th metronome, and report the minimum value of the sum of all d_i.", "constraint": "", "input": "The input is given in the following format.\n\nN\nt_1\nt_2\n:\nt_N\n\nThe first line provides the number of metronomes N (1 <= N <= 10^5). Each of the subsequent N lines provides the preset ticking interval t_i (1 <= t_i <= 10^4) of the i-th metronome.", "output": "Output the minimum value.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3\n6\n8\n output: 3\nIf we have three metronomes each with a ticking interval of 3,6, and 8 seconds, respectively, simultaneous activation of these will produce a tick in unison every 24 seconds. By extending the interval by 1 second for the first, and 2 seconds for the second metronome, the interval of ticking in unison will be reduced to 8 seconds, which is the shortest possible for the system.", "input: 2\n10\n10\n output: 0\n\nIf two metronomes are both set to 10 seconds, then simultaneous activation will produce a tick in unison every 10 seconds, which is the shortest possible for this system."], "Pid": "p00366", "ProblemText": "Task Description: A boy PCK is playing with N electric metronomes. The i-th metronome is set to tick every t_i seconds. He started all of them simultaneously.\n\nHe noticed that, even though each metronome has its own ticking interval, all of them tick simultaneously from time to time in certain intervals. To explore this interesting phenomenon more fully, he is now trying to shorten the interval of ticking in unison by adjusting some of the metronomes ' interval settings. Note, however, that the metronomes do not allow any shortening of the intervals.\n \n\n Given the number of metronomes and their preset intervals t_i (sec), write a program to make the tick-in-unison interval shortest by adding a non-negative integer d_i to the current interval setting of the i-th metronome, and report the minimum value of the sum of all d_i.\nTask Input: The input is given in the following format.\n\nN\nt_1\nt_2\n:\nt_N\n\nThe first line provides the number of metronomes N (1 <= N <= 10^5). Each of the subsequent N lines provides the preset ticking interval t_i (1 <= t_i <= 10^4) of the i-th metronome.\nTask Output: Output the minimum value.\nTask Samples: input: 3\n3\n6\n8\n output: 3\nIf we have three metronomes each with a ticking interval of 3,6, and 8 seconds, respectively, simultaneous activation of these will produce a tick in unison every 24 seconds. By extending the interval by 1 second for the first, and 2 seconds for the second metronome, the interval of ticking in unison will be reduced to 8 seconds, which is the shortest possible for the system.\ninput: 2\n10\n10\n output: 0\n\nIf two metronomes are both set to 10 seconds, then simultaneous activation will produce a tick in unison every 10 seconds, which is the shortest possible for this system.\n\n" }, { "title": "Three Meals", "content": "You are running a restaurant that serves dishes only three times a day. Each of your customer has his/her own separate time zones for eating breakfast, lunch and supper. Thus, your customer enjoys your dish only when he/she visits your restaurant to meet your serving time settings. Your wish is to modify your serving time arrangement so that as many as possible of your customers can enjoy your meals three times a day.\n \n\n Write a program to enable as many as possible of customers can enjoy your service three times a day, i. e. breakfast, lunch, and supper. A list of customers eating time zones is given, which you cannot change. Settings of your service time are your option. Coincidence between your service time and either edge of customer 's time zone (start or end time) does not hinder you to provide your service.", "constraint": "", "input": "The input is given in the following format.\n\nN\nast_1 aet_1 hst_1 het_1 bst_1 bet_1\nast_2 aet_2 hst_2 het_2 bst_2 bet_2\n:\nast_N aet_N hst_N het_N bst_N bet_N\n\nThe first line provides the number of customers N(1<=N<=50). Each of subsequent N lines provides time zone information of i-th customer: start and end time of breakfast zone (ast_i, aet_i), those of lunch zone (hst_i, het_i) and those of supper zone (bst_i, bet_i). The end time must be later in time as the start time. Time zones do not overlap, i. e. hst_i is later in time than aet_i, and so on. Each time settings must not cross 0: 00 midnight.\n\nh m\n\n Each time information is given by hour h (0<=h<=23) and minute m(0<=m<=59).", "output": "Output the maximum number of customers that can be served all three meals (breakfast, lunch, and supper).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 0 2 0 3 30 4 30 6 0 7 0\n2 30 3 0 4 0 5 0 5 30 6 30\n1 30 2 30 4 30 5 0 6 30 7 0\n2 30 3 0 5 0 6 0 6 30 7 0\n1 0 2 0 3 0 3 30 4 0 5 0\n output: 3"], "Pid": "p00367", "ProblemText": "Task Description: You are running a restaurant that serves dishes only three times a day. Each of your customer has his/her own separate time zones for eating breakfast, lunch and supper. Thus, your customer enjoys your dish only when he/she visits your restaurant to meet your serving time settings. Your wish is to modify your serving time arrangement so that as many as possible of your customers can enjoy your meals three times a day.\n \n\n Write a program to enable as many as possible of customers can enjoy your service three times a day, i. e. breakfast, lunch, and supper. A list of customers eating time zones is given, which you cannot change. Settings of your service time are your option. Coincidence between your service time and either edge of customer 's time zone (start or end time) does not hinder you to provide your service.\nTask Input: The input is given in the following format.\n\nN\nast_1 aet_1 hst_1 het_1 bst_1 bet_1\nast_2 aet_2 hst_2 het_2 bst_2 bet_2\n:\nast_N aet_N hst_N het_N bst_N bet_N\n\nThe first line provides the number of customers N(1<=N<=50). Each of subsequent N lines provides time zone information of i-th customer: start and end time of breakfast zone (ast_i, aet_i), those of lunch zone (hst_i, het_i) and those of supper zone (bst_i, bet_i). The end time must be later in time as the start time. Time zones do not overlap, i. e. hst_i is later in time than aet_i, and so on. Each time settings must not cross 0: 00 midnight.\n\nh m\n\n Each time information is given by hour h (0<=h<=23) and minute m(0<=m<=59).\nTask Output: Output the maximum number of customers that can be served all three meals (breakfast, lunch, and supper).\nTask Samples: input: 5\n1 0 2 0 3 30 4 30 6 0 7 0\n2 30 3 0 4 0 5 0 5 30 6 30\n1 30 2 30 4 30 5 0 6 30 7 0\n2 30 3 0 5 0 6 0 6 30 7 0\n1 0 2 0 3 0 3 30 4 0 5 0\n output: 3\n\n" }, { "title": "Checkered Pattern", "content": "You have a cross-section paper with W x H squares, and each of them is painted either in white or black. You want to re-arrange the squares into a neat checkered pattern, in which black and white squares are arranged alternately both in horizontal and vertical directions (the figure shown below is a checkered patter with W = 5 and H = 5). To achieve this goal, you can perform the following two operations as many times you like in an arbitrary sequence: swapping of two arbitrarily chosen columns, and swapping of two arbitrarily chosen rows.\n\n Create a program to determine, starting from the given cross-section paper, if you can re-arrange them into a checkered pattern.", "constraint": "", "input": "The input is given in the following format.\n\nW H\nc_1,1 c_1,2 . . . c_1, W\nc_2,1 c_2,2 . . . c_2, W\n:\nc_H, 1 c_H, 2 . . . c_H, W\n\n The first line provides the number of squares in horizontal direction W (2<=W<=1000) and those in vertical direction H(2<=H<=1000). Each of subsequent H lines provides an array of W integers c_i, j corresponding to a square of i-th row and j-th column. The color of the square is white if c_i, j is 0, and black if it is 1.", "output": "Output \"yes\" if the goal is achievable and \"no\" otherwise.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 2\n1 1 0\n0 0 1\n output: yes", "input: 2 2\n0 0\n1 1\n output: no"], "Pid": "p00368", "ProblemText": "Task Description: You have a cross-section paper with W x H squares, and each of them is painted either in white or black. You want to re-arrange the squares into a neat checkered pattern, in which black and white squares are arranged alternately both in horizontal and vertical directions (the figure shown below is a checkered patter with W = 5 and H = 5). To achieve this goal, you can perform the following two operations as many times you like in an arbitrary sequence: swapping of two arbitrarily chosen columns, and swapping of two arbitrarily chosen rows.\n\n Create a program to determine, starting from the given cross-section paper, if you can re-arrange them into a checkered pattern.\nTask Input: The input is given in the following format.\n\nW H\nc_1,1 c_1,2 . . . c_1, W\nc_2,1 c_2,2 . . . c_2, W\n:\nc_H, 1 c_H, 2 . . . c_H, W\n\n The first line provides the number of squares in horizontal direction W (2<=W<=1000) and those in vertical direction H(2<=H<=1000). Each of subsequent H lines provides an array of W integers c_i, j corresponding to a square of i-th row and j-th column. The color of the square is white if c_i, j is 0, and black if it is 1.\nTask Output: Output \"yes\" if the goal is achievable and \"no\" otherwise.\nTask Samples: input: 3 2\n1 1 0\n0 0 1\n output: yes\ninput: 2 2\n0 0\n1 1\n output: no\n\n" }, { "title": "Paper Fortune", "content": "If you visit Aizu Akabeko shrine, you will find a unique paper fortune on which a number with more than one digit is written. \n\nEach digit ranges from 1 to 9 (zero is avoided because it is considered a bad omen in this shrine). Using this string of numeric values, you can predict how many years it will take before your dream comes true. Cut up the string into more than one segment and compare their values. The difference between the largest and smallest value will give you the number of years before your wish will be fulfilled. Therefore, the result varies depending on the way you cut up the string. For example, if you are given a string 11121314 and divide it into segments, say, as 1,11,21,3,14, then the difference between the largest and smallest is 21 - 1 = 20. Another division 11,12,13,14 produces 3 (i. e. 14 - 11) years. Any random division produces a game of luck. However, you can search the minimum number of years using a program.\n \n\nGiven a string of numerical characters, write a program to search the minimum years before your wish will be fulfilled.", "constraint": "", "input": "The input is given in the following format.\n\nn\n\n An integer n is given. Its number of digits is from 2 to 100,000, and each digit ranges from 1 to 9.", "output": "Output the minimum number of years before your wish will be fulfilled.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11121314\n output: 3", "input: 123125129\n output: 6", "input: 119138\n output: 5"], "Pid": "p00369", "ProblemText": "Task Description: If you visit Aizu Akabeko shrine, you will find a unique paper fortune on which a number with more than one digit is written. \n\nEach digit ranges from 1 to 9 (zero is avoided because it is considered a bad omen in this shrine). Using this string of numeric values, you can predict how many years it will take before your dream comes true. Cut up the string into more than one segment and compare their values. The difference between the largest and smallest value will give you the number of years before your wish will be fulfilled. Therefore, the result varies depending on the way you cut up the string. For example, if you are given a string 11121314 and divide it into segments, say, as 1,11,21,3,14, then the difference between the largest and smallest is 21 - 1 = 20. Another division 11,12,13,14 produces 3 (i. e. 14 - 11) years. Any random division produces a game of luck. However, you can search the minimum number of years using a program.\n \n\nGiven a string of numerical characters, write a program to search the minimum years before your wish will be fulfilled.\nTask Input: The input is given in the following format.\n\nn\n\n An integer n is given. Its number of digits is from 2 to 100,000, and each digit ranges from 1 to 9.\nTask Output: Output the minimum number of years before your wish will be fulfilled.\nTask Samples: input: 11121314\n output: 3\ninput: 123125129\n output: 6\ninput: 119138\n output: 5\n\n" }, { "title": "Lake Survery", "content": "The Onogawa Expedition is planning to conduct a survey of the Aizu nature reserve. The expedition planner wants to take the shortest possible route from the start to end point of the survey, while the expedition has to go around the coast of the Lake of Onogawa en route. The expedition walks along the coast of the lake, but can not wade across the lake.\n\n Based on the base information including the start and end point of the survey and the area of Lake Onogawa as convex polygon data, make a program to find the shortest possible route for the expedition and calculate its distance. Note that the expedition can move along the polygonal lines passing through the nodes, but never enter within the area enclosed by the polygon.", "constraint": "", "input": "The input is given in the following format.\n\nx_s y_s\nx_g y_g\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\nThe first line provides the start point of the survey x_s, y_s (0<=x_s, y_s<=10^4), and the second line provides the end point x_g, y_g (0 <= x_g, y_g <= 10^4) all in integers. The third line provides the number of apexes N (3 <= N <= 100) of the polygon that represents the lake, and each of the subsequent N lines provides the coordinate of the i-th apex x_i, y_i (0 <= x_i, y_i <= 10^4) in counter-clockwise order. These data satisfy the following criteria:\n\nStart and end points of the expedition are not within the area enclosed by the polygon nor on boundaries.\n\nStart and end points of the expedition are not identical, i. e. , x_s ! = x_g or y_s ! = y_g.\n\nNo duplicate coordinates are given, i. e. , if i ! = j then x_i ! = x_r or y_i ! = y_j.\n\nThe area enclosed by the polygon has a positive value.\n\nAny three coordinates that define an area are not aligned on a line.", "output": "Output the distance of the shortest possible expedition route. Any number of decimal places can be selected as long as the error does not exceed ± 10^-3.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0\n4 0\n4\n1 1\n2 1\n3 3\n1 2\n output: 4.472136", "input: 4 4\n0 0\n4\n1 1\n3 1\n3 3\n1 3\n output: 6.32455"], "Pid": "p00370", "ProblemText": "Task Description: The Onogawa Expedition is planning to conduct a survey of the Aizu nature reserve. The expedition planner wants to take the shortest possible route from the start to end point of the survey, while the expedition has to go around the coast of the Lake of Onogawa en route. The expedition walks along the coast of the lake, but can not wade across the lake.\n\n Based on the base information including the start and end point of the survey and the area of Lake Onogawa as convex polygon data, make a program to find the shortest possible route for the expedition and calculate its distance. Note that the expedition can move along the polygonal lines passing through the nodes, but never enter within the area enclosed by the polygon.\nTask Input: The input is given in the following format.\n\nx_s y_s\nx_g y_g\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\nThe first line provides the start point of the survey x_s, y_s (0<=x_s, y_s<=10^4), and the second line provides the end point x_g, y_g (0 <= x_g, y_g <= 10^4) all in integers. The third line provides the number of apexes N (3 <= N <= 100) of the polygon that represents the lake, and each of the subsequent N lines provides the coordinate of the i-th apex x_i, y_i (0 <= x_i, y_i <= 10^4) in counter-clockwise order. These data satisfy the following criteria:\n\nStart and end points of the expedition are not within the area enclosed by the polygon nor on boundaries.\n\nStart and end points of the expedition are not identical, i. e. , x_s ! = x_g or y_s ! = y_g.\n\nNo duplicate coordinates are given, i. e. , if i ! = j then x_i ! = x_r or y_i ! = y_j.\n\nThe area enclosed by the polygon has a positive value.\n\nAny three coordinates that define an area are not aligned on a line.\nTask Output: Output the distance of the shortest possible expedition route. Any number of decimal places can be selected as long as the error does not exceed ± 10^-3.\nTask Samples: input: 0 0\n4 0\n4\n1 1\n2 1\n3 3\n1 2\n output: 4.472136\ninput: 4 4\n0 0\n4\n1 1\n3 1\n3 3\n1 3\n output: 6.32455\n\n" }, { "title": "Lottery Box", "content": "A lottery is being held in a corner of the venue of the Aizu festival. Several types of balls are inside the lottery box and each type has its unique integer printed on the surfaces of the balls. An integer T is printed on the lottery box.\n\nIn the lottery, you first declare two integers A and B, and draw up to M balls from the box. Let the sum of the integers printed on the balls be S. You can get a wonderful gift if the following two criteria are met: S divided by T gives a remainder greater than or equal to A, and S divided by T gives a quotient (fractional portion dropped) greater than or equal to B.\n\n Write a program to determine if you have any chance of getting the gift given the following information: the number of ball types, ball-type specific integers, the maximum number of balls to be drawn from the box, the integer printed on the lottery box, and two integers declared before drawing. Assume that each ball type has sufficient (>=M) population in the box. Note also that there may be a chance of getting the gift even without drawing any ball.", "constraint": "", "input": "The input is given in the following format.\n\nN M T\na_1\na_2\n:\na_N\nQ\nA_1 B_1\nA_2 B_2\n:\nA_Q B_Q\n\nThe first line provides the number of ball types N(1<=N<=10^5), the maximum number of balls you can draw from the box M(1<=M<=10^5), and the integer printed on the box T(1<=T<=1000). Each of the subsequent N lines provides an integer a_i (1<=a_i<=10^9) printed on the i-th ball type. The next line following these provides the number of declarations Q (1<=Q<=10^5). Each of the Q lines following this provides a pair of integers A_i (0 <= A_i < T), B_i (0 <= B_i <= 10^9) that constitute the i-th declaration.", "output": "Output a line for each pair of declaration A and B that contains \"yes\" if there is a chance of getting the gift or \"no\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 7\n8\n3\n6\n5\n2 2\n3 2\n4 1\n6 1\n6 0\n output: yes\nno\nyes\nno\nyes"], "Pid": "p00371", "ProblemText": "Task Description: A lottery is being held in a corner of the venue of the Aizu festival. Several types of balls are inside the lottery box and each type has its unique integer printed on the surfaces of the balls. An integer T is printed on the lottery box.\n\nIn the lottery, you first declare two integers A and B, and draw up to M balls from the box. Let the sum of the integers printed on the balls be S. You can get a wonderful gift if the following two criteria are met: S divided by T gives a remainder greater than or equal to A, and S divided by T gives a quotient (fractional portion dropped) greater than or equal to B.\n\n Write a program to determine if you have any chance of getting the gift given the following information: the number of ball types, ball-type specific integers, the maximum number of balls to be drawn from the box, the integer printed on the lottery box, and two integers declared before drawing. Assume that each ball type has sufficient (>=M) population in the box. Note also that there may be a chance of getting the gift even without drawing any ball.\nTask Input: The input is given in the following format.\n\nN M T\na_1\na_2\n:\na_N\nQ\nA_1 B_1\nA_2 B_2\n:\nA_Q B_Q\n\nThe first line provides the number of ball types N(1<=N<=10^5), the maximum number of balls you can draw from the box M(1<=M<=10^5), and the integer printed on the box T(1<=T<=1000). Each of the subsequent N lines provides an integer a_i (1<=a_i<=10^9) printed on the i-th ball type. The next line following these provides the number of declarations Q (1<=Q<=10^5). Each of the Q lines following this provides a pair of integers A_i (0 <= A_i < T), B_i (0 <= B_i <= 10^9) that constitute the i-th declaration.\nTask Output: Output a line for each pair of declaration A and B that contains \"yes\" if there is a chance of getting the gift or \"no\" otherwise.\nTask Samples: input: 3 2 7\n8\n3\n6\n5\n2 2\n3 2\n4 1\n6 1\n6 0\n output: yes\nno\nyes\nno\nyes\n\n" }, { "title": "Party", "content": "The students in a class in Akabe high-school define the relation “acquaintance” as: \n\nIf A and B are friends, then A is acquainted with B.\n\nIf A and B are friends and B is acquainted with C, then A is acquainted with C.\n They define the relation “companion” as:\n\n\n\n Suppose A is acquainted with B, and two classmates who have been friend distance. If A is still acquainted with B, then A and B are companions.\n \nA boy PCK joined the class recently and wishes to hold a party inviting his class fellows. He wishes to invite as many boys and girls as possible to the party and has written up an invitation list. In arranging the list, he placed the following conditions based on the acquaintanceship within the class before he joined.\n\n When T is in the list:\n\nU is listed if he/she is a companion of T.\n\nIf U is not a companion of T, U is not listed if he/she and T are friends, or he/she and some of T 's companions are friends.\n PCK made the invitation list so that the maximum number of his classmates is included.\n\n Given the number of classmates N and the friendships among them, write a program to estimate the number of boys and girls in the list. All the classmates are identified by an index that ranges from 0 to N-1.", "constraint": "", "input": "The input is given in the following format.\n\nN M\ns_1 t_1\ns_2 t_2\n:\ns_M t_M\n\nThe first line provides the number of classmates N (2 <= N <= 10^5) and the number of friendships M (1 <= M <= 2*10^5). Each of the M subsequent lines provides two of the classmates s_i, t_i (0 <= s_i, t_i <= N-1) indicating they are friends. No duplicate relationship appears among these lines.", "output": "Output the maximum number of classmates PCK invited to the party.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 8\n0 1\n1 2\n1 3\n2 3\n0 4\n4 5\n4 6\n5 6\n output: 6", "input: 3 2\n0 1\n1 2\n output: 2"], "Pid": "p00372", "ProblemText": "Task Description: The students in a class in Akabe high-school define the relation “acquaintance” as: \n\nIf A and B are friends, then A is acquainted with B.\n\nIf A and B are friends and B is acquainted with C, then A is acquainted with C.\n They define the relation “companion” as:\n\n\n\n Suppose A is acquainted with B, and two classmates who have been friend distance. If A is still acquainted with B, then A and B are companions.\n \nA boy PCK joined the class recently and wishes to hold a party inviting his class fellows. He wishes to invite as many boys and girls as possible to the party and has written up an invitation list. In arranging the list, he placed the following conditions based on the acquaintanceship within the class before he joined.\n\n When T is in the list:\n\nU is listed if he/she is a companion of T.\n\nIf U is not a companion of T, U is not listed if he/she and T are friends, or he/she and some of T 's companions are friends.\n PCK made the invitation list so that the maximum number of his classmates is included.\n\n Given the number of classmates N and the friendships among them, write a program to estimate the number of boys and girls in the list. All the classmates are identified by an index that ranges from 0 to N-1.\nTask Input: The input is given in the following format.\n\nN M\ns_1 t_1\ns_2 t_2\n:\ns_M t_M\n\nThe first line provides the number of classmates N (2 <= N <= 10^5) and the number of friendships M (1 <= M <= 2*10^5). Each of the M subsequent lines provides two of the classmates s_i, t_i (0 <= s_i, t_i <= N-1) indicating they are friends. No duplicate relationship appears among these lines.\nTask Output: Output the maximum number of classmates PCK invited to the party.\nTask Samples: input: 7 8\n0 1\n1 2\n1 3\n2 3\n0 4\n4 5\n4 6\n5 6\n output: 6\ninput: 3 2\n0 1\n1 2\n output: 2\n\n" }, { "title": "Aerial Photos", "content": "Hideyo has come by two aerial photos of the same scale and orientation. You can see various types of buildings, but some areas are hidden by clouds. Apparently, they are of the same area, and the area covered by the second photograph falls entirely within the first. However, because they were taken at different time points, different shapes and distribution of clouds obscure identification where the area in the second photograph is located in the first. There may even be more than one area within the first that the second fits equally well.\n\n A set of pixel information is given for each of the photographs. Write a program to extract candidate sub-areas within the first photograph that compare with the second equally well and output the number of the candidates.", "constraint": "", "input": "The input is given in the following format.\n\nAW AH BW BH\narow_1\narow_2\n:\narow_AH\nbrow_1\nbrow_2\n:\nbrow_BH\n\nThe first line provides the number of pixels in the horizontal and the vertical direction AW (1 <= AW <= 800) and AH (1 <= AH <= 800) for the first photograph, followed by those for the second BW (1 <= BW <= 100) and BH (1 <= BH <= 100) (AW >= BW and AH >= BH). Each of the subsequent AH lines provides pixel information (arow_i) of the i-th row from the top of the first photograph. Each of the BH lines that follows provides pixel information (brow_i) of the i-th row from the top of the second photograph.\n Each of the pixel information arow_i and brow_i is a string of length AW and BW, respectively, consisting of upper/lower-case letters, numeric characters, or \"? \". Each one character represents a pixel, whereby upper/lower-case letters and numeric characters represent a type of building, and \"? \" indicates a cloud-covered area.", "output": "Output the number of the candidates.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5 3 3\nAF??z\nW?p88\n???Hk\npU?m?\nF???c\nF??\np?8\n?H?\n output: 4", "input: 6 5 4 2\naaaaaa\naaaaaa\naaaaaa\naaaaaa\naaaaaa\naaaa\naaaa\n output: 12"], "Pid": "p00373", "ProblemText": "Task Description: Hideyo has come by two aerial photos of the same scale and orientation. You can see various types of buildings, but some areas are hidden by clouds. Apparently, they are of the same area, and the area covered by the second photograph falls entirely within the first. However, because they were taken at different time points, different shapes and distribution of clouds obscure identification where the area in the second photograph is located in the first. There may even be more than one area within the first that the second fits equally well.\n\n A set of pixel information is given for each of the photographs. Write a program to extract candidate sub-areas within the first photograph that compare with the second equally well and output the number of the candidates.\nTask Input: The input is given in the following format.\n\nAW AH BW BH\narow_1\narow_2\n:\narow_AH\nbrow_1\nbrow_2\n:\nbrow_BH\n\nThe first line provides the number of pixels in the horizontal and the vertical direction AW (1 <= AW <= 800) and AH (1 <= AH <= 800) for the first photograph, followed by those for the second BW (1 <= BW <= 100) and BH (1 <= BH <= 100) (AW >= BW and AH >= BH). Each of the subsequent AH lines provides pixel information (arow_i) of the i-th row from the top of the first photograph. Each of the BH lines that follows provides pixel information (brow_i) of the i-th row from the top of the second photograph.\n Each of the pixel information arow_i and brow_i is a string of length AW and BW, respectively, consisting of upper/lower-case letters, numeric characters, or \"? \". Each one character represents a pixel, whereby upper/lower-case letters and numeric characters represent a type of building, and \"? \" indicates a cloud-covered area.\nTask Output: Output the number of the candidates.\nTask Samples: input: 5 5 3 3\nAF??z\nW?p88\n???Hk\npU?m?\nF???c\nF??\np?8\n?H?\n output: 4\ninput: 6 5 4 2\naaaaaa\naaaaaa\naaaaaa\naaaaaa\naaaaaa\naaaa\naaaa\n output: 12\n\n" }, { "title": "Iron Bars", "content": "A boy PCK had N straight iron bars, which were serially indexed. Unfortunately, the first M bars (0 <= M <= N) among them were bent during transportation. They all suffered a perpendicular bend at one point.\n\n He is planning to make a cube using a set of bars selected using the following rules: X bars from bent ones, Y bars from straight ones, where 2X + Y = 12. Any two bars can be jointed only at the apexes of the cube. He wants to count how many types of rectangular parallelepipeds (hereafter RP) he can make using these bars.\n\nMake a program to count out types (different shapes) of RPs that PCK can make using the following information: the number of bars and length of each one, position of the bend, and the number of bars to be used to construct an RP. Note that any two RPs similar in shape are considered identical: namely if the length of three defining sides of two RPs coincide if arranged in increasing/decreasing order (e. g. , three sides of RP i and j are A_i, B_i, C_i, and A_j, B_j and C_j in increasing order, then the relations A_i = A_j, B_i = B_j, and C_i = C_j hold. Note also that the bars are sufficiently thin to allow you to consider them as idealized lines.", "constraint": "", "input": "The input is given in the following format.\n\nN M X Y\na_1\na_2\n:\na_N\nb_1\nb_2\n:\nb_M\n\nThe first line provides the total number of iron bars and bent bars, and those straight and bent bars used to construct an RP: N (6 <= N <= 6000), M (0 <= M <= N), X (0 <= X <= 6), and Y (0 <= Y <= 12). The following relations always hold for them: 2X+Y=12, X+Y <= N, X <= M. Each of the subsequent N lines provides the length of the i-th bar a_i (1 <= a_i <= 6000) in integers. Furthermore, each of the subsequent M lines provides the location at which the i-th bent bar suffered a perpendicular bend b_i (1 <= b_i <= 3000) in centimeters from one end of the bar (note: 1 <= a_i-b_i <= 3000).", "output": "Output the number of constructible rectangular parallelepipeds.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 18 8 3 6\n4\n3\n3\n3\n3\n2\n2\n2\n1\n1\n1\n1\n1\n2\n2\n3\n3\n3\n1\n1\n1\n1\n1\n1\n1\n1\n output: 3"], "Pid": "p00374", "ProblemText": "Task Description: A boy PCK had N straight iron bars, which were serially indexed. Unfortunately, the first M bars (0 <= M <= N) among them were bent during transportation. They all suffered a perpendicular bend at one point.\n\n He is planning to make a cube using a set of bars selected using the following rules: X bars from bent ones, Y bars from straight ones, where 2X + Y = 12. Any two bars can be jointed only at the apexes of the cube. He wants to count how many types of rectangular parallelepipeds (hereafter RP) he can make using these bars.\n\nMake a program to count out types (different shapes) of RPs that PCK can make using the following information: the number of bars and length of each one, position of the bend, and the number of bars to be used to construct an RP. Note that any two RPs similar in shape are considered identical: namely if the length of three defining sides of two RPs coincide if arranged in increasing/decreasing order (e. g. , three sides of RP i and j are A_i, B_i, C_i, and A_j, B_j and C_j in increasing order, then the relations A_i = A_j, B_i = B_j, and C_i = C_j hold. Note also that the bars are sufficiently thin to allow you to consider them as idealized lines.\nTask Input: The input is given in the following format.\n\nN M X Y\na_1\na_2\n:\na_N\nb_1\nb_2\n:\nb_M\n\nThe first line provides the total number of iron bars and bent bars, and those straight and bent bars used to construct an RP: N (6 <= N <= 6000), M (0 <= M <= N), X (0 <= X <= 6), and Y (0 <= Y <= 12). The following relations always hold for them: 2X+Y=12, X+Y <= N, X <= M. Each of the subsequent N lines provides the length of the i-th bar a_i (1 <= a_i <= 6000) in integers. Furthermore, each of the subsequent M lines provides the location at which the i-th bent bar suffered a perpendicular bend b_i (1 <= b_i <= 3000) in centimeters from one end of the bar (note: 1 <= a_i-b_i <= 3000).\nTask Output: Output the number of constructible rectangular parallelepipeds.\nTask Samples: input: 18 8 3 6\n4\n3\n3\n3\n3\n2\n2\n2\n1\n1\n1\n1\n1\n2\n2\n3\n3\n3\n1\n1\n1\n1\n1\n1\n1\n1\n output: 3\n\n" }, { "title": "Celsius/Fahrenheit", "content": "In Japan, temperature is usually expressed using the Celsius (℃) scale. In America, they used the Fahrenheit (℉) scale instead. $20$ degrees Celsius is roughly equal to $68$ degrees Fahrenheit. A phrase such as \"Today 's temperature is $68$ degrees\" is commonly encountered while you are in America.\n\nA value in Fahrenheit can be converted to Celsius by first subtracting $32$ and then multiplying by $\\frac{5}{9}$. A simplified method may be used to produce a rough estimate: first subtract $30$ and then divide by $2$. Using the latter method, $68$ Fahrenheit is converted to $19$ Centigrade, i. e. , $\\frac{(68-30)}{2}$.\n\n Make a program to convert Fahrenheit to Celsius using the simplified method: $C = \\frac{F - 30}{2}$.", "constraint": "", "input": "The input is given in the following format.\n\n$F$\n\n The input line provides a temperature in Fahrenheit $F$ ($30 <= F <= 100$), which is an integer divisible by $2$.", "output": "Output the converted Celsius temperature in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 68\n output: 19", "input: 50\n output: 10"], "Pid": "p00375", "ProblemText": "Task Description: In Japan, temperature is usually expressed using the Celsius (℃) scale. In America, they used the Fahrenheit (℉) scale instead. $20$ degrees Celsius is roughly equal to $68$ degrees Fahrenheit. A phrase such as \"Today 's temperature is $68$ degrees\" is commonly encountered while you are in America.\n\nA value in Fahrenheit can be converted to Celsius by first subtracting $32$ and then multiplying by $\\frac{5}{9}$. A simplified method may be used to produce a rough estimate: first subtract $30$ and then divide by $2$. Using the latter method, $68$ Fahrenheit is converted to $19$ Centigrade, i. e. , $\\frac{(68-30)}{2}$.\n\n Make a program to convert Fahrenheit to Celsius using the simplified method: $C = \\frac{F - 30}{2}$.\nTask Input: The input is given in the following format.\n\n$F$\n\n The input line provides a temperature in Fahrenheit $F$ ($30 <= F <= 100$), which is an integer divisible by $2$.\nTask Output: Output the converted Celsius temperature in a line.\nTask Samples: input: 68\n output: 19\ninput: 50\n output: 10\n\n" }, { "title": "Red Dragonfly", "content": "It 's still hot every day, but September has already come. It 's autumn according to the calendar. Looking around, I see two red dragonflies at rest on the wall in front of me. It 's autumn indeed.\n\n When two red dragonflies ' positional information as measured from the end of the wall is given, make a program to calculate the distance between their heads.", "constraint": "", "input": "The input is given in the following format.\n\n$x_1$ $x_2$\n\n The input line provides dragonflies ' head positions $x_1$ and $x_2$ ($0 <= x_1, x_2 <= 100$) as integers.", "output": "Output the distance between the two red dragonflies in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 20 30\n output: 10", "input: 50 25\n output: 25", "input: 25 25\n output: 0"], "Pid": "p00376", "ProblemText": "Task Description: It 's still hot every day, but September has already come. It 's autumn according to the calendar. Looking around, I see two red dragonflies at rest on the wall in front of me. It 's autumn indeed.\n\n When two red dragonflies ' positional information as measured from the end of the wall is given, make a program to calculate the distance between their heads.\nTask Input: The input is given in the following format.\n\n$x_1$ $x_2$\n\n The input line provides dragonflies ' head positions $x_1$ and $x_2$ ($0 <= x_1, x_2 <= 100$) as integers.\nTask Output: Output the distance between the two red dragonflies in a line.\nTask Samples: input: 20 30\n output: 10\ninput: 50 25\n output: 25\ninput: 25 25\n output: 0\n\n" }, { "title": "Cake Party", "content": "I 'm planning to have a party on my birthday. Many of my friends will come to the party. Some of them will come with one or more pieces of cakes, but it is not certain if the number of the cakes is a multiple of the number of people coming.\n \n I wish to enjoy the cakes equally among the partiers. So, I decided to apply the following rules. First, all the party attendants are given the same number of cakes. If some remainder occurs, a piece goes on a priority basis to the party host (that 's me! ). How many pieces of cake can I enjoy?\n Given the number of my friends and cake information, make a program to calculate how many pieces of cake I can enjoy. Note that I am not counted in the number of my friends.", "constraint": "", "input": "The input is given in the following format.\n\n$N$ $C$\n$p_1$ $p_2$ . . . $p_C$\n\nThe first line provides the number of my friends $N$ ($1 <= N <= 100$) and the number of those among them who brought one or more pieces of cake with them $C$ ($1 <= C <= N$). The second line provides an array of integers $p_i$ ($1 <= p_i <=100$), each of which shows the number of cakes of the $i$-th friend of mine who was willing to come up with one or more pieces of cake.", "output": "Output the number of cakes I can enjoy.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n5 5 6 5\n output: 4", "input: 7 5\n8 8 8 8 8\n output: 5", "input: 100 3\n3 3 3\n output: 1"], "Pid": "p00377", "ProblemText": "Task Description: I 'm planning to have a party on my birthday. Many of my friends will come to the party. Some of them will come with one or more pieces of cakes, but it is not certain if the number of the cakes is a multiple of the number of people coming.\n \n I wish to enjoy the cakes equally among the partiers. So, I decided to apply the following rules. First, all the party attendants are given the same number of cakes. If some remainder occurs, a piece goes on a priority basis to the party host (that 's me! ). How many pieces of cake can I enjoy?\n Given the number of my friends and cake information, make a program to calculate how many pieces of cake I can enjoy. Note that I am not counted in the number of my friends.\nTask Input: The input is given in the following format.\n\n$N$ $C$\n$p_1$ $p_2$ . . . $p_C$\n\nThe first line provides the number of my friends $N$ ($1 <= N <= 100$) and the number of those among them who brought one or more pieces of cake with them $C$ ($1 <= C <= N$). The second line provides an array of integers $p_i$ ($1 <= p_i <=100$), each of which shows the number of cakes of the $i$-th friend of mine who was willing to come up with one or more pieces of cake.\nTask Output: Output the number of cakes I can enjoy.\nTask Samples: input: 5 4\n5 5 6 5\n output: 4\ninput: 7 5\n8 8 8 8 8\n output: 5\ninput: 100 3\n3 3 3\n output: 1\n\n" }, { "title": "Heat Stroke", "content": "We have had record hot temperatures this summer. To avoid heat stroke, you decided to buy a quantity of drinking water at the nearby supermarket. Two types of bottled water, 1 and 0.5 liter, are on sale at respective prices there. You have a definite quantity in your mind, but are willing to buy a quantity larger than that if: no combination of these bottles meets the quantity, or, the total price becomes lower.\n\n Given the prices for each bottle of water and the total quantity needed, make a program to seek the lowest price to buy greater than or equal to the quantity required.", "constraint": "", "input": "The input is given in the following format.\n\n$A$ $B$ $X$\n\n The first line provides the prices for a 1-liter bottle $A$ ($1<= A <= 1000$), 500-milliliter bottle $B$ ($1 <= B <= 1000$), and the total water quantity needed $X$ ($1 <= X <= 20000$). All these values are given as integers, and the quantity of water in milliliters.", "output": "Output the total price.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 180 100 2400\n output: 460", "input: 200 90 2018\n output: 450"], "Pid": "p00378", "ProblemText": "Task Description: We have had record hot temperatures this summer. To avoid heat stroke, you decided to buy a quantity of drinking water at the nearby supermarket. Two types of bottled water, 1 and 0.5 liter, are on sale at respective prices there. You have a definite quantity in your mind, but are willing to buy a quantity larger than that if: no combination of these bottles meets the quantity, or, the total price becomes lower.\n\n Given the prices for each bottle of water and the total quantity needed, make a program to seek the lowest price to buy greater than or equal to the quantity required.\nTask Input: The input is given in the following format.\n\n$A$ $B$ $X$\n\n The first line provides the prices for a 1-liter bottle $A$ ($1<= A <= 1000$), 500-milliliter bottle $B$ ($1 <= B <= 1000$), and the total water quantity needed $X$ ($1 <= X <= 20000$). All these values are given as integers, and the quantity of water in milliliters.\nTask Output: Output the total price.\nTask Samples: input: 180 100 2400\n output: 460\ninput: 200 90 2018\n output: 450\n\n" }, { "title": "Dudeney Number", "content": "A Dudeney number is a positive integer for which the sum of its decimal digits is equal to the cube root of the number. For example, $512$ is a Dudeney number because it is the cube of $8$, which is the sum of its decimal digits ($5 + 1 + 2$).\n\n In this problem, we think of a type similar to Dudeney numbers and try to enumerate them.\n\n Given a non-negative integer $a$, an integer $n$ greater than or equal to 2 and an upper limit $m$, make a program to enumerate all $x$ 's such that the sum of its decimal digits $y$ satisfies the relation $x = (y + a)^n$, and $x <= m$.", "constraint": "", "input": "The input is given in the following format.\n\n$a$ $n$ $m$\n\n The input line provides three integers: $a$ ($0 <= a <= 50$), $n$ ($2 <= n <= 10$) and the upper limit $m$ ($1000 <= m <= 10^8$).", "output": "Output the number of integers that meet the above criteria.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 16 2 1000\n output: 2\n Two: $400 = (4 + 0 + 0 + 16)^2$ and $841 = (8 + 4 + 1 + 16)^2$", "input: 0 3 5000\n output: 3\n Three: $1=1^3$, $512 = (5 + 1 + 2)^3$ and $4913 = (4 + 9 + 1 + 3)^3$.", "input: 2 3 100000\n output: 0\n There is no such number $x$ in the range below $100,000$ such that its sum of decimal digits $y$ satisfies the relation $(y+2)^3 = x$."], "Pid": "p00379", "ProblemText": "Task Description: A Dudeney number is a positive integer for which the sum of its decimal digits is equal to the cube root of the number. For example, $512$ is a Dudeney number because it is the cube of $8$, which is the sum of its decimal digits ($5 + 1 + 2$).\n\n In this problem, we think of a type similar to Dudeney numbers and try to enumerate them.\n\n Given a non-negative integer $a$, an integer $n$ greater than or equal to 2 and an upper limit $m$, make a program to enumerate all $x$ 's such that the sum of its decimal digits $y$ satisfies the relation $x = (y + a)^n$, and $x <= m$.\nTask Input: The input is given in the following format.\n\n$a$ $n$ $m$\n\n The input line provides three integers: $a$ ($0 <= a <= 50$), $n$ ($2 <= n <= 10$) and the upper limit $m$ ($1000 <= m <= 10^8$).\nTask Output: Output the number of integers that meet the above criteria.\nTask Samples: input: 16 2 1000\n output: 2\n Two: $400 = (4 + 0 + 0 + 16)^2$ and $841 = (8 + 4 + 1 + 16)^2$\ninput: 0 3 5000\n output: 3\n Three: $1=1^3$, $512 = (5 + 1 + 2)^3$ and $4913 = (4 + 9 + 1 + 3)^3$.\ninput: 2 3 100000\n output: 0\n There is no such number $x$ in the range below $100,000$ such that its sum of decimal digits $y$ satisfies the relation $(y+2)^3 = x$.\n\n" }, { "title": "Bozosort", "content": "Bozosort, as well as Bogosort, is a very inefficient sort algorithm. It is a random number-based algorithm that sorts sequence elements following the steps as below:\n\n Randomly select two elements and swap them.\n\n Verify if all the elements are sorted in increasing order.\n\n Finish if sorted, else return to 1.\n To analyze Bozosort, you have decided to simulate the process using several predetermined pairs of elements.\n\n You are given several commands to swap two elements. Make a program to evaluate how many times you have to run the command before the sequence is aligned in increasing order.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$a_1$ $a_2$ . . . $a_N$\n$Q$\n$x_1$ $y_1$\n$x_2$ $y_2$\n$. . . $\n$x_Q$ $y_Q$\n\nThe first line provides the number of sequence elements $N$ ($2 <= N <= 300,000$). The second line provides an array of integers $a_i$ ($1 <= a_i <= 10^9$) that constitutes the sequence. Each of the subsequent $Q$ lines provides a pair of integers $x_i, y_i$ ($1 <= x_i, y_i <= N$) that represent the $i$-th command, which swaps the two elements indicated by $x_i$ and $y_i$ ($x_i \\ne y_i$).", "output": "If neat alignment in increasing order is realized the first time after execution of multiple commands, output at what time it was. Output 0 if the initial sequence is aligned in increasing order, and -1 if exhaustive execution still failed to attain the goal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n9 7 5 6 3 1\n3\n1 6\n2 5\n3 4\n output: 2", "input: 4\n4 3 2 1\n2\n1 2\n3 4\n output: -1", "input: 5\n1 1 1 2 2\n1\n1 2\n output: 0"], "Pid": "p00380", "ProblemText": "Task Description: Bozosort, as well as Bogosort, is a very inefficient sort algorithm. It is a random number-based algorithm that sorts sequence elements following the steps as below:\n\n Randomly select two elements and swap them.\n\n Verify if all the elements are sorted in increasing order.\n\n Finish if sorted, else return to 1.\n To analyze Bozosort, you have decided to simulate the process using several predetermined pairs of elements.\n\n You are given several commands to swap two elements. Make a program to evaluate how many times you have to run the command before the sequence is aligned in increasing order.\nTask Input: The input is given in the following format.\n\n$N$\n$a_1$ $a_2$ . . . $a_N$\n$Q$\n$x_1$ $y_1$\n$x_2$ $y_2$\n$. . . $\n$x_Q$ $y_Q$\n\nThe first line provides the number of sequence elements $N$ ($2 <= N <= 300,000$). The second line provides an array of integers $a_i$ ($1 <= a_i <= 10^9$) that constitutes the sequence. Each of the subsequent $Q$ lines provides a pair of integers $x_i, y_i$ ($1 <= x_i, y_i <= N$) that represent the $i$-th command, which swaps the two elements indicated by $x_i$ and $y_i$ ($x_i \\ne y_i$).\nTask Output: If neat alignment in increasing order is realized the first time after execution of multiple commands, output at what time it was. Output 0 if the initial sequence is aligned in increasing order, and -1 if exhaustive execution still failed to attain the goal.\nTask Samples: input: 6\n9 7 5 6 3 1\n3\n1 6\n2 5\n3 4\n output: 2\ninput: 4\n4 3 2 1\n2\n1 2\n3 4\n output: -1\ninput: 5\n1 1 1 2 2\n1\n1 2\n output: 0\n\n" }, { "title": "Transporter", "content": "In the year 30XX, an expedition team reached a planet and found a warp machine suggesting the existence of a mysterious supercivilization. When you go through one of its entrance gates, you can instantaneously move to the exit irrespective of how far away it is. You can move even to the end of the universe at will with this technology!\n\n The scientist team started examining the machine and successfully identified all the planets on which the entrances to the machine were located. Each of these N planets (identified by an index from $1$ to $N$) has an entrance to, and an exit from the warp machine. Each of the entrances and exits has a letter inscribed on it.\n\n The mechanism of spatial mobility through the warp machine is as follows:\n\nIf you go into an entrance gate labeled with c, then you can exit from any gate with label c.\n\nIf you go into an entrance located on the $i$-th planet, then you can exit from any gate located on the $j$-th planet where $i < j$.\n Once you have reached an exit of the warp machine on a planet, you can continue your journey by entering into the warp machine on the same planet. In this way, you can reach a faraway planet. Our human race has decided to dispatch an expedition to the star $N$, starting from Star $1$ and using the warp machine until it reaches Star $N$. To evaluate the possibility of successfully reaching the destination. it is highly desirable for us to know how many different routes are available for the expedition team to track.\n\n Given information regarding the stars, make a program to enumerate the passages from Star $1$ to Star $N$.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$s$\n$t$\n\n The first line provides the number of the stars on which the warp machine is located $N$ ($2 <= N <= 100,000$). The second line provides a string $s$ of length $N$, each component of which represents the letter inscribed on the entrance of the machine on the star. By the same token, the third line provides a string $t$ of length $N$ consisting of the letters inscribed on the exit of the machine. Two strings $s$ and $t$ consist all of lower-case alphabetical letters, and the $i$-th letter of these strings corresponds respectively to the entrance and exit of Star $i$ machine.", "output": "Divide the number of possible routes from Star $1$ to Star $N$ obtained above by 1,000,000,007, and output the remainder.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\nabbaba\nbaabab\n output: 5", "input: 25\nneihsokcpuziafoytisrevinu\nuniversityofaizupckoshien\n output: 4"], "Pid": "p00381", "ProblemText": "Task Description: In the year 30XX, an expedition team reached a planet and found a warp machine suggesting the existence of a mysterious supercivilization. When you go through one of its entrance gates, you can instantaneously move to the exit irrespective of how far away it is. You can move even to the end of the universe at will with this technology!\n\n The scientist team started examining the machine and successfully identified all the planets on which the entrances to the machine were located. Each of these N planets (identified by an index from $1$ to $N$) has an entrance to, and an exit from the warp machine. Each of the entrances and exits has a letter inscribed on it.\n\n The mechanism of spatial mobility through the warp machine is as follows:\n\nIf you go into an entrance gate labeled with c, then you can exit from any gate with label c.\n\nIf you go into an entrance located on the $i$-th planet, then you can exit from any gate located on the $j$-th planet where $i < j$.\n Once you have reached an exit of the warp machine on a planet, you can continue your journey by entering into the warp machine on the same planet. In this way, you can reach a faraway planet. Our human race has decided to dispatch an expedition to the star $N$, starting from Star $1$ and using the warp machine until it reaches Star $N$. To evaluate the possibility of successfully reaching the destination. it is highly desirable for us to know how many different routes are available for the expedition team to track.\n\n Given information regarding the stars, make a program to enumerate the passages from Star $1$ to Star $N$.\nTask Input: The input is given in the following format.\n\n$N$\n$s$\n$t$\n\n The first line provides the number of the stars on which the warp machine is located $N$ ($2 <= N <= 100,000$). The second line provides a string $s$ of length $N$, each component of which represents the letter inscribed on the entrance of the machine on the star. By the same token, the third line provides a string $t$ of length $N$ consisting of the letters inscribed on the exit of the machine. Two strings $s$ and $t$ consist all of lower-case alphabetical letters, and the $i$-th letter of these strings corresponds respectively to the entrance and exit of Star $i$ machine.\nTask Output: Divide the number of possible routes from Star $1$ to Star $N$ obtained above by 1,000,000,007, and output the remainder.\nTask Samples: input: 6\nabbaba\nbaabab\n output: 5\ninput: 25\nneihsokcpuziafoytisrevinu\nuniversityofaizupckoshien\n output: 4\n\n" }, { "title": "Taxi", "content": "PCK Taxi in Aizu city, owned by PCK company, has adopted a unique billing system: the user can decide the taxi fare. Today as usual, many people are waiting in a queue at the taxi stand in front of the station.\n\n In front of the station, there are $N$ parking spaces in row for PCK taxis, each with an index running from $1$ to $N$. Each of the parking areas is occupied by a taxi, and a queue of potential passengers is waiting for the ride. Each one in the queue has his/her own plan for how much to pay for the ride.\n\n To increase the company 's gain, the taxi driver is given the right to select the passenger who offers the highest taxi fare, rejecting others.\n\n The driver in the $i$-th parking space can perform the following actions any number of times in any sequence before he finally selects a passenger and starts driving.\n\nOffer a ride to the passenger who is at the head of the $i$-th parking space 's queue.\n\nReject to offer a ride to the passenger who is at the head of the $i$-th parking space 's queue. The passenger is removed from the queue.\n\nMove to the $i + 1$-th parking area if it is empty. If he is in the $N$-th parking area, he leaves the taxi stand to cruise the open road.\n A preliminary listening is made as to the fare the users offer. Your task is to maximize the sales volume of PCK Taxi in reference to the table of offered fares. A taxi cannot accommodate more than one passenger.\n\n Given the number of taxi parking spaces and information regarding the persons waiting in the parking areas, calculate the maximum possible volume of sales.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$s_1$\n$s_2$\n$. . . $\n$s_N$\n\nThe first line provides the number of taxi parking areas $N$ ($1 <= N <= 300,000$). Each of the subsequent $N$ lines provides information on the customers queueing in the $i$-th taxi parking area in the following format:\n\n$M$ $c_1$ $c_2$ . . . $c_M$\n\n The first integer $M$ ($1 <= M <= 300,000$) indicates the number of customers in the queue, and the subsequent array of integers $c_j$ ($1 <= c_j <= 10,000$) indicates the fare the $j$-th customer in the queue is willing to pay. The total number of customers in the taxi stand is equal to or less than $300,000$.", "output": "Output the maximum volume of sales.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 8 10 1\n4 7 1 2 15\n3 11 8 19\n output: 45"], "Pid": "p00382", "ProblemText": "Task Description: PCK Taxi in Aizu city, owned by PCK company, has adopted a unique billing system: the user can decide the taxi fare. Today as usual, many people are waiting in a queue at the taxi stand in front of the station.\n\n In front of the station, there are $N$ parking spaces in row for PCK taxis, each with an index running from $1$ to $N$. Each of the parking areas is occupied by a taxi, and a queue of potential passengers is waiting for the ride. Each one in the queue has his/her own plan for how much to pay for the ride.\n\n To increase the company 's gain, the taxi driver is given the right to select the passenger who offers the highest taxi fare, rejecting others.\n\n The driver in the $i$-th parking space can perform the following actions any number of times in any sequence before he finally selects a passenger and starts driving.\n\nOffer a ride to the passenger who is at the head of the $i$-th parking space 's queue.\n\nReject to offer a ride to the passenger who is at the head of the $i$-th parking space 's queue. The passenger is removed from the queue.\n\nMove to the $i + 1$-th parking area if it is empty. If he is in the $N$-th parking area, he leaves the taxi stand to cruise the open road.\n A preliminary listening is made as to the fare the users offer. Your task is to maximize the sales volume of PCK Taxi in reference to the table of offered fares. A taxi cannot accommodate more than one passenger.\n\n Given the number of taxi parking spaces and information regarding the persons waiting in the parking areas, calculate the maximum possible volume of sales.\nTask Input: The input is given in the following format.\n\n$N$\n$s_1$\n$s_2$\n$. . . $\n$s_N$\n\nThe first line provides the number of taxi parking areas $N$ ($1 <= N <= 300,000$). Each of the subsequent $N$ lines provides information on the customers queueing in the $i$-th taxi parking area in the following format:\n\n$M$ $c_1$ $c_2$ . . . $c_M$\n\n The first integer $M$ ($1 <= M <= 300,000$) indicates the number of customers in the queue, and the subsequent array of integers $c_j$ ($1 <= c_j <= 10,000$) indicates the fare the $j$-th customer in the queue is willing to pay. The total number of customers in the taxi stand is equal to or less than $300,000$.\nTask Output: Output the maximum volume of sales.\nTask Samples: input: 3\n3 8 10 1\n4 7 1 2 15\n3 11 8 19\n output: 45\n\n" }, { "title": "Points on a Straight Line", "content": "The university of A stages a programming contest this year as has been the case in the past. As a member of the team in charge of devising the problems, you have worked out a set of input data for a problem, which is an arrangement of points on a 2D plane in the coordinate system. The problem requires that any combination of these points greater than or equal to $K$ in number must not align on a line. You want to confirm that your data satisfies this requirement.\n\n Given the number of points $K$ and their respective 2D coordinates, make a program to check if any combination of points greater or equal to $K$ align on a line.", "constraint": "", "input": "The input is given in the following format.\n\n$N$ $K$\n$x_1$ $y_1$\n$x_2$ $y_2$\n$. . . $\n$x_N$ $y_N$\n The first line provides the number of points $N$ ($3 <= N <= 3000$) on the 2D coordinate system and an integer $K$ ($3 <= K <= N$). Each of the subsequent lines provides the $i$-th coordinate $x_i, y_i$ ($0 <= x_i, y_i <= 10000$) as integers. None of these coordinates coincide, i. e. , if $i \\ne j$, then $x_i \\ne x_j$ or $y_i \\ne y_j$.", "output": "Output 1 if any combination of points greater or equal to $K$ aligns on a line, or 0 otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n0 0\n1 0\n1 1\n0 1\n2 2\n output: 0", "input: 7 5\n0 0\n1 0\n1 1\n0 1\n2 0\n3 0\n4 0\n output: 1"], "Pid": "p00383", "ProblemText": "Task Description: The university of A stages a programming contest this year as has been the case in the past. As a member of the team in charge of devising the problems, you have worked out a set of input data for a problem, which is an arrangement of points on a 2D plane in the coordinate system. The problem requires that any combination of these points greater than or equal to $K$ in number must not align on a line. You want to confirm that your data satisfies this requirement.\n\n Given the number of points $K$ and their respective 2D coordinates, make a program to check if any combination of points greater or equal to $K$ align on a line.\nTask Input: The input is given in the following format.\n\n$N$ $K$\n$x_1$ $y_1$\n$x_2$ $y_2$\n$. . . $\n$x_N$ $y_N$\n The first line provides the number of points $N$ ($3 <= N <= 3000$) on the 2D coordinate system and an integer $K$ ($3 <= K <= N$). Each of the subsequent lines provides the $i$-th coordinate $x_i, y_i$ ($0 <= x_i, y_i <= 10000$) as integers. None of these coordinates coincide, i. e. , if $i \\ne j$, then $x_i \\ne x_j$ or $y_i \\ne y_j$.\nTask Output: Output 1 if any combination of points greater or equal to $K$ aligns on a line, or 0 otherwise.\nTask Samples: input: 5 4\n0 0\n1 0\n1 1\n0 1\n2 2\n output: 0\ninput: 7 5\n0 0\n1 0\n1 1\n0 1\n2 0\n3 0\n4 0\n output: 1\n\n" }, { "title": "Dungeon 2", "content": "Bob is playing a game called \"Dungeon 2\" which is the sequel to the popular \"Dungeon\" released last year. The game is played on a map consisting of $N$ rooms and $N-1$ roads connecting them. The roads allow bidirectional traffic and the player can start his tour from any room and reach any other room by way of multiple of roads. A point is printed in each of the rooms.\n\n Bob tries to accumulate the highest score by visiting the rooms by cleverly routing his character \"Tora-Tora. \" He can add the point printed in a room to his score only when he reaches the room for the first time. He can also add the points on the starting and ending rooms of Tora-Tora 's journey. The score is reduced by one each time Tora-Tore passes a road. Tora-Tora can start from any room and end his journey in any room.\n\n Given the map information, make a program to work out the maximum possible score Bob can gain.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$p_1$\n$p_2$\n$. . . $\n$p_N$\n$s_1$ $t_1$\n$s_2$ $t_2$\n$. . . $\n$s_{N-1}$ $t_{N-1}$\n\nThe first line provides the number of rooms $N$ ($1 <= N <= 100,000$). Each of the subsequent $N$ lines provides the point of the $i$-th room $p_i$ ($-100 <= p_i <= 100$) in integers. Each of the subsequent lines following these provides the information on the road directly connecting two rooms, where $s_i$ and $t_i$ ($1 <= s_i < t_i <= N$) represent the numbers of the two rooms connected by it. Not a single pair of rooms are connected by more than one road.", "output": "Output the maximum possible score Bob can gain.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n6\n1\n-1\n4\n3\n3\n1\n1 2\n2 3\n3 4\n3 5\n5 6\n5 7\n output: 10\n For example, the score is maximized by routing the rooms in the following sequence: $6 \\rightarrow 5 \\rightarrow 3 \\rightarrow 4 \\rightarrow 3 \\rightarrow 2 \\rightarrow 1$.", "input: 4\n5\n0\n1\n1\n1 2\n2 3\n2 4\n output: 5\n The score is maximized if Tora-Tora stats his journey from room 1 and ends in the same room."], "Pid": "p00384", "ProblemText": "Task Description: Bob is playing a game called \"Dungeon 2\" which is the sequel to the popular \"Dungeon\" released last year. The game is played on a map consisting of $N$ rooms and $N-1$ roads connecting them. The roads allow bidirectional traffic and the player can start his tour from any room and reach any other room by way of multiple of roads. A point is printed in each of the rooms.\n\n Bob tries to accumulate the highest score by visiting the rooms by cleverly routing his character \"Tora-Tora. \" He can add the point printed in a room to his score only when he reaches the room for the first time. He can also add the points on the starting and ending rooms of Tora-Tora 's journey. The score is reduced by one each time Tora-Tore passes a road. Tora-Tora can start from any room and end his journey in any room.\n\n Given the map information, make a program to work out the maximum possible score Bob can gain.\nTask Input: The input is given in the following format.\n\n$N$\n$p_1$\n$p_2$\n$. . . $\n$p_N$\n$s_1$ $t_1$\n$s_2$ $t_2$\n$. . . $\n$s_{N-1}$ $t_{N-1}$\n\nThe first line provides the number of rooms $N$ ($1 <= N <= 100,000$). Each of the subsequent $N$ lines provides the point of the $i$-th room $p_i$ ($-100 <= p_i <= 100$) in integers. Each of the subsequent lines following these provides the information on the road directly connecting two rooms, where $s_i$ and $t_i$ ($1 <= s_i < t_i <= N$) represent the numbers of the two rooms connected by it. Not a single pair of rooms are connected by more than one road.\nTask Output: Output the maximum possible score Bob can gain.\nTask Samples: input: 7\n6\n1\n-1\n4\n3\n3\n1\n1 2\n2 3\n3 4\n3 5\n5 6\n5 7\n output: 10\n For example, the score is maximized by routing the rooms in the following sequence: $6 \\rightarrow 5 \\rightarrow 3 \\rightarrow 4 \\rightarrow 3 \\rightarrow 2 \\rightarrow 1$.\ninput: 4\n5\n0\n1\n1\n1 2\n2 3\n2 4\n output: 5\n The score is maximized if Tora-Tora stats his journey from room 1 and ends in the same room.\n\n" }, { "title": "Disc", "content": "A mysterious device was discovered in an ancient ruin. The device consists of a disc with integers inscribed on both sides, a bundle of cards with an integer written on each of them and a pedestal within which the cards are placed. The disc rotates when the bundle of cards is put into the pedestal. Only one side of the disc is exposed to view at any one time.\n \n\n The disc is radially segmented in equal angles into $K$ sections, and an integer, from $1$ to $K$ in increasing order, is inscribed clockwise on each section on the front side. The sections on the back side share the same boundaries with the front side, and a negative counterpart of that in the section on the front side is inscribed, i. e. , if $X$ is inscribed in the front side section, $-X$ is inscribed on the counterpart section on the back side. There is a needle on the periphery of the disc, and it always points to the middle point of the arc that belongs to a section. Hereafter, we say \"the disc is set to $X$\" if the front side section just below the needle contains an integer $X$.\nFig. 1 Disc with 5 sections (i. e. , $K = 5$): When the disc is set to $1$ on the front side, it is set to $-1$ on the back side.\n \n\n Investigation of the behavior of the device revealed the following:\n\nWhen the bundle of cards is placed in the pedestal, the device sets the disc to 1. \nThen, the device reads the cards slice by slice from top downward and performs one of the following actions according to the integer $A$ on the card\n\nIf $A$ is a positive number, it rotates the disc clockwise by $|A|$ sections.\n\nIf $A$ is zero, it turns the disc back around the vertical line defined by the needle and the center of the disc.\n\nIf $A$ is a negative number, it rotates the disc counterclockwise by $|A|$ sections.\n It is provided that $|A|$ is the absolute value of $A$. The final state of the device (i. e. , to what section the needle is pointing) varies depending on the initial stacking sequence of the cards. To further investigate the behavior of the device, we swapped two arbitrary cards in the stack and placed the bundle in the pedestal to check what number the disc is set to. We performed this procedure over again and again.\n \n Given the information on the device and several commands to swap two cards, make a program to determine the number to which the device is set at the completion of all actions. Note that the stacking sequence of the cards continues to change as a new trial is made.", "constraint": "", "input": "The input is given in the following format.\n\n$K$ $N$ $Q$\n$A_1$ $A_2$ . . . $A_N$\n$L_1$ $R_1$\n$L_2$ $R_2$\n$. . . $\n$L_Q$ $R_Q$\n\n The first line provides the number of sections $K$ ($2 <= K <= 10^9$), the slices of cards $N$ ($2 <= N <= 100,000$), and the number of commands $Q$ ($1 <= Q <= 100,000$). The second line provides an array of $N$ integers inscribed on the sections of the disc. $A_i$ ($-10^9 <= A_i <= 10^9$) represents the number written on the $i$-th card from the top. Each of the subsequent $Q$ lines defines the $i$-th command $L_i, R_i$ ($1 <= L_ i < R_i <= N$) indicating a swapping of $L_i$-th and $R_i$-th cards from the top followed by placing the card bundle in the device.", "output": "For each command, output a line containing the number to which the device is set at the completion of all actions.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 3 1\n1 -2 0\n2 3\n output: -3\nThe device moves as follows while it is performing the first command.\n1 0 -2\n When the first command is performed, the stacking sequence of the card bundle, from top to bottom, changes to the sequence shown below.\n \nFig.2 An illustrative example of how the device works\n\n Therefore, the device is set to -3 after all actions have completed. Output this value.", "input: 5 7 5\n0 0 3 3 3 3 3\n1 2\n2 3\n3 4\n4 5\n5 6\n output: 1\n2\n3\n4\n5"], "Pid": "p00385", "ProblemText": "Task Description: A mysterious device was discovered in an ancient ruin. The device consists of a disc with integers inscribed on both sides, a bundle of cards with an integer written on each of them and a pedestal within which the cards are placed. The disc rotates when the bundle of cards is put into the pedestal. Only one side of the disc is exposed to view at any one time.\n \n\n The disc is radially segmented in equal angles into $K$ sections, and an integer, from $1$ to $K$ in increasing order, is inscribed clockwise on each section on the front side. The sections on the back side share the same boundaries with the front side, and a negative counterpart of that in the section on the front side is inscribed, i. e. , if $X$ is inscribed in the front side section, $-X$ is inscribed on the counterpart section on the back side. There is a needle on the periphery of the disc, and it always points to the middle point of the arc that belongs to a section. Hereafter, we say \"the disc is set to $X$\" if the front side section just below the needle contains an integer $X$.\nFig. 1 Disc with 5 sections (i. e. , $K = 5$): When the disc is set to $1$ on the front side, it is set to $-1$ on the back side.\n \n\n Investigation of the behavior of the device revealed the following:\n\nWhen the bundle of cards is placed in the pedestal, the device sets the disc to 1. \nThen, the device reads the cards slice by slice from top downward and performs one of the following actions according to the integer $A$ on the card\n\nIf $A$ is a positive number, it rotates the disc clockwise by $|A|$ sections.\n\nIf $A$ is zero, it turns the disc back around the vertical line defined by the needle and the center of the disc.\n\nIf $A$ is a negative number, it rotates the disc counterclockwise by $|A|$ sections.\n It is provided that $|A|$ is the absolute value of $A$. The final state of the device (i. e. , to what section the needle is pointing) varies depending on the initial stacking sequence of the cards. To further investigate the behavior of the device, we swapped two arbitrary cards in the stack and placed the bundle in the pedestal to check what number the disc is set to. We performed this procedure over again and again.\n \n Given the information on the device and several commands to swap two cards, make a program to determine the number to which the device is set at the completion of all actions. Note that the stacking sequence of the cards continues to change as a new trial is made.\nTask Input: The input is given in the following format.\n\n$K$ $N$ $Q$\n$A_1$ $A_2$ . . . $A_N$\n$L_1$ $R_1$\n$L_2$ $R_2$\n$. . . $\n$L_Q$ $R_Q$\n\n The first line provides the number of sections $K$ ($2 <= K <= 10^9$), the slices of cards $N$ ($2 <= N <= 100,000$), and the number of commands $Q$ ($1 <= Q <= 100,000$). The second line provides an array of $N$ integers inscribed on the sections of the disc. $A_i$ ($-10^9 <= A_i <= 10^9$) represents the number written on the $i$-th card from the top. Each of the subsequent $Q$ lines defines the $i$-th command $L_i, R_i$ ($1 <= L_ i < R_i <= N$) indicating a swapping of $L_i$-th and $R_i$-th cards from the top followed by placing the card bundle in the device.\nTask Output: For each command, output a line containing the number to which the device is set at the completion of all actions.\nTask Samples: input: 5 3 1\n1 -2 0\n2 3\n output: -3\nThe device moves as follows while it is performing the first command.\n1 0 -2\n When the first command is performed, the stacking sequence of the card bundle, from top to bottom, changes to the sequence shown below.\n \nFig.2 An illustrative example of how the device works\n\n Therefore, the device is set to -3 after all actions have completed. Output this value.\ninput: 5 7 5\n0 0 3 3 3 3 3\n1 2\n2 3\n3 4\n4 5\n5 6\n output: 1\n2\n3\n4\n5\n\n" }, { "title": "Meeting in a City", "content": "You are a teacher at Iazu High School is the Zuia Kingdom. There are $N$ cities and $N-1$ roads connecting them that allow you to move from one city to another by way of more than one road. Each of the roads allows bidirectional traffic and has a known length.\n \nAs a part of class activities, you are planning the following action assignment for your students. First, you come up with several themes commonly applicable to three different cities. Second, you assign each of the themes to a group of three students. Then, each student of a group is assigned to one of the three cities and conducts a survey on it. Finally, all students of the group get together in one of the $N$ cities and compile their results.\n \n\n After a theme group has completed its survey, the three members move from the city on which they studied to the city for getting together. The longest distance they have to travel for getting together is defined as the cost of the theme. You want to select the meeting city so that the cost for each theme becomes minimum.\n\n Given the number of cities, road information and $Q$ sets of three cities for each theme, make a program to work out the minimum cost for each theme.", "constraint": "", "input": "The input is given in the following format.\n\n$N$ $Q$ \n$u_1$ $v_1$ $w_1$\n$u_2$ $v_2$ $w_2$\n$. . . $\n$u_{N-1}$ $v_{N-1}$ $w_{N-1}$\n$a_1$ $b_1$ $c_1$\n$a_2$ $b_2$ $c_2$\n$. . . $\n$a_Q$ $b_Q$ $c_Q$\n\nThe first line provides the number of cities in the Zuia Kingdom $N$ ($3 <= N <= 100,000$) and the number of themes $Q$ ($1 <= Q <= 100,000$). Each of the subsequent $N-1$ lines provides the information regarding the $i$-th road $u_i, v_i, w_i$ ($ 1 <= u_i < v_i <= N, 1 <= w_i <= 10,000$), indicating that the road connects cities $u_i$ and $v_i$, and the road distance between the two is $w_i$. Each of the $Q$ lines that follows the above provides the three cities assigned to the $i$-th theme: $a_i, b_i, c_i$ ($1 <= a_i < b_i < c_i <= N$).", "output": "For each theme, output the cost in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n1 2 3\n2 3 4\n2 4 2\n4 5 3\n1 3 4\n1 4 5\n1 2 3\n2 4 5\n output: 4\n5\n4\n3\nIn the first theme, traveling distance from City 3 (the student conducts survey) to City 2 (meeting venue) determines the cost 4. As no other meeting city can provide smaller cost, you should output 4. In the second theme, you can minimize the cost down to 5 by selecting City 2 or City 4 as the meeting venue.", "input: 5 3\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n1 2 3\n1 3 5\n1 2 4\n output: 1\n2\n2", "input: 15 15\n1 2 45\n2 3 81\n1 4 29\n1 5 2\n5 6 25\n4 7 84\n7 8 56\n4 9 2\n4 10 37\n7 11 39\n1 12 11\n11 13 6\n3 14 68\n2 15 16\n10 13 14\n13 14 15\n2 14 15\n7 12 15\n10 14 15\n9 10 15\n9 14 15\n8 13 15\n5 6 13\n11 13 15\n12 13 14\n2 3 10\n5 13 15\n10 11 14\n6 8 11\n output: 194\n194\n97\n90\n149\n66\n149\n140\n129\n129\n194\n111\n129\n194\n140"], "Pid": "p00386", "ProblemText": "Task Description: You are a teacher at Iazu High School is the Zuia Kingdom. There are $N$ cities and $N-1$ roads connecting them that allow you to move from one city to another by way of more than one road. Each of the roads allows bidirectional traffic and has a known length.\n \nAs a part of class activities, you are planning the following action assignment for your students. First, you come up with several themes commonly applicable to three different cities. Second, you assign each of the themes to a group of three students. Then, each student of a group is assigned to one of the three cities and conducts a survey on it. Finally, all students of the group get together in one of the $N$ cities and compile their results.\n \n\n After a theme group has completed its survey, the three members move from the city on which they studied to the city for getting together. The longest distance they have to travel for getting together is defined as the cost of the theme. You want to select the meeting city so that the cost for each theme becomes minimum.\n\n Given the number of cities, road information and $Q$ sets of three cities for each theme, make a program to work out the minimum cost for each theme.\nTask Input: The input is given in the following format.\n\n$N$ $Q$ \n$u_1$ $v_1$ $w_1$\n$u_2$ $v_2$ $w_2$\n$. . . $\n$u_{N-1}$ $v_{N-1}$ $w_{N-1}$\n$a_1$ $b_1$ $c_1$\n$a_2$ $b_2$ $c_2$\n$. . . $\n$a_Q$ $b_Q$ $c_Q$\n\nThe first line provides the number of cities in the Zuia Kingdom $N$ ($3 <= N <= 100,000$) and the number of themes $Q$ ($1 <= Q <= 100,000$). Each of the subsequent $N-1$ lines provides the information regarding the $i$-th road $u_i, v_i, w_i$ ($ 1 <= u_i < v_i <= N, 1 <= w_i <= 10,000$), indicating that the road connects cities $u_i$ and $v_i$, and the road distance between the two is $w_i$. Each of the $Q$ lines that follows the above provides the three cities assigned to the $i$-th theme: $a_i, b_i, c_i$ ($1 <= a_i < b_i < c_i <= N$).\nTask Output: For each theme, output the cost in one line.\nTask Samples: input: 5 4\n1 2 3\n2 3 4\n2 4 2\n4 5 3\n1 3 4\n1 4 5\n1 2 3\n2 4 5\n output: 4\n5\n4\n3\nIn the first theme, traveling distance from City 3 (the student conducts survey) to City 2 (meeting venue) determines the cost 4. As no other meeting city can provide smaller cost, you should output 4. In the second theme, you can minimize the cost down to 5 by selecting City 2 or City 4 as the meeting venue.\ninput: 5 3\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n1 2 3\n1 3 5\n1 2 4\n output: 1\n2\n2\ninput: 15 15\n1 2 45\n2 3 81\n1 4 29\n1 5 2\n5 6 25\n4 7 84\n7 8 56\n4 9 2\n4 10 37\n7 11 39\n1 12 11\n11 13 6\n3 14 68\n2 15 16\n10 13 14\n13 14 15\n2 14 15\n7 12 15\n10 14 15\n9 10 15\n9 14 15\n8 13 15\n5 6 13\n11 13 15\n12 13 14\n2 3 10\n5 13 15\n10 11 14\n6 8 11\n output: 194\n194\n97\n90\n149\n66\n149\n140\n129\n129\n194\n111\n129\n194\n140\n\n" }, { "title": "Party Dress", "content": "Yae joins a journey plan, in which parties will be held several times during the itinerary. She wants to participate in all of them and will carry several dresses with her. But the number of dresses she can carry with her may be smaller than that of the party opportunities. In that case, she has to wear some of her dresses more than once. \n\n Fashion-conscious Yae wants to avoid that. At least, she wants to reduce the maximum number of times she has to wear the same dress as far as possible.\n\n Given the number of dresses and frequency of parties, make a program to determine how she can reduce the maximum frequency of wearing the most reused dress.", "constraint": "", "input": "The input is given in the following format.\n\n$A$ $B$\n\n The input line provides the number of dresses $A$ ($1 <= A <= 10^5$) and frequency of parties $B$ ($1 <= B <= 10^5$).", "output": "Output the frequency she has to wear the most reused dress.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n output: 2", "input: 25 10\n output: 1"], "Pid": "p00387", "ProblemText": "Task Description: Yae joins a journey plan, in which parties will be held several times during the itinerary. She wants to participate in all of them and will carry several dresses with her. But the number of dresses she can carry with her may be smaller than that of the party opportunities. In that case, she has to wear some of her dresses more than once. \n\n Fashion-conscious Yae wants to avoid that. At least, she wants to reduce the maximum number of times she has to wear the same dress as far as possible.\n\n Given the number of dresses and frequency of parties, make a program to determine how she can reduce the maximum frequency of wearing the most reused dress.\nTask Input: The input is given in the following format.\n\n$A$ $B$\n\n The input line provides the number of dresses $A$ ($1 <= A <= 10^5$) and frequency of parties $B$ ($1 <= B <= 10^5$).\nTask Output: Output the frequency she has to wear the most reused dress.\nTask Samples: input: 3 5\n output: 2\ninput: 25 10\n output: 1\n\n" }, { "title": "Design of a Mansion", "content": "Our master carpenter is designing a condominium called Bange Hills Mansion. The condominium is constructed by stacking up floors of the same height. The height of each floor is designed so that the total height of the stacked floors coincides with the predetermined height of the condominium. The height of each floor can be adjusted freely with a certain range.\n\n The final outcome of the building depends on clever height allotment for each floor. So, he plans to calculate possible combinations of per-floor heights to check how many options he has.\n\n Given the height of the condominium and the adjustable range of each floor 's height, make a program to enumerate the number of choices for a floor.", "constraint": "", "input": "The input is given in the following format.\n\n$H$ $A$ $B$\n\nThe input line provides the height of the condominium $H$ ($1 <= H <= 10^5$) and the upper and lower limits $A$ and $B$ of the height adjustable range for one floor ($1 <= A <= B <= H$). All data are given as integers.", "output": "Output the number of possible height selections for each floor in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100 2 4\n output: 2", "input: 101 3 5\n output: 0"], "Pid": "p00388", "ProblemText": "Task Description: Our master carpenter is designing a condominium called Bange Hills Mansion. The condominium is constructed by stacking up floors of the same height. The height of each floor is designed so that the total height of the stacked floors coincides with the predetermined height of the condominium. The height of each floor can be adjusted freely with a certain range.\n\n The final outcome of the building depends on clever height allotment for each floor. So, he plans to calculate possible combinations of per-floor heights to check how many options he has.\n\n Given the height of the condominium and the adjustable range of each floor 's height, make a program to enumerate the number of choices for a floor.\nTask Input: The input is given in the following format.\n\n$H$ $A$ $B$\n\nThe input line provides the height of the condominium $H$ ($1 <= H <= 10^5$) and the upper and lower limits $A$ and $B$ of the height adjustable range for one floor ($1 <= A <= B <= H$). All data are given as integers.\nTask Output: Output the number of possible height selections for each floor in a line.\nTask Samples: input: 100 2 4\n output: 2\ninput: 101 3 5\n output: 0\n\n" }, { "title": "Pilling Blocks", "content": "We make a tower by stacking up blocks. The tower consists of several stages and each stage is constructed by connecting blocks horizontally. Each block is of the same weight and is tough enough to withstand the weight equivalent to up to $K$ blocks without crushing.\n\n We have to build the tower abiding by the following conditions:\n\nEvery stage of the tower has one or more blocks on it.\n\nEach block is loaded with weight that falls within the withstanding range of the block. The weight loaded on a block in a stage is evaluated by: total weight of all blocks above the stage divided by the number of blocks within the stage.\n Given the number of blocks and the strength, make a program to evaluate the maximum height (i. e. , stages) of the tower than can be constructed.", "constraint": "", "input": "The input is given in the following format.\n\n$N$ $K$\n\n The input line provides the number of blocks available $N$ ($1 <= N <= 10^5$) and the strength of the block $K$ ($1 <= K <= 10^5$).", "output": "Output the maximum possible number of stages.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n output: 3", "input: 5 2\n output: 4"], "Pid": "p00389", "ProblemText": "Task Description: We make a tower by stacking up blocks. The tower consists of several stages and each stage is constructed by connecting blocks horizontally. Each block is of the same weight and is tough enough to withstand the weight equivalent to up to $K$ blocks without crushing.\n\n We have to build the tower abiding by the following conditions:\n\nEvery stage of the tower has one or more blocks on it.\n\nEach block is loaded with weight that falls within the withstanding range of the block. The weight loaded on a block in a stage is evaluated by: total weight of all blocks above the stage divided by the number of blocks within the stage.\n Given the number of blocks and the strength, make a program to evaluate the maximum height (i. e. , stages) of the tower than can be constructed.\nTask Input: The input is given in the following format.\n\n$N$ $K$\n\n The input line provides the number of blocks available $N$ ($1 <= N <= 10^5$) and the strength of the block $K$ ($1 <= K <= 10^5$).\nTask Output: Output the maximum possible number of stages.\nTask Samples: input: 4 2\n output: 3\ninput: 5 2\n output: 4\n\n" }, { "title": "Round Table of Sages", "content": "$N$ sages are sitting around a round table with $N$ seats. Each sage holds chopsticks with his dominant hand to eat his dinner. The following happens in this situation.\n\nIf sage $i$ is right-handed and a left-handed sage sits on his right, a level of frustration $w_i$ occurs to him. A right-handed sage on his right does not cause such frustration at all.\n\nIf sage $i$ is left-handed and a right-handed sage sits on his left, a level of frustration $w_i$ occurs to him. A left-handed sage on his left does not cause such frustration at all.\n You wish you could minimize the total amount of frustration by clever sitting order arrangement.\n\n Given the number of sages with his dominant hand information, make a program to evaluate the minimum frustration achievable.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$a_1$ $a_2$ $. . . $ $a_N$\n$w_1$ $w_2$ $. . . $ $w_N$ \n\nThe first line provides the number of sages $N$ ($3 <= N <= 10$). The second line provides an array of integers $a_i$ (0 or 1) which indicate if the $i$-th sage is right-handed (0) or left-handed (1). The third line provides an array of integers $w_i$ ($1 <= w_i <= 1000$) which indicate the level of frustration the $i$-th sage bears.", "output": "Output the minimum total frustration the sages bear.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 0 0 1 0\n2 3 5 1 2\n output: 3", "input: 3\n0 0 0\n1 2 3\n output: 0"], "Pid": "p00390", "ProblemText": "Task Description: $N$ sages are sitting around a round table with $N$ seats. Each sage holds chopsticks with his dominant hand to eat his dinner. The following happens in this situation.\n\nIf sage $i$ is right-handed and a left-handed sage sits on his right, a level of frustration $w_i$ occurs to him. A right-handed sage on his right does not cause such frustration at all.\n\nIf sage $i$ is left-handed and a right-handed sage sits on his left, a level of frustration $w_i$ occurs to him. A left-handed sage on his left does not cause such frustration at all.\n You wish you could minimize the total amount of frustration by clever sitting order arrangement.\n\n Given the number of sages with his dominant hand information, make a program to evaluate the minimum frustration achievable.\nTask Input: The input is given in the following format.\n\n$N$\n$a_1$ $a_2$ $. . . $ $a_N$\n$w_1$ $w_2$ $. . . $ $w_N$ \n\nThe first line provides the number of sages $N$ ($3 <= N <= 10$). The second line provides an array of integers $a_i$ (0 or 1) which indicate if the $i$-th sage is right-handed (0) or left-handed (1). The third line provides an array of integers $w_i$ ($1 <= w_i <= 1000$) which indicate the level of frustration the $i$-th sage bears.\nTask Output: Output the minimum total frustration the sages bear.\nTask Samples: input: 5\n1 0 0 1 0\n2 3 5 1 2\n output: 3\ninput: 3\n0 0 0\n1 2 3\n output: 0\n\n" }, { "title": "Treasure Map", "content": "Mr. Kobou found a bundle of old paper when he was cleaning his family home. On each paper, two series of numbers are written. Strange as it appeared to him, Mr. Kobou further went through the storehouse and found out a note his ancestor left. According to it, the bundle of paper is a treasure map, in which the two sequences of numbers seem to give a clue to the whereabouts of the treasure the ancestor buried.\n\n Mr. Kobou 's ancestor divided the area where he buried his treasure in a reticular pattern and used only some of the grid sections. The two series of numbers indicate the locations: the $i$-th member of the first series indicates the number of locations in the $i$-th column (form left) of the grid sections where a part of the treasure is buried, and the $j$-th member of the second indicates the same information regarding the $j$-th row from the top. No more than one piece of treasure is buried in one grid section. An example of a 5 * 4 case is shown below. If the pieces of treasure are buried in the grid sections noted as \"#\" the two series of numbers become \"0,2,2,1,1\" and \"1,1,1,3\".\n\n
\n \n 0 2 2 1 1 \n \n 1 # \n \n 1 # \n \n 1 # \n \n 3 # # # \n \n\nMr. Kobou 's ancestor seems to be a very careful person. He slipped some pieces of paper with completely irrelevant information into the bundle. For example, a set of number series \"3,2,3,0,0\" and \"4,2,0,0,2\" does not match any combination of 5 * 5 matrixes. So, Mr. Kobou has first to exclude these pieces of garbage information.\n\n Given the set of information written on the pieces of paper, make a program to judge if the information is relevant.", "constraint": "", "input": "The input is given in the following format.\n\n$W$ $H$\n$a_1$ $a_2$ $. . . $ $a_W$\n$b_1$ $b_2$ $. . . $ $b_H$ \n\nThe first line provides the number of horizontal partitions $W$ ($1 <= W <= 1000$) and vertical partitions $H$ ($1 <= H <= 1000$). The second line provides the $i$-th member of the first number series $a_i$ ($0 <= a_i <= H$) written on the paper, and the third line the $j$-th member of the second series $b_j$ ($0 <= b_j <= W$).", "output": "Output \"1\" if the information written on the paper is relevant, or \"0\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n0 2 2 1 1\n1 1 1 3\n output: 1", "input: 5 5\n3 2 3 0 0\n4 2 0 0 2\n output: 0"], "Pid": "p00391", "ProblemText": "Task Description: Mr. Kobou found a bundle of old paper when he was cleaning his family home. On each paper, two series of numbers are written. Strange as it appeared to him, Mr. Kobou further went through the storehouse and found out a note his ancestor left. According to it, the bundle of paper is a treasure map, in which the two sequences of numbers seem to give a clue to the whereabouts of the treasure the ancestor buried.\n\n Mr. Kobou 's ancestor divided the area where he buried his treasure in a reticular pattern and used only some of the grid sections. The two series of numbers indicate the locations: the $i$-th member of the first series indicates the number of locations in the $i$-th column (form left) of the grid sections where a part of the treasure is buried, and the $j$-th member of the second indicates the same information regarding the $j$-th row from the top. No more than one piece of treasure is buried in one grid section. An example of a 5 * 4 case is shown below. If the pieces of treasure are buried in the grid sections noted as \"#\" the two series of numbers become \"0,2,2,1,1\" and \"1,1,1,3\".\n\n
\n \n 0 2 2 1 1 \n \n 1 # \n \n 1 # \n \n 1 # \n \n 3 # # # \n \n\nMr. Kobou 's ancestor seems to be a very careful person. He slipped some pieces of paper with completely irrelevant information into the bundle. For example, a set of number series \"3,2,3,0,0\" and \"4,2,0,0,2\" does not match any combination of 5 * 5 matrixes. So, Mr. Kobou has first to exclude these pieces of garbage information.\n\n Given the set of information written on the pieces of paper, make a program to judge if the information is relevant.\nTask Input: The input is given in the following format.\n\n$W$ $H$\n$a_1$ $a_2$ $. . . $ $a_W$\n$b_1$ $b_2$ $. . . $ $b_H$ \n\nThe first line provides the number of horizontal partitions $W$ ($1 <= W <= 1000$) and vertical partitions $H$ ($1 <= H <= 1000$). The second line provides the $i$-th member of the first number series $a_i$ ($0 <= a_i <= H$) written on the paper, and the third line the $j$-th member of the second series $b_j$ ($0 <= b_j <= W$).\nTask Output: Output \"1\" if the information written on the paper is relevant, or \"0\" otherwise.\nTask Samples: input: 5 4\n0 2 2 1 1\n1 1 1 3\n output: 1\ninput: 5 5\n3 2 3 0 0\n4 2 0 0 2\n output: 0\n\n" }, { "title": "Common-Prime Sort", "content": "You are now examining a unique method to sort a sequence of numbers in increasing order. The method only allows swapping of two numbers that have a common prime factor. For example, a sequence [6,4,2,3,7] can be sorted using the following steps.\n\nStep 0: 6 4 2 3 7 (given sequence)\nStep 1: 2 4 6 3 7 (elements 6 and 2 swapped)\nStep 2: 2 6 4 3 7 (elements 4 and 6 swapped)\nStep 3: 2 3 4 6 7 (elements 6 and 3 swapped)\n\n Depending on the nature of the sequence, however, this approach may fail to complete the sorting. You have given a name \"Coprime sort\" to this approach and are now examining if a given sequence is coprime-sortable.\n\n Make a program to determine if a given sequence can be sorted in increasing order by iterating an arbitrary number of swapping operations of two elements that have a common prime number.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$a_1$ $a_2$ $. . . $ $a_N$\n\nThe first line provides the number of elements included in the sequence $N$ ($2 <= N <= 10^5$). The second line provides an array of integers $a_i$ ($2 <= a_i <= 10^5$) that constitute the sequence.", "output": "Output \"1\" if the sequence is coprime-sortable in increasing order, or \"0\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n6 4 2 3 7\n output: 1", "input: 7\n2 9 6 5 6 7 3\n output: 0"], "Pid": "p00392", "ProblemText": "Task Description: You are now examining a unique method to sort a sequence of numbers in increasing order. The method only allows swapping of two numbers that have a common prime factor. For example, a sequence [6,4,2,3,7] can be sorted using the following steps.\n\nStep 0: 6 4 2 3 7 (given sequence)\nStep 1: 2 4 6 3 7 (elements 6 and 2 swapped)\nStep 2: 2 6 4 3 7 (elements 4 and 6 swapped)\nStep 3: 2 3 4 6 7 (elements 6 and 3 swapped)\n\n Depending on the nature of the sequence, however, this approach may fail to complete the sorting. You have given a name \"Coprime sort\" to this approach and are now examining if a given sequence is coprime-sortable.\n\n Make a program to determine if a given sequence can be sorted in increasing order by iterating an arbitrary number of swapping operations of two elements that have a common prime number.\nTask Input: The input is given in the following format.\n\n$N$\n$a_1$ $a_2$ $. . . $ $a_N$\n\nThe first line provides the number of elements included in the sequence $N$ ($2 <= N <= 10^5$). The second line provides an array of integers $a_i$ ($2 <= a_i <= 10^5$) that constitute the sequence.\nTask Output: Output \"1\" if the sequence is coprime-sortable in increasing order, or \"0\" otherwise.\nTask Samples: input: 5\n6 4 2 3 7\n output: 1\ninput: 7\n2 9 6 5 6 7 3\n output: 0\n\n" }, { "title": "Beautiful Sequence", "content": "Alice is spending his time on an independent study to apply to the Nationwide Mathematics Contest. This year 's theme is \"Beautiful Sequence. \" As Alice is interested in the working of computers, she wants to create a beautiful sequence using only 0 and 1. She defines a \"Beautiful\" sequence of length $N$ that consists only of 0 and 1 if it includes $M$ successive array of 1s as its sub-sequence.\n \n\n Using his skills in programming, Alice decided to calculate how many \"Beautiful sequences\" she can generate and compile a report on it.\n\n Make a program to evaluate the possible number of \"Beautiful sequences\" given the sequence length $N$ and sub-sequence length $M$ that consists solely of 1. As the answer can be extremely large, divide it by $1,000,000,007 (= 10^9 + 7)$ and output the remainder.", "constraint": "", "input": "The input is given in the following format.\n\n$N$ $M$ \n\nThe input line provides the length of sequence $N$ ($1 <= N <= 10^5$) and the length $M$ ($1 <= M <= N$) of the array that solely consists of 1s.", "output": "Output the number of Beautiful sequences in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n output: 3\n The sequences with length 4 that include 1s in successive array of length 3 are: 0111,1110 and 1111.", "input: 4 2\n output: 8\n The sequences with length 4 that include 1s in successive array of length 2 are: 0011,0110,0111,1011,1100,1101,1110 and 1111."], "Pid": "p00393", "ProblemText": "Task Description: Alice is spending his time on an independent study to apply to the Nationwide Mathematics Contest. This year 's theme is \"Beautiful Sequence. \" As Alice is interested in the working of computers, she wants to create a beautiful sequence using only 0 and 1. She defines a \"Beautiful\" sequence of length $N$ that consists only of 0 and 1 if it includes $M$ successive array of 1s as its sub-sequence.\n \n\n Using his skills in programming, Alice decided to calculate how many \"Beautiful sequences\" she can generate and compile a report on it.\n\n Make a program to evaluate the possible number of \"Beautiful sequences\" given the sequence length $N$ and sub-sequence length $M$ that consists solely of 1. As the answer can be extremely large, divide it by $1,000,000,007 (= 10^9 + 7)$ and output the remainder.\nTask Input: The input is given in the following format.\n\n$N$ $M$ \n\nThe input line provides the length of sequence $N$ ($1 <= N <= 10^5$) and the length $M$ ($1 <= M <= N$) of the array that solely consists of 1s.\nTask Output: Output the number of Beautiful sequences in a line.\nTask Samples: input: 4 3\n output: 3\n The sequences with length 4 that include 1s in successive array of length 3 are: 0111,1110 and 1111.\ninput: 4 2\n output: 8\n The sequences with length 4 that include 1s in successive array of length 2 are: 0011,0110,0111,1011,1100,1101,1110 and 1111.\n\n" }, { "title": "Payroll", "content": "PCK company has $N$ salaried staff and they have specific ID numbers that run from $0$ to $N-1$. The company provides $N$ types of work that are also identified by ID numbers from $0$ to $N-1$. The time required to complete work $j$ is $t_j$.\n\nTo get each of the working staff to learn as many types of work as possible, the company shifts work assignment in the following fashion.\nOn the $d$-th day of a shift (the first day is counted as $0$th day), work $j$ is assigned to the staff $(j + d) \\% N$, where the notation $p \\% q$ indicates the remainder when $p$ is divided by $q$.\n \nSalaries in the PCK company are paid on a daily basis based on the hourly rate. When a staff whose hourly rate is $a$ carries out work $j$, his/her salary will amount to $a * t_j$. The initial hourly rate for a staff $i$ is $s_i$ yen. To boost staff 's motivation, the company employs a unique scheme for raising hourly rates. The promotion scheme table of the company contains a list of factors $f_k$ ($0 <= k <= M-1$), and the hourly rate of a staff is raised based on the following rule.\n At the completion of the $d$-th day 's work (the first day is counted as the $0$th day), the hourly rate of the staff with ID number $d \\% N$ is raised by $f_{(d \\% M)}$ yen. The salary raise takes effect after the day 's pay has been made.\n \n As the person in charge of accounting in PCK company, you have to calculate the total amount of pay for $D$ days from the $0$-th day.\n\n Make a program to work out the total amount of salary given the following information: initial hourly rate of each staff, hours required to complete a job, a table of promotion coefficients, and the number of days. Because the total may become excessively large, report the remainder when the total salary amount is divided by $1,000,000,007(= 10^9 + 7)$.", "constraint": "", "input": "The input is given in the following format.\n\n$N$ $M$ $D$\n$s_0$ $s_1$ $. . . $ $s_{N-1}$\n$t_0$ $t_1$ $. . . $ $t_{N-1}$\n$f_0$ $f_1$ $. . . $ $f_{M-1}$\n\nThe first line provides the number of working staff and types of work $N$ ($1 <= N <= 100$), the number of factors $M$ ($1 <= M <= 100$)and the number of days $D$ ($1 <= D <= 10^{15}$). Note that $M + N$ is equal to or less than 100. The second line provides the initial hourly rate for each staff $s_i$ ($1 <= s_i <= 10^8$) as integers. The third line provides the hours $t_j$ ($1 <= t_j <= 10^8$) required to complete each type of job as integers. The fourth line lists the factors $f_k$ ($1 <= f_k <= 10^8$) in the promotion scheme table.", "output": "Output the total amount of the salary.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 2\n3 2 1\n1 2 3\n1 2\n output: 26", "input: 3 2 5\n3 2 1\n1 2 3\n1 2\n output: 91"], "Pid": "p00394", "ProblemText": "Task Description: PCK company has $N$ salaried staff and they have specific ID numbers that run from $0$ to $N-1$. The company provides $N$ types of work that are also identified by ID numbers from $0$ to $N-1$. The time required to complete work $j$ is $t_j$.\n\nTo get each of the working staff to learn as many types of work as possible, the company shifts work assignment in the following fashion.\nOn the $d$-th day of a shift (the first day is counted as $0$th day), work $j$ is assigned to the staff $(j + d) \\% N$, where the notation $p \\% q$ indicates the remainder when $p$ is divided by $q$.\n \nSalaries in the PCK company are paid on a daily basis based on the hourly rate. When a staff whose hourly rate is $a$ carries out work $j$, his/her salary will amount to $a * t_j$. The initial hourly rate for a staff $i$ is $s_i$ yen. To boost staff 's motivation, the company employs a unique scheme for raising hourly rates. The promotion scheme table of the company contains a list of factors $f_k$ ($0 <= k <= M-1$), and the hourly rate of a staff is raised based on the following rule.\n At the completion of the $d$-th day 's work (the first day is counted as the $0$th day), the hourly rate of the staff with ID number $d \\% N$ is raised by $f_{(d \\% M)}$ yen. The salary raise takes effect after the day 's pay has been made.\n \n As the person in charge of accounting in PCK company, you have to calculate the total amount of pay for $D$ days from the $0$-th day.\n\n Make a program to work out the total amount of salary given the following information: initial hourly rate of each staff, hours required to complete a job, a table of promotion coefficients, and the number of days. Because the total may become excessively large, report the remainder when the total salary amount is divided by $1,000,000,007(= 10^9 + 7)$.\nTask Input: The input is given in the following format.\n\n$N$ $M$ $D$\n$s_0$ $s_1$ $. . . $ $s_{N-1}$\n$t_0$ $t_1$ $. . . $ $t_{N-1}$\n$f_0$ $f_1$ $. . . $ $f_{M-1}$\n\nThe first line provides the number of working staff and types of work $N$ ($1 <= N <= 100$), the number of factors $M$ ($1 <= M <= 100$)and the number of days $D$ ($1 <= D <= 10^{15}$). Note that $M + N$ is equal to or less than 100. The second line provides the initial hourly rate for each staff $s_i$ ($1 <= s_i <= 10^8$) as integers. The third line provides the hours $t_j$ ($1 <= t_j <= 10^8$) required to complete each type of job as integers. The fourth line lists the factors $f_k$ ($1 <= f_k <= 10^8$) in the promotion scheme table.\nTask Output: Output the total amount of the salary.\nTask Samples: input: 3 2 2\n3 2 1\n1 2 3\n1 2\n output: 26\ninput: 3 2 5\n3 2 1\n1 2 3\n1 2\n output: 91\n\n" }, { "title": "Maze & Items", "content": "Maze & Items is a puzzle game in which the player tries to reach the goal while collecting items. The maze consists of $W * H$ grids, and some of them are inaccessible to the player depending on the items he/she has now. The score the player earns is defined according to the order of collecting items. The objective of the game is, after starting from a defined point, to collect all the items using the least number of moves before reaching the goal. There may be multiple routes that allow the least number of moves. In that case, the player seeks to maximize his/her score.\n\nOne of the following symbols is assigned to each of the grids. You can move to one of the neighboring grids (horizontally or vertically, but not diagonally) in one time, but you cannot move to the area outside the maze.\n
\n Symbol Description \n\n \n . Always accessible \n \n # Always inaccessible \n \n Number 0,1, . . , 9 Always accessible and an item (with its specific number) is located in the grid. \n \n Capital letter A, B, . . . , J Accessible only when the player does NOT have the corresponding item. Each of A, B, . . . , J takes a value from 0 to 9. \n \n Small letter a, b, . . . , j Accessible only when the player DOES have the corresponding item. Each of a, b, . . . , j takes one value from 0 to 9. \n \n S Starting grid. Always accessible. \n \n T Goal grid. Always accessible. \n\n \nThe player fails to complete the game if he/she has not collected all the items before reaching the goal. When entering a grid in which an item is located, it 's the player 's option to collect it or not. The player must keep the item once he/she collects it, and it disappears from the maze.\n\nGiven the state information of the maze and a table that defines the collecting order dependent scores, make a program that works out the minimum number of moves required to collect all the items before reaching the goal, and the maximum score gained through performing the moves.", "constraint": "", "input": "The input is given in the following format.\n\n$W$ $H$\n$row_1$\n$row_2$\n. . .\n$row_H$\n$s_{00}$ $s_{01}$ . . . $s_{09}$\n$s_{10}$ $s_{11}$ . . . $s_{19}$\n. . .\n$s_{90}$ $s_{91}$ . . . $s_{99}$\n\nThe first line provides the number of horizontal and vertical grids in the maze $W$ ($4 <= W <= 1000$) and $H$ ($4 <= H <= 1000$). Each of the subsequent $H$ lines provides the information on the grid $row_i$ in the $i$-th row from the top of the maze, where $row_i$ is a string of length $W$ defined in the table above. A letter represents a grid. Each of the subsequent 10 lines provides the table that defines collecting order dependent scores. An element in the table $s_{ij}$ ($0 <= s_{ij} <= 100$) is an integer that defines the score when item $j$ is collected after the item $i$ (without any item between them). Note that $s_{ii} = 0$.\n\n The grid information satisfies the following conditions:\n\nEach of S, T, 0,1, . . . , 9 appears in the maze once and only once.\n\nEach of A, B, . . . , J, a, b, . . . , j appears in the maze no more than once.", "output": "Output two items in a line separated by a space: the minimum number of moves and the maximum score associated with that sequence of moves. Output \"-1\" if unable to attain the game 's objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12 5\n.....S......\n.abcdefghij.\n.0123456789.\n.ABCDEFGHIJ.\n.....T......\n0 1 0 0 0 0 0 0 0 0\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 26 2", "input: 4 5\n0jSB\n###.\n1234\n5678\n9..T\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 31 0", "input: 7 7\n1.3#8.0\n#.###.#\n#.###.#\n5..S..9\n#.#T#.#\n#.###.#\n4.2#6.7\n0 0 0 0 0 0 0 0 1 0\n0 0 0 1 0 0 0 0 0 0\n0 0 0 0 7 0 0 0 0 0\n0 2 0 0 0 0 0 0 0 0\n0 0 3 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 8 0 0 0\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 53 19", "input: 5 6\n..S..\n#####\n01234\n56789\n#####\n..T..\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: -1"], "Pid": "p00395", "ProblemText": "Task Description: Maze & Items is a puzzle game in which the player tries to reach the goal while collecting items. The maze consists of $W * H$ grids, and some of them are inaccessible to the player depending on the items he/she has now. The score the player earns is defined according to the order of collecting items. The objective of the game is, after starting from a defined point, to collect all the items using the least number of moves before reaching the goal. There may be multiple routes that allow the least number of moves. In that case, the player seeks to maximize his/her score.\n\nOne of the following symbols is assigned to each of the grids. You can move to one of the neighboring grids (horizontally or vertically, but not diagonally) in one time, but you cannot move to the area outside the maze.\n
\n Symbol Description \n\n \n . Always accessible \n \n # Always inaccessible \n \n Number 0,1, . . , 9 Always accessible and an item (with its specific number) is located in the grid. \n \n Capital letter A, B, . . . , J Accessible only when the player does NOT have the corresponding item. Each of A, B, . . . , J takes a value from 0 to 9. \n \n Small letter a, b, . . . , j Accessible only when the player DOES have the corresponding item. Each of a, b, . . . , j takes one value from 0 to 9. \n \n S Starting grid. Always accessible. \n \n T Goal grid. Always accessible. \n\n \nThe player fails to complete the game if he/she has not collected all the items before reaching the goal. When entering a grid in which an item is located, it 's the player 's option to collect it or not. The player must keep the item once he/she collects it, and it disappears from the maze.\n\nGiven the state information of the maze and a table that defines the collecting order dependent scores, make a program that works out the minimum number of moves required to collect all the items before reaching the goal, and the maximum score gained through performing the moves.\nTask Input: The input is given in the following format.\n\n$W$ $H$\n$row_1$\n$row_2$\n. . .\n$row_H$\n$s_{00}$ $s_{01}$ . . . $s_{09}$\n$s_{10}$ $s_{11}$ . . . $s_{19}$\n. . .\n$s_{90}$ $s_{91}$ . . . $s_{99}$\n\nThe first line provides the number of horizontal and vertical grids in the maze $W$ ($4 <= W <= 1000$) and $H$ ($4 <= H <= 1000$). Each of the subsequent $H$ lines provides the information on the grid $row_i$ in the $i$-th row from the top of the maze, where $row_i$ is a string of length $W$ defined in the table above. A letter represents a grid. Each of the subsequent 10 lines provides the table that defines collecting order dependent scores. An element in the table $s_{ij}$ ($0 <= s_{ij} <= 100$) is an integer that defines the score when item $j$ is collected after the item $i$ (without any item between them). Note that $s_{ii} = 0$.\n\n The grid information satisfies the following conditions:\n\nEach of S, T, 0,1, . . . , 9 appears in the maze once and only once.\n\nEach of A, B, . . . , J, a, b, . . . , j appears in the maze no more than once.\nTask Output: Output two items in a line separated by a space: the minimum number of moves and the maximum score associated with that sequence of moves. Output \"-1\" if unable to attain the game 's objective.\nTask Samples: input: 12 5\n.....S......\n.abcdefghij.\n.0123456789.\n.ABCDEFGHIJ.\n.....T......\n0 1 0 0 0 0 0 0 0 0\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 26 2\ninput: 4 5\n0jSB\n###.\n1234\n5678\n9..T\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 31 0\ninput: 7 7\n1.3#8.0\n#.###.#\n#.###.#\n5..S..9\n#.#T#.#\n#.###.#\n4.2#6.7\n0 0 0 0 0 0 0 0 1 0\n0 0 0 1 0 0 0 0 0 0\n0 0 0 0 7 0 0 0 0 0\n0 2 0 0 0 0 0 0 0 0\n0 0 3 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 8 0 0 0\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 53 19\ninput: 5 6\n..S..\n#####\n01234\n56789\n#####\n..T..\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: -1\n\n" }, { "title": "playing with stones", "content": "Koshiro and Ukiko are playing a game with black and white stones. The rules of the game are as follows:\nBefore starting the game, they define some small areas and place \"one or more black stones and one or more white stones\" in each of the areas.\n \nKoshiro and Ukiko alternately select an area and perform one of the following operations. \n \n(a) Remove a white stone from the area\n(b) Remove one or more black stones from the area. Note, however, that the number of the black stones must be less than or equal to white ones in the area. \n(c) Pick up a white stone from the stone pod and replace it with a black stone. There are plenty of white stones in the pod so that there will be no shortage during the game. \nIf either Koshiro or Ukiko cannot perform 2 anymore, he/she loses.\n They played the game several times, with Koshiro 's first move and Ukiko 's second move, and felt the winner was determined at the onset of the game. So, they tried to calculate the winner assuming both players take optimum actions.\n\n Given the initial allocation of black and white stones in each area, make a program to determine which will win assuming both players take optimum actions.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$w_1$ $b_1$\n$w_2$ $b_2$\n:\n$w_N$ $b_N$\n\n The first line provides the number of areas $N$ ($1 <= N <= 10000$). Each of the subsequent $N$ lines provides the number of white stones $w_i$ and black stones $b_i$ ($1 <= w_i, b_i <= 100$) in the $i$-th area.", "output": "Output 0 if Koshiro wins and 1 if Ukiko wins.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 46\n94 8\n46 57\n output: 0", "input: 3\n2 46\n94 8\n46 57\n output: 1"], "Pid": "p00396", "ProblemText": "Task Description: Koshiro and Ukiko are playing a game with black and white stones. The rules of the game are as follows:\nBefore starting the game, they define some small areas and place \"one or more black stones and one or more white stones\" in each of the areas.\n \nKoshiro and Ukiko alternately select an area and perform one of the following operations. \n \n(a) Remove a white stone from the area\n(b) Remove one or more black stones from the area. Note, however, that the number of the black stones must be less than or equal to white ones in the area. \n(c) Pick up a white stone from the stone pod and replace it with a black stone. There are plenty of white stones in the pod so that there will be no shortage during the game. \nIf either Koshiro or Ukiko cannot perform 2 anymore, he/she loses.\n They played the game several times, with Koshiro 's first move and Ukiko 's second move, and felt the winner was determined at the onset of the game. So, they tried to calculate the winner assuming both players take optimum actions.\n\n Given the initial allocation of black and white stones in each area, make a program to determine which will win assuming both players take optimum actions.\nTask Input: The input is given in the following format.\n\n$N$\n$w_1$ $b_1$\n$w_2$ $b_2$\n:\n$w_N$ $b_N$\n\n The first line provides the number of areas $N$ ($1 <= N <= 10000$). Each of the subsequent $N$ lines provides the number of white stones $w_i$ and black stones $b_i$ ($1 <= w_i, b_i <= 100$) in the $i$-th area.\nTask Output: Output 0 if Koshiro wins and 1 if Ukiko wins.\nTask Samples: input: 3\n2 46\n94 8\n46 57\n output: 0\ninput: 3\n2 46\n94 8\n46 57\n output: 1\n\n" }, { "title": "K-th Exclusive OR", "content": "Exclusive OR (XOR) is an operation on two binary numbers $x$ and $y$ (0 or 1) that produces 0 if $x = y$ and $1$ if $x \\ne y$. This operation is represented by the symbol $\\oplus$. From the definition: $0 \\oplus 0 = 0$, $0 \\oplus 1 = 1$, $1 \\oplus 0 = 1$, $1 \\oplus 1 = 0$.\n\nExclusive OR on two non-negative integers comprises the following procedures: binary representation of the two integers are XORed on bit by bit bases, and the resultant bit array constitute a new integer. This operation is also represented by the same symbol $\\oplus$. For example, XOR of decimal numbers $3$ and $5$ is equivalent to binary operation $011 \\oplus 101$ which results in $110$, or $6$ in decimal format.\n\n Bitwise XOR operation on a sequence $Z$ consisting of $M$ non-negative integers $z_1, z_2, . . . , z_M$ is defined as follows:\n\n $v_0 = 0, v_i = v_{i - 1} \\oplus z_i$ ($1 <= i <= M$)\n\nBitwise XOR on series $Z$ is defined as $v_M$.\nYou have a sequence $A$ consisting of $N$ non-negative integers, ample sheets of papers and an empty box. You performed each of the following operations once on every combinations of integers ($L, R$), where $1 <= L <= R <= N$.\n\nPerform the bitwise XOR operation on the sub-sequence (from $L$-th to $R$-th elements) and name the result as $B$.\n\nSelect a sheet of paper and write $B$ on it, then put it in the box.\n Assume that ample sheets of paper are available to complete the trials. You select a positive integer $K$ and line up the sheets of paper inside the box in decreasing order of the number written on them. What you want to know is the number written on the $K$-th sheet of paper.\n \n You are given a series and perform all the operations described above. Then, you line up the sheets of paper in decreasing order of the numbers written on them. Make a program to determine the $K$-th number in the series.", "constraint": "", "input": "The input is given in the following format.\n\n$N$ $K$\n$a_1$ $a_2$ . . . $a_N$\n\n The first line provides the number of elements in the series $N$ ($1 <= N <= 10^5$) and the selected number $K$ ($1 <= K <= N(N+1)/2$). The second line provides an array of elements $a_i$ ($0 <= a_i <= 10^6$).", "output": "", "content_img": false, "lang": "en", "error": true, "samples": ["input: 3 3\n1 2 3\n output: 2\n After all operations have been completed, the numbers written on the paper inside the box are as follows (sorted in decreasing order)\n\n$3,3,2,1,1,0$\n\n 3番目の数は2であるため、2を出力する。", "input: 7 1\n1 0 1 0 1 0 1\n output: 1", "input: 5 10\n1 2 4 8 16\n output: 7"], "Pid": "p00397", "ProblemText": "Task Description: Exclusive OR (XOR) is an operation on two binary numbers $x$ and $y$ (0 or 1) that produces 0 if $x = y$ and $1$ if $x \\ne y$. This operation is represented by the symbol $\\oplus$. From the definition: $0 \\oplus 0 = 0$, $0 \\oplus 1 = 1$, $1 \\oplus 0 = 1$, $1 \\oplus 1 = 0$.\n\nExclusive OR on two non-negative integers comprises the following procedures: binary representation of the two integers are XORed on bit by bit bases, and the resultant bit array constitute a new integer. This operation is also represented by the same symbol $\\oplus$. For example, XOR of decimal numbers $3$ and $5$ is equivalent to binary operation $011 \\oplus 101$ which results in $110$, or $6$ in decimal format.\n\n Bitwise XOR operation on a sequence $Z$ consisting of $M$ non-negative integers $z_1, z_2, . . . , z_M$ is defined as follows:\n\n $v_0 = 0, v_i = v_{i - 1} \\oplus z_i$ ($1 <= i <= M$)\n\nBitwise XOR on series $Z$ is defined as $v_M$.\nYou have a sequence $A$ consisting of $N$ non-negative integers, ample sheets of papers and an empty box. You performed each of the following operations once on every combinations of integers ($L, R$), where $1 <= L <= R <= N$.\n\nPerform the bitwise XOR operation on the sub-sequence (from $L$-th to $R$-th elements) and name the result as $B$.\n\nSelect a sheet of paper and write $B$ on it, then put it in the box.\n Assume that ample sheets of paper are available to complete the trials. You select a positive integer $K$ and line up the sheets of paper inside the box in decreasing order of the number written on them. What you want to know is the number written on the $K$-th sheet of paper.\n \n You are given a series and perform all the operations described above. Then, you line up the sheets of paper in decreasing order of the numbers written on them. Make a program to determine the $K$-th number in the series.\nTask Input: The input is given in the following format.\n\n$N$ $K$\n$a_1$ $a_2$ . . . $a_N$\n\n The first line provides the number of elements in the series $N$ ($1 <= N <= 10^5$) and the selected number $K$ ($1 <= K <= N(N+1)/2$). The second line provides an array of elements $a_i$ ($0 <= a_i <= 10^6$).\nTask Output: \nTask Samples: input: 3 3\n1 2 3\n output: 2\n After all operations have been completed, the numbers written on the paper inside the box are as follows (sorted in decreasing order)\n\n$3,3,2,1,1,0$\n\n 3番目の数は2であるため、2を出力する。\ninput: 7 1\n1 0 1 0 1 0 1\n output: 1\ninput: 5 10\n1 2 4 8 16\n output: 7\n\n" }, { "title": "Road Construction", "content": "The Zuia Kingdom has finally emerged through annexation of $N$ cities, which are identified by index from $1$ to $N$. You are appointed the Minister of Transport of the newly born kingdom to construct the inter-city road network.\n\nTo simplify the conceptual design planning, you opted to consider each city as a point on the map, so that the $i$-th city can be represented by an coordinate ($x_i, y_i$).\n\n The cost of road construction connecting $u$-th and $v$-th cities is equal to the distance $|x_u - x_v|$ or $|y_u - y_v|$, whichever the larger. The notation $|A|$ represents the absolute value of $A$. The object here is to explore the minimum cost required to construct the road network in such a way that people can move between different cities along one or more roads.\n\n Make a program to calculate the minimum of total road construction cost from the number of cities and their coordinates.", "constraint": "", "input": "The input is given in the following format.\n\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . .\n$x_N$ $y_N$\n\nThe first line provides the number of cities $N$ ($2 <= N <= 10^5$). Each of the subsequent $N$ lines provides the coordinate of the $i$-th city $x_i, y_i$ ($0 <= x_i, y_i <= 10^9$) as integers. Note that none of these coordinates coincides if: $i \\ne j$, then $x_i \\ne x_j$ or $y_i \\ne y_j$.", "output": "Output the minimum road construction cost.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n3 4\n10 1\n output: 9\n The road connecting city 1 and 2 can be constructed at the cost of 2, and that connecting city 2 and 3 at the cost of 7. Therefore, the total cost becomes 9, which is the minimum.", "input: 3\n1 2\n3 4\n3 2\n output: 4", "input: 5\n7 41\n10 0\n99 27\n71 87\n14 25\n output: 163"], "Pid": "p00398", "ProblemText": "Task Description: The Zuia Kingdom has finally emerged through annexation of $N$ cities, which are identified by index from $1$ to $N$. You are appointed the Minister of Transport of the newly born kingdom to construct the inter-city road network.\n\nTo simplify the conceptual design planning, you opted to consider each city as a point on the map, so that the $i$-th city can be represented by an coordinate ($x_i, y_i$).\n\n The cost of road construction connecting $u$-th and $v$-th cities is equal to the distance $|x_u - x_v|$ or $|y_u - y_v|$, whichever the larger. The notation $|A|$ represents the absolute value of $A$. The object here is to explore the minimum cost required to construct the road network in such a way that people can move between different cities along one or more roads.\n\n Make a program to calculate the minimum of total road construction cost from the number of cities and their coordinates.\nTask Input: The input is given in the following format.\n\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . .\n$x_N$ $y_N$\n\nThe first line provides the number of cities $N$ ($2 <= N <= 10^5$). Each of the subsequent $N$ lines provides the coordinate of the $i$-th city $x_i, y_i$ ($0 <= x_i, y_i <= 10^9$) as integers. Note that none of these coordinates coincides if: $i \\ne j$, then $x_i \\ne x_j$ or $y_i \\ne y_j$.\nTask Output: Output the minimum road construction cost.\nTask Samples: input: 3\n1 2\n3 4\n10 1\n output: 9\n The road connecting city 1 and 2 can be constructed at the cost of 2, and that connecting city 2 and 3 at the cost of 7. Therefore, the total cost becomes 9, which is the minimum.\ninput: 3\n1 2\n3 4\n3 2\n output: 4\ninput: 5\n7 41\n10 0\n99 27\n71 87\n14 25\n output: 163\n\n" }, { "title": "Foehn Phenomena", "content": "In the Kingdom of IOI, the wind always blows from sea to land. There are $N + 1$ spots numbered from $0$ to $N$. The wind from Spot $0$ to Spot $N$ in order. Mr. JOI has a house at Spot $N$. The altitude of Spot $0$ is $A_0 = 0$, and the altitude of Spot $i$ ($1 <= i <= N$) is $A_i$.\n \nThe wind blows on the surface of the ground. The temperature of the wind changes according to the change of the altitude. The temperature of the wind at Spot $0$, which is closest to the sea, is $0$ degree. For each $i$ ($0 <= i <= N - 1$), the change of the temperature of the wind from Spot $i$ to Spot $i + 1$ depends only on the values of $A_i$ and $A_{i+1}$ in the following way:\n \nIf $A_i < A_{i+1}$, the temperature of the wind decreases by $S$ degrees per altitude. \n\nIf $A_i >= A_{i+1}$, the temperature of the wind increases by $T$ degrees per altitude. \nThe tectonic movement is active in the land of the Kingdom of IOI. You have the data of tectonic movements for $Q$ days. In the $j$-th ($1 <= j <= Q$) day, the change of the altitude of Spot $k$ for $L_j <= k <= R_j$ ($1 <= L_j <= R_j <= N$) is described by $X_j$. If $X_j$ is not negative, the altitude increases by $X_j$. If $X_j$ is negative, the altitude decreases by $|X_j|$.\n\nYour task is to calculate the temperature of the wind at the house of Mr. JOI after each tectonic movement.\n task:\nGiven the data of tectonic movements, write a program which calculates, for each $j$ ($1 <= j <= Q$), the temperature of the wind at the house of Mr. JOI after the tectonic movement on the $j$-th day.", "constraint": "All input data satisfy the following conditions.\n\n$1 <= N <= 200 000．$\n\n$1 <= Q <= 200 000．$\n\n$1 <= S <= 1 000 000．$\n\n$1 <= T <= 1 000 000．$\n\n$A_0 = 0．$\n\n$-1 000 000 <= A_i <= 1 000 000 (1 <= i <= N)．$\n\n$1 <= L_j <= R_j <= N (1 <= j <= Q)．$\n\n$ -1 000 000 <= X_j <= 1 000 000 (1 <= j <= Q)．$", "input": "Read the following data from the standard input.\n\nThe first line of input contains four space separated integers $N$, $Q$, $S$, $T$. This means there is a house of Mr. JOI at Spot $N$, there are $Q$ tectonic movements, the temperature of the wind decreases by $S$ degrees per altitude if the altitude increases, and the temperature of the wind increases by $T$ degrees per altitude if the altitude decreases.\n\nThe $i$-th line ($1 <= i <= N +1$) of the following $N +1$ lines contains an integer $A_{i-1}$, which is the initial altitude at Spot ($i - 1$) before tectonic movements.\n\nThe $j$-th line ($1 <= j <= Q$) of the following $Q$ lines contains three space separated integers $L_j$, $R_j$, $X_j$. This means, for the tectonic movement on the $j$-th day, the change of the altitude at the spots from $L_j$ to $R_j$ is described by $X_j$.", "output": "Write $Q$ lines to the standard output. The $j$-th line ($1 <= j <= Q$) of output contains the temperature of the wind\nat the house of Mr. JOI after the tectonic movement on the $j$-th day.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 5 1 2\n0\n4\n1\n8\n1 2 2\n1 1 -2\n2 3 5\n1 2 -1\n1 3 5\n output: -5\n-7\n-13\n-13\n-18\nInitially, the altitudes of the Spot 0,1,2,3 are 0,4,1,8, respectively. After the tectonic movement on the first day, the altitudes become 0,6,3,8, respectively. At that moment, the temperatures of the wind are 0, -6,0, -5,respectively.", "input: 2 2 5 5\n0\n6\n-1\n1 1 4\n1 2 8\n output: 5\n-35", "input: 7 8 8 13\n0\n4\n-9\n4\n-2\n3\n10\n-9\n1 4 8\n3 5 -2\n3 3 9\n1 7 4\n3 5 -1\n5 6 3\n4 4 9\n6 7 -10\n output: 277\n277\n322\n290\n290\n290\n290\n370"], "Pid": "p00559", "ProblemText": "Task Description: In the Kingdom of IOI, the wind always blows from sea to land. There are $N + 1$ spots numbered from $0$ to $N$. The wind from Spot $0$ to Spot $N$ in order. Mr. JOI has a house at Spot $N$. The altitude of Spot $0$ is $A_0 = 0$, and the altitude of Spot $i$ ($1 <= i <= N$) is $A_i$.\n \nThe wind blows on the surface of the ground. The temperature of the wind changes according to the change of the altitude. The temperature of the wind at Spot $0$, which is closest to the sea, is $0$ degree. For each $i$ ($0 <= i <= N - 1$), the change of the temperature of the wind from Spot $i$ to Spot $i + 1$ depends only on the values of $A_i$ and $A_{i+1}$ in the following way:\n \nIf $A_i < A_{i+1}$, the temperature of the wind decreases by $S$ degrees per altitude. \n\nIf $A_i >= A_{i+1}$, the temperature of the wind increases by $T$ degrees per altitude. \nThe tectonic movement is active in the land of the Kingdom of IOI. You have the data of tectonic movements for $Q$ days. In the $j$-th ($1 <= j <= Q$) day, the change of the altitude of Spot $k$ for $L_j <= k <= R_j$ ($1 <= L_j <= R_j <= N$) is described by $X_j$. If $X_j$ is not negative, the altitude increases by $X_j$. If $X_j$ is negative, the altitude decreases by $|X_j|$.\n\nYour task is to calculate the temperature of the wind at the house of Mr. JOI after each tectonic movement.\n task:\nGiven the data of tectonic movements, write a program which calculates, for each $j$ ($1 <= j <= Q$), the temperature of the wind at the house of Mr. JOI after the tectonic movement on the $j$-th day.\nTask Constraint: All input data satisfy the following conditions.\n\n$1 <= N <= 200 000．$\n\n$1 <= Q <= 200 000．$\n\n$1 <= S <= 1 000 000．$\n\n$1 <= T <= 1 000 000．$\n\n$A_0 = 0．$\n\n$-1 000 000 <= A_i <= 1 000 000 (1 <= i <= N)．$\n\n$1 <= L_j <= R_j <= N (1 <= j <= Q)．$\n\n$ -1 000 000 <= X_j <= 1 000 000 (1 <= j <= Q)．$\nTask Input: Read the following data from the standard input.\n\nThe first line of input contains four space separated integers $N$, $Q$, $S$, $T$. This means there is a house of Mr. JOI at Spot $N$, there are $Q$ tectonic movements, the temperature of the wind decreases by $S$ degrees per altitude if the altitude increases, and the temperature of the wind increases by $T$ degrees per altitude if the altitude decreases.\n\nThe $i$-th line ($1 <= i <= N +1$) of the following $N +1$ lines contains an integer $A_{i-1}$, which is the initial altitude at Spot ($i - 1$) before tectonic movements.\n\nThe $j$-th line ($1 <= j <= Q$) of the following $Q$ lines contains three space separated integers $L_j$, $R_j$, $X_j$. This means, for the tectonic movement on the $j$-th day, the change of the altitude at the spots from $L_j$ to $R_j$ is described by $X_j$.\nTask Output: Write $Q$ lines to the standard output. The $j$-th line ($1 <= j <= Q$) of output contains the temperature of the wind\nat the house of Mr. JOI after the tectonic movement on the $j$-th day.\nTask Samples: input: 3 5 1 2\n0\n4\n1\n8\n1 2 2\n1 1 -2\n2 3 5\n1 2 -1\n1 3 5\n output: -5\n-7\n-13\n-13\n-18\nInitially, the altitudes of the Spot 0,1,2,3 are 0,4,1,8, respectively. After the tectonic movement on the first day, the altitudes become 0,6,3,8, respectively. At that moment, the temperatures of the wind are 0, -6,0, -5,respectively.\ninput: 2 2 5 5\n0\n6\n-1\n1 1 4\n1 2 8\n output: 5\n-35\ninput: 7 8 8 13\n0\n4\n-9\n4\n-2\n3\n10\n-9\n1 4 8\n3 5 -2\n3 3 9\n1 7 4\n3 5 -1\n5 6 3\n4 4 9\n6 7 -10\n output: 277\n277\n322\n290\n290\n290\n290\n370\n\n" }, { "title": "Semiexpress", "content": "The JOI Railways is the only railway company in the Kingdom of JOI. There are $N$ stations numbered from $1$ to $N$ along a railway. Currently, two kinds of trains are operated; one is express and the other one is local.\n\n A local train stops at every station. For each $i$ ($1 <= i < N$), by a local train, it takes $A$ minutes from the station $i$ to the station ($i + 1$).\n\t \n An express train stops only at the stations $S_1, S_2, . . . , S_M$ ($1 = S_1 < S_2 < . . . < S_M = N$). For each $i$ ($1 <= i < N$), by an express train, it takes $B$ minutes from the station $i$ to the station ($i + 1$).\n\n The JOI Railways plans to operate another kind of trains called \"semiexpress. \" For each $i$ ($1 <= i < N$), by a semiexpress train, it takes $C$ minutes from the station $i$ to the station ($i + 1$). The stops of semiexpress trains are not yet determined. But they must satisfy the following conditions:\n\n Semiexpress trains must stop at every station where express trains stop.\n\n Semiexpress trains must stop at $K$ stations exactly.\n The JOI Railways wants to maximize the number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes. The JOI Railways plans to determine the stops of semiexpress trains so that this number is maximized. We do not count the standing time of trains.\n\n When we travel from the station 1 to another station, we can take trains only to the direction where the numbers of stations increase. If several kinds of trains stop at the station $i$ ($2 <= i <= N - 1$), you can transfer between any trains which stop at that station.\n\nWhen the stops of semiexpress trains are determined appropriately, what is the maximum number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes?\n task:\nGiven the number of stations of the JOI Railways, the stops of express trains, the speeds of the trains, and maximum travel time, write a program which calculates the maximum number of stations which satisfy the condition on the travel time.", "constraint": "All input data satisfy the following conditions.\n\n$2 <= N <= 1 000 000 000．$\n\n$2 <= M <= K <= 3 000．$\n\n$K <= N．$\n\n$1 <= B < C < A <= 1 000 000 000．$\n\n$1 <= T <= 10^{18}$\n\n$1 = S_1 < S_2 < ... < S_M = N$", "input": "Read the following data from the standard input.\n\n The first line of input contains three space separated integers $N$, $M$, $K$. This means there are $N$ stations of the JOI Railways, an express train stops at $M$ stations, and a semiexpress train stops at $K$ stations,\n\nThe second line of input contains three space separated integers $A$, $B$, $C$. This means it takes $A$, $B$, $C$ minutes by a local, express, semiexpress train to travel from a station to the next station, respectively.\n\n>li> The third line of input contains an integer $T$. This means the JOI Railways wants to maximize the number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes.\n The $i$-th line ($1 <= i <= M$) of the following $M$ lines contains an integer $S_i$. This means an express train stops at the station $S_i$.", "output": "Write one line to the standard output. The output contains the maximum number of stations satisfying the condition on the travel time.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10 3 5\n10 3 5\n30\n1\n6\n10\n output: 8\n In this sample input, there are 10 stations of the JOI Railways. An express train stops at three stations 1,6,10. Assume that the stops of an semiexpress train are 1,5,6,8,10. Then, among the stations 2,3, ...10, we can travel from the station 1 to every station except for the station 9 within 30 minutes.\nFor some $i$, the travel time and the route from the station 1 to the station $i$ are as follows:\n\nFrom the station 1 to the station 3, we can travel using a local train only. The travel time is 20 minutes.\n From the station 1 to the station 7, we travel from the station 1 to the station 6 by an express train, and transfer to a local train. The travel time is 25 minutes.\n From the station 1 to the station 8, we travel from the station 1 to the station 6 by an express train, and transfer to a semiexpress train. The travel time is 25 minutes.\n From the station 1 to the station 9, we travel from the station 1 to the station 6 by an express train, from the station 6 to the station 8 by a semiexpress train, and from the station 8 to the station 9 by a local train. In total, the travel time is 35 minutes.", "input: 10 3 5\n10 3 5\n25\n1\n6\n10\n output: 2", "input: 90 10 12\n100000 1000 10000\n10000\n1\n10\n20\n30\n40\n50\n60\n70\n80\n90\n output: 2", "input: 12 3 4\n10 1 2\n30\n1\n11\n12\n output: 8", "input: 300 8 16\n345678901 123456789 234567890\n12345678901\n1\n10\n77\n82\n137\n210\n297\n300\n output: 72", "input: 1000000000 2 3000\n1000000000 1 2\n1000000000\n1\n1000000000\n output: 3000"], "Pid": "p00560", "ProblemText": "Task Description: The JOI Railways is the only railway company in the Kingdom of JOI. There are $N$ stations numbered from $1$ to $N$ along a railway. Currently, two kinds of trains are operated; one is express and the other one is local.\n\n A local train stops at every station. For each $i$ ($1 <= i < N$), by a local train, it takes $A$ minutes from the station $i$ to the station ($i + 1$).\n\t \n An express train stops only at the stations $S_1, S_2, . . . , S_M$ ($1 = S_1 < S_2 < . . . < S_M = N$). For each $i$ ($1 <= i < N$), by an express train, it takes $B$ minutes from the station $i$ to the station ($i + 1$).\n\n The JOI Railways plans to operate another kind of trains called \"semiexpress. \" For each $i$ ($1 <= i < N$), by a semiexpress train, it takes $C$ minutes from the station $i$ to the station ($i + 1$). The stops of semiexpress trains are not yet determined. But they must satisfy the following conditions:\n\n Semiexpress trains must stop at every station where express trains stop.\n\n Semiexpress trains must stop at $K$ stations exactly.\n The JOI Railways wants to maximize the number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes. The JOI Railways plans to determine the stops of semiexpress trains so that this number is maximized. We do not count the standing time of trains.\n\n When we travel from the station 1 to another station, we can take trains only to the direction where the numbers of stations increase. If several kinds of trains stop at the station $i$ ($2 <= i <= N - 1$), you can transfer between any trains which stop at that station.\n\nWhen the stops of semiexpress trains are determined appropriately, what is the maximum number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes?\n task:\nGiven the number of stations of the JOI Railways, the stops of express trains, the speeds of the trains, and maximum travel time, write a program which calculates the maximum number of stations which satisfy the condition on the travel time.\nTask Constraint: All input data satisfy the following conditions.\n\n$2 <= N <= 1 000 000 000．$\n\n$2 <= M <= K <= 3 000．$\n\n$K <= N．$\n\n$1 <= B < C < A <= 1 000 000 000．$\n\n$1 <= T <= 10^{18}$\n\n$1 = S_1 < S_2 < ... < S_M = N$\nTask Input: Read the following data from the standard input.\n\n The first line of input contains three space separated integers $N$, $M$, $K$. This means there are $N$ stations of the JOI Railways, an express train stops at $M$ stations, and a semiexpress train stops at $K$ stations,\n\nThe second line of input contains three space separated integers $A$, $B$, $C$. This means it takes $A$, $B$, $C$ minutes by a local, express, semiexpress train to travel from a station to the next station, respectively.\n\n>li> The third line of input contains an integer $T$. This means the JOI Railways wants to maximize the number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes.\n The $i$-th line ($1 <= i <= M$) of the following $M$ lines contains an integer $S_i$. This means an express train stops at the station $S_i$.\nTask Output: Write one line to the standard output. The output contains the maximum number of stations satisfying the condition on the travel time.\nTask Samples: input: 10 3 5\n10 3 5\n30\n1\n6\n10\n output: 8\n In this sample input, there are 10 stations of the JOI Railways. An express train stops at three stations 1,6,10. Assume that the stops of an semiexpress train are 1,5,6,8,10. Then, among the stations 2,3, ...10, we can travel from the station 1 to every station except for the station 9 within 30 minutes.\nFor some $i$, the travel time and the route from the station 1 to the station $i$ are as follows:\n\nFrom the station 1 to the station 3, we can travel using a local train only. The travel time is 20 minutes.\n From the station 1 to the station 7, we travel from the station 1 to the station 6 by an express train, and transfer to a local train. The travel time is 25 minutes.\n From the station 1 to the station 8, we travel from the station 1 to the station 6 by an express train, and transfer to a semiexpress train. The travel time is 25 minutes.\n From the station 1 to the station 9, we travel from the station 1 to the station 6 by an express train, from the station 6 to the station 8 by a semiexpress train, and from the station 8 to the station 9 by a local train. In total, the travel time is 35 minutes.\ninput: 10 3 5\n10 3 5\n25\n1\n6\n10\n output: 2\ninput: 90 10 12\n100000 1000 10000\n10000\n1\n10\n20\n30\n40\n50\n60\n70\n80\n90\n output: 2\ninput: 12 3 4\n10 1 2\n30\n1\n11\n12\n output: 8\ninput: 300 8 16\n345678901 123456789 234567890\n12345678901\n1\n10\n77\n82\n137\n210\n297\n300\n output: 72\ninput: 1000000000 2 3000\n1000000000 1 2\n1000000000\n1\n1000000000\n output: 3000\n\n" }, { "title": "Kingdom of JOIOI", "content": "The Kingdom of JOIOI is a rectangular grid of $H * W$ cells. In the Kingdom of JOIOI, in order to improve efficiency of administrative institutions, the country will be divided into two regions called \"JOI\" and \"IOI. \"\n\n Since we do not want to divide it in a complicated way, the division must satisfy the following conditions:\n\n Each region must contain at least one cell.\n\n Each cell must belong to exactly one of two regions.\n\n For every pair of cells in the JOI region, we can travel from one to the other by passing through cells belonging to the JOI region only. When move from a cell to another cell, the two cells must share an edge. The same is true for the IOI region.\n\n For each row or column, if we take all the cells in that row or column, the cells belonging to each region must be connected. All the cells in a row or column may belong to the same region.\n Each cell has an integer called the altitude. After we divide the country into two regions, it is expected that traveling in each region will be active. But, if the difference of the altitudes of cells are large, traveling between them becomes hard. Therefore, we would like to minimize the maximum of the difference of the altitudes between cells belonging to the same region. In other words, we would like to minimize the larger value of\n\n the difference between the maximum and the minimum altitudes in the JOI region, and\n\n the difference between the maximum and the minimum altitudes in the IOI region.\n\n task:\n Given the altitudes of cells in the Kingdom of JOIOI, write a program which calculates the minimum of the larger value of the difference between the maximum and the minimum altitudes in the JOI region and the difference between the maximum and the minimum altitudes in the IOI region when we divide the country into two regions.", "constraint": "All input data satisfy the following conditions.\n\n$2 <= H <= 2 000．$\n\n$2 <= W <= 2 000．$\n\n$1 <= A_{i, j} <= 1 000 000 000 (1 <= i <= H, 1 <= j <= W)．$", "input": "Read the following data from the standard input.\n\n The first line of input contains two space separated integers $H$, $W$. This means the Kingdom of JOIOI is a rectangular grid of $H * W$ cells.\n\n The $i$-th line ($1 <= i <= H$) of the following $H$ lines contains $W$ space separated integers $A_{i, 1}, A_{i, 2}, . . . , A_{i, W}$. This means the cell in the $i$-th row from above and $j$-th column from left ($1 <= j <= W$) has altitude $A_{i, j}$.", "output": "Write one line to the standard output. The output contains the minimum of the larger value of the difference between the maximum and the minimum altitudes in the JOI region and the difference between the maximum and the minimum altitudes in the IOI region when we divide the country into two regions.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 4\n1 12 6 11\n11 10 2 14\n10 1 9 20\n4 17 19 10\n output: 11\n For example, in this sample input, we divide the country into two regions as follows. Here, ‘J' denotes the JOI region, and ‘I' denotes the IOI region.\nThe following division does not satisfy the condition because, in the third column from left, cells with ‘I' are not connected.", "input: 8 6\n23 23 10 11 16 21\n15 26 19 28 19 20\n25 26 28 16 15 11\n11 8 19 11 15 24\n14 19 15 14 24 11\n10 8 11 7 6 14\n23 5 19 23 17 17\n18 11 21 14 20 16\n output: 18"], "Pid": "p00561", "ProblemText": "Task Description: The Kingdom of JOIOI is a rectangular grid of $H * W$ cells. In the Kingdom of JOIOI, in order to improve efficiency of administrative institutions, the country will be divided into two regions called \"JOI\" and \"IOI. \"\n\n Since we do not want to divide it in a complicated way, the division must satisfy the following conditions:\n\n Each region must contain at least one cell.\n\n Each cell must belong to exactly one of two regions.\n\n For every pair of cells in the JOI region, we can travel from one to the other by passing through cells belonging to the JOI region only. When move from a cell to another cell, the two cells must share an edge. The same is true for the IOI region.\n\n For each row or column, if we take all the cells in that row or column, the cells belonging to each region must be connected. All the cells in a row or column may belong to the same region.\n Each cell has an integer called the altitude. After we divide the country into two regions, it is expected that traveling in each region will be active. But, if the difference of the altitudes of cells are large, traveling between them becomes hard. Therefore, we would like to minimize the maximum of the difference of the altitudes between cells belonging to the same region. In other words, we would like to minimize the larger value of\n\n the difference between the maximum and the minimum altitudes in the JOI region, and\n\n the difference between the maximum and the minimum altitudes in the IOI region.\n\n task:\n Given the altitudes of cells in the Kingdom of JOIOI, write a program which calculates the minimum of the larger value of the difference between the maximum and the minimum altitudes in the JOI region and the difference between the maximum and the minimum altitudes in the IOI region when we divide the country into two regions.\nTask Constraint: All input data satisfy the following conditions.\n\n$2 <= H <= 2 000．$\n\n$2 <= W <= 2 000．$\n\n$1 <= A_{i, j} <= 1 000 000 000 (1 <= i <= H, 1 <= j <= W)．$\nTask Input: Read the following data from the standard input.\n\n The first line of input contains two space separated integers $H$, $W$. This means the Kingdom of JOIOI is a rectangular grid of $H * W$ cells.\n\n The $i$-th line ($1 <= i <= H$) of the following $H$ lines contains $W$ space separated integers $A_{i, 1}, A_{i, 2}, . . . , A_{i, W}$. This means the cell in the $i$-th row from above and $j$-th column from left ($1 <= j <= W$) has altitude $A_{i, j}$.\nTask Output: Write one line to the standard output. The output contains the minimum of the larger value of the difference between the maximum and the minimum altitudes in the JOI region and the difference between the maximum and the minimum altitudes in the IOI region when we divide the country into two regions.\nTask Samples: input: 4 4\n1 12 6 11\n11 10 2 14\n10 1 9 20\n4 17 19 10\n output: 11\n For example, in this sample input, we divide the country into two regions as follows. Here, ‘J' denotes the JOI region, and ‘I' denotes the IOI region.\nThe following division does not satisfy the condition because, in the third column from left, cells with ‘I' are not connected.\ninput: 8 6\n23 23 10 11 16 21\n15 26 19 28 19 20\n25 26 28 16 15 11\n11 8 19 11 15 24\n14 19 15 14 24 11\n10 8 11 7 6 14\n23 5 19 23 17 17\n18 11 21 14 20 16\n output: 18\n\n" }, { "title": "Soccer", "content": "You are a manager of a prestigious soccer team in the JOI league.\n\n The team has $N$ players numbered from 1 to $N$. The players are practicing hard in order to win the tournament game. The field is a rectangle whose height is $H$ meters and width is $W$ meters. The vertical line of the field is in the north-south direction, and the horizontal line of the field is in the east-west direction. A point in the field is denoted by ($i, j$) if it is $i$-meters to the south and $j$ meters to the east from the northwest corner of the field.\n\n After the practice finishes, players must clear the ball. In the beginning of the clearance, the player $i$ ($1 <= i <= N$) stands at ($S_i, T_i$). There is only one ball in the field, and the player 1 has it. You stand at ($S_N, T_N$) with the player $N$. The clearance is finished if the ball is passed to ($S_N, T_N$), and you catch it. You cannot move during the clearance process.\n\n You can ask players to act. But, if a player acts, his fatigue degree will be increased according to the action. Here is a list of possible actions of the players. If a player has the ball, he can act (i), (ii), or (iii). Otherwise, he can act (ii) or (iv).\n\n (i) Choose one of the 4 directions (east/west/south/north), and choose a positive integer $p$. Kick the ball to that direction. Then, the ball moves exactly p meters. The kicker does not move by this action, and he loses the ball. His fatigue degree is increased by $A * p + B$.\n(ii) Choose one of the 4 directions (east/west/south/north), and move 1 meter to that direction. If he has the ball, he moves with it. His fatigue degree is increased by $C$ regardless of whether he has the ball or not.\n(iii) Place the ball where he stands. He loses the ball. His fatigue degree does not change.\n (iv) Take the ball. His fatigue degree does not change. A player can take this action only if he stands at the same place as the ball, and nobody has the ball.\n\n Note that it is possible for a player or a ball to leave the field. More than one players can stand at the same place.\n\nSince the players just finished the practice, their fatigue degrees must not be increased too much. You want to calculate the minimum possible value of the sum of fatigue degrees of the players for the clearance process.\n task:\nGiven the size of the field and the positions of the players, write a program which calculates the minimum possible value of the sum of fatigue degrees of the players for the clearance process.", "constraint": "all input data satisfy the following conditions.\n \n$1 <= h <= 500. $\n$1 <= w <= 500. $\n$0 <= a <= 1 000 000 000. $\n$0 <= b <= 1 000 000 000. $\n$0 <= c <= 1 000 000 000. $\n$2 <= n <= 100 000. $\n$0 <= s_i <= h (1 <= i <= n). $\n$0 <= t_i <= w (1 <= i <= n). $\n$(s_1, t_1) <> (s_n, t_n). $", "input": "Read the following data from the standard input.\n The first line of input contains two space separated integers $H$, $W$. This means the field is a rectangle whose height is $H$ meters and width is $W$ meters.\n The second line contains three space separated integers $A$, $B$, $C$ describing the increment of the fatigue degree by actions.\n The third line contains an integer N, the number of players.\n The $i$-th line ($1 <= i <= N$) of the following $N$ lines contains two space separated integers $S_i$, $T_i$. This means, in the beginning of the clearance, the player $i$ ($1 <= i <= N$) stands at ($S_i, T_i$).", "output": "Write one line to the standard output. The output contains the minimum possible value of the sum of fatigue degrees of the players for the clearance process.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 5\n1 3 6\n3\n1 1\n0 4\n6 5\n output: 26\n \n in this sample input, the initial status of the field is as in the following figure. the white circles are the players. the black circle is the ball. you stand at (6,5).the initial status of the field\n \n the players act as follows:\n . the player 1 kicks the ball to the east for $3$ meters. his fatigue degree is increased by $1 * 3 + 3 = 6$. the ball moves to ($1,4$).\n the player 2 moves $1$ meter to the south, and he has the ball. his fatigue degree is increased by $6$.\n the player 2 moves $1$ meter to the east. his fatigue degree is increased by $6$.\n the player 2 kicks the ball to the south for $5$ meters. his fatigue degree is increased by $1 * 5 + 3 = 8$. the ball moves to ($6,5$). \nin these actions, the sum of fatigue degrees is $6 + 6 + 6 + 8 = 26$, which is the minimum possible value.\n \n\nthe actions in an optimal solution", "input: 3 3\n0 50 10\n2\n0 0\n3 3\n output: 60\n in sample input 2, it not not necessary to", "input: 4 3\n0 15 10\n2\n0 0\n4 3\n output: 45", "input: 4 6\n0 5 1000\n6\n3 1\n4 6\n3 0\n3 0\n4 0\n0 4\n output: 2020\n \nthat more than one players can stand at the same place."], "Pid": "p00562", "ProblemText": "Task Description: You are a manager of a prestigious soccer team in the JOI league.\n\n The team has $N$ players numbered from 1 to $N$. The players are practicing hard in order to win the tournament game. The field is a rectangle whose height is $H$ meters and width is $W$ meters. The vertical line of the field is in the north-south direction, and the horizontal line of the field is in the east-west direction. A point in the field is denoted by ($i, j$) if it is $i$-meters to the south and $j$ meters to the east from the northwest corner of the field.\n\n After the practice finishes, players must clear the ball. In the beginning of the clearance, the player $i$ ($1 <= i <= N$) stands at ($S_i, T_i$). There is only one ball in the field, and the player 1 has it. You stand at ($S_N, T_N$) with the player $N$. The clearance is finished if the ball is passed to ($S_N, T_N$), and you catch it. You cannot move during the clearance process.\n\n You can ask players to act. But, if a player acts, his fatigue degree will be increased according to the action. Here is a list of possible actions of the players. If a player has the ball, he can act (i), (ii), or (iii). Otherwise, he can act (ii) or (iv).\n\n (i) Choose one of the 4 directions (east/west/south/north), and choose a positive integer $p$. Kick the ball to that direction. Then, the ball moves exactly p meters. The kicker does not move by this action, and he loses the ball. His fatigue degree is increased by $A * p + B$.\n(ii) Choose one of the 4 directions (east/west/south/north), and move 1 meter to that direction. If he has the ball, he moves with it. His fatigue degree is increased by $C$ regardless of whether he has the ball or not.\n(iii) Place the ball where he stands. He loses the ball. His fatigue degree does not change.\n (iv) Take the ball. His fatigue degree does not change. A player can take this action only if he stands at the same place as the ball, and nobody has the ball.\n\n Note that it is possible for a player or a ball to leave the field. More than one players can stand at the same place.\n\nSince the players just finished the practice, their fatigue degrees must not be increased too much. You want to calculate the minimum possible value of the sum of fatigue degrees of the players for the clearance process.\n task:\nGiven the size of the field and the positions of the players, write a program which calculates the minimum possible value of the sum of fatigue degrees of the players for the clearance process.\nTask Constraint: all input data satisfy the following conditions.\n \n$1 <= h <= 500. $\n$1 <= w <= 500. $\n$0 <= a <= 1 000 000 000. $\n$0 <= b <= 1 000 000 000. $\n$0 <= c <= 1 000 000 000. $\n$2 <= n <= 100 000. $\n$0 <= s_i <= h (1 <= i <= n). $\n$0 <= t_i <= w (1 <= i <= n). $\n$(s_1, t_1) <> (s_n, t_n). $\nTask Input: Read the following data from the standard input.\n The first line of input contains two space separated integers $H$, $W$. This means the field is a rectangle whose height is $H$ meters and width is $W$ meters.\n The second line contains three space separated integers $A$, $B$, $C$ describing the increment of the fatigue degree by actions.\n The third line contains an integer N, the number of players.\n The $i$-th line ($1 <= i <= N$) of the following $N$ lines contains two space separated integers $S_i$, $T_i$. This means, in the beginning of the clearance, the player $i$ ($1 <= i <= N$) stands at ($S_i, T_i$).\nTask Output: Write one line to the standard output. The output contains the minimum possible value of the sum of fatigue degrees of the players for the clearance process.\nTask Samples: input: 6 5\n1 3 6\n3\n1 1\n0 4\n6 5\n output: 26\n \n in this sample input, the initial status of the field is as in the following figure. the white circles are the players. the black circle is the ball. you stand at (6,5).the initial status of the field\n \n the players act as follows:\n . the player 1 kicks the ball to the east for $3$ meters. his fatigue degree is increased by $1 * 3 + 3 = 6$. the ball moves to ($1,4$).\n the player 2 moves $1$ meter to the south, and he has the ball. his fatigue degree is increased by $6$.\n the player 2 moves $1$ meter to the east. his fatigue degree is increased by $6$.\n the player 2 kicks the ball to the south for $5$ meters. his fatigue degree is increased by $1 * 5 + 3 = 8$. the ball moves to ($6,5$). \nin these actions, the sum of fatigue degrees is $6 + 6 + 6 + 8 = 26$, which is the minimum possible value.\n \n\nthe actions in an optimal solution\ninput: 3 3\n0 50 10\n2\n0 0\n3 3\n output: 60\n in sample input 2, it not not necessary to\ninput: 4 3\n0 15 10\n2\n0 0\n4 3\n output: 45\ninput: 4 6\n0 5 1000\n6\n3 1\n4 6\n3 0\n3 0\n4 0\n0 4\n output: 2020\n \nthat more than one players can stand at the same place.\n\n" }, { "title": "Rope", "content": "JOI is a baby playing with a rope. The rope has length $N$, and it is placed as a straight line from left to right. The rope consists of $N$ cords. The cords are connected as a straight line. Each cord has length 1 and thickness 1. In total, $M$ colors are used for the rope. The color of the $i$-th cord from left is $C_i$ ($1 <= C_i <= M$).\n\n JOI is making the rope shorter. JOI repeats the following procedure until the length of the rope becomes 2.\n\n Let $L$ be the length of the rope. Choose an integer $j$ ($1 <= j < L$). Shorten the rope by combining cords so that the point of length $j$ from left on the rope becomes the leftmost point. More precisely, do the following:\n \n If $j <= L/2$, for each $i$ ($1 <= i <= j$), combine the $i$-th cord from left with the ($2j - i + 1$)-th cord from left. By this procedure, the rightmost point of the rope becomes the rightmost point. The length of the rope becomes $L - j$.\n\n If $j > L/2$, for each $i$ ($2j - L + 1 <= i <= j$), combine the $i$-th cord from left with the ($2j - i + 1$)-th cord from left. By this procedure, the leftmost point of the rope becomes the rightmost point. The length of the rope becomes $j$.\n \n If a cord is combined with another cord, the colors of the two cords must be the same. We can change the color of a cord before it is combined with another cord. The cost to change the color of a cord is equal to the thickness of it. After adjusting the colors of two cords, they are combined into a single cord; its thickness is equal to the sum of thicknesses of the two cords.\n \n JOI wants to minimize the total cost of procedures to shorten the rope until it becomes length 2. For each color, JOI wants to calculate the minimum total cost of procedures to shorten the rope so that the final rope of length 2 contains a cord with that color.\n\nYour task is to solve this problem instead of JOI.\n task:\nGiven the colors of the cords in the initial rope, write a program which calculates, for each color, the minimum total cost of procedures to shorten the rope so that the final rope of length 2 contains a cord with that color.", "constraint": "All input data satisfy the following conditions.\n\n$ 2 <= N <= 1 000 000． $\n\n$ 1 <= M <= N．$\n\n$ 1 <= C_i <= M (1 <= i <= N)．$\n\nFor each $c$ with $1 <= c <= M$, there exists an integer $i$ with $C_i = c$.", "input": "Read the following data from the standard input.\n\n The first line of input contains two space separated integers $N$, $M$. This means the rope consists of $N$ cords, and $M$ colors are used for the cords.\n\n The second line contains $N$ space separated integers $C_1, C_2, . . . , C_N$. This means the color of the $i$-th cord from left is $C_i$ ($1 <= C_i <= M$).", "output": "Write $M$ lines to the standard output. The $c$-th line ($1 <= c <= M$) contains the minimum total cost of procedures to shorten the rope so that the final rope of length 2 contains a cord with color $c$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 3\n1 2 3 3 2\n output: 2\n1\n1\n By the following procedures, we can shorten the rope so that the final rope of length 2 contains a cord with color 1. The total cost is 2.\n\n Change the color of the second cord from left to 1. Shorten the rope so that the point of length 1 from left on the rope becomes the leftmost point. The colors of cords become 1,3,3,2. The thicknesses of cords become 2,1,1,1.\n Change the color of the 4-th cord from left to 1. Shorten the rope so that the point of length 2 from left on the rope becomes the leftmost point. The colors of cords become 3,1. The thicknesses of cords become 2,3.\n\n By the following procedures, we can shorten the rope so that the final rope of length 2 contains a cord with color 2,3. The total cost is 1.\n\n Shorten the rope so that the point of length 3 from left on the rope becomes the leftmost point. The colors of cords become 3,2,1. The thicknesses of cords become 2,2,1.\n Change the color of the third cord from left to 2. Shorten the rope so that the point of length 2 from left on the rope becomes the leftmost point. The colors of cords become 2,3. The thicknesses of cords become 3,2.", "input: 7 3\n1 2 2 1 3 3 3\n output: 2\n2\n2\n By the following procedures, we can shorten the rope so that the final rope of length 2 contains a cord with color 1. The total cost is 2.\n\n Shorten the rope so that the point of length 2 from left on the rope becomes the leftmost point.\n Change the color of the leftmost cord to 1. Shorten the rope so that the point of length 1 from left on the rope becomes the leftmost point. Note that the cost to change the color is 2 because the thickness of the cord is 2.\n Shorten the rope so that the point of length 3 from left on the rope becomes the leftmost point.\n Shorten the rope so that the point of length 1 from left on the rope becomes the leftmost point.", "input: 10 3\n2 2 1 1 3 3 2 1 1 2\n output: 3\n3\n4\nBefore shortening the rope, we may change the colors of several cords."], "Pid": "p00563", "ProblemText": "Task Description: JOI is a baby playing with a rope. The rope has length $N$, and it is placed as a straight line from left to right. The rope consists of $N$ cords. The cords are connected as a straight line. Each cord has length 1 and thickness 1. In total, $M$ colors are used for the rope. The color of the $i$-th cord from left is $C_i$ ($1 <= C_i <= M$).\n\n JOI is making the rope shorter. JOI repeats the following procedure until the length of the rope becomes 2.\n\n Let $L$ be the length of the rope. Choose an integer $j$ ($1 <= j < L$). Shorten the rope by combining cords so that the point of length $j$ from left on the rope becomes the leftmost point. More precisely, do the following:\n \n If $j <= L/2$, for each $i$ ($1 <= i <= j$), combine the $i$-th cord from left with the ($2j - i + 1$)-th cord from left. By this procedure, the rightmost point of the rope becomes the rightmost point. The length of the rope becomes $L - j$.\n\n If $j > L/2$, for each $i$ ($2j - L + 1 <= i <= j$), combine the $i$-th cord from left with the ($2j - i + 1$)-th cord from left. By this procedure, the leftmost point of the rope becomes the rightmost point. The length of the rope becomes $j$.\n \n If a cord is combined with another cord, the colors of the two cords must be the same. We can change the color of a cord before it is combined with another cord. The cost to change the color of a cord is equal to the thickness of it. After adjusting the colors of two cords, they are combined into a single cord; its thickness is equal to the sum of thicknesses of the two cords.\n \n JOI wants to minimize the total cost of procedures to shorten the rope until it becomes length 2. For each color, JOI wants to calculate the minimum total cost of procedures to shorten the rope so that the final rope of length 2 contains a cord with that color.\n\nYour task is to solve this problem instead of JOI.\n task:\nGiven the colors of the cords in the initial rope, write a program which calculates, for each color, the minimum total cost of procedures to shorten the rope so that the final rope of length 2 contains a cord with that color.\nTask Constraint: All input data satisfy the following conditions.\n\n$ 2 <= N <= 1 000 000． $\n\n$ 1 <= M <= N．$\n\n$ 1 <= C_i <= M (1 <= i <= N)．$\n\nFor each $c$ with $1 <= c <= M$, there exists an integer $i$ with $C_i = c$.\nTask Input: Read the following data from the standard input.\n\n The first line of input contains two space separated integers $N$, $M$. This means the rope consists of $N$ cords, and $M$ colors are used for the cords.\n\n The second line contains $N$ space separated integers $C_1, C_2, . . . , C_N$. This means the color of the $i$-th cord from left is $C_i$ ($1 <= C_i <= M$).\nTask Output: Write $M$ lines to the standard output. The $c$-th line ($1 <= c <= M$) contains the minimum total cost of procedures to shorten the rope so that the final rope of length 2 contains a cord with color $c$.\nTask Samples: input: 5 3\n1 2 3 3 2\n output: 2\n1\n1\n By the following procedures, we can shorten the rope so that the final rope of length 2 contains a cord with color 1. The total cost is 2.\n\n Change the color of the second cord from left to 1. Shorten the rope so that the point of length 1 from left on the rope becomes the leftmost point. The colors of cords become 1,3,3,2. The thicknesses of cords become 2,1,1,1.\n Change the color of the 4-th cord from left to 1. Shorten the rope so that the point of length 2 from left on the rope becomes the leftmost point. The colors of cords become 3,1. The thicknesses of cords become 2,3.\n\n By the following procedures, we can shorten the rope so that the final rope of length 2 contains a cord with color 2,3. The total cost is 1.\n\n Shorten the rope so that the point of length 3 from left on the rope becomes the leftmost point. The colors of cords become 3,2,1. The thicknesses of cords become 2,2,1.\n Change the color of the third cord from left to 2. Shorten the rope so that the point of length 2 from left on the rope becomes the leftmost point. The colors of cords become 2,3. The thicknesses of cords become 3,2.\ninput: 7 3\n1 2 2 1 3 3 3\n output: 2\n2\n2\n By the following procedures, we can shorten the rope so that the final rope of length 2 contains a cord with color 1. The total cost is 2.\n\n Shorten the rope so that the point of length 2 from left on the rope becomes the leftmost point.\n Change the color of the leftmost cord to 1. Shorten the rope so that the point of length 1 from left on the rope becomes the leftmost point. Note that the cost to change the color is 2 because the thickness of the cord is 2.\n Shorten the rope so that the point of length 3 from left on the rope becomes the leftmost point.\n Shorten the rope so that the point of length 1 from left on the rope becomes the leftmost point.\ninput: 10 3\n2 2 1 1 3 3 2 1 1 2\n output: 3\n3\n4\nBefore shortening the rope, we may change the colors of several cords.\n\n" }, { "title": "A + B Problem", "content": "Compute A + B. \n sample program: \n \n \n\n#include\n\nint main(){\n int a, b;\n while( scanf(\"%d %d\", &a, &b) ! = EOF ){\n printf(\"%d\\n\", a + b);\n }\n return 0;\n}\n\n \n
", "constraint": "-1000 <= A, B <= 1000", "input": "The input will consist of a series of pairs of integers A and B separated by a space, one pair of integers per line. The input will be terminated by EOF.", "output": "For each pair of input integers A and B, you must output the sum of A and B in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 2\n10 5\n100 20\n output: 3\n15\n120"], "Pid": "p00586", "ProblemText": "Task Description: Compute A + B. \n sample program: \n \n \n\n#include\n\nint main(){\n int a, b;\n while( scanf(\"%d %d\", &a, &b) ! = EOF ){\n printf(\"%d\\n\", a + b);\n }\n return 0;\n}\n\n \n\nTask Constraint: -1000 <= A, B <= 1000\nTask Input: The input will consist of a series of pairs of integers A and B separated by a space, one pair of integers per line. The input will be terminated by EOF.\nTask Output: For each pair of input integers A and B, you must output the sum of A and B in one line.\nTask Samples: input: 1 2\n10 5\n100 20\n output: 3\n15\n120\n\n" }, { "title": "Binary Tree Intersection And Union", "content": "Given two binary trees, we consider the “intersection” and “union” of them.\nHere, we distinguish the left and right child of a node when it has only one\nchild. The definitions of them are very simple. First of all, draw a complete\nbinary tree (a tree whose nodes have either 0 or 2 children and leaves have\nthe same depth) with sufficiently large depth. Then, starting from its root,\nwrite on it a number, say, 1 for each position of first tree, and draw different\nnumber, say, 2 for second tree. The “intersection” of two trees is a tree with\nnodes numbered both 1 and 2, and the “union” is a tree with nodes numbered\neither 1 or 2, or both. For example, the intersection of trees in Figures 1 and\n2 is a tree in Figure 3, and the union of them is a tree in Figure 4.\n\nA node of a tree is expressed by a sequence of characters, “(, )“. If a node\nhas a left child, the expression of the child is inserted between '( ' and ', '.\nThe expression of a right child is inserted between ', ' and ') '. For exam-\nple, the expression of trees in Figures 1 and 2 are “((, ), (, ))“ and “((, (, )), )“,\nrespectively.", "constraint": "", "input": "Each line of the input contains an operation. An operation starts with a\ncharacter which specifies the type of operation, either 'i ' or 'u ': 'i ' means\nintersection, and 'u ' means union. Following the character and a space,\ntwo tree expressions are given, separated by a space. It is assumed that\n1 <= #nodes in a tree <= 100, and no tree expression contains spaces and\nsyntax errors. Input is terminated by EOF.", "output": "For each line of the input, output a tree expression, without any space, for\nthe result of the operation.", "content_img": true, "lang": "en", "error": false, "samples": ["input: i ((,),(,)) ((,(,)),)\nu ((,),(,)) ((,(,)),)\n output: ((,),)\n((,(,)),(,))"], "Pid": "p00587", "ProblemText": "Task Description: Given two binary trees, we consider the “intersection” and “union” of them.\nHere, we distinguish the left and right child of a node when it has only one\nchild. The definitions of them are very simple. First of all, draw a complete\nbinary tree (a tree whose nodes have either 0 or 2 children and leaves have\nthe same depth) with sufficiently large depth. Then, starting from its root,\nwrite on it a number, say, 1 for each position of first tree, and draw different\nnumber, say, 2 for second tree. The “intersection” of two trees is a tree with\nnodes numbered both 1 and 2, and the “union” is a tree with nodes numbered\neither 1 or 2, or both. For example, the intersection of trees in Figures 1 and\n2 is a tree in Figure 3, and the union of them is a tree in Figure 4.\n\nA node of a tree is expressed by a sequence of characters, “(, )“. If a node\nhas a left child, the expression of the child is inserted between '( ' and ', '.\nThe expression of a right child is inserted between ', ' and ') '. For exam-\nple, the expression of trees in Figures 1 and 2 are “((, ), (, ))“ and “((, (, )), )“,\nrespectively.\nTask Input: Each line of the input contains an operation. An operation starts with a\ncharacter which specifies the type of operation, either 'i ' or 'u ': 'i ' means\nintersection, and 'u ' means union. Following the character and a space,\ntwo tree expressions are given, separated by a space. It is assumed that\n1 <= #nodes in a tree <= 100, and no tree expression contains spaces and\nsyntax errors. Input is terminated by EOF.\nTask Output: For each line of the input, output a tree expression, without any space, for\nthe result of the operation.\nTask Samples: input: i ((,),(,)) ((,(,)),)\nu ((,),(,)) ((,(,)),)\n output: ((,),)\n((,(,)),(,))\n\n" }, { "title": "Extraordinary Girl (I)", "content": "She is an extraordinary girl. She works for a library. Since she is young\nand cute, she is forced to do a lot of laborious jobs. The most annoying job\nfor her is to put returned books into shelves, carrying them by a cart. The\ncart is large enough to carry many books, but too heavy for her. Since she\nis delicate, she wants to walk as short as possible when doing this job.\n The library has 4N shelves (1 <= N <= 10000), three main passages, and\nN + 1 sub passages. Each shelf is numbered between 1 to 4N as shown in\nFigure 1. Horizontal dashed lines correspond to main passages, while vertical\ndashed lines correspond to sub passages. She starts to return books from the\nposition with white circle in the figure and ends at the position with black\ncircle. For simplicity, assume she can only stop at either the middle of shelves\nor the intersection of passages. At the middle of shelves, she put books with\nthe same ID as the shelves. For example, when she stops at the middle of\nshelf 2 and 3, she can put books with ID 2 and 3.\n\n Since she is so lazy that she doesn 't want to memorize a complicated\nroute, she only walks main passages in forward direction (see an arrow in\nFigure 1). The walk from an intersection to its adjacent intersections takes 1\ncost. It means the walk from the middle of shelves to its adjacent intersection,\nand vice versa, takes 0.5 cost. You, as only a programmer amoung her friends,\nare to help her compute the minimum possible cost she takes to put all books\nin the shelves.", "constraint": "", "input": "The first line of input contains the number of test cases, T . Then T test\ncases follow. Each test case consists of two lines. The first line contains the\nnumber N , and the second line contains 4N characters, either Y or N . Y in\nn-th position means there are some books with ID n, and N means no book\nwith ID n.", "output": "The output should consists of T lines, each of which contains one integer,\nthe minimum possible cost, for each test case.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n2\nYNNNNYYY\n4\nNYNNYYNNNYNYYNNN\n output: 6\n9"], "Pid": "p00588", "ProblemText": "Task Description: She is an extraordinary girl. She works for a library. Since she is young\nand cute, she is forced to do a lot of laborious jobs. The most annoying job\nfor her is to put returned books into shelves, carrying them by a cart. The\ncart is large enough to carry many books, but too heavy for her. Since she\nis delicate, she wants to walk as short as possible when doing this job.\n The library has 4N shelves (1 <= N <= 10000), three main passages, and\nN + 1 sub passages. Each shelf is numbered between 1 to 4N as shown in\nFigure 1. Horizontal dashed lines correspond to main passages, while vertical\ndashed lines correspond to sub passages. She starts to return books from the\nposition with white circle in the figure and ends at the position with black\ncircle. For simplicity, assume she can only stop at either the middle of shelves\nor the intersection of passages. At the middle of shelves, she put books with\nthe same ID as the shelves. For example, when she stops at the middle of\nshelf 2 and 3, she can put books with ID 2 and 3.\n\n Since she is so lazy that she doesn 't want to memorize a complicated\nroute, she only walks main passages in forward direction (see an arrow in\nFigure 1). The walk from an intersection to its adjacent intersections takes 1\ncost. It means the walk from the middle of shelves to its adjacent intersection,\nand vice versa, takes 0.5 cost. You, as only a programmer amoung her friends,\nare to help her compute the minimum possible cost she takes to put all books\nin the shelves.\nTask Input: The first line of input contains the number of test cases, T . Then T test\ncases follow. Each test case consists of two lines. The first line contains the\nnumber N , and the second line contains 4N characters, either Y or N . Y in\nn-th position means there are some books with ID n, and N means no book\nwith ID n.\nTask Output: The output should consists of T lines, each of which contains one integer,\nthe minimum possible cost, for each test case.\nTask Samples: input: 2\n2\nYNNNNYYY\n4\nNYNNYYNNNYNYYNNN\n output: 6\n9\n\n" }, { "title": "Extraordinary Girl (II)", "content": "She loves e-mail so much! She sends e-mails by her cellular phone to\nher friends when she has breakfast, she talks with other friends, and even\nwhen she works in the library! Her cellular phone has somewhat simple\nlayout (Figure 1). Pushing button 1 once displays a character ( '), pushing\n\nit twice in series displays a character (, ), and so on, and pushing it 6 times\ndisplays ( ') again. Button 2 corresponds to charaters (abc ABC), and, for\nexample, pushing it four times displays (A). Button 3-9 have is similar to\nbutton 1. Button 0 is a special button: pushing it once make her possible\nto input characters in the same button in series. For example, she has to\npush “20202” to display “aaa” and “660666” to display “no”. In addition,\npushing button 0 n times in series (n > 1) displays n - 1 spaces. She never\npushes button 0 at the very beginning of her input. Here are some examples\nof her input and output:\n\n 666660666 --> No\n44444416003334446633111 --> I 'm fine.\n20202202000333003330333 --> aaba f ff\n\n One day, the chief librarian of the library got very angry with her and\nhacked her cellular phone when she went to the second floor of the library\nto return books in shelves. Now her cellular phone can only display button\nnumbers she pushes. Your task is to write a program to convert the sequence\nof button numbers into correct characters and help her continue her e-mails!", "constraint": "", "input": "Input consists of several lines. Each line contains the sequence of button\nnumbers without any spaces. You may assume one line contains no more\nthan 10000 numbers. Input terminates with EOF.", "output": "For each line of input, output the corresponding sequence of characters in\none line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 666660666\n44444416003334446633111\n20202202000333003330333\n output: No\nI'm fine.\naaba f ff"], "Pid": "p00589", "ProblemText": "Task Description: She loves e-mail so much! She sends e-mails by her cellular phone to\nher friends when she has breakfast, she talks with other friends, and even\nwhen she works in the library! Her cellular phone has somewhat simple\nlayout (Figure 1). Pushing button 1 once displays a character ( '), pushing\n\nit twice in series displays a character (, ), and so on, and pushing it 6 times\ndisplays ( ') again. Button 2 corresponds to charaters (abc ABC), and, for\nexample, pushing it four times displays (A). Button 3-9 have is similar to\nbutton 1. Button 0 is a special button: pushing it once make her possible\nto input characters in the same button in series. For example, she has to\npush “20202” to display “aaa” and “660666” to display “no”. In addition,\npushing button 0 n times in series (n > 1) displays n - 1 spaces. She never\npushes button 0 at the very beginning of her input. Here are some examples\nof her input and output:\n\n 666660666 --> No\n44444416003334446633111 --> I 'm fine.\n20202202000333003330333 --> aaba f ff\n\n One day, the chief librarian of the library got very angry with her and\nhacked her cellular phone when she went to the second floor of the library\nto return books in shelves. Now her cellular phone can only display button\nnumbers she pushes. Your task is to write a program to convert the sequence\nof button numbers into correct characters and help her continue her e-mails!\nTask Input: Input consists of several lines. Each line contains the sequence of button\nnumbers without any spaces. You may assume one line contains no more\nthan 10000 numbers. Input terminates with EOF.\nTask Output: For each line of input, output the corresponding sequence of characters in\none line.\nTask Samples: input: 666660666\n44444416003334446633111\n20202202000333003330333\n output: No\nI'm fine.\naaba f ff\n\n" }, { "title": "Pair of Primes", "content": "We arrange the numbers between 1 and N (1 <= N <= 10000) in increasing\norder and decreasing order like this:\n\n1 2 3 4 5 6 7 8 9 . . . N\nN . . . 9 8 7 6 5 4 3 2 1\n\nTwo numbers faced each other form a pair. Your task is to compute the number of pairs P such that both\nnumbers in the pairs are prime.", "constraint": "", "input": "Input contains several test cases. Each test case consists of an integer N in\none line.", "output": "For each line of input, output P .", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n4\n7\n51\n output: 0\n2\n2\n6"], "Pid": "p00590", "ProblemText": "Task Description: We arrange the numbers between 1 and N (1 <= N <= 10000) in increasing\norder and decreasing order like this:\n\n1 2 3 4 5 6 7 8 9 . . . N\nN . . . 9 8 7 6 5 4 3 2 1\n\nTwo numbers faced each other form a pair. Your task is to compute the number of pairs P such that both\nnumbers in the pairs are prime.\nTask Input: Input contains several test cases. Each test case consists of an integer N in\none line.\nTask Output: For each line of input, output P .\nTask Samples: input: 1\n4\n7\n51\n output: 0\n2\n2\n6\n\n" }, { "title": "Advanced Algorithm Class", "content": "In the advanced algorithm class, n^2 students sit in n rows and\nn columns. One day, a professor who teaches this subject comes into the class, asks the shortest student in each row to lift up his left hand, and the tallest student in each column to lift up his right hand.\nWhat is the height of the student whose both hands are up ? The student will\nbecome a target for professor 's questions.\n\n Given the size of the class, and the height of the students in the class, you\nhave to print the height of the student who has both his hands up in the class.", "constraint": "", "input": "The input will consist of several cases. the first line of each case will be n(0 < n < 100), the number of rows and columns in the class. It will then\nbe followed by a n-by-n matrix, each row of the matrix appearing on a single\nline. Note that the elements of the matrix may not be necessarily distinct. The\ninput will be terminated by the case n = 0.", "output": "For each input case, you have to print the height of the student in the class\nwhose both hands are up. If there is no such student, then print 0 for that case.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3\n4 5 6\n7 8 9\n3\n1 2 3\n7 8 9\n4 5 6\n0\n output: 7\n7"], "Pid": "p00591", "ProblemText": "Task Description: In the advanced algorithm class, n^2 students sit in n rows and\nn columns. One day, a professor who teaches this subject comes into the class, asks the shortest student in each row to lift up his left hand, and the tallest student in each column to lift up his right hand.\nWhat is the height of the student whose both hands are up ? The student will\nbecome a target for professor 's questions.\n\n Given the size of the class, and the height of the students in the class, you\nhave to print the height of the student who has both his hands up in the class.\nTask Input: The input will consist of several cases. the first line of each case will be n(0 < n < 100), the number of rows and columns in the class. It will then\nbe followed by a n-by-n matrix, each row of the matrix appearing on a single\nline. Note that the elements of the matrix may not be necessarily distinct. The\ninput will be terminated by the case n = 0.\nTask Output: For each input case, you have to print the height of the student in the class\nwhose both hands are up. If there is no such student, then print 0 for that case.\nTask Samples: input: 3\n1 2 3\n4 5 6\n7 8 9\n3\n1 2 3\n7 8 9\n4 5 6\n0\n output: 7\n7\n\n" }, { "title": "Boring Commercial", "content": "Now it is spring holidays. A lazy student has finally passed all final examination, and he decided to just kick back and just watch TV all day. Oh, his\nonly source of entertainment is watching TV. And TV commercial, as usual, are\na big nuisance for him. He can watch any thing on television, but cannot bear\neven a single second of commercial. So to prevent himself from the boredom of\nseeing the boring commercial, he keeps shuffling through the TV channels, so\nthat he can watch programs on different channels without seeing even a single\ncommercial.\nGiven the number of channels, and the duration at which the TV commercials\nare showed on each of the channels, you have to write a program which will\nprint the longest interval for which the lazy student can watch the television by\nshuffling between the different channels without ever seeing an TV commercial.\n \nFor example, consider the simplified situation where there are only three\ntelevision channels, and suppose that he is watching TV from 2100 hrs to 2400\nhrs. Suppose that the commercials are displayed at following time on each of\nthe channels.\n\n Channel 1: 2100 to 2130,2200 to 2230 and 2300 to 2330\n\n Channel 2: 2130 to 2200,2330 to 2400\n\n Channel 3: 2100 to 2130,2330 to 2400\n Then in this case, he can watch TV without getting interrupted by commercials for full 3 hours by watching Channel 2 from 2100 to 2130, then Channel 3\nfrom 2130 to 2330, and then Channel 1 from 2330 to 2400.", "constraint": "", "input": "The input will consist of several cases. In each case, the first line of the input\nwill be n, the number of channels, which will then be followed by p and q, the\ntime interval between which he will be watching the TV. It will be followed by\n2n lines, giving the time slots for each of the channels. For each channel, the\nfirst line will be k, the number of commercial slots, and it will then be followed\nby 2k numbers giving the commercial slots in order.\n\n The input will be terminated by values 0 for each of n, p, q. This case should\nnot be processed.", "output": "For each case, you have to output the maximum duration (in minutes) for which\nhe can watch television without seeing any commercial.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2100 2400\n1\n2130 2200\n3 2100 2400\n3\n2100 2130 2200 2230 2300 2330\n2\n2130 2200 2330 2400\n2\n2100 2130 2330 2400\n0 0 0\n output: 120\n180"], "Pid": "p00592", "ProblemText": "Task Description: Now it is spring holidays. A lazy student has finally passed all final examination, and he decided to just kick back and just watch TV all day. Oh, his\nonly source of entertainment is watching TV. And TV commercial, as usual, are\na big nuisance for him. He can watch any thing on television, but cannot bear\neven a single second of commercial. So to prevent himself from the boredom of\nseeing the boring commercial, he keeps shuffling through the TV channels, so\nthat he can watch programs on different channels without seeing even a single\ncommercial.\nGiven the number of channels, and the duration at which the TV commercials\nare showed on each of the channels, you have to write a program which will\nprint the longest interval for which the lazy student can watch the television by\nshuffling between the different channels without ever seeing an TV commercial.\n \nFor example, consider the simplified situation where there are only three\ntelevision channels, and suppose that he is watching TV from 2100 hrs to 2400\nhrs. Suppose that the commercials are displayed at following time on each of\nthe channels.\n\n Channel 1: 2100 to 2130,2200 to 2230 and 2300 to 2330\n\n Channel 2: 2130 to 2200,2330 to 2400\n\n Channel 3: 2100 to 2130,2330 to 2400\n Then in this case, he can watch TV without getting interrupted by commercials for full 3 hours by watching Channel 2 from 2100 to 2130, then Channel 3\nfrom 2130 to 2330, and then Channel 1 from 2330 to 2400.\nTask Input: The input will consist of several cases. In each case, the first line of the input\nwill be n, the number of channels, which will then be followed by p and q, the\ntime interval between which he will be watching the TV. It will be followed by\n2n lines, giving the time slots for each of the channels. For each channel, the\nfirst line will be k, the number of commercial slots, and it will then be followed\nby 2k numbers giving the commercial slots in order.\n\n The input will be terminated by values 0 for each of n, p, q. This case should\nnot be processed.\nTask Output: For each case, you have to output the maximum duration (in minutes) for which\nhe can watch television without seeing any commercial.\nTask Samples: input: 1 2100 2400\n1\n2130 2200\n3 2100 2400\n3\n2100 2130 2200 2230 2300 2330\n2\n2130 2200 2330 2400\n2\n2100 2130 2330 2400\n0 0 0\n output: 120\n180\n\n" }, { "title": "JPEG Compression", "content": "The fundamental idea in the JPEG compression algorithm is to sort coeffi-\ncient of given image by zigzag path and encode it. In this problem, we don 't\ndiscuss about details of the algorithm, but you are asked to make simple pro-\ngram. You are given single integer N , and you must output zigzag path on\na matrix where size is N by N . The zigzag scanning is start at the upper-left\ncorner (0,0) and end up at the bottom-right corner. See the following Figure\nand sample output to make sure rule of the zigzag scanning. For example, if you\nare given N = 8, corresponding output should be a matrix shown in right-side\nof the Figure. This matrix consists of visited time for each element.", "constraint": "", "input": "Several test cases are given. Each test case consists of one integer N (0 < N <\n10) in a line. The input will end at a line contains single zero.", "output": "For each input, you must output a matrix where each element is the visited\ntime. All numbers in the matrix must be right justified in a field of width 3.\nEach matrix should be prefixed by a header “Case x: ” where x equals test case\nnumber.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n4\n0\n output: Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7\n 3 5 8 13\n 4 9 12 14\n 10 11 15 16"], "Pid": "p00593", "ProblemText": "Task Description: The fundamental idea in the JPEG compression algorithm is to sort coeffi-\ncient of given image by zigzag path and encode it. In this problem, we don 't\ndiscuss about details of the algorithm, but you are asked to make simple pro-\ngram. You are given single integer N , and you must output zigzag path on\na matrix where size is N by N . The zigzag scanning is start at the upper-left\ncorner (0,0) and end up at the bottom-right corner. See the following Figure\nand sample output to make sure rule of the zigzag scanning. For example, if you\nare given N = 8, corresponding output should be a matrix shown in right-side\nof the Figure. This matrix consists of visited time for each element.\nTask Input: Several test cases are given. Each test case consists of one integer N (0 < N <\n10) in a line. The input will end at a line contains single zero.\nTask Output: For each input, you must output a matrix where each element is the visited\ntime. All numbers in the matrix must be right justified in a field of width 3.\nEach matrix should be prefixed by a header “Case x: ” where x equals test case\nnumber.\nTask Samples: input: 3\n4\n0\n output: Case 1:\n 1 2 6\n 3 5 7\n 4 8 9\nCase 2:\n 1 2 6 7\n 3 5 8 13\n 4 9 12 14\n 10 11 15 16\n\n" }, { "title": "What Color Is The Universe?", "content": "There are many stars in the space. What color is the universe if I look up it from outside? \"Until he found the answer to this question, he couldn't sleep. After a moment's thought, he proposed a hypothesis, \"When I observe the stars in the sky, if more than half of the stars have the same color, that is the color of the universe. \"He has collected data of stars in the universe after consistently observing them. However, when he try to count the number of star, he was in bed sick with a cold. You decided to help him by developing a program to identify the color of the universe. You are given an array A. Let |A| be the number of element in A, and let N_m be the number of m in A. For example, if A = {3,1,2,3,3,1,5,3}, |A| = 8, N_3 = 4, N_1 = 2, N_5 = 1. Your program have to find m such that: N_m >= (|A| / 2)If there is no such m, you also have to report the fact. There is no such m for the above example, but for a array A = {5,2,5,3,4,5,5}, 5 is the answer.", "constraint": "", "input": "There are several test cases. For each test case, in the first line |A| is given. In the next line, there will be |A| integers. The integers are less than 2^31 and |A| < 1,000,000. The input terminate with a line which contains single 0.", "output": "For each test case, output m in a line. If there is no answer, output \"NO COLOR\" in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8\n3 1 2 3 3 1 5 3\n7\n5 2 5 3 4 5 5\n0\n output: NO COLOR\n5"], "Pid": "p00594", "ProblemText": "Task Description: There are many stars in the space. What color is the universe if I look up it from outside? \"Until he found the answer to this question, he couldn't sleep. After a moment's thought, he proposed a hypothesis, \"When I observe the stars in the sky, if more than half of the stars have the same color, that is the color of the universe. \"He has collected data of stars in the universe after consistently observing them. However, when he try to count the number of star, he was in bed sick with a cold. You decided to help him by developing a program to identify the color of the universe. You are given an array A. Let |A| be the number of element in A, and let N_m be the number of m in A. For example, if A = {3,1,2,3,3,1,5,3}, |A| = 8, N_3 = 4, N_1 = 2, N_5 = 1. Your program have to find m such that: N_m >= (|A| / 2)If there is no such m, you also have to report the fact. There is no such m for the above example, but for a array A = {5,2,5,3,4,5,5}, 5 is the answer.\nTask Input: There are several test cases. For each test case, in the first line |A| is given. In the next line, there will be |A| integers. The integers are less than 2^31 and |A| < 1,000,000. The input terminate with a line which contains single 0.\nTask Output: For each test case, output m in a line. If there is no answer, output \"NO COLOR\" in a line.\nTask Samples: input: 8\n3 1 2 3 3 1 5 3\n7\n5 2 5 3 4 5 5\n0\n output: NO COLOR\n5\n\n" }, { "title": "Problem A: Greatest Common Divisor", "content": "Please find the greatest common divisor of two natural numbers. A clue is: The Euclid's algorithm is a way to resolve this task.", "constraint": "", "input": "The input file consists of several lines with pairs of two natural numbers in each line. The numbers do not exceed 100000.\n\nThe number of pairs (datasets) is less than 50.", "output": "Your program has to print the greatest common divisor for each pair of input numbers. Print each result on a new line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 57 38\n60 84\n output: 19\n12"], "Pid": "p00595", "ProblemText": "Task Description: Please find the greatest common divisor of two natural numbers. A clue is: The Euclid's algorithm is a way to resolve this task.\nTask Input: The input file consists of several lines with pairs of two natural numbers in each line. The numbers do not exceed 100000.\n\nThe number of pairs (datasets) is less than 50.\nTask Output: Your program has to print the greatest common divisor for each pair of input numbers. Print each result on a new line.\nTask Samples: input: 57 38\n60 84\n output: 19\n12\n\n" }, { "title": "Problem B: Dominoes Arrangement", "content": "[0,0]\n[0,1] [1,1]\n[0,2] [1,2] [2,2]\n[0,3] [1,3] [2,3] [3,3]\n[0,4] [1,4] [2,4] [3,4] [4,4]\n[0,5] [1,5] [2,5] [3,5] [4,5] [5,5]\n[0,6] [1,6] [2,6] [3,6] [4,6] [5,6] [6,6]\n\nConsider the standard set of 28 western dominoes as shown in the above figure. Given a subset of the standard set dominoes, decide whether this subset can be arranged in a straight row in accordance with the familiar playing rule that touching ends must match. For example, the subset [1,1], [2,2], [1,2] can be arranged in a row (as [1,1] followed by [1,2] followed by [2,2]), while the subset [1,1], [0,3], [1,4] can not be arranged in one row. Note that as in usual dominoes playing any pair [i, j] can also be treated as [j, i].\n\nYour task is to write a program that takes as input any subset of the dominoes and output either yes (if the input subset can be arranged in one row) or no (if the input set can not be arranged in one row).", "constraint": "", "input": "Input file consists of pairs of lines. The first line of each pair is the number of elements N (1 <= N <= 18) in the subset, and the second line is the elements of the subset separated by blanks, see the input sample below.\n\nThe number of pairs (datasets) is less than 30.", "output": "For each pair of lines of the input file, the corresponding output is either Yes or No, based on whether the input subset can be arranged in one line or not.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n13 23 14 24 15 25\n10\n00 01 11 02 12 22 03 13 23 33\n output: Yes\nNo"], "Pid": "p00596", "ProblemText": "Task Description: [0,0]\n[0,1] [1,1]\n[0,2] [1,2] [2,2]\n[0,3] [1,3] [2,3] [3,3]\n[0,4] [1,4] [2,4] [3,4] [4,4]\n[0,5] [1,5] [2,5] [3,5] [4,5] [5,5]\n[0,6] [1,6] [2,6] [3,6] [4,6] [5,6] [6,6]\n\nConsider the standard set of 28 western dominoes as shown in the above figure. Given a subset of the standard set dominoes, decide whether this subset can be arranged in a straight row in accordance with the familiar playing rule that touching ends must match. For example, the subset [1,1], [2,2], [1,2] can be arranged in a row (as [1,1] followed by [1,2] followed by [2,2]), while the subset [1,1], [0,3], [1,4] can not be arranged in one row. Note that as in usual dominoes playing any pair [i, j] can also be treated as [j, i].\n\nYour task is to write a program that takes as input any subset of the dominoes and output either yes (if the input subset can be arranged in one row) or no (if the input set can not be arranged in one row).\nTask Input: Input file consists of pairs of lines. The first line of each pair is the number of elements N (1 <= N <= 18) in the subset, and the second line is the elements of the subset separated by blanks, see the input sample below.\n\nThe number of pairs (datasets) is less than 30.\nTask Output: For each pair of lines of the input file, the corresponding output is either Yes or No, based on whether the input subset can be arranged in one line or not.\nTask Samples: input: 6\n13 23 14 24 15 25\n10\n00 01 11 02 12 22 03 13 23 33\n output: Yes\nNo\n\n" }, { "title": "Problem C: Finding the Largest Carbon Compound Given Its Longest Chain", "content": "An bydrocarbon is an organic compound which contains only carbons and hydrogens. An isomer is a compound that has the same number of carbons but different structures. Heptane, for example, is a hydrocarbon with 7 carbons. It has nine isomers. The structural formula of three are shown in Figure 1. Carbons are represented by the letter C, and bonds between carbons are represented by a straight line. In all figures, hydrogens are not represented for simplicity. Each carbon can be connected to a maximum of 4 carbons.\n\n \n \n\n \n \n Figure 1: These three examples of isomers of heptane have the same number of carbons but different structures. \n\n \n\nLet define a chain in an isomer as a sequence of connected carbons without branches. An isomer can have many chains of the same length. Figure 2 shows the longest chain of carbons for each of the represented isomer. Note that there can be many instances of longest chain in an isomer.\n\n \n \n\n \n \n Figure 2: The figures shows one instance of longest chain of carbons in each isomer. The first and the second isomers show longest chains of 5 carbons. The longest chain in the third isomer has 4 carbons. \n\n \n\nYour task is to identify the number of carbons of the largest possible carbon compound whose longest carbon chain has n (1 <= n <= 30) carbons.", "constraint": "", "input": "Each input contains a list of number of carbons, i. e. the length of a carbon chain.\n\nThe number of input lines is less than or equal to 30.", "output": "For each number n in input, identify the number of carbons of the largest possible carbon compound whose longest carbon chain has n carbons.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n4\n output: 1\n8"], "Pid": "p00597", "ProblemText": "Task Description: An bydrocarbon is an organic compound which contains only carbons and hydrogens. An isomer is a compound that has the same number of carbons but different structures. Heptane, for example, is a hydrocarbon with 7 carbons. It has nine isomers. The structural formula of three are shown in Figure 1. Carbons are represented by the letter C, and bonds between carbons are represented by a straight line. In all figures, hydrogens are not represented for simplicity. Each carbon can be connected to a maximum of 4 carbons.\n\n \n \n\n \n \n Figure 1: These three examples of isomers of heptane have the same number of carbons but different structures. \n\n \n\nLet define a chain in an isomer as a sequence of connected carbons without branches. An isomer can have many chains of the same length. Figure 2 shows the longest chain of carbons for each of the represented isomer. Note that there can be many instances of longest chain in an isomer.\n\n \n \n\n \n \n Figure 2: The figures shows one instance of longest chain of carbons in each isomer. The first and the second isomers show longest chains of 5 carbons. The longest chain in the third isomer has 4 carbons. \n\n \n\nYour task is to identify the number of carbons of the largest possible carbon compound whose longest carbon chain has n (1 <= n <= 30) carbons.\nTask Input: Each input contains a list of number of carbons, i. e. the length of a carbon chain.\n\nThe number of input lines is less than or equal to 30.\nTask Output: For each number n in input, identify the number of carbons of the largest possible carbon compound whose longest carbon chain has n carbons.\nTask Samples: input: 1\n4\n output: 1\n8\n\n" }, { "title": "Problem D: Operations with Finite Sets", "content": "Let A, B, C, D, E be sets of integers and let U is a universal set that includes all sets under consideration. All elements in any set are different (no repetitions).\n\nu - union of two sets, Au B = {x ∈ U : x ∈ A or x ∈ B} is the set of all elements which belong to A or B.\n\ni - intersection of two sets, Ai B = {x ∈ U : x ∈ A and x ∈ B} is the set of all elements which belong to both A and B.\n\nd - difference of two sets, Ad B = {x ∈ U : x ∈ A, x ∉ B} is the set of those elements of A which do not belong to B.\n\ns - symmetric difference of two sets, As B = (Ad B)u(Bd A) consists of those elements which belong to A or B but not to both.\n\nc - complement of a set, c A = {x ∈ U : x ∉ A}, is set of elements which belong to U but do not belong to A. Unary operator c has higest precedence.\n\nThe universal set U is defined as a union of all sets specified in data. \n\nYour task is to determine the result of an expression, which includes sets, set operations and parenthesis (any number of parenthesis and any correct enclosure of parenthesis may take place).", "constraint": "", "input": "Input consists of several pairs of lines difining sets and one pair of lines defining an expression. Each pair of lines for set definition includes the following.\n\nLine 1: Set name (A, B, C, D, E), number of elements in a set.\n\nLine 2: Set elements separated by blanks.\n\nPair of lines for expression definition:\n\nLine 1: R 0\n\nLine 2: Expression consisting of set names, operators and parenthesis (no blanks).\n\nNumber of sets can vary from 1 to 5. Set names can be specified in any order. Each set consists of 1-100 elements. Pair of lines for expression definition signals the end of data set. Input file includes several data sets. The number of datasets is less than 20.", "output": "For each data set, the output should contain one line with resulting set elements sorted in ascending order separated by blanks. If the result contains no set elements then the line should contain the text NULL.", "content_img": false, "lang": "en", "error": false, "samples": ["input: A 3\n1 3 -1\nB 4\n3 1 5 7\nD 1\n5\nR 0\ncAiBdD\nC 3\n1 2 3\nA 4\n2 10 8 3\nB 3\n2 4 8\nR 0\n(As(AiB))uC\n output: 7\n1 2 3 10"], "Pid": "p00598", "ProblemText": "Task Description: Let A, B, C, D, E be sets of integers and let U is a universal set that includes all sets under consideration. All elements in any set are different (no repetitions).\n\nu - union of two sets, Au B = {x ∈ U : x ∈ A or x ∈ B} is the set of all elements which belong to A or B.\n\ni - intersection of two sets, Ai B = {x ∈ U : x ∈ A and x ∈ B} is the set of all elements which belong to both A and B.\n\nd - difference of two sets, Ad B = {x ∈ U : x ∈ A, x ∉ B} is the set of those elements of A which do not belong to B.\n\ns - symmetric difference of two sets, As B = (Ad B)u(Bd A) consists of those elements which belong to A or B but not to both.\n\nc - complement of a set, c A = {x ∈ U : x ∉ A}, is set of elements which belong to U but do not belong to A. Unary operator c has higest precedence.\n\nThe universal set U is defined as a union of all sets specified in data. \n\nYour task is to determine the result of an expression, which includes sets, set operations and parenthesis (any number of parenthesis and any correct enclosure of parenthesis may take place).\nTask Input: Input consists of several pairs of lines difining sets and one pair of lines defining an expression. Each pair of lines for set definition includes the following.\n\nLine 1: Set name (A, B, C, D, E), number of elements in a set.\n\nLine 2: Set elements separated by blanks.\n\nPair of lines for expression definition:\n\nLine 1: R 0\n\nLine 2: Expression consisting of set names, operators and parenthesis (no blanks).\n\nNumber of sets can vary from 1 to 5. Set names can be specified in any order. Each set consists of 1-100 elements. Pair of lines for expression definition signals the end of data set. Input file includes several data sets. The number of datasets is less than 20.\nTask Output: For each data set, the output should contain one line with resulting set elements sorted in ascending order separated by blanks. If the result contains no set elements then the line should contain the text NULL.\nTask Samples: input: A 3\n1 3 -1\nB 4\n3 1 5 7\nD 1\n5\nR 0\ncAiBdD\nC 3\n1 2 3\nA 4\n2 10 8 3\nB 3\n2 4 8\nR 0\n(As(AiB))uC\n output: 7\n1 2 3 10\n\n" }, { "title": "Problem E: Combinatorial Topology", "content": "It was long believed that a 2-dimensional place can not be filled with a finite set of polygons in aperiodic way. British mathematician, Sir Roger Penrose, developed an aperiodic tiling over the years and established a theory of what is known today as quasicrystals.\n\nThe classic Penrose tiles consist of two rhombi with angles 36 and 72 degrees, see Figure 1. The edges of the rhombi are all of equal unit length, 1. These can fill the entire place without holes and overlaps (see Figure 2). Example: the bold line boundary in Figure 1 is filled with 20 thin tiles and 20 thick tiles.\n\nGiven a boundary (set of adjacent vertices counter-clock-wise oriented), how many thin tiles (36 degrees) and how many thick tiles (72 degrees) do you need to fill it (without any holes and intersections)?", "constraint": "", "input": "Each data set is defined as follows:\n\nLine 1: Number of vertices N (N < 100).\n\nN lines: x and y coordinates of each vertex per line separated by blanks (|x| < 100, |y| < 100).\n\nAll floats in the input have 6 digits after the decimal point. \n\nThe required precision is 4 digits. \n\nInput file includes several data sets. The number of data sets is less than 20.", "output": "Each line contains the solution for one set. First, there is the number of thin tiles, then the number of thick tiles, separated by a space. If the boundary is illegal for the above problem, the output should be \"-1 -1\".", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n-5.000000 0.000000\n5.000000 0.000000\n9.635255 14.265848\n-0.364745 14.265848\n3\n-1.000000 0.000000\n0.000000 0.000000\n0.000000 1.000000\n output: 0 150\n-1 -1"], "Pid": "p00599", "ProblemText": "Task Description: It was long believed that a 2-dimensional place can not be filled with a finite set of polygons in aperiodic way. British mathematician, Sir Roger Penrose, developed an aperiodic tiling over the years and established a theory of what is known today as quasicrystals.\n\nThe classic Penrose tiles consist of two rhombi with angles 36 and 72 degrees, see Figure 1. The edges of the rhombi are all of equal unit length, 1. These can fill the entire place without holes and overlaps (see Figure 2). Example: the bold line boundary in Figure 1 is filled with 20 thin tiles and 20 thick tiles.\n\nGiven a boundary (set of adjacent vertices counter-clock-wise oriented), how many thin tiles (36 degrees) and how many thick tiles (72 degrees) do you need to fill it (without any holes and intersections)?\nTask Input: Each data set is defined as follows:\n\nLine 1: Number of vertices N (N < 100).\n\nN lines: x and y coordinates of each vertex per line separated by blanks (|x| < 100, |y| < 100).\n\nAll floats in the input have 6 digits after the decimal point. \n\nThe required precision is 4 digits. \n\nInput file includes several data sets. The number of data sets is less than 20.\nTask Output: Each line contains the solution for one set. First, there is the number of thin tiles, then the number of thick tiles, separated by a space. If the boundary is illegal for the above problem, the output should be \"-1 -1\".\nTask Samples: input: 4\n-5.000000 0.000000\n5.000000 0.000000\n9.635255 14.265848\n-0.364745 14.265848\n3\n-1.000000 0.000000\n0.000000 0.000000\n0.000000 1.000000\n output: 0 150\n-1 -1\n\n" }, { "title": "Problem F: Computation of Minimum Length of Pipeline", "content": "The Aizu Wakamatsu city office decided to lay a hot water pipeline covering the whole area of the city to heat houses. The pipeline starts from some hot springs and connects every district in the city. The pipeline can fork at a hot spring or a district, but no cycle is allowed. The city office wants to minimize the length of pipeline in order to build it at the least possible expense.\n\nWrite a program to compute the minimal length of the pipeline. The program reads an input that consists of the following three parts:\n hint:\nThe first line correspondings to the first part: there are three hot springs and five districts. The following three lines are the second part: the distances between a hot spring and a district. For instance, the distance between the first hot spring and the third district is 25. The last four lines are the third part: the distances between two districts. For instance, the distance between the second and the third districts is 9. The second hot spring and the fourth district are not connectable The second and the fifth districts are not connectable, either.", "constraint": "", "input": "The first part consists of two positive integers in one line, which represent the number s of hot springs and the number d of districts in the city, respectively.\n\nThe second part consists of s lines: each line contains d non-negative integers. The i-th integer in the j-th line represents the distance between the j-th hot spring and the i-th district if it is non-zero. If zero it means they are not connectable due to an obstacle between them.\n\nThe third part consists of d-1 lines. The i-th line has d - i non-negative integers. The i-th integer in the j-th line represents the distance between the j-th and the (i + j)-th districts if it is non-zero. The meaning of zero is the same as mentioned above.\nFor the sake of simplicity, you can assume the following:\n\nThe number of hot springs and that of districts do not exceed 50.\n\nEach distance is no more than 100.\n\nEach line in the input file contains at most 256 characters.\n\nEach number is delimited by either whitespace or tab.\nThe input has several test cases. The input terminate with a line which has two 0. The number of test cases is less than 20.", "output": "Output the minimum length of pipeline for each test case.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n12 8 25 19 23\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0\n output: 38"], "Pid": "p00600", "ProblemText": "Task Description: The Aizu Wakamatsu city office decided to lay a hot water pipeline covering the whole area of the city to heat houses. The pipeline starts from some hot springs and connects every district in the city. The pipeline can fork at a hot spring or a district, but no cycle is allowed. The city office wants to minimize the length of pipeline in order to build it at the least possible expense.\n\nWrite a program to compute the minimal length of the pipeline. The program reads an input that consists of the following three parts:\n hint:\nThe first line correspondings to the first part: there are three hot springs and five districts. The following three lines are the second part: the distances between a hot spring and a district. For instance, the distance between the first hot spring and the third district is 25. The last four lines are the third part: the distances between two districts. For instance, the distance between the second and the third districts is 9. The second hot spring and the fourth district are not connectable The second and the fifth districts are not connectable, either.\nTask Input: The first part consists of two positive integers in one line, which represent the number s of hot springs and the number d of districts in the city, respectively.\n\nThe second part consists of s lines: each line contains d non-negative integers. The i-th integer in the j-th line represents the distance between the j-th hot spring and the i-th district if it is non-zero. If zero it means they are not connectable due to an obstacle between them.\n\nThe third part consists of d-1 lines. The i-th line has d - i non-negative integers. The i-th integer in the j-th line represents the distance between the j-th and the (i + j)-th districts if it is non-zero. The meaning of zero is the same as mentioned above.\nFor the sake of simplicity, you can assume the following:\n\nThe number of hot springs and that of districts do not exceed 50.\n\nEach distance is no more than 100.\n\nEach line in the input file contains at most 256 characters.\n\nEach number is delimited by either whitespace or tab.\nThe input has several test cases. The input terminate with a line which has two 0. The number of test cases is less than 20.\nTask Output: Output the minimum length of pipeline for each test case.\nTask Samples: input: 3 5\n12 8 25 19 23\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0\n output: 38\n\n" }, { "title": "Problem G: Dominating Set", "content": "What you have in your hands is a map of Aizu-Wakamatsu City. The lines on this map represent streets and the dots are street corners. Lion Dor Company is going to build food stores at some street corners where people can go to buy food. It is unnecessary and expensive to build a food store on every corner. Their plan is to build the food stores so that people could get food either right there on the corner where they live, or at the very most, have to walk down only one street to find a corner where there was a food store. Now, all they have to do is figure out where to put the food store.\n\nThe problem can be simplified as follows. Let G = (V, E) be unweighted undirected graph. A dominating set D of G is a subset of V such that every vertex in V - D is adjacent to at least one vertex in D. A minimum dominating set is a dominating set of minimum number of vertices for G. In the example graph given below, the black vertices are the members of the minimum dominating sets.\n\nDesign and implement an algorithm for the minimum domminating set problem.", "constraint": "n <= 30\n\n m <= 50", "input": "Input has several test cases. Each test case consists of the number of nodes n and the number of edges m in the first line. In the following m lines, edges are given by a pair of nodes connected by the edge. The graph nodess are named with the numbers 0,1, . . . , n - 1 respectively.\n\nThe input terminate with a line containing two 0. The number of test cases is less than 20.", "output": "Output the size of minimum dominating set for each test case.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 4\n0 1\n0 4\n1 2\n3 4\n5 4\n0 1\n0 4\n1 2\n3 4\n0 0\n output: 2\n2"], "Pid": "p00601", "ProblemText": "Task Description: What you have in your hands is a map of Aizu-Wakamatsu City. The lines on this map represent streets and the dots are street corners. Lion Dor Company is going to build food stores at some street corners where people can go to buy food. It is unnecessary and expensive to build a food store on every corner. Their plan is to build the food stores so that people could get food either right there on the corner where they live, or at the very most, have to walk down only one street to find a corner where there was a food store. Now, all they have to do is figure out where to put the food store.\n\nThe problem can be simplified as follows. Let G = (V, E) be unweighted undirected graph. A dominating set D of G is a subset of V such that every vertex in V - D is adjacent to at least one vertex in D. A minimum dominating set is a dominating set of minimum number of vertices for G. In the example graph given below, the black vertices are the members of the minimum dominating sets.\n\nDesign and implement an algorithm for the minimum domminating set problem.\nTask Constraint: n <= 30\n\n m <= 50\nTask Input: Input has several test cases. Each test case consists of the number of nodes n and the number of edges m in the first line. In the following m lines, edges are given by a pair of nodes connected by the edge. The graph nodess are named with the numbers 0,1, . . . , n - 1 respectively.\n\nThe input terminate with a line containing two 0. The number of test cases is less than 20.\nTask Output: Output the size of minimum dominating set for each test case.\nTask Samples: input: 5 4\n0 1\n0 4\n1 2\n3 4\n5 4\n0 1\n0 4\n1 2\n3 4\n0 0\n output: 2\n2\n\n" }, { "title": "Problem H: Fibonacci Sets", "content": "Fibonacci number f(i) appear in a variety of puzzles in nature and math, including packing problems, family trees or Pythagorean triangles. They obey the rule f(i) = f(i - 1) + f(i - 2), where we set f(0) = 1 = f(-1).\n\nLet V and d be two certain positive integers and be N ≡ 1001 a constant. Consider a set of V nodes, each node i having a Fibonacci label F[i] = (f(i) mod N) assigned for i = 1, . . . , V <= N. If |F(i) - F(j)| < d, then the nodes i and j are connected.\n\nGiven V and d, how many connected subsets of nodes will you obtain?\nFigure 1: There are 4 connected subsets for V = 20 and d = 100.", "constraint": "1 <= V <= 1000\n\n1 <= d <= 150", "input": "Each data set is defined as one line with two integers as follows:\n\nLine 1: Number of nodes V and the distance d.\n\nInput includes several data sets (i. e. , several lines). The number of dat sets is less than or equal to 50.", "output": "Output line contains one integer - the number of connected subsets - for each input line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 5\n50 1\n13 13\n output: 2\n50\n8"], "Pid": "p00602", "ProblemText": "Task Description: Fibonacci number f(i) appear in a variety of puzzles in nature and math, including packing problems, family trees or Pythagorean triangles. They obey the rule f(i) = f(i - 1) + f(i - 2), where we set f(0) = 1 = f(-1).\n\nLet V and d be two certain positive integers and be N ≡ 1001 a constant. Consider a set of V nodes, each node i having a Fibonacci label F[i] = (f(i) mod N) assigned for i = 1, . . . , V <= N. If |F(i) - F(j)| < d, then the nodes i and j are connected.\n\nGiven V and d, how many connected subsets of nodes will you obtain?\nFigure 1: There are 4 connected subsets for V = 20 and d = 100.\nTask Constraint: 1 <= V <= 1000\n\n1 <= d <= 150\nTask Input: Each data set is defined as one line with two integers as follows:\n\nLine 1: Number of nodes V and the distance d.\n\nInput includes several data sets (i. e. , several lines). The number of dat sets is less than or equal to 50.\nTask Output: Output line contains one integer - the number of connected subsets - for each input line.\nTask Samples: input: 5 5\n50 1\n13 13\n output: 2\n50\n8\n\n" }, { "title": "Problem I: Riffle Shuffle", "content": "There are a number of ways to shuffle a deck of cards. Riffle shuffle is one such example. The following is how to perform riffle shuffle.\n\n There is a deck of n cards. First, we divide it into two decks; deck A which consists of the top half of it and deck B of the bottom half. Deck A will have one more card when n is odd. \n\n Next, c cards are pulled from bottom of deck A and are stacked on deck C, which is empty initially. Then c cards are pulled from bottom of deck B and stacked on deck C, likewise. This operation is repeated until deck A and B become empty. When the number of cards of deck A(B) is less than c, all cards are pulled.\n Finally we obtain shuffled deck C. See an example below:\n\n - A single riffle operation where n = 9, c = 3\n \n for given deck [0 1 2 3 4 5 6 7 8] (right is top)\n\n - Step 0\n deck A [4 5 6 7 8]\n deck B [0 1 2 3]\n deck C []\n\n - Step 1\n deck A [7 8]\n deck B [0 1 2 3]\n deck C [4 5 6]\n\n - Step 2\n deck A [7 8]\n deck B [3]\n deck C [4 5 6 0 1 2]\n\n - Step 3\n deck A []\n deck B [3]\n deck C [4 5 6 0 1 2 7 8]\n\n - Step 4\n deck A []\n deck B []\n deck C [4 5 6 0 1 2 7 8 3]\n\n shuffled deck [4 5 6 0 1 2 7 8 3]\n\n This operation, called riffle operation, is repeated several times.\n\n Write a program that simulates Riffle shuffle and answer which card will be finally placed on the top of the deck.", "constraint": "", "input": "The input consists of multiple data sets. Each data set starts with a line containing two positive integers n(1 <= n <= 50) and r(1 <= r <= 50); n and r are the number of cards in the deck and the number of riffle operations, respectively.\n\nr more positive integers follow, each of which represents a riffle operation. These riffle operations are performed in the listed order. Each integer represents c, which is explained above.\n\n The end of the input is indicated by EOF. The number of data sets is less than 100. ", "output": "For each data set in the input, your program should print the number of the top card after the shuffle. Assume that at the beginning the cards are numbered from 0 to n-1, from the bottom to the top. Each number should be written in a sparate line without any superfluous characters such as leading or following spaces.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 1\n3\n9 4\n1 2 3 4\n output: 3\n0"], "Pid": "p00603", "ProblemText": "Task Description: There are a number of ways to shuffle a deck of cards. Riffle shuffle is one such example. The following is how to perform riffle shuffle.\n\n There is a deck of n cards. First, we divide it into two decks; deck A which consists of the top half of it and deck B of the bottom half. Deck A will have one more card when n is odd. \n\n Next, c cards are pulled from bottom of deck A and are stacked on deck C, which is empty initially. Then c cards are pulled from bottom of deck B and stacked on deck C, likewise. This operation is repeated until deck A and B become empty. When the number of cards of deck A(B) is less than c, all cards are pulled.\n Finally we obtain shuffled deck C. See an example below:\n\n - A single riffle operation where n = 9, c = 3\n \n for given deck [0 1 2 3 4 5 6 7 8] (right is top)\n\n - Step 0\n deck A [4 5 6 7 8]\n deck B [0 1 2 3]\n deck C []\n\n - Step 1\n deck A [7 8]\n deck B [0 1 2 3]\n deck C [4 5 6]\n\n - Step 2\n deck A [7 8]\n deck B [3]\n deck C [4 5 6 0 1 2]\n\n - Step 3\n deck A []\n deck B [3]\n deck C [4 5 6 0 1 2 7 8]\n\n - Step 4\n deck A []\n deck B []\n deck C [4 5 6 0 1 2 7 8 3]\n\n shuffled deck [4 5 6 0 1 2 7 8 3]\n\n This operation, called riffle operation, is repeated several times.\n\n Write a program that simulates Riffle shuffle and answer which card will be finally placed on the top of the deck.\nTask Input: The input consists of multiple data sets. Each data set starts with a line containing two positive integers n(1 <= n <= 50) and r(1 <= r <= 50); n and r are the number of cards in the deck and the number of riffle operations, respectively.\n\nr more positive integers follow, each of which represents a riffle operation. These riffle operations are performed in the listed order. Each integer represents c, which is explained above.\n\n The end of the input is indicated by EOF. The number of data sets is less than 100. \nTask Output: For each data set in the input, your program should print the number of the top card after the shuffle. Assume that at the beginning the cards are numbered from 0 to n-1, from the bottom to the top. Each number should be written in a sparate line without any superfluous characters such as leading or following spaces.\nTask Samples: input: 9 1\n3\n9 4\n1 2 3 4\n output: 3\n0\n\n" }, { "title": "Problem J: Cheating on ICPC", "content": "Peter loves any kinds of cheating. A week before ICPC, he broke into Doctor's PC and sneaked a look at all the problems that would be given in ICPC. He solved the problems, printed programs out, and brought into ICPC. Since electronic preparation is strictly prohibited, he had to type these programs again during the contest.\n Although he believes that he can solve every problems thanks to carefully debugged programs, he still has to find an optimal strategy to make certain of his victory.\n\n Teams are ranked by following rules.\n\n Team that solved more problems is ranked higher.\n\n In case of tie (solved same number of problems), team that received less Penalty is ranked higher.\n Here, Penalty is calculated by these rules.\n\n When the team solves a problem, time that the team spent to solve it (i. e. (time of submission) - (time of beginning of the contest)) are added to penalty.\n\n For each submittion that doesn't solve a problem, 20 minutes of Penalty are added. However, if the problem wasn't solved eventually, Penalty for it is not added.\n You must find that order of solving will affect result of contest. For example, there are three problem named A, B, and C, which takes 10 minutes, 20 minutes, and 30 minutes to solve, respectively. If you solve A, B, and C in this order, Penalty will be 10 + 30 + 60 = 100 minutes. However, If you do in reverse order, 30 + 50 + 60 = 140 minutes of Penalty will be given.\n\n Peter can easily estimate time to need to solve each problem (actually it depends only on length of his program. ) You, Peter's teammate, are asked to calculate minimal possible Penalty when he solve all the problems.", "constraint": "", "input": "Input file consists of multiple datasets. The first line of a dataset is non-negative integer N (0 <= N <= 100) which stands for number of problem. Next N Integers P[1], P[2], . . . , P[N] (0 <= P[i] <= 10800) represents time to solve problems.\n\n Input ends with EOF. The number of datasets is less than or equal to 100. ", "output": "Output minimal possible Penalty, one line for one dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10 20 30\n7\n56 26 62 43 25 80 7\n output: 100\n873"], "Pid": "p00604", "ProblemText": "Task Description: Peter loves any kinds of cheating. A week before ICPC, he broke into Doctor's PC and sneaked a look at all the problems that would be given in ICPC. He solved the problems, printed programs out, and brought into ICPC. Since electronic preparation is strictly prohibited, he had to type these programs again during the contest.\n Although he believes that he can solve every problems thanks to carefully debugged programs, he still has to find an optimal strategy to make certain of his victory.\n\n Teams are ranked by following rules.\n\n Team that solved more problems is ranked higher.\n\n In case of tie (solved same number of problems), team that received less Penalty is ranked higher.\n Here, Penalty is calculated by these rules.\n\n When the team solves a problem, time that the team spent to solve it (i. e. (time of submission) - (time of beginning of the contest)) are added to penalty.\n\n For each submittion that doesn't solve a problem, 20 minutes of Penalty are added. However, if the problem wasn't solved eventually, Penalty for it is not added.\n You must find that order of solving will affect result of contest. For example, there are three problem named A, B, and C, which takes 10 minutes, 20 minutes, and 30 minutes to solve, respectively. If you solve A, B, and C in this order, Penalty will be 10 + 30 + 60 = 100 minutes. However, If you do in reverse order, 30 + 50 + 60 = 140 minutes of Penalty will be given.\n\n Peter can easily estimate time to need to solve each problem (actually it depends only on length of his program. ) You, Peter's teammate, are asked to calculate minimal possible Penalty when he solve all the problems.\nTask Input: Input file consists of multiple datasets. The first line of a dataset is non-negative integer N (0 <= N <= 100) which stands for number of problem. Next N Integers P[1], P[2], . . . , P[N] (0 <= P[i] <= 10800) represents time to solve problems.\n\n Input ends with EOF. The number of datasets is less than or equal to 100. \nTask Output: Output minimal possible Penalty, one line for one dataset.\nTask Samples: input: 3\n10 20 30\n7\n56 26 62 43 25 80 7\n output: 100\n873\n\n" }, { "title": "Problem A: Vampirish Night", "content": "There is a vampire family of N members. Vampires are also known as extreme gourmets. Of course vampires' foods are human blood. However, not all kinds of blood is acceptable for them. Vampires drink blood that K blood types of ones are mixed, and each vampire has his/her favorite amount for each blood type.\n\nYou, cook of the family, are looking inside a fridge to prepare dinner. Your first task is to write a program that judges if all family members' dinner can be prepared using blood in the fridge.", "constraint": "Judge data includes at most 100 data sets.\n\n1 <= N <= 100\n\n1 <= K <= 100\n\n0 <= S_i <= 100000\n\n0 <= B_ij <= 1000", "input": "Input file consists of a number of data sets.\nOne data set is given in following format:\n\nN K\nS_1 S_2 . . . S_K\nB_11 B_12 . . . B_1K\nB_21 B_22 . . . B_2K\n:\nB_N1 B_N2 . . . B_NK\n\nN and K indicate the number of family members and the number of blood types respectively.\nS_i is an integer that indicates the amount of blood of the i-th blood type that is in a fridge.\n\nB_ij is an integer that indicates the amount of blood of the j-th blood type that the i-th vampire uses.\n\nThe end of input is indicated by a case where N = K = 0. You should print nothing for this data set.", "output": "For each set, print \"Yes\" if everyone's dinner can be prepared using blood in a fridge, \"No\" otherwise (without quotes).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n5 4 5\n1 2 3\n3 2 1\n3 5\n1 2 3 4 5\n0 1 0 1 2\n0 1 1 2 2\n1 0 3 1 1\n0 0\n output: Yes\nNo"], "Pid": "p00605", "ProblemText": "Task Description: There is a vampire family of N members. Vampires are also known as extreme gourmets. Of course vampires' foods are human blood. However, not all kinds of blood is acceptable for them. Vampires drink blood that K blood types of ones are mixed, and each vampire has his/her favorite amount for each blood type.\n\nYou, cook of the family, are looking inside a fridge to prepare dinner. Your first task is to write a program that judges if all family members' dinner can be prepared using blood in the fridge.\nTask Constraint: Judge data includes at most 100 data sets.\n\n1 <= N <= 100\n\n1 <= K <= 100\n\n0 <= S_i <= 100000\n\n0 <= B_ij <= 1000\nTask Input: Input file consists of a number of data sets.\nOne data set is given in following format:\n\nN K\nS_1 S_2 . . . S_K\nB_11 B_12 . . . B_1K\nB_21 B_22 . . . B_2K\n:\nB_N1 B_N2 . . . B_NK\n\nN and K indicate the number of family members and the number of blood types respectively.\nS_i is an integer that indicates the amount of blood of the i-th blood type that is in a fridge.\n\nB_ij is an integer that indicates the amount of blood of the j-th blood type that the i-th vampire uses.\n\nThe end of input is indicated by a case where N = K = 0. You should print nothing for this data set.\nTask Output: For each set, print \"Yes\" if everyone's dinner can be prepared using blood in a fridge, \"No\" otherwise (without quotes).\nTask Samples: input: 2 3\n5 4 5\n1 2 3\n3 2 1\n3 5\n1 2 3 4 5\n0 1 0 1 2\n0 1 1 2 2\n1 0 3 1 1\n0 0\n output: Yes\nNo\n\n" }, { "title": "Problem B: Cleaning Robot", "content": "Dr. Asimov, a robotics researcher, loves to research, but hates houseworks and his house were really dirty. So, he has developed a cleaning robot.\n\nAs shown in the following figure, his house has 9 rooms, where each room is identified by an alphabet:\n\nThe robot he developed operates as follows:\nIf the battery runs down, the robot stops.\n If not so, the robot chooses a direction from four cardinal points with the equal probability, and moves to the room in that direction. Then, the robot clean the room and consumes 1 point of the battery. \n\nHowever, if there is no room in that direction, the robot does not move and remains the same room. In addition, there is a junk room in the house where the robot can not enter, and the robot also remains when it tries to enter the junk room. The robot also consumes 1 point of the battery when it remains the same place.\n\nA battery charger for the robot is in a room. It would be convenient for Dr. Asimov if the robot stops at the battery room when its battery run down.\n\nYour task is to write a program which computes the probability of the robot stopping at the battery room.", "constraint": "Judge data includes at most 100 data sets.\n\nn <= 15\n\ns, t, b are distinct.", "input": "The input consists of several datasets. Each dataset consists of:\n\nn\ns t b\n\nn is an integer that indicates the initial battery point. s, t, b are alphabets respectively represent the room where the robot is initially, the battery room, and the junk room.\n\nThe input ends with a dataset which consists of single 0 for n. Your program should not output for this dataset.", "output": "For each dataset, print the probability as a floating point number in a line. The answer may not have an error greater than 0.000001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\nE A C\n1\nE B C\n2\nE A B\n0\n output: 0.00000000\n0.25000000\n0.06250000"], "Pid": "p00606", "ProblemText": "Task Description: Dr. Asimov, a robotics researcher, loves to research, but hates houseworks and his house were really dirty. So, he has developed a cleaning robot.\n\nAs shown in the following figure, his house has 9 rooms, where each room is identified by an alphabet:\n\nThe robot he developed operates as follows:\nIf the battery runs down, the robot stops.\n If not so, the robot chooses a direction from four cardinal points with the equal probability, and moves to the room in that direction. Then, the robot clean the room and consumes 1 point of the battery. \n\nHowever, if there is no room in that direction, the robot does not move and remains the same room. In addition, there is a junk room in the house where the robot can not enter, and the robot also remains when it tries to enter the junk room. The robot also consumes 1 point of the battery when it remains the same place.\n\nA battery charger for the robot is in a room. It would be convenient for Dr. Asimov if the robot stops at the battery room when its battery run down.\n\nYour task is to write a program which computes the probability of the robot stopping at the battery room.\nTask Constraint: Judge data includes at most 100 data sets.\n\nn <= 15\n\ns, t, b are distinct.\nTask Input: The input consists of several datasets. Each dataset consists of:\n\nn\ns t b\n\nn is an integer that indicates the initial battery point. s, t, b are alphabets respectively represent the room where the robot is initially, the battery room, and the junk room.\n\nThe input ends with a dataset which consists of single 0 for n. Your program should not output for this dataset.\nTask Output: For each dataset, print the probability as a floating point number in a line. The answer may not have an error greater than 0.000001.\nTask Samples: input: 1\nE A C\n1\nE B C\n2\nE A B\n0\n output: 0.00000000\n0.25000000\n0.06250000\n\n" }, { "title": "Problem C: Emacs-like Editor", "content": "Emacs is a text editor which is widely used by many programmers.\n\nThe advantage of Emacs is that we can move a cursor without arrow keys and the mice. For example, the cursor can be moved right, left, down, and up by pushing f, b, n, p with the Control Key respectively. In addition, cut-and-paste can be performed without the mouse.\n\nYour task is to write a program which simulates key operations in the Emacs-like editor. The program should read a text and print the corresponding edited text.\n\nThe text consists of several lines and each line consists of zero or more alphabets and space characters. A line, which does not have any character, is a blank line.\n\nThe editor has a cursor which can point out a character or the end-of-line in the corresponding line. The cursor can also point out the end-of-line in a blank line.\n\nIn addition, the editor has a buffer which can hold either a string (a sequence of characters) or a linefeed.\n\nThe editor accepts the following set of commands (If the corresponding line is a blank line, the word \"the first character\" should be \"the end-of-line\"):\na\nMove the cursor to the first character of the current line.\n\ne\nMove the cursor to the end-of-line of the current line.\n\np\nMove the cursor to the first character of the next upper line, if it exists. \nIf there is no line above the current line, move the cursor to the first character of the current line.\n\nn\nMove the cursor to the first character of the next lower line, if it exists. \nIf there is no line below the current line, move the cursor to the first character of the current line.\n\nf\nMove the cursor by one character to the right, unless the cursor points out the end-of-line. \nIf the cursor points out the end-of-line and there is a line below the current line, move the cursor to the first character of the next lower line. Otherwise, do nothing.\n\nb\nMove the cursor by one character to the left, unless the cursor points out the first character. \nIf the cursor points out the first character and there is a line above the current line, move the cursor to the end-of-line of the next upper line. Otherwise, do nothing.\n\nd\nIf the cursor points out a character, delete the character (Characters and end-of-line next to the deleted character are shifted to the left). \nIf the cursor points out the end-of-line and there is a line below, the next lower line is appended to the end-of-line of the current line (Lines below the current line are shifted to the upper). Otherwise, do nothing.\n\nk\nIf the cursor points out the end-of-line and there is a line below the current line, perform the command d mentioned above, and record a linefeed on the buffer. \nIf the cursor does not point out the end-of-line, cut characters between the cursor (inclusive) and the end-of-line, and record them on the buffer. After this operation, the cursor indicates the end-of-line of the current line.\n\ny\nIf the buffer is empty, do nothing. \nIf the buffer is holding a linefeed, insert the linefeed at the cursor. The cursor moves to the first character of the new line. \nIf the buffer is holding characters, insert the characters at the cursor. The cursor moves to the character or end-of-line which is originally pointed by the cursor.\n\nThe cursor position just after reading the text is the beginning of the first line, and the initial buffer is empty.", "constraint": "The number of lines in the text given as input <= 10\n\nThe number of characters in a line given as input <= 20 \n\nThe number of commands <= 300 \n\nThe maximum possible number of lines in the text during operations <= 100 \n\nThe maximum possible number of characters in a line during operations <= 1000", "input": "The input consists of only one data-set which includes two parts. The first part gives a text consisting of several lines. The end of the text is indicated by a line (without quotes):\n\"END_OF_TEXT\"\n\n

\nThis line should not be included in the text.\nNext part gives a series of commands. Each command is given in a line. The end of the commands is indicated by a character '-'.", "output": "For the input text, print the text edited by the commands.", "content_img": false, "lang": "en", "error": false, "samples": ["input: hyo\nni\nEND_OF_TEXT\nf\nd\nf\nf\nk\np\np\ne\ny\na\nk\ny\ny\nn\ny\n-\n output: honihoni\nhoni"], "Pid": "p00607", "ProblemText": "Task Description: Emacs is a text editor which is widely used by many programmers.\n\nThe advantage of Emacs is that we can move a cursor without arrow keys and the mice. For example, the cursor can be moved right, left, down, and up by pushing f, b, n, p with the Control Key respectively. In addition, cut-and-paste can be performed without the mouse.\n\nYour task is to write a program which simulates key operations in the Emacs-like editor. The program should read a text and print the corresponding edited text.\n\nThe text consists of several lines and each line consists of zero or more alphabets and space characters. A line, which does not have any character, is a blank line.\n\nThe editor has a cursor which can point out a character or the end-of-line in the corresponding line. The cursor can also point out the end-of-line in a blank line.\n\nIn addition, the editor has a buffer which can hold either a string (a sequence of characters) or a linefeed.\n\nThe editor accepts the following set of commands (If the corresponding line is a blank line, the word \"the first character\" should be \"the end-of-line\"):\na\nMove the cursor to the first character of the current line.\n\ne\nMove the cursor to the end-of-line of the current line.\n\np\nMove the cursor to the first character of the next upper line, if it exists. \nIf there is no line above the current line, move the cursor to the first character of the current line.\n\nn\nMove the cursor to the first character of the next lower line, if it exists. \nIf there is no line below the current line, move the cursor to the first character of the current line.\n\nf\nMove the cursor by one character to the right, unless the cursor points out the end-of-line. \nIf the cursor points out the end-of-line and there is a line below the current line, move the cursor to the first character of the next lower line. Otherwise, do nothing.\n\nb\nMove the cursor by one character to the left, unless the cursor points out the first character. \nIf the cursor points out the first character and there is a line above the current line, move the cursor to the end-of-line of the next upper line. Otherwise, do nothing.\n\nd\nIf the cursor points out a character, delete the character (Characters and end-of-line next to the deleted character are shifted to the left). \nIf the cursor points out the end-of-line and there is a line below, the next lower line is appended to the end-of-line of the current line (Lines below the current line are shifted to the upper). Otherwise, do nothing.\n\nk\nIf the cursor points out the end-of-line and there is a line below the current line, perform the command d mentioned above, and record a linefeed on the buffer. \nIf the cursor does not point out the end-of-line, cut characters between the cursor (inclusive) and the end-of-line, and record them on the buffer. After this operation, the cursor indicates the end-of-line of the current line.\n\ny\nIf the buffer is empty, do nothing. \nIf the buffer is holding a linefeed, insert the linefeed at the cursor. The cursor moves to the first character of the new line. \nIf the buffer is holding characters, insert the characters at the cursor. The cursor moves to the character or end-of-line which is originally pointed by the cursor.\n\nThe cursor position just after reading the text is the beginning of the first line, and the initial buffer is empty.\nTask Constraint: The number of lines in the text given as input <= 10\n\nThe number of characters in a line given as input <= 20 \n\nThe number of commands <= 300 \n\nThe maximum possible number of lines in the text during operations <= 100 \n\nThe maximum possible number of characters in a line during operations <= 1000\nTask Input: The input consists of only one data-set which includes two parts. The first part gives a text consisting of several lines. The end of the text is indicated by a line (without quotes):\n\"END_OF_TEXT\"\n\n

\nThis line should not be included in the text.\nNext part gives a series of commands. Each command is given in a line. The end of the commands is indicated by a character '-'.\nTask Output: For the input text, print the text edited by the commands.\nTask Samples: input: hyo\nni\nEND_OF_TEXT\nf\nd\nf\nf\nk\np\np\ne\ny\na\nk\ny\ny\nn\ny\n-\n output: honihoni\nhoni\n\n" }, { "title": "Problem D: Indian Puzzle", "content": "In the Indian Puzzle, one is intended to fill out blanks with numbers and operators in a n by n grid in order to make equalities in the grid true (See Figure 1).\nFigure 1\n\nA blank cell should be filled out with a number (from 0 to 9 inclusive) or an operator (+, -, *, ÷, =), and black cells split equalities. Initially, some cells are already filled with numbers or operators.\n\nThe objective of this puzzle is to fill out all the blank cells with numbers (from 0 to 9 inclusive) and operators (+, -, *, ÷) in a given list. All the numbers and operators in the list must be used to fill out the blank cells.\n\nA equality is organized by more than 2 consecutive left-to-right or top-to-bottom white cells. You can assume that a equality contains exactly one cell with '=' which connects two expressions.\n\nThe expressions conform to the order of operations and semantics of conventional four arithmetic operations. First, do all multiplication and division, starting from the left (top). Then, do all addition and subtraction, starting from the left (top). In addition, this puzzle has the following rules:\n\nDivision by zero and division leaving a remainder, are not allowed.\n\nLeading zeros are not allowed.\n\nUnary operators like 3*-8=-24 are not allowed.\nIn a formal description, the equality must conform the syntax in the following BNF:\n\n : : = = \n : : = | \n : : = | 0\n : : = | | 0\n : : = + | - | * | ÷\n : : = 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9\n\nOf course, puzzle creators must make solvable puzzle.\nYour task is to write a program which verifies whether given puzzle is solvable or not.", "constraint": "Judge data includes at most 100 data sets.\n\nH, W <= 10\n\nn <= 10", "input": "Input consists of several datasets. Each dataset consists of:\n\nH W\nH * W characters\nn\nn characters\n\nThe integers H and W are the numbers of rows and columns of the grid, respectively. H * W characters denote the grid which contains '. ' representing a blank cell, '#' representing a black cell, numbers (from 0 to 9 inclusive), operators('+', '-', '*', '/', '=')(* is represented by '*' and ÷ is represented by '/').\n\nThe integer n is the number of characters in the list. The last line of a dataset contains n characters indicating numbers and operators for the blank cells.\n\nThe end of input is indicated by a line containing two zeros separated by a space.", "output": "For each dataset, print \"Yes\" if the given puzzle is solvable, \"No\" if not.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 5\n4=..2\n+#=#+\n.-2=.\n=#*#=\n.-.=3\n6\n7 3 1 4 / 8\n1 6\n8..3=2\n2\n2 +\n0 0\n output: Yes\nNo"], "Pid": "p00608", "ProblemText": "Task Description: In the Indian Puzzle, one is intended to fill out blanks with numbers and operators in a n by n grid in order to make equalities in the grid true (See Figure 1).\nFigure 1\n\nA blank cell should be filled out with a number (from 0 to 9 inclusive) or an operator (+, -, *, ÷, =), and black cells split equalities. Initially, some cells are already filled with numbers or operators.\n\nThe objective of this puzzle is to fill out all the blank cells with numbers (from 0 to 9 inclusive) and operators (+, -, *, ÷) in a given list. All the numbers and operators in the list must be used to fill out the blank cells.\n\nA equality is organized by more than 2 consecutive left-to-right or top-to-bottom white cells. You can assume that a equality contains exactly one cell with '=' which connects two expressions.\n\nThe expressions conform to the order of operations and semantics of conventional four arithmetic operations. First, do all multiplication and division, starting from the left (top). Then, do all addition and subtraction, starting from the left (top). In addition, this puzzle has the following rules:\n\nDivision by zero and division leaving a remainder, are not allowed.\n\nLeading zeros are not allowed.\n\nUnary operators like 3*-8=-24 are not allowed.\nIn a formal description, the equality must conform the syntax in the following BNF:\n\n : : = = \n : : = | \n : : = | 0\n : : = | | 0\n : : = + | - | * | ÷\n : : = 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9\n\nOf course, puzzle creators must make solvable puzzle.\nYour task is to write a program which verifies whether given puzzle is solvable or not.\nTask Constraint: Judge data includes at most 100 data sets.\n\nH, W <= 10\n\nn <= 10\nTask Input: Input consists of several datasets. Each dataset consists of:\n\nH W\nH * W characters\nn\nn characters\n\nThe integers H and W are the numbers of rows and columns of the grid, respectively. H * W characters denote the grid which contains '. ' representing a blank cell, '#' representing a black cell, numbers (from 0 to 9 inclusive), operators('+', '-', '*', '/', '=')(* is represented by '*' and ÷ is represented by '/').\n\nThe integer n is the number of characters in the list. The last line of a dataset contains n characters indicating numbers and operators for the blank cells.\n\nThe end of input is indicated by a line containing two zeros separated by a space.\nTask Output: For each dataset, print \"Yes\" if the given puzzle is solvable, \"No\" if not.\nTask Samples: input: 5 5\n4=..2\n+#=#+\n.-2=.\n=#*#=\n.-.=3\n6\n7 3 1 4 / 8\n1 6\n8..3=2\n2\n2 +\n0 0\n output: Yes\nNo\n\n" }, { "title": "Problem E: Amazing Graze", "content": "In 2215 A. D. , a war between two planets, ACM and ICPC, is being more and more intense.\n\nACM introduced new combat planes. These planes have a special system that is called Graze, and fighting power of a plane increases when it is close to energy bullets that ICPC combat planes shoot.\n\nBoth combat planes and energy bullets have a shape of a sphere with a radius of R. Precisely, fighting power of a plane is equivalent to the number of energy bullet where distance from the plane is less than or equals to 2R.\n\nYou, helper of captain of intelligence units, are asked to analyze a war situation. The information given to you is coordinates of AN combat planes and BN energy bullets. Additionally, you know following things:\n\n All combat planes and energy bullet has same z-coordinates. In other word, z-coordinate can be ignored.\n\n No two combat planes, no two energy bullets, and no pair of combat plane and energy bullet collide (i. e. have positive common volume) each other.\nYour task is to write a program that outputs total fighting power of all combat planes.", "constraint": "Jude data includes at most 20 data sets.\n\n1 <= AN, BN <= 100000\n\n0 < R <= 10 \n\n0 <= (coordinate values) < 10000", "input": "Input file consists of a number of data sets.\nOne data set is given in following format:\n\nAN BN R\nXA_1 YA_1\nXA_2 YA_2\n:\nXA_AN YA_AN\nXB_1 YB_1\nXB_2 YB_2\n:\nXB_BN YB_BN\n\nAN, BN, R are integers that describe the number of combat planes, energy bullets, and their radius respectively.\n\nFollowing AN lines indicate coordinates of the center of combat planes. Each line has two integers that describe x-coordinate and y-coordinate.\n\nFollowing BN lines indicate coordinates of the center of energy bullets, in the same format as that of combat planes.\n\nInput ends when AN = BN = 0. You should output nothing for this case.", "output": "For each data set, output the total fighting power.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 1\n0 0\n0 4\n2 2\n2 8\n0 0 0\n output: 2"], "Pid": "p00609", "ProblemText": "Task Description: In 2215 A. D. , a war between two planets, ACM and ICPC, is being more and more intense.\n\nACM introduced new combat planes. These planes have a special system that is called Graze, and fighting power of a plane increases when it is close to energy bullets that ICPC combat planes shoot.\n\nBoth combat planes and energy bullets have a shape of a sphere with a radius of R. Precisely, fighting power of a plane is equivalent to the number of energy bullet where distance from the plane is less than or equals to 2R.\n\nYou, helper of captain of intelligence units, are asked to analyze a war situation. The information given to you is coordinates of AN combat planes and BN energy bullets. Additionally, you know following things:\n\n All combat planes and energy bullet has same z-coordinates. In other word, z-coordinate can be ignored.\n\n No two combat planes, no two energy bullets, and no pair of combat plane and energy bullet collide (i. e. have positive common volume) each other.\nYour task is to write a program that outputs total fighting power of all combat planes.\nTask Constraint: Jude data includes at most 20 data sets.\n\n1 <= AN, BN <= 100000\n\n0 < R <= 10 \n\n0 <= (coordinate values) < 10000\nTask Input: Input file consists of a number of data sets.\nOne data set is given in following format:\n\nAN BN R\nXA_1 YA_1\nXA_2 YA_2\n:\nXA_AN YA_AN\nXB_1 YB_1\nXB_2 YB_2\n:\nXB_BN YB_BN\n\nAN, BN, R are integers that describe the number of combat planes, energy bullets, and their radius respectively.\n\nFollowing AN lines indicate coordinates of the center of combat planes. Each line has two integers that describe x-coordinate and y-coordinate.\n\nFollowing BN lines indicate coordinates of the center of energy bullets, in the same format as that of combat planes.\n\nInput ends when AN = BN = 0. You should output nothing for this case.\nTask Output: For each data set, output the total fighting power.\nTask Samples: input: 2 2 1\n0 0\n0 4\n2 2\n2 8\n0 0 0\n output: 2\n\n" }, { "title": "Problem F: Cleaning Robot 2.0", "content": "Dr. Asimov, a robotics researcher, released cleaning robots he developed (see Problem B). His robots soon became very popular and he got much income. Now he is pretty rich. Wonderful.\n\nFirst, he renovated his house. Once his house had 9 rooms that were arranged in a square, but now his house has N * N rooms arranged in a square likewise. Then he laid either black or white carpet on each room.\n\nSince still enough money remained, he decided to spend them for development of a new robot. And finally he completed.\n\nThe new robot operates as follows:\n\nThe robot is set on any of N * N rooms, with directing any of north, east, west and south.\n\nThe robot detects color of carpets of lefthand, righthand, and forehand adjacent rooms if exists. If there is exactly one room that its carpet has the same color as carpet of room where it is, the robot changes direction to and moves to and then cleans the room. Otherwise, it halts. Note that halted robot doesn't clean any longer. Following is some examples of robot's movement.\n\nFigure 1. An example of the room\n\nIn Figure 1,\n\nrobot that is on room (1,1) and directing north directs east and goes to (1,2).\n\nrobot that is on room (0,2) and directing north directs west and goes to (0,1).\n\nrobot that is on room (0,0) and directing west halts.\nSince the robot powered by contactless battery chargers that are installed in every rooms, unlike the previous robot, it never stops because of running down of its battery. It keeps working until it halts.\nDoctor's house has become larger by the renovation. Therefore, it is not efficient to let only one robot clean. Fortunately, he still has enough budget. So he decided to make a number of same robots and let them clean simultaneously.\n\nThe robots interacts as follows:\n\n No two robots can be set on same room.\n\n It is still possible for a robot to detect a color of carpet of a room even if the room is occupied by another robot.\n\n All robots go ahead simultaneously.\n\n When robots collide (namely, two or more robots are in a single room, or two robots exchange their position after movement), they all halt. Working robots can take such halted robot away.\nOn every room dust stacks slowly but constantly. To keep his house pure, he wants his robots to work so that dust that stacked on any room at any time will eventually be cleaned.\n\nAfter thinking deeply, he realized that there exists a carpet layout such that no matter how initial placements of robots are, this condition never can be satisfied. Your task is to output carpet layout that there exists at least one initial placements of robots that meets above condition. Since there may be two or more such layouts, please output the K-th one lexicographically.", "constraint": "Judge data consists of at most 100 data sets.\n\n1 <= N < 64\n\n1 <= K < 2^63", "input": "Input file contains several data sets.\nOne data set is given in following format:\n\nN K\n\nHere, N and K are integers that are explained in the problem description.\n\nThe end of input is described by a case where N = K = 0. You should output nothing for this case.", "output": "Print the K-th carpet layout if exists, \"No\" (without quotes) otherwise.\n\nThe carpet layout is denoted by N lines of string that each has exactly N letters. A room with black carpet and a room with white carpet is denoted by a letter 'E' and '. ' respectively. Lexicographically order of carpet layout is defined as that of a string that is obtained by concatenating the first row, the second row, . . . , and the N-th row in this order.\n\nOutput a blank line after each data set.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 1\n2 3\n6 4\n0 0\n output: ..\n..\n\nNo\n\n..EEEE\n..E..E\nEEE..E\nE..EEE\nE..E..\nEEEE.."], "Pid": "p00610", "ProblemText": "Task Description: Dr. Asimov, a robotics researcher, released cleaning robots he developed (see Problem B). His robots soon became very popular and he got much income. Now he is pretty rich. Wonderful.\n\nFirst, he renovated his house. Once his house had 9 rooms that were arranged in a square, but now his house has N * N rooms arranged in a square likewise. Then he laid either black or white carpet on each room.\n\nSince still enough money remained, he decided to spend them for development of a new robot. And finally he completed.\n\nThe new robot operates as follows:\n\nThe robot is set on any of N * N rooms, with directing any of north, east, west and south.\n\nThe robot detects color of carpets of lefthand, righthand, and forehand adjacent rooms if exists. If there is exactly one room that its carpet has the same color as carpet of room where it is, the robot changes direction to and moves to and then cleans the room. Otherwise, it halts. Note that halted robot doesn't clean any longer. Following is some examples of robot's movement.\n\nFigure 1. An example of the room\n\nIn Figure 1,\n\nrobot that is on room (1,1) and directing north directs east and goes to (1,2).\n\nrobot that is on room (0,2) and directing north directs west and goes to (0,1).\n\nrobot that is on room (0,0) and directing west halts.\nSince the robot powered by contactless battery chargers that are installed in every rooms, unlike the previous robot, it never stops because of running down of its battery. It keeps working until it halts.\nDoctor's house has become larger by the renovation. Therefore, it is not efficient to let only one robot clean. Fortunately, he still has enough budget. So he decided to make a number of same robots and let them clean simultaneously.\n\nThe robots interacts as follows:\n\n No two robots can be set on same room.\n\n It is still possible for a robot to detect a color of carpet of a room even if the room is occupied by another robot.\n\n All robots go ahead simultaneously.\n\n When robots collide (namely, two or more robots are in a single room, or two robots exchange their position after movement), they all halt. Working robots can take such halted robot away.\nOn every room dust stacks slowly but constantly. To keep his house pure, he wants his robots to work so that dust that stacked on any room at any time will eventually be cleaned.\n\nAfter thinking deeply, he realized that there exists a carpet layout such that no matter how initial placements of robots are, this condition never can be satisfied. Your task is to output carpet layout that there exists at least one initial placements of robots that meets above condition. Since there may be two or more such layouts, please output the K-th one lexicographically.\nTask Constraint: Judge data consists of at most 100 data sets.\n\n1 <= N < 64\n\n1 <= K < 2^63\nTask Input: Input file contains several data sets.\nOne data set is given in following format:\n\nN K\n\nHere, N and K are integers that are explained in the problem description.\n\nThe end of input is described by a case where N = K = 0. You should output nothing for this case.\nTask Output: Print the K-th carpet layout if exists, \"No\" (without quotes) otherwise.\n\nThe carpet layout is denoted by N lines of string that each has exactly N letters. A room with black carpet and a room with white carpet is denoted by a letter 'E' and '. ' respectively. Lexicographically order of carpet layout is defined as that of a string that is obtained by concatenating the first row, the second row, . . . , and the N-th row in this order.\n\nOutput a blank line after each data set.\nTask Samples: input: 2 1\n2 3\n6 4\n0 0\n output: ..\n..\n\nNo\n\n..EEEE\n..E..E\nEEE..E\nE..EEE\nE..E..\nEEEE..\n\n" }, { "title": "Problem G: Building Water Ways", "content": "In ancient times, Romans constructed numerous water ways to supply water to cities and industrial sites. These water ways were amongst the greatest engineering feats of the ancient world.\n\nThese water ways contributed to social infrastructures which improved people's quality of life. On the other hand, problems related to the water control and the water facilities are still interesting as a lot of games of water ways construction have been developed.\n\nYour task is to write a program which reads a map and computes the minimum possible cost of constructing water ways from sources to all the cities.\n\nAs shown in Figure 1, the map is represented by H * W grid cells, where each cell represents source, city, flatland, or obstacle.\n\nYou can construct only one water way from a source, but there are no limitations on the length of that water way and it can provide water to any number of cities located on its path. You can not construct water ways on the obstacles.\n\nYour objective is to bring water to all the city and minimize the number of cells which represent water ways. In the Figure 1, water ways are constructed in 14 cells which is the minimum cost.\n\nThe water ways must satisfy the following conditions:\n\na water way cell is adjacent to at most 2 water way cells in four cardinal points.\n\na source cell is adjacent to at most 1 water way cell in four cardinal points.\n\nthere is no path from a source to other sources through water ways.", "constraint": "Judge data contains at most 60 data sets.\n\n3 <= H, W <= 10\n\n1 <= the number of sources, the number of cities <= 8\n\nThe map is surrounded by obstacles.\n\nSources are not adjacent each other(on the left, right, top and bottom)\n\nThere is a solution.", "input": "The input consists of multiple datasets. Each dataset consists of:\n\nH W\nH * W characters\n\nThe integers H and W are the numbers of rows and columns of the map. H * W characters denote the cells which contain:\n\n'P': source\n\n'*': city\n\n'. ': flatland\n\n'#': obstacle\nThe end of input is indicated by a line containing two zeros separated by a space.", "output": "For each dataset, print the minimum cost to construct the water ways.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 8\n########\n#P....*#\n########\n10 10\n##########\n#P.......#\n#..#*....#\n#..#*.#.*#\n#.....#*.#\n#*.......#\n#..##....#\n#...#.P..#\n#P......P#\n##########\n0 0\n output: 5\n14"], "Pid": "p00611", "ProblemText": "Task Description: In ancient times, Romans constructed numerous water ways to supply water to cities and industrial sites. These water ways were amongst the greatest engineering feats of the ancient world.\n\nThese water ways contributed to social infrastructures which improved people's quality of life. On the other hand, problems related to the water control and the water facilities are still interesting as a lot of games of water ways construction have been developed.\n\nYour task is to write a program which reads a map and computes the minimum possible cost of constructing water ways from sources to all the cities.\n\nAs shown in Figure 1, the map is represented by H * W grid cells, where each cell represents source, city, flatland, or obstacle.\n\nYou can construct only one water way from a source, but there are no limitations on the length of that water way and it can provide water to any number of cities located on its path. You can not construct water ways on the obstacles.\n\nYour objective is to bring water to all the city and minimize the number of cells which represent water ways. In the Figure 1, water ways are constructed in 14 cells which is the minimum cost.\n\nThe water ways must satisfy the following conditions:\n\na water way cell is adjacent to at most 2 water way cells in four cardinal points.\n\na source cell is adjacent to at most 1 water way cell in four cardinal points.\n\nthere is no path from a source to other sources through water ways.\nTask Constraint: Judge data contains at most 60 data sets.\n\n3 <= H, W <= 10\n\n1 <= the number of sources, the number of cities <= 8\n\nThe map is surrounded by obstacles.\n\nSources are not adjacent each other(on the left, right, top and bottom)\n\nThere is a solution.\nTask Input: The input consists of multiple datasets. Each dataset consists of:\n\nH W\nH * W characters\n\nThe integers H and W are the numbers of rows and columns of the map. H * W characters denote the cells which contain:\n\n'P': source\n\n'*': city\n\n'. ': flatland\n\n'#': obstacle\nThe end of input is indicated by a line containing two zeros separated by a space.\nTask Output: For each dataset, print the minimum cost to construct the water ways.\nTask Samples: input: 3 8\n########\n#P....*#\n########\n10 10\n##########\n#P.......#\n#..#*....#\n#..#*.#.*#\n#.....#*.#\n#*.......#\n#..##....#\n#...#.P..#\n#P......P#\n##########\n0 0\n output: 5\n14\n\n" }, { "title": "Problem H: Hedro's Hexahedron", "content": "Dr. Hedro is astonished. According to his theory, we can make sludge that can dissolve almost everything on the earth. Now he's trying to produce the sludge to verify his theory.\n\nThe sludge is produced in a rectangular solid shaped tank whose size is N * N * 2. Let coordinate of two corner points of tank be (-N/2, -N/2, -1), (N/2, N/2,1) as shown in Figure 1.\nFigure 1\n\n Doctor pours liquid that is ingredient of the sludge until height of the liquid becomes 1. Next, he get a lid on a tank and rotates slowly, without ruffling, with respect to z axis (Figure 2). After rotating enough long time, sludge is produced. Volume of liquid never changes through this operation.\nFigure 2\n\nNeedless to say, ordinary materials cannot be the tank. According to Doctor's theory, there is only one material that is not dissolved by the sludge on the earth. Doctor named it finaldefenceproblem (for short, FDP). To attach FDP tiles inside the tank allows to produce the sludge.\n\nSince to produce FDP is very difficult, the size of FDP tiles are limited to 1 * 1. At first, doctor tried to cover entire the entire inside of the tank. However, it turned out that to make enough number FDP tiles that can cover completely is impossible because it takes too long time. Therefore, he decided to replace FDP tiles where an area the sludge touches is zero with those of ordinary materials. All tiles are very thin, so never affects height of the sludge.\n\nHow many number of FDP tiles does doctor need? He has imposed this tough problem on you, his helper.", "constraint": "Judge data consists of at most 150 datasets.\n\n2 <= N <= 10^12\n\nN is even number", "input": "Input file contains several data sets.\nEach data set has one integer that describes N.\n\nInput ends when N = 0. You should output nothing for this case.", "output": "For each data set, print the number of tiles in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n4\n0\n output: 24\n64"], "Pid": "p00612", "ProblemText": "Task Description: Dr. Hedro is astonished. According to his theory, we can make sludge that can dissolve almost everything on the earth. Now he's trying to produce the sludge to verify his theory.\n\nThe sludge is produced in a rectangular solid shaped tank whose size is N * N * 2. Let coordinate of two corner points of tank be (-N/2, -N/2, -1), (N/2, N/2,1) as shown in Figure 1.\nFigure 1\n\n Doctor pours liquid that is ingredient of the sludge until height of the liquid becomes 1. Next, he get a lid on a tank and rotates slowly, without ruffling, with respect to z axis (Figure 2). After rotating enough long time, sludge is produced. Volume of liquid never changes through this operation.\nFigure 2\n\nNeedless to say, ordinary materials cannot be the tank. According to Doctor's theory, there is only one material that is not dissolved by the sludge on the earth. Doctor named it finaldefenceproblem (for short, FDP). To attach FDP tiles inside the tank allows to produce the sludge.\n\nSince to produce FDP is very difficult, the size of FDP tiles are limited to 1 * 1. At first, doctor tried to cover entire the entire inside of the tank. However, it turned out that to make enough number FDP tiles that can cover completely is impossible because it takes too long time. Therefore, he decided to replace FDP tiles where an area the sludge touches is zero with those of ordinary materials. All tiles are very thin, so never affects height of the sludge.\n\nHow many number of FDP tiles does doctor need? He has imposed this tough problem on you, his helper.\nTask Constraint: Judge data consists of at most 150 datasets.\n\n2 <= N <= 10^12\n\nN is even number\nTask Input: Input file contains several data sets.\nEach data set has one integer that describes N.\n\nInput ends when N = 0. You should output nothing for this case.\nTask Output: For each data set, print the number of tiles in a line.\nTask Samples: input: 2\n4\n0\n output: 24\n64\n\n" }, { "title": "Problem I: A Piece of Cake", "content": "In the city, there are two pastry shops. One shop was very popular because its cakes are pretty tasty. \nHowever, there was a man who is displeased at the shop. He was an owner of another shop. Although cause of his shop's unpopularity is incredibly awful taste of its cakes, he never improved it. He was just growing hate, ill, envy, and jealousy.\n\nFinally, he decided to vandalize the rival.\n\nHis vandalize is to mess up sales record of cakes. The rival shop sells K kinds of cakes and sales quantity is recorded for each kind. He calculates sum of sales quantities for all pairs of cakes. Getting K(K-1)/2 numbers, then he rearranges them randomly, and replace an original sales record with them.\n\nAn owner of the rival shop is bothered. Could you write, at least, a program that finds total sales quantity of all cakes for the pitiful owner?", "constraint": "Judge data contains at most 100 data sets.\n\n2 <= K <= 100\n\n0 <= c_i <= 100", "input": "Input file contains several data sets.\nA single data set has following format:\n\nK\nc_1 c_2 . . . c_K*(K-1)/2\n\nK is an integer that denotes how many kinds of cakes are sold. c_i is an integer that denotes a number written on the card.\n\nThe end of input is denoted by a case where K = 0. You should output nothing for this case.", "output": "For each data set, output the total sales quantity in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n2\n3\n5 4 3\n0\n output: 2\n6"], "Pid": "p00613", "ProblemText": "Task Description: In the city, there are two pastry shops. One shop was very popular because its cakes are pretty tasty. \nHowever, there was a man who is displeased at the shop. He was an owner of another shop. Although cause of his shop's unpopularity is incredibly awful taste of its cakes, he never improved it. He was just growing hate, ill, envy, and jealousy.\n\nFinally, he decided to vandalize the rival.\n\nHis vandalize is to mess up sales record of cakes. The rival shop sells K kinds of cakes and sales quantity is recorded for each kind. He calculates sum of sales quantities for all pairs of cakes. Getting K(K-1)/2 numbers, then he rearranges them randomly, and replace an original sales record with them.\n\nAn owner of the rival shop is bothered. Could you write, at least, a program that finds total sales quantity of all cakes for the pitiful owner?\nTask Constraint: Judge data contains at most 100 data sets.\n\n2 <= K <= 100\n\n0 <= c_i <= 100\nTask Input: Input file contains several data sets.\nA single data set has following format:\n\nK\nc_1 c_2 . . . c_K*(K-1)/2\n\nK is an integer that denotes how many kinds of cakes are sold. c_i is an integer that denotes a number written on the card.\n\nThe end of input is denoted by a case where K = 0. You should output nothing for this case.\nTask Output: For each data set, output the total sales quantity in one line.\nTask Samples: input: 2\n2\n3\n5 4 3\n0\n output: 2\n6\n\n" }, { "title": "Problem J: ICPC: Ideal Coin Payment and Change", "content": "Taro, a boy who hates any inefficiencies, pays coins so that the number of coins to be returned as change is minimized in order to do smoothly when he buys something.\n\nOne day, however, he doubt if this way is really efficient. When he pays more number of coins, a clerk consumes longer time to find the total value. Maybe he should pay with least possible number of coins.\n\nThinking for a while, he has decided to take the middle course. So he tries to minimize total number of paid coins and returned coins as change.\n\nNow he is going to buy a product of P yen having several coins. Since he is not good at calculation, please write a program that computes the minimal number of coins.\n\nYou may assume following things:\n\nThere are 6 kinds of coins, 1 yen, 5 yen, 10 yen, 50 yen, 100 yen and 500 yen.\n\nThe total value of coins he has is at least P yen.\n\nA clerk will return the change with least number of coins.", "constraint": "Judge data contains at most 100 data sets.\n\n0 <= N_i <= 1000", "input": "Input file contains several data sets.\nOne data set has following format:\n\nP N_1 N_5 N_10 N_50 N_100 N_500\n\nN_i is an integer and is the number of coins of i yen that he have.\n\nThe end of input is denoted by a case where P = 0. You should output nothing for this data set.", "output": "Output total number of coins that are paid and are returned.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 123 3 0 2 0 1 1\n999 9 9 9 9 9 9\n0 0 0 0 0 0 0\n output: 6\n3"], "Pid": "p00614", "ProblemText": "Task Description: Taro, a boy who hates any inefficiencies, pays coins so that the number of coins to be returned as change is minimized in order to do smoothly when he buys something.\n\nOne day, however, he doubt if this way is really efficient. When he pays more number of coins, a clerk consumes longer time to find the total value. Maybe he should pay with least possible number of coins.\n\nThinking for a while, he has decided to take the middle course. So he tries to minimize total number of paid coins and returned coins as change.\n\nNow he is going to buy a product of P yen having several coins. Since he is not good at calculation, please write a program that computes the minimal number of coins.\n\nYou may assume following things:\n\nThere are 6 kinds of coins, 1 yen, 5 yen, 10 yen, 50 yen, 100 yen and 500 yen.\n\nThe total value of coins he has is at least P yen.\n\nA clerk will return the change with least number of coins.\nTask Constraint: Judge data contains at most 100 data sets.\n\n0 <= N_i <= 1000\nTask Input: Input file contains several data sets.\nOne data set has following format:\n\nP N_1 N_5 N_10 N_50 N_100 N_500\n\nN_i is an integer and is the number of coins of i yen that he have.\n\nThe end of input is denoted by a case where P = 0. You should output nothing for this data set.\nTask Output: Output total number of coins that are paid and are returned.\nTask Samples: input: 123 3 0 2 0 1 1\n999 9 9 9 9 9 9\n0 0 0 0 0 0 0\n output: 6\n3\n\n" }, { "title": "Problem A: Traffic Analysis", "content": "There are two cameras which observe the up line and the down line respectively on the double lane (please see the following figure). These cameras are located on a line perpendicular to the lane, and we call the line 'monitoring line. ' (the red line in the figure)\n\nMonitoring systems are connected to the cameras respectively.\nWhen a car passes through the monitoring line, the corresponding monitoring system records elapsed time (sec) from the start of monitoring.\n\nYour task is to write a program which reads records of the two monitoring systems and prints the maximum time interval where cars did not pass through the monitoring line.\n\nThe two monitoring system start monitoring simultaneously. The end of monitoring is indicated by the latest time in the records.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset consists of:\n\nn m\ntl_1 tl_2 . . . tl_n\ntr_1 tr_2 . . . tr_m\n\nn, m are integers which represent the number of cars passed through monitoring line on the up line and the down line respectively. tl_i, tr_i are integers which denote the elapsed time when i-th car passed through the monitoring line for the up line and the down line respectively. You can assume that tl_1 < tl_2 < . . . < tl_n、 tr_1 < tr_2 < . . . < tr_m.\n\nYou can also assume that n, m <= 10000, and 1 <= tl_i, tr_i <= 1,000,000.\n\nThe end of input is indicated by a line including two zero.", "output": "For each dataset, print the maximum value in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 5\n20 35 60 70\n15 30 40 80 90\n3 2\n10 20 30\n42 60\n0 1\n100\n1 1\n10\n50\n0 0\n output: 20\n18\n100\n40"], "Pid": "p00615", "ProblemText": "Task Description: There are two cameras which observe the up line and the down line respectively on the double lane (please see the following figure). These cameras are located on a line perpendicular to the lane, and we call the line 'monitoring line. ' (the red line in the figure)\n\nMonitoring systems are connected to the cameras respectively.\nWhen a car passes through the monitoring line, the corresponding monitoring system records elapsed time (sec) from the start of monitoring.\n\nYour task is to write a program which reads records of the two monitoring systems and prints the maximum time interval where cars did not pass through the monitoring line.\n\nThe two monitoring system start monitoring simultaneously. The end of monitoring is indicated by the latest time in the records.\nTask Input: The input consists of multiple datasets. Each dataset consists of:\n\nn m\ntl_1 tl_2 . . . tl_n\ntr_1 tr_2 . . . tr_m\n\nn, m are integers which represent the number of cars passed through monitoring line on the up line and the down line respectively. tl_i, tr_i are integers which denote the elapsed time when i-th car passed through the monitoring line for the up line and the down line respectively. You can assume that tl_1 < tl_2 < . . . < tl_n、 tr_1 < tr_2 < . . . < tr_m.\n\nYou can also assume that n, m <= 10000, and 1 <= tl_i, tr_i <= 1,000,000.\n\nThe end of input is indicated by a line including two zero.\nTask Output: For each dataset, print the maximum value in a line.\nTask Samples: input: 4 5\n20 35 60 70\n15 30 40 80 90\n3 2\n10 20 30\n42 60\n0 1\n100\n1 1\n10\n50\n0 0\n output: 20\n18\n100\n40\n\n" }, { "title": "Problem A: Citation Format", "content": "To write a research paper, you should definitely follow the structured format. This format, in many cases, is strictly defined, and students who try to write their papers have a hard time with it.\n\nOne of such formats is related to citations. If you refer several pages of a material, you should enumerate their page numbers in ascending order. However, enumerating many page numbers waste space, so you should use the following abbreviated notation:\n\nWhen you refer all pages between page a and page b (a < b), you must use the notation \"a-b\". For example, when you refer pages 1,2,3,4, you must write \"1-4\" not \"1 2 3 4\". You must not write, for example, \"1-2 3-4\", \"1-3 4\", \"1-3 2-4\" and so on. When you refer one page and do not refer the previous and the next page of that page, you can write just the number of that page, but you must follow the notation when you refer successive pages (more than or equal to 2). Typically, commas are used to separate page numbers, in this problem we use space to separate the page numbers.\n\nYou, a kind senior, decided to write a program which generates the abbreviated notation for your junior who struggle with the citation.", "constraint": "1 <= n <= 50", "input": "Input consists of several datasets.\n\nThe first line of the dataset indicates the number of pages n.\n\nNext line consists of n integers. These integers are arranged in ascending order and they are differ from each other.\n\nInput ends when n = 0.", "output": "For each dataset, output the abbreviated notation in a line. Your program should not print extra space. Especially, be careful about the space at the end of line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 5 6\n3\n7 8 9\n0\n output: 1-3 5-6\n7-9"], "Pid": "p00637", "ProblemText": "Task Description: To write a research paper, you should definitely follow the structured format. This format, in many cases, is strictly defined, and students who try to write their papers have a hard time with it.\n\nOne of such formats is related to citations. If you refer several pages of a material, you should enumerate their page numbers in ascending order. However, enumerating many page numbers waste space, so you should use the following abbreviated notation:\n\nWhen you refer all pages between page a and page b (a < b), you must use the notation \"a-b\". For example, when you refer pages 1,2,3,4, you must write \"1-4\" not \"1 2 3 4\". You must not write, for example, \"1-2 3-4\", \"1-3 4\", \"1-3 2-4\" and so on. When you refer one page and do not refer the previous and the next page of that page, you can write just the number of that page, but you must follow the notation when you refer successive pages (more than or equal to 2). Typically, commas are used to separate page numbers, in this problem we use space to separate the page numbers.\n\nYou, a kind senior, decided to write a program which generates the abbreviated notation for your junior who struggle with the citation.\nTask Constraint: 1 <= n <= 50\nTask Input: Input consists of several datasets.\n\nThe first line of the dataset indicates the number of pages n.\n\nNext line consists of n integers. These integers are arranged in ascending order and they are differ from each other.\n\nInput ends when n = 0.\nTask Output: For each dataset, output the abbreviated notation in a line. Your program should not print extra space. Especially, be careful about the space at the end of line.\nTask Samples: input: 5\n1 2 3 5 6\n3\n7 8 9\n0\n output: 1-3 5-6\n7-9\n\n" }, { "title": "Problem B: Old Bridges", "content": "Long long ago, there was a thief. Looking for treasures, he was running about all over the world. One day, he heard a rumor that there were islands that had large amount of treasures, so he decided to head for there.\n\nFinally he found n islands that had treasures and one island that had nothing. Most of islands had seashore and he can land only on an island which had nothing. He walked around the island and found that there was an old bridge between this island and each of all other n islands.\n\nHe tries to visit all islands one by one and pick all the treasures up. Since he is afraid to be stolen, he visits with bringing all treasures that he has picked up. He is a strong man and can bring all the treasures at a time, but the old bridges will break if he cross it with taking certain or more amount of treasures.\n\nPlease write a program that judges if he can collect all the treasures and can be back to the island where he land on by properly selecting an order of his visit.", "constraint": "1 <= n <= 25", "input": "Input consists of several datasets.\n\nThe first line of each dataset contains an integer n.\nNext n lines represents information of the islands. Each line has two integers, which means the amount of treasures of the island and the maximal amount that he can take when he crosses the bridge to the islands, respectively.\n\nThe end of input is represented by a case with n = 0.", "output": "For each dataset, if he can collect all the treasures and can be back, print \"Yes\" Otherwise print \"No\"", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3\n3 6\n1 2\n3\n2 3\n3 5\n1 2\n0\n output: Yes\nNo"], "Pid": "p00638", "ProblemText": "Task Description: Long long ago, there was a thief. Looking for treasures, he was running about all over the world. One day, he heard a rumor that there were islands that had large amount of treasures, so he decided to head for there.\n\nFinally he found n islands that had treasures and one island that had nothing. Most of islands had seashore and he can land only on an island which had nothing. He walked around the island and found that there was an old bridge between this island and each of all other n islands.\n\nHe tries to visit all islands one by one and pick all the treasures up. Since he is afraid to be stolen, he visits with bringing all treasures that he has picked up. He is a strong man and can bring all the treasures at a time, but the old bridges will break if he cross it with taking certain or more amount of treasures.\n\nPlease write a program that judges if he can collect all the treasures and can be back to the island where he land on by properly selecting an order of his visit.\nTask Constraint: 1 <= n <= 25\nTask Input: Input consists of several datasets.\n\nThe first line of each dataset contains an integer n.\nNext n lines represents information of the islands. Each line has two integers, which means the amount of treasures of the island and the maximal amount that he can take when he crosses the bridge to the islands, respectively.\n\nThe end of input is represented by a case with n = 0.\nTask Output: For each dataset, if he can collect all the treasures and can be back, print \"Yes\" Otherwise print \"No\"\nTask Samples: input: 3\n2 3\n3 6\n1 2\n3\n2 3\n3 5\n1 2\n0\n output: Yes\nNo\n\n" }, { "title": "Problem C: Accelerated Railgun", "content": "She catched the thrown coin that draws parabolic curve with her sparkling fingers. She is an ESPer. Yes, she is an electro-master who has the third strongest power among more than one million ESPers in the city. Being flicked by her thumb, the coin is accelerated by electromagnetic force and is shot as Fleming's right-hand rule. Even if she holds back the initial velocity of the coin exceeds three times of the speed of sound. The coin that is shot in such velocity is heated because of air friction and adiabatic compression. As a result coin melts and shines in orange. This is her special ability, called railgun. The strength of railgun can make a hole of two meters in diameter on a concrete wall.\n\nShe had defeated criminals such as post office robberies and bank robberies in the city with her ability. And today, she decided to destroy a laboratory that is suspected to making some inhumane experiments on human body. Only her railgun can shoot it.\n\nThe railgun with a coin cannot destroy the laboratory because of lack of power. Since she have found a powered-suit nearby, so she decided to use it as a projectile. However, in this case it is difficult to take sight properly because the suit is much bigger and heavier than coins. Therefore she only can shoot the suit with certain velocity vector from her current position. Depending on the position of the laboratory, her railgun may not hit it and become a firework.\n\nTherefore she asked cooperation to the strongest ESPer in the city. He can change direction of a moving object as one of uncountable application of his ESP. Let's consider a 2-dimensional plane where the laboratory is on the origin (0,0). She shoots a projectile from P = (px, py) with velocity vector V = (vx, vy). His ESP makes a virtual wall of radius R (= 1.0) centered on the origin. When projectile collides with the wall, it is reflected so that incident angle will be equal to reflection angle.\n\nRange of railgun is limited to D, because air friction decreases velocity of projectile and heat may melts projectile completely. Under these conditions, please write a program that judges if the railgun hits the laboratory. Size of the laboratory and the suit is ignorablly small. After the railgun is shot, it is allowed to pass through P again.", "constraint": "Judge data never include dataset where the answer is (D - 1.0e-3) or bigger. \n\n0.0001 <= |V| <= 0.9999\n\n0.0001 <= |P| <= 0.9999\n\nD <= 50", "input": "Input consists of several datasets.\n\nThe first line of each dataset contains a real number D.\n\nNext line contains 4 real numbers, which means px, py, vx, vy, respectively.\n\nInput terminates when D = 0.", "output": "For each dataset, if the railgun hits, output the distance it moved until hits. Otherwise output 'impossible' (without quotes).\n\nYou can print any number of digits and answer with an error less than 1.0e-6 will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10.0\n0.5 0.0 -0.2 0.0\n1.0\n0.1 0.0 0.2 0.2\n0\n output: 0.50000000\nimpossible"], "Pid": "p00639", "ProblemText": "Task Description: She catched the thrown coin that draws parabolic curve with her sparkling fingers. She is an ESPer. Yes, she is an electro-master who has the third strongest power among more than one million ESPers in the city. Being flicked by her thumb, the coin is accelerated by electromagnetic force and is shot as Fleming's right-hand rule. Even if she holds back the initial velocity of the coin exceeds three times of the speed of sound. The coin that is shot in such velocity is heated because of air friction and adiabatic compression. As a result coin melts and shines in orange. This is her special ability, called railgun. The strength of railgun can make a hole of two meters in diameter on a concrete wall.\n\nShe had defeated criminals such as post office robberies and bank robberies in the city with her ability. And today, she decided to destroy a laboratory that is suspected to making some inhumane experiments on human body. Only her railgun can shoot it.\n\nThe railgun with a coin cannot destroy the laboratory because of lack of power. Since she have found a powered-suit nearby, so she decided to use it as a projectile. However, in this case it is difficult to take sight properly because the suit is much bigger and heavier than coins. Therefore she only can shoot the suit with certain velocity vector from her current position. Depending on the position of the laboratory, her railgun may not hit it and become a firework.\n\nTherefore she asked cooperation to the strongest ESPer in the city. He can change direction of a moving object as one of uncountable application of his ESP. Let's consider a 2-dimensional plane where the laboratory is on the origin (0,0). She shoots a projectile from P = (px, py) with velocity vector V = (vx, vy). His ESP makes a virtual wall of radius R (= 1.0) centered on the origin. When projectile collides with the wall, it is reflected so that incident angle will be equal to reflection angle.\n\nRange of railgun is limited to D, because air friction decreases velocity of projectile and heat may melts projectile completely. Under these conditions, please write a program that judges if the railgun hits the laboratory. Size of the laboratory and the suit is ignorablly small. After the railgun is shot, it is allowed to pass through P again.\nTask Constraint: Judge data never include dataset where the answer is (D - 1.0e-3) or bigger. \n\n0.0001 <= |V| <= 0.9999\n\n0.0001 <= |P| <= 0.9999\n\nD <= 50\nTask Input: Input consists of several datasets.\n\nThe first line of each dataset contains a real number D.\n\nNext line contains 4 real numbers, which means px, py, vx, vy, respectively.\n\nInput terminates when D = 0.\nTask Output: For each dataset, if the railgun hits, output the distance it moved until hits. Otherwise output 'impossible' (without quotes).\n\nYou can print any number of digits and answer with an error less than 1.0e-6 will be accepted.\nTask Samples: input: 10.0\n0.5 0.0 -0.2 0.0\n1.0\n0.1 0.0 0.2 0.2\n0\n output: 0.50000000\nimpossible\n\n" }, { "title": "Problem D: Distorted Love", "content": "Saying that it is not surprising that people want to know about their love, she has checked up his address, name, age, phone number, hometown, medical history, political party and even his sleeping position, every piece of his personal information. The word \"privacy\" is not in her dictionary. A person like her is called \"stoker\" or \"yandere\", but it doesn't mean much to her.\n\nTo know about him, she set up spyware to his PC. This spyware can record his mouse operations while he is browsing websites. After a while, she could successfully obtain the record from the spyware in absolute secrecy.\n\nWell, we want you to write a program which extracts web pages he visited from the records.\n\nAll pages have the same size H * W where upper-left corner is (0,0) and lower right corner is (W, H). A page includes several (or many) rectangular buttons (parallel to the page). Each button has a link to another page, and when a button is clicked the browser leads you to the corresponding page.\n\nHis browser manages history and the current page in the following way:\n\nThe browser has a buffer of 1-dimensional array with enough capacity to store pages, and a pointer to indicate a page in the buffer. A page indicated by the pointer is shown on the browser. At first, a predetermined page is stored and the pointer indicates that page. When the link button is clicked, all pages recorded in the right side from the pointer are removed from the buffer. Then, the page indicated by the link button is stored into the right-most position of the buffer, and the pointer moves to right. As a result, the user browse the page indicated by the button.\n\nThe browser also has special buttons 'back to the previous page' (back button) and 'forward to the next page' (forward button). When the user clicks the back button, the pointer moves to left, and the user clicks the forward button, the pointer moves to right. But in both cases, if there are no such pages in the buffer, nothing happen.\n\nThe record consists of the following operations:\n\nclick x y\n\nIt means to click (x, y). If there is a button on the point (x, y), he moved to the corresponding page. If there is nothing in the point, nothing happen. The button is clicked if x1 <= x <= x2 and y1 <= y <= y2 where x1, x2 means the leftmost and rightmost coordinate and y1, y2 means the topmost and bottommost coordinate of the corresponding button respectively.\n\nback\n\nIt means to click the Back button.\n\nforward\n\nIt means to click the Forward button.\n\nIn addition, there is a special operation show. Your program should print the name of current page for each show operation.\n\nBy the way, setting spyware into computers of others may conflict with the law. Do not attempt, or you will be reprimanded by great men.", "constraint": "1 <= n <= 100\n\nb[i] <= 100\n\n1 <= the number of characters in the name <= 20\n\nButtons are not touch, overlapped nor run over from the browser.", "input": "Input consists of several datasets.\n\nEach dataset starts with an integer n which represents the number of pages in the dataset.\n\nNext line contains two integers W and H.\n\nNext, information of each page are given. Each page starts with a string of characters and b[i], the number of buttons the page has. Following b[i] lines give information of buttons. Each button consists of four integers representing the coordinate (x1, y1) of upper left corner and the coordinate (x2, y2) of lower right corner of the button and a string of characters, which represents the name of page that the link of the button represents.\n\nNext, the number of operation m is given. Following m lines represent the record of operations. Please see the above description for the operation.\n\nThe first page is stored in the buffer at first.\n\nInput ends when n = 0.", "output": "For each dataset, output the name of current page for each show operation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n800 600\nindex 1\n500 100 700 200 profile\nprofile 2\n100 100 400 200 index\n100 400 400 500 link\nlink 1\n100 100 300 200 index\n9\nclick 600 150\nshow\nclick 200 450\nshow\nback\nback\nshow\nforward\nshow\n0\n output: profile\nlink\nindex\nprofile"], "Pid": "p00640", "ProblemText": "Task Description: Saying that it is not surprising that people want to know about their love, she has checked up his address, name, age, phone number, hometown, medical history, political party and even his sleeping position, every piece of his personal information. The word \"privacy\" is not in her dictionary. A person like her is called \"stoker\" or \"yandere\", but it doesn't mean much to her.\n\nTo know about him, she set up spyware to his PC. This spyware can record his mouse operations while he is browsing websites. After a while, she could successfully obtain the record from the spyware in absolute secrecy.\n\nWell, we want you to write a program which extracts web pages he visited from the records.\n\nAll pages have the same size H * W where upper-left corner is (0,0) and lower right corner is (W, H). A page includes several (or many) rectangular buttons (parallel to the page). Each button has a link to another page, and when a button is clicked the browser leads you to the corresponding page.\n\nHis browser manages history and the current page in the following way:\n\nThe browser has a buffer of 1-dimensional array with enough capacity to store pages, and a pointer to indicate a page in the buffer. A page indicated by the pointer is shown on the browser. At first, a predetermined page is stored and the pointer indicates that page. When the link button is clicked, all pages recorded in the right side from the pointer are removed from the buffer. Then, the page indicated by the link button is stored into the right-most position of the buffer, and the pointer moves to right. As a result, the user browse the page indicated by the button.\n\nThe browser also has special buttons 'back to the previous page' (back button) and 'forward to the next page' (forward button). When the user clicks the back button, the pointer moves to left, and the user clicks the forward button, the pointer moves to right. But in both cases, if there are no such pages in the buffer, nothing happen.\n\nThe record consists of the following operations:\n\nclick x y\n\nIt means to click (x, y). If there is a button on the point (x, y), he moved to the corresponding page. If there is nothing in the point, nothing happen. The button is clicked if x1 <= x <= x2 and y1 <= y <= y2 where x1, x2 means the leftmost and rightmost coordinate and y1, y2 means the topmost and bottommost coordinate of the corresponding button respectively.\n\nback\n\nIt means to click the Back button.\n\nforward\n\nIt means to click the Forward button.\n\nIn addition, there is a special operation show. Your program should print the name of current page for each show operation.\n\nBy the way, setting spyware into computers of others may conflict with the law. Do not attempt, or you will be reprimanded by great men.\nTask Constraint: 1 <= n <= 100\n\nb[i] <= 100\n\n1 <= the number of characters in the name <= 20\n\nButtons are not touch, overlapped nor run over from the browser.\nTask Input: Input consists of several datasets.\n\nEach dataset starts with an integer n which represents the number of pages in the dataset.\n\nNext line contains two integers W and H.\n\nNext, information of each page are given. Each page starts with a string of characters and b[i], the number of buttons the page has. Following b[i] lines give information of buttons. Each button consists of four integers representing the coordinate (x1, y1) of upper left corner and the coordinate (x2, y2) of lower right corner of the button and a string of characters, which represents the name of page that the link of the button represents.\n\nNext, the number of operation m is given. Following m lines represent the record of operations. Please see the above description for the operation.\n\nThe first page is stored in the buffer at first.\n\nInput ends when n = 0.\nTask Output: For each dataset, output the name of current page for each show operation.\nTask Samples: input: 3\n800 600\nindex 1\n500 100 700 200 profile\nprofile 2\n100 100 400 200 index\n100 400 400 500 link\nlink 1\n100 100 300 200 index\n9\nclick 600 150\nshow\nclick 200 450\nshow\nback\nback\nshow\nforward\nshow\n0\n output: profile\nlink\nindex\nprofile\n\n" }, { "title": "Problem E: Huge Family", "content": "Mr. Dango's family has extremely huge number of members. Once it had about 100 members, and now it has as many as population of a city. It is jokingly guessed that the member might fill this planet in near future. They all have warm and gracious personality and are close each other.\n\nThey usually communicate by a phone. Of course, They are all taking a family plan. This family plan is such a thing: when a choose b, and b choose a as a partner, a family plan can be applied between them and then the calling fee per unit time between them discounted to f(a, b), which is cheaper than a default fee. Each person can apply a family plan at most 2 times, but no same pair of persons can apply twice. Now, choosing their partner appropriately, all members of Mr. Dango's family applied twice.\n\nSince there are huge number of people, it is very difficult to send a message to all family members by a phone call. Mr. Dang have decided to make a phone calling network that is named 'clan' using the family plan. Let us present a definition of clan.\n\nLet S be an any subset of all phone calls that family plan is applied. Clan is S such that:\n\n For any two persons (let them be i and j), if i can send a message to j through phone calls that family plan is applied (directly or indirectly), then i can send a message to j through only phone calls in S (directly or indirectly).\n\n Meets condition 1 and a sum of the calling fee per unit time in S is minimized.\n\nClan allows to send a message efficiently. For example, we suppose that one have sent a message through all calls related to him in the clan. Additionaly we suppose that every people follow a rule, \"when he/she receives a message through a call in clan, he/she relays the message all other neibors in respect to clan. \" Then, we can prove that this message will surely be derivered to every people that is connected by all discounted calls, and that the message will never be derivered two or more times to same person.\n\nBy the way, you are given information about application of family plan of Mr. Dango's family. Please write a program that calculates that in how many ways a different clan can be constructed. You should output the answer modulo 10007 because it may be very big.", "constraint": "3 <= n <= 100,000", "input": "The input consists of several datasets.\n\nThe first line of each dataset contains an integer n, which indicates the number of members in the family.\n\nNext n lines represents information of the i-th member with four integers. The first two integers respectively represent b[0] (the partner of i) and f(i, b[0]) (the calling fee per unit time between i and b[0]). The following two integers represent b[1] and f(i, b[1]) in the same manner.\n\nInput terminates with a dataset where n = 0.", "output": "For each dataset, output the number of clan modulo 10007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1 2 3\n0 1 2 2\n1 2 0 3\n7\n1 2 2 1\n0 2 3 2\n0 1 3 1\n2 1 1 2\n5 3 6 2\n4 3 6 1\n4 2 5 1\n0\n output: 1\n2"], "Pid": "p00641", "ProblemText": "Task Description: Mr. Dango's family has extremely huge number of members. Once it had about 100 members, and now it has as many as population of a city. It is jokingly guessed that the member might fill this planet in near future. They all have warm and gracious personality and are close each other.\n\nThey usually communicate by a phone. Of course, They are all taking a family plan. This family plan is such a thing: when a choose b, and b choose a as a partner, a family plan can be applied between them and then the calling fee per unit time between them discounted to f(a, b), which is cheaper than a default fee. Each person can apply a family plan at most 2 times, but no same pair of persons can apply twice. Now, choosing their partner appropriately, all members of Mr. Dango's family applied twice.\n\nSince there are huge number of people, it is very difficult to send a message to all family members by a phone call. Mr. Dang have decided to make a phone calling network that is named 'clan' using the family plan. Let us present a definition of clan.\n\nLet S be an any subset of all phone calls that family plan is applied. Clan is S such that:\n\n For any two persons (let them be i and j), if i can send a message to j through phone calls that family plan is applied (directly or indirectly), then i can send a message to j through only phone calls in S (directly or indirectly).\n\n Meets condition 1 and a sum of the calling fee per unit time in S is minimized.\n\nClan allows to send a message efficiently. For example, we suppose that one have sent a message through all calls related to him in the clan. Additionaly we suppose that every people follow a rule, \"when he/she receives a message through a call in clan, he/she relays the message all other neibors in respect to clan. \" Then, we can prove that this message will surely be derivered to every people that is connected by all discounted calls, and that the message will never be derivered two or more times to same person.\n\nBy the way, you are given information about application of family plan of Mr. Dango's family. Please write a program that calculates that in how many ways a different clan can be constructed. You should output the answer modulo 10007 because it may be very big.\nTask Constraint: 3 <= n <= 100,000\nTask Input: The input consists of several datasets.\n\nThe first line of each dataset contains an integer n, which indicates the number of members in the family.\n\nNext n lines represents information of the i-th member with four integers. The first two integers respectively represent b[0] (the partner of i) and f(i, b[0]) (the calling fee per unit time between i and b[0]). The following two integers represent b[1] and f(i, b[1]) in the same manner.\n\nInput terminates with a dataset where n = 0.\nTask Output: For each dataset, output the number of clan modulo 10007.\nTask Samples: input: 3\n1 1 2 3\n0 1 2 2\n1 2 0 3\n7\n1 2 2 1\n0 2 3 2\n0 1 3 1\n2 1 1 2\n5 3 6 2\n4 3 6 1\n4 2 5 1\n0\n output: 1\n2\n\n" }, { "title": "Problem F: Ben Toh", "content": "As usual, those who called wolves get together on 8 p. m. at the supermarket. The thing they want is only one, a box lunch that is labeled half price. Scrambling for a few discounted box lunch, they fiercely fight every day. And those who are blessed by hunger and appetite the best can acquire the box lunch, while others have to have cup ramen or something with tear in their eyes.\n\nA senior high school student, Sato, is one of wolves. A dormitry he lives doesn't serve a dinner, and his parents don't send so much money. Therefore he absolutely acquire the half-priced box lunch and save his money. Otherwise he have to give up comic books and video games, or begin part-time job.\n\nSince Sato is an excellent wolf, he can acquire the discounted box lunch in 100% probability on the first day. But on the next day, many other wolves cooperate to block him and the probability to get a box lunch will be 50%. Even though he can get, the probability to get will be 25% on the next day of the day. Likewise, if he gets a box lunch on a certain day, the probability to get on the next day will be half. Once he failed to get a box lunch, probability to get would be back to 100%.\n\nHe continue to go to supermaket and try to get the discounted box lunch for n days. Please write a program to computes the expected value of the number of the discounted box lunches he can acquire.", "constraint": "1 <= n <= 100,000", "input": "Input consists of several datasets.\n\nInput for a single dataset is given as a single integer n.\n\nInput terminates with a dataset where n = 0.", "output": "For each dataset, write a line that contains an expected value. You may print any number of digits after the decimal point. Answers that have an error less than 1.0e-2 will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n2\n3\n0\n output: 1.00000000\n1.50000000\n2.12500000"], "Pid": "p00642", "ProblemText": "Task Description: As usual, those who called wolves get together on 8 p. m. at the supermarket. The thing they want is only one, a box lunch that is labeled half price. Scrambling for a few discounted box lunch, they fiercely fight every day. And those who are blessed by hunger and appetite the best can acquire the box lunch, while others have to have cup ramen or something with tear in their eyes.\n\nA senior high school student, Sato, is one of wolves. A dormitry he lives doesn't serve a dinner, and his parents don't send so much money. Therefore he absolutely acquire the half-priced box lunch and save his money. Otherwise he have to give up comic books and video games, or begin part-time job.\n\nSince Sato is an excellent wolf, he can acquire the discounted box lunch in 100% probability on the first day. But on the next day, many other wolves cooperate to block him and the probability to get a box lunch will be 50%. Even though he can get, the probability to get will be 25% on the next day of the day. Likewise, if he gets a box lunch on a certain day, the probability to get on the next day will be half. Once he failed to get a box lunch, probability to get would be back to 100%.\n\nHe continue to go to supermaket and try to get the discounted box lunch for n days. Please write a program to computes the expected value of the number of the discounted box lunches he can acquire.\nTask Constraint: 1 <= n <= 100,000\nTask Input: Input consists of several datasets.\n\nInput for a single dataset is given as a single integer n.\n\nInput terminates with a dataset where n = 0.\nTask Output: For each dataset, write a line that contains an expected value. You may print any number of digits after the decimal point. Answers that have an error less than 1.0e-2 will be accepted.\nTask Samples: input: 1\n2\n3\n0\n output: 1.00000000\n1.50000000\n2.12500000\n\n" }, { "title": "Problem G: Rolling Dice", "content": "The north country is conquered by the great shogun-sama (which means\nking). Recently many beautiful dice which were made by order of the\ngreat shogun-sama were given to all citizens of the country. All\ncitizens received the beautiful dice with a tear of delight. Now they\nare enthusiastically playing a game with the dice.\n\nThe game is played on grid of h * w cells that each of which has a\nnumber, which is designed by the great shogun-sama's noble philosophy.\nA player put his die on a starting cell and move it to a destination\ncell with rolling the die. After rolling the die once, he takes a\npenalty which is multiple of the number written on current cell and\nthe number printed on a bottom face of the die, because of malicious\nconspiracy of an enemy country. Since the great shogun-sama strongly\nwishes, it is decided that the beautiful dice are initially put so\nthat 1 faces top, 2 faces south, and 3 faces east. You will find that\nthe number initially faces north is 5, as sum of numbers on opposite\nfaces of a die is always 7. Needless to say, idiots those who move his\ndie outside the grid are punished immediately.\n\nThe great shogun-sama is pleased if some citizens can move the\nbeautiful dice with the least penalty when a grid and a starting cell\nand a destination cell is given. Other citizens should be sent to coal\nmine (which may imply labor as slaves). Write a program so that\ncitizens can deal with the great shogun-sama's expectations.", "constraint": "1 <= h, w <= 10\n\n0 <= number assinged to a cell <= 9\n\nthe start point and the goal point are different.", "input": "The first line of each data set has two numbers h and w, which stands\nfor the number of rows and columns of the grid.\n\nNext h line has w integers, which stands for the number printed on the\ngrid. Top-left corner corresponds to northwest corner.\n\nRow number and column number of the starting cell are given in the\nfollowing line, and those of the destination cell are given in the next\nline. Rows and columns are numbered 0 to h-1,0 to w-1, respectively.\n\nInput terminates when h = w = 0.", "output": "For each dataset, output the least penalty.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2\n8 8\n0 0\n0 1\n3 3\n1 2 5\n2 8 3\n0 1 2\n0 0\n2 2\n3 3\n1 2 5\n2 8 3\n0 1 2\n0 0\n1 2\n2 2\n1 2\n3 4\n0 0\n0 1\n2 3\n1 2 3\n4 5 6\n0 0\n1 2\n0 0\n output: 24\n19\n17\n6\n21"], "Pid": "p00643", "ProblemText": "Task Description: The north country is conquered by the great shogun-sama (which means\nking). Recently many beautiful dice which were made by order of the\ngreat shogun-sama were given to all citizens of the country. All\ncitizens received the beautiful dice with a tear of delight. Now they\nare enthusiastically playing a game with the dice.\n\nThe game is played on grid of h * w cells that each of which has a\nnumber, which is designed by the great shogun-sama's noble philosophy.\nA player put his die on a starting cell and move it to a destination\ncell with rolling the die. After rolling the die once, he takes a\npenalty which is multiple of the number written on current cell and\nthe number printed on a bottom face of the die, because of malicious\nconspiracy of an enemy country. Since the great shogun-sama strongly\nwishes, it is decided that the beautiful dice are initially put so\nthat 1 faces top, 2 faces south, and 3 faces east. You will find that\nthe number initially faces north is 5, as sum of numbers on opposite\nfaces of a die is always 7. Needless to say, idiots those who move his\ndie outside the grid are punished immediately.\n\nThe great shogun-sama is pleased if some citizens can move the\nbeautiful dice with the least penalty when a grid and a starting cell\nand a destination cell is given. Other citizens should be sent to coal\nmine (which may imply labor as slaves). Write a program so that\ncitizens can deal with the great shogun-sama's expectations.\nTask Constraint: 1 <= h, w <= 10\n\n0 <= number assinged to a cell <= 9\n\nthe start point and the goal point are different.\nTask Input: The first line of each data set has two numbers h and w, which stands\nfor the number of rows and columns of the grid.\n\nNext h line has w integers, which stands for the number printed on the\ngrid. Top-left corner corresponds to northwest corner.\n\nRow number and column number of the starting cell are given in the\nfollowing line, and those of the destination cell are given in the next\nline. Rows and columns are numbered 0 to h-1,0 to w-1, respectively.\n\nInput terminates when h = w = 0.\nTask Output: For each dataset, output the least penalty.\nTask Samples: input: 1 2\n8 8\n0 0\n0 1\n3 3\n1 2 5\n2 8 3\n0 1 2\n0 0\n2 2\n3 3\n1 2 5\n2 8 3\n0 1 2\n0 0\n1 2\n2 2\n1 2\n3 4\n0 0\n0 1\n2 3\n1 2 3\n4 5 6\n0 0\n1 2\n0 0\n output: 24\n19\n17\n6\n21\n\n" }, { "title": "Problem H: Winter Bells", "content": "The best night ever in the world has come! It's 8 p. m. of December 24th, yes, the night of Cristmas Eve. Santa Clause comes to a silent city with ringing bells. Overtaking north wind, from a sleigh a reindeer pulls she shoot presents to soxes hanged near windows for children.\n\nThe sleigh she is on departs from a big christmas tree on the fringe of the city. Miracle power that the christmas tree spread over the sky like a web and form a paths that the sleigh can go on. Since the paths with thicker miracle power is easier to go, these paths can be expressed as undirected weighted graph.\n\nDerivering the present is very strict about time. When it begins dawning the miracle power rapidly weakens and Santa Clause can not continue derivering any more. Her pride as a Santa Clause never excuses such a thing, so she have to finish derivering before dawning.\n\nThe sleigh a reindeer pulls departs from christmas tree (which corresponds to 0th node), and go across the city to the opposite fringe (n-1 th node) along the shortest path. Santa Clause create presents from the miracle power and shoot them from the sleigh the reindeer pulls at his full power. If there are two or more shortest paths, the reindeer selects one of all shortest paths with equal probability and go along it.\n\nBy the way, in this city there are p children that wish to see Santa Clause and are looking up the starlit sky from their home. Above the i-th child's home there is a cross point of the miracle power that corresponds to c[i]-th node of the graph. The child can see Santa Clause if (and only if) Santa Clause go through the node.\n\nPlease find the probability that each child can see Santa Clause.", "constraint": "3 <= n <= 100\n\nThere are no parallel edges and a edge whose end points are identical.\n\n 0 < weight of the edge < 10000", "input": "Input consists of several datasets.\n\nThe first line of each dataset contains three integers n, m, p, which means the number of nodes and edges of the graph, and the number of the children. Each node are numbered 0 to n-1.\n\nFollowing m lines contains information about edges. Each line has three integers. The first two integers means nodes on two endpoints of the edge. The third one is weight of the edge.\n\nNext p lines represent c[i] respectively.\n\nInput terminates when n = m = p = 0.", "output": "For each dataset, output p decimal values in same order as input. Write a blank line after that.\n\nYou may output any number of digit and may contain an error less than 1.0e-6.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 1\n0 1 2\n1 2 3\n1\n4 5 2\n0 1 1\n0 2 1\n1 2 1\n1 3 1\n2 3 1\n1\n2\n0 0 0\n output: 1.00000000\n\n0.50000000\n0.50000000"], "Pid": "p00644", "ProblemText": "Task Description: The best night ever in the world has come! It's 8 p. m. of December 24th, yes, the night of Cristmas Eve. Santa Clause comes to a silent city with ringing bells. Overtaking north wind, from a sleigh a reindeer pulls she shoot presents to soxes hanged near windows for children.\n\nThe sleigh she is on departs from a big christmas tree on the fringe of the city. Miracle power that the christmas tree spread over the sky like a web and form a paths that the sleigh can go on. Since the paths with thicker miracle power is easier to go, these paths can be expressed as undirected weighted graph.\n\nDerivering the present is very strict about time. When it begins dawning the miracle power rapidly weakens and Santa Clause can not continue derivering any more. Her pride as a Santa Clause never excuses such a thing, so she have to finish derivering before dawning.\n\nThe sleigh a reindeer pulls departs from christmas tree (which corresponds to 0th node), and go across the city to the opposite fringe (n-1 th node) along the shortest path. Santa Clause create presents from the miracle power and shoot them from the sleigh the reindeer pulls at his full power. If there are two or more shortest paths, the reindeer selects one of all shortest paths with equal probability and go along it.\n\nBy the way, in this city there are p children that wish to see Santa Clause and are looking up the starlit sky from their home. Above the i-th child's home there is a cross point of the miracle power that corresponds to c[i]-th node of the graph. The child can see Santa Clause if (and only if) Santa Clause go through the node.\n\nPlease find the probability that each child can see Santa Clause.\nTask Constraint: 3 <= n <= 100\n\nThere are no parallel edges and a edge whose end points are identical.\n\n 0 < weight of the edge < 10000\nTask Input: Input consists of several datasets.\n\nThe first line of each dataset contains three integers n, m, p, which means the number of nodes and edges of the graph, and the number of the children. Each node are numbered 0 to n-1.\n\nFollowing m lines contains information about edges. Each line has three integers. The first two integers means nodes on two endpoints of the edge. The third one is weight of the edge.\n\nNext p lines represent c[i] respectively.\n\nInput terminates when n = m = p = 0.\nTask Output: For each dataset, output p decimal values in same order as input. Write a blank line after that.\n\nYou may output any number of digit and may contain an error less than 1.0e-6.\nTask Samples: input: 3 2 1\n0 1 2\n1 2 3\n1\n4 5 2\n0 1 1\n0 2 1\n1 2 1\n1 3 1\n2 3 1\n1\n2\n0 0 0\n output: 1.00000000\n\n0.50000000\n0.50000000\n\n" }, { "title": "Problem I: Mysterious Onslaught", "content": "In 2012, human beings have been exposed to fierce onslaught of unidentified mysterious extra-terrestrial creatures. We have exhaused because of the long war and can't regist against them any longer. Only you, an excellent wizard, can save us. Yes, it's time to stand up!\n\nThe enemies are dispatched to the earth with being aligned like an n * n square. Appearently some of them have already lost their fighting capabilities for some unexpected reason. You have invented a highest grade magic spell 'MYON' to defeat them all. An attack of this magic covers any rectangles (which is parallel to axis). Once you cast a spell \"myon, \" then all the enemies which the magic covers will lose their fighting capabilities because of tremendous power of the magic. However, the magic seems to activate enemies' self-repairing circuit. Therefore if any enemy which have already lost its fighting capability is exposed to the magic, the enemy repossesses its fighting capability. You will win the war when all the enemies will lose their fighting capabilities.\n\nLet me show an example. An array of enemies below have dispatched:\n\n1 1 1 1 1\n1 0 0 0 1\n1 0 1 0 1\n1 0 0 0 1\n1 1 1 1 1\n\nHere, '0' means an enemy that doesn't possess fighting capability, and '1' means an enemy that possesses.\nFirst, you cast a spell \"myon\" with covering all the enemies, which results in;\n \n0 0 0 0 0\n0 1 1 1 0\n0 1 0 1 0\n0 1 1 1 0\n0 0 0 0 0\n\nNext, cast once again with covering central 3 * 3 enemies.\n\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n\nNow you can defeat them all by casting a spell covers remaining one. Therefore you can cast \"myonmyonmyon, \" which is the shortest spell for this case.\n\nYou are given the information of the array. Please write a program that generates the shortest spell that can defeat them all.", "constraint": "1 <= n <= 5", "input": "The first line of each test case has an integer n. Following n lines are information of an array of enemies. The format is same as described in the problem statement.\n\nInput terminates when n = 0.\nYou may assume that one or more enemy have fighting capability.", "output": "For each dataset, output the shortest spell.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 1 1 1 1\n1 0 0 0 1\n1 0 1 0 1\n1 0 0 0 1\n1 1 1 1 1\n3\n1 1 1\n1 1 1\n1 1 1\n5\n1 1 1 1 0\n1 1 1 1 0\n1 0 0 0 1\n0 1 1 1 1\n0 1 1 1 1\n0\n output: myonmyonmyon\nmyon\nmyonmyon"], "Pid": "p00645", "ProblemText": "Task Description: In 2012, human beings have been exposed to fierce onslaught of unidentified mysterious extra-terrestrial creatures. We have exhaused because of the long war and can't regist against them any longer. Only you, an excellent wizard, can save us. Yes, it's time to stand up!\n\nThe enemies are dispatched to the earth with being aligned like an n * n square. Appearently some of them have already lost their fighting capabilities for some unexpected reason. You have invented a highest grade magic spell 'MYON' to defeat them all. An attack of this magic covers any rectangles (which is parallel to axis). Once you cast a spell \"myon, \" then all the enemies which the magic covers will lose their fighting capabilities because of tremendous power of the magic. However, the magic seems to activate enemies' self-repairing circuit. Therefore if any enemy which have already lost its fighting capability is exposed to the magic, the enemy repossesses its fighting capability. You will win the war when all the enemies will lose their fighting capabilities.\n\nLet me show an example. An array of enemies below have dispatched:\n\n1 1 1 1 1\n1 0 0 0 1\n1 0 1 0 1\n1 0 0 0 1\n1 1 1 1 1\n\nHere, '0' means an enemy that doesn't possess fighting capability, and '1' means an enemy that possesses.\nFirst, you cast a spell \"myon\" with covering all the enemies, which results in;\n \n0 0 0 0 0\n0 1 1 1 0\n0 1 0 1 0\n0 1 1 1 0\n0 0 0 0 0\n\nNext, cast once again with covering central 3 * 3 enemies.\n\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n\nNow you can defeat them all by casting a spell covers remaining one. Therefore you can cast \"myonmyonmyon, \" which is the shortest spell for this case.\n\nYou are given the information of the array. Please write a program that generates the shortest spell that can defeat them all.\nTask Constraint: 1 <= n <= 5\nTask Input: The first line of each test case has an integer n. Following n lines are information of an array of enemies. The format is same as described in the problem statement.\n\nInput terminates when n = 0.\nYou may assume that one or more enemy have fighting capability.\nTask Output: For each dataset, output the shortest spell.\nTask Samples: input: 5\n1 1 1 1 1\n1 0 0 0 1\n1 0 1 0 1\n1 0 0 0 1\n1 1 1 1 1\n3\n1 1 1\n1 1 1\n1 1 1\n5\n1 1 1 1 0\n1 1 1 1 0\n1 0 0 0 1\n0 1 1 1 1\n0 1 1 1 1\n0\n output: myonmyonmyon\nmyon\nmyonmyon\n\n" }, { "title": "Problem J: No Story", "content": "Since I got tired to write long problem statements, I decided to make this problem statement short. For given positive integer L, how many pairs of positive integers a, b (a <= b) such that LCM(a, b) = L are there? Here, LCM(a, b) stands for the least common multiple of a and b.", "constraint": "1 <= L <= 10^12", "input": "For each dataset, an integer L is given in a line. Input terminates when L = 0.", "output": "For each dataset, output the number of pairs of a and b.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12\n9\n2\n0\n output: 8\n3\n2"], "Pid": "p00646", "ProblemText": "Task Description: Since I got tired to write long problem statements, I decided to make this problem statement short. For given positive integer L, how many pairs of positive integers a, b (a <= b) such that LCM(a, b) = L are there? Here, LCM(a, b) stands for the least common multiple of a and b.\nTask Constraint: 1 <= L <= 10^12\nTask Input: For each dataset, an integer L is given in a line. Input terminates when L = 0.\nTask Output: For each dataset, output the number of pairs of a and b.\nTask Samples: input: 12\n9\n2\n0\n output: 8\n3\n2\n\n" }, { "title": "Problem A: It's our delight! !", "content": "You are a student of University of Aizu.\nAnd you work part-time at a restaurant.\n\nStaffs of the restaurant are well trained to be delighted to provide more delicious products faster.\n\nThe speed providing products particularly depends on skill of the staff.\nSo, the manager of the restaurant want to know how long it takes to provide products.\n\nThough some restaurants employ a system which calculates how long it takes to provide products automatically,\nthe restaurant where you work employs a system which calculates it manually.\n\nYou, a student of University of Aizu, want to write a program to calculate it, and you hope that your program makes the task easier.\nYou are given the checks in a day.\nIf the length of time it takes to provide the products of a check is shorter than or equal to 8 minutes, it is \"ok\" check.\nWrite a program to output the ratio of \"ok\" checks to the total in percentage.\n hint:\nIf you want to read three integers in the following format, \ninteger: integer(space)integer\nyou can read them by scanf(\"%d%*c%d%d\", &a, &b, &c); in C.", "constraint": "", "input": "The input consists of multiple datasets.\nThe last dataset is followed by a line containing a single zero.\nYou don't have to process this data.\nThe first line of each dataset contains a single integer n.\n

\nn (0 < n <= 100) is the number of checks.\nEach of following n lines gives the details of a check in the following format.\n\nhh: mm MM\n\n

\nhh: mm is the clock time to print the check.\nMM is minute of the clock time to provide products.\nThe clock time is expressed according to the 24 hour clock. \nFor example, \"eleven one PM\" is expressed by \"23: 01\". \nYou can assume that the all of products are provided within fifteen minutes.\nThe restaurant is open from AM 11: 00 to AM 02: 00.\nAfter AM 02: 00, no check is printed.\nAlso at AM 02: 00, no check is printed.", "output": "Your program has to print in the following format for each dataset.\n\nlunch L\ndinner D\nmidnight M\n\n L is ratio of \"ok\" check printed to the total in lunch time.\n D is ratio of \"ok\" check printed to the total in dinner time.\n M is ratio of \"ok\" check printed to the total in midnight time.\nYou can truncate digits number after the decimal point of the ratio on the percentage. Lunch, dinner, and midnight times are defined as follows:\n\nLunch time is 11: 00 ~ 14: 59.\nDinner time is 18: 00 ~ 20: 59.\nMidnight time is 21: 00 ~ 01: 59.\n\nIf a check is not printed in the three range of time, you don't have to process it.\nIf no check is in the range of time, you should print \"no guest\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n12:57 59\n20:12 15\n12:19 21\n18:52 03\n16:09 14\n0\n output: lunch 100\ndinner 50\nmidnight no guest"], "Pid": "p00647", "ProblemText": "Task Description: You are a student of University of Aizu.\nAnd you work part-time at a restaurant.\n\nStaffs of the restaurant are well trained to be delighted to provide more delicious products faster.\n\nThe speed providing products particularly depends on skill of the staff.\nSo, the manager of the restaurant want to know how long it takes to provide products.\n\nThough some restaurants employ a system which calculates how long it takes to provide products automatically,\nthe restaurant where you work employs a system which calculates it manually.\n\nYou, a student of University of Aizu, want to write a program to calculate it, and you hope that your program makes the task easier.\nYou are given the checks in a day.\nIf the length of time it takes to provide the products of a check is shorter than or equal to 8 minutes, it is \"ok\" check.\nWrite a program to output the ratio of \"ok\" checks to the total in percentage.\n hint:\nIf you want to read three integers in the following format, \ninteger: integer(space)integer\nyou can read them by scanf(\"%d%*c%d%d\", &a, &b, &c); in C.\nTask Input: The input consists of multiple datasets.\nThe last dataset is followed by a line containing a single zero.\nYou don't have to process this data.\nThe first line of each dataset contains a single integer n.\n

\nn (0 < n <= 100) is the number of checks.\nEach of following n lines gives the details of a check in the following format.\n\nhh: mm MM\n\n

\nhh: mm is the clock time to print the check.\nMM is minute of the clock time to provide products.\nThe clock time is expressed according to the 24 hour clock. \nFor example, \"eleven one PM\" is expressed by \"23: 01\". \nYou can assume that the all of products are provided within fifteen minutes.\nThe restaurant is open from AM 11: 00 to AM 02: 00.\nAfter AM 02: 00, no check is printed.\nAlso at AM 02: 00, no check is printed.\nTask Output: Your program has to print in the following format for each dataset.\n\nlunch L\ndinner D\nmidnight M\n\n L is ratio of \"ok\" check printed to the total in lunch time.\n D is ratio of \"ok\" check printed to the total in dinner time.\n M is ratio of \"ok\" check printed to the total in midnight time.\nYou can truncate digits number after the decimal point of the ratio on the percentage. Lunch, dinner, and midnight times are defined as follows:\n\nLunch time is 11: 00 ~ 14: 59.\nDinner time is 18: 00 ~ 20: 59.\nMidnight time is 21: 00 ~ 01: 59.\n\nIf a check is not printed in the three range of time, you don't have to process it.\nIf no check is in the range of time, you should print \"no guest\".\nTask Samples: input: 5\n12:57 59\n20:12 15\n12:19 21\n18:52 03\n16:09 14\n0\n output: lunch 100\ndinner 50\nmidnight no guest\n\n" }, { "title": "Problem B: Watchin' TVA", "content": "Animation is one of methods for making movies and in Japan, it is popular to broadcast as a television program or perform as a movie. Many people, especially the young, love one. And here is an anime lover called Jack. We say he is an mysterious guy with uncertain age. He likes anime which are broadcasted in midnight and early morning especially.\n\nIn his room, there is a huge piece of paper on the wall. He writes a timetable of TV anime on it. In his house, he can watch all Japanese TV anime programs that are broadcasted in Japan using a secret and countrywide live system. However he can not watch all anime and must give up to watch some programs because they are \"broadcasted at the same time\" in a season. Here, programs are \"broadcasted at the same time\" means that two or more programs have one or more common minutes in broadcasting time. Increasing the number of anime programs in recent makes him nervous. Actually, some people buy DVDs after the program series ends or visit a web site called vhefoo. Anyway, he loves to watch programs on his live system. Of course, he is not able to watch two or more programs at the same time. However, as described above, he must give up some programs broadcasted at the same time. Therefore, he has a set of programs F and he watches programs in a set F absolutely.\n\nYour task is to write a program that reads a timetable and outputs the maximum number of watchable programs, keeping that Jack watches all programs in the set F. Of course, there are multiple choices of programs, so we want the number of programs he can watch. If two or more programs in a set F are broadcasted at the same time, you must give Jack an unfortunate announcement. In this case, your program outputs -1. In addition, each anime program is a program of 30 minutes.\n hint:\nSecond dataset: He can watch program E after watching B. Then he can choose a program either I or J after watching H. Therefore he can watch maximum 4 programs.", "constraint": "The number of datasets is less than or equal to 400.
\n1<=N<=500", "input": "Input consists of multiple datasets. \nA dataset is given in a following format.\n\nN\nPROGRAM_1\nPROGRAM_2\n. . .\nPROGRAM_N\nP\nFAV_1\nFAV_2\n. . .\nFAV_P\n\nN is the number of programs in a season. \nPROGRAM_i(1<=i<=N)is a string which has the following format.\n\nname weekday start\n\nname is a program name. This is a a string having between 1 and 32 characters and these names do not overlap each other program. A name consists of alphanumeric characters and '_'(underscore).\n\nweekday is a broadcasting weekday about the corresponding program. This is an integer. 0 means Sunday and 1 is Monday and so on (2: Tuesday, 3: Wednesday, 4: Thursday, 5: Friday, 6: Saturday).\n\nstart is a starting time of the program broadcasting. This is an integer between 600 and 2929. First one or two digits represent hour and the last two digits represent minute. If the hour has one digit it will be a representation \"900\" for example. Note: a program may have an integer more than or equal to 2400 as start, if the program begins the next day. For example, a program begins from 2500 on Monday should be interpreted as a program begins from 0100 on Tuesday. There are no input the minute of start exceeds 59. And when the hour of start is equal to 29, there are no input the minute of start exceeds 29.\nP is an integer and represents the number of elements in the set F. And FAV_i(1<=i<=P<=N) is a string for a program name which Jack watches absolutely. You can assume names which are not given in program descriptions will not appear in the set F. \nThe last line contains a single 0 which represents the end of input.", "output": "For each dataset, output an integer S that represents maximum number of programs Jack can watch in the following format.\n\nS", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\ngalaxy_angel 0 600\n1\ngalaxy_angel\n11\nA 0 600\nB 0 610\nC 0 610\nD 0 610\nE 0 640\nEE 0 700\nF 0 710\nG 0 710\nH 0 710\nI 0 740\nJ 0 750\n2\nB\nH\n42\nnchj 6 2620\nanhnnnmewbktthsrn 4 2515\ngntmdsh 1 1800\nachnnl 4 2540\nhnskirh 0 2200\naonexrcst 0 1700\ndgdys 6 2330\nhdnnara 4 2525\ndnpaonntssotk 4 2555\nddmnwndrlnd 6 2500\nC 4 2445\nastrttnomch 0 2330\nseknnqasr 1 2630\nsftnt 4 2630\nstnsgt 2 2605\ndrrnenmknmrmr 4 2610\nhnzm 6 2713\nyndmsoazzlsn 6 2658\nmrahlcalv 4 2615\nhshzrhkkrhs 1 900\nortchntsbshni 0 2430\nkmnmzshrski 1 2530\nsktdnc 4 1800\ngykkybrkjhkirkhn 2 2459\ntrk 0 900\n30zzsinhkntiik 3 2700\nsngkotmmmirprdx 1 2600\nyran 2 2529\ntntissygntinybu 1 2614\nskiichhtki 5 2505\ntgrbnny 6 2558\ndnbrsnki 3 1927\nyugozxl 1 1930\nfrbllchrmn 1 1928\nfjrg 1 1955\nshwmngtr 0 2200\nxmn 5 2200\nrngnkkrskitikihn 0 2100\nszysz 0 1254\nprttyrythmaulrdrm 6 1000\nsckiesfrntrqst 5 1820\nmshdr 1 2255\n1\nmrahlcalv\n0\n output: 1\n4\n31"], "Pid": "p00648", "ProblemText": "Task Description: Animation is one of methods for making movies and in Japan, it is popular to broadcast as a television program or perform as a movie. Many people, especially the young, love one. And here is an anime lover called Jack. We say he is an mysterious guy with uncertain age. He likes anime which are broadcasted in midnight and early morning especially.\n\nIn his room, there is a huge piece of paper on the wall. He writes a timetable of TV anime on it. In his house, he can watch all Japanese TV anime programs that are broadcasted in Japan using a secret and countrywide live system. However he can not watch all anime and must give up to watch some programs because they are \"broadcasted at the same time\" in a season. Here, programs are \"broadcasted at the same time\" means that two or more programs have one or more common minutes in broadcasting time. Increasing the number of anime programs in recent makes him nervous. Actually, some people buy DVDs after the program series ends or visit a web site called vhefoo. Anyway, he loves to watch programs on his live system. Of course, he is not able to watch two or more programs at the same time. However, as described above, he must give up some programs broadcasted at the same time. Therefore, he has a set of programs F and he watches programs in a set F absolutely.\n\nYour task is to write a program that reads a timetable and outputs the maximum number of watchable programs, keeping that Jack watches all programs in the set F. Of course, there are multiple choices of programs, so we want the number of programs he can watch. If two or more programs in a set F are broadcasted at the same time, you must give Jack an unfortunate announcement. In this case, your program outputs -1. In addition, each anime program is a program of 30 minutes.\n hint:\nSecond dataset: He can watch program E after watching B. Then he can choose a program either I or J after watching H. Therefore he can watch maximum 4 programs.\nTask Constraint: The number of datasets is less than or equal to 400.
\n1<=N<=500\nTask Input: Input consists of multiple datasets. \nA dataset is given in a following format.\n\nN\nPROGRAM_1\nPROGRAM_2\n. . .\nPROGRAM_N\nP\nFAV_1\nFAV_2\n. . .\nFAV_P\n\nN is the number of programs in a season. \nPROGRAM_i(1<=i<=N)is a string which has the following format.\n\nname weekday start\n\nname is a program name. This is a a string having between 1 and 32 characters and these names do not overlap each other program. A name consists of alphanumeric characters and '_'(underscore).\n\nweekday is a broadcasting weekday about the corresponding program. This is an integer. 0 means Sunday and 1 is Monday and so on (2: Tuesday, 3: Wednesday, 4: Thursday, 5: Friday, 6: Saturday).\n\nstart is a starting time of the program broadcasting. This is an integer between 600 and 2929. First one or two digits represent hour and the last two digits represent minute. If the hour has one digit it will be a representation \"900\" for example. Note: a program may have an integer more than or equal to 2400 as start, if the program begins the next day. For example, a program begins from 2500 on Monday should be interpreted as a program begins from 0100 on Tuesday. There are no input the minute of start exceeds 59. And when the hour of start is equal to 29, there are no input the minute of start exceeds 29.\nP is an integer and represents the number of elements in the set F. And FAV_i(1<=i<=P<=N) is a string for a program name which Jack watches absolutely. You can assume names which are not given in program descriptions will not appear in the set F. \nThe last line contains a single 0 which represents the end of input.\nTask Output: For each dataset, output an integer S that represents maximum number of programs Jack can watch in the following format.\n\nS\nTask Samples: input: 1\ngalaxy_angel 0 600\n1\ngalaxy_angel\n11\nA 0 600\nB 0 610\nC 0 610\nD 0 610\nE 0 640\nEE 0 700\nF 0 710\nG 0 710\nH 0 710\nI 0 740\nJ 0 750\n2\nB\nH\n42\nnchj 6 2620\nanhnnnmewbktthsrn 4 2515\ngntmdsh 1 1800\nachnnl 4 2540\nhnskirh 0 2200\naonexrcst 0 1700\ndgdys 6 2330\nhdnnara 4 2525\ndnpaonntssotk 4 2555\nddmnwndrlnd 6 2500\nC 4 2445\nastrttnomch 0 2330\nseknnqasr 1 2630\nsftnt 4 2630\nstnsgt 2 2605\ndrrnenmknmrmr 4 2610\nhnzm 6 2713\nyndmsoazzlsn 6 2658\nmrahlcalv 4 2615\nhshzrhkkrhs 1 900\nortchntsbshni 0 2430\nkmnmzshrski 1 2530\nsktdnc 4 1800\ngykkybrkjhkirkhn 2 2459\ntrk 0 900\n30zzsinhkntiik 3 2700\nsngkotmmmirprdx 1 2600\nyran 2 2529\ntntissygntinybu 1 2614\nskiichhtki 5 2505\ntgrbnny 6 2558\ndnbrsnki 3 1927\nyugozxl 1 1930\nfrbllchrmn 1 1928\nfjrg 1 1955\nshwmngtr 0 2200\nxmn 5 2200\nrngnkkrskitikihn 0 2100\nszysz 0 1254\nprttyrythmaulrdrm 6 1000\nsckiesfrntrqst 5 1820\nmshdr 1 2255\n1\nmrahlcalv\n0\n output: 1\n4\n31\n\n" }, { "title": "Problem C: Yanagi's Comic", "content": "Yanagi is a high school student, and she is called \"Hime\" by her boyfriend who is a ninja fanboy. She likes picture books very much, so she often writes picture books by herself.\nShe always asks you to make her picture book as an assistant.\nToday, you got asked to help her with making a comic.\n\nShe sometimes reads her picture books for children in kindergartens.\nSince Yanagi wants to let the children read,\nshe wants to insert numbers to frames in order.\nOf course, such a task should be done by the assistant, you.\n\nYou want to do the task easily and fast, so you decide to write a program to output the order of reading frames based on the positions of the frames.\n\nWrite a program to print the number of order for each frame.\n\nThe comics in this problem satisfy the following rules.\n\nThe each comic is drawn on a sheet of rectangle paper.\nYou can assume that the top side of the paper is on the x-axis.\nAnd you can assume that the right-hand side of the paper is on the y-axis.\nThe positive direction of the x-axis is leftward.\nThe positive direction of the y-axis is down direction.\nThe paper is large enough to include all frames of the comic.\nIn other words, no area in a frame is out of the paper.\n\nThe area of each frame is at least one.\nAll sides of each frame are parallel to the x-axis or the y-axis.\nThe frames can't overlap one another.\nHowever the frames may share the line of side.\n\nYou must decide the order to read K , where K is a set of frames, with the following steps.\n\nStep 1: You must choose an unread frame at the right-most position in K.\n If you find such frames multiple, you must choose the frame at the top position among them.\n If you can't find any unread frames, you stop reading K.\n The frame you chose is \"Starting Frame\".\n In step 1, you assume that the position of a frame is the top-right point of the frame.\n\nStep 2: You should draw a line from the right-bottom point of \"Starting Frame\" to leftward horizontally.\n If the line touch the right-hand side of other frame, you should stop drawing.\n If the line is on the side of other frame, you should not stop drawing.\n If the line touch the edge of paper, you should stop drawing.\n\nStep 3: The set of the unread frames which are above the line ( they may be the bottom-side on the line ) drawn at Step 2 is L.\n And you should read L.\n\nStep 4: Go back to Step 1.", "constraint": "0 < n < 10
\n(x_0i != x_1i) and (y_0i != y_1i)
\n0 <= x_0i , y_0i , x_1i , y_1i <= 500
", "input": "The input consists of multiple datasets.\nThe last dataset is followed by a line containing one zero.\nYou don't have to process this data.\n\nEach datasets is in the following format.\n\nn\nx_01 y_01 x_11 y_11\nx_02 y_02 x_12 y_12\n. . . .\nx_0n y_0n x_1n y_1n\n\nAll numbers of the datasets are integer.\nThey are separated by a space.\nThe first line of a dataset contains one integer.\nn is the number of frames of the comic.\n x_0i , y_0i , x_1i , y_1i are two non-neighboring points of i th frame in the line.", "output": "Print n lines for each dataset.\nPrint the number of order for ith frame in the ith line.\nAnd you should print blank line between the datasets. \nOutput format:\nnum_1\nnum_2\n. . .\nnum_i\n. . .\nnum_n", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n0 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0\n output: 1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\nThese pictures are related to first sample and second sample.\nGray frames have been read already.\nA red line denotes the line drawn at Step 2. Numbers in the figures denote the order of frames given by input.This is related to the first sample.These are related to the second sample."], "Pid": "p00649", "ProblemText": "Task Description: Yanagi is a high school student, and she is called \"Hime\" by her boyfriend who is a ninja fanboy. She likes picture books very much, so she often writes picture books by herself.\nShe always asks you to make her picture book as an assistant.\nToday, you got asked to help her with making a comic.\n\nShe sometimes reads her picture books for children in kindergartens.\nSince Yanagi wants to let the children read,\nshe wants to insert numbers to frames in order.\nOf course, such a task should be done by the assistant, you.\n\nYou want to do the task easily and fast, so you decide to write a program to output the order of reading frames based on the positions of the frames.\n\nWrite a program to print the number of order for each frame.\n\nThe comics in this problem satisfy the following rules.\n\nThe each comic is drawn on a sheet of rectangle paper.\nYou can assume that the top side of the paper is on the x-axis.\nAnd you can assume that the right-hand side of the paper is on the y-axis.\nThe positive direction of the x-axis is leftward.\nThe positive direction of the y-axis is down direction.\nThe paper is large enough to include all frames of the comic.\nIn other words, no area in a frame is out of the paper.\n\nThe area of each frame is at least one.\nAll sides of each frame are parallel to the x-axis or the y-axis.\nThe frames can't overlap one another.\nHowever the frames may share the line of side.\n\nYou must decide the order to read K , where K is a set of frames, with the following steps.\n\nStep 1: You must choose an unread frame at the right-most position in K.\n If you find such frames multiple, you must choose the frame at the top position among them.\n If you can't find any unread frames, you stop reading K.\n The frame you chose is \"Starting Frame\".\n In step 1, you assume that the position of a frame is the top-right point of the frame.\n\nStep 2: You should draw a line from the right-bottom point of \"Starting Frame\" to leftward horizontally.\n If the line touch the right-hand side of other frame, you should stop drawing.\n If the line is on the side of other frame, you should not stop drawing.\n If the line touch the edge of paper, you should stop drawing.\n\nStep 3: The set of the unread frames which are above the line ( they may be the bottom-side on the line ) drawn at Step 2 is L.\n And you should read L.\n\nStep 4: Go back to Step 1.\nTask Constraint: 0 < n < 10
\n(x_0i != x_1i) and (y_0i != y_1i)
\n0 <= x_0i , y_0i , x_1i , y_1i <= 500
\nTask Input: The input consists of multiple datasets.\nThe last dataset is followed by a line containing one zero.\nYou don't have to process this data.\n\nEach datasets is in the following format.\n\nn\nx_01 y_01 x_11 y_11\nx_02 y_02 x_12 y_12\n. . . .\nx_0n y_0n x_1n y_1n\n\nAll numbers of the datasets are integer.\nThey are separated by a space.\nThe first line of a dataset contains one integer.\nn is the number of frames of the comic.\n x_0i , y_0i , x_1i , y_1i are two non-neighboring points of i th frame in the line.\nTask Output: Print n lines for each dataset.\nPrint the number of order for ith frame in the ith line.\nAnd you should print blank line between the datasets. \nOutput format:\nnum_1\nnum_2\n. . .\nnum_i\n. . .\nnum_n\nTask Samples: input: 4\n0 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0\n output: 1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\nThese pictures are related to first sample and second sample.\nGray frames have been read already.\nA red line denotes the line drawn at Step 2. Numbers in the figures denote the order of frames given by input.This is related to the first sample.These are related to the second sample.\n\n" }, { "title": "Problem D: The House of Huge Family", "content": "Mr. Dango's family has an extremely huge number of members.\nOnce it had about 100 members, and now it has as many as population of a city.\nIt is jokingly guessed that the member might fill this planet in the near future.\n\nMr. Dango's family, the huge family, is getting their new house.\nScale of the house is as large as that of town.\n\nThey all had warm and gracious personality and were close each other.\nHowever, in this year the two members of them became to hate each other.\nSince the two members had enormous influence in the family, they were split into two groups.\n\nThey hope that the two groups don't meet each other in the new house.\nThough they are in the same building, they can avoid to meet each other by adjusting passageways.\n\nNow, you have a figure of room layout. Your task is written below.\n\nYou have to decide the two groups each room should belong to.\nBesides you must make it impossible that they move from any rooms belonging to one group to any rooms belonging to the other group.\nAll of the rooms need to belong to exactly one group.\nAnd any group has at least one room.\n\nTo do the task, you can cancel building passageway.\nBecause the house is under construction, to cancel causes some cost.\nYou'll be given the number of rooms and information of passageway.\nYou have to do the task by the lowest cost.\n\nPlease answer the lowest cost.\n\nBy characteristics of Mr. Dango's family, they move very slowly.\nSo all passageways are escalators.\nBecause of it, the passageways are one-way.", "constraint": "2 <= n <= 100\n\n-10,000 <= C_i <= 10,000\n\nY_1 ... Y_m can't be duplicated integer by each other.", "input": "The input consists of multiple datasets.\nEach dataset is given in the following format.\n\nn m\nX_1 Y_1 C_1\n. . .\nX_m Y_m C_m\n\nAll numbers in each datasets are integers.\nThe integers in each line are separated by a space.\n\nThe first line of each datasets contains two integers.\nn is the number of rooms in the house, m is the number of passageways in the house.\nEach room is indexed from 0 to n-1.\n\nEach of following m lines gives the details of the passageways in the house.\nEach line contains three integers.\nThe first integer X_i is an index of the room, the starting point of the passageway.\nThe second integer Y_i is an index of the room, the end point of the passageway.\nThe third integer C_i is the cost to cancel construction of the passageway.\nThe passageways, they are escalators, are one-way.\nThe last dataset is followed by a line containing two zeros (separated by a space).", "output": "For each dataset, print the lowest cost in a line. You may assume that the all of integers of both the answers and the input can be represented by 32 bits signed integers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n0 1 2\n1 2 1\n2 1\n0 1 100\n2 1\n0 1 0\n2 1\n0 1 -1\n0 0\n output: 1\n100\n0\n-1"], "Pid": "p00650", "ProblemText": "Task Description: Mr. Dango's family has an extremely huge number of members.\nOnce it had about 100 members, and now it has as many as population of a city.\nIt is jokingly guessed that the member might fill this planet in the near future.\n\nMr. Dango's family, the huge family, is getting their new house.\nScale of the house is as large as that of town.\n\nThey all had warm and gracious personality and were close each other.\nHowever, in this year the two members of them became to hate each other.\nSince the two members had enormous influence in the family, they were split into two groups.\n\nThey hope that the two groups don't meet each other in the new house.\nThough they are in the same building, they can avoid to meet each other by adjusting passageways.\n\nNow, you have a figure of room layout. Your task is written below.\n\nYou have to decide the two groups each room should belong to.\nBesides you must make it impossible that they move from any rooms belonging to one group to any rooms belonging to the other group.\nAll of the rooms need to belong to exactly one group.\nAnd any group has at least one room.\n\nTo do the task, you can cancel building passageway.\nBecause the house is under construction, to cancel causes some cost.\nYou'll be given the number of rooms and information of passageway.\nYou have to do the task by the lowest cost.\n\nPlease answer the lowest cost.\n\nBy characteristics of Mr. Dango's family, they move very slowly.\nSo all passageways are escalators.\nBecause of it, the passageways are one-way.\nTask Constraint: 2 <= n <= 100\n\n-10,000 <= C_i <= 10,000\n\nY_1 ... Y_m can't be duplicated integer by each other.\nTask Input: The input consists of multiple datasets.\nEach dataset is given in the following format.\n\nn m\nX_1 Y_1 C_1\n. . .\nX_m Y_m C_m\n\nAll numbers in each datasets are integers.\nThe integers in each line are separated by a space.\n\nThe first line of each datasets contains two integers.\nn is the number of rooms in the house, m is the number of passageways in the house.\nEach room is indexed from 0 to n-1.\n\nEach of following m lines gives the details of the passageways in the house.\nEach line contains three integers.\nThe first integer X_i is an index of the room, the starting point of the passageway.\nThe second integer Y_i is an index of the room, the end point of the passageway.\nThe third integer C_i is the cost to cancel construction of the passageway.\nThe passageways, they are escalators, are one-way.\nThe last dataset is followed by a line containing two zeros (separated by a space).\nTask Output: For each dataset, print the lowest cost in a line. You may assume that the all of integers of both the answers and the input can be represented by 32 bits signed integers.\nTask Samples: input: 3 2\n0 1 2\n1 2 1\n2 1\n0 1 100\n2 1\n0 1 0\n2 1\n0 1 -1\n0 0\n output: 1\n100\n0\n-1\n\n" }, { "title": "Problem E: Legend of Storia", "content": "In Storia Kingdom, there is an artifact called \"Perfect Sphere\" made by a great meister Es. This is handed down for generations in the royal palace as a treasure. Es left a memo and filled mysterious values in it. Within achievements of researches, it has been revealed that the values denote coordinate values. However it is still unknown the definition of the coordinate system.\n\nBy the way, you are a person who lived in age of Es lived. The values which meister Es left are defined by following. Es set an moving object in the artifact sphere. Surprisingly, that is rigid body and perpetual organization. The object rotates inside the sphere and it is always touching the inside surface of the sphere. This value is a coordinate of the tangent point by the object and the sphere, but it is not a three dimensional value. The object is a plate and this is a simple polygon. Here, \"simple\" means \"non self-intersected\". This rotates while touching a great circle of the sphere. Here, assume that the great circle is a circle O centered in the origin in the xy plane. (It is two-dimensional Cartesian coordinate system, the direction of positive x-value is right and the direction of positive y-value is up). This plate touches the circle O with a single point at the beginning of the movement. And it rotates in counterclockwise as the current touching point is the rotation fulcrum. When another point X of the plate touches the circle O newly, the plate continue to rotate as described above, but in the next rotation, the rotation fulcrum point is changed. This will be the point X. If two or more points can be interpreted as the point X, the point X is a most distant point from the currently touching point X'. Here, that distance is the length of the arc of the circle O from the point X' to the point X in clockwise.\n\nEs asked you, an excellent assistant, to write a program that enumerates Q tangent points (fulcrum points while the movement) by the plate and the circle O while the movement of the plate described above in the chronological order. Of course, one and the previous one must be distinct points. Following figures show you examples of the movement of the plate inside the circle O.\n\n1\n2\n3\n4", "constraint": "The number of datasets is less than or equal to 400.
\n3<=N<=25
\n1<=R<=1000
\n0<=Q<=100", "input": "Input consists of multiple datasets. \nA dataset is given in a following format.\n\nN R Q\nx_1 y_1\nx_2 y_2\n. . .\nx_N y_N\n\nN, R, Q are integers that represent the number of points of the plate, the radius of the circle, and the number of points Es needs respectively. \nFollowing N lines contain 2N integers that represent coordinates of the plate's points ( x_k , y_k ) in the circle. (1<=k<=N)\n\nYou can assume following conditions.\nPoints of the plate are given in counterclockwise.\n\nNo three points are co-linear.\n\nN-1 points of the plate are given inside of the circle (distances between the center of the circle and these points are less than R). And 1 point is on the circle edge.\n\nN=R=Q=0 shows the end of input.", "output": "For each dataset, output (Px Py: real number) in Q in the following format.\n\nPx_1 Px_1\nPx_2 Py_2\n. . .\nPx_N+1 Py_N+1\n\nThese answers must satisfy |Tx_i-Px_i|<=0.0001 and |Ty_i-Py_i|<=0.0001. \nHere, Px_i, Py_i(1<=i<=Q) are your output and Tx_i, Ty_i(1<=i<=Q) are judge's output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 10 8\n0 -10\n3 -7\n0 -4\n-3 -7\n0 0 0\n output: -4.146082488326 -9.100000000000\n-7.545870128753 -6.562000000000\n-9.587401146004 -2.842840000000\n-9.903199956975 1.388031200000\n-8.436422775690 5.369056784000\n-5.451089494781 8.383652146880\n-1.484560104812 9.889190123322\n2.749190104024 9.614673877565"], "Pid": "p00651", "ProblemText": "Task Description: In Storia Kingdom, there is an artifact called \"Perfect Sphere\" made by a great meister Es. This is handed down for generations in the royal palace as a treasure. Es left a memo and filled mysterious values in it. Within achievements of researches, it has been revealed that the values denote coordinate values. However it is still unknown the definition of the coordinate system.\n\nBy the way, you are a person who lived in age of Es lived. The values which meister Es left are defined by following. Es set an moving object in the artifact sphere. Surprisingly, that is rigid body and perpetual organization. The object rotates inside the sphere and it is always touching the inside surface of the sphere. This value is a coordinate of the tangent point by the object and the sphere, but it is not a three dimensional value. The object is a plate and this is a simple polygon. Here, \"simple\" means \"non self-intersected\". This rotates while touching a great circle of the sphere. Here, assume that the great circle is a circle O centered in the origin in the xy plane. (It is two-dimensional Cartesian coordinate system, the direction of positive x-value is right and the direction of positive y-value is up). This plate touches the circle O with a single point at the beginning of the movement. And it rotates in counterclockwise as the current touching point is the rotation fulcrum. When another point X of the plate touches the circle O newly, the plate continue to rotate as described above, but in the next rotation, the rotation fulcrum point is changed. This will be the point X. If two or more points can be interpreted as the point X, the point X is a most distant point from the currently touching point X'. Here, that distance is the length of the arc of the circle O from the point X' to the point X in clockwise.\n\nEs asked you, an excellent assistant, to write a program that enumerates Q tangent points (fulcrum points while the movement) by the plate and the circle O while the movement of the plate described above in the chronological order. Of course, one and the previous one must be distinct points. Following figures show you examples of the movement of the plate inside the circle O.\n\n1\n2\n3\n4\nTask Constraint: The number of datasets is less than or equal to 400.
\n3<=N<=25
\n1<=R<=1000
\n0<=Q<=100\nTask Input: Input consists of multiple datasets. \nA dataset is given in a following format.\n\nN R Q\nx_1 y_1\nx_2 y_2\n. . .\nx_N y_N\n\nN, R, Q are integers that represent the number of points of the plate, the radius of the circle, and the number of points Es needs respectively. \nFollowing N lines contain 2N integers that represent coordinates of the plate's points ( x_k , y_k ) in the circle. (1<=k<=N)\n\nYou can assume following conditions.\nPoints of the plate are given in counterclockwise.\n\nNo three points are co-linear.\n\nN-1 points of the plate are given inside of the circle (distances between the center of the circle and these points are less than R). And 1 point is on the circle edge.\n\nN=R=Q=0 shows the end of input.\nTask Output: For each dataset, output (Px Py: real number) in Q in the following format.\n\nPx_1 Px_1\nPx_2 Py_2\n. . .\nPx_N+1 Py_N+1\n\nThese answers must satisfy |Tx_i-Px_i|<=0.0001 and |Ty_i-Py_i|<=0.0001. \nHere, Px_i, Py_i(1<=i<=Q) are your output and Tx_i, Ty_i(1<=i<=Q) are judge's output.\nTask Samples: input: 4 10 8\n0 -10\n3 -7\n0 -4\n-3 -7\n0 0 0\n output: -4.146082488326 -9.100000000000\n-7.545870128753 -6.562000000000\n-9.587401146004 -2.842840000000\n-9.903199956975 1.388031200000\n-8.436422775690 5.369056784000\n-5.451089494781 8.383652146880\n-1.484560104812 9.889190123322\n2.749190104024 9.614673877565\n\n" }, { "title": "Problem F: Cutting a Chocolate", "content": "Turtle Shi-ta and turtle Be-ko decided to divide a chocolate.\nThe shape of the chocolate is rectangle. The corners of the chocolate are put on (0,0), (w, 0), (w, h) and (0, h).\nThe chocolate has lines for cutting.\nThey cut the chocolate only along some of these lines.\n\nThe lines are expressed as follows.\nThere are m points on the line connected between (0,0) and (0, h), and between (w, 0) and (w, h).\nEach i-th point, ordered by y value (i = 0 then y =0), is connected as cutting line.\nThese lines do not share any point where 0 < x < w .\nThey can share points where x = 0 or x = w .\nHowever, (0, l_i ) = (0, l_j ) and (w, r_i ) = (w, r_j ) implies i = j .\nThe following figure shows the example of the chocolate.\n\nThere are n special almonds, so delicious but high in calories on the chocolate.\nAlmonds are circle but their radius is too small. You can ignore radius of almonds.\nThe position of almond is expressed as (x, y) coordinate.\n\nTwo turtles are so selfish. Both of them have requirement for cutting.\n\nShi-ta's requirement is that the piece for her is continuous.\nIt is possible for her that she cannot get any chocolate.\nAssume that the minimum index of the piece is i and the maximum is k .\nShe must have all pieces between i and k .\nFor example, chocolate piece 1,2,3 is continuous but 1,3 or 0,2,4 is not continuous.\n\nBe-ko requires that the area of her chocolate is at least S .\nShe is worry about her weight. So she wants the number of almond on her chocolate is as few as possible.\n\nThey doesn't want to make remainder of the chocolate because the chocolate is expensive.\n\nYour task is to compute the minumum number of Beko's almonds if both of their requirment are satisfied.", "constraint": "", "input": "Input consists of multiple test cases. \nEach dataset is given in the following format.\n\nn m w h S\nl_0 r_0\n. . .\nl_m-1 r_m-1\nx_0 y_0\n. . .\nx_n-1 y_n-1\n\nThe last line contains five 0s.\nn is the number of almonds.\nm is the number of lines.\nw is the width of the chocolate.\nh is the height of the chocolate.\nS is the area that Be-ko wants to eat.\nInput is integer except x_i y_i.\n\nInput satisfies following constraints. \n1 <= n <= 30000\n1 <= m <= 30000\n1 <= w <= 200\n1 <= h <= 1000000\n0 <= S <= w*h\n\nIf i < j then l_i <= l_j and r_i <= r_j and then i -th lines and j -th lines share at most 1 point.\nIt is assured that l_m-1 and r_m-1 are h.\nx_i y_i is floating point number with ten digits.\nIt is assured that they are inside of the chocolate.\nIt is assured that the distance between points and any lines is at least 0.00001.", "output": "You should output the minumum number of almonds for Be-ko.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 3 10 10 50\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 70\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 30\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 40\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 100\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n0 0 0 0 0\n output: 1\n1\n0\n1\n2"], "Pid": "p00652", "ProblemText": "Task Description: Turtle Shi-ta and turtle Be-ko decided to divide a chocolate.\nThe shape of the chocolate is rectangle. The corners of the chocolate are put on (0,0), (w, 0), (w, h) and (0, h).\nThe chocolate has lines for cutting.\nThey cut the chocolate only along some of these lines.\n\nThe lines are expressed as follows.\nThere are m points on the line connected between (0,0) and (0, h), and between (w, 0) and (w, h).\nEach i-th point, ordered by y value (i = 0 then y =0), is connected as cutting line.\nThese lines do not share any point where 0 < x < w .\nThey can share points where x = 0 or x = w .\nHowever, (0, l_i ) = (0, l_j ) and (w, r_i ) = (w, r_j ) implies i = j .\nThe following figure shows the example of the chocolate.\n\nThere are n special almonds, so delicious but high in calories on the chocolate.\nAlmonds are circle but their radius is too small. You can ignore radius of almonds.\nThe position of almond is expressed as (x, y) coordinate.\n\nTwo turtles are so selfish. Both of them have requirement for cutting.\n\nShi-ta's requirement is that the piece for her is continuous.\nIt is possible for her that she cannot get any chocolate.\nAssume that the minimum index of the piece is i and the maximum is k .\nShe must have all pieces between i and k .\nFor example, chocolate piece 1,2,3 is continuous but 1,3 or 0,2,4 is not continuous.\n\nBe-ko requires that the area of her chocolate is at least S .\nShe is worry about her weight. So she wants the number of almond on her chocolate is as few as possible.\n\nThey doesn't want to make remainder of the chocolate because the chocolate is expensive.\n\nYour task is to compute the minumum number of Beko's almonds if both of their requirment are satisfied.\nTask Input: Input consists of multiple test cases. \nEach dataset is given in the following format.\n\nn m w h S\nl_0 r_0\n. . .\nl_m-1 r_m-1\nx_0 y_0\n. . .\nx_n-1 y_n-1\n\nThe last line contains five 0s.\nn is the number of almonds.\nm is the number of lines.\nw is the width of the chocolate.\nh is the height of the chocolate.\nS is the area that Be-ko wants to eat.\nInput is integer except x_i y_i.\n\nInput satisfies following constraints. \n1 <= n <= 30000\n1 <= m <= 30000\n1 <= w <= 200\n1 <= h <= 1000000\n0 <= S <= w*h\n\nIf i < j then l_i <= l_j and r_i <= r_j and then i -th lines and j -th lines share at most 1 point.\nIt is assured that l_m-1 and r_m-1 are h.\nx_i y_i is floating point number with ten digits.\nIt is assured that they are inside of the chocolate.\nIt is assured that the distance between points and any lines is at least 0.00001.\nTask Output: You should output the minumum number of almonds for Be-ko.\nTask Samples: input: 2 3 10 10 50\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 70\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 30\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 40\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n2 3 10 10 100\n3 3\n6 6\n10 10\n4.0000000000 4.0000000000\n7.0000000000 7.0000000000\n0 0 0 0 0\n output: 1\n1\n0\n1\n2\n\n" }, { "title": "Problem G: School of Killifish", "content": "Jon is the leader of killifish.\nJon have a problem in these days.\nJon has a plan to built new town in a pond.\nOf course new towns should have a school for children. But there are some natural enemies in a pond.\nJon thinks that the place of a school should be the safest place in a pond for children.\n\nJon has asked by some construction companies to make construction plans and Jon has q construction plans now.\nThe plan is selected by voting. But for each plan, the safest place for the school should be decided before voting.\n\nA pond is expressed by a 2D grid whose size is r*c.\nThe grid has r rows and c columns. The coordinate of the top-left cell is (0,0). The coordinate of the bottom-right cell is expressed as (r-1, c-1).\nEach cell has an integer which implies a dangerousness.\nThe lower value implies safer than the higher value.\nq plans are given by four integer r1 , c1 , r2 and c2 which represent the subgrid. \nThe top-left corner is (r1, c1) and the bottom-right corner is (r2, c2).\n\nYou have the r*c grid and q plans. Your task is to find the safest point for each plan.\nYou should find the lowest value in the subgrid.", "constraint": "", "input": "Input consists of multiple datasets. \nEach dataset is given in the following format.\n\nr c q\ngrid_0,0 grid_0,1 . . . grid_0, c-1\n. . .\ngrid_r-1,0 . . . grid_r-1, c-1\nr1 c1 r2 c2\n. . .\nr1 c1 r2 c2\n\nThe first line consists of 3 integers, r , c , and q .\nNext r lines have c integers.\ngrid_i, j means a dangerousness of the grid.\nAnd you can assume 0 <= grid_i, j <= 2^31-1.\nAfter that, q queries, r1, c1, r2 and c2, are given.\n\nThe dataset satisfies following constraints. \nr*c <= 10^6\nq <= 10^4\nFor each query, you can assume that r1<= r2 and c1 <= c2 .\n\nIf r * c <= 250000, q <= 100 is assured.\nIf r * c > 250000, Input consists of only that case.", "output": "For each query you should print the lowest value in the subgrid in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 4\n1 2 3\n4 2 2\n2 1 1\n0 0 2 2\n0 0 1 1\n1 0 1 0\n0 1 1 2\n1 10 4\n1 2 3 4 5 6 7 8 9 10\n0 0 0 9\n0 0 0 4\n0 5 0 9\n0 4 0 5\n0 0 0\n output: 1\n1\n4\n2\n1\n1\n6\n5"], "Pid": "p00653", "ProblemText": "Task Description: Jon is the leader of killifish.\nJon have a problem in these days.\nJon has a plan to built new town in a pond.\nOf course new towns should have a school for children. But there are some natural enemies in a pond.\nJon thinks that the place of a school should be the safest place in a pond for children.\n\nJon has asked by some construction companies to make construction plans and Jon has q construction plans now.\nThe plan is selected by voting. But for each plan, the safest place for the school should be decided before voting.\n\nA pond is expressed by a 2D grid whose size is r*c.\nThe grid has r rows and c columns. The coordinate of the top-left cell is (0,0). The coordinate of the bottom-right cell is expressed as (r-1, c-1).\nEach cell has an integer which implies a dangerousness.\nThe lower value implies safer than the higher value.\nq plans are given by four integer r1 , c1 , r2 and c2 which represent the subgrid. \nThe top-left corner is (r1, c1) and the bottom-right corner is (r2, c2).\n\nYou have the r*c grid and q plans. Your task is to find the safest point for each plan.\nYou should find the lowest value in the subgrid.\nTask Input: Input consists of multiple datasets. \nEach dataset is given in the following format.\n\nr c q\ngrid_0,0 grid_0,1 . . . grid_0, c-1\n. . .\ngrid_r-1,0 . . . grid_r-1, c-1\nr1 c1 r2 c2\n. . .\nr1 c1 r2 c2\n\nThe first line consists of 3 integers, r , c , and q .\nNext r lines have c integers.\ngrid_i, j means a dangerousness of the grid.\nAnd you can assume 0 <= grid_i, j <= 2^31-1.\nAfter that, q queries, r1, c1, r2 and c2, are given.\n\nThe dataset satisfies following constraints. \nr*c <= 10^6\nq <= 10^4\nFor each query, you can assume that r1<= r2 and c1 <= c2 .\n\nIf r * c <= 250000, q <= 100 is assured.\nIf r * c > 250000, Input consists of only that case.\nTask Output: For each query you should print the lowest value in the subgrid in a line.\nTask Samples: input: 3 3 4\n1 2 3\n4 2 2\n2 1 1\n0 0 2 2\n0 0 1 1\n1 0 1 0\n0 1 1 2\n1 10 4\n1 2 3 4 5 6 7 8 9 10\n0 0 0 9\n0 0 0 4\n0 5 0 9\n0 4 0 5\n0 0 0\n output: 1\n1\n4\n2\n1\n1\n6\n5\n\n" }, { "title": "", "content": "A sequence b ={a_i + a_j | i < j } is generated from a sequence a ={a_0 , . . . , a_n | a_i is even if i is 0, otherwise a_i is odd}. Given the sequence b , find the sequence a . This problem is easy for Eiko and she feels boring. So, she made a new problem by modifying this problem . A sequence b ={a_i *a_j | i < j } is generated from a sequence a ={ a_0, . . . , a_n | a_i is even if i is 0, otherwise a_i is odd}. Given the sequence b , find the sequence a . Your task is to solve the problem made by Eiko.", "constraint": "", "input": "Input consists of multiple datasets. \nEach dataset is given by following formats.\n\nn\nb_0 b_1 . . . b_n*(n+1)/2-1\n\nn is the number of odd integers in the sequence a. The range of n is 2 <= n <= 250.\nb_i is separated by a space.\nEach b_i is 1 <= b_i <= 2^63-1.\nThe end of the input consists of a single 0.", "output": "For each dataset, you should output two lines.\nFirst line contains a_0, an even number in the sequence a.\nThe second line contains n odd elements separated by a space. The odd elements are sorted by increasing order.\nYou can assume that the result is greater than or equal to 1 and less than or equal to 2^31-1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n6 10 14 15 21 35\n2\n30 42 35\n0\n output: 2\n3 5 7\n6\n5 7"], "Pid": "p00654", "ProblemText": "Task Description: A sequence b ={a_i + a_j | i < j } is generated from a sequence a ={a_0 , . . . , a_n | a_i is even if i is 0, otherwise a_i is odd}. Given the sequence b , find the sequence a . This problem is easy for Eiko and she feels boring. So, she made a new problem by modifying this problem . A sequence b ={a_i *a_j | i < j } is generated from a sequence a ={ a_0, . . . , a_n | a_i is even if i is 0, otherwise a_i is odd}. Given the sequence b , find the sequence a . Your task is to solve the problem made by Eiko.\nTask Input: Input consists of multiple datasets. \nEach dataset is given by following formats.\n\nn\nb_0 b_1 . . . b_n*(n+1)/2-1\n\nn is the number of odd integers in the sequence a. The range of n is 2 <= n <= 250.\nb_i is separated by a space.\nEach b_i is 1 <= b_i <= 2^63-1.\nThe end of the input consists of a single 0.\nTask Output: For each dataset, you should output two lines.\nFirst line contains a_0, an even number in the sequence a.\nThe second line contains n odd elements separated by a space. The odd elements are sorted by increasing order.\nYou can assume that the result is greater than or equal to 1 and less than or equal to 2^31-1.\nTask Samples: input: 3\n6 10 14 15 21 35\n2\n30 42 35\n0\n output: 2\n3 5 7\n6\n5 7\n\n" }, { "title": "Problem I: FIMO sequence", "content": "Your task is to simulate the sequence defined in the remaining part of the problem description.\n\nThis sequence is empty at first.\n i -th element of this sequence is expressed as a_i .\nThe first element of this sequence is a_1 if the sequence is not empty.\nThe operation is given by integer from 0 to 9.\nThe operation is described below.\n\n0:\nThis query is given with some integer x.\nIf this query is given, the integer x is inserted into the sequence.\nIf the sequence is empty, a_1 = x.\nIf the sequence has n elements, a_n+1 = x.\nSame integer will not appear more than once as x.\n\n1:\nIf this query is given, one element in the sequence is deleted.\nThe value in the middle of the sequence is deleted.\nIf the sequence has n elements and n is even, a_n/2 will be deleted.\nIf n is odd, a_⌈n/2⌉ will be deleted.\nThis query is not given when the sequence is empty.\n\nAssume that the sequence has a_1 =1, a_2 =2, a_3 =3, a_4 =4 and a_5 =5.\nIn this case, a_3 will be deleted.\nAfter deletion, the sequence will be a_1 =1, a_2 =2, a_3 =4, a_4 =5.\n\nAssume that the sequence has a_1 =1, a_2 =2, a_3 =3 and a_4 =4,\nIn this case, a_2 will be deleted.\nAfter deletion, the sequence will be a_1 =1, a_2 =3, a_3 =4.\n\n2:\nThe first half of the sequence is defined by the index from 1 to ⌈n/2⌉ .\nIf this query is given, you should compute the minimum element of the first half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {6,2,3,4,5,1,8}.\nIn this case, the minimum element of the first half of the sequence, {6,2,3,4} is 2.\n\n3:\nThe latter half of the sequence is elements that do not belong to the first half of the sequence.\nIf this query is given, you should compute the minimum element of the latter half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {6,2,3,4,5,1,8}.\nIn this case the answer for this query is 1 from {5,1,8}.\n\n4:\nThis query is given with an integer i.\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the first half of the sequence will become the answer for query 2.\nYou should compute the i -th minimum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th minimum element exists when this query is given.\n\nLet me show an example.\n\nAssume that deletion will be repeated to the sequence {6,2,3,4,5,1,8}.\n{6,2,3,4,5,1,8} The minimum element in the first half of the sequence is 2.\n{6,2,3,5,1,8} The minimum element in the first half of the sequence is 2.\n{6,2,5,1,8} The minimum element in the first half of the sequence is 2.\n{6,2,1,8} The minimum element in the first half of the sequence is 2.\n{6,1,8} The minimum element in the first half of the sequence is 1.\n{6,8} The minimum element in the first half of the sequence is 6.\n{8} The minimum element in the first half of the sequence is 8.\n{} The first half of the sequence is empty.\n\nFor the initial state, {6,2,3,4} is the first half of the sequence.\n2 and 6 become the minimum element of the first half of the sequence.\nIn this example, the 1-st minimum element is 2 and the 2-nd is 6.\n\n5:\nThis query is given with an integer i .\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the latter half of the sequence will become the answer for query 3.\nYou should compute the i -th minimum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th minimum element exists when this query is given.\n\nLet me show an example.\n\nAssume that deletion will be repeated to the sequence {6,2,3,4,5,1,8}.\n{6,2,3,4,5,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,2,3,5,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,2,5,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,2,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,1,8} The minimum elemets in the latter half of the sequence is 8.\n{6,8} The minimum elemets in the latter half of the sequence is 8.\n{8} The latter half of the sequence is empty.\n{} The latter half of the sequence is empty.\n\nFor the initial state, {5,1,8} is the latter half of the sequence.\n1 and 8 becomes the minimum element of the latter half ot the sequence.\nIn this example, the 1-st minimum element is 1 and the 2-nd is 8.\n\n6:\nIf this query is given, you should compute the maximum element of the first half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {1,3,2,5,9,6,7}.\nIn this case, the maximum element of the first half of the sequence, {1,3,2,5}, is 5.\n\n7:\nIf this query is given, you should compute the maximum element of the latter half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {1,3,2,5,9,6,7}.\nIn this case, the maximum element of the latter half of the sequence, {9,6,7}, is 9.\n\n8:\nThis query is given with an integer i .\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the first half of the sequence will become the answer for query 6.\nYou should compute the i -th maximum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th maximum elements exists when this query is given.\nLet me show an example.\nAssume that deletion will be repeated to the sequence {1,3,2,5,9,6,7}.\n{1,3,2,5,9,6,7} The maximum element in the first half of the sequence is 5.\n{1,3,2,9,6,7} The maximum element in the first half of the sequence is 3.\n{1,3,9,6,7} The maximum element in the first half of the sequence is 9.\n{1,3,6,7} The maximum element in the first half of the sequence is 3.\n{1,6,7} The maximum element in the first half of the sequence is 6.\n{1,7} The maximum element in the first half of the sequence is 1.\n{7} The maximum element in the first half of the sequence is 7.\n{} The first half of the sequence is empty.\n\nFor the initial state, {1,3,2,5} is the first half of the sequence.\n1,3 and 5 becomes the maximum element of the first half of the sequence.\nIn this example, the 1-st maximum element is 5, the 2-nd is 3 and the 3-rd is 1.\n\n9:\nThis query is given with an integer i .\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the latter half of the sequence will become the answer for query 7.\nYou should compute the i -th maximum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th maximum elements exists when this query is given.\nLet me show an example.\nAssume that deletion will be repeated to the sequence {1,3,2,5,9,6,7}.\n{1,3,2,5,9,6,7} The maximum element in the latter half of the sequence is 9.\n{1,3,2,9,6,7} The maximum element in the latter half of the sequence is 9.\n{1,3,9,6,7} The maximum element in the latter half of the sequence is 7.\n{1,3,6,7} The maximum element in the latter half of the sequence is 7.\n{1,6,7} The maximum element in the latter half of the sequence is 7.\n{1,7} The maximum element in the latter half of the sequence is 7.\n{7} The latter half of the sequence is empty.\n{} The latter half of the sequence is empty.\n\nFor the initial state, {9,6,7} is the latter half of the sequence.\n7 and 9 becomes the maximum element of the latter half of the sequence.\nIn this example, the 1-st maximum element is 9 and the 2-nd is 7.", "constraint": "", "input": "Input consists of multiple test cases.\nThe first line is the number of queries.\nFollowing q lines are queries.\n\nq\nquery_0\n. . .\nquery_i\n. . .\nqurey__q-1\n\nThe sum of the number of queries in the input data is less than 200001.\nIf query_i = 0,4,5,8, and 9 are consists of pair of integers.\nOther queries are given with a single integer.\nYou can assume that the length of the sequence doesn't exceed 20000.", "output": "If the query is 0, you don't output any numbers.\nIf the query is 1, you should output the deleted number.\nFor other queries, you should output the computed value.\nFor each case, you should output \"end\" (without quates) after you process all queries.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 1\n0 2\n0 3\n0 4\n1\n6\n0 1\n0 2\n0 3\n0 4\n0 5\n1\n31\n0 6\n0 2\n0 3\n0 4\n0 5\n0 1\n0 8\n4 1\n4 2\n5 1\n5 2\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n1\n32\n0 1\n0 3\n0 2\n0 5\n0 9\n0 6\n0 7\n8 1\n8 2\n8 3\n9 1\n9 2\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n1\n0\n output: 2\nend\n3\nend\n2\n6\n1\n8\n2\n1\n4\n2\n1\n3\n2\n1\n5\n2\n1\n2\n1\n8\n1\n6\n8\n6\n8\n8\nend\n5\n3\n1\n9\n7\n5\n9\n5\n3\n9\n2\n9\n7\n9\n3\n7\n3\n6\n7\n6\n1\n7\n1\n7\n7\nend"], "Pid": "p00655", "ProblemText": "Task Description: Your task is to simulate the sequence defined in the remaining part of the problem description.\n\nThis sequence is empty at first.\n i -th element of this sequence is expressed as a_i .\nThe first element of this sequence is a_1 if the sequence is not empty.\nThe operation is given by integer from 0 to 9.\nThe operation is described below.\n\n0:\nThis query is given with some integer x.\nIf this query is given, the integer x is inserted into the sequence.\nIf the sequence is empty, a_1 = x.\nIf the sequence has n elements, a_n+1 = x.\nSame integer will not appear more than once as x.\n\n1:\nIf this query is given, one element in the sequence is deleted.\nThe value in the middle of the sequence is deleted.\nIf the sequence has n elements and n is even, a_n/2 will be deleted.\nIf n is odd, a_⌈n/2⌉ will be deleted.\nThis query is not given when the sequence is empty.\n\nAssume that the sequence has a_1 =1, a_2 =2, a_3 =3, a_4 =4 and a_5 =5.\nIn this case, a_3 will be deleted.\nAfter deletion, the sequence will be a_1 =1, a_2 =2, a_3 =4, a_4 =5.\n\nAssume that the sequence has a_1 =1, a_2 =2, a_3 =3 and a_4 =4,\nIn this case, a_2 will be deleted.\nAfter deletion, the sequence will be a_1 =1, a_2 =3, a_3 =4.\n\n2:\nThe first half of the sequence is defined by the index from 1 to ⌈n/2⌉ .\nIf this query is given, you should compute the minimum element of the first half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {6,2,3,4,5,1,8}.\nIn this case, the minimum element of the first half of the sequence, {6,2,3,4} is 2.\n\n3:\nThe latter half of the sequence is elements that do not belong to the first half of the sequence.\nIf this query is given, you should compute the minimum element of the latter half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {6,2,3,4,5,1,8}.\nIn this case the answer for this query is 1 from {5,1,8}.\n\n4:\nThis query is given with an integer i.\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the first half of the sequence will become the answer for query 2.\nYou should compute the i -th minimum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th minimum element exists when this query is given.\n\nLet me show an example.\n\nAssume that deletion will be repeated to the sequence {6,2,3,4,5,1,8}.\n{6,2,3,4,5,1,8} The minimum element in the first half of the sequence is 2.\n{6,2,3,5,1,8} The minimum element in the first half of the sequence is 2.\n{6,2,5,1,8} The minimum element in the first half of the sequence is 2.\n{6,2,1,8} The minimum element in the first half of the sequence is 2.\n{6,1,8} The minimum element in the first half of the sequence is 1.\n{6,8} The minimum element in the first half of the sequence is 6.\n{8} The minimum element in the first half of the sequence is 8.\n{} The first half of the sequence is empty.\n\nFor the initial state, {6,2,3,4} is the first half of the sequence.\n2 and 6 become the minimum element of the first half of the sequence.\nIn this example, the 1-st minimum element is 2 and the 2-nd is 6.\n\n5:\nThis query is given with an integer i .\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the latter half of the sequence will become the answer for query 3.\nYou should compute the i -th minimum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th minimum element exists when this query is given.\n\nLet me show an example.\n\nAssume that deletion will be repeated to the sequence {6,2,3,4,5,1,8}.\n{6,2,3,4,5,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,2,3,5,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,2,5,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,2,1,8} The minimum elemets in the latter half of the sequence is 1.\n{6,1,8} The minimum elemets in the latter half of the sequence is 8.\n{6,8} The minimum elemets in the latter half of the sequence is 8.\n{8} The latter half of the sequence is empty.\n{} The latter half of the sequence is empty.\n\nFor the initial state, {5,1,8} is the latter half of the sequence.\n1 and 8 becomes the minimum element of the latter half ot the sequence.\nIn this example, the 1-st minimum element is 1 and the 2-nd is 8.\n\n6:\nIf this query is given, you should compute the maximum element of the first half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {1,3,2,5,9,6,7}.\nIn this case, the maximum element of the first half of the sequence, {1,3,2,5}, is 5.\n\n7:\nIf this query is given, you should compute the maximum element of the latter half of the sequence.\nThis query is not given when the sequence is empty.\n\nLet me show an example. \nAssume that the sequence is {1,3,2,5,9,6,7}.\nIn this case, the maximum element of the latter half of the sequence, {9,6,7}, is 9.\n\n8:\nThis query is given with an integer i .\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the first half of the sequence will become the answer for query 6.\nYou should compute the i -th maximum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th maximum elements exists when this query is given.\nLet me show an example.\nAssume that deletion will be repeated to the sequence {1,3,2,5,9,6,7}.\n{1,3,2,5,9,6,7} The maximum element in the first half of the sequence is 5.\n{1,3,2,9,6,7} The maximum element in the first half of the sequence is 3.\n{1,3,9,6,7} The maximum element in the first half of the sequence is 9.\n{1,3,6,7} The maximum element in the first half of the sequence is 3.\n{1,6,7} The maximum element in the first half of the sequence is 6.\n{1,7} The maximum element in the first half of the sequence is 1.\n{7} The maximum element in the first half of the sequence is 7.\n{} The first half of the sequence is empty.\n\nFor the initial state, {1,3,2,5} is the first half of the sequence.\n1,3 and 5 becomes the maximum element of the first half of the sequence.\nIn this example, the 1-st maximum element is 5, the 2-nd is 3 and the 3-rd is 1.\n\n9:\nThis query is given with an integer i .\nAssume that deletion is repeated until the sequence is empty.\nSome elements in the latter half of the sequence will become the answer for query 7.\nYou should compute the i -th maximum element from the answers.\nThis query is not given when the sequence is empty.\nYou can assume that i -th maximum elements exists when this query is given.\nLet me show an example.\nAssume that deletion will be repeated to the sequence {1,3,2,5,9,6,7}.\n{1,3,2,5,9,6,7} The maximum element in the latter half of the sequence is 9.\n{1,3,2,9,6,7} The maximum element in the latter half of the sequence is 9.\n{1,3,9,6,7} The maximum element in the latter half of the sequence is 7.\n{1,3,6,7} The maximum element in the latter half of the sequence is 7.\n{1,6,7} The maximum element in the latter half of the sequence is 7.\n{1,7} The maximum element in the latter half of the sequence is 7.\n{7} The latter half of the sequence is empty.\n{} The latter half of the sequence is empty.\n\nFor the initial state, {9,6,7} is the latter half of the sequence.\n7 and 9 becomes the maximum element of the latter half of the sequence.\nIn this example, the 1-st maximum element is 9 and the 2-nd is 7.\nTask Input: Input consists of multiple test cases.\nThe first line is the number of queries.\nFollowing q lines are queries.\n\nq\nquery_0\n. . .\nquery_i\n. . .\nqurey__q-1\n\nThe sum of the number of queries in the input data is less than 200001.\nIf query_i = 0,4,5,8, and 9 are consists of pair of integers.\nOther queries are given with a single integer.\nYou can assume that the length of the sequence doesn't exceed 20000.\nTask Output: If the query is 0, you don't output any numbers.\nIf the query is 1, you should output the deleted number.\nFor other queries, you should output the computed value.\nFor each case, you should output \"end\" (without quates) after you process all queries.\nTask Samples: input: 5\n0 1\n0 2\n0 3\n0 4\n1\n6\n0 1\n0 2\n0 3\n0 4\n0 5\n1\n31\n0 6\n0 2\n0 3\n0 4\n0 5\n0 1\n0 8\n4 1\n4 2\n5 1\n5 2\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n3\n1\n2\n1\n32\n0 1\n0 3\n0 2\n0 5\n0 9\n0 6\n0 7\n8 1\n8 2\n8 3\n9 1\n9 2\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n7\n1\n6\n1\n0\n output: 2\nend\n3\nend\n2\n6\n1\n8\n2\n1\n4\n2\n1\n3\n2\n1\n5\n2\n1\n2\n1\n8\n1\n6\n8\n6\n8\n8\nend\n5\n3\n1\n9\n7\n5\n9\n5\n3\n9\n2\n9\n7\n9\n3\n7\n3\n6\n7\n6\n1\n7\n1\n7\n7\nend\n\n" }, { "title": "Problem J: BD Shelf", "content": "Remember the boy called Jack. He likes anime, especially programs broadcasting in midnight or early morning. In his room, there is a big shelf and it is kept organized well. And there are anime BD/DVDs which he watched or gave up because of overlapping of broadcasting time with other animes. His money is tight, but he succeeded to get W hundreds dollars because of an unexpected event. And he came up with enhancing the content of his BD shelf.\n\nHe is troubled about the usage of the unexpected income. He has a good judge for anime to choose the anime he can enjoy because he is a great anime lover. Therefore, first of all, he listed up expectable animes and assigned each anime a value that represents \"a magnitude of expectation\". Moreover Jack tagged a mysterious string M for each anime. However Jack did not tell you the meaning of the string M.\n\nYour task is to write a program that reads a string X and that maximizes the sum of magnitudes of expectation when Jack bought BD/DVD boxes of anime with the budget of W hundreds dollars. Here, Jack must buy anime's BD/DVD box that have a string X as a sub-string of the string M assigned the anime. If he can not buy any boxes, output -1.\n\nA sequence of string X is given in order in the input as query. Assume two strings X_1 and X_2 are given as string X, and X_1 is the prefix of X_2. If X_1 is given in the input preceding X_2, you must not buy an anime which has the minimum magnitude of expectation among animes extracted by X_1 in the calculation for X_2. And vice versa (X_1 is the prefix of X_2 and if X_2 is given in the input preceding X_1, . . . ) .\nFor example, If three strings \"a\", \"abc\" and \"ab\" are given in this order in the input, In the processing for string \"abc\", you must not extract an anime which has the minimum magnitude of expectation among animes extracted by the processing of the string \"a\". In the processing for string \"ab\", you must not extract an anime has minimum magnitude of expectation among animes extracted by the processing of the string \"abc\" and \"a\".", "constraint": "There are 4 test cases. This is given by the following order.
\nIn the first testcase, 4 datasets satisfy N<=10 and Q<=10,6 datasets satisfy N<=5000 and Q<=5000.
\nIn the 2nd, 3rd and 4th testcase, each satisfies N<=20000 and Q<=20000.
\nThe time limit for this problem is the limit for each testcase.
\n1<=N<=20000
\n1<=W<=20
\n1<=(the length of string_i(1<=i<=N))<=10
\n1<=price_i(1<=i<=N)<=20
\n1<=expectation_i(1<=i<=N)<=7000000
\n1<=Q<=20000
\n1<=(the length of query_i(1<=i<=Q))<=5
\nIt is assured that all values for expectation are different.", "input": "Input consists of multiple datasets. \nA dataset is given in the following format.\n

\n\nN W\nstring_1 expectation_1 price_1\nstring_2 expectation_2 price_2\n. . .\nstring_N expectation_N price_N\nQ\nquery_1\nquery_2\n. . .\nquery_Q\n\n

\nN is an integer that represents the number of anime. Following N lines contains the information of each anime. \nstring_i(1<=i<=N) is a string consists of lowercase letters that represents string M assigned i-th anime by Jack. No two characters in this string are same. \nexpectation_i(1<=i<=N) is a natural number that represents a magnitude of expectation of the i-th anime. \nprice_i(1<=i<=N) is a natural number that represents a price(cost) in hundreds to buy the i-th anime.\nQ is an integer that represents the number of queries. \nquery_i(1<=i<=Q) is a string consists of lowercase letters. This is a string X described in the problem statement. \nN=W=0 shows the end of the input.", "output": "For each query, output an integer S on a line that represents the maximum sum of magnitudes of expectation in the following format.\n\nS", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\nabc 1 1\nabc 10 1\nabc 100 1\n3\na\nabc\nab\n3 4\nab 1 1\nab 10 1\nabc 100 1\n3\nabc\nab\na\n3 4\nabc 1 1\nabc 10 1\nabc 100 1\n3\nab\nab\nab\n8 20\nabcdef 100 2\nbcdef 200 1\ncfghj 300 3\nksjirto 400 6\nksitoew 500 2\nqwertyl 600 2\nkjhbvc 700 2\nedfghucb 800 1\n10\nks\ncd\nhj\ne\na\ng\nh\nj\ni\na\n0 0\n output: 111\n110\n100\n100\n11\n10\n111\n110\n100\n900\n300\n300\n2200\n100\n1100\n1500\n1400\n900\n-1"], "Pid": "p00656", "ProblemText": "Task Description: Remember the boy called Jack. He likes anime, especially programs broadcasting in midnight or early morning. In his room, there is a big shelf and it is kept organized well. And there are anime BD/DVDs which he watched or gave up because of overlapping of broadcasting time with other animes. His money is tight, but he succeeded to get W hundreds dollars because of an unexpected event. And he came up with enhancing the content of his BD shelf.\n\nHe is troubled about the usage of the unexpected income. He has a good judge for anime to choose the anime he can enjoy because he is a great anime lover. Therefore, first of all, he listed up expectable animes and assigned each anime a value that represents \"a magnitude of expectation\". Moreover Jack tagged a mysterious string M for each anime. However Jack did not tell you the meaning of the string M.\n\nYour task is to write a program that reads a string X and that maximizes the sum of magnitudes of expectation when Jack bought BD/DVD boxes of anime with the budget of W hundreds dollars. Here, Jack must buy anime's BD/DVD box that have a string X as a sub-string of the string M assigned the anime. If he can not buy any boxes, output -1.\n\nA sequence of string X is given in order in the input as query. Assume two strings X_1 and X_2 are given as string X, and X_1 is the prefix of X_2. If X_1 is given in the input preceding X_2, you must not buy an anime which has the minimum magnitude of expectation among animes extracted by X_1 in the calculation for X_2. And vice versa (X_1 is the prefix of X_2 and if X_2 is given in the input preceding X_1, . . . ) .\nFor example, If three strings \"a\", \"abc\" and \"ab\" are given in this order in the input, In the processing for string \"abc\", you must not extract an anime which has the minimum magnitude of expectation among animes extracted by the processing of the string \"a\". In the processing for string \"ab\", you must not extract an anime has minimum magnitude of expectation among animes extracted by the processing of the string \"abc\" and \"a\".\nTask Constraint: There are 4 test cases. This is given by the following order.
\nIn the first testcase, 4 datasets satisfy N<=10 and Q<=10,6 datasets satisfy N<=5000 and Q<=5000.
\nIn the 2nd, 3rd and 4th testcase, each satisfies N<=20000 and Q<=20000.
\nThe time limit for this problem is the limit for each testcase.
\n1<=N<=20000
\n1<=W<=20
\n1<=(the length of string_i(1<=i<=N))<=10
\n1<=price_i(1<=i<=N)<=20
\n1<=expectation_i(1<=i<=N)<=7000000
\n1<=Q<=20000
\n1<=(the length of query_i(1<=i<=Q))<=5
\nIt is assured that all values for expectation are different.\nTask Input: Input consists of multiple datasets. \nA dataset is given in the following format.\n

\n\nN W\nstring_1 expectation_1 price_1\nstring_2 expectation_2 price_2\n. . .\nstring_N expectation_N price_N\nQ\nquery_1\nquery_2\n. . .\nquery_Q\n\n

\nN is an integer that represents the number of anime. Following N lines contains the information of each anime. \nstring_i(1<=i<=N) is a string consists of lowercase letters that represents string M assigned i-th anime by Jack. No two characters in this string are same. \nexpectation_i(1<=i<=N) is a natural number that represents a magnitude of expectation of the i-th anime. \nprice_i(1<=i<=N) is a natural number that represents a price(cost) in hundreds to buy the i-th anime.\nQ is an integer that represents the number of queries. \nquery_i(1<=i<=Q) is a string consists of lowercase letters. This is a string X described in the problem statement. \nN=W=0 shows the end of the input.\nTask Output: For each query, output an integer S on a line that represents the maximum sum of magnitudes of expectation in the following format.\n\nS\nTask Samples: input: 3 4\nabc 1 1\nabc 10 1\nabc 100 1\n3\na\nabc\nab\n3 4\nab 1 1\nab 10 1\nabc 100 1\n3\nabc\nab\na\n3 4\nabc 1 1\nabc 10 1\nabc 100 1\n3\nab\nab\nab\n8 20\nabcdef 100 2\nbcdef 200 1\ncfghj 300 3\nksjirto 400 6\nksitoew 500 2\nqwertyl 600 2\nkjhbvc 700 2\nedfghucb 800 1\n10\nks\ncd\nhj\ne\na\ng\nh\nj\ni\na\n0 0\n output: 111\n110\n100\n100\n11\n10\n111\n110\n100\n900\n300\n300\n2200\n100\n1100\n1500\n1400\n900\n-1\n\n" }, { "title": "Problem K: Rearranging Seats", "content": "Haruna is a high school student.\nShe must remember the seating arrangements in her class because she is a class president.\nIt is too difficult task to remember if there are so many students.\n\nThat is the reason why seating rearrangement is depress task for her.\nBut students have a complaint if seating is fixed.\n\nOne day, she made a rule that all students must move but they don't move so far as the result of seating rearrangement.\n\nThe following is the rule.\nThe class room consists of r*c seats.\nEach r row has c seats.\nThe coordinate of the front row and most left is (1,1). The last row and right most is (r, c).\nAfter seating rearrangement, all students must move next to their seat.\nIf a student sit (y, x) before seating arrangement, his/her seat must be (y, x+1) , (y, x-1), (y+1, x) or (y-1, x).\nThe new seat must be inside of the class room. For example (0,1) or (r+1, c) is not allowed.\n\nYour task is to check whether it is possible to rearrange seats based on the above rule.\n hint:\nFor the second case, before seat rearrangement, the state is shown as follows.\n\n1 2\n3 4\n\nThere are some possible arrangements.\nFor example\n\n2 4\n1 3\n\nor\n\n2 1\n4 3\n\nis valid arrangement.", "constraint": "", "input": "Input consists of multiple datasets.\nEach dataset consists of 2 integers.\nThe last input contains two 0.\nA dataset is given by the following format.\n\nr c\n\nInput satisfies the following constraint. \n1 <= r <= 19,1 <= c <= 19", "output": "Print \"yes\" without quates in one line if it is possible to rearrange the seats, otherwise print \"no\" without quates in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1\n2 2\n0 0\n output: no\nyes"], "Pid": "p00657", "ProblemText": "Task Description: Haruna is a high school student.\nShe must remember the seating arrangements in her class because she is a class president.\nIt is too difficult task to remember if there are so many students.\n\nThat is the reason why seating rearrangement is depress task for her.\nBut students have a complaint if seating is fixed.\n\nOne day, she made a rule that all students must move but they don't move so far as the result of seating rearrangement.\n\nThe following is the rule.\nThe class room consists of r*c seats.\nEach r row has c seats.\nThe coordinate of the front row and most left is (1,1). The last row and right most is (r, c).\nAfter seating rearrangement, all students must move next to their seat.\nIf a student sit (y, x) before seating arrangement, his/her seat must be (y, x+1) , (y, x-1), (y+1, x) or (y-1, x).\nThe new seat must be inside of the class room. For example (0,1) or (r+1, c) is not allowed.\n\nYour task is to check whether it is possible to rearrange seats based on the above rule.\n hint:\nFor the second case, before seat rearrangement, the state is shown as follows.\n\n1 2\n3 4\n\nThere are some possible arrangements.\nFor example\n\n2 4\n1 3\n\nor\n\n2 1\n4 3\n\nis valid arrangement.\nTask Input: Input consists of multiple datasets.\nEach dataset consists of 2 integers.\nThe last input contains two 0.\nA dataset is given by the following format.\n\nr c\n\nInput satisfies the following constraint. \n1 <= r <= 19,1 <= c <= 19\nTask Output: Print \"yes\" without quates in one line if it is possible to rearrange the seats, otherwise print \"no\" without quates in one line.\nTask Samples: input: 1 1\n2 2\n0 0\n output: no\nyes\n\n" }, { "title": "Problem L: The Tower", "content": "Your task is to write a program that reads some lines of command for the following game and simulates operations until the player reaches the game over. We call following 2-dimensional grid of m by n characters Tower. The objective of this game is to move blocks in the tower to climb to a goal block. In the following grid, the bottom line is the first row and the top one is the n-th row. The leftmost column is the first column and the rightmost one is the m-th column.\n\n. . . . . . . . . . . . . . . . . . . . (n=13 th row)\n. . . . . #. . . . . G. . . . . . . .\n. . . . ##. . . . . ##. . . . . ##\n. . . ####. . . IIII. . . ###\n. . ####. . . . . ##. . . . . ##\n. . . ####B. . ####. . . . ##\n. . . . ###. . . . #33##. . ##\n. . . . . ####. . . #33#3. ##\n. ##CCCC#####2##. ####\n. . #####. . ###. #. . . ###\n. . . ###. . . . ###. . . . . #1\n. . . . ####. . ##. . . . . . . #\nS. . ###. . #. ####. . . . . # (1st row)\nExplanation of cell marks:\n'#' : Normal blockNormal block.\n\n'I' : Ice blockBlock made of the ice. This has different features from the normal one.\n\n'G' : Goal blockIf the player climbs to this, game is over and clear.\n\n'C' : Fixed blockThe player can not move this directly.\n\n'B' : Different dimensional blockIf the player climbs to this, game is over and lose.\n\n'. ' : SpaceEmpty place.\n\n'3' : Fragile block(3)A fragile block of count 3.\n\n'2' : Fragile block(2)A fragile block of count 2.\n\n'1' : Fragile block(1)A fragile block of count 1. If the count is zero, this block will be broken and become a space.\n\n'S' : PlayerThe player.\n\nExplanation of relative positions:\n123\n4S5\n678\n\nIn the following description, assume that left up is the position of 1, up(over S) is 2, right up is 3, left is 4, right is 5, left down is 6, down(under S) is 7, right down is 8 for S.\nMovements of the player\nThe player must not go out of the tower. The outside of the tower is considered as space cells.\n\nMoveThe player can move everywhere in the current row as long as some of the following conditions are satisfied.\n\nThe player is in the first row and the target cell is a space.\n\nThere are blocks under the route connecting the current cell and the target cell (horizontal segment) and the target cell is a space. It is OK that some blocks in the horizontal segment. And the case that some of blocks under the segment are different dimensional ones, it is also OK.\nClimb\nIf the player at the row below the n-th row (from 1st to n-1 th row) and there is a block in the right(left) and both of a cell over the player (up cell) and a right up(left up) cell are space, the player can move to the right up(left up) cell.\n\nGet down\nIf the player at the row above the 1st row (from 2nd to n-th row), he can get down to right(left) down. If the direction for getting down is right(left) and if there is no blocks in the right down (left down) cell and the right (left) cell, the player can move to the right down (left down) cell.\n\nPush\nIf there is a block or continuous blocks in the right or left of the player, he can push the blocks to the direction one cell. Here, blocks are \"continuous\" if there are two or more blocks and no space exist between them. However, if there is a fixed block in pushing blocks, the player can not push them. Pushed blocks will not stop the end of the row of the tower (1st and mth column). If the pushed blocks go out of the tower, this will be vanished. In the result of pushing, a block moved over the ice block continues to move to the pushed direction as long as there is a space in the progress direction, there is an ice block under the block and the pushed block is not vanished. \nIf the pushed block is an ice block, this continues to move to the pushed direction as long as there is a block under the ice block, there is a space in the progress direction and the pushed ice block is not vanished. However, for an ice block in the first row, the below the block do not have to be a space. And here, if the player pushes continuous blocks, pushing movements begin from the most distant block to a nearest block. Here, the distance is manhattan distance at the gird.\n\nPull\nIf there is a block in the right(left) of the player and the left(right) cell is space, the player can pull the block. However, if the pulling block is fixed one, he can not pull this. If the player pulls block, the player will move one cell to the direction of pulling.\nAutomated operations after the player operation: \nAutomated operations occur in the following order. This repeats in this order as long as the cells of the tower are changed by this operations. After this operations, the player can do the next operation.\n\nCountdown of fragile blocks\nIf the player over a fragile block moved to somewhere else, that fragile block's count will decrease by one. However, this count does not change if the player over the fragile block is moved to somewhere else by the automated operations.\n\nErasing blocksA block over an different dimensional block will be vanished.\n\nFalling of the playerIf there is no block under the player, the player continues to fall as long as satisfying this condition or come to 1st row.\n\nFalling of blocksIf there is no block under a block and left down and right down of a certain block, the block in the row over the 1st row (from 2nd to n-th row) continues to fall as long as satisfying this condition. Falling of blocks begins from lower blocks of the tower and then lefter blocks.\n\nConditions for game over: \nAfter the movement of the player or the automated operations, the game is over when the one of next conditions is satisfied. These conditions are judged in the following order. Note that, the condition (E) should not be judged after the movement of the player.\n\n(A) The player is over the goal block.\n\n(B) The player is over the different dimensional block.\n\n(C) The player and a block is in the same cell.\n\n(D) The goal block is moved from its initial position.\n\n(E) There is no next commands.\n\nFinally, show some examples. \nDocuments of commands will be give in the description of Input. \n\n Movement orAutomated operation Before After Command \n\n Move . #S### S#. ### MOVETO 1 \n Climb . . . 3S# S. . 3. # CLIMB LEFT \n Get down S. . 3. # . . . 2S# GETDOWN RIGHT \n Push . #S#####. . ###II. I. I. . #S. ####. ####II. I. I. PUSH RIGHT \n Push . #SI. . . ###. ### . #S. . . . ###. ### PUSH RIGHT \n Push . #. . . S####. ### . . . . . S. ###. ### PUSH RIGHT \n Pull . . S#####. . ###. #. #. #. . S#. ####. . ###. #. #. #. PULL LEFT \n Falling of the player . #S#. #. #. #. #. #. # . #. #. #. #. #. #. #S# - \n Falling of blocks . ###. #. . . ##. . . ##. . . #. #. # . #. #. #. . . ##. . . ##. #. #. #. # -", "constraint": "3<=m<=50
\n3<=n<=50
\nCharacters 'S' and 'G' will appear exactly once in the tower description.", "input": "Input consists of multiple datasets. \nA dataset is given in the following format.\n\nn m\nD_n, 1 D_n, 2 . . . D_n, m\nD_n-1,1 D_n-1,2 . . . D_n-1, m\n. . .\nD_1,1 D_1,2 . . . D_1, m\nT\nCommand_1\nCommand_2\n. . .\nCommand_T\n\nHere, m, n is the width and height of the tower. D_i, j(1<=i<=n and 1<=j<=m) is a mark of the cell. The explanation of marks described above. Command_k(1<=k<=T) is the k-th player operation (movement). This is a string and one of following strings.\n\n\"MOVETO s\" means move to s-th column cell in the same row.\n\"PUSH RIGHT\" means push right block(s).\n\"PUSH LEFT\" means push left block(s).\n\"PULL RIGHT\" means pull the left block to right.\n\"PULL LEFT\" means pull the right block to left.\n\"GETDOWN RIGHT\" means get down to right down.\n\"GETDOWN LEFT\" means get down to left down.\n\"CLIMB RIGHT\" means climb to the right block.\n\"CLIMB LEFT\" means climb to the left block.\n\nSome of commands are invalid. You must ignore these commands. And after game is over, the command input may continue in case. In this case, you must also ignore following commands. m=n=0 shows the end of input.", "output": "Each dataset, output a string that represents the result of the game in the following format.\n\nResult\nHere, Result is a string and one of the following strings (quotes for clarity).\n\"Game Over : Cleared\" (A)\n\n\"Game Over : Death by Hole\" (B)\n\n\"Game Over : Death by Block\" (C)\n\n\"Game Over : Death by Walking Goal\" (D)\n\n\"Game Over : Gave Up\" (E)", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 8\n........\n........\n....###.\n...#.#.G\nS#B...##\n#ICII.I#\n#..#.#.#\n.#..#.#.\n7\nPUSH RIGHT\nMOVETO 2\nCLIMB RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\n8 8\n........\n........\n........\n...G....\nS#B.....\n#ICIIIII\n#..#.#.#\n.#..#.#.\n4\nPUSH RIGHT\nMOVETO 2\nCLIMB RIGHT\nCLIMB RIGHT\n8 8\n........\n....#.#.\n.....#.G\n...#..#.\nS#B....#\n#ICIII.#\n#..#.#.#\n.#..#.#.\n8\nPUSH RIGHT\nMOVETO 2\nCLIMB RIGHT\nCLIMB RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\n0 0\n output: Game Over : Death by Hole\nGame Over : Cleared\nGame Over : Death by Walking Goal"], "Pid": "p00658", "ProblemText": "Task Description: Your task is to write a program that reads some lines of command for the following game and simulates operations until the player reaches the game over. We call following 2-dimensional grid of m by n characters Tower. The objective of this game is to move blocks in the tower to climb to a goal block. In the following grid, the bottom line is the first row and the top one is the n-th row. The leftmost column is the first column and the rightmost one is the m-th column.\n\n. . . . . . . . . . . . . . . . . . . . (n=13 th row)\n. . . . . #. . . . . G. . . . . . . .\n. . . . ##. . . . . ##. . . . . ##\n. . . ####. . . IIII. . . ###\n. . ####. . . . . ##. . . . . ##\n. . . ####B. . ####. . . . ##\n. . . . ###. . . . #33##. . ##\n. . . . . ####. . . #33#3. ##\n. ##CCCC#####2##. ####\n. . #####. . ###. #. . . ###\n. . . ###. . . . ###. . . . . #1\n. . . . ####. . ##. . . . . . . #\nS. . ###. . #. ####. . . . . # (1st row)\nExplanation of cell marks:\n'#' : Normal blockNormal block.\n\n'I' : Ice blockBlock made of the ice. This has different features from the normal one.\n\n'G' : Goal blockIf the player climbs to this, game is over and clear.\n\n'C' : Fixed blockThe player can not move this directly.\n\n'B' : Different dimensional blockIf the player climbs to this, game is over and lose.\n\n'. ' : SpaceEmpty place.\n\n'3' : Fragile block(3)A fragile block of count 3.\n\n'2' : Fragile block(2)A fragile block of count 2.\n\n'1' : Fragile block(1)A fragile block of count 1. If the count is zero, this block will be broken and become a space.\n\n'S' : PlayerThe player.\n\nExplanation of relative positions:\n123\n4S5\n678\n\nIn the following description, assume that left up is the position of 1, up(over S) is 2, right up is 3, left is 4, right is 5, left down is 6, down(under S) is 7, right down is 8 for S.\nMovements of the player\nThe player must not go out of the tower. The outside of the tower is considered as space cells.\n\nMoveThe player can move everywhere in the current row as long as some of the following conditions are satisfied.\n\nThe player is in the first row and the target cell is a space.\n\nThere are blocks under the route connecting the current cell and the target cell (horizontal segment) and the target cell is a space. It is OK that some blocks in the horizontal segment. And the case that some of blocks under the segment are different dimensional ones, it is also OK.\nClimb\nIf the player at the row below the n-th row (from 1st to n-1 th row) and there is a block in the right(left) and both of a cell over the player (up cell) and a right up(left up) cell are space, the player can move to the right up(left up) cell.\n\nGet down\nIf the player at the row above the 1st row (from 2nd to n-th row), he can get down to right(left) down. If the direction for getting down is right(left) and if there is no blocks in the right down (left down) cell and the right (left) cell, the player can move to the right down (left down) cell.\n\nPush\nIf there is a block or continuous blocks in the right or left of the player, he can push the blocks to the direction one cell. Here, blocks are \"continuous\" if there are two or more blocks and no space exist between them. However, if there is a fixed block in pushing blocks, the player can not push them. Pushed blocks will not stop the end of the row of the tower (1st and mth column). If the pushed blocks go out of the tower, this will be vanished. In the result of pushing, a block moved over the ice block continues to move to the pushed direction as long as there is a space in the progress direction, there is an ice block under the block and the pushed block is not vanished. \nIf the pushed block is an ice block, this continues to move to the pushed direction as long as there is a block under the ice block, there is a space in the progress direction and the pushed ice block is not vanished. However, for an ice block in the first row, the below the block do not have to be a space. And here, if the player pushes continuous blocks, pushing movements begin from the most distant block to a nearest block. Here, the distance is manhattan distance at the gird.\n\nPull\nIf there is a block in the right(left) of the player and the left(right) cell is space, the player can pull the block. However, if the pulling block is fixed one, he can not pull this. If the player pulls block, the player will move one cell to the direction of pulling.\nAutomated operations after the player operation: \nAutomated operations occur in the following order. This repeats in this order as long as the cells of the tower are changed by this operations. After this operations, the player can do the next operation.\n\nCountdown of fragile blocks\nIf the player over a fragile block moved to somewhere else, that fragile block's count will decrease by one. However, this count does not change if the player over the fragile block is moved to somewhere else by the automated operations.\n\nErasing blocksA block over an different dimensional block will be vanished.\n\nFalling of the playerIf there is no block under the player, the player continues to fall as long as satisfying this condition or come to 1st row.\n\nFalling of blocksIf there is no block under a block and left down and right down of a certain block, the block in the row over the 1st row (from 2nd to n-th row) continues to fall as long as satisfying this condition. Falling of blocks begins from lower blocks of the tower and then lefter blocks.\n\nConditions for game over: \nAfter the movement of the player or the automated operations, the game is over when the one of next conditions is satisfied. These conditions are judged in the following order. Note that, the condition (E) should not be judged after the movement of the player.\n\n(A) The player is over the goal block.\n\n(B) The player is over the different dimensional block.\n\n(C) The player and a block is in the same cell.\n\n(D) The goal block is moved from its initial position.\n\n(E) There is no next commands.\n\nFinally, show some examples. \nDocuments of commands will be give in the description of Input.
Example table
\n\n Movement orAutomated operation Before After Command \n\n Move . #S### S#. ### MOVETO 1 \n Climb . . . 3S# S. . 3. # CLIMB LEFT \n Get down S. . 3. # . . . 2S# GETDOWN RIGHT \n Push . #S#####. . ###II. I. I. . #S. ####. ####II. I. I. PUSH RIGHT \n Push . #SI. . . ###. ### . #S. . . . ###. ### PUSH RIGHT \n Push . #. . . S####. ### . . . . . S. ###. ### PUSH RIGHT \n Pull . . S#####. . ###. #. #. #. . S#. ####. . ###. #. #. #. PULL LEFT \n Falling of the player . #S#. #. #. #. #. #. # . #. #. #. #. #. #. #S# - \n Falling of blocks . ###. #. . . ##. . . ##. . . #. #. # . #. #. #. . . ##. . . ##. #. #. #. # -\nTask Constraint: 3<=m<=50
\n3<=n<=50
\nCharacters 'S' and 'G' will appear exactly once in the tower description.\nTask Input: Input consists of multiple datasets. \nA dataset is given in the following format.\n\nn m\nD_n, 1 D_n, 2 . . . D_n, m\nD_n-1,1 D_n-1,2 . . . D_n-1, m\n. . .\nD_1,1 D_1,2 . . . D_1, m\nT\nCommand_1\nCommand_2\n. . .\nCommand_T\n\nHere, m, n is the width and height of the tower. D_i, j(1<=i<=n and 1<=j<=m) is a mark of the cell. The explanation of marks described above. Command_k(1<=k<=T) is the k-th player operation (movement). This is a string and one of following strings.\n\n\"MOVETO s\" means move to s-th column cell in the same row.\n\"PUSH RIGHT\" means push right block(s).\n\"PUSH LEFT\" means push left block(s).\n\"PULL RIGHT\" means pull the left block to right.\n\"PULL LEFT\" means pull the right block to left.\n\"GETDOWN RIGHT\" means get down to right down.\n\"GETDOWN LEFT\" means get down to left down.\n\"CLIMB RIGHT\" means climb to the right block.\n\"CLIMB LEFT\" means climb to the left block.\n\nSome of commands are invalid. You must ignore these commands. And after game is over, the command input may continue in case. In this case, you must also ignore following commands. m=n=0 shows the end of input.\nTask Output: Each dataset, output a string that represents the result of the game in the following format.\n\nResult\nHere, Result is a string and one of the following strings (quotes for clarity).\n\"Game Over : Cleared\" (A)\n\n\"Game Over : Death by Hole\" (B)\n\n\"Game Over : Death by Block\" (C)\n\n\"Game Over : Death by Walking Goal\" (D)\n\n\"Game Over : Gave Up\" (E)\nTask Samples: input: 8 8\n........\n........\n....###.\n...#.#.G\nS#B...##\n#ICII.I#\n#..#.#.#\n.#..#.#.\n7\nPUSH RIGHT\nMOVETO 2\nCLIMB RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\n8 8\n........\n........\n........\n...G....\nS#B.....\n#ICIIIII\n#..#.#.#\n.#..#.#.\n4\nPUSH RIGHT\nMOVETO 2\nCLIMB RIGHT\nCLIMB RIGHT\n8 8\n........\n....#.#.\n.....#.G\n...#..#.\nS#B....#\n#ICIII.#\n#..#.#.#\n.#..#.#.\n8\nPUSH RIGHT\nMOVETO 2\nCLIMB RIGHT\nCLIMB RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\nCLIMB RIGHT\nGETDOWN RIGHT\n0 0\n output: Game Over : Death by Hole\nGame Over : Cleared\nGame Over : Death by Walking Goal\n\n" }, { "title": "Area of Polygons", "content": "Polygons are the most fundamental objects in geometric processing.\nComplex figures are often represented and handled as polygons\nwith many short sides.\nIf you are interested in the processing of geometric data,\nyou'd better try some programming exercises about basic\noperations on polygons.\n\nYour job in this problem is to write a program that computes the area of polygons.\n\nA polygon is represented by a sequence of points that are its vertices.\nIf the vertices p_1, p_2, . . . , p_n are given, line segments connecting\np_i and p_i+1 (1 <= i <= n-1) are sides of the polygon.\nThe line segment connecting p_n and p_1 is also a side of the polygon.\n\nYou can assume that the polygon is not degenerate.\nNamely, the following facts can be assumed without any input data checking.\n\nNo point will occur as a vertex more than once.\n\nTwo sides can intersect only at a common endpoint (vertex).\n\nThe polygon has at least 3 vertices.\nNote that the polygon is not necessarily convex.\nIn other words, an inner angle may be larger than 180 degrees.", "constraint": "", "input": "The input contains multiple data sets, each representing a polygon.\nA data set is given in the following format.\n n\n x1 y1\n x2 y2\n . . .\n xn yn\nThe first integer n is the number of vertices,\nsuch that 3 <= n <= 50.\nThe coordinate of a vertex p_i is given by (x_i, y_i).\nx_i and y_i are integers between 0 and 1000 inclusive.\nThe coordinates of vertices are given in the order\nof clockwise visit of them. The end of input is indicated by a data set with 0 as the value of n.", "output": "For each data set, your program should output its sequence number\n(1 for the first data set, 2 for the second, etc. ) and the area of the polygon separated by a single space. The area should be printed with one digit to the right of the decimal point. The sequence number and the area should be printed on the same line.\nSince your result is checked by an automatic grading program,\nyou should not insert any extra characters nor lines on the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1\n3 4\n6 0\n\n7\n0 0\n10 10\n0 20\n10 30\n0 40\n100 40\n100 0\n\n0\n output: 1 8.5\n2 3800.0"], "Pid": "p00682", "ProblemText": "Task Description: Polygons are the most fundamental objects in geometric processing.\nComplex figures are often represented and handled as polygons\nwith many short sides.\nIf you are interested in the processing of geometric data,\nyou'd better try some programming exercises about basic\noperations on polygons.\n\nYour job in this problem is to write a program that computes the area of polygons.\n\nA polygon is represented by a sequence of points that are its vertices.\nIf the vertices p_1, p_2, . . . , p_n are given, line segments connecting\np_i and p_i+1 (1 <= i <= n-1) are sides of the polygon.\nThe line segment connecting p_n and p_1 is also a side of the polygon.\n\nYou can assume that the polygon is not degenerate.\nNamely, the following facts can be assumed without any input data checking.\n\nNo point will occur as a vertex more than once.\n\nTwo sides can intersect only at a common endpoint (vertex).\n\nThe polygon has at least 3 vertices.\nNote that the polygon is not necessarily convex.\nIn other words, an inner angle may be larger than 180 degrees.\nTask Input: The input contains multiple data sets, each representing a polygon.\nA data set is given in the following format.\n n\n x1 y1\n x2 y2\n . . .\n xn yn\nThe first integer n is the number of vertices,\nsuch that 3 <= n <= 50.\nThe coordinate of a vertex p_i is given by (x_i, y_i).\nx_i and y_i are integers between 0 and 1000 inclusive.\nThe coordinates of vertices are given in the order\nof clockwise visit of them. The end of input is indicated by a data set with 0 as the value of n.\nTask Output: For each data set, your program should output its sequence number\n(1 for the first data set, 2 for the second, etc. ) and the area of the polygon separated by a single space. The area should be printed with one digit to the right of the decimal point. The sequence number and the area should be printed on the same line.\nSince your result is checked by an automatic grading program,\nyou should not insert any extra characters nor lines on the output.\nTask Samples: input: 3\n1 1\n3 4\n6 0\n\n7\n0 0\n10 10\n0 20\n10 30\n0 40\n100 40\n100 0\n\n0\n output: 1 8.5\n2 3800.0\n\n" }, { "title": "A Simple Offline Text Editor", "content": "A text editor is a useful software tool that can help people in various situations including writing and programming. Your job in this problem is to construct an offline text editor, i. e. , to write a program that first reads a given text and a sequence of editing commands and finally reports the text obtained by performing successively the commands in the given sequence. The editor has a text buffer and a cursor. The target text is stored in the text buffer and most editing commands are performed around the cursor. The cursor has its position that is either the beginning of the text, the end of the text, or between two consecutive characters in the text. The initial cursor position (i. e. , the cursor position just after reading the initial text) is the beginning of the text. A text manipulated by the editor is a single line consisting of a sequence of characters, each of which must be one of the following: 'a' through 'z', 'A' through 'Z', '0' through '9', '. ' (period), ', ' (comma), and ' ' (blank). You can assume that any other characters never occur in the text buffer. You can also assume that the target text consists of at most 1,000 characters at any time. The definition of words in this problem is a little strange: a word is a non-empty character sequence delimited by not only blank characters but also the cursor. For instance, in the following text with a cursor represented as '^', \n\nHe^llo, World. \n the words are the following. \n\nHe\nllo,\nWorld. \n Notice that punctuation characters may appear in words as shown in this example. The editor accepts the following set of commands. In the command list, \"any-text\" represents any text surrounded by a pair of double quotation marks such as \"abc\" and \"Co. , Ltd. \".
Example table
\n
\nCommand \n\n

Descriptions \n

\nforward char \n\nMove the cursor by one character to the right, unless the cursor is already at the end of the text. \n \nforward word \n\nMove the cursor to the end of the leftmost word in the right. If no words occur in the right, move it to the end of the text. \n \nbackward char \n\nMove the cursor by one character to the left, unless the cursor is already at the beginning of the text. \n \nbackward word \n\nMove the cursor to the beginning of the rightmost word in the left. If no words occur in the left, move it to the beginning of the text. \n \ninsert \"any-text\" \n\nInsert any-text (excluding double quotation marks) at the position specified by the cursor. After performing this command, the new cursor position is at the end of the inserted text. The length of any-text is less than or equal to 100. \n \ndelete char \n\nDelete the character that is right next to the cursor, if it exists. \n \ndelete word \n\nDelete the leftmost word in the right of the cursor. If one or more blank characters occur between the cursor and the word before performing this command, delete these blanks, too. If no words occur in the right, delete no characters in the text buffer.", "constraint": "", "input": "The first input line contains a positive integer, which represents the number of texts the editor will edit. For each text, the input contains the following descriptions:\n\nThe first line is an initial text whose length is at most 100.\n\nThe second line contains an integer M representing the number of editing commands.\n\nEach of the third through the M+2nd lines contains an editing command.\n\nYou can assume that every input line is in a proper format or has no syntax errors. You can also assume that every input line has no leading or trailing spaces and that just a single blank character occurs between a command name (e. g. , forward) and its argument (e. g. , char).", "output": "For each input text, print the final text with a character '^' representing the cursor position. Each output line shall contain exactly a single text with a character '^'.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nA sample input\n9\nforward word\ndelete char\nforward word\ndelete char\nforward word\ndelete char\nbackward word\nbackward word\nforward word\nHallow, Word.\n7\nforward char\ndelete word\ninsert \"ello, \"\nforward word\nbackward char\nbackward char\ninsert \"l\"\n\n3\nforward word\nbackward word\ndelete word\n output: \nAsampleinput^\nHello, Worl^d.\n^"], "Pid": "p00683", "ProblemText": "Task Description: A text editor is a useful software tool that can help people in various situations including writing and programming. Your job in this problem is to construct an offline text editor, i. e. , to write a program that first reads a given text and a sequence of editing commands and finally reports the text obtained by performing successively the commands in the given sequence. The editor has a text buffer and a cursor. The target text is stored in the text buffer and most editing commands are performed around the cursor. The cursor has its position that is either the beginning of the text, the end of the text, or between two consecutive characters in the text. The initial cursor position (i. e. , the cursor position just after reading the initial text) is the beginning of the text. A text manipulated by the editor is a single line consisting of a sequence of characters, each of which must be one of the following: 'a' through 'z', 'A' through 'Z', '0' through '9', '. ' (period), ', ' (comma), and ' ' (blank). You can assume that any other characters never occur in the text buffer. You can also assume that the target text consists of at most 1,000 characters at any time. The definition of words in this problem is a little strange: a word is a non-empty character sequence delimited by not only blank characters but also the cursor. For instance, in the following text with a cursor represented as '^', \n\nHe^llo, World. \n the words are the following. \n\nHe\nllo,\nWorld. \n Notice that punctuation characters may appear in words as shown in this example. The editor accepts the following set of commands. In the command list, \"any-text\" represents any text surrounded by a pair of double quotation marks such as \"abc\" and \"Co. , Ltd. \". \n
\nCommand \n\n

Descriptions \n

\nforward char \n\nMove the cursor by one character to the right, unless the cursor is already at the end of the text. \n \nforward word \n\nMove the cursor to the end of the leftmost word in the right. If no words occur in the right, move it to the end of the text. \n \nbackward char \n\nMove the cursor by one character to the left, unless the cursor is already at the beginning of the text. \n \nbackward word \n\nMove the cursor to the beginning of the rightmost word in the left. If no words occur in the left, move it to the beginning of the text. \n \ninsert \"any-text\" \n\nInsert any-text (excluding double quotation marks) at the position specified by the cursor. After performing this command, the new cursor position is at the end of the inserted text. The length of any-text is less than or equal to 100. \n \ndelete char \n\nDelete the character that is right next to the cursor, if it exists. \n \ndelete word \n\nDelete the leftmost word in the right of the cursor. If one or more blank characters occur between the cursor and the word before performing this command, delete these blanks, too. If no words occur in the right, delete no characters in the text buffer.\nTask Input: The first input line contains a positive integer, which represents the number of texts the editor will edit. For each text, the input contains the following descriptions:\n\nThe first line is an initial text whose length is at most 100.\n\nThe second line contains an integer M representing the number of editing commands.\n\nEach of the third through the M+2nd lines contains an editing command.\n\nYou can assume that every input line is in a proper format or has no syntax errors. You can also assume that every input line has no leading or trailing spaces and that just a single blank character occurs between a command name (e. g. , forward) and its argument (e. g. , char).\nTask Output: For each input text, print the final text with a character '^' representing the cursor position. Each output line shall contain exactly a single text with a character '^'.\nTask Samples: input: 3\nA sample input\n9\nforward word\ndelete char\nforward word\ndelete char\nforward word\ndelete char\nbackward word\nbackward word\nforward word\nHallow, Word.\n7\nforward char\ndelete word\ninsert \"ello, \"\nforward word\nbackward char\nbackward char\ninsert \"l\"\n\n3\nforward word\nbackward word\ndelete word\n output: \nAsampleinput^\nHello, Worl^d.\n^\n\n" }, { "title": "Calculation of Expressions", "content": "Write a program to calculate values of arithmetic expressions which may\ninvolve complex numbers. Details of the expressions are described below. In this problem, basic elements of expressions are \nnon-negative integer numbers and\nthe special symbol \"i\". Integer numbers are sequences\nof digits of arbitrary length and are in decimal notation. \"i\" denotes the\nunit imaginary number i, i. e. i^ 2 = -1. Operators appearing in expressions are + (addition), -\n(subtraction), and * (multiplication). Division is excluded from\nthe repertoire of the operators. All three operators are only used as binary\noperators. Unary plus and minus operators (e. g. , -100) are also\nexcluded from the repertoire. Note that the multiplication symbol *\nmay not be omitted in any case. For example, the expression 1+3i\nin mathematics should be written as 1+3*i. Usual formation rules of arithmetic expressions apply. Namely, (1) The\noperator * binds its operands stronger than the operators +\nand -. (2) The operators + and - have the same\nstrength in operand binding. (3) Two operators of the same strength bind\nfrom left to right. (4) Parentheses are used to designate specific order\nof binding. The consequence of these rules can easily be understood from the following\nexamples. \n\n(1) 3+4*5 is 3+(4*5), not (3+4)*5\n (2) 5-6+7 is (5-6)+7, not 5-(6+7)\n (3) 1+2+3 is (1+2)+3, not 1+(2+3)\n\nYour program should successively read expressions, calculate them and\n print their results. Overflow should be detected. Whenever an abnormal value is yielded as a result of applying an operator\nappearing in the given expression, \nyour program should report that the calculation failed due to overflow. \nBy \"an abnormal value\", we mean a value \nwhose real part or imaginary part is\ngreater than 10000 or less than -10000. Here are examples: \n \n
10000+1+(0-10) \noverflow, not 9991 \n\n \n(10*i+100)*(101+20*i) \n9900+3010i , not overflow \n\n \n4000000-4000000 \noverflow, not 0 \n\n \nNote that the law of associativity does not necessarily hold in this\nproblem. For example, in the first example, \noverflow is detected by interpreting\nthe expression as (10000+1)+(0-10) following the binding rules,\nwhereas overflow could not be detected \nif you interpreted it as 10000+(1+(0-10)).\nMoreover, overflow detection should take place for resulting value of each\noperation. In the second example, a value which exceeds 10000 appears\nin the calculation process of one multiplication \nif you use the mathematical rule\n(a+b i)(c+d i)=(ac-bd)+(ad+bc)i\n .\nBut the yielded result 9900+3010i does not contain any number\nwhich exceeds 10000 and, therefore, overflow should not be reported.", "constraint": "", "input": "A sequence of lines each of which contains an expression is given as\ninput. Each line consists of less than 100 characters and does not contain\nany blank spaces. You may assume that all expressions given in the sequence\nare syntactically correct.", "output": "Your program should produce output for each expression line by line.\nIf overflow is detected, output should be \na character string \"overflow\".\nOtherwise, output should be the resulting value of calculation\nin the following fashion.\n0 , if the result is 0+0i.\n -123 , if the result is -123+0i.\n 45i , if the result is 0+45i.\n 3+1i , if the result is 3+i.\n 123-45i , if the result is 123-45i.\n\nOutput should not contain any blanks, surplus 0,\n+, or -.", "content_img": false, "lang": "en", "error": false, "samples": ["input: (1-10*i)+00007+(3+10*i)\n3+4*i*(4+10*i)\n(102+10*i)*(99+10*i)\n2*i+3+9999*i+4\n output: 11\n-37+16i\n9998+2010i\noverflow"], "Pid": "p00684", "ProblemText": "Task Description: Write a program to calculate values of arithmetic expressions which may\ninvolve complex numbers. Details of the expressions are described below. In this problem, basic elements of expressions are \nnon-negative integer numbers and\nthe special symbol \"i\". Integer numbers are sequences\nof digits of arbitrary length and are in decimal notation. \"i\" denotes the\nunit imaginary number i, i. e. i^ 2 = -1. Operators appearing in expressions are + (addition), -\n(subtraction), and * (multiplication). Division is excluded from\nthe repertoire of the operators. All three operators are only used as binary\noperators. Unary plus and minus operators (e. g. , -100) are also\nexcluded from the repertoire. Note that the multiplication symbol *\nmay not be omitted in any case. For example, the expression 1+3i\nin mathematics should be written as 1+3*i. Usual formation rules of arithmetic expressions apply. Namely, (1) The\noperator * binds its operands stronger than the operators +\nand -. (2) The operators + and - have the same\nstrength in operand binding. (3) Two operators of the same strength bind\nfrom left to right. (4) Parentheses are used to designate specific order\nof binding. The consequence of these rules can easily be understood from the following\nexamples. \n\n(1) 3+4*5 is 3+(4*5), not (3+4)*5\n (2) 5-6+7 is (5-6)+7, not 5-(6+7)\n (3) 1+2+3 is (1+2)+3, not 1+(2+3)\n\nYour program should successively read expressions, calculate them and\n print their results. Overflow should be detected. Whenever an abnormal value is yielded as a result of applying an operator\nappearing in the given expression, \nyour program should report that the calculation failed due to overflow. \nBy \"an abnormal value\", we mean a value \nwhose real part or imaginary part is\ngreater than 10000 or less than -10000. Here are examples: \n \n\n \n \n \n\n \n Figure 1. given circles \n Figure 2. rope layout \n We want to enclose all these circles by a rope. Of course, the length of the \nrope should be minimized. For example, given circles of Figure 1, the rope \nshould run as shown in Figure 2. Your job is to write a program which finds the rope layout, and computes the \nminimum length of the rope. The thickness of the rope is negligible.", "constraint": "", "input": "The input consists of multiple data sets. Each data set is given in the \nfollowing format. n\nx_1 y_1 r_1\nx_2 y_2 r_2\n. . .\nx_n y_n r_n\nThe first line of a data set contains an integer n, which is the \nnumber of circles. n is positive, and does not exceed 100. The following n lines are descriptions of circles. Three values in a \nline are x-coordinate and y-coordinate of the center, and radius \n(called r in the rest of the problem) of the circle, in this order. Each \nvalue is given by a decimal fraction, with 3 digits after the decimal point. \nValues are separated by a space character. Each of x, y and r is never less than 0.01, and is never \ngreater than 100.0. Two circles are never the same. Speaking more precisely, at \nleast one of x, y or r of two circles has a difference \nlarger than 0.01. The end of the input is indicated by a line containing a zero.", "output": "For each data set, the minimum length of the rope should be printed, each in \na separate line. The printed values should have 5 digits after the decimal \npoint. They may not have an error greater than 0.00001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n10.000 10.000 10.000\n4\n10.000 10.000 5.000\n30.000 10.000 5.000\n30.000 30.000 5.000\n10.000 30.000 5.000\n6\n10.000 20.000 10.000\n20.000 50.000 5.000\n30.000 40.000 2.000\n1.000 2.000 3.000\n10.000 20.000 20.000\n20.000 40.000 1.500\n0\n output: 62.83185\n111.41593\n153.16052"], "Pid": "p00704", "ProblemText": "Task Description: A number of circles are given. A circle may be disjoint from other circles, \noverlapping with some other circles, or even totally surrounding or surrounded \nby another circle. \n\n \n \n \n\n \n Figure 1. given circles \n Figure 2. rope layout \n We want to enclose all these circles by a rope. Of course, the length of the \nrope should be minimized. For example, given circles of Figure 1, the rope \nshould run as shown in Figure 2. Your job is to write a program which finds the rope layout, and computes the \nminimum length of the rope. The thickness of the rope is negligible.\nTask Input: The input consists of multiple data sets. Each data set is given in the \nfollowing format. n\nx_1 y_1 r_1\nx_2 y_2 r_2\n. . .\nx_n y_n r_n\nThe first line of a data set contains an integer n, which is the \nnumber of circles. n is positive, and does not exceed 100. The following n lines are descriptions of circles. Three values in a \nline are x-coordinate and y-coordinate of the center, and radius \n(called r in the rest of the problem) of the circle, in this order. Each \nvalue is given by a decimal fraction, with 3 digits after the decimal point. \nValues are separated by a space character. Each of x, y and r is never less than 0.01, and is never \ngreater than 100.0. Two circles are never the same. Speaking more precisely, at \nleast one of x, y or r of two circles has a difference \nlarger than 0.01. The end of the input is indicated by a line containing a zero.\nTask Output: For each data set, the minimum length of the rope should be printed, each in \na separate line. The printed values should have 5 digits after the decimal \npoint. They may not have an error greater than 0.00001.\nTask Samples: input: 1\n10.000 10.000 10.000\n4\n10.000 10.000 5.000\n30.000 10.000 5.000\n30.000 30.000 5.000\n10.000 30.000 5.000\n6\n10.000 20.000 10.000\n20.000 50.000 5.000\n30.000 40.000 2.000\n1.000 2.000 3.000\n10.000 20.000 20.000\n20.000 40.000 1.500\n0\n output: 62.83185\n111.41593\n153.16052\n\n" }, { "title": "When Can We Meet?", "content": "The ICPC committee would like to have its meeting as soon as\npossible to address every little issue of the next contest. \nHowever, members of the committee are so busy maniacally developing\n(possibly useless) programs that it is very difficult to arrange\ntheir schedules for the meeting.\nSo, in order to settle the meeting date, the chairperson requested every\nmember to send back a list of convenient dates by E-mail.\nYour mission is to help the chairperson, who is now dedicated to other\nissues of the contest, by writing a program that \nchooses the best date from the submitted lists.\nYour program should find the date convenient for the most members.\nIf there is more than one such day, the earliest is the best.", "constraint": "", "input": "The input has multiple data sets, each starting with a line\ncontaining the number of committee members and the quorum of the meeting.\nN Q\n

\nHere, N, meaning the size of the committee, and Q\nmeaning the quorum, are positive integers. N is less than 50,\nand, of course, Q is less than or equal to N. \nN lines follow, each describing convenient dates for a\ncommittee\nmember in the following format.\n\nM Date_1\nDate_2 . . . Date_M\n\n

\nHere, M means the number of convenient dates for\nthe member, which is an integer greater than or equal to zero.\nThe remaining items in the line are his/her dates of convenience,\nwhich are positive integers less than 100, that is, 1 means tomorrow, \n2 means the day after tomorrow, and so on.\nThey are in ascending order without any repetition \nand separated by a space character.\nLines have neither leading nor trailing spaces.\nA line containing two zeros indicates the end of the input.", "output": "For each data set, print a single line containing the date number\nconvenient for the largest number of committee members.\n If there is more than one\nsuch date, print the earliest. However, if no dates are convenient\nfor more than or equal to the quorum number of members, print 0 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n2 1 4\n0\n3 3 4 8\n3 2\n4 1 5 8 9\n3 2 5 9\n5 2 4 5 7 9\n3 3\n2 1 4\n3 2 5 9\n2 2 4\n3 3\n2 1 2\n3 1 2 9\n2 2 4\n0 0\n output: 4\n5\n0\n2"], "Pid": "p00705", "ProblemText": "Task Description: The ICPC committee would like to have its meeting as soon as\npossible to address every little issue of the next contest. \nHowever, members of the committee are so busy maniacally developing\n(possibly useless) programs that it is very difficult to arrange\ntheir schedules for the meeting.\nSo, in order to settle the meeting date, the chairperson requested every\nmember to send back a list of convenient dates by E-mail.\nYour mission is to help the chairperson, who is now dedicated to other\nissues of the contest, by writing a program that \nchooses the best date from the submitted lists.\nYour program should find the date convenient for the most members.\nIf there is more than one such day, the earliest is the best.\nTask Input: The input has multiple data sets, each starting with a line\ncontaining the number of committee members and the quorum of the meeting.\nN Q\n

\nHere, N, meaning the size of the committee, and Q\nmeaning the quorum, are positive integers. N is less than 50,\nand, of course, Q is less than or equal to N. \nN lines follow, each describing convenient dates for a\ncommittee\nmember in the following format.\n\nM Date_1\nDate_2 . . . Date_M\n\n

\nHere, M means the number of convenient dates for\nthe member, which is an integer greater than or equal to zero.\nThe remaining items in the line are his/her dates of convenience,\nwhich are positive integers less than 100, that is, 1 means tomorrow, \n2 means the day after tomorrow, and so on.\nThey are in ascending order without any repetition \nand separated by a space character.\nLines have neither leading nor trailing spaces.\nA line containing two zeros indicates the end of the input.\nTask Output: For each data set, print a single line containing the date number\nconvenient for the largest number of committee members.\n If there is more than one\nsuch date, print the earliest. However, if no dates are convenient\nfor more than or equal to the quorum number of members, print 0 instead.\nTask Samples: input: 3 2\n2 1 4\n0\n3 3 4 8\n3 2\n4 1 5 8 9\n3 2 5 9\n5 2 4 5 7 9\n3 3\n2 1 4\n3 2 5 9\n2 2 4\n3 3\n2 1 2\n3 1 2 9\n2 2 4\n0 0\n output: 4\n5\n0\n2\n\n" }, { "title": "Get Many Persimmon Trees", "content": "Seiji Hayashi had been a professor of the Nisshinkan Samurai School\nin the domain of Aizu for a long time in the 18th century.\nIn order to reward him for his meritorious career in education,\nKatanobu Matsudaira, the lord of the domain of Aizu, had decided to\ngrant him a rectangular estate within a large field in the Aizu Basin.\nAlthough the size (width and height) of the estate was strictly specified\nby the lord, he was allowed to choose any location for the estate\nin the field.\nInside the field which had also a rectangular shape,\nmany Japanese persimmon trees,\nwhose fruit was one of the famous products of the Aizu region\nknown as 'Mishirazu Persimmon', were planted.\nSince persimmon was Hayashi's favorite fruit, he wanted to have\nas many persimmon trees as possible in the estate given by the lord.\n\nFor example, in Figure 1, the entire field is a rectangular grid whose\nwidth and height are 10 and 8 respectively. Each asterisk (*)\nrepresents a place of a persimmon tree. If the specified width and\nheight of the estate are 4 and 3 respectively, the area surrounded by\nthe solid line contains the most persimmon trees. Similarly, if the\nestate's width is 6 and its height is 4, the area surrounded by the\ndashed line has the most, and if the estate's width and height are 3\nand 4 respectively, the area surrounded by the dotted line contains\nthe most persimmon trees. Note that the width and height cannot be\nswapped; the sizes 4 by 3 and 3 by 4 are different, as shown in Figure\n1. \n Figure 1: Examples of Rectangular Estates \n \n\nYour task is to find the estate of a given size (width and height)\nthat contains the largest number of persimmon trees.", "constraint": "", "input": "The input consists of multiple data sets.\nEach data set is given in the following format.\n\nN\nW H\nx_1 y_1\nx_2 y_2\n. . . \nx_N y_N\nS T\n\nN is the number of persimmon trees,\nwhich is a positive integer less than 500.\nW and H are the width and the height of the entire field\nrespectively.\nYou can assume that both W and H are positive integers\nwhose values are less than 100.\nFor each i (1 <= i <= N), \nx_i and y_i are\ncoordinates of the i-th persimmon tree in the grid.\nNote that the origin of each coordinate is 1.\nYou can assume that 1 <= x_i <= W\nand 1 <= y_i <= H,\nand no two trees have the same positions.\nBut you should not assume that the persimmon trees are sorted in some order\naccording to their positions.\nLastly, S and T are positive integers of\nthe width and height respectively of the estate given by the lord.\nYou can also assume that 1 <= S <= W\nand 1 <= T <= H.\n\nThe end of the input is indicated by a line that solely contains a zero.", "output": "For each data set, you are requested to print one line containing the\nmaximum possible number of persimmon trees that can be included in an\nestate of the given size.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 16\n10 8\n2 2\n2 5\n2 7\n3 3\n3 8\n4 2\n4 5\n4 8\n6 4\n6 7\n7 5\n7 8\n8 1\n8 4\n9 6\n10 3\n4 3\n8\n6 4\n1 2\n2 1\n2 4\n3 4\n4 2\n5 3\n6 1\n6 2\n3 2\n0\n output: 4\n3"], "Pid": "p00706", "ProblemText": "Task Description: Seiji Hayashi had been a professor of the Nisshinkan Samurai School\nin the domain of Aizu for a long time in the 18th century.\nIn order to reward him for his meritorious career in education,\nKatanobu Matsudaira, the lord of the domain of Aizu, had decided to\ngrant him a rectangular estate within a large field in the Aizu Basin.\nAlthough the size (width and height) of the estate was strictly specified\nby the lord, he was allowed to choose any location for the estate\nin the field.\nInside the field which had also a rectangular shape,\nmany Japanese persimmon trees,\nwhose fruit was one of the famous products of the Aizu region\nknown as 'Mishirazu Persimmon', were planted.\nSince persimmon was Hayashi's favorite fruit, he wanted to have\nas many persimmon trees as possible in the estate given by the lord.\n\nFor example, in Figure 1, the entire field is a rectangular grid whose\nwidth and height are 10 and 8 respectively. Each asterisk (*)\nrepresents a place of a persimmon tree. If the specified width and\nheight of the estate are 4 and 3 respectively, the area surrounded by\nthe solid line contains the most persimmon trees. Similarly, if the\nestate's width is 6 and its height is 4, the area surrounded by the\ndashed line has the most, and if the estate's width and height are 3\nand 4 respectively, the area surrounded by the dotted line contains\nthe most persimmon trees. Note that the width and height cannot be\nswapped; the sizes 4 by 3 and 3 by 4 are different, as shown in Figure\n1. \n Figure 1: Examples of Rectangular Estates \n \n\nYour task is to find the estate of a given size (width and height)\nthat contains the largest number of persimmon trees.\nTask Input: The input consists of multiple data sets.\nEach data set is given in the following format.\n\nN\nW H\nx_1 y_1\nx_2 y_2\n. . . \nx_N y_N\nS T\n\nN is the number of persimmon trees,\nwhich is a positive integer less than 500.\nW and H are the width and the height of the entire field\nrespectively.\nYou can assume that both W and H are positive integers\nwhose values are less than 100.\nFor each i (1 <= i <= N), \nx_i and y_i are\ncoordinates of the i-th persimmon tree in the grid.\nNote that the origin of each coordinate is 1.\nYou can assume that 1 <= x_i <= W\nand 1 <= y_i <= H,\nand no two trees have the same positions.\nBut you should not assume that the persimmon trees are sorted in some order\naccording to their positions.\nLastly, S and T are positive integers of\nthe width and height respectively of the estate given by the lord.\nYou can also assume that 1 <= S <= W\nand 1 <= T <= H.\n\nThe end of the input is indicated by a line that solely contains a zero.\nTask Output: For each data set, you are requested to print one line containing the\nmaximum possible number of persimmon trees that can be included in an\nestate of the given size.\nTask Samples: input: 16\n10 8\n2 2\n2 5\n2 7\n3 3\n3 8\n4 2\n4 5\n4 8\n6 4\n6 7\n7 5\n7 8\n8 1\n8 4\n9 6\n10 3\n4 3\n8\n6 4\n1 2\n2 1\n2 4\n3 4\n4 2\n5 3\n6 1\n6 2\n3 2\n0\n output: 4\n3\n\n" }, { "title": "The Secret Number", "content": "Your job is to find out the secret number hidden in a matrix,\neach of whose element is a digit ('0'-'9') or a letter\n('A'-'Z'). You can see an example matrix in Figure 1.\nFigure 1: A Matrix\n\nThe secret number and other non-secret ones are coded in a\nmatrix as sequences of digits in a decimal format. You should\nonly consider sequences of digits D_1\nD_2 . . . D_n such that\nD_k+1 (1 <= k < n)\nis either right next to or immediately below\nD_k in the matrix. The secret you are\nseeking is the largest number coded in this manner.\n\nFour coded numbers in the matrix in Figure 1, i. e. , 908820,\n23140037,23900037, and 9930, are depicted in Figure 2. As you\nmay see, in general, two or more coded numbers may share a\ncommon subsequence. In this case, the secret number is\n23900037, which is the largest among the set of all coded numbers\nin the matrix.\nFigure 2: Coded Numbers\n\nIn contrast, the sequences illustrated in Figure 3 should be\nexcluded: 908A2 includes a letter; the fifth digit of 23149930\nis above the fourth; the third digit of 90037 is below right of\nthe second.\nFigure 3: Inappropriate Sequences\n\nWrite a program to figure out the secret number from a given\nmatrix.", "constraint": "", "input": "The input consists of multiple data sets, each data set\nrepresenting a matrix. The format of each data set is as\nfollows.\n\nW H\nC_11C_12 . . . C_1W\nC_21C_22 . . . C_2W\n. . . \nC_H1C_H2 . . . C_HW\n\nIn the first line of a data set, two positive integers W\nand H are given. W indicates the width (the\nnumber of columns) of the matrix, and H indicates the\nheight (the number of rows) of the matrix. W+H is less\nthan or equal to 70.\n\nH lines follow the first line, each of which corresponds\nto a row of the matrix in top to bottom order. The i-th\nrow consists of W characters\nC_i1C_i2\n. . . C_i W in left to right order. You may\nassume that the matrix includes at least one non-zero digit.\n\nFollowing the last data set, two zeros in a line indicate the\nend of the input.", "output": "For each data set, print the secret number on a line. Leading zeros\nshould be suppressed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 7 4\n9R2A993\n0E314A0\n8A900DE\n820R037\n6 7\nJH03HE\nID7722\n0DA1AH\n30C9G5\n99971A\nCA7EAI\nAHLBEM\n20 2\nA1234567891234CBDEGH\nBDEDF908034265091499\n0 0\n output: 23900037\n771971\n12345908034265091499"], "Pid": "p00707", "ProblemText": "Task Description: Your job is to find out the secret number hidden in a matrix,\neach of whose element is a digit ('0'-'9') or a letter\n('A'-'Z'). You can see an example matrix in Figure 1.\nFigure 1: A Matrix\n\nThe secret number and other non-secret ones are coded in a\nmatrix as sequences of digits in a decimal format. You should\nonly consider sequences of digits D_1\nD_2 . . . D_n such that\nD_k+1 (1 <= k < n)\nis either right next to or immediately below\nD_k in the matrix. The secret you are\nseeking is the largest number coded in this manner.\n\nFour coded numbers in the matrix in Figure 1, i. e. , 908820,\n23140037,23900037, and 9930, are depicted in Figure 2. As you\nmay see, in general, two or more coded numbers may share a\ncommon subsequence. In this case, the secret number is\n23900037, which is the largest among the set of all coded numbers\nin the matrix.\nFigure 2: Coded Numbers\n\nIn contrast, the sequences illustrated in Figure 3 should be\nexcluded: 908A2 includes a letter; the fifth digit of 23149930\nis above the fourth; the third digit of 90037 is below right of\nthe second.\nFigure 3: Inappropriate Sequences\n\nWrite a program to figure out the secret number from a given\nmatrix.\nTask Input: The input consists of multiple data sets, each data set\nrepresenting a matrix. The format of each data set is as\nfollows.\n\nW H\nC_11C_12 . . . C_1W\nC_21C_22 . . . C_2W\n. . . \nC_H1C_H2 . . . C_HW\n\nIn the first line of a data set, two positive integers W\nand H are given. W indicates the width (the\nnumber of columns) of the matrix, and H indicates the\nheight (the number of rows) of the matrix. W+H is less\nthan or equal to 70.\n\nH lines follow the first line, each of which corresponds\nto a row of the matrix in top to bottom order. The i-th\nrow consists of W characters\nC_i1C_i2\n. . . C_i W in left to right order. You may\nassume that the matrix includes at least one non-zero digit.\n\nFollowing the last data set, two zeros in a line indicate the\nend of the input.\nTask Output: For each data set, print the secret number on a line. Leading zeros\nshould be suppressed.\nTask Samples: input: 7 4\n9R2A993\n0E314A0\n8A900DE\n820R037\n6 7\nJH03HE\nID7722\n0DA1AH\n30C9G5\n99971A\nCA7EAI\nAHLBEM\n20 2\nA1234567891234CBDEGH\nBDEDF908034265091499\n0 0\n output: 23900037\n771971\n12345908034265091499\n\n" }, { "title": "Building a Space Station", "content": "You are a member of the space station engineering team,\nand are assigned a task in the construction process of the station.\nYou are expected to write a computer program to complete the task.\n\nThe space station is made up with a number of units, called cells. \nAll cells are sphere-shaped, but their sizes are not necessarily uniform.\nEach cell is fixed at its predetermined position\nshortly after the station is successfully put into its orbit.\nIt is quite strange that two cells may be touching each other,\nor even may be overlapping.\nIn an extreme case, a cell may be totally enclosing another one.\nI do not know how such arrangements are possible.\n\nAll the cells must be connected,\nsince crew members should be able to walk\nfrom any cell to any other cell.\nThey can walk from a cell A to another cell B, if,\n(1) A and B are touching each other or overlapping,\n(2) A and B are connected by a `corridor',\nor (3) there is a cell C such that walking from A to C, and also from B to C\nare both possible.\nNote that the condition (3) should be interpreted transitively.\n\nYou are expected to design a configuration,\nnamely, which pairs of cells are to be connected with corridors.\nThere is some freedom in the corridor configuration.\nFor example, if there are three cells A, B and C,\nnot touching nor overlapping each other,\nat least three plans are possible in order to connect all three cells.\nThe first is to build corridors A-B and A-C,\nthe second B-C and B-A, the third C-A and C-B.\nThe cost of building a corridor is proportional to its length.\nTherefore, you should choose a plan with the shortest\ntotal length of the corridors.\n\nYou can ignore the width of a corridor.\nA corridor is built between points on two cells' surfaces.\nIt can be made arbitrarily long, but of course the shortest one is chosen.\nEven if two corridors A-B and C-D intersect in space, they are\nnot considered to form a connection path between (for example) A and C.\nIn other words, you may consider that two corridors never intersect.", "constraint": "", "input": "The input consists of multiple data sets.\nEach data set is given in the following format.\n\nn\nx_1 y_1 z_1 r_1\nx_2 y_2 z_2 r_2\n. . . \nx_n y_n z_n r_n\n\nThe first line of a data set contains an integer n,\nwhich is the number of cells.\nn is positive, and does not exceed 100.\n\nThe following n lines are descriptions of cells.\nFour values in a line are x-, y- and z-coordinates of\nthe center, and radius (called r in the rest of the problem) of\nthe sphere, in this order.\nEach value is given by a decimal fraction, with\n3 digits after the decimal point.\nValues are separated by a space character.\n\nEach of x, y, z and r is positive\nand is less than 100.0.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each data set, the shortest total length of the corridors\nshould be printed, each in a separate line.\nThe printed values should have 3 digits after the decimal point.\nThey may not have an error greater than 0.001.\n\nNote that if no corridors are necessary, that is,\nif all the cells are connected without corridors,\nthe shortest total length of the corridors is 0.000.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10.000 10.000 50.000 10.000\n40.000 10.000 50.000 10.000\n40.000 40.000 50.000 10.000\n2\n30.000 30.000 30.000 20.000\n40.000 40.000 40.000 20.000\n5\n5.729 15.143 3.996 25.837\n6.013 14.372 4.818 10.671\n80.115 63.292 84.477 15.120\n64.095 80.924 70.029 14.881\n39.472 85.116 71.369 5.553\n0\n output: 20.000\n0.000\n73.834"], "Pid": "p00708", "ProblemText": "Task Description: You are a member of the space station engineering team,\nand are assigned a task in the construction process of the station.\nYou are expected to write a computer program to complete the task.\n\nThe space station is made up with a number of units, called cells. \nAll cells are sphere-shaped, but their sizes are not necessarily uniform.\nEach cell is fixed at its predetermined position\nshortly after the station is successfully put into its orbit.\nIt is quite strange that two cells may be touching each other,\nor even may be overlapping.\nIn an extreme case, a cell may be totally enclosing another one.\nI do not know how such arrangements are possible.\n\nAll the cells must be connected,\nsince crew members should be able to walk\nfrom any cell to any other cell.\nThey can walk from a cell A to another cell B, if,\n(1) A and B are touching each other or overlapping,\n(2) A and B are connected by a `corridor',\nor (3) there is a cell C such that walking from A to C, and also from B to C\nare both possible.\nNote that the condition (3) should be interpreted transitively.\n\nYou are expected to design a configuration,\nnamely, which pairs of cells are to be connected with corridors.\nThere is some freedom in the corridor configuration.\nFor example, if there are three cells A, B and C,\nnot touching nor overlapping each other,\nat least three plans are possible in order to connect all three cells.\nThe first is to build corridors A-B and A-C,\nthe second B-C and B-A, the third C-A and C-B.\nThe cost of building a corridor is proportional to its length.\nTherefore, you should choose a plan with the shortest\ntotal length of the corridors.\n\nYou can ignore the width of a corridor.\nA corridor is built between points on two cells' surfaces.\nIt can be made arbitrarily long, but of course the shortest one is chosen.\nEven if two corridors A-B and C-D intersect in space, they are\nnot considered to form a connection path between (for example) A and C.\nIn other words, you may consider that two corridors never intersect.\nTask Input: The input consists of multiple data sets.\nEach data set is given in the following format.\n\nn\nx_1 y_1 z_1 r_1\nx_2 y_2 z_2 r_2\n. . . \nx_n y_n z_n r_n\n\nThe first line of a data set contains an integer n,\nwhich is the number of cells.\nn is positive, and does not exceed 100.\n\nThe following n lines are descriptions of cells.\nFour values in a line are x-, y- and z-coordinates of\nthe center, and radius (called r in the rest of the problem) of\nthe sphere, in this order.\nEach value is given by a decimal fraction, with\n3 digits after the decimal point.\nValues are separated by a space character.\n\nEach of x, y, z and r is positive\nand is less than 100.0.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each data set, the shortest total length of the corridors\nshould be printed, each in a separate line.\nThe printed values should have 3 digits after the decimal point.\nThey may not have an error greater than 0.001.\n\nNote that if no corridors are necessary, that is,\nif all the cells are connected without corridors,\nthe shortest total length of the corridors is 0.000.\nTask Samples: input: 3\n10.000 10.000 50.000 10.000\n40.000 10.000 50.000 10.000\n40.000 40.000 50.000 10.000\n2\n30.000 30.000 30.000 20.000\n40.000 40.000 40.000 20.000\n5\n5.729 15.143 3.996 25.837\n6.013 14.372 4.818 10.671\n80.115 63.292 84.477 15.120\n64.095 80.924 70.029 14.881\n39.472 85.116 71.369 5.553\n0\n output: 20.000\n0.000\n73.834\n\n" }, { "title": "Square Carpets", "content": "Mr. Frugal bought a new house.\nHe feels deeply in love with his new house\nbecause it has a comfortable living room\nin which he can put himself completely at ease.\nHe thinks his new house is a really good buy.\n\nBut, to his disappointment, \nthe floor of its living room has some scratches on it.\n\nThe floor has a rectangle shape, covered with square panels.\nHe wants to replace all the scratched panels with flawless panels, \nbut he cannot afford to do so.\nThen, he decides to cover all the scratched panels \nwith carpets.\n\nThe features of the carpets he can use are as follows.\n\n Carpets are square-shaped.\n Carpets may overlap each other.\n Carpets cannot be folded.\n Different sizes of carpets are available.\nLengths of sides of carpets are multiples of that of the panels.\n\nThe carpets must cover all the scratched panels,\nbut must not cover any of the flawless ones.\n\nFor example, \nif the scratched panels are as shown in Figure 1, \nat least 6 carpets are needed. \n Figure 1: Example Covering \n \n\nAs carpets cost the same irrespective of their sizes, \nMr. Frugal would like to use as few number of carpets as possible.\n\nYour job is to write a program which tells the minimum number \nof the carpets to cover all the scratched panels.", "constraint": "", "input": "The input consists of multiple data sets.\n\nAs in the following, the end of the input is indicated by a line\ncontaining two zeros.\n\nData Set_1\nData Set_2\n. . . \nData Set_n\n0 0\n\nEach data set (Data Set_i) represents the\nstate of a floor. The format of a data set is as follows.\n\nW H\nP_11 P_12 P_13 . . . P_1W\nP_21 P_22 P_23 . . . P_2W\n. . . \nP_H1 P_H2\nP_H3 . . . P_HW\n\nThe positive integers W and H are the numbers of panels\non the living room\nin the x- and y- direction, respectively.\nThe values of W and H are no more than 10.\nThe integer P_yx represents the state of the panel.\nThe value of P_yx means,\n\n0: flawless panel (must not be covered), \n1: scratched panel (must be covered).", "output": "For each data set,\nyour program should output a line containing one integer which \nrepresents the minimum number of the carpets to cover \nall of the scratched panels.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 3\n0 1 1 1\n1 1 1 1\n1 1 1 1\n8 5\n0 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n1 1 1 0 1 1 1 1\n0 1 1 1 0 1 1 1\n8 8\n0 1 1 0 0 1 1 0\n1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n0 1 1 0 0 1 1 0\n0 1 1 0 0 1 1 0\n1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n0 1 1 0 0 1 1 0\n10 10\n1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1\n1 1 0 1 1 0 1 1 0 1\n1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1\n1 1 0 1 1 0 1 1 0 1\n1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1\n1 1 0 1 1 0 1 1 0 1\n1 1 1 1 1 1 1 1 1 1\n0 0\n output: 2\n6\n14\n29"], "Pid": "p00709", "ProblemText": "Task Description: Mr. Frugal bought a new house.\nHe feels deeply in love with his new house\nbecause it has a comfortable living room\nin which he can put himself completely at ease.\nHe thinks his new house is a really good buy.\n\nBut, to his disappointment, \nthe floor of its living room has some scratches on it.\n\nThe floor has a rectangle shape, covered with square panels.\nHe wants to replace all the scratched panels with flawless panels, \nbut he cannot afford to do so.\nThen, he decides to cover all the scratched panels \nwith carpets.\n\nThe features of the carpets he can use are as follows.\n\n Carpets are square-shaped.\n Carpets may overlap each other.\n Carpets cannot be folded.\n Different sizes of carpets are available.\nLengths of sides of carpets are multiples of that of the panels.\n\nThe carpets must cover all the scratched panels,\nbut must not cover any of the flawless ones.\n\nFor example, \nif the scratched panels are as shown in Figure 1, \nat least 6 carpets are needed. \n Figure 1: Example Covering \n \n\nAs carpets cost the same irrespective of their sizes, \nMr. Frugal would like to use as few number of carpets as possible.\n\nYour job is to write a program which tells the minimum number \nof the carpets to cover all the scratched panels.\nTask Input: The input consists of multiple data sets.\n\nAs in the following, the end of the input is indicated by a line\ncontaining two zeros.\n\nData Set_1\nData Set_2\n. . . \nData Set_n\n0 0\n\nEach data set (Data Set_i) represents the\nstate of a floor. The format of a data set is as follows.\n\nW H\nP_11 P_12 P_13 . . . P_1W\nP_21 P_22 P_23 . . . P_2W\n. . . \nP_H1 P_H2\nP_H3 . . . P_HW\n\nThe positive integers W and H are the numbers of panels\non the living room\nin the x- and y- direction, respectively.\nThe values of W and H are no more than 10.\nThe integer P_yx represents the state of the panel.\nThe value of P_yx means,\n\n0: flawless panel (must not be covered), \n1: scratched panel (must be covered).\nTask Output: For each data set,\nyour program should output a line containing one integer which \nrepresents the minimum number of the carpets to cover \nall of the scratched panels.\nTask Samples: input: 4 3\n0 1 1 1\n1 1 1 1\n1 1 1 1\n8 5\n0 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n1 1 1 0 1 1 1 1\n0 1 1 1 0 1 1 1\n8 8\n0 1 1 0 0 1 1 0\n1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n0 1 1 0 0 1 1 0\n0 1 1 0 0 1 1 0\n1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1\n0 1 1 0 0 1 1 0\n10 10\n1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1\n1 1 0 1 1 0 1 1 0 1\n1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1\n1 1 0 1 1 0 1 1 0 1\n1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1\n1 1 0 1 1 0 1 1 0 1\n1 1 1 1 1 1 1 1 1 1\n0 0\n output: 2\n6\n14\n29\n\n" }, { "title": "Problem A: Hanafuda Shuffle", "content": "There are a number of ways to shuffle a deck of cards. Hanafuda \nshuffling for Japanese card game 'Hanafuda' is one such example.\nThe following is how to perform Hanafuda shuffling.\nThere is a deck of n cards. Starting from the p-th card \nfrom the top of the deck, c cards are pulled out\nand put on the top of the deck, as shown in Figure 1.\nThis operation, called a cutting operation, is repeated.\n\nWrite a program that simulates Hanafuda shuffling and answers which \ncard will be finally placed on the top of the deck. \n Figure 1: Cutting operation", "constraint": "", "input": "The input consists of multiple data sets.\nEach data set starts with a line containing two positive integers n \n(1 <= n <= 50) and r (1 <= r <= 50); n and \n r are the number of cards in the deck and the number of cutting \noperations, respectively.\n\n There are r more lines in the data set, each of which\n represents a cutting operation. These cutting operations \nare performed in the listed order.\nEach line contains two positive integers p and c \n(p + c <= n + 1).\nStarting from the p-th card from the top of the deck, c\ncards should be pulled out and put on the top.\n\nThe end of the input is indicated by a line which contains two zeros.\n\nEach input line contains exactly two integers separated by a space \ncharacter.\nThere are no other characters in the line.", "output": "For each data set in the input, your program \nshould write the number of the top card after the shuffle.\nAssume that at the beginning the cards \nare numbered from 1 to n, from the bottom to the top.\nEach number should be written in a separate line \nwithout any superfluous characters such as leading or following spaces.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 2\n3 1\n3 1\n10 3\n1 10\n10 1\n8 3\n0 0\n output: 4\n4"], "Pid": "p00710", "ProblemText": "Task Description: There are a number of ways to shuffle a deck of cards. Hanafuda \nshuffling for Japanese card game 'Hanafuda' is one such example.\nThe following is how to perform Hanafuda shuffling.\nThere is a deck of n cards. Starting from the p-th card \nfrom the top of the deck, c cards are pulled out\nand put on the top of the deck, as shown in Figure 1.\nThis operation, called a cutting operation, is repeated.\n\nWrite a program that simulates Hanafuda shuffling and answers which \ncard will be finally placed on the top of the deck. \n Figure 1: Cutting operation\nTask Input: The input consists of multiple data sets.\nEach data set starts with a line containing two positive integers n \n(1 <= n <= 50) and r (1 <= r <= 50); n and \n r are the number of cards in the deck and the number of cutting \noperations, respectively.\n\n There are r more lines in the data set, each of which\n represents a cutting operation. These cutting operations \nare performed in the listed order.\nEach line contains two positive integers p and c \n(p + c <= n + 1).\nStarting from the p-th card from the top of the deck, c\ncards should be pulled out and put on the top.\n\nThe end of the input is indicated by a line which contains two zeros.\n\nEach input line contains exactly two integers separated by a space \ncharacter.\nThere are no other characters in the line.\nTask Output: For each data set in the input, your program \nshould write the number of the top card after the shuffle.\nAssume that at the beginning the cards \nare numbered from 1 to n, from the bottom to the top.\nEach number should be written in a separate line \nwithout any superfluous characters such as leading or following spaces.\nTask Samples: input: 5 2\n3 1\n3 1\n10 3\n1 10\n10 1\n8 3\n0 0\n output: 4\n4\n\n" }, { "title": "Problem B: Red and Black", "content": "There is a rectangular room, covered with square tiles. Each tile is\ncolored either red or black. A man is standing on a black tile.\nFrom a tile, he can move to one of four adjacent tiles. But he can't \nmove on red tiles, he can move only on black tiles.\n\n Write a program to count the number of black tiles which he can reach \nby repeating the moves described above.", "constraint": "", "input": "The input consists of multiple data sets.\n A data set starts with a line containing two positive integers W and H;\n W and H are the numbers of tiles in the x-\n and y- directions, respectively. W and H are \nnot more than 20.\n\n There are H more lines in the data set, each of which\nincludes W characters. Each character represents the color of a\ntile as follows.\n\n'. ' - a black tile\n'#' - a red tile\n'@' - a man on a black tile(appears exactly once in a data set)\nThe end of the input is indicated by a line consisting of two zeros.", "output": "For each data set, your program \nshould output a line which contains the number of \ntiles he can reach from the initial tile (including itself).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 9\n....#.\n.....#\n......\n......\n......\n......\n......\n#@...#\n.#..#.\n11 9\n.#.........\n.#.#######.\n.#.#.....#.\n.#.#.###.#.\n.#.#..@#.#.\n.#.#####.#.\n.#.......#.\n.#########.\n...........\n11 6\n..#..#..#..\n..#..#..#..\n..#..#..###\n..#..#..#@.\n..#..#..#..\n..#..#..#..\n7 7\n..#.#..\n..#.#..\n###.###\n...@...\n###.###\n..#.#..\n..#.#..\n0 0\n output: 45\n59\n6\n13"], "Pid": "p00711", "ProblemText": "Task Description: There is a rectangular room, covered with square tiles. Each tile is\ncolored either red or black. A man is standing on a black tile.\nFrom a tile, he can move to one of four adjacent tiles. But he can't \nmove on red tiles, he can move only on black tiles.\n\n Write a program to count the number of black tiles which he can reach \nby repeating the moves described above.\nTask Input: The input consists of multiple data sets.\n A data set starts with a line containing two positive integers W and H;\n W and H are the numbers of tiles in the x-\n and y- directions, respectively. W and H are \nnot more than 20.\n\n There are H more lines in the data set, each of which\nincludes W characters. Each character represents the color of a\ntile as follows.\n\n'. ' - a black tile\n'#' - a red tile\n'@' - a man on a black tile(appears exactly once in a data set)\nThe end of the input is indicated by a line consisting of two zeros.\nTask Output: For each data set, your program \nshould output a line which contains the number of \ntiles he can reach from the initial tile (including itself).\nTask Samples: input: 6 9\n....#.\n.....#\n......\n......\n......\n......\n......\n#@...#\n.#..#.\n11 9\n.#.........\n.#.#######.\n.#.#.....#.\n.#.#.###.#.\n.#.#..@#.#.\n.#.#####.#.\n.#.......#.\n.#########.\n...........\n11 6\n..#..#..#..\n..#..#..#..\n..#..#..###\n..#..#..#@.\n..#..#..#..\n..#..#..#..\n7 7\n..#.#..\n..#.#..\n###.###\n...@...\n###.###\n..#.#..\n..#.#..\n0 0\n output: 45\n59\n6\n13\n\n" }, { "title": "Problem C: Unit Fraction Partition", "content": "A fraction whose numerator is 1\nand whose denominator is a positive integer\nis called a unit fraction.\nA representation of a positive rational number\np/q\nas the sum of finitely many unit fractions is called a partition of\np/q\ninto unit fractions.\nFor example,\n1/2 + 1/6\nis a partition of\n2/3\ninto unit fractions.\nThe difference in the order of addition is disregarded.\nFor example, we do not distinguish\n1/6 + 1/2\nfrom\n1/2 + 1/6.\n\nFor given four positive integers\np,\nq,\na, and\nn,\ncount the number\nof partitions of\np/q\ninto unit fractions satisfying the following two conditions.\nThe partition is the sum of at most\nn\nmany unit fractions.\n\nThe product of the denominators of the unit fractions in the\npartition is less than or equal to\na.\n\nFor example, if\n(p, q, a, n) = (2,3,120,3),\nyou should report 4 since\n\nenumerates all of the valid partitions.", "constraint": "", "input": "The input is a sequence of at most 1000 data sets followed by a terminator.\n\nA data set is a line containing four positive integers\np,\nq,\na, and\nn\nsatisfying\np, q <= 800,\na <= 12000\nand\nn <= 7.\nThe integers are separated by a space.\n\nThe terminator is composed of just one line\nwhich contains four zeros separated by a space.\nIt is not a part of the input data but a mark for the end of the input.", "output": "The output should be composed of lines\neach of which contains a single integer.\nNo other characters should appear in the output.\n\nThe output integer corresponding to a data set\np,\nq,\na,\nn\nshould be the number of all partitions of\np/q\ninto at most\nn\nmany unit fractions such that the product of the denominators of the\nunit fractions is less than or equal to\na.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 3 120 3\n2 3 300 3\n2 3 299 3\n2 3 12 3\n2 3 12000 7\n54 795 12000 7\n2 3 300 1\n2 1 200 5\n2 4 54 2\n0 0 0 0\n output: 4\n7\n6\n2\n42\n1\n0\n9\n3"], "Pid": "p00712", "ProblemText": "Task Description: A fraction whose numerator is 1\nand whose denominator is a positive integer\nis called a unit fraction.\nA representation of a positive rational number\np/q\nas the sum of finitely many unit fractions is called a partition of\np/q\ninto unit fractions.\nFor example,\n1/2 + 1/6\nis a partition of\n2/3\ninto unit fractions.\nThe difference in the order of addition is disregarded.\nFor example, we do not distinguish\n1/6 + 1/2\nfrom\n1/2 + 1/6.\n\nFor given four positive integers\np,\nq,\na, and\nn,\ncount the number\nof partitions of\np/q\ninto unit fractions satisfying the following two conditions.\nThe partition is the sum of at most\nn\nmany unit fractions.\n\nThe product of the denominators of the unit fractions in the\npartition is less than or equal to\na.\n\nFor example, if\n(p, q, a, n) = (2,3,120,3),\nyou should report 4 since\n\nenumerates all of the valid partitions.\nTask Input: The input is a sequence of at most 1000 data sets followed by a terminator.\n\nA data set is a line containing four positive integers\np,\nq,\na, and\nn\nsatisfying\np, q <= 800,\na <= 12000\nand\nn <= 7.\nThe integers are separated by a space.\n\nThe terminator is composed of just one line\nwhich contains four zeros separated by a space.\nIt is not a part of the input data but a mark for the end of the input.\nTask Output: The output should be composed of lines\neach of which contains a single integer.\nNo other characters should appear in the output.\n\nThe output integer corresponding to a data set\np,\nq,\na,\nn\nshould be the number of all partitions of\np/q\ninto at most\nn\nmany unit fractions such that the product of the denominators of the\nunit fractions is less than or equal to\na.\nTask Samples: input: 2 3 120 3\n2 3 300 3\n2 3 299 3\n2 3 12 3\n2 3 12000 7\n54 795 12000 7\n2 3 300 1\n2 1 200 5\n2 4 54 2\n0 0 0 0\n output: 4\n7\n6\n2\n42\n1\n0\n9\n3\n\n" }, { "title": "Problem D: Circle and Points", "content": "You are given N points in the xy-plane. You have a\ncircle of radius one and move it on the xy-plane, so as to\nenclose as many of the points as possible. Find how many points can be\nsimultaneously enclosed at the maximum. A point is considered\nenclosed by a circle when it is inside or on the circle.\nFig 1. Circle and Points", "constraint": "", "input": "The input consists of a series of data sets, followed by a single line\nonly containing a single character '0', which indicates the end of the\ninput. Each data set begins with a line containing an integer N,\nwhich indicates the number of points in the data set. It is\nfollowed by N lines describing the coordinates of the\npoints. Each of the N lines has two decimal fractions X\nand Y, describing the x- and y-coordinates of a\npoint, respectively. They are given with five digits after the decimal\npoint.\n\nYou may assume 1 <= N <= 300, 0.0 <= X <= 10.0, and 0.0\n<= Y <= 10.0. No two points are closer than 0.0001. No two\npoints in a data set are approximately at a distance of 2.0. More\nprecisely, for any two points in a data set, the distance d\nbetween the two never satisfies 1.9999 <= d <= 2.0001. Finally,\nno three points in a data set are simultaneously very close to a\nsingle circle of radius one. More precisely,\nlet P_1, P_2, and P_3 be any three points in a\ndata set, and d_1, d_2, and d_3\nthe distances from an arbitrarily selected point in the xy-plane to each of them\nrespectively. Then it never simultaneously holds that 0.9999 <=\nd_i <= 1.0001 (i = 1,2,3).", "output": "For each data set, print a single line containing the maximum number\nof points in the data set that can be simultaneously enclosed by a\ncircle of radius one. No other characters including leading and\ntrailing spaces should be printed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n6.47634 7.69628\n5.16828 4.79915\n6.69533 6.20378\n6\n7.15296 4.08328\n6.50827 2.69466\n5.91219 3.86661\n5.29853 4.16097\n6.10838 3.46039\n6.34060 2.41599\n8\n7.90650 4.01746\n4.10998 4.18354\n4.67289 4.01887\n6.33885 4.28388\n4.98106 3.82728\n5.12379 5.16473\n7.84664 4.67693\n4.02776 3.87990\n20\n6.65128 5.47490\n6.42743 6.26189\n6.35864 4.61611\n6.59020 4.54228\n4.43967 5.70059\n4.38226 5.70536\n5.50755 6.18163\n7.41971 6.13668\n6.71936 3.04496\n5.61832 4.23857\n5.99424 4.29328\n5.60961 4.32998\n6.82242 5.79683\n5.44693 3.82724\n6.70906 3.65736\n7.89087 5.68000\n6.23300 4.59530\n5.92401 4.92329\n6.24168 3.81389\n6.22671 3.62210\n0\n output: 2\n5\n5\n11"], "Pid": "p00713", "ProblemText": "Task Description: You are given N points in the xy-plane. You have a\ncircle of radius one and move it on the xy-plane, so as to\nenclose as many of the points as possible. Find how many points can be\nsimultaneously enclosed at the maximum. A point is considered\nenclosed by a circle when it is inside or on the circle.\nFig 1. Circle and Points\nTask Input: The input consists of a series of data sets, followed by a single line\nonly containing a single character '0', which indicates the end of the\ninput. Each data set begins with a line containing an integer N,\nwhich indicates the number of points in the data set. It is\nfollowed by N lines describing the coordinates of the\npoints. Each of the N lines has two decimal fractions X\nand Y, describing the x- and y-coordinates of a\npoint, respectively. They are given with five digits after the decimal\npoint.\n\nYou may assume 1 <= N <= 300, 0.0 <= X <= 10.0, and 0.0\n<= Y <= 10.0. No two points are closer than 0.0001. No two\npoints in a data set are approximately at a distance of 2.0. More\nprecisely, for any two points in a data set, the distance d\nbetween the two never satisfies 1.9999 <= d <= 2.0001. Finally,\nno three points in a data set are simultaneously very close to a\nsingle circle of radius one. More precisely,\nlet P_1, P_2, and P_3 be any three points in a\ndata set, and d_1, d_2, and d_3\nthe distances from an arbitrarily selected point in the xy-plane to each of them\nrespectively. Then it never simultaneously holds that 0.9999 <=\nd_i <= 1.0001 (i = 1,2,3).\nTask Output: For each data set, print a single line containing the maximum number\nof points in the data set that can be simultaneously enclosed by a\ncircle of radius one. No other characters including leading and\ntrailing spaces should be printed.\nTask Samples: input: 3\n6.47634 7.69628\n5.16828 4.79915\n6.69533 6.20378\n6\n7.15296 4.08328\n6.50827 2.69466\n5.91219 3.86661\n5.29853 4.16097\n6.10838 3.46039\n6.34060 2.41599\n8\n7.90650 4.01746\n4.10998 4.18354\n4.67289 4.01887\n6.33885 4.28388\n4.98106 3.82728\n5.12379 5.16473\n7.84664 4.67693\n4.02776 3.87990\n20\n6.65128 5.47490\n6.42743 6.26189\n6.35864 4.61611\n6.59020 4.54228\n4.43967 5.70059\n4.38226 5.70536\n5.50755 6.18163\n7.41971 6.13668\n6.71936 3.04496\n5.61832 4.23857\n5.99424 4.29328\n5.60961 4.32998\n6.82242 5.79683\n5.44693 3.82724\n6.70906 3.65736\n7.89087 5.68000\n6.23300 4.59530\n5.92401 4.92329\n6.24168 3.81389\n6.22671 3.62210\n0\n output: 2\n5\n5\n11\n\n" }, { "title": "Problem E: Water Tank", "content": "Mr. Denjiro is a science teacher.\n\nToday he has just received a specially ordered water tank that\nwill certainly be useful for his innovative experiments on water\nflow. \n Figure 1: The water tank \n \n\nThe size of the tank is 100cm (Width) * 50cm (Height) * 30cm (Depth)\n (see Figure 1).\n\nFor the experiments, he fits several partition boards inside of\nthe tank parallel to the sideboards.\n\nThe width of each board is equal to the depth of the tank, i. e. 30cm.\nThe height of each board is less than that of the tank, i. e. 50 cm,\nand differs one another.\n\nThe boards are so thin that he can neglect the thickness in the experiments. \n Figure 2: The front view of the tank \n \n\nThe front view of the tank is shown in Figure 2.\n\n There are several faucets above the tank and he turns them on at\n the beginning of his experiment. The tank is initially empty.\n Your mission is to write a\n computer program to simulate water flow in the tank.", "constraint": "", "input": "The input consists of multiple data sets.\n\nD is the number of the data sets.\n\nD\nData Set_1\nData Set_2\n. . . \nData Set_D\n \nThe format of each data set \n(Data Set_d , 1 <= d <= D) \nis as follows.\n\nN\nB_1 H_1\nB_2 H_2\n. . . \nB_N H_N\nM\nF_1 A_1\nF_2 A_2\n. . . \nF_M A_M\nL\nP_1 T_1\nP_2 T_2\n. . . \nP_L T_L\n \nEach line in the data set contains one or two integers.\n\nN is the number of the boards he sets in the tank .\nB_i and H_i\n are the x-position (cm) and the height (cm) \nof the i-th board, \nwhere 1 <= i <= N .\n\nH_i s differ from one another. You may assume the\n following.\n\n0 < N < 10 , \n0 < B_1 < B_2 < . . . < B_N < 100 , \n0 < H_1 < 50 ,\n0 < H_2 < 50 ,\n . . . , 0 < H_N < 50.\n\nM is the number of the faucets above the tank .\nF_j and A_j are \nthe x-position (cm) and the amount of water flow (cm^3/second)\nof the j-th faucet ,\nwhere 1 <= j <= M .\n\nThere is no faucet just above any boards .\nNamely, none of F_j is equal to B_i .\n\nYou may assume the following .\n\n0 < M <10 , \n0 < F_1 < F_2 < . . . \n< F_M < 100 , \n0 < A_1 < 100, \n0 < A_2 < 100, . . .\n0 < A_M < 100.\n\nL is the number of observation time and location.\nP_k is the x-position (cm) of the k-th\nobservation point.\nT_k is the k-th observation time in seconds from the beginning.\n\nNone of P_k \nis equal to B_i .\n\nYou may assume the following .\n\n0 < L < 10 , \n0 < P_1 < 100,\n0 < P_2 < 100, . . . , \n0 < P_L < 100 , \n0 < T_1 < 1000000, \n0 < T_2 < 1000000, \n. . . ,\n0 < T_L < 1000000.", "output": "For each data set,\nyour program should output L lines each containing \none real number which represents the height (cm) of the water level specified \nby the x-position P_k \nat the time T_k.\n\nEach answer may not have an error greater than 0.001.\nAs long as this condition is satisfied,\nyou may output any number of digits after the decimal point.\n\nAfter the water tank is filled to the brim,\nthe water level at any P_k is equal to the\nheight of the tank, that is, 50 cm.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n5\n15 40\n35 20\n50 45\n70 30\n80 10\n3\n20 3\n60 2\n65 2\n6\n40 4100\n25 7500\n10 18000\n90 7000\n25 15000\n25 22000\n5\n15 40\n35 20\n50 45\n70 30\n80 10\n2\n60 4\n75 1\n3\n60 6000\n75 6000\n85 6000\n output: 0.666667\n21.4286\n36.6667\n11.1111\n40.0\n50.0\n30.0\n13.3333\n13.3333"], "Pid": "p00714", "ProblemText": "Task Description: Mr. Denjiro is a science teacher.\n\nToday he has just received a specially ordered water tank that\nwill certainly be useful for his innovative experiments on water\nflow. \n Figure 1: The water tank \n \n\nThe size of the tank is 100cm (Width) * 50cm (Height) * 30cm (Depth)\n (see Figure 1).\n\nFor the experiments, he fits several partition boards inside of\nthe tank parallel to the sideboards.\n\nThe width of each board is equal to the depth of the tank, i. e. 30cm.\nThe height of each board is less than that of the tank, i. e. 50 cm,\nand differs one another.\n\nThe boards are so thin that he can neglect the thickness in the experiments. \n Figure 2: The front view of the tank \n \n\nThe front view of the tank is shown in Figure 2.\n\n There are several faucets above the tank and he turns them on at\n the beginning of his experiment. The tank is initially empty.\n Your mission is to write a\n computer program to simulate water flow in the tank.\nTask Input: The input consists of multiple data sets.\n\nD is the number of the data sets.\n\nD\nData Set_1\nData Set_2\n. . . \nData Set_D\n \nThe format of each data set \n(Data Set_d , 1 <= d <= D) \nis as follows.\n\nN\nB_1 H_1\nB_2 H_2\n. . . \nB_N H_N\nM\nF_1 A_1\nF_2 A_2\n. . . \nF_M A_M\nL\nP_1 T_1\nP_2 T_2\n. . . \nP_L T_L\n \nEach line in the data set contains one or two integers.\n\nN is the number of the boards he sets in the tank .\nB_i and H_i\n are the x-position (cm) and the height (cm) \nof the i-th board, \nwhere 1 <= i <= N .\n\nH_i s differ from one another. You may assume the\n following.\n\n0 < N < 10 , \n0 < B_1 < B_2 < . . . < B_N < 100 , \n0 < H_1 < 50 ,\n0 < H_2 < 50 ,\n . . . , 0 < H_N < 50.\n\nM is the number of the faucets above the tank .\nF_j and A_j are \nthe x-position (cm) and the amount of water flow (cm^3/second)\nof the j-th faucet ,\nwhere 1 <= j <= M .\n\nThere is no faucet just above any boards .\nNamely, none of F_j is equal to B_i .\n\nYou may assume the following .\n\n0 < M <10 , \n0 < F_1 < F_2 < . . . \n< F_M < 100 , \n0 < A_1 < 100, \n0 < A_2 < 100, . . .\n0 < A_M < 100.\n\nL is the number of observation time and location.\nP_k is the x-position (cm) of the k-th\nobservation point.\nT_k is the k-th observation time in seconds from the beginning.\n\nNone of P_k \nis equal to B_i .\n\nYou may assume the following .\n\n0 < L < 10 , \n0 < P_1 < 100,\n0 < P_2 < 100, . . . , \n0 < P_L < 100 , \n0 < T_1 < 1000000, \n0 < T_2 < 1000000, \n. . . ,\n0 < T_L < 1000000.\nTask Output: For each data set,\nyour program should output L lines each containing \none real number which represents the height (cm) of the water level specified \nby the x-position P_k \nat the time T_k.\n\nEach answer may not have an error greater than 0.001.\nAs long as this condition is satisfied,\nyou may output any number of digits after the decimal point.\n\nAfter the water tank is filled to the brim,\nthe water level at any P_k is equal to the\nheight of the tank, that is, 50 cm.\nTask Samples: input: 2\n5\n15 40\n35 20\n50 45\n70 30\n80 10\n3\n20 3\n60 2\n65 2\n6\n40 4100\n25 7500\n10 18000\n90 7000\n25 15000\n25 22000\n5\n15 40\n35 20\n50 45\n70 30\n80 10\n2\n60 4\n75 1\n3\n60 6000\n75 6000\n85 6000\n output: 0.666667\n21.4286\n36.6667\n11.1111\n40.0\n50.0\n30.0\n13.3333\n13.3333\n\n" }, { "title": "Problem F: Name the Crossing", "content": "The city of Kyoto is well-known for its Chinese plan: streets are\neither North-South or East-West. Some streets are numbered, but most\nof them have real names.\n\nCrossings are named after the two streets crossing there,\ne. g. Kawaramachi-Sanjo is the crossing of Kawaramachi street and Sanjo\nstreet. But there is a problem: which name should come first?\nAt first the order seems quite arbitrary: one says Kawaramachi-Sanjo\n(North-South first) but Shijo-Kawaramachi (East-West first). With some\nexperience, one realizes that actually there\nseems to be an \"order\" on the streets, for instance in the above\nShijo is \"stronger\" than Kawaramachi, which in turn is \"stronger\" than\nSanjo.\nOne can use this order to deduce the names of other crossings.\n\nYou are given as input a list of known crossing names X-Y.\nStreets are either North-South or East-West, and only orthogonal streets\nmay cross.\n\nAs your list is very incomplete, you start by completing it using\nthe following rule:\n two streets A and B have equal strength if (1) to (3) are\n all true:\n\n they both cross the same third street C in the input \n\n there is no street D such that D-A and B-D appear in the input \n\n there is no street E such that A-E and E-B appear in the input \n\nWe use this definition to extend our strength relation:\n A is stronger than B, when there is a\n sequence A = A_1, A_2, . . . , A_n = B,\n with n at least 2, \n where, for any i in 1 . . n-1, either\n A_i-A_i+1 is an input crossing or\n A_i and A_i+1 have equal strength.\n\nThen you are asked whether some other possible crossing names X-Y are\nvalid. You should answer affirmatively if you can infer the validity of a\nname, negatively if you cannot. Concretely:\n YES if you can infer that the two streets are orthogonal, and X\n is stronger than Y\n\n NO otherwise", "constraint": "", "input": "The input is a sequence of data sets, each of the form\n\nN\nCrossing_1\n. . .\nCrossing_N\nM\nQuestion_1\n. . .\nQuestion_M\n\nBoth Crossings and Questions are of the form\n\nX-Y\n\nwhere X and Y are strings of alphanumerical characters,\nof lengths no more than 16. There is no white space, and case matters\nfor alphabetical characters.\n\nN and M are between 1 and 1000 inclusive, and there are\nno more than 200 streets in a data set.\n\nThe last data set is followed by a line containing a zero.", "output": "The output for each data set should be composed of M+1 lines,\nthe first one containing the number of streets\nin the Crossing part of the input, followed by the answers to\neach question, either YES or NO without any spaces.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\nShijo-Kawaramachi\nKarasuma-Imadegawa\nKawaramachi-Imadegawa\nNishioji-Shijo\nKarasuma-Gojo\nTorimaru-Rokujo\nRokujo-Karasuma\n6\nShijo-Karasuma\nImadegawa-Nishioji\nNishioji-Gojo\nShijo-Torimaru\nTorimaru-Gojo\nShijo-Kawabata\n4\n1jo-Midosuji\nMidosuji-2jo\n2jo-Omotesando\nOmotesando-1jo\n4\nMidosuji-1jo\n1jo-Midosuji\nMidosuji-Omotesando\n1jo-1jo\n0\n output: 8\nYES\nNO\nYES\nNO\nYES\nNO\n4\nYES\nYES\nNO\nNO"], "Pid": "p00715", "ProblemText": "Task Description: The city of Kyoto is well-known for its Chinese plan: streets are\neither North-South or East-West. Some streets are numbered, but most\nof them have real names.\n\nCrossings are named after the two streets crossing there,\ne. g. Kawaramachi-Sanjo is the crossing of Kawaramachi street and Sanjo\nstreet. But there is a problem: which name should come first?\nAt first the order seems quite arbitrary: one says Kawaramachi-Sanjo\n(North-South first) but Shijo-Kawaramachi (East-West first). With some\nexperience, one realizes that actually there\nseems to be an \"order\" on the streets, for instance in the above\nShijo is \"stronger\" than Kawaramachi, which in turn is \"stronger\" than\nSanjo.\nOne can use this order to deduce the names of other crossings.\n\nYou are given as input a list of known crossing names X-Y.\nStreets are either North-South or East-West, and only orthogonal streets\nmay cross.\n\nAs your list is very incomplete, you start by completing it using\nthe following rule:\n two streets A and B have equal strength if (1) to (3) are\n all true:\n\n they both cross the same third street C in the input \n\n there is no street D such that D-A and B-D appear in the input \n\n there is no street E such that A-E and E-B appear in the input \n\nWe use this definition to extend our strength relation:\n A is stronger than B, when there is a\n sequence A = A_1, A_2, . . . , A_n = B,\n with n at least 2, \n where, for any i in 1 . . n-1, either\n A_i-A_i+1 is an input crossing or\n A_i and A_i+1 have equal strength.\n\nThen you are asked whether some other possible crossing names X-Y are\nvalid. You should answer affirmatively if you can infer the validity of a\nname, negatively if you cannot. Concretely:\n YES if you can infer that the two streets are orthogonal, and X\n is stronger than Y\n\n NO otherwise\nTask Input: The input is a sequence of data sets, each of the form\n\nN\nCrossing_1\n. . .\nCrossing_N\nM\nQuestion_1\n. . .\nQuestion_M\n\nBoth Crossings and Questions are of the form\n\nX-Y\n\nwhere X and Y are strings of alphanumerical characters,\nof lengths no more than 16. There is no white space, and case matters\nfor alphabetical characters.\n\nN and M are between 1 and 1000 inclusive, and there are\nno more than 200 streets in a data set.\n\nThe last data set is followed by a line containing a zero.\nTask Output: The output for each data set should be composed of M+1 lines,\nthe first one containing the number of streets\nin the Crossing part of the input, followed by the answers to\neach question, either YES or NO without any spaces.\nTask Samples: input: 7\nShijo-Kawaramachi\nKarasuma-Imadegawa\nKawaramachi-Imadegawa\nNishioji-Shijo\nKarasuma-Gojo\nTorimaru-Rokujo\nRokujo-Karasuma\n6\nShijo-Karasuma\nImadegawa-Nishioji\nNishioji-Gojo\nShijo-Torimaru\nTorimaru-Gojo\nShijo-Kawabata\n4\n1jo-Midosuji\nMidosuji-2jo\n2jo-Omotesando\nOmotesando-1jo\n4\nMidosuji-1jo\n1jo-Midosuji\nMidosuji-Omotesando\n1jo-1jo\n0\n output: 8\nYES\nNO\nYES\nNO\nYES\nNO\n4\nYES\nYES\nNO\nNO\n\n" }, { "title": "Problem A: Ohgas' Fortune", "content": "The Ohgas are a prestigious family based on Hachioji. The head of the family,\nMr. Nemochi Ohga, a famous wealthy man, wishes to increase his fortune\nby depositing his money to an operation company. You are asked to help\nMr. Ohga maximize his profit by operating the given money during a specified\nperiod.\n\nFrom a given list of possible operations, \nyou choose an operation to deposit the given fund to. \nYou commit on the single operation throughout the period and\ndeposit all the fund to it.\n\nEach operation specifies an annual interest rate, whether the interest\nis simple or compound, and an annual operation charge.\n\nAn annual operation charge is a constant \nnot depending on the balance of the fund.\n\nThe amount of interest is calculated at the end of every year, by\nmultiplying the balance of the fund under operation by the annual\ninterest rate, and then rounding off its fractional part. For compound\ninterest, it is added to the balance of the fund under operation, and\nthus becomes a subject of interest for the following years. For\nsimple interest, on the other hand, it is saved somewhere else and\ndoes not enter the balance of the fund under operation (i. e. it is\nnot a subject of interest in the following years).\n\nAn operation charge is then subtracted from the balance of the fund\nunder operation. You may assume here that you can always pay the\noperation charge (i. e. the balance of the fund under operation is\nnever less than the operation charge).\n\nThe amount of money you obtain after the specified years of operation\nis called ``the final amount of fund. '' For simple interest, it is\nthe sum of the balance of the fund under operation at the end of the\nfinal year, plus the amount of interest accumulated throughout the\nperiod. For compound interest, it is simply the balance of the fund\nunder operation at the end of the final year.\nOperation companies use C, C++, Java, etc. , to perform their\ncalculations, so they pay a special attention to their interest\nrates. That is, in these companies, an interest rate is always an\nintegral multiple of 0.0001220703125 and between 0.0001220703125 and\n0.125 (inclusive). 0.0001220703125 is a decimal representation of\n1/8192. Thus, interest rates' being its multiples means that they can\nbe represented with no errors under the double-precision binary\nrepresentation of floating-point numbers.\n\nFor example, if you operate 1000000 JPY for five years with an annual,\ncompound interest rate of 0.03125 (3.125 %) and an annual operation charge of 3000 JPY, the balance changes as\nfollows.\n The balance of the fund under operation\n(at the beginning of year) \n Interest \nThe balance of the fund under operation (at the end of year) \n\n A B = A * 0.03125 (and rounding off fractions) \n A + B - 3000 \n\n 1000000 31250 1028250 \n\n 1028250 32132 1057382 \n\n 1057382 33043 1087425 \n\n 1087425 33982 1118407 \n\n 1118407 34950 1150357 \n\n \nAfter the five years of operation, the final amount of fund is 1150357 JPY.\n\nIf the interest is simple with all other parameters being equal, \nit looks like:\n \n \nThe balance of the fund under operation (at the beginning of year) \n Interest \n The balance of the fund under operation (at the end of year) \n Cumulative interest \n\n \n A B = A * 0.03125 (and rounding off fractions) A - 3000 \n 1000000 31250 997000 31250 \n\n 997000 31156 994000 62406 \n\n 994000 31062 991000 93468 \n\n 991000 30968 988000 124436 \n\n 988000 30875 985000 155311 \n\n In this case the final amount of fund is the total of the fund under\noperation, 985000 JPY, and the cumulative interests, 155311 JPY, which\nis 1140311 JPY.", "constraint": "", "input": "The input consists of datasets. The entire input looks like:\n\nthe number of datasets (=m) \n1st dataset \n2nd dataset \n. . . \nm-th dataset \n\nThe number of datasets, m, is no more than 100.\nEach dataset is formatted as follows.\n\nthe initial amount of the fund for operation \nthe number of years of operation \nthe number of available operations (=n) \noperation 1 \noperation 2 \n. . . \noperation n \n\nThe initial amount of the fund for operation, the number of years of operation, \nand the number of available operations are all positive integers.\nThe first is no more than 100000000, the second no more than 10, and \nthe third no more than 100.\n\nEach ``operation'' is formatted as follows.\n\nsimple-or-compound annual-interest-rate annual-operation-charge\n\nwhere simple-or-compound is a single character of either '0' or '1', \nwith '0' indicating\nsimple interest and '1' compound. annual-interest-rate is represented\nby a decimal fraction and is an integral multiple of 1/8192.\nannual-operation-charge is an integer not exceeding 100000.", "output": "For each dataset, print a line having a decimal integer indicating the\nfinal amount of fund for the best operation. The best operation is the\none that yields the maximum final amount among the available\noperations. Each line should not have any character other than \nthis number.\n\nYou may assume the final balance never exceeds 1000000000.\nYou may also assume that at least one operation has the final amount of the\nfund no less than the initial amount of the fund.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1000000\n5\n2\n0 0.03125 3000\n1 0.03125 3000\n6620000\n7\n2\n0 0.0732421875 42307\n1 0.0740966796875 40942\n39677000\n4\n4\n0 0.0709228515625 30754\n1 0.00634765625 26165\n0 0.03662109375 79468\n0 0.0679931640625 10932\n10585000\n6\n4\n1 0.0054931640625 59759\n1 0.12353515625 56464\n0 0.0496826171875 98193\n0 0.0887451171875 78966\n output: 1150357\n10559683\n50796918\n20829397"], "Pid": "p00716", "ProblemText": "Task Description: The Ohgas are a prestigious family based on Hachioji. The head of the family,\nMr. Nemochi Ohga, a famous wealthy man, wishes to increase his fortune\nby depositing his money to an operation company. You are asked to help\nMr. Ohga maximize his profit by operating the given money during a specified\nperiod.\n\nFrom a given list of possible operations, \nyou choose an operation to deposit the given fund to. \nYou commit on the single operation throughout the period and\ndeposit all the fund to it.\n\nEach operation specifies an annual interest rate, whether the interest\nis simple or compound, and an annual operation charge.\n\nAn annual operation charge is a constant \nnot depending on the balance of the fund.\n\nThe amount of interest is calculated at the end of every year, by\nmultiplying the balance of the fund under operation by the annual\ninterest rate, and then rounding off its fractional part. For compound\ninterest, it is added to the balance of the fund under operation, and\nthus becomes a subject of interest for the following years. For\nsimple interest, on the other hand, it is saved somewhere else and\ndoes not enter the balance of the fund under operation (i. e. it is\nnot a subject of interest in the following years).\n\nAn operation charge is then subtracted from the balance of the fund\nunder operation. You may assume here that you can always pay the\noperation charge (i. e. the balance of the fund under operation is\nnever less than the operation charge).\n\nThe amount of money you obtain after the specified years of operation\nis called ``the final amount of fund. '' For simple interest, it is\nthe sum of the balance of the fund under operation at the end of the\nfinal year, plus the amount of interest accumulated throughout the\nperiod. For compound interest, it is simply the balance of the fund\nunder operation at the end of the final year.\nOperation companies use C, C++, Java, etc. , to perform their\ncalculations, so they pay a special attention to their interest\nrates. That is, in these companies, an interest rate is always an\nintegral multiple of 0.0001220703125 and between 0.0001220703125 and\n0.125 (inclusive). 0.0001220703125 is a decimal representation of\n1/8192. Thus, interest rates' being its multiples means that they can\nbe represented with no errors under the double-precision binary\nrepresentation of floating-point numbers.\n\nFor example, if you operate 1000000 JPY for five years with an annual,\ncompound interest rate of 0.03125 (3.125 %) and an annual operation charge of 3000 JPY, the balance changes as\nfollows.\n The balance of the fund under operation\n(at the beginning of year) \n Interest \nThe balance of the fund under operation (at the end of year) \n\n A B = A * 0.03125 (and rounding off fractions) \n A + B - 3000 \n\n 1000000 31250 1028250 \n\n 1028250 32132 1057382 \n\n 1057382 33043 1087425 \n\n 1087425 33982 1118407 \n\n 1118407 34950 1150357 \n\n \nAfter the five years of operation, the final amount of fund is 1150357 JPY.\n\nIf the interest is simple with all other parameters being equal, \nit looks like:\n \n \nThe balance of the fund under operation (at the beginning of year) \n Interest \n The balance of the fund under operation (at the end of year) \n Cumulative interest \n\n \n A B = A * 0.03125 (and rounding off fractions) A - 3000 \n 1000000 31250 997000 31250 \n\n 997000 31156 994000 62406 \n\n 994000 31062 991000 93468 \n\n 991000 30968 988000 124436 \n\n 988000 30875 985000 155311 \n\n In this case the final amount of fund is the total of the fund under\noperation, 985000 JPY, and the cumulative interests, 155311 JPY, which\nis 1140311 JPY.\nTask Input: The input consists of datasets. The entire input looks like:\n\nthe number of datasets (=m) \n1st dataset \n2nd dataset \n. . . \nm-th dataset \n\nThe number of datasets, m, is no more than 100.\nEach dataset is formatted as follows.\n\nthe initial amount of the fund for operation \nthe number of years of operation \nthe number of available operations (=n) \noperation 1 \noperation 2 \n. . . \noperation n \n\nThe initial amount of the fund for operation, the number of years of operation, \nand the number of available operations are all positive integers.\nThe first is no more than 100000000, the second no more than 10, and \nthe third no more than 100.\n\nEach ``operation'' is formatted as follows.\n\nsimple-or-compound annual-interest-rate annual-operation-charge\n\nwhere simple-or-compound is a single character of either '0' or '1', \nwith '0' indicating\nsimple interest and '1' compound. annual-interest-rate is represented\nby a decimal fraction and is an integral multiple of 1/8192.\nannual-operation-charge is an integer not exceeding 100000.\nTask Output: For each dataset, print a line having a decimal integer indicating the\nfinal amount of fund for the best operation. The best operation is the\none that yields the maximum final amount among the available\noperations. Each line should not have any character other than \nthis number.\n\nYou may assume the final balance never exceeds 1000000000.\nYou may also assume that at least one operation has the final amount of the\nfund no less than the initial amount of the fund.\nTask Samples: input: 4\n1000000\n5\n2\n0 0.03125 3000\n1 0.03125 3000\n6620000\n7\n2\n0 0.0732421875 42307\n1 0.0740966796875 40942\n39677000\n4\n4\n0 0.0709228515625 30754\n1 0.00634765625 26165\n0 0.03662109375 79468\n0 0.0679931640625 10932\n10585000\n6\n4\n1 0.0054931640625 59759\n1 0.12353515625 56464\n0 0.0496826171875 98193\n0 0.0887451171875 78966\n output: 1150357\n10559683\n50796918\n20829397\n\n" }, { "title": "Problem B: Polygonal Line Search", "content": "Multiple polygonal lines are given on the xy-plane.\nGiven a list of polygonal lines and a template,\nyou must find out polygonal lines\nwhich have the same shape as the template.\n\nA polygonal line consists of several line segments parallel to x-axis or\ny-axis. It is defined by a list of xy-coordinates of vertices from the start-point to the end-point in order,\nand always turns 90 degrees at each vertex.\nA single polygonal line does not pass the same point twice.\n\nTwo polygonal lines have the same shape when they\nfully overlap each other only with rotation and translation\nwithin xy-plane (i. e. without magnification or a flip).\nThe vertices given in reverse order from the start-point to the end-point is the\nsame as that given in order.\n\nFigure 1 shows examples of polygonal lines.\nIn this figure, polygonal lines A and B have the same shape.\n\nWrite a program that answers polygonal lines which have the same shape as\nthe template. \n Figure 1: Polygonal lines", "constraint": "", "input": "The input consists of multiple datasets.\nThe end of the input is indicated by a line which contains a zero.\n\nA dataset is given as follows.\n\nn\nPolygonal line_0\nPolygonal line_1\nPolygonal line_2\n. . . \nPolygonal line_n\n\nn is the number of polygonal lines for the object of search on\nxy-plane.\nn is an integer, and 1 <= n <= 50.\nPolygonal line_0 indicates the template.\n\nA polygonal line is given as follows. \n\nm\nx_1 y_1\nx_2 y_2\n. . . \nx_m y_m\n\nm is the number of the vertices of a polygonal line (3 <= m <= 10).\n\nx_i and y_i, separated by a space,\nare the x- and y-coordinates\n of a vertex, respectively (-10000 < x_i < 10000, -10000 \nThe two MCXI-strings are separated by a space.\nYou may assume that the sum of the two MCXI-values \nof the two MCXI-strings in each specification \nis less than or equal to 9999.", "output": "For each specification,\nyour program should print an MCXI-string in a line.\nIts MCXI-value should be the sum of the two MCXI-values\nof the MCXI-strings in the specification.\nNo other characters should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\nxi x9i\ni 9i\nc2x2i 4c8x8i\nm2ci 4m7c9x8i\n9c9x9i i\ni 9m9c9x8i\nm i\ni m\nm9i i\n9m8c7xi c2x8i\n output: 3x\nx\n6cx\n5m9c9x9i\nm\n9m9c9x9i\nmi\nmi\nmx\n9m9c9x9i"], "Pid": "p00718", "ProblemText": "Task Description: Prof. Hachioji has devised a new numeral system of\nintegral numbers with four lowercase letters \"m\", \"c\", \"x\", \"i\"\nand with eight digits \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\". \nHe doesn't use digit \"0\" nor digit \"1\" in this system.\n\nThe letters \"m\", \"c\", \"x\" and \"i\" correspond to 1000,100,10 and 1,\nrespectively, \nand the digits \"2\", . . . , \"9\" correspond to 2, . . . , 9, respectively.\nThis system has nothing to do with the Roman numeral system.\n\nFor example,\ncharacter strings\n\n \"5m2c3x4i\", \"m2c4i\" and \"5m2c3x\"\n\ncorrespond to the integral numbers \n5234 (=5*1000+2*100+3*10+4*1),\n1204 (=1000+2*100+4*1),\n and 5230 (=5*1000+2*100+3*10), \nrespectively. \nThe parts of strings in the above example, \"5m\", \"2c\", \"3x\" and \"4i\" \nrepresent 5000 (=5*1000), 200 (=2*100), 30 (=3*10) and 4 (=4*1),\nrespectively. \n\nEach of the letters \"m\", \"c\", \"x\" and \"i\" may\n be prefixed by one of the digits\n\"2\", \"3\", . . . , \"9\". \nIn that case, the prefix digit and the letter are regarded \nas a pair.\nA pair that consists of a prefix digit and a letter \ncorresponds to an integer that is equal to\nthe original value of the letter multiplied by \nthe value of the prefix digit.\n\nFor each letter \"m\", \"c\", \"x\" and \"i\", \nthe number of its occurrence in a string is at most one.\nWhen it has a prefix digit, it should appear together with the prefix digit.\nThe letters \"m\", \"c\", \"x\" and \"i\" must appear in this order, from left to right.\nMoreover, when a digit exists in a string,\nit should appear as the prefix digit of the following letter.\nEach letter may be omitted in a string, but\nthe whole string must not be empty.\nA string made in this manner is called an MCXI-string.\n\nAn MCXI-string corresponds to a positive integer \nthat is the sum of the values of the letters\nand those of the pairs contained in it as mentioned above. \nThe positive integer corresponding to an MCXI-string is called its\nMCXI-value.\nMoreover, given an integer from 1 to 9999,\nthere is a unique MCXI-string whose MCXI-value is equal \nto the given integer.\nFor example,\nthe MCXI-value of an MCXI-string \"m2c4i\" is \n1204 that is equal to 1000 + 2*100 + 4*1.\nThere are no MCXI-strings but \"m2c4i\" that correspond to 1204.\nNote\nthat strings \"1m2c4i\", \"mcc4i\", \"m2c0x4i\", and \"2cm4i\" are\nnot valid MCXI-strings. \nThe reasons are use of \"1\",\nmultiple occurrences of \"c\", use of \"0\", and the wrong order of \"c\" and \"m\",\nrespectively.\n\nYour job is to write a program for Prof. Hachioji\nthat reads two MCXI-strings, \ncomputes the sum of their MCXI-values, and\nprints the MCXI-string corresponding to the result.\nTask Input: The input is as follows.\nThe first line contains a positive integer n (<= 500) that \nindicates the number of the following lines. \nThe k+1 th line is the specification of \nthe k th computation (k=1, . . . , n).\n\nn \nspecification_1 \nspecification_2 \n . . . \nspecification_n \n\nEach specification is described in a line:\n\nMCXI-string_1 MCXI-string_2\n\n

\nThe two MCXI-strings are separated by a space.\nYou may assume that the sum of the two MCXI-values \nof the two MCXI-strings in each specification \nis less than or equal to 9999.\nTask Output: For each specification,\nyour program should print an MCXI-string in a line.\nIts MCXI-value should be the sum of the two MCXI-values\nof the MCXI-strings in the specification.\nNo other characters should appear in the output.\nTask Samples: input: 10\nxi x9i\ni 9i\nc2x2i 4c8x8i\nm2ci 4m7c9x8i\n9c9x9i i\ni 9m9c9x8i\nm i\ni m\nm9i i\n9m8c7xi c2x8i\n output: 3x\nx\n6cx\n5m9c9x9i\nm\n9m9c9x9i\nmi\nmi\nmx\n9m9c9x9i\n\n" }, { "title": "Problem D: Traveling by Stagecoach", "content": "Once upon a time, there was a traveler.\n\nHe plans to travel using stagecoaches (horse wagons).\nHis starting point and destination are fixed,\nbut he cannot determine his route.\nYour job in this problem is to write a program\nwhich determines the route for him.\n\nThere are several cities in the country,\nand a road network connecting them.\nIf there is a road between two cities, one can travel by a stagecoach\nfrom one of them to the other.\nA coach ticket is needed for a coach ride.\nThe number of horses is specified in each of the tickets.\nOf course, with more horses, the coach runs faster.\n\nAt the starting point, the traveler has a number of coach tickets.\nBy considering these tickets and the information on the road network,\nyou should find the best possible route that takes him to the destination\nin the shortest time.\nThe usage of coach tickets should be taken into account.\n\nThe following conditions are assumed.\n A coach ride takes the traveler from one city to another \ndirectly connected by a road.\nIn other words, on each arrival to a city, he must change the coach. \n\n Only one ticket can be used for a coach ride between two cities\ndirectly connected by a road. \n\n Each ticket can be used only once. \n\n The time needed for a coach ride is the distance between two cities\ndivided by the number of horses. \n\n The time needed for the coach change should be ignored.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\nThe last dataset is followed by a line containing five zeros\n(separated by a space).\n\nn m p a b\nt_1 t_2 . . . t_n\nx_1 y_1 z_1\nx_2 y_2 z_2\n. . . \nx_p y_p z_p\n\nEvery input item in a dataset is a non-negative integer.\nIf a line contains two or more input items, they are separated by a space.\n\nn is the number of coach tickets.\nYou can assume that the number of tickets is between 1 and 8.\nm is the number of cities in the network.\nYou can assume that the number of cities is between 2 and 30.\np is the number of roads between cities, which may be zero.\n\na is the city index of the starting city.\nb is the city index of the destination city.\na is not equal to b.\nYou can assume that all city indices in a dataset (including the above two)\nare between 1 and m.\n\nThe second line of a dataset gives the details of coach tickets.\nt_i is the number of horses specified in the i-th\ncoach ticket (1<=i<=n).\nYou can assume that the number of horses is between 1 and 10.\n\nThe following p lines give the details of roads between cities.\nThe i-th road connects two cities with city indices\nx_i and y_i,\nand has a distance z_i (1<=i<=p).\nYou can assume that the distance is between 1 and 100.\n\nNo two roads connect the same pair of cities.\nA road never connects a city with itself.\nEach road can be traveled in both directions.", "output": "For each dataset in the input, one line should be output as specified below.\nAn output line should not contain extra characters such as spaces.\n\nIf the traveler can reach the destination, the time needed\nfor the best route (a route with the shortest time) should be printed.\nThe answer should not have an error greater than 0.001.\nYou may output any number of digits after the decimal point,\nprovided that the above accuracy condition is satisfied.\n\nIf the traveler cannot reach the destination,\nthe string \"Impossible\" should be printed.\nOne cannot reach the destination either when there are no routes\nleading to the destination, or when the number of tickets is not sufficient.\nNote that the first letter of \"Impossible\" is in uppercase,\nwhile the other letters are in lowercase.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 3 1 4\n3 1 2\n1 2 10\n2 3 30\n3 4 20\n2 4 4 2 1\n3 1\n2 3 3\n1 3 3\n4 1 2\n4 2 5\n2 4 3 4 1\n5 5\n1 2 10\n2 3 10\n3 4 10\n1 2 0 1 2\n1\n8 5 10 1 5\n2 7 1 8 4 5 6 3\n1 2 5\n2 3 4\n3 4 7\n4 5 3\n1 3 25\n2 4 23\n3 5 22\n1 4 45\n2 5 51\n1 5 99\n0 0 0 0 0\n output: 30.000\n3.667\nImpossible\nImpossible\n2.856"], "Pid": "p00719", "ProblemText": "Task Description: Once upon a time, there was a traveler.\n\nHe plans to travel using stagecoaches (horse wagons).\nHis starting point and destination are fixed,\nbut he cannot determine his route.\nYour job in this problem is to write a program\nwhich determines the route for him.\n\nThere are several cities in the country,\nand a road network connecting them.\nIf there is a road between two cities, one can travel by a stagecoach\nfrom one of them to the other.\nA coach ticket is needed for a coach ride.\nThe number of horses is specified in each of the tickets.\nOf course, with more horses, the coach runs faster.\n\nAt the starting point, the traveler has a number of coach tickets.\nBy considering these tickets and the information on the road network,\nyou should find the best possible route that takes him to the destination\nin the shortest time.\nThe usage of coach tickets should be taken into account.\n\nThe following conditions are assumed.\n A coach ride takes the traveler from one city to another \ndirectly connected by a road.\nIn other words, on each arrival to a city, he must change the coach. \n\n Only one ticket can be used for a coach ride between two cities\ndirectly connected by a road. \n\n Each ticket can be used only once. \n\n The time needed for a coach ride is the distance between two cities\ndivided by the number of horses. \n\n The time needed for the coach change should be ignored.\nTask Input: The input consists of multiple datasets, each in the following format.\nThe last dataset is followed by a line containing five zeros\n(separated by a space).\n\nn m p a b\nt_1 t_2 . . . t_n\nx_1 y_1 z_1\nx_2 y_2 z_2\n. . . \nx_p y_p z_p\n\nEvery input item in a dataset is a non-negative integer.\nIf a line contains two or more input items, they are separated by a space.\n\nn is the number of coach tickets.\nYou can assume that the number of tickets is between 1 and 8.\nm is the number of cities in the network.\nYou can assume that the number of cities is between 2 and 30.\np is the number of roads between cities, which may be zero.\n\na is the city index of the starting city.\nb is the city index of the destination city.\na is not equal to b.\nYou can assume that all city indices in a dataset (including the above two)\nare between 1 and m.\n\nThe second line of a dataset gives the details of coach tickets.\nt_i is the number of horses specified in the i-th\ncoach ticket (1<=i<=n).\nYou can assume that the number of horses is between 1 and 10.\n\nThe following p lines give the details of roads between cities.\nThe i-th road connects two cities with city indices\nx_i and y_i,\nand has a distance z_i (1<=i<=p).\nYou can assume that the distance is between 1 and 100.\n\nNo two roads connect the same pair of cities.\nA road never connects a city with itself.\nEach road can be traveled in both directions.\nTask Output: For each dataset in the input, one line should be output as specified below.\nAn output line should not contain extra characters such as spaces.\n\nIf the traveler can reach the destination, the time needed\nfor the best route (a route with the shortest time) should be printed.\nThe answer should not have an error greater than 0.001.\nYou may output any number of digits after the decimal point,\nprovided that the above accuracy condition is satisfied.\n\nIf the traveler cannot reach the destination,\nthe string \"Impossible\" should be printed.\nOne cannot reach the destination either when there are no routes\nleading to the destination, or when the number of tickets is not sufficient.\nNote that the first letter of \"Impossible\" is in uppercase,\nwhile the other letters are in lowercase.\nTask Samples: input: 3 4 3 1 4\n3 1 2\n1 2 10\n2 3 30\n3 4 20\n2 4 4 2 1\n3 1\n2 3 3\n1 3 3\n4 1 2\n4 2 5\n2 4 3 4 1\n5 5\n1 2 10\n2 3 10\n3 4 10\n1 2 0 1 2\n1\n8 5 10 1 5\n2 7 1 8 4 5 6 3\n1 2 5\n2 3 4\n3 4 7\n4 5 3\n1 3 25\n2 4 23\n3 5 22\n1 4 45\n2 5 51\n1 5 99\n0 0 0 0 0\n output: 30.000\n3.667\nImpossible\nImpossible\n2.856\n\n" }, { "title": "Problem E: Earth Observation with a Mobile Robot Team", "content": "A new type of mobile robot has been developed for environmental earth\nobservation.\nIt moves around on the ground, acquiring and recording various sorts of\nobservational data using high precision sensors.\nRobots of this type have short range wireless communication devices and can\nexchange observational data with ones nearby.\nThey also have large capacity memory units, on which they record data\nobserved by themselves and those received from others.\n\nFigure 1 illustrates the current positions of three robots A, B, and C and\nthe geographic coverage of their wireless devices.\nEach circle represents the wireless coverage of a robot, with its\ncenter representing the position of the robot.\nIn this figure, two robots A and B are in the positions where A can\ntransmit data to B, and vice versa.\nIn contrast, C cannot communicate with A or B, since it is too remote\nfrom them.\nStill, however, once B moves towards C as in Figure 2, B and C can\nstart communicating with each other.\nIn this manner, B can relay observational data from A to C.\nFigure 3 shows another example, in which data propagate among several robots \ninstantaneously. \n Figure 1: The initial configuration of three robots \n Figure 2: Mobile relaying \n Figure 3: Instantaneous relaying among multiple robots \n \n\nAs you may notice from these examples, if a team of robots move\nproperly, observational data quickly spread over a large number of them.\nYour mission is to write a program that simulates how information\nspreads among robots.\nSuppose that, regardless of data size, the time necessary for\ncommunication is negligible.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nN T R\nnickname and travel route of the first robot\nnickname and travel route of the second robot\n. . . \nnickname and travel route of the N-th robot\n\nThe first line contains three integers N, T, and\nR that are the number of robots, the length of the simulation\nperiod, and the maximum distance wireless signals can reach,\nrespectively, and satisfy that 1 <=N <= 100,1 <=\nT <= 1000, and 1 <= R <= 10.\n\nThe nickname and travel route of each robot are given in the\nfollowing format.\n\nnickname\nt_0 x_0 y_0\nt_1 vx_1 vy_1\nt_2 vx_2 vy_2\n. . . \nt_k vx_k vy_k \n\nNickname is a character string of length between one and eight that\nonly contains lowercase letters.\nNo two robots in a dataset may have the same nickname.\nEach of the lines following nickname contains three integers,\nsatisfying the following conditions.\n\n0 = t_0 < t_1 < . . . < t_k = T\n-10 <= vx_1, vy_1, . . . , vx_k, vy_k<= 10\n\nA robot moves around on a two dimensional plane.\n(x_0, y_0) is the location of the\nrobot at time 0.\nFrom time t_i-1 to t_i (0\n< i <= k), the velocities in the x and\ny directions are vx_i and\nvy_i, respectively.\nTherefore, the travel route of a robot is piecewise linear.\nNote that it may self-overlap or self-intersect.\n\nYou may assume that each dataset satisfies the following conditions.\nThe distance between any two robots at time 0 is not exactly R. \n\nThe x- and y-coordinates\nof each robot are always between -500 and 500, inclusive.\n\nOnce any robot approaches within R + 10^-6 of any\nother, the distance between them will become smaller than\nR - 10^-6 while maintaining the velocities.\n\nOnce any robot moves away up to R - 10^-6 of any\nother, the distance between them will become larger than R\n+ 10^-6 while maintaining the velocities.\n\nIf any pair of robots mutually enter the wireless area of the\nopposite ones at time t and any pair, which may share one or\ntwo members with the aforementioned pair, mutually leave the wireless\narea of the opposite ones at time t', the difference between\nt and t' is no smaller than 10^-6 time unit, that is,\n|t - t' | >= 10^-6.\nA dataset may include two or more robots that share the same location\nat the same time.\nHowever, you should still consider that they can move with the\ndesignated velocities.\n\nThe end of the input is indicated by a line containing three zeros.", "output": "For each dataset in the input, your program \nshould print the nickname of each robot that have got until time\nT the observational data originally acquired by the first robot\nat time 0. \nEach nickname should be written in a separate line in dictionary order\nwithout any superfluous characters such as leading or trailing spaces.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 5 10\nred\n0 0 0\n5 0 0\ngreen\n0 5 5\n5 6 1\nblue\n0 40 5\n5 0 0\n3 10 5\natom\n0 47 32\n5 -10 -7\n10 1 0\npluto\n0 0 0\n7 0 0\n10 3 3\ngesicht\n0 25 7\n5 -7 -2\n10 -1 10\n4 100 7\nimpulse\n0 -500 0\n100 10 1\nfreedom\n0 -491 0\n100 9 2\ndestiny\n0 -472 0\n100 7 4\nstrike\n0 -482 0\n100 8 3\n0 0 0\n output: blue\ngreen\nred\natom\ngesicht\npluto\nfreedom\nimpulse\nstrike"], "Pid": "p00720", "ProblemText": "Task Description: A new type of mobile robot has been developed for environmental earth\nobservation.\nIt moves around on the ground, acquiring and recording various sorts of\nobservational data using high precision sensors.\nRobots of this type have short range wireless communication devices and can\nexchange observational data with ones nearby.\nThey also have large capacity memory units, on which they record data\nobserved by themselves and those received from others.\n\nFigure 1 illustrates the current positions of three robots A, B, and C and\nthe geographic coverage of their wireless devices.\nEach circle represents the wireless coverage of a robot, with its\ncenter representing the position of the robot.\nIn this figure, two robots A and B are in the positions where A can\ntransmit data to B, and vice versa.\nIn contrast, C cannot communicate with A or B, since it is too remote\nfrom them.\nStill, however, once B moves towards C as in Figure 2, B and C can\nstart communicating with each other.\nIn this manner, B can relay observational data from A to C.\nFigure 3 shows another example, in which data propagate among several robots \ninstantaneously. \n Figure 1: The initial configuration of three robots \n Figure 2: Mobile relaying \n Figure 3: Instantaneous relaying among multiple robots \n \n\nAs you may notice from these examples, if a team of robots move\nproperly, observational data quickly spread over a large number of them.\nYour mission is to write a program that simulates how information\nspreads among robots.\nSuppose that, regardless of data size, the time necessary for\ncommunication is negligible.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nN T R\nnickname and travel route of the first robot\nnickname and travel route of the second robot\n. . . \nnickname and travel route of the N-th robot\n\nThe first line contains three integers N, T, and\nR that are the number of robots, the length of the simulation\nperiod, and the maximum distance wireless signals can reach,\nrespectively, and satisfy that 1 <=N <= 100,1 <=\nT <= 1000, and 1 <= R <= 10.\n\nThe nickname and travel route of each robot are given in the\nfollowing format.\n\nnickname\nt_0 x_0 y_0\nt_1 vx_1 vy_1\nt_2 vx_2 vy_2\n. . . \nt_k vx_k vy_k \n\nNickname is a character string of length between one and eight that\nonly contains lowercase letters.\nNo two robots in a dataset may have the same nickname.\nEach of the lines following nickname contains three integers,\nsatisfying the following conditions.\n\n0 = t_0 < t_1 < . . . < t_k = T\n-10 <= vx_1, vy_1, . . . , vx_k, vy_k<= 10\n\nA robot moves around on a two dimensional plane.\n(x_0, y_0) is the location of the\nrobot at time 0.\nFrom time t_i-1 to t_i (0\n< i <= k), the velocities in the x and\ny directions are vx_i and\nvy_i, respectively.\nTherefore, the travel route of a robot is piecewise linear.\nNote that it may self-overlap or self-intersect.\n\nYou may assume that each dataset satisfies the following conditions.\nThe distance between any two robots at time 0 is not exactly R. \n\nThe x- and y-coordinates\nof each robot are always between -500 and 500, inclusive.\n\nOnce any robot approaches within R + 10^-6 of any\nother, the distance between them will become smaller than\nR - 10^-6 while maintaining the velocities.\n\nOnce any robot moves away up to R - 10^-6 of any\nother, the distance between them will become larger than R\n+ 10^-6 while maintaining the velocities.\n\nIf any pair of robots mutually enter the wireless area of the\nopposite ones at time t and any pair, which may share one or\ntwo members with the aforementioned pair, mutually leave the wireless\narea of the opposite ones at time t', the difference between\nt and t' is no smaller than 10^-6 time unit, that is,\n|t - t' | >= 10^-6.\nA dataset may include two or more robots that share the same location\nat the same time.\nHowever, you should still consider that they can move with the\ndesignated velocities.\n\nThe end of the input is indicated by a line containing three zeros.\nTask Output: For each dataset in the input, your program \nshould print the nickname of each robot that have got until time\nT the observational data originally acquired by the first robot\nat time 0. \nEach nickname should be written in a separate line in dictionary order\nwithout any superfluous characters such as leading or trailing spaces.\nTask Samples: input: 3 5 10\nred\n0 0 0\n5 0 0\ngreen\n0 5 5\n5 6 1\nblue\n0 40 5\n5 0 0\n3 10 5\natom\n0 47 32\n5 -10 -7\n10 1 0\npluto\n0 0 0\n7 0 0\n10 3 3\ngesicht\n0 25 7\n5 -7 -2\n10 -1 10\n4 100 7\nimpulse\n0 -500 0\n100 10 1\nfreedom\n0 -491 0\n100 9 2\ndestiny\n0 -472 0\n100 7 4\nstrike\n0 -482 0\n100 8 3\n0 0 0\n output: blue\ngreen\nred\natom\ngesicht\npluto\nfreedom\nimpulse\nstrike\n\n" }, { "title": "Problem F: Cleaning Robot", "content": "Here, we want to solve path planning for a mobile robot cleaning a\nrectangular room floor with furniture.\n\nConsider the room floor paved with square tiles whose size fits \nthe cleaning robot (1 * 1).\nThere are 'clean tiles' and 'dirty tiles', and the robot can change\na 'dirty tile' to a 'clean tile' by visiting the tile.\nAlso there may be some obstacles (furniture) whose size fits a\ntile in the room. If there is an obstacle on a tile, the robot cannot visit \nit.\nThe robot moves to an adjacent tile with one move.\nThe tile onto which the robot moves must be one of four tiles \n(i. e. , east, west, north or south) adjacent to the tile where the \nrobot is present. The robot may visit a tile twice or more.\n\nYour task is to write a program which computes the minimum number of\nmoves for the robot to change all 'dirty tiles' to 'clean tiles', \nif ever possible.", "constraint": "", "input": "The input consists of multiple maps, each representing the size \nand arrangement of the room. A map is given in the following format.\n\nw h\n\nc_11 c_12 c_13 . . . c_1w\nc_21 c_22 c_23 . . . c_2w\n. . . \nc_h1 c_h2 c_h3 . . . c_hw\n\nThe integers w and h are the lengths of the two sides \nof the floor of the room in terms of widths of floor tiles. w and h \nare less than or equal to 20. The character c_yx represents \nwhat is initially on the tile with coordinates (x, y) as follows. \n\n'. ' : a clean tile\n'*' : a dirty tile \n'x' : a piece of furniture (obstacle) \n'o' : the robot (initial position)\n\nIn the map the number of 'dirty tiles' does not exceed 10.\nThere is only one 'robot'.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each map, your program should output a line containing the minimum \nnumber of moves. If the map includes 'dirty tiles' which the robot cannot reach, \nyour program should output -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 5\n.......\n.o...*.\n.......\n.*...*.\n.......\n15 13\n.......x.......\n...o...x....*..\n.......x.......\n.......x.......\n.......x.......\n...............\nxxxxx.....xxxxx\n...............\n.......x.......\n.......x.......\n.......x.......\n..*....x....*..\n.......x.......\n10 10\n..........\n..o.......\n..........\n..........\n..........\n.....xxxxx\n.....x....\n.....x.*..\n.....x....\n.....x....\n0 0\n output: 8\n49\n-1"], "Pid": "p00721", "ProblemText": "Task Description: Here, we want to solve path planning for a mobile robot cleaning a\nrectangular room floor with furniture.\n\nConsider the room floor paved with square tiles whose size fits \nthe cleaning robot (1 * 1).\nThere are 'clean tiles' and 'dirty tiles', and the robot can change\na 'dirty tile' to a 'clean tile' by visiting the tile.\nAlso there may be some obstacles (furniture) whose size fits a\ntile in the room. If there is an obstacle on a tile, the robot cannot visit \nit.\nThe robot moves to an adjacent tile with one move.\nThe tile onto which the robot moves must be one of four tiles \n(i. e. , east, west, north or south) adjacent to the tile where the \nrobot is present. The robot may visit a tile twice or more.\n\nYour task is to write a program which computes the minimum number of\nmoves for the robot to change all 'dirty tiles' to 'clean tiles', \nif ever possible.\nTask Input: The input consists of multiple maps, each representing the size \nand arrangement of the room. A map is given in the following format.\n\nw h\n\nc_11 c_12 c_13 . . . c_1w\nc_21 c_22 c_23 . . . c_2w\n. . . \nc_h1 c_h2 c_h3 . . . c_hw\n\nThe integers w and h are the lengths of the two sides \nof the floor of the room in terms of widths of floor tiles. w and h \nare less than or equal to 20. The character c_yx represents \nwhat is initially on the tile with coordinates (x, y) as follows. \n\n'. ' : a clean tile\n'*' : a dirty tile \n'x' : a piece of furniture (obstacle) \n'o' : the robot (initial position)\n\nIn the map the number of 'dirty tiles' does not exceed 10.\nThere is only one 'robot'.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each map, your program should output a line containing the minimum \nnumber of moves. If the map includes 'dirty tiles' which the robot cannot reach, \nyour program should output -1.\nTask Samples: input: 7 5\n.......\n.o...*.\n.......\n.*...*.\n.......\n15 13\n.......x.......\n...o...x....*..\n.......x.......\n.......x.......\n.......x.......\n...............\nxxxxx.....xxxxx\n...............\n.......x.......\n.......x.......\n.......x.......\n..*....x....*..\n.......x.......\n10 10\n..........\n..o.......\n..........\n..........\n..........\n.....xxxxx\n.....x....\n.....x.*..\n.....x....\n.....x....\n0 0\n output: 8\n49\n-1\n\n" }, { "title": "Problem A: Dirichlet's Theorem on Arithmetic Progressions", "content": "Good evening, contestants.\n\nIf a and d are relatively prime positive integers,\nthe arithmetic sequence beginning with a\nand increasing by d, i. e. ,\na,\na + d,\na + 2d,\na + 3d,\na + 4d,\n. . . ,\ncontains infinitely many prime numbers.\nThis fact is known as Dirichlet's Theorem on Arithmetic Progressions,\nwhich had been conjectured by Johann Carl Friedrich Gauss (1777 - 1855)\nand was proved by Johann Peter Gustav Lejeune Dirichlet (1805 - 1859)\nin 1837.\n\nFor example,\nthe arithmetic sequence beginning with 2 and increasing by 3,\ni. e. ,\n\n2,\n5,\n8,\n11,\n14,\n17,\n20,\n23,\n26,\n29,\n32,\n35,\n38,\n41,\n44,\n47,\n50,\n53,\n56,\n59,\n62,\n65,\n68,\n71,\n74,\n77,\n80,\n83,\n86,\n89,\n92,\n95,\n98,\n. . .\n,\n\ncontains infinitely many prime numbers\n\n2,\n5,\n11,\n17,\n23,\n29,\n41,\n47,\n53,\n59,\n71,\n83,\n89,\n. . .\n\n.\n\nYour mission, should you decide to accept it,\nis to write a program to find\nthe nth prime number in this arithmetic sequence\nfor given positive integers a, d, and n.\n\nAs always, should you or any of your team be tired or confused,\nthe secretary disavow any knowledge of your actions.\nThis judge system will self-terminate in three hours.\nGood luck!", "constraint": "", "input": "The input is a sequence of datasets.\nA dataset is a line containing three positive integers\na, d, and n separated by a space.\na and d are relatively prime.\nYou may assume a <= 9307, d <= 346,\nand n <= 210.\n\nThe end of the input is indicated by a line\ncontaining three zeros separated by a space.\nIt is not a dataset.", "output": "The output should be composed of\nas many lines as the number of the input datasets.\nEach line should contain a single integer\nand should never contain extra characters.\n\nThe output integer corresponding to\na dataset a, d, n should be\nthe nth \nprime number among those contained\nin the arithmetic sequence beginning with a\nand increasing by d.\n\nFYI, it is known that the result is always less than\n10^6 (one million)\nunder this input condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 367 186 151\n179 10 203\n271 37 39\n103 230 1\n27 104 185\n253 50 85\n1 1 1\n9075 337 210\n307 24 79\n331 221 177\n259 170 40\n269 58 102\n0 0 0\n output: 92809\n6709\n12037\n103\n93523\n14503\n2\n899429\n5107\n412717\n22699\n25673"], "Pid": "p00722", "ProblemText": "Task Description: Good evening, contestants.\n\nIf a and d are relatively prime positive integers,\nthe arithmetic sequence beginning with a\nand increasing by d, i. e. ,\na,\na + d,\na + 2d,\na + 3d,\na + 4d,\n. . . ,\ncontains infinitely many prime numbers.\nThis fact is known as Dirichlet's Theorem on Arithmetic Progressions,\nwhich had been conjectured by Johann Carl Friedrich Gauss (1777 - 1855)\nand was proved by Johann Peter Gustav Lejeune Dirichlet (1805 - 1859)\nin 1837.\n\nFor example,\nthe arithmetic sequence beginning with 2 and increasing by 3,\ni. e. ,\n\n2,\n5,\n8,\n11,\n14,\n17,\n20,\n23,\n26,\n29,\n32,\n35,\n38,\n41,\n44,\n47,\n50,\n53,\n56,\n59,\n62,\n65,\n68,\n71,\n74,\n77,\n80,\n83,\n86,\n89,\n92,\n95,\n98,\n. . .\n,\n\ncontains infinitely many prime numbers\n\n2,\n5,\n11,\n17,\n23,\n29,\n41,\n47,\n53,\n59,\n71,\n83,\n89,\n. . .\n\n.\n\nYour mission, should you decide to accept it,\nis to write a program to find\nthe nth prime number in this arithmetic sequence\nfor given positive integers a, d, and n.\n\nAs always, should you or any of your team be tired or confused,\nthe secretary disavow any knowledge of your actions.\nThis judge system will self-terminate in three hours.\nGood luck!\nTask Input: The input is a sequence of datasets.\nA dataset is a line containing three positive integers\na, d, and n separated by a space.\na and d are relatively prime.\nYou may assume a <= 9307, d <= 346,\nand n <= 210.\n\nThe end of the input is indicated by a line\ncontaining three zeros separated by a space.\nIt is not a dataset.\nTask Output: The output should be composed of\nas many lines as the number of the input datasets.\nEach line should contain a single integer\nand should never contain extra characters.\n\nThe output integer corresponding to\na dataset a, d, n should be\nthe nth \nprime number among those contained\nin the arithmetic sequence beginning with a\nand increasing by d.\n\nFYI, it is known that the result is always less than\n10^6 (one million)\nunder this input condition.\nTask Samples: input: 367 186 151\n179 10 203\n271 37 39\n103 230 1\n27 104 185\n253 50 85\n1 1 1\n9075 337 210\n307 24 79\n331 221 177\n259 170 40\n269 58 102\n0 0 0\n output: 92809\n6709\n12037\n103\n93523\n14503\n2\n899429\n5107\n412717\n22699\n25673\n\n" }, { "title": "Problem B: Organize Your Train part II", "content": "RJ Freight, a Japanese railroad company for freight operations\nhas recently constructed exchange lines at Hazawa, Yokohama.\nThe layout of the lines is shown in Figure B-1.\n\nFigure B-1: Layout of the exchange lines\nA freight train consists of 2 to 72 freight cars. There are 26\ntypes of freight cars, which are denoted by 26 lowercase letters\nfrom \"a\" to \"z\". The cars of the same type are indistinguishable from\neach other, and each car's direction doesn't matter either.\nThus, a string of lowercase letters of length 2 to 72 is sufficient\nto completely express the configuration of a train.\n\nUpon arrival at the exchange lines, a train is divided into two\nsub-trains at an arbitrary position (prior to entering the\nstorage lines). Each of the sub-trains may have its direction\nreversed (using the reversal line). Finally, the two sub-trains\nare connected in either order to form the final configuration.\nNote that the reversal operation is optional for each of the\nsub-trains.\n\nFor example, if the arrival configuration is \"abcd\", the train\nis split into two sub-trains of either 3: 1,2: 2 or 1: 3 cars.\nFor each of the splitting, possible final configurations are\nas follows (\"+\" indicates final concatenation position):\n [3: 1]\n abc+d cba+d d+abc d+cba\n [2: 2]\n ab+cd ab+dc ba+cd ba+dc cd+ab cd+ba dc+ab dc+ba\n [1: 3]\n a+bcd a+dcb bcd+a dcb+a\nExcluding duplicates, 12 distinct configurations are possible.\n\nGiven an arrival configuration, answer \nthe number of distinct configurations which can be\nconstructed using the exchange lines described above.", "constraint": "", "input": "The entire input looks like the following. \nthe number of datasets = m\n1st dataset \n2nd dataset \n. . . \nm-th dataset \n\nEach dataset represents an arriving train, and is a string of\n2 to 72 lowercase letters in an input line.", "output": "For each dataset, output the number of possible train configurations\nin a line. No other characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\naa\nabba\nabcd\nabcde\n output: 1\n6\n12\n18"], "Pid": "p00723", "ProblemText": "Task Description: RJ Freight, a Japanese railroad company for freight operations\nhas recently constructed exchange lines at Hazawa, Yokohama.\nThe layout of the lines is shown in Figure B-1.\n\nFigure B-1: Layout of the exchange lines\nA freight train consists of 2 to 72 freight cars. There are 26\ntypes of freight cars, which are denoted by 26 lowercase letters\nfrom \"a\" to \"z\". The cars of the same type are indistinguishable from\neach other, and each car's direction doesn't matter either.\nThus, a string of lowercase letters of length 2 to 72 is sufficient\nto completely express the configuration of a train.\n\nUpon arrival at the exchange lines, a train is divided into two\nsub-trains at an arbitrary position (prior to entering the\nstorage lines). Each of the sub-trains may have its direction\nreversed (using the reversal line). Finally, the two sub-trains\nare connected in either order to form the final configuration.\nNote that the reversal operation is optional for each of the\nsub-trains.\n\nFor example, if the arrival configuration is \"abcd\", the train\nis split into two sub-trains of either 3: 1,2: 2 or 1: 3 cars.\nFor each of the splitting, possible final configurations are\nas follows (\"+\" indicates final concatenation position):\n [3: 1]\n abc+d cba+d d+abc d+cba\n [2: 2]\n ab+cd ab+dc ba+cd ba+dc cd+ab cd+ba dc+ab dc+ba\n [1: 3]\n a+bcd a+dcb bcd+a dcb+a\nExcluding duplicates, 12 distinct configurations are possible.\n\nGiven an arrival configuration, answer \nthe number of distinct configurations which can be\nconstructed using the exchange lines described above.\nTask Input: The entire input looks like the following. \nthe number of datasets = m\n1st dataset \n2nd dataset \n. . . \nm-th dataset \n\nEach dataset represents an arriving train, and is a string of\n2 to 72 lowercase letters in an input line.\nTask Output: For each dataset, output the number of possible train configurations\nin a line. No other characters should appear in the output.\nTask Samples: input: 4\naa\nabba\nabcd\nabcde\n output: 1\n6\n12\n18\n\n" }, { "title": "Problem C: Hexerpents of Hexwamp", "content": "Hexwamp is a strange swamp, paved with regular hexagonal dimples.\nHexerpents crawling in this area are serpents adapted to the\nenvironment, consisting of a chain of regular hexagonal sections. Each\nsection fits in one dimple.\n\nHexerpents crawl moving some of their sections from the dimples they\nare in to adjacent ones. To avoid breaking their bodies, sections\nthat are adjacent to each other before the move should also be\nadjacent after the move. When one section moves, sections adjacent to\nit support the move, and thus they cannot move at that time. Any\nnumber of sections, as far as no two of them are adjacent to each\nother, can move at the same time.\n\nYou can easily find that a hexerpent can move its sections at its\neither end to only up to two dimples, and can move intermediate\nsections to only one dimple, if any.\n\nFor example, without any obstacles, a hexerpent can crawl forward\ntwisting its body as shown in Figure C-1, left to right. In this\nfigure, the serpent moves four of its eight sections at a time, and\nmoves its body forward by one dimple unit after four steps of moves.\nActually, they are much better in crawling sideways, like sidewinders.\nFigure C-1: Crawling forward\nTheir skin is so sticky that if two sections of a serpent that are not\noriginally adjacent come to adjacent dimples (Figure C-2), they will\nstick together and the serpent cannot but die. Two sections cannot\nfit in one dimple, of course. This restricts serpents' moves\nfurther. Sometimes, they have to make some efforts to get a food\npiece even when it is in the dimple next to their head.\nFigure C-2: Fatal case\nHexwamp has rocks here and there. Each rock fits in a dimple.\nHexerpents' skin does not stick to rocks, but they cannot crawl over\nthe rocks. Although avoiding dimples with rocks restricts their\nmoves, they know the geography so well that they can plan the fastest\npaths.\n\nYou are appointed to take the responsibility of the head of the\nscientist team to carry out academic research on this swamp and the\nserpents. You are expected to accomplish the research, but never at\nthe sacrifice of any casualty. Your task now is to estimate how soon\na man-eating hexerpent may move its head (the first section) to the\nposition of a scientist in the swamp. Their body sections except for\nthe head are quite harmless and the scientist wearing high-tech\nanti-sticking suit can stay in the same dimple with a body section of\nthe hexerpent.", "constraint": "", "input": "The input is a sequence of several datasets, and the end of the input\nis indicated by a line containing a single zero. The number of\ndatasets never exceeds 10.\n\nEach dataset looks like the following.\n\nthe number of sections the serpent has (=n) \nx_1 y_1\nx_2 y_2\n. . . \nx_n y_n\nthe number of rocks the swamp has (=k) \nu_1 v_1\nu_2 v_2\n. . . \nu_k v_k\nX Y\nThe first line of the dataset has an integer n that indicates\nthe number of sections the hexerpent has, which is 2 or greater and\nnever exceeds 8. Each of the n following lines contains two\nintegers x and y that indicate the coordinates of a\nserpent's section. The lines show the initial positions of the\nsections from the serpent's head to its tail, in this order.\n

\nThe next line of the dataset indicates the number of rocks k\nthe swamp has, which is a non-negative integer not exceeding 100.\nEach of the k following lines contains two integers u\nand v that indicate the position of a rock.\n\nFinally comes a line containing two integers X and Y,\nindicating the goal position of the hexerpent, where the scientist is.\nThe serpent's head is not initially here.\n\nAll of the coordinates x, y, u, v, X, and Y are between\n-999999 and 999999, inclusive. Two integers in a line are\nseparated by a single space. No characters other than decimal digits,\nminus signs, and spaces to separate two integers appear in the input.\nThe coordinate system used to indicate a position is as shown in\nFigure C-3.\nFigure C-3: The coordinate system", "output": "For each dataset, output a line that contains a decimal integer that\nindicates the minimum number of steps the serpent requires for moving\nits head to the goal position. Output lines should not contain any\nother characters.\n\nYou can assume that the hexerpent can reach the goal within 20 steps.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n2 -2\n2 -1\n1 0\n1\n0 2\n0 0\n4\n2 -2\n2 -1\n2 0\n3 0\n2\n1 -1\n0 2\n0 0\n8\n-6 0\n-5 0\n-4 0\n-3 0\n-2 0\n-1 0\n0 0\n1 0\n1\n-1 1\n0 0\n6\n2 -3\n3 -3\n3 -2\n3 -1\n3 0\n2 1\n3\n1 -1\n1 0\n1 1\n0 0\n3\n-8000 4996\n-8000 4997\n-8000 4998\n2\n-7999 4999\n-8001 5000\n-8000 5000\n8\n10 -8\n9 -7\n9 -6\n9 -5\n9 -4\n9 -3\n9 -2\n9 -1\n0\n0 0\n0\n output: 3\n9\n18\n18\n19\n20"], "Pid": "p00724", "ProblemText": "Task Description: Hexwamp is a strange swamp, paved with regular hexagonal dimples.\nHexerpents crawling in this area are serpents adapted to the\nenvironment, consisting of a chain of regular hexagonal sections. Each\nsection fits in one dimple.\n\nHexerpents crawl moving some of their sections from the dimples they\nare in to adjacent ones. To avoid breaking their bodies, sections\nthat are adjacent to each other before the move should also be\nadjacent after the move. When one section moves, sections adjacent to\nit support the move, and thus they cannot move at that time. Any\nnumber of sections, as far as no two of them are adjacent to each\nother, can move at the same time.\n\nYou can easily find that a hexerpent can move its sections at its\neither end to only up to two dimples, and can move intermediate\nsections to only one dimple, if any.\n\nFor example, without any obstacles, a hexerpent can crawl forward\ntwisting its body as shown in Figure C-1, left to right. In this\nfigure, the serpent moves four of its eight sections at a time, and\nmoves its body forward by one dimple unit after four steps of moves.\nActually, they are much better in crawling sideways, like sidewinders.\nFigure C-1: Crawling forward\nTheir skin is so sticky that if two sections of a serpent that are not\noriginally adjacent come to adjacent dimples (Figure C-2), they will\nstick together and the serpent cannot but die. Two sections cannot\nfit in one dimple, of course. This restricts serpents' moves\nfurther. Sometimes, they have to make some efforts to get a food\npiece even when it is in the dimple next to their head.\nFigure C-2: Fatal case\nHexwamp has rocks here and there. Each rock fits in a dimple.\nHexerpents' skin does not stick to rocks, but they cannot crawl over\nthe rocks. Although avoiding dimples with rocks restricts their\nmoves, they know the geography so well that they can plan the fastest\npaths.\n\nYou are appointed to take the responsibility of the head of the\nscientist team to carry out academic research on this swamp and the\nserpents. You are expected to accomplish the research, but never at\nthe sacrifice of any casualty. Your task now is to estimate how soon\na man-eating hexerpent may move its head (the first section) to the\nposition of a scientist in the swamp. Their body sections except for\nthe head are quite harmless and the scientist wearing high-tech\nanti-sticking suit can stay in the same dimple with a body section of\nthe hexerpent.\nTask Input: The input is a sequence of several datasets, and the end of the input\nis indicated by a line containing a single zero. The number of\ndatasets never exceeds 10.\n\nEach dataset looks like the following.\n\nthe number of sections the serpent has (=n) \nx_1 y_1\nx_2 y_2\n. . . \nx_n y_n\nthe number of rocks the swamp has (=k) \nu_1 v_1\nu_2 v_2\n. . . \nu_k v_k\nX Y\nThe first line of the dataset has an integer n that indicates\nthe number of sections the hexerpent has, which is 2 or greater and\nnever exceeds 8. Each of the n following lines contains two\nintegers x and y that indicate the coordinates of a\nserpent's section. The lines show the initial positions of the\nsections from the serpent's head to its tail, in this order.\n

\nThe next line of the dataset indicates the number of rocks k\nthe swamp has, which is a non-negative integer not exceeding 100.\nEach of the k following lines contains two integers u\nand v that indicate the position of a rock.\n\nFinally comes a line containing two integers X and Y,\nindicating the goal position of the hexerpent, where the scientist is.\nThe serpent's head is not initially here.\n\nAll of the coordinates x, y, u, v, X, and Y are between\n-999999 and 999999, inclusive. Two integers in a line are\nseparated by a single space. No characters other than decimal digits,\nminus signs, and spaces to separate two integers appear in the input.\nThe coordinate system used to indicate a position is as shown in\nFigure C-3.\nFigure C-3: The coordinate system\nTask Output: For each dataset, output a line that contains a decimal integer that\nindicates the minimum number of steps the serpent requires for moving\nits head to the goal position. Output lines should not contain any\nother characters.\n\nYou can assume that the hexerpent can reach the goal within 20 steps.\nTask Samples: input: 3\n2 -2\n2 -1\n1 0\n1\n0 2\n0 0\n4\n2 -2\n2 -1\n2 0\n3 0\n2\n1 -1\n0 2\n0 0\n8\n-6 0\n-5 0\n-4 0\n-3 0\n-2 0\n-1 0\n0 0\n1 0\n1\n-1 1\n0 0\n6\n2 -3\n3 -3\n3 -2\n3 -1\n3 0\n2 1\n3\n1 -1\n1 0\n1 1\n0 0\n3\n-8000 4996\n-8000 4997\n-8000 4998\n2\n-7999 4999\n-8001 5000\n-8000 5000\n8\n10 -8\n9 -7\n9 -6\n9 -5\n9 -4\n9 -3\n9 -2\n9 -1\n0\n0 0\n0\n output: 3\n9\n18\n18\n19\n20\n\n" }, { "title": "Problem D: Curling 2.0", "content": "On Planet MM-21, after their Olympic games this year, curling is getting popular.\nBut the rules are somewhat different from ours.\nThe game is played on an ice game board on which a square mesh is marked.\nThey use only a single stone.\nThe purpose of the game is to lead the stone from the start\nto the goal with the minimum number of moves.\n\nFig. D-1 shows an example of a game board.\nSome squares may be occupied with blocks.\nThere are two special squares namely the start and the goal,\nwhich are not occupied with blocks.\n(These two squares are distinct. )\nOnce the stone begins to move, it will proceed until it hits a block.\nIn order to bring the stone to the goal,\nyou may have to stop the stone by hitting it against a block,\nand throw again.\nFig. D-1: Example of board (S: start, G: goal)\nThe movement of the stone obeys the following rules:\n\n At the beginning, the stone stands still at the start square.\n\n The movements of the stone are restricted to x and y directions.\nDiagonal moves are prohibited.\n\n When the stone stands still, you can make it moving by throwing it.\nYou may throw it to any direction\nunless it is blocked immediately(Fig. D-2(a)).\n\n Once thrown, the stone keeps moving to the same direction until\none of the following occurs:\n\n The stone hits a block (Fig. D-2(b), (c)).\n \n The stone stops at the square next to the block it hit.\n \n The block disappears.\n \n The stone gets out of the board.\n \n The game ends in failure.\n \n The stone reaches the goal square.\n \n The stone stops there and the game ends in success.\n \n You cannot throw the stone more than 10 times in a game.\nIf the stone does not reach the goal in 10 moves, the game ends in failure.\n\nFig. D-2: Stone movements\nUnder the rules, we would like to know whether the stone at the start\ncan reach the goal and, if yes, the minimum number of moves required.\n\nWith the initial configuration shown in Fig. D-1,4 moves are required\nto bring the stone from the start to the goal.\nThe route is shown in Fig. D-3(a).\nNotice when the stone reaches the goal, the board configuration has changed\nas in Fig. D-3(b).\nFig. D-3: The solution for Fig. D-1 and the final board configuration", "constraint": "", "input": "The input is a sequence of datasets.\nThe end of the input is indicated by a line\ncontaining two zeros separated by a space.\nThe number of datasets never exceeds 100.\nEach dataset is formatted as follows.\n\nthe width(=w) and the height(=h) of the board \nFirst row of the board \n. . . \nh-th row of the board \nThe width and the height of the board satisfy:\n 2 <= w <= 20,1 <= h <= 20.\n\nEach line consists of w decimal numbers delimited by a space.\nThe number describes the status of the corresponding square.\n\n \n

0 vacant square \n\n 1 block \n\n 2 start position \n\n 3 goal position \n\n \n\n

\nThe dataset for Fig. D-1 is as follows:\n\n6 6 \n1 0 0 2 1 0 \n1 1 0 0 0 0 \n0 0 0 0 0 3 \n0 0 0 0 0 0 \n1 0 0 0 0 1 \n0 1 1 1 1 1", "output": "For each dataset, print a line having a decimal integer indicating the\nminimum number of moves along a route from the start to the goal.\nIf there are no such routes, print -1 instead.\nEach line should not have any character other than \nthis number.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 1\n3 2\n6 6\n1 0 0 2 1 0\n1 1 0 0 0 0\n0 0 0 0 0 3\n0 0 0 0 0 0\n1 0 0 0 0 1\n0 1 1 1 1 1\n6 1\n1 1 2 1 1 3\n6 1\n1 0 2 1 1 3\n12 1\n2 0 1 1 1 1 1 1 1 1 1 3\n13 1\n2 0 1 1 1 1 1 1 1 1 1 1 3\n0 0\n output: 1\n4\n-1\n4\n10\n-1"], "Pid": "p00725", "ProblemText": "Task Description: On Planet MM-21, after their Olympic games this year, curling is getting popular.\nBut the rules are somewhat different from ours.\nThe game is played on an ice game board on which a square mesh is marked.\nThey use only a single stone.\nThe purpose of the game is to lead the stone from the start\nto the goal with the minimum number of moves.\n\nFig. D-1 shows an example of a game board.\nSome squares may be occupied with blocks.\nThere are two special squares namely the start and the goal,\nwhich are not occupied with blocks.\n(These two squares are distinct. )\nOnce the stone begins to move, it will proceed until it hits a block.\nIn order to bring the stone to the goal,\nyou may have to stop the stone by hitting it against a block,\nand throw again.\nFig. D-1: Example of board (S: start, G: goal)\nThe movement of the stone obeys the following rules:\n\n At the beginning, the stone stands still at the start square.\n\n The movements of the stone are restricted to x and y directions.\nDiagonal moves are prohibited.\n\n When the stone stands still, you can make it moving by throwing it.\nYou may throw it to any direction\nunless it is blocked immediately(Fig. D-2(a)).\n\n Once thrown, the stone keeps moving to the same direction until\none of the following occurs:\n\n The stone hits a block (Fig. D-2(b), (c)).\n \n The stone stops at the square next to the block it hit.\n \n The block disappears.\n \n The stone gets out of the board.\n \n The game ends in failure.\n \n The stone reaches the goal square.\n \n The stone stops there and the game ends in success.\n \n You cannot throw the stone more than 10 times in a game.\nIf the stone does not reach the goal in 10 moves, the game ends in failure.\n\nFig. D-2: Stone movements\nUnder the rules, we would like to know whether the stone at the start\ncan reach the goal and, if yes, the minimum number of moves required.\n\nWith the initial configuration shown in Fig. D-1,4 moves are required\nto bring the stone from the start to the goal.\nThe route is shown in Fig. D-3(a).\nNotice when the stone reaches the goal, the board configuration has changed\nas in Fig. D-3(b).\nFig. D-3: The solution for Fig. D-1 and the final board configuration\nTask Input: The input is a sequence of datasets.\nThe end of the input is indicated by a line\ncontaining two zeros separated by a space.\nThe number of datasets never exceeds 100.\nEach dataset is formatted as follows.\n\nthe width(=w) and the height(=h) of the board \nFirst row of the board \n. . . \nh-th row of the board \nThe width and the height of the board satisfy:\n 2 <= w <= 20,1 <= h <= 20.\n\nEach line consists of w decimal numbers delimited by a space.\nThe number describes the status of the corresponding square.\n\n \n

0 vacant square \n\n 1 block \n\n 2 start position \n\n 3 goal position \n\n \n\n

\nThe dataset for Fig. D-1 is as follows:\n\n6 6 \n1 0 0 2 1 0 \n1 1 0 0 0 0 \n0 0 0 0 0 3 \n0 0 0 0 0 0 \n1 0 0 0 0 1 \n0 1 1 1 1 1\nTask Output: For each dataset, print a line having a decimal integer indicating the\nminimum number of moves along a route from the start to the goal.\nIf there are no such routes, print -1 instead.\nEach line should not have any character other than \nthis number.\nTask Samples: input: 2 1\n3 2\n6 6\n1 0 0 2 1 0\n1 1 0 0 0 0\n0 0 0 0 0 3\n0 0 0 0 0 0\n1 0 0 0 0 1\n0 1 1 1 1 1\n6 1\n1 1 2 1 1 3\n6 1\n1 0 2 1 1 3\n12 1\n2 0 1 1 1 1 1 1 1 1 1 3\n13 1\n2 0 1 1 1 1 1 1 1 1 1 1 3\n0 0\n output: 1\n4\n-1\n4\n10\n-1\n\n" }, { "title": "Problem E: The Genome Database of All Space Life", "content": "In 2300, the Life Science Division of Federal Republic of Space starts\na very ambitious project to complete the genome sequencing of all\nliving creatures in the entire universe and develop the genomic\ndatabase of all space life.\nThanks to scientific research over many years, it has been known that\nthe genome of any species consists of at most 26 kinds of\nmolecules, denoted by English capital letters (i. e. A\nto Z).\nWhat will be stored into the database are plain strings consisting of\nEnglish capital letters.\nIn general, however, the genome sequences of space life include\nfrequent repetitions and can be awfully long.\nSo, for efficient utilization of storage, we compress N-times\nrepetitions of a letter sequence seq into\nN(seq), where N is a natural \nnumber greater than or equal to two and the length of seq is at\nleast one.\nWhen seq consists of just one letter c, we may omit parentheses and write Nc.\nFor example, a fragment of a genome sequence:\nABABABABXYXYXYABABABABXYXYXYCCCCCCCCCC\ncan be compressed into:\n4(AB)XYXYXYABABABABXYXYXYCCCCCCCCCC\nby replacing the first occurrence of ABABABAB with its compressed form.\nSimilarly, by replacing the following repetitions of XY,\nAB, and C, we get:\n4(AB)3(XY)4(AB)3(XY)10C\nSince C is a single letter, parentheses are omitted in this\ncompressed representation.\nFinally, we have:\n2(4(AB)3(XY))10C\nby compressing the repetitions of 4(AB)3(XY).\nAs you may notice from this example, parentheses can be nested.\nYour mission is to write a program that uncompress compressed genome\nsequences.", "constraint": "", "input": "the input consists of multiple lines, each of which contains a\ncharacter string s and an integer i separated by a\nsingle space. \n \nthe character string s, in the aforementioned manner,\nrepresents a genome sequence.\nyou may assume that the length of s is between 1 and 100,\ninclusive.\nhowever, of course, the genome sequence represented by s may be\nmuch, much, and much longer than 100.\nyou may also assume that each natural number in s representing the\nnumber of repetitions is at most 1,000. \n \nthe integer i is at least zero and at most one million. \n \na line containing two zeros separated by a space follows the last input line and indicates\nthe end of the input.", "output": "for each input line, your program should print a line containing the\ni-th letter in the genome sequence that s represents.\nif the genome sequence is too short to have the i-th element,\nit should just print a zero.\nno other characters should be printed in the output lines.\nnote that in this problem the index number begins from zero rather\nthan one and therefore the initial letter of a sequence is its zeroth element.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ABC 3\nABC 0\n2(4(AB)3(XY))10C 30\n1000(1000(1000(1000(1000(1000(NM)))))) 999999\n0 0\n output: 0\nA\nC\nM"], "Pid": "p00726", "ProblemText": "Task Description: In 2300, the Life Science Division of Federal Republic of Space starts\na very ambitious project to complete the genome sequencing of all\nliving creatures in the entire universe and develop the genomic\ndatabase of all space life.\nThanks to scientific research over many years, it has been known that\nthe genome of any species consists of at most 26 kinds of\nmolecules, denoted by English capital letters (i. e. A\nto Z).\nWhat will be stored into the database are plain strings consisting of\nEnglish capital letters.\nIn general, however, the genome sequences of space life include\nfrequent repetitions and can be awfully long.\nSo, for efficient utilization of storage, we compress N-times\nrepetitions of a letter sequence seq into\nN(seq), where N is a natural \nnumber greater than or equal to two and the length of seq is at\nleast one.\nWhen seq consists of just one letter c, we may omit parentheses and write Nc.\nFor example, a fragment of a genome sequence:\nABABABABXYXYXYABABABABXYXYXYCCCCCCCCCC\ncan be compressed into:\n4(AB)XYXYXYABABABABXYXYXYCCCCCCCCCC\nby replacing the first occurrence of ABABABAB with its compressed form.\nSimilarly, by replacing the following repetitions of XY,\nAB, and C, we get:\n4(AB)3(XY)4(AB)3(XY)10C\nSince C is a single letter, parentheses are omitted in this\ncompressed representation.\nFinally, we have:\n2(4(AB)3(XY))10C\nby compressing the repetitions of 4(AB)3(XY).\nAs you may notice from this example, parentheses can be nested.\nYour mission is to write a program that uncompress compressed genome\nsequences.\nTask Input: the input consists of multiple lines, each of which contains a\ncharacter string s and an integer i separated by a\nsingle space. \n \nthe character string s, in the aforementioned manner,\nrepresents a genome sequence.\nyou may assume that the length of s is between 1 and 100,\ninclusive.\nhowever, of course, the genome sequence represented by s may be\nmuch, much, and much longer than 100.\nyou may also assume that each natural number in s representing the\nnumber of repetitions is at most 1,000. \n \nthe integer i is at least zero and at most one million. \n \na line containing two zeros separated by a space follows the last input line and indicates\nthe end of the input.\nTask Output: for each input line, your program should print a line containing the\ni-th letter in the genome sequence that s represents.\nif the genome sequence is too short to have the i-th element,\nit should just print a zero.\nno other characters should be printed in the output lines.\nnote that in this problem the index number begins from zero rather\nthan one and therefore the initial letter of a sequence is its zeroth element.\nTask Samples: input: ABC 3\nABC 0\n2(4(AB)3(XY))10C 30\n1000(1000(1000(1000(1000(1000(NM)))))) 999999\n0 0\n output: 0\nA\nC\nM\n\n" }, { "title": "Problem F Secrets in Shadows", "content": "Long long ago, there were several identical columns (or cylinders) built vertically in a big open space near Yokohama (Fig. F-1). In the daytime, the shadows of the columns were moving on the ground as the sun moves in the sky. Each column was very tall so that its shadow was very long. The top view of the shadows is shown in Fig. F-2.\n\t\nThe directions of the sun that minimizes and maximizes the widths of the shadows of the columns were said to give the important keys to the secrets of ancient treasures.\n\tFig. F-1: Columns (or cylinders) \n Gig. F-2: Top view of the columns (Fig. F-1) and their shadows \nThe width of the shadow of each column is the same as the diameter of the base disk. But the width of the whole shadow (the union of the shadows of all the columns) alters according to the direction of the sun since the shadows of some columns may overlap those of other columns.\n \nFig. F-3 shows the direction of the sun that minimizes the width of the whole shadow for the arrangement of columns in Fig. F-2. \n Fig. F-3: The direction of the sun for the minimal width of the whole shadow Fig. F-4 shows the direction of the sun that maximizes the width of the whole shadow. When the whole shadow is separated into several parts (two parts in this case), the width of the whole shadow is defined as the sum of the widths of the parts. Fig. F-4: The direction of the sun for the maximal width of the whole shadow\nA direction of the sun is specified by an angle θ defined in Fig. F-5. For example, the east is indicated by θ = 0, the south by θ = π/2, and the west by θ = π. You may assume that the sun rises in the east (θ = 0) and sets in the west (θ = π).\n\nYour job is to write a program that, given an arrangement of columns, computes two directions θ_min and θ_max of the sun that give the minimal width and the maximal width of the whole shadow, respectively.\n\nThe position of the center of the base disk of each column is specified by its (x, y) coordinates. The x-axis and y-axis are parallel to the line between the east and the west and that between the north and the south, respectively. Their positive directions indicate the east and the north, respectively.\n\nYou can assume that the big open space is a plane surface. \nFig. F-5: The definition of the angle of the direction of the sun \nThere may be more than one θ_min or θ_max for some arrangements in general, but here, you may assume that we only consider the arrangements that have unique θ_min and θ_max in the range 0 <= θ_min < π,0 <= θ_max < π.", "constraint": "", "input": "The input consists of multiple datasets, followed by the last line\ncontaining a single zero.\n\nEach dataset is formatted as follows.\n n\n x_1 y_1\n x_2 y_2\n . . .\n x_n y_n\n\nn is the number of the columns in the big open space. It is a positive integer no more than 100.\n\nx_k and y_k are the values of x-coordinate and y-coordinate of the center of the base disk of the k-th column (k=1, . . . , n). They are positive integers no more than 30. They are separated by a space.\n\nNote that the radius of the base disk of each column is one unit (the diameter is two units). You may assume that some columns may touch each other but no columns overlap others.\n\nFor example, a dataset\n\n 3\n 1 1\n 3 1\n 4 3\n\ncorresponds to the arrangement of three columns depicted in Fig. F-6. Two of them touch each other.\nFig. F-6: An arrangement of three columns\n ", "output": "For each dataset in the input, two lines should be output as specified below. The output lines should not contain extra characters such as spaces.\n\nIn the first line, the angle θ_min, the direction of the sun giving the minimal width, should be printed. In the second line, the other angle θ_max, the direction of the sun giving the maximal width, should be printed.\n\nEach angle should be contained in the interval between 0 and π (abbreviated to [0, π]) and should not have an error greater than ε=0.0000000001 (=10^-10).\n\nWhen the correct angle θ is in [0, ε], approximate values in [0, θ+ε] or in [π+θ-ε, π] are accepted. When the correct angle θ is in [π-ε, π], approximate values in [0, θ+ε-π] or in [θ-ε, π] are accepted.\n\nYou may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n1 1\n3 1\n4 3\n4\n1 1\n2 3\n3 8\n1 9\n8\n1 1\n3 1\n6 1\n1 3\n5 3\n1 7\n3 5\n5 5\n8\n20 7\n1 27\n30 14\n9 6\n17 13\n4 2\n17 7\n8 9\n0\n output: 2.553590050042226\n0.982793723247329\n1.570796326794896\n2.819842099193151\n1.325817663668032\n2.094395102393196\n2.777613697080149\n0.588002603547568"], "Pid": "p00727", "ProblemText": "Task Description: Long long ago, there were several identical columns (or cylinders) built vertically in a big open space near Yokohama (Fig. F-1). In the daytime, the shadows of the columns were moving on the ground as the sun moves in the sky. Each column was very tall so that its shadow was very long. The top view of the shadows is shown in Fig. F-2.\n\t\nThe directions of the sun that minimizes and maximizes the widths of the shadows of the columns were said to give the important keys to the secrets of ancient treasures.\n\tFig. F-1: Columns (or cylinders) \n Gig. F-2: Top view of the columns (Fig. F-1) and their shadows \nThe width of the shadow of each column is the same as the diameter of the base disk. But the width of the whole shadow (the union of the shadows of all the columns) alters according to the direction of the sun since the shadows of some columns may overlap those of other columns.\n \nFig. F-3 shows the direction of the sun that minimizes the width of the whole shadow for the arrangement of columns in Fig. F-2. \n Fig. F-3: The direction of the sun for the minimal width of the whole shadow Fig. F-4 shows the direction of the sun that maximizes the width of the whole shadow. When the whole shadow is separated into several parts (two parts in this case), the width of the whole shadow is defined as the sum of the widths of the parts. Fig. F-4: The direction of the sun for the maximal width of the whole shadow\nA direction of the sun is specified by an angle θ defined in Fig. F-5. For example, the east is indicated by θ = 0, the south by θ = π/2, and the west by θ = π. You may assume that the sun rises in the east (θ = 0) and sets in the west (θ = π).\n\nYour job is to write a program that, given an arrangement of columns, computes two directions θ_min and θ_max of the sun that give the minimal width and the maximal width of the whole shadow, respectively.\n\nThe position of the center of the base disk of each column is specified by its (x, y) coordinates. The x-axis and y-axis are parallel to the line between the east and the west and that between the north and the south, respectively. Their positive directions indicate the east and the north, respectively.\n\nYou can assume that the big open space is a plane surface. \nFig. F-5: The definition of the angle of the direction of the sun \nThere may be more than one θ_min or θ_max for some arrangements in general, but here, you may assume that we only consider the arrangements that have unique θ_min and θ_max in the range 0 <= θ_min < π,0 <= θ_max < π.\nTask Input: The input consists of multiple datasets, followed by the last line\ncontaining a single zero.\n\nEach dataset is formatted as follows.\n n\n x_1 y_1\n x_2 y_2\n . . .\n x_n y_n\n\nn is the number of the columns in the big open space. It is a positive integer no more than 100.\n\nx_k and y_k are the values of x-coordinate and y-coordinate of the center of the base disk of the k-th column (k=1, . . . , n). They are positive integers no more than 30. They are separated by a space.\n\nNote that the radius of the base disk of each column is one unit (the diameter is two units). You may assume that some columns may touch each other but no columns overlap others.\n\nFor example, a dataset\n\n 3\n 1 1\n 3 1\n 4 3\n\ncorresponds to the arrangement of three columns depicted in Fig. F-6. Two of them touch each other.\nFig. F-6: An arrangement of three columns\n \nTask Output: For each dataset in the input, two lines should be output as specified below. The output lines should not contain extra characters such as spaces.\n\nIn the first line, the angle θ_min, the direction of the sun giving the minimal width, should be printed. In the second line, the other angle θ_max, the direction of the sun giving the maximal width, should be printed.\n\nEach angle should be contained in the interval between 0 and π (abbreviated to [0, π]) and should not have an error greater than ε=0.0000000001 (=10^-10).\n\nWhen the correct angle θ is in [0, ε], approximate values in [0, θ+ε] or in [π+θ-ε, π] are accepted. When the correct angle θ is in [π-ε, π], approximate values in [0, θ+ε-π] or in [θ-ε, π] are accepted.\n\nYou may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied.\nTask Samples: input: 3\n1 1\n3 1\n4 3\n4\n1 1\n2 3\n3 8\n1 9\n8\n1 1\n3 1\n6 1\n1 3\n5 3\n1 7\n3 5\n5 5\n8\n20 7\n1 27\n30 14\n9 6\n17 13\n4 2\n17 7\n8 9\n0\n output: 2.553590050042226\n0.982793723247329\n1.570796326794896\n2.819842099193151\n1.325817663668032\n2.094395102393196\n2.777613697080149\n0.588002603547568\n\n" }, { "title": "Problem A: ICPC Score Totalizer Software", "content": "The International Clown and Pierrot Competition (ICPC), is one of the\nmost distinguished and also the most popular events on earth in the\nshow business.\n\nOne of the unique features of this contest is the great number of\njudges that sometimes counts up to one hundred. The number of judges\nmay differ from one contestant to another, because judges with any\nrelationship whatsoever with a specific contestant are temporarily\nexcluded for scoring his/her performance.\n\nBasically, scores given to a contestant's performance by the judges\nare averaged to decide his/her score. To avoid letting judges with\neccentric viewpoints too much influence the score, the highest and the\nlowest scores are set aside in this calculation. If the same highest\nscore is marked by two or more judges, only one of them is ignored.\nThe same is with the lowest score. The average, which may contain\nfractions, are truncated down to obtain final score as an integer.\n\nYou are asked to write a program that computes the scores of\nperformances, given the scores of all the judges, to speed up the event\nto be suited for a TV program.", "constraint": "", "input": "The input consists of a number of datasets, each corresponding to a\ncontestant's performance. There are no more than 20 datasets in the input.\n\nA dataset begins with a line with an integer n, the number of\njudges participated in scoring the performance (3 <= n <=\n100). Each of the n lines following it has an integral\nscore s (0 <= s <= 1000) marked by a judge. No\nother characters except for digits to express these numbers are in the\ninput. Judges' names are kept secret.\n\nThe end of the input is indicated by a line with a single zero in it.", "output": "For each dataset, a line containing a single decimal integer\nindicating the score for the corresponding performance should be\noutput. No other characters should be on the output line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n1000\n342\n0\n5\n2\n2\n9\n11\n932\n5\n300\n1000\n0\n200\n400\n8\n353\n242\n402\n274\n283\n132\n402\n523\n0\n output: 342\n7\n300\n326"], "Pid": "p00728", "ProblemText": "Task Description: The International Clown and Pierrot Competition (ICPC), is one of the\nmost distinguished and also the most popular events on earth in the\nshow business.\n\nOne of the unique features of this contest is the great number of\njudges that sometimes counts up to one hundred. The number of judges\nmay differ from one contestant to another, because judges with any\nrelationship whatsoever with a specific contestant are temporarily\nexcluded for scoring his/her performance.\n\nBasically, scores given to a contestant's performance by the judges\nare averaged to decide his/her score. To avoid letting judges with\neccentric viewpoints too much influence the score, the highest and the\nlowest scores are set aside in this calculation. If the same highest\nscore is marked by two or more judges, only one of them is ignored.\nThe same is with the lowest score. The average, which may contain\nfractions, are truncated down to obtain final score as an integer.\n\nYou are asked to write a program that computes the scores of\nperformances, given the scores of all the judges, to speed up the event\nto be suited for a TV program.\nTask Input: The input consists of a number of datasets, each corresponding to a\ncontestant's performance. There are no more than 20 datasets in the input.\n\nA dataset begins with a line with an integer n, the number of\njudges participated in scoring the performance (3 <= n <=\n100). Each of the n lines following it has an integral\nscore s (0 <= s <= 1000) marked by a judge. No\nother characters except for digits to express these numbers are in the\ninput. Judges' names are kept secret.\n\nThe end of the input is indicated by a line with a single zero in it.\nTask Output: For each dataset, a line containing a single decimal integer\nindicating the score for the corresponding performance should be\noutput. No other characters should be on the output line.\nTask Samples: input: 3\n1000\n342\n0\n5\n2\n2\n9\n11\n932\n5\n300\n1000\n0\n200\n400\n8\n353\n242\n402\n274\n283\n132\n402\n523\n0\n output: 342\n7\n300\n326\n\n" }, { "title": "Problem B: Analyzing Login/Logout Records", "content": "You have a computer literacy course in your university. In the computer\nsystem, the login/logout records of all PCs in a day are stored in a\nfile. Although students may use two or more PCs at a time, no one can\nlog in to a PC which has been logged in by someone who has not\nlogged out of that PC yet.\nYou are asked to write a program that calculates the total time of a\nstudent that he/she used at least one PC in a given time period\n(probably in a laboratory class) based on the records in the file.\n The following are example login/logout records.\n The student 1 logged in to the PC 1 at 12: 55\n The student 2 logged in to the PC 4 at 13: 00\n The student 1 logged in to the PC 2 at 13: 10\n The student 1 logged out of the PC 2 at 13: 20\n The student 1 logged in to the PC 3 at 13: 30\n The student 1 logged out of the PC 1 at 13: 40\n The student 1 logged out of the PC 3 at 13: 45\n The student 1 logged in to the PC 1 at 14: 20\n The student 2 logged out of the PC 4 at 14: 30\n The student 1 logged out of the PC 1 at 14: 40\nFor a query such as \"Give usage of the student 1 between 13: 00 and\n14: 30\", your program should answer \"55 minutes\", that is, the sum of\n45 minutes from 13: 00 to 13: 45 and 10 minutes from 14: 20 to 14: 30, as\ndepicted in the following figure.", "constraint": "", "input": "The input is a sequence of a number of datasets.\nThe end of the input is indicated by a line containing two zeros\nseparated by a space.\nThe number of datasets never exceeds 10.\n\nEach dataset is formatted as follows.\n\nN M \nr \nrecord_1\n. . . \nrecord_r \nq  \nquery_1\n. . . \nquery_q \n\nThe numbers N  and M  in the first line are the numbers of\nPCs and the students, respectively. r  is the number of\nrecords. q  is the number of queries. These four are integers\nsatisfying the following.\n\n1 <= N  <= 1000,1 <= M  <= 10000,2 <= r  <= 1000,1 <= q  <= 50\n\nEach record consists of four integers, delimited by a space, as follows.\n\nt  n  m  s \n\ns  is 0 or 1.\nIf s  is 1, this line means that the student m  logged in\nto the PC n  at time t . If s  is 0, it means that\nthe student m  logged out of the PC n  at time t .\nThe time is expressed as elapsed minutes from 0: 00 of the day.\nt , n  and m  satisfy the following.\n\n540 <= t  <= 1260,\n1 <= n  <= N ,1 <= m  <= M \n\n

\n\nYou may assume the following about the records.\n\nRecords are stored in ascending order of time t.  \n No two records for the same PC has the same time t.  \n No PCs are being logged in before the time of the first record\n nor after that of the last record in the file.\n Login and logout records for one PC appear alternatingly, and each of the login-logout record pairs is for the same student.\n\nEach query consists of three integers delimited by a space, as follows.\n\nt_s  t_e  m \n\nIt represents \"Usage of the student m  between \nt_s  and t_e \".\nt_s , t_e  and m \nsatisfy the following.\n\n540 <= t_s  < t_e  <= 1260,\n1 <= m  <= M", "output": "For each query, print a line having a decimal integer indicating the\ntime of usage in minutes. Output lines should not have any character\nother than this number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0\n output: 55\n70\n30\n0\n0\n50\n10\n50\n0"], "Pid": "p00729", "ProblemText": "Task Description: You have a computer literacy course in your university. In the computer\nsystem, the login/logout records of all PCs in a day are stored in a\nfile. Although students may use two or more PCs at a time, no one can\nlog in to a PC which has been logged in by someone who has not\nlogged out of that PC yet.\nYou are asked to write a program that calculates the total time of a\nstudent that he/she used at least one PC in a given time period\n(probably in a laboratory class) based on the records in the file.\n The following are example login/logout records.\n The student 1 logged in to the PC 1 at 12: 55\n The student 2 logged in to the PC 4 at 13: 00\n The student 1 logged in to the PC 2 at 13: 10\n The student 1 logged out of the PC 2 at 13: 20\n The student 1 logged in to the PC 3 at 13: 30\n The student 1 logged out of the PC 1 at 13: 40\n The student 1 logged out of the PC 3 at 13: 45\n The student 1 logged in to the PC 1 at 14: 20\n The student 2 logged out of the PC 4 at 14: 30\n The student 1 logged out of the PC 1 at 14: 40\nFor a query such as \"Give usage of the student 1 between 13: 00 and\n14: 30\", your program should answer \"55 minutes\", that is, the sum of\n45 minutes from 13: 00 to 13: 45 and 10 minutes from 14: 20 to 14: 30, as\ndepicted in the following figure.\nTask Input: The input is a sequence of a number of datasets.\nThe end of the input is indicated by a line containing two zeros\nseparated by a space.\nThe number of datasets never exceeds 10.\n\nEach dataset is formatted as follows.\n\nN M \nr \nrecord_1\n. . . \nrecord_r \nq  \nquery_1\n. . . \nquery_q \n\nThe numbers N  and M  in the first line are the numbers of\nPCs and the students, respectively. r  is the number of\nrecords. q  is the number of queries. These four are integers\nsatisfying the following.\n\n1 <= N  <= 1000,1 <= M  <= 10000,2 <= r  <= 1000,1 <= q  <= 50\n\nEach record consists of four integers, delimited by a space, as follows.\n\nt  n  m  s \n\ns  is 0 or 1.\nIf s  is 1, this line means that the student m  logged in\nto the PC n  at time t . If s  is 0, it means that\nthe student m  logged out of the PC n  at time t .\nThe time is expressed as elapsed minutes from 0: 00 of the day.\nt , n  and m  satisfy the following.\n\n540 <= t  <= 1260,\n1 <= n  <= N ,1 <= m  <= M \n\n

\n\nYou may assume the following about the records.\n\nRecords are stored in ascending order of time t.  \n No two records for the same PC has the same time t.  \n No PCs are being logged in before the time of the first record\n nor after that of the last record in the file.\n Login and logout records for one PC appear alternatingly, and each of the login-logout record pairs is for the same student.\n\nEach query consists of three integers delimited by a space, as follows.\n\nt_s  t_e  m \n\nIt represents \"Usage of the student m  between \nt_s  and t_e \".\nt_s , t_e  and m \nsatisfy the following.\n\n540 <= t_s  < t_e  <= 1260,\n1 <= m  <= M\nTask Output: For each query, print a line having a decimal integer indicating the\ntime of usage in minutes. Output lines should not have any character\nother than this number.\nTask Samples: input: 4 2\n10\n775 1 1 1\n780 4 2 1\n790 2 1 1\n800 2 1 0\n810 3 1 1\n820 1 1 0\n825 3 1 0\n860 1 1 1\n870 4 2 0\n880 1 1 0\n1\n780 870 1\n13 15\n12\n540 12 13 1\n600 12 13 0\n650 13 15 1\n660 12 15 1\n665 11 13 1\n670 13 15 0\n675 11 13 0\n680 12 15 0\n1000 11 14 1\n1060 12 14 1\n1060 11 14 0\n1080 12 14 0\n3\n540 700 13\n600 1000 15\n1000 1200 11\n1 1\n2\n600 1 1 1\n700 1 1 0\n5\n540 600 1\n550 650 1\n610 620 1\n650 750 1\n700 800 1\n0 0\n output: 55\n70\n30\n0\n0\n50\n10\n50\n0\n\n" }, { "title": "Problem C: Cut the Cake", "content": "Today is the birthday of Mr. Bon Vivant, who is known as one of the greatest pâtissiers in the world.\nThose who are invited to his birthday party are gourmets from around the world.\nThey are eager to see and eat his extremely creative cakes.\nNow a large box-shaped cake is being carried into the party.\nIt is not beautifully decorated and looks rather simple, but it must be delicious beyond anyone's imagination.\nLet us cut it into pieces with a knife and serve them to the guests attending the party.\n\nThe cake looks rectangular, viewing from above (Figure C-1).\nAs exemplified in Figure C-2, the cake will iteratively be cut into pieces, where on each cut exactly a single piece is cut into two smaller pieces.\nEach cut surface must be orthogonal to the bottom face and must be orthogonal or parallel to a side face.\nSo, every piece shall be rectangular looking from above and every side face vertical.\n\nFigure C-1: The top view of the cake \n\nFigure C-2: Cutting the cake into pieces\nPiece sizes in Figure C-2 vary significantly and it may look unfair, but you don't have to worry.\nThose guests who would like to eat as many sorts of cakes as possible often prefer smaller pieces.\nOf course, some prefer larger ones.\nYour mission of this problem is to write a computer program that simulates the cutting process of the cake and reports the size of each piece.", "constraint": "", "input": "The input is a sequence of datasets, each of which is of the following format.\n\nn  w  d\np_1  s_1\n. . . \np_n  s_n\n\nThe first line starts with an integer n that is between 0 and 100 inclusive.\nIt is the number of cuts to be performed.\nThe following w and d in the same line are integers between 1 and 100 inclusive.\nThey denote the width and depth of the cake, respectively.\nAssume in the sequel that the cake is placed so that w and d are the lengths in the east-west and north-south directions, respectively.\n\nEach of the following n lines specifies a single cut, cutting one and only one piece into two.\np_i is an integer between 1 and i inclusive and is the identification number of the piece that is the target of the i-th cut.\nNote that, just before the i-th cut, there exist exactly i pieces.\nEach piece in this stage has a unique identification number that is one of 1,2, . . . , i and is defined as follows:\nThe earlier a piece was born, the smaller its identification number is.\n\nOf the two pieces born at a time by the same cut, the piece with the smaller area (looking from above) has the smaller identification number.\nIf their areas are the same, you may define as you like the order between them, since your choice in this case has no influence on the final answer.\n\nNote that identification numbers are adjusted after each cut.\n\ns_i is an integer between 1 and 1000 inclusive and specifies the starting point of the i-th cut.\nFrom the northwest corner of the piece whose identification number is p_i, you can reach the starting point by traveling s_i in the clockwise direction around the piece. \nYou may assume that the starting point determined in this way cannot be any one of the four corners of the piece.\nThe i-th cut surface is orthogonal to the side face on which the starting point exists.\n

\nThe end of the input is indicated by a line with three zeros.", "output": "For each dataset, print in a line the areas looking from above of all the pieces that exist upon completion of the n cuts specified in the dataset.\nThey should be in ascending order and separated by a space.\nWhen multiple pieces have the same area, print it as many times as the number of the pieces.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 5 6\n1 18\n2 19\n1 2\n3 4 1\n1 1\n2 1\n3 1\n0 2 5\n0 0 0\n output: 4 4 6 16\n1 1 1 1\n10"], "Pid": "p00730", "ProblemText": "Task Description: Today is the birthday of Mr. Bon Vivant, who is known as one of the greatest pâtissiers in the world.\nThose who are invited to his birthday party are gourmets from around the world.\nThey are eager to see and eat his extremely creative cakes.\nNow a large box-shaped cake is being carried into the party.\nIt is not beautifully decorated and looks rather simple, but it must be delicious beyond anyone's imagination.\nLet us cut it into pieces with a knife and serve them to the guests attending the party.\n\nThe cake looks rectangular, viewing from above (Figure C-1).\nAs exemplified in Figure C-2, the cake will iteratively be cut into pieces, where on each cut exactly a single piece is cut into two smaller pieces.\nEach cut surface must be orthogonal to the bottom face and must be orthogonal or parallel to a side face.\nSo, every piece shall be rectangular looking from above and every side face vertical.\n\nFigure C-1: The top view of the cake \n\nFigure C-2: Cutting the cake into pieces\nPiece sizes in Figure C-2 vary significantly and it may look unfair, but you don't have to worry.\nThose guests who would like to eat as many sorts of cakes as possible often prefer smaller pieces.\nOf course, some prefer larger ones.\nYour mission of this problem is to write a computer program that simulates the cutting process of the cake and reports the size of each piece.\nTask Input: The input is a sequence of datasets, each of which is of the following format.\n\nn  w  d\np_1  s_1\n. . . \np_n  s_n\n\nThe first line starts with an integer n that is between 0 and 100 inclusive.\nIt is the number of cuts to be performed.\nThe following w and d in the same line are integers between 1 and 100 inclusive.\nThey denote the width and depth of the cake, respectively.\nAssume in the sequel that the cake is placed so that w and d are the lengths in the east-west and north-south directions, respectively.\n\nEach of the following n lines specifies a single cut, cutting one and only one piece into two.\np_i is an integer between 1 and i inclusive and is the identification number of the piece that is the target of the i-th cut.\nNote that, just before the i-th cut, there exist exactly i pieces.\nEach piece in this stage has a unique identification number that is one of 1,2, . . . , i and is defined as follows:\nThe earlier a piece was born, the smaller its identification number is.\n\nOf the two pieces born at a time by the same cut, the piece with the smaller area (looking from above) has the smaller identification number.\nIf their areas are the same, you may define as you like the order between them, since your choice in this case has no influence on the final answer.\n\nNote that identification numbers are adjusted after each cut.\n\ns_i is an integer between 1 and 1000 inclusive and specifies the starting point of the i-th cut.\nFrom the northwest corner of the piece whose identification number is p_i, you can reach the starting point by traveling s_i in the clockwise direction around the piece. \nYou may assume that the starting point determined in this way cannot be any one of the four corners of the piece.\nThe i-th cut surface is orthogonal to the side face on which the starting point exists.\n

\nThe end of the input is indicated by a line with three zeros.\nTask Output: For each dataset, print in a line the areas looking from above of all the pieces that exist upon completion of the n cuts specified in the dataset.\nThey should be in ascending order and separated by a space.\nWhen multiple pieces have the same area, print it as many times as the number of the pieces.\nTask Samples: input: 3 5 6\n1 18\n2 19\n1 2\n3 4 1\n1 1\n2 1\n3 1\n0 2 5\n0 0 0\n output: 4 4 6 16\n1 1 1 1\n10\n\n" }, { "title": "Problem D: Cliff Climbing", "content": "At 17: 00, special agent Jack starts to escape from the enemy camp.\nThere is a cliff in between the camp and the nearest safety zone.\nJack has to climb the almost vertical cliff \nby stepping his feet on the blocks that cover the cliff.\nThe cliff has slippery blocks where Jack has to\nspend time to take each step. \nHe also has to bypass some blocks that are too loose to support his weight.\nYour mission is to write a program that calculates the minimum time to complete climbing. \n\nFigure D-1 shows an example of cliff data that you will\nreceive.\nThe cliff is covered with square blocks.\nJack starts cliff climbing from the ground under the cliff,\nby stepping his left or right foot on one of the blocks marked with\n'S' at the bottom row.\nThe numbers on the blocks are the \"slippery levels\". It takes\nt time units for him to safely put his foot on a\nblock marked with t, where 1 <= t <= 9.\nHe cannot put his feet on blocks marked with 'X'.\nHe completes the climbing when he puts \neither of his feet on one of the blocks marked with 'T' at the top row.\n\nFigure D-1: Example of Cliff Data\nJack's movement must meet the following constraints. \nAfter putting his left (or right) foot on a block, he can only move\nhis right (or left, respectively) foot.\nHis left foot position (lx, ly) and his right foot position\n(rx, ry) should satisfy\nlx < rx and | lx - rx | + | ly - ry | <= 3.\nThis implies that, given a position of his left foot in Figure D-2 (a), he has to\nplace his right foot on one of the nine blocks marked with blue color.\nSimilarly, given a position of his right foot in Figure D-2 (b),\nhe has to place his\nleft foot on one of the nine blocks marked with blue color.\n\nFigure D-2: Possible Placements of Feet", "constraint": "", "input": "The input is a sequence of datasets.\nThe end of the input is indicated by a line containing two zeros separated by a space.\nEach dataset is formatted as follows:\n\nw h\ns(1,1) . . . s(1, w)\ns(2,1) . . . s(2, w)\n. . . \ns(h, 1) . . . s(h, w)\n\nThe integers w and h are the width and the height of \nthe matrix data of the cliff. You may assume 2 <= w <= 30 and 5 <= h <= 60.\nEach of the following h lines consists of w characters\ndelimited by a space.\nThe character s(y, x) represents the state of the block at\nposition \n(x, y) as follows:\n\n 'S': Jack can start cliff climbing from this block. \n\n 'T': Jack finishes climbing when he reaches this block. \n\n 'X': Jack cannot put his feet on this block. \n\n '1' - '9' (= t): Jack has to spend t time units\nto put either of his feet on this block. \n\nYou can assume that it takes no time to put a foot on a block marked with 'S' or 'T'.", "output": "For each dataset, print a line only having a decimal integer indicating \nthe minimum time required for the cliff climbing,\nwhen Jack can complete it.\nOtherwise, print a line only having \"-1\" for the dataset.\nEach line should not have any characters other than these numbers.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 6\n4 4 X X T T\n4 7 8 2 X 7\n3 X X X 1 8\n1 2 X X X 6\n1 1 2 4 4 7\nS S 2 3 X X\n2 10\nT 1\n1 X\n1 X\n1 X\n1 1\n1 X\n1 X\n1 1\n1 X\nS S\n2 10\nT X\n1 X\n1 X\n1 X\n1 1\n1 X\n1 X\n1 1\n1 X\nS S\n10 10\nT T T T T T T T T T\nX 2 X X X X X 3 4 X\n9 8 9 X X X 2 9 X 9\n7 7 X 7 3 X X 8 9 X\n8 9 9 9 6 3 X 5 X 5\n8 9 9 9 6 X X 5 X 5\n8 6 5 4 6 8 X 5 X 5\n8 9 3 9 6 8 X 5 X 5\n8 3 9 9 6 X X X 5 X\nS S S S S S S S S S\n10 7\n2 3 2 3 2 3 2 3 T T\n1 2 3 2 3 2 3 2 3 2\n3 2 3 2 3 2 3 2 3 4\n3 2 3 2 3 2 3 2 3 5\n3 2 3 1 3 2 3 2 3 5\n2 2 3 2 4 2 3 2 3 5\nS S 2 3 2 1 2 3 2 3\n0 0\n output: 12\n5\n-1\n22\n12"], "Pid": "p00731", "ProblemText": "Task Description: At 17: 00, special agent Jack starts to escape from the enemy camp.\nThere is a cliff in between the camp and the nearest safety zone.\nJack has to climb the almost vertical cliff \nby stepping his feet on the blocks that cover the cliff.\nThe cliff has slippery blocks where Jack has to\nspend time to take each step. \nHe also has to bypass some blocks that are too loose to support his weight.\nYour mission is to write a program that calculates the minimum time to complete climbing. \n\nFigure D-1 shows an example of cliff data that you will\nreceive.\nThe cliff is covered with square blocks.\nJack starts cliff climbing from the ground under the cliff,\nby stepping his left or right foot on one of the blocks marked with\n'S' at the bottom row.\nThe numbers on the blocks are the \"slippery levels\". It takes\nt time units for him to safely put his foot on a\nblock marked with t, where 1 <= t <= 9.\nHe cannot put his feet on blocks marked with 'X'.\nHe completes the climbing when he puts \neither of his feet on one of the blocks marked with 'T' at the top row.\n\nFigure D-1: Example of Cliff Data\nJack's movement must meet the following constraints. \nAfter putting his left (or right) foot on a block, he can only move\nhis right (or left, respectively) foot.\nHis left foot position (lx, ly) and his right foot position\n(rx, ry) should satisfy\nlx < rx and | lx - rx | + | ly - ry | <= 3.\nThis implies that, given a position of his left foot in Figure D-2 (a), he has to\nplace his right foot on one of the nine blocks marked with blue color.\nSimilarly, given a position of his right foot in Figure D-2 (b),\nhe has to place his\nleft foot on one of the nine blocks marked with blue color.\n\nFigure D-2: Possible Placements of Feet\nTask Input: The input is a sequence of datasets.\nThe end of the input is indicated by a line containing two zeros separated by a space.\nEach dataset is formatted as follows:\n\nw h\ns(1,1) . . . s(1, w)\ns(2,1) . . . s(2, w)\n. . . \ns(h, 1) . . . s(h, w)\n\nThe integers w and h are the width and the height of \nthe matrix data of the cliff. You may assume 2 <= w <= 30 and 5 <= h <= 60.\nEach of the following h lines consists of w characters\ndelimited by a space.\nThe character s(y, x) represents the state of the block at\nposition \n(x, y) as follows:\n\n 'S': Jack can start cliff climbing from this block. \n\n 'T': Jack finishes climbing when he reaches this block. \n\n 'X': Jack cannot put his feet on this block. \n\n '1' - '9' (= t): Jack has to spend t time units\nto put either of his feet on this block. \n\nYou can assume that it takes no time to put a foot on a block marked with 'S' or 'T'.\nTask Output: For each dataset, print a line only having a decimal integer indicating \nthe minimum time required for the cliff climbing,\nwhen Jack can complete it.\nOtherwise, print a line only having \"-1\" for the dataset.\nEach line should not have any characters other than these numbers.\nTask Samples: input: 6 6\n4 4 X X T T\n4 7 8 2 X 7\n3 X X X 1 8\n1 2 X X X 6\n1 1 2 4 4 7\nS S 2 3 X X\n2 10\nT 1\n1 X\n1 X\n1 X\n1 1\n1 X\n1 X\n1 1\n1 X\nS S\n2 10\nT X\n1 X\n1 X\n1 X\n1 1\n1 X\n1 X\n1 1\n1 X\nS S\n10 10\nT T T T T T T T T T\nX 2 X X X X X 3 4 X\n9 8 9 X X X 2 9 X 9\n7 7 X 7 3 X X 8 9 X\n8 9 9 9 6 3 X 5 X 5\n8 9 9 9 6 X X 5 X 5\n8 6 5 4 6 8 X 5 X 5\n8 9 3 9 6 8 X 5 X 5\n8 3 9 9 6 X X X 5 X\nS S S S S S S S S S\n10 7\n2 3 2 3 2 3 2 3 T T\n1 2 3 2 3 2 3 2 3 2\n3 2 3 2 3 2 3 2 3 4\n3 2 3 2 3 2 3 2 3 5\n3 2 3 1 3 2 3 2 3 5\n2 2 3 2 4 2 3 2 3 5\nS S 2 3 2 1 2 3 2 3\n0 0\n output: 12\n5\n-1\n22\n12\n\n" }, { "title": "Problem E: Twirl Around", "content": "Let's think about a bar rotating clockwise as if it were a\ntwirling baton moving on a planar surface surrounded by a\npolygonal wall (see Figure 1).\nFigure 1. A bar rotating in a polygon\nInitially, an end of the bar (called \"end A\") is at (0,0), and\nthe other end (called \"end B\") is at (0, L) where L is the\nlength of the bar. Initially, the bar is touching the wall only\nat the end A.\n\nThe bar turns fixing a touching point as the center.\nThe center changes as a new point touches the wall.\n\nYour task is to calculate the coordinates of the end A when the\nbar has fully turned by the given count R.\nFigure 2. Examples of turning bars\n\nIn Figure 2, some examples are shown. In cases (D) and\n(E), the bar is stuck prematurely (cannot rotate clockwise anymore \nwith any point touching the wall as the center)\nbefore R rotations. In such cases, you should answer the\ncoordinates of the end A in that (stuck) position. You can assume the following: \n\nWhen the bar's length L changes by ε (|ε| <\n0.00001), the final (x, y) coordinates\nwill not change more than 0.0005.", "constraint": "", "input": "The input consists of multiple datasets. The number of\ndatasets is no more than 100. The end of the input is represented\nby \"0 0 0\".\nThe format of each dataset is as follows:\n\nL R N\nX_1 Y_1\nX_2 Y_2\n. . .\nX_N Y_N\n\nL is the length of the bar.\nThe bar rotates 2π* R radians (if it is not\nstuck prematurely).\nN is the number of vertices which make the polygon.\n\nThe vertices of the polygon are arranged in a counter-clockwise order.\nYou may assume that the polygon is simple, that is,\nits border never crosses or touches itself.\n\nN, X_i and Y_i are\ninteger numbers; R and L are decimal fractions.\nRanges of those values are as follows:\n\n1.0 <= L <= 500.0,\n1.0 <= R <= 10.0,\n3 <= N <= 100,\n-1000 <= X_i <= 1000,\n-1000 <= Y_i <= 1000,\n\nX_1 <= -1, Y_1 = 0,\nX_2 >= 1, Y_2 = 0.", "output": "For each dataset, print one line containing x- and\ny-coordinates of the final position of the end A,\nseparated by a space.\nThe value may contain an error less than or equal to 0.001.\nYou may print any number of digits after the decimal point.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4.0 2.0 8\n-1 0\n5 0\n5 -2\n7 -2\n7 0\n18 0\n18 6\n-1 6\n4.0 2.0 4\n-1 0\n10 0\n10 12\n-1 12\n4.0 1.0 7\n-1 0\n2 0\n-1 -3\n-1 -8\n6 -8\n6 6\n-1 6\n4.0 2.0 6\n-1 0\n10 0\n10 3\n7 3\n7 5\n-1 5\n5.0 2.0 6\n-1 0\n2 0\n2 -4\n6 -4\n6 6\n-1 6\n6.0 1.0 8\n-1 0\n8 0\n7 2\n9 2\n8 4\n11 4\n11 12\n-1 12\n0 0 0\n output: 16.0 0.0\n9.999999999999998 7.4641016151377535\n0.585786437626906 -5.414213562373095\n8.0 0.0\n6.0 0.0\n9.52786404500042 4.0\nNote that the above sample input corresponds to the\ncases in Figure 2. For convenience, in Figure 3, we will show an\nanimation and corresponding photographic playback for the case (C)."], "Pid": "p00732", "ProblemText": "Task Description: Let's think about a bar rotating clockwise as if it were a\ntwirling baton moving on a planar surface surrounded by a\npolygonal wall (see Figure 1).\nFigure 1. A bar rotating in a polygon\nInitially, an end of the bar (called \"end A\") is at (0,0), and\nthe other end (called \"end B\") is at (0, L) where L is the\nlength of the bar. Initially, the bar is touching the wall only\nat the end A.\n\nThe bar turns fixing a touching point as the center.\nThe center changes as a new point touches the wall.\n\nYour task is to calculate the coordinates of the end A when the\nbar has fully turned by the given count R.\nFigure 2. Examples of turning bars\n\nIn Figure 2, some examples are shown. In cases (D) and\n(E), the bar is stuck prematurely (cannot rotate clockwise anymore \nwith any point touching the wall as the center)\nbefore R rotations. In such cases, you should answer the\ncoordinates of the end A in that (stuck) position. You can assume the following: \n\nWhen the bar's length L changes by ε (|ε| <\n0.00001), the final (x, y) coordinates\nwill not change more than 0.0005.\nTask Input: The input consists of multiple datasets. The number of\ndatasets is no more than 100. The end of the input is represented\nby \"0 0 0\".\nThe format of each dataset is as follows:\n\nL R N\nX_1 Y_1\nX_2 Y_2\n. . .\nX_N Y_N\n\nL is the length of the bar.\nThe bar rotates 2π* R radians (if it is not\nstuck prematurely).\nN is the number of vertices which make the polygon.\n\nThe vertices of the polygon are arranged in a counter-clockwise order.\nYou may assume that the polygon is simple, that is,\nits border never crosses or touches itself.\n\nN, X_i and Y_i are\ninteger numbers; R and L are decimal fractions.\nRanges of those values are as follows:\n\n1.0 <= L <= 500.0,\n1.0 <= R <= 10.0,\n3 <= N <= 100,\n-1000 <= X_i <= 1000,\n-1000 <= Y_i <= 1000,\n\nX_1 <= -1, Y_1 = 0,\nX_2 >= 1, Y_2 = 0.\nTask Output: For each dataset, print one line containing x- and\ny-coordinates of the final position of the end A,\nseparated by a space.\nThe value may contain an error less than or equal to 0.001.\nYou may print any number of digits after the decimal point.\nTask Samples: input: 4.0 2.0 8\n-1 0\n5 0\n5 -2\n7 -2\n7 0\n18 0\n18 6\n-1 6\n4.0 2.0 4\n-1 0\n10 0\n10 12\n-1 12\n4.0 1.0 7\n-1 0\n2 0\n-1 -3\n-1 -8\n6 -8\n6 6\n-1 6\n4.0 2.0 6\n-1 0\n10 0\n10 3\n7 3\n7 5\n-1 5\n5.0 2.0 6\n-1 0\n2 0\n2 -4\n6 -4\n6 6\n-1 6\n6.0 1.0 8\n-1 0\n8 0\n7 2\n9 2\n8 4\n11 4\n11 12\n-1 12\n0 0 0\n output: 16.0 0.0\n9.999999999999998 7.4641016151377535\n0.585786437626906 -5.414213562373095\n8.0 0.0\n6.0 0.0\n9.52786404500042 4.0\nNote that the above sample input corresponds to the\ncases in Figure 2. For convenience, in Figure 3, we will show an\nanimation and corresponding photographic playback for the case (C).\n\n" }, { "title": "Problem F: Dr. Podboq or: How We Became Asymmetric", "content": "After long studying how embryos of organisms become asymmetric during\ntheir development, Dr. Podboq, a famous biologist, has reached his new\nhypothesis. Dr. Podboq is now preparing a poster for the coming\nacademic conference, which shows a tree representing the development\nprocess of an embryo through repeated cell divisions starting from one\ncell. Your job is to write a program that transforms given trees into\nforms satisfying some conditions so that it is easier for the audience\nto get the idea.\n\nA tree representing the process of cell divisions has a form described\nbelow.\n\nThe starting cell is represented by a circle placed at the top.\n\nEach cell either terminates the division activity or divides into\ntwo cells. Therefore, from each circle representing a cell, there are\neither no branch downward, or two branches down to its\ntwo child cells.\nBelow is an example of such a tree.\nFigure F-1: A tree representing a process of cell divisions\n\nAccording to Dr. Podboq's hypothesis, we can determine which cells\nhave stronger or weaker asymmetricity by looking at the structure of\nthis tree representation. First, his hypothesis defines \"left-right\nsimilarity\" of cells as follows:\n\nThe left-right similarity of a cell that did not divide further is\n0.\n For a cell that did divide further, we collect the partial\ntrees starting from its child or descendant cells, and count how\nmany kinds of structures they have. Then, the left-right similarity of\nthe cell is defined to be the ratio of the number of structures\nthat appear both in\nthe right child side and the left child side. We regard two trees\nhave the same structure if we can make them have exactly the same shape by\ninterchanging two child cells of arbitrary cells.\nFor example, suppose we have a tree shown below:\nFigure F-2: An example tree\n\nThe left-right similarity of the cell A is computed as follows.\nFirst, within the descendants of the cell B, which is the left child\ncell of A, the following three kinds of structures appear. Notice that\nthe rightmost structure appears three times, but when we count the number\nof structures, we count it only once.\nFigure F-3: Structures appearing within the descendants of the cell B\n\nOn the other hand, within the descendants of the cell C, which is the\nright child cell of A, the following four kinds of structures appear.\nFigure F-4: Structures appearing within the descendants of the cell C\n\nAmong them, the first, second, and third ones within the B side are\nregarded as the same structure as the second, third, and fourth ones\nwithin the C side, respectively. Therefore, there are four structures\nin total, and three among them are common to the left side and the\nright side, which means the left-right similarity of A is 3/4.\n\nGiven the left-right similarity of each cell, Dr. Podboq's hypothesis\nsays we can determine which of the cells X and Y has\nstronger asymmetricity by the following rules.\n\nIf X and Y have different left-right similarities, the\none with lower left-right similarity has stronger asymmetricity.\nOtherwise, if neither X nor Y has child cells, they\nhave completely equal asymmetricity.\nOtherwise, both X and Y must have two child cells. In this case,\nwe compare the child cell of X with stronger (or equal)\nasymmetricity (than the other child cell of X) and the child\ncell of Y with stronger (or equal) asymmetricity (than the other child cell\nof Y), and the one having a child with stronger asymmetricity\nhas stronger asymmetricity.\n\nIf we still have a tie, we compare the other child cells of X\nand Y with weaker (or equal) asymmetricity, and the one having a child with\nstronger asymmetricity has stronger asymmetricity.\n\nIf we still have a tie again, X and Y have\ncompletely equal asymmetricity.\nWhen we compare child cells in some rules above, we recursively apply\nthis rule set.\n\nNow, your job is to write a program that transforms a given tree\nrepresenting a process of cell divisions, by interchanging two child cells\nof arbitrary cells, into a tree where the following conditions are\nsatisfied.\n\nFor every cell X which is the starting cell of the given\ntree or a left child cell of some parent cell, if X has two\nchild cells, the one at left has stronger (or equal) asymmetricity than the one\nat right.\n\nFor every cell X which is a right child cell of some parent\ncell, if X has two child cells, the one at right has stronger (or equal)\nasymmetricity than the one at left.\nIn case two child cells have equal asymmetricity, their order is\narbitrary because either order would results in trees of the same shape.\n\nFor example, suppose we are given the tree in Figure F-2. First we\ncompare B and C, and because B has lower left-right similarity, which means stronger asymmetricity, we\nkeep B at left and C at right. Next, because B is the left child cell\nof A, we compare two child cells of B, and the one with stronger\nasymmetricity is positioned at left. On the other hand, because C is\nthe right child cell of A, we compare two child cells of C, and the one\nwith stronger asymmetricity is positioned at right. We examine the\nother cells in the same way, and the tree is finally transformed into\nthe tree shown below.\nFigure F-5: The example tree after the transformation\n\nPlease be warned that the only operation allowed in the transformation\nof a tree is to interchange two child cells of some parent cell. For\nexample, you are not allowed to transform the tree in Figure F-2 into the tree\nbelow.\nFigure F-6: An example of disallowed transformation", "constraint": "", "input": "The input consists of n lines (1<=n<=100) describing\nn trees followed by a line only containing a single zero which\nrepresents the end of the input. Each tree includes at least 1 and at\nmost 127 cells. Below is an example of a tree description.\n\n((x (x x)) x)\n\nThis description represents the tree shown in Figure F-1. More\nformally, the description of a tree is in either of the following two formats.\n\n\"(\" \")\"\nor\n\"x\"\n\nThe former is the description of a tree whose starting cell has two\nchild cells, and the latter is the description of a tree whose starting\ncell has no child cell.", "output": "For each tree given in the input, print a line describing the result\nof the tree transformation. In the output, trees should be described in\nthe same formats as the input, and the tree descriptions must\nappear in the same order as the input. Each line should have no extra\ncharacter other than one tree description.", "content_img": true, "lang": "en", "error": false, "samples": ["input: (((x x) x) ((x x) (x (x x))))\n(((x x) (x x)) ((x x) ((x x) (x x))))\n(((x x) ((x x) x)) (((x (x x)) x) (x x)))\n(((x x) x) ((x x) (((((x x) x) x) x) x)))\n(((x x) x) ((x (x x)) (x (x x))))\n((((x (x x)) x) (x ((x x) x))) ((x (x x)) (x x)))\n((((x x) x) ((x x) (x (x x)))) (((x x) (x x)) ((x x) ((x x) (x x)))))\n0\n output: ((x (x x)) ((x x) ((x x) x)))\n(((x x) ((x x) (x x))) ((x x) (x x)))\n(((x ((x x) x)) (x x)) ((x x) ((x x) x)))\n(((x ((x ((x x) x)) x)) (x x)) ((x x) x))\n((x (x x)) ((x (x x)) ((x x) x)))\n(((x (x x)) (x x)) ((x ((x x) x)) ((x (x x)) x)))\n(((x (x x)) ((x x) ((x x) x))) (((x x) (x x)) (((x x) (x x)) (x x))))"], "Pid": "p00733", "ProblemText": "Task Description: After long studying how embryos of organisms become asymmetric during\ntheir development, Dr. Podboq, a famous biologist, has reached his new\nhypothesis. Dr. Podboq is now preparing a poster for the coming\nacademic conference, which shows a tree representing the development\nprocess of an embryo through repeated cell divisions starting from one\ncell. Your job is to write a program that transforms given trees into\nforms satisfying some conditions so that it is easier for the audience\nto get the idea.\n\nA tree representing the process of cell divisions has a form described\nbelow.\n\nThe starting cell is represented by a circle placed at the top.\n\nEach cell either terminates the division activity or divides into\ntwo cells. Therefore, from each circle representing a cell, there are\neither no branch downward, or two branches down to its\ntwo child cells.\nBelow is an example of such a tree.\nFigure F-1: A tree representing a process of cell divisions\n\nAccording to Dr. Podboq's hypothesis, we can determine which cells\nhave stronger or weaker asymmetricity by looking at the structure of\nthis tree representation. First, his hypothesis defines \"left-right\nsimilarity\" of cells as follows:\n\nThe left-right similarity of a cell that did not divide further is\n0.\n For a cell that did divide further, we collect the partial\ntrees starting from its child or descendant cells, and count how\nmany kinds of structures they have. Then, the left-right similarity of\nthe cell is defined to be the ratio of the number of structures\nthat appear both in\nthe right child side and the left child side. We regard two trees\nhave the same structure if we can make them have exactly the same shape by\ninterchanging two child cells of arbitrary cells.\nFor example, suppose we have a tree shown below:\nFigure F-2: An example tree\n\nThe left-right similarity of the cell A is computed as follows.\nFirst, within the descendants of the cell B, which is the left child\ncell of A, the following three kinds of structures appear. Notice that\nthe rightmost structure appears three times, but when we count the number\nof structures, we count it only once.\nFigure F-3: Structures appearing within the descendants of the cell B\n\nOn the other hand, within the descendants of the cell C, which is the\nright child cell of A, the following four kinds of structures appear.\nFigure F-4: Structures appearing within the descendants of the cell C\n\nAmong them, the first, second, and third ones within the B side are\nregarded as the same structure as the second, third, and fourth ones\nwithin the C side, respectively. Therefore, there are four structures\nin total, and three among them are common to the left side and the\nright side, which means the left-right similarity of A is 3/4.\n\nGiven the left-right similarity of each cell, Dr. Podboq's hypothesis\nsays we can determine which of the cells X and Y has\nstronger asymmetricity by the following rules.\n\nIf X and Y have different left-right similarities, the\none with lower left-right similarity has stronger asymmetricity.\nOtherwise, if neither X nor Y has child cells, they\nhave completely equal asymmetricity.\nOtherwise, both X and Y must have two child cells. In this case,\nwe compare the child cell of X with stronger (or equal)\nasymmetricity (than the other child cell of X) and the child\ncell of Y with stronger (or equal) asymmetricity (than the other child cell\nof Y), and the one having a child with stronger asymmetricity\nhas stronger asymmetricity.\n\nIf we still have a tie, we compare the other child cells of X\nand Y with weaker (or equal) asymmetricity, and the one having a child with\nstronger asymmetricity has stronger asymmetricity.\n\nIf we still have a tie again, X and Y have\ncompletely equal asymmetricity.\nWhen we compare child cells in some rules above, we recursively apply\nthis rule set.\n\nNow, your job is to write a program that transforms a given tree\nrepresenting a process of cell divisions, by interchanging two child cells\nof arbitrary cells, into a tree where the following conditions are\nsatisfied.\n\nFor every cell X which is the starting cell of the given\ntree or a left child cell of some parent cell, if X has two\nchild cells, the one at left has stronger (or equal) asymmetricity than the one\nat right.\n\nFor every cell X which is a right child cell of some parent\ncell, if X has two child cells, the one at right has stronger (or equal)\nasymmetricity than the one at left.\nIn case two child cells have equal asymmetricity, their order is\narbitrary because either order would results in trees of the same shape.\n\nFor example, suppose we are given the tree in Figure F-2. First we\ncompare B and C, and because B has lower left-right similarity, which means stronger asymmetricity, we\nkeep B at left and C at right. Next, because B is the left child cell\nof A, we compare two child cells of B, and the one with stronger\nasymmetricity is positioned at left. On the other hand, because C is\nthe right child cell of A, we compare two child cells of C, and the one\nwith stronger asymmetricity is positioned at right. We examine the\nother cells in the same way, and the tree is finally transformed into\nthe tree shown below.\nFigure F-5: The example tree after the transformation\n\nPlease be warned that the only operation allowed in the transformation\nof a tree is to interchange two child cells of some parent cell. For\nexample, you are not allowed to transform the tree in Figure F-2 into the tree\nbelow.\nFigure F-6: An example of disallowed transformation\nTask Input: The input consists of n lines (1<=n<=100) describing\nn trees followed by a line only containing a single zero which\nrepresents the end of the input. Each tree includes at least 1 and at\nmost 127 cells. Below is an example of a tree description.\n\n((x (x x)) x)\n\nThis description represents the tree shown in Figure F-1. More\nformally, the description of a tree is in either of the following two formats.\n\n\"(\" \")\"\nor\n\"x\"\n\nThe former is the description of a tree whose starting cell has two\nchild cells, and the latter is the description of a tree whose starting\ncell has no child cell.\nTask Output: For each tree given in the input, print a line describing the result\nof the tree transformation. In the output, trees should be described in\nthe same formats as the input, and the tree descriptions must\nappear in the same order as the input. Each line should have no extra\ncharacter other than one tree description.\nTask Samples: input: (((x x) x) ((x x) (x (x x))))\n(((x x) (x x)) ((x x) ((x x) (x x))))\n(((x x) ((x x) x)) (((x (x x)) x) (x x)))\n(((x x) x) ((x x) (((((x x) x) x) x) x)))\n(((x x) x) ((x (x x)) (x (x x))))\n((((x (x x)) x) (x ((x x) x))) ((x (x x)) (x x)))\n((((x x) x) ((x x) (x (x x)))) (((x x) (x x)) ((x x) ((x x) (x x)))))\n0\n output: ((x (x x)) ((x x) ((x x) x)))\n(((x x) ((x x) (x x))) ((x x) (x x)))\n(((x ((x x) x)) (x x)) ((x x) ((x x) x)))\n(((x ((x ((x x) x)) x)) (x x)) ((x x) x))\n((x (x x)) ((x (x x)) ((x x) x)))\n(((x (x x)) (x x)) ((x ((x x) x)) ((x (x x)) x)))\n(((x (x x)) ((x x) ((x x) x))) (((x x) (x x)) (((x x) (x x)) (x x))))\n\n" }, { "title": "Problem A: Equal Total Scores", "content": "Taro and Hanako have numbers of cards in their hands. \nEach of the cards has a score on it.\nTaro and Hanako wish to make the total scores of their cards equal\nby exchanging one card in one's hand with one card in the other's hand.\nWhich of the cards should be exchanged with which?\n\nNote that they have to exchange their\ncards even if they already have cards of the same total score.", "constraint": "", "input": "The input consists of a number of datasets. \nEach dataset is formatted as follows.\n\nn m\ns_1 \ns_2 \n. . . \ns_n \ns_n+1 \ns_n+2 \n. . . \ns_n+m \n\nThe first line of a dataset contains two numbers\nn and m delimited by a space, where n\nis the number of cards that Taro has\nand m is the number of cards that Hanako has. \nThe subsequent n+m lines \nlist the score for each of the cards,\none score per line. The first n scores\n(from s_1 up to s_n)\nare the scores of Taro's cards \nand the remaining m scores \n(from s_n+1 up to s_n+m)\nare Hanako's.\n\nThe numbers n and m\nare positive integers no greater than 100. Each score\nis a non-negative integer no greater than 100.\n\nThe end of the input is indicated by a line containing two zeros delimited\nby a single space.", "output": "For each dataset, output a single line containing two numbers delimited\nby a single space, where the first number is the score of the card Taro\ngives to Hanako and the second number is the score of the card Hanako gives\nto Taro. \nIf there is more than one way to exchange a pair of cards\nthat makes the total scores equal, \noutput a pair of scores whose sum is the smallest.\n\nIn case no exchange can make the total scores equal, output a\nsingle line containing solely -1.\nThe output must not contain any superfluous characters\nthat do not conform to the format.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n1\n5\n3\n7\n6 5\n3\n9\n5\n2\n3\n3\n12\n2\n7\n3\n5\n4 5\n10\n0\n3\n8\n1\n9\n6\n0\n6\n7 4\n1\n1\n2\n1\n2\n1\n4\n2\n3\n4\n3\n2 3\n1\n1\n2\n2\n2\n0 0\n output: 1 3\n3 5\n-1\n2 2\n-1"], "Pid": "p00734", "ProblemText": "Task Description: Taro and Hanako have numbers of cards in their hands. \nEach of the cards has a score on it.\nTaro and Hanako wish to make the total scores of their cards equal\nby exchanging one card in one's hand with one card in the other's hand.\nWhich of the cards should be exchanged with which?\n\nNote that they have to exchange their\ncards even if they already have cards of the same total score.\nTask Input: The input consists of a number of datasets. \nEach dataset is formatted as follows.\n\nn m\ns_1 \ns_2 \n. . . \ns_n \ns_n+1 \ns_n+2 \n. . . \ns_n+m \n\nThe first line of a dataset contains two numbers\nn and m delimited by a space, where n\nis the number of cards that Taro has\nand m is the number of cards that Hanako has. \nThe subsequent n+m lines \nlist the score for each of the cards,\none score per line. The first n scores\n(from s_1 up to s_n)\nare the scores of Taro's cards \nand the remaining m scores \n(from s_n+1 up to s_n+m)\nare Hanako's.\n\nThe numbers n and m\nare positive integers no greater than 100. Each score\nis a non-negative integer no greater than 100.\n\nThe end of the input is indicated by a line containing two zeros delimited\nby a single space.\nTask Output: For each dataset, output a single line containing two numbers delimited\nby a single space, where the first number is the score of the card Taro\ngives to Hanako and the second number is the score of the card Hanako gives\nto Taro. \nIf there is more than one way to exchange a pair of cards\nthat makes the total scores equal, \noutput a pair of scores whose sum is the smallest.\n\nIn case no exchange can make the total scores equal, output a\nsingle line containing solely -1.\nThe output must not contain any superfluous characters\nthat do not conform to the format.\nTask Samples: input: 2 2\n1\n5\n3\n7\n6 5\n3\n9\n5\n2\n3\n3\n12\n2\n7\n3\n5\n4 5\n10\n0\n3\n8\n1\n9\n6\n0\n6\n7 4\n1\n1\n2\n1\n2\n1\n4\n2\n3\n4\n3\n2 3\n1\n1\n2\n2\n2\n0 0\n output: 1 3\n3 5\n-1\n2 2\n-1\n\n" }, { "title": "Problem B: Monday-Saturday Prime Factors", "content": "Chief Judge's log, stardate 48642.5.\nWe have decided to make a problem from elementary number theory.\nThe problem looks like finding all prime factors of a positive integer,\nbut it is not.\n\nA positive integer whose remainder divided by 7 is either 1 or 6 is called\na 7N+{1,6} number.\nBut as it is hard to pronounce,\nwe shall call it a Monday-Saturday number.\n\nFor Monday-Saturday numbers a and b,\nwe say a is a Monday-Saturday divisor of b\nif there exists a Monday-Saturday number x\nsuch that ax = b.\nIt is easy to show that\nfor any Monday-Saturday numbers a and b,\nit holds that a is\na Monday-Saturday divisor of b\nif and only if\na is a divisor of b in the usual sense.\n\nWe call a Monday-Saturday number a Monday-Saturday prime\nif it is greater than 1 and has no Monday-Saturday divisors\nother than itself and 1.\nA Monday-Saturday number which is a prime in the usual sense\nis a Monday-Saturday prime\nbut the converse does not always hold.\nFor example, 27 is a Monday-Saturday prime\nalthough it is not a prime in the usual sense.\nWe call a Monday-Saturday prime\nwhich is a Monday-Saturday divisor of a Monday-Saturday number a\na Monday-Saturday prime factor of a.\nFor example, 27 is one of the Monday-Saturday prime factors of 216,\nsince 27 is a Monday-Saturday prime\nand 216 = 27 * 8 holds.\nAny Monday-Saturday number greater than 1\ncan be expressed as a product of one or more Monday-Saturday primes.\nThe expression is not always unique\neven if differences in order are ignored.\nFor example,\n\n216 = 6 * 6 * 6 = 8 * 27\n\nholds.\nOur contestants should write a program that outputs\nall Monday-Saturday prime factors\nof each input Monday-Saturday number.", "constraint": "", "input": "The input is a sequence of lines each of which contains a single\nMonday-Saturday number.\nEach Monday-Saturday number is greater than 1\nand less than 300000 (three hundred thousand).\nThe end of the input is indicated by a line\ncontaining a single digit 1.", "output": "For each input Monday-Saturday number,\nit should be printed, followed by a colon `: '\nand the list of its Monday-Saturday prime factors on a single line.\nMonday-Saturday prime factors should be listed in ascending order\nand each should be preceded by a space.\nAll the Monday-Saturday prime factors should be printed only once\neven if they divide the input Monday-Saturday number more than once.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 205920\n262144\n262200\n279936\n299998\n1\n output: 205920: 6 8 13 15 20 22 55 99\n262144: 8\n262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185\n279936: 6 8 27\n299998: 299998"], "Pid": "p00735", "ProblemText": "Task Description: Chief Judge's log, stardate 48642.5.\nWe have decided to make a problem from elementary number theory.\nThe problem looks like finding all prime factors of a positive integer,\nbut it is not.\n\nA positive integer whose remainder divided by 7 is either 1 or 6 is called\na 7N+{1,6} number.\nBut as it is hard to pronounce,\nwe shall call it a Monday-Saturday number.\n\nFor Monday-Saturday numbers a and b,\nwe say a is a Monday-Saturday divisor of b\nif there exists a Monday-Saturday number x\nsuch that ax = b.\nIt is easy to show that\nfor any Monday-Saturday numbers a and b,\nit holds that a is\na Monday-Saturday divisor of b\nif and only if\na is a divisor of b in the usual sense.\n\nWe call a Monday-Saturday number a Monday-Saturday prime\nif it is greater than 1 and has no Monday-Saturday divisors\nother than itself and 1.\nA Monday-Saturday number which is a prime in the usual sense\nis a Monday-Saturday prime\nbut the converse does not always hold.\nFor example, 27 is a Monday-Saturday prime\nalthough it is not a prime in the usual sense.\nWe call a Monday-Saturday prime\nwhich is a Monday-Saturday divisor of a Monday-Saturday number a\na Monday-Saturday prime factor of a.\nFor example, 27 is one of the Monday-Saturday prime factors of 216,\nsince 27 is a Monday-Saturday prime\nand 216 = 27 * 8 holds.\nAny Monday-Saturday number greater than 1\ncan be expressed as a product of one or more Monday-Saturday primes.\nThe expression is not always unique\neven if differences in order are ignored.\nFor example,\n\n216 = 6 * 6 * 6 = 8 * 27\n\nholds.\nOur contestants should write a program that outputs\nall Monday-Saturday prime factors\nof each input Monday-Saturday number.\nTask Input: The input is a sequence of lines each of which contains a single\nMonday-Saturday number.\nEach Monday-Saturday number is greater than 1\nand less than 300000 (three hundred thousand).\nThe end of the input is indicated by a line\ncontaining a single digit 1.\nTask Output: For each input Monday-Saturday number,\nit should be printed, followed by a colon `: '\nand the list of its Monday-Saturday prime factors on a single line.\nMonday-Saturday prime factors should be listed in ascending order\nand each should be preceded by a space.\nAll the Monday-Saturday prime factors should be printed only once\neven if they divide the input Monday-Saturday number more than once.\nTask Samples: input: 205920\n262144\n262200\n279936\n299998\n1\n output: 205920: 6 8 13 15 20 22 55 99\n262144: 8\n262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185\n279936: 6 8 27\n299998: 299998\n\n" }, { "title": "Problem C: How can I satisfy thee? Let me count the ways. . .", "content": "Three-valued logic is a logic system that has, in addition to \"true\" and \n\"false\", \"unknown\" as a valid value. \n\nIn the following, logical values \"false\", \"unknown\" and \"true\" are \nrepresented by 0,1 and 2 respectively. \n\nLet \"-\" be a unary operator (i. e. a symbol representing one argument function) \nand let both \"*\" and \"+\" be binary operators (i. e. symbols representing \ntwo argument functions). \nThese operators represent negation (NOT), conjunction (AND) and \ndisjunction (OR) respectively. \nThese operators in three-valued logic can be defined in Table C-1.\nTable C-1: Truth tables of three-valued logic operators\n \n

-X (X*Y) (X+Y) \n \n \n \n\n \n\nLet P, Q and R be variables ranging over three-valued logic values. \nFor a given formula, you are asked to answer the number of triples (P, Q, R) \nthat satisfy the formula, that is, those which make the value of the \ngiven formula 2. \nA formula is one of the following form (X and Y represent formulas). \n\n Constants: 0,1 or 2\n Variables: P, Q or R\n Negations: -X\n Conjunctions: (X*Y)\n Disjunctions: (X+Y)\nNote that conjunctions and disjunctions of two formulas are always \nparenthesized. \nFor example, when formula (P*Q) is given as an input, the value of \nthis formula is 2 when and only when (P, Q, R) is (2,2,0), (2,2,1) or (2,2,2). \nTherefore, you should output 3.", "constraint": "", "input": "The input consists of one or more lines. Each line contains a formula. \nA formula is a string which consists of 0,1,2, P, Q, R, -, *, +, (, ). \nOther characters such as spaces are not contained. \nThe grammar of formulas is given by the following BNF. \n\n : : = 0 | 1 | 2 | P | Q | R |\n - | (*) | (+)\n\nAll the formulas obey this syntax and thus you do not have to care about \ngrammatical errors.\nInput lines never exceed 80 characters. \n\nFinally, a line which\ncontains only a \". \" (period) comes, indicating the end of the input.", "output": "You should answer the number (in decimal) of triples (P, Q, R) that make the \nvalue of the given formula 2. One line containing the number should be \noutput for each of the formulas, and no other characters should be output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: (P*Q)\n(--R+(P*Q))\n(P*-P)\n2\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.\n output: 3\n11\n0\n27\n0\n7"], "Pid": "p00736", "ProblemText": "Task Description: Three-valued logic is a logic system that has, in addition to \"true\" and \n\"false\", \"unknown\" as a valid value. \n\nIn the following, logical values \"false\", \"unknown\" and \"true\" are \nrepresented by 0,1 and 2 respectively. \n\nLet \"-\" be a unary operator (i. e. a symbol representing one argument function) \nand let both \"*\" and \"+\" be binary operators (i. e. symbols representing \ntwo argument functions). \nThese operators represent negation (NOT), conjunction (AND) and \ndisjunction (OR) respectively. \nThese operators in three-valued logic can be defined in Table C-1.\nTable C-1: Truth tables of three-valued logic operators\n \n -X (X*Y) (X+Y) \n \n \n \n\n \n\nLet P, Q and R be variables ranging over three-valued logic values. \nFor a given formula, you are asked to answer the number of triples (P, Q, R) \nthat satisfy the formula, that is, those which make the value of the \ngiven formula 2. \nA formula is one of the following form (X and Y represent formulas). \n\n Constants: 0,1 or 2\n Variables: P, Q or R\n Negations: -X\n Conjunctions: (X*Y)\n Disjunctions: (X+Y)\nNote that conjunctions and disjunctions of two formulas are always \nparenthesized. \nFor example, when formula (P*Q) is given as an input, the value of \nthis formula is 2 when and only when (P, Q, R) is (2,2,0), (2,2,1) or (2,2,2). \nTherefore, you should output 3.\nTask Input: The input consists of one or more lines. Each line contains a formula. \nA formula is a string which consists of 0,1,2, P, Q, R, -, *, +, (, ). \nOther characters such as spaces are not contained. \nThe grammar of formulas is given by the following BNF. \n\n : : = 0 | 1 | 2 | P | Q | R |\n - | (*) | (+)\n\nAll the formulas obey this syntax and thus you do not have to care about \ngrammatical errors.\nInput lines never exceed 80 characters. \n\nFinally, a line which\ncontains only a \". \" (period) comes, indicating the end of the input.\nTask Output: You should answer the number (in decimal) of triples (P, Q, R) that make the \nvalue of the given formula 2. One line containing the number should be \noutput for each of the formulas, and no other characters should be output.\nTask Samples: input: (P*Q)\n(--R+(P*Q))\n(P*-P)\n2\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.\n output: 3\n11\n0\n27\n0\n7\n\n" }, { "title": "Problem D: Twirling Robot", "content": "Let's play a game using a robot on a rectangular board \ncovered with a square mesh (Figure D-1).\nThe robot is initially set at the start square in the northwest corner\nfacing the east direction.\nThe goal of this game is to lead the robot\nto the goal square in the southeast corner.\n\nFigure D-1: Example of a board\nThe robot can execute the following five types of commands.\n
\n
\"Straight\":
\n
Keep the current direction of the robot, and move forward to the next square.
\n
\"Right\":
\n
Turn right with 90 degrees from the current direction, and move forward to the next square.
\n
\"Back\":
\n
Turn to the reverse direction, and move forward to the next square.
\n
\"Left\":
\n
Turn left with 90 degrees from the current direction, and move forward to the next square.
\n
\"Halt\":
\n
Stop at the current square to finish the game.
\n
\n\nEach square has one of these commands assigned as shown in Figure D-2.\nThe robot executes the command assigned to the square where it resides,\nunless the player gives another command to be executed instead.\nEach time the player gives an explicit command, \nthe player has to pay the cost that depends on the command type.\n\nFigure D-2: Example of commands assigned to squares\nThe robot can visit the same square several times during a game.\nThe player loses the game when the robot goes out of the board\nor it executes a \"Halt\" command before arriving at the goal square.\n\nYour task is to write a program that calculates the minimum cost to lead the robot\nfrom the start square to the goal one.", "constraint": "", "input": "The input is a sequence of datasets. \nThe end of the input is indicated by a line containing two zeros separated by a space.\nEach dataset is formatted as follows.\n\nw h\ns(1,1) . . . s(1, w)\ns(2,1) . . . s(2, w)\n. . . \ns(h, 1) . . . s(h, w)\nc_0 c_1 c_2 c_3\n\nThe integers h and w are the numbers of rows and columns of the board, \nrespectively.\nYou may assume 2 <= h <= 30 and 2 <= w <= 30. \nEach of the following h lines consists of w numbers delimited by a space.\nThe number s(i, j) represents the command assigned to the square \nin the i-th row and the j-th column as follows.\n\n 0: \"Straight\"\n\n 1: \"Right\"\n\n 2: \"Back\"\n\n 3: \"Left\"\n\n 4: \"Halt\"\n\nYou can assume that a \"Halt\" command is assigned to the goal square.\nNote that \"Halt\" commands may be assigned to other squares, too.\n\nThe last line of a dataset contains four integers \nc_0, c_1, c_2, and c_3, delimited by a space, \nindicating the costs that the player has to pay \nwhen the player gives\n\"Straight\", \"Right\", \"Back\", and \"Left\" commands\nrespectively.\nThe player cannot give \"Halt\" commands.\nYou can assume that all the values of \nc_0, c_1, c_2, and c_3\nare between 1 and 9, inclusive.", "output": "For each dataset, print a line only having a decimal integer indicating the minimum cost \nrequired to lead the robot to the goal.\nNo other characters should be on the output line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8 3\n0 0 0 0 0 0 0 1\n2 3 0 1 4 0 0 1\n3 3 0 0 0 0 0 4\n9 9 1 9\n4 4\n3 3 4 0\n1 2 4 4\n1 1 1 0\n0 2 4 4\n8 7 2 1\n2 8\n2 2\n4 1\n0 4\n1 3\n1 0\n2 1\n0 3\n1 4\n1 9 3 1\n0 0\n output: 1\n11\n6"], "Pid": "p00737", "ProblemText": "Task Description: Let's play a game using a robot on a rectangular board \ncovered with a square mesh (Figure D-1).\nThe robot is initially set at the start square in the northwest corner\nfacing the east direction.\nThe goal of this game is to lead the robot\nto the goal square in the southeast corner.\n\nFigure D-1: Example of a board\nThe robot can execute the following five types of commands.\n
\n
\"Straight\":
\n
Keep the current direction of the robot, and move forward to the next square.
\n
\"Right\":
\n
Turn right with 90 degrees from the current direction, and move forward to the next square.
\n
\"Back\":
\n
Turn to the reverse direction, and move forward to the next square.
\n
\"Left\":
\n
Turn left with 90 degrees from the current direction, and move forward to the next square.
\n
\"Halt\":
\n
Stop at the current square to finish the game.
\n
\n\nEach square has one of these commands assigned as shown in Figure D-2.\nThe robot executes the command assigned to the square where it resides,\nunless the player gives another command to be executed instead.\nEach time the player gives an explicit command, \nthe player has to pay the cost that depends on the command type.\n\nFigure D-2: Example of commands assigned to squares\nThe robot can visit the same square several times during a game.\nThe player loses the game when the robot goes out of the board\nor it executes a \"Halt\" command before arriving at the goal square.\n\nYour task is to write a program that calculates the minimum cost to lead the robot\nfrom the start square to the goal one.\nTask Input: The input is a sequence of datasets. \nThe end of the input is indicated by a line containing two zeros separated by a space.\nEach dataset is formatted as follows.\n\nw h\ns(1,1) . . . s(1, w)\ns(2,1) . . . s(2, w)\n. . . \ns(h, 1) . . . s(h, w)\nc_0 c_1 c_2 c_3\n\nThe integers h and w are the numbers of rows and columns of the board, \nrespectively.\nYou may assume 2 <= h <= 30 and 2 <= w <= 30. \nEach of the following h lines consists of w numbers delimited by a space.\nThe number s(i, j) represents the command assigned to the square \nin the i-th row and the j-th column as follows.\n\n 0: \"Straight\"\n\n 1: \"Right\"\n\n 2: \"Back\"\n\n 3: \"Left\"\n\n 4: \"Halt\"\n\nYou can assume that a \"Halt\" command is assigned to the goal square.\nNote that \"Halt\" commands may be assigned to other squares, too.\n\nThe last line of a dataset contains four integers \nc_0, c_1, c_2, and c_3, delimited by a space, \nindicating the costs that the player has to pay \nwhen the player gives\n\"Straight\", \"Right\", \"Back\", and \"Left\" commands\nrespectively.\nThe player cannot give \"Halt\" commands.\nYou can assume that all the values of \nc_0, c_1, c_2, and c_3\nare between 1 and 9, inclusive.\nTask Output: For each dataset, print a line only having a decimal integer indicating the minimum cost \nrequired to lead the robot to the goal.\nNo other characters should be on the output line.\nTask Samples: input: 8 3\n0 0 0 0 0 0 0 1\n2 3 0 1 4 0 0 1\n3 3 0 0 0 0 0 4\n9 9 1 9\n4 4\n3 3 4 0\n1 2 4 4\n1 1 1 0\n0 2 4 4\n8 7 2 1\n2 8\n2 2\n4 1\n0 4\n1 3\n1 0\n2 1\n0 3\n1 4\n1 9 3 1\n0 0\n output: 1\n11\n6\n\n" }, { "title": "Problem E: Roll-A-Big-Ball", "content": "ACM University holds its sports day in every July. The \"Roll-A-Big-Ball\" \nis the highlight of the day. In the game, players roll a ball\non a straight course drawn on the ground. There are \nrectangular parallelepiped blocks on the ground as obstacles, which are fixed on the ground.\nDuring the game, the ball may not collide with any blocks.\nThe bottom point of the ball may not leave the course. \n\nTo have more fun, the university wants to use the largest possible ball\nfor the game. You must\nwrite a program that finds the largest radius of the ball that can reach\nthe goal without colliding any obstacle block.\n\nThe ball is a perfect sphere, and the ground is a plane.\nEach block is a rectangular parallelepiped. The four edges of its bottom rectangle are on the ground, and parallel to either x- or y-axes. \nThe course is given as a line segment from a start point to an end point.\nThe ball starts with its bottom point touching the start point, and goals when\nits bottom point touches the end point.\n\nThe positions of the ball and a block can be like in Figure E-1 (a) and (b).\n\nFigure E-1: Possible positions of the ball and a block", "constraint": "", "input": "The input consists of a number of datasets. \nEach dataset is formatted as follows. \n\nN\nsx sy ex ey\nminx_1 miny_1 maxx_1 maxy_1 h_1\nminx_2 miny_2 maxx_2 maxy_2 h_2\n. . . \nminx_N miny_N maxx_N maxy_N h_N\n\nA dataset begins with a line with an integer N, the number of\nblocks (1 <= N <= 50). The next line consists of four integers,\ndelimited by a space,\nindicating the start point (sx, sy) and the end point (ex, ey).\n\nThe following N lines give the placement of blocks. \nEach line, representing a block, consists of five integers delimited by a space. These integers indicate the two vertices (minx, miny), (maxx, maxy) of the \nbottom surface and the height h of the block.\nThe integers sx, sy, ex, ey, minx, miny, \nmaxx, maxy and h satisfy the following conditions.\n\n-10000 <= sx, sy, ex, ey <= 10000\n-10000 <= minx_i < maxx_i <= 10000\n-10000 <= miny_i < maxy_i <= 10000\n1 <= h_i <= 1000\n\nThe last dataset is followed by a line with a single zero in it.", "output": "For each dataset, output a separate line containing the largest radius. \nYou may assume that the largest radius never exceeds 1000 for each dataset.\nIf there are any blocks on the course line, the largest radius is defined to be zero.\nThe value may contain an error less than or equal to 0.001.\nYou may print any number of digits after the decimal point.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n-40 -40 100 30\n-100 -100 -50 -30 1\n30 -70 90 -30 10\n2\n-4 -4 10 3\n-10 -10 -5 -3 1\n3 -7 9 -3 1\n2\n-40 -40 100 30\n-100 -100 -50 -30 3\n30 -70 90 -30 10\n2\n-400 -400 1000 300\n-800 -800 -500 -300 7\n300 -700 900 -300 20\n3\n20 70 150 70\n0 0 50 50 4\n40 100 60 120 8\n130 80 200 200 1\n3\n20 70 150 70\n0 0 50 50 4\n40 100 60 120 10\n130 80 200 200 1\n3\n20 70 150 70\n0 0 50 50 10\n40 100 60 120 10\n130 80 200 200 3\n1\n2 4 8 8\n0 0 10 10 1\n1\n1 4 9 9\n2 2 7 7 1\n0\n output: 30\n1\n18.16666666667\n717.7857142857\n50.5\n50\n18.16666666667\n0\n0"], "Pid": "p00738", "ProblemText": "Task Description: ACM University holds its sports day in every July. The \"Roll-A-Big-Ball\" \nis the highlight of the day. In the game, players roll a ball\non a straight course drawn on the ground. There are \nrectangular parallelepiped blocks on the ground as obstacles, which are fixed on the ground.\nDuring the game, the ball may not collide with any blocks.\nThe bottom point of the ball may not leave the course. \n\nTo have more fun, the university wants to use the largest possible ball\nfor the game. You must\nwrite a program that finds the largest radius of the ball that can reach\nthe goal without colliding any obstacle block.\n\nThe ball is a perfect sphere, and the ground is a plane.\nEach block is a rectangular parallelepiped. The four edges of its bottom rectangle are on the ground, and parallel to either x- or y-axes. \nThe course is given as a line segment from a start point to an end point.\nThe ball starts with its bottom point touching the start point, and goals when\nits bottom point touches the end point.\n\nThe positions of the ball and a block can be like in Figure E-1 (a) and (b).\n\nFigure E-1: Possible positions of the ball and a block\nTask Input: The input consists of a number of datasets. \nEach dataset is formatted as follows. \n\nN\nsx sy ex ey\nminx_1 miny_1 maxx_1 maxy_1 h_1\nminx_2 miny_2 maxx_2 maxy_2 h_2\n. . . \nminx_N miny_N maxx_N maxy_N h_N\n\nA dataset begins with a line with an integer N, the number of\nblocks (1 <= N <= 50). The next line consists of four integers,\ndelimited by a space,\nindicating the start point (sx, sy) and the end point (ex, ey).\n\nThe following N lines give the placement of blocks. \nEach line, representing a block, consists of five integers delimited by a space. These integers indicate the two vertices (minx, miny), (maxx, maxy) of the \nbottom surface and the height h of the block.\nThe integers sx, sy, ex, ey, minx, miny, \nmaxx, maxy and h satisfy the following conditions.\n\n-10000 <= sx, sy, ex, ey <= 10000\n-10000 <= minx_i < maxx_i <= 10000\n-10000 <= miny_i < maxy_i <= 10000\n1 <= h_i <= 1000\n\nThe last dataset is followed by a line with a single zero in it.\nTask Output: For each dataset, output a separate line containing the largest radius. \nYou may assume that the largest radius never exceeds 1000 for each dataset.\nIf there are any blocks on the course line, the largest radius is defined to be zero.\nThe value may contain an error less than or equal to 0.001.\nYou may print any number of digits after the decimal point.\nTask Samples: input: 2\n-40 -40 100 30\n-100 -100 -50 -30 1\n30 -70 90 -30 10\n2\n-4 -4 10 3\n-10 -10 -5 -3 1\n3 -7 9 -3 1\n2\n-40 -40 100 30\n-100 -100 -50 -30 3\n30 -70 90 -30 10\n2\n-400 -400 1000 300\n-800 -800 -500 -300 7\n300 -700 900 -300 20\n3\n20 70 150 70\n0 0 50 50 4\n40 100 60 120 8\n130 80 200 200 1\n3\n20 70 150 70\n0 0 50 50 4\n40 100 60 120 10\n130 80 200 200 1\n3\n20 70 150 70\n0 0 50 50 10\n40 100 60 120 10\n130 80 200 200 3\n1\n2 4 8 8\n0 0 10 10 1\n1\n1 4 9 9\n2 2 7 7 1\n0\n output: 30\n1\n18.16666666667\n717.7857142857\n50.5\n50\n18.16666666667\n0\n0\n\n" }, { "title": "Problem F: ICPC: Intelligent Congruent Partition of Chocolate", "content": "The twins named Tatsuya and Kazuya love chocolate.\nThey have found a bar of their favorite chocolate in a very strange shape.\nThe chocolate bar looks to have been eaten partially by Mam.\nThey, of course, claim to eat it and then \nwill cut it into two pieces for their portions. \nSince they want to be sure that the chocolate bar is fairly divided, \nthey demand that the shapes of the two pieces are congruent\nand that each piece is connected.\n\nThe chocolate bar consists of many square shaped blocks of chocolate\nconnected to the adjacent square blocks of chocolate at their edges.\nThe whole chocolate bar is also connected. \n\nCutting the chocolate bar along with some edges of square blocks, \nyou should help them to divide it into two congruent and connected pieces of\nchocolate. That is, one piece fits into the other\nafter it is rotated, turned over and moved properly. \n\nFigure F-1: A partially eaten chocolate bar with 18 square blocks of chocolate\nFor example, there is a partially eaten chocolate bar\nwith 18 square blocks of chocolate as depicted in Figure F-1.\nCutting it along with some edges of square blocks, \nyou get two pieces of chocolate\nwith 9 square blocks each as depicted in Figure F-2.\n\nFigure F-2: Partitioning of the chocolate bar in Figure F-1\nYou get two congruent and connected pieces as the result. \nOne of them consists of 9 square blocks hatched with horizontal lines \nand the other with vertical lines.\nRotated clockwise with a right angle and turned over on a horizontal line,\nthe upper piece exactly fits into the lower piece.\n\nFigure F-3: A shape that cannot be partitioned \ninto two congruent and connected pieces\nTwo square blocks touching only at their corners\nare regarded as they are not connected to each other.\nFigure F-3 is an example shape that cannot be partitioned into\ntwo congruent and connected pieces.\nNote that, without the connectivity requirement,\nthis shape can be partitioned into two congruent pieces\nwith three squares (Figure F-4).\n\nFigure F-4: Two congruent but disconnected pieces\nYour job is to write a program that judges whether a given bar \nof chocolate can be partitioned into such two \ncongruent and connected pieces or not.", "constraint": "", "input": "The input is a sequence of datasets.\nThe end of the input is indicated by \na line containing two zeros separated by a space.\nEach dataset is formatted as follows.\n\nw h\nr(1,1) . . . r(1, w)\nr(2,1) . . . r(2, w)\n. . . \nr(h, 1) . . . r(h, w)\n\nThe integers w and h are the width and the height of \na chocolate bar, respectively. \nYou may assume 2 <= w <= 10 and 2 <= \nh <= 10.\nEach of the following h lines consists of w digits\ndelimited by a space.\nThe digit r(i, j) represents the existence of a square block of\nchocolate at the position \n(i, j) as follows.\n\n '0': There is no chocolate (i. e. , already eaten). \n\n '1': There is a square block of chocolate. \n\nYou can assume that there are at most 36 square blocks of \nchocolate in the bar, i. e. ,\nthe number of digit '1's representing square blocks of chocolate\nis at most 36 in each dataset.\nYou can also assume that there is at least one square block of chocolate in\neach row and each column.\n\nYou can assume that the chocolate bar is connected.\nSince Mam does not eat chocolate bars making holes in them,\nyou can assume that there is no dataset that represents \na bar in a shape with hole(s) as depicted in Figure F-5.\n\nFigure F-5: A partially eaten chocolate bar with a hole\n(You can assume that there is no dataset like this example)", "output": "For each dataset, output a line containing one of two uppercase character \nstrings \"YES\" or \"NO\".\n\"YES\" means the chocolate bar indicated by the dataset can be \npartitioned into two congruent and connected \npieces, and \"NO\" means it cannot be partitioned into such \ntwo pieces.\nNo other characters should be on the output line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 2\n1 1\n1 1\n3 3\n0 1 0\n1 1 0\n1 1 1\n4 6\n1 1 1 0\n1 1 1 1\n1 1 1 0\n1 1 1 0\n0 1 1 0\n1 1 1 0\n7 5\n0 0 1 0 0 1 1\n0 1 1 1 1 1 0\n0 1 1 1 1 1 0\n1 1 1 1 1 1 0\n1 0 0 0 1 1 0\n9 7\n0 0 1 0 0 0 0 0 0\n0 0 1 1 0 0 0 0 0\n1 1 1 1 1 1 1 1 0\n1 1 1 1 1 1 1 1 0\n0 1 1 1 1 1 1 1 1\n0 0 0 1 1 0 0 0 0\n0 0 0 1 0 0 0 0 0\n9 7\n0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0\n1 1 1 1 1 1 1 1 0\n1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1\n0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0\n7 6\n1 1 1 1 1 1 1\n1 1 1 1 1 1 1\n1 1 1 1 1 1 0\n1 1 1 1 1 1 0\n0 1 1 1 1 1 0\n0 1 1 1 1 1 0\n10 10\n0 1 1 1 1 1 1 1 1 1\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 1 0 0 0 0 0 1 0\n1 1 1 1 1 1 1 1 1 0\n0 0\n output: YES\nNO\nYES\nYES\nYES\nNO\nNO\nYES"], "Pid": "p00739", "ProblemText": "Task Description: The twins named Tatsuya and Kazuya love chocolate.\nThey have found a bar of their favorite chocolate in a very strange shape.\nThe chocolate bar looks to have been eaten partially by Mam.\nThey, of course, claim to eat it and then \nwill cut it into two pieces for their portions. \nSince they want to be sure that the chocolate bar is fairly divided, \nthey demand that the shapes of the two pieces are congruent\nand that each piece is connected.\n\nThe chocolate bar consists of many square shaped blocks of chocolate\nconnected to the adjacent square blocks of chocolate at their edges.\nThe whole chocolate bar is also connected. \n\nCutting the chocolate bar along with some edges of square blocks, \nyou should help them to divide it into two congruent and connected pieces of\nchocolate. That is, one piece fits into the other\nafter it is rotated, turned over and moved properly. \n\nFigure F-1: A partially eaten chocolate bar with 18 square blocks of chocolate\nFor example, there is a partially eaten chocolate bar\nwith 18 square blocks of chocolate as depicted in Figure F-1.\nCutting it along with some edges of square blocks, \nyou get two pieces of chocolate\nwith 9 square blocks each as depicted in Figure F-2.\n\nFigure F-2: Partitioning of the chocolate bar in Figure F-1\nYou get two congruent and connected pieces as the result. \nOne of them consists of 9 square blocks hatched with horizontal lines \nand the other with vertical lines.\nRotated clockwise with a right angle and turned over on a horizontal line,\nthe upper piece exactly fits into the lower piece.\n\nFigure F-3: A shape that cannot be partitioned \ninto two congruent and connected pieces\nTwo square blocks touching only at their corners\nare regarded as they are not connected to each other.\nFigure F-3 is an example shape that cannot be partitioned into\ntwo congruent and connected pieces.\nNote that, without the connectivity requirement,\nthis shape can be partitioned into two congruent pieces\nwith three squares (Figure F-4).\n\nFigure F-4: Two congruent but disconnected pieces\nYour job is to write a program that judges whether a given bar \nof chocolate can be partitioned into such two \ncongruent and connected pieces or not.\nTask Input: The input is a sequence of datasets.\nThe end of the input is indicated by \na line containing two zeros separated by a space.\nEach dataset is formatted as follows.\n\nw h\nr(1,1) . . . r(1, w)\nr(2,1) . . . r(2, w)\n. . . \nr(h, 1) . . . r(h, w)\n\nThe integers w and h are the width and the height of \na chocolate bar, respectively. \nYou may assume 2 <= w <= 10 and 2 <= \nh <= 10.\nEach of the following h lines consists of w digits\ndelimited by a space.\nThe digit r(i, j) represents the existence of a square block of\nchocolate at the position \n(i, j) as follows.\n\n '0': There is no chocolate (i. e. , already eaten). \n\n '1': There is a square block of chocolate. \n\nYou can assume that there are at most 36 square blocks of \nchocolate in the bar, i. e. ,\nthe number of digit '1's representing square blocks of chocolate\nis at most 36 in each dataset.\nYou can also assume that there is at least one square block of chocolate in\neach row and each column.\n\nYou can assume that the chocolate bar is connected.\nSince Mam does not eat chocolate bars making holes in them,\nyou can assume that there is no dataset that represents \na bar in a shape with hole(s) as depicted in Figure F-5.\n\nFigure F-5: A partially eaten chocolate bar with a hole\n(You can assume that there is no dataset like this example)\nTask Output: For each dataset, output a line containing one of two uppercase character \nstrings \"YES\" or \"NO\".\n\"YES\" means the chocolate bar indicated by the dataset can be \npartitioned into two congruent and connected \npieces, and \"NO\" means it cannot be partitioned into such \ntwo pieces.\nNo other characters should be on the output line.\nTask Samples: input: 2 2\n1 1\n1 1\n3 3\n0 1 0\n1 1 0\n1 1 1\n4 6\n1 1 1 0\n1 1 1 1\n1 1 1 0\n1 1 1 0\n0 1 1 0\n1 1 1 0\n7 5\n0 0 1 0 0 1 1\n0 1 1 1 1 1 0\n0 1 1 1 1 1 0\n1 1 1 1 1 1 0\n1 0 0 0 1 1 0\n9 7\n0 0 1 0 0 0 0 0 0\n0 0 1 1 0 0 0 0 0\n1 1 1 1 1 1 1 1 0\n1 1 1 1 1 1 1 1 0\n0 1 1 1 1 1 1 1 1\n0 0 0 1 1 0 0 0 0\n0 0 0 1 0 0 0 0 0\n9 7\n0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0\n1 1 1 1 1 1 1 1 0\n1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1\n0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0\n7 6\n1 1 1 1 1 1 1\n1 1 1 1 1 1 1\n1 1 1 1 1 1 0\n1 1 1 1 1 1 0\n0 1 1 1 1 1 0\n0 1 1 1 1 1 0\n10 10\n0 1 1 1 1 1 1 1 1 1\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0\n1 1 1 0 0 0 0 0 1 0\n1 1 1 1 1 1 1 1 1 0\n0 0\n output: YES\nNO\nYES\nYES\nYES\nNO\nNO\nYES\n\n" }, { "title": "Problem A: Next Mayor", "content": "One of the oddest traditions of the town of Gameston may be that even\nthe town mayor of the next term is chosen according to the result of a game.\nWhen the expiration of the term of the mayor approaches, at least\nthree candidates, including the mayor of the time, play a game of\npebbles, and the winner will be the next mayor.\n\nThe rule of the game of pebbles is as follows.\nIn what follows, n is the number of participating candidates.\n
\n
Requisites\n
A round table, a bowl, and plenty of pebbles.\n
Start of the Game\n
\n\nA number of pebbles are put into the bowl;\nthe number is decided by the Administration Commission using\nsome secret stochastic process.\nAll the candidates, numbered from 0 to n-1 sit around the round table, \nin a counterclockwise order. Initially, the bowl is handed to the \nserving mayor at the time, who is numbered 0.\n
Game Steps\n
\nWhen a candidate is handed the bowl and if any pebbles are in it,\none pebble is taken out of the bowl and is\nkept, together with those already at hand, if any.\nIf no pebbles are left in the bowl, the candidate puts\nall the kept pebbles, if any, into the bowl. Then, in either case, the bowl is\nhanded to the next candidate to the right.\n\nThis step is repeated until the winner is decided.\n
End of the Game\n
\nWhen a candidate takes the last pebble in the bowl, and no other\ncandidates keep any pebbles, the game ends and that candidate with all\nthe pebbles is the winner.\n
\nA math teacher of Gameston High, through his analysis, concluded that this game will always end within a finite number of steps, although the number of required steps can be very large.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is a line\ncontaining two integers n and p separated by a single\nspace. The integer n is the number of the candidates including\nthe current mayor, and the integer p is the total number of the\npebbles initially put in the bowl. You may assume 3 <= n <= 50\nand 2 <= p <= 50.\n\nWith the settings given in the input datasets, the game will end within 1000000 (one million) steps.\n\nThe end of the input is indicated by a line\ncontaining two zeros separated by a single space.", "output": "The output should be composed of lines corresponding to input datasets\nin the same order, each line of which containing the candidate number\nof the winner.\nNo other characters should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n3 3\n3 50\n10 29\n31 32\n50 2\n50 50\n0 0\n output: 1\n0\n1\n5\n30\n1\n13"], "Pid": "p00740", "ProblemText": "Task Description: One of the oddest traditions of the town of Gameston may be that even\nthe town mayor of the next term is chosen according to the result of a game.\nWhen the expiration of the term of the mayor approaches, at least\nthree candidates, including the mayor of the time, play a game of\npebbles, and the winner will be the next mayor.\n\nThe rule of the game of pebbles is as follows.\nIn what follows, n is the number of participating candidates.\n
\n
Requisites\n
A round table, a bowl, and plenty of pebbles.\n
Start of the Game\n
\n\nA number of pebbles are put into the bowl;\nthe number is decided by the Administration Commission using\nsome secret stochastic process.\nAll the candidates, numbered from 0 to n-1 sit around the round table, \nin a counterclockwise order. Initially, the bowl is handed to the \nserving mayor at the time, who is numbered 0.\n
Game Steps\n
\nWhen a candidate is handed the bowl and if any pebbles are in it,\none pebble is taken out of the bowl and is\nkept, together with those already at hand, if any.\nIf no pebbles are left in the bowl, the candidate puts\nall the kept pebbles, if any, into the bowl. Then, in either case, the bowl is\nhanded to the next candidate to the right.\n\nThis step is repeated until the winner is decided.\n
End of the Game\n
\nWhen a candidate takes the last pebble in the bowl, and no other\ncandidates keep any pebbles, the game ends and that candidate with all\nthe pebbles is the winner.\n
\nA math teacher of Gameston High, through his analysis, concluded that this game will always end within a finite number of steps, although the number of required steps can be very large.\nTask Input: The input is a sequence of datasets. Each dataset is a line\ncontaining two integers n and p separated by a single\nspace. The integer n is the number of the candidates including\nthe current mayor, and the integer p is the total number of the\npebbles initially put in the bowl. You may assume 3 <= n <= 50\nand 2 <= p <= 50.\n\nWith the settings given in the input datasets, the game will end within 1000000 (one million) steps.\n\nThe end of the input is indicated by a line\ncontaining two zeros separated by a single space.\nTask Output: The output should be composed of lines corresponding to input datasets\nin the same order, each line of which containing the candidate number\nof the winner.\nNo other characters should appear in the output.\nTask Samples: input: 3 2\n3 3\n3 50\n10 29\n31 32\n50 2\n50 50\n0 0\n output: 1\n0\n1\n5\n30\n1\n13\n\n" }, { "title": "Problem B: How Many Islands?", "content": "You are given a marine area map that is a mesh of squares, each\nrepresenting either a land or sea area.\nFigure B-1 is an example of a map.\n\nFigure B-1: A marine area map \nYou can walk from a square land area to another if they are horizontally,\nvertically, or diagonally adjacent to each other on the map.\nTwo areas are on the same island if and only if you can\nwalk from one to the other possibly through other land areas.\nThe marine area on the map is surrounded by the sea and therefore you\ncannot go outside of the area on foot.\n\nYou are requested to write a program that reads the map and counts the\nnumber of islands on it. \nFor instance, the map in Figure B-1 includes three islands.", "constraint": "", "input": "The input consists of a series of datasets, each being in the following format.\n\nw h\nc_1,1 c_1,2 . . . c_1, w\nc_2,1 c_2,2 . . . c_2, w\n. . . \nc_h, 1 c_h, 2 . . . c_h, w\n\nw and h are positive integers no more than 50 that\nrepresent the width and the height of the given map, respectively.\nIn other words, the map consists of w*h squares of the same size.\nw and h are separated by a single space.\nc_i, j is either 0 or 1 and delimited by a single space.\nIf c_i, j = 0, the square that is the i-th from\nthe left and j-th from the top on the map represents a sea\narea.\nOtherwise, that is, if c_i, j = 1, it represents a land area.\nThe end of the input is indicated by a line containing two zeros\nseparated by a single space.", "output": "For each dataset, output the number of the islands in a line.\nNo extra characters should occur in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 1\n0\n2 2\n0 1\n1 0\n3 2\n1 1 1\n1 1 1\n5 4\n1 0 1 0 0\n1 0 0 0 0\n1 0 1 0 1\n1 0 0 1 0\n5 4\n1 1 1 0 1\n1 0 1 0 1\n1 0 1 0 1\n1 0 1 1 1\n5 5\n1 0 1 0 1\n0 0 0 0 0\n1 0 1 0 1\n0 0 0 0 0\n1 0 1 0 1\n0 0\n output: 0\n1\n1\n3\n1\n9"], "Pid": "p00741", "ProblemText": "Task Description: You are given a marine area map that is a mesh of squares, each\nrepresenting either a land or sea area.\nFigure B-1 is an example of a map.\n\nFigure B-1: A marine area map \nYou can walk from a square land area to another if they are horizontally,\nvertically, or diagonally adjacent to each other on the map.\nTwo areas are on the same island if and only if you can\nwalk from one to the other possibly through other land areas.\nThe marine area on the map is surrounded by the sea and therefore you\ncannot go outside of the area on foot.\n\nYou are requested to write a program that reads the map and counts the\nnumber of islands on it. \nFor instance, the map in Figure B-1 includes three islands.\nTask Input: The input consists of a series of datasets, each being in the following format.\n\nw h\nc_1,1 c_1,2 . . . c_1, w\nc_2,1 c_2,2 . . . c_2, w\n. . . \nc_h, 1 c_h, 2 . . . c_h, w\n\nw and h are positive integers no more than 50 that\nrepresent the width and the height of the given map, respectively.\nIn other words, the map consists of w*h squares of the same size.\nw and h are separated by a single space.\nc_i, j is either 0 or 1 and delimited by a single space.\nIf c_i, j = 0, the square that is the i-th from\nthe left and j-th from the top on the map represents a sea\narea.\nOtherwise, that is, if c_i, j = 1, it represents a land area.\nThe end of the input is indicated by a line containing two zeros\nseparated by a single space.\nTask Output: For each dataset, output the number of the islands in a line.\nNo extra characters should occur in the output.\nTask Samples: input: 1 1\n0\n2 2\n0 1\n1 0\n3 2\n1 1 1\n1 1 1\n5 4\n1 0 1 0 0\n1 0 0 0 0\n1 0 1 0 1\n1 0 0 1 0\n5 4\n1 1 1 0 1\n1 0 1 0 1\n1 0 1 0 1\n1 0 1 1 1\n5 5\n1 0 1 0 1\n0 0 0 0 0\n1 0 1 0 1\n0 0 0 0 0\n1 0 1 0 1\n0 0\n output: 0\n1\n1\n3\n1\n9\n\n" }, { "title": "Problem C: Verbal Arithmetic", "content": "Let's think about verbal arithmetic. \n\nThe material of this puzzle is a summation\nof non-negative integers represented in a decimal format,\nfor example, as follows.\n\n 905 + 125 = 1030\n\nIn verbal arithmetic, every digit appearing in the equation is masked with an alphabetic character. A problem which has the above equation as one of its answers, for example, is the following.\n\n ACM + IBM = ICPC\n\nSolving this puzzle means finding possible digit assignments\nto the alphabetic characters in the verbal equation.\n\nThe rules of this puzzle are the following.\nEach integer in the equation is expressed in terms of one or more\ndigits '0'-'9', but all the digits are masked with some alphabetic\ncharacters 'A'-'Z'.\n\nThe same alphabetic character appearing in multiple places \nof the equation masks the same digit.\nMoreover, all appearances of the same digit are masked with a single\nalphabetic character.\nThat is, different alphabetic characters mean different digits.\n\nThe most significant digit must not be '0',\nexcept when a zero is expressed as a single digit '0'.\nThat is, expressing numbers as \"00\" or \"0123\" is not permitted.\n\nThere are 4 different digit assignments for the verbal equation above\nas shown in the following table.\n
10000+1+(0-10) \noverflow, not 9991 \n\n \n(10*i+100)*(101+20*i) \n9900+3010i , not overflow \n\n \n4000000-4000000 \noverflow, not 0 \n\n \nNote that the law of associativity does not necessarily hold in this\nproblem. For example, in the first example, \noverflow is detected by interpreting\nthe expression as (10000+1)+(0-10) following the binding rules,\nwhereas overflow could not be detected \nif you interpreted it as 10000+(1+(0-10)).\nMoreover, overflow detection should take place for resulting value of each\noperation. In the second example, a value which exceeds 10000 appears\nin the calculation process of one multiplication \nif you use the mathematical rule\n(a+b i)(c+d i)=(ac-bd)+(ad+bc)i\n .\nBut the yielded result 9900+3010i does not contain any number\nwhich exceeds 10000 and, therefore, overflow should not be reported.\nTask Input: A sequence of lines each of which contains an expression is given as\ninput. Each line consists of less than 100 characters and does not contain\nany blank spaces. You may assume that all expressions given in the sequence\nare syntactically correct.\nTask Output: Your program should produce output for each expression line by line.\nIf overflow is detected, output should be \na character string \"overflow\".\nOtherwise, output should be the resulting value of calculation\nin the following fashion.\n0 , if the result is 0+0i.\n -123 , if the result is -123+0i.\n 45i , if the result is 0+45i.\n 3+1i , if the result is 3+i.\n 123-45i , if the result is 123-45i.\n\nOutput should not contain any blanks, surplus 0,\n+, or -.\nTask Samples: input: (1-10*i)+00007+(3+10*i)\n3+4*i*(4+10*i)\n(102+10*i)*(99+10*i)\n2*i+3+9999*i+4\n output: 11\n-37+16i\n9998+2010i\noverflow\n\n" }, { "title": "Board Arrangements for Concentration Games", "content": "You have to organize a wedding party. The program of the\nparty will include a concentration game played by the\nbride and groom. The arrangement of the concentration game\nshould be easy since this game will be played to make the\nparty fun. We have a 4x4 board and 8 pairs of cards (denoted by `A' to `H')\nfor the concentration game:\n +---+---+---+---+ \n | | | | | A A B B\n +---+---+---+---+ C C D D\n | | | | | E E F F\n +---+---+---+---+ G G H H\n | | | | |\n +---+---+---+---+ \n | | | | |\n +---+---+---+---+ \nTo start the game, it is necessary to arrange all 16 cards\nface down on the board. For example:\n +---+---+---+---+ \n | A | B | A | B |\n +---+---+---+---+\n | C | D | C | D |\n +---+---+---+---+\n | E | F | G | H |\n +---+---+---+---+ \n | G | H | E | F |\n +---+---+---+---+ \nThe purpose of the concentration game is to expose as many\ncards as possible by repeatedly performing the following\nprocedure: (1) expose two cards, (2) keep them open if they\nmatch or replace them face down if they do not. Since the arrangements should be simple, every pair of cards\non the board must obey the following condition: the\nrelative position of one card to the other card of the pair must be\none of 4 given relative positions.\nThe 4 relative positions are different from one another and\nthey are selected from the following 24 candidates:\n (1,0), (2,0), (3,0),\n (-3,1), (-2,1), (-1,1), (0,1), (1,1), (2,1), (3,1),\n (-3,2), (-2,2), (-1,2), (0,2), (1,2), (2,2), (3,2),\n (-3,3), (-2,3), (-1,3), (0,3), (1,3), (2,3), (3,3).\nYour job in this problem is to write a program that\nreports the total number of board arrangements which satisfy\nthe given constraint. For example, if relative positions\n(-2,1), (-1,1), (1,1), (1,2) are given, the total number\nof board arrangements is two, where the following two\narrangements satisfy the given constraint:\n X0 X1 X2 X3 X0 X1 X2 X3\n +---+---+---+---+ +---+---+---+---+ \n Y0 | A | B | C | D | Y0 | A | B | C | D | \n +---+---+---+---+ +---+---+---+---+ \n Y1 | B | A | D | C | Y1 | B | D | E | C | \n +---+---+---+---+ +---+---+---+---+ \n Y2 | E | F | G | H | Y2 | F | A | G | H | \n +---+---+---+---+ +---+---+---+---+ \n Y3 | F | E | H | G | Y3 | G | F | H | E | \n +---+---+---+---+ +---+---+---+---+ \n the relative positions: the relative positions:\n A: (1,1), B: (-1,1) A: (1,2), B: (-1,1)\n C: (1,1), D: (-1,1) C: (1,1), D: (-2,1)\n E: (1,1), F: (-1,1) E: (1,2), F: ( 1,1)\n G: (1,1), H: (-1,1) G: (-2,1), H: (-1,1)\nArrangements of the same pattern should be counted only once. Two\nboard arrangements are said to have the same pattern if they are\nobtained from each other by repeatedly making any two pairs exchange\ntheir positions. For example, the following two arrangements have the\nsame pattern:\n X0 X1 X2 X3 X0 X1 X2 X3\n +---+---+---+---+ +---+---+---+---+ \n Y0 | H | G | F | E | Y0 | A | B | C | D | \n +---+---+---+---+ +---+---+---+---+ \n Y1 | G | E | D | F | Y1 | B | D | E | C | \n +---+---+---+---+ +---+---+---+---+ \n Y2 | C | H | B | A | Y2 | F | A | G | H | \n +---+---+---+---+ +---+---+---+---+ \n Y3 | B | C | A | D | Y3 | G | F | H | E | \n +---+---+---+---+ +---+---+---+---+", "constraint": "", "input": "The input contains multiple data sets, each representing 4 relative \npositions. A data set is given as a line in the following format. \n x_1 y_1 \n x_2 y_2 \n x_3 y_3 \n x_4 y_4 \n\n The i-th relative position is given by (x_i, y_i).\nYou may assume that the given relative positions are different from one \nanother and each of them is one of the 24 candidates. The end of input is indicated by the line which contains\na single number greater than 4.", "output": "For each data set, your program should output the total number\nof board arrangements (or more precisely, the total number of \npatterns). Each number should be printed in one line. Since your result is \nchecked by an automatic grading program,\nyou should not insert any extra characters nor lines on the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: -2 1 -1 1 1 1 1 2\n1 0 2 1 2 2 3 3\n5\n output: \n2\n15"], "Pid": "p00685", "ProblemText": "Task Description: You have to organize a wedding party. The program of the\nparty will include a concentration game played by the\nbride and groom. The arrangement of the concentration game\nshould be easy since this game will be played to make the\nparty fun. We have a 4x4 board and 8 pairs of cards (denoted by `A' to `H')\nfor the concentration game:\n +---+---+---+---+ \n | | | | | A A B B\n +---+---+---+---+ C C D D\n | | | | | E E F F\n +---+---+---+---+ G G H H\n | | | | |\n +---+---+---+---+ \n | | | | |\n +---+---+---+---+ \nTo start the game, it is necessary to arrange all 16 cards\nface down on the board. For example:\n +---+---+---+---+ \n | A | B | A | B |\n +---+---+---+---+\n | C | D | C | D |\n +---+---+---+---+\n | E | F | G | H |\n +---+---+---+---+ \n | G | H | E | F |\n +---+---+---+---+ \nThe purpose of the concentration game is to expose as many\ncards as possible by repeatedly performing the following\nprocedure: (1) expose two cards, (2) keep them open if they\nmatch or replace them face down if they do not. Since the arrangements should be simple, every pair of cards\non the board must obey the following condition: the\nrelative position of one card to the other card of the pair must be\none of 4 given relative positions.\nThe 4 relative positions are different from one another and\nthey are selected from the following 24 candidates:\n (1,0), (2,0), (3,0),\n (-3,1), (-2,1), (-1,1), (0,1), (1,1), (2,1), (3,1),\n (-3,2), (-2,2), (-1,2), (0,2), (1,2), (2,2), (3,2),\n (-3,3), (-2,3), (-1,3), (0,3), (1,3), (2,3), (3,3).\nYour job in this problem is to write a program that\nreports the total number of board arrangements which satisfy\nthe given constraint. For example, if relative positions\n(-2,1), (-1,1), (1,1), (1,2) are given, the total number\nof board arrangements is two, where the following two\narrangements satisfy the given constraint:\n X0 X1 X2 X3 X0 X1 X2 X3\n +---+---+---+---+ +---+---+---+---+ \n Y0 | A | B | C | D | Y0 | A | B | C | D | \n +---+---+---+---+ +---+---+---+---+ \n Y1 | B | A | D | C | Y1 | B | D | E | C | \n +---+---+---+---+ +---+---+---+---+ \n Y2 | E | F | G | H | Y2 | F | A | G | H | \n +---+---+---+---+ +---+---+---+---+ \n Y3 | F | E | H | G | Y3 | G | F | H | E | \n +---+---+---+---+ +---+---+---+---+ \n the relative positions: the relative positions:\n A: (1,1), B: (-1,1) A: (1,2), B: (-1,1)\n C: (1,1), D: (-1,1) C: (1,1), D: (-2,1)\n E: (1,1), F: (-1,1) E: (1,2), F: ( 1,1)\n G: (1,1), H: (-1,1) G: (-2,1), H: (-1,1)\nArrangements of the same pattern should be counted only once. Two\nboard arrangements are said to have the same pattern if they are\nobtained from each other by repeatedly making any two pairs exchange\ntheir positions. For example, the following two arrangements have the\nsame pattern:\n X0 X1 X2 X3 X0 X1 X2 X3\n +---+---+---+---+ +---+---+---+---+ \n Y0 | H | G | F | E | Y0 | A | B | C | D | \n +---+---+---+---+ +---+---+---+---+ \n Y1 | G | E | D | F | Y1 | B | D | E | C | \n +---+---+---+---+ +---+---+---+---+ \n Y2 | C | H | B | A | Y2 | F | A | G | H | \n +---+---+---+---+ +---+---+---+---+ \n Y3 | B | C | A | D | Y3 | G | F | H | E | \n +---+---+---+---+ +---+---+---+---+\nTask Input: The input contains multiple data sets, each representing 4 relative \npositions. A data set is given as a line in the following format. \n x_1 y_1 \n x_2 y_2 \n x_3 y_3 \n x_4 y_4 \n\n The i-th relative position is given by (x_i, y_i).\nYou may assume that the given relative positions are different from one \nanother and each of them is one of the 24 candidates. The end of input is indicated by the line which contains\na single number greater than 4.\nTask Output: For each data set, your program should output the total number\nof board arrangements (or more precisely, the total number of \npatterns). Each number should be printed in one line. Since your result is \nchecked by an automatic grading program,\nyou should not insert any extra characters nor lines on the output.\nTask Samples: input: -2 1 -1 1 1 1 1 2\n1 0 2 1 2 2 3 3\n5\n output: \n2\n15\n\n" }, { "title": "Where's Your Robot?", "content": "You have full control over a robot that walks around in a rectangular\nfield paved with square tiles like a chessboard. There are m\ncolumns of tiles from west to east, and n rows of tiles from\nsouth to north (1 <= m, n <= 100). Each tile is given a pair\nof coordinates, such as (i, j), where 1 <= i <= m\nand 1 <= j <= n. \n\nYour robot is initially on the center of the tile at (1,1), that is,\none at the southwest corner of the field, facing straight north. It\ncan move either forward or backward, or can change its facing\ndirection by ninety degrees at a time, according to a command you give\nto it, which is one of the following.\n\nFORWARD k\nGo forward by k tiles to its facing direction (1 <= k < 100).\n\nBACKWARD k\nGo backward by k tiles, without changing its facing direction\n(1 <= k < 100). \n\nRIGHT\nTurn to the right by ninety degrees.\n\nLEFT\nTurn to the left by ninety degrees.\n\nSTOP\nStop.\nWhile executing either a \"FORWARD\" or a\n\"BACKWARD\" command, the robot may bump against the\nwall surrounding the field. If that happens, the robot gives up the\ncommand execution there and stands at the center of the tile right in\nfront of the wall, without changing its direction.\nAfter finishing or giving up execution of a given command, your robot\nwill stand by for your next command.", "constraint": "", "input": "The input consists of one or more command sequences. Each input line\nhas at most fifty characters.\nThe first line of a command sequence contains two integer numbers\ntelling the size of the field, the first number being the number of\ncolumns and the second being the number of rows. There might be white\nspaces (blanks and/or tabs) before, in between, or after the two numbers.\nTwo zeros as field size indicates the end of input.\nEach of the following lines of a command sequence contains a command\nto the robot. When a command has an argument, one or more white\nspaces are put between them. White spaces may also appear before and\nafter the command and/or its argument.\nA command sequence is terminated by a line containing a\n\"STOP\" command. The next command sequence, if any,\nstarts from the next line.", "output": "The output should be one line for each command sequence in the input.\nIt should contain two numbers i and j of the coordinate pair\n(i, j), in this order, of the tile on which your robot stops.\nTwo numbers should be separated by one white spaces.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 5\nFORWARD 3\nRIGHT\nFORWARD 5\nLEFT\nBACKWARD 2\nSTOP\n3 1\nFORWARD 2\nSTOP\n0 0\n output: 6 2\n1 1"], "Pid": "p00686", "ProblemText": "Task Description: You have full control over a robot that walks around in a rectangular\nfield paved with square tiles like a chessboard. There are m\ncolumns of tiles from west to east, and n rows of tiles from\nsouth to north (1 <= m, n <= 100). Each tile is given a pair\nof coordinates, such as (i, j), where 1 <= i <= m\nand 1 <= j <= n. \n\nYour robot is initially on the center of the tile at (1,1), that is,\none at the southwest corner of the field, facing straight north. It\ncan move either forward or backward, or can change its facing\ndirection by ninety degrees at a time, according to a command you give\nto it, which is one of the following.\n\nFORWARD k\nGo forward by k tiles to its facing direction (1 <= k < 100).\n\nBACKWARD k\nGo backward by k tiles, without changing its facing direction\n(1 <= k < 100). \n\nRIGHT\nTurn to the right by ninety degrees.\n\nLEFT\nTurn to the left by ninety degrees.\n\nSTOP\nStop.\nWhile executing either a \"FORWARD\" or a\n\"BACKWARD\" command, the robot may bump against the\nwall surrounding the field. If that happens, the robot gives up the\ncommand execution there and stands at the center of the tile right in\nfront of the wall, without changing its direction.\nAfter finishing or giving up execution of a given command, your robot\nwill stand by for your next command.\nTask Input: The input consists of one or more command sequences. Each input line\nhas at most fifty characters.\nThe first line of a command sequence contains two integer numbers\ntelling the size of the field, the first number being the number of\ncolumns and the second being the number of rows. There might be white\nspaces (blanks and/or tabs) before, in between, or after the two numbers.\nTwo zeros as field size indicates the end of input.\nEach of the following lines of a command sequence contains a command\nto the robot. When a command has an argument, one or more white\nspaces are put between them. White spaces may also appear before and\nafter the command and/or its argument.\nA command sequence is terminated by a line containing a\n\"STOP\" command. The next command sequence, if any,\nstarts from the next line.\nTask Output: The output should be one line for each command sequence in the input.\nIt should contain two numbers i and j of the coordinate pair\n(i, j), in this order, of the tile on which your robot stops.\nTwo numbers should be separated by one white spaces.\nTask Samples: input: 6 5\nFORWARD 3\nRIGHT\nFORWARD 5\nLEFT\nBACKWARD 2\nSTOP\n3 1\nFORWARD 2\nSTOP\n0 0\n output: 6 2\n1 1\n\n" }, { "title": "Unable Count", "content": "I would, if I could, \n If I couldn't how could I? \n I couldn't, without I could, could I? \n Could you, without you could, could ye? \n Could ye? could ye? \n Could you, without you could, could ye? It is true, as this old rhyme says, that we can only DO what\nwe can DO and we cannot DO what we cannot DO. Changing some of\nDOs with COUNTs, we have another statement that we can only COUNT\nwhat we can DO and we cannot COUNT what we cannot DO, which looks\nrather false. We could count what we could do as well as we could\ncount what we couldn't do. Couldn't we, if we confine ourselves\nto finite issues? Surely we can count, in principle, both what we can do and\nwhat we cannot do, if the object space is finite. Yet, sometimes\nwe cannot count in practice what we can do or what we cannot do.\nHere, you are challenged, in a set of all positive integers up\nto (and including) a given bound n, to count\nall the integers that cannot be represented by a formula of\nthe form a*i+b*j, where a and\nb are given positive integers and i and j\nare variables ranging over non-negative integers. You are requested\nto report only the result of the count, i. e. how many integers\nare not representable.\nFor example, given n = 7, a = 2, b = 5,\nyou should answer 2, since 1 and 3 cannot be represented in a\nspecified form, and the other five numbers are representable as follows:\n 2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,\n 6 = 2*3 + 5*0, 7 = 2*1 + 5*1.", "constraint": "", "input": "The input is a sequence of lines. Each line consists of three integers,\nn, a and b, in this order, separated by a\nspace. The integers n, a and b are\nall positive and at most one million, except those in the last\nline. The last line consists of three zeros.", "output": "For each input line except the last one, your program should\nwrite out a line that contains only the result of the count.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 2 3\n10 2 5\n100 5 25\n0 0 0\n output: 1\n2\n80"], "Pid": "p00687", "ProblemText": "Task Description: I would, if I could, \n If I couldn't how could I? \n I couldn't, without I could, could I? \n Could you, without you could, could ye? \n Could ye? could ye? \n Could you, without you could, could ye? It is true, as this old rhyme says, that we can only DO what\nwe can DO and we cannot DO what we cannot DO. Changing some of\nDOs with COUNTs, we have another statement that we can only COUNT\nwhat we can DO and we cannot COUNT what we cannot DO, which looks\nrather false. We could count what we could do as well as we could\ncount what we couldn't do. Couldn't we, if we confine ourselves\nto finite issues? Surely we can count, in principle, both what we can do and\nwhat we cannot do, if the object space is finite. Yet, sometimes\nwe cannot count in practice what we can do or what we cannot do.\nHere, you are challenged, in a set of all positive integers up\nto (and including) a given bound n, to count\nall the integers that cannot be represented by a formula of\nthe form a*i+b*j, where a and\nb are given positive integers and i and j\nare variables ranging over non-negative integers. You are requested\nto report only the result of the count, i. e. how many integers\nare not representable.\nFor example, given n = 7, a = 2, b = 5,\nyou should answer 2, since 1 and 3 cannot be represented in a\nspecified form, and the other five numbers are representable as follows:\n 2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,\n 6 = 2*3 + 5*0, 7 = 2*1 + 5*1.\nTask Input: The input is a sequence of lines. Each line consists of three integers,\nn, a and b, in this order, separated by a\nspace. The integers n, a and b are\nall positive and at most one million, except those in the last\nline. The last line consists of three zeros.\nTask Output: For each input line except the last one, your program should\nwrite out a line that contains only the result of the count.\nTask Samples: input: 10 2 3\n10 2 5\n100 5 25\n0 0 0\n output: 1\n2\n80\n\n" }, { "title": "Factorization of Quadratic Formula", "content": "As the first step in algebra, students learn quadratic formulas and\ntheir factorization. Often, the factorization is a severe burden\nfor them. A large number of students cannot master the factorization;\nsuch students cannot be aware of the elegance of advanced algebra.\nIt might be the case that the factorization increases the number of people\nwho hate mathematics. Your job here is to write a program which helps students of\nan algebra course. Given a quadratic formula, your program should report\nhow the formula can be factorized into two linear formulas.\nAll coefficients of quadratic formulas and those of resultant\nlinear formulas are integers in this problem. The coefficients a, b and c of a quadratic formula\nax^2 + bx + c are given.\nThe values of a, b and c are integers,\nand their absolute values do not exceed 10000.\nFrom these values, your program is requested to find four integers\np, q, r and s, such that\nax^2 + bx + c =\n(px + q)(rx + s). Since we are considering integer coefficients only, it is not\nalways possible to factorize a quadratic formula into linear formulas.\nIf the factorization of the given formula is impossible,\nyour program should report that fact.", "constraint": "", "input": "The input is a sequence of lines, each representing\na quadratic formula.\nAn input line is given in the following format. \na b c\nEach of a, b and c is an integer.\nThey satisfy the following inequalities.\n\n 0 < a <= 10000\n\n -10000 <= b <= 10000\n\n -10000 <= c <= 10000\n\n

The greatest common divisor of a, b and c is 1.\nThat is, there is no integer k, greater than 1,\nsuch that all of a, b and c are divisible by k.\nThe end of input is indicated by a line consisting of three 0's.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5 2\n1 1 1\n10 -7 0\n1 0 -3\n0 0 0\n output: 2 1 1 2\nImpossible\n10 -7 1 0\nImpossible"], "output": "For each input line, your program should output the four integers\np, q, r and s in a line, if they exist.\nThese integers should be output in this order, separated by\none or more white spaces.\nIf the factorization is impossible, your program should output a line\nwhich contains the string \"Impossible\" only. The following relations should hold between the values\nof the four coefficients. \np > 0\n\nr > 0\n\n (p > r) or (p = r and q >= s)\nThese relations, together with the fact that the greatest common\ndivisor of a, b and c is 1,\nassure the uniqueness of the solution.\nIf you find a way to factorize the formula, it is not necessary\nto seek another way to factorize it.", "Pid": "p00688", "ProblemText": "Task Description: As the first step in algebra, students learn quadratic formulas and\ntheir factorization. Often, the factorization is a severe burden\nfor them. A large number of students cannot master the factorization;\nsuch students cannot be aware of the elegance of advanced algebra.\nIt might be the case that the factorization increases the number of people\nwho hate mathematics. Your job here is to write a program which helps students of\nan algebra course. Given a quadratic formula, your program should report\nhow the formula can be factorized into two linear formulas.\nAll coefficients of quadratic formulas and those of resultant\nlinear formulas are integers in this problem. The coefficients a, b and c of a quadratic formula\nax^2 + bx + c are given.\nThe values of a, b and c are integers,\nand their absolute values do not exceed 10000.\nFrom these values, your program is requested to find four integers\np, q, r and s, such that\nax^2 + bx + c =\n(px + q)(rx + s). Since we are considering integer coefficients only, it is not\nalways possible to factorize a quadratic formula into linear formulas.\nIf the factorization of the given formula is impossible,\nyour program should report that fact.\nTask Input: The input is a sequence of lines, each representing\na quadratic formula.\nAn input line is given in the following format. \na b c\nEach of a, b and c is an integer.\nThey satisfy the following inequalities.\n\n 0 < a <= 10000\n\n -10000 <= b <= 10000\n\n -10000 <= c <= 10000\n\n

The greatest common divisor of a, b and c is 1.\nThat is, there is no integer k, greater than 1,\nsuch that all of a, b and c are divisible by k.\nThe end of input is indicated by a line consisting of three 0's.\nTask Output: For each input line, your program should output the four integers\np, q, r and s in a line, if they exist.\nThese integers should be output in this order, separated by\none or more white spaces.\nIf the factorization is impossible, your program should output a line\nwhich contains the string \"Impossible\" only. The following relations should hold between the values\nof the four coefficients. \np > 0\n\nr > 0\n\n (p > r) or (p = r and q >= s)\nThese relations, together with the fact that the greatest common\ndivisor of a, b and c is 1,\nassure the uniqueness of the solution.\nIf you find a way to factorize the formula, it is not necessary\nto seek another way to factorize it.\nTask Samples: input: 2 5 2\n1 1 1\n10 -7 0\n1 0 -3\n0 0 0\n output: 2 1 1 2\nImpossible\n10 -7 1 0\nImpossible\n\n" }, { "title": "Spiral Footrace", "content": "Let us enjoy extraordinary footraces at an athletic field.\nBefore starting the race, small flags representing checkpoints are set up\nat random on the field. Every runner has to pass all the checkpoints one by\none in the spiral order specified below.\nThe starting point is the southwest corner of the athletic field. \nAt the starting point, runners are facing north.\nDuring the race, they run clockwise in a spiral passing\nevery checkpoint as illustrated in the following figure.\nWhen moving from one flag to the next, they take a straight path.\nThis means that the course of a race is always piecewise linear. \n\nUpon arriving at some flag, a runner has to determine the next flag\namong those that are not yet visited.\nThat flag shall be the one at the smallest angle to the right of the direction\nthat the runner is facing. When more than two flags are on the same straight\nline, the runner visits the nearest flag first.\nThe goal position is the place of the last visited flag.\nYour job is to write a program that calculates the length of the course from\nthe starting point to the goal, supposing that the course consists of\nline segments connected by flags.\nThe position of each flag is given by a coordinate pair\n(x_i, y_i), which is limited\nto the first quadrant. The starting point is fixed to the origin (0,0) where a\nflag is always set up.", "constraint": "", "input": "The input contains multiple data sets, each representing a collection of\nflag positions for a footrace. A data set is given in the following\nformat. \n\n n\n\nx_1 y_1\n\nx_2 y_2\n\n . . .\n\nx_n y_n\n\nHere, n is the number of flag positions (1 <= n <= 400).\nThe position of the i-th flag is given by\n(x_i, y_i), where \nx_i and y_i are integers\nin meter between 0 and 500 inclusive. \nThere may be white spaces (blanks and/or tabs) before, in between, or after\nx_i and y_i.\nOnce a certain\ncoordinate pair (x_i, y_i) is given,\nthe same one will not appear later in the data set, and the origin (0,0)\nwill not appear either.\nA data set beginning with n = 0 indicates end of the input.", "output": "For each data set, your program should output the length of the running course\nin meter. Each length should appear on a separate line, with\none digit to the right of the decimal point, after rounding it to one\ndecimal place.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8\n 60 70\n 20 40\n 50 50\n 70 10\n 10 70\n 80 90\n 70 50\n 100 50\n5\n 60 50\n 0 80\n 60 20\n 10 20\n 60 80\n0\n output: 388.9\n250.0"], "Pid": "p00689", "ProblemText": "Task Description: Let us enjoy extraordinary footraces at an athletic field.\nBefore starting the race, small flags representing checkpoints are set up\nat random on the field. Every runner has to pass all the checkpoints one by\none in the spiral order specified below.\nThe starting point is the southwest corner of the athletic field. \nAt the starting point, runners are facing north.\nDuring the race, they run clockwise in a spiral passing\nevery checkpoint as illustrated in the following figure.\nWhen moving from one flag to the next, they take a straight path.\nThis means that the course of a race is always piecewise linear. \n\nUpon arriving at some flag, a runner has to determine the next flag\namong those that are not yet visited.\nThat flag shall be the one at the smallest angle to the right of the direction\nthat the runner is facing. When more than two flags are on the same straight\nline, the runner visits the nearest flag first.\nThe goal position is the place of the last visited flag.\nYour job is to write a program that calculates the length of the course from\nthe starting point to the goal, supposing that the course consists of\nline segments connected by flags.\nThe position of each flag is given by a coordinate pair\n(x_i, y_i), which is limited\nto the first quadrant. The starting point is fixed to the origin (0,0) where a\nflag is always set up.\nTask Input: The input contains multiple data sets, each representing a collection of\nflag positions for a footrace. A data set is given in the following\nformat. \n\n n\n\nx_1 y_1\n\nx_2 y_2\n\n . . .\n\nx_n y_n\n\nHere, n is the number of flag positions (1 <= n <= 400).\nThe position of the i-th flag is given by\n(x_i, y_i), where \nx_i and y_i are integers\nin meter between 0 and 500 inclusive. \nThere may be white spaces (blanks and/or tabs) before, in between, or after\nx_i and y_i.\nOnce a certain\ncoordinate pair (x_i, y_i) is given,\nthe same one will not appear later in the data set, and the origin (0,0)\nwill not appear either.\nA data set beginning with n = 0 indicates end of the input.\nTask Output: For each data set, your program should output the length of the running course\nin meter. Each length should appear on a separate line, with\none digit to the right of the decimal point, after rounding it to one\ndecimal place.\nTask Samples: input: 8\n 60 70\n 20 40\n 50 50\n 70 10\n 10 70\n 80 90\n 70 50\n 100 50\n5\n 60 50\n 0 80\n 60 20\n 10 20\n 60 80\n0\n output: 388.9\n250.0\n\n" }, { "title": "A Long Ride on a Railway", "content": "Travelling by train is fun and exciting. But more than that indeed. Young\nchallenging boys often tried to purchase the longest single tickets and to\nsingle ride the longest routes of various railway systems. Route planning was\nlike solving puzzles. However, once assisted by computers, and supplied with\nmachine readable databases, it is not any more than elaborating or hacking\non the depth-first search algorithms.\nMap of a railway system is essentially displayed in the form of a graph. (See\nthe Figures below. ) The vertices (i. e. points) correspond to stations and the\nedges (i. e. lines) correspond to direct routes between stations. The station\nnames (denoted by positive integers and shown in the upright letters in the\nFigures) and direct route distances (shown in the slanted letters) are also\ngiven.\nThe problem is to find the length of the longest path and to form the\ncorresponding list of stations on the path for each system. The longest of\nsuch paths is one that starts from one station and, after travelling many\ndirect routes as far as possible without passing any direct route more than\nonce, arrives at a station which may be the starting station or different one\nand is longer than any other sequence of direct routes. Any station may be\nvisited any number of times in travelling the path if you like.", "constraint": "", "input": "The graph of a system is defined by a set of lines of integers of the\nform:\n \n ns nl \n\n s_1,1 \n s_1,2 \n d_1 \n\n s_2,1 \n s_2,2 \n d_2 \n\n . . . \n\n s_nl, 1 \n s_nl, 2 \n d_nl \n\n \nHere 1 <= ns <= 10 is the number of stations (so, station names are 1,2,\n. . . , ns), and 1 <= nl <= 20 is the number of direct routes in this\ngraph. \ns_i, 1 and s_i, 2\n(i = 1,2, . . . , nl) are station names at the both ends of the\ni-th direct route. d_i >= 1 (i = 1,2, . . . , \nnl) is the direct route distance between two different stations\ns_i, 1 and s_i, 2. \nIt is also known that there is at most one direct route between any pair of\nstations, and all direct routes can be travelled in either directions. Each\nstation has at most four direct routes leaving from it.\nThe integers in an input line are separated by at least one white space (i. e. a\nspace character (ASCII code 32) or a tab character (ASCII code 9)), and possibly\npreceded and followed by a number of white spaces.\n\nThe whole input of this problem consists of a few number of sets each of which\nrepresents one graph (i. e. system) and the input terminates with two integer\n0's in the line of next ns and nl.", "output": "Paths may be travelled from either end; loops can be traced clockwise or\nanticlockwise. So, the station lists for the longest path for Figure A are\nmultiple like (in lexicographic order):\n2 3 4 5\n5 4 3 2\n\nFor Figure B, the station lists for the longest path are also multiple like\n(again in lexicographic order):\n6 2 5 9 6 7\n6 9 5 2 6 7\n7 6 2 5 9 6\n7 6 9 5 2 6\n\nYet there may be the case where the longest paths are not unique. (That is,\nmultiple independent paths happen to have the same longest distance. ) To make\nthe answer canonical, it is required to answer the lexicographically least\nstation list of the path(s) for each set. Thus for Figure A,\n\n2 3 4 5\n\nand for Figure B,\n\n6 2 5 9 6 7\nmust be reported as the answer station list in a single line. The integers in a\nstation list must be separated by at least one white space. The line of\nstation list must be preceded by a separate line that gives the length of the\ncorresponding path. Every output line may start with white spaces. (See output\nsample. )", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 5\n 1 3 10\n 2 3 12\n 3 4 2\n 4 5 13\n 4 6 11\n10 10 \n 1 2 11\n 2 3 25\n 2 5 81\n 2 6 82\n 4 5 58\n 5 9 68\n 6 7 80\n 6 9 67\n 8 9 44\n 9 10 21\n 0 0 \nWarning: The station names are given in the lexicographic order here. The\ncontestants should not depend on the order.\n output: 27\n2 3 4 5\n378\n6 2 5 9 6 7"], "Pid": "p00690", "ProblemText": "Task Description: Travelling by train is fun and exciting. But more than that indeed. Young\nchallenging boys often tried to purchase the longest single tickets and to\nsingle ride the longest routes of various railway systems. Route planning was\nlike solving puzzles. However, once assisted by computers, and supplied with\nmachine readable databases, it is not any more than elaborating or hacking\non the depth-first search algorithms.\nMap of a railway system is essentially displayed in the form of a graph. (See\nthe Figures below. ) The vertices (i. e. points) correspond to stations and the\nedges (i. e. lines) correspond to direct routes between stations. The station\nnames (denoted by positive integers and shown in the upright letters in the\nFigures) and direct route distances (shown in the slanted letters) are also\ngiven.\nThe problem is to find the length of the longest path and to form the\ncorresponding list of stations on the path for each system. The longest of\nsuch paths is one that starts from one station and, after travelling many\ndirect routes as far as possible without passing any direct route more than\nonce, arrives at a station which may be the starting station or different one\nand is longer than any other sequence of direct routes. Any station may be\nvisited any number of times in travelling the path if you like.\nTask Input: The graph of a system is defined by a set of lines of integers of the\nform:\n \n ns nl \n\n s_1,1 \n s_1,2 \n d_1 \n\n s_2,1 \n s_2,2 \n d_2 \n\n . . . \n\n s_nl, 1 \n s_nl, 2 \n d_nl \n\n \nHere 1 <= ns <= 10 is the number of stations (so, station names are 1,2,\n. . . , ns), and 1 <= nl <= 20 is the number of direct routes in this\ngraph. \ns_i, 1 and s_i, 2\n(i = 1,2, . . . , nl) are station names at the both ends of the\ni-th direct route. d_i >= 1 (i = 1,2, . . . , \nnl) is the direct route distance between two different stations\ns_i, 1 and s_i, 2. \nIt is also known that there is at most one direct route between any pair of\nstations, and all direct routes can be travelled in either directions. Each\nstation has at most four direct routes leaving from it.\nThe integers in an input line are separated by at least one white space (i. e. a\nspace character (ASCII code 32) or a tab character (ASCII code 9)), and possibly\npreceded and followed by a number of white spaces.\n\nThe whole input of this problem consists of a few number of sets each of which\nrepresents one graph (i. e. system) and the input terminates with two integer\n0's in the line of next ns and nl.\nTask Output: Paths may be travelled from either end; loops can be traced clockwise or\nanticlockwise. So, the station lists for the longest path for Figure A are\nmultiple like (in lexicographic order):\n2 3 4 5\n5 4 3 2\n\nFor Figure B, the station lists for the longest path are also multiple like\n(again in lexicographic order):\n6 2 5 9 6 7\n6 9 5 2 6 7\n7 6 2 5 9 6\n7 6 9 5 2 6\n\nYet there may be the case where the longest paths are not unique. (That is,\nmultiple independent paths happen to have the same longest distance. ) To make\nthe answer canonical, it is required to answer the lexicographically least\nstation list of the path(s) for each set. Thus for Figure A,\n\n2 3 4 5\n\nand for Figure B,\n\n6 2 5 9 6 7\nmust be reported as the answer station list in a single line. The integers in a\nstation list must be separated by at least one white space. The line of\nstation list must be preceded by a separate line that gives the length of the\ncorresponding path. Every output line may start with white spaces. (See output\nsample. )\nTask Samples: input: 6 5\n 1 3 10\n 2 3 12\n 3 4 2\n 4 5 13\n 4 6 11\n10 10 \n 1 2 11\n 2 3 25\n 2 5 81\n 2 6 82\n 4 5 58\n 5 9 68\n 6 7 80\n 6 9 67\n 8 9 44\n 9 10 21\n 0 0 \nWarning: The station names are given in the lexicographic order here. The\ncontestants should not depend on the order.\n output: 27\n2 3 4 5\n378\n6 2 5 9 6 7\n\n" }, { "title": "Fermat's Last Theorem", "content": "In the 17th century, Fermat wrote that he proved for any integer $n >= 3$,\nthere exist no positive integers $x$, $y$, $z$ such that\n$x^n + y^n = z^n$.\nHowever he never disclosed the proof. Later, this claim was named\nFermat's Last Theorem or Fermat's Conjecture.\n\nIf Fermat's Last Theorem holds in case of $n$, then it also holds\nin case of any multiple of $n$.\nThus it suffices to prove cases where $n$ is a prime number\nand the special case $n$ = 4.\n\nA proof for the case $n$ = 4 was found in Fermat's own memorandum.\nThe case $n$ = 3 was proved by Euler in the 18th century.\nAfter that, many mathematicians attacked Fermat's Last Theorem.\nSome of them proved some part of the theorem, which was a\npartial success.\nMany others obtained nothing.\nIt was a long history.\nFinally, Wiles proved Fermat's Last Theorem in 1994.\n\nFermat's Last Theorem implies that for any integers $n >= 3$\nand $z > 1$, it always holds that\n\n$z^n > $ max { $x^n + y^n | x > 0, y > 0, x^n + y^n <= z^n$ }.\nYour mission is to write a program that verifies this in the case\n$n$ = 3 for a given $z$. Your program should read in\ninteger numbers greater than 1, and, corresponding to each input\n$z$, it should output the following:\n\n$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 <= z^3$ }.", "constraint": "", "input": "The input is a sequence of lines each containing one positive integer\nnumber followed by a line containing a zero. You may assume that all of\nthe input integers are greater than 1 and less than 1111.", "output": "The output should consist of lines each containing a single\ninteger number. Each output integer should be\n$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 <= z^3$ }.\n\n

\nfor the corresponding input integer z.\nNo other characters should appear in any output line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n4\n2\n0\n output: 27\n10\n6"], "Pid": "p00691", "ProblemText": "Task Description: In the 17th century, Fermat wrote that he proved for any integer $n >= 3$,\nthere exist no positive integers $x$, $y$, $z$ such that\n$x^n + y^n = z^n$.\nHowever he never disclosed the proof. Later, this claim was named\nFermat's Last Theorem or Fermat's Conjecture.\n\nIf Fermat's Last Theorem holds in case of $n$, then it also holds\nin case of any multiple of $n$.\nThus it suffices to prove cases where $n$ is a prime number\nand the special case $n$ = 4.\n\nA proof for the case $n$ = 4 was found in Fermat's own memorandum.\nThe case $n$ = 3 was proved by Euler in the 18th century.\nAfter that, many mathematicians attacked Fermat's Last Theorem.\nSome of them proved some part of the theorem, which was a\npartial success.\nMany others obtained nothing.\nIt was a long history.\nFinally, Wiles proved Fermat's Last Theorem in 1994.\n\nFermat's Last Theorem implies that for any integers $n >= 3$\nand $z > 1$, it always holds that\n\n$z^n > $ max { $x^n + y^n | x > 0, y > 0, x^n + y^n <= z^n$ }.\nYour mission is to write a program that verifies this in the case\n$n$ = 3 for a given $z$. Your program should read in\ninteger numbers greater than 1, and, corresponding to each input\n$z$, it should output the following:\n\n$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 <= z^3$ }.\nTask Input: The input is a sequence of lines each containing one positive integer\nnumber followed by a line containing a zero. You may assume that all of\nthe input integers are greater than 1 and less than 1111.\nTask Output: The output should consist of lines each containing a single\ninteger number. Each output integer should be\n$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 <= z^3$ }.\n\n

\nfor the corresponding input integer z.\nNo other characters should appear in any output line.\nTask Samples: input: 6\n4\n2\n0\n output: 27\n10\n6\n\n" }, { "title": "Patience", "content": "As the proverb says,\n\n\"Patience is bitter, but its fruit is sweet. \"\n\nWriting programs within the limited time may impose \nsome patience on you, but you enjoy it and win the contest, we hope.\n\nThe word \"patience\" has the meaning of perseverance, \nbut it has another meaning in card games.\nCard games for one player are called \"patience\" in the UK\nand \"solitaire\" in the US.\nLet's play a patience in this problem.\n\nIn this card game, you use only twenty cards whose \nface values are positive and less than or equal to 5 (Ace's value\nis 1 as usual).\nJust four cards are available for each face value.\n\nAt the beginning, the twenty cards are laid\nin five rows by four columns (See Figure 1).\nAll the cards are dealt face up.\n\nAn example of the initial layout is shown in Figure 2. \n \n \n \n \n Figure 1: Initial layout \n Figure 2: Example of the initial layout \n \n\nThe purpose of the game is to remove as many cards as possible\nby repeatedly removing a pair of neighboring cards \nof the same face value.\nLet us call such a pair a matching pair.\n\nThe phrase \"a pair of neighboring cards\" means a pair of cards which are\nadjacent to each other.\nFor example, in Figure 1, C_6 is adjacent to any of\nthe following eight cards:\nC_1C_2C_3C_5C_7C_9C_10C_11C_3C_2C_6C_7\nEvery time you remove a pair, you must rearrange the remaining cards \nas compact as possible. \nTo put it concretely, each remaining card C_i \nmust be examined in turn\nin its subscript order to be shifted to the uppermost-leftmost\nspace.\n\nHow to play:\n\n Search a matching pair.\n When you find more than one pair, choose one. \nIn Figure 3, you decided to remove the pair of \nC_6 and C_9.\n Remove the pair. (See Figure 4)\n Shift the remaining cards to the uppermost-leftmost space\n(See Figure 5,6).\n Repeat the above procedure until you cannot remove any pair.\n \n Figure 3: A matching pair found \n Figure 4: Remove the matching pair \n \n \n \n \n \n Figure 5: Shift the remaining cards \n Figure 6: Rearranged layout \n \nIf you can remove all the twenty cards, you win the game \nand your penalty is 0.\nIf you leave some cards,\nyou lose the game and \nyour penalty is the number of the remaining cards.\n\nWhenever you find multiple matching pairs,\nyou must choose one pair out of them \nas in the step 2 of the above procedure.\nThe result of the game depends on these choices.\n\nYour job is to write a program which answers the minimal penalty\nfor each initial layout.", "constraint": "", "input": "The input consists of multiple card layouts.\nThe input is given in the following format.\n\n N\n Layout_0\n Layout_1\n . . .\n Layout_N-1\n\nN is the number of card layouts.\nEach card layout gives the initial state of a game.\nA card layout is given in the following format.\n\n C_0 C_1 C_2 C_3\n C_4 C_5 C_6 C_7\n C_8 C_9 C_10 C_11\n C_12 C_13 C_14 C_15\n C_16 C_17 C_18 C_19\n\nC_i (0 <= i <= 19) is an integer \nfrom 1 to 5 which represents the face value of the card.", "output": "For every initial card layout, the minimal penalty should be output,\neach in a separate line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1 4 5 2\n3 1 4 3\n5 4 2 2\n4 5 2 3\n1 1 3 5\n5 1 5 1\n4 5 3 2\n3 2 1 4\n1 4 5 3\n2 3 4 2\n1 2 1 2\n5 4 5 4\n2 1 2 1\n3 5 3 4\n3 3 5 4\n4 2 3 1\n2 5 3 1\n3 5 4 2\n1 5 4 1\n4 5 3 2\n output: 0\n4\n12\n0"], "Pid": "p00692", "ProblemText": "Task Description: As the proverb says,\n\n\"Patience is bitter, but its fruit is sweet. \"\n\nWriting programs within the limited time may impose \nsome patience on you, but you enjoy it and win the contest, we hope.\n\nThe word \"patience\" has the meaning of perseverance, \nbut it has another meaning in card games.\nCard games for one player are called \"patience\" in the UK\nand \"solitaire\" in the US.\nLet's play a patience in this problem.\n\nIn this card game, you use only twenty cards whose \nface values are positive and less than or equal to 5 (Ace's value\nis 1 as usual).\nJust four cards are available for each face value.\n\nAt the beginning, the twenty cards are laid\nin five rows by four columns (See Figure 1).\nAll the cards are dealt face up.\n\nAn example of the initial layout is shown in Figure 2. \n \n \n \n \n Figure 1: Initial layout \n Figure 2: Example of the initial layout \n \n\nThe purpose of the game is to remove as many cards as possible\nby repeatedly removing a pair of neighboring cards \nof the same face value.\nLet us call such a pair a matching pair.\n\nThe phrase \"a pair of neighboring cards\" means a pair of cards which are\nadjacent to each other.\nFor example, in Figure 1, C_6 is adjacent to any of\nthe following eight cards:\nC_1C_2C_3C_5C_7C_9C_10C_11C_3C_2C_6C_7\nEvery time you remove a pair, you must rearrange the remaining cards \nas compact as possible. \nTo put it concretely, each remaining card C_i \nmust be examined in turn\nin its subscript order to be shifted to the uppermost-leftmost\nspace.\n\nHow to play:\n\n Search a matching pair.\n When you find more than one pair, choose one. \nIn Figure 3, you decided to remove the pair of \nC_6 and C_9.\n Remove the pair. (See Figure 4)\n Shift the remaining cards to the uppermost-leftmost space\n(See Figure 5,6).\n Repeat the above procedure until you cannot remove any pair.\n \n Figure 3: A matching pair found \n Figure 4: Remove the matching pair \n \n \n \n \n \n Figure 5: Shift the remaining cards \n Figure 6: Rearranged layout \n \nIf you can remove all the twenty cards, you win the game \nand your penalty is 0.\nIf you leave some cards,\nyou lose the game and \nyour penalty is the number of the remaining cards.\n\nWhenever you find multiple matching pairs,\nyou must choose one pair out of them \nas in the step 2 of the above procedure.\nThe result of the game depends on these choices.\n\nYour job is to write a program which answers the minimal penalty\nfor each initial layout.\nTask Input: The input consists of multiple card layouts.\nThe input is given in the following format.\n\n N\n Layout_0\n Layout_1\n . . .\n Layout_N-1\n\nN is the number of card layouts.\nEach card layout gives the initial state of a game.\nA card layout is given in the following format.\n\n C_0 C_1 C_2 C_3\n C_4 C_5 C_6 C_7\n C_8 C_9 C_10 C_11\n C_12 C_13 C_14 C_15\n C_16 C_17 C_18 C_19\n\nC_i (0 <= i <= 19) is an integer \nfrom 1 to 5 which represents the face value of the card.\nTask Output: For every initial card layout, the minimal penalty should be output,\neach in a separate line.\nTask Samples: input: 4\n1 4 5 2\n3 1 4 3\n5 4 2 2\n4 5 2 3\n1 1 3 5\n5 1 5 1\n4 5 3 2\n3 2 1 4\n1 4 5 3\n2 3 4 2\n1 2 1 2\n5 4 5 4\n2 1 2 1\n3 5 3 4\n3 3 5 4\n4 2 3 1\n2 5 3 1\n3 5 4 2\n1 5 4 1\n4 5 3 2\n output: 0\n4\n12\n0\n\n" }, { "title": "Cyber Guardian", "content": "In the good old days, the Internet was free from fears and\nterrorism. People did not have to worry about any cyber criminals or mad\ncomputer scientists. Today, however, you are facing atrocious crackers \nwherever you are, unless being disconnected. You have to protect\nyourselves against their attacks. Counting upon your excellent talent for software construction and\nstrong sense of justice, you are invited to work as a cyber\nguardian. Your ultimate mission is to create a perfect firewall system\nthat can completely shut out any intruders invading networks and protect\nchildren from harmful information exposed on the Net. However, it is\nextremely difficult and none have ever achieved it before. As the first \nstep, instead, you are now requested to write a software simulator\nunder much simpler assumptions. In general, a firewall system works at the entrance of a local network\nof an organization (e. g. , a company or a university) and enforces its local\nadministrative policy. It receives both inbound and outbound packets\n(note: data transmitted on the Net are divided into small segments\ncalled packets) and carefully inspects them one by one whether or not\neach of them is legal. The definition of the legality may\nvary from site to site or depend upon the local administrative\npolicy of an organization. Your simulator should accept data representing\nnot only received packets but also the local administrative policy. For simplicity in this problem we assume that each network packet\nconsists of three fields: its source address, destination address, and\nmessage body. The source address specifies the computer or appliance\nthat transmits the packet and the destination address specifies the\ncomputer or appliance to which the packet is transmitted. An address\nin your simulator is represented as eight digits such as 03214567 or\n31415926, instead of using the standard notation of IP addresses\nsuch as 192.168.1.1. Administrative policy is described in\nfiltering rules, each of which specifies some collection of\nsource-destination address pairs and defines those packets with the\nspecified address pairs either legal or illegal.", "constraint": "", "input": "The input consists of several data sets, each of which represents\nfiltering rules and received packets in the following format: \nn m\nrule_1\nrule_2\n. . . \nrule_n\npacket_1\npacket_2\n. . . \npacket_m\n The first line consists of two non-negative integers n and\nm. If both n and m are zeros, this means the end\nof input. Otherwise, n lines, each representing a filtering\nrule, and m lines, each representing an arriving packet, follow\nin this order. You may assume that n and m are less than\nor equal to 1,024. Each rule_i is in one of the following formats: \npermit source-pattern destination-pattern\ndeny source-pattern destination-pattern\n A source-pattern or destination-pattern is a\ncharacter string of length eight, where each character is either a\ndigit ('0' to '9') or a wildcard character '? '. For instance,\n\"1? ? ? ? 5? ? \" matches any address whose first and fifth digits are '1'\nand '5', respectively. In general, a wildcard character matches any\nsingle digit while a digit matches only itself. With the keywords \"permit\" and \"deny\", filtering rules specify\nlegal and illegal packets, respectively. That is, \nif the source and destination addresses of a packed are matched with\nsource-pattern and destination-pattern, respectively, it \nis permitted to pass the firewall or the request is\ndenied according to the keyword. Note that a permit rule \nand a deny rule can contradict since they may share the same source\nand destination address pair. For the purpose of conflict resolution,\nwe define a priority rule: rule_i has a higher priority over\nrule_j if and only if i > j. For\ncompleteness, we define the default rule: any packet is illegal unless\nbeing explicitly specified legal by some given rule. A packet is in the following format: \nsource-address destination-address message-body\n Each of the first two is a character string of length eight that\nconsists solely of digits. The last one is a character string\nconsisting solely of alphanumeric characters ('a' to 'z', 'A' to 'Z',\nand '0' to '9'). Neither whitespaces nor special characters can occur\nin a message body. You may assume that it is not empty and that its\nlength is at most 50. You may also assume that there is exactly one\nspace character between any two adjacent fields in an input line\nrepresenting a rule or a packet.", "output": "For each data set, print the number of legal packets in the first\nline, followed by all legal packets in the same order as they occur in\nthe data set. Each packet must be written exactly in one line. If the\ndata set includes two packets consisting of the same source and\ndestination addresses and the same message body, you should consider\nthem different packets and so they must be written in different\nlines. Any extra whitespaces or extra empty lines must not be\nwritten.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5\npermit 192168?? ?12??34?\ndeny 19216899 012343?5\n19216711 11233340 HiIamACracker\n19216891 01234345 Hello\n19216899 01234345 HiIamAlsoACracker\n19216809 11200340 World\n00000000 99999999 TheEndOfTheWorld\n1 2\npermit 12345678 23456789\n19216891 01234345 Hello\n12345678 23456789 Hello\n0 0\n output: 2\n19216891 01234345 Hello\n19216809 11200340 World\n1\n12345678 23456789 Hello"], "Pid": "p00693", "ProblemText": "Task Description: In the good old days, the Internet was free from fears and\nterrorism. People did not have to worry about any cyber criminals or mad\ncomputer scientists. Today, however, you are facing atrocious crackers \nwherever you are, unless being disconnected. You have to protect\nyourselves against their attacks. Counting upon your excellent talent for software construction and\nstrong sense of justice, you are invited to work as a cyber\nguardian. Your ultimate mission is to create a perfect firewall system\nthat can completely shut out any intruders invading networks and protect\nchildren from harmful information exposed on the Net. However, it is\nextremely difficult and none have ever achieved it before. As the first \nstep, instead, you are now requested to write a software simulator\nunder much simpler assumptions. In general, a firewall system works at the entrance of a local network\nof an organization (e. g. , a company or a university) and enforces its local\nadministrative policy. It receives both inbound and outbound packets\n(note: data transmitted on the Net are divided into small segments\ncalled packets) and carefully inspects them one by one whether or not\neach of them is legal. The definition of the legality may\nvary from site to site or depend upon the local administrative\npolicy of an organization. Your simulator should accept data representing\nnot only received packets but also the local administrative policy. For simplicity in this problem we assume that each network packet\nconsists of three fields: its source address, destination address, and\nmessage body. The source address specifies the computer or appliance\nthat transmits the packet and the destination address specifies the\ncomputer or appliance to which the packet is transmitted. An address\nin your simulator is represented as eight digits such as 03214567 or\n31415926, instead of using the standard notation of IP addresses\nsuch as 192.168.1.1. Administrative policy is described in\nfiltering rules, each of which specifies some collection of\nsource-destination address pairs and defines those packets with the\nspecified address pairs either legal or illegal.\nTask Input: The input consists of several data sets, each of which represents\nfiltering rules and received packets in the following format: \nn m\nrule_1\nrule_2\n. . . \nrule_n\npacket_1\npacket_2\n. . . \npacket_m\n The first line consists of two non-negative integers n and\nm. If both n and m are zeros, this means the end\nof input. Otherwise, n lines, each representing a filtering\nrule, and m lines, each representing an arriving packet, follow\nin this order. You may assume that n and m are less than\nor equal to 1,024. Each rule_i is in one of the following formats: \npermit source-pattern destination-pattern\ndeny source-pattern destination-pattern\n A source-pattern or destination-pattern is a\ncharacter string of length eight, where each character is either a\ndigit ('0' to '9') or a wildcard character '? '. For instance,\n\"1? ? ? ? 5? ? \" matches any address whose first and fifth digits are '1'\nand '5', respectively. In general, a wildcard character matches any\nsingle digit while a digit matches only itself. With the keywords \"permit\" and \"deny\", filtering rules specify\nlegal and illegal packets, respectively. That is, \nif the source and destination addresses of a packed are matched with\nsource-pattern and destination-pattern, respectively, it \nis permitted to pass the firewall or the request is\ndenied according to the keyword. Note that a permit rule \nand a deny rule can contradict since they may share the same source\nand destination address pair. For the purpose of conflict resolution,\nwe define a priority rule: rule_i has a higher priority over\nrule_j if and only if i > j. For\ncompleteness, we define the default rule: any packet is illegal unless\nbeing explicitly specified legal by some given rule. A packet is in the following format: \nsource-address destination-address message-body\n Each of the first two is a character string of length eight that\nconsists solely of digits. The last one is a character string\nconsisting solely of alphanumeric characters ('a' to 'z', 'A' to 'Z',\nand '0' to '9'). Neither whitespaces nor special characters can occur\nin a message body. You may assume that it is not empty and that its\nlength is at most 50. You may also assume that there is exactly one\nspace character between any two adjacent fields in an input line\nrepresenting a rule or a packet.\nTask Output: For each data set, print the number of legal packets in the first\nline, followed by all legal packets in the same order as they occur in\nthe data set. Each packet must be written exactly in one line. If the\ndata set includes two packets consisting of the same source and\ndestination addresses and the same message body, you should consider\nthem different packets and so they must be written in different\nlines. Any extra whitespaces or extra empty lines must not be\nwritten.\nTask Samples: input: 2 5\npermit 192168?? ?12??34?\ndeny 19216899 012343?5\n19216711 11233340 HiIamACracker\n19216891 01234345 Hello\n19216899 01234345 HiIamAlsoACracker\n19216809 11200340 World\n00000000 99999999 TheEndOfTheWorld\n1 2\npermit 12345678 23456789\n19216891 01234345 Hello\n12345678 23456789 Hello\n0 0\n output: 2\n19216891 01234345 Hello\n19216809 11200340 World\n1\n12345678 23456789 Hello\n\n" }, { "title": "Strange Key", "content": "Professor Tsukuba invented a mysterious jewelry box that can be opened\nwith a special gold key whose shape is very strange. It is composed\nof gold bars joined at their ends. Each gold bar\nhas the same length and is placed parallel to one of the three\northogonal axes in a three dimensional space, \ni. e. , x-axis, y-axis and z-axis.\nThe locking mechanism of the jewelry box\nis truly mysterious, but the shape of the key is known.\nTo identify the key of the jewelry box, he gave a way to describe \nits shape.\nThe description \nindicates a list of connected paths that completely defines the shape\nof the key: the gold bars of the key are arranged along the paths and \njoined at their ends.\nExcept for the first path, \neach path must start from an end point of a gold bar on a previously\ndefined path.\nEach path is represented by a sequence of elements, each of which is one\nof six symbols (+x, -x, +y, -y, +z and -z) or a positive integer.\nEach symbol indicates the direction from an end point to the other end\npoint of a gold bar along the path. Since each gold bar is\nparallel to one of the three orthogonal axes, the 6 symbols are enough to\nindicate the direction. Note that a description of a path has\ndirection but the gold bars themselves have no direction.\n\nAn end point of a gold bar can have a label, which is a positive integer.\nThe labeled point may be referred to as the beginnings of other paths.\nIn a key description, the first occurrence of a positive integer \ndefines a label of a point and each subsequent occurrence of the same\npositive integer indicates the beginning of a new path at the point.\n\nAn example of a key composed of 13 gold bars is depicted \nin Figure 1. The following sequence of lines\n 19\n 1 +x 1 +y +z 3 +z \n 3 +y -z +x +y -z -x +z 2 +z \n 2 +y\n\nis a description of the key in Figure 1.\nNote that newlines have the same role as space characters in the\ndescription, so that \"19 1 +x 1 +y +z 3 +z 3 +y -z +x +y -z -x +z\n2 +z 2 +y\" has the same meaning.\n\nThe meaning of this description is quite simple.\nThe first integer \"19\" means the number of\nthe following elements in this description.\nEach element is one of the 6 symbols or a positive integer.\n\nThe integer \"1\" at the head of the second line \nis a label attached to the starting point of the first path.\nWithout loss of generality, \nit can be assumed that the starting point of the first path is the\norigin, i. e. , (0,0,0), and that the length of each gold bar is 1.\nThe next element \"+x\" indicates that the first gold bar\nis parallel to the x-axis, \nso that the other end point of the gold bar is at (1,0,0).\nThese two elements \"1\" and \"+x\" indicates\nthe first path consisting of only one gold bar.\nThe third element of the second line in the description is the positive\ninteger \"1\", meaning that the point with the label \"1\", i. e. , the\norigin (0,0,0) is the beginning of a new path.\nThe following elements \"+y\", \"+z\", \"3\", and \"+z\" indicate the second\npath consisting of three gold bars. Note that this \"3\" is its first\noccurrence so that the point with coordinates (0,1,1) is labeled \"3\". \nThe head of the third line \"3\" indicates\nthe beginning of the third path and so on.\nConsequently, there are four paths by which the shape of the key in\nFigure 1 is completely defined.\n\nNote that there are various descriptions of the same key since there\nare various sets of paths that cover the shape of the key.\nFor example,\nthe following sequence of lines\n 19 \n 1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y \n 3 +z \n 2 +z\n\nis another description of the key in Figure 1, since\nthe gold bars are placed in the same way.\n\nFurthermore, the key may be turned 90-degrees around \nx-axis, y-axis or z-axis several times and may be moved parallelly.\nSince any combinations of rotations and parallel moves don't change\nthe shape of the key, a description of a rotated and moved key also\nrepresent the same shape of the original key. For example, a\nsequence\n 17 \n +y 1 +y -z +x\n 1 +z +y +x +z +y -x -y 2 -y\n 2 +z\n\nis a description of a key in Figure 2 that represents the same key \nas in Figure 1.\nIndeed, they are congruent under a rotation around x-axis and \na parallel move.\n\nYour job is to write a program to\njudge whether or not the given two descriptions define the same key.\n\nNote that paths may make a cycle.\nFor example, \"4 +x +y -x -y\" and \"6 1 +x 1 +y +x -y\"\nare valid descriptions. However, two or more gold bars must not be placed at the same position.\nFor example, key descriptions\n\"2 +x -x\" \nand\n\"7 1 +x 1 +y +x -y -x\" are invalid.", "constraint": "", "input": "An input data is a list of pairs of key descriptions followed by\na zero that indicates the end of the input.\nFor p pairs of key descriptions, the input is given in the\nfollowing format.\n\nkey-description_1-a\nkey-description_1-b\nkey-description_2-a\nkey-description_2-b\n. . . \nkey-description_p-a\nkey-description_p-b\n0\n\nEach key description (key-description) has the following format.\nn \ne_1 e_2 \n. . . \ne_k \n. . . \ne_n\n\nThe positive integer n indicates the number of the following elements \ne_1, . . . ,\ne_n .\nThey are separated by one or more space characters and/or newlines.\nEach element e_k is \none of the six symbols\n(+x, -x, +y, -y, +z and -z)\nor a positive integer.\n\nYou can assume that each label is a positive integer that is less than 51,\nthe number of elements in a single key description is less than 301,\nand the number of characters in a line is less than 80.\nYou can also assume that the given key descriptions are valid and \ncontain at least one gold bar.", "output": "The number of output lines should be equal to that of\npairs of key descriptions given in the input.\nIn each line, you should output one of two words \"SAME\",\nwhen the two key descriptions represent the same key, and \n\"DIFFERENT\", when they are different.\nNote that the letters should be in upper case.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 19\n 1 +x 1 +y +z 3 +z \n 3 +y -z +x +y -z -x +z 2 +z \n 2 +y\n19\n 1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y \n 3 +z \n 2 +z\n19\n 1 +x 1 +y +z 3 +z \n 3 +y -z +x +y -z -x +z 2 +y \n 2 +z\n18\n 1 -y\n 1 +y -z +x\n 1 +z +y +x +z +y -x -y 2 -y\n 2 +z\n3 +x +y +z\n3 +y +z -x\n0\n output: SAME\nSAME\nDIFFERENT"], "Pid": "p00694", "ProblemText": "Task Description: Professor Tsukuba invented a mysterious jewelry box that can be opened\nwith a special gold key whose shape is very strange. It is composed\nof gold bars joined at their ends. Each gold bar\nhas the same length and is placed parallel to one of the three\northogonal axes in a three dimensional space, \ni. e. , x-axis, y-axis and z-axis.\nThe locking mechanism of the jewelry box\nis truly mysterious, but the shape of the key is known.\nTo identify the key of the jewelry box, he gave a way to describe \nits shape.\nThe description \nindicates a list of connected paths that completely defines the shape\nof the key: the gold bars of the key are arranged along the paths and \njoined at their ends.\nExcept for the first path, \neach path must start from an end point of a gold bar on a previously\ndefined path.\nEach path is represented by a sequence of elements, each of which is one\nof six symbols (+x, -x, +y, -y, +z and -z) or a positive integer.\nEach symbol indicates the direction from an end point to the other end\npoint of a gold bar along the path. Since each gold bar is\nparallel to one of the three orthogonal axes, the 6 symbols are enough to\nindicate the direction. Note that a description of a path has\ndirection but the gold bars themselves have no direction.\n\nAn end point of a gold bar can have a label, which is a positive integer.\nThe labeled point may be referred to as the beginnings of other paths.\nIn a key description, the first occurrence of a positive integer \ndefines a label of a point and each subsequent occurrence of the same\npositive integer indicates the beginning of a new path at the point.\n\nAn example of a key composed of 13 gold bars is depicted \nin Figure 1. The following sequence of lines\n 19\n 1 +x 1 +y +z 3 +z \n 3 +y -z +x +y -z -x +z 2 +z \n 2 +y\n\nis a description of the key in Figure 1.\nNote that newlines have the same role as space characters in the\ndescription, so that \"19 1 +x 1 +y +z 3 +z 3 +y -z +x +y -z -x +z\n2 +z 2 +y\" has the same meaning.\n\nThe meaning of this description is quite simple.\nThe first integer \"19\" means the number of\nthe following elements in this description.\nEach element is one of the 6 symbols or a positive integer.\n\nThe integer \"1\" at the head of the second line \nis a label attached to the starting point of the first path.\nWithout loss of generality, \nit can be assumed that the starting point of the first path is the\norigin, i. e. , (0,0,0), and that the length of each gold bar is 1.\nThe next element \"+x\" indicates that the first gold bar\nis parallel to the x-axis, \nso that the other end point of the gold bar is at (1,0,0).\nThese two elements \"1\" and \"+x\" indicates\nthe first path consisting of only one gold bar.\nThe third element of the second line in the description is the positive\ninteger \"1\", meaning that the point with the label \"1\", i. e. , the\norigin (0,0,0) is the beginning of a new path.\nThe following elements \"+y\", \"+z\", \"3\", and \"+z\" indicate the second\npath consisting of three gold bars. Note that this \"3\" is its first\noccurrence so that the point with coordinates (0,1,1) is labeled \"3\". \nThe head of the third line \"3\" indicates\nthe beginning of the third path and so on.\nConsequently, there are four paths by which the shape of the key in\nFigure 1 is completely defined.\n\nNote that there are various descriptions of the same key since there\nare various sets of paths that cover the shape of the key.\nFor example,\nthe following sequence of lines\n 19 \n 1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y \n 3 +z \n 2 +z\n\nis another description of the key in Figure 1, since\nthe gold bars are placed in the same way.\n\nFurthermore, the key may be turned 90-degrees around \nx-axis, y-axis or z-axis several times and may be moved parallelly.\nSince any combinations of rotations and parallel moves don't change\nthe shape of the key, a description of a rotated and moved key also\nrepresent the same shape of the original key. For example, a\nsequence\n 17 \n +y 1 +y -z +x\n 1 +z +y +x +z +y -x -y 2 -y\n 2 +z\n\nis a description of a key in Figure 2 that represents the same key \nas in Figure 1.\nIndeed, they are congruent under a rotation around x-axis and \na parallel move.\n\nYour job is to write a program to\njudge whether or not the given two descriptions define the same key.\n\nNote that paths may make a cycle.\nFor example, \"4 +x +y -x -y\" and \"6 1 +x 1 +y +x -y\"\nare valid descriptions. However, two or more gold bars must not be placed at the same position.\nFor example, key descriptions\n\"2 +x -x\" \nand\n\"7 1 +x 1 +y +x -y -x\" are invalid.\nTask Input: An input data is a list of pairs of key descriptions followed by\na zero that indicates the end of the input.\nFor p pairs of key descriptions, the input is given in the\nfollowing format.\n\nkey-description_1-a\nkey-description_1-b\nkey-description_2-a\nkey-description_2-b\n. . . \nkey-description_p-a\nkey-description_p-b\n0\n\nEach key description (key-description) has the following format.\nn \ne_1 e_2 \n. . . \ne_k \n. . . \ne_n\n\nThe positive integer n indicates the number of the following elements \ne_1, . . . ,\ne_n .\nThey are separated by one or more space characters and/or newlines.\nEach element e_k is \none of the six symbols\n(+x, -x, +y, -y, +z and -z)\nor a positive integer.\n\nYou can assume that each label is a positive integer that is less than 51,\nthe number of elements in a single key description is less than 301,\nand the number of characters in a line is less than 80.\nYou can also assume that the given key descriptions are valid and \ncontain at least one gold bar.\nTask Output: The number of output lines should be equal to that of\npairs of key descriptions given in the input.\nIn each line, you should output one of two words \"SAME\",\nwhen the two key descriptions represent the same key, and \n\"DIFFERENT\", when they are different.\nNote that the letters should be in upper case.\nTask Samples: input: 19\n 1 +x 1 +y +z 3 +z \n 3 +y -z +x +y -z -x +z 2 +z \n 2 +y\n19\n 1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y \n 3 +z \n 2 +z\n19\n 1 +x 1 +y +z 3 +z \n 3 +y -z +x +y -z -x +z 2 +y \n 2 +z\n18\n 1 -y\n 1 +y -z +x\n 1 +z +y +x +z +y -x -y 2 -y\n 2 +z\n3 +x +y +z\n3 +y +z -x\n0\n output: SAME\nSAME\nDIFFERENT\n\n" }, { "title": "Get a Rectangular Field", "content": "Karnaugh is a poor farmer who has a very small field. He wants to reclaim wasteland in the kingdom to get a new field. But the king who loves regular shape made a rule that a settler can only get a rectangular land as his field. Thus, Karnaugh should get the largest rectangular land suitable for reclamation. The map of the wasteland is represented with a 5 x 5 grid as shown in the following figures, where '1' represents a place suitable for reclamation and '0' represents a sandy place. Your task is to find the largest rectangle consisting only of 1's in the map, and to report the size of the rectangle. The size of a rectangle is defined by the number of 1's in it. Note that there may be two or more largest rectangles of the same size.", "constraint": "", "input": "The input consists of maps preceded by an integer m \nindicating the number of input maps.\n\nm\nmap_1\n\nmap_2\n\nmap_3\n\n. . .\n\nmap_m\n \nTwo maps are separated by an empty line. \nEach map_k is in the following format:\n\n p p p p p \n p p p p p \n p p p p p \n p p p p p \n p p p p p \n\n \nEach p is a character either '1' or '0'.\nTwo p's in the same line are separated by a space character.\nHere, the character '1' shows a place suitable for reclamation\nand '0' shows a sandy place.\nEach map contains at least one '1'.", "output": "The size of the largest\nrectangle(s) for each input map should be shown each in a separate line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1 0 1 0\n0 1 1 1 1\n1 0 1 0 1\n0 1 1 1 0\n0 1 1 0 0\n\n0 1 0 1 1\n0 1 0 1 0\n0 0 1 0 0\n0 0 1 1 0\n1 0 1 0 0\n\n1 1 1 1 0\n0 1 1 1 0\n0 1 1 0 1\n0 1 1 1 0\n0 0 0 0 1\n output: 4\n3\n8"], "Pid": "p00695", "ProblemText": "Task Description: Karnaugh is a poor farmer who has a very small field. He wants to reclaim wasteland in the kingdom to get a new field. But the king who loves regular shape made a rule that a settler can only get a rectangular land as his field. Thus, Karnaugh should get the largest rectangular land suitable for reclamation. The map of the wasteland is represented with a 5 x 5 grid as shown in the following figures, where '1' represents a place suitable for reclamation and '0' represents a sandy place. Your task is to find the largest rectangle consisting only of 1's in the map, and to report the size of the rectangle. The size of a rectangle is defined by the number of 1's in it. Note that there may be two or more largest rectangles of the same size.\nTask Input: The input consists of maps preceded by an integer m \nindicating the number of input maps.\n\nm\nmap_1\n\nmap_2\n\nmap_3\n\n. . .\n\nmap_m\n \nTwo maps are separated by an empty line. \nEach map_k is in the following format:\n\n p p p p p \n p p p p p \n p p p p p \n p p p p p \n p p p p p \n\n \nEach p is a character either '1' or '0'.\nTwo p's in the same line are separated by a space character.\nHere, the character '1' shows a place suitable for reclamation\nand '0' shows a sandy place.\nEach map contains at least one '1'.\nTask Output: The size of the largest\nrectangle(s) for each input map should be shown each in a separate line.\nTask Samples: input: 3\n1 1 0 1 0\n0 1 1 1 1\n1 0 1 0 1\n0 1 1 1 0\n0 1 1 0 0\n\n0 1 0 1 1\n0 1 0 1 0\n0 0 1 0 0\n0 0 1 1 0\n1 0 1 0 0\n\n1 1 1 1 0\n0 1 1 1 0\n0 1 1 0 1\n0 1 1 1 0\n0 0 0 0 1\n output: 4\n3\n8\n\n" }, { "title": "Multi-column List", "content": "Ever since Mr. Ikra became the chief manager of his office,\nhe has had little time for his favorites, programming and debugging.\nSo he wants to check programs in trains to and from his office\nwith program lists.\nHe has wished for the tool that prints source programs \nas multi-column lists so that each column just fits in\na pocket of his business suit.\nIn this problem, you should help him by making a program that prints\nthe given input text in a multi-column format. Since his business\nsuits have various sizes of pockets, your program should be flexible\nenough and accept four parameters, (1) the number of lines in a\ncolumn, (2) the number of columns in a page, (3) the width of each\ncolumn, and (4) the width of the column spacing. \nWe assume that a fixed-width font is used for printing and so the\ncolumn width is given as the maximum number of characters in a line.\nThe column spacing is also specified as the number of\ncharacters filling it.", "constraint": "", "input": "In one file, stored are data sets in a form shown below.\nplen_1\ncnum_1\nwidth_1\ncspace_1\nline_1_1\nline_1_2\n. . . .\nline_1_i\n. . . .\n?\nplen_2\ncnum_2\nwidth_2\ncspace_2\ntext_2\nline_2_1\nline_2_2\n. . . .\nline_2_i\n. . . .\n?\n0\nThe first four lines of each data set give \npositive integers specifying the output format.\nPlen (1 <= plen <= 100) is the number of lines in a column.\nCnum is the number of columns in one page.\nWidth is the column width, i. e. , the number of characters in one column.\nCspace is the number of spacing characters between each pair of\nneighboring columns.\nYou may assume \n1 <= (cnum * width + cspace * (cnum-1)) <= 50.\nThe subsequent lines terminated by a line consisting solely of '? '\nare the input text.\nAny lines of the input text do not include any characters except\nalphanumeric characters '0'-'9', 'A'-'Z', and 'a'-'z'.\nNote that some of input lines may be empty. \nNo input lines have more than 1,000 characters.", "output": "Print the formatted pages in the order of input data sets.\nFill the gaps among them with dot('. ') characters.\nIf an output line is shorter than width, also fill its\ntrailing space with dot characters. \nAn input line that is empty shall occupy a single line on an output\ncolumn.\nThis empty output line is naturally filled with dot characters.\nAn input text that is empty, however, shall not occupy any page.\nA line larger than width is wrapped around \nand printed on multiple lines.\nAt the end of each page, print a line consisting only of '#'.\nAt the end of each data set, print a line consisting only of '? '.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n2\n8\n1\nAZXU5\n1GU2D4B\nK\nPO4IUTFV\nTHE\nQ34NBVC78\nT\n1961\nXWS34WQ\n\nLNGLNSNXTTPG\nED\nMN\nMLMNG\n?\n4\n2\n6\n2\nQWERTY\nFLHL\n?\n0\n output: You Should see the following section with a fixed-width font. \n\nAZXU5....8.......\n1GU2D4B..T.......\nK........1961....\nPO4IUTFV.XWS34WQ.\nTHE.............. \nQ34NBVC7.LNGLNSNX\n#\nTTPG.............\nED...............\nMN...............\nMLMNG............\n.................\n.................\n#\n?\nQWERTY........\nFLHL..........\n..............\n..............\n#\n?"], "Pid": "p00696", "ProblemText": "Task Description: Ever since Mr. Ikra became the chief manager of his office,\nhe has had little time for his favorites, programming and debugging.\nSo he wants to check programs in trains to and from his office\nwith program lists.\nHe has wished for the tool that prints source programs \nas multi-column lists so that each column just fits in\na pocket of his business suit.\nIn this problem, you should help him by making a program that prints\nthe given input text in a multi-column format. Since his business\nsuits have various sizes of pockets, your program should be flexible\nenough and accept four parameters, (1) the number of lines in a\ncolumn, (2) the number of columns in a page, (3) the width of each\ncolumn, and (4) the width of the column spacing. \nWe assume that a fixed-width font is used for printing and so the\ncolumn width is given as the maximum number of characters in a line.\nThe column spacing is also specified as the number of\ncharacters filling it.\nTask Input: In one file, stored are data sets in a form shown below.\nplen_1\ncnum_1\nwidth_1\ncspace_1\nline_1_1\nline_1_2\n. . . .\nline_1_i\n. . . .\n?\nplen_2\ncnum_2\nwidth_2\ncspace_2\ntext_2\nline_2_1\nline_2_2\n. . . .\nline_2_i\n. . . .\n?\n0\nThe first four lines of each data set give \npositive integers specifying the output format.\nPlen (1 <= plen <= 100) is the number of lines in a column.\nCnum is the number of columns in one page.\nWidth is the column width, i. e. , the number of characters in one column.\nCspace is the number of spacing characters between each pair of\nneighboring columns.\nYou may assume \n1 <= (cnum * width + cspace * (cnum-1)) <= 50.\nThe subsequent lines terminated by a line consisting solely of '? '\nare the input text.\nAny lines of the input text do not include any characters except\nalphanumeric characters '0'-'9', 'A'-'Z', and 'a'-'z'.\nNote that some of input lines may be empty. \nNo input lines have more than 1,000 characters.\nTask Output: Print the formatted pages in the order of input data sets.\nFill the gaps among them with dot('. ') characters.\nIf an output line is shorter than width, also fill its\ntrailing space with dot characters. \nAn input line that is empty shall occupy a single line on an output\ncolumn.\nThis empty output line is naturally filled with dot characters.\nAn input text that is empty, however, shall not occupy any page.\nA line larger than width is wrapped around \nand printed on multiple lines.\nAt the end of each page, print a line consisting only of '#'.\nAt the end of each data set, print a line consisting only of '? '.\nTask Samples: input: 6\n2\n8\n1\nAZXU5\n1GU2D4B\nK\nPO4IUTFV\nTHE\nQ34NBVC78\nT\n1961\nXWS34WQ\n\nLNGLNSNXTTPG\nED\nMN\nMLMNG\n?\n4\n2\n6\n2\nQWERTY\nFLHL\n?\n0\n output: You Should see the following section with a fixed-width font. \n\nAZXU5....8.......\n1GU2D4B..T.......\nK........1961....\nPO4IUTFV.XWS34WQ.\nTHE.............. \nQ34NBVC7.LNGLNSNX\n#\nTTPG.............\nED...............\nMN...............\nMLMNG............\n.................\n.................\n#\n?\nQWERTY........\nFLHL..........\n..............\n..............\n#\n?\n\n" }, { "title": "Jigsaw Puzzles for Computers", "content": "Ordinary Jigsaw puzzles are solved with visual hints;\nplayers solve a puzzle with the picture which the puzzle shows on finish,\nand the diverse patterns of pieces. \nSuch Jigsaw puzzles may be suitable for human players,\nbecause they require abilities of pattern recognition and imagination.\n\n On the other hand,\n\"Jigsaw puzzles\" described below may be just the things for\nsimple-minded computers.\n\n As shown in Figure 1,\n a puzzle is composed of nine square pieces, and each of the four edges\nof a piece is labeled with one of the following eight symbols: \n\n\"R\", \"G\", \"B\", \"W\", \"r\", \"g\", \"b\", and \"w\".\n \n \n\n Figure 1: The nine pieces of a puzzle \n\n \n In a completed puzzle, the nine pieces are arranged in a 3 x 3 grid,\nand each of the 12 pairs of edges facing each other \nmust be labeled with one of the\nfollowing four combinations of symbols: \n\n\"R\" with \"r\", \"G\" with \"g\",\n\t\"B\" with \"b\", and \"W\" with \"w\".\n\nFor example, an edge labeled \"R\" can only face an edge with \"r\".\nFigure 2 is an example of a completed state of a puzzle.\nIn the figure, edges under this restriction are indicated by shadowing their labels.\nThe player can freely move and rotate the pieces, but cannot turn them over.\nThere are no symbols on the reverse side of a piece !\n \n \n\n Figure 2: A completed puzzle example \n\n \n Each piece is represented by a sequence of the four symbols\non the piece, starting with the symbol of the top edge,\nfollowed by the symbols of the right edge, the bottom edge,\nand the left edge.\nFor example, gwg W represents the leftmost piece in Figure 1.\nNote that the same piece can be represented as \nwg Wg,\ng Wgw \nor Wgwg\nsince you can rotate it in 90,180 or 270 degrees.\n\nThe mission for you is to create a program which counts the number\nof solutions.\nIt is needless to say that these numbers must be multiples of four,\nbecause, as shown in Figure 3,\na configuration created by rotating a solution in 90,180 or 270 degrees\nis also a solution.\n \n \n\n Figure 3: Four obvious variations for a completed puzzle \n\n \n A term \"rotationally equal\" is defined; if two different pieces are\nidentical when one piece is rotated (in 90,180 or 270 degrees),\nthey are rotationally equal. For example,\nWg Wr and Wr Wg are rotationally equal.\n\n Another term \"rotationally symmetric\" is defined; if a piece is\nrotationally equal to itself, it is rotationally symmetric. \nFor example, a piece g Wg W is rotationally symmetric. \n\n Given puzzles satisfy the following three conditions:\n\nThere is no identical pair of pieces in a puzzle.\nThere is no rotationally equal pair of pieces in a puzzle.\nThere is no rotationally symmetric piece in a puzzle.", "constraint": "", "input": "The input consists of multiple puzzles.\n\n\tN\n\tPuzzle_1\n\tPuzzle_2\n\t. . . \n\tPuzzle_N\n\nN is the number of puzzles. Each Puzzle_i\ngives a puzzle with a single line\nof 44 characters, consisting of four-character representations of the nine\npieces of the puzzle, separated by a space character. \nFor example, the following line represents the puzzle\nin Figure 1. \n\n\tgwg W RBb W GWrb GRRb BWGr Rbgw r Gb R g Brg GRwb", "output": "For each Puzzle_i , the number of its solutions\nshould be the output, each in a separate line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6\nWwRR wwrg RRGb rGBG RGrb RrRg RGrg rgBB Wrgr\nRrGb WWGR rGgb Wbrg wgBb GgBg WbBG Wwwg WWGG\nRBbr Wrbr wGGG wggR WgGR WBWb WRgB wBgG WBgG\nwBrg rGgb WRrB WWbw wRRB RbbB WRrb wrbb WgrG\nWrwB WWww wRRB WGGb Wbbg WBgG WrbG Wrww RBgg\nWWgg RBrr Rggr RGBg Wbgr WGbg WBbr WGWB GGGg\n output: 40\n8\n32\n4\n12\n0"], "Pid": "p00697", "ProblemText": "Task Description: Ordinary Jigsaw puzzles are solved with visual hints;\nplayers solve a puzzle with the picture which the puzzle shows on finish,\nand the diverse patterns of pieces. \nSuch Jigsaw puzzles may be suitable for human players,\nbecause they require abilities of pattern recognition and imagination.\n\n On the other hand,\n\"Jigsaw puzzles\" described below may be just the things for\nsimple-minded computers.\n\n As shown in Figure 1,\n a puzzle is composed of nine square pieces, and each of the four edges\nof a piece is labeled with one of the following eight symbols: \n\n\"R\", \"G\", \"B\", \"W\", \"r\", \"g\", \"b\", and \"w\".\n \n \n\n Figure 1: The nine pieces of a puzzle \n\n \n In a completed puzzle, the nine pieces are arranged in a 3 x 3 grid,\nand each of the 12 pairs of edges facing each other \nmust be labeled with one of the\nfollowing four combinations of symbols: \n\n\"R\" with \"r\", \"G\" with \"g\",\n\t\"B\" with \"b\", and \"W\" with \"w\".\n\nFor example, an edge labeled \"R\" can only face an edge with \"r\".\nFigure 2 is an example of a completed state of a puzzle.\nIn the figure, edges under this restriction are indicated by shadowing their labels.\nThe player can freely move and rotate the pieces, but cannot turn them over.\nThere are no symbols on the reverse side of a piece !\n \n \n\n Figure 2: A completed puzzle example \n\n \n Each piece is represented by a sequence of the four symbols\non the piece, starting with the symbol of the top edge,\nfollowed by the symbols of the right edge, the bottom edge,\nand the left edge.\nFor example, gwg W represents the leftmost piece in Figure 1.\nNote that the same piece can be represented as \nwg Wg,\ng Wgw \nor Wgwg\nsince you can rotate it in 90,180 or 270 degrees.\n\nThe mission for you is to create a program which counts the number\nof solutions.\nIt is needless to say that these numbers must be multiples of four,\nbecause, as shown in Figure 3,\na configuration created by rotating a solution in 90,180 or 270 degrees\nis also a solution.\n \n \n\n Figure 3: Four obvious variations for a completed puzzle \n\n \n A term \"rotationally equal\" is defined; if two different pieces are\nidentical when one piece is rotated (in 90,180 or 270 degrees),\nthey are rotationally equal. For example,\nWg Wr and Wr Wg are rotationally equal.\n\n Another term \"rotationally symmetric\" is defined; if a piece is\nrotationally equal to itself, it is rotationally symmetric. \nFor example, a piece g Wg W is rotationally symmetric. \n\n Given puzzles satisfy the following three conditions:\n\nThere is no identical pair of pieces in a puzzle.\nThere is no rotationally equal pair of pieces in a puzzle.\nThere is no rotationally symmetric piece in a puzzle.\nTask Input: The input consists of multiple puzzles.\n\n\tN\n\tPuzzle_1\n\tPuzzle_2\n\t. . . \n\tPuzzle_N\n\nN is the number of puzzles. Each Puzzle_i\ngives a puzzle with a single line\nof 44 characters, consisting of four-character representations of the nine\npieces of the puzzle, separated by a space character. \nFor example, the following line represents the puzzle\nin Figure 1. \n\n\tgwg W RBb W GWrb GRRb BWGr Rbgw r Gb R g Brg GRwb\nTask Output: For each Puzzle_i , the number of its solutions\nshould be the output, each in a separate line.\nTask Samples: input: 6\nWwRR wwrg RRGb rGBG RGrb RrRg RGrg rgBB Wrgr\nRrGb WWGR rGgb Wbrg wgBb GgBg WbBG Wwwg WWGG\nRBbr Wrbr wGGG wggR WgGR WBWb WRgB wBgG WBgG\nwBrg rGgb WRrB WWbw wRRB RbbB WRrb wrbb WgrG\nWrwB WWww wRRB WGGb Wbbg WBgG WrbG Wrww RBgg\nWWgg RBrr Rggr RGBg Wbgr WGbg WBbr WGWB GGGg\n output: 40\n8\n32\n4\n12\n0\n\n" }, { "title": "Missing Numbers", "content": "Toshizo is the manager of a convenience store chain in Hakodate.\nEvery day, each of the stores in his chain sends him a table of the\nproducts that they have sold. Toshizo's job is to compile these\nfigures and calculate how much the stores have sold in total.\nThe type of a table that is sent to Toshizo by the stores looks like this\n(all numbers represent units of products sold):\n Store1 Store2 Store3 Totals\n Product A -5 40 70 | 105\n Product B 20 50 80 | 150\n Product C 30 60 90 | 180\n -----------------------------------------------------------\n Store's total sales 45 150 240 435\nBy looking at the table, Toshizo can tell at a glance which goods are\nselling well or selling badly, and which stores are paying well and\nwhich stores are too empty. Sometimes, customers will bring products\nback, so numbers in a table can be negative as well as positive.\nToshizo reports these figures to his boss in Tokyo, and together they\nsometimes decide to close stores that are not doing well and sometimes\ndecide to open new stores in places that they think will be profitable.\nSo, the total number of stores managed by Toshizo is not fixed. Also,\nthey often decide to discontinue selling some products that are not\npopular, as well as deciding to stock new items that are likely to be\npopular. So, the number of products that Toshizo has to monitor is also\nnot fixed.\nOne New Year, it is very cold in Hakodate. A water pipe bursts in\nToshizo's office and floods his desk. When Toshizo comes to work, he\nfinds that the latest sales table is not legible. He can make out some\nof the figures, but not all of them. He wants to call his boss in\nTokyo to tell him that the figures will be late, but he knows that his\nboss will expect him to reconstruct the table if at all possible.\nWaiting until the next day won't help, because it is the New Year, and\nhis shops will be on holiday. So, Toshizo decides either to work out\nthe values for himself, or to be sure that there really is no unique\nsolution. Only then can he call his boss and tell him what has\nhappened.\nBut Toshizo also wants to be sure that a problem like this never\nhappens again. So he decides to write a computer program that all the\nmanagers in his company can use if some of the data goes missing\nfrom their sales tables. For instance, if they have a table like:\n Store 1 Store 2 Store 3 Totals\n Product A ? ? 70 | 105\n Product B ? 50 ? | 150\n Product C 30 60 90 | 180\n --------------------------------------------------------\n Store's total sales 45 150 240 435\nthen Toshizo's program will be able to tell them the correct figures\nto replace the question marks.\nIn some cases, however, even his program will not be able to replace\nall the question marks, in general.\nFor instance, if a table like:\n Store 1 Store 2 Totals\n Product A ? ? | 40\n Product B ? ? | 40\n ---------------------------------------------\n Store's total sales 40 40 80\nis given, there are infinitely many possible solutions.\nIn this sort of case, his program will just say \"NO\". \nToshizo's program works for any data where the totals row and column\nare still intact.\nCan you reproduce Toshizo's program?", "constraint": "", "input": "The input consists of multiple data sets, each in the following\nformat:\np s\nrow_1\nrow_2\n. . .\nrow_p\ntotals\n\nThe first line consists of two integers p and s,\nrepresenting the numbers of products and stores, respectively.\nThe former is less than 100 and the latter is less than 10.\nThey are separated by a blank character.\nEach of the subsequent lines represents a row of the table and\nconsists of s+1 elements, each of which is either an integer or\na question mark.\nThe i-th line (1 <= i <= p) corresponds to\nthe i-th product and the last line the totals row.\nThe first s elements in a line represent the sales of each\nstore and the last one the total sales of the product.\nNumbers or question marks in a line are separated by a blank character.\nThere are no missing numbers in the totals column or row. \nThere is at least one question mark in each data set.\nThe known numbers in the table except the totals row and column is\nbetween -1,000 and 1,000, inclusive.\nHowever, unknown numbers, represented by question marks, may not be in\nthis range.\nThe total sales number of each product is between -10,000 and\n10,000, inclusive. \nThe total sales number of each store is between -100,000 and\n100,000, inclusive. \nThere is a blank line between each data set in the input, and the input\nis terminated by a line consisting of a zero.", "output": "When there is a unique solution, your program should print the missing\nnumbers in the occurrence order in the input data set.\nOtherwise, your program should print just \"NO\".\nThe answers of consecutive data sets should be separated by an empty\nline.\nEach non-empty output line contains only a single number or \"NO\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n? ? 70 105\n? 50 ? 150\n30 60 90 180\n45 150 240 435\n \n2 2\n? ? 40\n? ? 40\n40 40 80\n\n2 3\n? 30 40 90\n50 60 70 180\n70 90 110 270\n\n0\n output: -5\n40\n20\n80\n \nNO\n\n20"], "Pid": "p00698", "ProblemText": "Task Description: Toshizo is the manager of a convenience store chain in Hakodate.\nEvery day, each of the stores in his chain sends him a table of the\nproducts that they have sold. Toshizo's job is to compile these\nfigures and calculate how much the stores have sold in total.\nThe type of a table that is sent to Toshizo by the stores looks like this\n(all numbers represent units of products sold):\n Store1 Store2 Store3 Totals\n Product A -5 40 70 | 105\n Product B 20 50 80 | 150\n Product C 30 60 90 | 180\n -----------------------------------------------------------\n Store's total sales 45 150 240 435\nBy looking at the table, Toshizo can tell at a glance which goods are\nselling well or selling badly, and which stores are paying well and\nwhich stores are too empty. Sometimes, customers will bring products\nback, so numbers in a table can be negative as well as positive.\nToshizo reports these figures to his boss in Tokyo, and together they\nsometimes decide to close stores that are not doing well and sometimes\ndecide to open new stores in places that they think will be profitable.\nSo, the total number of stores managed by Toshizo is not fixed. Also,\nthey often decide to discontinue selling some products that are not\npopular, as well as deciding to stock new items that are likely to be\npopular. So, the number of products that Toshizo has to monitor is also\nnot fixed.\nOne New Year, it is very cold in Hakodate. A water pipe bursts in\nToshizo's office and floods his desk. When Toshizo comes to work, he\nfinds that the latest sales table is not legible. He can make out some\nof the figures, but not all of them. He wants to call his boss in\nTokyo to tell him that the figures will be late, but he knows that his\nboss will expect him to reconstruct the table if at all possible.\nWaiting until the next day won't help, because it is the New Year, and\nhis shops will be on holiday. So, Toshizo decides either to work out\nthe values for himself, or to be sure that there really is no unique\nsolution. Only then can he call his boss and tell him what has\nhappened.\nBut Toshizo also wants to be sure that a problem like this never\nhappens again. So he decides to write a computer program that all the\nmanagers in his company can use if some of the data goes missing\nfrom their sales tables. For instance, if they have a table like:\n Store 1 Store 2 Store 3 Totals\n Product A ? ? 70 | 105\n Product B ? 50 ? | 150\n Product C 30 60 90 | 180\n --------------------------------------------------------\n Store's total sales 45 150 240 435\nthen Toshizo's program will be able to tell them the correct figures\nto replace the question marks.\nIn some cases, however, even his program will not be able to replace\nall the question marks, in general.\nFor instance, if a table like:\n Store 1 Store 2 Totals\n Product A ? ? | 40\n Product B ? ? | 40\n ---------------------------------------------\n Store's total sales 40 40 80\nis given, there are infinitely many possible solutions.\nIn this sort of case, his program will just say \"NO\". \nToshizo's program works for any data where the totals row and column\nare still intact.\nCan you reproduce Toshizo's program?\nTask Input: The input consists of multiple data sets, each in the following\nformat:\np s\nrow_1\nrow_2\n. . .\nrow_p\ntotals\n\nThe first line consists of two integers p and s,\nrepresenting the numbers of products and stores, respectively.\nThe former is less than 100 and the latter is less than 10.\nThey are separated by a blank character.\nEach of the subsequent lines represents a row of the table and\nconsists of s+1 elements, each of which is either an integer or\na question mark.\nThe i-th line (1 <= i <= p) corresponds to\nthe i-th product and the last line the totals row.\nThe first s elements in a line represent the sales of each\nstore and the last one the total sales of the product.\nNumbers or question marks in a line are separated by a blank character.\nThere are no missing numbers in the totals column or row. \nThere is at least one question mark in each data set.\nThe known numbers in the table except the totals row and column is\nbetween -1,000 and 1,000, inclusive.\nHowever, unknown numbers, represented by question marks, may not be in\nthis range.\nThe total sales number of each product is between -10,000 and\n10,000, inclusive. \nThe total sales number of each store is between -100,000 and\n100,000, inclusive. \nThere is a blank line between each data set in the input, and the input\nis terminated by a line consisting of a zero.\nTask Output: When there is a unique solution, your program should print the missing\nnumbers in the occurrence order in the input data set.\nOtherwise, your program should print just \"NO\".\nThe answers of consecutive data sets should be separated by an empty\nline.\nEach non-empty output line contains only a single number or \"NO\".\nTask Samples: input: 3 3\n? ? 70 105\n? 50 ? 150\n30 60 90 180\n45 150 240 435\n \n2 2\n? ? 40\n? ? 40\n40 40 80\n\n2 3\n? 30 40 90\n50 60 70 180\n70 90 110 270\n\n0\n output: -5\n40\n20\n80\n \nNO\n\n20\n\n" }, { "title": "Nets of Dice", "content": "In mathematics, some plain words have special meanings.\nThe word \"net\" is one of such technical terms.\nIn mathematics, the word \"net\" is sometimes used to\nmean a plane shape \nwhich can be folded into some solid shape.\nThe following are a solid shape (Figure 1) and one of its net (Figure 2).\nNets corresponding to a solid shape are not unique.\nFor example, Figure 3 shows three of the nets of a cube.\nIn this problem, we consider nets of dice.\nThe definition of a die is as follows.\n A die is a cube, each face marked with a number between one and six.\n Numbers on faces of a die are different from each other.\n The sum of two numbers on the opposite faces is always 7.\nUsually, a die is used in pair with another die.\nThe plural form of the word \"die\" is \"dice\".\nSome examples of proper nets of dice are shown in Figure 4,\nand those of improper ones are shown in Figure 5.\nThe reasons why each example in Figure 5 is improper are as follows.\n(a) The sum of two numbers on the opposite faces is not always 7.\n(b) Some faces are marked with the same number.\n(c) This is not a net of a cube. Some faces overlap each other.\n(d) This is not a net of a cube.\nSome faces overlap each other and one face of a cube is not covered.\n(e) This is not a net of a cube. \nThe plane shape is cut off into two parts.\nThe face marked with '2' is isolated.\n(f) This is not a net of a cube.\nThe plane shape is cut off into two parts.\n(g) There is an extra face marked with '5'.\nNotice that there are two kinds of dice.\nFor example, the solid shapes formed from \nthe first two examples in Figure 4 \nare mirror images of each other.\nAny net of a die can be expressed on a sheet of 5x5 mesh like the one in Figure 6.\nIn the figure, gray squares are the parts to be cut off.\nWhen we represent the sheet of mesh by numbers as in Figure 7,\nsquares cut off are marked with zeros.\nYour job is to write a program which tells\nthe proper nets of a die from the improper ones automatically.", "constraint": "", "input": "The input consists of multiple sheets of 5x5 mesh.\n \n N \n\n Mesh_0 \n\n Mesh_1 \n\n . . . \n\n Mesh_N-1 \n\n \nN is the number of sheets of mesh.\nEach Mesh_i gives a sheet of mesh\non which a net of a die is expressed.\nMesh_i is in the following format.\n \n \n F_00 \n F_01 \n F_02 \n F_03 \n F_04 \n \n F_10 \n F_11 \n F_12 \n F_13 \n F_14 \n \n F_20 \n F_21 \n F_22 \n F_23 \n F_24 \n \n F_30 \n F_31 \n F_32 \n F_33 \n F_34 \n \n F_40 \n F_41 \n F_42 \n F_43 \n F_44 \n \nEach F_ij is an integer between 0 and 6.\nThey are separated by a space character.", "output": "For each Mesh_i, \nthe truth value, true or false, \nshould be output, each in a separate line.\nWhen the net of a die expressed on the Mesh_i is proper, \noutput \"true\".\nOtherwise, output \"false\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n0 0 0 0 0\n0 0 0 0 6\n0 2 4 5 3\n0 0 1 0 0\n0 0 0 0 0\n0 0 3 0 0\n0 0 2 0 0\n0 0 4 1 0\n0 0 0 5 0\n0 0 0 6 0\n0 0 0 3 0\n0 0 2 5 0\n0 4 1 0 0\n0 0 6 0 0\n0 0 0 0 0\n0 6 2 0 0\n0 0 4 0 0\n0 1 5 0 0\n0 0 3 0 0\n0 0 0 0 0\n0 0 0 0 6\n0 2 4 5 3\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 1 0\n0 0 0 0 6\n0 2 4 5 3\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 1 0\n output: true\ntrue\nfalse\nfalse\nfalse\nfalse"], "Pid": "p00699", "ProblemText": "Task Description: In mathematics, some plain words have special meanings.\nThe word \"net\" is one of such technical terms.\nIn mathematics, the word \"net\" is sometimes used to\nmean a plane shape \nwhich can be folded into some solid shape.\nThe following are a solid shape (Figure 1) and one of its net (Figure 2).\nNets corresponding to a solid shape are not unique.\nFor example, Figure 3 shows three of the nets of a cube.\nIn this problem, we consider nets of dice.\nThe definition of a die is as follows.\n A die is a cube, each face marked with a number between one and six.\n Numbers on faces of a die are different from each other.\n The sum of two numbers on the opposite faces is always 7.\nUsually, a die is used in pair with another die.\nThe plural form of the word \"die\" is \"dice\".\nSome examples of proper nets of dice are shown in Figure 4,\nand those of improper ones are shown in Figure 5.\nThe reasons why each example in Figure 5 is improper are as follows.\n(a) The sum of two numbers on the opposite faces is not always 7.\n(b) Some faces are marked with the same number.\n(c) This is not a net of a cube. Some faces overlap each other.\n(d) This is not a net of a cube.\nSome faces overlap each other and one face of a cube is not covered.\n(e) This is not a net of a cube. \nThe plane shape is cut off into two parts.\nThe face marked with '2' is isolated.\n(f) This is not a net of a cube.\nThe plane shape is cut off into two parts.\n(g) There is an extra face marked with '5'.\nNotice that there are two kinds of dice.\nFor example, the solid shapes formed from \nthe first two examples in Figure 4 \nare mirror images of each other.\nAny net of a die can be expressed on a sheet of 5x5 mesh like the one in Figure 6.\nIn the figure, gray squares are the parts to be cut off.\nWhen we represent the sheet of mesh by numbers as in Figure 7,\nsquares cut off are marked with zeros.\nYour job is to write a program which tells\nthe proper nets of a die from the improper ones automatically.\nTask Input: The input consists of multiple sheets of 5x5 mesh.\n \n N \n\n Mesh_0 \n\n Mesh_1 \n\n . . . \n\n Mesh_N-1 \n\n \nN is the number of sheets of mesh.\nEach Mesh_i gives a sheet of mesh\non which a net of a die is expressed.\nMesh_i is in the following format.\n \n \n F_00 \n F_01 \n F_02 \n F_03 \n F_04 \n \n F_10 \n F_11 \n F_12 \n F_13 \n F_14 \n \n F_20 \n F_21 \n F_22 \n F_23 \n F_24 \n \n F_30 \n F_31 \n F_32 \n F_33 \n F_34 \n \n F_40 \n F_41 \n F_42 \n F_43 \n F_44 \n \nEach F_ij is an integer between 0 and 6.\nThey are separated by a space character.\nTask Output: For each Mesh_i, \nthe truth value, true or false, \nshould be output, each in a separate line.\nWhen the net of a die expressed on the Mesh_i is proper, \noutput \"true\".\nOtherwise, output \"false\".\nTask Samples: input: 6\n0 0 0 0 0\n0 0 0 0 6\n0 2 4 5 3\n0 0 1 0 0\n0 0 0 0 0\n0 0 3 0 0\n0 0 2 0 0\n0 0 4 1 0\n0 0 0 5 0\n0 0 0 6 0\n0 0 0 3 0\n0 0 2 5 0\n0 4 1 0 0\n0 0 6 0 0\n0 0 0 0 0\n0 6 2 0 0\n0 0 4 0 0\n0 1 5 0 0\n0 0 3 0 0\n0 0 0 0 0\n0 0 0 0 6\n0 2 4 5 3\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 1 0\n0 0 0 0 6\n0 2 4 5 3\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 1 0\n output: true\ntrue\nfalse\nfalse\nfalse\nfalse\n\n" }, { "title": "Exploring Caves", "content": "There are many caves deep in mountains found in the countryside. In legend, \neach cave has a treasure hidden within the farthest room from the cave's \nentrance. The Shogun has ordered his Samurais to explore these caves with \nKarakuri dolls (robots) and to find all treasures. These robots move in the \ncaves and log relative distances and directions between rooms. Each room in a cave is mapped to a point on an integer grid (x, y >= 0). \nFor each cave, the robot always starts from its entrance, runs along the grid \nand returns to the entrance (which also serves as the exit). The treasure in \neach cave is hidden in the farthest room from the entrance, using Euclid \ndistance for measurement, i. e. the distance of the room at point (x, y) from the \nentrance (0,0) is defined as the square root of (x*x+y*y). If more than one \nroom has the same farthest distance from the entrance, the treasure is hidden in \nthe room having the greatest value of x. While the robot explores a cave, it \nrecords how it has moved. Each time it takes a new direction at a room, it notes \nthe difference (dx, dy) from the last time it changed its direction. For \nexample, suppose the robot is currently in the room at point (2,4). If it moves \nto room (6,4), the robot records (4,0), i. e. dx=6-2 and dy=4-4. The first data \nis defined as the difference from the entrance. The following figure shows rooms \nin the first cave of the Sample Input. In the figure, the farthest room is the \nsquare root of 61 distant from the entrance. Based on the records that the robots bring back, your job is to determine the \nrooms where treasures are hidden.", "constraint": "", "input": "In the first line of the input, an integer N showing the number of \ncaves in the input is given. Integers dx_i and \ndy_i are i-th data showing the differences between \nrooms. Note that since the robot moves along the grid, either \ndx_i or dy_i is zero. An integer pair \ndx_i = dy_i = 0 signals the end of one cave's \ndata which means the robot finished the exploration for the cave and returned \nback to the entrance. The coordinates are limited to (0,0)-(1000,1000).", "output": "Print the position (x, y) of the treasure room on a line for each cave.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n1 0\n0 1\n-1 0\n1 0\n0 5\n-1 0\n0 -1\n5 0\n0 1\n0 -1\n1 0\n0 -4\n-3 0\n0 3\n2 0\n0 -2\n-1 0\n0 1\n0 -1\n1 0\n0 2\n-2 0\n0 -3\n3 0\n0 4\n-4 0\n0 -5\n-2 0\n0 0\n1 0\n-1 0\n0 0\n2 0\n0 1\n-1 0\n0 1\n-1 0\n0 -2\n0 0\n output: 6 5\n1 0\n2 1"], "Pid": "p00700", "ProblemText": "Task Description: There are many caves deep in mountains found in the countryside. In legend, \neach cave has a treasure hidden within the farthest room from the cave's \nentrance. The Shogun has ordered his Samurais to explore these caves with \nKarakuri dolls (robots) and to find all treasures. These robots move in the \ncaves and log relative distances and directions between rooms. Each room in a cave is mapped to a point on an integer grid (x, y >= 0). \nFor each cave, the robot always starts from its entrance, runs along the grid \nand returns to the entrance (which also serves as the exit). The treasure in \neach cave is hidden in the farthest room from the entrance, using Euclid \ndistance for measurement, i. e. the distance of the room at point (x, y) from the \nentrance (0,0) is defined as the square root of (x*x+y*y). If more than one \nroom has the same farthest distance from the entrance, the treasure is hidden in \nthe room having the greatest value of x. While the robot explores a cave, it \nrecords how it has moved. Each time it takes a new direction at a room, it notes \nthe difference (dx, dy) from the last time it changed its direction. For \nexample, suppose the robot is currently in the room at point (2,4). If it moves \nto room (6,4), the robot records (4,0), i. e. dx=6-2 and dy=4-4. The first data \nis defined as the difference from the entrance. The following figure shows rooms \nin the first cave of the Sample Input. In the figure, the farthest room is the \nsquare root of 61 distant from the entrance. Based on the records that the robots bring back, your job is to determine the \nrooms where treasures are hidden.\nTask Input: In the first line of the input, an integer N showing the number of \ncaves in the input is given. Integers dx_i and \ndy_i are i-th data showing the differences between \nrooms. Note that since the robot moves along the grid, either \ndx_i or dy_i is zero. An integer pair \ndx_i = dy_i = 0 signals the end of one cave's \ndata which means the robot finished the exploration for the cave and returned \nback to the entrance. The coordinates are limited to (0,0)-(1000,1000).\nTask Output: Print the position (x, y) of the treasure room on a line for each cave.\nTask Samples: input: 3\n1 0\n0 1\n-1 0\n1 0\n0 5\n-1 0\n0 -1\n5 0\n0 1\n0 -1\n1 0\n0 -4\n-3 0\n0 3\n2 0\n0 -2\n-1 0\n0 1\n0 -1\n1 0\n0 2\n-2 0\n0 -3\n3 0\n0 4\n-4 0\n0 -5\n-2 0\n0 0\n1 0\n-1 0\n0 0\n2 0\n0 1\n-1 0\n0 1\n-1 0\n0 -2\n0 0\n output: 6 5\n1 0\n2 1\n\n" }, { "title": "Pile Up!", "content": "There are cubes of the same size and a simple robot named Masato. Initially, \nall cubes are on the floor. Masato can be instructed to pick up a cube and put \nit on another cube, to make piles of cubes. Each instruction is of the form \n`pick up cube A and put it on cube B (or on the floor). ' When he is to pick up a cube, he does so after taking off all the cubes on \nand above it in the same pile (if any) onto the floor. In contrast, when he is \nto put a cube on another, he puts the former on top of the pile including the \nlatter without taking any cubes off. When he is instructed to put a cube on another cube and both cubes are \nalready in the same pile, there are two cases. If the former cube is stacked \nsomewhere below the latter, he put off all the cube above it onto the floor. \nAfterwards he puts the former cube on the latter cube. If the former cube is \nstacked somewhere above the latter, he just ignores the instruction. When he is instructed to put a cube on the floor, there are also two cases. \nIf the cube is already on the floor (including the case that the cube is stacked \nin the bottom of some pile), he just ignores the instruction. Otherwise, he puts \noff all the cube on and up above the pile (if any) onto the floor before moving \nthe cube onto the floor. He also ignores the instruction when told to put a cube on top of itself \n(this is impossible). Given the number of the cubes and a series of instructions, simulate actions \nof Masato and calculate the heights of piles when Masato has finished his job.", "constraint": "", "input": "The input consists of a series of data sets. One data set contains the number \nof cubes as its first line, and a series of instructions, each described in a \nseparate line. The number of cubes does not exceed 100. Each instruction \nconsists of two numbers; the former number indicates which cube to pick up, and \nthe latter number indicates on which cube to put it. The end of the instructions \nis marked by two zeros. The end of the input is marked by the line containing a single zero. One data set has the following form: m\nI_1 J_1\nI_2 J_2\n. . .\nI_n J_n\n0 0\nEach cube is identified by its number (1 through m). \nI_k indicates which cube to pick up and \nJ_k indicates on which cube to put it. The latter may be \nzero, instructing to put the cube on the floor.", "output": "Output the height of each pile (the number of cubes in the pile) in ascending \norder, separated by newlines. A single cube by itself also counts as \"a pile. \" \nEnd of output for one data set should be marked by a line containing the \ncharacter sequence `end' by itself.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 3\n2 0\n0 0\n4\n4 1\n3 1\n1 2\n0 0\n5\n2 1\n3 1\n4 1\n3 2\n1 1\n0 0\n0\n output: 1\n2\nend\n1\n1\n2\nend\n1\n4\nend"], "Pid": "p00701", "ProblemText": "Task Description: There are cubes of the same size and a simple robot named Masato. Initially, \nall cubes are on the floor. Masato can be instructed to pick up a cube and put \nit on another cube, to make piles of cubes. Each instruction is of the form \n`pick up cube A and put it on cube B (or on the floor). ' When he is to pick up a cube, he does so after taking off all the cubes on \nand above it in the same pile (if any) onto the floor. In contrast, when he is \nto put a cube on another, he puts the former on top of the pile including the \nlatter without taking any cubes off. When he is instructed to put a cube on another cube and both cubes are \nalready in the same pile, there are two cases. If the former cube is stacked \nsomewhere below the latter, he put off all the cube above it onto the floor. \nAfterwards he puts the former cube on the latter cube. If the former cube is \nstacked somewhere above the latter, he just ignores the instruction. When he is instructed to put a cube on the floor, there are also two cases. \nIf the cube is already on the floor (including the case that the cube is stacked \nin the bottom of some pile), he just ignores the instruction. Otherwise, he puts \noff all the cube on and up above the pile (if any) onto the floor before moving \nthe cube onto the floor. He also ignores the instruction when told to put a cube on top of itself \n(this is impossible). Given the number of the cubes and a series of instructions, simulate actions \nof Masato and calculate the heights of piles when Masato has finished his job.\nTask Input: The input consists of a series of data sets. One data set contains the number \nof cubes as its first line, and a series of instructions, each described in a \nseparate line. The number of cubes does not exceed 100. Each instruction \nconsists of two numbers; the former number indicates which cube to pick up, and \nthe latter number indicates on which cube to put it. The end of the instructions \nis marked by two zeros. The end of the input is marked by the line containing a single zero. One data set has the following form: m\nI_1 J_1\nI_2 J_2\n. . .\nI_n J_n\n0 0\nEach cube is identified by its number (1 through m). \nI_k indicates which cube to pick up and \nJ_k indicates on which cube to put it. The latter may be \nzero, instructing to put the cube on the floor.\nTask Output: Output the height of each pile (the number of cubes in the pile) in ascending \norder, separated by newlines. A single cube by itself also counts as \"a pile. \" \nEnd of output for one data set should be marked by a line containing the \ncharacter sequence `end' by itself.\nTask Samples: input: 3\n1 3\n2 0\n0 0\n4\n4 1\n3 1\n1 2\n0 0\n5\n2 1\n3 1\n4 1\n3 2\n1 1\n0 0\n0\n output: 1\n2\nend\n1\n1\n2\nend\n1\n4\nend\n\n" }, { "title": "Kanglish : Analysis on Artificial Language", "content": "The late Prof. Kanazawa made an artificial language named Kanglish, which is \nsimilar to English, for studying mythology. Words and sentences of Kanglish are \nwritten with its own special characters called \"Kan-characters\". The size of the \nset of the Kan-characters is 38, i. e. , there are 38 different Kan-characters in \nthe set. Since Kan-characters cannot be directly stored in a computer because of \nthe lack of a coded character set, Prof. Kanazawa devised a way to represent \neach Kan-character as an alphabetical letter or an ordered combination of two \nalphabetical letters. Thus, each Kan-character is represented as one of the \nfollowing 26 letters \n\"a\", \"b\", \"c\", \"d\", \"e\", \"f\", \"g\", \"h\", \"i\", \"j\", \"k\", \"l\", \"m\", \n \"n\", \"o\", \"p\", \"q\", \"r\", \"s\", \"t\", \"u\", \"v\", \"w\", \"x\", \"y\", and \"z\", \nor one of the following 12 combinations of letters \n\"ld\", \"mb\", \"mp\", \"nc\", \"nd\", \"ng\", \"nt\", \"nw\", \"ps\", \"qu\", \"cw\", \n and \"ts\". \nIn addition, the Kan-characters are ordered according to \nthe above alphabetical representation. The order is named Kan-order in which the \nKan-character represented by \"a\" is the first one, that by \"b\" is the second, \nthat by \"z\" is the 26th, that by \"ld\" is the 27th, and that by \"ts\" is the 38th \n(the last). \nThe representations of words in Kanglish are separated by spaces. Each \nsentence is written in one line, so there are no periods or full stops in \nKanglish. All alphabetical letters are in lower case, i. e. , there are no \ncapitalizations. \nWe currently have many documents written in Kanglish with the alphabetical \nrepresentation. However, we have lost most of Prof. Kanazawa's work on how they \ncan be translated. To recognize his work, we have decided to first analyze them \nstatistically. The first analysis is to check sequences of consecutive \nKan-characters in words. \nFor example, a substring \"ic\" in a word \"quice\" indicates an ordered pair of \ntwo adjacent Kan-characters that are represented by \"i\" and \"c\". For simplicity, \nwe make a rule that, in the alphabetical representation of a word, a \nKan-character is recognized as the longest possible alphabetical representation \nfrom left to right. Thus, a substring \"ncw\" should be considered as a pair of \n\"nc\" and \"w\". It does not consist of \"n\" and \"cw\", nor \"n\", \"c\", and \"w\". \nFor each Kan-character, there are 38 possible pairs of that Kan-character and \nanother Kan-character, e. g. \"aa\", \"ab\", . . . , \"az\", \"ald\", . . . , \"ats\". Thus, \nmathematically, there is a total of 1444 (i. e. , 38x38) possible pairs, including \npairs such as \"n\" and \"cw\", which is actually not allowed according to the above \nrule. \nYour job is to write a program that counts how many times each pair occurs in \ninput data. For example, in the sentence qua ist qda quang quice\nthe Kan-character represented by \"qu\" appears \nthree times. There are two occurrences of the pair of \"qu\" and \"a\", and one \noccurrence of the pair of \"qu\" and \"i\". Note that the alphabetical letter \"q\" \nappears four times in the example sentence, but the Kan-character represented by \n\"q\" occurs only once, because \"qu\" represents another Kan-character that is \ndifferent from the Kan-character represented by \"q\". \nFor simplicity, a newline at the end of a line is considered as a space. Thus \nin the above example, \"e\" is followed by a space.", "constraint": "", "input": "n\nline_1\nline_2\n. . .\nline_n\nThe first line of the input is an integer n, which indicates the \nnumber of lines that follow. Each line except for the first line represents one \nKanglish sentence. You may assume that n <= 1000 and that each line \nhas at most 59 alphabetical letters including spaces.", "output": "a kc_1 m_1\nb kc_2 m_2\nc kc_3 m_3\n. . .\nts kc_38 m_38\nThe output consists of 38 lines for the whole input lines. Each line of the \noutput has two strings and an integer. In the i-th line in the output, \nthe first string is the alphabetical representation of the i-th \nKan-character in the Kan-order. For example, the first string of the first line \nis \"a\", that of the third line is \"c\", and that of the 37th line is \"cw\". The \nfirst string is followed by a space. The second string in the i-th line (denoted by kc_i \nabove) shows the alphabetical representation of a Kan-character that most often \noccurred directly after the first Kan-character. If there are two or more such \nKan-characters, the first one in the Kan-order should be printed. The second \nstring is followed by a space. The integer (denoted by m_i above) in the i-th line \nshows the number of times that the second Kan-character occurred directly after \nthe first Kan-character. In other words, the integer shows the number of times \nthat ``the ordered pair of the first Kan-character and the second \nKan-character'' appeared in the input. The integer is followed by a newline. \nSuppose the 28th output line is as follows: \nmb e 4\n\"mb\" is output because it is the 28th character in \nthe Kanglish alphabet. \"e 4\" means that the pair \"mbe\" appeared 4 times in the \ninput, and that there were no pairs beginning with \"mb\" that appeared more than \n4 times. \n

\nNote that if the i-th Kan-character does not appear in the input, or \nif the i-th Kan-character is not followed by any other Kan-characters but \nspaces, the second string in the i-th output line should be \"a\" and the \nthird item should be zero. \nAlthough the output does not include spaces, Kan-characters that appear with \na space in-between is not considered as a pair. Thus, in the following example \nabc def\n\n\"d\" is not counted as occurring after \"c\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nnai tiruvantel ar varyuvantel i valar tielyama nu vilya\nqua ist qda quang ncw psts\nsvampti tsuldya jay quadal ciszeriol\n output: a r 3\nb a 0\nc i 1\nd a 2\ne l 3\nf a 0\ng a 0\nh a 0\ni s 2\nj a 1\nk a 0\nl y 2\nm a 1\nn a 1\no l 1\np a 0\nq d 1\nr i 1\ns t 1\nt i 3\nu v 2\nv a 5\nw a 0\nx a 0\ny a 3\nz e 1\nld y 1\nmb a 0\nmp t 1\nnc w 1\nnd a 0\nng a 0\nnt e 2\nnw a 0\nps ts 1\nqu a 3\ncw a 0\nts u 1"], "Pid": "p00702", "ProblemText": "Task Description: The late Prof. Kanazawa made an artificial language named Kanglish, which is \nsimilar to English, for studying mythology. Words and sentences of Kanglish are \nwritten with its own special characters called \"Kan-characters\". The size of the \nset of the Kan-characters is 38, i. e. , there are 38 different Kan-characters in \nthe set. Since Kan-characters cannot be directly stored in a computer because of \nthe lack of a coded character set, Prof. Kanazawa devised a way to represent \neach Kan-character as an alphabetical letter or an ordered combination of two \nalphabetical letters. Thus, each Kan-character is represented as one of the \nfollowing 26 letters \n\"a\", \"b\", \"c\", \"d\", \"e\", \"f\", \"g\", \"h\", \"i\", \"j\", \"k\", \"l\", \"m\", \n \"n\", \"o\", \"p\", \"q\", \"r\", \"s\", \"t\", \"u\", \"v\", \"w\", \"x\", \"y\", and \"z\", \nor one of the following 12 combinations of letters \n\"ld\", \"mb\", \"mp\", \"nc\", \"nd\", \"ng\", \"nt\", \"nw\", \"ps\", \"qu\", \"cw\", \n and \"ts\". \nIn addition, the Kan-characters are ordered according to \nthe above alphabetical representation. The order is named Kan-order in which the \nKan-character represented by \"a\" is the first one, that by \"b\" is the second, \nthat by \"z\" is the 26th, that by \"ld\" is the 27th, and that by \"ts\" is the 38th \n(the last). \nThe representations of words in Kanglish are separated by spaces. Each \nsentence is written in one line, so there are no periods or full stops in \nKanglish. All alphabetical letters are in lower case, i. e. , there are no \ncapitalizations. \nWe currently have many documents written in Kanglish with the alphabetical \nrepresentation. However, we have lost most of Prof. Kanazawa's work on how they \ncan be translated. To recognize his work, we have decided to first analyze them \nstatistically. The first analysis is to check sequences of consecutive \nKan-characters in words. \nFor example, a substring \"ic\" in a word \"quice\" indicates an ordered pair of \ntwo adjacent Kan-characters that are represented by \"i\" and \"c\". For simplicity, \nwe make a rule that, in the alphabetical representation of a word, a \nKan-character is recognized as the longest possible alphabetical representation \nfrom left to right. Thus, a substring \"ncw\" should be considered as a pair of \n\"nc\" and \"w\". It does not consist of \"n\" and \"cw\", nor \"n\", \"c\", and \"w\". \nFor each Kan-character, there are 38 possible pairs of that Kan-character and \nanother Kan-character, e. g. \"aa\", \"ab\", . . . , \"az\", \"ald\", . . . , \"ats\". Thus, \nmathematically, there is a total of 1444 (i. e. , 38x38) possible pairs, including \npairs such as \"n\" and \"cw\", which is actually not allowed according to the above \nrule. \nYour job is to write a program that counts how many times each pair occurs in \ninput data. For example, in the sentence qua ist qda quang quice\nthe Kan-character represented by \"qu\" appears \nthree times. There are two occurrences of the pair of \"qu\" and \"a\", and one \noccurrence of the pair of \"qu\" and \"i\". Note that the alphabetical letter \"q\" \nappears four times in the example sentence, but the Kan-character represented by \n\"q\" occurs only once, because \"qu\" represents another Kan-character that is \ndifferent from the Kan-character represented by \"q\". \nFor simplicity, a newline at the end of a line is considered as a space. Thus \nin the above example, \"e\" is followed by a space.\nTask Input: n\nline_1\nline_2\n. . .\nline_n\nThe first line of the input is an integer n, which indicates the \nnumber of lines that follow. Each line except for the first line represents one \nKanglish sentence. You may assume that n <= 1000 and that each line \nhas at most 59 alphabetical letters including spaces.\nTask Output: a kc_1 m_1\nb kc_2 m_2\nc kc_3 m_3\n. . .\nts kc_38 m_38\nThe output consists of 38 lines for the whole input lines. Each line of the \noutput has two strings and an integer. In the i-th line in the output, \nthe first string is the alphabetical representation of the i-th \nKan-character in the Kan-order. For example, the first string of the first line \nis \"a\", that of the third line is \"c\", and that of the 37th line is \"cw\". The \nfirst string is followed by a space. The second string in the i-th line (denoted by kc_i \nabove) shows the alphabetical representation of a Kan-character that most often \noccurred directly after the first Kan-character. If there are two or more such \nKan-characters, the first one in the Kan-order should be printed. The second \nstring is followed by a space. The integer (denoted by m_i above) in the i-th line \nshows the number of times that the second Kan-character occurred directly after \nthe first Kan-character. In other words, the integer shows the number of times \nthat ``the ordered pair of the first Kan-character and the second \nKan-character'' appeared in the input. The integer is followed by a newline. \nSuppose the 28th output line is as follows: \nmb e 4\n\"mb\" is output because it is the 28th character in \nthe Kanglish alphabet. \"e 4\" means that the pair \"mbe\" appeared 4 times in the \ninput, and that there were no pairs beginning with \"mb\" that appeared more than \n4 times. \n

\nNote that if the i-th Kan-character does not appear in the input, or \nif the i-th Kan-character is not followed by any other Kan-characters but \nspaces, the second string in the i-th output line should be \"a\" and the \nthird item should be zero. \nAlthough the output does not include spaces, Kan-characters that appear with \na space in-between is not considered as a pair. Thus, in the following example \nabc def\n\n\"d\" is not counted as occurring after \"c\".\nTask Samples: input: 3\nnai tiruvantel ar varyuvantel i valar tielyama nu vilya\nqua ist qda quang ncw psts\nsvampti tsuldya jay quadal ciszeriol\n output: a r 3\nb a 0\nc i 1\nd a 2\ne l 3\nf a 0\ng a 0\nh a 0\ni s 2\nj a 1\nk a 0\nl y 2\nm a 1\nn a 1\no l 1\np a 0\nq d 1\nr i 1\ns t 1\nt i 3\nu v 2\nv a 5\nw a 0\nx a 0\ny a 3\nz e 1\nld y 1\nmb a 0\nmp t 1\nnc w 1\nnd a 0\nng a 0\nnt e 2\nnw a 0\nps ts 1\nqu a 3\ncw a 0\nts u 1\n\n" }, { "title": "What is the Number in my Mind ?", "content": "Let us enjoy a number guess game. \nA number containing L digits is in my mind (where 4 < = L < = 10). You \nshould guess what number it is. It is composed of any of the following ten \ndigits: \"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", and \"9\".\nNo digits appear twice in the number. For example, when L = 4, \"1234\" is a\nlegitimate candidate but \"1123\" is not (since \"1\" appears twice). \nThe number may begin with \"0\", and a number \"05678\" should be distinct from a \nnumber \"5678\", for example. \nIf you and your computer cannot see through my mind by telepathy, a group of \nhints will be needed in order for you to identify the number in my mind. \nA hint is a triple of numbers named try, hit, and \nblow. \nThe try is a number containing L decimal digits. No digits appear \ntwice in the try, and this number may also begin with \"0\". \nThe hit value indicates the count of digits that the try and \nthe number in my mind have in common, and that are exactly in the same position. \nThe blow value indicates the count of digits that the try and\nthe number in my mind have in common, but that are NOT in the same position. \nThey are arranged in one line as follows. try hit blow\nFor example, if L = 4 and the number in my mind is 9876, then the\nfollowing is an example of hint-set consisting of legitimate hints. 7360 0 2\n\t\"2507 0 1\n\t\"9713 1 1\n\t\"9678 2 2\nThe above hint-set should be sufficient for you to guess the number and\nthe answer should be 9876. \nIn contrast, the following hint-set is not sufficient to guess the\nnumber.\t\"7360 0 2\n\t\"9713 1 1\n\t\"9678 2 2\nNo number is consistent with the following hint-set.\t\"9678 2 2\n\t\"1234 2 2\nAnswers for last two hint-sets should be NO.\nYour job is to write a program identifying the numbers in my mind using given\nhint-sets.", "constraint": "", "input": "The input consists of multiple hint-sets as follows. Each of them corresponds \nto a number in my mind. < HINT-SET__1 >\n< HINT-SET__2 >\n. . . \n< HINT-SET_i >\n. . . \n< HINT-SET_n >\nA is composed of one header line in the \nfollowing format (L and H should be separated by a single space \ncharacter. ): L H\nand H lines of hints in the following format (1 <= j <= \nH ) : TRY_1 HIT_1 BLOW_1\nTRY_2 HIT_2 BLOW_2\n. . . \nTRY_j HIT_j BLOW_j\n. . . \nTRY_H HIT_H BLOW_H\n

L indicates the number of digits of the number in my mind and \nTRY_j . HIT_j and BLOW_j \nindicate hit and blow values between the TRY_j and the number \nin my mind. (They are separated by a single space character. ) \n

The end of the input is indicated by a header line with L = 0 and \nH = 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 4\n160348 0 4\n913286 2 3\n431289 3 1\n671283 3 3\n10 8\n3827690415 2 8\n0482691573 1 9\n1924730586 3 7\n1378490256 1 9\n6297830541 1 9\n4829531706 3 7\n4621570983 1 9\n9820147536 6 4\n4 4\n2713 0 3\n1247 2 0\n1230 1 1\n1387 2 1\n6 5\n605743 0 4\n593026 2 2\n792456 1 2\n143052 1 3\n093614 3 3\n5 2\n12345 5 0\n67890 0 5\n0 0\n output: 637281\n7820914536\n3287\nNO\nNO"], "output": "For each hint-set, the answer should be printed, each in a separate line. If \nyou can successfully identify the number for a given hint-set, the answer should \nbe the number. If you cannot identify the number, the answer should be \nNO.", "Pid": "p00703", "ProblemText": "Task Description: Let us enjoy a number guess game. \nA number containing L digits is in my mind (where 4 < = L < = 10). You \nshould guess what number it is. It is composed of any of the following ten \ndigits: \"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", and \"9\".\nNo digits appear twice in the number. For example, when L = 4, \"1234\" is a\nlegitimate candidate but \"1123\" is not (since \"1\" appears twice). \nThe number may begin with \"0\", and a number \"05678\" should be distinct from a \nnumber \"5678\", for example. \nIf you and your computer cannot see through my mind by telepathy, a group of \nhints will be needed in order for you to identify the number in my mind. \nA hint is a triple of numbers named try, hit, and \nblow. \nThe try is a number containing L decimal digits. No digits appear \ntwice in the try, and this number may also begin with \"0\". \nThe hit value indicates the count of digits that the try and \nthe number in my mind have in common, and that are exactly in the same position. \nThe blow value indicates the count of digits that the try and\nthe number in my mind have in common, but that are NOT in the same position. \nThey are arranged in one line as follows. try hit blow\nFor example, if L = 4 and the number in my mind is 9876, then the\nfollowing is an example of hint-set consisting of legitimate hints. 7360 0 2\n\t\"2507 0 1\n\t\"9713 1 1\n\t\"9678 2 2\nThe above hint-set should be sufficient for you to guess the number and\nthe answer should be 9876. \nIn contrast, the following hint-set is not sufficient to guess the\nnumber.\t\"7360 0 2\n\t\"9713 1 1\n\t\"9678 2 2\nNo number is consistent with the following hint-set.\t\"9678 2 2\n\t\"1234 2 2\nAnswers for last two hint-sets should be NO.\nYour job is to write a program identifying the numbers in my mind using given\nhint-sets.\nTask Input: The input consists of multiple hint-sets as follows. Each of them corresponds \nto a number in my mind. < HINT-SET__1 >\n< HINT-SET__2 >\n. . . \n< HINT-SET_i >\n. . . \n< HINT-SET_n >\nA is composed of one header line in the \nfollowing format (L and H should be separated by a single space \ncharacter. ): L H\nand H lines of hints in the following format (1 <= j <= \nH ) : TRY_1 HIT_1 BLOW_1\nTRY_2 HIT_2 BLOW_2\n. . . \nTRY_j HIT_j BLOW_j\n. . . \nTRY_H HIT_H BLOW_H\n

L indicates the number of digits of the number in my mind and \nTRY_j . HIT_j and BLOW_j \nindicate hit and blow values between the TRY_j and the number \nin my mind. (They are separated by a single space character. ) \n

The end of the input is indicated by a header line with L = 0 and \nH = 0.\nTask Output: For each hint-set, the answer should be printed, each in a separate line. If \nyou can successfully identify the number for a given hint-set, the answer should \nbe the number. If you cannot identify the number, the answer should be \nNO.\nTask Samples: input: 6 4\n160348 0 4\n913286 2 3\n431289 3 1\n671283 3 3\n10 8\n3827690415 2 8\n0482691573 1 9\n1924730586 3 7\n1378490256 1 9\n6297830541 1 9\n4829531706 3 7\n4621570983 1 9\n9820147536 6 4\n4 4\n2713 0 3\n1247 2 0\n1230 1 1\n1387 2 1\n6 5\n605743 0 4\n593026 2 2\n792456 1 2\n143052 1 3\n093614 3 3\n5 2\n12345 5 0\n67890 0 5\n0 0\n output: 637281\n7820914536\n3287\nNO\nNO\n\n" }, { "title": "Enclosing Circles", "content": "A number of circles are given. A circle may be disjoint from other circles, \noverlapping with some other circles, or even totally surrounding or surrounded \nby another circle. \n

\n Mask A B C I M P \n\n Case 1 9 2 0 1 5 3 \n\n Case 2 9 3 0 1 5 4 \n\n Case 3 9 6 0 1 5 7 \n\n Case 4 9 7 0 1 5 8 \n\n \nYour job is to write a program which solves this puzzle.", "constraint": "", "input": "The input consists of a number of datasets.\nThe end of the input is indicated by a line containing a zero.\n\n

\nThe number of datasets is no more than 100.\nEach dataset is formatted as follows.\n\nN \nSTRING _1 \nSTRING _2 \n. . . \nSTRING _N \n\n

\n\nThe first line of a dataset contains an integer N \nwhich is the number of integers appearing in the equation.\nEach of the following N lines contains a string\ncomposed of uppercase alphabetic characters 'A'-'Z'\nwhich mean masked digits.\n\nEach dataset expresses the following equation.\n\nSTRING _1 + STRING _2 + . . . + STRING _N -1 = STRING _N\n\nThe integer N is greater than 2 and less than 13.\nThe length of STRING _i is greater than 0\nand less than 9.\nThe number of different alphabetic characters appearing \nin each dataset is greater than 0 and less than 11.", "output": "For each dataset, output a single line containing \nthe number of different digit assignments that satisfy the equation.\n\nThe output must not contain any superfluous characters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nACM\nIBM\nICPC\n3\nGAME\nBEST\nGAMER\n4\nA\nB\nC\nAB\n3\nA\nB\nCD\n3\nONE\nTWO\nTHREE\n3\nTWO\nTHREE\nFIVE\n3\nMOV\nPOP\nDIV\n9\nA\nB\nC\nD\nE\nF\nG\nH\nIJ\n0\n output: 4\n1\n8\n30\n0\n0\n0\n40320"], "Pid": "p00742", "ProblemText": "Task Description: Let's think about verbal arithmetic. \n\nThe material of this puzzle is a summation\nof non-negative integers represented in a decimal format,\nfor example, as follows.\n\n 905 + 125 = 1030\n\nIn verbal arithmetic, every digit appearing in the equation is masked with an alphabetic character. A problem which has the above equation as one of its answers, for example, is the following.\n\n ACM + IBM = ICPC\n\nSolving this puzzle means finding possible digit assignments\nto the alphabetic characters in the verbal equation.\n\nThe rules of this puzzle are the following.\nEach integer in the equation is expressed in terms of one or more\ndigits '0'-'9', but all the digits are masked with some alphabetic\ncharacters 'A'-'Z'.\n\nThe same alphabetic character appearing in multiple places \nof the equation masks the same digit.\nMoreover, all appearances of the same digit are masked with a single\nalphabetic character.\nThat is, different alphabetic characters mean different digits.\n\nThe most significant digit must not be '0',\nexcept when a zero is expressed as a single digit '0'.\nThat is, expressing numbers as \"00\" or \"0123\" is not permitted.\n\nThere are 4 different digit assignments for the verbal equation above\nas shown in the following table.\n

\n Mask A B C I M P \n\n Case 1 9 2 0 1 5 3 \n\n Case 2 9 3 0 1 5 4 \n\n Case 3 9 6 0 1 5 7 \n\n Case 4 9 7 0 1 5 8 \n\n \nYour job is to write a program which solves this puzzle.\nTask Input: The input consists of a number of datasets.\nThe end of the input is indicated by a line containing a zero.\n\n

\nThe number of datasets is no more than 100.\nEach dataset is formatted as follows.\n\nN \nSTRING _1 \nSTRING _2 \n. . . \nSTRING _N \n\n

\n\nThe first line of a dataset contains an integer N \nwhich is the number of integers appearing in the equation.\nEach of the following N lines contains a string\ncomposed of uppercase alphabetic characters 'A'-'Z'\nwhich mean masked digits.\n\nEach dataset expresses the following equation.\n\nSTRING _1 + STRING _2 + . . . + STRING _N -1 = STRING _N\n\nThe integer N is greater than 2 and less than 13.\nThe length of STRING _i is greater than 0\nand less than 9.\nThe number of different alphabetic characters appearing \nin each dataset is greater than 0 and less than 11.\nTask Output: For each dataset, output a single line containing \nthe number of different digit assignments that satisfy the equation.\n\nThe output must not contain any superfluous characters.\nTask Samples: input: 3\nACM\nIBM\nICPC\n3\nGAME\nBEST\nGAMER\n4\nA\nB\nC\nAB\n3\nA\nB\nCD\n3\nONE\nTWO\nTHREE\n3\nTWO\nTHREE\nFIVE\n3\nMOV\nPOP\nDIV\n9\nA\nB\nC\nD\nE\nF\nG\nH\nIJ\n0\n output: 4\n1\n8\n30\n0\n0\n0\n40320\n\n" }, { "title": "Problem D: Discrete Speed", "content": "Consider car trips in a country where there is no friction.\nCars in this country do not have engines.\nOnce a car started to move at a speed, it keeps moving at the same speed.\nThere are acceleration devices on some points on the road,\nwhere a car can increase or decrease its speed by 1.\nIt can also keep its speed there.\nYour job in this problem is to write a program\nwhich determines the route with the shortest time\nto travel from a starting city to a goal city.\nThere are several cities in the country,\nand a road network connecting them.\nEach city has an acceleration device.\nAs mentioned above, if a car arrives at a city at a speed v ,\nit leaves the city at one of v - 1, v , or v + 1.\nThe first road leaving the starting city must be run at the speed 1.\nSimilarly, the last road arriving at the goal city must be run at the speed 1.\nThe starting city and the goal city are given.\nThe problem is to find the best route which leads to the goal city\ngoing through several cities on the road network.\nWhen the car arrives at a city, it cannot immediately go back the road\nit used to reach the city. No U-turns are allowed.\nExcept this constraint, one can choose any route on the road network.\nIt is allowed to visit the same city or use the same road multiple times.\nThe starting city and the goal city may be visited during the trip.\nFor each road on the network, its distance and speed limit are given.\nA car must run a road at a speed less than or equal to its speed limit.\nThe time needed to run a road is the distance divided by the speed.\nThe time needed within cities including that for acceleration or deceleration should be ignored.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn m \ns g \n\nx_ 1 y_ 1 d_ 1 c_ 1\n. . . \n\nx_m y_m d_m c_m \n\nEvery input item in a dataset is a non-negative integer.\nInput items in the same line are separated by a space.\n\nThe first line gives the size of the road network.\nn is the number of cities in the network.\nYou can assume that the number of cities is between 2 and 30, inclusive.\nm is the number of roads between cities, which may be zero.\nThe second line gives the trip.\ns is the city index of the starting city.\ng is the city index of the goal city.\ns is not equal to g .\nYou can assume that all city indices in a dataset (including the above two)\nare between 1 and n , inclusive.\nThe following m lines give the details of roads between cities.\nThe i -th road connects two cities with city indices\nx_i and y_i ,\nand has a distance d_i (1 <= i <= m ).\nYou can assume that the distance is between 1 and 100, inclusive.\nThe speed limit of the road is specified by c_i .\nYou can assume that the speed limit is between 1 and 30, inclusive.\nNo two roads connect the same pair of cities.\nA road never connects a city with itself.\nEach road can be traveled in both directions.\n\nThe last dataset is followed by a line containing two zeros\n(separated by a space).", "output": "For each dataset in the input, one line should be output as specified below.\nAn output line should not contain extra characters such as spaces.\n\nIf one can travel from the starting city to the goal city,\nthe time needed for the best route (a route with the shortest time)\nshould be printed.\nThe answer should not have an error greater than 0.001.\nYou may output any number of digits after the decimal point,\nprovided that the above accuracy condition is satisfied.\n\nIf it is impossible to reach the goal city,\nthe string \"unreachable\" should be printed.\nNote that all the letters of \"unreachable\" are in lowercase.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 0\n1 2\n5 4\n1 5\n1 2 1 1\n2 3 2 2\n3 4 2 2\n4 5 1 1\n6 6\n1 6\n1 2 2 1\n2 3 2 1\n3 6 2 1\n1 4 2 30\n4 5 3 30\n5 6 2 30\n6 7\n1 6\n1 2 1 30\n2 3 1 30\n3 1 1 30\n3 4 100 30\n4 5 1 30\n5 6 1 30\n6 4 1 30\n0 0\n output: unreachable\n4.00000\n5.50000\n11.25664"], "Pid": "p00743", "ProblemText": "Task Description: Consider car trips in a country where there is no friction.\nCars in this country do not have engines.\nOnce a car started to move at a speed, it keeps moving at the same speed.\nThere are acceleration devices on some points on the road,\nwhere a car can increase or decrease its speed by 1.\nIt can also keep its speed there.\nYour job in this problem is to write a program\nwhich determines the route with the shortest time\nto travel from a starting city to a goal city.\nThere are several cities in the country,\nand a road network connecting them.\nEach city has an acceleration device.\nAs mentioned above, if a car arrives at a city at a speed v ,\nit leaves the city at one of v - 1, v , or v + 1.\nThe first road leaving the starting city must be run at the speed 1.\nSimilarly, the last road arriving at the goal city must be run at the speed 1.\nThe starting city and the goal city are given.\nThe problem is to find the best route which leads to the goal city\ngoing through several cities on the road network.\nWhen the car arrives at a city, it cannot immediately go back the road\nit used to reach the city. No U-turns are allowed.\nExcept this constraint, one can choose any route on the road network.\nIt is allowed to visit the same city or use the same road multiple times.\nThe starting city and the goal city may be visited during the trip.\nFor each road on the network, its distance and speed limit are given.\nA car must run a road at a speed less than or equal to its speed limit.\nThe time needed to run a road is the distance divided by the speed.\nThe time needed within cities including that for acceleration or deceleration should be ignored.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn m \ns g \n\nx_ 1 y_ 1 d_ 1 c_ 1\n. . . \n\nx_m y_m d_m c_m \n\nEvery input item in a dataset is a non-negative integer.\nInput items in the same line are separated by a space.\n\nThe first line gives the size of the road network.\nn is the number of cities in the network.\nYou can assume that the number of cities is between 2 and 30, inclusive.\nm is the number of roads between cities, which may be zero.\nThe second line gives the trip.\ns is the city index of the starting city.\ng is the city index of the goal city.\ns is not equal to g .\nYou can assume that all city indices in a dataset (including the above two)\nare between 1 and n , inclusive.\nThe following m lines give the details of roads between cities.\nThe i -th road connects two cities with city indices\nx_i and y_i ,\nand has a distance d_i (1 <= i <= m ).\nYou can assume that the distance is between 1 and 100, inclusive.\nThe speed limit of the road is specified by c_i .\nYou can assume that the speed limit is between 1 and 30, inclusive.\nNo two roads connect the same pair of cities.\nA road never connects a city with itself.\nEach road can be traveled in both directions.\n\nThe last dataset is followed by a line containing two zeros\n(separated by a space).\nTask Output: For each dataset in the input, one line should be output as specified below.\nAn output line should not contain extra characters such as spaces.\n\nIf one can travel from the starting city to the goal city,\nthe time needed for the best route (a route with the shortest time)\nshould be printed.\nThe answer should not have an error greater than 0.001.\nYou may output any number of digits after the decimal point,\nprovided that the above accuracy condition is satisfied.\n\nIf it is impossible to reach the goal city,\nthe string \"unreachable\" should be printed.\nNote that all the letters of \"unreachable\" are in lowercase.\nTask Samples: input: 2 0\n1 2\n5 4\n1 5\n1 2 1 1\n2 3 2 2\n3 4 2 2\n4 5 1 1\n6 6\n1 6\n1 2 2 1\n2 3 2 1\n3 6 2 1\n1 4 2 30\n4 5 3 30\n5 6 2 30\n6 7\n1 6\n1 2 1 30\n2 3 1 30\n3 1 1 30\n3 4 100 30\n4 5 1 30\n5 6 1 30\n6 4 1 30\n0 0\n output: unreachable\n4.00000\n5.50000\n11.25664\n\n" }, { "title": "Problem E: Cards", "content": "There are many blue cards and red cards on the table.\nFor each card, an integer number greater than 1 is printed on its face.\nThe same number may be printed on several cards.\nA blue card and a red card can be paired when both of the numbers\nprinted on them have a common divisor greater than 1.\nThere may be more than one red card that can be paired with one blue card.\nAlso, there may be more than one blue card that can be paired with one red card.\nWhen a blue card and a red card are chosen and paired,\nthese two cards are removed from the whole cards on the table.\n\nFigure E-1: Four blue cards and three red cards\nFor example, in Figure E-1,\nthere are four blue cards and three red cards.\nNumbers 2,6,6 and 15 are printed on the faces of the four blue cards, \nand 2,3 and 35 are printed on those of the three red cards.\nHere, you can make pairs of blue cards and red cards as follows.\nFirst,\nthe blue card with number 2 on it and the red card with 2 are paired and removed.\nSecond,\none of the two blue cards with 6 and the red card with 3 are paired and removed.\nFinally,\nthe blue card with 15 and the red card with 35 are paired and removed.\nThus the number of removed pairs is three.\n\nNote that the total number of the pairs depends on\nthe way of choosing cards to be paired.\nThe blue card with 15 and the red card with 3 might be paired \nand removed at the beginning.\nIn this case, there are only one more pair that can be removed\nand the total number of the removed pairs is two.\n\nYour job is to find the largest number of pairs that can be removed from the given set of cards on the table.", "constraint": "", "input": "The input is a sequence of datasets.\nThe number of the datasets is less than or equal to 100.\nEach dataset is formatted as follows.\n\nm n \nb_1 . . . b_k\n. . . b_m \nr_1 . . . r_k\n. . . r_n \n\nThe integers m and n are the number of blue cards\nand that of red cards, respectively.\nYou may assume 1 <= m <= 500 and 1<= n <= 500.\n\nb_k (1 <= k <= m) and\nr_k (1 <= k <= n) are\nnumbers printed on the blue cards and the red cards respectively,\nthat are integers greater than or equal to 2 and less than \n10000000 (=10^7). \nThe input integers are separated by a space or a newline.\nEach of b_m and r_n is\nfollowed by a newline.\nThere are no other characters in the dataset.\nThe end of the input is indicated by a line containing two zeros\nseparated by a space.", "output": "For each dataset, output a line containing an integer that indicates\nthe maximum of the number of the pairs.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 3\n2 6 6 15\n2 3 5\n2 3\n4 9\n8 16 32\n4 2\n4 9 11 13\n5 7\n5 5\n2 3 5 1001 1001\n7 11 13 30 30\n10 10\n2 3 5 7 9 11 13 15 17 29\n4 6 10 14 18 22 26 30 34 38\n20 20\n195 144 903 63 137 513 44 626 75 473\n876 421 568 519 755 840 374 368 570 872\n363 650 155 265 64 26 426 391 15 421\n373 984 564 54 823 477 565 866 879 638\n100 100\n195 144 903 63 137 513 44 626 75 473\n876 421 568 519 755 840 374 368 570 872\n363 650 155 265 64 26 426 391 15 421\n373 984 564 54 823 477 565 866 879 638\n117 755 835 683 52 369 302 424 513 870\n75 874 299 228 140 361 30 342 750 819\n761 123 804 325 952 405 578 517 49 457\n932 941 988 767 624 41 912 702 241 426\n351 92 300 648 318 216 785 347 556 535\n166 318 434 746 419 386 928 996 680 975\n231 390 916 220 933 319 37 846 797 54\n272 924 145 348 350 239 563 135 362 119\n446 305 213 879 51 631 43 755 405 499\n509 412 887 203 408 821 298 443 445 96\n274 715 796 417 839 147 654 402 280 17\n298 725 98 287 382 923 694 201 679 99\n699 188 288 364 389 694 185 464 138 406\n558 188 897 354 603 737 277 35 139 556\n826 213 59 922 499 217 846 193 416 525\n69 115 489 355 256 654 49 439 118 961\n0 0\n output: 3\n1\n0\n4\n9\n18\n85"], "Pid": "p00744", "ProblemText": "Task Description: There are many blue cards and red cards on the table.\nFor each card, an integer number greater than 1 is printed on its face.\nThe same number may be printed on several cards.\nA blue card and a red card can be paired when both of the numbers\nprinted on them have a common divisor greater than 1.\nThere may be more than one red card that can be paired with one blue card.\nAlso, there may be more than one blue card that can be paired with one red card.\nWhen a blue card and a red card are chosen and paired,\nthese two cards are removed from the whole cards on the table.\n\nFigure E-1: Four blue cards and three red cards\nFor example, in Figure E-1,\nthere are four blue cards and three red cards.\nNumbers 2,6,6 and 15 are printed on the faces of the four blue cards, \nand 2,3 and 35 are printed on those of the three red cards.\nHere, you can make pairs of blue cards and red cards as follows.\nFirst,\nthe blue card with number 2 on it and the red card with 2 are paired and removed.\nSecond,\none of the two blue cards with 6 and the red card with 3 are paired and removed.\nFinally,\nthe blue card with 15 and the red card with 35 are paired and removed.\nThus the number of removed pairs is three.\n\nNote that the total number of the pairs depends on\nthe way of choosing cards to be paired.\nThe blue card with 15 and the red card with 3 might be paired \nand removed at the beginning.\nIn this case, there are only one more pair that can be removed\nand the total number of the removed pairs is two.\n\nYour job is to find the largest number of pairs that can be removed from the given set of cards on the table.\nTask Input: The input is a sequence of datasets.\nThe number of the datasets is less than or equal to 100.\nEach dataset is formatted as follows.\n\nm n \nb_1 . . . b_k\n. . . b_m \nr_1 . . . r_k\n. . . r_n \n\nThe integers m and n are the number of blue cards\nand that of red cards, respectively.\nYou may assume 1 <= m <= 500 and 1<= n <= 500.\n\nb_k (1 <= k <= m) and\nr_k (1 <= k <= n) are\nnumbers printed on the blue cards and the red cards respectively,\nthat are integers greater than or equal to 2 and less than \n10000000 (=10^7). \nThe input integers are separated by a space or a newline.\nEach of b_m and r_n is\nfollowed by a newline.\nThere are no other characters in the dataset.\nThe end of the input is indicated by a line containing two zeros\nseparated by a space.\nTask Output: For each dataset, output a line containing an integer that indicates\nthe maximum of the number of the pairs.\nTask Samples: input: 4 3\n2 6 6 15\n2 3 5\n2 3\n4 9\n8 16 32\n4 2\n4 9 11 13\n5 7\n5 5\n2 3 5 1001 1001\n7 11 13 30 30\n10 10\n2 3 5 7 9 11 13 15 17 29\n4 6 10 14 18 22 26 30 34 38\n20 20\n195 144 903 63 137 513 44 626 75 473\n876 421 568 519 755 840 374 368 570 872\n363 650 155 265 64 26 426 391 15 421\n373 984 564 54 823 477 565 866 879 638\n100 100\n195 144 903 63 137 513 44 626 75 473\n876 421 568 519 755 840 374 368 570 872\n363 650 155 265 64 26 426 391 15 421\n373 984 564 54 823 477 565 866 879 638\n117 755 835 683 52 369 302 424 513 870\n75 874 299 228 140 361 30 342 750 819\n761 123 804 325 952 405 578 517 49 457\n932 941 988 767 624 41 912 702 241 426\n351 92 300 648 318 216 785 347 556 535\n166 318 434 746 419 386 928 996 680 975\n231 390 916 220 933 319 37 846 797 54\n272 924 145 348 350 239 563 135 362 119\n446 305 213 879 51 631 43 755 405 499\n509 412 887 203 408 821 298 443 445 96\n274 715 796 417 839 147 654 402 280 17\n298 725 98 287 382 923 694 201 679 99\n699 188 288 364 389 694 185 464 138 406\n558 188 897 354 603 737 277 35 139 556\n826 213 59 922 499 217 846 193 416 525\n69 115 489 355 256 654 49 439 118 961\n0 0\n output: 3\n1\n0\n4\n9\n18\n85\n\n" }, { "title": "Problem F: Tighten Up!", "content": "We have a flat panel with two holes. Pins are nailed on its\nsurface. From the back of the panel, a string comes out through one\nof the holes to the surface. The string is then laid on the surface\nin a form of a polygonal chain, and goes out to the panel's back through\nthe other hole. Initially, the string does not touch any pins.\n\nFigures F-1, F-2, and F-3 show three example layouts of holes, pins and\nstrings. In each layout, white squares and circles denote holes and\npins, respectively. A polygonal chain of solid segments denotes the\nstring.\nFigure F-1: An example layout of holes, pins and a string\nFigure F-2: An example layout of holes, pins and a string\nFigure F-3: An example layout of holes, pins and a string\n\nWhen we tie a pair of equal weight stones to the both ends of the\nstring, the stones slowly straighten the string until there is no\nloose part. The string eventually forms a different polygonal chain as it is\nobstructed by some of the pins. (There are also cases when the\nstring is obstructed by no pins, though. )\n\nThe string does not hook itself while being straightened. A fully\ntightened string thus draws a polygonal chain on the surface of the\npanel, whose vertices are the positions of some pins with the end\nvertices at the two holes. The layouts in Figures F-1, F-2, and F-3 result in the\nrespective polygonal chains in Figures F-4, F-5, and F-6. Write a program that\ncalculates the length of the tightened polygonal chain.\nFigure F-4: Tightened polygonal chains from the example in Figure F-1.\nFigure F-5: Tightened polygonal chains from the example in Figure F-2.\nFigure F-6: Tightened polygonal chains from the example in Figure F-3.\n\nNote that the strings, pins and holes are thin enough so that you\ncan ignore their diameters.", "constraint": "", "input": "The input consists of multiple datasets, followed by a line containing\ntwo zeros separated by a space. Each dataset gives the initial shape of the string (i. e. , the positions of holes and vertices) and the positions of\npins in the\nfollowing format.\n\nm n \nx_1 y_1 \n. . . \nx_l y_l \n\nThe first line has two integers m and n (2 <= m \n\n<= 100,0 <= n <= 100), representing the number of\nvertices including two holes that give the initial string shape (m) and the number\nof pins (n). Each of the following l = m\n+ n lines has two integers x_i\n\nand y_i (0 <= x_i <= 1000,0 <= y_i <= 1000), representing a position P_i =\n(x_i , y_i ) on the surface of the\npanel.\nPositions P_1, . . . , P_m give the initial shape of\n the string; i. e. , the two holes are at P_1\n and P_m , and the string's shape is a polygonal\n chain whose vertices are P_i (i =\n 1, . . . , m), in this order.\n\n Positions P_m+1, . . . , P_m+n are the positions of\n the pins.\n \n\nNote that no two points are at the same position. No three points are\nexactly on\na straight line.", "output": "For each dataset, the length of the part of the tightened string that\nremains on the surface of the panel should be output in a line.\nNo extra characters\nshould appear in the output.\n\nNo lengths in the output should have an error greater than 0.001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 16\n5 4\n11 988\n474 975\n459 16\n985 12\n984 982\n242 227\n140 266\n45 410\n92 570\n237 644\n370 567\n406 424\n336 290\n756 220\n634 251\n511 404\n575 554\n726 643\n868 571\n907 403\n845 283\n10 4\n261 196\n943 289\n859 925\n56 822\n112 383\n514 0\n1000 457\n514 1000\n0 485\n233 224\n710 242\n850 654\n485 915\n140 663\n26 5\n0 953\n180 0\n299 501\n37 301\n325 124\n162 507\n84 140\n913 409\n635 157\n645 555\n894 229\n598 223\n783 514\n765 137\n599 445\n695 126\n859 462\n599 312\n838 167\n708 563\n565 258\n945 283\n251 454\n125 111\n28 469\n1000 1000\n185 319\n717 296\n9 315\n372 249\n203 528\n15 15\n200 247\n859 597\n340 134\n967 247\n421 623\n1000 427\n751 1000\n102 737\n448 0\n978 510\n556 907\n0 582\n627 201\n697 963\n616 608\n345 819\n810 809\n437 706\n702 695\n448 474\n605 474\n329 355\n691 350\n816 231\n313 216\n864 360\n772 278\n756 747\n529 639\n513 525\n0 0\n output: 2257.0518296609\n3609.92159564177\n2195.83727086364\n3619.77160684813"], "Pid": "p00745", "ProblemText": "Task Description: We have a flat panel with two holes. Pins are nailed on its\nsurface. From the back of the panel, a string comes out through one\nof the holes to the surface. The string is then laid on the surface\nin a form of a polygonal chain, and goes out to the panel's back through\nthe other hole. Initially, the string does not touch any pins.\n\nFigures F-1, F-2, and F-3 show three example layouts of holes, pins and\nstrings. In each layout, white squares and circles denote holes and\npins, respectively. A polygonal chain of solid segments denotes the\nstring.\nFigure F-1: An example layout of holes, pins and a string\nFigure F-2: An example layout of holes, pins and a string\nFigure F-3: An example layout of holes, pins and a string\n\nWhen we tie a pair of equal weight stones to the both ends of the\nstring, the stones slowly straighten the string until there is no\nloose part. The string eventually forms a different polygonal chain as it is\nobstructed by some of the pins. (There are also cases when the\nstring is obstructed by no pins, though. )\n\nThe string does not hook itself while being straightened. A fully\ntightened string thus draws a polygonal chain on the surface of the\npanel, whose vertices are the positions of some pins with the end\nvertices at the two holes. The layouts in Figures F-1, F-2, and F-3 result in the\nrespective polygonal chains in Figures F-4, F-5, and F-6. Write a program that\ncalculates the length of the tightened polygonal chain.\nFigure F-4: Tightened polygonal chains from the example in Figure F-1.\nFigure F-5: Tightened polygonal chains from the example in Figure F-2.\nFigure F-6: Tightened polygonal chains from the example in Figure F-3.\n\nNote that the strings, pins and holes are thin enough so that you\ncan ignore their diameters.\nTask Input: The input consists of multiple datasets, followed by a line containing\ntwo zeros separated by a space. Each dataset gives the initial shape of the string (i. e. , the positions of holes and vertices) and the positions of\npins in the\nfollowing format.\n\nm n \nx_1 y_1 \n. . . \nx_l y_l \n\nThe first line has two integers m and n (2 <= m \n\n<= 100,0 <= n <= 100), representing the number of\nvertices including two holes that give the initial string shape (m) and the number\nof pins (n). Each of the following l = m\n+ n lines has two integers x_i\n\nand y_i (0 <= x_i <= 1000,0 <= y_i <= 1000), representing a position P_i =\n(x_i , y_i ) on the surface of the\npanel.\nPositions P_1, . . . , P_m give the initial shape of\n the string; i. e. , the two holes are at P_1\n and P_m , and the string's shape is a polygonal\n chain whose vertices are P_i (i =\n 1, . . . , m), in this order.\n\n Positions P_m+1, . . . , P_m+n are the positions of\n the pins.\n \n\nNote that no two points are at the same position. No three points are\nexactly on\na straight line.\nTask Output: For each dataset, the length of the part of the tightened string that\nremains on the surface of the panel should be output in a line.\nNo extra characters\nshould appear in the output.\n\nNo lengths in the output should have an error greater than 0.001.\nTask Samples: input: 6 16\n5 4\n11 988\n474 975\n459 16\n985 12\n984 982\n242 227\n140 266\n45 410\n92 570\n237 644\n370 567\n406 424\n336 290\n756 220\n634 251\n511 404\n575 554\n726 643\n868 571\n907 403\n845 283\n10 4\n261 196\n943 289\n859 925\n56 822\n112 383\n514 0\n1000 457\n514 1000\n0 485\n233 224\n710 242\n850 654\n485 915\n140 663\n26 5\n0 953\n180 0\n299 501\n37 301\n325 124\n162 507\n84 140\n913 409\n635 157\n645 555\n894 229\n598 223\n783 514\n765 137\n599 445\n695 126\n859 462\n599 312\n838 167\n708 563\n565 258\n945 283\n251 454\n125 111\n28 469\n1000 1000\n185 319\n717 296\n9 315\n372 249\n203 528\n15 15\n200 247\n859 597\n340 134\n967 247\n421 623\n1000 427\n751 1000\n102 737\n448 0\n978 510\n556 907\n0 582\n627 201\n697 963\n616 608\n345 819\n810 809\n437 706\n702 695\n448 474\n605 474\n329 355\n691 350\n816 231\n313 216\n864 360\n772 278\n756 747\n529 639\n513 525\n0 0\n output: 2257.0518296609\n3609.92159564177\n2195.83727086364\n3619.77160684813\n\n" }, { "title": "Problem A: Pablo Squarson's Headache", "content": "Pablo Squarson is a well-known cubism artist. This year's theme for Pablo Squarson is \"Squares\". Today we are visiting his studio to see how his masterpieces are given birth. At the center of his studio, there is a huuuuuge table and beside it are many, many squares of the same size. Pablo Squarson puts one of the squares on the table. Then he places some other squares on the table in sequence. It seems his methodical nature forces him to place each square side by side to the one that he already placed on, with machine-like precision. Oh! The first piece of artwork is done. Pablo Squarson seems satisfied with it. Look at his happy face. Oh, what's wrong with Pablo? He is tearing his hair! Oh, I see. He wants to find a box that fits the new piece of work but he has trouble figuring out its size. Let's help him! Your mission is to write a program that takes instructions that record how Pablo made a piece of his artwork and computes its width and height. It is known that the size of each square is 1. You may assume that Pablo does not put a square on another. I hear someone murmured \"A smaller box will do\". No, poor Pablo, shaking his head, is grumbling \"My square style does not seem to be understood by illiterates\".", "constraint": "", "input": "The input consists of a number of datasets. Each dataset represents the way Pablo made a piece of his artwork. The format of a dataset is as follows.\nN\nn_1 d_1\nn_2 d_2\n. . . \nn_N_-1 d_N_-1\nThe first line contains the number of squares (= N) used to make the piece of artwork. The number is a positive integer and is smaller than 200.\n

The remaining (N-1) lines in the dataset are square placement instructions. The line “n_i d_i” indicates placement of the square numbered i (<= N-1). The rules of numbering squares are as follows. The first square is numbered \"zero\". Subsequently placed squares are numbered 1,2, . . . , (N-1). Note that the input does not give any placement instruction to the first square, which is numbered zero.\nA square placement instruction for the square numbered i, namely “n_i d_i”, directs it to be placed next to the one that is numbered n_i, towards the direction given by d_i, which denotes leftward (= 0), downward (= 1), rightward (= 2), and upward (= 3).\nFor example, pieces of artwork corresponding to the four datasets shown in Sample Input are depicted below. Squares are labeled by their numbers.\n\nThe end of the input is indicated by a line that contains a single zero.", "output": "For each dataset, output a line that contains the width and the height of the piece of artwork as decimal numbers, separated by a space. Each line should not contain any other characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n5\n0 0\n0 1\n0 2\n0 3\n12\n0 0\n1 0\n2 0\n3 1\n4 1\n5 1\n6 2\n7 2\n8 2\n9 3\n10 3\n10\n0 2\n1 2\n2 2\n3 2\n2 1\n5 1\n6 1\n7 1\n8 1\n0\n output: 1 1\n3 3\n4 4\n5 6"], "Pid": "p00746", "ProblemText": "Task Description: Pablo Squarson is a well-known cubism artist. This year's theme for Pablo Squarson is \"Squares\". Today we are visiting his studio to see how his masterpieces are given birth. At the center of his studio, there is a huuuuuge table and beside it are many, many squares of the same size. Pablo Squarson puts one of the squares on the table. Then he places some other squares on the table in sequence. It seems his methodical nature forces him to place each square side by side to the one that he already placed on, with machine-like precision. Oh! The first piece of artwork is done. Pablo Squarson seems satisfied with it. Look at his happy face. Oh, what's wrong with Pablo? He is tearing his hair! Oh, I see. He wants to find a box that fits the new piece of work but he has trouble figuring out its size. Let's help him! Your mission is to write a program that takes instructions that record how Pablo made a piece of his artwork and computes its width and height. It is known that the size of each square is 1. You may assume that Pablo does not put a square on another. I hear someone murmured \"A smaller box will do\". No, poor Pablo, shaking his head, is grumbling \"My square style does not seem to be understood by illiterates\".\nTask Input: The input consists of a number of datasets. Each dataset represents the way Pablo made a piece of his artwork. The format of a dataset is as follows.\nN\nn_1 d_1\nn_2 d_2\n. . . \nn_N_-1 d_N_-1\nThe first line contains the number of squares (= N) used to make the piece of artwork. The number is a positive integer and is smaller than 200.\n

The remaining (N-1) lines in the dataset are square placement instructions. The line “n_i d_i” indicates placement of the square numbered i (<= N-1). The rules of numbering squares are as follows. The first square is numbered \"zero\". Subsequently placed squares are numbered 1,2, . . . , (N-1). Note that the input does not give any placement instruction to the first square, which is numbered zero.\nA square placement instruction for the square numbered i, namely “n_i d_i”, directs it to be placed next to the one that is numbered n_i, towards the direction given by d_i, which denotes leftward (= 0), downward (= 1), rightward (= 2), and upward (= 3).\nFor example, pieces of artwork corresponding to the four datasets shown in Sample Input are depicted below. Squares are labeled by their numbers.\n\nThe end of the input is indicated by a line that contains a single zero.\nTask Output: For each dataset, output a line that contains the width and the height of the piece of artwork as decimal numbers, separated by a space. Each line should not contain any other characters.\nTask Samples: input: 1\n5\n0 0\n0 1\n0 2\n0 3\n12\n0 0\n1 0\n2 0\n3 1\n4 1\n5 1\n6 2\n7 2\n8 2\n9 3\n10 3\n10\n0 2\n1 2\n2 2\n3 2\n2 1\n5 1\n6 1\n7 1\n8 1\n0\n output: 1 1\n3 3\n4 4\n5 6\n\n" }, { "title": "Problem B: Amazing Mazes", "content": "You are requested to solve maze problems. Without passing through\nthese mazes, you might not be able to pass through the domestic \ncontest!\n\nA maze here is a rectangular area of a number of squares, lined up\nboth lengthwise and widthwise, The area is surrounded by walls except\nfor its entry and exit. The entry to the maze is at the leftmost part\nof the upper side of the rectangular area, that is, the upper side of\nthe uppermost leftmost square of the maze is open. The exit is\nlocated at the rightmost part of the lower side, likewise.\n\nIn the maze, you can move from a square to one of the squares\nadjoining either horizontally or vertically. Adjoining squares,\nhowever, may be separated by a wall, and when they are, you cannot go\nthrough the wall.\n\nYour task is to find the length of the shortest path from the entry to\nthe exit. Note that there may be more than one shortest paths, or\nthere may be none.", "constraint": "", "input": "The input consists of one or more datasets, each of which represents a\nmaze.\n\nThe first line of a dataset contains two integer numbers, the\nwidth w and the height h of the rectangular area, in\nthis order.\n\nThe following 2 * h - 1 lines of a dataset describe\nwhether there are walls between squares or not. The first line starts\nwith a space and the rest of the line contains w - 1\nintegers, 1 or 0, separated by a space. These indicate whether walls\nseparate horizontally adjoining squares in the first row. An integer\n1 indicates a wall is placed, and 0 indicates no wall is there. The\nsecond line starts without a space and contains w integers, 1 or 0,\nseparated by a space. These indicate whether walls separate\nvertically adjoining squares in the first and the second rows. An\ninteger 1/0 indicates a wall is placed or not. The following lines\nindicate placing of walls between horizontally and vertically\nadjoining squares, alternately, in the same manner.\n\nThe end of the input is indicated by a line containing two zeros.\n\nThe number of datasets is no more than 100. Both the widths and the\nheights of rectangular areas are no less than 2 and no more than 30.", "output": "For each dataset, output a line having an integer indicating the\nlength of the shortest path from the entry to the exit. The length of\na path is given by the number of visited squares. If there exists\nno path to go through the maze, output a line containing a single\nzero. The line should not contain any character other than this\nnumber.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 3\n 1\n0 1\n 0\n1 0\n 1\n9 4\n 1 0 1 0 0 0 0 0\n0 1 1 0 1 1 0 0 0\n 1 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 1 1\n 0 0 0 1 0 0 1 1\n0 0 0 0 1 1 0 0 0\n 0 0 0 0 0 0 1 0\n12 5\n 1 0 0 0 0 0 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0 0 0\n 1 0 1 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 1 0 0 0 0\n 0 0 1 0 0 1 0 1 0 0 0\n0 0 0 1 1 0 1 1 0 1 1 0\n 0 0 0 0 0 1 0 0 1 0 0\n0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 1 0 0\n0 0\n\n
output: 4\n0\n20"], "Pid": "p00747", "ProblemText": "Task Description: You are requested to solve maze problems. Without passing through\nthese mazes, you might not be able to pass through the domestic \ncontest!\n\nA maze here is a rectangular area of a number of squares, lined up\nboth lengthwise and widthwise, The area is surrounded by walls except\nfor its entry and exit. The entry to the maze is at the leftmost part\nof the upper side of the rectangular area, that is, the upper side of\nthe uppermost leftmost square of the maze is open. The exit is\nlocated at the rightmost part of the lower side, likewise.\n\nIn the maze, you can move from a square to one of the squares\nadjoining either horizontally or vertically. Adjoining squares,\nhowever, may be separated by a wall, and when they are, you cannot go\nthrough the wall.\n\nYour task is to find the length of the shortest path from the entry to\nthe exit. Note that there may be more than one shortest paths, or\nthere may be none.\nTask Input: The input consists of one or more datasets, each of which represents a\nmaze.\n\nThe first line of a dataset contains two integer numbers, the\nwidth w and the height h of the rectangular area, in\nthis order.\n\nThe following 2 * h - 1 lines of a dataset describe\nwhether there are walls between squares or not. The first line starts\nwith a space and the rest of the line contains w - 1\nintegers, 1 or 0, separated by a space. These indicate whether walls\nseparate horizontally adjoining squares in the first row. An integer\n1 indicates a wall is placed, and 0 indicates no wall is there. The\nsecond line starts without a space and contains w integers, 1 or 0,\nseparated by a space. These indicate whether walls separate\nvertically adjoining squares in the first and the second rows. An\ninteger 1/0 indicates a wall is placed or not. The following lines\nindicate placing of walls between horizontally and vertically\nadjoining squares, alternately, in the same manner.\n\nThe end of the input is indicated by a line containing two zeros.\n\nThe number of datasets is no more than 100. Both the widths and the\nheights of rectangular areas are no less than 2 and no more than 30.\nTask Output: For each dataset, output a line having an integer indicating the\nlength of the shortest path from the entry to the exit. The length of\na path is given by the number of visited squares. If there exists\nno path to go through the maze, output a line containing a single\nzero. The line should not contain any character other than this\nnumber.\nTask Samples: input: 2 3\n 1\n0 1\n 0\n1 0\n 1\n9 4\n 1 0 1 0 0 0 0 0\n0 1 1 0 1 1 0 0 0\n 1 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 1 1\n 0 0 0 1 0 0 1 1\n0 0 0 0 1 1 0 0 0\n 0 0 0 0 0 0 1 0\n12 5\n 1 0 0 0 0 0 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0 0 0\n 1 0 1 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 1 0 0 0 0\n 0 0 1 0 0 1 0 1 0 0 0\n0 0 0 1 1 0 1 1 0 1 1 0\n 0 0 0 0 0 1 0 0 1 0 0\n0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 1 0 0\n0 0\n\n
output: 4\n0\n20\n\n" }, { "title": "Problem C: Pollock's conjecture", "content": "The nth triangular number is\ndefined as\nthe sum of the first n positive integers.\nThe nth tetrahedral number is\ndefined as\nthe sum of the first n triangular numbers.\nIt is easy to show that\nthe nth tetrahedral number is equal to\nn(n+1)(n+2) ⁄ 6.\nFor example,\nthe 5th tetrahedral number is\n1+(1+2)+(1+2+3)+(1+2+3+4)+(1+2+3+4+5)\n= 5*6*7 ⁄ 6\n= 35.\n

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\n\nThe first 5 triangular numbers\n\n1,3,6,10,15\n
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\n\n
\n
\n\nThe first 5 tetrahedral numbers\n\n1,4,10,20,35\n
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\n\n
\n
\nIn 1850,\nSir Frederick Pollock, 1st Baronet,\nwho was not a professional mathematician\nbut a British lawyer and Tory (currently known as Conservative) politician,\nconjectured\nthat every positive integer can be represented\nas the sum of at most five tetrahedral numbers.\nHere,\na tetrahedral number may occur in the sum more than once\nand,\nin such a case, each occurrence is counted separately.\nThe conjecture has been open for more than one and a half century.\n\nYour mission is to write a program\nto verify Pollock's conjecture for individual integers.\nYour program should make a calculation of\nthe least number of tetrahedral numbers\nto represent each input integer as their sum.\nIn addition,\nfor some unknown reason,\nyour program should make a similar calculation\nwith only odd tetrahedral numbers available.\n\nFor example,\none can represent 40 as the sum of 2 tetrahedral numbers,\n4*5*6 ⁄ 6 + 4*5*6 ⁄ 6,\nbut 40 itself is not a tetrahedral number.\nOne can represent 40 as the sum of 6 odd tetrahedral numbers,\n5*6*7 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6,\nbut cannot represent as the sum of fewer odd tetrahedral numbers.\nThus, your program should report 2 and 6 if 40 is given.", "constraint": "", "input": "The input is a sequence of lines each of which contains a single positive integer less than 10^6.\nThe end of the input is indicated by a line containing a single zero.", "output": "For each input positive integer,\noutput a line containing two integers separated by a space.\nThe first integer should be\nthe least number of tetrahedral numbers\nto represent the input integer as their sum.\nThe second integer should be\nthe least number of odd tetrahedral numbers\nto represent the input integer as their sum.\nNo extra characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 40\n14\n5\n165\n120\n103\n106\n139\n0\n output: 2 6\n2 14\n2 5\n1 1\n1 18\n5 35\n4 4\n3 37"], "Pid": "p00748", "ProblemText": "Task Description: The nth triangular number is\ndefined as\nthe sum of the first n positive integers.\nThe nth tetrahedral number is\ndefined as\nthe sum of the first n triangular numbers.\nIt is easy to show that\nthe nth tetrahedral number is equal to\nn(n+1)(n+2) ⁄ 6.\nFor example,\nthe 5th tetrahedral number is\n1+(1+2)+(1+2+3)+(1+2+3+4)+(1+2+3+4+5)\n= 5*6*7 ⁄ 6\n= 35.\n
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\n\nThe first 5 triangular numbers\n\n1,3,6,10,15\n
\n
\n\n
\n
\n\nThe first 5 tetrahedral numbers\n\n1,4,10,20,35\n
\n
\n\n
\n
\nIn 1850,\nSir Frederick Pollock, 1st Baronet,\nwho was not a professional mathematician\nbut a British lawyer and Tory (currently known as Conservative) politician,\nconjectured\nthat every positive integer can be represented\nas the sum of at most five tetrahedral numbers.\nHere,\na tetrahedral number may occur in the sum more than once\nand,\nin such a case, each occurrence is counted separately.\nThe conjecture has been open for more than one and a half century.\n\nYour mission is to write a program\nto verify Pollock's conjecture for individual integers.\nYour program should make a calculation of\nthe least number of tetrahedral numbers\nto represent each input integer as their sum.\nIn addition,\nfor some unknown reason,\nyour program should make a similar calculation\nwith only odd tetrahedral numbers available.\n\nFor example,\none can represent 40 as the sum of 2 tetrahedral numbers,\n4*5*6 ⁄ 6 + 4*5*6 ⁄ 6,\nbut 40 itself is not a tetrahedral number.\nOne can represent 40 as the sum of 6 odd tetrahedral numbers,\n5*6*7 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6 + 1*2*3 ⁄ 6,\nbut cannot represent as the sum of fewer odd tetrahedral numbers.\nThus, your program should report 2 and 6 if 40 is given.\nTask Input: The input is a sequence of lines each of which contains a single positive integer less than 10^6.\nThe end of the input is indicated by a line containing a single zero.\nTask Output: For each input positive integer,\noutput a line containing two integers separated by a space.\nThe first integer should be\nthe least number of tetrahedral numbers\nto represent the input integer as their sum.\nThe second integer should be\nthe least number of odd tetrahedral numbers\nto represent the input integer as their sum.\nNo extra characters should appear in the output.\nTask Samples: input: 40\n14\n5\n165\n120\n103\n106\n139\n0\n output: 2 6\n2 14\n2 5\n1 1\n1 18\n5 35\n4 4\n3 37\n\n" }, { "title": "Problem D: Off Balance", "content": "You are working for an administration office of the International\nCenter for Picassonian Cubism (ICPC), which plans to build a new art\ngallery for young artists. The center is organizing an architectural\ndesign competition to find the best design for the new building.\nSubmitted designs will look like a screenshot of a well known\ngame as shown below.\n\nThis is because the center specifies that \nthe building should be constructed by stacking regular units\ncalled pieces, each of which consists of four cubic blocks.\nIn addition, the center requires the competitors to submit designs\nthat satisfy the following restrictions.\n\nAll the pieces are aligned. When two pieces touch each other, the faces of\nthe touching blocks must be placed exactly at the same position.\nAll the pieces are stable. Since pieces are merely stacked, \ntheir centers of masses must be carefully positioned so as not to \ncollapse.\nThe pieces are stacked in a tree-like form \nin order to symbolize boundless potentiality of young artists.\nIn other words, one and only one\npiece touches the ground, and each of other pieces touches one and\nonly one piece on its bottom faces.\nThe building has a flat shape.\n This is because the construction site\n is a narrow area located between a\n straight moat and an expressway where \n no more than one block can be placed \n between the moat and the\nexpressway as illustrated below.\nIt will take many days to fully check stability of designs as it requires \ncomplicated structural calculation.\nTherefore, you are\nasked to quickly check obviously unstable designs by focusing on \ncenters of masses. The rules of your quick check are as follows. Assume the center of mass of a block is located at the center of the\nblock, and all blocks have the same weight. \nWe denote a location of a block by xy-coordinates of its\nleft-bottom corner. The unit length is the edge length of a block.\n \nAmong the blocks of the piece that touch another piece or the ground on their\nbottom faces, let x_L be the leftmost x-coordinate of \nthe leftmost block, and let x_R be the rightmost\nx-coordinate of the rightmost block.\nLet the x-coordinate of its accumulated center of mass of\nthe piece be M, where the accumulated center of mass of a piece P\nis the center of the mass of the pieces that are directly and indirectly \nsupported by P, in addition to P itself. Then the piece is\nstable, if and only if\nx_L < M < x_R. Otherwise, it is\nunstable. A design of a building is unstable if any of its pieces is unstable.\n\nNote that the above rules could judge some designs to be unstable even \nif it would not collapse in reality. For example, the left one of the\nfollowing designs shall be judged to be unstable.\n \n \n \n \n\n Also note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable.\n\nWrite a program that judges stability of each design based on the above quick check rules.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is\nindicated by a line containing two zeros separated by a space. Each\ndataset, which represents a front view of a building, is formatted as follows.\n\nw h \np_0(h-1)p_1(h-1). . . p_(w-1)(h-1) \n. . .\t\t \t \np_01p_11. . . p_(w-1)1 \np_00p_10. . . p_(w-1)0 \n\nThe integers w and h separated by a space are the numbers of columns\nand rows of the layout, respectively. You may assume 1 <= w <=\n10 and 1 <= h <= 60. The next h lines specify the placement of\nthe pieces. The character p_xy indicates the status of a block at\n(x, y), either `. ', meaning empty, or one digit character between\n`1' and `9', inclusive, meaning a block of a piece. \n(As mentioned earlier, we denote a location of a block by xy-coordinates of its\nleft-bottom corner. )\n\nWhen two blocks with the same number touch each other by any of their\ntop, bottom, left or right face, those blocks are of the same piece.\n(Note that there might be two different pieces that are denoted by \nthe same number. )\nThe bottom of a block at (x, 0) touches the ground.\n\nYou may assume that the pieces in each dataset are stacked in a tree-like form.", "output": "For each dataset, output a line containing a word STABLE\nwhen the design is stable with respect to the above quick check rules.\nOtherwise, output UNSTABLE. The output\nshould be written with uppercase letters, and should not contain any other extra characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n output: STABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE"], "Pid": "p00749", "ProblemText": "Task Description: You are working for an administration office of the International\nCenter for Picassonian Cubism (ICPC), which plans to build a new art\ngallery for young artists. The center is organizing an architectural\ndesign competition to find the best design for the new building.\nSubmitted designs will look like a screenshot of a well known\ngame as shown below.\n\nThis is because the center specifies that \nthe building should be constructed by stacking regular units\ncalled pieces, each of which consists of four cubic blocks.\nIn addition, the center requires the competitors to submit designs\nthat satisfy the following restrictions.\n\nAll the pieces are aligned. When two pieces touch each other, the faces of\nthe touching blocks must be placed exactly at the same position.\nAll the pieces are stable. Since pieces are merely stacked, \ntheir centers of masses must be carefully positioned so as not to \ncollapse.\nThe pieces are stacked in a tree-like form \nin order to symbolize boundless potentiality of young artists.\nIn other words, one and only one\npiece touches the ground, and each of other pieces touches one and\nonly one piece on its bottom faces.\nThe building has a flat shape.\n This is because the construction site\n is a narrow area located between a\n straight moat and an expressway where \n no more than one block can be placed \n between the moat and the\nexpressway as illustrated below.\nIt will take many days to fully check stability of designs as it requires \ncomplicated structural calculation.\nTherefore, you are\nasked to quickly check obviously unstable designs by focusing on \ncenters of masses. The rules of your quick check are as follows. Assume the center of mass of a block is located at the center of the\nblock, and all blocks have the same weight. \nWe denote a location of a block by xy-coordinates of its\nleft-bottom corner. The unit length is the edge length of a block.\n \nAmong the blocks of the piece that touch another piece or the ground on their\nbottom faces, let x_L be the leftmost x-coordinate of \nthe leftmost block, and let x_R be the rightmost\nx-coordinate of the rightmost block.\nLet the x-coordinate of its accumulated center of mass of\nthe piece be M, where the accumulated center of mass of a piece P\nis the center of the mass of the pieces that are directly and indirectly \nsupported by P, in addition to P itself. Then the piece is\nstable, if and only if\nx_L < M < x_R. Otherwise, it is\nunstable. A design of a building is unstable if any of its pieces is unstable.\n\nNote that the above rules could judge some designs to be unstable even \nif it would not collapse in reality. For example, the left one of the\nfollowing designs shall be judged to be unstable.\n \n \n \n \n\n Also note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable.\n\nWrite a program that judges stability of each design based on the above quick check rules.\nTask Input: The input is a sequence of datasets. The end of the input is\nindicated by a line containing two zeros separated by a space. Each\ndataset, which represents a front view of a building, is formatted as follows.\n\nw h \np_0(h-1)p_1(h-1). . . p_(w-1)(h-1) \n. . .\t\t \t \np_01p_11. . . p_(w-1)1 \np_00p_10. . . p_(w-1)0 \n\nThe integers w and h separated by a space are the numbers of columns\nand rows of the layout, respectively. You may assume 1 <= w <=\n10 and 1 <= h <= 60. The next h lines specify the placement of\nthe pieces. The character p_xy indicates the status of a block at\n(x, y), either `. ', meaning empty, or one digit character between\n`1' and `9', inclusive, meaning a block of a piece. \n(As mentioned earlier, we denote a location of a block by xy-coordinates of its\nleft-bottom corner. )\n\nWhen two blocks with the same number touch each other by any of their\ntop, bottom, left or right face, those blocks are of the same piece.\n(Note that there might be two different pieces that are denoted by \nthe same number. )\nThe bottom of a block at (x, 0) touches the ground.\n\nYou may assume that the pieces in each dataset are stacked in a tree-like form.\nTask Output: For each dataset, output a line containing a word STABLE\nwhen the design is stable with respect to the above quick check rules.\nOtherwise, output UNSTABLE. The output\nshould be written with uppercase letters, and should not contain any other extra characters.\nTask Samples: input: 4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n output: STABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n\n" }, { "title": "Problem E: The Most Powerful Spell", "content": "Long long ago, there lived a wizard who invented a lot of \"magical patterns. \"\nIn a room where one of his magical patterns is drawn on the floor,\nanyone can use magic by casting magic spells!\nThe set of spells usable in the room depends on the drawn magical pattern.\nYour task is to compute, for each given magical pattern,\nthe most powerful spell enabled by the pattern.\n\nA spell is a string of lowercase letters.\nAmong the spells, lexicographically earlier one is more powerful.\nNote that a string w is defined to be lexicographically earlier than a string u\nwhen w has smaller letter\nin the order a 1 --\"cada\"--> 3 --\"bra\"--> 2.\n\nAnother example is \"oilcadabraketdadabra\", obtained from the path\n\n    \n 0 --\"oil\"--> 1 --\"cada\"--> 3 --\"bra\"--> 2 --\"ket\"--> 3 --\"da\"--> 3 --\"da\"--> 3 --\"bra\"--> 2.\n\nThe spell \"abracadabra\" is more powerful than \"oilcadabraketdadabra\"\nbecause it is lexicographically earlier.\nIn fact, no other spell enabled by the magical pattern is more powerful than \"abracadabra\".\nThus \"abracadabra\" is the answer you have to compute.\n\nWhen you cannot determine the most powerful spell, please answer \"NO\".\nThere are two such cases.\nOne is the case when no path exists from the star node to the gold node.\nThe other case is when for every usable spell there always exist more powerful spells.\nThe situation is exemplified in the following figure:\n\"ab\" is more powerful than \"b\", and \"aab\" is more powerful than \"ab\", and so on.\nFor any spell, by prepending \"a\", we obtain a lexicographically earlier\n (hence more powerful) spell.\n", "constraint": "", "input": "The input consists of at most 150 datasets.\nEach dataset is formatted as follows.\n\nn a s g\nx_1 y_1 lab_1\nx_2 y_2 lab_2\n. . . \nx_a y_a lab_a\n\nThe first line of a dataset contains four integers.\n n is the number of the nodes, and a is the number of the arrows.\n The numbers s and g indicate the star node and the gold node, respectively.\nThen a lines describing the arrows follow.\nEach line consists of two integers and one string.\nThe line \"x_i y_i lab_i\" represents\nan arrow from the node x_i to the node y_i\nwith the associated label lab_i .\nValues in the dataset satisfy:\n2 <= n <= 40,\n0 <= a <= 400,\n0 <= s, g, x_i , y_i < n ,\ns ! =g,\nand\nlab_i is a string of 1 to 6 lowercase letters.\nBe careful that there may be self-connecting arrows (i. e. , x_i = y_i ),\nand multiple arrows connecting the same pair of nodes\n(i. e. , x_i = x_j and y_i = y_j\n for some i ! = j ).\n\nThe end of the input is indicated by a line containing four zeros.", "output": "For each dataset, output a line containing the most powerful spell for the magical pattern.\nIf there does not exist such a spell, output \"NO\" (without quotes).\nEach line should not have any other characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 7 0 2\n0 1 abra\n0 1 oil\n2 0 ket\n1 3 cada\n3 3 da\n3 2 bra\n2 3 ket\n2 2 0 1\n0 0 a\n0 1 b\n5 6 3 0\n3 1 op\n3 2 op\n3 4 opq\n1 0 st\n2 0 qr\n4 0 r\n2 1 0 1\n1 1 loooop\n0 0 0 0\n output: abracadabra\nNO\nopqr\nNO"], "Pid": "p00750", "ProblemText": "Task Description: Long long ago, there lived a wizard who invented a lot of \"magical patterns. \"\nIn a room where one of his magical patterns is drawn on the floor,\nanyone can use magic by casting magic spells!\nThe set of spells usable in the room depends on the drawn magical pattern.\nYour task is to compute, for each given magical pattern,\nthe most powerful spell enabled by the pattern.\n\nA spell is a string of lowercase letters.\nAmong the spells, lexicographically earlier one is more powerful.\nNote that a string w is defined to be lexicographically earlier than a string u\nwhen w has smaller letter\nin the order a 1 --\"cada\"--> 3 --\"bra\"--> 2.\n\nAnother example is \"oilcadabraketdadabra\", obtained from the path\n\n    \n 0 --\"oil\"--> 1 --\"cada\"--> 3 --\"bra\"--> 2 --\"ket\"--> 3 --\"da\"--> 3 --\"da\"--> 3 --\"bra\"--> 2.\n\nThe spell \"abracadabra\" is more powerful than \"oilcadabraketdadabra\"\nbecause it is lexicographically earlier.\nIn fact, no other spell enabled by the magical pattern is more powerful than \"abracadabra\".\nThus \"abracadabra\" is the answer you have to compute.\n\nWhen you cannot determine the most powerful spell, please answer \"NO\".\nThere are two such cases.\nOne is the case when no path exists from the star node to the gold node.\nThe other case is when for every usable spell there always exist more powerful spells.\nThe situation is exemplified in the following figure:\n\"ab\" is more powerful than \"b\", and \"aab\" is more powerful than \"ab\", and so on.\nFor any spell, by prepending \"a\", we obtain a lexicographically earlier\n (hence more powerful) spell.\n\nTask Input: The input consists of at most 150 datasets.\nEach dataset is formatted as follows.\n\nn a s g\nx_1 y_1 lab_1\nx_2 y_2 lab_2\n. . . \nx_a y_a lab_a\n\nThe first line of a dataset contains four integers.\n n is the number of the nodes, and a is the number of the arrows.\n The numbers s and g indicate the star node and the gold node, respectively.\nThen a lines describing the arrows follow.\nEach line consists of two integers and one string.\nThe line \"x_i y_i lab_i\" represents\nan arrow from the node x_i to the node y_i\nwith the associated label lab_i .\nValues in the dataset satisfy:\n2 <= n <= 40,\n0 <= a <= 400,\n0 <= s, g, x_i , y_i < n ,\ns ! =g,\nand\nlab_i is a string of 1 to 6 lowercase letters.\nBe careful that there may be self-connecting arrows (i. e. , x_i = y_i ),\nand multiple arrows connecting the same pair of nodes\n(i. e. , x_i = x_j and y_i = y_j\n for some i ! = j ).\n\nThe end of the input is indicated by a line containing four zeros.\nTask Output: For each dataset, output a line containing the most powerful spell for the magical pattern.\nIf there does not exist such a spell, output \"NO\" (without quotes).\nEach line should not have any other characters.\nTask Samples: input: 4 7 0 2\n0 1 abra\n0 1 oil\n2 0 ket\n1 3 cada\n3 3 da\n3 2 bra\n2 3 ket\n2 2 0 1\n0 0 a\n0 1 b\n5 6 3 0\n3 1 op\n3 2 op\n3 4 opq\n1 0 st\n2 0 qr\n4 0 r\n2 1 0 1\n1 1 loooop\n0 0 0 0\n output: abracadabra\nNO\nopqr\nNO\n\n" }, { "title": "Problem F: Old Memories", "content": "In 4272 A. D. , Master of Programming Literature, Dr. Isaac Cornell Panther-Carol,\nwho has miraculously survived through the three World Computer Virus Wars and reached 90 years old this year,\nwon a Nobel Prize for Literature.\nMedia reported every detail of his life.\nHowever, there was one thing they could not report — that is, an essay written by him when he was an elementary school boy.\nAlthough he had a copy and was happy to let them see it, \nthe biggest problem was that his copy of the essay was infected by a computer virus several times during the World Computer Virus War III\nand therefore the computer virus could have altered the text.\n\nFurther investigation showed that his copy was altered indeed. Why could we know that?\nMore than 80 years ago his classmates transferred the original essay to their brain before infection.\nWith the advent of Solid State Brain, one can now retain a text perfectly over centuries once it is transferred to his or her brain.\nNo one could remember the entire text due to the limited capacity,\nbut we managed to retrieve a part of the text from the brain of one of his classmates; sadly, it did not match perfectly to the copy at hand.\nIt would not have happened without virus infection.\n\nAt the moment, what we know about the computer virus is that each time the virus infects an essay it does one of the following:\n\nthe virus inserts one random character to a random position in the text. (e. g. , \"ABCD\" → \"ABCZD\")\n\nthe virus picks up one character in the text randomly, and then changes it into another character. (e. g. , \"ABCD\" → \"ABXD\")\n\nthe virus picks up one character in the text randomly, and then removes it from the text. (e. g. , \"ABCD\" → \"ACD\")\nYou also know the maximum number of times the computer virus infected the copy, because you could deduce it from the amount of the intrusion log.\nFortunately, most of his classmates seemed to remember at least one part of the essay (we call it a piece hereafter).\nConsidering all evidences together, the original essay might be reconstructed.\nYou, as a journalist and computer scientist, would like to reconstruct the original essay by writing a computer program to calculate the possible original text(s) that fits to the given pieces and the altered copy at hand.", "constraint": "", "input": "The input consists of multiple datasets. The number of datasets is no more than 100.\nEach dataset is formatted as follows:\n\nd n\nthe altered text\npiece_1\npiece_2\n. . . \npiece_n\n\nThe first line of a dataset contains two positive integers d (d <= 2) and n (n <= 30),\nwhere d is the maximum number of times the virus infected the copy and n is the number of pieces.\n\nThe second line is the text of the altered copy at hand. We call it the altered text hereafter.\nThe length of the altered text is less than or equal to 40 characters.\n\nThe following n lines are pieces, each of which is a part of the original essay remembered by one of his classmates.\nEach piece has at least 13 characters but no more than 20 characters. All pieces are of the same length.\nCharacters in the altered text and pieces are uppercase letters (`A' to `Z') and a period (`. ').\nSince the language he used does not leave a space between words, no spaces appear in the text.\n\nA line containing two zeros terminates the input.\n\nHis classmates were so many that you can assume that any character that appears in the original essay is covered by at least one piece.\nA piece might cover the original essay more than once; the original essay may contain repetitions.\nPlease note that some pieces may not appear in the original essay because some of his classmates might have mistaken to provide irrelevant pieces.", "output": "Below we explain what you should output for each dataset.\nSuppose if there are c possibilities for the original essay that fit to the given pieces and the given altered text.\nFirst, print a line containing c.\nIf c is less than or equal to 5, then print in lexicographical order c lines, each of which contains an individual possibility.\nNote that, in lexicographical order, '. ' comes before any other characters.\nYou can assume that c is always non-zero.\nThe output should not include any characters other than those mentioned above.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 4\nAABBCCDDEEFFGGHHIJJKKLLMMNNOOPP\nAABBCCDDEEFFGG\nCCDDEEFFGGHHII\nFFGGHHIIJJKKLL\nJJKKLLMMNNOOPP\n2 3\nABRACADABRA.ABBRACADABRA.\nABRACADABRA.A\n.ABRACADABRA.\nBRA.ABRACADAB\n2 2\nAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAA\nAAAAAAAAAAAAA\n2 3\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\nXXXXXXAXXXXXX\nXXXXXXBXXXXXX\nXXXXXXXXXXXXX\n0 0\n output: 1\nAABBCCDDEEFFGGHHIIJJKKLLMMNNOOPP\n5\n.ABRACADABRA.ABRACADABRA.\nABRACADABRA.A.ABRACADABRA.\nABRACADABRA.AABRACADABRA.A\nABRACADABRA.ABRACADABRA.\nABRACADABRA.ABRACADABRA.A\n5\nAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAA\n257"], "Pid": "p00751", "ProblemText": "Task Description: In 4272 A. D. , Master of Programming Literature, Dr. Isaac Cornell Panther-Carol,\nwho has miraculously survived through the three World Computer Virus Wars and reached 90 years old this year,\nwon a Nobel Prize for Literature.\nMedia reported every detail of his life.\nHowever, there was one thing they could not report — that is, an essay written by him when he was an elementary school boy.\nAlthough he had a copy and was happy to let them see it, \nthe biggest problem was that his copy of the essay was infected by a computer virus several times during the World Computer Virus War III\nand therefore the computer virus could have altered the text.\n\nFurther investigation showed that his copy was altered indeed. Why could we know that?\nMore than 80 years ago his classmates transferred the original essay to their brain before infection.\nWith the advent of Solid State Brain, one can now retain a text perfectly over centuries once it is transferred to his or her brain.\nNo one could remember the entire text due to the limited capacity,\nbut we managed to retrieve a part of the text from the brain of one of his classmates; sadly, it did not match perfectly to the copy at hand.\nIt would not have happened without virus infection.\n\nAt the moment, what we know about the computer virus is that each time the virus infects an essay it does one of the following:\n\nthe virus inserts one random character to a random position in the text. (e. g. , \"ABCD\" → \"ABCZD\")\n\nthe virus picks up one character in the text randomly, and then changes it into another character. (e. g. , \"ABCD\" → \"ABXD\")\n\nthe virus picks up one character in the text randomly, and then removes it from the text. (e. g. , \"ABCD\" → \"ACD\")\nYou also know the maximum number of times the computer virus infected the copy, because you could deduce it from the amount of the intrusion log.\nFortunately, most of his classmates seemed to remember at least one part of the essay (we call it a piece hereafter).\nConsidering all evidences together, the original essay might be reconstructed.\nYou, as a journalist and computer scientist, would like to reconstruct the original essay by writing a computer program to calculate the possible original text(s) that fits to the given pieces and the altered copy at hand.\nTask Input: The input consists of multiple datasets. The number of datasets is no more than 100.\nEach dataset is formatted as follows:\n\nd n\nthe altered text\npiece_1\npiece_2\n. . . \npiece_n\n\nThe first line of a dataset contains two positive integers d (d <= 2) and n (n <= 30),\nwhere d is the maximum number of times the virus infected the copy and n is the number of pieces.\n\nThe second line is the text of the altered copy at hand. We call it the altered text hereafter.\nThe length of the altered text is less than or equal to 40 characters.\n\nThe following n lines are pieces, each of which is a part of the original essay remembered by one of his classmates.\nEach piece has at least 13 characters but no more than 20 characters. All pieces are of the same length.\nCharacters in the altered text and pieces are uppercase letters (`A' to `Z') and a period (`. ').\nSince the language he used does not leave a space between words, no spaces appear in the text.\n\nA line containing two zeros terminates the input.\n\nHis classmates were so many that you can assume that any character that appears in the original essay is covered by at least one piece.\nA piece might cover the original essay more than once; the original essay may contain repetitions.\nPlease note that some pieces may not appear in the original essay because some of his classmates might have mistaken to provide irrelevant pieces.\nTask Output: Below we explain what you should output for each dataset.\nSuppose if there are c possibilities for the original essay that fit to the given pieces and the given altered text.\nFirst, print a line containing c.\nIf c is less than or equal to 5, then print in lexicographical order c lines, each of which contains an individual possibility.\nNote that, in lexicographical order, '. ' comes before any other characters.\nYou can assume that c is always non-zero.\nThe output should not include any characters other than those mentioned above.\nTask Samples: input: 1 4\nAABBCCDDEEFFGGHHIJJKKLLMMNNOOPP\nAABBCCDDEEFFGG\nCCDDEEFFGGHHII\nFFGGHHIIJJKKLL\nJJKKLLMMNNOOPP\n2 3\nABRACADABRA.ABBRACADABRA.\nABRACADABRA.A\n.ABRACADABRA.\nBRA.ABRACADAB\n2 2\nAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAA\nAAAAAAAAAAAAA\n2 3\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\nXXXXXXAXXXXXX\nXXXXXXBXXXXXX\nXXXXXXXXXXXXX\n0 0\n output: 1\nAABBCCDDEEFFGGHHIIJJKKLLMMNNOOPP\n5\n.ABRACADABRA.ABRACADABRA.\nABRACADABRA.A.ABRACADABRA.\nABRACADABRA.AABRACADABRA.A\nABRACADABRA.ABRACADABRA.\nABRACADABRA.ABRACADABRA.A\n5\nAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAA\n257\n\n" }, { "title": "Problem G: Laser Beam Reflections", "content": "A laser beam generator, a target object and some mirrors are \nplaced on a plane.\nThe mirrors stand upright on the plane,\nand both sides of the mirrors are flat and can reflect beams.\nTo point the beam at the target,\nyou may set the beam to several directions because of different reflections.\nYour job is to find the shortest beam path\nfrom the generator to the target and answer the length of the path.\n\nFigure G-1 shows examples of possible beam paths,\nwhere the bold line represents the shortest one.\n\nFigure G-1: Examples of possible paths", "constraint": "", "input": "The input consists of a number of datasets. The end of the input is indicated by a line containing a zero. \n\nEach dataset is formatted as follows. \nEach value in the dataset except n is an integer no less than 0 and no more than 100.\n\nn\nPX_1 PY_1 QX_1 QY_1\n. . . \nPX_n PY_n QX_n QY_n\nTX TY\nLX LY\n\nThe first line of a dataset contains an integer n (1 <= n <= 5),\nrepresenting the number of mirrors.\nThe following n lines list the arrangement of mirrors on the plane.\nThe coordinates\n(PX_i, PY_i) and \n(QX_i, QY_i) represent\nthe positions of both ends of the mirror.\nMirrors are apart from each other.\nThe last two lines represent the target position (TX, TY)\nand the position of the beam generator (LX, LY).\nThe positions of the target and the generator are apart from each other,\nand these positions are also apart from mirrors.\n\nThe sizes of the target object and the beam generator are small enough to be ignored.\nYou can also ignore the thicknesses of mirrors.\n\nIn addition, you can assume the following conditions on the given datasets.\n\nThere is at least one possible path from the beam generator to the target.\nThe number of reflections along the shortest path is less than 6.\n\nThe shortest path does not cross or touch a plane containing a mirror\nsurface at any points within 0.001 unit distance from either end of the mirror.\n\nEven if the beam could arbitrarily select reflection or passage \nwhen it reaches each plane containing a mirror surface\nat a point within 0.001 unit distance from one of the mirror ends,\nany paths from the generator to the target would not be \nshorter than the shortest path.\n\nWhen the beam is shot from the generator in an arbitrary direction and \nit reflects on a mirror or passes the mirror within 0.001 unit distance from the mirror,\nthe angle θ formed by the beam and the mirror \nsatisfies sin(θ) > 0.1, \nuntil the beam reaches the 6th reflection point (exclusive).\nFigure G-1 corresponds to the first dataset of the Sample Input below.\nFigure G-2 shows the shortest paths for the subsequent datasets of the Sample Input.\n\nFigure G-2: Examples of the shortest paths", "output": "For each dataset, output a single line containing the length of the shortest path from\nthe beam generator to the target.\nThe value should not have an error greater than 0.001.\nNo extra characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n30 10 30 75\n60 30 60 95\n90 0\n0 100\n1\n20 81 90 90\n10 90\n90 10\n2\n10 0 10 58\n20 20 20 58\n0 70\n30 0\n4\n8 0 8 60\n16 16 16 48\n16 10 28 30\n16 52 28 34\n24 0\n24 64\n5\n8 0 8 60\n16 16 16 48\n16 10 28 30\n16 52 28 34\n100 0 100 50\n24 0\n24 64\n0\n output: 180.27756377319946\n113.13708498984761\n98.99494936611666\n90.50966799187809\n90.50966799187809"], "Pid": "p00752", "ProblemText": "Task Description: A laser beam generator, a target object and some mirrors are \nplaced on a plane.\nThe mirrors stand upright on the plane,\nand both sides of the mirrors are flat and can reflect beams.\nTo point the beam at the target,\nyou may set the beam to several directions because of different reflections.\nYour job is to find the shortest beam path\nfrom the generator to the target and answer the length of the path.\n\nFigure G-1 shows examples of possible beam paths,\nwhere the bold line represents the shortest one.\n\nFigure G-1: Examples of possible paths\nTask Input: The input consists of a number of datasets. The end of the input is indicated by a line containing a zero. \n\nEach dataset is formatted as follows. \nEach value in the dataset except n is an integer no less than 0 and no more than 100.\n\nn\nPX_1 PY_1 QX_1 QY_1\n. . . \nPX_n PY_n QX_n QY_n\nTX TY\nLX LY\n\nThe first line of a dataset contains an integer n (1 <= n <= 5),\nrepresenting the number of mirrors.\nThe following n lines list the arrangement of mirrors on the plane.\nThe coordinates\n(PX_i, PY_i) and \n(QX_i, QY_i) represent\nthe positions of both ends of the mirror.\nMirrors are apart from each other.\nThe last two lines represent the target position (TX, TY)\nand the position of the beam generator (LX, LY).\nThe positions of the target and the generator are apart from each other,\nand these positions are also apart from mirrors.\n\nThe sizes of the target object and the beam generator are small enough to be ignored.\nYou can also ignore the thicknesses of mirrors.\n\nIn addition, you can assume the following conditions on the given datasets.\n\nThere is at least one possible path from the beam generator to the target.\nThe number of reflections along the shortest path is less than 6.\n\nThe shortest path does not cross or touch a plane containing a mirror\nsurface at any points within 0.001 unit distance from either end of the mirror.\n\nEven if the beam could arbitrarily select reflection or passage \nwhen it reaches each plane containing a mirror surface\nat a point within 0.001 unit distance from one of the mirror ends,\nany paths from the generator to the target would not be \nshorter than the shortest path.\n\nWhen the beam is shot from the generator in an arbitrary direction and \nit reflects on a mirror or passes the mirror within 0.001 unit distance from the mirror,\nthe angle θ formed by the beam and the mirror \nsatisfies sin(θ) > 0.1, \nuntil the beam reaches the 6th reflection point (exclusive).\nFigure G-1 corresponds to the first dataset of the Sample Input below.\nFigure G-2 shows the shortest paths for the subsequent datasets of the Sample Input.\n\nFigure G-2: Examples of the shortest paths\nTask Output: For each dataset, output a single line containing the length of the shortest path from\nthe beam generator to the target.\nThe value should not have an error greater than 0.001.\nNo extra characters should appear in the output.\nTask Samples: input: 2\n30 10 30 75\n60 30 60 95\n90 0\n0 100\n1\n20 81 90 90\n10 90\n90 10\n2\n10 0 10 58\n20 20 20 58\n0 70\n30 0\n4\n8 0 8 60\n16 16 16 48\n16 10 28 30\n16 52 28 34\n24 0\n24 64\n5\n8 0 8 60\n16 16 16 48\n16 10 28 30\n16 52 28 34\n100 0 100 50\n24 0\n24 64\n0\n output: 180.27756377319946\n113.13708498984761\n98.99494936611666\n90.50966799187809\n90.50966799187809\n\n" }, { "title": "Chebyshev's Theorem", "content": "\nIf n is a positive integer,\nthere exists at least one prime number greater than n and less than or equal to 2n.\nThis fact is known as Chebyshev's theorem or the Bertrand-Chebyshev theorem,\nwhich had been conjectured by Joseph Louis François Bertrand (1822–1900)\nand was proven by Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв,1821–1894) in 1850.\nSrinivasa Aiyangar Ramanujan (1887–1920) gave an elementary proof in his paper published in 1919.\nPaul Erdős (1913–1996) discovered another elementary proof in 1932.\nFor example, there exist 4 prime numbers greater than 10 and less than or equal to 20, i. e. 11,13,17 and 19.\nThere exist 3 prime numbers greater than 14 and less than or equal to 28, i. e. 17,19 and 23.\nYour mission is to write a program that counts the prime numbers greater than n and less than or equal to 2n for each given positive integer n.\nUsing such a program, you can verify Chebyshev's theorem for individual positive integers.", "constraint": "", "input": "The input is a sequence of datasets.\nA dataset is a line containing a single positive integer n.\nYou may assume n <= 123456.\nThe end of the input is indicated by a line containing a single zero.\nIt is not a dataset.", "output": "The output should be composed of as many lines as the input datasets.\nEach line should contain a single integer and should never contain extra characters.\nThe output integer corresponding to a dataset consisting of an integer n should be the number of the prime numbers p satisfying n < p <= 2n.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n10\n13\n100\n1000\n10000\n100000\n0\n output: \n1\n4\n3\n21\n135\n1033\n8392"], "Pid": "p00753", "ProblemText": "Task Description: \nIf n is a positive integer,\nthere exists at least one prime number greater than n and less than or equal to 2n.\nThis fact is known as Chebyshev's theorem or the Bertrand-Chebyshev theorem,\nwhich had been conjectured by Joseph Louis François Bertrand (1822–1900)\nand was proven by Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв,1821–1894) in 1850.\nSrinivasa Aiyangar Ramanujan (1887–1920) gave an elementary proof in his paper published in 1919.\nPaul Erdős (1913–1996) discovered another elementary proof in 1932.\nFor example, there exist 4 prime numbers greater than 10 and less than or equal to 20, i. e. 11,13,17 and 19.\nThere exist 3 prime numbers greater than 14 and less than or equal to 28, i. e. 17,19 and 23.\nYour mission is to write a program that counts the prime numbers greater than n and less than or equal to 2n for each given positive integer n.\nUsing such a program, you can verify Chebyshev's theorem for individual positive integers.\nTask Input: The input is a sequence of datasets.\nA dataset is a line containing a single positive integer n.\nYou may assume n <= 123456.\nThe end of the input is indicated by a line containing a single zero.\nIt is not a dataset.\nTask Output: The output should be composed of as many lines as the input datasets.\nEach line should contain a single integer and should never contain extra characters.\nThe output integer corresponding to a dataset consisting of an integer n should be the number of the prime numbers p satisfying n < p <= 2n.\nTask Samples: input: 1\n10\n13\n100\n1000\n10000\n100000\n0\n output: \n1\n4\n3\n21\n135\n1033\n8392\n\n" }, { "title": "The Balance of the World", "content": "\nThe world should be finely balanced. Positive vs. negative,\nlight vs. shadow, and left vs. right brackets.\nYour mission is to write a program that judges whether a string is balanced\nwith respect to brackets so that we can observe the balance of the\nworld.\nA string that will be given to the program may have two kinds of brackets,\nround (“( )”) and square (“[ ]”).\nA string is balanced if and only if the following conditions hold.\n\nFor every left round bracket (“(”), there is a corresponding\n right round bracket (“)”) in the following part of the string.\n\nFor every left square bracket (“[”), there is a corresponding\n right square bracket (“]”) in the following part of the string.\n\nFor every right bracket, there is a left bracket corresponding to it.\n\nCorrespondences of brackets have to be one to one, that is, a\n single bracket never corresponds to two or more brackets.\n\nFor every pair of corresponding left and right brackets,\n the substring between them is balanced.", "constraint": "", "input": "The input consists of one or more lines, each of which being a dataset.\nA dataset is a string that consists of English alphabets,\nspace characters, and two kinds of brackets, round (“( )”) and square (“[ ]”),\nterminated by a period. You can assume that every line has 100\ncharacters or less.\nThe line formed by a single period indicates the end of the input,\nwhich is not a dataset.", "output": "For each dataset, output “yes” if the\nstring is balanced, or “no” otherwise, in a line.\nThere may not be any extra characters in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: So when I die (the [first] I will see in (heaven) is a score list).\n[ first in ] ( first out ).\nHalf Moon tonight (At least it is better than no Moon at all].\nA rope may form )( a trail in a maze.\nHelp( I[m being held prisoner in a fortune cookie factory)].\n([ (([( [ ] ) ( ) (( ))] )) ]).\n .\n.\n output: \nyes\nyes\nno\nno\nno\nyes\nyes"], "Pid": "p00754", "ProblemText": "Task Description: \nThe world should be finely balanced. Positive vs. negative,\nlight vs. shadow, and left vs. right brackets.\nYour mission is to write a program that judges whether a string is balanced\nwith respect to brackets so that we can observe the balance of the\nworld.\nA string that will be given to the program may have two kinds of brackets,\nround (“( )”) and square (“[ ]”).\nA string is balanced if and only if the following conditions hold.\n\nFor every left round bracket (“(”), there is a corresponding\n right round bracket (“)”) in the following part of the string.\n\nFor every left square bracket (“[”), there is a corresponding\n right square bracket (“]”) in the following part of the string.\n\nFor every right bracket, there is a left bracket corresponding to it.\n\nCorrespondences of brackets have to be one to one, that is, a\n single bracket never corresponds to two or more brackets.\n\nFor every pair of corresponding left and right brackets,\n the substring between them is balanced.\nTask Input: The input consists of one or more lines, each of which being a dataset.\nA dataset is a string that consists of English alphabets,\nspace characters, and two kinds of brackets, round (“( )”) and square (“[ ]”),\nterminated by a period. You can assume that every line has 100\ncharacters or less.\nThe line formed by a single period indicates the end of the input,\nwhich is not a dataset.\nTask Output: For each dataset, output “yes” if the\nstring is balanced, or “no” otherwise, in a line.\nThere may not be any extra characters in the output.\nTask Samples: input: So when I die (the [first] I will see in (heaven) is a score list).\n[ first in ] ( first out ).\nHalf Moon tonight (At least it is better than no Moon at all].\nA rope may form )( a trail in a maze.\nHelp( I[m being held prisoner in a fortune cookie factory)].\n([ (([( [ ] ) ( ) (( ))] )) ]).\n .\n.\n output: \nyes\nyes\nno\nno\nno\nyes\nyes\n\n" }, { "title": "Identically Colored Panels Connection", "content": "\nDr. Fukuoka has invented fancy panels.\n\nEach panel has a square shape of a unit size and \nhas one of the six colors, namely, yellow, pink, red, purple, green and blue.\n\nThe panel has two remarkable properties.\n\nOne property is that, when two or more panels with the same color\nare placed adjacently, their touching edges melt a little\nand they are fused each other.\nThe fused panels are united into a polygonally shaped panel.\nThe other property is that the color of a panel can be changed \nto one of six colors by giving an electrical shock.\nThe resulting color can be controlled by its waveform.\nThe electrical shock to an already united panel changes\nthe color of the whole to a specified single color.\nSince he wants to investigate the strength with respect to the\ncolor and the size of a united panel compared to unit panels,\nhe tries to unite panels into a polygonal panel with a specified color.\n\nFigure C-1: panels and their initial colors\nSince many panels are simultaneously synthesized and generated on a base plate \nthrough some complex chemical processes,\nthe fabricated panels are randomly colored and\nthey are arranged in a rectangular shape on the base plate (Figure C-1).\n\nNote that the two purple (color 4) panels in Figure C-1 are\nalready united at the initial state since they are \nadjacent to each other.\nInstalling electrodes to a panel, and\nchanging its color several times by giving electrical shocks\naccording to an appropriate sequence for a specified target color,\nhe can make a united panel merge the adjacent panels \nto unite them step by step\nand can obtain a larger panel with the target color.\n\nUnfortunately, panels will be broken when\nthey are struck by the sixth electrical shock.\n\nThat is, he can change the color of a panel or a united panel only \nfive times.\nLet us consider a case\nwhere the panel at the upper left corner of the panel configuration\n(Figure C-1) is attached with the electrodes.\nFirst, changing the color of the panel from yellow to blue,\nthe two adjacent panels are fused into a united panel (Figure C-2).\nFigure C-2: \nChange of the color of the panel at the upper left corner,\nfrom yellow (color 1) to blue (color 6). \n\nSecond, changing the color of the upper left united panel from blue\nto red, a united red panel that consists of three unit panels is newly formed\n(Figure C-3).\nThen, changing the color of the united panel from red to purple,\npanels are united again to form a united panel of five unit panels\n(Figure C-4).\nFigure C-3: \nChange of the color of the panel at the upper left corner,\nfrom blue (color 6) to red (color 3).\nFigure C-4: \nChange of the color of the panel at the upper left corner,\nfrom red (color 3) to purple (color 4).\nFurthermore, through making a pink united panel in Figure C-5 by\nchanging the color from purple to pink, \nthen, the green united panel in Figure C-6 is obtained\nby changing the color from pink to green.\nThe green united panel consists of ten unit panels.\nFigure C-5: \nChange of the color of the panel at the upper left corner, \nfrom purple (color 4) to pink (color 2). \n\nFigure C-6: \nChange of the color of the panel at the upper left corner,\nfrom pink (color 2) to green (color 5). \n\nIn order to check the strength of united panels with \nvarious sizes and colors, he needs to unite as many panels\nas possible with the target color.\n\nYour job is to write a program that finds a sequence to change \nthe colors five times \nin order to get the largest united panel with the target color.\n\nNote that the electrodes are fixed to the panel at the upper left corner.", "constraint": "", "input": "The input consists of multiple datasets, each being in the following format.\n\nh w c\np_1,1 p_1,2 . . . p_1, w\np_2,1 p_2,2 . . . p_2, w \n. . . \np_h, 1 p_h, 2 . . . p_h, w\n\nh and w are positive integers no more than 8 that\nrepresent the height and the width of the given rectangle.\nc is a positive integer no more than 6 that represents\nthe target color of the finally united panel.\n\np_i, j is a positive integer no more than 6\nthat represents the initial color of the panel at the position\n(i, j).\n\nThe end of the input is indicated by a line that consists of \nthree zeros separated by single spaces.", "output": "For each dataset, output the largest possible number of unit panels\nin the united panel at the upper left corner with the target color\nafter five times of color changes of the panel \nat the upper left corner.\nNo extra characters should occur in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 5 5\n1 6 3 2 5\n2 5 4 6 1\n1 2 4 1 5\n4 5 6\n1 5 6 1 2\n1 4 6 3 2\n1 5 2 3 2\n1 1 2 3 2\n1 1 5\n1\n1 8 6\n1 2 3 4 5 1 2 3\n8 1 1\n1\n2\n3\n4\n5\n1\n2\n3\n8 8 6\n5 2 5 2 6 5 4 2\n4 2 2 2 5 2 2 2\n4 4 4 2 5 2 2 2\n6 4 5 2 2 2 6 6\n6 6 5 5 2 2 6 6\n6 2 5 4 2 2 6 6\n2 4 4 4 6 2 2 6\n2 2 2 5 5 2 2 2\n8 8 2\n3 3 5 4 1 6 2 3\n2 3 6 4 3 6 2 2\n4 1 6 6 6 4 4 4\n2 5 3 6 3 6 3 5\n3 1 3 4 1 5 6 3\n1 6 6 3 5 1 5 3\n2 4 2 2 2 6 5 3\n4 1 3 6 1 5 5 4\n0 0 0\n output: \n10\n18\n1\n5\n6\n64\n33"], "Pid": "p00755", "ProblemText": "Task Description: \nDr. Fukuoka has invented fancy panels.\n\nEach panel has a square shape of a unit size and \nhas one of the six colors, namely, yellow, pink, red, purple, green and blue.\n\nThe panel has two remarkable properties.\n\nOne property is that, when two or more panels with the same color\nare placed adjacently, their touching edges melt a little\nand they are fused each other.\nThe fused panels are united into a polygonally shaped panel.\nThe other property is that the color of a panel can be changed \nto one of six colors by giving an electrical shock.\nThe resulting color can be controlled by its waveform.\nThe electrical shock to an already united panel changes\nthe color of the whole to a specified single color.\nSince he wants to investigate the strength with respect to the\ncolor and the size of a united panel compared to unit panels,\nhe tries to unite panels into a polygonal panel with a specified color.\n\nFigure C-1: panels and their initial colors\nSince many panels are simultaneously synthesized and generated on a base plate \nthrough some complex chemical processes,\nthe fabricated panels are randomly colored and\nthey are arranged in a rectangular shape on the base plate (Figure C-1).\n\nNote that the two purple (color 4) panels in Figure C-1 are\nalready united at the initial state since they are \nadjacent to each other.\nInstalling electrodes to a panel, and\nchanging its color several times by giving electrical shocks\naccording to an appropriate sequence for a specified target color,\nhe can make a united panel merge the adjacent panels \nto unite them step by step\nand can obtain a larger panel with the target color.\n\nUnfortunately, panels will be broken when\nthey are struck by the sixth electrical shock.\n\nThat is, he can change the color of a panel or a united panel only \nfive times.\nLet us consider a case\nwhere the panel at the upper left corner of the panel configuration\n(Figure C-1) is attached with the electrodes.\nFirst, changing the color of the panel from yellow to blue,\nthe two adjacent panels are fused into a united panel (Figure C-2).\nFigure C-2: \nChange of the color of the panel at the upper left corner,\nfrom yellow (color 1) to blue (color 6). \n\nSecond, changing the color of the upper left united panel from blue\nto red, a united red panel that consists of three unit panels is newly formed\n(Figure C-3).\nThen, changing the color of the united panel from red to purple,\npanels are united again to form a united panel of five unit panels\n(Figure C-4).\nFigure C-3: \nChange of the color of the panel at the upper left corner,\nfrom blue (color 6) to red (color 3).\nFigure C-4: \nChange of the color of the panel at the upper left corner,\nfrom red (color 3) to purple (color 4).\nFurthermore, through making a pink united panel in Figure C-5 by\nchanging the color from purple to pink, \nthen, the green united panel in Figure C-6 is obtained\nby changing the color from pink to green.\nThe green united panel consists of ten unit panels.\nFigure C-5: \nChange of the color of the panel at the upper left corner, \nfrom purple (color 4) to pink (color 2). \n\nFigure C-6: \nChange of the color of the panel at the upper left corner,\nfrom pink (color 2) to green (color 5). \n\nIn order to check the strength of united panels with \nvarious sizes and colors, he needs to unite as many panels\nas possible with the target color.\n\nYour job is to write a program that finds a sequence to change \nthe colors five times \nin order to get the largest united panel with the target color.\n\nNote that the electrodes are fixed to the panel at the upper left corner.\nTask Input: The input consists of multiple datasets, each being in the following format.\n\nh w c\np_1,1 p_1,2 . . . p_1, w\np_2,1 p_2,2 . . . p_2, w \n. . . \np_h, 1 p_h, 2 . . . p_h, w\n\nh and w are positive integers no more than 8 that\nrepresent the height and the width of the given rectangle.\nc is a positive integer no more than 6 that represents\nthe target color of the finally united panel.\n\np_i, j is a positive integer no more than 6\nthat represents the initial color of the panel at the position\n(i, j).\n\nThe end of the input is indicated by a line that consists of \nthree zeros separated by single spaces.\nTask Output: For each dataset, output the largest possible number of unit panels\nin the united panel at the upper left corner with the target color\nafter five times of color changes of the panel \nat the upper left corner.\nNo extra characters should occur in the output.\nTask Samples: input: 3 5 5\n1 6 3 2 5\n2 5 4 6 1\n1 2 4 1 5\n4 5 6\n1 5 6 1 2\n1 4 6 3 2\n1 5 2 3 2\n1 1 2 3 2\n1 1 5\n1\n1 8 6\n1 2 3 4 5 1 2 3\n8 1 1\n1\n2\n3\n4\n5\n1\n2\n3\n8 8 6\n5 2 5 2 6 5 4 2\n4 2 2 2 5 2 2 2\n4 4 4 2 5 2 2 2\n6 4 5 2 2 2 6 6\n6 6 5 5 2 2 6 6\n6 2 5 4 2 2 6 6\n2 4 4 4 6 2 2 6\n2 2 2 5 5 2 2 2\n8 8 2\n3 3 5 4 1 6 2 3\n2 3 6 4 3 6 2 2\n4 1 6 6 6 4 4 4\n2 5 3 6 3 6 3 5\n3 1 3 4 1 5 6 3\n1 6 6 3 5 1 5 3\n2 4 2 2 2 6 5 3\n4 1 3 6 1 5 5 4\n0 0 0\n output: \n10\n18\n1\n5\n6\n64\n33\n\n" }, { "title": "And Then, How Many Are There?", "content": "\nTo Mr. Solitarius, who is a famous solo play game creator, a new idea\noccurs like every day.\nHis new game requires discs of various colors and sizes.\nTo start with, all the discs are randomly scattered around the\ncenter of a table.\nDuring the play, you can remove a pair of discs of the same color if\nneither of them has any discs on top of it.\nNote that a disc is not considered to be on top of another when they\nare externally tangent to each other.\n\nFigure D-1: Seven discs on the table\nFor example, in Figure D-1, you can only remove the two black\ndiscs first and then their removal makes it possible to remove the two\nwhite ones.\nIn contrast, gray ones never become removable.\nYou are requested to write a computer program that, for given colors,\nsizes, and initial placings of discs, calculates the maximum number of discs\nthat can be removed.", "constraint": "", "input": "The input consists of multiple datasets, each being in the\nfollowing format and representing the state of a game just after all\nthe discs are scattered.\n\nn\nx_1 y_1 r_1 c_1\nx_2 y_2 r_2 c_2\n. . . \nx_n y_n r_n c_n\n\nThe first line consists of a positive integer n representing\nthe number of discs.\nThe following n lines, each containing 4 integers separated by\na single space, represent the colors, sizes, and initial placings of\nthe n discs in the following manner:\n(x_i, y_i), \nr_i, and \nc_i are\nthe xy-coordinates of the center, the radius, and the color index\nnumber, respectively, of the i-th disc, and\n\nwhenever the i-th disc is put on top of the j-th\ndisc, i < j must be satisfied.\n\nYou may assume that every color index number is between 1 and 4,\ninclusive, and at most 6 discs in a dataset are of the same\ncolor.\nYou may also assume that the x- and y-coordinates of the\ncenter of every disc are between 0 and 100, inclusive, and the radius\nbetween 1 and 100, inclusive.\nThe end of the input is indicated by a single zero.", "output": "For each dataset, print a line containing an integer indicating the\nmaximum number of discs that can be removed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n0 0 50 1\n0 0 50 2\n100 0 50 1\n0 0 100 2\n7\n12 40 8 1\n10 40 10 2\n30 40 10 2\n10 10 10 1\n20 10 9 3\n30 10 8 3\n40 10 7 3\n2\n0 0 100 1\n100 32 5 1\n0\n output: \n2\n4\n0"], "Pid": "p00756", "ProblemText": "Task Description: \nTo Mr. Solitarius, who is a famous solo play game creator, a new idea\noccurs like every day.\nHis new game requires discs of various colors and sizes.\nTo start with, all the discs are randomly scattered around the\ncenter of a table.\nDuring the play, you can remove a pair of discs of the same color if\nneither of them has any discs on top of it.\nNote that a disc is not considered to be on top of another when they\nare externally tangent to each other.\n\nFigure D-1: Seven discs on the table\nFor example, in Figure D-1, you can only remove the two black\ndiscs first and then their removal makes it possible to remove the two\nwhite ones.\nIn contrast, gray ones never become removable.\nYou are requested to write a computer program that, for given colors,\nsizes, and initial placings of discs, calculates the maximum number of discs\nthat can be removed.\nTask Input: The input consists of multiple datasets, each being in the\nfollowing format and representing the state of a game just after all\nthe discs are scattered.\n\nn\nx_1 y_1 r_1 c_1\nx_2 y_2 r_2 c_2\n. . . \nx_n y_n r_n c_n\n\nThe first line consists of a positive integer n representing\nthe number of discs.\nThe following n lines, each containing 4 integers separated by\na single space, represent the colors, sizes, and initial placings of\nthe n discs in the following manner:\n(x_i, y_i), \nr_i, and \nc_i are\nthe xy-coordinates of the center, the radius, and the color index\nnumber, respectively, of the i-th disc, and\n\nwhenever the i-th disc is put on top of the j-th\ndisc, i < j must be satisfied.\n\nYou may assume that every color index number is between 1 and 4,\ninclusive, and at most 6 discs in a dataset are of the same\ncolor.\nYou may also assume that the x- and y-coordinates of the\ncenter of every disc are between 0 and 100, inclusive, and the radius\nbetween 1 and 100, inclusive.\nThe end of the input is indicated by a single zero.\nTask Output: For each dataset, print a line containing an integer indicating the\nmaximum number of discs that can be removed.\nTask Samples: input: 4\n0 0 50 1\n0 0 50 2\n100 0 50 1\n0 0 100 2\n7\n12 40 8 1\n10 40 10 2\n30 40 10 2\n10 10 10 1\n20 10 9 3\n30 10 8 3\n40 10 7 3\n2\n0 0 100 1\n100 32 5 1\n0\n output: \n2\n4\n0\n\n" }, { "title": "Planning Rolling Blackouts", "content": "\n\nFaced with seriously tight power supply-demand balance, the\nelectric power company for which you are working implemented rolling\n blackouts in this spring. It divided the servicing area into several\ngroups of towns, and divided a day into several blackout periods. At\neach blackout period of a day, one of the groups, which alternates\nfrom one group to another, is cut off the electricity. By keeping the total demand of\nelectricity used by the rest of the towns within the supply\ncapacity, the company avoided unforeseeable large-scale blackout.\nWorking at the customer relations department, you had to listen to\nso many complaints from the customers, which made you think that you\ncould have a better implementation. Most of the complaints are about the\nfrequent cut-offs. But you could have divided the area into a larger number of\ngroups, which resulted in less frequent cut-offs for each group. The\nother complaints are about the complicated grouping (in fact, someone\nsaid that the shapes of the groups are fractals), which makes it\nimpossible to understand which town belongs to which group without\nclosely inspecting into the grouping list publicized by the company.\nWith the rectangular servicing area and towns located in a grid form,\nyou could have made a simpler grouping.\n\nWhen you talked your analysis directly to the president of the company, you are\nappointed to plan rolling blackouts for this summer. Be careful what\nyou propose. Anyway, you need to divide the servicing area into\nas many groups as possible with keeping total demand of electricity\nwithin the supply capacity. It should also divide the towns into\nsimple and easy to remember groups.\nYour task is to write a program, given a demand table (a table showing\nelectricity demand of each town) and the supply capacity, that answers\na grouping of towns that satisfy the following conditions.\nThe grouping should be made by horizontally or vertically splitting\n the area in a recursive manner. In other words, the grouping must\n be a set of areas after applied the following splitting\n procedure to a set containing only the entire area for zero or\n more times:\n (The splitting procedure) remove one area from the set,\n either vertically or horizontally split it into two sub-areas,\n and put the sub-areas into the set.\n\n\n\nThe maximum suppressed demand of the grouping, which is the greatest total demand of the\n all but one group, is no more than the supply capacity.\n\nThe grouping has the largest number of groups among the groupings\n that satisfy the above conditions 1 and 2.\n\nThe grouping has the greatest amount of reserve power among the\n groupings that satisfy the above conditions 1,2 and 3, where the\n reserve power of a grouping is the difference between the supply\n capacity and the maximum suppressed demand.\nNote that the condition 1 does not allow such a grouping shown in Figure E-1.\nFigure E-1: A grouping that violates the condition 1", "constraint": "", "input": "The input consists of one or more datasets. Each dataset is given in\nthe following format.\n\nh w s \nu_11 u_12 . . . u_1w\nu_21 u_22 . . . u_2w\n. . . \nu_h1 u_h2 . . . u_hw\n\nThe first line contains three positive integer numbers,\nnamely h, w and s, denoting the height and width\nof the demand table and the power supply capacity. The following h\nlines, each of which contains w integer numbers, denote demands of towns at respective\nlocations. Those figures are constrained as follows.\n\n1 <= h, w <= 32 \n1 <= u_ij <= 100\n\nRegrettably, you may assume that the supply capacity is less than the total demand of the area.\nThe last dataset is followed by a line containing three zeros.", "output": "For each dataset, print a line having two integers indicating the\nnumber of groups in the grouping that satisfies the conditions, and\nthe amount of the reserve power. Each line should not have any\ncharacter other than those numbers and a space in between.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3 33\n4 4 2\n2 9 6\n6 5 3\n3 4 15\n1 2 1 2\n2 1 2 1\n1 2 1 2\n32 32 1112\n1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 2\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1\n2 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1\n1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1\n1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1\n1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1\n2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1\n2 1 1 1 1 1 1 1 2 1 1 1 2 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1\n1 1 1 2 1 1 2 1 1 1 2 1 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n0 0 0\n output: \n4 1\n6 0\n553 0"], "Pid": "p00757", "ProblemText": "Task Description: \n\nFaced with seriously tight power supply-demand balance, the\nelectric power company for which you are working implemented rolling\n blackouts in this spring. It divided the servicing area into several\ngroups of towns, and divided a day into several blackout periods. At\neach blackout period of a day, one of the groups, which alternates\nfrom one group to another, is cut off the electricity. By keeping the total demand of\nelectricity used by the rest of the towns within the supply\ncapacity, the company avoided unforeseeable large-scale blackout.\nWorking at the customer relations department, you had to listen to\nso many complaints from the customers, which made you think that you\ncould have a better implementation. Most of the complaints are about the\nfrequent cut-offs. But you could have divided the area into a larger number of\ngroups, which resulted in less frequent cut-offs for each group. The\nother complaints are about the complicated grouping (in fact, someone\nsaid that the shapes of the groups are fractals), which makes it\nimpossible to understand which town belongs to which group without\nclosely inspecting into the grouping list publicized by the company.\nWith the rectangular servicing area and towns located in a grid form,\nyou could have made a simpler grouping.\n\nWhen you talked your analysis directly to the president of the company, you are\nappointed to plan rolling blackouts for this summer. Be careful what\nyou propose. Anyway, you need to divide the servicing area into\nas many groups as possible with keeping total demand of electricity\nwithin the supply capacity. It should also divide the towns into\nsimple and easy to remember groups.\nYour task is to write a program, given a demand table (a table showing\nelectricity demand of each town) and the supply capacity, that answers\na grouping of towns that satisfy the following conditions.\nThe grouping should be made by horizontally or vertically splitting\n the area in a recursive manner. In other words, the grouping must\n be a set of areas after applied the following splitting\n procedure to a set containing only the entire area for zero or\n more times:\n (The splitting procedure) remove one area from the set,\n either vertically or horizontally split it into two sub-areas,\n and put the sub-areas into the set.\n\n\n\nThe maximum suppressed demand of the grouping, which is the greatest total demand of the\n all but one group, is no more than the supply capacity.\n\nThe grouping has the largest number of groups among the groupings\n that satisfy the above conditions 1 and 2.\n\nThe grouping has the greatest amount of reserve power among the\n groupings that satisfy the above conditions 1,2 and 3, where the\n reserve power of a grouping is the difference between the supply\n capacity and the maximum suppressed demand.\nNote that the condition 1 does not allow such a grouping shown in Figure E-1.\nFigure E-1: A grouping that violates the condition 1\nTask Input: The input consists of one or more datasets. Each dataset is given in\nthe following format.\n\nh w s \nu_11 u_12 . . . u_1w\nu_21 u_22 . . . u_2w\n. . . \nu_h1 u_h2 . . . u_hw\n\nThe first line contains three positive integer numbers,\nnamely h, w and s, denoting the height and width\nof the demand table and the power supply capacity. The following h\nlines, each of which contains w integer numbers, denote demands of towns at respective\nlocations. Those figures are constrained as follows.\n\n1 <= h, w <= 32 \n1 <= u_ij <= 100\n\nRegrettably, you may assume that the supply capacity is less than the total demand of the area.\nThe last dataset is followed by a line containing three zeros.\nTask Output: For each dataset, print a line having two integers indicating the\nnumber of groups in the grouping that satisfies the conditions, and\nthe amount of the reserve power. Each line should not have any\ncharacter other than those numbers and a space in between.\nTask Samples: input: 3 3 33\n4 4 2\n2 9 6\n6 5 3\n3 4 15\n1 2 1 2\n2 1 2 1\n1 2 1 2\n32 32 1112\n1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 2\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1\n2 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1\n1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1\n1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1\n1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1\n2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1\n2 1 1 1 1 1 1 1 2 1 1 1 2 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1\n1 1 1 2 1 1 2 1 1 1 2 1 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n0 0 0\n output: \n4 1\n6 0\n553 0\n\n" }, { "title": "Watchdog Corporation", "content": "\nIn Northern Kyushu, you are running a company\nwhich rents watchdogs in response to the customers' order.\nThe distinguishing point of your service is that you also\ninstall fences to enhance the performance of watchdogs.\nThe dog is put on a leash, which is tied up to a peg.\nYou are installing fences at the\nborder of the dog's reach, so that strangers approaching the\nfence are taken care of by your dog.\nThere may be a rectangular building near the dog; the dog cannot\nenter the building, but can go around it as long as the length of\nthe leash permits, as in Figure F-1. You do not need fences along the\nbuilding's wall.\n\nFigure F-1: Example fence layouts (some parts of the fences are omitted. )\nGiven the length of the leash and the position and the size of the\nbuilding, your program should calculate the length of the fence.", "constraint": "", "input": "The input consists of multiple datasets each consisting of \nfive integers in a line of the following format.\n\nlen x_1 y_1\nx_2 y_2\n\nlen indicates the length of the leash.\nx_1, y_1, x_2\nand y_2 indicate the size and position of the\nbuilding in that a point with coordinate (x, y)\nsuch that x_1 < x \nIn Northern Kyushu, you are running a company\nwhich rents watchdogs in response to the customers' order.\nThe distinguishing point of your service is that you also\ninstall fences to enhance the performance of watchdogs.\nThe dog is put on a leash, which is tied up to a peg.\nYou are installing fences at the\nborder of the dog's reach, so that strangers approaching the\nfence are taken care of by your dog.\nThere may be a rectangular building near the dog; the dog cannot\nenter the building, but can go around it as long as the length of\nthe leash permits, as in Figure F-1. You do not need fences along the\nbuilding's wall.\n\nFigure F-1: Example fence layouts (some parts of the fences are omitted. )\nGiven the length of the leash and the position and the size of the\nbuilding, your program should calculate the length of the fence.\nTask Input: The input consists of multiple datasets each consisting of \nfive integers in a line of the following format.\n\nlen x_1 y_1\nx_2 y_2\n\nlen indicates the length of the leash.\nx_1, y_1, x_2\nand y_2 indicate the size and position of the\nbuilding in that a point with coordinate (x, y)\nsuch that x_1 < x \nThere is a rectangular maze consisting of a number of square rooms\narranged in grid. The maze is surrounded by\nwalls except for its entry and exit. The entry to the maze is at the\nleftmost part of the upper side of the rectangular area, that is, the\nupper side of the uppermost leftmost room of the maze is open. The\nexit is located at the rightmost part of the lower side, likewise.\nThere is a wall between each pair of vertically or horizontally adjacent rooms. Such a wall has either\na door with a card key lock, or no door at all. If you insert a card\nto a door, the door opens and you can pass the door. The opened door\nwill close immediately, and the inserted card won't return. You can\nopen any door with any card. You cannot go\nthrough a wall that has no door.\nWhen a maze map is given, you can easily determine how many cards are\nneeded to pass through the maze from the entry to the exit. In the\nmaze in Figure G-1, you can pass through it with ten cards,\nfollowing the path represented by the green arrows () in Figure G-2.\n\nFigure G-1: A map of a maze\n\nFigure G-2: One of the shortest paths\n\n \nNow, you are informed that one of the doors is broken and can't be\npassed. But you don't know which door is broken. If you insert a card\nto a broken door, the inserted card immediately returns. However,\nyou can't tell a broken door from a working door just by its\nappearance.\n\nFigure G-3: A maze that potentially can't be passed through\nIf the door marked with a red X () in Figure G-3 is broken, you have no way to pass through\nthe maze from the entry to the exit. However, you can pass the maze in\nFigure G-1 whichever door is broken. When you intend to follow the\nshortest path in Figure G-2, and find that the door marked with a red X in Figure G-4 is broken, you\nmight follow the path represented as green arrows. In this case, you\nneed twenty cards.\n\nFigure G-4: A maze with a broken door\nHowever, you can pass through the maze with less cards. You should\nfollow the path in Figure G-5, until you find the broken door.\nThe path is not the shortest path because it needs twelve\ncards at least. After you've found a broken door on the path, you\nshould follow the shortest path to the exit that doesn't use the broken\ndoor. With this strategy, you can pass the maze with sixteen cards\nwhichever door is broken. Figure G-6 shows one of the worst cases of\nthis strategy; it needs sixteen cards.\n\nFigure G-5: The path before you find the broken door\n\nFigure G-6: One of the worst cases of the strategy\nYou are requested to write a program that prints the minimum number of\ncards to pass the maze whichever door is broken.", "constraint": "", "input": "The input consists of one or more datasets, each of which represents a\nmaze. The number of datasets is no more than 100. \nThe first line of a dataset contains two integer numbers, the\nheight h and the width w of the rectangular maze, in\nthis order. You may assume that 2 <= h, w <= 30.\nThe following 2 * h - 1 lines of a dataset describe\nwhether there are doors between rooms or not. The first line starts\nwith a space and the rest of the line contains w - 1\nintegers, 1 or 0, separated by a space. These indicate whether doors\nconnect horizontally adjoining rooms in the first row. An integer\n0 indicates a door is placed, and 1 indicates no door is there. The\nsecond line starts without a space and contains w integers, 1 or 0,\nseparated by a space. These indicate whether doors connect\nvertically adjoining rooms in the first and the second rows. An\ninteger 0/1 indicates a door is placed or not. The following lines\nindicate placing of doors between horizontally and vertically\nadjoining rooms, alternately, in the same manner.\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output a line having an integer indicating the\nminimum number of cards needed. \nIf there exists no path to pass through the maze when a certain door is broken, output a line containing -1.\nThe line should not contain any character other than this number.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 8\n 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 1\n 0 0 0 0 1 0 0\n0 1 1 1 1 0 0 0\n 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n 0 0 0 0 0 1 0\n4 8\n 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 1\n 0 0 0 0 1 0 0\n0 1 1 1 1 0 0 0\n 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 1\n2 2\n 0\n0 0\n 0\n3 3\n 0 0\n0 1 0\n 0 1\n0 0 0\n 0 0\n2 4\n 1 0 1\n0 0 0 0\n 0 1 0\n6 12\n 0 0 0 1 1 0 0 0 0 0 0\n0 1 1 0 0 0 0 0 0 1 1 0\n 1 0 0 1 0 0 0 0 1 0 0\n0 0 0 0 0 0 0 0 0 0 0 0\n 1 0 0 1 1 0 0 1 1 0 0\n0 0 0 0 0 0 0 0 0 0 0 0\n 1 0 0 1 1 0 0 1 1 0 0\n0 0 0 1 0 0 0 0 0 0 0 0\n 0 0 0 0 1 0 0 1 1 0 0\n0 0 0 0 0 1 1 0 0 1 0 0\n 1 0 0 0 0 0 0 1 0 0 0\n20 20\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0\n output: \n16\n-1\n4\n10\n-1\n32\n40"], "Pid": "p00759", "ProblemText": "Task Description: \nThere is a rectangular maze consisting of a number of square rooms\narranged in grid. The maze is surrounded by\nwalls except for its entry and exit. The entry to the maze is at the\nleftmost part of the upper side of the rectangular area, that is, the\nupper side of the uppermost leftmost room of the maze is open. The\nexit is located at the rightmost part of the lower side, likewise.\nThere is a wall between each pair of vertically or horizontally adjacent rooms. Such a wall has either\na door with a card key lock, or no door at all. If you insert a card\nto a door, the door opens and you can pass the door. The opened door\nwill close immediately, and the inserted card won't return. You can\nopen any door with any card. You cannot go\nthrough a wall that has no door.\nWhen a maze map is given, you can easily determine how many cards are\nneeded to pass through the maze from the entry to the exit. In the\nmaze in Figure G-1, you can pass through it with ten cards,\nfollowing the path represented by the green arrows () in Figure G-2.\n\nFigure G-1: A map of a maze\n\nFigure G-2: One of the shortest paths\n\n \nNow, you are informed that one of the doors is broken and can't be\npassed. But you don't know which door is broken. If you insert a card\nto a broken door, the inserted card immediately returns. However,\nyou can't tell a broken door from a working door just by its\nappearance.\n\nFigure G-3: A maze that potentially can't be passed through\nIf the door marked with a red X () in Figure G-3 is broken, you have no way to pass through\nthe maze from the entry to the exit. However, you can pass the maze in\nFigure G-1 whichever door is broken. When you intend to follow the\nshortest path in Figure G-2, and find that the door marked with a red X in Figure G-4 is broken, you\nmight follow the path represented as green arrows. In this case, you\nneed twenty cards.\n\nFigure G-4: A maze with a broken door\nHowever, you can pass through the maze with less cards. You should\nfollow the path in Figure G-5, until you find the broken door.\nThe path is not the shortest path because it needs twelve\ncards at least. After you've found a broken door on the path, you\nshould follow the shortest path to the exit that doesn't use the broken\ndoor. With this strategy, you can pass the maze with sixteen cards\nwhichever door is broken. Figure G-6 shows one of the worst cases of\nthis strategy; it needs sixteen cards.\n\nFigure G-5: The path before you find the broken door\n\nFigure G-6: One of the worst cases of the strategy\nYou are requested to write a program that prints the minimum number of\ncards to pass the maze whichever door is broken.\nTask Input: The input consists of one or more datasets, each of which represents a\nmaze. The number of datasets is no more than 100. \nThe first line of a dataset contains two integer numbers, the\nheight h and the width w of the rectangular maze, in\nthis order. You may assume that 2 <= h, w <= 30.\nThe following 2 * h - 1 lines of a dataset describe\nwhether there are doors between rooms or not. The first line starts\nwith a space and the rest of the line contains w - 1\nintegers, 1 or 0, separated by a space. These indicate whether doors\nconnect horizontally adjoining rooms in the first row. An integer\n0 indicates a door is placed, and 1 indicates no door is there. The\nsecond line starts without a space and contains w integers, 1 or 0,\nseparated by a space. These indicate whether doors connect\nvertically adjoining rooms in the first and the second rows. An\ninteger 0/1 indicates a door is placed or not. The following lines\nindicate placing of doors between horizontally and vertically\nadjoining rooms, alternately, in the same manner.\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output a line having an integer indicating the\nminimum number of cards needed. \nIf there exists no path to pass through the maze when a certain door is broken, output a line containing -1.\nThe line should not contain any character other than this number.\nTask Samples: input: 4 8\n 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 1\n 0 0 0 0 1 0 0\n0 1 1 1 1 0 0 0\n 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n 0 0 0 0 0 1 0\n4 8\n 0 0 0 0 0 0 1\n0 0 0 0 0 0 0 1\n 0 0 0 0 1 0 0\n0 1 1 1 1 0 0 0\n 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 1\n2 2\n 0\n0 0\n 0\n3 3\n 0 0\n0 1 0\n 0 1\n0 0 0\n 0 0\n2 4\n 1 0 1\n0 0 0 0\n 0 1 0\n6 12\n 0 0 0 1 1 0 0 0 0 0 0\n0 1 1 0 0 0 0 0 0 1 1 0\n 1 0 0 1 0 0 0 0 1 0 0\n0 0 0 0 0 0 0 0 0 0 0 0\n 1 0 0 1 1 0 0 1 1 0 0\n0 0 0 0 0 0 0 0 0 0 0 0\n 1 0 0 1 1 0 0 1 1 0 0\n0 0 0 1 0 0 0 0 0 0 0 0\n 0 0 0 0 1 0 0 1 1 0 0\n0 0 0 0 0 1 1 0 0 1 0 0\n 1 0 0 0 0 0 0 1 0 0 0\n20 20\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0\n output: \n16\n-1\n4\n10\n-1\n32\n40\n\n" }, { "title": "Millennium", "content": "A wise king declared a new calendar. \"Tomorrow shall be the first day of the calendar, that is, the day 1 of the month 1 of the year 1. Each year consists of 10 months, from month 1 through month 10, and starts from a big month. A common year shall start with a big month, followed by small months and big months one after another. Therefore the first month is a big month, the second month is a small month, the third a big month, . . . , and the 10th and last month a small one. A big month consists of 20 days and a small month consists of 19 days. However years which are multiples of three, that are year 3, year 6, year 9, and so on, shall consist of 10 big months and no small month. \"Many years have passed since the calendar started to be used. For celebration of the millennium day (the year 1000, month 1, day 1), a royal lottery is going to be organized to send gifts to those who have lived as many days as the number chosen by the lottery. Write a program that helps people calculate the number of days since their birthdate to the millennium day.", "constraint": "", "input": "The input is formatted as follows.\n\nn\nY_1 M_1 D_1\nY_2 M_2 D_2\n . . . \nY_n M_n D_n\n\nHere, the first line gives the number of datasets as a positive integer n, which is less than or equal to 100. It is followed by n datasets. Each dataset is formatted in a line and gives three positive integers, Y_i (< 1000), M_i (<= 10), and D_i (<= 20), that correspond to the year, month and day, respectively, of a person's birthdate in the king's calendar. These three numbers are separated by a space.", "output": "For the birthdate specified in each dataset, print in a line the number of days from the birthdate, inclusive, to the millennium day, exclusive. Output lines should not contain any character other than this number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n1 1 1\n344 3 1\n696 5 1\n182 9 5\n998 8 7\n344 2 19\n696 4 19\n999 10 20\n output: 196470\n128976\n59710\n160715\n252\n128977\n59712\n1"], "Pid": "p00760", "ProblemText": "Task Description: A wise king declared a new calendar. \"Tomorrow shall be the first day of the calendar, that is, the day 1 of the month 1 of the year 1. Each year consists of 10 months, from month 1 through month 10, and starts from a big month. A common year shall start with a big month, followed by small months and big months one after another. Therefore the first month is a big month, the second month is a small month, the third a big month, . . . , and the 10th and last month a small one. A big month consists of 20 days and a small month consists of 19 days. However years which are multiples of three, that are year 3, year 6, year 9, and so on, shall consist of 10 big months and no small month. \"Many years have passed since the calendar started to be used. For celebration of the millennium day (the year 1000, month 1, day 1), a royal lottery is going to be organized to send gifts to those who have lived as many days as the number chosen by the lottery. Write a program that helps people calculate the number of days since their birthdate to the millennium day.\nTask Input: The input is formatted as follows.\n\nn\nY_1 M_1 D_1\nY_2 M_2 D_2\n . . . \nY_n M_n D_n\n\nHere, the first line gives the number of datasets as a positive integer n, which is less than or equal to 100. It is followed by n datasets. Each dataset is formatted in a line and gives three positive integers, Y_i (< 1000), M_i (<= 10), and D_i (<= 20), that correspond to the year, month and day, respectively, of a person's birthdate in the king's calendar. These three numbers are separated by a space.\nTask Output: For the birthdate specified in each dataset, print in a line the number of days from the birthdate, inclusive, to the millennium day, exclusive. Output lines should not contain any character other than this number.\nTask Samples: input: 8\n1 1 1\n344 3 1\n696 5 1\n182 9 5\n998 8 7\n344 2 19\n696 4 19\n999 10 20\n output: 196470\n128976\n59710\n160715\n252\n128977\n59712\n1\n\n" }, { "title": "Recurring Decimals", "content": "A decimal representation of an integer can be transformed to another integer by rearranging the order of digits.\nLet us make a sequence using this fact.\n\nA non-negative integer a_0 and the number of digits L are given first.\nApplying the following rules, we obtain a_i+1 from a_i.\n Express the integer a_i in decimal notation with L digits. Leading zeros are added if necessary. For example, the decimal notation with six digits of the number 2012 is 002012.\n \n\n Rearranging the digits, find the largest possible integer and the smallest possible integer;\n In the example above, the largest possible integer is 221000 and the smallest is 000122 = 122.\n \n\n A new integer a_i+1 is obtained by subtracting the smallest possible integer from the largest.\n In the example above, we obtain 220878 subtracting 122 from 221000.\n \n\nWhen you repeat this calculation, you will get a sequence of integers \na_0 , \na_1 , \na_2 , . . . .\n\nFor example, starting with the integer 83268 and with the number of digits 6,\nyou will get the following sequence of integers\na_0 , \na_1 , \na_2 , . . . .\n\na_0 = 083268\na_1 = 886320 - 023688 = 862632\na_2 = 866322 - 223668 = 642654\na_3 = 665442 - 244566 = 420876\na_4 = 876420 - 024678 = 851742\na_5 = 875421 - 124578 = 750843\na_6 = 875430 - 034578 = 840852\na_7 = 885420 - 024588 = 860832\na_8 = 886320 - 023688 = 862632\n   …\n\nBecause the number of digits to express integers is fixed, \nyou will encounter occurrences of the same integer in the sequence\na_0 , \na_1 , \na_2 , . . .\neventually.\n\nTherefore you can always find a pair of i  and j  \nthat satisfies the condition a_i = a_j  \n(i  > j  ).\nIn the example above, the pair (i = 8, j = 1) satisfies the condition because a_8 = a_1 = 862632.\n\nWrite a program that,\ngiven an initial integer a_0 and a number of digits L,\nfinds the smallest i that satisfies the condition a_i = a_j   (i  > j  ).", "constraint": "", "input": "The input consists of multiple datasets.\nA dataset is a line containing two integers a_0  and L \nseparated by a space.\na_0  and L  \nrepresent the initial integer of the sequence and the number of digits, respectively,\nwhere \n1 <= L  <= 6\nand \n0 <= a_0  < 10^L .\n\nThe end of the input is indicated by a line containing two zeros;\nit is not a dataset.", "output": "For each dataset, \nfind the smallest number i  \nthat satisfies the condition\na_i = a_j   (i  > j  )\nand print a line containing three integers,\nj , \na_i   and\ni  - j.\nNumbers should be separated by a space.\nLeading zeros should be suppressed.\nOutput lines should not contain extra characters.\n\nYou can assume that the above i  is not\ngreater than 20.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2012 4\n83268 6\n1112 4\n0 1\n99 2\n0 0\n output: 3 6174 1\n1 862632 7\n5 6174 1\n0 0 1\n1 0 1"], "Pid": "p00761", "ProblemText": "Task Description: A decimal representation of an integer can be transformed to another integer by rearranging the order of digits.\nLet us make a sequence using this fact.\n\nA non-negative integer a_0 and the number of digits L are given first.\nApplying the following rules, we obtain a_i+1 from a_i.\n Express the integer a_i in decimal notation with L digits. Leading zeros are added if necessary. For example, the decimal notation with six digits of the number 2012 is 002012.\n \n\n Rearranging the digits, find the largest possible integer and the smallest possible integer;\n In the example above, the largest possible integer is 221000 and the smallest is 000122 = 122.\n \n\n A new integer a_i+1 is obtained by subtracting the smallest possible integer from the largest.\n In the example above, we obtain 220878 subtracting 122 from 221000.\n \n\nWhen you repeat this calculation, you will get a sequence of integers \na_0 , \na_1 , \na_2 , . . . .\n\nFor example, starting with the integer 83268 and with the number of digits 6,\nyou will get the following sequence of integers\na_0 , \na_1 , \na_2 , . . . .\n\na_0 = 083268\na_1 = 886320 - 023688 = 862632\na_2 = 866322 - 223668 = 642654\na_3 = 665442 - 244566 = 420876\na_4 = 876420 - 024678 = 851742\na_5 = 875421 - 124578 = 750843\na_6 = 875430 - 034578 = 840852\na_7 = 885420 - 024588 = 860832\na_8 = 886320 - 023688 = 862632\n   …\n\nBecause the number of digits to express integers is fixed, \nyou will encounter occurrences of the same integer in the sequence\na_0 , \na_1 , \na_2 , . . .\neventually.\n\nTherefore you can always find a pair of i  and j  \nthat satisfies the condition a_i = a_j  \n(i  > j  ).\nIn the example above, the pair (i = 8, j = 1) satisfies the condition because a_8 = a_1 = 862632.\n\nWrite a program that,\ngiven an initial integer a_0 and a number of digits L,\nfinds the smallest i that satisfies the condition a_i = a_j   (i  > j  ).\nTask Input: The input consists of multiple datasets.\nA dataset is a line containing two integers a_0  and L \nseparated by a space.\na_0  and L  \nrepresent the initial integer of the sequence and the number of digits, respectively,\nwhere \n1 <= L  <= 6\nand \n0 <= a_0  < 10^L .\n\nThe end of the input is indicated by a line containing two zeros;\nit is not a dataset.\nTask Output: For each dataset, \nfind the smallest number i  \nthat satisfies the condition\na_i = a_j   (i  > j  )\nand print a line containing three integers,\nj , \na_i   and\ni  - j.\nNumbers should be separated by a space.\nLeading zeros should be suppressed.\nOutput lines should not contain extra characters.\n\nYou can assume that the above i  is not\ngreater than 20.\nTask Samples: input: 2012 4\n83268 6\n1112 4\n0 1\n99 2\n0 0\n output: 3 6174 1\n1 862632 7\n5 6174 1\n0 0 1\n1 0 1\n\n" }, { "title": "Biased Dice", "content": "Professor Random, known for his research on randomized algorithms, is now conducting an experiment on biased dice. His experiment consists of dropping a number of dice onto a plane, one after another from a fixed position above the plane. The dice fall onto the plane or dice already there, without rotating, and may roll and fall according to their property. Then he observes and records the status of the stack formed on the plane, specifically, how many times each number appears on the faces visible from above. All the dice have the same size and their face numbering is identical, which we show in Figure C-1.\n\nFigure C-1: Numbering of a die\nThe dice have very special properties, as in the following.\n\n(1) Ordinary dice can roll in four directions, but the dice used in this experiment never roll in the directions of faces 1,2 and 3; they can only roll in the directions of faces 4,5 and 6. In the situation shown in Figure C-2, our die can only roll to one of two directions.\n\nFigure C-2: An ordinary die and a biased die\n(2) The die can only roll when it will fall down after rolling, as shown in Figure C-3. When multiple possibilities exist, the die rolls towards the face with the largest number among those directions it can roll to.\n\nFigure C-3: A die can roll only when it can fall\n(3) When a die rolls, it rolls exactly 90 degrees, and then falls straight down until its bottom face touches another die or the plane, as in the case [B] or [C] of Figure C-4.\n\n(4) After rolling and falling, the die repeatedly does so according to the rules (1) to (3) above.\n\nFigure C-4: Example stacking of biased dice\nFor example, when we drop four dice all in the same orientation, 6 at the top and 4 at the front, then a stack will be formed as shown in Figure C-4.\n\nFigure C-5: Example records\nAfter forming the stack, we count the numbers of faces with 1 through 6 visible from above and record them. For example, in the left case of Figure C-5, the record will be \"0 2 1 0 0 0\", and in the right case, \"0 1 1 0 0 1\".", "constraint": "", "input": "The input consists of several datasets each in the following format.\n\nn \nt_1  f_1\nt_2  f_2\n. . . \nt_n  f_n\n\nHere, n (1 <= n <= 100) is an integer and is the number of the dice to be dropped. t_i and f_i (1 <= t_i, f_i <= 6) are two integers separated by a space and represent the numbers on the top and the front faces of the i-th die, when it is released, respectively.\n\nThe end of the input is indicated by a line containing a single zero.", "output": "For each dataset, output six integers separated by a space. The integers represent the numbers of faces with 1 through 6 correspondingly, visible from above. There may not be any other characters in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n6 4\n6 4\n6 4\n6 4\n2\n5 3\n5 3\n8\n4 2\n4 2\n4 2\n4 2\n4 2\n4 2\n4 2\n4 2\n6\n4 6\n1 5\n2 3\n5 3\n2 4\n4 2\n0\n output: 0 1 1 0 0 1\n1 0 0 0 1 0\n1 2 2 1 0 0\n2 3 0 0 0 0"], "Pid": "p00762", "ProblemText": "Task Description: Professor Random, known for his research on randomized algorithms, is now conducting an experiment on biased dice. His experiment consists of dropping a number of dice onto a plane, one after another from a fixed position above the plane. The dice fall onto the plane or dice already there, without rotating, and may roll and fall according to their property. Then he observes and records the status of the stack formed on the plane, specifically, how many times each number appears on the faces visible from above. All the dice have the same size and their face numbering is identical, which we show in Figure C-1.\n\nFigure C-1: Numbering of a die\nThe dice have very special properties, as in the following.\n\n(1) Ordinary dice can roll in four directions, but the dice used in this experiment never roll in the directions of faces 1,2 and 3; they can only roll in the directions of faces 4,5 and 6. In the situation shown in Figure C-2, our die can only roll to one of two directions.\n\nFigure C-2: An ordinary die and a biased die\n(2) The die can only roll when it will fall down after rolling, as shown in Figure C-3. When multiple possibilities exist, the die rolls towards the face with the largest number among those directions it can roll to.\n\nFigure C-3: A die can roll only when it can fall\n(3) When a die rolls, it rolls exactly 90 degrees, and then falls straight down until its bottom face touches another die or the plane, as in the case [B] or [C] of Figure C-4.\n\n(4) After rolling and falling, the die repeatedly does so according to the rules (1) to (3) above.\n\nFigure C-4: Example stacking of biased dice\nFor example, when we drop four dice all in the same orientation, 6 at the top and 4 at the front, then a stack will be formed as shown in Figure C-4.\n\nFigure C-5: Example records\nAfter forming the stack, we count the numbers of faces with 1 through 6 visible from above and record them. For example, in the left case of Figure C-5, the record will be \"0 2 1 0 0 0\", and in the right case, \"0 1 1 0 0 1\".\nTask Input: The input consists of several datasets each in the following format.\n\nn \nt_1  f_1\nt_2  f_2\n. . . \nt_n  f_n\n\nHere, n (1 <= n <= 100) is an integer and is the number of the dice to be dropped. t_i and f_i (1 <= t_i, f_i <= 6) are two integers separated by a space and represent the numbers on the top and the front faces of the i-th die, when it is released, respectively.\n\nThe end of the input is indicated by a line containing a single zero.\nTask Output: For each dataset, output six integers separated by a space. The integers represent the numbers of faces with 1 through 6 correspondingly, visible from above. There may not be any other characters in the output.\nTask Samples: input: 4\n6 4\n6 4\n6 4\n6 4\n2\n5 3\n5 3\n8\n4 2\n4 2\n4 2\n4 2\n4 2\n4 2\n4 2\n4 2\n6\n4 6\n1 5\n2 3\n5 3\n2 4\n4 2\n0\n output: 0 1 1 0 0 1\n1 0 0 0 1 0\n1 2 2 1 0 0\n2 3 0 0 0 0\n\n" }, { "title": "Railway Connection", "content": "Tokyo has a very complex railway system.\nFor example, there exists a partial map of lines and stations\nas shown in Figure D-1.\n\nFigure D-1: A sample railway network\n\nSuppose you are going to station D from station A.\nObviously, the path with the shortest distance is A→B→D.\nHowever, the path with the shortest distance does not necessarily\nmean the minimum cost.\nAssume the lines A-B, B-C, and C-D are operated by one railway company,\nand the line B-D is operated by another company.\nIn this case, the path A→B→C→D may cost less than A→B→D.\nOne of the reasons is that the fare is not proportional to the distance.\nUsually, the longer the distance is, the fare per unit distance is lower.\nIf one uses lines of more than one railway company,\nthe fares charged by these companies are simply added together,\nand consequently the total cost may become higher although the distance is shorter\nthan the path using lines of only one company.\n\nIn this problem, a railway network including multiple railway companies is given.\nThe fare table (the rule to calculate the fare from the distance) of each company is also given.\nYour task is, given the starting point and the goal point, to write a program\nthat computes the path with the least total fare.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn m c s g\nx_1 y_1 d_1 c_1\n. . . \nx_m y_m d_m c_m\np_1 . . . p_c\nq_1,1 . . . q_1, p1-1\nr_1,1 . . . r_1, p1\n. . . \nq_c, 1 . . . q_c, pc-1\nr_c, 1 . . . r_c, pc\n\nEvery input item in a dataset is a non-negative integer.\nInput items in the same input line are separated by a space.\n\nThe first input line gives the size of the railway network and the intended trip.\nn is the number of stations (2 <= n <= 100).\nm is the number of lines connecting two stations (0 <= m <= 10000).\nc is the number of railway companies (1 <= c <= 20).\ns is the station index of the starting point (1 <= s <= n ).\ng is the station index of the goal point (1 <= g <= n, g ! = s ).\n\nThe following m input lines give the details of (railway) lines.\nThe i -th line connects two stations\nx_i and y_i \n(1 <= x_i <= n,\n1 <= y_i <= n,\nx_i ! = y_i ).\nEach line can be traveled in both directions.\nThere may be two or more lines connecting the same pair of stations.\nd_i is the distance of the i -th line (1 <= d_i <= 200).\nc_i is the company index of the railway company operating the line (1 <= c_i <= c ).\n\nThe fare table (the relation between the distance and the fare)\nof each railway company can be expressed as a line chart.\nFor the railway company j ,\nthe number of sections of the line chart is given by p_j \n(1 <= p_j <= 50).\nq_j, k (1 <= k <= p_j-1) gives\nthe distance separating two sections of the chart\n(1 <= q_j, k <= 10000).\nr_j, k (1 <= k <= p_j ) gives\nthe fare increment per unit distance for the corresponding section of the chart\n(1 <= r_j, k <= 100).\nMore precisely, with the fare for the distance z denoted by\nf_j (z ),\nthe fare for distance z satisfying\nq_j, k-1+1 <= z <= q_j, k \nis computed by the recurrence relation\nf_j (z) = f_j (z-1)+r_j, k.\nAssume that q_j, 0 and f_j (0) are zero,\nand q_j, pj is infinity.\n\nFor example, assume p_j = 3,\nq_j, 1 = 3,\nq_j, 2 = 6,\nr_j, 1 = 10,\nr_j, 2 = 5, and\nr_j, 3 = 3.\nThe fare table in this case is as follows.\n
\n distance 1 2 3 4 5 6 7 8 9 \n\n fare 10 20 30 35 40 45 48 51 54 \n\n \nq_j, k increase monotonically with respect to k .\nr_j, k decrease monotonically with respect to k .\n\nThe last dataset is followed by an input line containing five zeros\n(separated by a space).", "output": "For each dataset in the input, the total fare for the best route\n(the route with the minimum total fare)\nshould be output as a line.\nIf the goal cannot be reached from the start, output \"-1\".\nAn output line should not contain extra characters such as spaces.\n\nOnce a route from the start to the goal is determined,\nthe total fare of the route is computed as follows.\nIf two or more lines of the same railway company are used contiguously,\nthe total distance of these lines is used to compute the fare of this section.\nThe total fare of the route is the sum of fares of such \"sections consisting\nof contiguous lines of the same company\".\nEven if one uses two lines of the same company, if a line of another company\nis used between these two lines, the fares of sections including these two\nlines are computed independently.\nNo company offers transit discount.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 4 2 1 4\n1 2 2 1\n2 3 2 1\n3 4 5 1\n2 4 4 2\n3 1\n3 6\n10 5 3\n\n10\n2 0 1 1 2\n1\n\n1\n4 5 2 4 1\n4 3 10 1\n3 2 2 1\n3 2 1 2\n3 2 5 2\n2 1 10 1\n3 3\n20 30\n3 2 1\n5 10\n3 2 1\n5 5 2 1 5\n1 2 10 2\n1 3 20 2\n2 4 20 1\n3 4 10 1\n4 5 20 1\n2 2\n20\n4 1\n20\n3 1\n0 0 0 0 0\n output: 54\n-1\n63\n130"], "Pid": "p00763", "ProblemText": "Task Description: Tokyo has a very complex railway system.\nFor example, there exists a partial map of lines and stations\nas shown in Figure D-1.\n\nFigure D-1: A sample railway network\n\nSuppose you are going to station D from station A.\nObviously, the path with the shortest distance is A→B→D.\nHowever, the path with the shortest distance does not necessarily\nmean the minimum cost.\nAssume the lines A-B, B-C, and C-D are operated by one railway company,\nand the line B-D is operated by another company.\nIn this case, the path A→B→C→D may cost less than A→B→D.\nOne of the reasons is that the fare is not proportional to the distance.\nUsually, the longer the distance is, the fare per unit distance is lower.\nIf one uses lines of more than one railway company,\nthe fares charged by these companies are simply added together,\nand consequently the total cost may become higher although the distance is shorter\nthan the path using lines of only one company.\n\nIn this problem, a railway network including multiple railway companies is given.\nThe fare table (the rule to calculate the fare from the distance) of each company is also given.\nYour task is, given the starting point and the goal point, to write a program\nthat computes the path with the least total fare.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn m c s g\nx_1 y_1 d_1 c_1\n. . . \nx_m y_m d_m c_m\np_1 . . . p_c\nq_1,1 . . . q_1, p1-1\nr_1,1 . . . r_1, p1\n. . . \nq_c, 1 . . . q_c, pc-1\nr_c, 1 . . . r_c, pc\n\nEvery input item in a dataset is a non-negative integer.\nInput items in the same input line are separated by a space.\n\nThe first input line gives the size of the railway network and the intended trip.\nn is the number of stations (2 <= n <= 100).\nm is the number of lines connecting two stations (0 <= m <= 10000).\nc is the number of railway companies (1 <= c <= 20).\ns is the station index of the starting point (1 <= s <= n ).\ng is the station index of the goal point (1 <= g <= n, g ! = s ).\n\nThe following m input lines give the details of (railway) lines.\nThe i -th line connects two stations\nx_i and y_i \n(1 <= x_i <= n,\n1 <= y_i <= n,\nx_i ! = y_i ).\nEach line can be traveled in both directions.\nThere may be two or more lines connecting the same pair of stations.\nd_i is the distance of the i -th line (1 <= d_i <= 200).\nc_i is the company index of the railway company operating the line (1 <= c_i <= c ).\n\nThe fare table (the relation between the distance and the fare)\nof each railway company can be expressed as a line chart.\nFor the railway company j ,\nthe number of sections of the line chart is given by p_j \n(1 <= p_j <= 50).\nq_j, k (1 <= k <= p_j-1) gives\nthe distance separating two sections of the chart\n(1 <= q_j, k <= 10000).\nr_j, k (1 <= k <= p_j ) gives\nthe fare increment per unit distance for the corresponding section of the chart\n(1 <= r_j, k <= 100).\nMore precisely, with the fare for the distance z denoted by\nf_j (z ),\nthe fare for distance z satisfying\nq_j, k-1+1 <= z <= q_j, k \nis computed by the recurrence relation\nf_j (z) = f_j (z-1)+r_j, k.\nAssume that q_j, 0 and f_j (0) are zero,\nand q_j, pj is infinity.\n\nFor example, assume p_j = 3,\nq_j, 1 = 3,\nq_j, 2 = 6,\nr_j, 1 = 10,\nr_j, 2 = 5, and\nr_j, 3 = 3.\nThe fare table in this case is as follows.\n
\n distance 1 2 3 4 5 6 7 8 9 \n\n fare 10 20 30 35 40 45 48 51 54 \n\n \nq_j, k increase monotonically with respect to k .\nr_j, k decrease monotonically with respect to k .\n\nThe last dataset is followed by an input line containing five zeros\n(separated by a space).\nTask Output: For each dataset in the input, the total fare for the best route\n(the route with the minimum total fare)\nshould be output as a line.\nIf the goal cannot be reached from the start, output \"-1\".\nAn output line should not contain extra characters such as spaces.\n\nOnce a route from the start to the goal is determined,\nthe total fare of the route is computed as follows.\nIf two or more lines of the same railway company are used contiguously,\nthe total distance of these lines is used to compute the fare of this section.\nThe total fare of the route is the sum of fares of such \"sections consisting\nof contiguous lines of the same company\".\nEven if one uses two lines of the same company, if a line of another company\nis used between these two lines, the fares of sections including these two\nlines are computed independently.\nNo company offers transit discount.\nTask Samples: input: 4 4 2 1 4\n1 2 2 1\n2 3 2 1\n3 4 5 1\n2 4 4 2\n3 1\n3 6\n10 5 3\n\n10\n2 0 1 1 2\n1\n\n1\n4 5 2 4 1\n4 3 10 1\n3 2 2 1\n3 2 1 2\n3 2 5 2\n2 1 10 1\n3 3\n20 30\n3 2 1\n5 10\n3 2 1\n5 5 2 1 5\n1 2 10 2\n1 3 20 2\n2 4 20 1\n3 4 10 1\n4 5 20 1\n2 2\n20\n4 1\n20\n3 1\n0 0 0 0 0\n output: 54\n-1\n63\n130\n\n" }, { "title": "Chain-Confined Path", "content": "There is a chain consisting of multiple circles on a plane.\nThe first (last) circle of the chain only intersects with the next (previous) circle,\nand each intermediate circle intersects only with the two neighboring circles.\n\nYour task is to find the shortest path that satisfies the following conditions.\n\nThe path connects the centers of the first circle and the last circle.\n\nThe path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles.\nFigure E-1 shows an example of such a chain and the corresponding shortest path.\n\nFigure E-1: An example chain and the corresponding shortest path", "constraint": "", "input": "The input consists of multiple datasets.\nEach dataset represents the shape of a chain in the following format.\n\nn\nx_1 y_1 r_1 \nx_2 y_2 r_2 \n. . . \nx_n y_n r_n \n\nThe first line of a dataset contains an integer n (3 <= n <= 100) \nrepresenting the number of the circles.\nEach of the following n lines contains three integers separated by a single space.\n(x_i, y_i) \nand r_i represent \nthe center position and the radius of the i-th circle C_i.\nYou can assume that 0 <= x_i <= 1000, \n0 <= y_i <= 1000, and\n1 <= r_i <= 25.\n\nYou can assume that C_i and \nC_i+1 (1 <= i <= n-1) intersect at two separate points.\nWhen j >= i+2, C_i and C_j are apart and either of them does not contain the other.\nIn addition, you can assume that any circle does not contain the center of any other circle.\n\nThe end of the input is indicated by a line containing a zero. \n\nFigure E-1 corresponds to the first dataset of Sample Input below.\nFigure E-2 shows the shortest paths for the subsequent datasets of Sample Input. \nFigure E-2: Example chains and the corresponding shortest paths", "output": "For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle.\nThe value should not have an error greater than 0.001.\nNo extra characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10\n802 0 10\n814 0 4\n820 1 4\n826 1 4\n832 3 5\n838 5 5\n845 7 3\n849 10 3\n853 14 4\n857 18 3\n3\n0 0 5\n8 0 5\n8 8 5\n3\n0 0 5\n7 3 6\n16 0 5\n9\n0 3 5\n8 0 8\n19 2 8\n23 14 6\n23 21 6\n23 28 6\n19 40 8\n8 42 8\n0 39 5\n11\n0 0 5\n8 0 5\n18 8 10\n8 16 5\n0 16 5\n0 24 5\n3 32 5\n10 32 5\n17 28 8\n27 25 3\n30 18 5\n0\n output: 58.953437\n11.414214\n16.0\n61.874812\n63.195179"], "Pid": "p00764", "ProblemText": "Task Description: There is a chain consisting of multiple circles on a plane.\nThe first (last) circle of the chain only intersects with the next (previous) circle,\nand each intermediate circle intersects only with the two neighboring circles.\n\nYour task is to find the shortest path that satisfies the following conditions.\n\nThe path connects the centers of the first circle and the last circle.\n\nThe path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles.\nFigure E-1 shows an example of such a chain and the corresponding shortest path.\n\nFigure E-1: An example chain and the corresponding shortest path\nTask Input: The input consists of multiple datasets.\nEach dataset represents the shape of a chain in the following format.\n\nn\nx_1 y_1 r_1 \nx_2 y_2 r_2 \n. . . \nx_n y_n r_n \n\nThe first line of a dataset contains an integer n (3 <= n <= 100) \nrepresenting the number of the circles.\nEach of the following n lines contains three integers separated by a single space.\n(x_i, y_i) \nand r_i represent \nthe center position and the radius of the i-th circle C_i.\nYou can assume that 0 <= x_i <= 1000, \n0 <= y_i <= 1000, and\n1 <= r_i <= 25.\n\nYou can assume that C_i and \nC_i+1 (1 <= i <= n-1) intersect at two separate points.\nWhen j >= i+2, C_i and C_j are apart and either of them does not contain the other.\nIn addition, you can assume that any circle does not contain the center of any other circle.\n\nThe end of the input is indicated by a line containing a zero. \n\nFigure E-1 corresponds to the first dataset of Sample Input below.\nFigure E-2 shows the shortest paths for the subsequent datasets of Sample Input. \nFigure E-2: Example chains and the corresponding shortest paths\nTask Output: For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle.\nThe value should not have an error greater than 0.001.\nNo extra characters should appear in the output.\nTask Samples: input: 10\n802 0 10\n814 0 4\n820 1 4\n826 1 4\n832 3 5\n838 5 5\n845 7 3\n849 10 3\n853 14 4\n857 18 3\n3\n0 0 5\n8 0 5\n8 8 5\n3\n0 0 5\n7 3 6\n16 0 5\n9\n0 3 5\n8 0 8\n19 2 8\n23 14 6\n23 21 6\n23 28 6\n19 40 8\n8 42 8\n0 39 5\n11\n0 0 5\n8 0 5\n18 8 10\n8 16 5\n0 16 5\n0 24 5\n3 32 5\n10 32 5\n17 28 8\n27 25 3\n30 18 5\n0\n output: 58.953437\n11.414214\n16.0\n61.874812\n63.195179\n\n" }, { "title": "Generic Poker", "content": "You have a deck of N * M cards. Each card in the deck has a rank. The range of ranks is 1 through M, and the deck includes N cards of each rank.\n\nWe denote a card with rank m by m here.\n\nYou can draw a hand of L cards at random from the deck.\nIf the hand matches the given pattern,\nsome bonus will be rewarded.\nA pattern is described as follows.\n\nhand_pattern = card_pattern_1 ' ' card_pattern_2 ' ' . . . ' ' card_pattern_L\ncard_pattern = '*' | var_plus\nvar_plus = variable | var_plus '+'\nvariable = 'a' | 'b' | 'c'\n\n
\n
hand_pattern\n
\n\nA hand matches the hand_pattern if each card_pattern in the hand_pattern matches with a distinct card in the hand.\n\n
card_pattern\n
\n\nIf the card_pattern is an asterisk ('*'), it matches any card. \nCharacters 'a', 'b', and 'c' denote variables and all the occurrences of the same variable match cards of the same rank.\nA card_pattern with a variable followed by plus ('+')\ncharacters matches a card whose rank is the sum of the rank corresponding to the variable\nand the number of plus characters.\n\nYou can assume that, when a hand_pattern includes a card_pattern with\na variable followed by some number of plus characters, it also\nincludes card_patterns with that variable and all smaller numbers (including zero) of plus characters.\nFor example, if 'a+++' appears in a hand_pattern, card_patterns 'a',\n'a+', and 'a++' also appear in the hand_pattern.\n\n
\n\nThere is no restriction on which ranks different variables mean.\nFor example, 'a' and 'b' may or may not match cards of the same rank.\n\nWe show some example hand_patterns. The pattern\n\na * b a b \n\nmatches the hand:\n\n3 3 10 10 9\n\nwith 'a's and 'b's meaning 3 and 10 (or 10 and 3),\nrespectively. This pattern also matches the following hand.\n\n3 3 3 3 9\n\nIn this case, both 'a's and 'b's mean 3. The pattern\n\na a+ a++ a+++ a++++\n\nmatches the following hand.\n\n4 5 6 7 8\n\nIn this case, 'a' should mean 4. \n\nYour mission is to write a program that computes the probability that\na hand randomly drawn from the deck matches the given hand_pattern.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN M L\ncard_pattern_1 card_pattern_2 . . . card_pattern_L\n\nThe first line consists of three positive integers N, M, and L.\nN indicates the number of cards in each rank, M indicates the number of ranks, and L indicates the number of cards in a hand. N, M, and L are constrained as follows.\n\n1 <= N <= 7\n1 <= M <= 60\n1 <= L <= 7\nL <= N * M\n\nThe second line describes a hand_pattern.\n\nThe end of the input is indicated by a line containing three zeros \nseparated by a single space.", "output": "For each dataset, output a line containing a decimal fraction which means the probability of a hand matching the hand_pattern.\n\nThe output should not contain an error greater than 10^-8.\n\nNo other characters should be contained in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 1\na\n3 3 4\na+ * a *\n2 2 3\na a b\n2 2 3\n* * *\n2 2 3\n* b b\n2 2 2\na a\n2 3 3\na a+ a++\n2 6 6\na a+ a++ b b+ b++\n4 13 5\na a * * *\n4 13 5\na a b b *\n4 13 5\na a a * *\n4 13 5\na a+ a++ a+++ a++++\n4 13 5\n* * * * *\n4 13 5\na a a b b\n4 13 5\na a a a *\n7 60 7\na b a b c c *\n7 60 7\n* * * * * * *\n7 60 7\na a+ a++ a+++ a++++ a+++++ a++++++\n1 14 4\nb a+ a a\n0 0 0\n output: 1.0000000000\n0.8809523810\n1.0000000000\n1.0000000000\n1.0000000000\n0.3333333333\n0.4000000000\n0.1212121212\n0.4929171669\n0.0492196879\n0.0228091236\n0.0035460338\n1.0000000000\n0.0014405762\n0.0002400960\n0.0002967709\n1.0000000000\n0.0000001022\n0.0000000000"], "Pid": "p00765", "ProblemText": "Task Description: You have a deck of N * M cards. Each card in the deck has a rank. The range of ranks is 1 through M, and the deck includes N cards of each rank.\n\nWe denote a card with rank m by m here.\n\nYou can draw a hand of L cards at random from the deck.\nIf the hand matches the given pattern,\nsome bonus will be rewarded.\nA pattern is described as follows.\n\nhand_pattern = card_pattern_1 ' ' card_pattern_2 ' ' . . . ' ' card_pattern_L\ncard_pattern = '*' | var_plus\nvar_plus = variable | var_plus '+'\nvariable = 'a' | 'b' | 'c'\n\n
\n
hand_pattern\n
\n\nA hand matches the hand_pattern if each card_pattern in the hand_pattern matches with a distinct card in the hand.\n\n
card_pattern\n
\n\nIf the card_pattern is an asterisk ('*'), it matches any card. \nCharacters 'a', 'b', and 'c' denote variables and all the occurrences of the same variable match cards of the same rank.\nA card_pattern with a variable followed by plus ('+')\ncharacters matches a card whose rank is the sum of the rank corresponding to the variable\nand the number of plus characters.\n\nYou can assume that, when a hand_pattern includes a card_pattern with\na variable followed by some number of plus characters, it also\nincludes card_patterns with that variable and all smaller numbers (including zero) of plus characters.\nFor example, if 'a+++' appears in a hand_pattern, card_patterns 'a',\n'a+', and 'a++' also appear in the hand_pattern.\n\n
\n\nThere is no restriction on which ranks different variables mean.\nFor example, 'a' and 'b' may or may not match cards of the same rank.\n\nWe show some example hand_patterns. The pattern\n\na * b a b \n\nmatches the hand:\n\n3 3 10 10 9\n\nwith 'a's and 'b's meaning 3 and 10 (or 10 and 3),\nrespectively. This pattern also matches the following hand.\n\n3 3 3 3 9\n\nIn this case, both 'a's and 'b's mean 3. The pattern\n\na a+ a++ a+++ a++++\n\nmatches the following hand.\n\n4 5 6 7 8\n\nIn this case, 'a' should mean 4. \n\nYour mission is to write a program that computes the probability that\na hand randomly drawn from the deck matches the given hand_pattern.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN M L\ncard_pattern_1 card_pattern_2 . . . card_pattern_L\n\nThe first line consists of three positive integers N, M, and L.\nN indicates the number of cards in each rank, M indicates the number of ranks, and L indicates the number of cards in a hand. N, M, and L are constrained as follows.\n\n1 <= N <= 7\n1 <= M <= 60\n1 <= L <= 7\nL <= N * M\n\nThe second line describes a hand_pattern.\n\nThe end of the input is indicated by a line containing three zeros \nseparated by a single space.\nTask Output: For each dataset, output a line containing a decimal fraction which means the probability of a hand matching the hand_pattern.\n\nThe output should not contain an error greater than 10^-8.\n\nNo other characters should be contained in the output.\nTask Samples: input: 1 1 1\na\n3 3 4\na+ * a *\n2 2 3\na a b\n2 2 3\n* * *\n2 2 3\n* b b\n2 2 2\na a\n2 3 3\na a+ a++\n2 6 6\na a+ a++ b b+ b++\n4 13 5\na a * * *\n4 13 5\na a b b *\n4 13 5\na a a * *\n4 13 5\na a+ a++ a+++ a++++\n4 13 5\n* * * * *\n4 13 5\na a a b b\n4 13 5\na a a a *\n7 60 7\na b a b c c *\n7 60 7\n* * * * * * *\n7 60 7\na a+ a++ a+++ a++++ a+++++ a++++++\n1 14 4\nb a+ a a\n0 0 0\n output: 1.0000000000\n0.8809523810\n1.0000000000\n1.0000000000\n1.0000000000\n0.3333333333\n0.4000000000\n0.1212121212\n0.4929171669\n0.0492196879\n0.0228091236\n0.0035460338\n1.0000000000\n0.0014405762\n0.0002400960\n0.0002967709\n1.0000000000\n0.0000001022\n0.0000000000\n\n" }, { "title": "Patisserie ACM", "content": "Amber Claes Maes, a patissier, opened her own shop last month.\nShe decided to submit her work to the International Chocolate\nPatissier Competition to promote her shop, and she\nwas pursuing a recipe of sweet chocolate bars.\nAfter thousands of trials, she finally reached the recipe.\nHowever, the recipe required high skill levels to form chocolate to\nan orderly rectangular shape.\nSadly, she has just made another strange-shaped chocolate bar as shown in\nFigure G-1.\n\nFigure G-1: A strange-shaped chocolate bar\nEach chocolate bar consists of many small rectangular segments\nof chocolate. \nAdjacent segments are separated with a groove in\nbetween them for ease of snapping.\nShe planned to cut the strange-shaped chocolate bars into several\nrectangular pieces and sell them in her shop.\nShe wants to cut each chocolate bar as follows.\n\nThe bar must be cut along grooves.\n\nThe bar must be cut into rectangular pieces.\n\nThe bar must be cut into as few pieces as possible.\nFollowing the rules, Figure G-2 can be an instance of cutting of\nthe chocolate bar shown in Figure G-1. Figures G-3 and G-4\ndo not meet the rules; Figure G-3 has\na non-rectangular piece, and Figure G-4 has more pieces\nthan Figure G-2.\n\nFigure G-2: An instance of cutting that follows the rules\n\nFigure G-3: An instance of cutting that leaves a non-rectangular piece\n\nFigure G-4: An instance of cutting that yields more pieces than Figure G-2\nYour job is to write a program that computes the number of pieces\nof chocolate after cutting according to the rules.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by\na line containing two zeros separated by a space. Each dataset is\nformatted as follows.\n\nh w\nr_(1,1) . . . r_(1, w)\nr_(2,1) . . . r_(2, w)\n. . . \nr_(h, 1) . . . r_(h, w)\n\nThe integers h and w are the lengths of the two orthogonal\ndimensions of the chocolate, in number of segments.\nYou may assume that 2 <= h <= 100 and 2 <= w <= 100.\nEach of the following h\nlines consists of w characters, each is either a\n\" . \" or a \" # \". The character\nr_(i, j) represents whether \nthe chocolate segment exists at the position (i, j )\nas follows.\n\n\" . \": There is no chocolate.\n\n\" # \": There is a segment of chocolate.\nYou can assume that there is no dataset that represents\neither multiple disconnected bars as depicted in Figure G-5\nor a bar in a shape with hole(s) as depicted in Figure G-6\nand G-7. You can also assume that there is at least one \" # \"\ncharacter in each dataset.\n\nFigure G-5: Disconnected chocolate bars\n\nFigure G-6: A chocolate bar with a hole\n\nFigure G-7: Another instance of a chocolate bar with a hole", "output": "For each dataset, output a line containing the integer representing\nthe number of chocolate pieces obtained by cutting according to the rules.\nNo other characters are allowed in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 5\n###.#\n#####\n###..\n4 5\n.#.##\n.####\n####.\n##.#.\n8 8\n.#.#.#.#\n########\n.######.\n########\n.######.\n########\n.######.\n########\n8 8\n.#.#.#.#\n########\n.##.#.#.\n##....##\n.##.###.\n##...###\n.##.###.\n###.#.##\n4 4\n####\n####\n####\n####\n0 0\n output: 3\n5\n11\n19\n1"], "Pid": "p00766", "ProblemText": "Task Description: Amber Claes Maes, a patissier, opened her own shop last month.\nShe decided to submit her work to the International Chocolate\nPatissier Competition to promote her shop, and she\nwas pursuing a recipe of sweet chocolate bars.\nAfter thousands of trials, she finally reached the recipe.\nHowever, the recipe required high skill levels to form chocolate to\nan orderly rectangular shape.\nSadly, she has just made another strange-shaped chocolate bar as shown in\nFigure G-1.\n\nFigure G-1: A strange-shaped chocolate bar\nEach chocolate bar consists of many small rectangular segments\nof chocolate. \nAdjacent segments are separated with a groove in\nbetween them for ease of snapping.\nShe planned to cut the strange-shaped chocolate bars into several\nrectangular pieces and sell them in her shop.\nShe wants to cut each chocolate bar as follows.\n\nThe bar must be cut along grooves.\n\nThe bar must be cut into rectangular pieces.\n\nThe bar must be cut into as few pieces as possible.\nFollowing the rules, Figure G-2 can be an instance of cutting of\nthe chocolate bar shown in Figure G-1. Figures G-3 and G-4\ndo not meet the rules; Figure G-3 has\na non-rectangular piece, and Figure G-4 has more pieces\nthan Figure G-2.\n\nFigure G-2: An instance of cutting that follows the rules\n\nFigure G-3: An instance of cutting that leaves a non-rectangular piece\n\nFigure G-4: An instance of cutting that yields more pieces than Figure G-2\nYour job is to write a program that computes the number of pieces\nof chocolate after cutting according to the rules.\nTask Input: The input is a sequence of datasets. The end of the input is indicated by\na line containing two zeros separated by a space. Each dataset is\nformatted as follows.\n\nh w\nr_(1,1) . . . r_(1, w)\nr_(2,1) . . . r_(2, w)\n. . . \nr_(h, 1) . . . r_(h, w)\n\nThe integers h and w are the lengths of the two orthogonal\ndimensions of the chocolate, in number of segments.\nYou may assume that 2 <= h <= 100 and 2 <= w <= 100.\nEach of the following h\nlines consists of w characters, each is either a\n\" . \" or a \" # \". The character\nr_(i, j) represents whether \nthe chocolate segment exists at the position (i, j )\nas follows.\n\n\" . \": There is no chocolate.\n\n\" # \": There is a segment of chocolate.\nYou can assume that there is no dataset that represents\neither multiple disconnected bars as depicted in Figure G-5\nor a bar in a shape with hole(s) as depicted in Figure G-6\nand G-7. You can also assume that there is at least one \" # \"\ncharacter in each dataset.\n\nFigure G-5: Disconnected chocolate bars\n\nFigure G-6: A chocolate bar with a hole\n\nFigure G-7: Another instance of a chocolate bar with a hole\nTask Output: For each dataset, output a line containing the integer representing\nthe number of chocolate pieces obtained by cutting according to the rules.\nNo other characters are allowed in the output.\nTask Samples: input: 3 5\n###.#\n#####\n###..\n4 5\n.#.##\n.####\n####.\n##.#.\n8 8\n.#.#.#.#\n########\n.######.\n########\n.######.\n########\n.######.\n########\n8 8\n.#.#.#.#\n########\n.##.#.#.\n##....##\n.##.###.\n##...###\n.##.###.\n###.#.##\n4 4\n####\n####\n####\n####\n0 0\n output: 3\n5\n11\n19\n1\n\n" }, { "title": "Integral Rectangles", "content": "Let us consider rectangles whose height, h, and\nwidth, w, are both integers. We call such rectangles \nintegral rectangles. In this problem, we consider only wide\nintegral rectangles, i. e. , those with w > h.\n\nWe define the following ordering of wide integral rectangles. Given\ntwo wide integral rectangles,\nThe one shorter in its diagonal line is smaller, and\n\nIf the two have diagonal lines with the same length, the one shorter\n in its height is smaller.\n\nGiven a wide integral rectangle, find the smallest wide integral\nrectangle bigger than the given one.", "constraint": "", "input": "The entire input consists of multiple datasets. The number of\n datasets is no more than 100. Each dataset describes a wide integral\n rectangle by specifying its height and width, namely h\n and w, separated by a space in a line, as follows.\n\nh w\n\nFor each dataset, h and w (>h) are both\nintegers greater than 0 and no more than 100. \n\nThe end of the input is indicated by a line of two zeros separated by a space.", "output": "For each dataset, print in a line two numbers describing the\nheight and width, namely h and w (> h), of the\nsmallest wide integral rectangle bigger than the one described in the\ndataset. Put a space between the numbers. No other\ncharacters are allowed in the output.\n\nFor any wide integral rectangle given in the input, the width and\nheight of the smallest wide integral rectangle bigger than the given\none are both known to be not greater than 150. \n\nIn addition, although\nthe ordering of wide integral rectangles uses the comparison of\nlengths of diagonal lines, this comparison can be replaced with that\nof squares (self-products) of lengths of diagonal lines, which can\navoid unnecessary troubles possibly caused by the use of floating-point\nnumbers.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 2\n1 3\n2 3\n1 4\n2 4\n5 6\n1 8\n4 7\n98 100\n99 100\n0 0\n output: 1 3\n2 3\n1 4\n2 4\n3 4\n1 8\n4 7\n2 8\n3 140\n89 109"], "Pid": "p00767", "ProblemText": "Task Description: Let us consider rectangles whose height, h, and\nwidth, w, are both integers. We call such rectangles \nintegral rectangles. In this problem, we consider only wide\nintegral rectangles, i. e. , those with w > h.\n\nWe define the following ordering of wide integral rectangles. Given\ntwo wide integral rectangles,\nThe one shorter in its diagonal line is smaller, and\n\nIf the two have diagonal lines with the same length, the one shorter\n in its height is smaller.\n\nGiven a wide integral rectangle, find the smallest wide integral\nrectangle bigger than the given one.\nTask Input: The entire input consists of multiple datasets. The number of\n datasets is no more than 100. Each dataset describes a wide integral\n rectangle by specifying its height and width, namely h\n and w, separated by a space in a line, as follows.\n\nh w\n\nFor each dataset, h and w (>h) are both\nintegers greater than 0 and no more than 100. \n\nThe end of the input is indicated by a line of two zeros separated by a space.\nTask Output: For each dataset, print in a line two numbers describing the\nheight and width, namely h and w (> h), of the\nsmallest wide integral rectangle bigger than the one described in the\ndataset. Put a space between the numbers. No other\ncharacters are allowed in the output.\n\nFor any wide integral rectangle given in the input, the width and\nheight of the smallest wide integral rectangle bigger than the given\none are both known to be not greater than 150. \n\nIn addition, although\nthe ordering of wide integral rectangles uses the comparison of\nlengths of diagonal lines, this comparison can be replaced with that\nof squares (self-products) of lengths of diagonal lines, which can\navoid unnecessary troubles possibly caused by the use of floating-point\nnumbers.\nTask Samples: input: 1 2\n1 3\n2 3\n1 4\n2 4\n5 6\n1 8\n4 7\n98 100\n99 100\n0 0\n output: 1 3\n2 3\n1 4\n2 4\n3 4\n1 8\n4 7\n2 8\n3 140\n89 109\n\n" }, { "title": "ICPC Ranking", "content": "Your mission in this problem is to write a program\nwhich, given the submission log of an ICPC (International Collegiate Programming Contest),\ndetermines team rankings.\n\nThe log is a sequence of records of program submission\nin the order of submission.\nA record has four fields: elapsed time, team number,\nproblem number, and judgment.\nThe elapsed time is the time elapsed from the beginning of the contest\nto the submission.\nThe judgment field tells whether the submitted program was\ncorrect or incorrect, and when incorrect,\nwhat kind of an error was found.\n\nThe team ranking is determined according to the following rules.\nNote that the rule set shown here is one used in the real ICPC World Finals and Regionals,\nwith some detail rules omitted for simplification.\nTeams that solved more problems are ranked higher.\n\nAmong teams that solve the same number of problems, \nones with smaller total consumed time are ranked higher.\nIf two or more teams solved the same number of problems, and their\ntotal consumed times are the same, they are ranked the same.\n\nThe total consumed time is the sum of the consumed time for each problem solved.\nThe consumed time for a solved problem is the elapsed time \nof the accepted submission plus 20 penalty minutes for every previously rejected submission for that problem.\n\nIf a team did not solve a problem, the consumed time for the problem is zero, and thus even if there are several incorrect submissions, no penalty is given.\n\nYou can assume that a team never submits a program for a problem\nafter the correct submission for the same problem.", "constraint": "", "input": "The input is a sequence of datasets each in the following format.\nThe last dataset is followed by a line with four zeros.\n\nM T P R \nm_1 t_1 p_1 j_1 \nm_2 t_2 p_2 j_2 \n. . . . . \nm_R t_R p_R j_R \n\nThe first line of a dataset contains four integers\nM, T, P, and R.\nM is the duration of the contest.\nT is the number of teams.\nP is the number of problems.\nR is the number of submission records.\nThe relations \n120 <= M <= 300,\n1 <= T <= 50,\n1 <= P <= 10,\nand 0 <= R <= 2000\nhold for these values.\nEach team is assigned a team number between 1 and T, inclusive.\nEach problem is assigned a problem number between 1 and P, inclusive.\n\nEach of the following R lines contains a submission record\nwith four integers\nm_k, t_k,\np_k, and j_k\n(1 <= k <= R).\nm_k is the elapsed time.\nt_k is the team number.\np_k is the problem number.\nj_k is the judgment\n(0 means correct, and other values mean incorrect).\nThe relations\n0 <= m_k <= M-1,\n1 <= t_k <= T,\n1 <= p_k <= P,\nand 0 <= j_k <= 10\nhold for these values.\n\nThe elapsed time fields are rounded off to the nearest minute.\n\nSubmission records are given in the order of submission.\nTherefore, if i < j,\nthe i-th submission is done before the j-th submission\n(m_i <= m_j).\nIn some cases, you can determine the ranking of two teams\nwith a difference less than a minute, by using this fact.\nHowever, such a fact is never used in the team ranking.\nTeams are ranked only using time information in minutes.", "output": "For each dataset, your program should output team numbers (from 1 to T),\nhigher ranked teams first.\nThe separator between two team numbers should be a comma.\nWhen two teams are ranked the same, the separator between them\nshould be an equal sign.\nTeams ranked the same should be listed\nin decreasing order of their team numbers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 300 10 8 5\n50 5 2 1\n70 5 2 0\n75 1 1 0\n100 3 1 0\n150 3 2 0\n240 5 5 7\n50 1 1 0\n60 2 2 0\n70 2 3 0\n90 1 3 0\n120 3 5 0\n140 4 1 0\n150 2 4 1\n180 3 5 4\n15 2 2 1\n20 2 2 1\n25 2 2 0\n60 1 1 0\n120 5 5 4\n15 5 4 1\n20 5 4 0\n40 1 1 0\n40 2 2 0\n120 2 3 4\n30 1 1 0\n40 2 1 0\n50 2 2 0\n60 1 2 0\n120 3 3 2\n0 1 1 0\n1 2 2 0\n300 5 8 0\n0 0 0 0\n output: 3,1,5,10=9=8=7=6=4=2\n2,1,3,4,5\n1,2,3\n5=2=1,4=3\n2=1\n1,2,3\n5=4=3=2=1"], "Pid": "p00768", "ProblemText": "Task Description: Your mission in this problem is to write a program\nwhich, given the submission log of an ICPC (International Collegiate Programming Contest),\ndetermines team rankings.\n\nThe log is a sequence of records of program submission\nin the order of submission.\nA record has four fields: elapsed time, team number,\nproblem number, and judgment.\nThe elapsed time is the time elapsed from the beginning of the contest\nto the submission.\nThe judgment field tells whether the submitted program was\ncorrect or incorrect, and when incorrect,\nwhat kind of an error was found.\n\nThe team ranking is determined according to the following rules.\nNote that the rule set shown here is one used in the real ICPC World Finals and Regionals,\nwith some detail rules omitted for simplification.\nTeams that solved more problems are ranked higher.\n\nAmong teams that solve the same number of problems, \nones with smaller total consumed time are ranked higher.\nIf two or more teams solved the same number of problems, and their\ntotal consumed times are the same, they are ranked the same.\n\nThe total consumed time is the sum of the consumed time for each problem solved.\nThe consumed time for a solved problem is the elapsed time \nof the accepted submission plus 20 penalty minutes for every previously rejected submission for that problem.\n\nIf a team did not solve a problem, the consumed time for the problem is zero, and thus even if there are several incorrect submissions, no penalty is given.\n\nYou can assume that a team never submits a program for a problem\nafter the correct submission for the same problem.\nTask Input: The input is a sequence of datasets each in the following format.\nThe last dataset is followed by a line with four zeros.\n\nM T P R \nm_1 t_1 p_1 j_1 \nm_2 t_2 p_2 j_2 \n. . . . . \nm_R t_R p_R j_R \n\nThe first line of a dataset contains four integers\nM, T, P, and R.\nM is the duration of the contest.\nT is the number of teams.\nP is the number of problems.\nR is the number of submission records.\nThe relations \n120 <= M <= 300,\n1 <= T <= 50,\n1 <= P <= 10,\nand 0 <= R <= 2000\nhold for these values.\nEach team is assigned a team number between 1 and T, inclusive.\nEach problem is assigned a problem number between 1 and P, inclusive.\n\nEach of the following R lines contains a submission record\nwith four integers\nm_k, t_k,\np_k, and j_k\n(1 <= k <= R).\nm_k is the elapsed time.\nt_k is the team number.\np_k is the problem number.\nj_k is the judgment\n(0 means correct, and other values mean incorrect).\nThe relations\n0 <= m_k <= M-1,\n1 <= t_k <= T,\n1 <= p_k <= P,\nand 0 <= j_k <= 10\nhold for these values.\n\nThe elapsed time fields are rounded off to the nearest minute.\n\nSubmission records are given in the order of submission.\nTherefore, if i < j,\nthe i-th submission is done before the j-th submission\n(m_i <= m_j).\nIn some cases, you can determine the ranking of two teams\nwith a difference less than a minute, by using this fact.\nHowever, such a fact is never used in the team ranking.\nTeams are ranked only using time information in minutes.\nTask Output: For each dataset, your program should output team numbers (from 1 to T),\nhigher ranked teams first.\nThe separator between two team numbers should be a comma.\nWhen two teams are ranked the same, the separator between them\nshould be an equal sign.\nTeams ranked the same should be listed\nin decreasing order of their team numbers.\nTask Samples: input: 300 10 8 5\n50 5 2 1\n70 5 2 0\n75 1 1 0\n100 3 1 0\n150 3 2 0\n240 5 5 7\n50 1 1 0\n60 2 2 0\n70 2 3 0\n90 1 3 0\n120 3 5 0\n140 4 1 0\n150 2 4 1\n180 3 5 4\n15 2 2 1\n20 2 2 1\n25 2 2 0\n60 1 1 0\n120 5 5 4\n15 5 4 1\n20 5 4 0\n40 1 1 0\n40 2 2 0\n120 2 3 4\n30 1 1 0\n40 2 1 0\n50 2 2 0\n60 1 2 0\n120 3 3 2\n0 1 1 0\n1 2 2 0\n300 5 8 0\n0 0 0 0\n output: 3,1,5,10=9=8=7=6=4=2\n2,1,3,4,5\n1,2,3\n5=2=1,4=3\n2=1\n1,2,3\n5=4=3=2=1\n\n" }, { "title": "Hierarchical Democracy", "content": "The presidential election in Republic of Democratia is carried out through multiple stages as follows.\n\nThere are exactly two presidential candidates.\n\nAt the first stage, eligible voters go to the polls of his/her electoral district.\nThe winner of the district is the candidate who takes a majority of the votes.\nVoters cast their ballots only at this first stage.\n\nA district of the k-th stage (k > 1) consists of multiple districts of the (k - 1)-th stage. In contrast, a district of the (k - 1)-th stage is a sub-district of one and only one district of the k-th stage. The winner of a district of the k-th stage is the candidate who wins in a majority of its sub-districts of the (k - 1)-th stage.\n\nThe final stage has just one nation-wide district. The winner of the final stage is chosen as the president.\nYou can assume the following about the presidential election of this country.\n\nEvery eligible voter casts a vote.\n\nThe number of the eligible voters of each electoral district of the first stage is odd.\n\nThe number of the sub-districts of the (k - 1)-th stage that constitute a district of the k-th stage (k > 1) is also odd.\nThis means that each district of every stage has its winner (there is no tie). \n\nYour mission is to write a program that finds a way to win the presidential election with the minimum number of votes.\nSuppose, for instance, that the district of the final stage has three sub-districts of the first stage and that the numbers of the eligible voters of the sub-districts are 123,4567, and 89, respectively.\nThe minimum number of votes required to be the winner is 107, that is, 62 from the first district and 45 from the third.\nIn this case, even if the other candidate were given all the 4567 votes in the second district, s/he would inevitably be the loser. \nAlthough you might consider this election system unfair, you should accept it as a reality.", "constraint": "", "input": "The entire input looks like: \nthe number of datasets (=n) \n1st dataset \n2nd dataset \n… \nn-th dataset \n\nThe number of datasets, n, is no more than 100.\n\nThe number of the eligible voters of each district and the part-whole relations among districts are denoted as follows.\n\nAn electoral district of the first stage is denoted as [c], where c is the number of the eligible voters of the district.\n\nA district of the k-th stage (k > 1) is denoted as [d_1d_2…d_m], where d_1, d_2, …, d_m denote its sub-districts of the (k - 1)-th stage in this notation.\nFor instance, an electoral district of the first stage that has 123 eligible voters is denoted as [123].\nA district of the second stage consisting of three sub-districts of the first stage that have 123,4567, and 89 eligible voters, respectively, is denoted as [[123][4567][89]].\n\nEach dataset is a line that contains the character string denoting the district of the final stage in the aforementioned notation.\nYou can assume the following.\n\nThe character string in each dataset does not include any characters except digits ('0', '1', …, '9') and square brackets ('[', ']'), and its length is between 11 and 10000, inclusive.\n\nThe number of the eligible voters of each electoral district of the first stage is between 3 and 9999, inclusive.\nThe number of stages is a nation-wide constant.\nSo, for instance, [[[9][9][9]][9][9]] never appears in the input.\n[[[[9]]]] may not appear either since each district of the second or later stage must have multiple sub-districts of the previous stage.", "output": "For each dataset, print the minimum number of votes required to be the winner of the presidential election in a line.\nNo output line may include any characters except the digits with which the number is written.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n[[123][4567][89]]\n[[5][3][7][3][9]]\n[[[99][59][63][85][51]][[1539][7995][467]][[51][57][79][99][3][91][59]]]\n[[[37][95][31][77][15]][[43][5][5][5][85]][[71][3][51][89][29]][[57][95][5][69][31]][[99][59][65][73][31]]]\n[[[[9][7][3]][[3][5][7]][[7][9][5]]][[[9][9][3]][[5][9][9]][[7][7][3]]][[[5][9][7]][[3][9][3]][[9][5][5]]]]\n[[8231][3721][203][3271][8843]]\n output: 107\n7\n175\n95\n21\n3599"], "Pid": "p00769", "ProblemText": "Task Description: The presidential election in Republic of Democratia is carried out through multiple stages as follows.\n\nThere are exactly two presidential candidates.\n\nAt the first stage, eligible voters go to the polls of his/her electoral district.\nThe winner of the district is the candidate who takes a majority of the votes.\nVoters cast their ballots only at this first stage.\n\nA district of the k-th stage (k > 1) consists of multiple districts of the (k - 1)-th stage. In contrast, a district of the (k - 1)-th stage is a sub-district of one and only one district of the k-th stage. The winner of a district of the k-th stage is the candidate who wins in a majority of its sub-districts of the (k - 1)-th stage.\n\nThe final stage has just one nation-wide district. The winner of the final stage is chosen as the president.\nYou can assume the following about the presidential election of this country.\n\nEvery eligible voter casts a vote.\n\nThe number of the eligible voters of each electoral district of the first stage is odd.\n\nThe number of the sub-districts of the (k - 1)-th stage that constitute a district of the k-th stage (k > 1) is also odd.\nThis means that each district of every stage has its winner (there is no tie). \n\nYour mission is to write a program that finds a way to win the presidential election with the minimum number of votes.\nSuppose, for instance, that the district of the final stage has three sub-districts of the first stage and that the numbers of the eligible voters of the sub-districts are 123,4567, and 89, respectively.\nThe minimum number of votes required to be the winner is 107, that is, 62 from the first district and 45 from the third.\nIn this case, even if the other candidate were given all the 4567 votes in the second district, s/he would inevitably be the loser. \nAlthough you might consider this election system unfair, you should accept it as a reality.\nTask Input: The entire input looks like: \nthe number of datasets (=n) \n1st dataset \n2nd dataset \n… \nn-th dataset \n\nThe number of datasets, n, is no more than 100.\n\nThe number of the eligible voters of each district and the part-whole relations among districts are denoted as follows.\n\nAn electoral district of the first stage is denoted as [c], where c is the number of the eligible voters of the district.\n\nA district of the k-th stage (k > 1) is denoted as [d_1d_2…d_m], where d_1, d_2, …, d_m denote its sub-districts of the (k - 1)-th stage in this notation.\nFor instance, an electoral district of the first stage that has 123 eligible voters is denoted as [123].\nA district of the second stage consisting of three sub-districts of the first stage that have 123,4567, and 89 eligible voters, respectively, is denoted as [[123][4567][89]].\n\nEach dataset is a line that contains the character string denoting the district of the final stage in the aforementioned notation.\nYou can assume the following.\n\nThe character string in each dataset does not include any characters except digits ('0', '1', …, '9') and square brackets ('[', ']'), and its length is between 11 and 10000, inclusive.\n\nThe number of the eligible voters of each electoral district of the first stage is between 3 and 9999, inclusive.\nThe number of stages is a nation-wide constant.\nSo, for instance, [[[9][9][9]][9][9]] never appears in the input.\n[[[[9]]]] may not appear either since each district of the second or later stage must have multiple sub-districts of the previous stage.\nTask Output: For each dataset, print the minimum number of votes required to be the winner of the presidential election in a line.\nNo output line may include any characters except the digits with which the number is written.\nTask Samples: input: 6\n[[123][4567][89]]\n[[5][3][7][3][9]]\n[[[99][59][63][85][51]][[1539][7995][467]][[51][57][79][99][3][91][59]]]\n[[[37][95][31][77][15]][[43][5][5][5][85]][[71][3][51][89][29]][[57][95][5][69][31]][[99][59][65][73][31]]]\n[[[[9][7][3]][[3][5][7]][[7][9][5]]][[[9][9][3]][[5][9][9]][[7][7][3]]][[[5][9][7]][[3][9][3]][[9][5][5]]]]\n[[8231][3721][203][3271][8843]]\n output: 107\n7\n175\n95\n21\n3599\n\n" }, { "title": "Prime Caves", "content": "An international expedition discovered abandoned Buddhist cave temples\nin a giant cliff standing on the middle of a desert. There were many\nsmall caves dug into halfway down the vertical cliff, which were\naligned on square grids. The archaeologists in the expedition were\nexcited by Buddha's statues in those caves. More excitingly, there\nwere scrolls of Buddhism sutras (holy books) hidden in some of the caves. Those\nscrolls, which estimated to be written more than\nthousand years ago, were of immeasurable value.\n\nThe leader of the expedition wanted to collect as many scrolls as\npossible. However, it was not easy to get into the caves as they were\nlocated in the middle of the cliff. The only way to enter a cave was to\nhang you from a helicopter. Once entered and explored a cave, you can\nclimb down to one of the three caves under your cave; i. e. , either the\ncave directly below your cave, the caves one left or right to the cave\ndirectly below your cave. This can be repeated for as many times as\nyou want, and then you can descent down to the ground by using a long rope.\n\nSo you can explore several caves in one attempt. But which caves\nyou should visit? By examining the results of the preliminary\nattempts, a mathematician member of the expedition discovered\nthat (1) the caves can be numbered from the central one, spiraling\nout as shown in Figure D-1; and (2) only those caves with their cave\nnumbers being prime (let's call such caves prime caves),\nwhich are circled in the figure, store scrolls. From the next\nattempt, you would be able to maximize the number of prime caves to\nexplore.\nFigure D-1: Numbering of the caves and the prime caves\n\nWrite a program, given the total number of the caves and the cave visited first, that finds the descending route containing the maximum number of prime caves.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has an\n integer m (1 <= m <= 10^6) and an integer n (1 <= n\n <= m) in one line, separated by a space. m represents the total number of caves. n\n represents the cave number of the cave from which you will start your exploration. The last\n dataset is followed by a line with two zeros.", "output": "For each dataset, find the path that starts from the cave n and\ncontains the largest number of prime caves, and output the number of\nthe prime caves on the path and the last prime cave number on the\npath in one line, separated by a space. The cave n, explored first, is included\nin the caves on the path.\nIf there is more than one such path, output for the path\nin which the last of the prime caves explored has the largest number among such paths.\nWhen there is no such path that explores prime caves, output \"0\n0\" (without quotation marks).", "content_img": true, "lang": "en", "error": false, "samples": ["input: 49 22\n46 37\n42 23\n945 561\n1081 681\n1056 452\n1042 862\n973 677\n1000000 1000000\n0 0\n output: 0 0\n6 43\n1 23\n20 829\n18 947\n10 947\n13 947\n23 947\n534 993541"], "Pid": "p00770", "ProblemText": "Task Description: An international expedition discovered abandoned Buddhist cave temples\nin a giant cliff standing on the middle of a desert. There were many\nsmall caves dug into halfway down the vertical cliff, which were\naligned on square grids. The archaeologists in the expedition were\nexcited by Buddha's statues in those caves. More excitingly, there\nwere scrolls of Buddhism sutras (holy books) hidden in some of the caves. Those\nscrolls, which estimated to be written more than\nthousand years ago, were of immeasurable value.\n\nThe leader of the expedition wanted to collect as many scrolls as\npossible. However, it was not easy to get into the caves as they were\nlocated in the middle of the cliff. The only way to enter a cave was to\nhang you from a helicopter. Once entered and explored a cave, you can\nclimb down to one of the three caves under your cave; i. e. , either the\ncave directly below your cave, the caves one left or right to the cave\ndirectly below your cave. This can be repeated for as many times as\nyou want, and then you can descent down to the ground by using a long rope.\n\nSo you can explore several caves in one attempt. But which caves\nyou should visit? By examining the results of the preliminary\nattempts, a mathematician member of the expedition discovered\nthat (1) the caves can be numbered from the central one, spiraling\nout as shown in Figure D-1; and (2) only those caves with their cave\nnumbers being prime (let's call such caves prime caves),\nwhich are circled in the figure, store scrolls. From the next\nattempt, you would be able to maximize the number of prime caves to\nexplore.\nFigure D-1: Numbering of the caves and the prime caves\n\nWrite a program, given the total number of the caves and the cave visited first, that finds the descending route containing the maximum number of prime caves.\nTask Input: The input consists of multiple datasets. Each dataset has an\n integer m (1 <= m <= 10^6) and an integer n (1 <= n\n <= m) in one line, separated by a space. m represents the total number of caves. n\n represents the cave number of the cave from which you will start your exploration. The last\n dataset is followed by a line with two zeros.\nTask Output: For each dataset, find the path that starts from the cave n and\ncontains the largest number of prime caves, and output the number of\nthe prime caves on the path and the last prime cave number on the\npath in one line, separated by a space. The cave n, explored first, is included\nin the caves on the path.\nIf there is more than one such path, output for the path\nin which the last of the prime caves explored has the largest number among such paths.\nWhen there is no such path that explores prime caves, output \"0\n0\" (without quotation marks).\nTask Samples: input: 49 22\n46 37\n42 23\n945 561\n1081 681\n1056 452\n1042 862\n973 677\n1000000 1000000\n0 0\n output: 0 0\n6 43\n1 23\n20 829\n18 947\n10 947\n13 947\n23 947\n534 993541\n\n" }, { "title": "Anchored Balloon", "content": "A balloon placed on the ground is connected to one or more anchors on the ground with ropes.\nEach rope is long enough to connect the balloon and the anchor.\nNo two ropes cross each other.\nFigure E-1 shows such a situation.\n\nFigure E-1: A balloon and ropes on the ground\n\nNow the balloon takes off, and your task is to find how high \nthe balloon can go up with keeping the rope connections.\nThe positions of the anchors are fixed.\nThe lengths of the ropes and the positions of the anchors are given.\nYou may assume that these ropes have no weight and\nthus can be straightened up when pulled to\nwhichever directions.\nFigure E-2 shows the highest position of the balloon for\nthe situation shown in Figure E-1.\n\nFigure E-2: The highest position of the balloon", "constraint": "", "input": "The input consists of multiple datasets, each in the following format. \n\nn\nx_1 y_1 l_1 \n. . . \nx_n y_n l_n \n\nThe first line of a dataset contains an integer n (1 <= n <= 10) representing the number of the ropes.\nEach of the following n lines contains three integers, \nx_i, y_i, and l_i, separated by a single space. \nP_i = \n(x_i, y_i) represents\nthe position of the anchor connecting the i-th rope,\nand l_i represents the length of the rope.\nYou can assume that \n-100 <= x_i <= 100, \n-100 <= y_i <= 100, and\n1 <= l_i <= 300.\nThe balloon is initially placed at (0,0) on the ground.\nYou can ignore the size of the balloon and the anchors.\n\nYou can assume that P_i and P_j \nrepresent different positions if i ! = j.\nYou can also assume that the distance between\nP_i and (0,0) is less than or equal to \nl_i-1.\nThis means that the balloon can go up at least 1 unit high.\n\nFigures E-1 and E-2 correspond to the first dataset of Sample Input below. \n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, \noutput a single line containing the maximum height that the balloon can go up.\nThe error of the value should be no greater than 0.00001. \nNo extra characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n10 10 20\n10 -10 20\n-10 10 120\n1\n10 10 16\n2\n10 10 20\n10 -10 20\n2\n100 0 101\n-90 0 91\n2\n0 0 53\n30 40 102\n3\n10 10 20\n10 -10 20\n-10 -10 20\n3\n1 5 13\n5 -3 13\n-3 -3 13\n3\n98 97 168\n-82 -80 193\n-99 -96 211\n4\n90 -100 160\n-80 -80 150\n90 80 150\n80 80 245\n4\n85 -90 290\n-80 -80 220\n-85 90 145\n85 90 170\n5\n0 0 4\n3 0 5\n-3 0 5\n0 3 5\n0 -3 5\n10\n95 -93 260\n-86 96 211\n91 90 177\n-81 -80 124\n-91 91 144\n97 94 165\n-90 -86 194\n89 85 167\n-93 -80 222\n92 -84 218\n0\n output: 17.3205081\n16.0000000\n17.3205081\n13.8011200\n53.0000000\n14.1421356\n12.0000000\n128.3928757\n94.1879092\n131.1240816\n4.0000000\n72.2251798"], "Pid": "p00771", "ProblemText": "Task Description: A balloon placed on the ground is connected to one or more anchors on the ground with ropes.\nEach rope is long enough to connect the balloon and the anchor.\nNo two ropes cross each other.\nFigure E-1 shows such a situation.\n\nFigure E-1: A balloon and ropes on the ground\n\nNow the balloon takes off, and your task is to find how high \nthe balloon can go up with keeping the rope connections.\nThe positions of the anchors are fixed.\nThe lengths of the ropes and the positions of the anchors are given.\nYou may assume that these ropes have no weight and\nthus can be straightened up when pulled to\nwhichever directions.\nFigure E-2 shows the highest position of the balloon for\nthe situation shown in Figure E-1.\n\nFigure E-2: The highest position of the balloon\nTask Input: The input consists of multiple datasets, each in the following format. \n\nn\nx_1 y_1 l_1 \n. . . \nx_n y_n l_n \n\nThe first line of a dataset contains an integer n (1 <= n <= 10) representing the number of the ropes.\nEach of the following n lines contains three integers, \nx_i, y_i, and l_i, separated by a single space. \nP_i = \n(x_i, y_i) represents\nthe position of the anchor connecting the i-th rope,\nand l_i represents the length of the rope.\nYou can assume that \n-100 <= x_i <= 100, \n-100 <= y_i <= 100, and\n1 <= l_i <= 300.\nThe balloon is initially placed at (0,0) on the ground.\nYou can ignore the size of the balloon and the anchors.\n\nYou can assume that P_i and P_j \nrepresent different positions if i ! = j.\nYou can also assume that the distance between\nP_i and (0,0) is less than or equal to \nl_i-1.\nThis means that the balloon can go up at least 1 unit high.\n\nFigures E-1 and E-2 correspond to the first dataset of Sample Input below. \n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, \noutput a single line containing the maximum height that the balloon can go up.\nThe error of the value should be no greater than 0.00001. \nNo extra characters should appear in the output.\nTask Samples: input: 3\n10 10 20\n10 -10 20\n-10 10 120\n1\n10 10 16\n2\n10 10 20\n10 -10 20\n2\n100 0 101\n-90 0 91\n2\n0 0 53\n30 40 102\n3\n10 10 20\n10 -10 20\n-10 -10 20\n3\n1 5 13\n5 -3 13\n-3 -3 13\n3\n98 97 168\n-82 -80 193\n-99 -96 211\n4\n90 -100 160\n-80 -80 150\n90 80 150\n80 80 245\n4\n85 -90 290\n-80 -80 220\n-85 90 145\n85 90 170\n5\n0 0 4\n3 0 5\n-3 0 5\n0 3 5\n0 -3 5\n10\n95 -93 260\n-86 96 211\n91 90 177\n-81 -80 124\n-91 91 144\n97 94 165\n-90 -86 194\n89 85 167\n-93 -80 222\n92 -84 218\n0\n output: 17.3205081\n16.0000000\n17.3205081\n13.8011200\n53.0000000\n14.1421356\n12.0000000\n128.3928757\n94.1879092\n131.1240816\n4.0000000\n72.2251798\n\n" }, { "title": "Rotate and Rewrite", "content": "Two sequences of integers\nA: A_1 A_2 . . . A_n and\nB: B_1 B_2 . . . B_m and\na set of rewriting rules of the form\n\"x_1 x_2 . . . x_k → y\"\nare given.\nThe following transformations on each of the sequences are allowed\nan arbitrary number of times in an arbitrary order independently.\nRotate:\n Moving the first element of a sequence to the last.\n That is, transforming a sequence c_1 c_2 . . . c_p\n to c_2 . . . c_p c_1.\n\nRewrite:\n With a rewriting rule\n \"x_1 x_2 . . . x_k → y\",\n transforming a sequence\n c_1 c_2 . . . c_i x_1 x_2 . . . x_k d_1 d_2 . . . d_j\n to\nc_1 c_2 . . . c_i y d_1 d_2 . . . d_j.\n\t\nYour task is to determine whether it is possible to transform the two sequences A and B into the same sequence.\nIf possible, compute the length of the longest of the sequences after such a transformation.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following form. \nn m r \nA_1 A_2 . . . A_n\nB_1 B_2 . . . B_m\nR_1\n. . . \nR_r\n\nThe first line of a dataset consists of three positive integers n, m, and r, \nwhere \nn (n <= 25) is the length of the sequence A,\nm (m <= 25) is the length of the sequence B, and\nr (r <= 60) is the number of rewriting rules.\nThe second line contains n integers representing the n elements of A.\nThe third line contains m integers representing the m elements of B.\nEach of the last r lines describes a rewriting rule in the following form.\n\nk x_1 x_2 . . . x_k y\n\nThe first k is an integer (2 <= k <= 10), which is the length of the left-hand side of the rule.\nIt is followed by k integers x_1 x_2 . . . x_k,\nrepresenting the left-hand side of the rule.\nFinally comes an integer y, representing the right-hand side.\n\nAll of A_1, . . , A_n, B_1, . . . , B_m, x_1, . . . , x_k, and y\nare in the range between 1 and 30, inclusive.\nA line \"0 0 0\" denotes the end of the input.", "output": "For each dataset, if it is possible to transform A and B\nto the same sequence, print the length of the longest of\nthe sequences after such a transformation.\nPrint -1 if it is impossible.", "content_img": false, "lang": "ca", "error": false, "samples": ["input: 3 3 3\n1 2 3\n4 5 6\n2 1 2 5\n2 6 4 3\n2 5 3 1\n3 3 2\n1 1 1\n2 2 1\n2 1 1 2\n2 2 2 1\n7 1 2\n1 1 2 1 4 1 2\n4\n3 1 4 1 4\n3 2 4 2 4\n16 14 5\n2 1 2 2 1 3 2 1 3 2 2 1 1 3 1 2\n2 1 3 1 1 2 3 1 2 2 2 2 1 3\n2 3 1 3\n3 2 2 2 1\n3 2 2 1 2\n3 1 2 2 2\n4 2 1 2 2 2\n0 0 0\n output: 2\n-1\n1\n9"], "Pid": "p00772", "ProblemText": "Task Description: Two sequences of integers\nA: A_1 A_2 . . . A_n and\nB: B_1 B_2 . . . B_m and\na set of rewriting rules of the form\n\"x_1 x_2 . . . x_k → y\"\nare given.\nThe following transformations on each of the sequences are allowed\nan arbitrary number of times in an arbitrary order independently.\nRotate:\n Moving the first element of a sequence to the last.\n That is, transforming a sequence c_1 c_2 . . . c_p\n to c_2 . . . c_p c_1.\n\nRewrite:\n With a rewriting rule\n \"x_1 x_2 . . . x_k → y\",\n transforming a sequence\n c_1 c_2 . . . c_i x_1 x_2 . . . x_k d_1 d_2 . . . d_j\n to\nc_1 c_2 . . . c_i y d_1 d_2 . . . d_j.\n\t\nYour task is to determine whether it is possible to transform the two sequences A and B into the same sequence.\nIf possible, compute the length of the longest of the sequences after such a transformation.\nTask Input: The input consists of multiple datasets. Each dataset has the following form. \nn m r \nA_1 A_2 . . . A_n\nB_1 B_2 . . . B_m\nR_1\n. . . \nR_r\n\nThe first line of a dataset consists of three positive integers n, m, and r, \nwhere \nn (n <= 25) is the length of the sequence A,\nm (m <= 25) is the length of the sequence B, and\nr (r <= 60) is the number of rewriting rules.\nThe second line contains n integers representing the n elements of A.\nThe third line contains m integers representing the m elements of B.\nEach of the last r lines describes a rewriting rule in the following form.\n\nk x_1 x_2 . . . x_k y\n\nThe first k is an integer (2 <= k <= 10), which is the length of the left-hand side of the rule.\nIt is followed by k integers x_1 x_2 . . . x_k,\nrepresenting the left-hand side of the rule.\nFinally comes an integer y, representing the right-hand side.\n\nAll of A_1, . . , A_n, B_1, . . . , B_m, x_1, . . . , x_k, and y\nare in the range between 1 and 30, inclusive.\nA line \"0 0 0\" denotes the end of the input.\nTask Output: For each dataset, if it is possible to transform A and B\nto the same sequence, print the length of the longest of\nthe sequences after such a transformation.\nPrint -1 if it is impossible.\nTask Samples: input: 3 3 3\n1 2 3\n4 5 6\n2 1 2 5\n2 6 4 3\n2 5 3 1\n3 3 2\n1 1 1\n2 2 1\n2 1 1 2\n2 2 2 1\n7 1 2\n1 1 2 1 4 1 2\n4\n3 1 4 1 4\n3 2 4 2 4\n16 14 5\n2 1 2 2 1 3 2 1 3 2 2 1 1 3 1 2\n2 1 3 1 1 2 3 1 2 2 2 2 1 3\n2 3 1 3\n3 2 2 2 1\n3 2 2 1 2\n3 1 2 2 2\n4 2 1 2 2 2\n0 0 0\n output: 2\n-1\n1\n9\n\n" }, { "title": "Tax Rate Changed", "content": "VAT (value-added tax) is a tax imposed at a certain rate proportional to the sale price.\n \n Our store uses the following rules to calculate the after-tax prices.\n \n\n\tWhen the VAT rate is x%,\n\tfor an item with the before-tax price of p yen,\n\tits after-tax price of the item is p (100+x) / 100 yen, fractions rounded off.\n \n\tThe total after-tax price of multiple items paid at once is\n\tthe sum of after-tax prices of the items.\n \n The VAT rate is changed quite often.\n Our accountant has become aware that\n \"different pairs of items that had the same total after-tax price\n may have different total after-tax prices after VAT rate changes. \"\n For example, when the VAT rate rises from 5% to 8%,\n a pair of items that had the total after-tax prices of 105 yen before\n can now have after-tax prices either of 107,108, or 109 yen, as shown in the table below.\n \n
\n
Before-tax prices of two items After-tax price with 5% VAT After-tax price with 8% VAT \n\n 20,80 21 + 84 = 105 21 + 86 = 107 \n\n 2,99 2 + 103 = 105 2 + 106 = 108 \n\n 13,88 13 + 92 = 105 14 + 95 = 109 \n\n \n\n Our accountant is examining effects of VAT-rate changes on after-tax prices.\n You are asked to write a program that calculates the possible maximum\n total after-tax price of two items with the new VAT rate,\n knowing their total after-tax price before the VAT rate change.\n hints:\n In the following table,\n an instance of a before-tax price pair that has the maximum after-tax price after the VAT-rate change\n is given for each dataset of the sample input.\n \n
Dataset Before-tax prices After-tax price with y% VAT \n\n 5 8 105 13,88 14 + 95 = 109 \n\n 8 5 105 12,87 12 + 91 = 103 \n\n 1 2 24 1,23 1 + 23 = 24 \n\n 99 98 24 1,12 1 + 23 = 24 \n\n 12 13 26 1,23 1 + 25 = 26 \n\n 1 22 23 1,22 1 + 26 = 27 \n\n 1 13 201 1,199 1 +224 = 225 \n\n 13 16 112 25,75 29 + 87 = 116 \n\n 2 24 50 25,25 31 + 31 = 62 \n\n 1 82 61 11,50 20 + 91 = 111 \n\n 1 84 125 50,75 92 +138 = 230 \n\n 1 99 999 92,899 183+1789 =1972 \n\n 99 1 999 1,502 1 +507 = 508 \n\n 98 99 999 5,500 9 +995 =1004 \n\n 1 99 11 1,10 1 + 19 = 20 \n\n 99 1 12 1, 6 1 + 6 = 7", "constraint": "", "input": "The input consists of multiple datasets.\n Each dataset is in one line,\n which consists of three integers x, y, and s separated by a space.\n x is the VAT rate in percent before the VAT-rate change,\n y is the VAT rate in percent after the VAT-rate change,\n and s is the sum of after-tax prices of two items before the VAT-rate change.\n For these integers, 0 < x < 100,0 < y < 100,\n 10 < s < 1000, and x ! = y hold.\n For before-tax prices of items, all possibilities of 1 yen through s-1 yen should be considered.\n \n The end of the input is specified by three zeros separated by a space.", "output": "For each dataset,\n output in a line the possible maximum total after-tax price when the VAT rate is changed to y%.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 8 105\n8 5 105\n1 2 24\n99 98 24\n12 13 26\n1 22 23\n1 13 201\n13 16 112\n2 24 50\n1 82 61\n1 84 125\n1 99 999\n99 1 999\n98 99 999\n1 99 11\n99 1 12\n0 0 0\n output: 109\n103\n24\n24\n26\n27\n225\n116\n62\n111\n230\n1972\n508\n1004\n20\n7"], "Pid": "p00773", "ProblemText": "Task Description: VAT (value-added tax) is a tax imposed at a certain rate proportional to the sale price.\n \n Our store uses the following rules to calculate the after-tax prices.\n \n\n\tWhen the VAT rate is x%,\n\tfor an item with the before-tax price of p yen,\n\tits after-tax price of the item is p (100+x) / 100 yen, fractions rounded off.\n \n\tThe total after-tax price of multiple items paid at once is\n\tthe sum of after-tax prices of the items.\n \n The VAT rate is changed quite often.\n Our accountant has become aware that\n \"different pairs of items that had the same total after-tax price\n may have different total after-tax prices after VAT rate changes. \"\n For example, when the VAT rate rises from 5% to 8%,\n a pair of items that had the total after-tax prices of 105 yen before\n can now have after-tax prices either of 107,108, or 109 yen, as shown in the table below.\n \n\n
Before-tax prices of two items After-tax price with 5% VAT After-tax price with 8% VAT \n\n 20,80 21 + 84 = 105 21 + 86 = 107 \n\n 2,99 2 + 103 = 105 2 + 106 = 108 \n\n 13,88 13 + 92 = 105 14 + 95 = 109 \n\n \n\n Our accountant is examining effects of VAT-rate changes on after-tax prices.\n You are asked to write a program that calculates the possible maximum\n total after-tax price of two items with the new VAT rate,\n knowing their total after-tax price before the VAT rate change.\n hints:\n In the following table,\n an instance of a before-tax price pair that has the maximum after-tax price after the VAT-rate change\n is given for each dataset of the sample input.\n \n
Dataset Before-tax prices After-tax price with y% VAT \n\n 5 8 105 13,88 14 + 95 = 109 \n\n 8 5 105 12,87 12 + 91 = 103 \n\n 1 2 24 1,23 1 + 23 = 24 \n\n 99 98 24 1,12 1 + 23 = 24 \n\n 12 13 26 1,23 1 + 25 = 26 \n\n 1 22 23 1,22 1 + 26 = 27 \n\n 1 13 201 1,199 1 +224 = 225 \n\n 13 16 112 25,75 29 + 87 = 116 \n\n 2 24 50 25,25 31 + 31 = 62 \n\n 1 82 61 11,50 20 + 91 = 111 \n\n 1 84 125 50,75 92 +138 = 230 \n\n 1 99 999 92,899 183+1789 =1972 \n\n 99 1 999 1,502 1 +507 = 508 \n\n 98 99 999 5,500 9 +995 =1004 \n\n 1 99 11 1,10 1 + 19 = 20 \n\n 99 1 12 1, 6 1 + 6 = 7\nTask Input: The input consists of multiple datasets.\n Each dataset is in one line,\n which consists of three integers x, y, and s separated by a space.\n x is the VAT rate in percent before the VAT-rate change,\n y is the VAT rate in percent after the VAT-rate change,\n and s is the sum of after-tax prices of two items before the VAT-rate change.\n For these integers, 0 < x < 100,0 < y < 100,\n 10 < s < 1000, and x ! = y hold.\n For before-tax prices of items, all possibilities of 1 yen through s-1 yen should be considered.\n \n The end of the input is specified by three zeros separated by a space.\nTask Output: For each dataset,\n output in a line the possible maximum total after-tax price when the VAT rate is changed to y%.\nTask Samples: input: 5 8 105\n8 5 105\n1 2 24\n99 98 24\n12 13 26\n1 22 23\n1 13 201\n13 16 112\n2 24 50\n1 82 61\n1 84 125\n1 99 999\n99 1 999\n98 99 999\n1 99 11\n99 1 12\n0 0 0\n output: 109\n103\n24\n24\n26\n27\n225\n116\n62\n111\n230\n1972\n508\n1004\n20\n7\n\n" }, { "title": "Chain Disappearance Puzzle", "content": "We are playing a puzzle.\nAn upright board with H rows by 5 columns of cells, as shown in \nthe figure below, is used in this puzzle.\nA stone engraved with a digit, one of 1 through 9, is placed in each of \nthe cells.\nWhen three or more stones in horizontally adjacent cells are engraved \nwith the same digit, the stones will disappear.\nIf there are stones in the cells above the cell with a disappeared \nstone, the stones in the above cells will drop down, filling the \nvacancy.\n\nThe puzzle proceeds taking the following steps.\n\nWhen three or more stones in horizontally adjacent cells are \nengraved with the same digit, the stones will disappear. Disappearances \nof all such groups of stones take place simultaneously.\n\nWhen stones are in the cells above the emptied cells, these stones drop down so that the emptied cells are filled. \n\nAfter the completion of all stone drops, if one or more groups of \nstones satisfy the disappearance condition, repeat by returning to the \nstep 1.\nThe score of this puzzle is the sum of the digits on the disappeared stones.\n\nWrite a program that calculates the score of given configurations of stones.", "constraint": "", "input": "The input consists of multiple datasets.\nEach dataset is formed as follows.\n\nBoard height H\nStone placement of the row 1\nStone placement of the row 2\n. . . \nStone placement of the row H\n\nThe first line specifies the height ( H ) of the puzzle board (1 <= H <= 10).\nThe remaining H lines give placement of stones on each of the rows from top to bottom.\nThe placements are given by five digits (1 through 9), separated by a space.\nThese digits are engraved on the five stones in the corresponding row, in the same order.\n\nThe input ends with a line with a single zero.", "output": "For each dataset, output the score in a line.\nOutput lines may not include any characters except the digits expressing the scores.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n6 9 9 9 9\n5\n5 9 5 5 9\n5 5 6 9 9\n4 6 3 6 9\n3 3 2 9 9\n2 2 1 1 1\n10\n3 5 6 5 6\n2 2 2 8 3\n6 2 5 9 2\n7 7 7 6 1\n4 6 6 4 9\n8 9 1 1 8\n5 6 1 8 1\n6 8 2 1 2\n9 6 3 3 5\n5 3 8 8 8\n5\n1 2 3 4 5\n6 7 8 9 1\n2 3 4 5 6\n7 8 9 1 2\n3 4 5 6 7\n3\n2 2 8 7 4\n6 5 7 7 7\n8 8 9 9 9\n0\n output: 36\n38\n99\n0\n72"], "Pid": "p00774", "ProblemText": "Task Description: We are playing a puzzle.\nAn upright board with H rows by 5 columns of cells, as shown in \nthe figure below, is used in this puzzle.\nA stone engraved with a digit, one of 1 through 9, is placed in each of \nthe cells.\nWhen three or more stones in horizontally adjacent cells are engraved \nwith the same digit, the stones will disappear.\nIf there are stones in the cells above the cell with a disappeared \nstone, the stones in the above cells will drop down, filling the \nvacancy.\n\nThe puzzle proceeds taking the following steps.\n\nWhen three or more stones in horizontally adjacent cells are \nengraved with the same digit, the stones will disappear. Disappearances \nof all such groups of stones take place simultaneously.\n\nWhen stones are in the cells above the emptied cells, these stones drop down so that the emptied cells are filled. \n\nAfter the completion of all stone drops, if one or more groups of \nstones satisfy the disappearance condition, repeat by returning to the \nstep 1.\nThe score of this puzzle is the sum of the digits on the disappeared stones.\n\nWrite a program that calculates the score of given configurations of stones.\nTask Input: The input consists of multiple datasets.\nEach dataset is formed as follows.\n\nBoard height H\nStone placement of the row 1\nStone placement of the row 2\n. . . \nStone placement of the row H\n\nThe first line specifies the height ( H ) of the puzzle board (1 <= H <= 10).\nThe remaining H lines give placement of stones on each of the rows from top to bottom.\nThe placements are given by five digits (1 through 9), separated by a space.\nThese digits are engraved on the five stones in the corresponding row, in the same order.\n\nThe input ends with a line with a single zero.\nTask Output: For each dataset, output the score in a line.\nOutput lines may not include any characters except the digits expressing the scores.\nTask Samples: input: 1\n6 9 9 9 9\n5\n5 9 5 5 9\n5 5 6 9 9\n4 6 3 6 9\n3 3 2 9 9\n2 2 1 1 1\n10\n3 5 6 5 6\n2 2 2 8 3\n6 2 5 9 2\n7 7 7 6 1\n4 6 6 4 9\n8 9 1 1 8\n5 6 1 8 1\n6 8 2 1 2\n9 6 3 3 5\n5 3 8 8 8\n5\n1 2 3 4 5\n6 7 8 9 1\n2 3 4 5 6\n7 8 9 1 2\n3 4 5 6 7\n3\n2 2 8 7 4\n6 5 7 7 7\n8 8 9 9 9\n0\n output: 36\n38\n99\n0\n72\n\n" }, { "title": "Vampire", "content": "Mr. C is a vampire. If he is exposed to the sunlight directly, he turns \ninto ash.\nNevertheless, last night, he attended to the meeting of Immortal and \nCorpse Programmers\nCircle, and he has to go home in the near dawn.\nFortunately, there are many tall buildings around Mr. C's home, and \nwhile the sunlight is blocked by the buildings, he can move around \nsafely.\nThe top end of the sun has just reached the horizon now.\nIn how many seconds does Mr. C have to go into his safe coffin?\n\nTo simplify the problem, we represent the eastern dawn sky as a 2-dimensional\nx-y plane, where the x axis is horizontal and the y axis\nis vertical, and approximate building silhouettes by rectangles\nand the sun by a circle on this plane.\n\nThe x axis represents the horizon.\nWe denote the time by t, and the current time is t=0.\nThe radius of the sun is r and\nits center is at (0, -r) when the time t=0.\nThe sun moves on the x-y plane in a uniform linear motion at\na constant velocity of (0,1) per second.\n\nThe sunlight is blocked if and only if the entire region of the sun \n(including its edge) is included in the union of the silhouettes \n(including their edges) and the region below the horizon (y <= 0).\n\nWrite a program that computes the time of the last moment when the sunlight is blocked.\n\nThe following figure shows the layout of silhouettes and the position of the sun at\nthe last moment when the sunlight is blocked, that corresponds to the\nfirst dataset of Sample Input below. As this figure indicates, there are possibilities\nthat the last moment when the sunlight is blocked can be the time t=0.\n\nThe sunlight is blocked even when two silhouettes share parts of their edges.\n\nThe following figure shows the layout of silhouettes and the position of the sun at the\nlast moment when the sunlight is blocked, corresponding to the second\ndataset of Sample Input.\nIn this dataset the radius of the sun is 2 and there are two silhouettes:\nthe one with height 4 is in -2 <= x <= 0, and\nthe other with height 3 is in 0 <= x <= 2.", "constraint": "", "input": "The input consists of multiple datasets.\nThe first line of a dataset contains two\nintegers r and n separated by a space.\nr is the radius of the sun and n is the number of silhouettes\nof the buildings.\n(1 <= r <= 20,0 <= n <= 20)\n\nEach of following n lines contains three integers\nx_li, x_ri, h_i (1 <= i <= n) separated by a space.\n\nThese three integers represent a silhouette rectangle of a building.\nThe silhouette rectangle is parallel to the horizon, and its left and right edges\nare at x = x_li and x = x_ri, its top\nedge is at y = h_i, and its bottom edge is on\nthe horizon.\n(-20 <= x_li < x_ri <= 20,\n0 < h_i <= 20)\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\n\nNote that these silhouettes may overlap one another.", "output": "For each dataset, output a line containing the number indicating the time t of the last moment when the sunlight is blocked.\nThe value should not have an error greater than 0.001.\nNo extra characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 3\n-2 -1 3\n0 1 3\n2 3 3\n2 2\n-2 0 4\n0 2 3\n2 6\n-3 3 1\n-2 3 2\n-1 3 3\n0 3 4\n1 3 5\n2 3 6\n2 6\n-3 3 1\n-3 2 2\n-3 1 3\n-3 0 4\n-3 -1 5\n-3 -2 6\n0 0\n output: 0.0000\n3.0000\n2.2679\n2.2679"], "Pid": "p00775", "ProblemText": "Task Description: Mr. C is a vampire. If he is exposed to the sunlight directly, he turns \ninto ash.\nNevertheless, last night, he attended to the meeting of Immortal and \nCorpse Programmers\nCircle, and he has to go home in the near dawn.\nFortunately, there are many tall buildings around Mr. C's home, and \nwhile the sunlight is blocked by the buildings, he can move around \nsafely.\nThe top end of the sun has just reached the horizon now.\nIn how many seconds does Mr. C have to go into his safe coffin?\n\nTo simplify the problem, we represent the eastern dawn sky as a 2-dimensional\nx-y plane, where the x axis is horizontal and the y axis\nis vertical, and approximate building silhouettes by rectangles\nand the sun by a circle on this plane.\n\nThe x axis represents the horizon.\nWe denote the time by t, and the current time is t=0.\nThe radius of the sun is r and\nits center is at (0, -r) when the time t=0.\nThe sun moves on the x-y plane in a uniform linear motion at\na constant velocity of (0,1) per second.\n\nThe sunlight is blocked if and only if the entire region of the sun \n(including its edge) is included in the union of the silhouettes \n(including their edges) and the region below the horizon (y <= 0).\n\nWrite a program that computes the time of the last moment when the sunlight is blocked.\n\nThe following figure shows the layout of silhouettes and the position of the sun at\nthe last moment when the sunlight is blocked, that corresponds to the\nfirst dataset of Sample Input below. As this figure indicates, there are possibilities\nthat the last moment when the sunlight is blocked can be the time t=0.\n\nThe sunlight is blocked even when two silhouettes share parts of their edges.\n\nThe following figure shows the layout of silhouettes and the position of the sun at the\nlast moment when the sunlight is blocked, corresponding to the second\ndataset of Sample Input.\nIn this dataset the radius of the sun is 2 and there are two silhouettes:\nthe one with height 4 is in -2 <= x <= 0, and\nthe other with height 3 is in 0 <= x <= 2.\nTask Input: The input consists of multiple datasets.\nThe first line of a dataset contains two\nintegers r and n separated by a space.\nr is the radius of the sun and n is the number of silhouettes\nof the buildings.\n(1 <= r <= 20,0 <= n <= 20)\n\nEach of following n lines contains three integers\nx_li, x_ri, h_i (1 <= i <= n) separated by a space.\n\nThese three integers represent a silhouette rectangle of a building.\nThe silhouette rectangle is parallel to the horizon, and its left and right edges\nare at x = x_li and x = x_ri, its top\nedge is at y = h_i, and its bottom edge is on\nthe horizon.\n(-20 <= x_li < x_ri <= 20,\n0 < h_i <= 20)\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\n\nNote that these silhouettes may overlap one another.\nTask Output: For each dataset, output a line containing the number indicating the time t of the last moment when the sunlight is blocked.\nThe value should not have an error greater than 0.001.\nNo extra characters should appear in the output.\nTask Samples: input: 2 3\n-2 -1 3\n0 1 3\n2 3 3\n2 2\n-2 0 4\n0 2 3\n2 6\n-3 3 1\n-2 3 2\n-1 3 3\n0 3 4\n1 3 5\n2 3 6\n2 6\n-3 3 1\n-3 2 2\n-3 1 3\n-3 0 4\n-3 -1 5\n-3 -2 6\n0 0\n output: 0.0000\n3.0000\n2.2679\n2.2679\n\n" }, { "title": "Encryption System", "content": "A programmer developed a new encryption system.\nHowever, his system has an issue that\ntwo or more distinct strings are `encrypted' to the same string.\n\nWe have a string encrypted by his system. \nTo decode the original string, we want to enumerate all the candidates of the string before the encryption.\nYour mission is to write a program for this task.\n\nThe encryption is performed taking the following steps. Given a string that consists only of lowercase letters ('a' to 'z').\n\nChange the first 'b' to 'a'. If there is no 'b', do nothing.\n\nChange the first 'c' to 'b'. If there is no 'c', do nothing.\n\n. . .\n
  • Change the first 'z' to 'y'. If there is no 'z', do nothing.", "constraint": "", "input": "The input consists of at most 100 datasets.\nEach dataset is a line containing an encrypted string.\nThe encrypted string consists only of lowercase letters, and contains at least 1 and at most 20 characters.\n\nThe input ends with a line with a single '#' symbol.", "output": "For each dataset,\nthe number of candidates n of the string before encryption should be printed in a line first,\nfollowed by lines each containing a candidate of the string before encryption.\nIf n does not exceed 10, print all candidates in dictionary order;\notherwise, print the first five and the last five candidates in dictionary order.\n\nHere, dictionary order is recursively defined as follows.\nThe empty string comes the first in dictionary order.\nFor two nonempty strings x = x_1 . . . x_k and y = y_1 . . . y_l, \nthe string x precedes the string y in dictionary order if \n\nx_1 precedes y_1 in alphabetical order ('a' to 'z'), or\n\nx_1 and y_1 are the same character and x_2 . . . x_k precedes y_2 . . . y_l in dictionary order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: enw\nabc\nabcdefghijklmnopqrst\nz\n#\n output: 1\nfox\n5\nacc\nacd\nbbd\nbcc\nbcd\n17711\nacceeggiikkmmooqqssu\nacceeggiikkmmooqqstt\nacceeggiikkmmooqqstu\nacceeggiikkmmooqrrtt\nacceeggiikkmmooqrrtu\nbcdefghijklmnopqrrtt\nbcdefghijklmnopqrrtu\nbcdefghijklmnopqrssu\nbcdefghijklmnopqrstt\nbcdefghijklmnopqrstu\n0"], "Pid": "p00776", "ProblemText": "Task Description: A programmer developed a new encryption system.\nHowever, his system has an issue that\ntwo or more distinct strings are `encrypted' to the same string.\n\nWe have a string encrypted by his system. \nTo decode the original string, we want to enumerate all the candidates of the string before the encryption.\nYour mission is to write a program for this task.\n\nThe encryption is performed taking the following steps. Given a string that consists only of lowercase letters ('a' to 'z').\n\nChange the first 'b' to 'a'. If there is no 'b', do nothing.\n\nChange the first 'c' to 'b'. If there is no 'c', do nothing.\n\n. . .\n
  • Change the first 'z' to 'y'. If there is no 'z', do nothing.\nTask Input: The input consists of at most 100 datasets.\nEach dataset is a line containing an encrypted string.\nThe encrypted string consists only of lowercase letters, and contains at least 1 and at most 20 characters.\n\nThe input ends with a line with a single '#' symbol.\nTask Output: For each dataset,\nthe number of candidates n of the string before encryption should be printed in a line first,\nfollowed by lines each containing a candidate of the string before encryption.\nIf n does not exceed 10, print all candidates in dictionary order;\notherwise, print the first five and the last five candidates in dictionary order.\n\nHere, dictionary order is recursively defined as follows.\nThe empty string comes the first in dictionary order.\nFor two nonempty strings x = x_1 . . . x_k and y = y_1 . . . y_l, \nthe string x precedes the string y in dictionary order if \n\nx_1 precedes y_1 in alphabetical order ('a' to 'z'), or\n\nx_1 and y_1 are the same character and x_2 . . . x_k precedes y_2 . . . y_l in dictionary order.\nTask Samples: input: enw\nabc\nabcdefghijklmnopqrst\nz\n#\n output: 1\nfox\n5\nacc\nacd\nbbd\nbcc\nbcd\n17711\nacceeggiikkmmooqqssu\nacceeggiikkmmooqqstt\nacceeggiikkmmooqqstu\nacceeggiikkmmooqrrtt\nacceeggiikkmmooqrrtu\nbcdefghijklmnopqrrtt\nbcdefghijklmnopqrrtu\nbcdefghijklmnopqrssu\nbcdefghijklmnopqrstt\nbcdefghijklmnopqrstu\n0\n\n" }, { "title": "Bridge Removal", "content": "ICPC islands once had been a popular tourist destination.\nFor nature preservation, however, the government decided to prohibit entrance to the islands,\nand to remove all the man-made structures there.\nThe hardest part of the project is to remove all the bridges connecting the islands.\n\nThere are n islands and n-1 bridges.\nThe bridges are built so that all the islands are reachable from all the other islands by\ncrossing one or more bridges.\nThe bridge removal team can choose any island as the starting point, and can repeat either of the\nfollowing steps.\n\nMove to another island by crossing a bridge that is connected to the current island.\n\nRemove one bridge that is connected to the current island, and stay at the same island after the removal.\nOf course, a bridge, once removed, cannot be crossed in either direction.\nCrossing or removing a bridge both takes time proportional to the length of the bridge.\nYour task is to compute the shortest time necessary for removing all the bridges.\nNote that the island where the team starts can differ from where the team finishes the work.", "constraint": "", "input": "The input consists of at most 100 datasets.\nEach dataset is formatted as follows.\n\nn\np_2 p_3 . . . p_n \nd_2 d_3 . . . d_n\n\nThe first integer n (3 <= n <= 800) is the number of the islands.\nThe islands are numbered from 1 to n.\nThe second line contains n-1 island numbers p_i\n(1 <= p_i < i), and tells that for each i\nfrom 2 to n the island i and the island p_i are connected by a bridge.\nThe third line contains n-1 integers d_i (1 <= d_i <= 100,000)\neach denoting the length of the corresponding bridge.\nThat is, the length of the bridge connecting the island i and p_i\nis d_i. It takes d_i units of time to cross the bridge, and\nalso the same units of time to remove it.\n\nNote that, with this input format, it is assured that all the islands are reachable each other by\ncrossing one or more bridges.\n\nThe input ends with a line with a single zero.", "output": "For each dataset, print the minimum time units required to remove all the bridges in a single line.\nEach line should not have any character other than this number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 3\n10 20 30\n10\n1 2 2 1 5 5 1 8 8\n10 1 1 20 1 1 30 1 1\n3\n1 1\n1 1\n0\n output: 80\n136\n2"], "Pid": "p00777", "ProblemText": "Task Description: ICPC islands once had been a popular tourist destination.\nFor nature preservation, however, the government decided to prohibit entrance to the islands,\nand to remove all the man-made structures there.\nThe hardest part of the project is to remove all the bridges connecting the islands.\n\nThere are n islands and n-1 bridges.\nThe bridges are built so that all the islands are reachable from all the other islands by\ncrossing one or more bridges.\nThe bridge removal team can choose any island as the starting point, and can repeat either of the\nfollowing steps.\n\nMove to another island by crossing a bridge that is connected to the current island.\n\nRemove one bridge that is connected to the current island, and stay at the same island after the removal.\nOf course, a bridge, once removed, cannot be crossed in either direction.\nCrossing or removing a bridge both takes time proportional to the length of the bridge.\nYour task is to compute the shortest time necessary for removing all the bridges.\nNote that the island where the team starts can differ from where the team finishes the work.\nTask Input: The input consists of at most 100 datasets.\nEach dataset is formatted as follows.\n\nn\np_2 p_3 . . . p_n \nd_2 d_3 . . . d_n\n\nThe first integer n (3 <= n <= 800) is the number of the islands.\nThe islands are numbered from 1 to n.\nThe second line contains n-1 island numbers p_i\n(1 <= p_i < i), and tells that for each i\nfrom 2 to n the island i and the island p_i are connected by a bridge.\nThe third line contains n-1 integers d_i (1 <= d_i <= 100,000)\neach denoting the length of the corresponding bridge.\nThat is, the length of the bridge connecting the island i and p_i\nis d_i. It takes d_i units of time to cross the bridge, and\nalso the same units of time to remove it.\n\nNote that, with this input format, it is assured that all the islands are reachable each other by\ncrossing one or more bridges.\n\nThe input ends with a line with a single zero.\nTask Output: For each dataset, print the minimum time units required to remove all the bridges in a single line.\nEach line should not have any character other than this number.\nTask Samples: input: 4\n1 2 3\n10 20 30\n10\n1 2 2 1 5 5 1 8 8\n10 1 1 20 1 1 30 1 1\n3\n1 1\n1 1\n0\n output: 80\n136\n2\n\n" }, { "title": "A Die Maker", "content": "The work of die makers starts early in the morning.\n\nYou are a die maker.\nYou receive orders from customers, and make various kinds of dice every day.\nToday, you received an order of a cubic die with six numbers\nt_1, t_2, . . . , t_6 on whichever faces.\n\nFor making the ordered die, you use a tool of flat-board shape.\nYou initially have a die with a zero on each face.\nIf you rotate the die by 90 degrees on the tool towards one of northward, southward, eastward, and southward,\nthe number on the face that newly touches the tool is increased by one.\nBy rotating the die towards appropriate directions repeatedly,\nyou may obtain the ordered die.\n\nThe final numbers on the faces of the die\nis determined by the sequence of directions towards which you rotate the die.\nWe call the string that represents the sequence of directions an operation sequence. \nFormally, we define operation sequences as follows.\nAn operation sequence consists of n characters, where n is the number of rotations made.\nIf you rotate the die eastward in the i-th rotation,\nthe i-th character of the operation sequence is E.\nSimilarly, if you rotate it westward, it is W,\nif southward, it is S, otherwise,\nif northward, it is N.\nFor example, the operation sequence NWS represents\nthe sequence of three rotations, northward first, westward next,\nand finally southward.\n\nGiven six integers of the customer's order,\ncompute an operation sequence that makes a die to order.\nIf there are two or more possibilities, you should compute the earliest operation sequence in dictionary order.", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of datasets does not exceed 40.\nEach dataset has the following form.\n\nt_1 t_2 t_3 t_4 t_5 t_6\np q\n\nt_1, t_2, . . . , t_6 are integers that represent the order from the customer.\nFurther, p and q are positive integers that specify the output range of the operation sequence (see the details below).\n\nEach dataset satisfies\n0 <= t_1 <= t_2 <= . . . <= t_6 <= 5,000\nand\n1 <= p <= q <= t_1+t_2+. . . +t_6.\nA line containing six zeros denotes the end of the input.", "output": "For each dataset,\nprint the subsequence,\nfrom the p-th position to the q-th position, inclusively,\nof the operation sequence that is the earliest in dictionary order.\nIf it is impossible to make the ordered die, print impossible.\n\nHere, dictionary order is recursively defined as follows.\nThe empty string comes the first in dictionary order.\nFor two nonempty strings x = x_1 . . . x_k and y = y_1 . . . y_l, the string x precedes the string y in dictionary order if\n\n x_1 precedes y_1 in alphabetical order ('A' to 'Z'), or \n\n x_1 and y_1 are the same character and x_2 . . . x_k precedes y_2 . . . y_l in dictionary order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 1 1 1 1\n1 6\n1 1 1 1 1 1\n4 5\n0 0 0 0 0 2\n1 2\n0 0 2 2 2 4\n5 9\n1 2 3 4 5 6\n15 16\n0 1 2 3 5 9\n13 16\n2 13 22 27 31 91\n100 170\n0 0 0 0 0 0\n output: EEENEE\nNE\nimpossible\nNSSNW\nEN\nEWNS\nSNSNSNSNSNSNSNSNSNSNSNSSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNWEWE"], "Pid": "p00778", "ProblemText": "Task Description: The work of die makers starts early in the morning.\n\nYou are a die maker.\nYou receive orders from customers, and make various kinds of dice every day.\nToday, you received an order of a cubic die with six numbers\nt_1, t_2, . . . , t_6 on whichever faces.\n\nFor making the ordered die, you use a tool of flat-board shape.\nYou initially have a die with a zero on each face.\nIf you rotate the die by 90 degrees on the tool towards one of northward, southward, eastward, and southward,\nthe number on the face that newly touches the tool is increased by one.\nBy rotating the die towards appropriate directions repeatedly,\nyou may obtain the ordered die.\n\nThe final numbers on the faces of the die\nis determined by the sequence of directions towards which you rotate the die.\nWe call the string that represents the sequence of directions an operation sequence. \nFormally, we define operation sequences as follows.\nAn operation sequence consists of n characters, where n is the number of rotations made.\nIf you rotate the die eastward in the i-th rotation,\nthe i-th character of the operation sequence is E.\nSimilarly, if you rotate it westward, it is W,\nif southward, it is S, otherwise,\nif northward, it is N.\nFor example, the operation sequence NWS represents\nthe sequence of three rotations, northward first, westward next,\nand finally southward.\n\nGiven six integers of the customer's order,\ncompute an operation sequence that makes a die to order.\nIf there are two or more possibilities, you should compute the earliest operation sequence in dictionary order.\nTask Input: The input consists of multiple datasets.\nThe number of datasets does not exceed 40.\nEach dataset has the following form.\n\nt_1 t_2 t_3 t_4 t_5 t_6\np q\n\nt_1, t_2, . . . , t_6 are integers that represent the order from the customer.\nFurther, p and q are positive integers that specify the output range of the operation sequence (see the details below).\n\nEach dataset satisfies\n0 <= t_1 <= t_2 <= . . . <= t_6 <= 5,000\nand\n1 <= p <= q <= t_1+t_2+. . . +t_6.\nA line containing six zeros denotes the end of the input.\nTask Output: For each dataset,\nprint the subsequence,\nfrom the p-th position to the q-th position, inclusively,\nof the operation sequence that is the earliest in dictionary order.\nIf it is impossible to make the ordered die, print impossible.\n\nHere, dictionary order is recursively defined as follows.\nThe empty string comes the first in dictionary order.\nFor two nonempty strings x = x_1 . . . x_k and y = y_1 . . . y_l, the string x precedes the string y in dictionary order if\n\n x_1 precedes y_1 in alphabetical order ('A' to 'Z'), or \n\n x_1 and y_1 are the same character and x_2 . . . x_k precedes y_2 . . . y_l in dictionary order.\nTask Samples: input: 1 1 1 1 1 1\n1 6\n1 1 1 1 1 1\n4 5\n0 0 0 0 0 2\n1 2\n0 0 2 2 2 4\n5 9\n1 2 3 4 5 6\n15 16\n0 1 2 3 5 9\n13 16\n2 13 22 27 31 91\n100 170\n0 0 0 0 0 0\n output: EEENEE\nNE\nimpossible\nNSSNW\nEN\nEWNS\nSNSNSNSNSNSNSNSNSNSNSNSSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNWEWE\n\n" }, { "title": "Don't Cross the Circles!", "content": "There are one or more circles on a plane.\nAny two circles have different center positions and/or different radiuses.\nA circle may intersect with another circle,\nbut no three or more circles have areas nor points shared by all of them.\nA circle may completely contain another circle or two circles may intersect at two separate points,\nbut you can assume that the circumferences of two circles never\ntouch at a single point.\n\nYour task is to judge\nwhether there exists a path that connects the given two points, P and Q,\nwithout crossing the circumferences of the circles.\nYou are given one or more point pairs for each layout of circles.\n\nIn the case of Figure G-1,\nwe can connect P and Q_1 without crossing the circumferences of the circles, but we cannot connect P with Q_2, Q_3, or Q_4 without crossing the circumferences of the circles.\nFigure G-1: Sample layout of circles and points", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn m\nCx_1 Cy_1 r_1 \n. . . \nCx_n Cy_n r_n \nPx_1 Py_1 Qx_1 Qy_1 \n. . . \nPx_m Py_m Qx_m Qy_m \n\nThe first line of a dataset contains two integers n and m\nseparated by a space.\nn represents the number of circles, and\nyou can assume 1 <= n <= 100.\nm represents the number of point pairs, and\nyou can assume 1 <= m <= 10.\nEach of the following n lines contains three integers separated by a single space.\n(Cx_i, Cy_i) and r_i represent the center position and the radius of the i-th circle, respectively.\nEach of the following m lines contains four integers separated by a single space.\nThese four integers represent coordinates of two separate points\nP_j = (Px_j, Py_j) and\nQ_j =(Qx_j, Qy_j).\nThese two points P_j and Q_j\nform the j-th point pair.\nYou can assume\n0 <= Cx_i <= 10000,\n0 <= Cy_i <= 10000,\n1 <= r_i <= 1000,\n0 <= Px_j <= 10000,\n0 <= Py_j <= 10000,\n0 <= Qx_j <= 10000,\n0 <= Qy_j <= 10000.\nIn addition,\nyou can assume\nP_j or Q_j\nare not located on the circumference of any circle.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\n\nFigure G-1 shows the layout of the circles and the points in the first dataset of the sample input below.\nFigure G-2 shows the layouts of the subsequent datasets in the sample input.\nFigure G-2: Sample layout of circles and points", "output": "For each dataset,\noutput a single line containing the m results separated by a space.\nThe j-th result should be \"YES\" if there exists a path connecting P_j and Q_j, and \"NO\" otherwise.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 3\n0 0 1000\n1399 1331 931\n0 1331 500\n1398 0 400\n2000 360 340\n450 950 1600 380\n450 950 1399 1331\n450 950 450 2000\n1 2\n50 50 50\n0 10 100 90\n0 10 50 50\n2 2\n50 50 50\n100 50 50\n40 50 110 50\n40 50 0 0\n4 1\n25 100 26\n75 100 26\n50 40 40\n50 160 40\n50 81 50 119\n6 1\n100 50 40\n0 50 40\n50 0 48\n50 50 3\n55 55 4\n55 105 48\n50 55 55 50\n20 6\n270 180 50\n360 170 50\n0 0 50\n10 0 10\n0 90 50\n0 180 50\n90 180 50\n180 180 50\n205 90 50\n180 0 50\n65 0 20\n75 30 16\n90 78 36\n105 30 16\n115 0 20\n128 48 15\n128 100 15\n280 0 30\n330 0 30\n305 65 42\n0 20 10 20\n0 20 10 0\n50 30 133 0\n50 30 133 30\n90 40 305 20\n90 40 240 30\n16 2\n0 0 50\n0 90 50\n0 180 50\n90 180 50\n180 180 50\n205 90 50\n180 0 50\n65 0 20\n115 0 20\n90 0 15\n280 0 30\n330 0 30\n305 65 42\n75 40 16\n90 88 36\n105 40 16\n128 35 250 30\n90 50 305 20\n0 0\n output: YES NO NO\nYES NO\nNO NO\nNO\nYES\nYES NO NO YES NO NO\nNO NO"], "Pid": "p00779", "ProblemText": "Task Description: There are one or more circles on a plane.\nAny two circles have different center positions and/or different radiuses.\nA circle may intersect with another circle,\nbut no three or more circles have areas nor points shared by all of them.\nA circle may completely contain another circle or two circles may intersect at two separate points,\nbut you can assume that the circumferences of two circles never\ntouch at a single point.\n\nYour task is to judge\nwhether there exists a path that connects the given two points, P and Q,\nwithout crossing the circumferences of the circles.\nYou are given one or more point pairs for each layout of circles.\n\nIn the case of Figure G-1,\nwe can connect P and Q_1 without crossing the circumferences of the circles, but we cannot connect P with Q_2, Q_3, or Q_4 without crossing the circumferences of the circles.\nFigure G-1: Sample layout of circles and points\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn m\nCx_1 Cy_1 r_1 \n. . . \nCx_n Cy_n r_n \nPx_1 Py_1 Qx_1 Qy_1 \n. . . \nPx_m Py_m Qx_m Qy_m \n\nThe first line of a dataset contains two integers n and m\nseparated by a space.\nn represents the number of circles, and\nyou can assume 1 <= n <= 100.\nm represents the number of point pairs, and\nyou can assume 1 <= m <= 10.\nEach of the following n lines contains three integers separated by a single space.\n(Cx_i, Cy_i) and r_i represent the center position and the radius of the i-th circle, respectively.\nEach of the following m lines contains four integers separated by a single space.\nThese four integers represent coordinates of two separate points\nP_j = (Px_j, Py_j) and\nQ_j =(Qx_j, Qy_j).\nThese two points P_j and Q_j\nform the j-th point pair.\nYou can assume\n0 <= Cx_i <= 10000,\n0 <= Cy_i <= 10000,\n1 <= r_i <= 1000,\n0 <= Px_j <= 10000,\n0 <= Py_j <= 10000,\n0 <= Qx_j <= 10000,\n0 <= Qy_j <= 10000.\nIn addition,\nyou can assume\nP_j or Q_j\nare not located on the circumference of any circle.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\n\nFigure G-1 shows the layout of the circles and the points in the first dataset of the sample input below.\nFigure G-2 shows the layouts of the subsequent datasets in the sample input.\nFigure G-2: Sample layout of circles and points\nTask Output: For each dataset,\noutput a single line containing the m results separated by a space.\nThe j-th result should be \"YES\" if there exists a path connecting P_j and Q_j, and \"NO\" otherwise.\nTask Samples: input: 5 3\n0 0 1000\n1399 1331 931\n0 1331 500\n1398 0 400\n2000 360 340\n450 950 1600 380\n450 950 1399 1331\n450 950 450 2000\n1 2\n50 50 50\n0 10 100 90\n0 10 50 50\n2 2\n50 50 50\n100 50 50\n40 50 110 50\n40 50 0 0\n4 1\n25 100 26\n75 100 26\n50 40 40\n50 160 40\n50 81 50 119\n6 1\n100 50 40\n0 50 40\n50 0 48\n50 50 3\n55 55 4\n55 105 48\n50 55 55 50\n20 6\n270 180 50\n360 170 50\n0 0 50\n10 0 10\n0 90 50\n0 180 50\n90 180 50\n180 180 50\n205 90 50\n180 0 50\n65 0 20\n75 30 16\n90 78 36\n105 30 16\n115 0 20\n128 48 15\n128 100 15\n280 0 30\n330 0 30\n305 65 42\n0 20 10 20\n0 20 10 0\n50 30 133 0\n50 30 133 30\n90 40 305 20\n90 40 240 30\n16 2\n0 0 50\n0 90 50\n0 180 50\n90 180 50\n180 180 50\n205 90 50\n180 0 50\n65 0 20\n115 0 20\n90 0 15\n280 0 30\n330 0 30\n305 65 42\n75 40 16\n90 88 36\n105 40 16\n128 35 250 30\n90 50 305 20\n0 0\n output: YES NO NO\nYES NO\nNO NO\nNO\nYES\nYES NO NO YES NO NO\nNO NO\n\n" }, { "title": "Problem A: Goldbach's Conjecture", "content": "Goldbach's Conjecture: For any even number n greater than or equal to 4, there exists at least one pair of prime numbers p_1 and p_2 such that n = p_1 + p_2.\n\nThis conjecture has not been proved nor refused yet. No one is sure whether this conjecture actually holds. However, one can find such a pair of prime numbers, if any, for a given even number. The problem here is to write a program that reports the number of all the pairs of prime numbers satisfying the condition in the conjecture for a given even number.\n\nA sequence of even numbers is given as input. Corresponding to each number, the program should output the number of pairs mentioned above. Notice that we are intereseted in the number of essentially different pairs and therefore you should not count (p_1, p_2) and (p_2, p_1) separately as two different pairs.", "constraint": "", "input": "An integer is given in each input line. You may assume that each integer is even, and is greater than or equal to 4 and less than 2^15. The end of the input is indicated by a number 0.", "output": "Each output line should contain an integer number. No other characters should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n10\n12\n0\n output: 1\n2\n1"], "Pid": "p00780", "ProblemText": "Task Description: Goldbach's Conjecture: For any even number n greater than or equal to 4, there exists at least one pair of prime numbers p_1 and p_2 such that n = p_1 + p_2.\n\nThis conjecture has not been proved nor refused yet. No one is sure whether this conjecture actually holds. However, one can find such a pair of prime numbers, if any, for a given even number. The problem here is to write a program that reports the number of all the pairs of prime numbers satisfying the condition in the conjecture for a given even number.\n\nA sequence of even numbers is given as input. Corresponding to each number, the program should output the number of pairs mentioned above. Notice that we are intereseted in the number of essentially different pairs and therefore you should not count (p_1, p_2) and (p_2, p_1) separately as two different pairs.\nTask Input: An integer is given in each input line. You may assume that each integer is even, and is greater than or equal to 4 and less than 2^15. The end of the input is indicated by a number 0.\nTask Output: Each output line should contain an integer number. No other characters should appear in the output.\nTask Samples: input: 6\n10\n12\n0\n output: 1\n2\n1\n\n" }, { "title": "Problem B: Lattice Practices", "content": "Once upon a time, there was a king who loved beautiful costumes very much. The king had a special cocoon bed to make excellent cloth of silk. The cocoon bed had 16 small square rooms, forming a 4 * 4 lattice, for 16 silkworms. The cocoon bed can be depicted as follows:\n\nThe cocoon bed can be divided into 10 rectangular boards, each of which has 5 slits:\n\nNote that, except for the slit depth, there is no difference between the left side and the right side of the board (or, between the front and the back); thus, we cannot distinguish a symmetric board from its rotated image as is shown in the following:\n\nSlits have two kinds of depth, either shallow or deep. The cocoon bed should be constructed by fitting five of the boards vertically and the others horizontally, matching a shallow slit with a deep slit.\n\nYour job is to write a program that calculates the number of possible configurations to make the lattice. You may assume that there is no pair of identical boards. Notice that we are interested in the number of essentially different configurations and therefore you should not count mirror image configurations and rotated configurations separately as different configurations.\n\nThe following is an example of mirror image and rotated configurations, showing vertical and horizontal boards separately, where shallow and deep slits are denoted by '1' and '0' respectively.\n\nNotice that a rotation may exchange position of a vertical board and a horizontal board.", "constraint": "", "input": "The input consists of multiple data sets, each in a line. A data set gives the patterns of slits of 10 boards used to construct the lattice. The format of a data set is as follows:\n\nXXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX\n\nEach x is either '0' or '1'. '0' means a deep slit, and '1' a shallow slit. A block of five slit descriptions corresponds to a board. There are 10 blocks of slit descriptions in a line. Two adjacent blocks are separated by a space.\n\nFor example, the first data set in the Sample Input means the set of the following 10 boards:\n\nThe end of the input is indicated by a line consisting solely of three characters \"END\".", "output": "For each data set, the number of possible configurations to make the lattice from the given 10 boards should be output, each in a separate line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10000 01000 00100 11000 01100 11111 01110 11100 10110 11110\n10101 01000 00000 11001 01100 11101 01110 11100 10110 11010\nEND\n output: 40\n6"], "Pid": "p00781", "ProblemText": "Task Description: Once upon a time, there was a king who loved beautiful costumes very much. The king had a special cocoon bed to make excellent cloth of silk. The cocoon bed had 16 small square rooms, forming a 4 * 4 lattice, for 16 silkworms. The cocoon bed can be depicted as follows:\n\nThe cocoon bed can be divided into 10 rectangular boards, each of which has 5 slits:\n\nNote that, except for the slit depth, there is no difference between the left side and the right side of the board (or, between the front and the back); thus, we cannot distinguish a symmetric board from its rotated image as is shown in the following:\n\nSlits have two kinds of depth, either shallow or deep. The cocoon bed should be constructed by fitting five of the boards vertically and the others horizontally, matching a shallow slit with a deep slit.\n\nYour job is to write a program that calculates the number of possible configurations to make the lattice. You may assume that there is no pair of identical boards. Notice that we are interested in the number of essentially different configurations and therefore you should not count mirror image configurations and rotated configurations separately as different configurations.\n\nThe following is an example of mirror image and rotated configurations, showing vertical and horizontal boards separately, where shallow and deep slits are denoted by '1' and '0' respectively.\n\nNotice that a rotation may exchange position of a vertical board and a horizontal board.\nTask Input: The input consists of multiple data sets, each in a line. A data set gives the patterns of slits of 10 boards used to construct the lattice. The format of a data set is as follows:\n\nXXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX\n\nEach x is either '0' or '1'. '0' means a deep slit, and '1' a shallow slit. A block of five slit descriptions corresponds to a board. There are 10 blocks of slit descriptions in a line. Two adjacent blocks are separated by a space.\n\nFor example, the first data set in the Sample Input means the set of the following 10 boards:\n\nThe end of the input is indicated by a line consisting solely of three characters \"END\".\nTask Output: For each data set, the number of possible configurations to make the lattice from the given 10 boards should be output, each in a separate line.\nTask Samples: input: 10000 01000 00100 11000 01100 11111 01110 11100 10110 11110\n10101 01000 00000 11001 01100 11101 01110 11100 10110 11010\nEND\n output: 40\n6\n\n" }, { "title": "Problem C: Mobile Phone Coverage", "content": "A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice.\n\nfor this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna A_i has power r_i, corresponding to \"radius\". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna (x_i, y_i) with radius r_i. However, in this city Maxnorm such a coverage region becomes the square [x_i - r_i, x_i + r_i] * [y_i - r_i, y_i + r_i]. In other words, the distance between two points (x_p, y_p) and (x_q, y_q) is measured by the max norm max{ |x_p - x_q|, |y_p - y_q|}, or, the L_∞ norm, in this city Maxnorm instead of the ordinary Euclidean norm √ {(x_p - x_q)^2 + (y_p - y_q)^2}.\n\nAs an example, consider the following collection of 3 antennas\n\n4.0 4.0 3.0\n5.0 6.0 3.0\n5.5 4.5 1.0\ndepicted in the following figure\nwhere the i-th row represents x_i, y_i r_i such that (x_i, y_i) is the position of the i-th antenna and r_i is its power. The area of regions of points covered by at least one antenna is 52.00 in this case.\n\nWrite a program that finds the area of coverage by a given collection of antenna locations.", "constraint": "", "input": "The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format.\n\nn\nx_1 y_1 r_1\nx_2 y_2 r_2\n. . .\nx_n y_n r_n\n\nThe first integer n is the number of antennas, such that 2 <= n <= 100. The coordinate of the i-th antenna is given by (x_i, y_i), and its power is r_i. x_i, y_i and r_i are fractional numbers between 0 and 200 inclusive.\n\nThe end of the input is indicated by a data set with 0 as the value of n.", "output": "For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc. ) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places.\n\nThe sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n4.0 4.0 3.0\n5.0 6.0 3.0\n5.5 4.5 1.0\n2\n3.0 3.0 3.0\n1.5 1.5 1.0\n0\n output: 1 52.00\n2 36.00"], "Pid": "p00782", "ProblemText": "Task Description: A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice.\n\nfor this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna A_i has power r_i, corresponding to \"radius\". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna (x_i, y_i) with radius r_i. However, in this city Maxnorm such a coverage region becomes the square [x_i - r_i, x_i + r_i] * [y_i - r_i, y_i + r_i]. In other words, the distance between two points (x_p, y_p) and (x_q, y_q) is measured by the max norm max{ |x_p - x_q|, |y_p - y_q|}, or, the L_∞ norm, in this city Maxnorm instead of the ordinary Euclidean norm √ {(x_p - x_q)^2 + (y_p - y_q)^2}.\n\nAs an example, consider the following collection of 3 antennas\n\n4.0 4.0 3.0\n5.0 6.0 3.0\n5.5 4.5 1.0\ndepicted in the following figure\nwhere the i-th row represents x_i, y_i r_i such that (x_i, y_i) is the position of the i-th antenna and r_i is its power. The area of regions of points covered by at least one antenna is 52.00 in this case.\n\nWrite a program that finds the area of coverage by a given collection of antenna locations.\nTask Input: The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format.\n\nn\nx_1 y_1 r_1\nx_2 y_2 r_2\n. . .\nx_n y_n r_n\n\nThe first integer n is the number of antennas, such that 2 <= n <= 100. The coordinate of the i-th antenna is given by (x_i, y_i), and its power is r_i. x_i, y_i and r_i are fractional numbers between 0 and 200 inclusive.\n\nThe end of the input is indicated by a data set with 0 as the value of n.\nTask Output: For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc. ) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places.\n\nThe sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space.\nTask Samples: input: 3\n4.0 4.0 3.0\n5.0 6.0 3.0\n5.5 4.5 1.0\n2\n3.0 3.0 3.0\n1.5 1.5 1.0\n0\n output: 1 52.00\n2 36.00\n\n" }, { "title": "Problem D: Napoleon's Grumble", "content": "Legend has it that, after being defeated in Waterloo, Napoleon Bonaparte, in retrospect of his days of glory, talked to himself \"Able was I ere I saw Elba. \" Although, it is quite doubtful that he should have said this in English, this phrase is widely known as a typical palindrome.\n\nA palindrome is a symmetric character sequence that looks the same when read backwards, right to left. In the above Napoleon's grumble, white spaces appear at the same positions when read backwards. This is not a required condition for a palindrome. The following, ignoring spaces and punctuation marks, are known as the first conversation and the first palindromes by human beings.\n\n\"Madam, I'm Adam. \"\n\"Eve. \"\n(by Mark Twain)\n\nWrite a program that finds palindromes in input lines.", "constraint": "", "input": "A multi-line text is given as the input. The input ends at the end of the file.\n\nThere are at most 100 lines in the input. Each line has less than 1,024 Roman alphabet characters.", "output": "Corresponding to each input line, a line consisting of all the character sequences that are palindromes in the input line should be output. However, trivial palindromes consisting of only one or two characters should not be reported.\n\nOn finding palindromes, any characters in the input except Roman alphabets, such as punctuation characters, digits, space, and tabs, should be ignored. Characters that differ only in their cases should be looked upon as the same character. Whether or not the character sequences represent a proper English word or sentence does not matter.\n\nPalindromes should be reported all in uppercase characters. When two or more palindromes are reported, they should be separated by a space character. You may report palindromes in any order.\n\nIf two or more occurrences of the same palindromes are found in the same input line, report only once. When a palindrome overlaps with another, even when one is completely included in the other, both should be reported. However, palindromes appearing in the center of another palindrome, whether or not they also appear elsewhere, should not be reported. For example, for an input line of \"AAAAAA\", two palindromes \"AAAAAA\" and \"AAAAA\" should be output, but not \"AAAA\" nor \"AAA\". For \"AABCAAAAAA\", the output remains the same.\n\nOne line should be output corresponding to one input line. If an input line does not contain any palindromes, an empty line should be output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: As the first man said to the\nfirst woman:\n\"Madam, I'm Adam.\"\nShe responded:\n\"Eve.\"\n output: TOT\n\nMADAMIMADAM MADAM\nERE DED\nEVE\nNote that the second line in the output is empty, corresponding to the second input line containing no palindromes. Also note that some of the palindromes in the third input line, namely \"ADA\", \"MIM\", \"AMIMA\", \"DAMIMAD\", and \"ADAMIMADA\", are not reported because they appear at the center of reported ones. \"MADAM\" is reported, as it does not appear in the center, but only once, disregarding its second occurrence."], "Pid": "p00783", "ProblemText": "Task Description: Legend has it that, after being defeated in Waterloo, Napoleon Bonaparte, in retrospect of his days of glory, talked to himself \"Able was I ere I saw Elba. \" Although, it is quite doubtful that he should have said this in English, this phrase is widely known as a typical palindrome.\n\nA palindrome is a symmetric character sequence that looks the same when read backwards, right to left. In the above Napoleon's grumble, white spaces appear at the same positions when read backwards. This is not a required condition for a palindrome. The following, ignoring spaces and punctuation marks, are known as the first conversation and the first palindromes by human beings.\n\n\"Madam, I'm Adam. \"\n\"Eve. \"\n(by Mark Twain)\n\nWrite a program that finds palindromes in input lines.\nTask Input: A multi-line text is given as the input. The input ends at the end of the file.\n\nThere are at most 100 lines in the input. Each line has less than 1,024 Roman alphabet characters.\nTask Output: Corresponding to each input line, a line consisting of all the character sequences that are palindromes in the input line should be output. However, trivial palindromes consisting of only one or two characters should not be reported.\n\nOn finding palindromes, any characters in the input except Roman alphabets, such as punctuation characters, digits, space, and tabs, should be ignored. Characters that differ only in their cases should be looked upon as the same character. Whether or not the character sequences represent a proper English word or sentence does not matter.\n\nPalindromes should be reported all in uppercase characters. When two or more palindromes are reported, they should be separated by a space character. You may report palindromes in any order.\n\nIf two or more occurrences of the same palindromes are found in the same input line, report only once. When a palindrome overlaps with another, even when one is completely included in the other, both should be reported. However, palindromes appearing in the center of another palindrome, whether or not they also appear elsewhere, should not be reported. For example, for an input line of \"AAAAAA\", two palindromes \"AAAAAA\" and \"AAAAA\" should be output, but not \"AAAA\" nor \"AAA\". For \"AABCAAAAAA\", the output remains the same.\n\nOne line should be output corresponding to one input line. If an input line does not contain any palindromes, an empty line should be output.\nTask Samples: input: As the first man said to the\nfirst woman:\n\"Madam, I'm Adam.\"\nShe responded:\n\"Eve.\"\n output: TOT\n\nMADAMIMADAM MADAM\nERE DED\nEVE\nNote that the second line in the output is empty, corresponding to the second input line containing no palindromes. Also note that some of the palindromes in the third input line, namely \"ADA\", \"MIM\", \"AMIMA\", \"DAMIMAD\", and \"ADAMIMADA\", are not reported because they appear at the center of reported ones. \"MADAM\" is reported, as it does not appear in the center, but only once, disregarding its second occurrence.\n\n" }, { "title": "Problem E: Pipeline Scheduling", "content": "An arithmetic pipeline is designed to process more than one task simultaneously in an overlapping manner. It includes function units and data paths among them. Tasks are processed by pipelining: at each clock, one or more units are dedicated to a task and the output produced for the task at the clock is cascading to the units that are responsible for the next stage; since each unit may work in parallel with the others at any clock, more than one task may be being processed at a time by a single pipeline.\n\nIn this problem, a pipeline may have a feedback structure, that is, data paths among function units may have directed loops as shown in the next figure.\n\nExample of a feed back pipeline\nSince an arithmetic pipeline in this problem is designed as special purpose dedicated hardware, we assume that it accepts just a single sort of task. Therefore, the timing information of a pipeline is fully described by a simple table called a reservation table, which specifies the function units that are busy at each clock when a task is processed without overlapping execution.\n\nExample of a \"reservation table\"\nIn reservation tables, 'X' means \"the function unit is busy at that clock\" and '. ' means \"the function unit is not busy at that clock. \" In this case, once a task enters the pipeline, it is processed by unit0 at the first clock, by unit1 at the second clock, and so on. It takes seven clock cycles to perform a task.\n\nNotice that no special hardware is provided to avoid simultaneous use of the same function unit.\n\nTherefore, a task must not be started if it would conflict with any tasks being processed. For instance, with the above reservation table, if two tasks, say task 0 and task 1, were started at clock 0 and clock 1, respectively, a conflict would occur on unit0 at clock 5. This means that you should not start two tasks with single cycle interval. This invalid schedule is depicted in the following process table, which is obtained by overlapping two copies of the reservation table with one being shifted to the right by 1 clock.\n\nExample of a \"conflict\"\n('0's and '1's in this table except those in the first row represent tasks 0 and 1, respectively, and 'C' means the conflict. )\nYour job is to write a program that reports the minimum number of clock cycles in which the given pipeline can process 10 tasks.", "constraint": "", "input": "The input consists of multiple data sets, each representing the reservation table of a pipeline. A data set is given in the following format.\n\nn\nx_0,0 x_0,1 . . . x_0, n-1\nx_1,0 x_1,1 . . . x_1, n-1\nx_2,0 x_2,1 . . . x_2, n-1\nx_3,0 x_3,1 . . . x_3, n-1\nx_4,0 x_4,1 . . . x_4, n-1\n\nThe integer n (< 20) in the first line is the width of the reservation table, or the number of clock cycles that is necessary to perform a single task. The second line represents the usage of unit0, the third line unit1, and so on. x_i, j is either 'X' or '. '. The former means reserved and the latter free. There are no spaces in any input line. For simplicity, we only consider those pipelines that consist of 5 function units. The end of the input is indicated by a data set with 0 as the value of n.", "output": "For each data set, your program should output a line containing an integer number that is the minimum number of clock cycles in which the given pipeline can process 10 tasks.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 7\nX...XX.\n.X.....\n..X....\n...X...\n......X\n0\n output: 34\nIn this sample case, it takes 41 clock cycles process 10 tasks if each task is started as early as possible under the condition that it never conflicts with any previous tasks being processed.\n(The digits in the table except those in the clock row represent the task number.)\n\nHowever, it takes only 34 clock cycles if each task is started at every third clock.\n(The digits in the table except those in the clock row represent the task number.)\n\nThis is the best possible schedule and therefore your program should report 34 in this case."], "Pid": "p00784", "ProblemText": "Task Description: An arithmetic pipeline is designed to process more than one task simultaneously in an overlapping manner. It includes function units and data paths among them. Tasks are processed by pipelining: at each clock, one or more units are dedicated to a task and the output produced for the task at the clock is cascading to the units that are responsible for the next stage; since each unit may work in parallel with the others at any clock, more than one task may be being processed at a time by a single pipeline.\n\nIn this problem, a pipeline may have a feedback structure, that is, data paths among function units may have directed loops as shown in the next figure.\n\nExample of a feed back pipeline\nSince an arithmetic pipeline in this problem is designed as special purpose dedicated hardware, we assume that it accepts just a single sort of task. Therefore, the timing information of a pipeline is fully described by a simple table called a reservation table, which specifies the function units that are busy at each clock when a task is processed without overlapping execution.\n\nExample of a \"reservation table\"\nIn reservation tables, 'X' means \"the function unit is busy at that clock\" and '. ' means \"the function unit is not busy at that clock. \" In this case, once a task enters the pipeline, it is processed by unit0 at the first clock, by unit1 at the second clock, and so on. It takes seven clock cycles to perform a task.\n\nNotice that no special hardware is provided to avoid simultaneous use of the same function unit.\n\nTherefore, a task must not be started if it would conflict with any tasks being processed. For instance, with the above reservation table, if two tasks, say task 0 and task 1, were started at clock 0 and clock 1, respectively, a conflict would occur on unit0 at clock 5. This means that you should not start two tasks with single cycle interval. This invalid schedule is depicted in the following process table, which is obtained by overlapping two copies of the reservation table with one being shifted to the right by 1 clock.\n\nExample of a \"conflict\"\n('0's and '1's in this table except those in the first row represent tasks 0 and 1, respectively, and 'C' means the conflict. )\nYour job is to write a program that reports the minimum number of clock cycles in which the given pipeline can process 10 tasks.\nTask Input: The input consists of multiple data sets, each representing the reservation table of a pipeline. A data set is given in the following format.\n\nn\nx_0,0 x_0,1 . . . x_0, n-1\nx_1,0 x_1,1 . . . x_1, n-1\nx_2,0 x_2,1 . . . x_2, n-1\nx_3,0 x_3,1 . . . x_3, n-1\nx_4,0 x_4,1 . . . x_4, n-1\n\nThe integer n (< 20) in the first line is the width of the reservation table, or the number of clock cycles that is necessary to perform a single task. The second line represents the usage of unit0, the third line unit1, and so on. x_i, j is either 'X' or '. '. The former means reserved and the latter free. There are no spaces in any input line. For simplicity, we only consider those pipelines that consist of 5 function units. The end of the input is indicated by a data set with 0 as the value of n.\nTask Output: For each data set, your program should output a line containing an integer number that is the minimum number of clock cycles in which the given pipeline can process 10 tasks.\nTask Samples: input: 7\nX...XX.\n.X.....\n..X....\n...X...\n......X\n0\n output: 34\nIn this sample case, it takes 41 clock cycles process 10 tasks if each task is started as early as possible under the condition that it never conflicts with any previous tasks being processed.\n(The digits in the table except those in the clock row represent the task number.)\n\nHowever, it takes only 34 clock cycles if each task is started at every third clock.\n(The digits in the table except those in the clock row represent the task number.)\n\nThis is the best possible schedule and therefore your program should report 34 in this case.\n\n" }, { "title": "Problem F: Triangle Partition", "content": "Suppose that a triangle and a number of points inside the triangle are given. Your job is to find a partition of the triangle so that the set of the given points are divided into three subsets of equal size.\n\nLet A, B and C denote the vertices of the triangle. There are n points, P_1, P_2, . . . , P_n, given inside ∆ABC. You are requested to find a point Q such that each of the three triangles ∆QBC, ∆QCA and ∆QAB contains at least n/3 points. Points on the boundary line are counted in both triangles. For example, a point on the line QA is counted in ∆QCA and also in ∆QAB. If Q coincides a point, the point is counted in all three triangles.\n\nIt can be proved that there always exists a point Q satisfying the above condition. The problem will be easily understood from the figure below.", "constraint": "", "input": "The input consists of multiple data sets, each representing a set of points. A data set is given in the following format.\n\nn\nx_1 y_1\nx_2 y_2\n. . .\nx_n y_n\n\nThe first integer n is the number of points, such that 3 <= n <= 300. n is always a multiple of 3. The coordinate of a point P_i is given by (x_i, y_i). x_i and y_i are integers between 0 and 1000.\n\nThe coordinates of the triangle ABC are fixed. They are A(0,0), B(1000,0) and C(0,1000).\n\nEach of P_i is located strictly inside the triangle ABC, not on the side BC, CA nor AB. No two points can be connected by a straight line running through one of the vertices of the triangle. Speaking more precisely, if you connect a point P_i with the vertex A by a straight line, another point P_j never appears on the line. The same holds for B and C.\n\nThe end of the input is indicated by a 0 as the value of n. The number of data sets does not exceed 10.", "output": "For each data set, your program should output the coordinate of the point Q. The format of the output is as follows.\n\nq_x q_y\n\nFor each data set, a line of this format should be given. No extra lines are allowed. On the contrary, any number of space characters may be inserted before q_x, between q_x and q_y or after q_y.\n\nEach of q_x and q_y should be represented by a fractional number (e. g. , 3.1416) but not with an exponential part (e. g. , 6.023e+23 is not allowed). Four digits should follow the decimal point.\n\nNote that there is no unique \"correct answer\" in this problem. In general, there are infinitely many points which satisfy the given condition. Your result may be any one of these \"possible answers\".\n\nIn your program you should be careful to minimize the effect of numeric errors in the handling of floating-point numbers. However, it seems inevitable that some rounding errors exist in the output. We expect that there is an error of 0.5 * 10^-4 in the output, and will judge your result accordingly.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n100 500\n200 500\n300 500\n6\n100 300\n100 600\n200 100\n200 700\n500 100\n600 300\n0\n output: 166.6667 555.5556\n333.3333 333.3333\nAs mentioned above, the results shown here are not the only solutions. Many other coordinates for the point Q are also acceptable. The title of this section should really be \"Sample Output for the Sample Input\"."], "Pid": "p00785", "ProblemText": "Task Description: Suppose that a triangle and a number of points inside the triangle are given. Your job is to find a partition of the triangle so that the set of the given points are divided into three subsets of equal size.\n\nLet A, B and C denote the vertices of the triangle. There are n points, P_1, P_2, . . . , P_n, given inside ∆ABC. You are requested to find a point Q such that each of the three triangles ∆QBC, ∆QCA and ∆QAB contains at least n/3 points. Points on the boundary line are counted in both triangles. For example, a point on the line QA is counted in ∆QCA and also in ∆QAB. If Q coincides a point, the point is counted in all three triangles.\n\nIt can be proved that there always exists a point Q satisfying the above condition. The problem will be easily understood from the figure below.\nTask Input: The input consists of multiple data sets, each representing a set of points. A data set is given in the following format.\n\nn\nx_1 y_1\nx_2 y_2\n. . .\nx_n y_n\n\nThe first integer n is the number of points, such that 3 <= n <= 300. n is always a multiple of 3. The coordinate of a point P_i is given by (x_i, y_i). x_i and y_i are integers between 0 and 1000.\n\nThe coordinates of the triangle ABC are fixed. They are A(0,0), B(1000,0) and C(0,1000).\n\nEach of P_i is located strictly inside the triangle ABC, not on the side BC, CA nor AB. No two points can be connected by a straight line running through one of the vertices of the triangle. Speaking more precisely, if you connect a point P_i with the vertex A by a straight line, another point P_j never appears on the line. The same holds for B and C.\n\nThe end of the input is indicated by a 0 as the value of n. The number of data sets does not exceed 10.\nTask Output: For each data set, your program should output the coordinate of the point Q. The format of the output is as follows.\n\nq_x q_y\n\nFor each data set, a line of this format should be given. No extra lines are allowed. On the contrary, any number of space characters may be inserted before q_x, between q_x and q_y or after q_y.\n\nEach of q_x and q_y should be represented by a fractional number (e. g. , 3.1416) but not with an exponential part (e. g. , 6.023e+23 is not allowed). Four digits should follow the decimal point.\n\nNote that there is no unique \"correct answer\" in this problem. In general, there are infinitely many points which satisfy the given condition. Your result may be any one of these \"possible answers\".\n\nIn your program you should be careful to minimize the effect of numeric errors in the handling of floating-point numbers. However, it seems inevitable that some rounding errors exist in the output. We expect that there is an error of 0.5 * 10^-4 in the output, and will judge your result accordingly.\nTask Samples: input: 3\n100 500\n200 500\n300 500\n6\n100 300\n100 600\n200 100\n200 700\n500 100\n600 300\n0\n output: 166.6667 555.5556\n333.3333 333.3333\nAs mentioned above, the results shown here are not the only solutions. Many other coordinates for the point Q are also acceptable. The title of this section should really be \"Sample Output for the Sample Input\".\n\n" }, { "title": "Problem G: BUT We Need a Diagram", "content": "Consider a data structure called BUT (Binary and/or Unary Tree). A BUT is defined inductively as follows:\n\nLet l be a letter of the English alphabet, either lowercase or uppercase (n the sequel, we say simply \"a letter\"). Then, the object that consists only of l, designating l as its label, is a BUT. In this case, it is called a 0-ary BUT.\n\nLet l be a letter and C a BUT. Then, the object that consists of l and C, designating l as its label and C as its component, is a BUT. In this case, it is called a unary BUT.\n\nLet l be a letter, L and R BUTs. Then, the object that consists of l, L and R, designating l as its label, L as its left component, and R as its right component, is a BUT. In this case, it is called a binary BUT.\nA BUT can be represented by a expression in the following way.\n\nWhen a BUT B is 0-ary, its representation is the letter of its label.\n\nWhen a BUT B is unary, its representation is the letter of its label followed by the parenthesized representation of its component.\n\nWhen a BUT B is binary, its representation is the letter of its label, a left parenthesis, the representation of its left component, a comma, the representation of its right component, and a right parenthesis, arranged in this order.\nHere are examples:\n\na\nA(b)\na(a, B)\na(B(c(D), E), f(g(H, i)))\n\nSuch an expression is concise, but a diagram is much more appealing to our eyes. We prefer a diagram:\n\nD H i\n- ---\nc E g\n--- -\n B f\n ----\n a\n\nto the expression a(B(c(D), E), f(g(H, i)))\n\nYour mission is to write a program that converts the expression representing a BUT into its diagram. We want to keep a diagram as compact as possible assuming that we display it on a conventional character terminal with a fixed pitch font such as Courier. Let's define the diagram D for BUT B inductively along the structure of B as follows:\n\nWhen B is 0-ary, D consists only of a letter of its label. The letter is called the root of D, and also called the leaf of D\n\nWhen B is unary, D consists of a letter l of its label, a minus symbol S, and the diagram C for its component, satisfying the following constraints:\n \nl is just below S\n\nThe root of C is just above S\nl is called the root of D, and the leaves of C are called the leaves of D.\nWhen B is binary, D consists of a letter l of its label, a sequence of minus symbols S, the diagram L for its left component, and the diagram R for its right component, satisfying the following constraints:\n \nS is contiguous, and is in a line.\n\nl is just below the central minus symbol of S, where, if the center of S locates on a minus symbol s, s is the central, and if the center of S locates between adjacent minus symbols, the left one of them is the central.\n\nThe root of L is just above the left most minus symbols of S, and the rot of R is just above the rightmost minus symbol of S\n\nIn any line of D, L and R do not touch or overlap each other.\n\nNo minus symbols are just above the leaves of L and R.\nl is called the root of D, and the leaves of L and R are called the leaves of D", "constraint": "", "input": "The input to the program is a sequence of expressions representing BUTs. Each expression except the last one is terminated by a semicolon. The last expression is terminated by a period. White spaces (tabs and blanks) should be ignored. An expression may extend over multiple lines. The number of letter, i. e. , the number of characters except parentheses, commas, and white spaces, in an expression is at most 80.\n\nYou may assume that the input is syntactically correct and need not take care of error cases.", "output": "Each expression is to be identified with a number starting with 1 in the order of occurrence in the input. Output should be produced in the order of the input.\n\nFor each expression, a line consisting of the identification number of the expression followed by a colon should be produced first, and then, the diagram for the BUT represented by the expression should be produced.\n\nFor diagram, output should consist of the minimum number of lines, which contain only letters or minus symbols together with minimum number of blanks required to obey the rules shown above.", "content_img": false, "lang": "en", "error": false, "samples": ["input: a(A,b(B,C));\nx( y( y( z(z), v( s, t ) ) ), u ) ;\n\na( b( c,\n d(\n e(f),\n g\n )\n ),\n h( i(\n j(\n k(k,k),\n l(l)\n ),\n m(m)\n )\n )\n );\n\na(B(C),d(e(f(g(h(i(j,k),l),m),n),o),p))\n.\n output: 1:\n B C\n ---\nA b\n---\n a\n2:\nz s t\n- ---\nz v\n----\n y\n -\n y u\n ---\n x\n3:\n k k l\n --- -\n f k l m\n - ---- -\n e g j m\n --- -----\nc d i\n--- -\n b h\n -------\n a\n4:\nj k\n---\n i l\n ---\n h m\n ---\n g n\n ---\n f o\n ---\n C e p\n - ---\n B d\n ----\n a"], "Pid": "p00786", "ProblemText": "Task Description: Consider a data structure called BUT (Binary and/or Unary Tree). A BUT is defined inductively as follows:\n\nLet l be a letter of the English alphabet, either lowercase or uppercase (n the sequel, we say simply \"a letter\"). Then, the object that consists only of l, designating l as its label, is a BUT. In this case, it is called a 0-ary BUT.\n\nLet l be a letter and C a BUT. Then, the object that consists of l and C, designating l as its label and C as its component, is a BUT. In this case, it is called a unary BUT.\n\nLet l be a letter, L and R BUTs. Then, the object that consists of l, L and R, designating l as its label, L as its left component, and R as its right component, is a BUT. In this case, it is called a binary BUT.\nA BUT can be represented by a expression in the following way.\n\nWhen a BUT B is 0-ary, its representation is the letter of its label.\n\nWhen a BUT B is unary, its representation is the letter of its label followed by the parenthesized representation of its component.\n\nWhen a BUT B is binary, its representation is the letter of its label, a left parenthesis, the representation of its left component, a comma, the representation of its right component, and a right parenthesis, arranged in this order.\nHere are examples:\n\na\nA(b)\na(a, B)\na(B(c(D), E), f(g(H, i)))\n\nSuch an expression is concise, but a diagram is much more appealing to our eyes. We prefer a diagram:\n\nD H i\n- ---\nc E g\n--- -\n B f\n ----\n a\n\nto the expression a(B(c(D), E), f(g(H, i)))\n\nYour mission is to write a program that converts the expression representing a BUT into its diagram. We want to keep a diagram as compact as possible assuming that we display it on a conventional character terminal with a fixed pitch font such as Courier. Let's define the diagram D for BUT B inductively along the structure of B as follows:\n\nWhen B is 0-ary, D consists only of a letter of its label. The letter is called the root of D, and also called the leaf of D\n\nWhen B is unary, D consists of a letter l of its label, a minus symbol S, and the diagram C for its component, satisfying the following constraints:\n \nl is just below S\n\nThe root of C is just above S\nl is called the root of D, and the leaves of C are called the leaves of D.\nWhen B is binary, D consists of a letter l of its label, a sequence of minus symbols S, the diagram L for its left component, and the diagram R for its right component, satisfying the following constraints:\n \nS is contiguous, and is in a line.\n\nl is just below the central minus symbol of S, where, if the center of S locates on a minus symbol s, s is the central, and if the center of S locates between adjacent minus symbols, the left one of them is the central.\n\nThe root of L is just above the left most minus symbols of S, and the rot of R is just above the rightmost minus symbol of S\n\nIn any line of D, L and R do not touch or overlap each other.\n\nNo minus symbols are just above the leaves of L and R.\nl is called the root of D, and the leaves of L and R are called the leaves of D\nTask Input: The input to the program is a sequence of expressions representing BUTs. Each expression except the last one is terminated by a semicolon. The last expression is terminated by a period. White spaces (tabs and blanks) should be ignored. An expression may extend over multiple lines. The number of letter, i. e. , the number of characters except parentheses, commas, and white spaces, in an expression is at most 80.\n\nYou may assume that the input is syntactically correct and need not take care of error cases.\nTask Output: Each expression is to be identified with a number starting with 1 in the order of occurrence in the input. Output should be produced in the order of the input.\n\nFor each expression, a line consisting of the identification number of the expression followed by a colon should be produced first, and then, the diagram for the BUT represented by the expression should be produced.\n\nFor diagram, output should consist of the minimum number of lines, which contain only letters or minus symbols together with minimum number of blanks required to obey the rules shown above.\nTask Samples: input: a(A,b(B,C));\nx( y( y( z(z), v( s, t ) ) ), u ) ;\n\na( b( c,\n d(\n e(f),\n g\n )\n ),\n h( i(\n j(\n k(k,k),\n l(l)\n ),\n m(m)\n )\n )\n );\n\na(B(C),d(e(f(g(h(i(j,k),l),m),n),o),p))\n.\n output: 1:\n B C\n ---\nA b\n---\n a\n2:\nz s t\n- ---\nz v\n----\n y\n -\n y u\n ---\n x\n3:\n k k l\n --- -\n f k l m\n - ---- -\n e g j m\n --- -----\nc d i\n--- -\n b h\n -------\n a\n4:\nj k\n---\n i l\n ---\n h m\n ---\n g n\n ---\n f o\n ---\n C e p\n - ---\n B d\n ----\n a\n\n" }, { "title": "Problem H: Digital Racing Circuit", "content": "You have an ideally small racing car on an x-y plane (0 <= x, y <= 255, where bigger y denotes upper coordinate). The racing circuit course is figured by two solid walls. Each wall is a closed loop of connected line segments. End point coordinates of every line segment are both integers (See Figure 1). Thus, a wall is represented by a list of end point integer coordinates (x_1, y_1), (x_2, y_2), . . . , (x_n, y_n). The start line and the goal line are identical.\nFigure 1. A Simple Course\n\nFor the qualification run, you start the car at any integer coordinate position on the start line, say (s_x, s_y).\n\nAt any clock t (>= 0), according to the acceleration parameter at t, (a_x, t, a_y, t), the velocity changes instantly to (v_x, t-1 + a_x, t, v_y, t-1 + a_y, t), if the velocity at t - 1 is (v_x, t-1, v_y, t-1). The velocity will be kept constant until the next clock. It is assumed that the velocity at clock -1, (v_x, -1, v_y, -1) is (0,0). Each of the acceleration components must be either -1,0, or 1, because your car does not have so fantastic engine and brake. In other words, any successive pair of velocities should not differ more than 1 for either x-component or y-component. Note that your trajectory will be piecewise linear as the walls are.\n\nYour car should not touch nor run over the circuit wall, or your car will be crashed, even at the start line. The referee watches your car's trajectory very carefully, checking whether or not the trajectory touches the wall or attempts to cross the wall.\n\nThe objective of the qualification run is to finish your run within as few clock units as possible, without suffering from any interference by other racing cars. That is, you run alone the circuit around clockwise and reach, namely touch or go across the goal line without having been crashed. Don't be crashed even in the last trajectory segment after you reach the goal line. But we don't care whatever happens after that clock\n\nYour final lap time is the clock t when you reach the goal line for the first time after you have once left the start line. But it needs a little adjustment at the goal instant. When you cross the goal line, only the necessary fraction of your car's last trajectory segment is counted. For example, if the length of your final trajectory segment is 3 and only its 1/3 fraction is needed to reach the goal line, you have to add only 0.333 instead of 1 clock unit.\n\nDrivers are requested to control their cars as cleverly as possible to run fast but avoiding crash. ALAS! The racing committee decided that it is too DANGEROUS to allow novices to run the circuit. In the last year, it was reported that some novices wrenched their fingers by typing too enthusiastically their programs. So, this year, you are invited as a referee assistant in order to accumulate the experience on this dangerous car race.\n\nA number of experienced drivers are now running the circuit for the qualification for semi-finals. They submit their driving records to the referee. The referee has to check the records one by one whether it is not a fake.\n\nNow, you are requested to make a program to check the validity of driving records for any given course configuration. Is the start point right on the start line without touching the walls? Is every value in the acceleration parameter list either one of -1,0, and 1? Does the length of acceleration parameter list match the reported lap time? That is, aren't there any excess acceleration parameters after the goal, or are these enough to reach the goal? Doesn't it involve any crash? Does it mean a clockwise running all around? (Note that it is not inhibited to run backward temporarily unless crossing the start line again. ) Is the lap time calculation correct? You should allow a rounding error up to 0.01 clock unit in the lap time.", "constraint": "", "input": "The input consists of a course configuration followed by a number of driving records on that course.\n\nA course configuration is given by two lists representing the inner wall and the outer wall, respectively. Each line shows the end point coordinates of the line segments that comprise the wall. A course configuration looks as follows:\n\ni_x, 1 i_y, 1 . . . . . i_x, N i_y, N 99999\no_x, 1 o_y, 1 . . . . . o_x, M o_y, M 99999\n\nwhere data are alternating x-coordinates and y-coordinates that are all non-negative integers (<= 255) terminated by 99999. The start/goal line is a line segment connecting the coordinates (i_x, 1, i_y, 1) and (o_x, 1, o_y, 1). For simplicity, i_y, 1 is assumed to be equal to o_y, 1; that is, the start/goal line is horizontal on the x-y plane. Note that N and M may vary among course configurations, but do not exceed 100, because too many curves involve much danger even for experienced drivers. You need not check the validity of the course configuration.\n\nA driving record consists of three parts, which is terminated by 99999: two integers s_x, s_y for the start position (s_x, s_y), the lap time with three digits after the decimal point, and the sequential list of acceleration parameters at all clocks until the goal. It is assumed that the length of the acceleration parameter list does not exceed 500. A driving record looks like the following:\n\ns_x s_y\nlap-time\na_x, 0 a_y, 0 a_x, 1 a_y, 1 . . . a_x, L a_y, L 99999\n\nInput is terminated by a null driving record; that is, it is terminated by a 99999 that immediately follows 99999 of the last driving record.", "output": "The test result should be reported by simply printing OK or NG for each driving record, each result in each line. No other letter is allowed in the result.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 28 6 32 25 32 26 27 26 24 6 24 99999\n2 28 2 35 30 35 30 20 2 20 99999\n\n3 28\n22.667\n0 1 1 1 1 0 0 -1 0 -1 1 0 0 0 1 0 -1 0 0 -1 -1 -1 -1 0 -1 0 -1 -1 -1 1 -1 1\n-1 1 -1 0 1 0 1 1 1 1 1 0 1 1 99999\n\n5 28\n22.667\n0 1 -1 1 1 0 1 -1 1 -1 1 0 1 0 1 0 -1 -1 -1 0 -1 -1 -1 0 -1 1 -1 -1 -1 1\n-1 0 -1 1 -1 0 1 0 1 0 1 1 1 1 1 1 99999\n\n4 28\n6.333\n0 1 0 1 1 -1 -1 -1 0 -1 0 -1 0 -1 99999\n\n3 28\n20.000\n0 -1 1 -1 1 0 1 1 1 1 1 0 -1 0 -1 0 -1 1 -1 1\n-1 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 1 0 1 -1 1 -1 1 -1 99999\n\n99999\n output: OK\nNG\nNG\nNG"], "Pid": "p00787", "ProblemText": "Task Description: You have an ideally small racing car on an x-y plane (0 <= x, y <= 255, where bigger y denotes upper coordinate). The racing circuit course is figured by two solid walls. Each wall is a closed loop of connected line segments. End point coordinates of every line segment are both integers (See Figure 1). Thus, a wall is represented by a list of end point integer coordinates (x_1, y_1), (x_2, y_2), . . . , (x_n, y_n). The start line and the goal line are identical.\nFigure 1. A Simple Course\n\nFor the qualification run, you start the car at any integer coordinate position on the start line, say (s_x, s_y).\n\nAt any clock t (>= 0), according to the acceleration parameter at t, (a_x, t, a_y, t), the velocity changes instantly to (v_x, t-1 + a_x, t, v_y, t-1 + a_y, t), if the velocity at t - 1 is (v_x, t-1, v_y, t-1). The velocity will be kept constant until the next clock. It is assumed that the velocity at clock -1, (v_x, -1, v_y, -1) is (0,0). Each of the acceleration components must be either -1,0, or 1, because your car does not have so fantastic engine and brake. In other words, any successive pair of velocities should not differ more than 1 for either x-component or y-component. Note that your trajectory will be piecewise linear as the walls are.\n\nYour car should not touch nor run over the circuit wall, or your car will be crashed, even at the start line. The referee watches your car's trajectory very carefully, checking whether or not the trajectory touches the wall or attempts to cross the wall.\n\nThe objective of the qualification run is to finish your run within as few clock units as possible, without suffering from any interference by other racing cars. That is, you run alone the circuit around clockwise and reach, namely touch or go across the goal line without having been crashed. Don't be crashed even in the last trajectory segment after you reach the goal line. But we don't care whatever happens after that clock\n\nYour final lap time is the clock t when you reach the goal line for the first time after you have once left the start line. But it needs a little adjustment at the goal instant. When you cross the goal line, only the necessary fraction of your car's last trajectory segment is counted. For example, if the length of your final trajectory segment is 3 and only its 1/3 fraction is needed to reach the goal line, you have to add only 0.333 instead of 1 clock unit.\n\nDrivers are requested to control their cars as cleverly as possible to run fast but avoiding crash. ALAS! The racing committee decided that it is too DANGEROUS to allow novices to run the circuit. In the last year, it was reported that some novices wrenched their fingers by typing too enthusiastically their programs. So, this year, you are invited as a referee assistant in order to accumulate the experience on this dangerous car race.\n\nA number of experienced drivers are now running the circuit for the qualification for semi-finals. They submit their driving records to the referee. The referee has to check the records one by one whether it is not a fake.\n\nNow, you are requested to make a program to check the validity of driving records for any given course configuration. Is the start point right on the start line without touching the walls? Is every value in the acceleration parameter list either one of -1,0, and 1? Does the length of acceleration parameter list match the reported lap time? That is, aren't there any excess acceleration parameters after the goal, or are these enough to reach the goal? Doesn't it involve any crash? Does it mean a clockwise running all around? (Note that it is not inhibited to run backward temporarily unless crossing the start line again. ) Is the lap time calculation correct? You should allow a rounding error up to 0.01 clock unit in the lap time.\nTask Input: The input consists of a course configuration followed by a number of driving records on that course.\n\nA course configuration is given by two lists representing the inner wall and the outer wall, respectively. Each line shows the end point coordinates of the line segments that comprise the wall. A course configuration looks as follows:\n\ni_x, 1 i_y, 1 . . . . . i_x, N i_y, N 99999\no_x, 1 o_y, 1 . . . . . o_x, M o_y, M 99999\n\nwhere data are alternating x-coordinates and y-coordinates that are all non-negative integers (<= 255) terminated by 99999. The start/goal line is a line segment connecting the coordinates (i_x, 1, i_y, 1) and (o_x, 1, o_y, 1). For simplicity, i_y, 1 is assumed to be equal to o_y, 1; that is, the start/goal line is horizontal on the x-y plane. Note that N and M may vary among course configurations, but do not exceed 100, because too many curves involve much danger even for experienced drivers. You need not check the validity of the course configuration.\n\nA driving record consists of three parts, which is terminated by 99999: two integers s_x, s_y for the start position (s_x, s_y), the lap time with three digits after the decimal point, and the sequential list of acceleration parameters at all clocks until the goal. It is assumed that the length of the acceleration parameter list does not exceed 500. A driving record looks like the following:\n\ns_x s_y\nlap-time\na_x, 0 a_y, 0 a_x, 1 a_y, 1 . . . a_x, L a_y, L 99999\n\nInput is terminated by a null driving record; that is, it is terminated by a 99999 that immediately follows 99999 of the last driving record.\nTask Output: The test result should be reported by simply printing OK or NG for each driving record, each result in each line. No other letter is allowed in the result.\nTask Samples: input: 6 28 6 32 25 32 26 27 26 24 6 24 99999\n2 28 2 35 30 35 30 20 2 20 99999\n\n3 28\n22.667\n0 1 1 1 1 0 0 -1 0 -1 1 0 0 0 1 0 -1 0 0 -1 -1 -1 -1 0 -1 0 -1 -1 -1 1 -1 1\n-1 1 -1 0 1 0 1 1 1 1 1 0 1 1 99999\n\n5 28\n22.667\n0 1 -1 1 1 0 1 -1 1 -1 1 0 1 0 1 0 -1 -1 -1 0 -1 -1 -1 0 -1 1 -1 -1 -1 1\n-1 0 -1 1 -1 0 1 0 1 0 1 1 1 1 1 1 99999\n\n4 28\n6.333\n0 1 0 1 1 -1 -1 -1 0 -1 0 -1 0 -1 99999\n\n3 28\n20.000\n0 -1 1 -1 1 0 1 1 1 1 1 0 -1 0 -1 0 -1 1 -1 1\n-1 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 1 0 1 -1 1 -1 1 -1 99999\n\n99999\n output: OK\nNG\nNG\nNG\n\n" }, { "title": "Problem A: Rational Irrationals", "content": "Rational numbers are numbers represented by ratios of two integers. For a prime number p, one of the elementary theorems in the number theory is that there is no rational number equal to √p. Such numbers are called irrational numbers. It is also known that there are rational numbers arbitrarily close to √p\n\nNow, given a positive integer n, we define a set Q_n of all rational numbers whose elements are represented by ratios of two positive integers both of which are less than or equal to n. For example, Q_4 is a set of 11 rational numbers {1/1,1/2,1/3,1/4,2/1,2/3,3/1,3/2,3/4,4/1,4/3}. 2/2,2/4,3/3,4/2 and 4/4 are not included here because they are equal to 1/1,1/2,1/1,2/1 and 1/1, respectively.\n\nYour job is to write a program that reads two integers p and n and reports two rational numbers x / y and u / v, where u / v < √p < x / y and there are no other elements of Q_n between u/v and x/y. When n is greater than √p, such a pair of rational numbers always exists.", "constraint": "", "input": "The input consists of lines each of which contains two positive integers, a prime number p and an integer n in the following format.\n\np n\n\nThey are separated by a space character. You can assume that p and n are less than 10000, and that n is greater than √p. The end of the input is indicated by a line consisting of two zeros.", "output": "For each input line, your program should output a line consisting of the two rational numbers x / y and u / v (x / y > u / v) separated by a space character in the following format.\n\nx/y u/v\n\nThey should be irreducible. For example, 6/14 and 15/3 are not accepted. They should be reduced to 3/7 and 5/1, respectively.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5\n3 10\n5 100\n0 0\n output: 3/2 4/3\n7/4 5/3\n85/38 38/17"], "Pid": "p00788", "ProblemText": "Task Description: Rational numbers are numbers represented by ratios of two integers. For a prime number p, one of the elementary theorems in the number theory is that there is no rational number equal to √p. Such numbers are called irrational numbers. It is also known that there are rational numbers arbitrarily close to √p\n\nNow, given a positive integer n, we define a set Q_n of all rational numbers whose elements are represented by ratios of two positive integers both of which are less than or equal to n. For example, Q_4 is a set of 11 rational numbers {1/1,1/2,1/3,1/4,2/1,2/3,3/1,3/2,3/4,4/1,4/3}. 2/2,2/4,3/3,4/2 and 4/4 are not included here because they are equal to 1/1,1/2,1/1,2/1 and 1/1, respectively.\n\nYour job is to write a program that reads two integers p and n and reports two rational numbers x / y and u / v, where u / v < √p < x / y and there are no other elements of Q_n between u/v and x/y. When n is greater than √p, such a pair of rational numbers always exists.\nTask Input: The input consists of lines each of which contains two positive integers, a prime number p and an integer n in the following format.\n\np n\n\nThey are separated by a space character. You can assume that p and n are less than 10000, and that n is greater than √p. The end of the input is indicated by a line consisting of two zeros.\nTask Output: For each input line, your program should output a line consisting of the two rational numbers x / y and u / v (x / y > u / v) separated by a space character in the following format.\n\nx/y u/v\n\nThey should be irreducible. For example, 6/14 and 15/3 are not accepted. They should be reduced to 3/7 and 5/1, respectively.\nTask Samples: input: 2 5\n3 10\n5 100\n0 0\n output: 3/2 4/3\n7/4 5/3\n85/38 38/17\n\n" }, { "title": "Problem B: Square Coins", "content": "People in Silverland use square coins. Not only they have square shapes but also their values are square numbers. Coins with values of all square numbers up to 289 (= 17^2), i. e. , 1-credit coins, 4-credit coins, 9-credit coins, . . . , and 289-credit coins, are available in Silverland.\n\nThere are four combinations of coins to pay ten credits:\n\nten 1-credit coins,\n\none 4-credit coin and six 1-credit coins,\n\ntwo 4-credit coins and two 1-credit coins, and\n\none 9-credit coin and one 1-credit coin.\nYour mission is to count the number of ways to pay a given amount using coins of Silverland.", "constraint": "", "input": "The input consists of lines each containing an integer meaning an amount to be paid, followed by a line containing a zero. You may assume that all the amounts are positive and less than 300.", "output": "For each of the given amount, one line containing a single integer representing the number of combinations of coins should be output. No other characters should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n10\n30\n0\n output: 1\n4\n27"], "Pid": "p00789", "ProblemText": "Task Description: People in Silverland use square coins. Not only they have square shapes but also their values are square numbers. Coins with values of all square numbers up to 289 (= 17^2), i. e. , 1-credit coins, 4-credit coins, 9-credit coins, . . . , and 289-credit coins, are available in Silverland.\n\nThere are four combinations of coins to pay ten credits:\n\nten 1-credit coins,\n\none 4-credit coin and six 1-credit coins,\n\ntwo 4-credit coins and two 1-credit coins, and\n\none 9-credit coin and one 1-credit coin.\nYour mission is to count the number of ways to pay a given amount using coins of Silverland.\nTask Input: The input consists of lines each containing an integer meaning an amount to be paid, followed by a line containing a zero. You may assume that all the amounts are positive and less than 300.\nTask Output: For each of the given amount, one line containing a single integer representing the number of combinations of coins should be output. No other characters should appear in the output.\nTask Samples: input: 2\n10\n30\n0\n output: 1\n4\n27\n\n" }, { "title": "Problem C: Die Game", "content": "Life is not easy. Sometimes it is beyond your control. Now, as contestants of ACM ICPC, you might be just tasting the bitter of life. But don't worry! Do not look only on the dark side of life, but look also on the bright side. Life may be an enjoyable game of chance, like throwing dice. Do or die! Then, at last, you might be able to find the route to victory.\n\nThis problem comes from a game using a die. By the way, do you know a die? It has nothing to do with \"death. \" A die is a cubic object with six faces, each of which represents a different number from one to six and is marked with the corresponding number of spots. Since it is usually used in pair, \"a die\" is rarely used word. You might have heard a famous phrase \"the die is cast, \" though.\n\nWhen a game starts, a die stands still on a flat table. During the game, the die is tumbled in all directions by the dealer. You will win the game if you can predict the number seen on the top face at the time when the die stops tumbling.\n\nNow you are requested to write a program that simulates the rolling of a die. For simplicity, we assume that the die neither slip nor jumps but just rolls on the table in four directions, that is, north, east, south, and west. At the beginning of every game, the dealer puts the die at the center of the table and adjusts its direction so that the numbers one, two, and three are seen on the top, north, and west faces, respectively. For the other three faces, we do not explicitly specify anything but tell you the golden rule: the sum of the numbers on any pair of opposite faces is always seven.\n\nYour program should accept a sequence of commands, each of which is either \"north\", \"east\", \"south\", or \"west\". A \"north\" command tumbles the die down to north, that is, the top face becomes the new north, the north becomes the new bottom, and so on. More precisely, the die is rotated around its north bottom edge to the north direction and the rotation angle is 9 degrees. Other commands also tumble the die accordingly to their own directions. Your program should calculate the number finally shown on the top after performing the commands in the sequence. Note that the table is sufficiently large and the die never falls off during the game.", "constraint": "", "input": "The input consists of one or more command sequences, each of which corresponds to a single game. The first line of a command sequence contains a positive integer, representing the number of the following command lines in the sequence. You may assume that this number is less than or equal to 1024. A line containing a zero indicates the end of the input. Each command line includes a command that is one of north, east, south, and west. You may assume that no white space occurs in any line.", "output": "For each command sequence, output one line containing solely the number of the top face at the time when the game is finished.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\nnorth\n3\nnorth\neast\nsouth\n0\n output: 5\n1"], "Pid": "p00790", "ProblemText": "Task Description: Life is not easy. Sometimes it is beyond your control. Now, as contestants of ACM ICPC, you might be just tasting the bitter of life. But don't worry! Do not look only on the dark side of life, but look also on the bright side. Life may be an enjoyable game of chance, like throwing dice. Do or die! Then, at last, you might be able to find the route to victory.\n\nThis problem comes from a game using a die. By the way, do you know a die? It has nothing to do with \"death. \" A die is a cubic object with six faces, each of which represents a different number from one to six and is marked with the corresponding number of spots. Since it is usually used in pair, \"a die\" is rarely used word. You might have heard a famous phrase \"the die is cast, \" though.\n\nWhen a game starts, a die stands still on a flat table. During the game, the die is tumbled in all directions by the dealer. You will win the game if you can predict the number seen on the top face at the time when the die stops tumbling.\n\nNow you are requested to write a program that simulates the rolling of a die. For simplicity, we assume that the die neither slip nor jumps but just rolls on the table in four directions, that is, north, east, south, and west. At the beginning of every game, the dealer puts the die at the center of the table and adjusts its direction so that the numbers one, two, and three are seen on the top, north, and west faces, respectively. For the other three faces, we do not explicitly specify anything but tell you the golden rule: the sum of the numbers on any pair of opposite faces is always seven.\n\nYour program should accept a sequence of commands, each of which is either \"north\", \"east\", \"south\", or \"west\". A \"north\" command tumbles the die down to north, that is, the top face becomes the new north, the north becomes the new bottom, and so on. More precisely, the die is rotated around its north bottom edge to the north direction and the rotation angle is 9 degrees. Other commands also tumble the die accordingly to their own directions. Your program should calculate the number finally shown on the top after performing the commands in the sequence. Note that the table is sufficiently large and the die never falls off during the game.\nTask Input: The input consists of one or more command sequences, each of which corresponds to a single game. The first line of a command sequence contains a positive integer, representing the number of the following command lines in the sequence. You may assume that this number is less than or equal to 1024. A line containing a zero indicates the end of the input. Each command line includes a command that is one of north, east, south, and west. You may assume that no white space occurs in any line.\nTask Output: For each command sequence, output one line containing solely the number of the top face at the time when the game is finished.\nTask Samples: input: 1\nnorth\n3\nnorth\neast\nsouth\n0\n output: 5\n1\n\n" }, { "title": "Problem D: Trapezoids", "content": "If you are a computer user, you should have seen pictures drawn with ASCII characters. Such a picture may not look as good as GIF or Postscript pictures, but is much easier to handle. ASCII pictures can easily be drawn using text editors, and can convey graphical information using only text-based media. Program s extracting information from such pictures may be useful.\n\nWe are interested in simple pictures of trapezoids, consisting only of asterisk('*') characters and blank spaces. A trapezoid (trapezium in the Queen's English) is a four-side polygon where at least one pair of its sides is parallel. Furthermore, the picture in this problem satisfies the following conditions.\n\nAll the asterisks in the picture belong to sides of some trapezoid.\n\nTwo sides of a trapezoid are horizontal and the other two are vertical or incline 45 degrees.\n\nEvery side is more than 2 characters long.\n\nTwo distinct trapezoids do not share any asterisk characters.\n\nSides of two trapezoids do not touch. That is, asterisks of one trapezoid do not appear in eight neighbors of asterisks of a different trapezoid. For example, the following arrangements never appear.\n **** | **** | ******\n * * | * * *** | * *\n **** | ******* * | ****\n **** | *** | ****\n * * | | * *\n **** | | ****\n\nSome trapezoids may appear inside others. For example, the following is a valid picture.\n\n*********\n* *\n* *** *\n* * * *\n* ***** *\n* *\n*********\n\nYour task is to recognize trapezoids in the picture and to calculate the area of each trapezoid. The area of a trapezoid is the number of characters on or inside its four sides, including the areas of the trapezoids inside it, if any.", "constraint": "", "input": "The input contains several descriptions of pictures. Each of then starts with a line containing an integer h (1 <= h <= 1000), where h is the height (number of lines) of the picture. Each line of the picture consists only of asterisk and space characters, and contains less than 80 characters. The lines of the picture do not necessarily have the same length and may contain redundant space characters at the end. After the last picture, and integer zero terminates the input.", "output": "For each picture, your program should produce output lines each containing two integers m and n is this order, which means there are n trapezoids of area m in the picture. output lines for one picture should be in ascending order on m and count all the trapezoids in the picture.\n\nOutput lines for two pictures should be separated by a line containing ten hyphen ('-') characters. This separator line should not appear before the output for the first picture nor after the output for the last.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n********\n* *\n* *** *\n* * * *\n* *** *\n* *\n********\n9\n\n***\n* *\n***** *****\n * *\n *** *****\n * *\n * *\n ***\n11\n **** *******************\n * * ********* * *\n ****** * * **** * ********* *\n * *** * * * * * * *\n*** * * * * **** ******* * * *** *** * *\n* * * ***** * * * * * * * * * * *\n*** * * *** * * *** *** * *\n ********* * * * *\n * ********************* *\n * *\n *****************************\n0\n(Spacing between lines in pictures is made narrower for better appearance. Note that a blank line exists as the first line of the second picture.)\n output: 9 1\n56 1\n----------\n12 2\n15 1\n----------\n9 3\n12 2\n15 2\n63 1\n105 1\n264 1"], "Pid": "p00791", "ProblemText": "Task Description: If you are a computer user, you should have seen pictures drawn with ASCII characters. Such a picture may not look as good as GIF or Postscript pictures, but is much easier to handle. ASCII pictures can easily be drawn using text editors, and can convey graphical information using only text-based media. Program s extracting information from such pictures may be useful.\n\nWe are interested in simple pictures of trapezoids, consisting only of asterisk('*') characters and blank spaces. A trapezoid (trapezium in the Queen's English) is a four-side polygon where at least one pair of its sides is parallel. Furthermore, the picture in this problem satisfies the following conditions.\n\nAll the asterisks in the picture belong to sides of some trapezoid.\n\nTwo sides of a trapezoid are horizontal and the other two are vertical or incline 45 degrees.\n\nEvery side is more than 2 characters long.\n\nTwo distinct trapezoids do not share any asterisk characters.\n\nSides of two trapezoids do not touch. That is, asterisks of one trapezoid do not appear in eight neighbors of asterisks of a different trapezoid. For example, the following arrangements never appear.\n **** | **** | ******\n * * | * * *** | * *\n **** | ******* * | ****\n **** | *** | ****\n * * | | * *\n **** | | ****\n\nSome trapezoids may appear inside others. For example, the following is a valid picture.\n\n*********\n* *\n* *** *\n* * * *\n* ***** *\n* *\n*********\n\nYour task is to recognize trapezoids in the picture and to calculate the area of each trapezoid. The area of a trapezoid is the number of characters on or inside its four sides, including the areas of the trapezoids inside it, if any.\nTask Input: The input contains several descriptions of pictures. Each of then starts with a line containing an integer h (1 <= h <= 1000), where h is the height (number of lines) of the picture. Each line of the picture consists only of asterisk and space characters, and contains less than 80 characters. The lines of the picture do not necessarily have the same length and may contain redundant space characters at the end. After the last picture, and integer zero terminates the input.\nTask Output: For each picture, your program should produce output lines each containing two integers m and n is this order, which means there are n trapezoids of area m in the picture. output lines for one picture should be in ascending order on m and count all the trapezoids in the picture.\n\nOutput lines for two pictures should be separated by a line containing ten hyphen ('-') characters. This separator line should not appear before the output for the first picture nor after the output for the last.\nTask Samples: input: 7\n********\n* *\n* *** *\n* * * *\n* *** *\n* *\n********\n9\n\n***\n* *\n***** *****\n * *\n *** *****\n * *\n * *\n ***\n11\n **** *******************\n * * ********* * *\n ****** * * **** * ********* *\n * *** * * * * * * *\n*** * * * * **** ******* * * *** *** * *\n* * * ***** * * * * * * * * * * *\n*** * * *** * * *** *** * *\n ********* * * * *\n * ********************* *\n * *\n *****************************\n0\n(Spacing between lines in pictures is made narrower for better appearance. Note that a blank line exists as the first line of the second picture.)\n output: 9 1\n56 1\n----------\n12 2\n15 1\n----------\n9 3\n12 2\n15 2\n63 1\n105 1\n264 1\n\n" }, { "title": "Problem E: Mirror Illusion", "content": "A rich man has a square room with mirrors for security or just for fun. Each side of the room is eight meters wide. The floor, the ceiling and the walls are not special; however, the room can be equipped with a lot of mirrors on the walls or as vertical partitions.\n\nEvery mirror is one meter wide, as tall as the wall, double-side, perfectly reflective, and ultimately thin.\n\nPoles to fix mirrors are located at the corners of the room, on the walls and inside the room. Their locations are the 81 lattice points at intervals of one meter. A mirror can be fixed between two poles which are one meter distant from each other. If we use the sign \"+\" to represent a pole, the overview of the room can be illustrated as follows.\n\nLet us denote a location on the floor by (x, y) in a rectangular coordinate system. For example, the rectangular coordinates of the four corners of the room are (0,0), (8,0), (0,8) and (8,8), respectively. The location (x, y) is in the room if and only if the conditions 0 <= x <= 8 and 0 <= y <= 8 are satisfied. If i and j are integers satisfying the conditions 0 <= i <= 8 and 0 <= j <= 8, we can denote by (i, j) the locations of poles.\n\nOne day a thief intruded into this room possibly by breaking the ceiling. He stood at (0.75,0.25) and looked almost toward the center of the room. Precisely speaking, he looked toward the point (1,0.5) of the same height as his eyes. So what did he see in the center of his sight? He would have seen one of the walls or himself as follows.\n\nIf there existed no mirror, he saw the wall at (8,7.5)\n\nIf there existed one mirror between two poles at (8,7) and (8,8), he saw the wall at (7.5,8). (Let us denote the line between these two poles by (8,7)-(8,8). )\n\nIf there were four mirrors on (8,7)-(8,8), (7,8)-(8,8), (0,0)-(0,1) and (0,0)-(1,0), he saw himself at (0.75,0.25).\n\nIf there were four mirrors on (2,1)-(2,2), (1,2)-(2,2), (0,0)-(0,1) and (0,0)-(1,0), he saw himself at (0.75,0.25)\nYour job is to write a program that reports the location at which the thief saw one of the walls or himself with the given mirror arrangements.", "constraint": "", "input": "The input contains multiple data sets, each representing how to equip the room with mirrors. A data set is given in the following format.\n\nn\nd_1 i_1 j_1\nd_2 i_2 j_2\n. . .\nd_n i_n j_n\n\nThe first integer n is the number of mirrors, such that 0 <= n <= 144. The way the k-th (1 <= k <= n) mirror is fixed is given by d_k and (i_k, j_k). d_k is either 'x' or 'y', which gives the direction of the mirror. If d_k is 'x', the mirror is fixed on (i_k, j_k)-(i_k + 1, j_k). If d_k is 'y', the mirror is fixed on (i_k, j_k) (i_k, j_k + 1). The end of the input is indicated by a negative integer.", "output": "For each data set, your program should output the location (x, y) at which the thief saw one of the walls or himself. The location should be reported in a line containing two integers which are separated by a single space and respectively represent x and y in centimeter as the unit of length. No extra lines nor spaces are allowed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0\n1\ny 8 7\n4\ny 8 7\nx 7 8\ny 0 0\nx 0 0\n4\ny 2 1\nx 1 2\ny 0 0\nx 0 0\n-1\n output: 800 750\n750 800\n75 25\n75 25"], "Pid": "p00792", "ProblemText": "Task Description: A rich man has a square room with mirrors for security or just for fun. Each side of the room is eight meters wide. The floor, the ceiling and the walls are not special; however, the room can be equipped with a lot of mirrors on the walls or as vertical partitions.\n\nEvery mirror is one meter wide, as tall as the wall, double-side, perfectly reflective, and ultimately thin.\n\nPoles to fix mirrors are located at the corners of the room, on the walls and inside the room. Their locations are the 81 lattice points at intervals of one meter. A mirror can be fixed between two poles which are one meter distant from each other. If we use the sign \"+\" to represent a pole, the overview of the room can be illustrated as follows.\n\nLet us denote a location on the floor by (x, y) in a rectangular coordinate system. For example, the rectangular coordinates of the four corners of the room are (0,0), (8,0), (0,8) and (8,8), respectively. The location (x, y) is in the room if and only if the conditions 0 <= x <= 8 and 0 <= y <= 8 are satisfied. If i and j are integers satisfying the conditions 0 <= i <= 8 and 0 <= j <= 8, we can denote by (i, j) the locations of poles.\n\nOne day a thief intruded into this room possibly by breaking the ceiling. He stood at (0.75,0.25) and looked almost toward the center of the room. Precisely speaking, he looked toward the point (1,0.5) of the same height as his eyes. So what did he see in the center of his sight? He would have seen one of the walls or himself as follows.\n\nIf there existed no mirror, he saw the wall at (8,7.5)\n\nIf there existed one mirror between two poles at (8,7) and (8,8), he saw the wall at (7.5,8). (Let us denote the line between these two poles by (8,7)-(8,8). )\n\nIf there were four mirrors on (8,7)-(8,8), (7,8)-(8,8), (0,0)-(0,1) and (0,0)-(1,0), he saw himself at (0.75,0.25).\n\nIf there were four mirrors on (2,1)-(2,2), (1,2)-(2,2), (0,0)-(0,1) and (0,0)-(1,0), he saw himself at (0.75,0.25)\nYour job is to write a program that reports the location at which the thief saw one of the walls or himself with the given mirror arrangements.\nTask Input: The input contains multiple data sets, each representing how to equip the room with mirrors. A data set is given in the following format.\n\nn\nd_1 i_1 j_1\nd_2 i_2 j_2\n. . .\nd_n i_n j_n\n\nThe first integer n is the number of mirrors, such that 0 <= n <= 144. The way the k-th (1 <= k <= n) mirror is fixed is given by d_k and (i_k, j_k). d_k is either 'x' or 'y', which gives the direction of the mirror. If d_k is 'x', the mirror is fixed on (i_k, j_k)-(i_k + 1, j_k). If d_k is 'y', the mirror is fixed on (i_k, j_k) (i_k, j_k + 1). The end of the input is indicated by a negative integer.\nTask Output: For each data set, your program should output the location (x, y) at which the thief saw one of the walls or himself. The location should be reported in a line containing two integers which are separated by a single space and respectively represent x and y in centimeter as the unit of length. No extra lines nor spaces are allowed.\nTask Samples: input: 0\n1\ny 8 7\n4\ny 8 7\nx 7 8\ny 0 0\nx 0 0\n4\ny 2 1\nx 1 2\ny 0 0\nx 0 0\n-1\n output: 800 750\n750 800\n75 25\n75 25\n\n" }, { "title": "Problem F: Heavenly Jewels", "content": "There is a flat island whose shape is a perfect square. On this island, there are three habitants whose names are IC, PC, and ACM Every day, one jewel is dropped from the heaven. Just as the jewel touches the ground, IC, PC, and ACM leave their houses simultaneously, run with the same speed, and then a person who first touched the jewel can get the jewel. Hence, the person whose house is nearest to the location of the jewel is the winner of that day.\n\nThey always have a quarrel with each other, and therefore their houses are located at distinct places. The locations of their houses are fixed. This jewel falls at a random point on the island, that is, all points on the island have even chance.\n\nWhen three are two or more persons whose houses are simultaneously nearest, the last person in the order of\n\nIC, PC, ACM\n\nobtains the jewel.\n\nOur interest is to know the probability for IC to get the jewel under this situation.", "constraint": "", "input": "The input describes one problem instance per line. Each line contains the x- and y-coordinates of IC's home, those of PC's, and those of ACM's in this order. Note that the houses of IC, PC and ACM are located at distinct places. The end of the input is indicated by a line with six zeros.\n\nThe coordinates of the whole island are given by (0,10000) * (0,10000) and coordinates of houses are given in integer numbers between 1 and 9999, inclusive. It should be noted that the locations of the jewels are arbitrary places on the island and their coordinate values are not necessarily integers.", "output": "For each input line, your program should output its sequence number starting from 1, and the probability for the instance. The computed probability values should have errors less than 10-5.\n\nThe sequence number and the probability should be printed on the same line. The two numbers should be separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2000 2000 8000 8000 9000 9500\n2500 2500 7500 2500 2500 7500\n0 0 0 0 0 0\n output: 1 0.50000\n2 0.25000"], "Pid": "p00793", "ProblemText": "Task Description: There is a flat island whose shape is a perfect square. On this island, there are three habitants whose names are IC, PC, and ACM Every day, one jewel is dropped from the heaven. Just as the jewel touches the ground, IC, PC, and ACM leave their houses simultaneously, run with the same speed, and then a person who first touched the jewel can get the jewel. Hence, the person whose house is nearest to the location of the jewel is the winner of that day.\n\nThey always have a quarrel with each other, and therefore their houses are located at distinct places. The locations of their houses are fixed. This jewel falls at a random point on the island, that is, all points on the island have even chance.\n\nWhen three are two or more persons whose houses are simultaneously nearest, the last person in the order of\n\nIC, PC, ACM\n\nobtains the jewel.\n\nOur interest is to know the probability for IC to get the jewel under this situation.\nTask Input: The input describes one problem instance per line. Each line contains the x- and y-coordinates of IC's home, those of PC's, and those of ACM's in this order. Note that the houses of IC, PC and ACM are located at distinct places. The end of the input is indicated by a line with six zeros.\n\nThe coordinates of the whole island are given by (0,10000) * (0,10000) and coordinates of houses are given in integer numbers between 1 and 9999, inclusive. It should be noted that the locations of the jewels are arbitrary places on the island and their coordinate values are not necessarily integers.\nTask Output: For each input line, your program should output its sequence number starting from 1, and the probability for the instance. The computed probability values should have errors less than 10-5.\n\nThe sequence number and the probability should be printed on the same line. The two numbers should be separated by a space.\nTask Samples: input: 2000 2000 8000 8000 9000 9500\n2500 2500 7500 2500 2500 7500\n0 0 0 0 0 0\n output: 1 0.50000\n2 0.25000\n\n" }, { "title": "Problem G: Walking Ant", "content": "Ants are quite diligent. They sometimes build their nests beneath flagstones.\n\nHere, an ant is walking in a rectangular area tiled with square flagstones, seeking the only hole leading to her nest.\n\nThe ant takes exactly one second to move from one flagstone to another. That is, if the ant is on the flagstone with coordinates (x, y) at time t, she will be on one of the five flagstones with the following coordinates at time t + 1:\n\n(x, y), (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1).\n\nThe ant cannot go out of the rectangular area. The ant can visit the same flagstone more than once.\n\nInsects are easy to starve. The ant has to go back to her nest without starving. Physical strength of the ant is expressed by the unit \"HP\". Initially, the ant has the strength of 6 HP. Every second, she loses 1 HP. When the ant arrives at a flagstone with some food on it, she eats a small piece of the food there, and recovers her strength to the maximum value, i. e. , 6 HP, without taking any time. The food is plenty enough, and she can eat it as many times as she wants.\n\nWhen the ant's strength gets down to 0 HP, she dies and will not move anymore. If the ant's strength gets down to 0 HP at the moment she moves to a flagstone, she does not effectively reach the flagstone: even if some food is on it, she cannot eat it; even if the hole is on that stone, she has to die at the entrance of her home.\n\nIf there is a puddle on a flagstone, the ant cannot move there.\n\nYour job is to write a program which computes the minimum possible time for the ant to reach the hole with positive strength from her start position, if ever possible.", "constraint": "", "input": "The input consists of multiple maps, each representing the size and the arrangement of the rectangular area. A map is given in the following format.\n\nw h\nd_11 d_12 d_13 . . . d_1w\nd_2 d_22 d_23 . . . d_2w\n . . .\nd_h1 d_h2 d_h3 . . . d_hw\n\nThe integers w and h are the numbers of flagstones in the x- and y-directions, respectively. w and h are less than or equal to 8. The integer d_yx represents the state of the flagstone with coordinates (x, y) as follows.\n\n0: There is a puddle on the flagstone, and the ant cannot move there.\n\n1,2: Nothing exists on the flagstone, and the ant can move there. '2' indicates where the ant initially stands.\n\n3: The hole to the nest is on the flagstone.\n\n4: Some food is on the flagstone.\n\nThere is one and only one flagstone with a hole. Not more than five flagstones have food on them.\n\nThe end of the input is indicated by a line with two zeros.\n\nInteger numbers in an input line are separated by at least one space character.", "output": "for each map in the input, your program should output one line containing one integer representing the minimum time. If the ant cannot return to her nest, your program should output -1 instead of the minimum time.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3\n2 1 1\n1 1 0\n1 1 3\n8 4\n2 1 1 0 1 1 1 0\n1 0 4 1 1 0 4 1\n1 0 0 0 0 0 0 1\n1 1 1 4 1 1 1 3\n8 5\n1 2 1 1 1 1 1 4\n1 0 0 0 1 0 0 1\n1 4 1 0 1 1 0 1\n1 0 0 0 0 3 0 1\n1 1 4 1 1 1 1 1\n0 0\n output: 4\n-1\n13"], "Pid": "p00794", "ProblemText": "Task Description: Ants are quite diligent. They sometimes build their nests beneath flagstones.\n\nHere, an ant is walking in a rectangular area tiled with square flagstones, seeking the only hole leading to her nest.\n\nThe ant takes exactly one second to move from one flagstone to another. That is, if the ant is on the flagstone with coordinates (x, y) at time t, she will be on one of the five flagstones with the following coordinates at time t + 1:\n\n(x, y), (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1).\n\nThe ant cannot go out of the rectangular area. The ant can visit the same flagstone more than once.\n\nInsects are easy to starve. The ant has to go back to her nest without starving. Physical strength of the ant is expressed by the unit \"HP\". Initially, the ant has the strength of 6 HP. Every second, she loses 1 HP. When the ant arrives at a flagstone with some food on it, she eats a small piece of the food there, and recovers her strength to the maximum value, i. e. , 6 HP, without taking any time. The food is plenty enough, and she can eat it as many times as she wants.\n\nWhen the ant's strength gets down to 0 HP, she dies and will not move anymore. If the ant's strength gets down to 0 HP at the moment she moves to a flagstone, she does not effectively reach the flagstone: even if some food is on it, she cannot eat it; even if the hole is on that stone, she has to die at the entrance of her home.\n\nIf there is a puddle on a flagstone, the ant cannot move there.\n\nYour job is to write a program which computes the minimum possible time for the ant to reach the hole with positive strength from her start position, if ever possible.\nTask Input: The input consists of multiple maps, each representing the size and the arrangement of the rectangular area. A map is given in the following format.\n\nw h\nd_11 d_12 d_13 . . . d_1w\nd_2 d_22 d_23 . . . d_2w\n . . .\nd_h1 d_h2 d_h3 . . . d_hw\n\nThe integers w and h are the numbers of flagstones in the x- and y-directions, respectively. w and h are less than or equal to 8. The integer d_yx represents the state of the flagstone with coordinates (x, y) as follows.\n\n0: There is a puddle on the flagstone, and the ant cannot move there.\n\n1,2: Nothing exists on the flagstone, and the ant can move there. '2' indicates where the ant initially stands.\n\n3: The hole to the nest is on the flagstone.\n\n4: Some food is on the flagstone.\n\nThere is one and only one flagstone with a hole. Not more than five flagstones have food on them.\n\nThe end of the input is indicated by a line with two zeros.\n\nInteger numbers in an input line are separated by at least one space character.\nTask Output: for each map in the input, your program should output one line containing one integer representing the minimum time. If the ant cannot return to her nest, your program should output -1 instead of the minimum time.\nTask Samples: input: 3 3\n2 1 1\n1 1 0\n1 1 3\n8 4\n2 1 1 0 1 1 1 0\n1 0 4 1 1 0 4 1\n1 0 0 0 0 0 0 1\n1 1 1 4 1 1 1 3\n8 5\n1 2 1 1 1 1 1 4\n1 0 0 0 1 0 0 1\n1 4 1 0 1 1 0 1\n1 0 0 0 0 3 0 1\n1 1 4 1 1 1 1 1\n0 0\n output: 4\n-1\n13\n\n" }, { "title": "Problem H: Co-occurrence Search", "content": "A huge amount of information is being heaped on WWW. Albeit it is not well-organized, users can browse WWW as an unbounded source of up-to-date information, instead of consulting established but a little out-of-date encyclopedia. However, you can further exploit WWW by learning more about keyword search algorithms.\n\nFor example, if you want to get information on recent comparison between Windows and UNIX, you may expect to get relevant description out of a big bunch of Web texts, by extracting texts that contain both keywords \"Windows\" and \"UNIX\" close together.\n\nHere we have a simplified version of this co-occurrence keyword search problem, where the text and keywords are replaced by a string and key characters, respectively. A character string S of length n (1 <= n <= 1,000,000) and a set K of k distinct key characters a_1, . . . , a_k (1 <= k <= 50) are given. Find every shortest substring of S that contains all of the key characters a_1, . . . , a_k.", "constraint": "", "input": "The input is a text file which contains only printable characters (ASCII codes 21 to 7E in hexadecimal) and newlines. No white space such as space or tab appears in the input.\n\nThe text is a sequence of the shortest string search problems described above. Each problem consists of character string S_i and key character set K_i (i = 1,2, . . . , p). Every S_i and K_i is followed by an empty line. However, any single newline between successive lines in a string should be ignored; that is, newlines are not part of the string. For various technical reasons, every line consists of at most 72 characters. Each key character set is given in a single line. The input is terminated by consecutive empty lines; p is not given explicitly.", "output": "All of p problems should be solved and their answers should be output in order. However, it is not requested to print all of the shortest substrings if more than one substring is found in a problem, since found substrings may be too much to check them all. Only the number of the substrings together with their representative is requested instead. That is, for each problem i, the number of the shortest substrings should be output followed by the first (or the leftmost) shortest substring s_i1, obeying the following format:\n\n\n the number of the shortest substrings for the i-th problem\n empty line\n the first line of s_i1\n the second line of s_i1\n . . .\n the last line of s_i1\n empty line for the substring termination \n\n\nwhere each line of the shortest substring s_i1 except for the last line should consist of exactly 72 characters and the last line (or the single line if the substring is shorter than or equal to 72 characters, of course) should not exceed 72 characters.\n\nIf there is no such substring for a problem, the output will be a 0 followed by an empty line; no more successive empty line should be output because there is no substring to be terminated.", "content_img": false, "lang": "en", "error": false, "samples": ["input: Thefirstexampleistrivial.\n\nmfv\n\nAhugeamountofinformationisbeingheapedonWWW.Albeititisnot\nwell-organized,userscanbrowseWWWasanunboundedsourceof\nup-to-dateinformation,insteadofconsultingestablishedbutalittle\nout-of-dateencyclopedia.However,youcanfurtherexploitWWWby\nlearningmoreaboutkeywordsearchalgorithms.Forexample,ifyou\nwanttogetinformationonrecentcomparisonbetweenWindowsandUNIX,\nyoumayexpecttogetrelevantdescriptionoutofabigbunchofWeb\ntexts,byextractingtextsthatcontainbothkeywords\"Windows\"and\"UNIX\"\nclosetogether.\n\nbWn\n\n3.1415926535897932384626433832795028841971693993751058209749445923078164\n\npi\n\nWagner,Bach,Beethoven,Chopin,Brahms,Hindemith,Ives,Suk,Mozart,Stravinsky\n\nWeary\n\nASCIIcharacterssuchas+,*,[,#,<,},_arenotexcludedinagivenstringas\nthisexampleillustratesbyitself.Youshouldnotforgetthem.Onemorefact\nyoushouldnoticeisthatuppercaselettersandlowercaselettersare\ndistinguishedinthisproblem.Don'tidentify\"g\"and\"G\",forexmaple.\nHowever,weareafraidthatthisexamplegivesyoutoomuchhint!\n\n![GsC_l\n\nETAONRISHDLFCMUGYPWBVKXJQZ\n\nABCDEFGHIJKLMNOPQRSTUVWXYZ\n output: 1\n\nfirstexampleistriv\n\n7\n\nnWWW.Alb\n\n0\n\n1\n\nWagner,Bach,Beethoven,Chopin,Brahms,Hindemith,Ives,Suk,Mozart,Stravinsky\n\n1\n\nCIIcharacterssuchas+,*,[,#,<,},_arenotexcludedinagivenstringasthisexampl\neillustratesbyitself.Youshouldnotforgetthem.Onemorefactyoushouldnoticeis\nthatuppercaselettersandlowercaselettersaredistinguishedinthisproblem.Don\n'tidentify\"g\"and\"G\",forexmaple.However,weareafraidthatthisexamplegivesyo\nutoomuchhint!\n\n1\n\nETAONRISHDLFCMUGYPWBVKXJQZ"], "Pid": "p00795", "ProblemText": "Task Description: A huge amount of information is being heaped on WWW. Albeit it is not well-organized, users can browse WWW as an unbounded source of up-to-date information, instead of consulting established but a little out-of-date encyclopedia. However, you can further exploit WWW by learning more about keyword search algorithms.\n\nFor example, if you want to get information on recent comparison between Windows and UNIX, you may expect to get relevant description out of a big bunch of Web texts, by extracting texts that contain both keywords \"Windows\" and \"UNIX\" close together.\n\nHere we have a simplified version of this co-occurrence keyword search problem, where the text and keywords are replaced by a string and key characters, respectively. A character string S of length n (1 <= n <= 1,000,000) and a set K of k distinct key characters a_1, . . . , a_k (1 <= k <= 50) are given. Find every shortest substring of S that contains all of the key characters a_1, . . . , a_k.\nTask Input: The input is a text file which contains only printable characters (ASCII codes 21 to 7E in hexadecimal) and newlines. No white space such as space or tab appears in the input.\n\nThe text is a sequence of the shortest string search problems described above. Each problem consists of character string S_i and key character set K_i (i = 1,2, . . . , p). Every S_i and K_i is followed by an empty line. However, any single newline between successive lines in a string should be ignored; that is, newlines are not part of the string. For various technical reasons, every line consists of at most 72 characters. Each key character set is given in a single line. The input is terminated by consecutive empty lines; p is not given explicitly.\nTask Output: All of p problems should be solved and their answers should be output in order. However, it is not requested to print all of the shortest substrings if more than one substring is found in a problem, since found substrings may be too much to check them all. Only the number of the substrings together with their representative is requested instead. That is, for each problem i, the number of the shortest substrings should be output followed by the first (or the leftmost) shortest substring s_i1, obeying the following format:\n\n\n the number of the shortest substrings for the i-th problem\n empty line\n the first line of s_i1\n the second line of s_i1\n . . .\n the last line of s_i1\n empty line for the substring termination \n\n\nwhere each line of the shortest substring s_i1 except for the last line should consist of exactly 72 characters and the last line (or the single line if the substring is shorter than or equal to 72 characters, of course) should not exceed 72 characters.\n\nIf there is no such substring for a problem, the output will be a 0 followed by an empty line; no more successive empty line should be output because there is no substring to be terminated.\nTask Samples: input: Thefirstexampleistrivial.\n\nmfv\n\nAhugeamountofinformationisbeingheapedonWWW.Albeititisnot\nwell-organized,userscanbrowseWWWasanunboundedsourceof\nup-to-dateinformation,insteadofconsultingestablishedbutalittle\nout-of-dateencyclopedia.However,youcanfurtherexploitWWWby\nlearningmoreaboutkeywordsearchalgorithms.Forexample,ifyou\nwanttogetinformationonrecentcomparisonbetweenWindowsandUNIX,\nyoumayexpecttogetrelevantdescriptionoutofabigbunchofWeb\ntexts,byextractingtextsthatcontainbothkeywords\"Windows\"and\"UNIX\"\nclosetogether.\n\nbWn\n\n3.1415926535897932384626433832795028841971693993751058209749445923078164\n\npi\n\nWagner,Bach,Beethoven,Chopin,Brahms,Hindemith,Ives,Suk,Mozart,Stravinsky\n\nWeary\n\nASCIIcharacterssuchas+,*,[,#,<,},_arenotexcludedinagivenstringas\nthisexampleillustratesbyitself.Youshouldnotforgetthem.Onemorefact\nyoushouldnoticeisthatuppercaselettersandlowercaselettersare\ndistinguishedinthisproblem.Don'tidentify\"g\"and\"G\",forexmaple.\nHowever,weareafraidthatthisexamplegivesyoutoomuchhint!\n\n![GsC_l\n\nETAONRISHDLFCMUGYPWBVKXJQZ\n\nABCDEFGHIJKLMNOPQRSTUVWXYZ\n output: 1\n\nfirstexampleistriv\n\n7\n\nnWWW.Alb\n\n0\n\n1\n\nWagner,Bach,Beethoven,Chopin,Brahms,Hindemith,Ives,Suk,Mozart,Stravinsky\n\n1\n\nCIIcharacterssuchas+,*,[,#,<,},_arenotexcludedinagivenstringasthisexampl\neillustratesbyitself.Youshouldnotforgetthem.Onemorefactyoushouldnoticeis\nthatuppercaselettersandlowercaselettersaredistinguishedinthisproblem.Don\n'tidentify\"g\"and\"G\",forexmaple.However,weareafraidthatthisexamplegivesyo\nutoomuchhint!\n\n1\n\nETAONRISHDLFCMUGYPWBVKXJQZ\n\n" }, { "title": "Problem A: Lost in Space", "content": "William Robinson was completely puzzled in the music room; he could not find his triangle in\nhis bag. He was sure that he had prepared it the night before. He remembered its clank when\nhe had stepped on the school bus early that morning. No, not in his dream. His triangle was\nquite unique: no two sides had the same length, which made his favorite peculiar jingle. He\ninsisted to the music teacher, Mr. Smith, that his triangle had probably been stolen by those\naliens and thrown away into deep space.\n\nYour mission is to help Will find his triangle in space. His triangle has been made invisible by the\naliens, but candidate positions of its vertices are somehow known. You have to tell which three\nof them make his triangle. Having gone through worm-holes, the triangle may have changed its\nsize. However, even in that case, all the sides are known to be enlarged or shrunk equally, that\nis, the transformed triangle is similar to the original.", "constraint": "", "input": "The very first line of the input has an integer which is the number of data sets. Each data set\ngives data for one incident such as that of Will 's. At least one and at most ten data sets are\ngiven.\n\nThe first line of each data set contains three decimals that give lengths of the sides of the original\ntriangle, measured in centimeters. Three vertices of the original triangle are named P, Q, and\nR. Three decimals given in the first line correspond to the lengths of sides QR, RP, and PQ, in\nthis order. They are separated by one or more space characters.\n\nThe second line of a data set has an integer which is the number of points in space to be\nconsidered as candidates for vertices. At least three and at most thirty points are considered.\n\nThe rest of the data set are lines containing coordinates of candidate points, in light years. Each\nline has three decimals, corresponding to x, y, and z coordinates, separated by one or more space\ncharacters. Points are numbered in the order of their appearances, starting from one.\n\nAmong all the triangles formed by three of the given points, only one of them is similar to the\noriginal, that is, ratios of the lengths of any two sides are equal to the corresponding ratios of\nthe original allowing an error of less than 0.01 percent. Other triangles have some of the ratios\ndifferent from the original by at least 0.1 percent.\n\nThe origin of the coordinate system is not the center of the earth but the center of our galaxy.\nNote that negative coordinate values may appear here. As they are all within or close to our galaxy, coordinate values are less than one hundred thousand light years. You don 't have to\ntake relativistic effects into account, i. e. , you may assume that we are in a Euclidean space. You\nmay also assume in your calculation that one light year is equal to 9.461 * 10^12 kilometers.\n\nA succeeding data set, if any, starts from the line immediately following the last line of the\npreceding data set.", "output": "For each data set, one line should be output. That line should contain the point numbers of the\nthree vertices of the similar triangle, separated by a space character. They should be reported\nin the order P, Q, and then R.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n 50.36493 81.61338 79.96592\n5\n -10293.83 -4800.033 -5296.238\n 14936.30 6964.826 7684.818\n -4516.069 25748.41 -27016.06\n 18301.59 -11946.25 5380.309\n 27115.20 43415.93 -71607.81\n 11.51547 13.35555 14.57307\n5\n -56292.27 2583.892 67754.62\n -567.5082 -756.2763 -118.7268\n -1235.987 -213.3318 -216.4862\n -317.6108 -54.81976 -55.63033\n 22505.44 -40752.88 27482.94\n output: 1 2 4\n3 4 2"], "Pid": "p00796", "ProblemText": "Task Description: William Robinson was completely puzzled in the music room; he could not find his triangle in\nhis bag. He was sure that he had prepared it the night before. He remembered its clank when\nhe had stepped on the school bus early that morning. No, not in his dream. His triangle was\nquite unique: no two sides had the same length, which made his favorite peculiar jingle. He\ninsisted to the music teacher, Mr. Smith, that his triangle had probably been stolen by those\naliens and thrown away into deep space.\n\nYour mission is to help Will find his triangle in space. His triangle has been made invisible by the\naliens, but candidate positions of its vertices are somehow known. You have to tell which three\nof them make his triangle. Having gone through worm-holes, the triangle may have changed its\nsize. However, even in that case, all the sides are known to be enlarged or shrunk equally, that\nis, the transformed triangle is similar to the original.\nTask Input: The very first line of the input has an integer which is the number of data sets. Each data set\ngives data for one incident such as that of Will 's. At least one and at most ten data sets are\ngiven.\n\nThe first line of each data set contains three decimals that give lengths of the sides of the original\ntriangle, measured in centimeters. Three vertices of the original triangle are named P, Q, and\nR. Three decimals given in the first line correspond to the lengths of sides QR, RP, and PQ, in\nthis order. They are separated by one or more space characters.\n\nThe second line of a data set has an integer which is the number of points in space to be\nconsidered as candidates for vertices. At least three and at most thirty points are considered.\n\nThe rest of the data set are lines containing coordinates of candidate points, in light years. Each\nline has three decimals, corresponding to x, y, and z coordinates, separated by one or more space\ncharacters. Points are numbered in the order of their appearances, starting from one.\n\nAmong all the triangles formed by three of the given points, only one of them is similar to the\noriginal, that is, ratios of the lengths of any two sides are equal to the corresponding ratios of\nthe original allowing an error of less than 0.01 percent. Other triangles have some of the ratios\ndifferent from the original by at least 0.1 percent.\n\nThe origin of the coordinate system is not the center of the earth but the center of our galaxy.\nNote that negative coordinate values may appear here. As they are all within or close to our galaxy, coordinate values are less than one hundred thousand light years. You don 't have to\ntake relativistic effects into account, i. e. , you may assume that we are in a Euclidean space. You\nmay also assume in your calculation that one light year is equal to 9.461 * 10^12 kilometers.\n\nA succeeding data set, if any, starts from the line immediately following the last line of the\npreceding data set.\nTask Output: For each data set, one line should be output. That line should contain the point numbers of the\nthree vertices of the similar triangle, separated by a space character. They should be reported\nin the order P, Q, and then R.\nTask Samples: input: 2\n 50.36493 81.61338 79.96592\n5\n -10293.83 -4800.033 -5296.238\n 14936.30 6964.826 7684.818\n -4516.069 25748.41 -27016.06\n 18301.59 -11946.25 5380.309\n 27115.20 43415.93 -71607.81\n 11.51547 13.35555 14.57307\n5\n -56292.27 2583.892 67754.62\n -567.5082 -756.2763 -118.7268\n -1235.987 -213.3318 -216.4862\n -317.6108 -54.81976 -55.63033\n 22505.44 -40752.88 27482.94\n output: 1 2 4\n3 4 2\n\n" }, { "title": "Problem B: Family Tree", "content": "A professor of anthropology was interested in people living in isolated islands and their history.\nHe collected their family trees to conduct some anthropological experiment. For the experiment,\nhe needed to process the family trees with a computer. For that purpose he translated them\ninto text files. The following is an example of a text file representing a family tree.\n\nJohn\n Robert\n Frank\n Andrew\n Nancy\n David\n\nEach line contains the given name of a person. The name in the first line is the oldest ancestor\nin this family tree. The family tree contains only the descendants of the oldest ancestor. Their\nhusbands and wives are not shown in the family tree. The children of a person are indented\nwith one more space than the parent. For example, Robert and Nancy are the children of John,\nand Frank and Andrew are the children of Robert. David is indented with one more space than\nRobert, but he is not a child of Robert, but of Nancy. To represent a family tree in this way,\nthe professor excluded some people from the family trees so that no one had both parents in a\nfamily tree.\n\nFor the experiment, the professor also collected documents of the families and extracted the\nset of statements about relations of two persons in each family tree. The following are some\nexamples of statements about the family above.\n\nJohn is the parent of Robert.\nRobert is a sibling of Nancy.\nDavid is a descendant of Robert.\n\nFor the experiment, he needs to check whether each statement is true or not. For example, the\nfirst two statements above are true and the last statement is false. Since this task is tedious, he\nwould like to check it by a computer program.", "constraint": "", "input": "The input contains several data sets. Each data set consists of a family tree and a set of\nstatements. The first line of each data set contains two integers n (0 < n < 1000) and m (0 < m < 1000) which represent the number of names in the family tree and the number of\nstatements, respectively. Each line of the input has less than 70 characters.\n\nAs a name, we consider any character string consisting of only alphabetic characters. The names\nin a family tree have less than 20 characters. The name in the first line of the family tree has\nno leading spaces. The other names in the family tree are indented with at least one space, i. e. ,\nthey are descendants of the person in the first line. You can assume that if a name in the family\ntree is indented with k spaces, the name in the next line is indented with at most k + 1 spaces.\nThis guarantees that each person except the oldest ancestor has his or her parent in the family\ntree. No name appears twice in the same family tree. Each line of the family tree contains no\nredundant spaces at the end.\n\nEach statement occupies one line and is written in one of the following formats, where X and\nY are different names in the family tree.\n\nX is a child of Y.\nX is the parent of Y.\nX is a sibling of Y.\nX is a descendant of Y.\nX is an ancestor of Y.\n\nNames not appearing in the family tree are never used in the statements. Consecutive words in\na statement are separated by a single space. Each statement contains no redundant spaces at\nthe beginning and at the end of the line.\n\nThe end of the input is indicated by two zeros.", "output": "For each statement in a data set, your program should output one line containing True or False.\nThe first letter of True or False in the output must be a capital. The output for each data set\nshould be followed by an empty line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 5\nJohn\n Robert\n Frank\n Andrew\n Nancy\n David\nRobert is a child of John.\nRobert is an ancestor of Andrew.\nRobert is a sibling of Nancy.\nNancy is the parent of Frank.\nJohn is a descendant of Andrew.\n2 1\nabc\n xyz\nxyz is a child of abc.\n0 0\n output: True\nTrue\nTrue\nFalse\nFalse\n\nTrue"], "Pid": "p00797", "ProblemText": "Task Description: A professor of anthropology was interested in people living in isolated islands and their history.\nHe collected their family trees to conduct some anthropological experiment. For the experiment,\nhe needed to process the family trees with a computer. For that purpose he translated them\ninto text files. The following is an example of a text file representing a family tree.\n\nJohn\n Robert\n Frank\n Andrew\n Nancy\n David\n\nEach line contains the given name of a person. The name in the first line is the oldest ancestor\nin this family tree. The family tree contains only the descendants of the oldest ancestor. Their\nhusbands and wives are not shown in the family tree. The children of a person are indented\nwith one more space than the parent. For example, Robert and Nancy are the children of John,\nand Frank and Andrew are the children of Robert. David is indented with one more space than\nRobert, but he is not a child of Robert, but of Nancy. To represent a family tree in this way,\nthe professor excluded some people from the family trees so that no one had both parents in a\nfamily tree.\n\nFor the experiment, the professor also collected documents of the families and extracted the\nset of statements about relations of two persons in each family tree. The following are some\nexamples of statements about the family above.\n\nJohn is the parent of Robert.\nRobert is a sibling of Nancy.\nDavid is a descendant of Robert.\n\nFor the experiment, he needs to check whether each statement is true or not. For example, the\nfirst two statements above are true and the last statement is false. Since this task is tedious, he\nwould like to check it by a computer program.\nTask Input: The input contains several data sets. Each data set consists of a family tree and a set of\nstatements. The first line of each data set contains two integers n (0 < n < 1000) and m (0 < m < 1000) which represent the number of names in the family tree and the number of\nstatements, respectively. Each line of the input has less than 70 characters.\n\nAs a name, we consider any character string consisting of only alphabetic characters. The names\nin a family tree have less than 20 characters. The name in the first line of the family tree has\nno leading spaces. The other names in the family tree are indented with at least one space, i. e. ,\nthey are descendants of the person in the first line. You can assume that if a name in the family\ntree is indented with k spaces, the name in the next line is indented with at most k + 1 spaces.\nThis guarantees that each person except the oldest ancestor has his or her parent in the family\ntree. No name appears twice in the same family tree. Each line of the family tree contains no\nredundant spaces at the end.\n\nEach statement occupies one line and is written in one of the following formats, where X and\nY are different names in the family tree.\n\nX is a child of Y.\nX is the parent of Y.\nX is a sibling of Y.\nX is a descendant of Y.\nX is an ancestor of Y.\n\nNames not appearing in the family tree are never used in the statements. Consecutive words in\na statement are separated by a single space. Each statement contains no redundant spaces at\nthe beginning and at the end of the line.\n\nThe end of the input is indicated by two zeros.\nTask Output: For each statement in a data set, your program should output one line containing True or False.\nThe first letter of True or False in the output must be a capital. The output for each data set\nshould be followed by an empty line.\nTask Samples: input: 6 5\nJohn\n Robert\n Frank\n Andrew\n Nancy\n David\nRobert is a child of John.\nRobert is an ancestor of Andrew.\nRobert is a sibling of Nancy.\nNancy is the parent of Frank.\nJohn is a descendant of Andrew.\n2 1\nabc\n xyz\nxyz is a child of abc.\n0 0\n output: True\nTrue\nTrue\nFalse\nFalse\n\nTrue\n\n" }, { "title": "Problem C: Push! !", "content": "Mr. Schwarz was a famous powerful pro wrestler. He starts a part time job as a warehouseman.\nHis task is to move a cargo to a goal by repeatedly pushing the cargo in the warehouse, of course,\nwithout breaking the walls and the pillars of the warehouse.\n\nThere may be some pillars in the warehouse. Except for the locations of the pillars, the floor of\nthe warehouse is paved with square tiles whose size fits with the cargo. Each pillar occupies the\nsame area as a tile.\n\nInitially, the cargo is on the center of a tile. With one push, he can move the cargo onto the\ncenter of an adjacent tile if he is in proper position. The tile onto which he will move the cargo\nmust be one of (at most) four tiles (i. e. , east, west, north or south) adjacent to the tile where\nthe cargo is present.\n\nTo push, he must also be on the tile adjacent to the present tile. He can only push the cargo in\nthe same direction as he faces to it and he cannot pull it. So, when the cargo is on the tile next\nto a wall (or a pillar), he can only move it along the wall (or the pillar). Furthermore, once he\nplaces it on a corner tile, he cannot move it anymore.\n\nHe can change his position, if there is a path to the position without obstacles (such as the cargo\nand pillars) in the way. The goal is not an obstacle. In addition, he can move only in the four\ndirections (i. e. , east, west, north or south) and change his direction only at the center of a tile.\n\nAs he is not so young, he wants to save his energy by keeping the number of required pushes\nas small as possible. But he does not mind the count of his pedometer, because walking is very\nlight exercise for him.\n\nYour job is to write a program that outputs the minimum number of pushes required to move\nthe cargo to the goal, if ever possible.", "constraint": "", "input": "The input consists of multiple maps, each representing the size and the arrangement of the\nwarehouse. A map is given in the following format.\n\nw h\nd_11 d_12 d_13 . . . d_1w\nd_21 d_22 d_23 . . . d_2w\n . . .\nd_h1 d_h2 d_h3 . . . d_hw\n\nThe integers w and h are the lengths of the two sides of the floor of the warehouse in terms of\nwidths of floor tiles. w and h are less than or equal to 7. The integer d_ij represents what is\ninitially on the corresponding floor area in the following way.\n 0: nothing (simply a floor tile) 1: a pillar 2: the cargo 3: the goal 4: the warehouseman (Mr. Schwarz)\nEach of the integers 2,3 and 4 appears exactly once as d_ij in the map. Integer numbers in an\ninput line are separated by at least one space character. The end of the input is indicated by a\nline containing two zeros.", "output": "For each map, your program should output a line containing the minimum number of pushes.\nIf the cargo cannot be moved to the goal, -1 should be output instead.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 5\n0 0 0 0 0\n4 2 0 1 1\n0 1 0 0 0\n1 0 0 0 3\n1 0 0 0 0\n5 3\n4 0 0 0 0\n2 0 0 0 0\n0 0 0 0 3\n7 5\n1 1 4 1 0 0 0\n1 1 2 1 0 0 0\n3 0 0 0 0 0 0\n0 1 0 1 0 0 0\n0 0 0 1 0 0 0\n6 6\n0 0 0 0 0 3\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 2 0 0 0 0\n4 0 0 0 0 0\n0 0\n output: 5\n-1\n11\n8"], "Pid": "p00798", "ProblemText": "Task Description: Mr. Schwarz was a famous powerful pro wrestler. He starts a part time job as a warehouseman.\nHis task is to move a cargo to a goal by repeatedly pushing the cargo in the warehouse, of course,\nwithout breaking the walls and the pillars of the warehouse.\n\nThere may be some pillars in the warehouse. Except for the locations of the pillars, the floor of\nthe warehouse is paved with square tiles whose size fits with the cargo. Each pillar occupies the\nsame area as a tile.\n\nInitially, the cargo is on the center of a tile. With one push, he can move the cargo onto the\ncenter of an adjacent tile if he is in proper position. The tile onto which he will move the cargo\nmust be one of (at most) four tiles (i. e. , east, west, north or south) adjacent to the tile where\nthe cargo is present.\n\nTo push, he must also be on the tile adjacent to the present tile. He can only push the cargo in\nthe same direction as he faces to it and he cannot pull it. So, when the cargo is on the tile next\nto a wall (or a pillar), he can only move it along the wall (or the pillar). Furthermore, once he\nplaces it on a corner tile, he cannot move it anymore.\n\nHe can change his position, if there is a path to the position without obstacles (such as the cargo\nand pillars) in the way. The goal is not an obstacle. In addition, he can move only in the four\ndirections (i. e. , east, west, north or south) and change his direction only at the center of a tile.\n\nAs he is not so young, he wants to save his energy by keeping the number of required pushes\nas small as possible. But he does not mind the count of his pedometer, because walking is very\nlight exercise for him.\n\nYour job is to write a program that outputs the minimum number of pushes required to move\nthe cargo to the goal, if ever possible.\nTask Input: The input consists of multiple maps, each representing the size and the arrangement of the\nwarehouse. A map is given in the following format.\n\nw h\nd_11 d_12 d_13 . . . d_1w\nd_21 d_22 d_23 . . . d_2w\n . . .\nd_h1 d_h2 d_h3 . . . d_hw\n\nThe integers w and h are the lengths of the two sides of the floor of the warehouse in terms of\nwidths of floor tiles. w and h are less than or equal to 7. The integer d_ij represents what is\ninitially on the corresponding floor area in the following way.\n 0: nothing (simply a floor tile) 1: a pillar 2: the cargo 3: the goal 4: the warehouseman (Mr. Schwarz)\nEach of the integers 2,3 and 4 appears exactly once as d_ij in the map. Integer numbers in an\ninput line are separated by at least one space character. The end of the input is indicated by a\nline containing two zeros.\nTask Output: For each map, your program should output a line containing the minimum number of pushes.\nIf the cargo cannot be moved to the goal, -1 should be output instead.\nTask Samples: input: 5 5\n0 0 0 0 0\n4 2 0 1 1\n0 1 0 0 0\n1 0 0 0 3\n1 0 0 0 0\n5 3\n4 0 0 0 0\n2 0 0 0 0\n0 0 0 0 3\n7 5\n1 1 4 1 0 0 0\n1 1 2 1 0 0 0\n3 0 0 0 0 0 0\n0 1 0 1 0 0 0\n0 0 0 1 0 0 0\n6 6\n0 0 0 0 0 3\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 2 0 0 0 0\n4 0 0 0 0 0\n0 0\n output: 5\n-1\n11\n8\n\n" }, { "title": "Problem D: Pump up Batteries", "content": "Bill is a boss of security guards. He has pride in that his men put on wearable computers on their\nduty. At the same time, it is his headache that capacities of commercially available batteries are\nfar too small to support those computers all day long. His men come back to the office to charge\nup their batteries and spend idle time until its completion. Bill has only one battery charger in\nthe office because it is very expensive.\n\nBill suspects that his men spend much idle time waiting in a queue for the charger. If it is the\ncase, Bill had better introduce another charger. Bill knows that his men are honest in some\nsense and blindly follow any given instructions or rules. Such a simple-minded way of life may\nlead to longer waiting time, but they cannot change their behavioral pattern.\n\nEach battery has a data sheet attached on it that indicates the best pattern of charging and\nconsuming cycle. The pattern is given as a sequence of pairs of consuming time and charging\ntime. The data sheet says the pattern should be followed cyclically to keep the battery in quality.\nA guard, trying to follow the suggested cycle strictly, will come back to the office exactly when\nthe consuming time passes out, stay there until the battery has been charged for the exact time\nperiod indicated, and then go back to his beat.\n\nThe guards are quite punctual. They spend not a second more in the office than the time\nnecessary for charging up their batteries. They will wait in a queue, however, if the charger is\noccupied by another guard, exactly on first-come-first-served basis. When two or more guards\ncome back to the office at the same instance of time, they line up in the order of their identifi-\ncation numbers, and, each of them, one by one in the order of that line, judges if he can use the\ncharger and, if not, goes into the queue. They do these actions in an instant.\n\nYour mission is to write a program that simulates those situations like Bill 's and reports how\nmuch time is wasted in waiting for the charger.", "constraint": "", "input": "The input consists of one or more data sets for simulation.\n\nThe first line of a data set consists of two positive integers separated by a space character: the\nnumber of guards and the simulation duration. The number of guards does not exceed one\nhundred. The guards have their identification numbers starting from one up to the number of\nguards. The simulation duration is measured in minutes, and is at most one week, i. e. , 10080\n(min. ).\nPatterns for batteries possessed by the guards follow the first line. For each guard, in the order\nof identification number, appears the pattern indicated on the data sheet attached to his battery.\nA pattern is a sequence of positive integers, whose length is a multiple of two and does not exceed\nfifty. The numbers in the sequence show consuming time and charging time alternately. Those\ntimes are also given in minutes and are at most one day, i. e. , 1440 (min. ). A space character or\na newline follows each number. A pattern is terminated with an additional zero followed by a\nnewline.\n\nEach data set is terminated with an additional empty line. The input is terminated with an\nadditional line that contains two zeros separated by a space character.", "output": "For each data set your program should simulate up to the given duration. Each guard should\nrepeat consuming of his battery (i. e. , being on his beat) and charging of his battery according\nto the given pattern cyclically. At the beginning, all the guards start their cycle simultaneously,\nthat is, they start their beats and, thus, start their first consuming period.\n\nFor each data set, your program should produce one line containing the total wait time of the\nguards in the queue up to the time when the simulation duration runs out. The output should\nnot contain any other characters.\n\nFor example, consider a data set:\n\n3 25\n3 1 2 1 4 1 0\n1 1 0\n2 1 3 2 0\n\nThe guard 1 tries to repeat 3 min. consuming, 1 min. charging, 2 min. consuming, 1 min.\ncharging, 4 min. consuming, and 1 min. charging, cyclically. Yet he has to wait sometimes to\nuse the charger, when he is on his duty together with the other guards 2 and 3. Thus, the actual\nbehavior of the guards looks like:\n\n 0 10 20\n | | | | | |\nguard 1: ***. **. ****. ***. **-. ****.\nguard 2: *. *-. *-. *-. *. *. *. *--. *. *-\nguard 3: **. ***--. . **-. ***. . **. ***\n\nwhere “*” represents a minute spent for consuming, “. ” for charging, and “-” for waiting in the\nqueue. At time 3, the guards 1 and 2 came back to the office and the guard 1 started charging\nwhile the guard 2 went into the queue. At time 6, all the guards came back to the office and the\nguard 1 started charging while the others went to the queue. When the charger got available\nat time 7, the guard 2 started charging, leaving the guard 3 in the queue. All those happened are consequences of rules stated above. And the total time wasted in waiting for the charger\nbecomes 10 minutes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 25\n3 1 2 1 4 1 0\n1 1 0\n2 1 3 2 0\n\n4 1000\n80 20 80 20 80 20 80 20 0\n80\n20\n0\n80 20 90\n10 80\n20\n0\n90 10\n0\n\n0 0\n output: 10\n110"], "Pid": "p00799", "ProblemText": "Task Description: Bill is a boss of security guards. He has pride in that his men put on wearable computers on their\nduty. At the same time, it is his headache that capacities of commercially available batteries are\nfar too small to support those computers all day long. His men come back to the office to charge\nup their batteries and spend idle time until its completion. Bill has only one battery charger in\nthe office because it is very expensive.\n\nBill suspects that his men spend much idle time waiting in a queue for the charger. If it is the\ncase, Bill had better introduce another charger. Bill knows that his men are honest in some\nsense and blindly follow any given instructions or rules. Such a simple-minded way of life may\nlead to longer waiting time, but they cannot change their behavioral pattern.\n\nEach battery has a data sheet attached on it that indicates the best pattern of charging and\nconsuming cycle. The pattern is given as a sequence of pairs of consuming time and charging\ntime. The data sheet says the pattern should be followed cyclically to keep the battery in quality.\nA guard, trying to follow the suggested cycle strictly, will come back to the office exactly when\nthe consuming time passes out, stay there until the battery has been charged for the exact time\nperiod indicated, and then go back to his beat.\n\nThe guards are quite punctual. They spend not a second more in the office than the time\nnecessary for charging up their batteries. They will wait in a queue, however, if the charger is\noccupied by another guard, exactly on first-come-first-served basis. When two or more guards\ncome back to the office at the same instance of time, they line up in the order of their identifi-\ncation numbers, and, each of them, one by one in the order of that line, judges if he can use the\ncharger and, if not, goes into the queue. They do these actions in an instant.\n\nYour mission is to write a program that simulates those situations like Bill 's and reports how\nmuch time is wasted in waiting for the charger.\nTask Input: The input consists of one or more data sets for simulation.\n\nThe first line of a data set consists of two positive integers separated by a space character: the\nnumber of guards and the simulation duration. The number of guards does not exceed one\nhundred. The guards have their identification numbers starting from one up to the number of\nguards. The simulation duration is measured in minutes, and is at most one week, i. e. , 10080\n(min. ).\nPatterns for batteries possessed by the guards follow the first line. For each guard, in the order\nof identification number, appears the pattern indicated on the data sheet attached to his battery.\nA pattern is a sequence of positive integers, whose length is a multiple of two and does not exceed\nfifty. The numbers in the sequence show consuming time and charging time alternately. Those\ntimes are also given in minutes and are at most one day, i. e. , 1440 (min. ). A space character or\na newline follows each number. A pattern is terminated with an additional zero followed by a\nnewline.\n\nEach data set is terminated with an additional empty line. The input is terminated with an\nadditional line that contains two zeros separated by a space character.\nTask Output: For each data set your program should simulate up to the given duration. Each guard should\nrepeat consuming of his battery (i. e. , being on his beat) and charging of his battery according\nto the given pattern cyclically. At the beginning, all the guards start their cycle simultaneously,\nthat is, they start their beats and, thus, start their first consuming period.\n\nFor each data set, your program should produce one line containing the total wait time of the\nguards in the queue up to the time when the simulation duration runs out. The output should\nnot contain any other characters.\n\nFor example, consider a data set:\n\n3 25\n3 1 2 1 4 1 0\n1 1 0\n2 1 3 2 0\n\nThe guard 1 tries to repeat 3 min. consuming, 1 min. charging, 2 min. consuming, 1 min.\ncharging, 4 min. consuming, and 1 min. charging, cyclically. Yet he has to wait sometimes to\nuse the charger, when he is on his duty together with the other guards 2 and 3. Thus, the actual\nbehavior of the guards looks like:\n\n 0 10 20\n | | | | | |\nguard 1: ***. **. ****. ***. **-. ****.\nguard 2: *. *-. *-. *-. *. *. *. *--. *. *-\nguard 3: **. ***--. . **-. ***. . **. ***\n\nwhere “*” represents a minute spent for consuming, “. ” for charging, and “-” for waiting in the\nqueue. At time 3, the guards 1 and 2 came back to the office and the guard 1 started charging\nwhile the guard 2 went into the queue. At time 6, all the guards came back to the office and the\nguard 1 started charging while the others went to the queue. When the charger got available\nat time 7, the guard 2 started charging, leaving the guard 3 in the queue. All those happened are consequences of rules stated above. And the total time wasted in waiting for the charger\nbecomes 10 minutes.\nTask Samples: input: 3 25\n3 1 2 1 4 1 0\n1 1 0\n2 1 3 2 0\n\n4 1000\n80 20 80 20 80 20 80 20 0\n80\n20\n0\n80 20 90\n10 80\n20\n0\n90 10\n0\n\n0 0\n output: 10\n110\n\n" }, { "title": "Problem E: The Devil of Gravity", "content": "Haven't you ever thought that programs written in Java, C++, Pascal, or any other modern computer languages look rather sparse? Although most editors provide sufficient screen space for at least 80 characters or so in a line, the average number of significant characters occurring in a line is just a fraction. Today, people usually prefer readability of programs to efficient use of screen real estate.\n\nDr. Faust, a radical computer scientist, believes that editors for real programmers shall be more space efficient. He has been doing research on saving space and invented various techniques for many years, but he has reached the point where no more essential improvements will be expected with his own ideas.\n\nAfter long thought, he has finally decided to take the ultimate but forbidden approach. He does not hesitate to sacrifice anything for his ambition, and asks a devil to give him supernatural intellectual powers in exchange with his soul. With the transcendental knowledge and ability, the devil provides new algorithms and data structures for space efficient implementations of editors.\n\nThe editor implemented with those evil techniques is beyond human imaginations and behaves somehow strange. The mighty devil Dr. Faust asks happens to be the devil of gravity. The editor under its control saves space with magical magnetic and gravitational forces.\n\nYour mission is to defeat Dr. Faust by re-implementing this strange editor without any help of the devil. At first glance, the editor looks like an ordinary text editor. It presents texts in two-dimensional layouts and accepts editing commands including those of cursor movements and character insertions and deletions. A text handled by the devil's editor, however, is partitioned into text segments, each of which is a horizontal block of non-blank characters. In the following figure, for instance, four text segments \"abcdef\", \"ghijkl\", \"mnop\", \"qrstuvw\" are present and the first two are placed in the same row.\n\nabcdef ghijkl\n mnop\nqrstuvw\n\nThe editor has the following unique features.\n\n A text segment without any supporting segments in the row immediately below it falls by the evil gravitational force.\n\n Text segments in the same row and contiguous to each other are concatenated by the evil magnetic force.\nFor instance, if characters in the segment \"mnop\" in the previous example are deleted, the two segments on top of it fall and we have the following.\n\nabcdef\nqrstuvw ghijkl\n\nAfter that, if \"x\" is added at the tail (i. e. , the right next of the rightmost column) of the segment \"qrstuvw\", the two segments in the bottom row are concatenated.\n\nabcdef\nqrstuvwxghijkl\n\nNow we have two text segments in this figure. By this way, the editor saves screen space but demands the users' extraordinary intellectual power.\n\nIn general, after a command execution, the following rules are applied, where S is a text segment, left(S) and right(S) are the leftmost and rightmost columns of S, respectively, and row(S) is the row number of S.\n\n If the columns from left(S) to right(S) in the row numbered row(S)-1 (i. e. , the row just below S) are empty (i. e. , any characters of any text segments do not exist there), S is pulled down to row(S)-1 vertically, preserving its column position. If the same ranges in row(S)-2, row(S)-3, and so on are also empty, S is further pulled down again and again. This process terminates sooner or later since the editor has the ultimate bottom, the row whose number is zero.\n\n If two text segments S and T are in the same row and right(S)+1 = left(T), that is, T starts at the right next column of the rightmost character of S, S and T are automatically concatenated to form a single text segment, which starts at left(S) and ends at right(T). Of course, the new segment is still in the original row.\nNote that any text segment has at least one character. Note also that the first rule is applied prior to any application of the second rule. This means that no concatenation may occur while falling segments exist. For instance, consider the following case.\n\n dddddddd\n cccccccc\nbbbb\naaa\n\nIf the last character of the text segment \"bbbb\" is deleted, the concatenation rule is not applied until the two segments \"cccccccc\" and \"dddddddd\" stop falling. This means that \"bbb\" and \"cccccccc\" are not concatenated.\n\nThe devil's editor has a cursor and it is always in a single text segment, which we call the current segment. The cursor is at some character position of the current segment or otherwise at its tail. Note that the cursor cannot be a support. For instance, in the previous example, even if the cursor is at the last character of \"bbbb\" and it stays at the same position after the deletion, it cannot support \"cccccccc\" and \"dddddddd\" any more by solely itself and thus those two segments shall fall. Finally, the cursor is at the leftmost \"d\"\n\nThe editor accepts the following commands, each represented by a single character.\n\n F: Move the cursor forward (i. e. , to the right) by one column in the current segment. If the cursor is at the tail of the current segment and thus it cannot move any more within the segment, an error occurs.\n\n B: Move the cursor backward (i. e. , to the left) by one column in the current segment. If the cursor is at the leftmost position of the current segment, an error occurs.\n\n P: Move the cursor upward by one row. The column position of the cursor does not change. If the new position would be out of the legal cursor range of any existing text segment, an error occurs.\n\n N: Move the cursor downward by one row. The column position of the cursor does not change. If the cursor is in the bottom row or the new position is out of the legal cursor range of any existing text segment, an error occurs.\n\n D: Delete the character at the cursor position. If the cursor is at the tail of the current segment and so no character is there, an error occurs. If the cursor is at some character, it is deleted and the current segment becomes shorter by one character. Neither the beginning (i. e. , leftmost) column of the current segment nor the column position of the cursor changes. However, if the current segment becomes empty, it is removed and the cursor falls by one row. If the new position would be out of the legal cursor range of any existing text segment, an error occurs. \n\n Note that after executing this command, some text segments may lose their supports and be pulled down toward the hell. If the current segment falls, the cursor also falls with it.\n\n C: Create a new segment of length one immediately above the current cursor position. It consists of a copy of the character under the cursor. If the cursor is at the tail, an error occurs. Also if the the position of the new segment is already occupied by another segment, an error occurs. After executing the command, the created segment becomes the new current segment and the column position of the cursor advances to the right by one column.\n\n Lowercase and numeric characters (`a' to `z' and `0' to `9'): Insert the character at the current cursor position. The current segment becomes longer by one character. The cursor moves forward by one column. The beginning column of the current segment does not change.\nOnce an error occurs, the entire editing session terminates abnormally.", "constraint": "", "input": "The first line of the input contains an integer that represents the number of editing sessions. Each of the following lines contains a character sequence, where the first character is the initial character and the rest represents a command sequence processed during a session. Each session starts with a single segment consisting of the initial character in the bottom row. The initial cursor position is at the tail of the segment. The editor processes each command represented by a character one by one in the manner described above.\n\nYou may assume that each command line is non-empty and its length is at most one hundred. A command sequence ends with a newline.", "output": "For each editing session specified by the input, if it terminates without errors, your program should print the current segment at the completion of the session in a line. If an error occurs during the session, just print \"ERROR\" in capital letters in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n12BC3BC4BNBBDD5\naaaBCNBBBCb\naaaBBCbNBC\n output: 15234\naba\nERROR"], "Pid": "p00800", "ProblemText": "Task Description: Haven't you ever thought that programs written in Java, C++, Pascal, or any other modern computer languages look rather sparse? Although most editors provide sufficient screen space for at least 80 characters or so in a line, the average number of significant characters occurring in a line is just a fraction. Today, people usually prefer readability of programs to efficient use of screen real estate.\n\nDr. Faust, a radical computer scientist, believes that editors for real programmers shall be more space efficient. He has been doing research on saving space and invented various techniques for many years, but he has reached the point where no more essential improvements will be expected with his own ideas.\n\nAfter long thought, he has finally decided to take the ultimate but forbidden approach. He does not hesitate to sacrifice anything for his ambition, and asks a devil to give him supernatural intellectual powers in exchange with his soul. With the transcendental knowledge and ability, the devil provides new algorithms and data structures for space efficient implementations of editors.\n\nThe editor implemented with those evil techniques is beyond human imaginations and behaves somehow strange. The mighty devil Dr. Faust asks happens to be the devil of gravity. The editor under its control saves space with magical magnetic and gravitational forces.\n\nYour mission is to defeat Dr. Faust by re-implementing this strange editor without any help of the devil. At first glance, the editor looks like an ordinary text editor. It presents texts in two-dimensional layouts and accepts editing commands including those of cursor movements and character insertions and deletions. A text handled by the devil's editor, however, is partitioned into text segments, each of which is a horizontal block of non-blank characters. In the following figure, for instance, four text segments \"abcdef\", \"ghijkl\", \"mnop\", \"qrstuvw\" are present and the first two are placed in the same row.\n\nabcdef ghijkl\n mnop\nqrstuvw\n\nThe editor has the following unique features.\n\n A text segment without any supporting segments in the row immediately below it falls by the evil gravitational force.\n\n Text segments in the same row and contiguous to each other are concatenated by the evil magnetic force.\nFor instance, if characters in the segment \"mnop\" in the previous example are deleted, the two segments on top of it fall and we have the following.\n\nabcdef\nqrstuvw ghijkl\n\nAfter that, if \"x\" is added at the tail (i. e. , the right next of the rightmost column) of the segment \"qrstuvw\", the two segments in the bottom row are concatenated.\n\nabcdef\nqrstuvwxghijkl\n\nNow we have two text segments in this figure. By this way, the editor saves screen space but demands the users' extraordinary intellectual power.\n\nIn general, after a command execution, the following rules are applied, where S is a text segment, left(S) and right(S) are the leftmost and rightmost columns of S, respectively, and row(S) is the row number of S.\n\n If the columns from left(S) to right(S) in the row numbered row(S)-1 (i. e. , the row just below S) are empty (i. e. , any characters of any text segments do not exist there), S is pulled down to row(S)-1 vertically, preserving its column position. If the same ranges in row(S)-2, row(S)-3, and so on are also empty, S is further pulled down again and again. This process terminates sooner or later since the editor has the ultimate bottom, the row whose number is zero.\n\n If two text segments S and T are in the same row and right(S)+1 = left(T), that is, T starts at the right next column of the rightmost character of S, S and T are automatically concatenated to form a single text segment, which starts at left(S) and ends at right(T). Of course, the new segment is still in the original row.\nNote that any text segment has at least one character. Note also that the first rule is applied prior to any application of the second rule. This means that no concatenation may occur while falling segments exist. For instance, consider the following case.\n\n dddddddd\n cccccccc\nbbbb\naaa\n\nIf the last character of the text segment \"bbbb\" is deleted, the concatenation rule is not applied until the two segments \"cccccccc\" and \"dddddddd\" stop falling. This means that \"bbb\" and \"cccccccc\" are not concatenated.\n\nThe devil's editor has a cursor and it is always in a single text segment, which we call the current segment. The cursor is at some character position of the current segment or otherwise at its tail. Note that the cursor cannot be a support. For instance, in the previous example, even if the cursor is at the last character of \"bbbb\" and it stays at the same position after the deletion, it cannot support \"cccccccc\" and \"dddddddd\" any more by solely itself and thus those two segments shall fall. Finally, the cursor is at the leftmost \"d\"\n\nThe editor accepts the following commands, each represented by a single character.\n\n F: Move the cursor forward (i. e. , to the right) by one column in the current segment. If the cursor is at the tail of the current segment and thus it cannot move any more within the segment, an error occurs.\n\n B: Move the cursor backward (i. e. , to the left) by one column in the current segment. If the cursor is at the leftmost position of the current segment, an error occurs.\n\n P: Move the cursor upward by one row. The column position of the cursor does not change. If the new position would be out of the legal cursor range of any existing text segment, an error occurs.\n\n N: Move the cursor downward by one row. The column position of the cursor does not change. If the cursor is in the bottom row or the new position is out of the legal cursor range of any existing text segment, an error occurs.\n\n D: Delete the character at the cursor position. If the cursor is at the tail of the current segment and so no character is there, an error occurs. If the cursor is at some character, it is deleted and the current segment becomes shorter by one character. Neither the beginning (i. e. , leftmost) column of the current segment nor the column position of the cursor changes. However, if the current segment becomes empty, it is removed and the cursor falls by one row. If the new position would be out of the legal cursor range of any existing text segment, an error occurs. \n\n Note that after executing this command, some text segments may lose their supports and be pulled down toward the hell. If the current segment falls, the cursor also falls with it.\n\n C: Create a new segment of length one immediately above the current cursor position. It consists of a copy of the character under the cursor. If the cursor is at the tail, an error occurs. Also if the the position of the new segment is already occupied by another segment, an error occurs. After executing the command, the created segment becomes the new current segment and the column position of the cursor advances to the right by one column.\n\n Lowercase and numeric characters (`a' to `z' and `0' to `9'): Insert the character at the current cursor position. The current segment becomes longer by one character. The cursor moves forward by one column. The beginning column of the current segment does not change.\nOnce an error occurs, the entire editing session terminates abnormally.\nTask Input: The first line of the input contains an integer that represents the number of editing sessions. Each of the following lines contains a character sequence, where the first character is the initial character and the rest represents a command sequence processed during a session. Each session starts with a single segment consisting of the initial character in the bottom row. The initial cursor position is at the tail of the segment. The editor processes each command represented by a character one by one in the manner described above.\n\nYou may assume that each command line is non-empty and its length is at most one hundred. A command sequence ends with a newline.\nTask Output: For each editing session specified by the input, if it terminates without errors, your program should print the current segment at the completion of the session in a line. If an error occurs during the session, just print \"ERROR\" in capital letters in a line.\nTask Samples: input: 3\n12BC3BC4BNBBDD5\naaaBCNBBBCb\naaaBBCbNBC\n output: 15234\naba\nERROR\n\n" }, { "title": "Problem F: Numoeba", "content": "A scientist discovered a strange variation of amoeba. The scientist named it numoeba. A numoeba, though it looks like an amoeba, is actually a community of cells, which always forms a tree.\n\nThe scientist called the cell leader that is at the root position of the tree. For example, in Fig. 1, the leader is A. In a numoeba, its leader may change time to time. For example, if E gets new leadership, the tree in Fig. 1 becomes one in Fig. 2. We will use the terms root, leaf, parent, child and subtree for a numoeba as defined in the graph theory.\n\nNumoeba changes its physical structure at every biological clock by cell division and cell death. The leader may change depending on this physical change.\n\nThe most astonishing fact about the numoeba cell is that it contains an organic unit called numbosome, which represents an odd integer within the range from 1 to 12,345,677. At every biological clock, the value of a numbosome changes from n to a new value as follows:\n\n The maximum odd factor of 3n + 1 is calculated. This value can be obtained from 3n + 1 by repeating division by 2 while even.\n\n If the resulting integer is greater than 12,345,678, then it is subtracted by 12,345,678.\nFor example, if the numbosome value of a cell is 13,13 * 3 + 1 = 40 is divided by 2^3 = 8 and a new numbosome value 5 is obtained. If the numbosome value of a cell is 11,111,111, it changes to 4,320,989, instead of 16,666,667. If 3n + 1 is a power of 2, yielding 1 as the result, it signifies the death of the cell as will be described below.\n\nAt every biological clock, the next numbosome value of every cell is calculated and the fate of the cell and thereby the fate of numoeba is determined according to the following steps.\n\n A cell that is a leaf and increases its numbosome value is designated as a candidate leaf. \n\n A cell dies if its numbosome value becomes 1. If the dying cell is the leader of the numoeba, the numoeba dies as a whole. Otherwise, all the cells in the subtree from the dying cell (including itself) die. However, there is an exceptional case where the cells in the subtree do not necessarily die; if there is only one child cell of the dying non-leader cell, the child cell will replace the dying cell. Thus, a straight chain simply shrinks if its non-leader constituent dies.\n\n For example, consider a numoeba with the leader A below. \nIf the leader A dies in (1), the numoeba dies. \nIf the cell D dies in (1), (1) will be as follows. \n\nAnd, if the cell E dies in (1), (1) will be as follows. \n Note that this procedure is executed sequentially, top-down from the root of the numoeba to leaves. If the cells E and F will die in (1), the death of F is not detected at the time the procedure examines the cell E. The numoeba, therefore, becomes (3). One should not consider in such a way that the death of F makes G the only child of E, and, therefore, G will replace the dying E.\n\n If a candidate leaf survives with the numbosome value of n, it spawns a cell as its child, thereby a new leaf, whose numbosome value is the least odd integer greater than or equal to (n + 1)/2. We call the child leaf bonus.\n\n Finally, a new leader of the numoeba is selected, who has a unique maximum numbosome value among all the constituent cells. The tree structure of the numoeba is changed so that the new leader is its root, like what is shown in Fig. 1 and Fig. 2. Note that the parent-child relationship of some cells may be reversed by this leader change. When a new leader of a unique maximum numbosome value, say m, is selected (it may be the same cell as the previous leader), it spawns a cell as its child with the numbosome whose value is the greatest odd integer less than or equal to (m + 1)/2. We call the child leader bonus. If there is more than one cell of the same maximum numbosome value, however, the leader does not change for the next period, and there is no leader bonus.\n\nThe following illustrates the growth and death of a numoeba starting from a single cell seed with the numbosome value 15, which plays both roles of the leader and a leaf at the start. In the figure, a cell is nicknamed with its numbosome value. Note that the order of the children of a parent is irrelevant. \n\nThe numoeba continues changing its structure, and at clock 104, it looks as follows.\n\nHere, two ambitious 2429's could not become the leader. The leader 5 will die without promoting these talented cells at the next clock. This alludes the fragility of a big organization.\n\nAnd, the numoeba dies at clock 105.\n\nYour job is to write a program that outputs statistics about the life of numoebae that start from a single cell seed at clock zero.", "constraint": "", "input": "A sequence of odd integers, each in a line. Each odd integer k_i (3 <= k_i <= 9,999) indicates the initial numbosome value of the starting cell. This sequence is terminated by a zero.", "output": "A sequence of pairs of integers: an integer that represents the numoeba's life time and an integer that represents the maximum number of constituent cells in its life. These two integers should be separated by a space character, and each pair should be followed immediately by a newline. Here, the lifetime means the clock when the numoeba dies.\n\nYou can use the fact that the life time is less than 500, and that the number of cells does not exceed 500 in any time, for any seed value given in the input. You might guess that the program would consume a lot of memory. It is true in general. But, don't mind. Referees will use a test data set consisting of no more than 10 starting values, and, starting from any of the those values, the total numbers of cells spawned during the lifetime will not exceed 5000.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n5\n7\n15\n655\n2711\n6395\n7195\n8465\n0\n output: 2 3\n1 1\n9 11\n105 65\n398 332\n415 332\n430 332\n428 332\n190 421"], "Pid": "p00801", "ProblemText": "Task Description: A scientist discovered a strange variation of amoeba. The scientist named it numoeba. A numoeba, though it looks like an amoeba, is actually a community of cells, which always forms a tree.\n\nThe scientist called the cell leader that is at the root position of the tree. For example, in Fig. 1, the leader is A. In a numoeba, its leader may change time to time. For example, if E gets new leadership, the tree in Fig. 1 becomes one in Fig. 2. We will use the terms root, leaf, parent, child and subtree for a numoeba as defined in the graph theory.\n\nNumoeba changes its physical structure at every biological clock by cell division and cell death. The leader may change depending on this physical change.\n\nThe most astonishing fact about the numoeba cell is that it contains an organic unit called numbosome, which represents an odd integer within the range from 1 to 12,345,677. At every biological clock, the value of a numbosome changes from n to a new value as follows:\n\n The maximum odd factor of 3n + 1 is calculated. This value can be obtained from 3n + 1 by repeating division by 2 while even.\n\n If the resulting integer is greater than 12,345,678, then it is subtracted by 12,345,678.\nFor example, if the numbosome value of a cell is 13,13 * 3 + 1 = 40 is divided by 2^3 = 8 and a new numbosome value 5 is obtained. If the numbosome value of a cell is 11,111,111, it changes to 4,320,989, instead of 16,666,667. If 3n + 1 is a power of 2, yielding 1 as the result, it signifies the death of the cell as will be described below.\n\nAt every biological clock, the next numbosome value of every cell is calculated and the fate of the cell and thereby the fate of numoeba is determined according to the following steps.\n\n A cell that is a leaf and increases its numbosome value is designated as a candidate leaf. \n\n A cell dies if its numbosome value becomes 1. If the dying cell is the leader of the numoeba, the numoeba dies as a whole. Otherwise, all the cells in the subtree from the dying cell (including itself) die. However, there is an exceptional case where the cells in the subtree do not necessarily die; if there is only one child cell of the dying non-leader cell, the child cell will replace the dying cell. Thus, a straight chain simply shrinks if its non-leader constituent dies.\n\n For example, consider a numoeba with the leader A below. \nIf the leader A dies in (1), the numoeba dies. \nIf the cell D dies in (1), (1) will be as follows. \n\nAnd, if the cell E dies in (1), (1) will be as follows. \n Note that this procedure is executed sequentially, top-down from the root of the numoeba to leaves. If the cells E and F will die in (1), the death of F is not detected at the time the procedure examines the cell E. The numoeba, therefore, becomes (3). One should not consider in such a way that the death of F makes G the only child of E, and, therefore, G will replace the dying E.\n\n If a candidate leaf survives with the numbosome value of n, it spawns a cell as its child, thereby a new leaf, whose numbosome value is the least odd integer greater than or equal to (n + 1)/2. We call the child leaf bonus.\n\n Finally, a new leader of the numoeba is selected, who has a unique maximum numbosome value among all the constituent cells. The tree structure of the numoeba is changed so that the new leader is its root, like what is shown in Fig. 1 and Fig. 2. Note that the parent-child relationship of some cells may be reversed by this leader change. When a new leader of a unique maximum numbosome value, say m, is selected (it may be the same cell as the previous leader), it spawns a cell as its child with the numbosome whose value is the greatest odd integer less than or equal to (m + 1)/2. We call the child leader bonus. If there is more than one cell of the same maximum numbosome value, however, the leader does not change for the next period, and there is no leader bonus.\n\nThe following illustrates the growth and death of a numoeba starting from a single cell seed with the numbosome value 15, which plays both roles of the leader and a leaf at the start. In the figure, a cell is nicknamed with its numbosome value. Note that the order of the children of a parent is irrelevant. \n\nThe numoeba continues changing its structure, and at clock 104, it looks as follows.\n\nHere, two ambitious 2429's could not become the leader. The leader 5 will die without promoting these talented cells at the next clock. This alludes the fragility of a big organization.\n\nAnd, the numoeba dies at clock 105.\n\nYour job is to write a program that outputs statistics about the life of numoebae that start from a single cell seed at clock zero.\nTask Input: A sequence of odd integers, each in a line. Each odd integer k_i (3 <= k_i <= 9,999) indicates the initial numbosome value of the starting cell. This sequence is terminated by a zero.\nTask Output: A sequence of pairs of integers: an integer that represents the numoeba's life time and an integer that represents the maximum number of constituent cells in its life. These two integers should be separated by a space character, and each pair should be followed immediately by a newline. Here, the lifetime means the clock when the numoeba dies.\n\nYou can use the fact that the life time is less than 500, and that the number of cells does not exceed 500 in any time, for any seed value given in the input. You might guess that the program would consume a lot of memory. It is true in general. But, don't mind. Referees will use a test data set consisting of no more than 10 starting values, and, starting from any of the those values, the total numbers of cells spawned during the lifetime will not exceed 5000.\nTask Samples: input: 3\n5\n7\n15\n655\n2711\n6395\n7195\n8465\n0\n output: 2 3\n1 1\n9 11\n105 65\n398 332\n415 332\n430 332\n428 332\n190 421\n\n" }, { "title": "Problem G: Telescope", "content": "Dr. Extreme experimentally made an extremely precise telescope to investigate extremely curious phenomena at an extremely distant place. In order to make the telescope so precise as to investigate phenomena at such an extremely distant place, even quite a small distortion is not allowed. However, he forgot the influence of the internal gas affected by low-frequency vibration of magnetic flux passing through the telescope. The cylinder of the telescope is not affected by the low-frequency vibration, but the internal gas is.\nThe cross section of the telescope forms a perfect circle. If he forms a coil by putting extremely thin wire along the (inner) circumference, he can measure (the average vertical component of) the temporal variation of magnetic flux: such measurement would be useful to estimate the influence. But points on the circumference at which the wire can be fixed are limited; furthermore, the number of special clips to fix the wire is also limited. To obtain the highest sensitivity, he wishes to form a coil of a polygon shape with the largest area by stringing the wire among carefully selected points on the circumference.\nYour job is to write a program which reports the maximum area of all possible m-polygons (polygons with exactly m vertices) each of whose vertices is one of the n points given on a circumference with a radius of 1. An example of the case n = 4 and m = 3 is illustrated below. \nIn the figure above, the equations such as \"p_1_ = 0.0\" indicate the locations of the n given points, and the decimals such as \"1.000000\" on m-polygons indicate the areas of m-polygons.\nParameter p_i_ denotes the location of the i-th given point on the circumference (1 <= i <= n). The location p of a point on the circumference is in the range 0 <= p < 1, corresponding to the range of rotation angles from 0 to 2π radians. That is, the rotation angle of a point at p to the point at 0 equals 2π radians. (π is the circular constant 3.14159265358979323846. . . . )\nYou may rely on the fact that the area of an isosceles triangle ABC (AB = AC = 1) with an interior angle BAC of α radians (0 < α < π ) is (1/2)sinα , and the area of a polygon inside a circle with a radius of 1 is less than π .", "constraint": "", "input": "The input consists of multiple subproblems followed by a line containing two zeros that indicates the end of the input. Each subproblem is given in the following format.\n\nn m\np_1_ p_2_ . . . p_n_\n\nn is the number of points on the circumference (3 <= n <= 40). m is the number of vertices to form m-polygons (3 <= m <= n). The locations of n points, p_1_, p_2_, . . . , p_n_, are given as decimals and they are separated by either a space character or a newline. In addition, you may assume that 0 <= p_1_ < p_2_ < . . . < p_n_ < 1.", "output": "For each subproblem, the maximum area should be output, each in a separate line. Each value in the output may not have an error greater than 0.000001 and its fractional part should be represented by 6 decimal digits after the decimal point.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n0.0 0.25 0.5 0.666666666666666666667\n4 4\n0.0 0.25 0.5 0.75\n30 15\n0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27\n0.30 0.33 0.36 0.39 0.42 0.45 0.48 0.51 0.54 0.57\n0.61 0.64 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.87\n40 20\n0.351 0.353 0.355 0.357 0.359 0.361 0.363 0.365 0.367 0.369\n0.371 0.373 0.375 0.377 0.379 0.381 0.383 0.385 0.387 0.389\n0.611 0.613 0.615 0.617 0.619 0.621 0.623 0.625 0.627 0.629\n0.631 0.633 0.635 0.637 0.639 0.641 0.643 0.645 0.647 0.649\n0 0\n output: 1.183013\n2.000000\n3.026998\n0.253581"], "Pid": "p00802", "ProblemText": "Task Description: Dr. Extreme experimentally made an extremely precise telescope to investigate extremely curious phenomena at an extremely distant place. In order to make the telescope so precise as to investigate phenomena at such an extremely distant place, even quite a small distortion is not allowed. However, he forgot the influence of the internal gas affected by low-frequency vibration of magnetic flux passing through the telescope. The cylinder of the telescope is not affected by the low-frequency vibration, but the internal gas is.\nThe cross section of the telescope forms a perfect circle. If he forms a coil by putting extremely thin wire along the (inner) circumference, he can measure (the average vertical component of) the temporal variation of magnetic flux: such measurement would be useful to estimate the influence. But points on the circumference at which the wire can be fixed are limited; furthermore, the number of special clips to fix the wire is also limited. To obtain the highest sensitivity, he wishes to form a coil of a polygon shape with the largest area by stringing the wire among carefully selected points on the circumference.\nYour job is to write a program which reports the maximum area of all possible m-polygons (polygons with exactly m vertices) each of whose vertices is one of the n points given on a circumference with a radius of 1. An example of the case n = 4 and m = 3 is illustrated below. \nIn the figure above, the equations such as \"p_1_ = 0.0\" indicate the locations of the n given points, and the decimals such as \"1.000000\" on m-polygons indicate the areas of m-polygons.\nParameter p_i_ denotes the location of the i-th given point on the circumference (1 <= i <= n). The location p of a point on the circumference is in the range 0 <= p < 1, corresponding to the range of rotation angles from 0 to 2π radians. That is, the rotation angle of a point at p to the point at 0 equals 2π radians. (π is the circular constant 3.14159265358979323846. . . . )\nYou may rely on the fact that the area of an isosceles triangle ABC (AB = AC = 1) with an interior angle BAC of α radians (0 < α < π ) is (1/2)sinα , and the area of a polygon inside a circle with a radius of 1 is less than π .\nTask Input: The input consists of multiple subproblems followed by a line containing two zeros that indicates the end of the input. Each subproblem is given in the following format.\n\nn m\np_1_ p_2_ . . . p_n_\n\nn is the number of points on the circumference (3 <= n <= 40). m is the number of vertices to form m-polygons (3 <= m <= n). The locations of n points, p_1_, p_2_, . . . , p_n_, are given as decimals and they are separated by either a space character or a newline. In addition, you may assume that 0 <= p_1_ < p_2_ < . . . < p_n_ < 1.\nTask Output: For each subproblem, the maximum area should be output, each in a separate line. Each value in the output may not have an error greater than 0.000001 and its fractional part should be represented by 6 decimal digits after the decimal point.\nTask Samples: input: 4 3\n0.0 0.25 0.5 0.666666666666666666667\n4 4\n0.0 0.25 0.5 0.75\n30 15\n0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27\n0.30 0.33 0.36 0.39 0.42 0.45 0.48 0.51 0.54 0.57\n0.61 0.64 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.87\n40 20\n0.351 0.353 0.355 0.357 0.359 0.361 0.363 0.365 0.367 0.369\n0.371 0.373 0.375 0.377 0.379 0.381 0.383 0.385 0.387 0.389\n0.611 0.613 0.615 0.617 0.619 0.621 0.623 0.625 0.627 0.629\n0.631 0.633 0.635 0.637 0.639 0.641 0.643 0.645 0.647 0.649\n0 0\n output: 1.183013\n2.000000\n3.026998\n0.253581\n\n" }, { "title": "Problem A: Starship Hakodate-maru", "content": "The surveyor starship Hakodate-maru is famous for her two fuel containers with unbounded capacities. They hold the same type of atomic fuel balls.\n\nThere, however, is an inconvenience. The shapes of the fuel containers #1 and #2 are always cubic and regular tetrahedral respectively. Both of the fuel containers should be either empty or filled according to their shapes. Otherwise, the fuel balls become extremely unstable and may explode in the fuel containers. Thus, the number of fuel balls for the container #1 should be a cubic number (n^3 for some n = 0,1,2,3, . . . ) and that for the container #2 should be a tetrahedral number ( n(n + 1)(n + 2)/6 for some n = 0,1,2,3, . . . ).\n\nHakodate-maru is now at the star base Goryokaku preparing for the next mission to create a precise and detailed chart of stars and interstellar matters. Both of the fuel containers are now empty. Commander Parus of Goryokaku will soon send a message to Captain Future of Hakodate-maru on how many fuel balls Goryokaku can supply. Captain Future should quickly answer to Commander Parus on how many fuel balls she requests before her ship leaves Goryokaku. Of course, Captain Future and her omcers want as many fuel balls as possible.\n\nFor example, consider the case Commander Parus offers 151200 fuel balls. If only the fuel container #1 were available (i. e. ifthe fuel container #2 were unavailable), at most 148877 fuel balls could be put into the fuel container since 148877 = 53 * 53 * 53 < 151200 < 54 * 54 * 54 . If only the fuel container #2 were available, at most 147440 fuel balls could be put into the fuel container since 147440 = 95 * 96 * 97/6 < 151200 < 96 * 97 * 98/6 . Using both of the fuel containers #1 and #2,151200 fuel balls can be put into the fuel containers since 151200 = 39 * 39 * 39 + 81 * 82 * 83/6 . In this case, Captain Future's answer should be \"151200\".\n\nCommander Parus's offer cannot be greater than 151200 because of the capacity of the fuel storages of Goryokaku. Captain Future and her omcers know that well.\n\nYou are a fuel engineer assigned to Hakodate-maru. Your duty today is to help Captain Future with calculating the number of fuel balls she should request.", "constraint": "", "input": "The input is a sequence of at most 1024 positive integers. Each line contains a single integer. The sequence is followed by a zero, which indicates the end of data and should not be treated as input. You may assume that none of the input integers is greater than 151200.", "output": "The output is composed of lines, each containing a single integer. Each output integer should be the greatest integer that is the sum of a nonnegative cubic number and a nonnegative tetrahedral number and that is not greater than the corresponding input number. No other characters should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100\n64\n50\n20\n151200\n0\n output: 99\n64\n47\n20\n151200"], "Pid": "p00803", "ProblemText": "Task Description: The surveyor starship Hakodate-maru is famous for her two fuel containers with unbounded capacities. They hold the same type of atomic fuel balls.\n\nThere, however, is an inconvenience. The shapes of the fuel containers #1 and #2 are always cubic and regular tetrahedral respectively. Both of the fuel containers should be either empty or filled according to their shapes. Otherwise, the fuel balls become extremely unstable and may explode in the fuel containers. Thus, the number of fuel balls for the container #1 should be a cubic number (n^3 for some n = 0,1,2,3, . . . ) and that for the container #2 should be a tetrahedral number ( n(n + 1)(n + 2)/6 for some n = 0,1,2,3, . . . ).\n\nHakodate-maru is now at the star base Goryokaku preparing for the next mission to create a precise and detailed chart of stars and interstellar matters. Both of the fuel containers are now empty. Commander Parus of Goryokaku will soon send a message to Captain Future of Hakodate-maru on how many fuel balls Goryokaku can supply. Captain Future should quickly answer to Commander Parus on how many fuel balls she requests before her ship leaves Goryokaku. Of course, Captain Future and her omcers want as many fuel balls as possible.\n\nFor example, consider the case Commander Parus offers 151200 fuel balls. If only the fuel container #1 were available (i. e. ifthe fuel container #2 were unavailable), at most 148877 fuel balls could be put into the fuel container since 148877 = 53 * 53 * 53 < 151200 < 54 * 54 * 54 . If only the fuel container #2 were available, at most 147440 fuel balls could be put into the fuel container since 147440 = 95 * 96 * 97/6 < 151200 < 96 * 97 * 98/6 . Using both of the fuel containers #1 and #2,151200 fuel balls can be put into the fuel containers since 151200 = 39 * 39 * 39 + 81 * 82 * 83/6 . In this case, Captain Future's answer should be \"151200\".\n\nCommander Parus's offer cannot be greater than 151200 because of the capacity of the fuel storages of Goryokaku. Captain Future and her omcers know that well.\n\nYou are a fuel engineer assigned to Hakodate-maru. Your duty today is to help Captain Future with calculating the number of fuel balls she should request.\nTask Input: The input is a sequence of at most 1024 positive integers. Each line contains a single integer. The sequence is followed by a zero, which indicates the end of data and should not be treated as input. You may assume that none of the input integers is greater than 151200.\nTask Output: The output is composed of lines, each containing a single integer. Each output integer should be the greatest integer that is the sum of a nonnegative cubic number and a nonnegative tetrahedral number and that is not greater than the corresponding input number. No other characters should appear in the output.\nTask Samples: input: 100\n64\n50\n20\n151200\n0\n output: 99\n64\n47\n20\n151200\n\n" }, { "title": "Problem B: e-Market", "content": "The city of Hakodate recently established a commodity exchange market. To participate in the market, each dealer transmits through the Internet an order consisting of his or her name, the type of the order (buy or sell), the name of the commodity, and the quoted price.\n\nIn this market a deal can be made only if the price of a sell order is lower than or equal to the price of a buy order. The price of the deal is the mean of the prices of the buy and sell orders, where the mean price is rounded downward to the nearest integer. To exclude dishonest deals, no deal is made between a pair of sell and buy orders from the same dealer. The system of the market maintains the list of orders for which a deal has not been made and processes a new order in the following manner.\n\n For a new sell order, a deal is made with the buy order with the highest price in the list satisfying the conditions. If there is more than one buy order with the same price, the deal is made with the earliest of them.\n\n For a new buy order, a deal is made with the sell order with the lowest price in the list satisfying the conditions. If there is more than one sell order with the same price, the deal is made with the earliest of them.\nThe market opens at 7: 00 and closes at 22: 00 everyday. When the market closes, all the remaining orders are cancelled. To keep complete record of the market, the system of the market saves all the orders it received everyday.\n\nThe manager of the market asked the system administrator to make a program which reports the activity of the market. The report must contain two kinds of information. For each commodity the report must contain informationon the lowest, the average and the highest prices of successful deals. For each dealer, the report must contain information on the amounts the dealer paid and received for commodities.", "constraint": "", "input": "The input contains several data sets. Each data set represents the record of the market on one day. The first line of each data set contains an integer n (n < 1000) which is the number of orders in the record. Each line of the record describes an order, consisting of the name of the dealer, the type of the order, the name of the commodity, and the quoted price. They are separated by a single space character.\n\nThe name of a dealer consists of capital alphabetical letters and is less than 10 characters in length. The type of an order is indicated by a string, \"BUY\" or \"SELL\". The name of a commodity is a single capital letter. The quoted price is a positive integer less than 1000.\n\nThe orders in a record are arranged according to time when they were received and the first line of the record corresponds to the oldest order.\n\nThe end of the input is indicated by a line containing a zero.", "output": "The output for each data set consists of two parts separated by a line containing two hyphen (`-') characters.\n\nThe first part is output for commodities. For each commodity, your program should output the name of the commodity and the lowest, the average and the highest prices of successful deals in one line. The name and the prices in a line should be separated by a space character. The average price is rounded downward to the nearest integer. The output should contain only the commodities for which deals are made and the order of the output must be alphabetic.\n\nThe second part is output for dealers. For each dealer, your program should output the name of the dealer, the amounts the dealer paid and received for commodities. The name and the numbers in a line should be separated by a space character. The output should contain all the dealers who transmitted orders. The order of dealers in the output must be lexicographic on their names. The lexicographic order is the order in which words in dictionaries are arranged.\n\nThe output for each data set should be followed by a linecontaining ten hyphen (`-') characters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nPERLIS SELL A 300\nWILKES BUY A 200\nHAMMING SELL A 100\n4\nBACKUS SELL A 10\nFLOYD BUY A 20\nIVERSON SELL B 30\nBACKUS BUY B 40\n7\nWILKINSON SELL A 500\nMCCARTHY BUY C 300\nWILKINSON SELL C 200\nDIJKSTRA SELL B 100\nBACHMAN BUY A 400\nDIJKSTRA BUY A 600\nWILKINSON SELL A 300\n2\nABCD SELL X 10\nABC BUY X 15\n2\nA SELL M 100\nA BUY M 100\n0\n output: A 150 150 150\n--\nHAMMING 0 150\nPERLIS 0 0\nWILKES 150 0\n----------\nA 15 15 15\nB 35 35 35\n--\nBACKUS 35 15\nFLOYD 15 0\nIVERSON 0 35\n----------\nA 350 450 550\nC 250 250 250\n--\nBACHMAN 350 0\nDIJKSTRA 550 0\nMCCARTHY 250 0\nWILKINSON 0 1150\n----------\nX 12 12 12\n--\nABC 12 0\nABCD 0 12\n----------\n--\nA 0 0\n----------"], "Pid": "p00804", "ProblemText": "Task Description: The city of Hakodate recently established a commodity exchange market. To participate in the market, each dealer transmits through the Internet an order consisting of his or her name, the type of the order (buy or sell), the name of the commodity, and the quoted price.\n\nIn this market a deal can be made only if the price of a sell order is lower than or equal to the price of a buy order. The price of the deal is the mean of the prices of the buy and sell orders, where the mean price is rounded downward to the nearest integer. To exclude dishonest deals, no deal is made between a pair of sell and buy orders from the same dealer. The system of the market maintains the list of orders for which a deal has not been made and processes a new order in the following manner.\n\n For a new sell order, a deal is made with the buy order with the highest price in the list satisfying the conditions. If there is more than one buy order with the same price, the deal is made with the earliest of them.\n\n For a new buy order, a deal is made with the sell order with the lowest price in the list satisfying the conditions. If there is more than one sell order with the same price, the deal is made with the earliest of them.\nThe market opens at 7: 00 and closes at 22: 00 everyday. When the market closes, all the remaining orders are cancelled. To keep complete record of the market, the system of the market saves all the orders it received everyday.\n\nThe manager of the market asked the system administrator to make a program which reports the activity of the market. The report must contain two kinds of information. For each commodity the report must contain informationon the lowest, the average and the highest prices of successful deals. For each dealer, the report must contain information on the amounts the dealer paid and received for commodities.\nTask Input: The input contains several data sets. Each data set represents the record of the market on one day. The first line of each data set contains an integer n (n < 1000) which is the number of orders in the record. Each line of the record describes an order, consisting of the name of the dealer, the type of the order, the name of the commodity, and the quoted price. They are separated by a single space character.\n\nThe name of a dealer consists of capital alphabetical letters and is less than 10 characters in length. The type of an order is indicated by a string, \"BUY\" or \"SELL\". The name of a commodity is a single capital letter. The quoted price is a positive integer less than 1000.\n\nThe orders in a record are arranged according to time when they were received and the first line of the record corresponds to the oldest order.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: The output for each data set consists of two parts separated by a line containing two hyphen (`-') characters.\n\nThe first part is output for commodities. For each commodity, your program should output the name of the commodity and the lowest, the average and the highest prices of successful deals in one line. The name and the prices in a line should be separated by a space character. The average price is rounded downward to the nearest integer. The output should contain only the commodities for which deals are made and the order of the output must be alphabetic.\n\nThe second part is output for dealers. For each dealer, your program should output the name of the dealer, the amounts the dealer paid and received for commodities. The name and the numbers in a line should be separated by a space character. The output should contain all the dealers who transmitted orders. The order of dealers in the output must be lexicographic on their names. The lexicographic order is the order in which words in dictionaries are arranged.\n\nThe output for each data set should be followed by a linecontaining ten hyphen (`-') characters.\nTask Samples: input: 3\nPERLIS SELL A 300\nWILKES BUY A 200\nHAMMING SELL A 100\n4\nBACKUS SELL A 10\nFLOYD BUY A 20\nIVERSON SELL B 30\nBACKUS BUY B 40\n7\nWILKINSON SELL A 500\nMCCARTHY BUY C 300\nWILKINSON SELL C 200\nDIJKSTRA SELL B 100\nBACHMAN BUY A 400\nDIJKSTRA BUY A 600\nWILKINSON SELL A 300\n2\nABCD SELL X 10\nABC BUY X 15\n2\nA SELL M 100\nA BUY M 100\n0\n output: A 150 150 150\n--\nHAMMING 0 150\nPERLIS 0 0\nWILKES 150 0\n----------\nA 15 15 15\nB 35 35 35\n--\nBACKUS 35 15\nFLOYD 15 0\nIVERSON 0 35\n----------\nA 350 450 550\nC 250 250 250\n--\nBACHMAN 350 0\nDIJKSTRA 550 0\nMCCARTHY 250 0\nWILKINSON 0 1150\n----------\nX 12 12 12\n--\nABC 12 0\nABCD 0 12\n----------\n--\nA 0 0\n----------\n\n" }, { "title": "Problem C: Fishnet", "content": "A fisherman named Etadokah awoke in a very small island. He could see calm, beautiful and blue sea around the island. The previous night he had encountered a terrible storm and had reached this uninhabited island. Some wrecks of his ship were spread around him. He found a square wood-frame and a long thread among the wrecks. He had to survive in this island until someone came and saved him.\n\nIn order to catch fish, he began to make a kind of fishnet by cutting the long thread into short threads and fixing them at pegs on the square wood-frame (Figure 1). He wanted to know the sizes of the meshes of the fishnet to see whether he could catch small fish as well as large ones.\n\nThe wood-frame is perfectly square with four thin edges one meter long. . a bottom edge, a top edge, a left edge, and a right edge. There are n pegs on each edge, and thus there are 4n pegs in total. The positions ofpegs are represented by their (x, y)-coordinates. Those of an example case with n = 2 are depicted in Figures 2 and 3. The position of the ith peg on the bottom edge is represented by (a_i, 0) . That on the top edge, on the left edge and on the right edge are represented by (b_i, 1) , (0, c_i), and (1, d_i), respectively. The long thread is cut into 2n threads with appropriate lengths. The threads are strained between (a_i, 0) and (b_i, 1) , and between (0, c_i) and (1, d_i) (i = 1, . . . , n) .\n\nYou should write a program that reports the size of the largest mesh among the (n + 1)^2 meshes of the fishnet made by fixing the threads at the pegs. You may assume that the thread he found is long enough to make the fishnet and that the wood-frame is thin enough for neglecting its thickness. \nFigure 1. A wood-frame with 8 pegs.\nFigure 2. Positions of pegs (indicated by small black circles)\nFigure 3. A fishnet and the largest mesh (shaded)", "constraint": "", "input": "The input consists of multiple subproblems followed by a line containing a zero that indicates the end of input. Each subproblem is given in the following format.\n\nn\na_1a_2 . . . a_n\nb_1b_2 . . . b_n\nc_1c_2 . . . c_n\nd_1d_2 . . . d_n\n\nAn integer n followed by a newline is the number of pegs on each edge. a_1, . . . , a_n, b_1, . . . , b_n, c_1, . . . , c_n, d_1, . . . , d_n are decimal fractions, and they are separated by a space character except that a_n, b_n, c_n and d_n are followed by a new line. Each a_i (i = 1, . . . , n) indicates the x-coordinate of the ith peg on the bottom edge. Each b_i (i = 1, . . . , n) indicates the x-coordinate of the ith peg on the top edge. Each c_i (i = 1, . . . , n) indicates the y-coordinate of the ith peg on the left edge. Each d_i (i = 1, . . . , n) indicates the y-coordinate of the ith peg on the right edge. The decimal fractions are represented by 7 digits after the decimal point. In addition you may assume that 0 < n <= 30 , 0 < a_1 < a_2 < . . . < a_n < 1,0 < b_1 < b_2 < . . . < b_n < 1 , 0 < c_1 < c_2 < . . . < c_n < 1 and 0 < d_1 <= d_2 < . . . < d_n < 1 .", "output": "For each subproblem, the size of the largest mesh should be printed followed by a new line. Each value should be represented by 6 digits after the decimal point, and it may not have an error greater than 0.000001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n0.2000000 0.6000000\n0.3000000 0.8000000\n0.3000000 0.5000000\n0.5000000 0.6000000\n2\n0.3333330 0.6666670\n0.3333330 0.6666670\n0.3333330 0.6666670\n0.3333330 0.6666670\n4\n0.2000000 0.4000000 0.6000000 0.8000000\n0.1000000 0.5000000 0.6000000 0.9000000\n0.2000000 0.4000000 0.6000000 0.8000000\n0.1000000 0.5000000 0.6000000 0.9000000\n2\n0.5138701 0.9476283\n0.1717362 0.1757412\n0.3086521 0.7022313\n0.2264312 0.5345343\n1\n0.4000000\n0.6000000\n0.3000000\n0.5000000\n0\n output: 0.215657\n0.111112\n0.078923\n0.279223\n0.348958"], "Pid": "p00805", "ProblemText": "Task Description: A fisherman named Etadokah awoke in a very small island. He could see calm, beautiful and blue sea around the island. The previous night he had encountered a terrible storm and had reached this uninhabited island. Some wrecks of his ship were spread around him. He found a square wood-frame and a long thread among the wrecks. He had to survive in this island until someone came and saved him.\n\nIn order to catch fish, he began to make a kind of fishnet by cutting the long thread into short threads and fixing them at pegs on the square wood-frame (Figure 1). He wanted to know the sizes of the meshes of the fishnet to see whether he could catch small fish as well as large ones.\n\nThe wood-frame is perfectly square with four thin edges one meter long. . a bottom edge, a top edge, a left edge, and a right edge. There are n pegs on each edge, and thus there are 4n pegs in total. The positions ofpegs are represented by their (x, y)-coordinates. Those of an example case with n = 2 are depicted in Figures 2 and 3. The position of the ith peg on the bottom edge is represented by (a_i, 0) . That on the top edge, on the left edge and on the right edge are represented by (b_i, 1) , (0, c_i), and (1, d_i), respectively. The long thread is cut into 2n threads with appropriate lengths. The threads are strained between (a_i, 0) and (b_i, 1) , and between (0, c_i) and (1, d_i) (i = 1, . . . , n) .\n\nYou should write a program that reports the size of the largest mesh among the (n + 1)^2 meshes of the fishnet made by fixing the threads at the pegs. You may assume that the thread he found is long enough to make the fishnet and that the wood-frame is thin enough for neglecting its thickness. \nFigure 1. A wood-frame with 8 pegs.\nFigure 2. Positions of pegs (indicated by small black circles)\nFigure 3. A fishnet and the largest mesh (shaded)\nTask Input: The input consists of multiple subproblems followed by a line containing a zero that indicates the end of input. Each subproblem is given in the following format.\n\nn\na_1a_2 . . . a_n\nb_1b_2 . . . b_n\nc_1c_2 . . . c_n\nd_1d_2 . . . d_n\n\nAn integer n followed by a newline is the number of pegs on each edge. a_1, . . . , a_n, b_1, . . . , b_n, c_1, . . . , c_n, d_1, . . . , d_n are decimal fractions, and they are separated by a space character except that a_n, b_n, c_n and d_n are followed by a new line. Each a_i (i = 1, . . . , n) indicates the x-coordinate of the ith peg on the bottom edge. Each b_i (i = 1, . . . , n) indicates the x-coordinate of the ith peg on the top edge. Each c_i (i = 1, . . . , n) indicates the y-coordinate of the ith peg on the left edge. Each d_i (i = 1, . . . , n) indicates the y-coordinate of the ith peg on the right edge. The decimal fractions are represented by 7 digits after the decimal point. In addition you may assume that 0 < n <= 30 , 0 < a_1 < a_2 < . . . < a_n < 1,0 < b_1 < b_2 < . . . < b_n < 1 , 0 < c_1 < c_2 < . . . < c_n < 1 and 0 < d_1 <= d_2 < . . . < d_n < 1 .\nTask Output: For each subproblem, the size of the largest mesh should be printed followed by a new line. Each value should be represented by 6 digits after the decimal point, and it may not have an error greater than 0.000001.\nTask Samples: input: 2\n0.2000000 0.6000000\n0.3000000 0.8000000\n0.3000000 0.5000000\n0.5000000 0.6000000\n2\n0.3333330 0.6666670\n0.3333330 0.6666670\n0.3333330 0.6666670\n0.3333330 0.6666670\n4\n0.2000000 0.4000000 0.6000000 0.8000000\n0.1000000 0.5000000 0.6000000 0.9000000\n0.2000000 0.4000000 0.6000000 0.8000000\n0.1000000 0.5000000 0.6000000 0.9000000\n2\n0.5138701 0.9476283\n0.1717362 0.1757412\n0.3086521 0.7022313\n0.2264312 0.5345343\n1\n0.4000000\n0.6000000\n0.3000000\n0.5000000\n0\n output: 0.215657\n0.111112\n0.078923\n0.279223\n0.348958\n\n" }, { "title": "Problem D: 77377", "content": "At the risk of its future, International Cellular Phones Corporation (ICPC) invests its resources in developing new mobile phones, which are planned to be equipped with Web browser, mailer, instant messenger, and many other advanced communication tools. Unless members of ICPC can complete this stiff job, it will eventually lose its market share.\n\nYou are now requested to help ICPC to develop intriguing text input software for small mobile terminals. As you may know, most phones today have twelve buttons, namely, ten number buttons from \"0\" to \"9\" and two special buttons \"*\" and \"#\". Although the company is very ambitious, it has decided to follow today's standards and conventions. You should not change the standard button layout, and should also pay attention to the following standard button assignment.\n\n \n
    button \tletters \tbutton letters \n \n 2 \ta, b, c \t6 \tm, n, o \n \n 3 \td, e, f \t7 \tp, q, r, s \n \n 4 \tg, h, i \t 8 \tt, u, v \n \n 5 \tj, k, l \t9 \tw, x, y, z \n \nThis means that you can only use eight buttons for text input.\n\nMost users of current ICPC phones are rushed enough to grudge wasting time on even a single button press. Your text input software should be economical of users' time so that a single button press is suffcient for each character input. In consequence, for instance, your program should accept a sequence of button presses \"77377\" and produce the word \"press\". Similarly, it should translate \"77377843288866\" into \"press the button\".\nUmmm. . . It seems impossible to build such text input software since more than one English letter is represented by a digit! . For instance, \"77377\" may represent not only \"press\" but also any one of 768 (= 4 * 4 * 3 * 4 * 4) character strings. However, we have the good news that the new model of ICPC mobile phones has enough memory to keep a dictionary. You may be able to write a program that filters out false words, i. e. , strings not listed in the dictionary.", "constraint": "", "input": "The input consists of multiple data sets, each of which represents a dictionary and a sequence of button presses in the following format.\n\nn\nword_1\n.\n.\n.\nword_n\nsequence\n\nn in the first line is a positive integer, representing the number of words in the dictionary. The next n lines, each representing a word in the dictionary, only contain lower case letters from `a' to `z'. The order of words in the dictionary is arbitrary (not necessarily in the lexicographic order). No words occur more than once in the dictionary. The last line, sequence, is the sequence of button presses, and only contains digits from `2' to `9'.\n\nYou may assume that a dictionary has at most one hundred words and that the length of each word is between one and fifty, inclusive. You may also assume that the number of input digits in the sequence is between one and three hundred, inclusive.\n\nA line containing a zero indicates the end of the input.", "output": "For each data set, your program should print all sequences that can be represented by the input sequence of button presses. Each sequence should be a sequence of words in the dictionary, and should appear in a single line. The order of lines does not matter.\n\nTwo adjacent words in a line should be separated by a single space character and the last word should be followed by a single period (`. ').\n\nFollowing those output lines, your program should also print a terminating line consisting solely of two hyphens (`--'). If there are no corresponding sequences of words, your program should only print the terminating line.\n\nYou may assume that for each data set the number of output lines is at most twenty, excluding the terminating line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\npush\npress\nthe\nbutton\nbottom\n77377843288866\n4\ni\nam\ngoing\ngo\n42646464\n3\na\nb\nc\n333\n0\n output: press the button.\n--\ni am going.\ni am go go i.\n--\n--"], "Pid": "p00806", "ProblemText": "Task Description: At the risk of its future, International Cellular Phones Corporation (ICPC) invests its resources in developing new mobile phones, which are planned to be equipped with Web browser, mailer, instant messenger, and many other advanced communication tools. Unless members of ICPC can complete this stiff job, it will eventually lose its market share.\n\nYou are now requested to help ICPC to develop intriguing text input software for small mobile terminals. As you may know, most phones today have twelve buttons, namely, ten number buttons from \"0\" to \"9\" and two special buttons \"*\" and \"#\". Although the company is very ambitious, it has decided to follow today's standards and conventions. You should not change the standard button layout, and should also pay attention to the following standard button assignment.\n\n \n
    button \tletters \tbutton letters \n \n 2 \ta, b, c \t6 \tm, n, o \n \n 3 \td, e, f \t7 \tp, q, r, s \n \n 4 \tg, h, i \t 8 \tt, u, v \n \n 5 \tj, k, l \t9 \tw, x, y, z \n \nThis means that you can only use eight buttons for text input.\n\nMost users of current ICPC phones are rushed enough to grudge wasting time on even a single button press. Your text input software should be economical of users' time so that a single button press is suffcient for each character input. In consequence, for instance, your program should accept a sequence of button presses \"77377\" and produce the word \"press\". Similarly, it should translate \"77377843288866\" into \"press the button\".\nUmmm. . . It seems impossible to build such text input software since more than one English letter is represented by a digit! . For instance, \"77377\" may represent not only \"press\" but also any one of 768 (= 4 * 4 * 3 * 4 * 4) character strings. However, we have the good news that the new model of ICPC mobile phones has enough memory to keep a dictionary. You may be able to write a program that filters out false words, i. e. , strings not listed in the dictionary.\nTask Input: The input consists of multiple data sets, each of which represents a dictionary and a sequence of button presses in the following format.\n\nn\nword_1\n.\n.\n.\nword_n\nsequence\n\nn in the first line is a positive integer, representing the number of words in the dictionary. The next n lines, each representing a word in the dictionary, only contain lower case letters from `a' to `z'. The order of words in the dictionary is arbitrary (not necessarily in the lexicographic order). No words occur more than once in the dictionary. The last line, sequence, is the sequence of button presses, and only contains digits from `2' to `9'.\n\nYou may assume that a dictionary has at most one hundred words and that the length of each word is between one and fifty, inclusive. You may also assume that the number of input digits in the sequence is between one and three hundred, inclusive.\n\nA line containing a zero indicates the end of the input.\nTask Output: For each data set, your program should print all sequences that can be represented by the input sequence of button presses. Each sequence should be a sequence of words in the dictionary, and should appear in a single line. The order of lines does not matter.\n\nTwo adjacent words in a line should be separated by a single space character and the last word should be followed by a single period (`. ').\n\nFollowing those output lines, your program should also print a terminating line consisting solely of two hyphens (`--'). If there are no corresponding sequences of words, your program should only print the terminating line.\n\nYou may assume that for each data set the number of output lines is at most twenty, excluding the terminating line.\nTask Samples: input: 5\npush\npress\nthe\nbutton\nbottom\n77377843288866\n4\ni\nam\ngoing\ngo\n42646464\n3\na\nb\nc\n333\n0\n output: press the button.\n--\ni am going.\ni am go go i.\n--\n--\n\n" }, { "title": "Problem E: Beehives", "content": "Taro and Hanako, students majoring in biology, have been engaged long in observations of beehives. Their interest is in finding any egg patterns laid by queen bees of a specific wild species. A queen bee is said to lay a batch ofeggs in a short time. Taro and Hanako have never seen queen bees laying eggs. Thus, every time they find beehives, they find eggs just laid in hive cells.\n\nTaro and Hanako have a convention to record an egg layout. . they assume the queen bee lays eggs, moving from one cell to an adjacent cell along a path containing no cycles. They record the path of cells with eggs. There is no guarantee in biology for them to find an acyclic path in every case. Yet they have never failed to do so in their observations. \n\nThere are only six possible movements from a cell to an adjacent one, and they agree to write down those six by letters a, b, c, d, e, and f ounterclockwise as shown in Figure 2. Thus the layout in Figure 1 may be written down as \"faafd\".\n\nTaro and Hanako have investigated beehives in a forest independently. Each has his/her own way to approach beehives, protecting oneself from possible bee attacks.\n\nThey are asked to report on their work jointly at a conference, and share their own observation records to draft a joint report. At this point they find a serious fault in their convention. They have never discussed which direction, in an absolute sense, should be taken as \"a\", and thus Figure 2 might be taken as, e. g. , Figure 3 or Figure 4. The layout shown in Figure 1 may be recorded differently, depending on the direction looking at the beehive and the path assumed: \"bcbdb\" with combination of Figure 3 and Figure 5, or \"bccac\" with combination of Figure 4 and Figure 6.\n\nA beehive can be observed only from its front side and never from its back, so a layout cannot be confused with its mirror image.\n\nSince they may have observed the same layout independently, they have to find duplicated records in their observations (Of course, they do not record the exact place and the exact time of each observation). Your mission is to help Taro and Hanako by writing a program that checks whether two observation records are made from the same layout.", "constraint": "", "input": "The input starts with a line containing the number of record pairs that follow. The number is given with at most three digits.\n\nEach record pair consists of two lines of layout records and a line containing a hyphen. Each layout record consists of a sequence of letters a, b, c, d, e, and f. Note that a layout record may be an empty sequence if a queen bee laid only one egg by some reason. You can trust Taro and Hanako in that any of the paths in the input does not force you to visit any cell more than once. Any of lines in the input contain no characters other than those described above, and contain at most one hundred characters.", "output": "For each pair of records, produce a line containing either \"true\" or \"false\": \"true\" if the two records represent the same layout, and \"false\" otherwise. A line should not contain any other characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\nfaafd\nbcbdb\n-\nbcbdb\nbccac\n-\nfaafd\naafdd\n-\naaafddd\naaaeff\n-\naaedd\naafdd\n-\n output: true\ntrue\nfalse\nfalse\nfalse"], "Pid": "p00807", "ProblemText": "Task Description: Taro and Hanako, students majoring in biology, have been engaged long in observations of beehives. Their interest is in finding any egg patterns laid by queen bees of a specific wild species. A queen bee is said to lay a batch ofeggs in a short time. Taro and Hanako have never seen queen bees laying eggs. Thus, every time they find beehives, they find eggs just laid in hive cells.\n\nTaro and Hanako have a convention to record an egg layout. . they assume the queen bee lays eggs, moving from one cell to an adjacent cell along a path containing no cycles. They record the path of cells with eggs. There is no guarantee in biology for them to find an acyclic path in every case. Yet they have never failed to do so in their observations. \n\nThere are only six possible movements from a cell to an adjacent one, and they agree to write down those six by letters a, b, c, d, e, and f ounterclockwise as shown in Figure 2. Thus the layout in Figure 1 may be written down as \"faafd\".\n\nTaro and Hanako have investigated beehives in a forest independently. Each has his/her own way to approach beehives, protecting oneself from possible bee attacks.\n\nThey are asked to report on their work jointly at a conference, and share their own observation records to draft a joint report. At this point they find a serious fault in their convention. They have never discussed which direction, in an absolute sense, should be taken as \"a\", and thus Figure 2 might be taken as, e. g. , Figure 3 or Figure 4. The layout shown in Figure 1 may be recorded differently, depending on the direction looking at the beehive and the path assumed: \"bcbdb\" with combination of Figure 3 and Figure 5, or \"bccac\" with combination of Figure 4 and Figure 6.\n\nA beehive can be observed only from its front side and never from its back, so a layout cannot be confused with its mirror image.\n\nSince they may have observed the same layout independently, they have to find duplicated records in their observations (Of course, they do not record the exact place and the exact time of each observation). Your mission is to help Taro and Hanako by writing a program that checks whether two observation records are made from the same layout.\nTask Input: The input starts with a line containing the number of record pairs that follow. The number is given with at most three digits.\n\nEach record pair consists of two lines of layout records and a line containing a hyphen. Each layout record consists of a sequence of letters a, b, c, d, e, and f. Note that a layout record may be an empty sequence if a queen bee laid only one egg by some reason. You can trust Taro and Hanako in that any of the paths in the input does not force you to visit any cell more than once. Any of lines in the input contain no characters other than those described above, and contain at most one hundred characters.\nTask Output: For each pair of records, produce a line containing either \"true\" or \"false\": \"true\" if the two records represent the same layout, and \"false\" otherwise. A line should not contain any other characters.\nTask Samples: input: 5\nfaafd\nbcbdb\n-\nbcbdb\nbccac\n-\nfaafd\naafdd\n-\naaafddd\naaaeff\n-\naaedd\naafdd\n-\n output: true\ntrue\nfalse\nfalse\nfalse\n\n" }, { "title": "Problem F: Young, Poor and Busy", "content": "Ken and Keiko are young, poor and busy. Short explanation: they are students, and ridden with part-time jobs. To make things worse, Ken lives in Hakodate and Keiko in Tokyo. They want to meet, but since they have neither time nor money, they have to go back to their respective jobs immediately after, and must be careful about transportation costs. Help them find the most economical meeting point.\n\nKen starts from Hakodate, Keiko from Tokyo. They know schedules and fares for all trains, and can choose to meet anywhere including their hometowns, but they cannot leave before 8am and must be back by 6pm in their respective towns. Train changes take no time (one can leave the same minute he/she arrives), but they want to meet for at least 30 minutes in the same city. \n\nThere can be up to 100 cities and 2000 direct connections, so you should devise an algorithm clever enough for the task.", "constraint": "", "input": "The input is a sequence of data sets.\n\nThe first line of a data set contains a single integer, the number of connections in the timetable. It is not greater than 2000.\n\nConnections are given one on a line, in the following format.\n\n Start_city HH: MM Arrival_city HH: MM price\n\nStart_city and Arrival_city are composed of up to 16 alphabetical characters, with only the first one in upper case. Departure and arrival times are given in hours and minutes (two digits each, separated by \": \") from 00: 00 to 23: 59. Arrival time is strictly after departure time. The price for one connection is an integer between 1 and 10000, inclusive. Fields are separated by spaces.\n\nThe end of the input is marked by a line containing a zero.", "output": "The output should contain one integer for each data set, the lowest cost possible. This is the total fare of all connections they use.\n\nIf there is no solution to a data set, you should output a zero.\n\nThe solution to each data set should be given in a separate line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nHakodate 08:15 Morioka 12:30 2500\nMorioka 14:05 Hakodate 17:30 2500\nMorioka 15:30 Hakodate 18:00 3000\nMorioka 14:30 Tokyo 17:50 3000\nTokyo 08:30 Morioka 13:35 3000\n4\nHakodate 08:15 Morioka 12:30 2500\nMorioka 14:04 Hakodate 17:30 2500\nMorioka 14:30 Tokyo 17:50 3000\nTokyo 08:30 Morioka 13:35 3000\n18\nHakodate 09:55 Akita 10:53 3840\nHakodate 14:14 Akita 16:09 1920\nHakodate 18:36 Akita 19:33 3840\nHakodate 08:00 Morioka 08:53 3550\nHakodate 22:40 Morioka 23:34 3550\nAkita 14:23 Tokyo 14:53 2010\nAkita 20:36 Tokyo 21:06 2010\nAkita 08:20 Hakodate 09:18 3840\nAkita 13:56 Hakodate 14:54 3840\nAkita 21:37 Hakodate 22:35 3840\nMorioka 09:51 Tokyo 10:31 2660\nMorioka 14:49 Tokyo 15:29 2660\nMorioka 19:42 Tokyo 20:22 2660\nMorioka 15:11 Hakodate 16:04 3550\nMorioka 23:03 Hakodate 23:56 3550\nTokyo 09:44 Morioka 11:04 1330\nTokyo 21:54 Morioka 22:34 2660\nTokyo 11:34 Akita 12:04 2010\n0\n output: 11000\n0\n11090"], "Pid": "p00808", "ProblemText": "Task Description: Ken and Keiko are young, poor and busy. Short explanation: they are students, and ridden with part-time jobs. To make things worse, Ken lives in Hakodate and Keiko in Tokyo. They want to meet, but since they have neither time nor money, they have to go back to their respective jobs immediately after, and must be careful about transportation costs. Help them find the most economical meeting point.\n\nKen starts from Hakodate, Keiko from Tokyo. They know schedules and fares for all trains, and can choose to meet anywhere including their hometowns, but they cannot leave before 8am and must be back by 6pm in their respective towns. Train changes take no time (one can leave the same minute he/she arrives), but they want to meet for at least 30 minutes in the same city. \n\nThere can be up to 100 cities and 2000 direct connections, so you should devise an algorithm clever enough for the task.\nTask Input: The input is a sequence of data sets.\n\nThe first line of a data set contains a single integer, the number of connections in the timetable. It is not greater than 2000.\n\nConnections are given one on a line, in the following format.\n\n Start_city HH: MM Arrival_city HH: MM price\n\nStart_city and Arrival_city are composed of up to 16 alphabetical characters, with only the first one in upper case. Departure and arrival times are given in hours and minutes (two digits each, separated by \": \") from 00: 00 to 23: 59. Arrival time is strictly after departure time. The price for one connection is an integer between 1 and 10000, inclusive. Fields are separated by spaces.\n\nThe end of the input is marked by a line containing a zero.\nTask Output: The output should contain one integer for each data set, the lowest cost possible. This is the total fare of all connections they use.\n\nIf there is no solution to a data set, you should output a zero.\n\nThe solution to each data set should be given in a separate line.\nTask Samples: input: 5\nHakodate 08:15 Morioka 12:30 2500\nMorioka 14:05 Hakodate 17:30 2500\nMorioka 15:30 Hakodate 18:00 3000\nMorioka 14:30 Tokyo 17:50 3000\nTokyo 08:30 Morioka 13:35 3000\n4\nHakodate 08:15 Morioka 12:30 2500\nMorioka 14:04 Hakodate 17:30 2500\nMorioka 14:30 Tokyo 17:50 3000\nTokyo 08:30 Morioka 13:35 3000\n18\nHakodate 09:55 Akita 10:53 3840\nHakodate 14:14 Akita 16:09 1920\nHakodate 18:36 Akita 19:33 3840\nHakodate 08:00 Morioka 08:53 3550\nHakodate 22:40 Morioka 23:34 3550\nAkita 14:23 Tokyo 14:53 2010\nAkita 20:36 Tokyo 21:06 2010\nAkita 08:20 Hakodate 09:18 3840\nAkita 13:56 Hakodate 14:54 3840\nAkita 21:37 Hakodate 22:35 3840\nMorioka 09:51 Tokyo 10:31 2660\nMorioka 14:49 Tokyo 15:29 2660\nMorioka 19:42 Tokyo 20:22 2660\nMorioka 15:11 Hakodate 16:04 3550\nMorioka 23:03 Hakodate 23:56 3550\nTokyo 09:44 Morioka 11:04 1330\nTokyo 21:54 Morioka 22:34 2660\nTokyo 11:34 Akita 12:04 2010\n0\n output: 11000\n0\n11090\n\n" }, { "title": "Problem G: Nim", "content": "Let's play a traditional game Nim. You and I are seated across a table and we have a hundred stones on the table (we know the number of stones exactly). We play in turn and at each turn, you or I can remove one to four stones from the heap. You play first and the one who removed the last stone loses.\n\nIn this game, you have a winning strategy. To see this, you first remove four stones and leave 96 stones. No matter how I play, I will end up with leaving 92-95 stones. Then you will in turn leave 91 stones for me (verify this is always possible). This way, you can always leave 5k + 1 stones for me and finally I get the last stone, sigh. If we initially had 101 stones, on the other hand, I have a winning strategy and you are doomed to lose.\n\nLet's generalize the game a little bit. First, let's make it a team game. Each team has n players and the 2n players are seated around the table, with each player having opponents at both sides. Turns round the table so the two teams play alternately. Second, let's vary the maximum number ofstones each player can take. That is, each player has his/her own maximum number ofstones he/she can take at each turn (The minimum is always one). So the game is asymmetric and may even be unfair.\n\nIn general, when played between two teams of experts, the outcome of a game is completely determined by the initial number ofstones and the minimum number of stones each player can take at each turn. In other words, either team has a winning strategy.\n\nYou are the head-coach of a team. In each game, the umpire shows both teams the initial number of stones and the maximum number of stones each player can take at each turn. Your team plays first. Your job is, given those numbers, to instantaneously judge whether your team has a winning strategy.\n\nIncidentally, there is a rumor that Captain Future and her officers of Hakodate-maru love this game, and they are killing their time playing it during their missions. You wonder where the stones are? . Well, they do not have stones but do have plenty of balls in the fuel containers! .", "constraint": "", "input": "The input is a sequence of lines, followed by the last line containing a zero. Each line except the last is a sequence of integers and has the following format.\n\nn S M_1 M_2 . . . M_2n\n\nwhere n is the number of players in a team, S the initial number of stones, and M_i the maximum number of stones i th player can take. 1st, 3rd, 5th, . . . players are your team's players and 2nd, 4th, 6th, . . . the opponents. Numbers are separated by a single space character. You may assume 1 <= n <= 10,1 <= M_i <= 16, and 1 <= S <= 2^13.", "output": "The out put should consist of lines each containing either a one, meaning your team has a winning strategy, or a zero otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 101 4 4\n1 100 4 4\n3 97 8 7 6 5 4 3\n0\n output: 0\n1\n1"], "Pid": "p00809", "ProblemText": "Task Description: Let's play a traditional game Nim. You and I are seated across a table and we have a hundred stones on the table (we know the number of stones exactly). We play in turn and at each turn, you or I can remove one to four stones from the heap. You play first and the one who removed the last stone loses.\n\nIn this game, you have a winning strategy. To see this, you first remove four stones and leave 96 stones. No matter how I play, I will end up with leaving 92-95 stones. Then you will in turn leave 91 stones for me (verify this is always possible). This way, you can always leave 5k + 1 stones for me and finally I get the last stone, sigh. If we initially had 101 stones, on the other hand, I have a winning strategy and you are doomed to lose.\n\nLet's generalize the game a little bit. First, let's make it a team game. Each team has n players and the 2n players are seated around the table, with each player having opponents at both sides. Turns round the table so the two teams play alternately. Second, let's vary the maximum number ofstones each player can take. That is, each player has his/her own maximum number ofstones he/she can take at each turn (The minimum is always one). So the game is asymmetric and may even be unfair.\n\nIn general, when played between two teams of experts, the outcome of a game is completely determined by the initial number ofstones and the minimum number of stones each player can take at each turn. In other words, either team has a winning strategy.\n\nYou are the head-coach of a team. In each game, the umpire shows both teams the initial number of stones and the maximum number of stones each player can take at each turn. Your team plays first. Your job is, given those numbers, to instantaneously judge whether your team has a winning strategy.\n\nIncidentally, there is a rumor that Captain Future and her officers of Hakodate-maru love this game, and they are killing their time playing it during their missions. You wonder where the stones are? . Well, they do not have stones but do have plenty of balls in the fuel containers! .\nTask Input: The input is a sequence of lines, followed by the last line containing a zero. Each line except the last is a sequence of integers and has the following format.\n\nn S M_1 M_2 . . . M_2n\n\nwhere n is the number of players in a team, S the initial number of stones, and M_i the maximum number of stones i th player can take. 1st, 3rd, 5th, . . . players are your team's players and 2nd, 4th, 6th, . . . the opponents. Numbers are separated by a single space character. You may assume 1 <= n <= 10,1 <= M_i <= 16, and 1 <= S <= 2^13.\nTask Output: The out put should consist of lines each containing either a one, meaning your team has a winning strategy, or a zero otherwise.\nTask Samples: input: 1 101 4 4\n1 100 4 4\n3 97 8 7 6 5 4 3\n0\n output: 0\n1\n1\n\n" }, { "title": "Problem H: Super Star", "content": "During a voyage of the starship Hakodate-maru (see Problem A), researchers found strange synchronized movements of stars. Having heard these observations, Dr. Extreme proposed a theory of \"super stars\". Do not take this term as a description of actors or singers. It is a revolutionary theory in astronomy.\n\nAccording to this theory, stars we are observing are not independent objects, but only small portions of larger objects called super stars. A super star is filled with invisible (or transparent) material, and only a number of points inside or on its surface shine. These points are observed as stars by us.\n\nIn order to verify this theory, Dr. Extreme wants to build motion equations of super stars and to compare the solutions of these equations with observed movements of stars. As the first step, he assumes that a super star is sphere-shaped, and has the smallest possible radius such that the sphere contains all given stars in or on it. This assumption makes it possible to estimate the volume of a super star, and thus its mass (the density of the invisible material is known).\n\nYou are asked to help Dr. Extreme by writing a program which, given the locations of a number of stars, finds the smallest sphere containing all of them in or on it. In this computation, you should ignore the sizes of stars. In other words, a star should be regarded as a point. You may assume the universe is a Euclidean space.", "constraint": "", "input": "The input consists of multiple data sets. Each data set is given in the following format.\n\nn\nx_1 y_1 z_1\nx_2 y_2 z_2\n. . .\nx_n y_n z_n\n\nThe first line of a data set contains an integer n, which is the number of points. It satisfies the condition 4 <= n <= 30.\n\nThe locations of n points are given by three-dimensional orthogonal coordinates: (x_i, y_i, z_i) (i = 1, . . . , n). Three coordinates of a point appear in a line, separated by a space character.\n\nEach value is given by a decimal fraction, and is between 0.0 and 100.0 (both ends inclusive). Points are at least 0.01 distant from each other.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each data set, the radius ofthe smallest sphere containing all given points should be printed, each in a separate line. The printed values should have 5 digits after the decimal point. They may not have an error greater than 0.00001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n10.00000 10.00000 10.00000\n20.00000 10.00000 10.00000\n20.00000 20.00000 10.00000\n10.00000 20.00000 10.00000\n4\n10.00000 10.00000 10.00000\n10.00000 50.00000 50.00000\n50.00000 10.00000 50.00000\n50.00000 50.00000 10.00000\n0\n output: 7.07107\n34.64102"], "Pid": "p00810", "ProblemText": "Task Description: During a voyage of the starship Hakodate-maru (see Problem A), researchers found strange synchronized movements of stars. Having heard these observations, Dr. Extreme proposed a theory of \"super stars\". Do not take this term as a description of actors or singers. It is a revolutionary theory in astronomy.\n\nAccording to this theory, stars we are observing are not independent objects, but only small portions of larger objects called super stars. A super star is filled with invisible (or transparent) material, and only a number of points inside or on its surface shine. These points are observed as stars by us.\n\nIn order to verify this theory, Dr. Extreme wants to build motion equations of super stars and to compare the solutions of these equations with observed movements of stars. As the first step, he assumes that a super star is sphere-shaped, and has the smallest possible radius such that the sphere contains all given stars in or on it. This assumption makes it possible to estimate the volume of a super star, and thus its mass (the density of the invisible material is known).\n\nYou are asked to help Dr. Extreme by writing a program which, given the locations of a number of stars, finds the smallest sphere containing all of them in or on it. In this computation, you should ignore the sizes of stars. In other words, a star should be regarded as a point. You may assume the universe is a Euclidean space.\nTask Input: The input consists of multiple data sets. Each data set is given in the following format.\n\nn\nx_1 y_1 z_1\nx_2 y_2 z_2\n. . .\nx_n y_n z_n\n\nThe first line of a data set contains an integer n, which is the number of points. It satisfies the condition 4 <= n <= 30.\n\nThe locations of n points are given by three-dimensional orthogonal coordinates: (x_i, y_i, z_i) (i = 1, . . . , n). Three coordinates of a point appear in a line, separated by a space character.\n\nEach value is given by a decimal fraction, and is between 0.0 and 100.0 (both ends inclusive). Points are at least 0.01 distant from each other.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each data set, the radius ofthe smallest sphere containing all given points should be printed, each in a separate line. The printed values should have 5 digits after the decimal point. They may not have an error greater than 0.00001.\nTask Samples: input: 4\n10.00000 10.00000 10.00000\n20.00000 10.00000 10.00000\n20.00000 20.00000 10.00000\n10.00000 20.00000 10.00000\n4\n10.00000 10.00000 10.00000\n10.00000 50.00000 50.00000\n50.00000 10.00000 50.00000\n50.00000 50.00000 10.00000\n0\n output: 7.07107\n34.64102\n\n" }, { "title": "Problem A: Calling Extraterrestrial Intelligence Again", "content": "A message from humans to extraterrestrial intelligence was sent through the Arecibo radio telescope in Puerto Rico on the afternoon of Saturday November l6, l974. The message consisted of l679 bits and was meant to be translated to a rectangular picture with 23 * 73 pixels. Since both 23 and 73 are prime numbers, 23 * 73 is the unique possible size of the translated rectangular picture each edge of which is longer than l pixel. Of course, there was no guarantee that the receivers would try to translate the message to a rectangular picture. Even if they would, they might put the pixels into the rectangle incorrectly. The senders of the Arecibo message were optimistic.\n\nWe are planning a similar project. Your task in the project is to find the most suitable width and height of the translated rectangular picture. The term ``most suitable'' is defined as follows. An integer m greater than 4 is given. A positive fraction a/b less than or equal to 1 is also given. The area of the picture should not be greater than m. Both of the width and the height of the translated picture should be prime numbers. The ratio of the width to the height should not be less than a/b nor greater than 1. You should maximize the area of the picture under these constraints.\n\nIn other words, you will receive an integer m and a fraction a/b . It holds that m > 4 and 0 < a/b <= 1 . You should find the pair of prime numbers p, q such that pq <= m and a/b <= p/q <= 1 , and furthermore, the product pq takes the maximum value among such pairs of two prime numbers. You should report p and q as the \"most suitable\" width and height of the translated picture.", "constraint": "", "input": "The input is a sequence of at most 2000 triplets of positive integers, delimited by a space character in between. Each line contains a single triplet. The sequence is followed by a triplet of zeros, 0 0 0, which indicates the end of the input and should not be treated as data to be processed.\n\nThe integers of each input triplet are the integer m, the numerator a, and the denominator b described above, in this order. You may assume 4 < m < 100000 and 1 <= a <= b <= 1000.", "output": "The output is a sequence of pairs of positive integers. The i-th output pair corresponds to the i-th input triplet. The integers of each output pair are the width p and the height q described above, in this order.\n\nEach output line contains a single pair. A space character is put between the integers as a delimiter. No other characters should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1 2\n99999 999 999\n1680 5 16\n1970 1 1\n2002 4 11\n0 0 0\n output: 2 2\n313 313\n23 73\n43 43\n37 53"], "Pid": "p00811", "ProblemText": "Task Description: A message from humans to extraterrestrial intelligence was sent through the Arecibo radio telescope in Puerto Rico on the afternoon of Saturday November l6, l974. The message consisted of l679 bits and was meant to be translated to a rectangular picture with 23 * 73 pixels. Since both 23 and 73 are prime numbers, 23 * 73 is the unique possible size of the translated rectangular picture each edge of which is longer than l pixel. Of course, there was no guarantee that the receivers would try to translate the message to a rectangular picture. Even if they would, they might put the pixels into the rectangle incorrectly. The senders of the Arecibo message were optimistic.\n\nWe are planning a similar project. Your task in the project is to find the most suitable width and height of the translated rectangular picture. The term ``most suitable'' is defined as follows. An integer m greater than 4 is given. A positive fraction a/b less than or equal to 1 is also given. The area of the picture should not be greater than m. Both of the width and the height of the translated picture should be prime numbers. The ratio of the width to the height should not be less than a/b nor greater than 1. You should maximize the area of the picture under these constraints.\n\nIn other words, you will receive an integer m and a fraction a/b . It holds that m > 4 and 0 < a/b <= 1 . You should find the pair of prime numbers p, q such that pq <= m and a/b <= p/q <= 1 , and furthermore, the product pq takes the maximum value among such pairs of two prime numbers. You should report p and q as the \"most suitable\" width and height of the translated picture.\nTask Input: The input is a sequence of at most 2000 triplets of positive integers, delimited by a space character in between. Each line contains a single triplet. The sequence is followed by a triplet of zeros, 0 0 0, which indicates the end of the input and should not be treated as data to be processed.\n\nThe integers of each input triplet are the integer m, the numerator a, and the denominator b described above, in this order. You may assume 4 < m < 100000 and 1 <= a <= b <= 1000.\nTask Output: The output is a sequence of pairs of positive integers. The i-th output pair corresponds to the i-th input triplet. The integers of each output pair are the width p and the height q described above, in this order.\n\nEach output line contains a single pair. A space character is put between the integers as a delimiter. No other characters should appear in the output.\nTask Samples: input: 5 1 2\n99999 999 999\n1680 5 16\n1970 1 1\n2002 4 11\n0 0 0\n output: 2 2\n313 313\n23 73\n43 43\n37 53\n\n" }, { "title": "Problem B: Equals are Equals", "content": "Mr. Simpson got up with a slight feeling of tiredness. It was the start of another day of hard work. A bunch of papers were waiting for his inspection on his desk in his office. The papers contained his students' answers to questions in his Math class, but the answers looked as if they were just stains of ink.\n\nHis headache came from the ``creativity'' of his students. They provided him a variety of ways to answer each problem. He has his own answer to each problem, which is correct, of course, and the best from his aesthetic point of view.\n\nSome of his students wrote algebraic expressions equivalent to the expected answer, but many of them look quite different from Mr. Simpson's answer in terms of their literal forms. Some wrote algebraic expressions not equivalent to his answer, but they look quite similar to it. Only a few of the students' answers were exactly the same as his.\n\nIt is his duty to check if each expression is mathematically equivalent to the answer he has prepared. This is to prevent expressions that are equivalent to his from being marked as ``incorrect'', even if they are not acceptable to his aesthetic moral.\n\nHe had now spent five days checking the expressions. Suddenly, he stood up and yelled, ``I've had enough! I must call for help. ''\n\nYour job is to write a program to help Mr. Simpson to judge if each answer is equivalent to the ``correct'' one. Algebraic expressions written on the papers are multi-variable polynomials over variable symbols a, b, . . . , z with integer coefficients, e. g. ,\n\n(a + b^2)(a - b^2), ax^2 +2bx + c and (x^2 +5x + 4)(x^2 + 5x + 6) + 1.\nMr. Simpson will input every answer expression as it is written on the papers; he promises you that an algebraic expression he inputs is a sequence of terms separated by additive operators `+' and `-', representing the sum of the terms with those operators, if any; a term is a juxtaposition of multiplicands, representing their product; and a multiplicand is either (a) a non-negative integer as a digit sequence in decimal, (b) a variable symbol (one of the lowercase letters `a' to `z'), possibly followed by a symbol `^' and a non-zero digit, which represents the power of that variable, or (c) a parenthesized algebraic expression, recursively. Note that the operator `+' or `-' appears only as a binary operator and not as a unary operator to specify the sing of its operand.\n\nHe says that he will put one or more space characters before an integer if it immediately follows another integer or a digit following the symbol `^'. He also says he may put spaces here and there in an expression as an attempt to make it readable, but he will never put a space between two consecutive digits of an integer. He remarks that the expressions are not so complicated, and that any expression, having its `-'s replaced with `+'s, if any, would have no variable raised to its 10th power, nor coefficient more than a billion, even if it is fully expanded into a form of a sum of products of coefficients and powered variables.", "constraint": "", "input": "The input to your program is a sequence of blocks of lines. A block consists of lines, each containing an expression, and a terminating line. After the last block, there is another terminating line. A terminating line is a line solely consisting of a period symbol.\n\nThe first expression of a block is one prepared by Mr. Simpson; all that follow in a block are answers by the students. An expression consists of lowercase letters, digits, operators `+', `-' and `^', parentheses `(' and `)', and spaces. A line containing an expression has no more than 80 characters.", "output": "Your program should produce a line solely consisting of ``yes'' or ``no'' for each answer by the students corresponding to whether or not it is mathematically equivalent to the expected answer. Your program should produce a line solely containing a period symbol after each block.", "content_img": false, "lang": "en", "error": false, "samples": ["input: a+b+c\n(a+b)+c\na- (b-c)+2\n.\n4ab\n(a - b) (0-b+a) - 1a ^ 2 - b ^ 2\n2 b 2 a\n.\n108 a\n2 2 3 3 3 a\n4 a^1 27\n.\n.\n output: yes\nno\n.\nno\nyes\n.\nyes\nyes\n."], "Pid": "p00812", "ProblemText": "Task Description: Mr. Simpson got up with a slight feeling of tiredness. It was the start of another day of hard work. A bunch of papers were waiting for his inspection on his desk in his office. The papers contained his students' answers to questions in his Math class, but the answers looked as if they were just stains of ink.\n\nHis headache came from the ``creativity'' of his students. They provided him a variety of ways to answer each problem. He has his own answer to each problem, which is correct, of course, and the best from his aesthetic point of view.\n\nSome of his students wrote algebraic expressions equivalent to the expected answer, but many of them look quite different from Mr. Simpson's answer in terms of their literal forms. Some wrote algebraic expressions not equivalent to his answer, but they look quite similar to it. Only a few of the students' answers were exactly the same as his.\n\nIt is his duty to check if each expression is mathematically equivalent to the answer he has prepared. This is to prevent expressions that are equivalent to his from being marked as ``incorrect'', even if they are not acceptable to his aesthetic moral.\n\nHe had now spent five days checking the expressions. Suddenly, he stood up and yelled, ``I've had enough! I must call for help. ''\n\nYour job is to write a program to help Mr. Simpson to judge if each answer is equivalent to the ``correct'' one. Algebraic expressions written on the papers are multi-variable polynomials over variable symbols a, b, . . . , z with integer coefficients, e. g. ,\n\n(a + b^2)(a - b^2), ax^2 +2bx + c and (x^2 +5x + 4)(x^2 + 5x + 6) + 1.\nMr. Simpson will input every answer expression as it is written on the papers; he promises you that an algebraic expression he inputs is a sequence of terms separated by additive operators `+' and `-', representing the sum of the terms with those operators, if any; a term is a juxtaposition of multiplicands, representing their product; and a multiplicand is either (a) a non-negative integer as a digit sequence in decimal, (b) a variable symbol (one of the lowercase letters `a' to `z'), possibly followed by a symbol `^' and a non-zero digit, which represents the power of that variable, or (c) a parenthesized algebraic expression, recursively. Note that the operator `+' or `-' appears only as a binary operator and not as a unary operator to specify the sing of its operand.\n\nHe says that he will put one or more space characters before an integer if it immediately follows another integer or a digit following the symbol `^'. He also says he may put spaces here and there in an expression as an attempt to make it readable, but he will never put a space between two consecutive digits of an integer. He remarks that the expressions are not so complicated, and that any expression, having its `-'s replaced with `+'s, if any, would have no variable raised to its 10th power, nor coefficient more than a billion, even if it is fully expanded into a form of a sum of products of coefficients and powered variables.\nTask Input: The input to your program is a sequence of blocks of lines. A block consists of lines, each containing an expression, and a terminating line. After the last block, there is another terminating line. A terminating line is a line solely consisting of a period symbol.\n\nThe first expression of a block is one prepared by Mr. Simpson; all that follow in a block are answers by the students. An expression consists of lowercase letters, digits, operators `+', `-' and `^', parentheses `(' and `)', and spaces. A line containing an expression has no more than 80 characters.\nTask Output: Your program should produce a line solely consisting of ``yes'' or ``no'' for each answer by the students corresponding to whether or not it is mathematically equivalent to the expected answer. Your program should produce a line solely containing a period symbol after each block.\nTask Samples: input: a+b+c\n(a+b)+c\na- (b-c)+2\n.\n4ab\n(a - b) (0-b+a) - 1a ^ 2 - b ^ 2\n2 b 2 a\n.\n108 a\n2 2 3 3 3 a\n4 a^1 27\n.\n.\n output: yes\nno\n.\nno\nyes\n.\nyes\nyes\n.\n\n" }, { "title": "Problem C: GIGA Universe Cup", "content": "Following FIFA World Cup, a larger competition called ``GIGA Universe Cup'' is taking place somewhere in our universe. Both FIFA World Cup and GIGA Universe Cup are two rounds competitions that consist of the first round, also known as ``group league, '' and the second called ``final tournament. '' In the first round, participating teams are divided into groups of four teams each. Each team in a group plays a match against each of the other teams in the same group. For example, let's say we have a group of the following four teams, ``Engband, Swedon, Argontina, and Nigerua. '' They play the following six matches: Engband - Swedon, Engband - Argontina, Engband - Nigerua, Swedon - Argontina, Swedon - Nigerua, and Argontina - Nigerua.\n\nThe result of a single match is shown by the number of goals scored by each team, like ``Engband 1 - 0 Argontina, '' which says Engband scored one goal whereas Argontina zero. Based on the result of a match, points are given to the two teams as follows and used to rank teams. If a team wins a match (i. e. , scores more goals than the other), three points are given to it and zero to the other. If a match draws (i. e. , the two teams score the same number of goals), one point is given to each.\n\nThe goal difference of a team in given matches is the total number of goals it scored minus the total number of goals its opponents scored in these matches. For example, if we have three matches ``Swedon 1 - 2 Engband, '' ``Swedon 3 - 4 Nigerua, '' and ``Swedon 5 - 6 Argontina, '' then the goal difference of Swedon in these three matches is (1 + 3 + 5) - (2 + 4+ 6) = -3.\n\nGiven the results of all the six matches in a group, teams are ranked by the following criteria, listed in the order of priority (that is, we first apply (a) to determine the ranking, with ties broken by (b), with ties broken by (c), and so on).\n(a) greater number of points in all the group matches; (b) greater goal difference in all the group matches; (c) greater number of goals scored in all the group matches. \nIf two or more teams are equal on the basis of the above three criteria, their place shall be determined by the following criteria, applied in this order:\n(d) greater number of points obtained in the group matches between the teams concerned; (e) greater goal difference resulting from the group matches between the teams concerned; (f) greater number of goals scored in the group matches between the teams concerned; \nIf two or more teams are sti Il equal, apply (d), (e), and (f) as necessary to each such group. Repeat this until those three rules to equal teams do not make any further resolution. Finally, teams that still remain equal are ordered by:\n(g) drawing lots by the Organizing Committee for the GIGA Universe Cup. \nThe two teams coming first and second in each group qualify for the second round.\n\nYour job is to write a program which, given the results of matches played so far in a group and one team specified in the group, calculates the probability that the specified team will qualify for the second round. You may assume each team has played exactly two matches and has one match to play. In total, four matches have been played and two matches are to be played.\n\nAssume the probability that any team scores (exactly) p goals in any match is:\n\nfor p <= 8, and zero for p > 8 . Assume the lot in the step (g) is fair.", "constraint": "", "input": "The first line of the input is an integer, less than 1000, that indicates the number of subsequent records.\n\nThe rest of the input is the indicated number of records. A single record has the following format:\n\nIn the above, <_> is a single underscore (_) and a sequence of exactly four underscores (____). Each of _1, . . . , _4 is either an asterisk character (*) followed by exactly three uppercase letters (e. g. , *ENG), or an underscore followed by exactly three uppercase letters (e. g. , _SWE). The former indicates that it is the team you are asked to calculate the probability of the second round qualification for. You may assume exactly one of _1, . . . , _4 is marked with an asterisk. Each _ij(1 <= i < j <= 4) is a match result between the _i and _j. Each match result is either __-_ (i. e. , two underscores, hyphen, and another underscore) or of the form _x-y where each of x and y is a single digit (<= 8) . The former indicates that the corresponding match has not been played, whereas the latter that the result of the match was x goals by _i and y goals by _j. Since each team has played exactly two matches, exactly two match results are in the former format.", "output": "The output should consist of n lines where n is the number of records in the input. The ith line should show the probability that the designated team (marked with an asterisk) will qualify for the second round in the ith record.\n\nNumbers should be printed with exactly seven digits after the decimal point. Each number should not contain an error greater than 10^-7.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n_____*AAA__BBB__CCC__DDD\n*AAA_______0-0__0-0___-_\n_BBB_____________-___0-0\n_CCC_________________0-0\n_DDD____________________\n______CHN__CRC__TUR_*BRA\n_CHN_______0-2___-___0-4\n_CRC____________1-1___-_\n_TUR_________________1-2\n*BRA____________________\n______CMR_*KSA__GER__IRL\n_CMR_______1-0___-___1-1\n*KSA____________0-8___-_\n_GER_________________1-1\n_IRL____________________\n______TUN__JPN_*BEL__RUS\n_TUN________-___1-1__0-2\n_JPN____________2-2__1-0\n*BEL__________________-_\n_RUS____________________\n______MEX__CRO_*ECU__ITA\n_MEX_______1-0__2-1___-_\n_CRO_____________-___2-1\n*ECU_________________0-2\n_ITA____________________\n output: 0.5000000\n1.0000000\n0.0000000\n0.3852746\n0.0353304"], "Pid": "p00813", "ProblemText": "Task Description: Following FIFA World Cup, a larger competition called ``GIGA Universe Cup'' is taking place somewhere in our universe. Both FIFA World Cup and GIGA Universe Cup are two rounds competitions that consist of the first round, also known as ``group league, '' and the second called ``final tournament. '' In the first round, participating teams are divided into groups of four teams each. Each team in a group plays a match against each of the other teams in the same group. For example, let's say we have a group of the following four teams, ``Engband, Swedon, Argontina, and Nigerua. '' They play the following six matches: Engband - Swedon, Engband - Argontina, Engband - Nigerua, Swedon - Argontina, Swedon - Nigerua, and Argontina - Nigerua.\n\nThe result of a single match is shown by the number of goals scored by each team, like ``Engband 1 - 0 Argontina, '' which says Engband scored one goal whereas Argontina zero. Based on the result of a match, points are given to the two teams as follows and used to rank teams. If a team wins a match (i. e. , scores more goals than the other), three points are given to it and zero to the other. If a match draws (i. e. , the two teams score the same number of goals), one point is given to each.\n\nThe goal difference of a team in given matches is the total number of goals it scored minus the total number of goals its opponents scored in these matches. For example, if we have three matches ``Swedon 1 - 2 Engband, '' ``Swedon 3 - 4 Nigerua, '' and ``Swedon 5 - 6 Argontina, '' then the goal difference of Swedon in these three matches is (1 + 3 + 5) - (2 + 4+ 6) = -3.\n\nGiven the results of all the six matches in a group, teams are ranked by the following criteria, listed in the order of priority (that is, we first apply (a) to determine the ranking, with ties broken by (b), with ties broken by (c), and so on).\n(a) greater number of points in all the group matches; (b) greater goal difference in all the group matches; (c) greater number of goals scored in all the group matches. \nIf two or more teams are equal on the basis of the above three criteria, their place shall be determined by the following criteria, applied in this order:\n(d) greater number of points obtained in the group matches between the teams concerned; (e) greater goal difference resulting from the group matches between the teams concerned; (f) greater number of goals scored in the group matches between the teams concerned; \nIf two or more teams are sti Il equal, apply (d), (e), and (f) as necessary to each such group. Repeat this until those three rules to equal teams do not make any further resolution. Finally, teams that still remain equal are ordered by:\n(g) drawing lots by the Organizing Committee for the GIGA Universe Cup. \nThe two teams coming first and second in each group qualify for the second round.\n\nYour job is to write a program which, given the results of matches played so far in a group and one team specified in the group, calculates the probability that the specified team will qualify for the second round. You may assume each team has played exactly two matches and has one match to play. In total, four matches have been played and two matches are to be played.\n\nAssume the probability that any team scores (exactly) p goals in any match is:\n\nfor p <= 8, and zero for p > 8 . Assume the lot in the step (g) is fair.\nTask Input: The first line of the input is an integer, less than 1000, that indicates the number of subsequent records.\n\nThe rest of the input is the indicated number of records. A single record has the following format:\n\nIn the above, <_> is a single underscore (_) and a sequence of exactly four underscores (____). Each of _1, . . . , _4 is either an asterisk character (*) followed by exactly three uppercase letters (e. g. , *ENG), or an underscore followed by exactly three uppercase letters (e. g. , _SWE). The former indicates that it is the team you are asked to calculate the probability of the second round qualification for. You may assume exactly one of _1, . . . , _4 is marked with an asterisk. Each _ij(1 <= i < j <= 4) is a match result between the _i and _j. Each match result is either __-_ (i. e. , two underscores, hyphen, and another underscore) or of the form _x-y where each of x and y is a single digit (<= 8) . The former indicates that the corresponding match has not been played, whereas the latter that the result of the match was x goals by _i and y goals by _j. Since each team has played exactly two matches, exactly two match results are in the former format.\nTask Output: The output should consist of n lines where n is the number of records in the input. The ith line should show the probability that the designated team (marked with an asterisk) will qualify for the second round in the ith record.\n\nNumbers should be printed with exactly seven digits after the decimal point. Each number should not contain an error greater than 10^-7.\nTask Samples: input: 5\n_____*AAA__BBB__CCC__DDD\n*AAA_______0-0__0-0___-_\n_BBB_____________-___0-0\n_CCC_________________0-0\n_DDD____________________\n______CHN__CRC__TUR_*BRA\n_CHN_______0-2___-___0-4\n_CRC____________1-1___-_\n_TUR_________________1-2\n*BRA____________________\n______CMR_*KSA__GER__IRL\n_CMR_______1-0___-___1-1\n*KSA____________0-8___-_\n_GER_________________1-1\n_IRL____________________\n______TUN__JPN_*BEL__RUS\n_TUN________-___1-1__0-2\n_JPN____________2-2__1-0\n*BEL__________________-_\n_RUS____________________\n______MEX__CRO_*ECU__ITA\n_MEX_______1-0__2-1___-_\n_CRO_____________-___2-1\n*ECU_________________0-2\n_ITA____________________\n output: 0.5000000\n1.0000000\n0.0000000\n0.3852746\n0.0353304\n\n" }, { "title": "Problem D: Life Line", "content": "Let's play a new board game 'Life Line'.\nThe number of the players is greater than 1 and less than 10.\nIn this game, the board is a regular triangle in which many small regular triangles are arranged (See Figure l). The edges of each small triangle are of the same length. \nThe size of the board is expressed by the number of vertices on the bottom edge of the outer triangle.\nFor example, the size of the board in Figure 1 is 4.\nAt the beginning of the game, each player is assigned his own identification number between 1 and 9, and is given some stones on which his identification number is written.\nEach player puts his stone in turn on one of the 'empty' vertices. An 'empty vertex' is a vertex that has no stone on it.\nWhen one player puts his stone on one of the vertices during his turn, some stones might be removed from the board. The player gains points which is equal to the number of the removed stones of others, but loses points which is equal to the number of the removed stones of himself. The points of a player for a single turn is the points he gained minus the points he lost in that turn.\nThe conditions for removing stones are as follows:\n The stones on the board are divided into groups. Each group contains a set of stones whose numbers are the same and placed adjacently. That is, if the same numbered stones are placed adjacently, they belong to the same group.\n If none of the stones in a group is adjacent to at least one 'empty' vertex, all the stones in that group are removed from the board.\nSuppose that the turn of the player '4' comes now. If he puts his stone on the vertex shown in Figure 3a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 3b). The player gains 6 points, because the 6 stones of others are removed from the board (See Figure 3c). \nAs another example, suppose that the turn of the player '2' comes in Figure 2. If the player puts his stone on the vertex shown in Figure 4a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 4b). The player gains 4 points, because the 4 stones of others are removed. But, at the same time, he loses 3 points, because his 3 stones are removed. As the result, the player's points of this turn is 4 - 3 = 1 (See Figure 4c).\nWhen each player puts all of his stones on the board, the game is over. The total score of a player is the summation of the points of all of his turns.\nYour job is to write a program that tells you the maximum points a player can get (i. e. , the points he gains - the points he loses) in his current turn.", "constraint": "", "input": "The input consists of multiple data. Each data represents the state of the board of the game still in progress.\n\nThe format of each data is as follows.\n\n N C\n\n S_1,1\n S_2,1 S_2,2\n S_3,1 S_3,2 S_3,3\n . . .\n S_N, 1 . . . S_N, N\n\nN is the size of the board (3 <= N <= 10).\n\nC is the identification number of the player whose turn comes now (1 <= C <= 9) . That is, your program must calculate his points in this turn.\n\nS_i, j is the state of the vertex on the board (0 <= S_i, j <= 9) . If the value of S_i, j is positive, it means that there is the stone numbered by S_i, j there. If the value of S_i, j is 0, it means that the vertex is 'empty'.\n\nTwo zeros in a line, i. e. , 0 0, represents the end of the input.", "output": "For each data, the maximum points the player can get in the turn should be output, each in a separate line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 2\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 0\n 0 0 0 0\n0 0 0 0 0\n5 3\n 3\n 3 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0\n output: 6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n5"], "Pid": "p00814", "ProblemText": "Task Description: Let's play a new board game 'Life Line'.\nThe number of the players is greater than 1 and less than 10.\nIn this game, the board is a regular triangle in which many small regular triangles are arranged (See Figure l). The edges of each small triangle are of the same length. \nThe size of the board is expressed by the number of vertices on the bottom edge of the outer triangle.\nFor example, the size of the board in Figure 1 is 4.\nAt the beginning of the game, each player is assigned his own identification number between 1 and 9, and is given some stones on which his identification number is written.\nEach player puts his stone in turn on one of the 'empty' vertices. An 'empty vertex' is a vertex that has no stone on it.\nWhen one player puts his stone on one of the vertices during his turn, some stones might be removed from the board. The player gains points which is equal to the number of the removed stones of others, but loses points which is equal to the number of the removed stones of himself. The points of a player for a single turn is the points he gained minus the points he lost in that turn.\nThe conditions for removing stones are as follows:\n The stones on the board are divided into groups. Each group contains a set of stones whose numbers are the same and placed adjacently. That is, if the same numbered stones are placed adjacently, they belong to the same group.\n If none of the stones in a group is adjacent to at least one 'empty' vertex, all the stones in that group are removed from the board.\nSuppose that the turn of the player '4' comes now. If he puts his stone on the vertex shown in Figure 3a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 3b). The player gains 6 points, because the 6 stones of others are removed from the board (See Figure 3c). \nAs another example, suppose that the turn of the player '2' comes in Figure 2. If the player puts his stone on the vertex shown in Figure 4a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 4b). The player gains 4 points, because the 4 stones of others are removed. But, at the same time, he loses 3 points, because his 3 stones are removed. As the result, the player's points of this turn is 4 - 3 = 1 (See Figure 4c).\nWhen each player puts all of his stones on the board, the game is over. The total score of a player is the summation of the points of all of his turns.\nYour job is to write a program that tells you the maximum points a player can get (i. e. , the points he gains - the points he loses) in his current turn.\nTask Input: The input consists of multiple data. Each data represents the state of the board of the game still in progress.\n\nThe format of each data is as follows.\n\n N C\n\n S_1,1\n S_2,1 S_2,2\n S_3,1 S_3,2 S_3,3\n . . .\n S_N, 1 . . . S_N, N\n\nN is the size of the board (3 <= N <= 10).\n\nC is the identification number of the player whose turn comes now (1 <= C <= 9) . That is, your program must calculate his points in this turn.\n\nS_i, j is the state of the vertex on the board (0 <= S_i, j <= 9) . If the value of S_i, j is positive, it means that there is the stone numbered by S_i, j there. If the value of S_i, j is 0, it means that the vertex is 'empty'.\n\nTwo zeros in a line, i. e. , 0 0, represents the end of the input.\nTask Output: For each data, the maximum points the player can get in the turn should be output, each in a separate line.\nTask Samples: input: 4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 2\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 0\n 0 0 0 0\n0 0 0 0 0\n5 3\n 3\n 3 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0\n output: 6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n5\n\n" }, { "title": "Problem E: Map of Ninja House", "content": "An old document says that a Ninja House in Kanazawa City was in fact a defensive fortress, which was designed like a maze. Its rooms were connected by hidden doors in a complicated manner, so that any invader would become lost. Each room has at least two doors.\n\nThe Ninja House can be modeled by a graph, as shown in Figure l. A circle represents a room. Each line connecting two circles represents a door between two rooms. \n \n \n\nFigure l. Graph Model of Ninja House.\n \n\nFigure 2. Ninja House exploration.\n \n \n\nI decided to draw a map, since no map was available. Your mission is to help me draw a map from the record of my exploration.\n\nI started exploring by entering a single entrance that was open to the outside. The path I walked is schematically shown in Figure 2, by a line with arrows. The rules for moving between rooms are described below.\n\n After entering a room, I first open the rightmost door and move to the next room. However, if the next room has already been visited, I close the door without entering, and open the next rightmost door, and so on. When I have inspected all the doors of a room, I go back through the door I used to enter the room. \n\nI have a counter with me to memorize the distance from the first room. The counter is incremented when I enter a new room, and decremented when I go back from a room. In Figure 2, each number in parentheses is the value of the counter when I have entered the room, i. e. , the distance from the first room. In contrast, the numbers not in parentheses represent the order of my visit.\n\nI take a record of my exploration. Every time I open a door, I record a single number, according to the following rules.\n\n If the opposite side of the door is a new room, I record the number of doors in that room, which is a positive number.\n\n If it is an already visited room, say R, I record ``the distance of R from the first room'' minus ``the distance of the current room from the first room'', which is a negative number.\nIn the example shown in Figure 2, as the first room has three doors connecting other rooms, I initially record ``3''. Then when I move to the second, third, and fourth rooms, which all have three doors, I append ``3 3 3'' to the record. When I skip the entry from the fourth room to the first room, the distance difference ``-3'' (minus three) will be appended, and so on. So, when I finish this exploration, its record is a sequence of numbers ``3 3 3 3 -3 3 2 -5 3 2 -5 -3''.\n\nThere are several dozens of Ninja Houses in the city. Given a sequence of numbers for each of these houses, you should produce a graph for each house.", "constraint": "", "input": "The first line of the input is a single integer n, indicating the number of records of Ninja Houses I have visited. You can assume that n is less than 100. Each of the following n records consists of numbers recorded on one exploration and a zero as a terminator. Each record consists of one or more lines whose lengths are less than 1000 characters. Each number is delimited by a space or a newline. You can assume that the number of rooms for each Ninja House is less than 100, and the number of doors in each room is less than 40.", "output": "For each Ninja House of m rooms, the output should consist of m lines. The j-th line of each such m lines should look as follows:\n\ni r_1 r_2 . . . r_ki\nr_1r_kiik_iir_1r_2r_kiir_1r_ki", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n3 3 3 3 -3 3 2 -5 3 2 -5 -3 0\n3 5 4 -2 4 -3 -2 -2 -1 0\n output: 1 2 4 6\n2 1 3 8\n3 2 4 7\n4 1 3 5\n5 4 6 7\n6 1 5\n7 3 5 8\n8 2 7\n1 2 3 4\n2 1 3 3 4 4\n3 1 2 2 4\n4 1 2 2 3"], "Pid": "p00815", "ProblemText": "Task Description: An old document says that a Ninja House in Kanazawa City was in fact a defensive fortress, which was designed like a maze. Its rooms were connected by hidden doors in a complicated manner, so that any invader would become lost. Each room has at least two doors.\n\nThe Ninja House can be modeled by a graph, as shown in Figure l. A circle represents a room. Each line connecting two circles represents a door between two rooms. \n \n \n\nFigure l. Graph Model of Ninja House.\n \n\nFigure 2. Ninja House exploration.\n \n \n\nI decided to draw a map, since no map was available. Your mission is to help me draw a map from the record of my exploration.\n\nI started exploring by entering a single entrance that was open to the outside. The path I walked is schematically shown in Figure 2, by a line with arrows. The rules for moving between rooms are described below.\n\n After entering a room, I first open the rightmost door and move to the next room. However, if the next room has already been visited, I close the door without entering, and open the next rightmost door, and so on. When I have inspected all the doors of a room, I go back through the door I used to enter the room. \n\nI have a counter with me to memorize the distance from the first room. The counter is incremented when I enter a new room, and decremented when I go back from a room. In Figure 2, each number in parentheses is the value of the counter when I have entered the room, i. e. , the distance from the first room. In contrast, the numbers not in parentheses represent the order of my visit.\n\nI take a record of my exploration. Every time I open a door, I record a single number, according to the following rules.\n\n If the opposite side of the door is a new room, I record the number of doors in that room, which is a positive number.\n\n If it is an already visited room, say R, I record ``the distance of R from the first room'' minus ``the distance of the current room from the first room'', which is a negative number.\nIn the example shown in Figure 2, as the first room has three doors connecting other rooms, I initially record ``3''. Then when I move to the second, third, and fourth rooms, which all have three doors, I append ``3 3 3'' to the record. When I skip the entry from the fourth room to the first room, the distance difference ``-3'' (minus three) will be appended, and so on. So, when I finish this exploration, its record is a sequence of numbers ``3 3 3 3 -3 3 2 -5 3 2 -5 -3''.\n\nThere are several dozens of Ninja Houses in the city. Given a sequence of numbers for each of these houses, you should produce a graph for each house.\nTask Input: The first line of the input is a single integer n, indicating the number of records of Ninja Houses I have visited. You can assume that n is less than 100. Each of the following n records consists of numbers recorded on one exploration and a zero as a terminator. Each record consists of one or more lines whose lengths are less than 1000 characters. Each number is delimited by a space or a newline. You can assume that the number of rooms for each Ninja House is less than 100, and the number of doors in each room is less than 40.\nTask Output: For each Ninja House of m rooms, the output should consist of m lines. The j-th line of each such m lines should look as follows:\n\ni r_1 r_2 . . . r_ki\nr_1r_kiik_iir_1r_2r_kiir_1r_ki\nTask Samples: input: 2\n3 3 3 3 -3 3 2 -5 3 2 -5 -3 0\n3 5 4 -2 4 -3 -2 -2 -1 0\n output: 1 2 4 6\n2 1 3 8\n3 2 4 7\n4 1 3 5\n5 4 6 7\n6 1 5\n7 3 5 8\n8 2 7\n1 2 3 4\n2 1 3 3 4 4\n3 1 2 2 4\n4 1 2 2 3\n\n" }, { "title": "Problem F: Shredding Company", "content": "You have just been put in charge of developing a new shredder for the Shredding Company. Although a 'normal' shredder would just shred sheets of paper into little pieces so that the contents would become unreadable, this new shredder needs to have the following unusual basic characteristics.\nThe shredder takes as input a target number and a sheet of paper with a number written on it.\nIt shreds (or cuts) the sheet into pieces each of which has one or more digits on it.\nThe sum of the numbers written on each piece is the closest possible number to the target number, without going over it.\nFor example, suppose that the target number is 50, and the sheet of paper has the number 12346. The shredder would cut the sheet into four pieces, where one piece has 1, another has 2, the third has 34, and the fourth has 6. This is because their sum 43 (= 1 + 2 + 34 + 6) is closest to the target number 50 of all possible combinations without going over 50. For example, a combination where the pieces are 1,23,4, and 6 is not valid, because the sum of this combination 34 (= 1 + 23 + 4 + 6) is less than the above combination's 43. The combination of 12,34, and 6 is not valid either, because the sum 52 (= 12+34+6) is greater than the target number of 50.\nThere are also three special rules:\nIf the target number is the same as the number on the sheet of paper, then the paper is not cut. For example, if the target number is 100 and the number on the sheet of paper is also 100, then the paper is not cut.\nIf it is not possible to make any combination whose sum is less than or equal to the target number, then error is printed on a display. For example, if the target number is 1 and the number on the sheet of paper is 123, it is not possible to make any valid combination, as the combination with the smallest possible sum is 1,2,3. The sum for this combination is 6, which is greater than the target number, and thus error is printed.\nIf there is more than one possible combination where the sum is closest to the target number without going over it, then rejected is printed on a display. For example, if the target number is 15, and the number on the sheet of paper is 111, then there are two possible combinations with the highest possible sum of 12: (a) 1 and 11 and (b) 11 and 1; thus rejected is printed.\nIn order to develop such a shredder, you have decided to first make a simple program that would simulate the above characteristics and rules. Given two numbers, where the first is the target number and the second is the number on the sheet of paper to be shredded, you need to figure out how the shredder should 'cut up' the second number.", "constraint": "", "input": "The input consists of several test cases, each on one line, as follows:\n\nt_1 num_1\nt_2 num_2\n. . .\nt_n num_n\n0 0\n\nEach test case consists of the following two positive integers, which are separated by one space: (1) the first integer (t_i above) is the target number; (2) the second integer (num_i above) is the number that is on the paper to be shredded.\n\nNeither integers may have a 0 as the first digit, e. g. , 123 is allowed but 0123 is not. You may assume that both integers are at most 6 digits in length. A line consisting of two zeros signals the end of the input.", "output": "For each test case in the input, the corresponding output takes one of the following three types:\n\n sum part_1 part_2 . . .\n rejected\n error\nIn the first type, part_j and sum have the following meaning:\n\n Each part_j is a number on one piece of shredded paper. The order of part_j corresponds to the order of the original digits on the sheet of paper.\n sum is the sum of the numbers after being shredded, i. e. , sum = part_1 + part_2 + . . . .\n\nEach number should be separated by one space.\n\nThe message \"error\" is printed if it is not possible to make any combination, and \"rejected\" if there is more than one possible combination.\n\nNo extra characters including spaces are allowed at the beginning of each line, nor at the end of each line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 50 12346\n376 144139\n927438 927438\n18 3312\n9 3142\n25 1299\n111 33333\n103 862150\n6 1104\n0 0\n output: 43 1 2 34 6\n283 144 139\n927438 927438\n18 3 3 12\nerror\n21 1 2 9 9\nrejected\n103 86 2 15 0\nrejected"], "Pid": "p00816", "ProblemText": "Task Description: You have just been put in charge of developing a new shredder for the Shredding Company. Although a 'normal' shredder would just shred sheets of paper into little pieces so that the contents would become unreadable, this new shredder needs to have the following unusual basic characteristics.\nThe shredder takes as input a target number and a sheet of paper with a number written on it.\nIt shreds (or cuts) the sheet into pieces each of which has one or more digits on it.\nThe sum of the numbers written on each piece is the closest possible number to the target number, without going over it.\nFor example, suppose that the target number is 50, and the sheet of paper has the number 12346. The shredder would cut the sheet into four pieces, where one piece has 1, another has 2, the third has 34, and the fourth has 6. This is because their sum 43 (= 1 + 2 + 34 + 6) is closest to the target number 50 of all possible combinations without going over 50. For example, a combination where the pieces are 1,23,4, and 6 is not valid, because the sum of this combination 34 (= 1 + 23 + 4 + 6) is less than the above combination's 43. The combination of 12,34, and 6 is not valid either, because the sum 52 (= 12+34+6) is greater than the target number of 50.\nThere are also three special rules:\nIf the target number is the same as the number on the sheet of paper, then the paper is not cut. For example, if the target number is 100 and the number on the sheet of paper is also 100, then the paper is not cut.\nIf it is not possible to make any combination whose sum is less than or equal to the target number, then error is printed on a display. For example, if the target number is 1 and the number on the sheet of paper is 123, it is not possible to make any valid combination, as the combination with the smallest possible sum is 1,2,3. The sum for this combination is 6, which is greater than the target number, and thus error is printed.\nIf there is more than one possible combination where the sum is closest to the target number without going over it, then rejected is printed on a display. For example, if the target number is 15, and the number on the sheet of paper is 111, then there are two possible combinations with the highest possible sum of 12: (a) 1 and 11 and (b) 11 and 1; thus rejected is printed.\nIn order to develop such a shredder, you have decided to first make a simple program that would simulate the above characteristics and rules. Given two numbers, where the first is the target number and the second is the number on the sheet of paper to be shredded, you need to figure out how the shredder should 'cut up' the second number.\nTask Input: The input consists of several test cases, each on one line, as follows:\n\nt_1 num_1\nt_2 num_2\n. . .\nt_n num_n\n0 0\n\nEach test case consists of the following two positive integers, which are separated by one space: (1) the first integer (t_i above) is the target number; (2) the second integer (num_i above) is the number that is on the paper to be shredded.\n\nNeither integers may have a 0 as the first digit, e. g. , 123 is allowed but 0123 is not. You may assume that both integers are at most 6 digits in length. A line consisting of two zeros signals the end of the input.\nTask Output: For each test case in the input, the corresponding output takes one of the following three types:\n\n sum part_1 part_2 . . .\n rejected\n error\nIn the first type, part_j and sum have the following meaning:\n\n Each part_j is a number on one piece of shredded paper. The order of part_j corresponds to the order of the original digits on the sheet of paper.\n sum is the sum of the numbers after being shredded, i. e. , sum = part_1 + part_2 + . . . .\n\nEach number should be separated by one space.\n\nThe message \"error\" is printed if it is not possible to make any combination, and \"rejected\" if there is more than one possible combination.\n\nNo extra characters including spaces are allowed at the beginning of each line, nor at the end of each line.\nTask Samples: input: 50 12346\n376 144139\n927438 927438\n18 3312\n9 3142\n25 1299\n111 33333\n103 862150\n6 1104\n0 0\n output: 43 1 2 34 6\n283 144 139\n927438 927438\n18 3 3 12\nerror\n21 1 2 9 9\nrejected\n103 86 2 15 0\nrejected\n\n" }, { "title": "Problem G: True Liars", "content": "After having drifted about in a small boat for a couple of days, Akira Crusoe Maeda was finally cast ashore on a foggy island. Though he was exhausted and despaired, he was still fortunate to remember a legend of the foggy island, which he had heard from patriarchs in his childhood. This must be the island in the legend.\n\nIn the legend, two tribes have inhabited the island, one is divine and the other is devilish; once members of the divine tribe bless you, your future is bright and promising, and your soul will eventually go to Heaven; in contrast, once members of the devilish tribe curse you, your future is bleak and hopeless, and your soul will eventually fall down to Hell.\n\nIn order to prevent the worst-case scenario, Akira should distinguish the devilish from the divine. But how? They looked exactly alike and he could not distinguish one from the other solely by their appearances. He still had his last hope, however. The members of the divine tribe are truth-tellers, that is, they always tell the truth and those of the devilish tribe are liars, that is, they always tell a lie.\n\nHe asked some of the whether or not some are divine. They knew one another very much and always responded to him \"faithfully\" according to their individual natures (i. e. , they always tell the truth or always a lie). He did not dare to ask any other forms of questions, since the legend says that a devilish member would curse a person forever when he did not like the question. He had another piece of useful information: the legend tells the populations of both tribes. These numbers in the legend are trustworthy since everyone living on this island is immortal and none have ever been born at least these millennia.\n\nYou are a good computer programmer and so requested to help Akira by writing a program that classifies the inhabitants according to their answers to his inquiries.", "constraint": "", "input": "The input consists of multiple data sets, each in the following format:\n\nn p_1 p_2\nx_1 y_1 a_1\nx_2 y_2 a_2\n. . .\nx_i y_i a_i\n. . .\nx_n y_n a_n\n\nThe first line has three non-negative integers n, p_1, and p_2. n is the number of questions Akira asked. p_1 and p_2 are the populations of the divine and devilish tribes, respectively, in the legend. Each of the following n lines has two integers x_i, y_i and one word a_i. x_i and y_i are the identification numbers of inhabitants, each of which is between 1 and p_1 + p_2, inclusive. a_i is either \"yes\", if the inhabitant x_i said that the inhabitant y_i was a member of the divine tribe, or \"no\", otherwise. Note that x_i and y_i can be the same number since \"are you a member of the divine tribe? \" is a valid question. Note also that two lines may have the same x's and y's since Akira was very upset and might have asked the same question to the same one more than once.\n\nYou may assume that n is less than 1000 and that p_1 and p_2 are less than 300. A line with three zeros, i. e. , \"0 0 0\", represents the end of the input. You can assume that each data set is consistent and no contradictory answers are included.", "output": "For each data set, if it includes sufficient information to classify all the inhabitants, print the identification numbers of all the divine ones in ascending order, one in a line. In addition, following the output numbers, print \"end\" in a line. Otherwise, i. e. , if a given data set does not include sufficient information to identify all the divine members, print \"no\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 1\n1 2 no\n2 1 no\n3 2 1\n1 1 yes\n2 2 yes\n3 3 yes\n2 2 1\n1 2 yes\n2 3 no\n5 4 3\n1 2 yes\n1 3 no\n4 5 yes\n5 6 yes\n6 7 no\n0 0 0\n output: no\nno\n1\n2\nend\n3\n4\n5\n6\nend"], "Pid": "p00817", "ProblemText": "Task Description: After having drifted about in a small boat for a couple of days, Akira Crusoe Maeda was finally cast ashore on a foggy island. Though he was exhausted and despaired, he was still fortunate to remember a legend of the foggy island, which he had heard from patriarchs in his childhood. This must be the island in the legend.\n\nIn the legend, two tribes have inhabited the island, one is divine and the other is devilish; once members of the divine tribe bless you, your future is bright and promising, and your soul will eventually go to Heaven; in contrast, once members of the devilish tribe curse you, your future is bleak and hopeless, and your soul will eventually fall down to Hell.\n\nIn order to prevent the worst-case scenario, Akira should distinguish the devilish from the divine. But how? They looked exactly alike and he could not distinguish one from the other solely by their appearances. He still had his last hope, however. The members of the divine tribe are truth-tellers, that is, they always tell the truth and those of the devilish tribe are liars, that is, they always tell a lie.\n\nHe asked some of the whether or not some are divine. They knew one another very much and always responded to him \"faithfully\" according to their individual natures (i. e. , they always tell the truth or always a lie). He did not dare to ask any other forms of questions, since the legend says that a devilish member would curse a person forever when he did not like the question. He had another piece of useful information: the legend tells the populations of both tribes. These numbers in the legend are trustworthy since everyone living on this island is immortal and none have ever been born at least these millennia.\n\nYou are a good computer programmer and so requested to help Akira by writing a program that classifies the inhabitants according to their answers to his inquiries.\nTask Input: The input consists of multiple data sets, each in the following format:\n\nn p_1 p_2\nx_1 y_1 a_1\nx_2 y_2 a_2\n. . .\nx_i y_i a_i\n. . .\nx_n y_n a_n\n\nThe first line has three non-negative integers n, p_1, and p_2. n is the number of questions Akira asked. p_1 and p_2 are the populations of the divine and devilish tribes, respectively, in the legend. Each of the following n lines has two integers x_i, y_i and one word a_i. x_i and y_i are the identification numbers of inhabitants, each of which is between 1 and p_1 + p_2, inclusive. a_i is either \"yes\", if the inhabitant x_i said that the inhabitant y_i was a member of the divine tribe, or \"no\", otherwise. Note that x_i and y_i can be the same number since \"are you a member of the divine tribe? \" is a valid question. Note also that two lines may have the same x's and y's since Akira was very upset and might have asked the same question to the same one more than once.\n\nYou may assume that n is less than 1000 and that p_1 and p_2 are less than 300. A line with three zeros, i. e. , \"0 0 0\", represents the end of the input. You can assume that each data set is consistent and no contradictory answers are included.\nTask Output: For each data set, if it includes sufficient information to classify all the inhabitants, print the identification numbers of all the divine ones in ascending order, one in a line. In addition, following the output numbers, print \"end\" in a line. Otherwise, i. e. , if a given data set does not include sufficient information to identify all the divine members, print \"no\" in a line.\nTask Samples: input: 2 1 1\n1 2 no\n2 1 no\n3 2 1\n1 1 yes\n2 2 yes\n3 3 yes\n2 2 1\n1 2 yes\n2 3 no\n5 4 3\n1 2 yes\n1 3 no\n4 5 yes\n5 6 yes\n6 7 no\n0 0 0\n output: no\nno\n1\n2\nend\n3\n4\n5\n6\nend\n\n" }, { "title": "Problem H: Viva Confetti", "content": "Do you know confetti? They are small discs of colored paper, and people throw them around during parties or festivals. Since people throw lots of confetti, they may end up stacked one on another, so there may be hidden ones underneath.\nA handful of various sized confetti have been dropped on a table. Given their positions and sizes, can you tell us how many of them you can see?\n\nThe following figure represents the disc configuration for the first sample input, where the bottom disc is still visible.", "constraint": "", "input": "The input is composed of a number of configurations of the following form.\n\nn \t\t\nx_1 y_1 z_1\nx_2 y_2 z_2\n.\n.\n.\nx_n y_n z_n\n\nThe first line in a configuration is the number of discs in the configuration (a positive integer not more than 100), followed by one Ine descriptions of each disc: coordinates of its center and radius, expressed as real numbers in decimal notation, with up to 12 digits after the decimal point. The imprecision margin is ±5 * 10^-13. That is, it is guaranteed that variations of less than ±5 * 10^-13 on input values do not change which discs are visible. Coordinates of all points contained in discs are between -10 and 10.\n\nConfetti are listed in their stacking order, x_1 y_1 r_1 being the bottom one and x_n y_n r_n the top one. You are observing from the top.\n\nThe end of the input is marked by a zero on a single line.", "output": "For each configuration you should output the number of visible confetti on a single line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n0 0 0.5\n-0.9 0 1.00000000001\n0.9 0 1.00000000001\n5\n0 1 0.5\n1 1 1.00000000001\n0 2 1.00000000001\n-1 1 1.00000000001\n0 -0.00001 1.00000000001\n5\n0 1 0.5\n1 1 1.00000000001\n0 2 1.00000000001\n-1 1 1.00000000001\n0 0 1.00000000001\n2\n0 0 1.0000001\n0 0 1\n2\n0 0 1\n0.00000001 0 1\n0\n output: 3\n5\n4\n2\n2"], "Pid": "p00818", "ProblemText": "Task Description: Do you know confetti? They are small discs of colored paper, and people throw them around during parties or festivals. Since people throw lots of confetti, they may end up stacked one on another, so there may be hidden ones underneath.\nA handful of various sized confetti have been dropped on a table. Given their positions and sizes, can you tell us how many of them you can see?\n\nThe following figure represents the disc configuration for the first sample input, where the bottom disc is still visible.\nTask Input: The input is composed of a number of configurations of the following form.\n\nn \t\t\nx_1 y_1 z_1\nx_2 y_2 z_2\n.\n.\n.\nx_n y_n z_n\n\nThe first line in a configuration is the number of discs in the configuration (a positive integer not more than 100), followed by one Ine descriptions of each disc: coordinates of its center and radius, expressed as real numbers in decimal notation, with up to 12 digits after the decimal point. The imprecision margin is ±5 * 10^-13. That is, it is guaranteed that variations of less than ±5 * 10^-13 on input values do not change which discs are visible. Coordinates of all points contained in discs are between -10 and 10.\n\nConfetti are listed in their stacking order, x_1 y_1 r_1 being the bottom one and x_n y_n r_n the top one. You are observing from the top.\n\nThe end of the input is marked by a zero on a single line.\nTask Output: For each configuration you should output the number of visible confetti on a single line.\nTask Samples: input: 3\n0 0 0.5\n-0.9 0 1.00000000001\n0.9 0 1.00000000001\n5\n0 1 0.5\n1 1 1.00000000001\n0 2 1.00000000001\n-1 1 1.00000000001\n0 -0.00001 1.00000000001\n5\n0 1 0.5\n1 1 1.00000000001\n0 2 1.00000000001\n-1 1 1.00000000001\n0 0 1.00000000001\n2\n0 0 1.0000001\n0 0 1\n2\n0 0 1\n0.00000001 0 1\n0\n output: 3\n5\n4\n2\n2\n\n" }, { "title": "Problem A: Unreliable Messengers", "content": "The King of a little Kingdom on a little island in the Pacific Ocean frequently has childish\nideas. One day he said, “You shall make use of a message relaying game when you inform me\nof something. ” In response to the King 's statement, six servants were selected as messengers\nwhose names were Mr. J, Miss C, Mr. E, Mr. A, Dr. P, and Mr. M. They had to relay a message\nto the next messenger until the message got to the King.\n\nMessages addressed to the King consist of digits (‘0 '-‘9 ') and alphabet characters (‘a '-‘z ', ‘A '-‘Z '). Capital and small letters are distinguished in messages. For example, “ke3E9Aa” is a\nmessage.\n\nContrary to King 's expectations, he always received wrong messages, because each messenger\nchanged messages a bit before passing them to the next messenger. Since it irritated the King, he\ntold you who are the Minister of the Science and Technology Agency of the Kingdom, “We don 't\nwant such a wrong message any more. You shall develop software to correct it! ” In response to\nthe King 's new statement, you analyzed the messengers ' mistakes with all technologies in the\nKingdom, and acquired the following features of mistakes of each messenger. A surprising point\nwas that each messenger made the same mistake whenever relaying a message. The following\nfacts were observed.\n\nMr. J rotates all characters of the message to the left by one. For example, he transforms\n“a B23d” to “B23da”.\n\nMiss C rotates all characters of the message to the right by one. For example, she transforms\n“a B23d” to “da B23”.\n\nMr. E swaps the left half of the message with the right half. If the message has an odd number\nof characters, the middle one does not move. For example, he transforms “e3ac” to “ace3”,\nand “a B23d” to “3d2a B”.\n\nMr. A reverses the message. For example, he transforms “a B23d” to “d32Ba”.\n\nDr. P increments by one all the digits in the message. If a digit is ‘9 ', it becomes ‘0 '. The\nalphabet characters do not change. For example, he transforms “a B23d” to “a B34d”, and “e9ac”\nto “e0ac”.\n\nMr. M decrements by one all the digits in the message. If a digit is ‘0 ', it becomes ‘9 '. The\nalphabet characters do not change. For example, he transforms “a B23d” to “a B12d”, and “e0ac”\nto “e9ac”.\nThe software you must develop is to infer the original message from the final message, given the\norder of the messengers. For example, if the order of the messengers is A -> J -> M -> P and the\nmessage given to the King is “a B23d”, what is the original message? According to the features\nof the messengers ' mistakes, the sequence leading to the final message is\n\n A J M P\n“32Bad” --> “da B23” --> “a B23d” --> “a B12d” --> “a B23d”.\n\nAs a result, the original message should be “32Bad”.", "constraint": "", "input": "The input format is as follows.\n\n n\n The order of messengers\n The message given to the King\n .\n .\n .\n The order of messengers\n The message given to the King\n\nThe first line of the input contains a positive integer n, which denotes the number of data sets.\nEach data set is a pair of the order of messengers and the message given to the King. The\nnumber of messengers relaying a message is between 1 and 6 inclusive. The same person may\nnot appear more than once in the order of messengers. The length of a message is between 1\nand 25 inclusive.", "output": "The inferred messages are printed each on a separate line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nAJMP\naB23d\nE\n86AE\nAM\n6\nJPEM\nWaEaETC302Q\nCP\nrTurnAGundam1isdefferentf\n output: 32Bad\nAE86\n7\nEC302QTWaEa\nTurnAGundam0isdefferentfr"], "Pid": "p00819", "ProblemText": "Task Description: The King of a little Kingdom on a little island in the Pacific Ocean frequently has childish\nideas. One day he said, “You shall make use of a message relaying game when you inform me\nof something. ” In response to the King 's statement, six servants were selected as messengers\nwhose names were Mr. J, Miss C, Mr. E, Mr. A, Dr. P, and Mr. M. They had to relay a message\nto the next messenger until the message got to the King.\n\nMessages addressed to the King consist of digits (‘0 '-‘9 ') and alphabet characters (‘a '-‘z ', ‘A '-‘Z '). Capital and small letters are distinguished in messages. For example, “ke3E9Aa” is a\nmessage.\n\nContrary to King 's expectations, he always received wrong messages, because each messenger\nchanged messages a bit before passing them to the next messenger. Since it irritated the King, he\ntold you who are the Minister of the Science and Technology Agency of the Kingdom, “We don 't\nwant such a wrong message any more. You shall develop software to correct it! ” In response to\nthe King 's new statement, you analyzed the messengers ' mistakes with all technologies in the\nKingdom, and acquired the following features of mistakes of each messenger. A surprising point\nwas that each messenger made the same mistake whenever relaying a message. The following\nfacts were observed.\n\nMr. J rotates all characters of the message to the left by one. For example, he transforms\n“a B23d” to “B23da”.\n\nMiss C rotates all characters of the message to the right by one. For example, she transforms\n“a B23d” to “da B23”.\n\nMr. E swaps the left half of the message with the right half. If the message has an odd number\nof characters, the middle one does not move. For example, he transforms “e3ac” to “ace3”,\nand “a B23d” to “3d2a B”.\n\nMr. A reverses the message. For example, he transforms “a B23d” to “d32Ba”.\n\nDr. P increments by one all the digits in the message. If a digit is ‘9 ', it becomes ‘0 '. The\nalphabet characters do not change. For example, he transforms “a B23d” to “a B34d”, and “e9ac”\nto “e0ac”.\n\nMr. M decrements by one all the digits in the message. If a digit is ‘0 ', it becomes ‘9 '. The\nalphabet characters do not change. For example, he transforms “a B23d” to “a B12d”, and “e0ac”\nto “e9ac”.\nThe software you must develop is to infer the original message from the final message, given the\norder of the messengers. For example, if the order of the messengers is A -> J -> M -> P and the\nmessage given to the King is “a B23d”, what is the original message? According to the features\nof the messengers ' mistakes, the sequence leading to the final message is\n\n A J M P\n“32Bad” --> “da B23” --> “a B23d” --> “a B12d” --> “a B23d”.\n\nAs a result, the original message should be “32Bad”.\nTask Input: The input format is as follows.\n\n n\n The order of messengers\n The message given to the King\n .\n .\n .\n The order of messengers\n The message given to the King\n\nThe first line of the input contains a positive integer n, which denotes the number of data sets.\nEach data set is a pair of the order of messengers and the message given to the King. The\nnumber of messengers relaying a message is between 1 and 6 inclusive. The same person may\nnot appear more than once in the order of messengers. The length of a message is between 1\nand 25 inclusive.\nTask Output: The inferred messages are printed each on a separate line.\nTask Samples: input: 5\nAJMP\naB23d\nE\n86AE\nAM\n6\nJPEM\nWaEaETC302Q\nCP\nrTurnAGundam1isdefferentf\n output: 32Bad\nAE86\n7\nEC302QTWaEa\nTurnAGundam0isdefferentfr\n\n" }, { "title": "Problem B: Lagrange's Four-Square Theorem", "content": "The fact that any positive integer has a representation as the sum of at most four positive\nsquares (i. e. squares of positive integers) is known as Lagrange 's Four-Square Theorem. The\nfirst published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission\nhowever is not to explain the original proof nor to discover a new proof but to show that the\ntheorem holds for some specific numbers by counting how many such possible representations\nthere are.\n\nFor a given positive integer n, you should report the number of all representations of n as the\nsum of at most four positive squares. The order of addition does not matter, e. g. you should\nconsider 4^2 + 3^2 and 3^2 + 4^2 are the same representation.\n\nFor example, let 's check the case of 25. This integer has just three representations 1^2 +2^2 +2^2 +4^2 ,\n3^2 + 4^2 , and 5^2 . Thus you should report 3 in this case. Be careful not to count 4^2 + 3^2 and\n3^2 + 4^2 separately.", "constraint": "", "input": "The input is composed of at most 255 lines, each containing a single positive integer less than\n2^15 , followed by a line containing a single zero. The last line is not a part of the input data.", "output": "The output should be composed of lines, each containing a single integer. No other characters\nshould appear in the output.\n\nThe output integer corresponding to the input integer n is the number of all representations\nof n as the sum of at most four positive squares.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n25\n2003\n211\n20007\n0\n output: 1\n3\n48\n7\n738"], "Pid": "p00820", "ProblemText": "Task Description: The fact that any positive integer has a representation as the sum of at most four positive\nsquares (i. e. squares of positive integers) is known as Lagrange 's Four-Square Theorem. The\nfirst published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission\nhowever is not to explain the original proof nor to discover a new proof but to show that the\ntheorem holds for some specific numbers by counting how many such possible representations\nthere are.\n\nFor a given positive integer n, you should report the number of all representations of n as the\nsum of at most four positive squares. The order of addition does not matter, e. g. you should\nconsider 4^2 + 3^2 and 3^2 + 4^2 are the same representation.\n\nFor example, let 's check the case of 25. This integer has just three representations 1^2 +2^2 +2^2 +4^2 ,\n3^2 + 4^2 , and 5^2 . Thus you should report 3 in this case. Be careful not to count 4^2 + 3^2 and\n3^2 + 4^2 separately.\nTask Input: The input is composed of at most 255 lines, each containing a single positive integer less than\n2^15 , followed by a line containing a single zero. The last line is not a part of the input data.\nTask Output: The output should be composed of lines, each containing a single integer. No other characters\nshould appear in the output.\n\nThe output integer corresponding to the input integer n is the number of all representations\nof n as the sum of at most four positive squares.\nTask Samples: input: 1\n25\n2003\n211\n20007\n0\n output: 1\n3\n48\n7\n738\n\n" }, { "title": "Problem C: Area of Polygons", "content": "Yoko 's math homework today was to calculate areas of polygons in the xy-plane. Vertices are\nall aligned to grid points (i. e. they have integer coordinates).\n\nYour job is to help Yoko, not good either at math or at computer programming, get her home-\nwork done. A polygon is given by listing the coordinates of its vertices. Your program should\napproximate its area by counting the number of unit squares (whose vertices are also grid points)\nintersecting the polygon. Precisely, a unit square “intersects the polygon” if and only if the in-\ntersection of the two has non-zero area. In the figure below, dashed horizontal and vertical lines\nare grid lines, and solid lines are edges of the polygon. Shaded unit squares are considered inter-\nsecting the polygon. Your program should output 55 for this polygon (as you see, the number\nof shaded unit squares is 55).\nFigure 1: A polygon and unit squares intersecting it", "constraint": "", "input": "The input file describes polygons one after another, followed by a terminating line that only\ncontains a single zero.\n\nA description of a polygon begins with a line containing a single integer, m (>= 3), that gives\nthe number of its vertices. It is followed by m lines, each containing two integers x and y, the coordinates of a vertex. The x and y are separated by a single space. The i-th of these m lines\ngives the coordinates of the i-th vertex (i = 1, . . . , m). For each i = 1, . . . , m - 1, the i-th vertex\nand the (i + 1)-th vertex are connected by an edge. The m-th vertex and the first vertex are\nalso connected by an edge (i. e. , the curve is closed). Edges intersect only at vertices. No three\nedges share a single vertex (i. e. , the curve is simple). The number of polygons is no more than\n100. For each polygon, the number of vertices (m) is no more than 100. All coordinates x and\ny satisfy -2000 <= x <= 2000 and -2000 <= y <= 2000.", "output": "The output should consist of as many lines as the number of polygons. The k-th output line\nshould print an integer which is the area of the k-th polygon, approximated in the way described\nabove. No other characters, including whitespaces, should be printed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n5 -3\n1 0\n1 7\n-7 -1\n3\n5 5\n18 5\n5 10\n3\n-5 -5\n-5 -10\n-18 -10\n5\n0 0\n20 2\n11 1\n21 2\n2 0\n0\n output: 55\n41\n41\n23"], "Pid": "p00821", "ProblemText": "Task Description: Yoko 's math homework today was to calculate areas of polygons in the xy-plane. Vertices are\nall aligned to grid points (i. e. they have integer coordinates).\n\nYour job is to help Yoko, not good either at math or at computer programming, get her home-\nwork done. A polygon is given by listing the coordinates of its vertices. Your program should\napproximate its area by counting the number of unit squares (whose vertices are also grid points)\nintersecting the polygon. Precisely, a unit square “intersects the polygon” if and only if the in-\ntersection of the two has non-zero area. In the figure below, dashed horizontal and vertical lines\nare grid lines, and solid lines are edges of the polygon. Shaded unit squares are considered inter-\nsecting the polygon. Your program should output 55 for this polygon (as you see, the number\nof shaded unit squares is 55).\nFigure 1: A polygon and unit squares intersecting it\nTask Input: The input file describes polygons one after another, followed by a terminating line that only\ncontains a single zero.\n\nA description of a polygon begins with a line containing a single integer, m (>= 3), that gives\nthe number of its vertices. It is followed by m lines, each containing two integers x and y, the coordinates of a vertex. The x and y are separated by a single space. The i-th of these m lines\ngives the coordinates of the i-th vertex (i = 1, . . . , m). For each i = 1, . . . , m - 1, the i-th vertex\nand the (i + 1)-th vertex are connected by an edge. The m-th vertex and the first vertex are\nalso connected by an edge (i. e. , the curve is closed). Edges intersect only at vertices. No three\nedges share a single vertex (i. e. , the curve is simple). The number of polygons is no more than\n100. For each polygon, the number of vertices (m) is no more than 100. All coordinates x and\ny satisfy -2000 <= x <= 2000 and -2000 <= y <= 2000.\nTask Output: The output should consist of as many lines as the number of polygons. The k-th output line\nshould print an integer which is the area of the k-th polygon, approximated in the way described\nabove. No other characters, including whitespaces, should be printed.\nTask Samples: input: 4\n5 -3\n1 0\n1 7\n-7 -1\n3\n5 5\n18 5\n5 10\n3\n-5 -5\n-5 -10\n-18 -10\n5\n0 0\n20 2\n11 1\n21 2\n2 0\n0\n output: 55\n41\n41\n23\n\n" }, { "title": "Problem D: Weather Forecast", "content": "You are the God of Wind.\n\nBy moving a big cloud around, you can decide the weather: it invariably rains under the cloud,\nand the sun shines everywhere else.\n\nBut you are a benign God: your goal is to give enough rain to every field in the countryside,\nand sun to markets and festivals. Small humans, in their poor vocabulary, only describe this as\n“weather forecast”.\n\nYou are in charge of a small country, called Paccimc. This country is constituted of 4 * 4 square\nareas, denoted by their numbers.\n\nYour cloud is of size 2 * 2, and may not cross the borders of the country.\n\nYou are given the schedule of markets and festivals in each area for a period of time.\n\nOn the first day of the period, it is raining in the central areas (6-7-10-11), independently of the\nschedule.\n\nOn each of the following days, you may move your cloud by 1 or 2 squares in one of the four\ncardinal directions (North, West, South, and East), or leave it in the same position. Diagonal\nmoves are not allowed. All moves occur at the beginning of the day.\n\nYou should not leave an area without rain for a full week (that is, you are allowed at most 6\nconsecutive days without rain). You don 't have to care about rain on days outside the period\nyou were given: i. e. you can assume it rains on the whole country the day before the period,\nand the day after it finishes.", "constraint": "", "input": "The input is a sequence of data sets, followed by a terminating line containing only a zero.\n\nA data set gives the number N of days (no more than 365) in the period on a single line, followed by N lines giving the schedule for markets and festivals. The i-th line gives the schedule for\nthe i-th day. It is composed of 16 numbers, either 0 or 1,0 standing for a normal day, and 1 a\nmarket or festival day. The numbers are separated by one or more spaces.", "output": "The answer is a 0 or 1 on a single line for each data set, 1 if you can satisfy everybody, 0 if there\nis no way to do it.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0\n7\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1\n0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1\n0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0\n0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0\n1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0\n7\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0\n0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0\n0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0\n15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0\n0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0\n0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0\n0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0\n1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0\n0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0\n0\n output: 0\n1\n0\n1"], "Pid": "p00822", "ProblemText": "Task Description: You are the God of Wind.\n\nBy moving a big cloud around, you can decide the weather: it invariably rains under the cloud,\nand the sun shines everywhere else.\n\nBut you are a benign God: your goal is to give enough rain to every field in the countryside,\nand sun to markets and festivals. Small humans, in their poor vocabulary, only describe this as\n“weather forecast”.\n\nYou are in charge of a small country, called Paccimc. This country is constituted of 4 * 4 square\nareas, denoted by their numbers.\n\nYour cloud is of size 2 * 2, and may not cross the borders of the country.\n\nYou are given the schedule of markets and festivals in each area for a period of time.\n\nOn the first day of the period, it is raining in the central areas (6-7-10-11), independently of the\nschedule.\n\nOn each of the following days, you may move your cloud by 1 or 2 squares in one of the four\ncardinal directions (North, West, South, and East), or leave it in the same position. Diagonal\nmoves are not allowed. All moves occur at the beginning of the day.\n\nYou should not leave an area without rain for a full week (that is, you are allowed at most 6\nconsecutive days without rain). You don 't have to care about rain on days outside the period\nyou were given: i. e. you can assume it rains on the whole country the day before the period,\nand the day after it finishes.\nTask Input: The input is a sequence of data sets, followed by a terminating line containing only a zero.\n\nA data set gives the number N of days (no more than 365) in the period on a single line, followed by N lines giving the schedule for markets and festivals. The i-th line gives the schedule for\nthe i-th day. It is composed of 16 numbers, either 0 or 1,0 standing for a normal day, and 1 a\nmarket or festival day. The numbers are separated by one or more spaces.\nTask Output: The answer is a 0 or 1 on a single line for each data set, 1 if you can satisfy everybody, 0 if there\nis no way to do it.\nTask Samples: input: 1\n0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0\n7\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1\n0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1\n0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0\n0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0\n1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1\n0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0\n7\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0\n0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0\n0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1\n0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0\n15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0\n0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0\n1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0\n0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0\n0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0\n1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0\n0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0\n0\n output: 0\n1\n0\n1\n\n" }, { "title": "Problem E: Molecular Formula", "content": "Your mission in this problem is to write a computer program that manipulates molecular for-\nmulae in virtual chemistry. As in real chemistry, each molecular formula represents a molecule\nconsisting of one or more atoms. However, it may not have chemical reality.\n\nThe following are the definitions of atomic symbols and molecular formulae you should consider.\n\n An atom in a molecule is represented by an atomic symbol, which is either a single capital\n letter or a capital letter followed by a small letter. For instance H and He are atomic\n symbols.\n\n A molecular formula is a non-empty sequence of atomic symbols. For instance, HHHe HHHe\n is a molecular formula, and represents a molecule consisting of four H 's and two He 's.\n\n For convenience, a repetition of the same sub-formula where n is an integer\n between 2 and 99 inclusive, can be abbreviated to (X)n. Parentheses can be omitted if\n X is an atomic symbol. For instance, HHHe HHHe is also written as H2He H2He, (HHHe)2,\n (H2He)2, or even ((H)2He)2.\nThe set of all molecular formulae can be viewed as a formal language. Summarizing the above\ndescription, the syntax of molecular formulae is defined as follows.\n\nEach atom in our virtual chemistry has its own atomic weight. Given the weights of atoms,\nyour program should calculate the weight of a molecule represented by a molecular formula.\nThe molecular weight is defined by the sum of the weights of the constituent atoms. For\ninstance, assuming that the atomic weights of the atoms whose symbols are H and He are 1 and\n4, respectively, the total weight of a molecule represented by (H2He)2 is 12.", "constraint": "", "input": "The input consists of two parts. The first part, the Atomic Table, is composed of a number of\nlines, each line including an atomic symbol, one or more spaces, and its atomic weight which is a positive integer no more than 1000. No two lines include the same atomic symbol.\n\nThe first part ends with a line containing only the string END OF FIRST PART.\n\nThe second part of the input is a sequence of lines. Each line is a molecular formula, not\nexceeding 80 characters, and contains no spaces. A molecule contains at most 10^5 atoms. Some\natomic symbols in a molecular formula may not appear in the Atomic Table.\n\nThe sequence is followed by a line containing a single zero, indicating the end of the input.", "output": "The output is a sequence of lines, one for each line of the second part of the input. Each line\ncontains either an integer, the molecular weight for a given molecular formula in the correspond-\ning input line if all its atomic symbols appear in the Atomic Table, or UNKNOWN otherwise. No\nextra characters are allowed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: H 1\nHe 4\nC 12\nO 16\nF 19\nNe 20\nCu 64\nCc 333\nEND_OF_FIRST_PART\nH2C\n(MgF)2As\nCu(OH)2\nH((CO)2F)99\n0\n output: 14\nUNKNOWN\n98\n7426"], "Pid": "p00823", "ProblemText": "Task Description: Your mission in this problem is to write a computer program that manipulates molecular for-\nmulae in virtual chemistry. As in real chemistry, each molecular formula represents a molecule\nconsisting of one or more atoms. However, it may not have chemical reality.\n\nThe following are the definitions of atomic symbols and molecular formulae you should consider.\n\n An atom in a molecule is represented by an atomic symbol, which is either a single capital\n letter or a capital letter followed by a small letter. For instance H and He are atomic\n symbols.\n\n A molecular formula is a non-empty sequence of atomic symbols. For instance, HHHe HHHe\n is a molecular formula, and represents a molecule consisting of four H 's and two He 's.\n\n For convenience, a repetition of the same sub-formula where n is an integer\n between 2 and 99 inclusive, can be abbreviated to (X)n. Parentheses can be omitted if\n X is an atomic symbol. For instance, HHHe HHHe is also written as H2He H2He, (HHHe)2,\n (H2He)2, or even ((H)2He)2.\nThe set of all molecular formulae can be viewed as a formal language. Summarizing the above\ndescription, the syntax of molecular formulae is defined as follows.\n\nEach atom in our virtual chemistry has its own atomic weight. Given the weights of atoms,\nyour program should calculate the weight of a molecule represented by a molecular formula.\nThe molecular weight is defined by the sum of the weights of the constituent atoms. For\ninstance, assuming that the atomic weights of the atoms whose symbols are H and He are 1 and\n4, respectively, the total weight of a molecule represented by (H2He)2 is 12.\nTask Input: The input consists of two parts. The first part, the Atomic Table, is composed of a number of\nlines, each line including an atomic symbol, one or more spaces, and its atomic weight which is a positive integer no more than 1000. No two lines include the same atomic symbol.\n\nThe first part ends with a line containing only the string END OF FIRST PART.\n\nThe second part of the input is a sequence of lines. Each line is a molecular formula, not\nexceeding 80 characters, and contains no spaces. A molecule contains at most 10^5 atoms. Some\natomic symbols in a molecular formula may not appear in the Atomic Table.\n\nThe sequence is followed by a line containing a single zero, indicating the end of the input.\nTask Output: The output is a sequence of lines, one for each line of the second part of the input. Each line\ncontains either an integer, the molecular weight for a given molecular formula in the correspond-\ning input line if all its atomic symbols appear in the Atomic Table, or UNKNOWN otherwise. No\nextra characters are allowed.\nTask Samples: input: H 1\nHe 4\nC 12\nO 16\nF 19\nNe 20\nCu 64\nCc 333\nEND_OF_FIRST_PART\nH2C\n(MgF)2As\nCu(OH)2\nH((CO)2F)99\n0\n output: 14\nUNKNOWN\n98\n7426\n\n" }, { "title": "Problem F: Gap", "content": "Let 's play a card game called Gap.\n\nYou have 28 cards labeled with two-digit numbers. The first digit (from 1 to 4) represents the\nsuit of the card, and the second digit (from 1 to 7) represents the value of the card.\n\nFirst, you shuffle the cards and lay them face up on the table in four rows of seven cards, leaving\na space of one card at the extreme left of each row. The following shows an example of initial\nlayout.\n\nNext, you remove all cards of value 1, and put them in the open space at the left end of the\nrows: “11” to the top row, “21” to the next, and so on.\n\nNow you have 28 cards and four spaces, called gaps, in four rows and eight columns. You start\nmoving cards from this layout.\n\nAt each move, you choose one of the four gaps and fill it with the successor of the left neighbor\nof the gap. The successor of a card is the next card in the same suit, when it exists. For instance\nthe successor of “42” is “43”, and “27” has no successor.\n\nIn the above layout, you can move “43” to the gap at the right of “42”, or “36” to the gap at\nthe right of “35”. If you move “43”, a new gap is generated to the right of “16”. You cannot\nmove any card to the right of a card of value 7, nor to the right of a gap.\n\nThe goal of the game is, by choosing clever moves, to make four ascending sequences of the same\nsuit, as follows.\n\nYour task is to find the minimum number of moves to reach the goal layout.", "constraint": "", "input": "The input starts with a line containing the number of initial layouts that follow.\n\nEach layout consists of five lines - a blank line and four lines which represent initial layouts of\nfour rows. Each row has seven two-digit numbers which correspond to the cards.", "output": "For each initial layout, produce a line with the minimum number of moves to reach the goal\nlayout. Note that this number should not include the initial four moves of the cards of value 1.\nIf there is no move sequence from the initial layout to the goal layout, produce “-1”.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n\n12 13 14 15 16 17 21\n22 23 24 25 26 27 31\n32 33 34 35 36 37 41\n42 43 44 45 46 47 11\n\n26 31 13 44 21 24 42\n17 45 23 25 41 36 11\n46 34 14 12 37 32 47\n16 43 27 35 22 33 15\n\n17 12 16 13 15 14 11\n27 22 26 23 25 24 21\n37 32 36 33 35 34 31\n47 42 46 43 45 44 41\n\n27 14 22 35 32 46 33\n13 17 36 24 44 21 15\n43 16 45 47 23 11 26\n25 37 41 34 42 12 31\n output: 0\n33\n60\n-1"], "Pid": "p00824", "ProblemText": "Task Description: Let 's play a card game called Gap.\n\nYou have 28 cards labeled with two-digit numbers. The first digit (from 1 to 4) represents the\nsuit of the card, and the second digit (from 1 to 7) represents the value of the card.\n\nFirst, you shuffle the cards and lay them face up on the table in four rows of seven cards, leaving\na space of one card at the extreme left of each row. The following shows an example of initial\nlayout.\n\nNext, you remove all cards of value 1, and put them in the open space at the left end of the\nrows: “11” to the top row, “21” to the next, and so on.\n\nNow you have 28 cards and four spaces, called gaps, in four rows and eight columns. You start\nmoving cards from this layout.\n\nAt each move, you choose one of the four gaps and fill it with the successor of the left neighbor\nof the gap. The successor of a card is the next card in the same suit, when it exists. For instance\nthe successor of “42” is “43”, and “27” has no successor.\n\nIn the above layout, you can move “43” to the gap at the right of “42”, or “36” to the gap at\nthe right of “35”. If you move “43”, a new gap is generated to the right of “16”. You cannot\nmove any card to the right of a card of value 7, nor to the right of a gap.\n\nThe goal of the game is, by choosing clever moves, to make four ascending sequences of the same\nsuit, as follows.\n\nYour task is to find the minimum number of moves to reach the goal layout.\nTask Input: The input starts with a line containing the number of initial layouts that follow.\n\nEach layout consists of five lines - a blank line and four lines which represent initial layouts of\nfour rows. Each row has seven two-digit numbers which correspond to the cards.\nTask Output: For each initial layout, produce a line with the minimum number of moves to reach the goal\nlayout. Note that this number should not include the initial four moves of the cards of value 1.\nIf there is no move sequence from the initial layout to the goal layout, produce “-1”.\nTask Samples: input: 4\n\n12 13 14 15 16 17 21\n22 23 24 25 26 27 31\n32 33 34 35 36 37 41\n42 43 44 45 46 47 11\n\n26 31 13 44 21 24 42\n17 45 23 25 41 36 11\n46 34 14 12 37 32 47\n16 43 27 35 22 33 15\n\n17 12 16 13 15 14 11\n27 22 26 23 25 24 21\n37 32 36 33 35 34 31\n47 42 46 43 45 44 41\n\n27 14 22 35 32 46 33\n13 17 36 24 44 21 15\n43 16 45 47 23 11 26\n25 37 41 34 42 12 31\n output: 0\n33\n60\n-1\n\n" }, { "title": "Problem G: Concert Hall Scheduling", "content": "You are appointed director of a famous concert hall, to save it from bankruptcy. The hall is very\npopular, and receives many requests to use its two fine rooms, but unfortunately the previous\ndirector was not very efficient, and it has been losing money for many years. The two rooms are\nof the same size and arrangement. Therefore, each applicant wishing to hold a concert asks for\na room without specifying which. Each room can be used for only one concert per day.\n\nIn order to make more money, you have decided to abandon the previous fixed price policy, and\nrather let applicants specify the price they are ready to pay. Each application shall specify a\nperiod [i, j] and an asking price w, where i and j are respectively the first and last days of the\nperiod (1 <= i <= j <= 365), and w is a positive integer in yen, indicating the amount the applicant\nis willing to pay to use a room for the whole period.\n\nYou have received applications for the next year, and you should now choose the applications\nyou will accept. Each application should be either accepted for its whole period or completely\nrejected. Each concert should use the same room during the whole applied period.\n\nConsidering the dire economic situation of the concert hall, artistic quality is to be ignored,\nand you should just try to maximize the total income for the whole year by accepting the most\nprofitable applications.", "constraint": "", "input": "The input has multiple data sets, each starting with a line consisting of a single integer n, the\nnumber of applications in the data set. Then, it is followed by n lines, each of which represents\none application with a period [i, j] and an asking price w yen in the following format.\n\n i j w\n\nA line containing a single zero indicates the end of the input.\n\nThe maximum number of applications in a data set is one thousand, and the maximum asking\nprice is one million yen.", "output": "For each data set, print a single line containing an integer, the maximum total income in yen\nfor the data set.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 10\n2 3 10\n3 3 10\n1 3 10\n6\n1 20 1000\n3 25 10000\n5 15 5000\n22 300 5500\n10 295 9000\n7 7 6000\n8\n32 251 2261\n123 281 1339\n211 235 5641\n162 217 7273\n22 139 7851\n194 198 9190\n119 274 878\n122 173 8640\n0\n output: 30\n25500\n38595"], "Pid": "p00825", "ProblemText": "Task Description: You are appointed director of a famous concert hall, to save it from bankruptcy. The hall is very\npopular, and receives many requests to use its two fine rooms, but unfortunately the previous\ndirector was not very efficient, and it has been losing money for many years. The two rooms are\nof the same size and arrangement. Therefore, each applicant wishing to hold a concert asks for\na room without specifying which. Each room can be used for only one concert per day.\n\nIn order to make more money, you have decided to abandon the previous fixed price policy, and\nrather let applicants specify the price they are ready to pay. Each application shall specify a\nperiod [i, j] and an asking price w, where i and j are respectively the first and last days of the\nperiod (1 <= i <= j <= 365), and w is a positive integer in yen, indicating the amount the applicant\nis willing to pay to use a room for the whole period.\n\nYou have received applications for the next year, and you should now choose the applications\nyou will accept. Each application should be either accepted for its whole period or completely\nrejected. Each concert should use the same room during the whole applied period.\n\nConsidering the dire economic situation of the concert hall, artistic quality is to be ignored,\nand you should just try to maximize the total income for the whole year by accepting the most\nprofitable applications.\nTask Input: The input has multiple data sets, each starting with a line consisting of a single integer n, the\nnumber of applications in the data set. Then, it is followed by n lines, each of which represents\none application with a period [i, j] and an asking price w yen in the following format.\n\n i j w\n\nA line containing a single zero indicates the end of the input.\n\nThe maximum number of applications in a data set is one thousand, and the maximum asking\nprice is one million yen.\nTask Output: For each data set, print a single line containing an integer, the maximum total income in yen\nfor the data set.\nTask Samples: input: 4\n1 2 10\n2 3 10\n3 3 10\n1 3 10\n6\n1 20 1000\n3 25 10000\n5 15 5000\n22 300 5500\n10 295 9000\n7 7 6000\n8\n32 251 2261\n123 281 1339\n211 235 5641\n162 217 7273\n22 139 7851\n194 198 9190\n119 274 878\n122 173 8640\n0\n output: 30\n25500\n38595\n\n" }, { "title": "Problem H: Monster Trap", "content": "Once upon a time when people still believed in magic, there was a great wizard Aranyaka\nGondlir. After twenty years of hard training in a deep forest, he had finally mastered ultimate\nmagic, and decided to leave the forest for his home.\n\nArriving at his home village, Aranyaka was very surprised at the extraordinary desolation. A\ngloom had settled over the village. Even the whisper of the wind could scare villagers. It was a\nmere shadow of what it had been.\n\nWhat had happened? Soon he recognized a sure sign of an evil monster that is immortal. Even\nthe great wizard could not kill it, and so he resolved to seal it with magic. Aranyaka could cast\na spell to create a monster trap: once he had drawn a line on the ground with his magic rod,\nthe line would function as a barrier wall that any monster could not get over. Since he could\nonly draw straight lines, he had to draw several lines to complete a monster trap, i. e. , magic\nbarrier walls enclosing the monster. If there was a gap between barrier walls, the monster could\neasily run away through the gap.\n\nFor instance, a complete monster trap without any gaps is built by the barrier walls in the left\nfigure, where “M” indicates the position of the monster. In contrast, the barrier walls in the\nright figure have a loophole, even though it is almost complete.\n\nYour mission is to write a program to tell whether or not the wizard has successfully sealed the\nmonster.", "constraint": "", "input": "The input consists of multiple data sets, each in the following format.\n\nn\nx_1 y_1 x'_1 y'_1\nx_2 y_2 x'_2 y'_2\n . . .\nx_n y_n x'_n y'_n\n\nThe first line of a data set contains a positive integer n, which is the number of the line segments\ndrawn by the wizard. Each of the following n input lines contains four integers x, y, x', and\ny', which represent the x- and y-coordinates of two points (x, y) and (x', y' ) connected by a line\nsegment. You may assume that all line segments have non-zero lengths. You may also assume\nthat n is less than or equal to 100 and that all coordinates are between -50 and 50, inclusive.\n\nFor your convenience, the coordinate system is arranged so that the monster is always on the\norigin (0,0). The wizard never draws lines crossing (0,0).\n\nYou may assume that any two line segments have at most one intersection point and that no\nthree line segments share the same intersection point. You may also assume that the distance\nbetween any two intersection points is greater than 10^-5.\n\nAn input line containing a zero indicates the end of the input.", "output": "For each data set, print “yes” or “no” in a line. If a monster trap is completed, print “yes”.\nOtherwise, i. e. , if there is a loophole, print “no”.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8\n-7 9 6 9\n-5 5 6 5\n-10 -5 10 -5\n-6 9 -9 -6\n6 9 9 -6\n-1 -2 -3 10\n1 -2 3 10\n-2 -3 2 -3\n8\n-7 9 5 7\n-5 5 6 5\n-10 -5 10 -5\n-6 9 -9 -6\n6 9 9 -6\n-1 -2 -3 10\n1 -2 3 10\n-2 -3 2 -3\n0\n output: yes\nno"], "Pid": "p00826", "ProblemText": "Task Description: Once upon a time when people still believed in magic, there was a great wizard Aranyaka\nGondlir. After twenty years of hard training in a deep forest, he had finally mastered ultimate\nmagic, and decided to leave the forest for his home.\n\nArriving at his home village, Aranyaka was very surprised at the extraordinary desolation. A\ngloom had settled over the village. Even the whisper of the wind could scare villagers. It was a\nmere shadow of what it had been.\n\nWhat had happened? Soon he recognized a sure sign of an evil monster that is immortal. Even\nthe great wizard could not kill it, and so he resolved to seal it with magic. Aranyaka could cast\na spell to create a monster trap: once he had drawn a line on the ground with his magic rod,\nthe line would function as a barrier wall that any monster could not get over. Since he could\nonly draw straight lines, he had to draw several lines to complete a monster trap, i. e. , magic\nbarrier walls enclosing the monster. If there was a gap between barrier walls, the monster could\neasily run away through the gap.\n\nFor instance, a complete monster trap without any gaps is built by the barrier walls in the left\nfigure, where “M” indicates the position of the monster. In contrast, the barrier walls in the\nright figure have a loophole, even though it is almost complete.\n\nYour mission is to write a program to tell whether or not the wizard has successfully sealed the\nmonster.\nTask Input: The input consists of multiple data sets, each in the following format.\n\nn\nx_1 y_1 x'_1 y'_1\nx_2 y_2 x'_2 y'_2\n . . .\nx_n y_n x'_n y'_n\n\nThe first line of a data set contains a positive integer n, which is the number of the line segments\ndrawn by the wizard. Each of the following n input lines contains four integers x, y, x', and\ny', which represent the x- and y-coordinates of two points (x, y) and (x', y' ) connected by a line\nsegment. You may assume that all line segments have non-zero lengths. You may also assume\nthat n is less than or equal to 100 and that all coordinates are between -50 and 50, inclusive.\n\nFor your convenience, the coordinate system is arranged so that the monster is always on the\norigin (0,0). The wizard never draws lines crossing (0,0).\n\nYou may assume that any two line segments have at most one intersection point and that no\nthree line segments share the same intersection point. You may also assume that the distance\nbetween any two intersection points is greater than 10^-5.\n\nAn input line containing a zero indicates the end of the input.\nTask Output: For each data set, print “yes” or “no” in a line. If a monster trap is completed, print “yes”.\nOtherwise, i. e. , if there is a loophole, print “no”.\nTask Samples: input: 8\n-7 9 6 9\n-5 5 6 5\n-10 -5 10 -5\n-6 9 -9 -6\n6 9 9 -6\n-1 -2 -3 10\n1 -2 3 10\n-2 -3 2 -3\n8\n-7 9 5 7\n-5 5 6 5\n-10 -5 10 -5\n-6 9 -9 -6\n6 9 9 -6\n-1 -2 -3 10\n1 -2 3 10\n-2 -3 2 -3\n0\n output: yes\nno\n\n" }, { "title": "Problem A: The Balance", "content": "Ms. Iyo Kiffa-Australis has a balance and only two kinds of weights to measure a dose of medicine.\n\nFor example, to measure 200mg of aspirin using 300mg weights and 700mg weights, she can put\none 700mg weight on the side of the medicine and three 300mg weights on the opposite side\n(Figure 1). Although she could put four 300mg weights on the medicine side and two 700mg\nweights on the other (Figure 2), she would not choose this solution because it is less convenient\nto use more weights.\n\nYou are asked to help her by calculating how many weights are required.\nFigure 1: To measure 200mg of aspirin using three 300mg weights and one 700mg weight\nFigure 2: To measure 200mg of aspirin using four 300mg weights and two 700mg weights", "constraint": "", "input": "The input is a sequence of datasets. A dataset is a line containing three positive integers a, b,\nand d separated by a space. The following relations hold: a ! = b, a <= 10000, b <= 10000, and\nd <= 50000. You may assume that it is possible to measure d mg using a combination of a mg\nand b mg weights. In other words, you need not consider “no solution” cases.\n\nThe end of the input is indicated by a line containing three zeros separated by a space. It is not\na dataset.", "output": "The output should be composed of lines, each corresponding to an input dataset (a, b, d). An\noutput line should contain two nonnegative integers x and y separated by a space. They should\nsatisfy the following three conditions.\n\n You can measure d mg using x many a mg weights and y many b mg weights.\n\n The total number of weights (x + y) is the smallest among those pairs of nonnegative\n integers satisfying the previous condition.\n\n The total mass of weights (ax + by) is the smallest among those pairs of nonnegative\n integers satisfying the previous two conditions.\nNo extra characters (e. g. extra spaces) should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 700 300 200\n500 200 300\n500 200 500\n275 110 330\n275 110 385\n648 375 4002\n3 1 10000\n0 0 0\n output: 1 3\n1 1\n1 0\n0 3\n1 1\n49 74\n3333 1"], "Pid": "p00827", "ProblemText": "Task Description: Ms. Iyo Kiffa-Australis has a balance and only two kinds of weights to measure a dose of medicine.\n\nFor example, to measure 200mg of aspirin using 300mg weights and 700mg weights, she can put\none 700mg weight on the side of the medicine and three 300mg weights on the opposite side\n(Figure 1). Although she could put four 300mg weights on the medicine side and two 700mg\nweights on the other (Figure 2), she would not choose this solution because it is less convenient\nto use more weights.\n\nYou are asked to help her by calculating how many weights are required.\nFigure 1: To measure 200mg of aspirin using three 300mg weights and one 700mg weight\nFigure 2: To measure 200mg of aspirin using four 300mg weights and two 700mg weights\nTask Input: The input is a sequence of datasets. A dataset is a line containing three positive integers a, b,\nand d separated by a space. The following relations hold: a ! = b, a <= 10000, b <= 10000, and\nd <= 50000. You may assume that it is possible to measure d mg using a combination of a mg\nand b mg weights. In other words, you need not consider “no solution” cases.\n\nThe end of the input is indicated by a line containing three zeros separated by a space. It is not\na dataset.\nTask Output: The output should be composed of lines, each corresponding to an input dataset (a, b, d). An\noutput line should contain two nonnegative integers x and y separated by a space. They should\nsatisfy the following three conditions.\n\n You can measure d mg using x many a mg weights and y many b mg weights.\n\n The total number of weights (x + y) is the smallest among those pairs of nonnegative\n integers satisfying the previous condition.\n\n The total mass of weights (ax + by) is the smallest among those pairs of nonnegative\n integers satisfying the previous two conditions.\nNo extra characters (e. g. extra spaces) should appear in the output.\nTask Samples: input: 700 300 200\n500 200 300\n500 200 500\n275 110 330\n275 110 385\n648 375 4002\n3 1 10000\n0 0 0\n output: 1 3\n1 1\n1 0\n0 3\n1 1\n49 74\n3333 1\n\n" }, { "title": "Problem B: Make a Sequence", "content": "Your company 's next product will be a new game, which is a three-dimensional variant of the\nclassic game “Tic-Tac-Toe”. Two players place balls in a three-dimensional space (board), and\ntry to make a sequence of a certain length.\n\nPeople believe that it is fun to play the game, but they still cannot fix the values of some\nparameters of the game. For example, what size of the board makes the game most exciting?\nParameters currently under discussion are the board size (we call it n in the following) and the\nlength of the sequence (m). In order to determine these parameter values, you are requested to\nwrite a computer simulator of the game.\n\nYou can see several snapshots of the game in Figures 1-3. These figures correspond to the three\ndatasets given in the Sample Input.\nFigure 1: A game with n = m = 3\n\nHere are the precise rules of the game.\n\n Two players, Black and White, play alternately. Black plays first.\n\n There are n * n vertical pegs. Each peg can accommodate up to n balls. A peg can be\n specified by its x- and y-coordinates (1 <= x, y <= n). A ball on a peg can be specified by\n its z-coordinate (1 <= z <= n). At the beginning of a game, there are no balls on any of the\n pegs.\nFigure 2: A game with n = m = 3 (White made a 3-sequence before Black)\n\n On his turn, a player chooses one of n * n pegs, and puts a ball of his color onto the peg.\n The ball follows the law of gravity. That is, the ball stays just above the top-most ball\n on the same peg or on the floor (if there are no balls on the peg). Speaking differently, a\n player can choose x- and y-coordinates of the ball, but he cannot choose its z-coordinate.\n\n The objective of the game is to make an m-sequence. If a player makes an m-sequence or\n longer of his color, he wins. An m-sequence is a row of m consecutive balls of the same\n color. For example, black balls in positions (5,1,2), (5,2,2) and (5,3,2) form a 3-sequence.\n A sequence can be horizontal, vertical, or diagonal. Precisely speaking, there are 13\n possible directions to make a sequence, categorized as follows.\nFigure 3: A game with n = 4, m = 3 (Black made two 4-sequences)\n(a) One-dimensional axes. For example, (3,1,2), (4,1,2) and (5,1,2) is a 3-sequence.\n There are three directions in this category. \n(b) Two-dimensional diagonals. For example, (2,3,1), (3,3,2) and (4,3,3) is a 3-sequence.\n There are six directions in this category. \n(c) Three-dimensional diagonals. For example, (5,1,3), (4,2,4) and (3,3,5) is a 3-\n sequence. There are four directions in this category.\n\nNote that we do not distinguish between opposite directions.\n\nAs the evaluation process of the game, people have been playing the game several times changing\nthe parameter values. You are given the records of these games. It is your job to write a computer\nprogram which determines the winner of each recorded game.\n\nSince it is difficult for a human to find three-dimensional sequences, players often do not notice\nthe end of the game, and continue to play uselessly. In these cases, moves after the end of the\ngame, i. e. after the winner is determined, should be ignored. For example, after a player won\nmaking an m-sequence, players may make additional m-sequences. In this case, all m-sequences\nbut the first should be ignored, and the winner of the game is unchanged.\n\nA game does not necessarily end with the victory of one of the players. If there are no pegs left\nto put a ball on, the game ends with a draw. Moreover, people may quit a game before making\nany m-sequence. In such cases also, the game ends with a draw.", "constraint": "", "input": "The input consists of multiple datasets each corresponding to the record of a game. A dataset\nstarts with a line containing three positive integers n, m, and p separated by a space. The\nrelations 3 <= m <= n <= 7 and 1 <= p <= n^3 hold between them. n and m are the parameter values\nof the game as described above. p is the number of moves in the game.\n\nThe rest of the dataset is p lines each containing two positive integers x and y. Each of these\nlines describes a move, i. e. the player on turn puts his ball on the peg specified. You can assume\nthat 1 <= x <= n and 1 <= y <= n. You can also assume that at most n balls are put on a peg\nthroughout a game.\n\nThe end of the input is indicated by a line with three zeros separated by a space.", "output": "For each dataset, a line describing the winner and the number of moves until the game ends\nshould be output. The winner is either “Black” or “White”. A single space should be inserted\nbetween the winner and the number of moves. No other extra characters are allowed in the\noutput.\n\nIn case of a draw, the output line should be “Draw”.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3 3\n1 1\n1 1\n1 1\n3 3 7\n2 2\n1 3\n1 1\n2 3\n2 1\n3 3\n3 1\n4 3 15\n1 1\n2 2\n1 1\n3 3\n3 3\n1 1\n3 3\n3 3\n4 4\n1 1\n4 4\n4 4\n4 4\n4 1\n2 2\n0 0 0\n output: Draw\nWhite 6\nBlack 15"], "Pid": "p00828", "ProblemText": "Task Description: Your company 's next product will be a new game, which is a three-dimensional variant of the\nclassic game “Tic-Tac-Toe”. Two players place balls in a three-dimensional space (board), and\ntry to make a sequence of a certain length.\n\nPeople believe that it is fun to play the game, but they still cannot fix the values of some\nparameters of the game. For example, what size of the board makes the game most exciting?\nParameters currently under discussion are the board size (we call it n in the following) and the\nlength of the sequence (m). In order to determine these parameter values, you are requested to\nwrite a computer simulator of the game.\n\nYou can see several snapshots of the game in Figures 1-3. These figures correspond to the three\ndatasets given in the Sample Input.\nFigure 1: A game with n = m = 3\n\nHere are the precise rules of the game.\n\n Two players, Black and White, play alternately. Black plays first.\n\n There are n * n vertical pegs. Each peg can accommodate up to n balls. A peg can be\n specified by its x- and y-coordinates (1 <= x, y <= n). A ball on a peg can be specified by\n its z-coordinate (1 <= z <= n). At the beginning of a game, there are no balls on any of the\n pegs.\nFigure 2: A game with n = m = 3 (White made a 3-sequence before Black)\n\n On his turn, a player chooses one of n * n pegs, and puts a ball of his color onto the peg.\n The ball follows the law of gravity. That is, the ball stays just above the top-most ball\n on the same peg or on the floor (if there are no balls on the peg). Speaking differently, a\n player can choose x- and y-coordinates of the ball, but he cannot choose its z-coordinate.\n\n The objective of the game is to make an m-sequence. If a player makes an m-sequence or\n longer of his color, he wins. An m-sequence is a row of m consecutive balls of the same\n color. For example, black balls in positions (5,1,2), (5,2,2) and (5,3,2) form a 3-sequence.\n A sequence can be horizontal, vertical, or diagonal. Precisely speaking, there are 13\n possible directions to make a sequence, categorized as follows.\nFigure 3: A game with n = 4, m = 3 (Black made two 4-sequences)\n(a) One-dimensional axes. For example, (3,1,2), (4,1,2) and (5,1,2) is a 3-sequence.\n There are three directions in this category. \n(b) Two-dimensional diagonals. For example, (2,3,1), (3,3,2) and (4,3,3) is a 3-sequence.\n There are six directions in this category. \n(c) Three-dimensional diagonals. For example, (5,1,3), (4,2,4) and (3,3,5) is a 3-\n sequence. There are four directions in this category.\n\nNote that we do not distinguish between opposite directions.\n\nAs the evaluation process of the game, people have been playing the game several times changing\nthe parameter values. You are given the records of these games. It is your job to write a computer\nprogram which determines the winner of each recorded game.\n\nSince it is difficult for a human to find three-dimensional sequences, players often do not notice\nthe end of the game, and continue to play uselessly. In these cases, moves after the end of the\ngame, i. e. after the winner is determined, should be ignored. For example, after a player won\nmaking an m-sequence, players may make additional m-sequences. In this case, all m-sequences\nbut the first should be ignored, and the winner of the game is unchanged.\n\nA game does not necessarily end with the victory of one of the players. If there are no pegs left\nto put a ball on, the game ends with a draw. Moreover, people may quit a game before making\nany m-sequence. In such cases also, the game ends with a draw.\nTask Input: The input consists of multiple datasets each corresponding to the record of a game. A dataset\nstarts with a line containing three positive integers n, m, and p separated by a space. The\nrelations 3 <= m <= n <= 7 and 1 <= p <= n^3 hold between them. n and m are the parameter values\nof the game as described above. p is the number of moves in the game.\n\nThe rest of the dataset is p lines each containing two positive integers x and y. Each of these\nlines describes a move, i. e. the player on turn puts his ball on the peg specified. You can assume\nthat 1 <= x <= n and 1 <= y <= n. You can also assume that at most n balls are put on a peg\nthroughout a game.\n\nThe end of the input is indicated by a line with three zeros separated by a space.\nTask Output: For each dataset, a line describing the winner and the number of moves until the game ends\nshould be output. The winner is either “Black” or “White”. A single space should be inserted\nbetween the winner and the number of moves. No other extra characters are allowed in the\noutput.\n\nIn case of a draw, the output line should be “Draw”.\nTask Samples: input: 3 3 3\n1 1\n1 1\n1 1\n3 3 7\n2 2\n1 3\n1 1\n2 3\n2 1\n3 3\n3 1\n4 3 15\n1 1\n2 2\n1 1\n3 3\n3 3\n1 1\n3 3\n3 3\n4 4\n1 1\n4 4\n4 4\n4 4\n4 1\n2 2\n0 0 0\n output: Draw\nWhite 6\nBlack 15\n\n" }, { "title": "Problem C: Leaky Cryptography", "content": "The ACM ICPC judges are very careful about not leaking their problems, and all communications are encrypted. However, one does sometimes make mistakes, like using too weak an\nencryption scheme. Here is an example of that.\n\nThe encryption chosen was very simple: encrypt each chunk of the input by flipping some bits\naccording to a shared key. To provide reasonable security, the size of both chunk and key is 32\nbits.\n\nThat is, suppose the input was a sequence of m 32-bit integers.\nN_1 N_2 N_3 . . . N_m\nAfter encoding with the key K it becomes the following sequence of m 32-bit integers.\n\n(N_1 ∧ K) (N_2 ∧ K) (N_3 ∧ K) . . . (N_m ∧ K)\nwhere (a ∧ b) is the bitwise exclusive or of a and b.\n\nExclusive or is the logical operator which is 1 when only one of its operands is 1, and 0 otherwise.\nHere is its definition for 1-bit integers.\n 0 ⊕ 0 = 0 0 ⊕ 1 = 1\n 1 ⊕ 0 = 1 1 ⊕ 1 =0\nAs you can see, it is identical to addition modulo 2. For two 32-bit integers a and b, their bitwise\nexclusive or a ∧ b is defined as follows, using their binary representations, composed of 0's and 1's.\na ∧ b = a_31 . . . a_1a_0 ∧ b_31 . . . b_1b_0 = c_31 . . . c_1c_0\nwhere\nc_i = a_i ⊕ b_i (i = 0,1, . . . , 31).\nFor instance, using binary notation, 11010110 ∧ 01010101 = 10100011, or using hexadecimal, \n\nd6 ∧ 55 = a3.\n\nSince this kind of encryption is notoriously weak to statistical attacks, the message has to be\ncompressed in advance, so that it has no statistical regularity. We suppose that N_1 N_2 . . . N_m\nis already in compressed form.\n\nHowever, the trouble is that the compression algorithm itself introduces some form of regularity:\nafter every 8 integers of compressed data, it inserts a checksum, the sum of these integers. That\nis, in the above input, N_9 = ∑^8_i=1 N_i = N_1 + . . . + N_8, where additions are modulo 2^32.\nLuckily, you could intercept a communication between the judges. Maybe it contains a problem for the finals!\n\nAs you are very clever, you have certainly seen that you can easily find the lowest bit of the key,\ndenoted by K_0. On the one hand, if K_0 = 1, then after encoding, the lowest bit of ∑^8_i=1 N_i ∧ K is unchanged, as K_0 is added an even number of times, but the lowest bit of N_9 ∧ K is changed,\nso they shall differ. On the other hand, if K_0 = 0, then after encoding, the lowest bit of ∑^8_i=1 N_i ∧ K shall still be identical to the lowest bit of N_9 ∧ K, as they do not change. For instance, if the lowest bits after encoding are 1 1 1 1 1 1 1 1 1 then K_0 must be 1, but if\nthey are 1 1 1 1 1 1 1 0 1 then K_0 must be 0.\n\nSo far, so good. Can you do better?\n\nYou should find the key used for encoding.", "constraint": "", "input": "The input starts with a line containing only a positive integer S, indicating the number of\ndatasets in the input. S is no more than 1000.\n\nIt is followed by S datasets. Each dataset is composed of nine 32-bit integers corresponding\nto the first nine chunks of a communication. They are written in hexadecimal notation, using\ndigits ‘0 ' to ‘9 ' and lowercase letters ‘a ' to ‘f ', and with no leading zeros. They are separated\nby a space or a newline. Each dataset is ended by a newline.", "output": "For each dataset you should output the key used for encoding. Each key shall appear alone on\nits line, and be written in hexadecimal notation, using digits ‘0 ' to ‘9 ' and lowercase letters ‘a '\nto ‘f ', and with no leading zeros.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n1 1 1 1 1 1 1 1 8\n3 2 3 2 3 2 3 2 6\n3 4 4 7 7 b a 2 2e\ne1 13 ce 28 ca 6 ab 46 a6d\nb08 49e2 6128 f27 8cf2 bc50 7380 7fe1 723b\n4eba eb4 a352 fd14 6ac1 eed1 dd06 bb83 392bc\nef593c08 847e522f 74c02b9c 26f3a4e1 e2720a01 6fe66007\n7a4e96ad 6ee5cef6 3853cd88\n60202fb8 757d6d66 9c3a9525 fbcd7983 82b9571c ddc54bab 853e52da\n22047c88 e5524401\n output: 0\n2\n6\n1c6\n4924afc7\nffff95c5\n546991d\n901c4a16"], "Pid": "p00829", "ProblemText": "Task Description: The ACM ICPC judges are very careful about not leaking their problems, and all communications are encrypted. However, one does sometimes make mistakes, like using too weak an\nencryption scheme. Here is an example of that.\n\nThe encryption chosen was very simple: encrypt each chunk of the input by flipping some bits\naccording to a shared key. To provide reasonable security, the size of both chunk and key is 32\nbits.\n\nThat is, suppose the input was a sequence of m 32-bit integers.\nN_1 N_2 N_3 . . . N_m\nAfter encoding with the key K it becomes the following sequence of m 32-bit integers.\n\n(N_1 ∧ K) (N_2 ∧ K) (N_3 ∧ K) . . . (N_m ∧ K)\nwhere (a ∧ b) is the bitwise exclusive or of a and b.\n\nExclusive or is the logical operator which is 1 when only one of its operands is 1, and 0 otherwise.\nHere is its definition for 1-bit integers.\n 0 ⊕ 0 = 0 0 ⊕ 1 = 1\n 1 ⊕ 0 = 1 1 ⊕ 1 =0\nAs you can see, it is identical to addition modulo 2. For two 32-bit integers a and b, their bitwise\nexclusive or a ∧ b is defined as follows, using their binary representations, composed of 0's and 1's.\na ∧ b = a_31 . . . a_1a_0 ∧ b_31 . . . b_1b_0 = c_31 . . . c_1c_0\nwhere\nc_i = a_i ⊕ b_i (i = 0,1, . . . , 31).\nFor instance, using binary notation, 11010110 ∧ 01010101 = 10100011, or using hexadecimal, \n\nd6 ∧ 55 = a3.\n\nSince this kind of encryption is notoriously weak to statistical attacks, the message has to be\ncompressed in advance, so that it has no statistical regularity. We suppose that N_1 N_2 . . . N_m\nis already in compressed form.\n\nHowever, the trouble is that the compression algorithm itself introduces some form of regularity:\nafter every 8 integers of compressed data, it inserts a checksum, the sum of these integers. That\nis, in the above input, N_9 = ∑^8_i=1 N_i = N_1 + . . . + N_8, where additions are modulo 2^32.\nLuckily, you could intercept a communication between the judges. Maybe it contains a problem for the finals!\n\nAs you are very clever, you have certainly seen that you can easily find the lowest bit of the key,\ndenoted by K_0. On the one hand, if K_0 = 1, then after encoding, the lowest bit of ∑^8_i=1 N_i ∧ K is unchanged, as K_0 is added an even number of times, but the lowest bit of N_9 ∧ K is changed,\nso they shall differ. On the other hand, if K_0 = 0, then after encoding, the lowest bit of ∑^8_i=1 N_i ∧ K shall still be identical to the lowest bit of N_9 ∧ K, as they do not change. For instance, if the lowest bits after encoding are 1 1 1 1 1 1 1 1 1 then K_0 must be 1, but if\nthey are 1 1 1 1 1 1 1 0 1 then K_0 must be 0.\n\nSo far, so good. Can you do better?\n\nYou should find the key used for encoding.\nTask Input: The input starts with a line containing only a positive integer S, indicating the number of\ndatasets in the input. S is no more than 1000.\n\nIt is followed by S datasets. Each dataset is composed of nine 32-bit integers corresponding\nto the first nine chunks of a communication. They are written in hexadecimal notation, using\ndigits ‘0 ' to ‘9 ' and lowercase letters ‘a ' to ‘f ', and with no leading zeros. They are separated\nby a space or a newline. Each dataset is ended by a newline.\nTask Output: For each dataset you should output the key used for encoding. Each key shall appear alone on\nits line, and be written in hexadecimal notation, using digits ‘0 ' to ‘9 ' and lowercase letters ‘a '\nto ‘f ', and with no leading zeros.\nTask Samples: input: 8\n1 1 1 1 1 1 1 1 8\n3 2 3 2 3 2 3 2 6\n3 4 4 7 7 b a 2 2e\ne1 13 ce 28 ca 6 ab 46 a6d\nb08 49e2 6128 f27 8cf2 bc50 7380 7fe1 723b\n4eba eb4 a352 fd14 6ac1 eed1 dd06 bb83 392bc\nef593c08 847e522f 74c02b9c 26f3a4e1 e2720a01 6fe66007\n7a4e96ad 6ee5cef6 3853cd88\n60202fb8 757d6d66 9c3a9525 fbcd7983 82b9571c ddc54bab 853e52da\n22047c88 e5524401\n output: 0\n2\n6\n1c6\n4924afc7\nffff95c5\n546991d\n901c4a16\n\n" }, { "title": "Problem D: Pathological Paths", "content": "Professor Pathfinder is a distinguished authority on the structure of hyperlinks in the World\nWide Web. For establishing his hypotheses, he has been developing software agents, which\nautomatically traverse hyperlinks and analyze the structure of the Web. Today, he has gotten\nan intriguing idea to improve his software agents. However, he is very busy and requires help\nfrom good programmers. You are now being asked to be involved in his development team and\nto create a small but critical software module of his new type of software agents.\n\nUpon traversal of hyperlinks, Pathfinder 's software agents incrementally generate a map of\nvisited portions of the Web. So the agents should maintain the list of traversed hyperlinks\nand visited web pages. One problem in keeping track of such information is that two or more\ndifferent URLs can point to the same web page. For instance, by typing any one of the following\nfive URLs, your favorite browsers probably bring you to the same web page, which as you may\nhave visited is the home page of the ACM ICPC Ehime contest.\n\n http: //www. ehime-u. ac. jp/ICPC/\n http: //www. ehime-u. ac. jp/ICPC\n http: //www. ehime-u. ac. jp/ICPC/. . /ICPC/\n http: //www. ehime-u. ac. jp/ICPC/. /\n http: //www. ehime-u. ac. jp/ICPC/index. html\n\nYour program should reveal such aliases for Pathfinder 's experiments.\n\nWell, . . . but it were a real challenge and to be perfect you might have to embed rather compli-\ncated logic into your program. We are afraid that even excellent programmers like you could\nnot complete it in five hours. So, we make the problem a little simpler and subtly unrealis-\ntic. You should focus on the path parts (i. e. /ICPC/, /ICPC, /ICPC/. . /ICPC/, /ICPC/. /, and\n/ICPC/index. html in the above example) of URLs and ignore the scheme parts (e. g. http: //),\nthe server parts (e. g. www. ehime-u. ac. jp), and other optional parts. You should carefully read\nthe rules described in the sequel since some of them may not be based on the reality of today 's\nWeb and URLs.\n\nEach path part in this problem is an absolute pathname, which specifies a path from the root\ndirectory to some web page in a hierarchical (tree-shaped) directory structure. A pathname\nalways starts with a slash (/), representing the root directory, followed by path segments delim-\nited by a slash. For instance, /ICPC/index. html is a pathname with two path segments ICPC and index. html.\n\nAll those path segments but the last should be directory names and the last one the name of an\nordinary file where a web page is stored. However, we have one exceptional rule: an ordinary\nfile name index. html at the end of a pathname may be omitted. For instance, a pathname\n/ICPC/index. html can be shortened to /ICPC/, if index. html is an existing ordinary file name.\nMore precisely, if ICPC is the name of an existing directory just under the root and index. html\nis the name of an existing ordinary file just under the /ICPC directory, /ICPC/index. html and\n/ICPC/ refer to the same web page. Furthermore, the last slash following the last path segment\ncan also be omitted. That is, for instance, /ICPC/ can be further shortened to /ICPC. However,\n/index. html can only be abbreviated to / (a single slash).\n\nYou should pay special attention to path segments consisting of a single period (. ) or a double\nperiod (. . ), both of which are always regarded as directory names. The former represents the\ndirectory itself and the latter represents its parent directory. Therefore, if /ICPC/ refers to some\nweb page, both /ICPC/. / and /ICPC/. . /ICPC/ refer to the same page. Also /ICPC2/. . /ICPC/\nrefers to the same page if ICPC2 is the name of an existing directory just under the root;\notherwise it does not refer to any web page. Note that the root directory does not have any\nparent directory and thus such pathnames as /. . / and /ICPC/. . /. . /index. html cannot point\nto any web page.\n\nYour job in this problem is to write a program that checks whether two given pathnames refer\nto existing web pages and, if so, examines whether they are the same.", "constraint": "", "input": "The input consists of multiple datasets. The first line of each dataset contains two positive\nintegers N and M, both of which are less than or equal to 100 and are separated by a single\nspace character.\n\nThe rest of the dataset consists of N + 2M lines, each of which contains a syntactically correct\npathname of at most 100 characters. You may assume that each path segment enclosed by two\nslashes is of length at least one. In other words, two consecutive slashes cannot occur in any\npathname. Each path segment does not include anything other than alphanumerical characters\n(i. e. ‘a '-‘z ', ‘A '-‘Z ', and ‘0 '-‘9 ') and periods (‘. ').\n\nThe first N pathnames enumerate all the web pages (ordinary files). Every existing directory\nname occurs at least once in these pathnames. You can assume that these pathnames do not\ninclude any path segments consisting solely of single or double periods and that the last path\nsegments are ordinary file names. Therefore, you do not have to worry about special rules for\nindex. html and single/double periods. You can also assume that no two of the N pathnames\npoint to the same page.\n\nEach of the following M pairs of pathnames is a question: do the two pathnames point to the\nsame web page? These pathnames may include single or double periods and may be terminated\nby a slash. They may include names that do not correspond to existing directories or ordinary\nfiles.\n\nTwo zeros in a line indicate the end of the input.", "output": "For each dataset, your program should output the M answers to the M questions, each in a\nseparate line. Each answer should be “yes” if both point to the same web page, “not found”\nif at least one of the pathnames does not point to any one of the first N web pages listed in the\ninput, or “no” otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 6\n/home/ACM/index.html\n/ICPC/index.html\n/ICPC/general.html\n/ICPC/japanese/index.html\n/ICPC/secret/confidential/2005/index.html\n/home/ACM/\n/home/ICPC/../ACM/\n/ICPC/secret/\n/ICPC/secret/index.html\n/ICPC\n/ICPC/../ICPC/index.html\n/ICPC\n/ICPC/general.html\n/ICPC/japanese/.././\n/ICPC/japanese/./../\n/home/ACM/index.html\n/home/ACM/index.html/\n1 4\n/index.html/index.html\n/\n/index.html/index.html\n/index.html\n/index.html/index.html\n/..\n/index.html/../..\n/index.html/\n/index.html/index.html/..\n0 0\n output: not found\nnot found\nyes\nno\nyes\nnot found\nnot found\nyes\nnot found\nnot found"], "Pid": "p00830", "ProblemText": "Task Description: Professor Pathfinder is a distinguished authority on the structure of hyperlinks in the World\nWide Web. For establishing his hypotheses, he has been developing software agents, which\nautomatically traverse hyperlinks and analyze the structure of the Web. Today, he has gotten\nan intriguing idea to improve his software agents. However, he is very busy and requires help\nfrom good programmers. You are now being asked to be involved in his development team and\nto create a small but critical software module of his new type of software agents.\n\nUpon traversal of hyperlinks, Pathfinder 's software agents incrementally generate a map of\nvisited portions of the Web. So the agents should maintain the list of traversed hyperlinks\nand visited web pages. One problem in keeping track of such information is that two or more\ndifferent URLs can point to the same web page. For instance, by typing any one of the following\nfive URLs, your favorite browsers probably bring you to the same web page, which as you may\nhave visited is the home page of the ACM ICPC Ehime contest.\n\n http: //www. ehime-u. ac. jp/ICPC/\n http: //www. ehime-u. ac. jp/ICPC\n http: //www. ehime-u. ac. jp/ICPC/. . /ICPC/\n http: //www. ehime-u. ac. jp/ICPC/. /\n http: //www. ehime-u. ac. jp/ICPC/index. html\n\nYour program should reveal such aliases for Pathfinder 's experiments.\n\nWell, . . . but it were a real challenge and to be perfect you might have to embed rather compli-\ncated logic into your program. We are afraid that even excellent programmers like you could\nnot complete it in five hours. So, we make the problem a little simpler and subtly unrealis-\ntic. You should focus on the path parts (i. e. /ICPC/, /ICPC, /ICPC/. . /ICPC/, /ICPC/. /, and\n/ICPC/index. html in the above example) of URLs and ignore the scheme parts (e. g. http: //),\nthe server parts (e. g. www. ehime-u. ac. jp), and other optional parts. You should carefully read\nthe rules described in the sequel since some of them may not be based on the reality of today 's\nWeb and URLs.\n\nEach path part in this problem is an absolute pathname, which specifies a path from the root\ndirectory to some web page in a hierarchical (tree-shaped) directory structure. A pathname\nalways starts with a slash (/), representing the root directory, followed by path segments delim-\nited by a slash. For instance, /ICPC/index. html is a pathname with two path segments ICPC and index. html.\n\nAll those path segments but the last should be directory names and the last one the name of an\nordinary file where a web page is stored. However, we have one exceptional rule: an ordinary\nfile name index. html at the end of a pathname may be omitted. For instance, a pathname\n/ICPC/index. html can be shortened to /ICPC/, if index. html is an existing ordinary file name.\nMore precisely, if ICPC is the name of an existing directory just under the root and index. html\nis the name of an existing ordinary file just under the /ICPC directory, /ICPC/index. html and\n/ICPC/ refer to the same web page. Furthermore, the last slash following the last path segment\ncan also be omitted. That is, for instance, /ICPC/ can be further shortened to /ICPC. However,\n/index. html can only be abbreviated to / (a single slash).\n\nYou should pay special attention to path segments consisting of a single period (. ) or a double\nperiod (. . ), both of which are always regarded as directory names. The former represents the\ndirectory itself and the latter represents its parent directory. Therefore, if /ICPC/ refers to some\nweb page, both /ICPC/. / and /ICPC/. . /ICPC/ refer to the same page. Also /ICPC2/. . /ICPC/\nrefers to the same page if ICPC2 is the name of an existing directory just under the root;\notherwise it does not refer to any web page. Note that the root directory does not have any\nparent directory and thus such pathnames as /. . / and /ICPC/. . /. . /index. html cannot point\nto any web page.\n\nYour job in this problem is to write a program that checks whether two given pathnames refer\nto existing web pages and, if so, examines whether they are the same.\nTask Input: The input consists of multiple datasets. The first line of each dataset contains two positive\nintegers N and M, both of which are less than or equal to 100 and are separated by a single\nspace character.\n\nThe rest of the dataset consists of N + 2M lines, each of which contains a syntactically correct\npathname of at most 100 characters. You may assume that each path segment enclosed by two\nslashes is of length at least one. In other words, two consecutive slashes cannot occur in any\npathname. Each path segment does not include anything other than alphanumerical characters\n(i. e. ‘a '-‘z ', ‘A '-‘Z ', and ‘0 '-‘9 ') and periods (‘. ').\n\nThe first N pathnames enumerate all the web pages (ordinary files). Every existing directory\nname occurs at least once in these pathnames. You can assume that these pathnames do not\ninclude any path segments consisting solely of single or double periods and that the last path\nsegments are ordinary file names. Therefore, you do not have to worry about special rules for\nindex. html and single/double periods. You can also assume that no two of the N pathnames\npoint to the same page.\n\nEach of the following M pairs of pathnames is a question: do the two pathnames point to the\nsame web page? These pathnames may include single or double periods and may be terminated\nby a slash. They may include names that do not correspond to existing directories or ordinary\nfiles.\n\nTwo zeros in a line indicate the end of the input.\nTask Output: For each dataset, your program should output the M answers to the M questions, each in a\nseparate line. Each answer should be “yes” if both point to the same web page, “not found”\nif at least one of the pathnames does not point to any one of the first N web pages listed in the\ninput, or “no” otherwise.\nTask Samples: input: 5 6\n/home/ACM/index.html\n/ICPC/index.html\n/ICPC/general.html\n/ICPC/japanese/index.html\n/ICPC/secret/confidential/2005/index.html\n/home/ACM/\n/home/ICPC/../ACM/\n/ICPC/secret/\n/ICPC/secret/index.html\n/ICPC\n/ICPC/../ICPC/index.html\n/ICPC\n/ICPC/general.html\n/ICPC/japanese/.././\n/ICPC/japanese/./../\n/home/ACM/index.html\n/home/ACM/index.html/\n1 4\n/index.html/index.html\n/\n/index.html/index.html\n/index.html\n/index.html/index.html\n/..\n/index.html/../..\n/index.html/\n/index.html/index.html/..\n0 0\n output: not found\nnot found\nyes\nno\nyes\nnot found\nnot found\nyes\nnot found\nnot found\n\n" }, { "title": "Problem E: Confusing Login Names", "content": "Meikyokan University is very famous for its research and education in the area of computer\nscience. This university has a computer center that has advanced and secure computing facilities\nincluding supercomputers and many personal computers connected to the Internet.\n\nOne of the policies of the computer center is to let the students select their own login names.\nUnfortunately, students are apt to select similar login names, and troubles caused by mistakes\nin entering or specifying login names are relatively common. These troubles are a burden on\nthe staff of the computer center.\n\nTo avoid such troubles, Dr. Choei Takano, the chief manager of the computer center, decided\nto stamp out similar and confusing login names. To this end, Takano has to develop a program\nthat detects confusing login names.\n\nBased on the following four operations on strings, the distance between two login names is\ndetermined as the minimum number of operations that transforms one login name to the other.\n\n Deleting a character at an arbitrary position.\n\n Inserting a character into an arbitrary position.\n\n Replacing a character at an arbitrary position with another character.\n\n Swapping two adjacent characters at an arbitrary position.\nFor example, the distance between “omura” and “murai” is two, because the following sequence\nof operations transforms “omura” to “murai”.\n\n delete ‘o ' insert ‘i '\n omura --> mura --> murai\n\nAnother example is that the distance between “akasan” and “kaason” is also two.\n\n swap ‘a ' and ‘k ' replace ‘a ' with ‘o '\n akasan --> kaasan --> kaason\n\nTakano decided that two login names with a small distance are confusing and thus must be\navoided.\n\nYour job is to write a program that enumerates all the confusing pairs of login names.\n\nBeware that the rules may combine in subtle ways. For instance, the distance between “ant”\nand “neat” is two.\n\n swap ‘a ' and ‘n ' insert ‘e '\n ant --> nat --> neat", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is given in the following format.\n\n n\n d\n name_1\n name_2\n . . .\n name_n\n\nThe first integer n is the number of login names. Then comes a positive integer d. Two login\nnames whose distance is less than or equal to d are deemed to be confusing. You may assume\nthat 0 < n <= 200 and 0 < d <= 2. The i-th student 's login name is given by name_i, which is\ncomposed of only lowercase letters. Its length is less than 16. You can assume that there are no\nduplicates in name_i (1 <= i <= n).\n\nThe end of the input is indicated by a line that solely contains a zero.", "output": "For each dataset, your program should output all pairs of confusing login names, one pair per\nline, followed by the total number of confusing pairs in the dataset.\n\nIn each pair, the two login names are to be separated only by a comma character (, ), and the\nlogin name that is alphabetically preceding the other should appear first. The entire output of\nconfusing pairs for each dataset must be sorted as follows. For two pairs “w_1, w_2” and “w_3, w_4”,\nif w_1 alphabetically precedes w_3, or they are the same and w_2 precedes w_4, then “w_1, w_2” must\nappear before “w_3, w_4”.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n2\nomura\ntoshio\nraku\ntanaka\nimura\nyoshoi\nhayashi\nmiura\n3\n1\ntasaka\nnakata\ntanaka\n1\n1\nfoo\n5\n2\npsqt\nabcdef\nabzdefa\npqrst\nabdxcef\n0\n output: imura,miura\nimura,omura\nmiura,omura\ntoshio,yoshoi\n4\ntanaka,tasaka\n1\n0\nabcdef,abdxcef\nabcdef,abzdefa\npqrst,psqt\n3"], "Pid": "p00831", "ProblemText": "Task Description: Meikyokan University is very famous for its research and education in the area of computer\nscience. This university has a computer center that has advanced and secure computing facilities\nincluding supercomputers and many personal computers connected to the Internet.\n\nOne of the policies of the computer center is to let the students select their own login names.\nUnfortunately, students are apt to select similar login names, and troubles caused by mistakes\nin entering or specifying login names are relatively common. These troubles are a burden on\nthe staff of the computer center.\n\nTo avoid such troubles, Dr. Choei Takano, the chief manager of the computer center, decided\nto stamp out similar and confusing login names. To this end, Takano has to develop a program\nthat detects confusing login names.\n\nBased on the following four operations on strings, the distance between two login names is\ndetermined as the minimum number of operations that transforms one login name to the other.\n\n Deleting a character at an arbitrary position.\n\n Inserting a character into an arbitrary position.\n\n Replacing a character at an arbitrary position with another character.\n\n Swapping two adjacent characters at an arbitrary position.\nFor example, the distance between “omura” and “murai” is two, because the following sequence\nof operations transforms “omura” to “murai”.\n\n delete ‘o ' insert ‘i '\n omura --> mura --> murai\n\nAnother example is that the distance between “akasan” and “kaason” is also two.\n\n swap ‘a ' and ‘k ' replace ‘a ' with ‘o '\n akasan --> kaasan --> kaason\n\nTakano decided that two login names with a small distance are confusing and thus must be\navoided.\n\nYour job is to write a program that enumerates all the confusing pairs of login names.\n\nBeware that the rules may combine in subtle ways. For instance, the distance between “ant”\nand “neat” is two.\n\n swap ‘a ' and ‘n ' insert ‘e '\n ant --> nat --> neat\nTask Input: The input consists of multiple datasets. Each dataset is given in the following format.\n\n n\n d\n name_1\n name_2\n . . .\n name_n\n\nThe first integer n is the number of login names. Then comes a positive integer d. Two login\nnames whose distance is less than or equal to d are deemed to be confusing. You may assume\nthat 0 < n <= 200 and 0 < d <= 2. The i-th student 's login name is given by name_i, which is\ncomposed of only lowercase letters. Its length is less than 16. You can assume that there are no\nduplicates in name_i (1 <= i <= n).\n\nThe end of the input is indicated by a line that solely contains a zero.\nTask Output: For each dataset, your program should output all pairs of confusing login names, one pair per\nline, followed by the total number of confusing pairs in the dataset.\n\nIn each pair, the two login names are to be separated only by a comma character (, ), and the\nlogin name that is alphabetically preceding the other should appear first. The entire output of\nconfusing pairs for each dataset must be sorted as follows. For two pairs “w_1, w_2” and “w_3, w_4”,\nif w_1 alphabetically precedes w_3, or they are the same and w_2 precedes w_4, then “w_1, w_2” must\nappear before “w_3, w_4”.\nTask Samples: input: 8\n2\nomura\ntoshio\nraku\ntanaka\nimura\nyoshoi\nhayashi\nmiura\n3\n1\ntasaka\nnakata\ntanaka\n1\n1\nfoo\n5\n2\npsqt\nabcdef\nabzdefa\npqrst\nabdxcef\n0\n output: imura,miura\nimura,omura\nmiura,omura\ntoshio,yoshoi\n4\ntanaka,tasaka\n1\n0\nabcdef,abdxcef\nabcdef,abzdefa\npqrst,psqt\n3\n\n" }, { "title": "Problem F: Dice Puzzle", "content": "Let 's try a dice puzzle. The rules of this puzzle are as follows.\nDice with six faces as shown in Figure 1 are used in the puzzle.\nFigure 1: Faces of a die\nWith twenty seven such dice, a 3 * 3 * 3 cube is built as shown in Figure 2.\nFigure 2: 3 * 3 * 3 cube\nWhen building up a cube made of dice, the sum of the numbers marked on the faces of adjacent dice that are placed against each other must be seven (See Figure 3). For example, if one face of the pair is marked “2”, then the other face must be “5”.\n\nFigure 3: A pair of faces placed against each other\nThe top and the front views of the cube are partially given, i. e. the numbers on faces of\nsome of the dice on the top and on the front are given.\nFigure 4: Top and front views of the cube\nThe goal of the puzzle is to find all the plausible dice arrangements that are consistent\nwith the given top and front view information.\n\nYour job is to write a program that solves this puzzle.", "constraint": "", "input": "The input consists of multiple datasets in the following format.\n\n N\n Dataset_1\n Dataset_2\n . . .\n Dataset_N\n\nN is the number of the datasets.\n\nThe format of each dataset is as follows.\n\nT_11 T_12 T_13\nT_21 T_22 T_23\nT_31 T_32 T_33\nF_11 F_12 F_13\nF_21 F_22 F_23\nF_31 F_32 F_33\n\nT_ij and F_ij (1 <= i <= 3,1 <= j <= 3) are the faces of dice appearing on the top and front views,\nas shown in Figure 2, or a zero. A zero means that the face at the corresponding position is\nunknown.", "output": "For each plausible arrangement of dice, compute the sum of the numbers marked on the nine\nfaces appearing on the right side of the cube, that is, with the notation given in Figure 2,\n\n∑^3_i=1∑^3_j=1R_ij.\n\nFor each dataset, you should output the right view sums for all the plausible arrangements, in\nascending order and without duplicates. Numbers should be separated by a single space.\n\nWhen there are no plausible arrangements for a dataset, output a zero.\n\nFor example, suppose that the top and the front views are given as follows.\nFigure 5: Example\nThere are four plausible right views as shown in Figure 6. The right view sums are 33,36,32,\nand 33, respectively. After rearranging them into ascending order and eliminating duplicates,\nthe answer should be “32 33 36”.\nFigure 6: Plausible right views\n\nThe output should be one line for each dataset. The output may have spaces at ends of lines.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1 1 1\n1 1 1\n1 1 1\n2 2 2\n2 2 2\n2 2 2\n4 3 3\n5 2 2\n4 3 3\n6 1 1\n6 1 1\n6 1 0\n1 0 0\n0 2 0\n0 0 0\n5 1 2\n5 1 2\n0 0 0\n2 0 0\n0 3 0\n0 0 0\n0 0 0\n0 0 0\n3 0 1\n output: 27\n24\n32 33 36\n0"], "Pid": "p00832", "ProblemText": "Task Description: Let 's try a dice puzzle. The rules of this puzzle are as follows.\nDice with six faces as shown in Figure 1 are used in the puzzle.\nFigure 1: Faces of a die\nWith twenty seven such dice, a 3 * 3 * 3 cube is built as shown in Figure 2.\nFigure 2: 3 * 3 * 3 cube\nWhen building up a cube made of dice, the sum of the numbers marked on the faces of adjacent dice that are placed against each other must be seven (See Figure 3). For example, if one face of the pair is marked “2”, then the other face must be “5”.\n\nFigure 3: A pair of faces placed against each other\nThe top and the front views of the cube are partially given, i. e. the numbers on faces of\nsome of the dice on the top and on the front are given.\nFigure 4: Top and front views of the cube\nThe goal of the puzzle is to find all the plausible dice arrangements that are consistent\nwith the given top and front view information.\n\nYour job is to write a program that solves this puzzle.\nTask Input: The input consists of multiple datasets in the following format.\n\n N\n Dataset_1\n Dataset_2\n . . .\n Dataset_N\n\nN is the number of the datasets.\n\nThe format of each dataset is as follows.\n\nT_11 T_12 T_13\nT_21 T_22 T_23\nT_31 T_32 T_33\nF_11 F_12 F_13\nF_21 F_22 F_23\nF_31 F_32 F_33\n\nT_ij and F_ij (1 <= i <= 3,1 <= j <= 3) are the faces of dice appearing on the top and front views,\nas shown in Figure 2, or a zero. A zero means that the face at the corresponding position is\nunknown.\nTask Output: For each plausible arrangement of dice, compute the sum of the numbers marked on the nine\nfaces appearing on the right side of the cube, that is, with the notation given in Figure 2,\n\n∑^3_i=1∑^3_j=1R_ij.\n\nFor each dataset, you should output the right view sums for all the plausible arrangements, in\nascending order and without duplicates. Numbers should be separated by a single space.\n\nWhen there are no plausible arrangements for a dataset, output a zero.\n\nFor example, suppose that the top and the front views are given as follows.\nFigure 5: Example\nThere are four plausible right views as shown in Figure 6. The right view sums are 33,36,32,\nand 33, respectively. After rearranging them into ascending order and eliminating duplicates,\nthe answer should be “32 33 36”.\nFigure 6: Plausible right views\n\nThe output should be one line for each dataset. The output may have spaces at ends of lines.\nTask Samples: input: 4\n1 1 1\n1 1 1\n1 1 1\n2 2 2\n2 2 2\n2 2 2\n4 3 3\n5 2 2\n4 3 3\n6 1 1\n6 1 1\n6 1 0\n1 0 0\n0 2 0\n0 0 0\n5 1 2\n5 1 2\n0 0 0\n2 0 0\n0 3 0\n0 0 0\n0 0 0\n0 0 0\n3 0 1\n output: 27\n24\n32 33 36\n0\n\n" }, { "title": "Problem G: Color the Map", "content": "You were lucky enough to get a map just before entering the legendary magical mystery world.\nThe map shows the whole area of your planned exploration, including several countries with\ncomplicated borders. The map is clearly drawn, but in sepia ink only; it is hard to recognize at\na glance which region belongs to which country, and this might bring you into severe danger. You\nhave decided to color the map before entering the area. “A good deal depends on preparation, ”\nyou talked to yourself.\n\nEach country has one or more territories, each of which has a polygonal shape. Territories\nbelonging to one country may or may not “touch” each other, i. e. there may be disconnected\nterritories. All the territories belonging to the same country must be assigned the same color.\nYou can assign the same color to more than one country, but, to avoid confusion, two countries\n“adjacent” to each other should be assigned different colors. Two countries are considered to be\n“adjacent” if any of their territories share a border of non-zero length.\n\nWrite a program that finds the least number of colors required to color the map.", "constraint": "", "input": "The input consists of multiple map data. Each map data starts with a line containing the total\nnumber of territories n, followed by the data for those territories. n is a positive integer not\nmore than 100. The data for a territory with m vertices has the following format:\n\n String\n x_1 y_1\n x_2 y_2\n . . .\n x_m y_m\n -1\n\n“String” (a sequence of alphanumerical characters) gives the name of the country it belongs to.\nA country name has at least one character and never has more than twenty. When a country\nhas multiple territories, its name appears in each of them.\n\nRemaining lines represent the vertices of the territory. A vertex data line has a pair of nonneg-\native integers which represent the x- and y-coordinates of a vertex. x- and y-coordinates are\nseparated by a single space, and y-coordinate is immediately followed by a newline. Edges of\nthe territory are obtained by connecting vertices given in two adjacent vertex data lines, and byconnecting vertices given in the last and the first vertex data lines. None of x- and y-coordinates\nexceeds 1000. Finally, -1 in a line marks the end of vertex data lines. The number of vertices\nm does not exceed 100.\n\nYou may assume that the contours of polygons are simple, i. e. they do not cross nor touch\nthemselves. No two polygons share a region of non-zero area. The number of countries in a map\ndoes not exceed 10.\n\nThe last map data is followed by a line containing only a zero, marking the end of the input\ndata.", "output": "For each map data, output one line containing the least possible number of colors required to\ncolor the map satisfying the specified conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\nBlizid\n0 0\n60 0\n60 60\n0 60\n0 50\n50 50\n50 10\n0 10\n-1\nBlizid\n0 10\n10 10\n10 50\n0 50\n-1\nWindom\n10 10\n50 10\n40 20\n20 20\n20 40\n10 50\n-1\nAccent\n50 10\n50 50\n35 50\n35 25\n-1\nPilot\n35 25\n35 50\n10 50\n-1\nBlizid\n20 20\n40 20\n20 40\n-1\n4\nA1234567890123456789\n0 0\n0 100\n100 100\n100 0\n-1\nB1234567890123456789\n100 100\n100 200\n200 200\n200 100\n-1\nC1234567890123456789\n0 100\n100 100\n100 200\n0 200\n-1\nD123456789012345678\n100 0\n100 100\n200 100\n200 0\n-1\n0\n output: 4\n2"], "Pid": "p00833", "ProblemText": "Task Description: You were lucky enough to get a map just before entering the legendary magical mystery world.\nThe map shows the whole area of your planned exploration, including several countries with\ncomplicated borders. The map is clearly drawn, but in sepia ink only; it is hard to recognize at\na glance which region belongs to which country, and this might bring you into severe danger. You\nhave decided to color the map before entering the area. “A good deal depends on preparation, ”\nyou talked to yourself.\n\nEach country has one or more territories, each of which has a polygonal shape. Territories\nbelonging to one country may or may not “touch” each other, i. e. there may be disconnected\nterritories. All the territories belonging to the same country must be assigned the same color.\nYou can assign the same color to more than one country, but, to avoid confusion, two countries\n“adjacent” to each other should be assigned different colors. Two countries are considered to be\n“adjacent” if any of their territories share a border of non-zero length.\n\nWrite a program that finds the least number of colors required to color the map.\nTask Input: The input consists of multiple map data. Each map data starts with a line containing the total\nnumber of territories n, followed by the data for those territories. n is a positive integer not\nmore than 100. The data for a territory with m vertices has the following format:\n\n String\n x_1 y_1\n x_2 y_2\n . . .\n x_m y_m\n -1\n\n“String” (a sequence of alphanumerical characters) gives the name of the country it belongs to.\nA country name has at least one character and never has more than twenty. When a country\nhas multiple territories, its name appears in each of them.\n\nRemaining lines represent the vertices of the territory. A vertex data line has a pair of nonneg-\native integers which represent the x- and y-coordinates of a vertex. x- and y-coordinates are\nseparated by a single space, and y-coordinate is immediately followed by a newline. Edges of\nthe territory are obtained by connecting vertices given in two adjacent vertex data lines, and byconnecting vertices given in the last and the first vertex data lines. None of x- and y-coordinates\nexceeds 1000. Finally, -1 in a line marks the end of vertex data lines. The number of vertices\nm does not exceed 100.\n\nYou may assume that the contours of polygons are simple, i. e. they do not cross nor touch\nthemselves. No two polygons share a region of non-zero area. The number of countries in a map\ndoes not exceed 10.\n\nThe last map data is followed by a line containing only a zero, marking the end of the input\ndata.\nTask Output: For each map data, output one line containing the least possible number of colors required to\ncolor the map satisfying the specified conditions.\nTask Samples: input: 6\nBlizid\n0 0\n60 0\n60 60\n0 60\n0 50\n50 50\n50 10\n0 10\n-1\nBlizid\n0 10\n10 10\n10 50\n0 50\n-1\nWindom\n10 10\n50 10\n40 20\n20 20\n20 40\n10 50\n-1\nAccent\n50 10\n50 50\n35 50\n35 25\n-1\nPilot\n35 25\n35 50\n10 50\n-1\nBlizid\n20 20\n40 20\n20 40\n-1\n4\nA1234567890123456789\n0 0\n0 100\n100 100\n100 0\n-1\nB1234567890123456789\n100 100\n100 200\n200 200\n200 100\n-1\nC1234567890123456789\n0 100\n100 100\n100 200\n0 200\n-1\nD123456789012345678\n100 0\n100 100\n200 100\n200 0\n-1\n0\n output: 4\n2\n\n" }, { "title": "Problem H: Inherit the Spheres", "content": "In the year 2xxx, an expedition team landing on a planet found strange objects made by an\nancient species living on that planet. They are transparent boxes containing opaque solid spheres\n(Figure 1). There are also many lithographs which seem to contain positions and radiuses of\nspheres.\nFigure 1: A strange object\n\nInitially their objective was unknown, but Professor Zambendorf found the cross section formed\nby a horizontal plane plays an important role. For example, the cross section of an object\nchanges as in Figure 2 by sliding the plane from bottom to top.\nFigure 2: Cross sections at different positions\n\nHe eventually found that some information is expressed by the transition of the number of\nconnected figures in the cross section, where each connected figure is a union of discs intersecting\nor touching each other, and each disc is a cross section of the corresponding solid sphere. For\ninstance, in Figure 2, whose geometry is described in the first sample dataset later, the number\nof connected figures changes as 0,1,2,1,2,3,2,1, and 0, at z = 0.0000,162.0000,167.0000,\n173.0004,185.0000,191.9996,198.0000,203.0000, and 205.0000, respectively. By assigning 1 for\nincrement and 0 for decrement, the transitions of this sequence can be expressed by an 8-bit\nbinary number 11011000.\n\nFor helping further analysis, write a program to determine the transitions when sliding the\nhorizontal plane from bottom (z = 0) to top (z = 36000).", "constraint": "", "input": "The input consists of a series of datasets. Each dataset begins with a line containing a positive\ninteger, which indicates the number of spheres N in the dataset. It is followed by N lines\ndescribing the centers and radiuses of the spheres. Each of the N lines has four positive integers\nX_i, Y_i, Z_i, and R_i (i = 1, . . . , N) describing the center and the radius of the i-th sphere,\nrespectively.\n\nYou may assume 1 <= N <= 100,1 <= R_i <= 2000,0 < X_i - R_i < X_i + R_i < 4000,0 < Y_i - R_i < Y_i + R_i < 16000, and 0 < Z_i - R_i < Z_i + R_i < 36000. Each solid sphere is defined as the set of\nall points (x, y, z) satisfying (x - X_i)^2 + (y - Y_i)^2 + (z - Z_i)^2 <= R_i^2.\n\nA sphere may contain other spheres. No two spheres are mutually tangent. Every Z_i ± R_i and\nminimum/maximum z coordinates of a circle formed by the intersection of any two spheres differ\nfrom each other by at least 0.01.\n\nThe end of the input is indicated by a line with one zero.", "output": "For each dataset, your program should output two lines. The first line should contain an integer\nM indicating the number of transitions. The second line should contain an M-bit binary number\nthat expresses the transitions of the number of connected figures as specified above.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n95 20 180 18\n125 20 185 18\n40 27 195 10\n1\n5 5 5 4\n2\n5 5 5 4\n5 5 5 3\n2\n5 5 5 4\n5 7 5 3\n16\n2338 3465 29034 710\n1571 14389 25019 842\n1706 8015 11324 1155\n1899 4359 33815 888\n2160 10364 20511 1264\n2048 8835 23706 1906\n2598 13041 23679 618\n1613 11112 8003 1125\n1777 4754 25986 929\n2707 9945 11458 617\n1153 10358 4305 755\n2462 8450 21838 934\n1822 11539 10025 1639\n1473 11939 12924 638\n1388 8519 18653 834\n2239 7384 32729 862\n0\n output: 8\n11011000\n2\n10\n2\n10\n2\n10\n28\n1011100100110101101000101100"], "Pid": "p00834", "ProblemText": "Task Description: In the year 2xxx, an expedition team landing on a planet found strange objects made by an\nancient species living on that planet. They are transparent boxes containing opaque solid spheres\n(Figure 1). There are also many lithographs which seem to contain positions and radiuses of\nspheres.\nFigure 1: A strange object\n\nInitially their objective was unknown, but Professor Zambendorf found the cross section formed\nby a horizontal plane plays an important role. For example, the cross section of an object\nchanges as in Figure 2 by sliding the plane from bottom to top.\nFigure 2: Cross sections at different positions\n\nHe eventually found that some information is expressed by the transition of the number of\nconnected figures in the cross section, where each connected figure is a union of discs intersecting\nor touching each other, and each disc is a cross section of the corresponding solid sphere. For\ninstance, in Figure 2, whose geometry is described in the first sample dataset later, the number\nof connected figures changes as 0,1,2,1,2,3,2,1, and 0, at z = 0.0000,162.0000,167.0000,\n173.0004,185.0000,191.9996,198.0000,203.0000, and 205.0000, respectively. By assigning 1 for\nincrement and 0 for decrement, the transitions of this sequence can be expressed by an 8-bit\nbinary number 11011000.\n\nFor helping further analysis, write a program to determine the transitions when sliding the\nhorizontal plane from bottom (z = 0) to top (z = 36000).\nTask Input: The input consists of a series of datasets. Each dataset begins with a line containing a positive\ninteger, which indicates the number of spheres N in the dataset. It is followed by N lines\ndescribing the centers and radiuses of the spheres. Each of the N lines has four positive integers\nX_i, Y_i, Z_i, and R_i (i = 1, . . . , N) describing the center and the radius of the i-th sphere,\nrespectively.\n\nYou may assume 1 <= N <= 100,1 <= R_i <= 2000,0 < X_i - R_i < X_i + R_i < 4000,0 < Y_i - R_i < Y_i + R_i < 16000, and 0 < Z_i - R_i < Z_i + R_i < 36000. Each solid sphere is defined as the set of\nall points (x, y, z) satisfying (x - X_i)^2 + (y - Y_i)^2 + (z - Z_i)^2 <= R_i^2.\n\nA sphere may contain other spheres. No two spheres are mutually tangent. Every Z_i ± R_i and\nminimum/maximum z coordinates of a circle formed by the intersection of any two spheres differ\nfrom each other by at least 0.01.\n\nThe end of the input is indicated by a line with one zero.\nTask Output: For each dataset, your program should output two lines. The first line should contain an integer\nM indicating the number of transitions. The second line should contain an M-bit binary number\nthat expresses the transitions of the number of connected figures as specified above.\nTask Samples: input: 3\n95 20 180 18\n125 20 185 18\n40 27 195 10\n1\n5 5 5 4\n2\n5 5 5 4\n5 5 5 3\n2\n5 5 5 4\n5 7 5 3\n16\n2338 3465 29034 710\n1571 14389 25019 842\n1706 8015 11324 1155\n1899 4359 33815 888\n2160 10364 20511 1264\n2048 8835 23706 1906\n2598 13041 23679 618\n1613 11112 8003 1125\n1777 4754 25986 929\n2707 9945 11458 617\n1153 10358 4305 755\n2462 8450 21838 934\n1822 11539 10025 1639\n1473 11939 12924 638\n1388 8519 18653 834\n2239 7384 32729 862\n0\n output: 8\n11011000\n2\n10\n2\n10\n2\n10\n28\n1011100100110101101000101100\n\n" }, { "title": "Problem I: Crossing Prisms", "content": "Prof. Bocchan is a mathematician and a sculptor. He likes to create sculptures with mathematics.\n\nHis style to make sculptures is very unique. He uses two identical prisms. Crossing them at right\nangles, he makes a polyhedron that is their intersection as a new work. Since he finishes it up\nwith painting, he needs to know the surface area of the polyhedron for estimating the amount\nof pigment needed.\n\nFor example, let us consider the two identical prisms in Figure 1. The definition of their cross\nsection is given in Figure 2. The prisms are put at right angles with each other and their\nintersection is the polyhedron depicted in Figure 3. An approximate value of its surface area\nis 194.8255.\nFigure 1: Two identical prisms at right angles\n\nGiven the shape of the cross section of the two identical prisms, your job is to calculate the\nsurface area of his sculpture.", "constraint": "", "input": "The input consists of multiple datasets, followed by a single line containing only a zero. The\nfirst line of each dataset contains an integer n indicating the number of the following lines, each\nof which contains two integers a_i and b_i (i = 1, . . . , n).\nFigure 2: Outline of the cross section\nFigure 3: The intersection\n\nA closed path formed by the given points (a_1, b_1), (a_2, b_2 ), . . . , (a_n, b_n), (a_n+1, b_n+1)(= (a_1, b_1))\nindicates the outline of the cross section of the prisms. The closed path is simple, that is, it does\nnot cross nor touch itself. The right-hand side of the line segment from (a_i, b_i) to (a_i+1 , b_i+1 ) is the inside of the section.\n\nYou may assume that 3 <= n <= 4,0 <= a_i <= 10 and 0 <= b_i <= 10 (i = 1, . . . , n).\n\nOne of the prisms is put along the x-axis so that the outline of its cross section at x = ζ is\nindicated by points (x_i, y_i, z_i ) = (ζ, a_i, b_i) (0 <= ζ <= 10, i = 1, . . . , n). The other prism is put\nalong the y-axis so that its cross section at y = η is indicated by points (x_i, y_i, z_i) = (a_i, η, b_i)\n(0 <= η <= 10, i = 1, . . . , n).", "output": "The output should consist of a series of lines each containing a single decimal fraction. Each\nnumber should indicate an approximate value of the surface area of the polyhedron defined by the corresponding dataset. The value may contain an error less than or equal to 0.0001. You\nmay print any number of digits below the decimal point.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n5 0\n0 10\n7 5\n10 5\n4\n7 5\n10 5\n5 0\n0 10\n4\n0 10\n10 10\n10 0\n0 0\n3\n0 0\n0 10\n10 0\n4\n0 10\n10 5\n0 0\n9 5\n4\n5 0\n0 10\n5 5\n10 10\n4\n0 5\n5 10\n10 5\n5 0\n4\n7 1\n4 1\n0 1\n9 5\n0\n output: 194.8255\n194.8255\n600.0000\n341.4214\n42.9519\n182.5141\n282.8427\n149.2470"], "Pid": "p00835", "ProblemText": "Task Description: Prof. Bocchan is a mathematician and a sculptor. He likes to create sculptures with mathematics.\n\nHis style to make sculptures is very unique. He uses two identical prisms. Crossing them at right\nangles, he makes a polyhedron that is their intersection as a new work. Since he finishes it up\nwith painting, he needs to know the surface area of the polyhedron for estimating the amount\nof pigment needed.\n\nFor example, let us consider the two identical prisms in Figure 1. The definition of their cross\nsection is given in Figure 2. The prisms are put at right angles with each other and their\nintersection is the polyhedron depicted in Figure 3. An approximate value of its surface area\nis 194.8255.\nFigure 1: Two identical prisms at right angles\n\nGiven the shape of the cross section of the two identical prisms, your job is to calculate the\nsurface area of his sculpture.\nTask Input: The input consists of multiple datasets, followed by a single line containing only a zero. The\nfirst line of each dataset contains an integer n indicating the number of the following lines, each\nof which contains two integers a_i and b_i (i = 1, . . . , n).\nFigure 2: Outline of the cross section\nFigure 3: The intersection\n\nA closed path formed by the given points (a_1, b_1), (a_2, b_2 ), . . . , (a_n, b_n), (a_n+1, b_n+1)(= (a_1, b_1))\nindicates the outline of the cross section of the prisms. The closed path is simple, that is, it does\nnot cross nor touch itself. The right-hand side of the line segment from (a_i, b_i) to (a_i+1 , b_i+1 ) is the inside of the section.\n\nYou may assume that 3 <= n <= 4,0 <= a_i <= 10 and 0 <= b_i <= 10 (i = 1, . . . , n).\n\nOne of the prisms is put along the x-axis so that the outline of its cross section at x = ζ is\nindicated by points (x_i, y_i, z_i ) = (ζ, a_i, b_i) (0 <= ζ <= 10, i = 1, . . . , n). The other prism is put\nalong the y-axis so that its cross section at y = η is indicated by points (x_i, y_i, z_i) = (a_i, η, b_i)\n(0 <= η <= 10, i = 1, . . . , n).\nTask Output: The output should consist of a series of lines each containing a single decimal fraction. Each\nnumber should indicate an approximate value of the surface area of the polyhedron defined by the corresponding dataset. The value may contain an error less than or equal to 0.0001. You\nmay print any number of digits below the decimal point.\nTask Samples: input: 4\n5 0\n0 10\n7 5\n10 5\n4\n7 5\n10 5\n5 0\n0 10\n4\n0 10\n10 10\n10 0\n0 0\n3\n0 0\n0 10\n10 0\n4\n0 10\n10 5\n0 0\n9 5\n4\n5 0\n0 10\n5 5\n10 10\n4\n0 5\n5 10\n10 5\n5 0\n4\n7 1\n4 1\n0 1\n9 5\n0\n output: 194.8255\n194.8255\n600.0000\n341.4214\n42.9519\n182.5141\n282.8427\n149.2470\n\n" }, { "title": "Problem A: Sum of Consecutive Prime Numbers", "content": "Some positive integers can be represented by a sum of one or more consecutive prime numbers.\nHow many such representations does a given positive integer have? For example, the integer 53\nhas two representations 5 + 7 + 11 + 13 + 17 and 53. The integer 41 has three representations\n2 + 3 + 5 + 7 + 11 + 13,11 + 13 + 17, and 41. The integer 3 has only one representation, which is\n3. The integer 20 has no such representations. Note that summands must be consecutive prime\nnumbers, so neither 7 + 13 nor 3 + 5 + 5 + 7 is a valid representation for the integer 20.\n\nYour mission is to write a program that reports the number of representations for the given\npositive integer.", "constraint": "", "input": "The input is a sequence of positive integers each in a separate line. The integers are between 2\nand 10 000, inclusive. The end of the input is indicated by a zero.", "output": "The output should be composed of lines each corresponding to an input line except the last zero.\nAn output line includes the number of representations for the input integer as the sum of one\nor more consecutive prime numbers. No other characters should be inserted in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3\n17\n41\n20\n666\n12\n53\n0\n output: 1\n1\n2\n3\n0\n0\n1\n2"], "Pid": "p00836", "ProblemText": "Task Description: Some positive integers can be represented by a sum of one or more consecutive prime numbers.\nHow many such representations does a given positive integer have? For example, the integer 53\nhas two representations 5 + 7 + 11 + 13 + 17 and 53. The integer 41 has three representations\n2 + 3 + 5 + 7 + 11 + 13,11 + 13 + 17, and 41. The integer 3 has only one representation, which is\n3. The integer 20 has no such representations. Note that summands must be consecutive prime\nnumbers, so neither 7 + 13 nor 3 + 5 + 5 + 7 is a valid representation for the integer 20.\n\nYour mission is to write a program that reports the number of representations for the given\npositive integer.\nTask Input: The input is a sequence of positive integers each in a separate line. The integers are between 2\nand 10 000, inclusive. The end of the input is indicated by a zero.\nTask Output: The output should be composed of lines each corresponding to an input line except the last zero.\nAn output line includes the number of representations for the input integer as the sum of one\nor more consecutive prime numbers. No other characters should be inserted in the output.\nTask Samples: input: 2\n3\n17\n41\n20\n666\n12\n53\n0\n output: 1\n1\n2\n3\n0\n0\n1\n2\n\n" }, { "title": "Problem B: Book Replacement", "content": "The deadline of Prof. Hachioji 's assignment is tomorrow. To complete the task, students have\nto copy pages of many reference books in the library.\n\nAll the reference books are in a storeroom and only the librarian is allowed to enter it. To obtain\na copy of a reference book 's page, a student should ask the librarian to make it. The librarian\nbrings books out of the storeroom and makes page copies according to the requests. The overall\nsituation is shown in Figure 1.\n\nStudents queue up in front of the counter. Only a single book can be requested at a time. If a\nstudent has more requests, the student goes to the end of the queue after the request has been\nserved.\n\nIn the storeroom, there are m desks D_1, . . . , D_m, and a shelf. They are placed in a line in this\norder, from the door to the back of the room. Up to c books can be put on each of the desks. If\na student requests a book, the librarian enters the storeroom and looks for it on D_1, . . . , D_m in\nthis order, and then on the shelf. After finding the book, the librarian takes it and gives a copy\nof a page to the student.\n\nThen the librarian returns to the storeroom with the requested book, to put it on D_1 according to the following procedure.\n\nIf D_1 is not full (in other words, the number of books on D_1 < c), the librarian puts the requested book there.\nIf D_1 is full, the librarian\n\n temporarily puts the requested book on the non-full desk closest to the entrance or,\n in case all the desks are full, on the shelf,\n\n finds the book on D_1 that has not been requested for the longest time (i. e. the least recently used book) and takes it,\n\n puts it on the non-full desk (except D_1 ) closest to the entrance or, in case all the desks except D_1 are full, on the shelf,\n\n takes the requested book from the temporary place,\n\n and finally puts it on D_1 .\nYour task is to write a program which simulates the behaviors of the students and the librarian,\nand evaluates the total cost of the overall process. Costs are associated with accessing a desk\nor the shelf, that is, putting/taking a book on/from it in the description above. The cost of an\naccess is i for desk D_i and m + 1 for the shelf. That is, an access to D_1, . . . , D_m , and the shelf\ncosts 1, . . . , m, and m + 1, respectively. Costs of other actions are ignored.\n\nInitially, no books are put on desks. No new students appear after opening the library.", "constraint": "", "input": "The input consists of multiple datasets. The end of the input is indicated by a line containing\nthree zeros separated by a space. It is not a dataset.\n\nThe format of each dataset is as follows.\n\n m c n\n k_1\n b_11 . . . b_1k1\n .\n .\n .\n k_n\n b_n1 . . . b_nkn\n\nHere, all data items are positive integers. m is the number of desks not exceeding 10. c is the number of books allowed to put on a desk, which does not exceed 30. n is the number of\nstudents not exceeding 100. k_i is the number of books requested by the i-th student, which does\nnot exceed 50. b_ij is the ID number of the book requested by the i-th student on the j-th turn.\nNo two books have the same ID number. Note that a student may request the same book more\nthan once. b_ij is less than 100.\n\nHere we show you an example of cost calculation for the following dataset.\n\n3 1 2\n3\n60 61 62\n2\n70 60\n\nIn this dataset, there are 3 desks (D_1, D_2, D_3 ). At most 1 book can be put on each desk. The\nnumber of students is 2. The first student requests 3 books of which IDs are 60,61, and 62,\nrespectively, and the second student 2 books of which IDs are 70 and 60, respectively.\n\nThe calculation of the cost for this dataset is done as follows. First, for the first request of the\nfirst student, the librarian takes the book 60 from the shelf and puts it on D_1 and the first\nstudent goes to the end of the queue, costing 5. Next, for the first request of the second student,\nthe librarian takes the book 70 from the shelf, puts it on D_2, moves the book 60 from D_1 to D_3 ,\nand finally moves the book 70 from D_2 to D_1 , costing 13. Similarly, the cost for the books 61,\n60, and 62, are calculated as 14,12,14, respectively. Therefore, the total cost is 58.", "output": "For each dataset, output the total cost of processing all the requests, in a separate line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 1 1\n1\n50\n2 1 2\n1\n50\n1\n60\n2 1 2\n2\n60 61\n1\n70\n4 2 3\n3\n60 61 62\n1\n70\n2\n80 81\n3 1 2\n3\n60 61 62\n2\n70 60\n1 2 5\n2\n87 95\n3\n96 71 35\n2\n68 2\n3\n3 18 93\n2\n57 2\n2 2 1\n5\n1 2 1 3 1\n0 0 0\n output: 4\n16\n28\n68\n58\n98\n23"], "Pid": "p00837", "ProblemText": "Task Description: The deadline of Prof. Hachioji 's assignment is tomorrow. To complete the task, students have\nto copy pages of many reference books in the library.\n\nAll the reference books are in a storeroom and only the librarian is allowed to enter it. To obtain\na copy of a reference book 's page, a student should ask the librarian to make it. The librarian\nbrings books out of the storeroom and makes page copies according to the requests. The overall\nsituation is shown in Figure 1.\n\nStudents queue up in front of the counter. Only a single book can be requested at a time. If a\nstudent has more requests, the student goes to the end of the queue after the request has been\nserved.\n\nIn the storeroom, there are m desks D_1, . . . , D_m, and a shelf. They are placed in a line in this\norder, from the door to the back of the room. Up to c books can be put on each of the desks. If\na student requests a book, the librarian enters the storeroom and looks for it on D_1, . . . , D_m in\nthis order, and then on the shelf. After finding the book, the librarian takes it and gives a copy\nof a page to the student.\n\nThen the librarian returns to the storeroom with the requested book, to put it on D_1 according to the following procedure.\n\nIf D_1 is not full (in other words, the number of books on D_1 < c), the librarian puts the requested book there.\nIf D_1 is full, the librarian\n\n temporarily puts the requested book on the non-full desk closest to the entrance or,\n in case all the desks are full, on the shelf,\n\n finds the book on D_1 that has not been requested for the longest time (i. e. the least recently used book) and takes it,\n\n puts it on the non-full desk (except D_1 ) closest to the entrance or, in case all the desks except D_1 are full, on the shelf,\n\n takes the requested book from the temporary place,\n\n and finally puts it on D_1 .\nYour task is to write a program which simulates the behaviors of the students and the librarian,\nand evaluates the total cost of the overall process. Costs are associated with accessing a desk\nor the shelf, that is, putting/taking a book on/from it in the description above. The cost of an\naccess is i for desk D_i and m + 1 for the shelf. That is, an access to D_1, . . . , D_m , and the shelf\ncosts 1, . . . , m, and m + 1, respectively. Costs of other actions are ignored.\n\nInitially, no books are put on desks. No new students appear after opening the library.\nTask Input: The input consists of multiple datasets. The end of the input is indicated by a line containing\nthree zeros separated by a space. It is not a dataset.\n\nThe format of each dataset is as follows.\n\n m c n\n k_1\n b_11 . . . b_1k1\n .\n .\n .\n k_n\n b_n1 . . . b_nkn\n\nHere, all data items are positive integers. m is the number of desks not exceeding 10. c is the number of books allowed to put on a desk, which does not exceed 30. n is the number of\nstudents not exceeding 100. k_i is the number of books requested by the i-th student, which does\nnot exceed 50. b_ij is the ID number of the book requested by the i-th student on the j-th turn.\nNo two books have the same ID number. Note that a student may request the same book more\nthan once. b_ij is less than 100.\n\nHere we show you an example of cost calculation for the following dataset.\n\n3 1 2\n3\n60 61 62\n2\n70 60\n\nIn this dataset, there are 3 desks (D_1, D_2, D_3 ). At most 1 book can be put on each desk. The\nnumber of students is 2. The first student requests 3 books of which IDs are 60,61, and 62,\nrespectively, and the second student 2 books of which IDs are 70 and 60, respectively.\n\nThe calculation of the cost for this dataset is done as follows. First, for the first request of the\nfirst student, the librarian takes the book 60 from the shelf and puts it on D_1 and the first\nstudent goes to the end of the queue, costing 5. Next, for the first request of the second student,\nthe librarian takes the book 70 from the shelf, puts it on D_2, moves the book 60 from D_1 to D_3 ,\nand finally moves the book 70 from D_2 to D_1 , costing 13. Similarly, the cost for the books 61,\n60, and 62, are calculated as 14,12,14, respectively. Therefore, the total cost is 58.\nTask Output: For each dataset, output the total cost of processing all the requests, in a separate line.\nTask Samples: input: 2 1 1\n1\n50\n2 1 2\n1\n50\n1\n60\n2 1 2\n2\n60 61\n1\n70\n4 2 3\n3\n60 61 62\n1\n70\n2\n80 81\n3 1 2\n3\n60 61 62\n2\n70 60\n1 2 5\n2\n87 95\n3\n96 71 35\n2\n68 2\n3\n3 18 93\n2\n57 2\n2 2 1\n5\n1 2 1 3 1\n0 0 0\n output: 4\n16\n28\n68\n58\n98\n23\n\n" }, { "title": "Problem C: Colored Cubes", "content": "There are several colored cubes. All of them are of the same size but they may be colored\ndifferently. Each face of these cubes has a single color. Colors of distinct faces of a cube may or\nmay not be the same.\n\nTwo cubes are said to be identically colored if some suitable rotations of one of the cubes give\nidentical looks to both of the cubes. For example, two cubes shown in Figure 2 are identically\ncolored. A set of cubes is said to be identically colored if every pair of them are identically\ncolored.\n\nA cube and its mirror image are not necessarily identically colored. For example, two cubes\nshown in Figure 3 are not identically colored.\n\nYou can make a given set of cubes identically colored by repainting some of the faces, whatever\ncolors the faces may have. In Figure 4, repainting four faces makes the three cubes identically\ncolored and repainting fewer faces will never do.\n\nYour task is to write a program to calculate the minimum number of faces that needs to be\nrepainted for a given set of cubes to become identically colored.", "constraint": "", "input": "The input is a sequence of datasets. A dataset consists of a header and a body appearing in this\norder. A header is a line containing one positive integer n and the body following it consists\nof n lines. You can assume that 1 <= n <= 4. Each line in a body contains six color names\nseparated by a space. A color name consists of a word or words connected with a hyphen (-).\nA word consists of one or more lowercase letters. You can assume that a color name is at most\n24-characters long including hyphens.\n\nA dataset corresponds to a set of colored cubes. The integer n corresponds to the number of\ncubes. Each line of the body corresponds to a cube and describes the colors of its faces. Color\nnames in a line is ordered in accordance with the numbering of faces shown in Figure 5. A line\n\n color_1 color_2 color_3 color_4 color_5 color_6\n\nThe end of the input is indicated by a line containing a single zero. It is not a dataset nor a\npart of a dataset.", "output": "For each dataset, output a line containing the minimum number of faces that need to be repainted\nto make the set of cubes identically colored.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\nscarlet green blue yellow magenta cyan\nblue pink green magenta cyan lemon\npurple red blue yellow cyan green\n2\nred green blue yellow magenta cyan\ncyan green blue yellow magenta red\n2\nred green gray gray magenta cyan\ncyan green gray gray magenta red\n2\nred green blue yellow magenta cyan\nmagenta red blue yellow cyan green\n3\nred green blue yellow magenta cyan\ncyan green blue yellow magenta red\nmagenta red blue yellow cyan green\n3\nblue green green green green blue\ngreen blue blue green green green\ngreen green green green green sea-green\n3\nred yellow red yellow red yellow\nred red yellow yellow red yellow\nred red red red red red\n4\nviolet violet salmon salmon salmon salmon\nviolet salmon salmon salmon salmon violet\nviolet violet salmon salmon violet violet\nviolet violet violet violet salmon salmon\n1\nred green blue yellow magenta cyan\n4\nmagenta pink red scarlet vermilion wine-red\naquamarine blue cyan indigo sky-blue turquoise-blue\nblond cream chrome-yellow lemon olive yellow\nchrome-green emerald-green green olive vilidian sky-blue\n0\n output: 4\n2\n0\n0\n2\n3\n4\n4\n0\n16"], "Pid": "p00838", "ProblemText": "Task Description: There are several colored cubes. All of them are of the same size but they may be colored\ndifferently. Each face of these cubes has a single color. Colors of distinct faces of a cube may or\nmay not be the same.\n\nTwo cubes are said to be identically colored if some suitable rotations of one of the cubes give\nidentical looks to both of the cubes. For example, two cubes shown in Figure 2 are identically\ncolored. A set of cubes is said to be identically colored if every pair of them are identically\ncolored.\n\nA cube and its mirror image are not necessarily identically colored. For example, two cubes\nshown in Figure 3 are not identically colored.\n\nYou can make a given set of cubes identically colored by repainting some of the faces, whatever\ncolors the faces may have. In Figure 4, repainting four faces makes the three cubes identically\ncolored and repainting fewer faces will never do.\n\nYour task is to write a program to calculate the minimum number of faces that needs to be\nrepainted for a given set of cubes to become identically colored.\nTask Input: The input is a sequence of datasets. A dataset consists of a header and a body appearing in this\norder. A header is a line containing one positive integer n and the body following it consists\nof n lines. You can assume that 1 <= n <= 4. Each line in a body contains six color names\nseparated by a space. A color name consists of a word or words connected with a hyphen (-).\nA word consists of one or more lowercase letters. You can assume that a color name is at most\n24-characters long including hyphens.\n\nA dataset corresponds to a set of colored cubes. The integer n corresponds to the number of\ncubes. Each line of the body corresponds to a cube and describes the colors of its faces. Color\nnames in a line is ordered in accordance with the numbering of faces shown in Figure 5. A line\n\n color_1 color_2 color_3 color_4 color_5 color_6\n\nThe end of the input is indicated by a line containing a single zero. It is not a dataset nor a\npart of a dataset.\nTask Output: For each dataset, output a line containing the minimum number of faces that need to be repainted\nto make the set of cubes identically colored.\nTask Samples: input: 3\nscarlet green blue yellow magenta cyan\nblue pink green magenta cyan lemon\npurple red blue yellow cyan green\n2\nred green blue yellow magenta cyan\ncyan green blue yellow magenta red\n2\nred green gray gray magenta cyan\ncyan green gray gray magenta red\n2\nred green blue yellow magenta cyan\nmagenta red blue yellow cyan green\n3\nred green blue yellow magenta cyan\ncyan green blue yellow magenta red\nmagenta red blue yellow cyan green\n3\nblue green green green green blue\ngreen blue blue green green green\ngreen green green green green sea-green\n3\nred yellow red yellow red yellow\nred red yellow yellow red yellow\nred red red red red red\n4\nviolet violet salmon salmon salmon salmon\nviolet salmon salmon salmon salmon violet\nviolet violet salmon salmon violet violet\nviolet violet violet violet salmon salmon\n1\nred green blue yellow magenta cyan\n4\nmagenta pink red scarlet vermilion wine-red\naquamarine blue cyan indigo sky-blue turquoise-blue\nblond cream chrome-yellow lemon olive yellow\nchrome-green emerald-green green olive vilidian sky-blue\n0\n output: 4\n2\n0\n0\n2\n3\n4\n4\n0\n16\n\n" }, { "title": "Problem D: Organize Your Train", "content": "In the good old Hachioji railroad station located in the west of Tokyo, there are several parking\nlines, and lots of freight trains come and go every day.\n\nAll freight trains travel at night, so these trains containing various types of cars are settled in\nyour parking lines early in the morning. Then, during the daytime, you must reorganize cars\nin these trains according to the request of the railroad clients, so that every line contains the\n“right” train, i. e. the right number of cars of the right types, in the right order.\n\nAs shown in Figure 7, all parking lines run in the East-West direction. There are exchange\nlines connecting them through which you can move cars. An exchange line connects two ends\nof different parking lines. Note that an end of a parking line can be connected to many ends of\nother lines. Also note that an exchange line may connect the East-end of a parking line and the\nWest-end of another.\n\nCars of the same type are not discriminated between each other. The cars are symmetric, so\ndirections of cars don 't matter either.\n\nYou can divide a train at an arbitrary position to make two sub-trains and move one of them\nthrough an exchange line connected to the end of its side. Alternatively, you may move a whole\ntrain as is without dividing it. Anyway, when a (sub-) train arrives at the destination parking\nline and the line already has another train in it, they are coupled to form a longer train.\n\nYour superautomatic train organization system can do these without any help of locomotive\nengines. Due to the limitation of the system, trains cannot stay on exchange lines; when you\nstart moving a (sub-) train, it must arrive at the destination parking line before moving another\ntrain.\n\nIn what follows, a letter represents a car type and a train is expressed as a sequence of letters.\nFor example in Figure 8, from an initial state having a train \"aabbccdee\" \non line 0 and no trains\non other lines, you can make \"bbaadeecc\" on line 2 with the four moves shown in the figure.\n\nTo cut the cost out, your boss wants to minimize the number of (sub-) train movements. For\nexample, in the case of Figure 8, the number of movements is 4 and this is the minimum.\n\nGiven the configurations of the train cars in the morning (arrival state) and evening (departure\nstate), your job is to write a program to find the optimal train reconfiguration plan.", "constraint": "", "input": "The input consists of one or more datasets. A dataset has the following format:\n\nx y\np_1 P_1 q_1 Q_1\np_2 P_2 q_2 Q_2\n.\n.\n.\np_y P_y q_y Q_y\ns_0\ns_1\n.\n.\n.\ns_x-1\nt_0\nt_1\n.\n.\n.\nt_x-1\n\nx is the number of parking lines, which are numbered from 0 to x-1. y is the number of exchange\nlines. Then y lines of the exchange line data follow, each describing two ends connected by the\nexchange line; p_i and q_i are integers between 0 and x - 1 which indicate parking line numbers,\nand P_i and Q_i are either \"E\" (East) or \"W\" (West) which indicate the ends of the parking lines.\n\nThen x lines of the arrival (initial) configuration data, s_0, . . . , s_x-1, and x lines of the departure\n(target) configuration data, t_0, . . . t_x-1, follow. Each of these lines contains one or more lowercase letters \"a\", \"b\", . . . , \"z\", which indicate types of cars of the train in the corresponding parking\nline, in west to east order, or alternatively, a single \"-\" when the parking line is empty.\n\nYou may assume that x does not exceed 4, the total number of cars contained in all the trains\ndoes not exceed 10, and every parking line has sufficient length to park all the cars.\n\nYou may also assume that each dataset has at least one solution and that the minimum number\nof moves is between one and six, inclusive.\n\nTwo zeros in a line indicate the end of the input.", "output": "For each dataset, output the number of moves for an optimal reconfiguration plan, in a separate\nline.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 5\n0W 1W\n0W 2W\n0W 2E\n0E 1E\n1E 2E\naabbccdee\n-\n-\n-\n-\nbbaadeecc\n3 3\n0E 1W\n1E 2W\n2E 0W\naabb\nbbcc\naa\nbbbb\ncc\naaaa\n3 4\n0E 1W\n0E 2E\n1E 2W\n2E 0W\nababab\n-\n-\naaabbb\n-\n-\n0 0\n output: 4\n2\n5"], "Pid": "p00839", "ProblemText": "Task Description: In the good old Hachioji railroad station located in the west of Tokyo, there are several parking\nlines, and lots of freight trains come and go every day.\n\nAll freight trains travel at night, so these trains containing various types of cars are settled in\nyour parking lines early in the morning. Then, during the daytime, you must reorganize cars\nin these trains according to the request of the railroad clients, so that every line contains the\n“right” train, i. e. the right number of cars of the right types, in the right order.\n\nAs shown in Figure 7, all parking lines run in the East-West direction. There are exchange\nlines connecting them through which you can move cars. An exchange line connects two ends\nof different parking lines. Note that an end of a parking line can be connected to many ends of\nother lines. Also note that an exchange line may connect the East-end of a parking line and the\nWest-end of another.\n\nCars of the same type are not discriminated between each other. The cars are symmetric, so\ndirections of cars don 't matter either.\n\nYou can divide a train at an arbitrary position to make two sub-trains and move one of them\nthrough an exchange line connected to the end of its side. Alternatively, you may move a whole\ntrain as is without dividing it. Anyway, when a (sub-) train arrives at the destination parking\nline and the line already has another train in it, they are coupled to form a longer train.\n\nYour superautomatic train organization system can do these without any help of locomotive\nengines. Due to the limitation of the system, trains cannot stay on exchange lines; when you\nstart moving a (sub-) train, it must arrive at the destination parking line before moving another\ntrain.\n\nIn what follows, a letter represents a car type and a train is expressed as a sequence of letters.\nFor example in Figure 8, from an initial state having a train \"aabbccdee\" \non line 0 and no trains\non other lines, you can make \"bbaadeecc\" on line 2 with the four moves shown in the figure.\n\nTo cut the cost out, your boss wants to minimize the number of (sub-) train movements. For\nexample, in the case of Figure 8, the number of movements is 4 and this is the minimum.\n\nGiven the configurations of the train cars in the morning (arrival state) and evening (departure\nstate), your job is to write a program to find the optimal train reconfiguration plan.\nTask Input: The input consists of one or more datasets. A dataset has the following format:\n\nx y\np_1 P_1 q_1 Q_1\np_2 P_2 q_2 Q_2\n.\n.\n.\np_y P_y q_y Q_y\ns_0\ns_1\n.\n.\n.\ns_x-1\nt_0\nt_1\n.\n.\n.\nt_x-1\n\nx is the number of parking lines, which are numbered from 0 to x-1. y is the number of exchange\nlines. Then y lines of the exchange line data follow, each describing two ends connected by the\nexchange line; p_i and q_i are integers between 0 and x - 1 which indicate parking line numbers,\nand P_i and Q_i are either \"E\" (East) or \"W\" (West) which indicate the ends of the parking lines.\n\nThen x lines of the arrival (initial) configuration data, s_0, . . . , s_x-1, and x lines of the departure\n(target) configuration data, t_0, . . . t_x-1, follow. Each of these lines contains one or more lowercase letters \"a\", \"b\", . . . , \"z\", which indicate types of cars of the train in the corresponding parking\nline, in west to east order, or alternatively, a single \"-\" when the parking line is empty.\n\nYou may assume that x does not exceed 4, the total number of cars contained in all the trains\ndoes not exceed 10, and every parking line has sufficient length to park all the cars.\n\nYou may also assume that each dataset has at least one solution and that the minimum number\nof moves is between one and six, inclusive.\n\nTwo zeros in a line indicate the end of the input.\nTask Output: For each dataset, output the number of moves for an optimal reconfiguration plan, in a separate\nline.\nTask Samples: input: 3 5\n0W 1W\n0W 2W\n0W 2E\n0E 1E\n1E 2E\naabbccdee\n-\n-\n-\n-\nbbaadeecc\n3 3\n0E 1W\n1E 2W\n2E 0W\naabb\nbbcc\naa\nbbbb\ncc\naaaa\n3 4\n0E 1W\n0E 2E\n1E 2W\n2E 0W\nababab\n-\n-\naaabbb\n-\n-\n0 0\n output: 4\n2\n5\n\n" }, { "title": "Problem E: Mobile Computing", "content": "There is a mysterious planet called Yaen, whose space is 2-dimensional. There are many beautiful\nstones on the planet, and the Yaen people love to collect them. They bring the stones back home\nand make nice mobile arts of them to decorate their 2-dimensional living rooms.\n\nIn their 2-dimensional world, a mobile is defined recursively as follows:\n\n a stone hung by a string, or\n\n a rod of length 1 with two sub-mobiles at both ends; the rod\n is hung by a string at the center of gravity of sub-mobiles.\n When the weights of the sub-mobiles are n and m, and their\n distances from the center of gravity are a and b respectively,\n the equation n * a = m * b holds.\nFor example, if you got three stones with weights 1,1, and 2, here are some possible mobiles\nand their widths:\n\nGiven the weights of stones and the width of the room, your task is to design the widest possible\nmobile satisfying both of the following conditions.\n\n It uses all the stones.\n\n Its width is less than the width of the room.\nYou should ignore the widths of stones.\nIn some cases two sub-mobiles hung from both ends of a rod might\noverlap (see the figure on the below). Such mobiles are acceptable.\nThe width of the example is (1/3) + 1 + (1/4).", "constraint": "", "input": "The first line of the input gives the number of datasets. Then the specified number of datasets\nfollow. A dataset has the following format.\n\n r\n s\n w_1\n .\n .\n .\n w_s\n\nr is a decimal fraction representing the width of the room, which satisfies 0 < r < 10. s is the\nnumber of the stones. You may assume 1 <= s <= 6. w_i is the weight of the i-th stone, which is\nan integer. You may assume 1 <= w_i <= 1000.\n\nYou can assume that no mobiles whose widths are between r - 0.00001 and r + 0.00001 can be made of given stones.", "output": "For each dataset in the input, one line containing a decimal fraction should be output. The\ndecimal fraction should give the width of the widest possible mobile as defined above. An\noutput line should not contain extra characters such as spaces.\n\nIn case there is no mobile which satisfies the requirement, answer -1 instead.\n\nThe answer should not have an error greater than 0.00000001. You may output any number of\ndigits after the decimal point, provided that the above accuracy condition is satisfied.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n1.3\n3\n1\n2\n1\n1.4\n3\n1\n2\n1\n2.0\n3\n1\n2\n1\n1.59\n4\n2\n1\n1\n3\n1.7143\n4\n1\n2\n3\n5\n output: -1\n1.3333333333333335\n1.6666666666666667\n1.5833333333333335\n1.7142857142857142"], "Pid": "p00840", "ProblemText": "Task Description: There is a mysterious planet called Yaen, whose space is 2-dimensional. There are many beautiful\nstones on the planet, and the Yaen people love to collect them. They bring the stones back home\nand make nice mobile arts of them to decorate their 2-dimensional living rooms.\n\nIn their 2-dimensional world, a mobile is defined recursively as follows:\n\n a stone hung by a string, or\n\n a rod of length 1 with two sub-mobiles at both ends; the rod\n is hung by a string at the center of gravity of sub-mobiles.\n When the weights of the sub-mobiles are n and m, and their\n distances from the center of gravity are a and b respectively,\n the equation n * a = m * b holds.\nFor example, if you got three stones with weights 1,1, and 2, here are some possible mobiles\nand their widths:\n\nGiven the weights of stones and the width of the room, your task is to design the widest possible\nmobile satisfying both of the following conditions.\n\n It uses all the stones.\n\n Its width is less than the width of the room.\nYou should ignore the widths of stones.\nIn some cases two sub-mobiles hung from both ends of a rod might\noverlap (see the figure on the below). Such mobiles are acceptable.\nThe width of the example is (1/3) + 1 + (1/4).\nTask Input: The first line of the input gives the number of datasets. Then the specified number of datasets\nfollow. A dataset has the following format.\n\n r\n s\n w_1\n .\n .\n .\n w_s\n\nr is a decimal fraction representing the width of the room, which satisfies 0 < r < 10. s is the\nnumber of the stones. You may assume 1 <= s <= 6. w_i is the weight of the i-th stone, which is\nan integer. You may assume 1 <= w_i <= 1000.\n\nYou can assume that no mobiles whose widths are between r - 0.00001 and r + 0.00001 can be made of given stones.\nTask Output: For each dataset in the input, one line containing a decimal fraction should be output. The\ndecimal fraction should give the width of the widest possible mobile as defined above. An\noutput line should not contain extra characters such as spaces.\n\nIn case there is no mobile which satisfies the requirement, answer -1 instead.\n\nThe answer should not have an error greater than 0.00000001. You may output any number of\ndigits after the decimal point, provided that the above accuracy condition is satisfied.\nTask Samples: input: 5\n1.3\n3\n1\n2\n1\n1.4\n3\n1\n2\n1\n2.0\n3\n1\n2\n1\n1.59\n4\n2\n1\n1\n3\n1.7143\n4\n1\n2\n3\n5\n output: -1\n1.3333333333333335\n1.6666666666666667\n1.5833333333333335\n1.7142857142857142\n\n" }, { "title": "Problem F: Atomic Car Race", "content": "In the year 2020, a race of atomically energized cars will be held. Unlike today 's car races, fueling\nis not a concern of racing teams. Cars can run throughout the course without any refueling.\nInstead, the critical factor is tire (tyre). Teams should carefully plan where to change tires of\ntheir cars.\n\nThe race is a road race having n checkpoints in the course. Their distances from the start are a_1, a_2, . . . , and a_n (in kilometers). The n-th checkpoint is the goal. At the i-th checkpoint (i < n),\ntires of a car can be changed. Of course, a team can choose whether to change or not to change\ntires at each checkpoint. It takes b seconds to change tires (including overhead for braking and\naccelerating). There is no time loss at a checkpoint if a team chooses not to change tires.\n\nA car cannot run fast for a while after a tire change, because the temperature of tires is lower\nthan the designed optimum. After running long without any tire changes, on the other hand,\na car cannot run fast because worn tires cannot grip the road surface well. The time to run\nan interval of one kilometer from x to x + 1 is given by the following expression (in seconds).\nHere x is a nonnegative integer denoting the distance (in kilometers) from the latest checkpoint\nwhere tires are changed (or the start). r, v, e and f are given constants.\n\n1/(v - e * (x - r)) (if x >= r)\n1/(v - f * (r - x)) (if x < r)\n\nYour mission is to write a program to determine the best strategy of tire changes which minimizes\nthe total time to the goal.", "constraint": "", "input": "The input consists of multiple datasets each corresponding to a race situation. The format of a\ndataset is as follows.\n\nn\na_1 a_2 . . . a_n\nb\nr v e f\n\nThe meaning of each of the input items is given in the problem statement. If an input line\ncontains two or more input items, they are separated by a space.\n\nn is a positive integer not exceeding 100. Each of a_1, a_2, . . . , and a_n is a positive integer satisfying 0 < a_1 < a_2 < . . . < a_n <= 10000. b is a positive decimal fraction not exceeding 100.0. r is a\nnonnegative integer satisfying 0 <= r <= a_n - 1. Each of v, e and f is a positive decimal fraction.\nYou can assume that v - e * (a_n - 1 - r) >= 0.01 and v - f * r >= 0.01.\n\nThe end of the input is indicated by a line with a single zero.", "output": "For each dataset in the input, one line containing a decimal fraction should be output. The\ndecimal fraction should give the elapsed time at the goal (in seconds) when the best strategy is\ntaken. An output line should not contain extra characters such as spaces.\n\nThe answer should not have an error greater than 0.001. You may output any number of digits\nafter the decimal point, provided that the above accuracy condition is satisfied.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n2 3\n1.0\n1 1.0 0.1 0.3\n5\n5 10 15 20 25\n0.15\n1 1.0 0.04 0.5\n10\n1783 3640 3991 4623 5465 5481 6369 6533 6865 8425\n4.172\n72 59.4705 0.0052834 0.0611224\n0\n output: 3.5397\n31.9249\n168.6682"], "Pid": "p00841", "ProblemText": "Task Description: In the year 2020, a race of atomically energized cars will be held. Unlike today 's car races, fueling\nis not a concern of racing teams. Cars can run throughout the course without any refueling.\nInstead, the critical factor is tire (tyre). Teams should carefully plan where to change tires of\ntheir cars.\n\nThe race is a road race having n checkpoints in the course. Their distances from the start are a_1, a_2, . . . , and a_n (in kilometers). The n-th checkpoint is the goal. At the i-th checkpoint (i < n),\ntires of a car can be changed. Of course, a team can choose whether to change or not to change\ntires at each checkpoint. It takes b seconds to change tires (including overhead for braking and\naccelerating). There is no time loss at a checkpoint if a team chooses not to change tires.\n\nA car cannot run fast for a while after a tire change, because the temperature of tires is lower\nthan the designed optimum. After running long without any tire changes, on the other hand,\na car cannot run fast because worn tires cannot grip the road surface well. The time to run\nan interval of one kilometer from x to x + 1 is given by the following expression (in seconds).\nHere x is a nonnegative integer denoting the distance (in kilometers) from the latest checkpoint\nwhere tires are changed (or the start). r, v, e and f are given constants.\n\n1/(v - e * (x - r)) (if x >= r)\n1/(v - f * (r - x)) (if x < r)\n\nYour mission is to write a program to determine the best strategy of tire changes which minimizes\nthe total time to the goal.\nTask Input: The input consists of multiple datasets each corresponding to a race situation. The format of a\ndataset is as follows.\n\nn\na_1 a_2 . . . a_n\nb\nr v e f\n\nThe meaning of each of the input items is given in the problem statement. If an input line\ncontains two or more input items, they are separated by a space.\n\nn is a positive integer not exceeding 100. Each of a_1, a_2, . . . , and a_n is a positive integer satisfying 0 < a_1 < a_2 < . . . < a_n <= 10000. b is a positive decimal fraction not exceeding 100.0. r is a\nnonnegative integer satisfying 0 <= r <= a_n - 1. Each of v, e and f is a positive decimal fraction.\nYou can assume that v - e * (a_n - 1 - r) >= 0.01 and v - f * r >= 0.01.\n\nThe end of the input is indicated by a line with a single zero.\nTask Output: For each dataset in the input, one line containing a decimal fraction should be output. The\ndecimal fraction should give the elapsed time at the goal (in seconds) when the best strategy is\ntaken. An output line should not contain extra characters such as spaces.\n\nThe answer should not have an error greater than 0.001. You may output any number of digits\nafter the decimal point, provided that the above accuracy condition is satisfied.\nTask Samples: input: 2\n2 3\n1.0\n1 1.0 0.1 0.3\n5\n5 10 15 20 25\n0.15\n1 1.0 0.04 0.5\n10\n1783 3640 3991 4623 5465 5481 6369 6533 6865 8425\n4.172\n72 59.4705 0.0052834 0.0611224\n0\n output: 3.5397\n31.9249\n168.6682\n\n" }, { "title": "Problem G: Network Mess", "content": "Gilbert is the network admin of Ginkgo company. His boss is mad about the messy network\ncables on the floor. He finally walked up to Gilbert and asked the lazy network admin to illustrate\nhow computers and switches are connected. Since he is a programmer, he is very reluctant to\nmove throughout the office and examine cables and switches with his eyes. He instead opted\nto get this job done by measurement and a little bit of mathematical thinking, sitting down in\nfront of his computer all the time. Your job is to help him by writing a program to reconstruct\nthe network topology from measurements.\n\nThere are a known number of computers and an unknown number of switches. Each computer\nis connected to one of the switches via a cable and to nothing else. Specifically, a computer\nis never connected to another computer directly, or never connected to two or more switches.\nSwitches are connected via cables to form a tree (a connected undirected graph with no cycles).\nNo switches are ‘useless. ' In other words, each switch is on the path between at least one pair\nof computers.\n\nAll in all, computers and switches together form a tree whose leaves are computers and whose\ninternal nodes switches (See Figure 9).\n\nGilbert measures the distances between all pairs of computers. The distance between two com-\nputers is simply the number of switches on the path between the two, plus one. Or equivalently,\nit is the number of cables used to connect them. You may wonder how Gilbert can actually\nobtain these distances solely based on measurement. Well, he can do so by a very sophisticated\nstatistical processing technique he invented. Please do not ask the details.\n\nYou are therefore given a matrix describing distances between leaves of a tree. Your job is to\nconstruct the tree from it.", "constraint": "", "input": "The input is a series of distance matrices, followed by a line consisting of a single '0'. Each\ndistance matrix is formatted as follows.\n\nN\na_11 a_12 . . . a_1N\na_21 a_22 . . . a_2N\n . . . .\n . . . .\n . . . .\na_N1 a_N2 . . . a_NN\nN is the size, i. e. the number of rows and the number of columns, of the matrix. a_ij gives the\ndistance between the i-th leaf node (computer) and the j-th. You may assume 2 <= N <= 50 and\nthe matrix is symmetric whose diagonal elements are all zeros. That is, a_ii = 0 and a_ij = a_ji\nfor each i and j. Each non-diagonal element a_ij (i ! = j) satisfies 2 <= a_ij <= 30. You may assume\nthere is always a solution. That is, there is a tree having the given distances between leaf nodes.", "output": "For each distance matrix, find a tree having the given distances between leaf nodes. Then output\nthe degree of each internal node (i. e. the number of cables adjoining each switch), all in a single\nline and in ascending order. Numbers in a line should be separated by a single space. A line\nshould not contain any other characters, including trailing spaces.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n 0 2 2 2\n 2 0 2 2\n 2 2 0 2\n 2 2 2 0\n4\n 0 2 4 4\n 2 0 4 4\n 4 4 0 2\n 4 4 2 0\n2\n 0 12\n 12 0\n0\n output: 4\n2 3 3\n2 2 2 2 2 2 2 2 2 2 2"], "Pid": "p00842", "ProblemText": "Task Description: Gilbert is the network admin of Ginkgo company. His boss is mad about the messy network\ncables on the floor. He finally walked up to Gilbert and asked the lazy network admin to illustrate\nhow computers and switches are connected. Since he is a programmer, he is very reluctant to\nmove throughout the office and examine cables and switches with his eyes. He instead opted\nto get this job done by measurement and a little bit of mathematical thinking, sitting down in\nfront of his computer all the time. Your job is to help him by writing a program to reconstruct\nthe network topology from measurements.\n\nThere are a known number of computers and an unknown number of switches. Each computer\nis connected to one of the switches via a cable and to nothing else. Specifically, a computer\nis never connected to another computer directly, or never connected to two or more switches.\nSwitches are connected via cables to form a tree (a connected undirected graph with no cycles).\nNo switches are ‘useless. ' In other words, each switch is on the path between at least one pair\nof computers.\n\nAll in all, computers and switches together form a tree whose leaves are computers and whose\ninternal nodes switches (See Figure 9).\n\nGilbert measures the distances between all pairs of computers. The distance between two com-\nputers is simply the number of switches on the path between the two, plus one. Or equivalently,\nit is the number of cables used to connect them. You may wonder how Gilbert can actually\nobtain these distances solely based on measurement. Well, he can do so by a very sophisticated\nstatistical processing technique he invented. Please do not ask the details.\n\nYou are therefore given a matrix describing distances between leaves of a tree. Your job is to\nconstruct the tree from it.\nTask Input: The input is a series of distance matrices, followed by a line consisting of a single '0'. Each\ndistance matrix is formatted as follows.\n\nN\na_11 a_12 . . . a_1N\na_21 a_22 . . . a_2N\n . . . .\n . . . .\n . . . .\na_N1 a_N2 . . . a_NN\nN is the size, i. e. the number of rows and the number of columns, of the matrix. a_ij gives the\ndistance between the i-th leaf node (computer) and the j-th. You may assume 2 <= N <= 50 and\nthe matrix is symmetric whose diagonal elements are all zeros. That is, a_ii = 0 and a_ij = a_ji\nfor each i and j. Each non-diagonal element a_ij (i ! = j) satisfies 2 <= a_ij <= 30. You may assume\nthere is always a solution. That is, there is a tree having the given distances between leaf nodes.\nTask Output: For each distance matrix, find a tree having the given distances between leaf nodes. Then output\nthe degree of each internal node (i. e. the number of cables adjoining each switch), all in a single\nline and in ascending order. Numbers in a line should be separated by a single space. A line\nshould not contain any other characters, including trailing spaces.\nTask Samples: input: 4\n 0 2 2 2\n 2 0 2 2\n 2 2 0 2\n 2 2 2 0\n4\n 0 2 4 4\n 2 0 4 4\n 4 4 0 2\n 4 4 2 0\n2\n 0 12\n 12 0\n0\n output: 4\n2 3 3\n2 2 2 2 2 2 2 2 2 2 2\n\n" }, { "title": "Problem H: Bingo", "content": "A Bingo game is played by one gamemaster and several players. At the beginning of a game,\neach player is given a card with M * M numbers in a matrix (See Figure 10).\n\nAs the game proceeds, the gamemaster announces a series of numbers one by one. Each player\npunches a hole in his card on the announced number, if any.\n\nWhen at least one 'Bingo' is made on the card, the player wins and leaves the game. The 'Bingo'\nmeans that all the M numbers in a line are punched vertically, horizontally or diagonally (See\nFigure 11).\n\nThe gamemaster continues announcing numbers until all the players make a Bingo.\n\nIn the ordinary Bingo games, the gamemaster chooses numbers by a random process and has no\ncontrol on them. But in this problem the gamemaster knows all the cards at the beginning of\nthe game and controls the game by choosing the number sequence to be announced at his will.\n\nSpecifically, he controls the game to satisfy the following condition.\n\nCard_i makes a Bingo no later than Card_j, for i < j. (*)\n\nFigure 12 shows an example of how a game proceeds. The gamemaster cannot announce '5'\nbefore '16', because Card_4 makes a Bingo before Card_2 and Card_3, violating the condition (*).\n\nYour job is to write a program which finds the minimum length of such sequence of numbers for\nthe given cards.", "constraint": "", "input": "The input consists of multiple datasets. The format of each dataset is as follows.\n\nAll data items are integers. P is the number of the cards, namely the number of the players. M is the number of rows and the number of columns of the matrix on each card. N^k_ij means the number written at the position (i, j) on the k-th card. If (i, j) ! = (p, q), then N^k_ij ! = N^k_pq. The parameters P, M, and N satisfy the conditions 2 <= P <= 4,3 <= M <= 4, and 0 <= N^k_ij <= 99.\nThe end of the input is indicated by a line containing two zeros separated by a space. It is not\na dataset.", "output": "For each dataset, output the minimum length of the sequence of numbers which satisfy the\ncondition (*). Output a zero if there are no such sequences. Output for each dataset must be\nprinted on a separate line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 3\n10 25 11 20 6 2 1 15 23\n5 21 3 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0\n output: 5\n4\n12\n0\nFor your convenience, sequences satisfying the condition (*) for the first three datasets are shown\nbelow. There may be other sequences of the same length satisfying the condition, but no shorter.\n11,2,23,16,5\n15,16,17,18\n11,12,13,21,22,23,31,32,33,41,42,43"], "Pid": "p00843", "ProblemText": "Task Description: A Bingo game is played by one gamemaster and several players. At the beginning of a game,\neach player is given a card with M * M numbers in a matrix (See Figure 10).\n\nAs the game proceeds, the gamemaster announces a series of numbers one by one. Each player\npunches a hole in his card on the announced number, if any.\n\nWhen at least one 'Bingo' is made on the card, the player wins and leaves the game. The 'Bingo'\nmeans that all the M numbers in a line are punched vertically, horizontally or diagonally (See\nFigure 11).\n\nThe gamemaster continues announcing numbers until all the players make a Bingo.\n\nIn the ordinary Bingo games, the gamemaster chooses numbers by a random process and has no\ncontrol on them. But in this problem the gamemaster knows all the cards at the beginning of\nthe game and controls the game by choosing the number sequence to be announced at his will.\n\nSpecifically, he controls the game to satisfy the following condition.\n\nCard_i makes a Bingo no later than Card_j, for i < j. (*)\n\nFigure 12 shows an example of how a game proceeds. The gamemaster cannot announce '5'\nbefore '16', because Card_4 makes a Bingo before Card_2 and Card_3, violating the condition (*).\n\nYour job is to write a program which finds the minimum length of such sequence of numbers for\nthe given cards.\nTask Input: The input consists of multiple datasets. The format of each dataset is as follows.\n\nAll data items are integers. P is the number of the cards, namely the number of the players. M is the number of rows and the number of columns of the matrix on each card. N^k_ij means the number written at the position (i, j) on the k-th card. If (i, j) ! = (p, q), then N^k_ij ! = N^k_pq. The parameters P, M, and N satisfy the conditions 2 <= P <= 4,3 <= M <= 4, and 0 <= N^k_ij <= 99.\nThe end of the input is indicated by a line containing two zeros separated by a space. It is not\na dataset.\nTask Output: For each dataset, output the minimum length of the sequence of numbers which satisfy the\ncondition (*). Output a zero if there are no such sequences. Output for each dataset must be\nprinted on a separate line.\nTask Samples: input: 4 3\n10 25 11 20 6 2 1 15 23\n5 21 3 12 23 17 7 26 2\n8 18 4 22 13 27 16 5 11\n19 9 24 2 11 5 14 28 16\n4 3\n12 13 20 24 28 32 15 16 17\n12 13 21 25 29 33 16 17 18\n12 13 22 26 30 34 17 18 15\n12 13 23 27 31 35 18 15 16\n4 3\n11 12 13 14 15 16 17 18 19\n21 22 23 24 25 26 27 28 29\n31 32 33 34 35 36 37 38 39\n41 42 43 44 45 46 47 48 49\n4 4\n2 6 9 21 15 23 17 31 33 12 25 4 8 24 13 36\n22 18 27 26 35 28 3 7 11 20 38 16 5 32 14 29\n26 7 16 29 27 3 38 14 18 28 20 32 22 35 11 5\n36 13 24 8 4 25 12 33 31 17 23 15 21 9 6 2\n0 0\n output: 5\n4\n12\n0\nFor your convenience, sequences satisfying the condition (*) for the first three datasets are shown\nbelow. There may be other sequences of the same length satisfying the condition, but no shorter.\n11,2,23,16,5\n15,16,17,18\n11,12,13,21,22,23,31,32,33,41,42,43\n\n" }, { "title": "Problem I: Shy Polygons", "content": "You are given two solid polygons and their positions on the xy-plane. You can move one\nof the two along the x-axis (they can overlap during the move). You cannot move it in other\ndirections. The goal is to place them as compactly as possible, subject to the following condition:\nthe distance between any point in one polygon and any point in the other must not be smaller\nthan a given minimum distance L.\n\nWe define the width of a placement as the difference between the maximum and the minimum\nx-coordinates of all points in the two polygons.\n\nYour job is to write a program to calculate the minimum width of placements satisfying the\nabove condition.\n\nLet's see an example. If the polygons in Figure 13 are placed with L = 10.0, the result will be 100. Figure 14 shows one of the optimal placements.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is given in the following format.\n\n L\n Polygon_1\n Polygon_2\n\nL is a decimal fraction, which means the required distance of two polygons. L is greater than\n0.1 and less than 50.0.\n\nThe format of each polygon is as follows.\n\nn\nx_1 y_1\nx_2 y_2\n.\n.\n.\nx_n y_n\n\nn is a positive integer, which represents the number of vertices of the polygon. n is greater than\n2 and less than 15.\n\nRemaining lines represent the vertices of the polygon. A vertex data line has a pair of nonneg-\native integers which represent the x- and y-coordinates of a vertex. x- and y-coordinates are\nseparated by a single space, and y-coordinate is immediately followed by a newline. x and y are\nless than 500.\n\nEdges of the polygon connect vertices given in two adjacent vertex data lines, and vertices given\nin the last and the first vertex data lines. You may assume that the vertices are given in the\ncounterclockwise order, and the contours of polygons are simple, i. e. they do not cross nor touch\nthemselves.\n\nAlso, you may assume that the result is not sensitive to errors. In concrete terms, for a given\npair of polygons, the minimum width is a function of the given minimum distance l. Let us\ndenote the function w(l). Then you can assume that |w(L ± 10^-7) - w(L)| < 10^-4.\n\nThe end of the input is indicated by a line that only contains a zero. It is not a part of a dataset.", "output": "The output should consist of a series of lines each containing a single decimal fraction. Each\nnumber should indicate the minimum width for the corresponding dataset. The answer should\nnot have an error greater than 0.0001. You may output any number of digits after the decimal\npoint, provided that the above accuracy condition is satisfied.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10.5235\n3\n0 0\n100 100\n0 100\n4\n0 50\n20 50\n20 80\n0 80\n10.0\n4\n120 45\n140 35\n140 65\n120 55\n8\n0 0\n100 0\n100 100\n0 100\n0 55\n80 90\n80 10\n0 45\n10.0\n3\n0 0\n1 0\n0 1\n3\n0 100\n1 101\n0 101\n10.0\n3\n0 0\n1 0\n0 100\n3\n0 50\n100 50\n0 51\n0\n output: 114.882476\n100\n1\n110.5005"], "Pid": "p00844", "ProblemText": "Task Description: You are given two solid polygons and their positions on the xy-plane. You can move one\nof the two along the x-axis (they can overlap during the move). You cannot move it in other\ndirections. The goal is to place them as compactly as possible, subject to the following condition:\nthe distance between any point in one polygon and any point in the other must not be smaller\nthan a given minimum distance L.\n\nWe define the width of a placement as the difference between the maximum and the minimum\nx-coordinates of all points in the two polygons.\n\nYour job is to write a program to calculate the minimum width of placements satisfying the\nabove condition.\n\nLet's see an example. If the polygons in Figure 13 are placed with L = 10.0, the result will be 100. Figure 14 shows one of the optimal placements.\nTask Input: The input consists of multiple datasets. Each dataset is given in the following format.\n\n L\n Polygon_1\n Polygon_2\n\nL is a decimal fraction, which means the required distance of two polygons. L is greater than\n0.1 and less than 50.0.\n\nThe format of each polygon is as follows.\n\nn\nx_1 y_1\nx_2 y_2\n.\n.\n.\nx_n y_n\n\nn is a positive integer, which represents the number of vertices of the polygon. n is greater than\n2 and less than 15.\n\nRemaining lines represent the vertices of the polygon. A vertex data line has a pair of nonneg-\native integers which represent the x- and y-coordinates of a vertex. x- and y-coordinates are\nseparated by a single space, and y-coordinate is immediately followed by a newline. x and y are\nless than 500.\n\nEdges of the polygon connect vertices given in two adjacent vertex data lines, and vertices given\nin the last and the first vertex data lines. You may assume that the vertices are given in the\ncounterclockwise order, and the contours of polygons are simple, i. e. they do not cross nor touch\nthemselves.\n\nAlso, you may assume that the result is not sensitive to errors. In concrete terms, for a given\npair of polygons, the minimum width is a function of the given minimum distance l. Let us\ndenote the function w(l). Then you can assume that |w(L ± 10^-7) - w(L)| < 10^-4.\n\nThe end of the input is indicated by a line that only contains a zero. It is not a part of a dataset.\nTask Output: The output should consist of a series of lines each containing a single decimal fraction. Each\nnumber should indicate the minimum width for the corresponding dataset. The answer should\nnot have an error greater than 0.0001. You may output any number of digits after the decimal\npoint, provided that the above accuracy condition is satisfied.\nTask Samples: input: 10.5235\n3\n0 0\n100 100\n0 100\n4\n0 50\n20 50\n20 80\n0 80\n10.0\n4\n120 45\n140 35\n140 65\n120 55\n8\n0 0\n100 0\n100 100\n0 100\n0 55\n80 90\n80 10\n0 45\n10.0\n3\n0 0\n1 0\n0 1\n3\n0 100\n1 101\n0 101\n10.0\n3\n0 0\n1 0\n0 100\n3\n0 50\n100 50\n0 51\n0\n output: 114.882476\n100\n1\n110.5005\n\n" }, { "title": "Problem A: How I Wonder What You Are!", "content": "One of the questions children often ask is \"How many stars are there in the sky? \" Under ideal conditions, even with the naked eye, nearly eight thousands are observable in the northern hemisphere. With a decent telescope, you may find many more, but, as the sight field will be\nlimited, you may find much less at a time.\n\nChildren may ask the same questions to their parents on a planet of some solar system billions\nof light-years away from the Earth. Their telescopes are similar to ours with circular sight fields,\nbut alien kids have many eyes and can look into different directions at a time through many\ntelescopes.\n\nGiven a set of positions of stars, a set of telescopes and the directions they are looking to, your\ntask is to count up how many stars can be seen through these telescopes.", "constraint": "", "input": "The input consists of one or more datasets. The number of datasets is less than 50. Each dataset\ndescribes stars and the parameters of the telescopes used.\n\nThe first line of a dataset contains a positive integer n not exceeding 500, meaning the number\nof stars. Each of the n lines following it contains three decimal fractions, s_x, s_y, and s_z. They\ngive the position (s_x, s_y, s_z) of the star described in Euclidean coordinates. You may assume\n-1000 <= s_x <= 1000, -1000 <= s_y <= 1000, -1000 <= s_z <= 1000 and (s_x, s_y, s_z) ! = (0,0,0).\n\nThen comes a line containing a positive integer m not exceeding 50, meaning the number of\ntelescopes. Each of the following m lines contains four decimal fractions, t_x, t_y, t_z, and φ, describing a telescope.\n\nThe first three numbers represent the direction of the telescope. All the telescopes are at the\norigin of the coordinate system (0,0,0) (we ignore the size of the planet). The three numbers give\nthe point (t_x, t_y, t_z) which can be seen in the center of the sight through the telescope. You may\nassume -1000 <= t_x <= 1000, -1000 <= t_y <= 1000, -1000 <= t_z <= 1000 and (t_x, t_y, t_z) ! = (0,0,0).\n\nThe fourth number φ (0 <= φ <= π/2) gives the angular radius, in radians, of the sight field of\nthe telescope.\n\nLet us defie that θ_i, j is the angle between the direction of the i-th star and the center direction\nof the j-th telescope and φ_jis the angular radius of the sight field of the j-th telescope. The i-th star is observable through the j-th telescope if and only if θ_i, j is less than . You may assume that |θ_i, j - φ_j| > 0.00000001 for all pairs of i and j.\n\nFigure 1: Direction and angular radius of a telescope\n\nThe end of the input is indicated with a line containing a single zero.", "output": "For each dataset, one line containing an integer meaning the number of stars observable through\nthe telescopes should be output. No other characters should be contained in the output. Note\nthat stars that can be seen through more than one telescope should not be counted twice or\nmore.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n100 0 500\n-500.243 -200.1 -300.5\n0 300 200\n2\n1 1 1 0.65\n-1 0 0 1.57\n3\n1 0 0\n0 1 0\n0 0 1\n4\n1 -1 -1 0.9553\n-1 1 -1 0.9554\n-1 -1 1 0.9553\n-1 1 -1 0.9554\n3\n1 0 0\n0 1 0\n0 0 1\n4\n1 -1 -1 0.9553\n-1 1 -1 0.9553\n-1 -1 1 0.9553\n-1 1 -1 0.9553\n0\n output: 2\n1\n0"], "Pid": "p00845", "ProblemText": "Task Description: One of the questions children often ask is \"How many stars are there in the sky? \" Under ideal conditions, even with the naked eye, nearly eight thousands are observable in the northern hemisphere. With a decent telescope, you may find many more, but, as the sight field will be\nlimited, you may find much less at a time.\n\nChildren may ask the same questions to their parents on a planet of some solar system billions\nof light-years away from the Earth. Their telescopes are similar to ours with circular sight fields,\nbut alien kids have many eyes and can look into different directions at a time through many\ntelescopes.\n\nGiven a set of positions of stars, a set of telescopes and the directions they are looking to, your\ntask is to count up how many stars can be seen through these telescopes.\nTask Input: The input consists of one or more datasets. The number of datasets is less than 50. Each dataset\ndescribes stars and the parameters of the telescopes used.\n\nThe first line of a dataset contains a positive integer n not exceeding 500, meaning the number\nof stars. Each of the n lines following it contains three decimal fractions, s_x, s_y, and s_z. They\ngive the position (s_x, s_y, s_z) of the star described in Euclidean coordinates. You may assume\n-1000 <= s_x <= 1000, -1000 <= s_y <= 1000, -1000 <= s_z <= 1000 and (s_x, s_y, s_z) ! = (0,0,0).\n\nThen comes a line containing a positive integer m not exceeding 50, meaning the number of\ntelescopes. Each of the following m lines contains four decimal fractions, t_x, t_y, t_z, and φ, describing a telescope.\n\nThe first three numbers represent the direction of the telescope. All the telescopes are at the\norigin of the coordinate system (0,0,0) (we ignore the size of the planet). The three numbers give\nthe point (t_x, t_y, t_z) which can be seen in the center of the sight through the telescope. You may\nassume -1000 <= t_x <= 1000, -1000 <= t_y <= 1000, -1000 <= t_z <= 1000 and (t_x, t_y, t_z) ! = (0,0,0).\n\nThe fourth number φ (0 <= φ <= π/2) gives the angular radius, in radians, of the sight field of\nthe telescope.\n\nLet us defie that θ_i, j is the angle between the direction of the i-th star and the center direction\nof the j-th telescope and φ_jis the angular radius of the sight field of the j-th telescope. The i-th star is observable through the j-th telescope if and only if θ_i, j is less than . You may assume that |θ_i, j - φ_j| > 0.00000001 for all pairs of i and j.\n\nFigure 1: Direction and angular radius of a telescope\n\nThe end of the input is indicated with a line containing a single zero.\nTask Output: For each dataset, one line containing an integer meaning the number of stars observable through\nthe telescopes should be output. No other characters should be contained in the output. Note\nthat stars that can be seen through more than one telescope should not be counted twice or\nmore.\nTask Samples: input: 3\n100 0 500\n-500.243 -200.1 -300.5\n0 300 200\n2\n1 1 1 0.65\n-1 0 0 1.57\n3\n1 0 0\n0 1 0\n0 0 1\n4\n1 -1 -1 0.9553\n-1 1 -1 0.9554\n-1 -1 1 0.9553\n-1 1 -1 0.9554\n3\n1 0 0\n0 1 0\n0 0 1\n4\n1 -1 -1 0.9553\n-1 1 -1 0.9553\n-1 -1 1 0.9553\n-1 1 -1 0.9553\n0\n output: 2\n1\n0\n\n" }, { "title": "Problem B: How I Mathematician Wonder What You Are!", "content": "After counting so many stars in the sky in his childhood, Isaac, now an astronomer and a\nmathematician, uses a big astronomical telescope and lets his image processing program count\nstars. The hardest part of the program is to judge if a shining object in the sky is really a star.\nAs a mathematician, the only way he knows is to apply a mathematical definition of stars.\n\nThe mathematical defiition of a star shape is as follows: A planar shape F is star-shaped if and\nonly if there is a point C ∈ F such that, for any point P ∈ F, the line segment CP is contained\nin F. Such a point C is called a center of F. To get accustomed to the definition, let's see some\nexamples below.\n\nFigure 2: Star shapes (the first row) and non-star shapes (the second row)\nThe firrst two are what you would normally call stars. According to the above definition, however,\nall shapes in the first row are star-shaped. The two in the second row are not. For each star\nshape, a center is indicated with a dot. Note that a star shape in general has infinitely many\ncenters. For example, for the third quadrangular shape, all points in it are centers.\n\nYour job is to write a program that tells whether a given polygonal shape is star-shaped or not.", "constraint": "", "input": "The input is a sequence of datasets followed by a line containing a single zero. Each dataset\nspecifies a polygon, and is formatted as follows.\n\n n\n x_1 y_1\n x_2 y_2\n . . .\n x_n y_n\n\nThe first line is the number of vertices, n, which satisfies 4 <= n <= 50. Subsequent n lines are the x- and y-coordinates of the n vertices. They are integers and satisfy 0 <= x_i <= 10000 and 0 <= y_i <= 10000 (i = 1, . . . , n). Line segments (x_i, y_i)-(x_i+1, y_i+1) (i = 1, . . . , n - 1) and the line segment (x_n, y_n)-(x_1, y_1) form the border of the polygon in the counterclockwise order. That is, these line segments see the inside of the polygon in the left of their directions.\n\nYou may assume that the polygon is simple, that is, its border never crosses or touches itself.\nYou may also assume that no three edges of the polygon meet at a single point even when they\nare infinitely extended.", "output": "For each dataset, output \"1\" if the polygon is star-shaped and \"0\" otherwise. Each number must be in a separate line and the line should not contain any other characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6\n66 13\n96 61\n76 98\n13 94\n4 0\n45 68\n8\n27 21\n55 14\n93 12\n56 95\n15 48\n38 46\n51 65\n64 31\n0\n output: 1\n0"], "Pid": "p00846", "ProblemText": "Task Description: After counting so many stars in the sky in his childhood, Isaac, now an astronomer and a\nmathematician, uses a big astronomical telescope and lets his image processing program count\nstars. The hardest part of the program is to judge if a shining object in the sky is really a star.\nAs a mathematician, the only way he knows is to apply a mathematical definition of stars.\n\nThe mathematical defiition of a star shape is as follows: A planar shape F is star-shaped if and\nonly if there is a point C ∈ F such that, for any point P ∈ F, the line segment CP is contained\nin F. Such a point C is called a center of F. To get accustomed to the definition, let's see some\nexamples below.\n\nFigure 2: Star shapes (the first row) and non-star shapes (the second row)\nThe firrst two are what you would normally call stars. According to the above definition, however,\nall shapes in the first row are star-shaped. The two in the second row are not. For each star\nshape, a center is indicated with a dot. Note that a star shape in general has infinitely many\ncenters. For example, for the third quadrangular shape, all points in it are centers.\n\nYour job is to write a program that tells whether a given polygonal shape is star-shaped or not.\nTask Input: The input is a sequence of datasets followed by a line containing a single zero. Each dataset\nspecifies a polygon, and is formatted as follows.\n\n n\n x_1 y_1\n x_2 y_2\n . . .\n x_n y_n\n\nThe first line is the number of vertices, n, which satisfies 4 <= n <= 50. Subsequent n lines are the x- and y-coordinates of the n vertices. They are integers and satisfy 0 <= x_i <= 10000 and 0 <= y_i <= 10000 (i = 1, . . . , n). Line segments (x_i, y_i)-(x_i+1, y_i+1) (i = 1, . . . , n - 1) and the line segment (x_n, y_n)-(x_1, y_1) form the border of the polygon in the counterclockwise order. That is, these line segments see the inside of the polygon in the left of their directions.\n\nYou may assume that the polygon is simple, that is, its border never crosses or touches itself.\nYou may also assume that no three edges of the polygon meet at a single point even when they\nare infinitely extended.\nTask Output: For each dataset, output \"1\" if the polygon is star-shaped and \"0\" otherwise. Each number must be in a separate line and the line should not contain any other characters.\nTask Samples: input: 6\n66 13\n96 61\n76 98\n13 94\n4 0\n45 68\n8\n27 21\n55 14\n93 12\n56 95\n15 48\n38 46\n51 65\n64 31\n0\n output: 1\n0\n\n" }, { "title": "Problem C: Cubic Eight-Puzzle", "content": "Let's play a puzzle using eight cubes placed on a 3 * 3 board leaving one empty square.\n\nFaces of cubes are painted with three colors. As a puzzle step, you can roll one of the cubes to\nthe adjacent empty square. Your goal is to make the specified color pattern visible from above\nby a number of such steps.\n\nThe rules of this puzzle are as follows.\nColoring of Cubes: All the cubes are colored in the same way as shown in Figure 3.\nThe opposite faces have the same color.\nFigure 3: Coloring of a cube\n\nInitial Board State: Eight cubes are placed on the 3 * 3 board leaving one empty square.\nAll the cubes have the same orientation as shown in Figure 4. As shown in the figure,\nsquares on the board are given x and y coordinates, (1,1), (1,2), . . . , and (3,3). The\nposition of the initially empty square may vary.\nFigure 4: Initial board state\n\nRolling Cubes: At each step, we can choose one of the cubes adjacent to the empty square and roll it into the empty square, leaving the original position empty. Figure 5\nshows an example.\nFigure 5: Rolling a cube\n\nGoal: The goal of this puzzle is to arrange the cubes so that their top faces form the\nspecified color pattern by a number of cube rolling steps described above.\nYour task is to write a program that finds the minimum number of steps required to make the\nspecified color pattern from the given initial state.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by a line containing two\nzeros separated by a space. The number of datasets is less than 16. Each dataset is formatted\nas follows.\n\n x y\n F_11 F_21 F_31\n F_12 F_22 F_32\n F_13 F_23 F_33\n \nThe first line contains two integers x and y separated by a space, indicating the position (x, y)\nof the initially empty square. The values of x and y are 1,2, or 3.\n\nThe following three lines specify the color pattern to make. Each line contains three characters\nF_1j, F_2j, and F_3j, separated by a space. Character F_ij indicates the top color of the cube, if any, at position (i, j) as follows:\n\n B: Blue\n W: White\n R: Red\n E: the square is Empty.\n\nThere is exactly one 'E' character in each dataset.", "output": "For each dataset, output the minimum number of steps to achieve the goal, when the goal can\nbe reached within 30 steps. Otherwise, output \"-1\" for the dataset.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 2\nW W W\nE W W\nW W W\n2 1\nR B W\nR W W\nE W W\n3 3\nW B W\nB R E\nR B R\n3 3\nB W R\nB W R\nB E R\n2 1\nB B B\nB R B\nB R E\n1 1\nR R R\nW W W\nR R E\n2 1\nR R R\nB W B\nR R E\n3 2\nR R R\nW E W\nR R R\n0 0\n output: 0\n3\n13\n23\n29\n30\n-1\n-1"], "Pid": "p00847", "ProblemText": "Task Description: Let's play a puzzle using eight cubes placed on a 3 * 3 board leaving one empty square.\n\nFaces of cubes are painted with three colors. As a puzzle step, you can roll one of the cubes to\nthe adjacent empty square. Your goal is to make the specified color pattern visible from above\nby a number of such steps.\n\nThe rules of this puzzle are as follows.\nColoring of Cubes: All the cubes are colored in the same way as shown in Figure 3.\nThe opposite faces have the same color.\nFigure 3: Coloring of a cube\n\nInitial Board State: Eight cubes are placed on the 3 * 3 board leaving one empty square.\nAll the cubes have the same orientation as shown in Figure 4. As shown in the figure,\nsquares on the board are given x and y coordinates, (1,1), (1,2), . . . , and (3,3). The\nposition of the initially empty square may vary.\nFigure 4: Initial board state\n\nRolling Cubes: At each step, we can choose one of the cubes adjacent to the empty square and roll it into the empty square, leaving the original position empty. Figure 5\nshows an example.\nFigure 5: Rolling a cube\n\nGoal: The goal of this puzzle is to arrange the cubes so that their top faces form the\nspecified color pattern by a number of cube rolling steps described above.\nYour task is to write a program that finds the minimum number of steps required to make the\nspecified color pattern from the given initial state.\nTask Input: The input is a sequence of datasets. The end of the input is indicated by a line containing two\nzeros separated by a space. The number of datasets is less than 16. Each dataset is formatted\nas follows.\n\n x y\n F_11 F_21 F_31\n F_12 F_22 F_32\n F_13 F_23 F_33\n \nThe first line contains two integers x and y separated by a space, indicating the position (x, y)\nof the initially empty square. The values of x and y are 1,2, or 3.\n\nThe following three lines specify the color pattern to make. Each line contains three characters\nF_1j, F_2j, and F_3j, separated by a space. Character F_ij indicates the top color of the cube, if any, at position (i, j) as follows:\n\n B: Blue\n W: White\n R: Red\n E: the square is Empty.\n\nThere is exactly one 'E' character in each dataset.\nTask Output: For each dataset, output the minimum number of steps to achieve the goal, when the goal can\nbe reached within 30 steps. Otherwise, output \"-1\" for the dataset.\nTask Samples: input: 1 2\nW W W\nE W W\nW W W\n2 1\nR B W\nR W W\nE W W\n3 3\nW B W\nB R E\nR B R\n3 3\nB W R\nB W R\nB E R\n2 1\nB B B\nB R B\nB R E\n1 1\nR R R\nW W W\nR R E\n2 1\nR R R\nB W B\nR R E\n3 2\nR R R\nW E W\nR R R\n0 0\n output: 0\n3\n13\n23\n29\n30\n-1\n-1\n\n" }, { "title": "Problem D: Sum of Different Primes", "content": "A positive integer may be expressed as a sum of different prime numbers (primes), in one way or\nanother. Given two positive integers n and k, you should count the number of ways to express\nn as a sum of k different primes. Here, two ways are considered to be the same if they sum up\nthe same set of the primes. For example, 8 can be expressed as 3 + 5 and 5+ 3 but they are not\ndistinguished.\n\nWhen n and k are 24 and 3 respectively, the answer is two because there are two sets {2,3,19} and {2,5,17} whose sums are equal to 24. There are no other sets of three primes that sum up\nto 24. For n = 24 and k = 2, the answer is three, because there are three sets {5,19}, {7,17} and {11,13}. For n = 2 and k = 1, the answer is one, because there is only one set {2} whose\nsum is 2. For n = 1 and k = 1, the answer is zero. As 1 is not a prime, you shouldn't count\n{1}. For n = 4 and k = 2, the answer is zero, because there are no sets of two diffrent primes\nwhose sums are 4.\n\nYour job is to write a program that reports the number of such ways for the given n and k.", "constraint": "", "input": "The input is a sequence of datasets followed by a line containing two zeros separated by a space.\nA dataset is a line containing two positive integers n and k separated by a space. You may\nassume that n <= 1120 and k <= 14.", "output": "The output should be composed of lines, each corresponding to an input dataset. An output\nline should contain one non-negative integer indicating the number of ways for n and k specified in the corresponding dataset. You may assume that it is less than 2^31.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 24 3\n24 2\n2 1\n1 1\n4 2\n18 3\n17 1\n17 3\n17 4\n100 5\n1000 10\n1120 14\n0 0\n output: 2\n3\n1\n0\n0\n2\n1\n0\n1\n55\n200102899\n2079324314"], "Pid": "p00848", "ProblemText": "Task Description: A positive integer may be expressed as a sum of different prime numbers (primes), in one way or\nanother. Given two positive integers n and k, you should count the number of ways to express\nn as a sum of k different primes. Here, two ways are considered to be the same if they sum up\nthe same set of the primes. For example, 8 can be expressed as 3 + 5 and 5+ 3 but they are not\ndistinguished.\n\nWhen n and k are 24 and 3 respectively, the answer is two because there are two sets {2,3,19} and {2,5,17} whose sums are equal to 24. There are no other sets of three primes that sum up\nto 24. For n = 24 and k = 2, the answer is three, because there are three sets {5,19}, {7,17} and {11,13}. For n = 2 and k = 1, the answer is one, because there is only one set {2} whose\nsum is 2. For n = 1 and k = 1, the answer is zero. As 1 is not a prime, you shouldn't count\n{1}. For n = 4 and k = 2, the answer is zero, because there are no sets of two diffrent primes\nwhose sums are 4.\n\nYour job is to write a program that reports the number of such ways for the given n and k.\nTask Input: The input is a sequence of datasets followed by a line containing two zeros separated by a space.\nA dataset is a line containing two positive integers n and k separated by a space. You may\nassume that n <= 1120 and k <= 14.\nTask Output: The output should be composed of lines, each corresponding to an input dataset. An output\nline should contain one non-negative integer indicating the number of ways for n and k specified in the corresponding dataset. You may assume that it is less than 2^31.\nTask Samples: input: 24 3\n24 2\n2 1\n1 1\n4 2\n18 3\n17 1\n17 3\n17 4\n100 5\n1000 10\n1120 14\n0 0\n output: 2\n3\n1\n0\n0\n2\n1\n0\n1\n55\n200102899\n2079324314\n\n" }, { "title": "Problem E: Manhattan Wiring", "content": "There is a rectangular area containing n * m cells. Two cells are marked with \"2\", and another two with \"3\". Some cells are occupied by obstacles. You should connect the two \"2\"s and also the two \"3\"s with non-intersecting lines. Lines can run only vertically or horizontally connecting\ncenters of cells without obstacles.\n\nLines cannot run on a cell with an obstacle. Only one line can run on a cell at most once. Hence,\na line cannot intersect with the other line, nor with itself. Under these constraints, the total\nlength of the two lines should be minimized. The length of a line is defined as the number of\ncell borders it passes. In particular, a line connecting cells sharing their border has length 1.\n\nFig. 6(a) shows an example setting. Fig. 6(b) shows two lines satisfying the constraints above\nwith minimum total length 18.\n\nFigure 6: An example setting and its solution", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\n n m\n row_1\n . . .\n row_n\n\nn is the number of rows which satisfies 2 <= n <= 9. m is the number of columns which satisfies\n2 <= m <= 9. Each row_i is a sequence of m digits separated by a space. The digits mean the\nfollowing.\n0: Empty1: Occupied by an obstacle2: Marked with \"2\"3: Marked with \"3\"\nThe end of the input is indicated with a line containing two zeros separated by a space.", "output": "For each dataset, one line containing the minimum total length of the two lines should be output.\nIf there is no pair of lines satisfying the requirement, answer \"0\" instead. No other characters\nshould be contained in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 5\n0 0 0 0 0\n0 0 0 3 0\n2 0 2 0 0\n1 0 1 1 1\n0 0 0 0 3\n2 3\n2 2 0\n0 3 3\n6 5\n2 0 0 0 0\n0 3 0 0 0\n0 0 0 0 0\n1 1 1 0 0\n0 0 0 0 0\n0 0 2 3 0\n5 9\n0 0 0 0 0 0 0 0 0\n0 0 0 0 3 0 0 0 0\n0 2 0 0 0 0 0 2 0\n0 0 0 0 3 0 0 0 0\n0 0 0 0 0 0 0 0 0\n9 9\n3 0 0 0 0 0 0 0 2\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n2 0 0 0 0 0 0 0 3\n9 9\n0 0 0 1 0 0 0 0 0\n0 2 0 1 0 0 0 0 3\n0 0 0 1 0 0 0 0 2\n0 0 0 1 0 0 0 0 3\n0 0 0 1 1 1 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n9 9\n0 0 0 0 0 0 0 0 0\n0 3 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 2 3 2\n0 0\n output: 18\n2\n17\n12\n0\n52\n43"], "Pid": "p00849", "ProblemText": "Task Description: There is a rectangular area containing n * m cells. Two cells are marked with \"2\", and another two with \"3\". Some cells are occupied by obstacles. You should connect the two \"2\"s and also the two \"3\"s with non-intersecting lines. Lines can run only vertically or horizontally connecting\ncenters of cells without obstacles.\n\nLines cannot run on a cell with an obstacle. Only one line can run on a cell at most once. Hence,\na line cannot intersect with the other line, nor with itself. Under these constraints, the total\nlength of the two lines should be minimized. The length of a line is defined as the number of\ncell borders it passes. In particular, a line connecting cells sharing their border has length 1.\n\nFig. 6(a) shows an example setting. Fig. 6(b) shows two lines satisfying the constraints above\nwith minimum total length 18.\n\nFigure 6: An example setting and its solution\nTask Input: The input consists of multiple datasets, each in the following format.\n\n n m\n row_1\n . . .\n row_n\n\nn is the number of rows which satisfies 2 <= n <= 9. m is the number of columns which satisfies\n2 <= m <= 9. Each row_i is a sequence of m digits separated by a space. The digits mean the\nfollowing.\n0: Empty1: Occupied by an obstacle2: Marked with \"2\"3: Marked with \"3\"\nThe end of the input is indicated with a line containing two zeros separated by a space.\nTask Output: For each dataset, one line containing the minimum total length of the two lines should be output.\nIf there is no pair of lines satisfying the requirement, answer \"0\" instead. No other characters\nshould be contained in the output.\nTask Samples: input: 5 5\n0 0 0 0 0\n0 0 0 3 0\n2 0 2 0 0\n1 0 1 1 1\n0 0 0 0 3\n2 3\n2 2 0\n0 3 3\n6 5\n2 0 0 0 0\n0 3 0 0 0\n0 0 0 0 0\n1 1 1 0 0\n0 0 0 0 0\n0 0 2 3 0\n5 9\n0 0 0 0 0 0 0 0 0\n0 0 0 0 3 0 0 0 0\n0 2 0 0 0 0 0 2 0\n0 0 0 0 3 0 0 0 0\n0 0 0 0 0 0 0 0 0\n9 9\n3 0 0 0 0 0 0 0 2\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n2 0 0 0 0 0 0 0 3\n9 9\n0 0 0 1 0 0 0 0 0\n0 2 0 1 0 0 0 0 3\n0 0 0 1 0 0 0 0 2\n0 0 0 1 0 0 0 0 3\n0 0 0 1 1 1 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n9 9\n0 0 0 0 0 0 0 0 0\n0 3 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 2 3 2\n0 0\n output: 18\n2\n17\n12\n0\n52\n43\n\n" }, { "title": "Problem F: Power Calculus", "content": "Starting with x and repeatedly multiplying by x, we can compute x^31 with thirty multiplications:\nx^2 = x * x, x^3 = x^2 * x, x^4 = x^3 * x, . . . , x^31 = x^30 * x.\nThe operation of squaring can appreciably shorten the sequence of multiplications. The following is a way to compute x^31 with eight multiplications:\nx^2 = x * x, x^3 = x^2 * x, x^6 = x^3 * x^3, x^7 = x^6 * x, x^14 = x^7 * x^7, \nx^15 = x^14 * x, x^30 = x^15 * x^15, x^31 = x^30 * x.\nThis is not the shortest sequence of multiplications to compute x^31. There are many ways with only seven multiplications. The following is one of them:\nx^2 = x * x, x^4 = x^2 * x^2, x^8 = x^4 * x^4, x^10 = x^8 * x^2, \nx^20 = x^10 * x^10, x^30 = x^20 * x^10, x^31 = x^30 * x.\nThere however is no way to compute x^31 with fewer multiplications. Thus this is one of the\nmost eficient ways to compute x^31 only by multiplications.\n\nIf division is also available, we can find a shorter sequence of operations. It is possible to\ncompute x^31 with six operations (five multiplications and one division):\nx^2 = x * x, x^4 = x^2 * x^2, x^8 = x^4 * x^4, x^16 = x^8 * x^8, x^32 = x^16 * x^16, \nx^31 = x^32 ÷ x.\nThis is one of the most eficient ways to compute x^31 if a division is as fast as a multiplication.\n\nYour mission is to write a program to find the least number of operations to compute x^n\nby multiplication and division starting with x for the given positive integer n. Products and\nquotients appearing in the sequence of operations should be x to a positive integer's power. In\nother words, x^-3, for example, should never appear.", "constraint": "", "input": "The input is a sequence of one or more lines each containing a single integer n. n is positive and\nless than or equal to 1000. The end of the input is indicated by a zero.", "output": "Your program should print the least total number of multiplications and divisions required to\ncompute x^n starting with x for the integer n. The numbers should be written each in a separate\nline without any superfluous characters such as leading or trailing spaces.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n31\n70\n91\n473\n512\n811\n953\n0\n output: 0\n6\n8\n9\n11\n9\n13\n12"], "Pid": "p00850", "ProblemText": "Task Description: Starting with x and repeatedly multiplying by x, we can compute x^31 with thirty multiplications:\nx^2 = x * x, x^3 = x^2 * x, x^4 = x^3 * x, . . . , x^31 = x^30 * x.\nThe operation of squaring can appreciably shorten the sequence of multiplications. The following is a way to compute x^31 with eight multiplications:\nx^2 = x * x, x^3 = x^2 * x, x^6 = x^3 * x^3, x^7 = x^6 * x, x^14 = x^7 * x^7, \nx^15 = x^14 * x, x^30 = x^15 * x^15, x^31 = x^30 * x.\nThis is not the shortest sequence of multiplications to compute x^31. There are many ways with only seven multiplications. The following is one of them:\nx^2 = x * x, x^4 = x^2 * x^2, x^8 = x^4 * x^4, x^10 = x^8 * x^2, \nx^20 = x^10 * x^10, x^30 = x^20 * x^10, x^31 = x^30 * x.\nThere however is no way to compute x^31 with fewer multiplications. Thus this is one of the\nmost eficient ways to compute x^31 only by multiplications.\n\nIf division is also available, we can find a shorter sequence of operations. It is possible to\ncompute x^31 with six operations (five multiplications and one division):\nx^2 = x * x, x^4 = x^2 * x^2, x^8 = x^4 * x^4, x^16 = x^8 * x^8, x^32 = x^16 * x^16, \nx^31 = x^32 ÷ x.\nThis is one of the most eficient ways to compute x^31 if a division is as fast as a multiplication.\n\nYour mission is to write a program to find the least number of operations to compute x^n\nby multiplication and division starting with x for the given positive integer n. Products and\nquotients appearing in the sequence of operations should be x to a positive integer's power. In\nother words, x^-3, for example, should never appear.\nTask Input: The input is a sequence of one or more lines each containing a single integer n. n is positive and\nless than or equal to 1000. The end of the input is indicated by a zero.\nTask Output: Your program should print the least total number of multiplications and divisions required to\ncompute x^n starting with x for the integer n. The numbers should be written each in a separate\nline without any superfluous characters such as leading or trailing spaces.\nTask Samples: input: 1\n31\n70\n91\n473\n512\n811\n953\n0\n output: 0\n6\n8\n9\n11\n9\n13\n12\n\n" }, { "title": "Problem G: Polygons on the Grid", "content": "The ultimate Tantra is said to have been kept in the most distinguished temple deep in the\nsacred forest somewhere in Japan. Paleographers finally identified its location, surprisingly a\nsmall temple in Hiyoshi, after years of eager research. The temple has an underground secret\nroom built with huge stones. This underground megalith is suspected to be where the Tantra\nis enshrined.\n\nThe room door is, however, securely locked. Legends tell that the key of the door lock was an\ninteger, that only highest priests knew. As the sect that built the temple decayed down, it is\nimpossible to know the integer now, and the Agency for Cultural Affairs bans breaking up the\ndoor. Fortunately, a figure of a number of rods that might be used as a clue to guess that secret\nnumber is engraved on the door.\n\nMany distinguished scholars have challenged the riddle, but no one could have ever succeeded\nin solving it, until recently a brilliant young computer scientist finally deciphered the puzzle.\nLengths of the rods are multiples of a certain unit length. He found that, to find the secret\nnumber, all the rods should be placed on a grid of the unit length to make one convex polygon.\nBoth ends of each rod must be set on grid points. Elementary mathematics tells that the\npolygon's area ought to be an integer multiple of the square of the unit length. The area size of\nthe polygon with the largest area is the secret number which is needed to unlock the door.\n\nFor example, if you have five rods whose lengths are 1,2,5,5, and 5, respectively, you can make\nessentially only three kinds of polygons, shown in Figure 7. Then, you know that the maximum\narea is 19.\n\nFigure 7: Convex polygons consisting of five rods of lengths 1,2,5,5, and 5\nYour task is to write a program to find the maximum area of convex polygons using all the given\nrods whose ends are on grid points.", "constraint": "", "input": "The input consists of multiple datasets, followed by a line containing a single zero which indicates\nthe end of the input. The format of a dataset is as follows.\n\n n\n r_1 r_2 . . . r_n\n\nn is an integer which means the number of rods and satisfies 3 <= n <= 6. r_i means the length of the i-th rod and satisfies 1 <= r_i <= 300.", "output": "For each dataset, output a line containing an integer which is the area of the largest convex\npolygon. When there are no possible convex polygons for a dataset, output \"-1\".", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n3 4 5\n5\n1 2 5 5 5\n6\n195 221 255 260 265 290\n6\n130 145 169 185 195 265\n3\n1 1 2\n6\n3 3 3 3 3 3\n0\n output: 6\n19\n158253\n-1\n-1\n18"], "Pid": "p00851", "ProblemText": "Task Description: The ultimate Tantra is said to have been kept in the most distinguished temple deep in the\nsacred forest somewhere in Japan. Paleographers finally identified its location, surprisingly a\nsmall temple in Hiyoshi, after years of eager research. The temple has an underground secret\nroom built with huge stones. This underground megalith is suspected to be where the Tantra\nis enshrined.\n\nThe room door is, however, securely locked. Legends tell that the key of the door lock was an\ninteger, that only highest priests knew. As the sect that built the temple decayed down, it is\nimpossible to know the integer now, and the Agency for Cultural Affairs bans breaking up the\ndoor. Fortunately, a figure of a number of rods that might be used as a clue to guess that secret\nnumber is engraved on the door.\n\nMany distinguished scholars have challenged the riddle, but no one could have ever succeeded\nin solving it, until recently a brilliant young computer scientist finally deciphered the puzzle.\nLengths of the rods are multiples of a certain unit length. He found that, to find the secret\nnumber, all the rods should be placed on a grid of the unit length to make one convex polygon.\nBoth ends of each rod must be set on grid points. Elementary mathematics tells that the\npolygon's area ought to be an integer multiple of the square of the unit length. The area size of\nthe polygon with the largest area is the secret number which is needed to unlock the door.\n\nFor example, if you have five rods whose lengths are 1,2,5,5, and 5, respectively, you can make\nessentially only three kinds of polygons, shown in Figure 7. Then, you know that the maximum\narea is 19.\n\nFigure 7: Convex polygons consisting of five rods of lengths 1,2,5,5, and 5\nYour task is to write a program to find the maximum area of convex polygons using all the given\nrods whose ends are on grid points.\nTask Input: The input consists of multiple datasets, followed by a line containing a single zero which indicates\nthe end of the input. The format of a dataset is as follows.\n\n n\n r_1 r_2 . . . r_n\n\nn is an integer which means the number of rods and satisfies 3 <= n <= 6. r_i means the length of the i-th rod and satisfies 1 <= r_i <= 300.\nTask Output: For each dataset, output a line containing an integer which is the area of the largest convex\npolygon. When there are no possible convex polygons for a dataset, output \"-1\".\nTask Samples: input: 3\n3 4 5\n5\n1 2 5 5 5\n6\n195 221 255 260 265 290\n6\n130 145 169 185 195 265\n3\n1 1 2\n6\n3 3 3 3 3 3\n0\n output: 6\n19\n158253\n-1\n-1\n18\n\n" }, { "title": "Problem H: The Best Name for Your Baby", "content": "In the year 29XX, the government of a small country somewhere on the earth introduced a law restricting first names of the people only to traditional names in their culture, in order to preserve their cultural uniqueness. The linguists of the country specifies a set of rules once every year, and only names conforming to the rules are allowed in that year. In addition, the law also requires each person to use a name of a specific length calculated from one's birth date because\notherwise too many people would use the same very popular names. Since the legislation of that law, the common task of the parents of new babies is to find the name that comes first in the alphabetical order among the legitimate names of the given length because names earlier in the alphabetical order have various benefits in their culture.\n\nLegitimate names are the strings consisting of only lowercase letters that can be obtained by\nrepeatedly applying the rule set to the initial string \"S\", a string consisting only of a single uppercase S.\n\nApplying the rule set to a string is to choose one of the rules and apply it to the string. Each\nof the rules has the form A -> α, where A is an uppercase letter and α is a string of lowercase and/or uppercase letters. Applying such a rule to a string is to replace an occurrence of the\nletter A in the string to the string α. That is, when the string has the form \"βAγ\", where β and\nγ are arbitrary (possibly empty) strings of letters, applying the rule rewrites it into the string \"βαγ\". If there are two or more occurrences of A in the original string, an arbitrary one of them\ncan be chosen for the replacement.\n\nBelow is an example set of rules.\n\nS -> a AB (1)\nA -> (2)\nA -> Aa (3)\nB -> Abb A (4)\n\nApplying the rule (1) to \"S\", \"a AB\" is obtained. Applying (2) to it results in \"a B\", as A is replaced by an empty string. Then, the rule (4) can be used to make it \"a Abb A\". Applying (3) to the first occurrence of A makes it \"a Aabb A\". Applying the rule (2) to the A at the end results in \"a Aabb\". Finally, applying the rule (2) again to the remaining A results in \"aabb\". As no uppercase letter remains in this string, \"aabb\" is a legitimate name. \n\nWe denote such a rewriting process as follows.\n\n (1) (2) (4) (3) (2) (2)\nS --> a AB --> a B --> a Abb A --> a Aabb A --> a Aabb --> aabb\n\nLinguists of the country may sometimes define a ridiculous rule set such as follows.\n\nS -> s A (1)\nA -> a S (2)\nB -> b (3)\n\nThe only possible rewriting sequence with this rule set is:\n\n (1) (2) (1) (2)\nS --> s A --> sa S --> sas A --> . . .\n\nwhich will never terminate. No legitimate names exist in this case. Also, the rule (3) can never be used, as its left hand side, B, does not appear anywhere else.\n\nIt may happen that no rules are supplied for some uppercase letters appearing in the rewriting steps. In its extreme case, even S might have no rules for it in the set, in which case there are no legitimate names, of course. Poor nameless babies, sigh!\n\nNow your job is to write a program that finds the name earliest in the alphabetical order among the legitimate names of the given length conforming to the given set of rules.", "constraint": "", "input": "The input is a sequence of datasets, followed by a line containing two zeros separated by a space representing the end of the input. Each dataset starts with a line including two integers n and l separated by a space, where n (1 <= n <= 50) is the number of rules and l (0 <= l <= 20) is the required length of the name. After that line, n lines each representing a rule follow. Each of these lines starts with one of uppercase letters, A to Z, followed by the character \"=\" (instead of \"->\") and then followed by the right hand side of the rule which is a string of letters A to\nZ and a to z. The length of the string does not exceed 10 and may be zero. There appears no space in the lines representing the rules.", "output": "The output consists of the lines showing the answer to each dataset in the same order as the input. Each line is a string of lowercase letters, a to z, which is the first legitimate name conforming to the rules and the length given in the corresponding input dataset. When the given set of rules has no conforming string of the given length, the corresponding line in the output should show a single hyphen, \"-\". No other characters should be included in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\nA=a\nA=\nS=ASb\nS=Ab\n2 5\nS=aSb\nS=\n1 5\nS=S\n1 0\nS=S\n1 0\nA=\n2 0\nA=\nS=AA\n4 5\nA=aB\nA=b\nB=SA\nS=A\n4 20\nS=AAAAAAAAAA\nA=aA\nA=bA\nA=\n0 0\n output: abb\n-\n-\n-\n-\n\naabbb\naaaaaaaaaaaaaaaaaaaa"], "Pid": "p00852", "ProblemText": "Task Description: In the year 29XX, the government of a small country somewhere on the earth introduced a law restricting first names of the people only to traditional names in their culture, in order to preserve their cultural uniqueness. The linguists of the country specifies a set of rules once every year, and only names conforming to the rules are allowed in that year. In addition, the law also requires each person to use a name of a specific length calculated from one's birth date because\notherwise too many people would use the same very popular names. Since the legislation of that law, the common task of the parents of new babies is to find the name that comes first in the alphabetical order among the legitimate names of the given length because names earlier in the alphabetical order have various benefits in their culture.\n\nLegitimate names are the strings consisting of only lowercase letters that can be obtained by\nrepeatedly applying the rule set to the initial string \"S\", a string consisting only of a single uppercase S.\n\nApplying the rule set to a string is to choose one of the rules and apply it to the string. Each\nof the rules has the form A -> α, where A is an uppercase letter and α is a string of lowercase and/or uppercase letters. Applying such a rule to a string is to replace an occurrence of the\nletter A in the string to the string α. That is, when the string has the form \"βAγ\", where β and\nγ are arbitrary (possibly empty) strings of letters, applying the rule rewrites it into the string \"βαγ\". If there are two or more occurrences of A in the original string, an arbitrary one of them\ncan be chosen for the replacement.\n\nBelow is an example set of rules.\n\nS -> a AB (1)\nA -> (2)\nA -> Aa (3)\nB -> Abb A (4)\n\nApplying the rule (1) to \"S\", \"a AB\" is obtained. Applying (2) to it results in \"a B\", as A is replaced by an empty string. Then, the rule (4) can be used to make it \"a Abb A\". Applying (3) to the first occurrence of A makes it \"a Aabb A\". Applying the rule (2) to the A at the end results in \"a Aabb\". Finally, applying the rule (2) again to the remaining A results in \"aabb\". As no uppercase letter remains in this string, \"aabb\" is a legitimate name. \n\nWe denote such a rewriting process as follows.\n\n (1) (2) (4) (3) (2) (2)\nS --> a AB --> a B --> a Abb A --> a Aabb A --> a Aabb --> aabb\n\nLinguists of the country may sometimes define a ridiculous rule set such as follows.\n\nS -> s A (1)\nA -> a S (2)\nB -> b (3)\n\nThe only possible rewriting sequence with this rule set is:\n\n (1) (2) (1) (2)\nS --> s A --> sa S --> sas A --> . . .\n\nwhich will never terminate. No legitimate names exist in this case. Also, the rule (3) can never be used, as its left hand side, B, does not appear anywhere else.\n\nIt may happen that no rules are supplied for some uppercase letters appearing in the rewriting steps. In its extreme case, even S might have no rules for it in the set, in which case there are no legitimate names, of course. Poor nameless babies, sigh!\n\nNow your job is to write a program that finds the name earliest in the alphabetical order among the legitimate names of the given length conforming to the given set of rules.\nTask Input: The input is a sequence of datasets, followed by a line containing two zeros separated by a space representing the end of the input. Each dataset starts with a line including two integers n and l separated by a space, where n (1 <= n <= 50) is the number of rules and l (0 <= l <= 20) is the required length of the name. After that line, n lines each representing a rule follow. Each of these lines starts with one of uppercase letters, A to Z, followed by the character \"=\" (instead of \"->\") and then followed by the right hand side of the rule which is a string of letters A to\nZ and a to z. The length of the string does not exceed 10 and may be zero. There appears no space in the lines representing the rules.\nTask Output: The output consists of the lines showing the answer to each dataset in the same order as the input. Each line is a string of lowercase letters, a to z, which is the first legitimate name conforming to the rules and the length given in the corresponding input dataset. When the given set of rules has no conforming string of the given length, the corresponding line in the output should show a single hyphen, \"-\". No other characters should be included in the output.\nTask Samples: input: 4 3\nA=a\nA=\nS=ASb\nS=Ab\n2 5\nS=aSb\nS=\n1 5\nS=S\n1 0\nS=S\n1 0\nA=\n2 0\nA=\nS=AA\n4 5\nA=aB\nA=b\nB=SA\nS=A\n4 20\nS=AAAAAAAAAA\nA=aA\nA=bA\nA=\n0 0\n output: abb\n-\n-\n-\n-\n\naabbb\naaaaaaaaaaaaaaaaaaaa\n\n" }, { "title": "Problem I: Enjoyable Commutation", "content": "Isaac is tired of his daily trip to his ofice, using the same shortest route everyday. Although this saves his time, he must see the same scenery again and again. He cannot stand such a boring commutation any more.\n\nOne day, he decided to improve the situation. He would change his route everyday at least slightly. His new scheme is as follows. On the first day, he uses the shortest route. On the second day, he uses the second shortest route, namely the shortest except one used on the first day. In general, on the k-th day, the k-th shortest route is chosen. Visiting the same place twice on a route should be avoided, of course.\n\nYou are invited to help Isaac, by writing a program which finds his route on the k-th day. The problem is easily modeled using terms in the graph theory. Your program should find the k-th shortest path in the given directed graph.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\n n m k a b\n x_1 y_1 d_1\n x_2 y_2 d_2\n . . .\n x_m y_m d_m\n\nEvery input item in a dataset is a non-negative integer. Two or more input items in a line are separated by a space.\n\nn is the number of nodes in the graph. You can assume the inequality 2 <= n <= 50. m is the number of (directed) edges. a is the start node, and b is the goal node. They are between 1 and n, inclusive. You are required to find the k-th shortest path from a to b. You can assume 1 <= k <= 200 and a ! = b.\n\nThe i-th edge is from the node x_i to y_i with the length d_i (1 <= i <= m). Both x_i and y_i are between 1 and n, inclusive. d_i is between 1 and 10000, inclusive. You can directly go from x_i to y_i, but not from y_i to x_i unless an edge from y_i to x_i is explicitly given. The edge connecting the same pair of nodes is unique, if any, that is, if i ! = j, it is never the case that x_i equals x_j and y_i equals y_j. Edges are not connecting a node to itself, that is, x_i never equals y_i . Thus the inequality 0 <= m <= n(n - 1) holds.\n\nNote that the given graph may be quite unrealistic as a road network. Both the cases m = 0 and m = n(n - 1) are included in the judges' data.\n\nThe last dataset is followed by a line containing five zeros (separated by a space).", "output": "For each dataset in the input, one line should be output as specified below. An output line should not contain extra characters such as spaces.\n\nIf the number of distinct paths from a to b is less than k, the string None should be printed. Note that the first letter of None is in uppercase, while the other letters are in lowercase.\n\nIf the number of distinct paths from a to b is k or more, the node numbers visited in the k-th shortest path should be printed in the visited order, separated by a hyphen (minus sign). Note that a must be the first, and b must be the last in the printed line.\n\nIn this problem the term shorter (thus shortest also) has a special meaning. A path P is defined to be shorter than Q, if and only if one of the following conditions holds.\n\n The length of P is less than the length of Q. The length of a path is defined to be the sum of lengths of edges on the path.\n\n The length of P is equal to the length of Q, and P's sequence of node numbers comes earlier than Q's in the dictionary order. Let's specify the latter condition more precisely. Denote P's sequence of node numbers by p_1, p_2, . . . , p_s, and Q's by q_1, q_2, . . . , q_t. p_1 = q_1 = a and p_s = q_t = b should be observed. The sequence P comes earlier than Q in the dictionary order, if for some r (1 <= r <= s and r <= t), p_1 = q_1, . . . , p_r-1 = q_r-1, and p_r < q_r (p_r is numerically smaller than q_r).\nA path visiting the same node twice or more is not allowed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 20 10 1 5\n1 2 1\n1 3 2\n1 4 1\n1 5 3\n2 1 1\n2 3 1\n2 4 2\n2 5 2\n3 1 1\n3 2 2\n3 4 1\n3 5 1\n4 1 1\n4 2 1\n4 3 1\n4 5 2\n5 1 1\n5 2 1\n5 3 1\n5 4 1\n4 6 1 1 4\n2 4 2\n1 3 2\n1 2 1\n1 4 3\n2 3 1\n3 4 1\n3 3 5 1 3\n1 2 1\n2 3 1\n1 3 1\n0 0 0 0 0\n output: 1-2-4-3-5\n1-2-3-4\nNone\nIn the case of the first dataset, there are 16 paths from the node 1 to 5. They are ordered as follows (The number in parentheses is the length of the path).\n1 (3) 1-2-3-5 9 (5) 1-2-3-4-5\n2 (3) 1-2-5 10 (5) 1-2-4-3-5\n3 (3) 1-3-5 11 (5) 1-2-4-5\n4 (3) 1-4-3-5 12 (5) 1-3-4-5\n5 (3) 1-4-5 13 (6) 1-3-2-5\n6 (3) 1-5 14 (6) 1-3-4-2-5\n7 (4) 1-4-2-3-5 15 (6) 1-4-3-2-5\n8 (4) 1-4-2-5 16 (8) 1-3-2-4-5"], "Pid": "p00853", "ProblemText": "Task Description: Isaac is tired of his daily trip to his ofice, using the same shortest route everyday. Although this saves his time, he must see the same scenery again and again. He cannot stand such a boring commutation any more.\n\nOne day, he decided to improve the situation. He would change his route everyday at least slightly. His new scheme is as follows. On the first day, he uses the shortest route. On the second day, he uses the second shortest route, namely the shortest except one used on the first day. In general, on the k-th day, the k-th shortest route is chosen. Visiting the same place twice on a route should be avoided, of course.\n\nYou are invited to help Isaac, by writing a program which finds his route on the k-th day. The problem is easily modeled using terms in the graph theory. Your program should find the k-th shortest path in the given directed graph.\nTask Input: The input consists of multiple datasets, each in the following format.\n\n n m k a b\n x_1 y_1 d_1\n x_2 y_2 d_2\n . . .\n x_m y_m d_m\n\nEvery input item in a dataset is a non-negative integer. Two or more input items in a line are separated by a space.\n\nn is the number of nodes in the graph. You can assume the inequality 2 <= n <= 50. m is the number of (directed) edges. a is the start node, and b is the goal node. They are between 1 and n, inclusive. You are required to find the k-th shortest path from a to b. You can assume 1 <= k <= 200 and a ! = b.\n\nThe i-th edge is from the node x_i to y_i with the length d_i (1 <= i <= m). Both x_i and y_i are between 1 and n, inclusive. d_i is between 1 and 10000, inclusive. You can directly go from x_i to y_i, but not from y_i to x_i unless an edge from y_i to x_i is explicitly given. The edge connecting the same pair of nodes is unique, if any, that is, if i ! = j, it is never the case that x_i equals x_j and y_i equals y_j. Edges are not connecting a node to itself, that is, x_i never equals y_i . Thus the inequality 0 <= m <= n(n - 1) holds.\n\nNote that the given graph may be quite unrealistic as a road network. Both the cases m = 0 and m = n(n - 1) are included in the judges' data.\n\nThe last dataset is followed by a line containing five zeros (separated by a space).\nTask Output: For each dataset in the input, one line should be output as specified below. An output line should not contain extra characters such as spaces.\n\nIf the number of distinct paths from a to b is less than k, the string None should be printed. Note that the first letter of None is in uppercase, while the other letters are in lowercase.\n\nIf the number of distinct paths from a to b is k or more, the node numbers visited in the k-th shortest path should be printed in the visited order, separated by a hyphen (minus sign). Note that a must be the first, and b must be the last in the printed line.\n\nIn this problem the term shorter (thus shortest also) has a special meaning. A path P is defined to be shorter than Q, if and only if one of the following conditions holds.\n\n The length of P is less than the length of Q. The length of a path is defined to be the sum of lengths of edges on the path.\n\n The length of P is equal to the length of Q, and P's sequence of node numbers comes earlier than Q's in the dictionary order. Let's specify the latter condition more precisely. Denote P's sequence of node numbers by p_1, p_2, . . . , p_s, and Q's by q_1, q_2, . . . , q_t. p_1 = q_1 = a and p_s = q_t = b should be observed. The sequence P comes earlier than Q in the dictionary order, if for some r (1 <= r <= s and r <= t), p_1 = q_1, . . . , p_r-1 = q_r-1, and p_r < q_r (p_r is numerically smaller than q_r).\nA path visiting the same node twice or more is not allowed.\nTask Samples: input: 5 20 10 1 5\n1 2 1\n1 3 2\n1 4 1\n1 5 3\n2 1 1\n2 3 1\n2 4 2\n2 5 2\n3 1 1\n3 2 2\n3 4 1\n3 5 1\n4 1 1\n4 2 1\n4 3 1\n4 5 2\n5 1 1\n5 2 1\n5 3 1\n5 4 1\n4 6 1 1 4\n2 4 2\n1 3 2\n1 2 1\n1 4 3\n2 3 1\n3 4 1\n3 3 5 1 3\n1 2 1\n2 3 1\n1 3 1\n0 0 0 0 0\n output: 1-2-4-3-5\n1-2-3-4\nNone\nIn the case of the first dataset, there are 16 paths from the node 1 to 5. They are ordered as follows (The number in parentheses is the length of the path).\n1 (3) 1-2-3-5 9 (5) 1-2-3-4-5\n2 (3) 1-2-5 10 (5) 1-2-4-3-5\n3 (3) 1-3-5 11 (5) 1-2-4-5\n4 (3) 1-4-3-5 12 (5) 1-3-4-5\n5 (3) 1-4-5 13 (6) 1-3-2-5\n6 (3) 1-5 14 (6) 1-3-4-2-5\n7 (4) 1-4-2-3-5 15 (6) 1-4-3-2-5\n8 (4) 1-4-2-5 16 (8) 1-3-2-4-5\n\n" }, { "title": "Problem A: And Then There Was One", "content": "Let 's play a stone removing game.\n\nInitially, n stones are arranged on a circle and numbered 1, . . . , n clockwise (Figure 1). You are also given two numbers k and m. From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone m. In step 2, locate the k-th next stone clockwise from m and remove it. In subsequent steps, start from the slot of the stone removed in the last step, make k hops clockwise on the remaining stones and remove the one you reach. In other words, skip (k - 1) remaining stones clockwise and remove the next one. Repeat this until only one stone is left and answer its number.\n\nFor example, the answer for the case n = 8, k = 5, m = 3 is 1, as shown in Figure 1.\n\nFigure 1: An example game\nInitial state: Eight stones are arranged on a circle.\n\nStep 1: Stone 3 is removed since m = 3.\n\nStep 2: You start from the slot that was occupied by stone 3. You skip four stones 4,5,6 and 7 (since k = 5), and remove the next one, which is 8.\n\nStep 3: You skip stones 1,2,4 and 5, and thus remove 6. Note that you only count stones that are still on the circle and ignore those already removed. Stone 3 is ignored in this case.\n\nSteps 4-7: You continue until only one stone is left. Notice that in later steps when only a few stones remain, the same stone may be skipped multiple times. For example, stones 1 and 4 are skipped twice in step 7.\n\nFinal State: Finally, only one stone, 1, is on the circle. This is the final state, so the answer is 1.", "constraint": "", "input": "The input consists of multiple datasets each of which is formatted as follows.\n\nn k m\n\nThe last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.\n 2 <= n <= 10000, 1 <= k <= 10000, 1 <= m <= n\nThe number of datasets is less than 100.", "output": "For each dataset, output a line containing the stone number left in the final state. No extra characters such as spaces should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8 5 3\n100 9999 98\n10000 10000 10000\n0 0 0\n output: 1\n93\n2019"], "Pid": "p00854", "ProblemText": "Task Description: Let 's play a stone removing game.\n\nInitially, n stones are arranged on a circle and numbered 1, . . . , n clockwise (Figure 1). You are also given two numbers k and m. From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone m. In step 2, locate the k-th next stone clockwise from m and remove it. In subsequent steps, start from the slot of the stone removed in the last step, make k hops clockwise on the remaining stones and remove the one you reach. In other words, skip (k - 1) remaining stones clockwise and remove the next one. Repeat this until only one stone is left and answer its number.\n\nFor example, the answer for the case n = 8, k = 5, m = 3 is 1, as shown in Figure 1.\n\nFigure 1: An example game\nInitial state: Eight stones are arranged on a circle.\n\nStep 1: Stone 3 is removed since m = 3.\n\nStep 2: You start from the slot that was occupied by stone 3. You skip four stones 4,5,6 and 7 (since k = 5), and remove the next one, which is 8.\n\nStep 3: You skip stones 1,2,4 and 5, and thus remove 6. Note that you only count stones that are still on the circle and ignore those already removed. Stone 3 is ignored in this case.\n\nSteps 4-7: You continue until only one stone is left. Notice that in later steps when only a few stones remain, the same stone may be skipped multiple times. For example, stones 1 and 4 are skipped twice in step 7.\n\nFinal State: Finally, only one stone, 1, is on the circle. This is the final state, so the answer is 1.\nTask Input: The input consists of multiple datasets each of which is formatted as follows.\n\nn k m\n\nThe last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.\n 2 <= n <= 10000, 1 <= k <= 10000, 1 <= m <= n\nThe number of datasets is less than 100.\nTask Output: For each dataset, output a line containing the stone number left in the final state. No extra characters such as spaces should appear in the output.\nTask Samples: input: 8 5 3\n100 9999 98\n10000 10000 10000\n0 0 0\n output: 1\n93\n2019\n\n" }, { "title": "Problem B: Prime Gap", "content": "The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and\nnot equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24,25,26,27,28) between 23 and 29 is a prime gap of length 6.\n\nYour mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap\ncontains k.", "constraint": "", "input": "The input is a sequence of lines each of which contains a single positive integer. Each positive\ninteger is greater than 1 and less than or equal to the 100000th prime number, which is 1299709.\nThe end of the input is indicated by a line containing a single zero.", "output": "The output should be composed of lines each of which contains a single non-negative integer. It\nis the length of the prime gap that contains the corresponding positive integer in the input if it\nis a composite number, or 0 otherwise. No other characters should occur in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\n11\n27\n2\n492170\n0\n output: 4\n0\n6\n0\n114"], "Pid": "p00855", "ProblemText": "Task Description: The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and\nnot equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24,25,26,27,28) between 23 and 29 is a prime gap of length 6.\n\nYour mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap\ncontains k.\nTask Input: The input is a sequence of lines each of which contains a single positive integer. Each positive\ninteger is greater than 1 and less than or equal to the 100000th prime number, which is 1299709.\nThe end of the input is indicated by a line containing a single zero.\nTask Output: The output should be composed of lines each of which contains a single non-negative integer. It\nis the length of the prime gap that contains the corresponding positive integer in the input if it\nis a composite number, or 0 otherwise. No other characters should occur in the output.\nTask Samples: input: 10\n11\n27\n2\n492170\n0\n output: 4\n0\n6\n0\n114\n\n" }, { "title": "Problem C: Minimal Backgammon", "content": "Here is a very simple variation of the game backgammon, named “Minimal Backgammon”. The game is played by only one player, using only one of the dice and only one checker (the token used by the player).\n\nThe game board is a line of (N + 1) squares labeled as 0 (the start) to N (the goal). At the beginning, the checker is placed on the start (square 0). The aim of the game is to bring the checker to the goal (square N). The checker proceeds as many squares as the roll of the dice. The dice generates six integers from 1 to 6 with equal probability.\n\nThe checker should not go beyond the goal. If the roll of the dice would bring the checker beyond the goal, the checker retreats from the goal as many squares as the excess. For example, if the checker is placed at the square (N - 3), the roll \"5\" brings the checker to the square (N - 2), because the excess beyond the goal is 2. At the next turn, the checker proceeds toward the goal\nas usual.\n\nEach square, except the start and the goal, may be given one of the following two special instructions.\n\nLose one turn (labeled \"L\" in Figure 2) If the checker stops here, you cannot move the checker in the next turn.\nGo back to the start (labeled \"B\" in Figure 2) If the checker stops here, the checker is brought back to the start.\nFigure 2: An example game\nGiven a game board configuration (the size N, and the placement of the special instructions), you are requested to compute the probability with which the game succeeds within a given number of turns.", "constraint": "", "input": "The input consists of multiple datasets, each containing integers in the following format.\n\nN T L B\nLose_1\n. . .\nLose_L\nBack_1\n. . .\nBack_B\n\nN is the index of the goal, which satisfies 5 <= N <= 100. T is the number of turns. You are requested to compute the probability of success within T turns. T satisfies 1 <= T <= 100. L is the number of squares marked “Lose one turn”, which satisfies 0 <= L <= N - 1. B is the number of squares marked “Go back to the start”, which satisfies 0 <= B <= N - 1. They are separated by a space.\n\nLose_i's are the indexes of the squares marked “Lose one turn”, which satisfy 1 <= Lose_i <= N - 1. All Lose_i's are distinct, and sorted in ascending order. Back_i's are the indexes of the squares marked “Go back to the start”, which satisfy 1 <= Back_i <= N - 1. All Back_i's are distinct, and sorted in ascending order. No numbers occur both in Lose_i's and Back_i's.\n\nThe end of the input is indicated by a line containing four zeros separated by a space.", "output": "For each dataset, you should answer the probability with which the game succeeds within the\ngiven number of turns. The output should not contain an error greater than 0.00001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 1 0 0\n7 1 0 0\n7 2 0 0\n6 6 1 1\n2\n5\n7 10 0 6\n1\n2\n3\n4\n5\n6\n0 0 0 0\n output: 0.166667\n0.000000\n0.166667\n0.619642\n0.000000"], "Pid": "p00856", "ProblemText": "Task Description: Here is a very simple variation of the game backgammon, named “Minimal Backgammon”. The game is played by only one player, using only one of the dice and only one checker (the token used by the player).\n\nThe game board is a line of (N + 1) squares labeled as 0 (the start) to N (the goal). At the beginning, the checker is placed on the start (square 0). The aim of the game is to bring the checker to the goal (square N). The checker proceeds as many squares as the roll of the dice. The dice generates six integers from 1 to 6 with equal probability.\n\nThe checker should not go beyond the goal. If the roll of the dice would bring the checker beyond the goal, the checker retreats from the goal as many squares as the excess. For example, if the checker is placed at the square (N - 3), the roll \"5\" brings the checker to the square (N - 2), because the excess beyond the goal is 2. At the next turn, the checker proceeds toward the goal\nas usual.\n\nEach square, except the start and the goal, may be given one of the following two special instructions.\n\nLose one turn (labeled \"L\" in Figure 2) If the checker stops here, you cannot move the checker in the next turn.\nGo back to the start (labeled \"B\" in Figure 2) If the checker stops here, the checker is brought back to the start.\nFigure 2: An example game\nGiven a game board configuration (the size N, and the placement of the special instructions), you are requested to compute the probability with which the game succeeds within a given number of turns.\nTask Input: The input consists of multiple datasets, each containing integers in the following format.\n\nN T L B\nLose_1\n. . .\nLose_L\nBack_1\n. . .\nBack_B\n\nN is the index of the goal, which satisfies 5 <= N <= 100. T is the number of turns. You are requested to compute the probability of success within T turns. T satisfies 1 <= T <= 100. L is the number of squares marked “Lose one turn”, which satisfies 0 <= L <= N - 1. B is the number of squares marked “Go back to the start”, which satisfies 0 <= B <= N - 1. They are separated by a space.\n\nLose_i's are the indexes of the squares marked “Lose one turn”, which satisfy 1 <= Lose_i <= N - 1. All Lose_i's are distinct, and sorted in ascending order. Back_i's are the indexes of the squares marked “Go back to the start”, which satisfy 1 <= Back_i <= N - 1. All Back_i's are distinct, and sorted in ascending order. No numbers occur both in Lose_i's and Back_i's.\n\nThe end of the input is indicated by a line containing four zeros separated by a space.\nTask Output: For each dataset, you should answer the probability with which the game succeeds within the\ngiven number of turns. The output should not contain an error greater than 0.00001.\nTask Samples: input: 6 1 0 0\n7 1 0 0\n7 2 0 0\n6 6 1 1\n2\n5\n7 10 0 6\n1\n2\n3\n4\n5\n6\n0 0 0 0\n output: 0.166667\n0.000000\n0.166667\n0.619642\n0.000000\n\n" }, { "title": "Problem D: Lowest Pyramid", "content": "You are constructing a triangular pyramid with a sheet of craft paper with grid lines. Its base\nand sides are all of triangular shape. You draw the base triangle and the three sides connected\nto the base on the paper, cut along the outer six edges, fold the edges of the base, and assemble\nthem up as a pyramid.\n\nYou are given the coordinates of the base's three vertices, and are to determine the coordinates\nof the other three. All the vertices must have integral X- and Y-coordinate values between -100 and +100 inclusive. Your goal is to minimize the height of the pyramid satisfying these\nconditions. Figure 3 shows some examples.\n\nFigure 3: Some craft paper drawings and side views of the assembled pyramids", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nX_0 Y_0 X_1 Y_1 X_2 Y_2\n\nThey are all integral numbers between -100 and +100 inclusive. (X_0, Y_0), (X_1, Y_1), (X_2, Y_2) are the coordinates of three vertices of the triangular base in counterclockwise order.\n\nThe end of the input is indicated by a line containing six zeros separated by a single space.", "output": "For each dataset, answer a single number in a separate line. If you can choose three vertices (X_a, Y_a), (X_b, Y_b) and (X_c, Y_c) whose coordinates are all integral values between -100 and +100 inclusive, and triangles (X_0, Y_0 )-(X_1, Y_1)-(X_a, Y_a), (X_1, Y_1)-(X_2, Y_2)-(X_b, Y_b), (X_2, Y_2)-(X_0, Y_0)-(X_c, Y_c) and (X_0, Y_0)-(X_1, Y_1)-(X_2, Y_2) do not overlap each other (in the XY-plane), and can be assembled as a triangular pyramid of positive (non-zero) height, output the minimum height among such pyramids. Otherwise, output -1.\n\nYou may assume that the height is, if positive (non-zero), not less than 0.00001. The output should not contain an error greater than 0.00001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 0 1 0 0 1\n0 0 5 0 2 5\n-100 -100 100 -100 0 100\n-72 -72 72 -72 0 72\n0 0 0 0 0 0\n output: 2\n1.49666\n-1\n8.52936"], "Pid": "p00857", "ProblemText": "Task Description: You are constructing a triangular pyramid with a sheet of craft paper with grid lines. Its base\nand sides are all of triangular shape. You draw the base triangle and the three sides connected\nto the base on the paper, cut along the outer six edges, fold the edges of the base, and assemble\nthem up as a pyramid.\n\nYou are given the coordinates of the base's three vertices, and are to determine the coordinates\nof the other three. All the vertices must have integral X- and Y-coordinate values between -100 and +100 inclusive. Your goal is to minimize the height of the pyramid satisfying these\nconditions. Figure 3 shows some examples.\n\nFigure 3: Some craft paper drawings and side views of the assembled pyramids\nTask Input: The input consists of multiple datasets, each in the following format.\n\nX_0 Y_0 X_1 Y_1 X_2 Y_2\n\nThey are all integral numbers between -100 and +100 inclusive. (X_0, Y_0), (X_1, Y_1), (X_2, Y_2) are the coordinates of three vertices of the triangular base in counterclockwise order.\n\nThe end of the input is indicated by a line containing six zeros separated by a single space.\nTask Output: For each dataset, answer a single number in a separate line. If you can choose three vertices (X_a, Y_a), (X_b, Y_b) and (X_c, Y_c) whose coordinates are all integral values between -100 and +100 inclusive, and triangles (X_0, Y_0 )-(X_1, Y_1)-(X_a, Y_a), (X_1, Y_1)-(X_2, Y_2)-(X_b, Y_b), (X_2, Y_2)-(X_0, Y_0)-(X_c, Y_c) and (X_0, Y_0)-(X_1, Y_1)-(X_2, Y_2) do not overlap each other (in the XY-plane), and can be assembled as a triangular pyramid of positive (non-zero) height, output the minimum height among such pyramids. Otherwise, output -1.\n\nYou may assume that the height is, if positive (non-zero), not less than 0.00001. The output should not contain an error greater than 0.00001.\nTask Samples: input: 0 0 1 0 0 1\n0 0 5 0 2 5\n-100 -100 100 -100 0 100\n-72 -72 72 -72 0 72\n0 0 0 0 0 0\n output: 2\n1.49666\n-1\n8.52936\n\n" }, { "title": "Problem E: Geometric Map", "content": "Your task in this problem is to create a program that finds the shortest path between two given\nlocations on a given street map, which is represented as a collection of line segments on a plane.\n\nFigure 4 is an example of a street map, where some line segments represent streets and the\nothers are signs indicating the directions in which cars cannot move. More concretely, AE, AM, MQ, EQ, CP and HJ represent the streets and the others are signs in this map. In general, an end point of a sign touches one and only one line segment representing a street and the other end point is open. Each end point of every street touches one or more streets, but no signs.\n\nThe sign BF, for instance, indicates that at B cars may move left to right but may not in the\nreverse direction. In general, cars may not move from the obtuse angle side to the acute angle\nside at a point where a sign touches a street (note that the angle CBF is obtuse and the angle ABF is acute). Cars may directly move neither from P to M nor from M to P since cars moving left\nto right may not go through N and those moving right to left may not go through O. In a special\ncase where the angle between a sign and a street is rectangular, cars may not move in either\ndirections at the point. For instance, cars may directly move neither from H to J nor from J to H.\n\nYou should write a program that finds the shortest path obeying these traffic rules. The length of a line segment between (x_1, y_1) and (x_2, y_2) is √{(x_2 - x_1)^2 + (y_2 - y_1 )^2} .", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn\nx_s y_s\nx_g y_g\nx_1^1 y_1^1 x_2^1 y_2^1\n .\n .\n .\nx_1^k y_1^k x_2^k y_2^k\n .\n .\n .\nx_1^n y_1^n x_2^n y_2^n\n\nn, representing the number of line segments, is a positive integer less than or equal to 200.\n\n(x_s, y_s) and (x_g, y_g) are the start and goal points, respectively. You can assume that (x_s, y_s) ! = (x_g, y_g) and that each of them is located on an end point of some line segment representing a street. You can also assume that the shortest path from (x_s, y_s) to (x_g, y_g) is unique.\n\n(x_1^k, y_1^k) and (x_2^k, y_2^k ) are the two end points of the kth line segment. You can assume that \n(x_1^k, y_1^k) ! =(x_2^k, y_2^k ).\nTwo line segments never cross nor overlap. That is, if they share a point, it is always one of their end points.\n\nAll the coordinates are non-negative integers less than or equal to 1000. The end of the input is indicated by a line containing a single zero.", "output": "For each input dataset, print every street intersection point on the shortest path from the start\npoint to the goal point, one in an output line in this order, and a zero in a line following\nthose points. Note that a street intersection point is a point where at least two line segments\nrepresenting streets meet. An output line for a street intersection point should contain its x- and y-coordinates separated by a space.\n\nPrint -1 if there are no paths from the start point to the goal point.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8\n1 1\n4 4\n1 1 4 1\n1 1 1 4\n3 1 3 4\n4 3 5 3\n2 4 3 5\n4 1 4 4\n3 3 2 2\n1 4 4 4\n9\n1 5\n5 1\n5 4 5 1\n1 5 1 1\n1 5 5 1\n2 3 2 4\n5 4 1 5\n3 2 2 1\n4 2 4 1\n1 1 5 1\n5 3 4 3\n11\n5 5\n1 0\n3 1 5 1\n4 3 4 2\n3 1 5 5\n2 3 2 2\n1 0 1 2\n1 2 3 4\n3 4 5 5\n1 0 5 2\n4 0 4 1\n5 5 5 1\n2 3 2 4\n0\n output: 1 1\n3 1\n3 4\n4 4\n0\n-1\n5 5\n5 2\n3 1\n1 0\n0"], "Pid": "p00858", "ProblemText": "Task Description: Your task in this problem is to create a program that finds the shortest path between two given\nlocations on a given street map, which is represented as a collection of line segments on a plane.\n\nFigure 4 is an example of a street map, where some line segments represent streets and the\nothers are signs indicating the directions in which cars cannot move. More concretely, AE, AM, MQ, EQ, CP and HJ represent the streets and the others are signs in this map. In general, an end point of a sign touches one and only one line segment representing a street and the other end point is open. Each end point of every street touches one or more streets, but no signs.\n\nThe sign BF, for instance, indicates that at B cars may move left to right but may not in the\nreverse direction. In general, cars may not move from the obtuse angle side to the acute angle\nside at a point where a sign touches a street (note that the angle CBF is obtuse and the angle ABF is acute). Cars may directly move neither from P to M nor from M to P since cars moving left\nto right may not go through N and those moving right to left may not go through O. In a special\ncase where the angle between a sign and a street is rectangular, cars may not move in either\ndirections at the point. For instance, cars may directly move neither from H to J nor from J to H.\n\nYou should write a program that finds the shortest path obeying these traffic rules. The length of a line segment between (x_1, y_1) and (x_2, y_2) is √{(x_2 - x_1)^2 + (y_2 - y_1 )^2} .\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn\nx_s y_s\nx_g y_g\nx_1^1 y_1^1 x_2^1 y_2^1\n .\n .\n .\nx_1^k y_1^k x_2^k y_2^k\n .\n .\n .\nx_1^n y_1^n x_2^n y_2^n\n\nn, representing the number of line segments, is a positive integer less than or equal to 200.\n\n(x_s, y_s) and (x_g, y_g) are the start and goal points, respectively. You can assume that (x_s, y_s) ! = (x_g, y_g) and that each of them is located on an end point of some line segment representing a street. You can also assume that the shortest path from (x_s, y_s) to (x_g, y_g) is unique.\n\n(x_1^k, y_1^k) and (x_2^k, y_2^k ) are the two end points of the kth line segment. You can assume that \n(x_1^k, y_1^k) ! =(x_2^k, y_2^k ).\nTwo line segments never cross nor overlap. That is, if they share a point, it is always one of their end points.\n\nAll the coordinates are non-negative integers less than or equal to 1000. The end of the input is indicated by a line containing a single zero.\nTask Output: For each input dataset, print every street intersection point on the shortest path from the start\npoint to the goal point, one in an output line in this order, and a zero in a line following\nthose points. Note that a street intersection point is a point where at least two line segments\nrepresenting streets meet. An output line for a street intersection point should contain its x- and y-coordinates separated by a space.\n\nPrint -1 if there are no paths from the start point to the goal point.\nTask Samples: input: 8\n1 1\n4 4\n1 1 4 1\n1 1 1 4\n3 1 3 4\n4 3 5 3\n2 4 3 5\n4 1 4 4\n3 3 2 2\n1 4 4 4\n9\n1 5\n5 1\n5 4 5 1\n1 5 1 1\n1 5 5 1\n2 3 2 4\n5 4 1 5\n3 2 2 1\n4 2 4 1\n1 1 5 1\n5 3 4 3\n11\n5 5\n1 0\n3 1 5 1\n4 3 4 2\n3 1 5 5\n2 3 2 2\n1 0 1 2\n1 2 3 4\n3 4 5 5\n1 0 5 2\n4 0 4 1\n5 5 5 1\n2 3 2 4\n0\n output: 1 1\n3 1\n3 4\n4 4\n0\n-1\n5 5\n5 2\n3 1\n1 0\n0\n\n" }, { "title": "Problem F: Slim Span", "content": "Given an undirected weighted graph G, you should find one of spanning trees specified as follows.\n\nThe graph G is an ordered pair (V, E), where V is a set of vertices {v_1, v_2, . . . , v_n} and E is a set of undirected edges {e_1, e_2, . . . , e_m}. Each edge e ∈ E has its weight w(e).\n\nA spanning tree T is a tree (a connected subgraph without cycles) which connects all the n\nvertices with n - 1 edges. The slimness of a spanning tree T is defined as the difference between\nthe largest weight and the smallest weight among the n - 1 edges of T.\n\nFigure 5: A graph G and the weights of the edges\nFor example, a graph G in Figure 5(a) has four vertices {v_1, v_2, v_3, v_4} and five undirected edges {e_1, e_2, e_3, e_4, e_5}. The weights of the edges are w(e_1) = 3, w(e_2) = 5, w(e_3) = 6, w(e_4) = 6, w(e_5) = 7 as shown in Figure 5(b).\n\nFigure 6: Examples of the spanning trees of G\nThere are several spanning trees for G. Four of them are depicted in Figure 6(a)-(d). The spanning tree T_a in Figure 6(a) has three edges whose weights are 3,6 and 7. The largest weight\nis 7 and the smallest weight is 3 so that the slimness of the tree T_a is 4. The slimnesses of\nspanning trees T_b , T_c and T_d shown in Figure 6(b), (c) and (d) are 3,2 and 1, respectively. You\ncan easily see the slimness of any other spanning tree is greater than or equal to 1, thus the\nspanning tree T_d in Figure 6(d) is one of the slimmest spanning trees whose slimness is 1.\n\nYour job is to write a program that computes the smallest slimness.", "constraint": "", "input": "The input consists of multiple datasets, followed by a line containing two zeros separated by a space. Each dataset has the following format.\n\nn m\na_1 b_1 w_1\n .\n .\n .\na_m b_m w_m\n\nEvery input item in a dataset is a non-negative integer. Items in a line are separated by a space.\n\nn is the number of the vertices and m the number of the edges. You can assume 2 <= n <= 100 and 0 <= m <= n(n - 1)/2. a_k and b_k (k = 1, . . . , m) are positive integers less than or equal to n, which represent the two vertices v_ak and v_bk connected by the kth edge e_k. w_k is a positive integer less than or equal to 10000, which indicates the weight of e_k . You can assume that the graph G = (V, E) is simple, that is, there are no self-loops (that connect the same vertex) nor parallel edges (that are two or more edges whose both ends are the same two vertices).", "output": "For each dataset, if the graph has spanning trees, the smallest slimness among them should be\nprinted. Otherwise, -1 should be printed. An output should not contain extra characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 5\n1 2 3\n1 3 5\n1 4 6\n2 4 6\n3 4 7\n4 6\n1 2 10\n1 3 100\n1 4 90\n2 3 20\n2 4 80\n3 4 40\n2 1\n1 2 1\n3 0\n3 1\n1 2 1\n3 3\n1 2 2\n2 3 5\n1 3 6\n5 10\n1 2 110\n1 3 120\n1 4 130\n1 5 120\n2 3 110\n2 4 120\n2 5 130\n3 4 120\n3 5 110\n4 5 120\n5 10\n1 2 9384\n1 3 887\n1 4 2778\n1 5 6916\n2 3 7794\n2 4 8336\n2 5 5387\n3 4 493\n3 5 6650\n4 5 1422\n5 8\n1 2 1\n2 3 100\n3 4 100\n4 5 100\n1 5 50\n2 5 50\n3 5 50\n4 1 150\n0 0\n output: 1\n20\n0\n-1\n-1\n1\n0\n1686\n50"], "Pid": "p00859", "ProblemText": "Task Description: Given an undirected weighted graph G, you should find one of spanning trees specified as follows.\n\nThe graph G is an ordered pair (V, E), where V is a set of vertices {v_1, v_2, . . . , v_n} and E is a set of undirected edges {e_1, e_2, . . . , e_m}. Each edge e ∈ E has its weight w(e).\n\nA spanning tree T is a tree (a connected subgraph without cycles) which connects all the n\nvertices with n - 1 edges. The slimness of a spanning tree T is defined as the difference between\nthe largest weight and the smallest weight among the n - 1 edges of T.\n\nFigure 5: A graph G and the weights of the edges\nFor example, a graph G in Figure 5(a) has four vertices {v_1, v_2, v_3, v_4} and five undirected edges {e_1, e_2, e_3, e_4, e_5}. The weights of the edges are w(e_1) = 3, w(e_2) = 5, w(e_3) = 6, w(e_4) = 6, w(e_5) = 7 as shown in Figure 5(b).\n\nFigure 6: Examples of the spanning trees of G\nThere are several spanning trees for G. Four of them are depicted in Figure 6(a)-(d). The spanning tree T_a in Figure 6(a) has three edges whose weights are 3,6 and 7. The largest weight\nis 7 and the smallest weight is 3 so that the slimness of the tree T_a is 4. The slimnesses of\nspanning trees T_b , T_c and T_d shown in Figure 6(b), (c) and (d) are 3,2 and 1, respectively. You\ncan easily see the slimness of any other spanning tree is greater than or equal to 1, thus the\nspanning tree T_d in Figure 6(d) is one of the slimmest spanning trees whose slimness is 1.\n\nYour job is to write a program that computes the smallest slimness.\nTask Input: The input consists of multiple datasets, followed by a line containing two zeros separated by a space. Each dataset has the following format.\n\nn m\na_1 b_1 w_1\n .\n .\n .\na_m b_m w_m\n\nEvery input item in a dataset is a non-negative integer. Items in a line are separated by a space.\n\nn is the number of the vertices and m the number of the edges. You can assume 2 <= n <= 100 and 0 <= m <= n(n - 1)/2. a_k and b_k (k = 1, . . . , m) are positive integers less than or equal to n, which represent the two vertices v_ak and v_bk connected by the kth edge e_k. w_k is a positive integer less than or equal to 10000, which indicates the weight of e_k . You can assume that the graph G = (V, E) is simple, that is, there are no self-loops (that connect the same vertex) nor parallel edges (that are two or more edges whose both ends are the same two vertices).\nTask Output: For each dataset, if the graph has spanning trees, the smallest slimness among them should be\nprinted. Otherwise, -1 should be printed. An output should not contain extra characters.\nTask Samples: input: 4 5\n1 2 3\n1 3 5\n1 4 6\n2 4 6\n3 4 7\n4 6\n1 2 10\n1 3 100\n1 4 90\n2 3 20\n2 4 80\n3 4 40\n2 1\n1 2 1\n3 0\n3 1\n1 2 1\n3 3\n1 2 2\n2 3 5\n1 3 6\n5 10\n1 2 110\n1 3 120\n1 4 130\n1 5 120\n2 3 110\n2 4 120\n2 5 130\n3 4 120\n3 5 110\n4 5 120\n5 10\n1 2 9384\n1 3 887\n1 4 2778\n1 5 6916\n2 3 7794\n2 4 8336\n2 5 5387\n3 4 493\n3 5 6650\n4 5 1422\n5 8\n1 2 1\n2 3 100\n3 4 100\n4 5 100\n1 5 50\n2 5 50\n3 5 50\n4 1 150\n0 0\n output: 1\n20\n0\n-1\n-1\n1\n0\n1686\n50\n\n" }, { "title": "Problem G: The Morning after Halloween", "content": "You are working for an amusement park as an operator of an obakeyashiki, or a haunted house,\nin which guests walk through narrow and dark corridors. The house is proud of their lively\nghosts, which are actually robots remotely controlled by the operator, hiding here and there in\nthe corridors. One morning, you found that the ghosts are not in the positions where they are\nsupposed to be. Ah, yesterday was Halloween. Believe or not, paranormal spirits have moved\nthem around the corridors in the night. You have to move them into their right positions before\nguests come. Your manager is eager to know how long it takes to restore the ghosts.\n\nIn this problem, you are asked to write a program that, given a floor map of a house, finds the\nsmallest number of steps to move all ghosts to the positions where they are supposed to be.\n\nA floor consists of a matrix of square cells. A cell is either a wall cell where ghosts cannot move\ninto or a corridor cell where they can.\n\nAt each step, you can move any number of ghosts simultaneously. Every ghost can either stay\nin the current cell, or move to one of the corridor cells in its 4-neighborhood (i. e. immediately\nleft, right, up or down), if the ghosts satisfy the following conditions:\n\n No more than one ghost occupies one position at the end of the step.\n\n No pair of ghosts exchange their positions one another in the step.\nFor example, suppose ghosts are located as shown in the following (partial) map, where a sharp sign ('#) represents a wall cell and 'a', 'b', and 'c' ghosts.\n\n ####\n ab#\n #c##\n ####\n\nThe following four maps show the only possible positions of the ghosts after one step.\n\n #### #### #### ####\n ab# a b# acb# ab #\n #c## #c## # ## #c##\n #### #### #### ####", "constraint": "", "input": "The input consists of at most 10 datasets, each of which represents a floor map of a house. The format of a dataset is as follows.\n\nw h n\nc_11c_12. . . c_1w\nc_21c_22. . . c_2w\n. . . . .\n. . .\n .\n. . .\nc_h1c_h2. . . c_hw\n\nw, h and n in the first line are integers, separated by a space. w and h are the floor width\nand height of the house, respectively. n is the number of ghosts. They satisfy the following constraints.\n 4 <= w <= 16\n 4 <= h <= 16\n 1 <= n <= 3\nSubsequent h lines of w characters are the floor map. Each of c_ij is either:\n\na '#' representing a wall cell,\n\n a lowercase letter representing a corridor cell which is the initial position of a ghost,\n\n an uppercase letter representing a corridor cell which is the position where the ghost corresponding to its lowercase letter is supposed to be, or\n\n a space representing a corridor cell that is none of the above.\nIn each map, each of the first n letters from a and the first n letters from A appears once and\nonly once. Outermost cells of a map are walls; i. e. all characters of the first and last lines are\nsharps; and the first and last characters on each line are also sharps. All corridor cells in a\nmap are connected; i. e. given a corridor cell, you can reach any other corridor cell by following\ncorridor cells in the 4-neighborhoods. Similarly, all wall cells are connected. Any 2 * 2 area on\nany map has at least one sharp. You can assume that every map has a sequence of moves of ghosts that restores all ghosts to the positions where they are supposed to be.\n\nThe last dataset is followed by a line containing three zeros separated by a space.", "output": "For each dataset in the input, one line containing the smallest number of steps to restore ghosts\ninto the positions where they are supposed to be should be output. An output line should not\ncontain extra characters such as spaces.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5 2\n#####\n#A#B#\n# #\n#b#a#\n#####\n16 4 3\n################\n## ########## ##\n# ABCcba #\n################\n16 16 3\n################\n### ## # ##\n## # ## # c#\n# ## ########b#\n# ## # # # #\n# # ## # # ##\n## a# # # # #\n### ## #### ## #\n## # # # #\n# ##### # ## ##\n#### #B# # #\n## C# # ###\n# # # ####### #\n# ###### A## #\n# # ##\n################\n0 0 0\n output: 7\n36\n77"], "Pid": "p00860", "ProblemText": "Task Description: You are working for an amusement park as an operator of an obakeyashiki, or a haunted house,\nin which guests walk through narrow and dark corridors. The house is proud of their lively\nghosts, which are actually robots remotely controlled by the operator, hiding here and there in\nthe corridors. One morning, you found that the ghosts are not in the positions where they are\nsupposed to be. Ah, yesterday was Halloween. Believe or not, paranormal spirits have moved\nthem around the corridors in the night. You have to move them into their right positions before\nguests come. Your manager is eager to know how long it takes to restore the ghosts.\n\nIn this problem, you are asked to write a program that, given a floor map of a house, finds the\nsmallest number of steps to move all ghosts to the positions where they are supposed to be.\n\nA floor consists of a matrix of square cells. A cell is either a wall cell where ghosts cannot move\ninto or a corridor cell where they can.\n\nAt each step, you can move any number of ghosts simultaneously. Every ghost can either stay\nin the current cell, or move to one of the corridor cells in its 4-neighborhood (i. e. immediately\nleft, right, up or down), if the ghosts satisfy the following conditions:\n\n No more than one ghost occupies one position at the end of the step.\n\n No pair of ghosts exchange their positions one another in the step.\nFor example, suppose ghosts are located as shown in the following (partial) map, where a sharp sign ('#) represents a wall cell and 'a', 'b', and 'c' ghosts.\n\n ####\n ab#\n #c##\n ####\n\nThe following four maps show the only possible positions of the ghosts after one step.\n\n #### #### #### ####\n ab# a b# acb# ab #\n #c## #c## # ## #c##\n #### #### #### ####\nTask Input: The input consists of at most 10 datasets, each of which represents a floor map of a house. The format of a dataset is as follows.\n\nw h n\nc_11c_12. . . c_1w\nc_21c_22. . . c_2w\n. . . . .\n. . .\n .\n. . .\nc_h1c_h2. . . c_hw\n\nw, h and n in the first line are integers, separated by a space. w and h are the floor width\nand height of the house, respectively. n is the number of ghosts. They satisfy the following constraints.\n 4 <= w <= 16\n 4 <= h <= 16\n 1 <= n <= 3\nSubsequent h lines of w characters are the floor map. Each of c_ij is either:\n\na '#' representing a wall cell,\n\n a lowercase letter representing a corridor cell which is the initial position of a ghost,\n\n an uppercase letter representing a corridor cell which is the position where the ghost corresponding to its lowercase letter is supposed to be, or\n\n a space representing a corridor cell that is none of the above.\nIn each map, each of the first n letters from a and the first n letters from A appears once and\nonly once. Outermost cells of a map are walls; i. e. all characters of the first and last lines are\nsharps; and the first and last characters on each line are also sharps. All corridor cells in a\nmap are connected; i. e. given a corridor cell, you can reach any other corridor cell by following\ncorridor cells in the 4-neighborhoods. Similarly, all wall cells are connected. Any 2 * 2 area on\nany map has at least one sharp. You can assume that every map has a sequence of moves of ghosts that restores all ghosts to the positions where they are supposed to be.\n\nThe last dataset is followed by a line containing three zeros separated by a space.\nTask Output: For each dataset in the input, one line containing the smallest number of steps to restore ghosts\ninto the positions where they are supposed to be should be output. An output line should not\ncontain extra characters such as spaces.\nTask Samples: input: 5 5 2\n#####\n#A#B#\n# #\n#b#a#\n#####\n16 4 3\n################\n## ########## ##\n# ABCcba #\n################\n16 16 3\n################\n### ## # ##\n## # ## # c#\n# ## ########b#\n# ## # # # #\n# # ## # # ##\n## a# # # # #\n### ## #### ## #\n## # # # #\n# ##### # ## ##\n#### #B# # #\n## C# # ###\n# # # ####### #\n# ###### A## #\n# # ##\n################\n0 0 0\n output: 7\n36\n77\n\n" }, { "title": "Problem H: Bug Hunt", "content": "In this problem, we consider a simple programming language that has only declarations of one-\ndimensional integer arrays and assignment statements. The problem is to find a bug in the given\nprogram.\n\nThe syntax of this language is given in BNF as follows:\n\nwhere denotes a new line character (LF).\n\nCharacters used in a program are alphabetical letters, decimal digits, =, [, ] and new line characters. No other characters appear in a program.\n\nA declaration declares an array and specifies its length. Valid indices of an array of length n are integers between 0 and n - 1, inclusive. Note that the array names are case sensitive, i. e.\narray a and array A are different arrays. The initial value of each element in the declared array is undefined.\n\nFor example, array a of length 10 and array b of length 5 are declared respectively as follows.\n\na[10]\nb[5]\n\nAn expression evaluates to a non-negative integer. A is interpreted as a decimal\ninteger. An [] evaluates to the value of the -th element of\nthe array. An assignment assigns the value denoted by the right hand side to the array element\nspecified by the left hand side.\n\nExamples of assignments are as follows.\n\na[0]=3\na[1]=0\na[2]=a[a[1]]\na[a[0]]=a[1]\n\nA program is executed from the first line, line by line. You can assume that an array is declared once and only once before any of its element is assigned or referred to.\n\nGiven a program, you are requested to find the following bugs.\n\n An index of an array is invalid.\n\n An array element that has not been assigned before is referred to in an assignment as an index of array or as the value to be assigned.\nYou can assume that other bugs, such as syntax errors, do not appear. You can also assume\nthat integers represented by s are between 0 and 2^31 - 1 (= 2147483647), inclusive.", "constraint": "", "input": "The input consists of multiple datasets followed by a line which contains only a single '. ' (period).\nEach dataset consists of a program also followed by a line which contains only a single '. ' (period).\nA program does not exceed 1000 lines. Any line does not exceed 80 characters excluding a new\nline character.", "output": "For each program in the input, you should answer the line number of the assignment in which\nthe first bug appears. The line numbers start with 1 for each program. If the program does not\nhave a bug, you should answer zero. The output should not contain extra characters such as\nspaces.", "content_img": true, "lang": "en", "error": false, "samples": ["input: a[3]\na[0]=a[1]\n.\nx[1]\nx[0]=x[0]\n.\na[0]\na[0]=1\n.\nb[2]\nb[0]=2\nb[1]=b[b[0]]\nb[0]=b[1]\n.\ng[2]\nG[10]\ng[0]=0\ng[1]=G[0]\n.\na[2147483647]\na[0]=1\nB[2]\nB[a[0]]=2\na[B[a[0]]]=3\na[2147483646]=a[2]\n.\n.\n output: 2\n2\n2\n3\n4\n0"], "Pid": "p00861", "ProblemText": "Task Description: In this problem, we consider a simple programming language that has only declarations of one-\ndimensional integer arrays and assignment statements. The problem is to find a bug in the given\nprogram.\n\nThe syntax of this language is given in BNF as follows:\n\nwhere denotes a new line character (LF).\n\nCharacters used in a program are alphabetical letters, decimal digits, =, [, ] and new line characters. No other characters appear in a program.\n\nA declaration declares an array and specifies its length. Valid indices of an array of length n are integers between 0 and n - 1, inclusive. Note that the array names are case sensitive, i. e.\narray a and array A are different arrays. The initial value of each element in the declared array is undefined.\n\nFor example, array a of length 10 and array b of length 5 are declared respectively as follows.\n\na[10]\nb[5]\n\nAn expression evaluates to a non-negative integer. A is interpreted as a decimal\ninteger. An [] evaluates to the value of the -th element of\nthe array. An assignment assigns the value denoted by the right hand side to the array element\nspecified by the left hand side.\n\nExamples of assignments are as follows.\n\na[0]=3\na[1]=0\na[2]=a[a[1]]\na[a[0]]=a[1]\n\nA program is executed from the first line, line by line. You can assume that an array is declared once and only once before any of its element is assigned or referred to.\n\nGiven a program, you are requested to find the following bugs.\n\n An index of an array is invalid.\n\n An array element that has not been assigned before is referred to in an assignment as an index of array or as the value to be assigned.\nYou can assume that other bugs, such as syntax errors, do not appear. You can also assume\nthat integers represented by s are between 0 and 2^31 - 1 (= 2147483647), inclusive.\nTask Input: The input consists of multiple datasets followed by a line which contains only a single '. ' (period).\nEach dataset consists of a program also followed by a line which contains only a single '. ' (period).\nA program does not exceed 1000 lines. Any line does not exceed 80 characters excluding a new\nline character.\nTask Output: For each program in the input, you should answer the line number of the assignment in which\nthe first bug appears. The line numbers start with 1 for each program. If the program does not\nhave a bug, you should answer zero. The output should not contain extra characters such as\nspaces.\nTask Samples: input: a[3]\na[0]=a[1]\n.\nx[1]\nx[0]=x[0]\n.\na[0]\na[0]=1\n.\nb[2]\nb[0]=2\nb[1]=b[b[0]]\nb[0]=b[1]\n.\ng[2]\nG[10]\ng[0]=0\ng[1]=G[0]\n.\na[2147483647]\na[0]=1\nB[2]\nB[a[0]]=2\na[B[a[0]]]=3\na[2147483646]=a[2]\n.\n.\n output: 2\n2\n2\n3\n4\n0\n\n" }, { "title": "Problem I: Most Distant Point from the Sea", "content": "The main land of Japan called Honshu is an island surrounded by the sea. In such an island, it\nis natural to ask a question: \"Where is the most distant point from the sea? \" The answer to\nthis question for Honshu was found in 1996. The most distant point is located in former Usuda\nTown, Nagano Prefecture, whose distance from the sea is 114.86 km.\n\nIn this problem, you are asked to write a program which, given a map of an island, finds the\nmost distant point from the sea in the island, and reports its distance from the sea. In order to\nsimplify the problem, we only consider maps representable by convex polygons.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset represents a map of an island, which is a convex polygon. The format of a dataset is as follows.\n\nn\nx_1 y_1\n .\n .\n .\nx_n y_n\n\nEvery input item in a dataset is a non-negative integer. Two input items in a line are separated by a space.\n\nn in the first line is the number of vertices of the polygon, satisfying 3 <= n <= 100. Subsequent\nn lines are the x- and y-coordinates of the n vertices. Line segments (x_i, y_i) - (x_i+1, y_i+1) (1 <= i <= n - 1) and the line segment (x_n, y_n) - (x_1, y_1) form the border of the polygon in counterclockwise order. That is, these line segments see the inside of the polygon in the left of their directions. All coordinate values are between 0 and 10000, inclusive.\n\nYou can assume that the polygon is simple, that is, its border never crosses or touches itself. As stated above, the given polygon is always a convex one.\n\nThe last dataset is followed by a line containing a single zero.", "output": "For each dataset in the input, one line containing the distance of the most distant point from\nthe sea should be output. An output line should not contain extra characters such as spaces.\n\nThe answer should not have an error greater than 0.00001 (10^-5 ). You may output any number\nof digits after the decimal point, provided that the above accuracy condition is satisfied.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n10000 0\n10000 10000\n0 10000\n3\n0 0\n10000 0\n7000 1000\n6\n0 40\n100 20\n250 40\n250 70\n100 90\n0 70\n3\n0 0\n10000 10000\n5000 5001\n0\n output: 5000.000000\n494.233641\n34.542948\n0.353553"], "Pid": "p00862", "ProblemText": "Task Description: The main land of Japan called Honshu is an island surrounded by the sea. In such an island, it\nis natural to ask a question: \"Where is the most distant point from the sea? \" The answer to\nthis question for Honshu was found in 1996. The most distant point is located in former Usuda\nTown, Nagano Prefecture, whose distance from the sea is 114.86 km.\n\nIn this problem, you are asked to write a program which, given a map of an island, finds the\nmost distant point from the sea in the island, and reports its distance from the sea. In order to\nsimplify the problem, we only consider maps representable by convex polygons.\nTask Input: The input consists of multiple datasets. Each dataset represents a map of an island, which is a convex polygon. The format of a dataset is as follows.\n\nn\nx_1 y_1\n .\n .\n .\nx_n y_n\n\nEvery input item in a dataset is a non-negative integer. Two input items in a line are separated by a space.\n\nn in the first line is the number of vertices of the polygon, satisfying 3 <= n <= 100. Subsequent\nn lines are the x- and y-coordinates of the n vertices. Line segments (x_i, y_i) - (x_i+1, y_i+1) (1 <= i <= n - 1) and the line segment (x_n, y_n) - (x_1, y_1) form the border of the polygon in counterclockwise order. That is, these line segments see the inside of the polygon in the left of their directions. All coordinate values are between 0 and 10000, inclusive.\n\nYou can assume that the polygon is simple, that is, its border never crosses or touches itself. As stated above, the given polygon is always a convex one.\n\nThe last dataset is followed by a line containing a single zero.\nTask Output: For each dataset in the input, one line containing the distance of the most distant point from\nthe sea should be output. An output line should not contain extra characters such as spaces.\n\nThe answer should not have an error greater than 0.00001 (10^-5 ). You may output any number\nof digits after the decimal point, provided that the above accuracy condition is satisfied.\nTask Samples: input: 4\n0 0\n10000 0\n10000 10000\n0 10000\n3\n0 0\n10000 0\n7000 1000\n6\n0 40\n100 20\n250 40\n250 70\n100 90\n0 70\n3\n0 0\n10000 10000\n5000 5001\n0\n output: 5000.000000\n494.233641\n34.542948\n0.353553\n\n" }, { "title": "Problem J: The Teacher's Side of Math", "content": "One of the tasks students routinely carry out in their mathematics classes is to solve a polynomial equation. It is, given a polynomial, say X^2 - 4X + 1, to find its roots (2 ± √3).\n\nIf the students ' task is to find the roots of a given polynomial, the teacher 's task is then to find a polynomial that has a given root. Ms. Galsone is an enthusiastic mathematics teacher who is bored with finding solutions of quadratic equations that are as simple as a + b√c. She wanted to make higher-degree equations whose solutions are a little more complicated. As usual in problems in mathematics classes, she wants to maintain all coefficients to be integers and keep the degree of the polynomial as small as possible (provided it has the specified root). Please help her by writing a program that carries out the task of the teacher 's side.\n\nYou are given a number t of the form:\n t = ^m√a+^n√b\nwhere a and b are distinct prime numbers, and m and n are integers greater than 1.\n\nIn this problem, you are asked to find t's minimal polynomial on integers, which is the polynomial F(X) = a_d X^d + a_d-1X^d-1 + . . . + a_1X + a_0 satisfying the following conditions.\n\n Coefficients a_0, . . . , a_d are integers and a_d > 0.\n\n F(t) = 0.\n\n The degree d is minimum among polynomials satisfying the above two conditions.\n\n F(X) is primitive. That is, coefficients a_0, . . . , a_d have no common divisors greater than one.\nFor example, the minimal polynomial of √3+ √2 on integers is F(X) = X^4 - 10X^2 + 1. Verifying F(t) = 0 is as simple as the following (α = 3, β = 2).\n\nF(t) = (α + β)^4 - 10(α + β)^2 + 1\n\n= (α^4 + 4α^3β + 6α^2β^2 + 4αβ^3 + β^4 ) - 10(α^2 + 2αβ + β^2) + 1\n\n= 9 + 12αβ + 36 + 8αβ + 4 - 10(3 + 2αβ + 2) + 1\n\n= (9 + 36 + 4 - 50 + 1) + (12 + 8 - 20)αβ\n\n = 0\n\nVerifying that the degree of F(t) is in fact minimum is a bit more difficult. Fortunately, under\nthe condition given in this problem, which is that a and b are distinct prime numbers and m and n greater than one, the degree of the minimal polynomial is always mn. Moreover, it is\nalways monic. That is, the coefficient of its highest-order term (a_d) is one.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\n a m b n\n\nThis line represents ^m√a + ^n√b. The last dataset is followed by a single line consisting of four zeros. Numbers in a single line are separated by a single space.\n\nEvery dataset satisfies the following conditions.\n\n ^m√a + ^n√b <= 4.\n\n mn <= 20.\n\n The coefficients of the answer a_0, . . . , a_d are between (-2^31 + 1) and (2^31 - 1), inclusive.", "output": "For each dataset, output the coefficients of its minimal polynomial on integers F(X) = a_d X^d + a_d-1X^d-1 + . . . + a_1X + a_0, in the following format.\n\na_d a_d-1 . . . a_1 a_0\nNon-negative integers must be printed without a sign (+ or -). Numbers in a single line must\nbe separated by a single space and no other characters or extra spaces may appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 2 2\n3 2 2 3\n2 2 3 4\n31 4 2 3\n3 2 2 7\n0 0 0 0\n output: 1 0 -10 0 1\n1 0 -9 -4 27 -36 -23\n1 0 -8 0 18 0 -104 0 1\n1 0 0 -8 -93 0 24 -2976 2883 -32 -3720 -23064 -29775\n1 0 -21 0 189 0 -945 -4 2835 -252 -5103 -1260 5103 -756 -2183"], "Pid": "p00863", "ProblemText": "Task Description: One of the tasks students routinely carry out in their mathematics classes is to solve a polynomial equation. It is, given a polynomial, say X^2 - 4X + 1, to find its roots (2 ± √3).\n\nIf the students ' task is to find the roots of a given polynomial, the teacher 's task is then to find a polynomial that has a given root. Ms. Galsone is an enthusiastic mathematics teacher who is bored with finding solutions of quadratic equations that are as simple as a + b√c. She wanted to make higher-degree equations whose solutions are a little more complicated. As usual in problems in mathematics classes, she wants to maintain all coefficients to be integers and keep the degree of the polynomial as small as possible (provided it has the specified root). Please help her by writing a program that carries out the task of the teacher 's side.\n\nYou are given a number t of the form:\n t = ^m√a+^n√b\nwhere a and b are distinct prime numbers, and m and n are integers greater than 1.\n\nIn this problem, you are asked to find t's minimal polynomial on integers, which is the polynomial F(X) = a_d X^d + a_d-1X^d-1 + . . . + a_1X + a_0 satisfying the following conditions.\n\n Coefficients a_0, . . . , a_d are integers and a_d > 0.\n\n F(t) = 0.\n\n The degree d is minimum among polynomials satisfying the above two conditions.\n\n F(X) is primitive. That is, coefficients a_0, . . . , a_d have no common divisors greater than one.\nFor example, the minimal polynomial of √3+ √2 on integers is F(X) = X^4 - 10X^2 + 1. Verifying F(t) = 0 is as simple as the following (α = 3, β = 2).\n\nF(t) = (α + β)^4 - 10(α + β)^2 + 1\n\n= (α^4 + 4α^3β + 6α^2β^2 + 4αβ^3 + β^4 ) - 10(α^2 + 2αβ + β^2) + 1\n\n= 9 + 12αβ + 36 + 8αβ + 4 - 10(3 + 2αβ + 2) + 1\n\n= (9 + 36 + 4 - 50 + 1) + (12 + 8 - 20)αβ\n\n = 0\n\nVerifying that the degree of F(t) is in fact minimum is a bit more difficult. Fortunately, under\nthe condition given in this problem, which is that a and b are distinct prime numbers and m and n greater than one, the degree of the minimal polynomial is always mn. Moreover, it is\nalways monic. That is, the coefficient of its highest-order term (a_d) is one.\nTask Input: The input consists of multiple datasets, each in the following format.\n\n a m b n\n\nThis line represents ^m√a + ^n√b. The last dataset is followed by a single line consisting of four zeros. Numbers in a single line are separated by a single space.\n\nEvery dataset satisfies the following conditions.\n\n ^m√a + ^n√b <= 4.\n\n mn <= 20.\n\n The coefficients of the answer a_0, . . . , a_d are between (-2^31 + 1) and (2^31 - 1), inclusive.\nTask Output: For each dataset, output the coefficients of its minimal polynomial on integers F(X) = a_d X^d + a_d-1X^d-1 + . . . + a_1X + a_0, in the following format.\n\na_d a_d-1 . . . a_1 a_0\nNon-negative integers must be printed without a sign (+ or -). Numbers in a single line must\nbe separated by a single space and no other characters or extra spaces may appear in the output.\nTask Samples: input: 3 2 2 2\n3 2 2 3\n2 2 3 4\n31 4 2 3\n3 2 2 7\n0 0 0 0\n output: 1 0 -10 0 1\n1 0 -9 -4 27 -36 -23\n1 0 -8 0 18 0 -104 0 1\n1 0 0 -8 -93 0 24 -2976 2883 -32 -3720 -23064 -29775\n1 0 -21 0 189 0 -945 -4 2835 -252 -5103 -1260 5103 -756 -2183\n\n" }, { "title": "Problem A: Grey Area", "content": "Dr. Grey is a data analyst, who visualizes various aspects of data received from all over the\nworld everyday. He is extremely good at sophisticated visualization tools, but yet his favorite is\na simple self-made histogram generator.\nFigure 1 is an example of histogram automatically produced by his histogram.\nA histogram is a visual display of frequencies of value occurrences as bars. In this example, values\nin the interval 0-9 occur five times, those in the interval 10-19 occur three times, and 20-29\nand 30-39 once each.\nDr. Grey's histogram generator is a simple tool. First, the height of the histogram is fixed, that\nis, the height of the highest bar is always the same and those of the others are automatically\nadjusted proportionately. Second, the widths of bars are also fixed. It can only produce a\nhistogram of uniform intervals, that is, each interval of a histogram should have the same width\n(10 in the above example). Finally, the bar for each interval is painted in a grey color, where\nthe colors of the leftmost and the rightmost intervals are black and white, respectively, and the\ndarkness of bars monotonically decreases at the same rate from left to right. For instance, in\nFigure 1, the darkness levels of the four bars are 1,2/3,1/3, and 0, respectively.\nIn this problem, you are requested to estimate ink consumption when printing a histogram on paper. The amount of ink necessary to draw a bar is proportional to both its area and darkness.", "constraint": "", "input": "The input consists of multiple datasets, each of which contains integers and specifies a value\ntable and intervals for the histogram generator, in the following format.\n\nn w\nv_1\nv_2\n. \n. \nv_n\n\nn is the total number of value occurrences for the histogram, and each of the n lines following\nthe first line contains a single value. Note that the same value may possibly occur multiple\ntimes.\n\nw is the interval width. A value v is in the first (i. e. leftmost) interval if 0 <= v < w, the second\none if w <= v < 2w, and so on. Note that the interval from 0 (inclusive) to w (exclusive) should\nbe regarded as the leftmost even if no values occur in this interval. The last (i. e. rightmost)\ninterval is the one that includes the largest value in the dataset.\n\nYou may assume the following.\n\n 1 <= n <= 100\n 10 <= w <= 50\n 0 <= v_i <= 100 for 1 <= i <= n\n\nYou can also assume that the maximum value is no less than w. This means that the histogram\nhas more than one interval.\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output a line containing the amount of ink consumed in printing the histogram.\n\nOne unit of ink is necessary to paint one highest bar black. Assume that 0.01 units of ink per\nhistogram is consumed for various purposes except for painting bars such as drawing lines and\ncharacters (see Figure 1). For instance, the amount of ink consumed in printing the histogram\nin Figure 1 is:\n\nEach output value should be in a decimal fraction and may have an error less than 10^-5 .", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 50\n100\n0\n100\n3 50\n100\n100\n50\n10 10\n1\n2\n3\n4\n5\n16\n17\n18\n29\n30\n0 0\n output: 0.51\n0.26\n1.4766666666666667"], "Pid": "p00864", "ProblemText": "Task Description: Dr. Grey is a data analyst, who visualizes various aspects of data received from all over the\nworld everyday. He is extremely good at sophisticated visualization tools, but yet his favorite is\na simple self-made histogram generator.\nFigure 1 is an example of histogram automatically produced by his histogram.\nA histogram is a visual display of frequencies of value occurrences as bars. In this example, values\nin the interval 0-9 occur five times, those in the interval 10-19 occur three times, and 20-29\nand 30-39 once each.\nDr. Grey's histogram generator is a simple tool. First, the height of the histogram is fixed, that\nis, the height of the highest bar is always the same and those of the others are automatically\nadjusted proportionately. Second, the widths of bars are also fixed. It can only produce a\nhistogram of uniform intervals, that is, each interval of a histogram should have the same width\n(10 in the above example). Finally, the bar for each interval is painted in a grey color, where\nthe colors of the leftmost and the rightmost intervals are black and white, respectively, and the\ndarkness of bars monotonically decreases at the same rate from left to right. For instance, in\nFigure 1, the darkness levels of the four bars are 1,2/3,1/3, and 0, respectively.\nIn this problem, you are requested to estimate ink consumption when printing a histogram on paper. The amount of ink necessary to draw a bar is proportional to both its area and darkness.\nTask Input: The input consists of multiple datasets, each of which contains integers and specifies a value\ntable and intervals for the histogram generator, in the following format.\n\nn w\nv_1\nv_2\n. \n. \nv_n\n\nn is the total number of value occurrences for the histogram, and each of the n lines following\nthe first line contains a single value. Note that the same value may possibly occur multiple\ntimes.\n\nw is the interval width. A value v is in the first (i. e. leftmost) interval if 0 <= v < w, the second\none if w <= v < 2w, and so on. Note that the interval from 0 (inclusive) to w (exclusive) should\nbe regarded as the leftmost even if no values occur in this interval. The last (i. e. rightmost)\ninterval is the one that includes the largest value in the dataset.\n\nYou may assume the following.\n\n 1 <= n <= 100\n 10 <= w <= 50\n 0 <= v_i <= 100 for 1 <= i <= n\n\nYou can also assume that the maximum value is no less than w. This means that the histogram\nhas more than one interval.\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output a line containing the amount of ink consumed in printing the histogram.\n\nOne unit of ink is necessary to paint one highest bar black. Assume that 0.01 units of ink per\nhistogram is consumed for various purposes except for painting bars such as drawing lines and\ncharacters (see Figure 1). For instance, the amount of ink consumed in printing the histogram\nin Figure 1 is:\n\nEach output value should be in a decimal fraction and may have an error less than 10^-5 .\nTask Samples: input: 3 50\n100\n0\n100\n3 50\n100\n100\n50\n10 10\n1\n2\n3\n4\n5\n16\n17\n18\n29\n30\n0 0\n output: 0.51\n0.26\n1.4766666666666667\n\n" }, { "title": "Problem B: Expected Allowance", "content": "Hideyuki is allowed by his father Ujisato some 1000 yen bills every month for his pocket money.\nIn the first day of every month, the number of bills is decided as follows. Ujisato prepares n\npieces of m-sided dice and declares the cutback k. Hideyuki rolls these dice. The number of\nbills given is the sum of the spots of the rolled dice decreased by the cutback. Fortunately to\nHideyuki, Ujisato promises him to give at least one bill, even if the sum of the spots does not\nexceed the cutback. Each of the dice has spots of 1 through m inclusive on each side, and the\nprobability of each side is the same.\n\nIn this problem, you are asked to write a program that finds the expected value of the number\nof given bills.\n\nFor example, when n = 2, m = 6 and k = 3, the probabilities of the number of bills being 1,2,3,4,5,6,7,8 and 9 are 1/36 + 2/36 + 3/36,4/36,5/36,6/36,5/36,4/36,3/36,2/36 and 1/36, respectively.\n\nTherefore, the expected value is\n\n(1/36 + 2/36 + 3/36) * 1 + 4/36 * 2 + 5/36 * 3 + 6/36 * 4 + 5/36 * 5 + 4/36 * 6 + 3/36 * 7 + 2/36 * 8 + 1/36 * 9, which is approximately 4.11111111.", "constraint": "", "input": "The input is a sequence of lines each of which contains three integers n, m and k in this order.\nThey satisfy the following conditions.\n\n1 <= n\n2 <= m\n0 <= k < nm\nnm * m^n < 100000000 (10^8)\n\nThe end of the input is indicated by a line containing three zeros.", "output": "The output should be comprised of lines each of which contains a single decimal fraction. It is\nthe expected number of bills and may have an error less than 10^-7 . No other characters should\noccur in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 6 0\n2 6 3\n3 10 9\n13 3 27\n1 2008 3\n0 0 0\n output: 7.00000000\n4.11111111\n7.71000000\n1.42902599\n1001.50298805"], "Pid": "p00865", "ProblemText": "Task Description: Hideyuki is allowed by his father Ujisato some 1000 yen bills every month for his pocket money.\nIn the first day of every month, the number of bills is decided as follows. Ujisato prepares n\npieces of m-sided dice and declares the cutback k. Hideyuki rolls these dice. The number of\nbills given is the sum of the spots of the rolled dice decreased by the cutback. Fortunately to\nHideyuki, Ujisato promises him to give at least one bill, even if the sum of the spots does not\nexceed the cutback. Each of the dice has spots of 1 through m inclusive on each side, and the\nprobability of each side is the same.\n\nIn this problem, you are asked to write a program that finds the expected value of the number\nof given bills.\n\nFor example, when n = 2, m = 6 and k = 3, the probabilities of the number of bills being 1,2,3,4,5,6,7,8 and 9 are 1/36 + 2/36 + 3/36,4/36,5/36,6/36,5/36,4/36,3/36,2/36 and 1/36, respectively.\n\nTherefore, the expected value is\n\n(1/36 + 2/36 + 3/36) * 1 + 4/36 * 2 + 5/36 * 3 + 6/36 * 4 + 5/36 * 5 + 4/36 * 6 + 3/36 * 7 + 2/36 * 8 + 1/36 * 9, which is approximately 4.11111111.\nTask Input: The input is a sequence of lines each of which contains three integers n, m and k in this order.\nThey satisfy the following conditions.\n\n1 <= n\n2 <= m\n0 <= k < nm\nnm * m^n < 100000000 (10^8)\n\nThe end of the input is indicated by a line containing three zeros.\nTask Output: The output should be comprised of lines each of which contains a single decimal fraction. It is\nthe expected number of bills and may have an error less than 10^-7 . No other characters should\noccur in the output.\nTask Samples: input: 2 6 0\n2 6 3\n3 10 9\n13 3 27\n1 2008 3\n0 0 0\n output: 7.00000000\n4.11111111\n7.71000000\n1.42902599\n1001.50298805\n\n" }, { "title": "Problem C: Stopped Watches", "content": "In the middle of Tyrrhenian Sea, there is a small volcanic island called Chronus. The island\nis now uninhabited but it used to be a civilized island. Some historical records imply that the\nisland was annihilated by an eruption of a volcano about 800 years ago and that most of the\npeople in the island were killed by pyroclastic flows caused by the volcanic activity. In 2003, a\nEuropean team of archaeologists launched an excavation project in Chronus Island. Since then,\nthe project has provided many significant historic insights. In particular the discovery made\nin the summer of 2008 astonished the world: the project team excavated several mechanical\nwatches worn by the victims of the disaster. This indicates that people in Chronus Island had\nsuch a highly advanced manufacturing technology.\n\nShortly after the excavation of the watches, archaeologists in the team tried to identify what\ntime of the day the disaster happened, but it was not successful due to several difficulties. First,\nthe extraordinary heat of pyroclastic flows severely damaged the watches and took away the\nletters and numbers printed on them. Second, every watch has a perfect round form and one\ncannot tell where the top of the watch is. Lastly, though every watch has three hands, they\nhave a completely identical look and therefore one cannot tell which is the hour, the minute,\nor the second (It is a mystery how the people in Chronus Island were distinguishing the three hands. Some archaeologists\nguess that the hands might be painted with different colors, but this is only a hypothesis, as the paint was lost\nby the heat.\n). This means that we cannot decide the time indicated by a watch uniquely;\nthere can be a number of candidates. We have to consider different rotations of the watch.\nFurthermore, since there are several possible interpretations of hands, we have also to consider\nall the permutations of hands.\n\nYou are an information archaeologist invited to the project team and are asked to induce the\nmost plausible time interval within which the disaster happened, from the set of excavated\nwatches.\n\nIn what follows, we express a time modulo 12 hours. We write a time by the notation hh: mm: ss,\nwhere hh, mm, and ss stand for the hour (hh = 00,01,02, . . . , 11), the minute (mm = 00,\n01,02, . . . , 59), and the second (ss = 00,01,02, . . . , 59), respectively. The time starts from\n00: 00: 00 and counts up every second 00: 00: 00,00: 00: 01,00: 00: 02, . . . , but it reverts to 00: 00: 00\nevery 12 hours.\n\nThe watches in Chronus Island obey the following conventions of modern analog watches.\n\nA watch has three hands, i. e. the hour hand, the minute hand, and the second hand,\nthough they look identical as mentioned above.\n\nEvery hand ticks 6 degrees clockwise in a discrete manner. That is, no hand stays between\nticks, and each hand returns to the same position every 60 ticks.\n\nThe second hand ticks every second.\n\nThe minute hand ticks every 60 seconds.\n\nThe hour hand ticks every 12 minutes.\nAt the time 00: 00: 00, all the three hands are located at the same position.\n\nBecause people in Chronus Island were reasonably keen to keep their watches correct and pyroclastic flows spread over the island quite rapidly, it can be assumed that all the watches were\nstopped in a short interval of time. Therefore it is highly expected that the time the disaster\nhappened is in the shortest time interval within which all the excavated watches have at least\none candidate time.\n\nYou must calculate the shortest time interval and report it to the project team.", "constraint": "", "input": "The input consists of multiple datasets, each of which is formatted as follows.\n\nn\ns_1 t_1 u_1\ns_2 t_2 u_2\n . \n . \n . \ns_n t_n u_n\n\nThe first line contains a single integer n (2 <= n <= 10), representing the number of the watches.\nThe three numbers s_i , t_i , u_i in each line are integers such that 0 <= s_i , t_i , u_i <= 59 and they specify\nthe positions of the three hands by the number of ticks relative to an arbitrarily chosen position.\n\nNote that the positions of the hands of a watch can be expressed in many different ways. For\nexample, if a watch was stopped at the time 11: 55: 03, the positions of hands can be expressed\ndifferently by rotating the watch arbitrarily (e. g. 59 55 3,0 56 4,1 57 5, etc. ) and as well by\npermuting the hour, minute, and second hands arbitrarily (e. g. 55 59 3,55 3 59,3 55 59, etc. ).\n\nThe end of the input is indicated by a line containing a single zero.", "output": "For each dataset, output the shortest time interval within which all the watches given in the\ndataset have at least one candidate time. The output must be written in a single line in the\nfollowing format for each dataset.\n\nhh: mm: ss h'h': m'm': s's'\n\nEach line contains a pair of times hh: mm: ss and, h'h': m'm': s's' indicating that the shortest\ninterval begins at hh: mm: ss and ends at h'h': m'm': s's' inclusive. The beginning time and the\nending time are separated by a single space and each of them should consist of hour, minute,\nand second in two digits separated by colons. No extra characters should appear in the output.\n\nIn calculating the shortest interval, you can exploit the facts that every watch has at least one\ncandidate time and that the shortest time interval contains 00: 00: 00 only if the interval starts\nfrom 00: 00: 00 (i. e. the shortest interval terminates before the time reverts to 00: 00: 00).\n\nIf there is more than one time interval that gives the shortest, output the one that first comes\nafter 00: 00: 00 inclusive.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n8 8 18\n32 32 32\n57 2 57\n5\n49 3 49\n7 30 44\n27 21 21\n33 56 56\n21 46 4\n3\n45 52 28\n36 26 36\n20 55 50\n10\n33 8 39\n50 57 43\n35 21 12\n21 17 11\n16 21 58\n45 40 53\n45 30 53\n39 1 8\n55 48 30\n7 48 15\n0\n output: 00:00:00 00:00:10\n06:14:56 06:32:09\n07:27:37 07:32:02\n05:17:40 05:21:03"], "Pid": "p00866", "ProblemText": "Task Description: In the middle of Tyrrhenian Sea, there is a small volcanic island called Chronus. The island\nis now uninhabited but it used to be a civilized island. Some historical records imply that the\nisland was annihilated by an eruption of a volcano about 800 years ago and that most of the\npeople in the island were killed by pyroclastic flows caused by the volcanic activity. In 2003, a\nEuropean team of archaeologists launched an excavation project in Chronus Island. Since then,\nthe project has provided many significant historic insights. In particular the discovery made\nin the summer of 2008 astonished the world: the project team excavated several mechanical\nwatches worn by the victims of the disaster. This indicates that people in Chronus Island had\nsuch a highly advanced manufacturing technology.\n\nShortly after the excavation of the watches, archaeologists in the team tried to identify what\ntime of the day the disaster happened, but it was not successful due to several difficulties. First,\nthe extraordinary heat of pyroclastic flows severely damaged the watches and took away the\nletters and numbers printed on them. Second, every watch has a perfect round form and one\ncannot tell where the top of the watch is. Lastly, though every watch has three hands, they\nhave a completely identical look and therefore one cannot tell which is the hour, the minute,\nor the second (It is a mystery how the people in Chronus Island were distinguishing the three hands. Some archaeologists\nguess that the hands might be painted with different colors, but this is only a hypothesis, as the paint was lost\nby the heat.\n). This means that we cannot decide the time indicated by a watch uniquely;\nthere can be a number of candidates. We have to consider different rotations of the watch.\nFurthermore, since there are several possible interpretations of hands, we have also to consider\nall the permutations of hands.\n\nYou are an information archaeologist invited to the project team and are asked to induce the\nmost plausible time interval within which the disaster happened, from the set of excavated\nwatches.\n\nIn what follows, we express a time modulo 12 hours. We write a time by the notation hh: mm: ss,\nwhere hh, mm, and ss stand for the hour (hh = 00,01,02, . . . , 11), the minute (mm = 00,\n01,02, . . . , 59), and the second (ss = 00,01,02, . . . , 59), respectively. The time starts from\n00: 00: 00 and counts up every second 00: 00: 00,00: 00: 01,00: 00: 02, . . . , but it reverts to 00: 00: 00\nevery 12 hours.\n\nThe watches in Chronus Island obey the following conventions of modern analog watches.\n\nA watch has three hands, i. e. the hour hand, the minute hand, and the second hand,\nthough they look identical as mentioned above.\n\nEvery hand ticks 6 degrees clockwise in a discrete manner. That is, no hand stays between\nticks, and each hand returns to the same position every 60 ticks.\n\nThe second hand ticks every second.\n\nThe minute hand ticks every 60 seconds.\n\nThe hour hand ticks every 12 minutes.\nAt the time 00: 00: 00, all the three hands are located at the same position.\n\nBecause people in Chronus Island were reasonably keen to keep their watches correct and pyroclastic flows spread over the island quite rapidly, it can be assumed that all the watches were\nstopped in a short interval of time. Therefore it is highly expected that the time the disaster\nhappened is in the shortest time interval within which all the excavated watches have at least\none candidate time.\n\nYou must calculate the shortest time interval and report it to the project team.\nTask Input: The input consists of multiple datasets, each of which is formatted as follows.\n\nn\ns_1 t_1 u_1\ns_2 t_2 u_2\n . \n . \n . \ns_n t_n u_n\n\nThe first line contains a single integer n (2 <= n <= 10), representing the number of the watches.\nThe three numbers s_i , t_i , u_i in each line are integers such that 0 <= s_i , t_i , u_i <= 59 and they specify\nthe positions of the three hands by the number of ticks relative to an arbitrarily chosen position.\n\nNote that the positions of the hands of a watch can be expressed in many different ways. For\nexample, if a watch was stopped at the time 11: 55: 03, the positions of hands can be expressed\ndifferently by rotating the watch arbitrarily (e. g. 59 55 3,0 56 4,1 57 5, etc. ) and as well by\npermuting the hour, minute, and second hands arbitrarily (e. g. 55 59 3,55 3 59,3 55 59, etc. ).\n\nThe end of the input is indicated by a line containing a single zero.\nTask Output: For each dataset, output the shortest time interval within which all the watches given in the\ndataset have at least one candidate time. The output must be written in a single line in the\nfollowing format for each dataset.\n\nhh: mm: ss h'h': m'm': s's'\n\nEach line contains a pair of times hh: mm: ss and, h'h': m'm': s's' indicating that the shortest\ninterval begins at hh: mm: ss and ends at h'h': m'm': s's' inclusive. The beginning time and the\nending time are separated by a single space and each of them should consist of hour, minute,\nand second in two digits separated by colons. No extra characters should appear in the output.\n\nIn calculating the shortest interval, you can exploit the facts that every watch has at least one\ncandidate time and that the shortest time interval contains 00: 00: 00 only if the interval starts\nfrom 00: 00: 00 (i. e. the shortest interval terminates before the time reverts to 00: 00: 00).\n\nIf there is more than one time interval that gives the shortest, output the one that first comes\nafter 00: 00: 00 inclusive.\nTask Samples: input: 3\n8 8 18\n32 32 32\n57 2 57\n5\n49 3 49\n7 30 44\n27 21 21\n33 56 56\n21 46 4\n3\n45 52 28\n36 26 36\n20 55 50\n10\n33 8 39\n50 57 43\n35 21 12\n21 17 11\n16 21 58\n45 40 53\n45 30 53\n39 1 8\n55 48 30\n7 48 15\n0\n output: 00:00:00 00:00:10\n06:14:56 06:32:09\n07:27:37 07:32:02\n05:17:40 05:21:03\n\n" }, { "title": "Problem D: Digits on the Floor", "content": "Taro attempts to tell digits to Hanako by putting straight bars on the floor. Taro wants to\nexpress each digit by making one of the forms shown in Figure 1.\n\nSince Taro may not have bars of desired lengths, Taro cannot always make forms exactly as\nshown in Figure 1. Fortunately, Hanako can recognize a form as a digit if the connection\nrelation between bars in the form is kept. Neither the lengths of bars nor the directions of forms\naffect Hanako 's perception as long as the connection relation remains the same. For example,\nHanako can recognize all the awkward forms in Figure 2 as digits. On the other hand, Hanako\ncannot recognize the forms in Figure 3 as digits. For clarity, touching bars are slightly separated\nin Figures 1,2 and 3. Actually, touching bars overlap exactly at one single point.\n\n \n \n\n Figure 1: Representation of digits \n\n \n\n \n \n\n Figure 2: Examples of forms recognized as digits \n\n \nIn the forms, when a bar touches another, the touching point is an end of at least one of them.\nThat is, bars never cross. In addition, the angle of such two bars is always a right angle.\n\nTo enable Taro to represent forms with his limited set of bars, positions and lengths of bars can\nbe changed as far as the connection relations are kept. Also, forms can be rotated.\n\nKeeping the connection relations means the following.\n\n \n \n\n Figure 3: Forms not recognized as digits (these kinds of forms are not contained in the dataset) \n\n \nSeparated bars are not made to touch.\n\nTouching bars are not made separate.\n\nWhen one end of a bar touches another bar, that end still touches the same bar. When it\ntouches a midpoint of the other bar, it remains to touch a midpoint of the same bar on\nthe same side.\nThe angle of touching two bars is kept to be the same right angle (90 degrees and -90\ndegrees are considered different, and forms for 2 and 5 are kept distinguished).\n\nYour task is to find how many times each digit appears on the floor.\n\nThe forms of some digits always contain the forms of other digits. For example, a form for\n9 always contains four forms for 1, one form for 4, and two overlapping forms for 7. In this\nproblem, ignore the forms contained in another form and count only the digit of the “largest”\nform composed of all mutually connecting bars. If there is one form for 9, it should be interpreted\nas one appearance of 9 and no appearance of 1,4, or 7.", "constraint": "", "input": "The input consists of a number of datasets. Each dataset is formatted as follows.\n\nn\nx_1a y_1a x_1b y_1b\nx_2a y_2a x_2b y_2b\n . \n . \n . \nx_na y_na x_nb y_nb\n\nIn the first line, n represents the number of bars in the dataset. For the rest of the lines, one\nline represents one bar. Four integers x_a, y_a , x_b , y_b , delimited by single spaces, are given in\neach line. x_a and y_a are the x- and y-coordinates of one end of the bar, respectively. x_b and\ny_b are those of the other end. The coordinate system is as shown in Figure 4. You can assume\n1 <= n <= 1000 and 0 <= x_a , y_a , x_b , y_b <= 1000.\n\nThe end of the input is indicated by a line containing one zero.\n\n \n \n\n Figure 4: The coordinate system \n\n \n\nYou can also assume the following conditions.\n\nMore than two bars do not overlap at one point.\n\nEvery bar is used as a part of a digit. Non-digit forms do not exist on the floor.\n\nA bar that makes up one digit does not touch nor cross any bar that makes up another\ndigit.\nThere is no bar whose length is zero.", "output": "For each dataset, output a single line containing ten integers delimited by single spaces. These\nintegers represent how many times 0,1,2, . . . , and 9 appear on the floor in this order. Output\nlines must not contain other characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 9\n60 140 200 300\n300 105 330 135\n330 135 250 215\n240 205 250 215\n298 167 285 154\n30 40 30 90\n30 90 150 90\n150 90 150 20\n30 40 150 40\n8\n320 20 300 60\n320 20 380 50\n380 50 240 330\n10 50 40 20\n10 50 110 150\n110 150 180 80\n40 20 37 17\n37 17 27 27\n20\n72 222 132 182\n204 154 204 54\n510 410 520 370\n404 54 204 54\n530 450 410 450\n204 68 404 68\n80 110 120 30\n130 160 180 60\n520 370 320 320\n310 360 320 320\n120 30 180 60\n60 100 80 110\n404 154 204 154\n80 60 60 100\n430 550 590 550\n510 410 310 360\n430 450 430 550\n404 54 404 154\n232 202 142 262\n142 262 102 202\n0\n output: 0 1 0 1 0 0 0 0 0 1\n0 0 0 0 0 1 0 1 0 0\n1 0 1 0 2 0 0 0 1 0"], "Pid": "p00867", "ProblemText": "Task Description: Taro attempts to tell digits to Hanako by putting straight bars on the floor. Taro wants to\nexpress each digit by making one of the forms shown in Figure 1.\n\nSince Taro may not have bars of desired lengths, Taro cannot always make forms exactly as\nshown in Figure 1. Fortunately, Hanako can recognize a form as a digit if the connection\nrelation between bars in the form is kept. Neither the lengths of bars nor the directions of forms\naffect Hanako 's perception as long as the connection relation remains the same. For example,\nHanako can recognize all the awkward forms in Figure 2 as digits. On the other hand, Hanako\ncannot recognize the forms in Figure 3 as digits. For clarity, touching bars are slightly separated\nin Figures 1,2 and 3. Actually, touching bars overlap exactly at one single point.\n\n \n \n\n Figure 1: Representation of digits \n\n \n\n \n \n\n Figure 2: Examples of forms recognized as digits \n\n \nIn the forms, when a bar touches another, the touching point is an end of at least one of them.\nThat is, bars never cross. In addition, the angle of such two bars is always a right angle.\n\nTo enable Taro to represent forms with his limited set of bars, positions and lengths of bars can\nbe changed as far as the connection relations are kept. Also, forms can be rotated.\n\nKeeping the connection relations means the following.\n\n \n \n\n Figure 3: Forms not recognized as digits (these kinds of forms are not contained in the dataset) \n\n \nSeparated bars are not made to touch.\n\nTouching bars are not made separate.\n\nWhen one end of a bar touches another bar, that end still touches the same bar. When it\ntouches a midpoint of the other bar, it remains to touch a midpoint of the same bar on\nthe same side.\nThe angle of touching two bars is kept to be the same right angle (90 degrees and -90\ndegrees are considered different, and forms for 2 and 5 are kept distinguished).\n\nYour task is to find how many times each digit appears on the floor.\n\nThe forms of some digits always contain the forms of other digits. For example, a form for\n9 always contains four forms for 1, one form for 4, and two overlapping forms for 7. In this\nproblem, ignore the forms contained in another form and count only the digit of the “largest”\nform composed of all mutually connecting bars. If there is one form for 9, it should be interpreted\nas one appearance of 9 and no appearance of 1,4, or 7.\nTask Input: The input consists of a number of datasets. Each dataset is formatted as follows.\n\nn\nx_1a y_1a x_1b y_1b\nx_2a y_2a x_2b y_2b\n . \n . \n . \nx_na y_na x_nb y_nb\n\nIn the first line, n represents the number of bars in the dataset. For the rest of the lines, one\nline represents one bar. Four integers x_a, y_a , x_b , y_b , delimited by single spaces, are given in\neach line. x_a and y_a are the x- and y-coordinates of one end of the bar, respectively. x_b and\ny_b are those of the other end. The coordinate system is as shown in Figure 4. You can assume\n1 <= n <= 1000 and 0 <= x_a , y_a , x_b , y_b <= 1000.\n\nThe end of the input is indicated by a line containing one zero.\n\n \n \n\n Figure 4: The coordinate system \n\n \n\nYou can also assume the following conditions.\n\nMore than two bars do not overlap at one point.\n\nEvery bar is used as a part of a digit. Non-digit forms do not exist on the floor.\n\nA bar that makes up one digit does not touch nor cross any bar that makes up another\ndigit.\nThere is no bar whose length is zero.\nTask Output: For each dataset, output a single line containing ten integers delimited by single spaces. These\nintegers represent how many times 0,1,2, . . . , and 9 appear on the floor in this order. Output\nlines must not contain other characters.\nTask Samples: input: 9\n60 140 200 300\n300 105 330 135\n330 135 250 215\n240 205 250 215\n298 167 285 154\n30 40 30 90\n30 90 150 90\n150 90 150 20\n30 40 150 40\n8\n320 20 300 60\n320 20 380 50\n380 50 240 330\n10 50 40 20\n10 50 110 150\n110 150 180 80\n40 20 37 17\n37 17 27 27\n20\n72 222 132 182\n204 154 204 54\n510 410 520 370\n404 54 204 54\n530 450 410 450\n204 68 404 68\n80 110 120 30\n130 160 180 60\n520 370 320 320\n310 360 320 320\n120 30 180 60\n60 100 80 110\n404 154 204 154\n80 60 60 100\n430 550 590 550\n510 410 310 360\n430 450 430 550\n404 54 404 154\n232 202 142 262\n142 262 102 202\n0\n output: 0 1 0 1 0 0 0 0 0 1\n0 0 0 0 0 1 0 1 0 0\n1 0 1 0 2 0 0 0 1 0\n\n" }, { "title": "Problem E: Spherical Mirrors", "content": "A long time ago in a galaxy, far, far away, there were N spheres with various radii.\nSpheres were mirrors, that is, they had reflective surfaces . . . .\n\nYou are standing at the origin of the galaxy (0,0,0), and emit a laser ray to the direction\n(u, v, w). The ray travels in a straight line.\n\nWhen the laser ray from I hits the surface of a sphere at Q, let N be a point outside of the\nsphere on the line connecting the sphere center and Q. The reflected ray goes to the direction\ntowards R that satisfies the following conditions: (1) R is on the plane formed by the three\npoints I, Q and N , (2) ∠ IQN = ∠ NQR, as shown in Figure 1.\n\n \n \n\n Figure 1: Laser ray reflection \n\n \n\nAfter it is reflected several times, finally it goes beyond our observation. Your mission is to write\na program that identifies the last reflection point.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\n N\n u v w\n x_1 y_1 z_1 r_1\n .\n .\n .\n x_N y_N z_N r_N\n\nThe first line of a dataset contains a positive integer N which is the number of spheres. The\nnext line contains three integers u, v and w separated by single spaces, where (u, v, w) is the\ndirection of the laser ray initially emitted from the origin.\n\nEach of the following N lines contains four integers separated by single spaces. The i-th line\ncorresponds to the i-th sphere, and the numbers represent the center position (x_i, y_i, z_i ) and the\nradius r_i .\n\nN, u, v, w, x_i, y_i, z_i and r_i satisfy the following conditions.\n\n 1 <= N <= 100 \n-100 <= u, v, w <= 100\n-100 <= x_i, y_i, z_i <= 100\n 5 <= r_i <= 30\nu^2 + v^2 + w^2 > 0\n\nYou can assume that the distance between the surfaces of any two spheres is no less than 0.1.\nYou can also assume that the origin (0,0,0) is located outside of any sphere, and is at least 0.1\ndistant from the surface of any sphere.\n\nThe ray is known to be reflected by the sphere surfaces at least once, and at most five times.\nYou can assume that the angle between the ray and the line connecting the sphere center and\nthe reflection point, which is known as the angle of reflection (i. e. θ in Figure 1), is less than 85\ndegrees for each point of reflection.\n\nThe last dataset is followed by a line containing a single zero.", "output": "For each dataset in the input, you should print the x-, y- and z-coordinates of the last reflection\npoint separated by single spaces in a line. No output line should contain extra characters.\n\nNo coordinate values in the output should have an error greater than 0.01.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n-20 -20 -24\n100 100 100 30\n10 8 3 5\n-70 -70 -84 5\n4\n0 47 84\n-23 41 42 8\n45 -10 14 19\n-5 28 47 12\n-27 68 34 14\n0\n output: 79.0940 79.0940 94.9128\n-21.8647 54.9770 34.1761"], "Pid": "p00868", "ProblemText": "Task Description: A long time ago in a galaxy, far, far away, there were N spheres with various radii.\nSpheres were mirrors, that is, they had reflective surfaces . . . .\n\nYou are standing at the origin of the galaxy (0,0,0), and emit a laser ray to the direction\n(u, v, w). The ray travels in a straight line.\n\nWhen the laser ray from I hits the surface of a sphere at Q, let N be a point outside of the\nsphere on the line connecting the sphere center and Q. The reflected ray goes to the direction\ntowards R that satisfies the following conditions: (1) R is on the plane formed by the three\npoints I, Q and N , (2) ∠ IQN = ∠ NQR, as shown in Figure 1.\n\n \n \n\n Figure 1: Laser ray reflection \n\n \n\nAfter it is reflected several times, finally it goes beyond our observation. Your mission is to write\na program that identifies the last reflection point.\nTask Input: The input consists of multiple datasets, each in the following format.\n\n N\n u v w\n x_1 y_1 z_1 r_1\n .\n .\n .\n x_N y_N z_N r_N\n\nThe first line of a dataset contains a positive integer N which is the number of spheres. The\nnext line contains three integers u, v and w separated by single spaces, where (u, v, w) is the\ndirection of the laser ray initially emitted from the origin.\n\nEach of the following N lines contains four integers separated by single spaces. The i-th line\ncorresponds to the i-th sphere, and the numbers represent the center position (x_i, y_i, z_i ) and the\nradius r_i .\n\nN, u, v, w, x_i, y_i, z_i and r_i satisfy the following conditions.\n\n 1 <= N <= 100 \n-100 <= u, v, w <= 100\n-100 <= x_i, y_i, z_i <= 100\n 5 <= r_i <= 30\nu^2 + v^2 + w^2 > 0\n\nYou can assume that the distance between the surfaces of any two spheres is no less than 0.1.\nYou can also assume that the origin (0,0,0) is located outside of any sphere, and is at least 0.1\ndistant from the surface of any sphere.\n\nThe ray is known to be reflected by the sphere surfaces at least once, and at most five times.\nYou can assume that the angle between the ray and the line connecting the sphere center and\nthe reflection point, which is known as the angle of reflection (i. e. θ in Figure 1), is less than 85\ndegrees for each point of reflection.\n\nThe last dataset is followed by a line containing a single zero.\nTask Output: For each dataset in the input, you should print the x-, y- and z-coordinates of the last reflection\npoint separated by single spaces in a line. No output line should contain extra characters.\n\nNo coordinate values in the output should have an error greater than 0.01.\nTask Samples: input: 3\n-20 -20 -24\n100 100 100 30\n10 8 3 5\n-70 -70 -84 5\n4\n0 47 84\n-23 41 42 8\n45 -10 14 19\n-5 28 47 12\n-27 68 34 14\n0\n output: 79.0940 79.0940 94.9128\n-21.8647 54.9770 34.1761\n\n" }, { "title": "Problem F: Traveling Cube", "content": "On a small planet named Bandai, a landing party of the starship Tadamigawa discovered colorful\ncubes traveling on flat areas of the planet surface, which the landing party named beds. A cube\nappears at a certain position on a bed, travels on the bed for a while, and then disappears. After\na longtime observation, a science officer Lt. Alyssa Ogawa of Tadamigawa found the rule how a\ncube travels on a bed.\n\nA bed is a rectangular area tiled with squares of the same size.\n One of the squares is colored red,\n\n one colored green,\n\n one colored blue,\n\n one colored cyan,\n\n one colored magenta,\n\n one colored yellow,\n\n one or more colored white, and\n\n all others, if any, colored black.\nInitially, a cube appears on one of the white squares. The cube 's faces are colored as follows.\n\n top red\n bottom cyan\n north green\n south magenta\n east blue\n west yellow\n\nThe cube can roll around a side of the current square at a step and thus rolls on to an adjacent\nsquare. When the cube rolls on to a chromatically colored (red, green, blue, cyan, magenta or\nyellow) square, the top face of the cube after the roll should be colored the same. When the\ncube rolls on to a white square, there is no such restriction. The cube should never roll on to a\nblack square.\n\nThroughout the travel, the cube can visit each of the chromatically colored squares only once,\nand any of the white squares arbitrarily many times. As already mentioned, the cube can never\nvisit any of the black squares. On visit to the final chromatically colored square, the cube\ndisappears. Somehow the order of visits to the chromatically colored squares is known to us\nbefore the travel starts.\n\nYour mission is to find the least number of steps for the cube to visit all the chromatically\ncolored squares in the given order.", "constraint": "", "input": "The input is a sequence of datasets. A dataset is formatted as follows:\n\n w d\n c_11 . . . c_w1\n . .\n . .\n . .\n c_1d . . . c_wd\n v_1v_2v_3v_4v_5v_6\n\nThe first line is a pair of positive integers w and d separated by a space. The next d lines are\nw-character-long strings c_11 . . . c_w1 , . . . , c_1d . . . c_wd with no spaces. Each character cij is one of\nthe letters r, g, b, c, m, y, w and k, which stands for red, green, blue, cyan, magenta, yellow,\nwhite and black respectively, or a sign #. Each of r, g, b, c, m, y and # occurs once and only once\nin a dataset. The last line is a six-character-long string v_1v_2v_3v_4v_5v_6 which is a permutation of\n“rgbcmy”.\n\nThe integers w and d denote the width (the length from the east end to the west end) and the\ndepth (the length from the north end to the south end) of a bed. The unit is the length of a\nside of a square. You can assume that neither w nor d is greater than 30.\n\nEach character c_ij shows the color of a square in the bed. The characters c_11 , c_w1 , c_1d and c_wd\ncorrespond to the north-west corner, the north-east corner, the south-west corner and the south-\neast corner of the bed respectively. If c_ij is a letter, it indicates the color of the corresponding\nsquare. If c_ij is a #, the corresponding square is colored white and is the initial position of the\ncube.\n\nThe string v_1v_2v_3v_4v_5v_6 shows the order of colors of squares to visit. The cube should visit the\nsquares colored v_1, v_2 , v_3 , v_4 , v_5 and v_6 in this order.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.", "output": "For each input dataset, output the least number of steps if there is a solution, or \"unreachable\"\nif there is no solution. In either case, print it in one line for each input dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 5\nkkkkkwwwww\nw#wwwrwwww\nwwwwbgwwww\nkwwmcwwwkk\nkkwywwwkkk\nrgbcmy\n10 5\nkkkkkkkkkk\nk#kkkkkkkk\nkwkkkkkwwk\nkcmyrgbwwk\nkwwwwwwwwk\ncmyrgb\n10 5\nkkkkkkkkkk\nk#kkkkkkkk\nkwkkkkkwkk\nkcmyrgbwwk\nkwwwwwwwwk\ncmyrgb\n0 0\n output: 9\n49\nunreachable"], "Pid": "p00869", "ProblemText": "Task Description: On a small planet named Bandai, a landing party of the starship Tadamigawa discovered colorful\ncubes traveling on flat areas of the planet surface, which the landing party named beds. A cube\nappears at a certain position on a bed, travels on the bed for a while, and then disappears. After\na longtime observation, a science officer Lt. Alyssa Ogawa of Tadamigawa found the rule how a\ncube travels on a bed.\n\nA bed is a rectangular area tiled with squares of the same size.\n One of the squares is colored red,\n\n one colored green,\n\n one colored blue,\n\n one colored cyan,\n\n one colored magenta,\n\n one colored yellow,\n\n one or more colored white, and\n\n all others, if any, colored black.\nInitially, a cube appears on one of the white squares. The cube 's faces are colored as follows.\n\n top red\n bottom cyan\n north green\n south magenta\n east blue\n west yellow\n\nThe cube can roll around a side of the current square at a step and thus rolls on to an adjacent\nsquare. When the cube rolls on to a chromatically colored (red, green, blue, cyan, magenta or\nyellow) square, the top face of the cube after the roll should be colored the same. When the\ncube rolls on to a white square, there is no such restriction. The cube should never roll on to a\nblack square.\n\nThroughout the travel, the cube can visit each of the chromatically colored squares only once,\nand any of the white squares arbitrarily many times. As already mentioned, the cube can never\nvisit any of the black squares. On visit to the final chromatically colored square, the cube\ndisappears. Somehow the order of visits to the chromatically colored squares is known to us\nbefore the travel starts.\n\nYour mission is to find the least number of steps for the cube to visit all the chromatically\ncolored squares in the given order.\nTask Input: The input is a sequence of datasets. A dataset is formatted as follows:\n\n w d\n c_11 . . . c_w1\n . .\n . .\n . .\n c_1d . . . c_wd\n v_1v_2v_3v_4v_5v_6\n\nThe first line is a pair of positive integers w and d separated by a space. The next d lines are\nw-character-long strings c_11 . . . c_w1 , . . . , c_1d . . . c_wd with no spaces. Each character cij is one of\nthe letters r, g, b, c, m, y, w and k, which stands for red, green, blue, cyan, magenta, yellow,\nwhite and black respectively, or a sign #. Each of r, g, b, c, m, y and # occurs once and only once\nin a dataset. The last line is a six-character-long string v_1v_2v_3v_4v_5v_6 which is a permutation of\n“rgbcmy”.\n\nThe integers w and d denote the width (the length from the east end to the west end) and the\ndepth (the length from the north end to the south end) of a bed. The unit is the length of a\nside of a square. You can assume that neither w nor d is greater than 30.\n\nEach character c_ij shows the color of a square in the bed. The characters c_11 , c_w1 , c_1d and c_wd\ncorrespond to the north-west corner, the north-east corner, the south-west corner and the south-\neast corner of the bed respectively. If c_ij is a letter, it indicates the color of the corresponding\nsquare. If c_ij is a #, the corresponding square is colored white and is the initial position of the\ncube.\n\nThe string v_1v_2v_3v_4v_5v_6 shows the order of colors of squares to visit. The cube should visit the\nsquares colored v_1, v_2 , v_3 , v_4 , v_5 and v_6 in this order.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\nTask Output: For each input dataset, output the least number of steps if there is a solution, or \"unreachable\"\nif there is no solution. In either case, print it in one line for each input dataset.\nTask Samples: input: 10 5\nkkkkkwwwww\nw#wwwrwwww\nwwwwbgwwww\nkwwmcwwwkk\nkkwywwwkkk\nrgbcmy\n10 5\nkkkkkkkkkk\nk#kkkkkkkk\nkwkkkkkwwk\nkcmyrgbwwk\nkwwwwwwwwk\ncmyrgb\n10 5\nkkkkkkkkkk\nk#kkkkkkkk\nkwkkkkkwkk\nkcmyrgbwwk\nkwwwwwwwwk\ncmyrgb\n0 0\n output: 9\n49\nunreachable\n\n" }, { "title": "Problem G: Search of Concatenated Strings", "content": "The amount of information on the World Wide Web is growing quite rapidly. In this information\nexplosion age, we must survive by accessing only the Web pages containing information relevant\nto our own needs. One of the key technologies for this purpose is keyword search. By using\nwell-known search engines, we can easily access those pages containing useful information about\nthe topic we want to know.\n\nThere are many variations in keyword search problems. If a single string is searched in a given\ntext, the problem is quite easy. If the pattern to be searched consists of multiple strings, or\nis given by some powerful notation such as regular expressions, the task requires elaborate\nalgorithms to accomplish efficiently.\n\nIn our problem, a number of strings (element strings) are given, but they are not directly\nsearched for. Concatenations of all the element strings in any order are the targets of the search\nhere.\n\nFor example, consider three element strings aa, b and ccc are given. In this case, the following\nsix concatenated strings are the targets of the search, i. e. they should be searched in the text.\n\naabccc\naacccb\nbaaccc\nbcccaa\ncccaab\ncccbaa\n\nThe text may contain several occurrences of these strings. You are requested to count the\nnumber of occurrences of these strings, or speaking more precisely, the number of positions of\noccurrences in the text.\n\nTwo or more concatenated strings may be identical. In such cases, it is necessary to consider\nsubtle aspects of the above problem statement. For example, if two element strings are x and\nxx, the string xxx is an occurrence of both the concatenation of x and xx and that of xx and x.\nSince the number of positions of occurrences should be counted, this case is counted as one, not\ntwo.\n\nTwo occurrences may overlap. For example, the string xxxx has occurrences of the concatenation\nxxx in two different positions. This case is counted as two.", "constraint": "", "input": "The input consists of a number of datasets, each giving a set of element strings and a text. The\nformat of a dataset is as follows.\n\nn m\ne_1\ne_2\n.\n.\n.\ne_n\nt_1\nt_2\n.\n.\n.\nt_m\n\nThe first line contains two integers separated by a space. n is the number of element strings. m\nis the number of lines used to represent the text. n is between 1 and 12, inclusive.\n\nEach of the following n lines gives an element string. The length (number of characters) of an\nelement string is between 1 and 20, inclusive.\nThe last m lines as a whole give the text. Since it is not desirable to have a very long line, the\ntext is separated into m lines by newlines, but these newlines should be ignored. They are not\nparts of the text. The length of each of these lines (not including the newline) is between 1 and\n100, inclusive. The length of the text is between 1 and 5000, inclusive.\n\nThe element strings and the text do not contain characters other than lowercase letters.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\n\nCAUTION! Although the sample input contains only small datasets, note that 12! * 5000 is far larger than 2^31 .", "output": "For each dataset in the input, one line containing the number of matched positions should be\noutput. An output line should not contain extra characters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\naa\nb\nccc\naabccczbaacccbaazaabbcccaa\n3 1\na\nb\nc\ncbbcbcbabaacabccaccbaacbccbcaaaccccbcbcbbcacbaacccaccbbcaacbbabbabaccc\n3 4\naaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n0 0\n output: 5\n12\n197"], "Pid": "p00870", "ProblemText": "Task Description: The amount of information on the World Wide Web is growing quite rapidly. In this information\nexplosion age, we must survive by accessing only the Web pages containing information relevant\nto our own needs. One of the key technologies for this purpose is keyword search. By using\nwell-known search engines, we can easily access those pages containing useful information about\nthe topic we want to know.\n\nThere are many variations in keyword search problems. If a single string is searched in a given\ntext, the problem is quite easy. If the pattern to be searched consists of multiple strings, or\nis given by some powerful notation such as regular expressions, the task requires elaborate\nalgorithms to accomplish efficiently.\n\nIn our problem, a number of strings (element strings) are given, but they are not directly\nsearched for. Concatenations of all the element strings in any order are the targets of the search\nhere.\n\nFor example, consider three element strings aa, b and ccc are given. In this case, the following\nsix concatenated strings are the targets of the search, i. e. they should be searched in the text.\n\naabccc\naacccb\nbaaccc\nbcccaa\ncccaab\ncccbaa\n\nThe text may contain several occurrences of these strings. You are requested to count the\nnumber of occurrences of these strings, or speaking more precisely, the number of positions of\noccurrences in the text.\n\nTwo or more concatenated strings may be identical. In such cases, it is necessary to consider\nsubtle aspects of the above problem statement. For example, if two element strings are x and\nxx, the string xxx is an occurrence of both the concatenation of x and xx and that of xx and x.\nSince the number of positions of occurrences should be counted, this case is counted as one, not\ntwo.\n\nTwo occurrences may overlap. For example, the string xxxx has occurrences of the concatenation\nxxx in two different positions. This case is counted as two.\nTask Input: The input consists of a number of datasets, each giving a set of element strings and a text. The\nformat of a dataset is as follows.\n\nn m\ne_1\ne_2\n.\n.\n.\ne_n\nt_1\nt_2\n.\n.\n.\nt_m\n\nThe first line contains two integers separated by a space. n is the number of element strings. m\nis the number of lines used to represent the text. n is between 1 and 12, inclusive.\n\nEach of the following n lines gives an element string. The length (number of characters) of an\nelement string is between 1 and 20, inclusive.\nThe last m lines as a whole give the text. Since it is not desirable to have a very long line, the\ntext is separated into m lines by newlines, but these newlines should be ignored. They are not\nparts of the text. The length of each of these lines (not including the newline) is between 1 and\n100, inclusive. The length of the text is between 1 and 5000, inclusive.\n\nThe element strings and the text do not contain characters other than lowercase letters.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\n\nCAUTION! Although the sample input contains only small datasets, note that 12! * 5000 is far larger than 2^31 .\nTask Output: For each dataset in the input, one line containing the number of matched positions should be\noutput. An output line should not contain extra characters.\nTask Samples: input: 3 1\naa\nb\nccc\naabccczbaacccbaazaabbcccaa\n3 1\na\nb\nc\ncbbcbcbabaacabccaccbaacbccbcaaaccccbcbcbbcacbaacccaccbbcaacbbabbabaccc\n3 4\naaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n0 0\n output: 5\n12\n197\n\n" }, { "title": "Problem H: Top Spinning", "content": "Spinning tops are one of the most popular and the most traditional toys. Not only spinning\nthem, but also making one 's own is a popular enjoyment.\n\nOne of the easiest way to make a top is to cut out a certain shape from a cardboard and pierce\nan axis stick through its center of mass. Professionally made tops usually have three dimensional\nshapes, but in this problem we consider only two dimensional ones.\n\nUsually, tops have rotationally symmetric shapes, such as a circle, a rectangle (with 2-fold\nrotational symmetry) or a regular triangle (with 3-fold symmetry). Although such symmetries\nare useful in determining their centers of mass, they are not definitely required; an asymmetric\ntop also spins quite well if its axis is properly pierced at the center of mass.\n\nWhen a shape of a top is given as a path to cut it out from a cardboard of uniform thickness,\nyour task is to find its center of mass to make it spin well. Also, you have to determine whether\nthe center of mass is on the part of the cardboard cut out. If not, you cannot pierce the axis\nstick, of course.\n hints:\nAn important nature of mass centers is that, when an object O can be decomposed into parts\nO_1 , . . . , O_n with masses M_1 , . . . , M_n , the center of mass of O can be computed by:\n\nwhere G_k is the vector pointing the center of mass of O_k.\n\nA circular segment with its radius r and angle θ (in radian) has its arc length s = rθ and its\nchord length c = r√(2 - 2cosθ). Its area size is A = r^2(θ - sinθ)/2 and its center of mass G is\ny = 2r^3sin^3(θ/2)/(3A) distant from the circle center.\nFigure 2: Circular segment and its center of mass\nFigure 3: The first sample top", "constraint": "", "input": "The input consists of multiple datasets, each of which describes a counterclockwise path on a\ncardboard to cut out a top. A path is indicated by a sequence of command lines, each of which\nspecifies a line segment or an arc.\n\nIn the description of commands below, the current position is the position to start the next cut,\nif any. After executing the cut specified by a command, the current position is moved to the\nend position of the cut made.\n\nThe commands given are one of those listed below. The command name starts from the first\ncolumn of a line and the command and its arguments are separated by a space. All the command\narguments are integers.\n\nstart x y\n\nSpecifies the start position of a path. This command itself does not specify any cutting;\nit only sets the current position to be (x, y).\n\nline x y\n\n Specifies a linear cut along a straight line from the current position to the position (x, y),\n which is not identical to the current position.\n\narc x y r\n\n Specifies a round cut along a circular arc. The arc starts from the current position and\n ends at (x, y), which is not identical to the current position. The arc has a radius of |r|.\n When r is negative, the center of the circle is to the left side of the direction of this round\n cut; when it is positive, it is to the right side (Figure 1). The absolute value of r is greater\n than the half distance of the two ends of the arc. Among two arcs connecting the start\n and the end positions with the specified radius, the arc specified is one with its central\n angle less than 180 degrees.\n\nclose\n\n Closes a path by making a linear cut to the initial start position and terminates a dataset.\n If the current position is already at the start position, this command simply indicates the\n end of a dataset.\n\nThe figure below gives an example of a command sequence and its corresponding path. Note\nthat, in this case, the given radius -r is negative and thus the center of the arc is to the left of\nthe arc. The arc command should be interpreted as shown in this figure and, not the other way\naround on the same circle.\nFigure 1: A partial command sequence and the path specified so far\n\nA dataset starts with a start command and ends with a close command.\n\nThe end of the input is specified by a line with a command end.\n\nThere are at most 100 commands in a dataset and at most 100 datasets are in the input.\nAbsolute values of all the coordinates and radii are less than or equal to 100.\n\nYou may assume that the path does not cross nor touch itself. You may also assume that paths\nwill never expand beyond edges of the cardboard, or, in other words, the cardboard is virtually\ninfinitely large.", "output": "For each of the dataset, output a line containing x- and y-coordinates of the center of mass of\nthe top cut out by the path specified, and then a character ‘+ ' or ‘- ' indicating whether this\ncenter is on the top or not, respectively. Two coordinates should be in decimal fractions. There\nshould be a space between two coordinates and between the y-coordinate and the character ‘+ '\nor ‘- '. No other characters should be output. The coordinates may have errors less than 10^-3 .\nYou may assume that the center of mass is at least 10^-3 distant from the path.", "content_img": true, "lang": "en", "error": false, "samples": ["input: start 0 0\narc 2 2 -2\nline 2 5\narc 0 3 -2\nclose\nstart -1 1\nline 2 1\nline 2 2\nline -2 2\narc -3 1 -1\nline -3 -2\narc -2 -3 -1\nline 2 -3\nline 2 -2\nline -1 -2\nline -1 -1\narc -1 0 2\nclose\nstart 0 0\nline 3 0\nline 5 -1\narc 4 -2 -1\nline 6 -2\nline 6 1\nline 7 3\narc 8 2 -1\nline 8 4\nline 5 4\nline 3 5\narc 4 6 -1\nline 2 6\nline 2 3\nline 1 1\narc 0 2 -1\nclose\nend\n output: 1.00000 2.50000 +\n-1.01522 -0.50000 -\n4.00000 2.00000 +"], "Pid": "p00871", "ProblemText": "Task Description: Spinning tops are one of the most popular and the most traditional toys. Not only spinning\nthem, but also making one 's own is a popular enjoyment.\n\nOne of the easiest way to make a top is to cut out a certain shape from a cardboard and pierce\nan axis stick through its center of mass. Professionally made tops usually have three dimensional\nshapes, but in this problem we consider only two dimensional ones.\n\nUsually, tops have rotationally symmetric shapes, such as a circle, a rectangle (with 2-fold\nrotational symmetry) or a regular triangle (with 3-fold symmetry). Although such symmetries\nare useful in determining their centers of mass, they are not definitely required; an asymmetric\ntop also spins quite well if its axis is properly pierced at the center of mass.\n\nWhen a shape of a top is given as a path to cut it out from a cardboard of uniform thickness,\nyour task is to find its center of mass to make it spin well. Also, you have to determine whether\nthe center of mass is on the part of the cardboard cut out. If not, you cannot pierce the axis\nstick, of course.\n hints:\nAn important nature of mass centers is that, when an object O can be decomposed into parts\nO_1 , . . . , O_n with masses M_1 , . . . , M_n , the center of mass of O can be computed by:\n\nwhere G_k is the vector pointing the center of mass of O_k.\n\nA circular segment with its radius r and angle θ (in radian) has its arc length s = rθ and its\nchord length c = r√(2 - 2cosθ). Its area size is A = r^2(θ - sinθ)/2 and its center of mass G is\ny = 2r^3sin^3(θ/2)/(3A) distant from the circle center.\nFigure 2: Circular segment and its center of mass\nFigure 3: The first sample top\nTask Input: The input consists of multiple datasets, each of which describes a counterclockwise path on a\ncardboard to cut out a top. A path is indicated by a sequence of command lines, each of which\nspecifies a line segment or an arc.\n\nIn the description of commands below, the current position is the position to start the next cut,\nif any. After executing the cut specified by a command, the current position is moved to the\nend position of the cut made.\n\nThe commands given are one of those listed below. The command name starts from the first\ncolumn of a line and the command and its arguments are separated by a space. All the command\narguments are integers.\n\nstart x y\n\nSpecifies the start position of a path. This command itself does not specify any cutting;\nit only sets the current position to be (x, y).\n\nline x y\n\n Specifies a linear cut along a straight line from the current position to the position (x, y),\n which is not identical to the current position.\n\narc x y r\n\n Specifies a round cut along a circular arc. The arc starts from the current position and\n ends at (x, y), which is not identical to the current position. The arc has a radius of |r|.\n When r is negative, the center of the circle is to the left side of the direction of this round\n cut; when it is positive, it is to the right side (Figure 1). The absolute value of r is greater\n than the half distance of the two ends of the arc. Among two arcs connecting the start\n and the end positions with the specified radius, the arc specified is one with its central\n angle less than 180 degrees.\n\nclose\n\n Closes a path by making a linear cut to the initial start position and terminates a dataset.\n If the current position is already at the start position, this command simply indicates the\n end of a dataset.\n\nThe figure below gives an example of a command sequence and its corresponding path. Note\nthat, in this case, the given radius -r is negative and thus the center of the arc is to the left of\nthe arc. The arc command should be interpreted as shown in this figure and, not the other way\naround on the same circle.\nFigure 1: A partial command sequence and the path specified so far\n\nA dataset starts with a start command and ends with a close command.\n\nThe end of the input is specified by a line with a command end.\n\nThere are at most 100 commands in a dataset and at most 100 datasets are in the input.\nAbsolute values of all the coordinates and radii are less than or equal to 100.\n\nYou may assume that the path does not cross nor touch itself. You may also assume that paths\nwill never expand beyond edges of the cardboard, or, in other words, the cardboard is virtually\ninfinitely large.\nTask Output: For each of the dataset, output a line containing x- and y-coordinates of the center of mass of\nthe top cut out by the path specified, and then a character ‘+ ' or ‘- ' indicating whether this\ncenter is on the top or not, respectively. Two coordinates should be in decimal fractions. There\nshould be a space between two coordinates and between the y-coordinate and the character ‘+ '\nor ‘- '. No other characters should be output. The coordinates may have errors less than 10^-3 .\nYou may assume that the center of mass is at least 10^-3 distant from the path.\nTask Samples: input: start 0 0\narc 2 2 -2\nline 2 5\narc 0 3 -2\nclose\nstart -1 1\nline 2 1\nline 2 2\nline -2 2\narc -3 1 -1\nline -3 -2\narc -2 -3 -1\nline 2 -3\nline 2 -2\nline -1 -2\nline -1 -1\narc -1 0 2\nclose\nstart 0 0\nline 3 0\nline 5 -1\narc 4 -2 -1\nline 6 -2\nline 6 1\nline 7 3\narc 8 2 -1\nline 8 4\nline 5 4\nline 3 5\narc 4 6 -1\nline 2 6\nline 2 3\nline 1 1\narc 0 2 -1\nclose\nend\n output: 1.00000 2.50000 +\n-1.01522 -0.50000 -\n4.00000 2.00000 +\n\n" }, { "title": "Problem I: Common Polynomial", "content": "Math teacher Mr. Matsudaira is teaching expansion and factoring of polynomials to his students.\nLast week he instructed the students to write two polynomials (with a single variable x), and\nto report GCM (greatest common measure) of them as a homework, but he found it boring to\ncheck their answers manually. So you are asked to write a program to check the answers.\n\nHereinafter, only those polynomials with integral coefficients, called integral polynomials, are\nconsidered.\n\nWhen two integral polynomials A and B are given, an integral polynomial C is a common factor\nof A and B if there are some integral polynomials X and Y such that A = CX and B = CY.\n\nGCM of two integral polynomials is a common factor which has the highest degree (for x, here);\nyou have to write a program which calculates the GCM of two polynomials.\n\nIt is known that GCM of given two polynomials is unique when constant multiplication factor is\nignored. That is, when C and D are both GCM of some two polynomials A and B, p * C = q * D\nfor some nonzero integers p and q.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset constitutes a pair of input lines, each\nrepresenting a polynomial as an expression defined below.\n\n A primary is a variable x, a sequence of digits 0 - 9, or an expression enclosed within ( . . . ). Examples: x, 99, (x+1)\n\n A factor is a primary by itself or a primary followed by an exponent. An exponent consists\n of a symbol ^ followed by a sequence of digits 0 - 9. Examples: x^05,1^15, (x+1)^3\n\n A term consists of one or more adjoining factors. Examples: 4x, (x+1)(x-2), 3(x+1)^2\n\n An expression is one or more terms connected by either + or -. Additionally, the first\n term of an expression may optionally be preceded with a minus sign -. Examples: -x+1,3(x+1)^2-x(x-1)^2\nInteger constants, exponents, multiplications (adjoining), additions (+) and subtractions/negations\n(-) have their ordinary meanings. A sequence of digits is always interpreted as an integer con-\nstant. For example, 99 means 99, not 9 * 9.\nAny subexpressions of the input, when fully expanded normalized, have coefficients less than\n100 and degrees of x less than 10. Digit sequences in exponents represent non-zero values.\n\nAll the datasets are designed so that a standard algorithm with 32-bit two 's complement integers\ncan solve the problem without overflows.\n\nThe end of the input is indicated by a line containing a period.", "output": "For each of the dataset, output GCM polynomial expression in a line, in the format below.\n\n c_0x^p_0 ± c_1x^p_1 . . . ± c_nx^p_n\n\nWhere c_i and p_i (i = 0, . . . , n) are positive integers with p_0 > p_1 > . . . > p_n, and the greatest\ncommon divisor of {c_i | i = 0, . . . , n} is 1.\n\nAdditionally:\n\n When c_i is equal to 1, it should be omitted unless corresponding p_i is 0,\n\n x^0 should be omitted as a whole, and\n\n x^1 should be written as x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: -(x^3-3x^2+3x-1)\n(x-1)^2\nx^2+10x+25\nx^2+6x+5\nx^3+1\nx-1\n.\n output: x^2-2x+1\nx+5\n1"], "Pid": "p00872", "ProblemText": "Task Description: Math teacher Mr. Matsudaira is teaching expansion and factoring of polynomials to his students.\nLast week he instructed the students to write two polynomials (with a single variable x), and\nto report GCM (greatest common measure) of them as a homework, but he found it boring to\ncheck their answers manually. So you are asked to write a program to check the answers.\n\nHereinafter, only those polynomials with integral coefficients, called integral polynomials, are\nconsidered.\n\nWhen two integral polynomials A and B are given, an integral polynomial C is a common factor\nof A and B if there are some integral polynomials X and Y such that A = CX and B = CY.\n\nGCM of two integral polynomials is a common factor which has the highest degree (for x, here);\nyou have to write a program which calculates the GCM of two polynomials.\n\nIt is known that GCM of given two polynomials is unique when constant multiplication factor is\nignored. That is, when C and D are both GCM of some two polynomials A and B, p * C = q * D\nfor some nonzero integers p and q.\nTask Input: The input consists of multiple datasets. Each dataset constitutes a pair of input lines, each\nrepresenting a polynomial as an expression defined below.\n\n A primary is a variable x, a sequence of digits 0 - 9, or an expression enclosed within ( . . . ). Examples: x, 99, (x+1)\n\n A factor is a primary by itself or a primary followed by an exponent. An exponent consists\n of a symbol ^ followed by a sequence of digits 0 - 9. Examples: x^05,1^15, (x+1)^3\n\n A term consists of one or more adjoining factors. Examples: 4x, (x+1)(x-2), 3(x+1)^2\n\n An expression is one or more terms connected by either + or -. Additionally, the first\n term of an expression may optionally be preceded with a minus sign -. Examples: -x+1,3(x+1)^2-x(x-1)^2\nInteger constants, exponents, multiplications (adjoining), additions (+) and subtractions/negations\n(-) have their ordinary meanings. A sequence of digits is always interpreted as an integer con-\nstant. For example, 99 means 99, not 9 * 9.\nAny subexpressions of the input, when fully expanded normalized, have coefficients less than\n100 and degrees of x less than 10. Digit sequences in exponents represent non-zero values.\n\nAll the datasets are designed so that a standard algorithm with 32-bit two 's complement integers\ncan solve the problem without overflows.\n\nThe end of the input is indicated by a line containing a period.\nTask Output: For each of the dataset, output GCM polynomial expression in a line, in the format below.\n\n c_0x^p_0 ± c_1x^p_1 . . . ± c_nx^p_n\n\nWhere c_i and p_i (i = 0, . . . , n) are positive integers with p_0 > p_1 > . . . > p_n, and the greatest\ncommon divisor of {c_i | i = 0, . . . , n} is 1.\n\nAdditionally:\n\n When c_i is equal to 1, it should be omitted unless corresponding p_i is 0,\n\n x^0 should be omitted as a whole, and\n\n x^1 should be written as x.\nTask Samples: input: -(x^3-3x^2+3x-1)\n(x-1)^2\nx^2+10x+25\nx^2+6x+5\nx^3+1\nx-1\n.\n output: x^2-2x+1\nx+5\n1\n\n" }, { "title": "Problem J: Zigzag", "content": "Given several points on a plane, let 's try to solve a puzzle connecting them with a zigzag line.\nThe puzzle is to find the zigzag line that passes through all the given points with the minimum\nnumber of turns. Moreover, when there are several zigzag lines with the minimum number of\nturns, the shortest one among them should be found.\n\nFor example, consider nine points given in Figure 1.\nFigure 1: Given nine points\n\nA zigzag line is composed of several straight line segments. Here, the rule requests that each\nline segment should pass through two or more given points.\n\nA zigzag line may turn at some of the given points or anywhere else. There may be some given\npoints passed more than once.\nFigure 2: Zigzag lines with three turning points.\n\nTwo zigzag lines with three turning points are depicted in Figure 2 (a) and (b) for the same\nset of given points shown in Figure 1. The length of the zigzag line in Figure 2 (a) is shorter than that in Figure 2 (b). In fact, the length of the zigzag line in Figure 2 (a) is the shortest\nso that it is the solution for the nine points given in Figure 1.\n\nAnother zigzag line with four turning points is depicted in Figure 3. Its length is shorter than\nthose in Figure 2, however, the number of turning points is greater than those in Figure 2,\nand thus, it is not the solution.\nFigure 3: Zigzag line with four turning points.\n\nThere are two zigzag lines that passes another set of given points depicted in Figure 4 (a) and\n(b).\n\nBoth have the same number of turning points, and the line in (a) is longer than that in (b).\nHowever, the solution is (a), because one of the segments of the zigzag line in (b) passes only\none given point, violating the rule.\nFigure 4: Zigzag line with two turning points (a), and not a zigzag line concerned (b).\n\nYour job is to write a program that solves this puzzle.", "constraint": "", "input": "The input consists of multiple datasets, followed by a line containing one zero. Each dataset\nhas the following format.\n\nn\nx_1 y_1\n .\n .\n .\nx_n y_n\n\nEvery input item in a dataset is a non-negative integer. Items in a line are separated by a single\nspace.\n\nn is the number of the given points. x_k and y_k (k = 1, . . . , n) indicate the position of the k-th\npoint. The order of the points is meaningless. You can assume that 2 <= n <= 10,0 <= x_k <= 10,\nand 0 <= y_k <= 10.", "output": "For each dataset, the minimum number of turning points and the length of the shortest zigzag\nline with that number of turning points should be printed, separated by a space in a line. The\nlength should be in a decimal fraction with an error less than 0.0001 (= 1.0 * 10^-4 ).\n\nYou may assume that the minimum number of turning points is at most four, that is, the number\nof line segments is at most five.\n\nThe example solutions for the first four datasets in the sample input are depicted in Figure 5\nand 6.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n0 0\n10 9\n4\n0 0\n3 1\n0 3\n3 3\n10\n2 2\n4 2\n6 2\n2 4\n4 4\n6 4\n2 6\n4 6\n6 6\n3 3\n10\n0 0\n2 0\n4 0\n0 2\n2 2\n4 2\n0 4\n2 4\n4 4\n6 8\n9\n0 0\n1 0\n3 0\n0 1\n1 1\n3 1\n0 2\n1 2\n2 2\n10\n0 0\n1 0\n0 1\n1 1\n9 9\n9 10\n10 9\n10 10\n0 2\n10 8\n10\n0 0\n0 10\n2 0\n2 1\n2 7\n2 10\n5 1\n6 7\n9 2\n10 9\n0\n output: 0 13.45362405\n1 18.48683298\n3 24.14213562\n4 24.94813673\n3 12.24264069\n3 60.78289622\n3 502.7804353\n\nFigure 5: Example solutions for the first and the second datasets in the sample inputs.\n\nFigure 6: Example solutions for the third and the fourth datasets in the sample inputs."], "Pid": "p00873", "ProblemText": "Task Description: Given several points on a plane, let 's try to solve a puzzle connecting them with a zigzag line.\nThe puzzle is to find the zigzag line that passes through all the given points with the minimum\nnumber of turns. Moreover, when there are several zigzag lines with the minimum number of\nturns, the shortest one among them should be found.\n\nFor example, consider nine points given in Figure 1.\nFigure 1: Given nine points\n\nA zigzag line is composed of several straight line segments. Here, the rule requests that each\nline segment should pass through two or more given points.\n\nA zigzag line may turn at some of the given points or anywhere else. There may be some given\npoints passed more than once.\nFigure 2: Zigzag lines with three turning points.\n\nTwo zigzag lines with three turning points are depicted in Figure 2 (a) and (b) for the same\nset of given points shown in Figure 1. The length of the zigzag line in Figure 2 (a) is shorter than that in Figure 2 (b). In fact, the length of the zigzag line in Figure 2 (a) is the shortest\nso that it is the solution for the nine points given in Figure 1.\n\nAnother zigzag line with four turning points is depicted in Figure 3. Its length is shorter than\nthose in Figure 2, however, the number of turning points is greater than those in Figure 2,\nand thus, it is not the solution.\nFigure 3: Zigzag line with four turning points.\n\nThere are two zigzag lines that passes another set of given points depicted in Figure 4 (a) and\n(b).\n\nBoth have the same number of turning points, and the line in (a) is longer than that in (b).\nHowever, the solution is (a), because one of the segments of the zigzag line in (b) passes only\none given point, violating the rule.\nFigure 4: Zigzag line with two turning points (a), and not a zigzag line concerned (b).\n\nYour job is to write a program that solves this puzzle.\nTask Input: The input consists of multiple datasets, followed by a line containing one zero. Each dataset\nhas the following format.\n\nn\nx_1 y_1\n .\n .\n .\nx_n y_n\n\nEvery input item in a dataset is a non-negative integer. Items in a line are separated by a single\nspace.\n\nn is the number of the given points. x_k and y_k (k = 1, . . . , n) indicate the position of the k-th\npoint. The order of the points is meaningless. You can assume that 2 <= n <= 10,0 <= x_k <= 10,\nand 0 <= y_k <= 10.\nTask Output: For each dataset, the minimum number of turning points and the length of the shortest zigzag\nline with that number of turning points should be printed, separated by a space in a line. The\nlength should be in a decimal fraction with an error less than 0.0001 (= 1.0 * 10^-4 ).\n\nYou may assume that the minimum number of turning points is at most four, that is, the number\nof line segments is at most five.\n\nThe example solutions for the first four datasets in the sample input are depicted in Figure 5\nand 6.\nTask Samples: input: 2\n0 0\n10 9\n4\n0 0\n3 1\n0 3\n3 3\n10\n2 2\n4 2\n6 2\n2 4\n4 4\n6 4\n2 6\n4 6\n6 6\n3 3\n10\n0 0\n2 0\n4 0\n0 2\n2 2\n4 2\n0 4\n2 4\n4 4\n6 8\n9\n0 0\n1 0\n3 0\n0 1\n1 1\n3 1\n0 2\n1 2\n2 2\n10\n0 0\n1 0\n0 1\n1 1\n9 9\n9 10\n10 9\n10 10\n0 2\n10 8\n10\n0 0\n0 10\n2 0\n2 1\n2 7\n2 10\n5 1\n6 7\n9 2\n10 9\n0\n output: 0 13.45362405\n1 18.48683298\n3 24.14213562\n4 24.94813673\n3 12.24264069\n3 60.78289622\n3 502.7804353\n\nFigure 5: Example solutions for the first and the second datasets in the sample inputs.\n\nFigure 6: Example solutions for the third and the fourth datasets in the sample inputs.\n\n" }, { "title": "Problem A: Cubist Artwork", "content": "International Center for Picassonian Cubism is a Spanish national museum of cubist artworks,\ndedicated to Pablo Picasso. The center held a competition for an artwork that will be displayed\nin front of the facade of the museum building. The artwork is a collection of cubes that are\npiled up on the ground and is intended to amuse visitors, who will be curious how the shape of\nthe collection of cubes changes when it is seen from the front and the sides.\n\nThe artwork is a collection of cubes with edges of one foot long and is built on a flat ground\nthat is divided into a grid of one foot by one foot squares. Due to some technical reasons, cubes\nof the artwork must be either put on the ground, fitting into a unit square in the grid, or put\non another cube in the way that the bottom face of the upper cube exactly meets the top face\nof the lower cube. No other way of putting cubes is possible.\n\nYou are a member of the judging committee responsible for selecting one out of a plenty of\nartwork proposals submitted to the competition. The decision is made primarily based on\nartistic quality but the cost for installing the artwork is another important factor. Your task is\nto investigate the installation cost for each proposal. The cost is proportional to the number of\ncubes, so you have to figure out the minimum number of cubes needed for installation.\n\nEach design proposal of an artwork consists of the front view and the side view (the view seen\nfrom the right-hand side), as shown in Figure 1.\nFigure 1: An example of an artwork proposal\n\nThe front view (resp. , the side view) indicates the maximum heights of piles of cubes for each\ncolumn line (resp. , row line) of the grid.\n\nThere are several ways to install this proposal of artwork, such as the following figures.\n\nIn these figures, the dotted lines on the ground indicate the grid lines. The left figure makes use\nof 16 cubes, which is not optimal. That is, the artwork can be installed with a fewer number\nof cubes. Actually, the right one is optimal and only uses 13 cubes. Note that, a single pile of\nheight three in the right figure plays the roles of two such piles in the left one.\n\nNotice that swapping columns of cubes does not change the side view. Similarly, swapping\nrows does not change the front view. Thus, such swaps do not change the costs of building the\nartworks.\n\nFor example, consider the artwork proposal given in Figure 2.\nFigure 2: Another example of artwork proposal\n\nAn optimal installation of this proposal of artwork can be achieved with 13 cubes, as shown\nin the following figure, which can be obtained by exchanging the rightmost two columns of the\noptimal installation of the artwork of Figure 1.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by a line containing two\nzeros separated by a space. Each dataset is formatted as follows.\n\nw d\nh_1 h_2 . . . h_w\nh'_1 h'_2 . . . h'_d\n\nThe integers w and d separated by a space are the numbers of columns and rows of the grid,\nrespectively. You may assume 1 <= w <= 10 and 1 <= d <= 10. The integers separated by a space\nin the second and third lines specify the shape of the artwork. The integers h_i (1 <= h_i <= 20,\n1 <= i <= w) in the second line give the front view, i. e. , the maximum heights of cubes per each\ncolumn line, ordered from left to right (seen from the front). The integers h_i (1 <= h_i <= 20,\n1 <= i <= d) in the third line give the side view, i. e. , the maximum heights of cubes per each row\nline, ordered from left to right (seen from the right-hand side).", "output": "For each dataset, output a line containing the minimum number of cubes. The output should\nnot contain any other extra characters.\n\nYou can assume that, for each dataset, there is at least one way to install the artwork.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 5\n1 2 3 4 5\n1 2 3 4 5\n5 5\n2 5 4 1 3\n4 1 5 3 2\n5 5\n1 2 3 4 5\n3 3 3 4 5\n3 3\n7 7 7\n7 7 7\n3 3\n4 4 4\n4 3 4\n4 3\n4 2 2 4\n4 2 1\n4 4\n2 8 8 8\n2 3 8 3\n10 10\n9 9 9 9 9 9 9 9 9 9\n9 9 9 9 9 9 9 9 9 9\n10 9\n20 1 20 20 20 20 20 18 20 20\n20 20 20 20 7 20 20 20 20\n0 0\n output: 15\n15\n21\n21\n15\n13\n32\n90\n186"], "Pid": "p00874", "ProblemText": "Task Description: International Center for Picassonian Cubism is a Spanish national museum of cubist artworks,\ndedicated to Pablo Picasso. The center held a competition for an artwork that will be displayed\nin front of the facade of the museum building. The artwork is a collection of cubes that are\npiled up on the ground and is intended to amuse visitors, who will be curious how the shape of\nthe collection of cubes changes when it is seen from the front and the sides.\n\nThe artwork is a collection of cubes with edges of one foot long and is built on a flat ground\nthat is divided into a grid of one foot by one foot squares. Due to some technical reasons, cubes\nof the artwork must be either put on the ground, fitting into a unit square in the grid, or put\non another cube in the way that the bottom face of the upper cube exactly meets the top face\nof the lower cube. No other way of putting cubes is possible.\n\nYou are a member of the judging committee responsible for selecting one out of a plenty of\nartwork proposals submitted to the competition. The decision is made primarily based on\nartistic quality but the cost for installing the artwork is another important factor. Your task is\nto investigate the installation cost for each proposal. The cost is proportional to the number of\ncubes, so you have to figure out the minimum number of cubes needed for installation.\n\nEach design proposal of an artwork consists of the front view and the side view (the view seen\nfrom the right-hand side), as shown in Figure 1.\nFigure 1: An example of an artwork proposal\n\nThe front view (resp. , the side view) indicates the maximum heights of piles of cubes for each\ncolumn line (resp. , row line) of the grid.\n\nThere are several ways to install this proposal of artwork, such as the following figures.\n\nIn these figures, the dotted lines on the ground indicate the grid lines. The left figure makes use\nof 16 cubes, which is not optimal. That is, the artwork can be installed with a fewer number\nof cubes. Actually, the right one is optimal and only uses 13 cubes. Note that, a single pile of\nheight three in the right figure plays the roles of two such piles in the left one.\n\nNotice that swapping columns of cubes does not change the side view. Similarly, swapping\nrows does not change the front view. Thus, such swaps do not change the costs of building the\nartworks.\n\nFor example, consider the artwork proposal given in Figure 2.\nFigure 2: Another example of artwork proposal\n\nAn optimal installation of this proposal of artwork can be achieved with 13 cubes, as shown\nin the following figure, which can be obtained by exchanging the rightmost two columns of the\noptimal installation of the artwork of Figure 1.\nTask Input: The input is a sequence of datasets. The end of the input is indicated by a line containing two\nzeros separated by a space. Each dataset is formatted as follows.\n\nw d\nh_1 h_2 . . . h_w\nh'_1 h'_2 . . . h'_d\n\nThe integers w and d separated by a space are the numbers of columns and rows of the grid,\nrespectively. You may assume 1 <= w <= 10 and 1 <= d <= 10. The integers separated by a space\nin the second and third lines specify the shape of the artwork. The integers h_i (1 <= h_i <= 20,\n1 <= i <= w) in the second line give the front view, i. e. , the maximum heights of cubes per each\ncolumn line, ordered from left to right (seen from the front). The integers h_i (1 <= h_i <= 20,\n1 <= i <= d) in the third line give the side view, i. e. , the maximum heights of cubes per each row\nline, ordered from left to right (seen from the right-hand side).\nTask Output: For each dataset, output a line containing the minimum number of cubes. The output should\nnot contain any other extra characters.\n\nYou can assume that, for each dataset, there is at least one way to install the artwork.\nTask Samples: input: 5 5\n1 2 3 4 5\n1 2 3 4 5\n5 5\n2 5 4 1 3\n4 1 5 3 2\n5 5\n1 2 3 4 5\n3 3 3 4 5\n3 3\n7 7 7\n7 7 7\n3 3\n4 4 4\n4 3 4\n4 3\n4 2 2 4\n4 2 1\n4 4\n2 8 8 8\n2 3 8 3\n10 10\n9 9 9 9 9 9 9 9 9 9\n9 9 9 9 9 9 9 9 9 9\n10 9\n20 1 20 20 20 20 20 18 20 20\n20 20 20 20 7 20 20 20 20\n0 0\n output: 15\n15\n21\n21\n15\n13\n32\n90\n186\n\n" }, { "title": "Problem B: Repeated Substitution with Sed", "content": "Do you know \"sed, \" a tool provided with Unix? Its most popular use is to substitute every\noccurrence of a string contained in the input string (actually each input line) with another\nstring β. More precisely, it proceeds as follows.\n\n Within the input string, every non-overlapping (but possibly adjacent) occurrences of α are\n marked. If there is more than one possibility for non-overlapping matching, the leftmost\n one is chosen.\n\n Each of the marked occurrences is substituted with β to obtain the output string; other\n parts of the input string remain intact.\nFor example, when α is \"aa\" and β is \"bca\", an input string \"aaxaaa\" will produce \"bcaxbcaa\",\nbut not \"aaxbcaa\" nor \"bcaxabca\". Further application of the same substitution to the string\n\"bcaxbcaa\" will result in \"bcaxbcbca\", but this is another substitution, which is counted as the\nsecond one.\n\nIn this problem, a set of substitution pairs (α_i, β_i) (i = 1,2, . . . , n), an initial string γ, and a\nfinal string δ are given, and you must investigate how to produce δ from γ with a minimum\nnumber of substitutions. A single substitution (α_i, β_i) here means simultaneously substituting\nall the non-overlapping occurrences of α_i, in the sense described above, with β_i.\n\nYou may use a specific substitution (α_i, β_i ) multiple times, including zero times.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn\nα_1 β_1\nα_2 β_2\n . \n . \n . \nα_n β_n\nγ\nδ\n\nn is a positive integer indicating the number of pairs. α_i and β_i are separated by a single space.\nYou may assume that 1 <= |α_i| < |β_i| <= 10 for any i (|s| means the length of the string s),\n\nα_i ! = α_j for any i ! = j, n <= 10 and 1 <= |γ| < |δ| <= 10. All the strings consist solely of lowercase\nletters. The end of the input is indicated by a line containing a single zero.", "output": "For each dataset, output the minimum number of substitutions to obtain δ from γ. If δ cannot\nbe produced from γ with the given set of substitutions, output -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\na bb\nb aa\na\nbbbbbbbb\n1\na aa\na\naaaaa\n3\nab aab\nabc aadc\nad dee\nabc\ndeeeeeeeec\n10\na abc\nb bai\nc acf\nd bed\ne abh\nf fag\ng abe\nh bag\ni aaj\nj bbb\na\nabacfaabe\n0\n output: 3\n-1\n7\n4"], "Pid": "p00875", "ProblemText": "Task Description: Do you know \"sed, \" a tool provided with Unix? Its most popular use is to substitute every\noccurrence of a string contained in the input string (actually each input line) with another\nstring β. More precisely, it proceeds as follows.\n\n Within the input string, every non-overlapping (but possibly adjacent) occurrences of α are\n marked. If there is more than one possibility for non-overlapping matching, the leftmost\n one is chosen.\n\n Each of the marked occurrences is substituted with β to obtain the output string; other\n parts of the input string remain intact.\nFor example, when α is \"aa\" and β is \"bca\", an input string \"aaxaaa\" will produce \"bcaxbcaa\",\nbut not \"aaxbcaa\" nor \"bcaxabca\". Further application of the same substitution to the string\n\"bcaxbcaa\" will result in \"bcaxbcbca\", but this is another substitution, which is counted as the\nsecond one.\n\nIn this problem, a set of substitution pairs (α_i, β_i) (i = 1,2, . . . , n), an initial string γ, and a\nfinal string δ are given, and you must investigate how to produce δ from γ with a minimum\nnumber of substitutions. A single substitution (α_i, β_i) here means simultaneously substituting\nall the non-overlapping occurrences of α_i, in the sense described above, with β_i.\n\nYou may use a specific substitution (α_i, β_i ) multiple times, including zero times.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn\nα_1 β_1\nα_2 β_2\n . \n . \n . \nα_n β_n\nγ\nδ\n\nn is a positive integer indicating the number of pairs. α_i and β_i are separated by a single space.\nYou may assume that 1 <= |α_i| < |β_i| <= 10 for any i (|s| means the length of the string s),\n\nα_i ! = α_j for any i ! = j, n <= 10 and 1 <= |γ| < |δ| <= 10. All the strings consist solely of lowercase\nletters. The end of the input is indicated by a line containing a single zero.\nTask Output: For each dataset, output the minimum number of substitutions to obtain δ from γ. If δ cannot\nbe produced from γ with the given set of substitutions, output -1.\nTask Samples: input: 2\na bb\nb aa\na\nbbbbbbbb\n1\na aa\na\naaaaa\n3\nab aab\nabc aadc\nad dee\nabc\ndeeeeeeeec\n10\na abc\nb bai\nc acf\nd bed\ne abh\nf fag\ng abe\nh bag\ni aaj\nj bbb\na\nabacfaabe\n0\n output: 3\n-1\n7\n4\n\n" }, { "title": "Problem C: Swimming Jam", "content": "Despite urging requests of the townspeople, the municipal office cannot afford to improve many\nof the apparently deficient city amenities under this recession. The city swimming pool is one\nof the typical examples. It has only two swimming lanes. The Municipal Fitness Agency, under\nthis circumstances, settled usage rules so that the limited facilities can be utilized fully.\n\nTwo lanes are to be used for one-way swimming of different directions. Swimmers are requested\nto start swimming in one of the lanes, from its one end to the other, and then change the lane to\nswim his/her way back. When he or she reaches the original starting end, he/she should return\nto his/her initial lane and starts swimming again.\n\nEach swimmer has his/her own natural constant pace. Swimmers, however, are not permitted\nto pass other swimmers except at the ends of the pool; as the lanes are not wide enough, that\nmight cause accidents. If a swimmer is blocked by a slower swimmer, he/she has to follow the\nslower swimmer at the slower pace until the end of the lane is reached. Note that the blocking\nswimmer 's natural pace may be faster than the blocked swimmer; the blocking swimmer might\nalso be blocked by another swimmer ahead, whose natural pace is slower than the blocked\nswimmer. Blocking would have taken place whether or not a faster swimmer was between them.\n\nSwimmers can change their order if they reach the end of the lane simultaneously. They change\ntheir order so that ones with faster natural pace swim in front. When a group of two or more\nswimmers formed by a congestion reaches the end of the lane, they are considered to reach there\nsimultaneously, and thus change their order there.\n\nThe number of swimmers, their natural paces in times to swim from one end to the other, and\nthe numbers of laps they plan to swim are given. Note that here one \"lap\" means swimming\nfrom one end to the other and then swimming back to the original end. Your task is to calculate\nthe time required for all the swimmers to finish their plans. All the swimmers start from the\nsame end of the pool at the same time, the faster swimmers in front.\n\nIn solving this problem, you can ignore the sizes of swimmers' bodies, and also ignore the time\nrequired to change the lanes and the order in a group of swimmers at an end of the lanes.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nn\nt_1 c_1\n. . . \nt_n c_n\n\nn is an integer (1 <= n <= 50) that represents the number of swimmers. t_i and c_i are integers\n(1 <= t_i <= 300,1 <= c_i <= 250) that represent the natural pace in times to swim from one end\nto the other and the number of planned laps for the i-th swimmer, respectively. ti and ci are\nseparated by a space.\n\nThe end of the input is indicated by a line containing one zero.", "output": "For each dataset, output the time required for all the swimmers to finish their plans in a line.\nNo extra characters should occur in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n10 30\n15 20\n2\n10 240\n15 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0\n output: 600\n4800\n36\n40"], "Pid": "p00876", "ProblemText": "Task Description: Despite urging requests of the townspeople, the municipal office cannot afford to improve many\nof the apparently deficient city amenities under this recession. The city swimming pool is one\nof the typical examples. It has only two swimming lanes. The Municipal Fitness Agency, under\nthis circumstances, settled usage rules so that the limited facilities can be utilized fully.\n\nTwo lanes are to be used for one-way swimming of different directions. Swimmers are requested\nto start swimming in one of the lanes, from its one end to the other, and then change the lane to\nswim his/her way back. When he or she reaches the original starting end, he/she should return\nto his/her initial lane and starts swimming again.\n\nEach swimmer has his/her own natural constant pace. Swimmers, however, are not permitted\nto pass other swimmers except at the ends of the pool; as the lanes are not wide enough, that\nmight cause accidents. If a swimmer is blocked by a slower swimmer, he/she has to follow the\nslower swimmer at the slower pace until the end of the lane is reached. Note that the blocking\nswimmer 's natural pace may be faster than the blocked swimmer; the blocking swimmer might\nalso be blocked by another swimmer ahead, whose natural pace is slower than the blocked\nswimmer. Blocking would have taken place whether or not a faster swimmer was between them.\n\nSwimmers can change their order if they reach the end of the lane simultaneously. They change\ntheir order so that ones with faster natural pace swim in front. When a group of two or more\nswimmers formed by a congestion reaches the end of the lane, they are considered to reach there\nsimultaneously, and thus change their order there.\n\nThe number of swimmers, their natural paces in times to swim from one end to the other, and\nthe numbers of laps they plan to swim are given. Note that here one \"lap\" means swimming\nfrom one end to the other and then swimming back to the original end. Your task is to calculate\nthe time required for all the swimmers to finish their plans. All the swimmers start from the\nsame end of the pool at the same time, the faster swimmers in front.\n\nIn solving this problem, you can ignore the sizes of swimmers' bodies, and also ignore the time\nrequired to change the lanes and the order in a group of swimmers at an end of the lanes.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nn\nt_1 c_1\n. . . \nt_n c_n\n\nn is an integer (1 <= n <= 50) that represents the number of swimmers. t_i and c_i are integers\n(1 <= t_i <= 300,1 <= c_i <= 250) that represent the natural pace in times to swim from one end\nto the other and the number of planned laps for the i-th swimmer, respectively. ti and ci are\nseparated by a space.\n\nThe end of the input is indicated by a line containing one zero.\nTask Output: For each dataset, output the time required for all the swimmers to finish their plans in a line.\nNo extra characters should occur in the output.\nTask Samples: input: 2\n10 30\n15 20\n2\n10 240\n15 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0\n output: 600\n4800\n36\n40\n\n" }, { "title": "Problem D: Separate Points", "content": "Numbers of black and white points are placed on a plane. Let's imagine that a straight line\nof infinite length is drawn on the plane. When the line does not meet any of the points, the\nline divides these points into two groups. If the division by such a line results in one group\nconsisting only of black points and the other consisting only of white points, we say that the\nline \"separates black and white points\".\n\nLet's see examples in Figure 3. In the leftmost example, you can easily find that the black and\nwhite points can be perfectly separated by the dashed line according to their colors. In the\nremaining three examples, there exists no such straight line that gives such a separation.\nFigure 3: Example planes\n\nIn this problem, given a set of points with their colors and positions, you are requested to decide\nwhether there exists a straight line that separates black and white points.", "constraint": "", "input": "The input is a sequence of datasets, each of which is formatted as follows.\nn mx_1y_1x_n y_nx_n+1y_n+1x_n+my_n+m\nThe first line contains two positive integers separated by a single space; n is the number of black\npoints, and m is the number of white points. They are less than or equal to 100. Then n + m\nlines representing the coordinates of points follow. Each line contains two integers x_i and y_i\nseparated by a space, where (x_i , y_i ) represents the x-coordinate and the y-coordinate of the i-th\npoint. The color of the i-th point is black for 1 <= i <= n, and is white for n + 1 <= i <= n + m.\n\nAll the points have integral x- and y-coordinate values between 0 and 10000 inclusive. You can\nalso assume that no two points have the same position.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.", "output": "For each dataset, output \"YES\" if there exists a line satisfying the condition. If not, output\n\"NO\". In either case, print it in one line for each input dataset.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3\n100 700\n200 200\n600 600\n500 100\n500 300\n800 500\n3 3\n100 300\n400 600\n400 100\n600 400\n500 900\n300 300\n3 4\n300 300\n500 300\n400 600\n100 100\n200 900\n500 900\n800 100\n1 2\n300 300\n100 100\n500 500\n1 1\n100 100\n200 100\n2 2\n0 0\n500 700\n1000 1400\n1500 2100\n2 2\n0 0\n1000 1000\n1000 0\n0 1000\n3 3\n0 100\n4999 102\n10000 103\n5001 102\n10000 102\n0 101\n3 3\n100 100\n200 100\n100 200\n0 0\n400 0\n0 400\n3 3\n2813 1640\n2583 2892\n2967 1916\n541 3562\n9298 3686\n7443 7921\n0 0\n output: YES\nNO\nNO\nNO\nYES\nYES\nNO\nNO\nNO\nYES"], "Pid": "p00877", "ProblemText": "Task Description: Numbers of black and white points are placed on a plane. Let's imagine that a straight line\nof infinite length is drawn on the plane. When the line does not meet any of the points, the\nline divides these points into two groups. If the division by such a line results in one group\nconsisting only of black points and the other consisting only of white points, we say that the\nline \"separates black and white points\".\n\nLet's see examples in Figure 3. In the leftmost example, you can easily find that the black and\nwhite points can be perfectly separated by the dashed line according to their colors. In the\nremaining three examples, there exists no such straight line that gives such a separation.\nFigure 3: Example planes\n\nIn this problem, given a set of points with their colors and positions, you are requested to decide\nwhether there exists a straight line that separates black and white points.\nTask Input: The input is a sequence of datasets, each of which is formatted as follows.\nn mx_1y_1x_n y_nx_n+1y_n+1x_n+my_n+m\nThe first line contains two positive integers separated by a single space; n is the number of black\npoints, and m is the number of white points. They are less than or equal to 100. Then n + m\nlines representing the coordinates of points follow. Each line contains two integers x_i and y_i\nseparated by a space, where (x_i , y_i ) represents the x-coordinate and the y-coordinate of the i-th\npoint. The color of the i-th point is black for 1 <= i <= n, and is white for n + 1 <= i <= n + m.\n\nAll the points have integral x- and y-coordinate values between 0 and 10000 inclusive. You can\nalso assume that no two points have the same position.\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\nTask Output: For each dataset, output \"YES\" if there exists a line satisfying the condition. If not, output\n\"NO\". In either case, print it in one line for each input dataset.\nTask Samples: input: 3 3\n100 700\n200 200\n600 600\n500 100\n500 300\n800 500\n3 3\n100 300\n400 600\n400 100\n600 400\n500 900\n300 300\n3 4\n300 300\n500 300\n400 600\n100 100\n200 900\n500 900\n800 100\n1 2\n300 300\n100 100\n500 500\n1 1\n100 100\n200 100\n2 2\n0 0\n500 700\n1000 1400\n1500 2100\n2 2\n0 0\n1000 1000\n1000 0\n0 1000\n3 3\n0 100\n4999 102\n10000 103\n5001 102\n10000 102\n0 101\n3 3\n100 100\n200 100\n100 200\n0 0\n400 0\n0 400\n3 3\n2813 1640\n2583 2892\n2967 1916\n541 3562\n9298 3686\n7443 7921\n0 0\n output: YES\nNO\nNO\nNO\nYES\nYES\nNO\nNO\nNO\nYES\n\n" }, { "title": "Problem E: Origami Through-Hole", "content": "Origami is the traditional Japanese art of paper folding. One day, Professor Egami found the\nmessage board decorated with some pieces of origami works pinned on it, and became interested\nin the pinholes on the origami paper. Your mission is to simulate paper folding and pin punching\non the folded sheet, and calculate the number of pinholes on the original sheet when unfolded.\n\nA sequence of folding instructions for a flat and square piece of paper and a single pinhole\nposition are specified. As a folding instruction, two points P and Q are given. The paper should\nbe folded so that P touches Q from above (Figure 4). To make a fold, we first divide the sheet\ninto two segments by creasing the sheet along the folding line, i. e. , the perpendicular bisector\nof the line segment PQ, and then turn over the segment containing P onto the other. You can\nignore the thickness of the paper.\nFigure 4: Simple case of paper folding\n\nThe original flat square piece of paper is folded into a structure consisting of layered paper\nsegments, which are connected by linear hinges. For each instruction, we fold one or more paper\nsegments along the specified folding line, dividing the original segments into new smaller ones.\nThe folding operation turns over some of the paper segments (not only the new smaller segments\nbut also some other segments that have no intersection with the folding line) to the reflective\nposition against the folding line. That is, for a paper segment that intersects with the folding\nline, one of the two new segments made by dividing the original is turned over; for a paper\nsegment that does not intersect with the folding line, the whole segment is simply turned over.\n\nThe folding operation is carried out repeatedly applying the following rules, until we have no\nsegment to turn over.\n\n Rule 1: The uppermost segment that contains P must be turned over.\n\n Rule 2: If a hinge of a segment is moved to the other side of the folding line by the\n operation, any segment that shares the same hinge must be turned over.\n\nRule 3: If two paper segments overlap and the lower segment is turned over, the upper\nsegment must be turned over too.\nIn the examples shown in Figure 5, (a) and (c) show cases where only Rule 1 is applied. (b)\nshows a case where Rule 1 and 2 are applied to turn over two paper segments connected by a\nhinge, and (d) shows a case where Rule 1,3 and 2 are applied to turn over three paper segments.\nFigure 5: Different cases of folding\n\nAfter processing all the folding instructions, the pinhole goes through all the layered segments\nof paper at that position. In the case of Figure 6, there are three pinholes on the unfolded sheet\nof paper.\nFigure 6: Number of pinholes on the unfolded sheet", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by a line containing a\nzero.\n\nEach dataset is formatted as follows.\n\nk\np_x^1 p_y^1 q_x^1 q_y^1\n. \n. \n. \np_x^k p_y^k q_x^k q_y^k\nh_x h_y\n\nFor all datasets, the size of the initial sheet is 100 mm square, and, using mm as the coordinate\nunit, the corners of the sheet are located at the coordinates (0,0), (100,0), (100,100) and\n(0,100). The integer k is the number of folding instructions and 1 <= k <= 10. Each of the\nfollowing k lines represents a single folding instruction and consists of four integers p_x^i, p_y^i, q_x^i, and q_y^i, delimited by a space. The positions of point P and Q for the i-th instruction are given by (p_x^i, p_y^i) and (q_x^i, q_y^i), respectively. You can assume that P ! = Q. You must carry out these\ninstructions in the given order. The last line of a dataset contains two integers h_x and h_y\ndelimited by a space, and (h_x, h_y ) represents the position of the pinhole.\n\nYou can assume the following properties:\n\n The points P and Q of the folding instructions are placed on some paper segments at the\n folding time, and P is at least 0.01 mm distant from any borders of the paper segments.\n\n The position of the pinhole also is at least 0.01 mm distant from any borders of the paper\n segments at the punching time.\n\n Every folding line, when infinitely extended to both directions, is at least 0.01 mm distant\n from any corners of the paper segments before the folding along that folding line.\n\n When two paper segments have any overlap, the overlapping area cannot be placed between\n any two parallel lines with 0.01 mm distance. When two paper segments do not overlap,\n any points on one segment are at least 0.01 mm distant from any points on the other\n segment.\nFor example, Figure 5 (a), (b), (c) and (d) correspond to the first four datasets of the sample\ninput.", "output": "For each dataset, output a single line containing the number of the pinholes on the sheet of\npaper, when unfolded. No extra characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n90 90 80 20\n80 20 75 50\n50 35\n2\n90 90 80 20\n75 50 80 20\n55 20\n3\n5 90 15 70\n95 90 85 75\n20 67 20 73\n20 75\n3\n5 90 15 70\n5 10 15 55\n20 67 20 73\n75 80\n8\n1 48 1 50\n10 73 10 75\n31 87 31 89\n91 94 91 96\n63 97 62 96\n63 80 61 82\n39 97 41 95\n62 89 62 90\n41 93\n5\n2 1 1 1\n-95 1 -96 1\n-190 1 -191 1\n-283 1 -284 1\n-373 1 -374 1\n-450 1\n2\n77 17 89 8\n103 13 85 10\n53 36\n0\n output: 3\n4\n3\n2\n32\n1\n0"], "Pid": "p00878", "ProblemText": "Task Description: Origami is the traditional Japanese art of paper folding. One day, Professor Egami found the\nmessage board decorated with some pieces of origami works pinned on it, and became interested\nin the pinholes on the origami paper. Your mission is to simulate paper folding and pin punching\non the folded sheet, and calculate the number of pinholes on the original sheet when unfolded.\n\nA sequence of folding instructions for a flat and square piece of paper and a single pinhole\nposition are specified. As a folding instruction, two points P and Q are given. The paper should\nbe folded so that P touches Q from above (Figure 4). To make a fold, we first divide the sheet\ninto two segments by creasing the sheet along the folding line, i. e. , the perpendicular bisector\nof the line segment PQ, and then turn over the segment containing P onto the other. You can\nignore the thickness of the paper.\nFigure 4: Simple case of paper folding\n\nThe original flat square piece of paper is folded into a structure consisting of layered paper\nsegments, which are connected by linear hinges. For each instruction, we fold one or more paper\nsegments along the specified folding line, dividing the original segments into new smaller ones.\nThe folding operation turns over some of the paper segments (not only the new smaller segments\nbut also some other segments that have no intersection with the folding line) to the reflective\nposition against the folding line. That is, for a paper segment that intersects with the folding\nline, one of the two new segments made by dividing the original is turned over; for a paper\nsegment that does not intersect with the folding line, the whole segment is simply turned over.\n\nThe folding operation is carried out repeatedly applying the following rules, until we have no\nsegment to turn over.\n\n Rule 1: The uppermost segment that contains P must be turned over.\n\n Rule 2: If a hinge of a segment is moved to the other side of the folding line by the\n operation, any segment that shares the same hinge must be turned over.\n\nRule 3: If two paper segments overlap and the lower segment is turned over, the upper\nsegment must be turned over too.\nIn the examples shown in Figure 5, (a) and (c) show cases where only Rule 1 is applied. (b)\nshows a case where Rule 1 and 2 are applied to turn over two paper segments connected by a\nhinge, and (d) shows a case where Rule 1,3 and 2 are applied to turn over three paper segments.\nFigure 5: Different cases of folding\n\nAfter processing all the folding instructions, the pinhole goes through all the layered segments\nof paper at that position. In the case of Figure 6, there are three pinholes on the unfolded sheet\nof paper.\nFigure 6: Number of pinholes on the unfolded sheet\nTask Input: The input is a sequence of datasets. The end of the input is indicated by a line containing a\nzero.\n\nEach dataset is formatted as follows.\n\nk\np_x^1 p_y^1 q_x^1 q_y^1\n. \n. \n. \np_x^k p_y^k q_x^k q_y^k\nh_x h_y\n\nFor all datasets, the size of the initial sheet is 100 mm square, and, using mm as the coordinate\nunit, the corners of the sheet are located at the coordinates (0,0), (100,0), (100,100) and\n(0,100). The integer k is the number of folding instructions and 1 <= k <= 10. Each of the\nfollowing k lines represents a single folding instruction and consists of four integers p_x^i, p_y^i, q_x^i, and q_y^i, delimited by a space. The positions of point P and Q for the i-th instruction are given by (p_x^i, p_y^i) and (q_x^i, q_y^i), respectively. You can assume that P ! = Q. You must carry out these\ninstructions in the given order. The last line of a dataset contains two integers h_x and h_y\ndelimited by a space, and (h_x, h_y ) represents the position of the pinhole.\n\nYou can assume the following properties:\n\n The points P and Q of the folding instructions are placed on some paper segments at the\n folding time, and P is at least 0.01 mm distant from any borders of the paper segments.\n\n The position of the pinhole also is at least 0.01 mm distant from any borders of the paper\n segments at the punching time.\n\n Every folding line, when infinitely extended to both directions, is at least 0.01 mm distant\n from any corners of the paper segments before the folding along that folding line.\n\n When two paper segments have any overlap, the overlapping area cannot be placed between\n any two parallel lines with 0.01 mm distance. When two paper segments do not overlap,\n any points on one segment are at least 0.01 mm distant from any points on the other\n segment.\nFor example, Figure 5 (a), (b), (c) and (d) correspond to the first four datasets of the sample\ninput.\nTask Output: For each dataset, output a single line containing the number of the pinholes on the sheet of\npaper, when unfolded. No extra characters should appear in the output.\nTask Samples: input: 2\n90 90 80 20\n80 20 75 50\n50 35\n2\n90 90 80 20\n75 50 80 20\n55 20\n3\n5 90 15 70\n95 90 85 75\n20 67 20 73\n20 75\n3\n5 90 15 70\n5 10 15 55\n20 67 20 73\n75 80\n8\n1 48 1 50\n10 73 10 75\n31 87 31 89\n91 94 91 96\n63 97 62 96\n63 80 61 82\n39 97 41 95\n62 89 62 90\n41 93\n5\n2 1 1 1\n-95 1 -96 1\n-190 1 -191 1\n-283 1 -284 1\n-373 1 -374 1\n-450 1\n2\n77 17 89 8\n103 13 85 10\n53 36\n0\n output: 3\n4\n3\n2\n32\n1\n0\n\n" }, { "title": "Problem F: Chemist's Math", "content": "You have probably learnt chemical equations (chemical reaction formulae) in your high-school\ndays. The following are some well-known equations.\n\n 2H_2 + O_2 → 2H_2O (1)\n C_a(OH)_2 + CO_2 → C_a CO_3 + H_2O (2)\n N_2 + 3H_2 → 2NH_3 (3)\nWhile Equations (1)–(3) all have balanced left-hand sides and right-hand sides, the following\nones do not.\n Al + O_2 → Al_2O_3 (wrong) (4)\n C_3H_8 + O_2 → CO_2 + H_2O (wrong) (5)\n\nThe equations must follow the law of conservation of mass; the quantity of each chemical element\n(such as H, O, Ca, Al) should not change with chemical reactions. So we should \"adjust\" the\nnumbers of molecules on the left-hand side and right-hand side:\n 4Al + 3O_2 → 2Al_2O_3 (correct) (6)\n C_3H_8 + 5O_2 → 3CO_2 + 4H_2O (correct) (7)\nThe coefficients of Equation (6) are (4,3,2) from left to right, and those of Equation (7) are\n(1,5,3,4) from left to right. Note that the coefficient 1 may be omitted from chemical equations.\n\nThe coefficients of a correct equation must satisfy the following conditions.\n\n The coefficients are all positive integers.\n\n The coefficients are relatively prime, that is, their greatest common divisor (g. c. d. ) is 1.\n\n The quantities of each chemical element on the left-hand side and the right-hand side are\n equal.\nConversely, if a chemical equation satisfies the above three conditions, we regard it as a correct\nequation, no matter whether the reaction or its constituent molecules can be chemically realized\nin the real world, and no matter whether it can be called a reaction (e. g. , H_2 → H_2 is considered\ncorrect). A chemical equation satisfying Conditions 1 and 3 (but not necessarily Condition 2)\nis called a balanced equation.\n\nYour goal is to read in chemical equations with missing coefficients like Equation (4) and (5),\nline by line, and output the sequences of coefficients that make the equations correct.\n\nNote that the above three conditions do not guarantee that a correct equation is uniquely\ndetermined. For example, if we \"mix\" the reactions generating H_2O and NH_3 , we would get\n\nxH_2 + yO_2 + zN_2 + uH_2 → vH_2O + wNH_3 (8)\n\nbut (x, y, z, u, v, w) = (2,1,1,3,2,2) does not represent a unique correct equation; for instance,\n(4,2,1,3,4,2) and (4,2,3,9,4,6) are also \"correct\" according to the above definition! However,\nwe guarantee that every chemical equation we give you will lead to a unique correct equation by\nadjusting their coefficients. In other words, we guarantee that (i) every chemical equation can be\nbalanced with positive coefficients, and that (ii) all balanced equations of the original equation\ncan be obtained by multiplying the coefficients of a unique correct equation by a positive integer.", "constraint": "", "input": "The input is a sequence of chemical equations (without coefficients) of the following syntax in\nthe Backus-Naur Form:\n\n : : = \"->\" \n : : = | \"+\" \n : : = | \n : : = | \n : : = | \"(\" \")\"\n : : = \n | \n : : = \"A\" | \"B\" | \"C\" | \"D\" | \"E\" | \"F\" | \"G\" | \"H\" | \"I\"\n | \"J\" | \"K\" | \"L\" | \"M\" | \"N\" | \"O\" | \"P\" | \"Q\" | \"R\"\n | \"S\" | \"T\" | \"U\" | \"V\" | \"W\" | \"X\" | \"Y\" | \"Z\"\n : : = \"a\" | \"b\" | \"c\" | \"d\" | \"e\" | \"f\" | \"g\" | \"h\" | \"i\"\n | \"j\" | \"k\" | \"l\" | \"m\" | \"n\" | \"o\" | \"p\" | \"q\" | \"r\"\n | \"s\" | \"t\" | \"u\" | \"v\" | \"w\" | \"x\" | \"y\" | \"z\"\n : : = \n | \n : : = \"1\" | \"2\" | \"3\" | \"4\" | \"5\" | \"6\" | \"7\" | \"8\" |\n : : = \"0\" | \n\nEach chemical equation is followed by a period and a newline. No other characters such as\nspaces do not appear in the input. For instance, the equation\nC_a(OH)_2 + CO_2 → C_a CO_3 + H_2O\n\nis represented as\n\nCa(OH)2+CO2->Ca CO3+H2O.\n\nEach chemical equation is no more than 80 characters long, and as the above syntax implies,\nthe 's are less than 100. Parentheses may be used but will not be nested (maybe a\ngood news to some of you! ). Each side of a chemical equation consists of no more than 10\ntop-level molecules. The coefficients that make the equations correct will not exceed 40000. The\nchemical equations in the input have been chosen so that 32-bit integer arithmetic would suffice\nwith appropriate precautions against possible arithmetic overflow. You are free to use 64-bit\narithmetic, however.\n\nThe end of the input is indicated by a line consisting of a single period.\n\nNote that our definition of above allows chemical elements that do not\nexist or unknown as of now, and excludes known chemical elements with three-letter names (e. g. ,\nununbium (Uub), with the atomic number 112).", "output": "For each chemical equation, output a line containing the sequence of positive integer coefficients\nthat make the chemical equation correct. Numbers in a line must be separated by a single space.\nNo extra characters should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: N2+H2->NH3.\nNa+Cl2->NaCl.\nCa(OH)2+CO2->CaCO3+H2O.\nCaCl2+AgNO3->Ca(NO3)2+AgCl.\nC2H5OH+O2->CO2+H2O.\nC4H10+O2->CO2+H2O.\nA12B23+C34D45+ABCD->A6D7+B8C9.\nA98B+B98C+C98->A98B99C99.\nA2+B3+C5+D7+E11+F13->ABCDEF.\n.\n output: 1 3 2\n2 1 2\n1 1 1 1\n1 2 1 2\n1 3 2 3\n2 13 8 10\n2 123 33042 5511 4136\n1 1 1 1\n15015 10010 6006 4290 2730 2310 30030"], "Pid": "p00879", "ProblemText": "Task Description: You have probably learnt chemical equations (chemical reaction formulae) in your high-school\ndays. The following are some well-known equations.\n\n 2H_2 + O_2 → 2H_2O (1)\n C_a(OH)_2 + CO_2 → C_a CO_3 + H_2O (2)\n N_2 + 3H_2 → 2NH_3 (3)\nWhile Equations (1)–(3) all have balanced left-hand sides and right-hand sides, the following\nones do not.\n Al + O_2 → Al_2O_3 (wrong) (4)\n C_3H_8 + O_2 → CO_2 + H_2O (wrong) (5)\n\nThe equations must follow the law of conservation of mass; the quantity of each chemical element\n(such as H, O, Ca, Al) should not change with chemical reactions. So we should \"adjust\" the\nnumbers of molecules on the left-hand side and right-hand side:\n 4Al + 3O_2 → 2Al_2O_3 (correct) (6)\n C_3H_8 + 5O_2 → 3CO_2 + 4H_2O (correct) (7)\nThe coefficients of Equation (6) are (4,3,2) from left to right, and those of Equation (7) are\n(1,5,3,4) from left to right. Note that the coefficient 1 may be omitted from chemical equations.\n\nThe coefficients of a correct equation must satisfy the following conditions.\n\n The coefficients are all positive integers.\n\n The coefficients are relatively prime, that is, their greatest common divisor (g. c. d. ) is 1.\n\n The quantities of each chemical element on the left-hand side and the right-hand side are\n equal.\nConversely, if a chemical equation satisfies the above three conditions, we regard it as a correct\nequation, no matter whether the reaction or its constituent molecules can be chemically realized\nin the real world, and no matter whether it can be called a reaction (e. g. , H_2 → H_2 is considered\ncorrect). A chemical equation satisfying Conditions 1 and 3 (but not necessarily Condition 2)\nis called a balanced equation.\n\nYour goal is to read in chemical equations with missing coefficients like Equation (4) and (5),\nline by line, and output the sequences of coefficients that make the equations correct.\n\nNote that the above three conditions do not guarantee that a correct equation is uniquely\ndetermined. For example, if we \"mix\" the reactions generating H_2O and NH_3 , we would get\n\nxH_2 + yO_2 + zN_2 + uH_2 → vH_2O + wNH_3 (8)\n\nbut (x, y, z, u, v, w) = (2,1,1,3,2,2) does not represent a unique correct equation; for instance,\n(4,2,1,3,4,2) and (4,2,3,9,4,6) are also \"correct\" according to the above definition! However,\nwe guarantee that every chemical equation we give you will lead to a unique correct equation by\nadjusting their coefficients. In other words, we guarantee that (i) every chemical equation can be\nbalanced with positive coefficients, and that (ii) all balanced equations of the original equation\ncan be obtained by multiplying the coefficients of a unique correct equation by a positive integer.\nTask Input: The input is a sequence of chemical equations (without coefficients) of the following syntax in\nthe Backus-Naur Form:\n\n : : = \"->\" \n : : = | \"+\" \n : : = | \n : : = | \n : : = | \"(\" \")\"\n : : = \n | \n : : = \"A\" | \"B\" | \"C\" | \"D\" | \"E\" | \"F\" | \"G\" | \"H\" | \"I\"\n | \"J\" | \"K\" | \"L\" | \"M\" | \"N\" | \"O\" | \"P\" | \"Q\" | \"R\"\n | \"S\" | \"T\" | \"U\" | \"V\" | \"W\" | \"X\" | \"Y\" | \"Z\"\n : : = \"a\" | \"b\" | \"c\" | \"d\" | \"e\" | \"f\" | \"g\" | \"h\" | \"i\"\n | \"j\" | \"k\" | \"l\" | \"m\" | \"n\" | \"o\" | \"p\" | \"q\" | \"r\"\n | \"s\" | \"t\" | \"u\" | \"v\" | \"w\" | \"x\" | \"y\" | \"z\"\n : : = \n | \n : : = \"1\" | \"2\" | \"3\" | \"4\" | \"5\" | \"6\" | \"7\" | \"8\" |\n : : = \"0\" | \n\nEach chemical equation is followed by a period and a newline. No other characters such as\nspaces do not appear in the input. For instance, the equation\nC_a(OH)_2 + CO_2 → C_a CO_3 + H_2O\n\nis represented as\n\nCa(OH)2+CO2->Ca CO3+H2O.\n\nEach chemical equation is no more than 80 characters long, and as the above syntax implies,\nthe 's are less than 100. Parentheses may be used but will not be nested (maybe a\ngood news to some of you! ). Each side of a chemical equation consists of no more than 10\ntop-level molecules. The coefficients that make the equations correct will not exceed 40000. The\nchemical equations in the input have been chosen so that 32-bit integer arithmetic would suffice\nwith appropriate precautions against possible arithmetic overflow. You are free to use 64-bit\narithmetic, however.\n\nThe end of the input is indicated by a line consisting of a single period.\n\nNote that our definition of above allows chemical elements that do not\nexist or unknown as of now, and excludes known chemical elements with three-letter names (e. g. ,\nununbium (Uub), with the atomic number 112).\nTask Output: For each chemical equation, output a line containing the sequence of positive integer coefficients\nthat make the chemical equation correct. Numbers in a line must be separated by a single space.\nNo extra characters should appear in the output.\nTask Samples: input: N2+H2->NH3.\nNa+Cl2->NaCl.\nCa(OH)2+CO2->CaCO3+H2O.\nCaCl2+AgNO3->Ca(NO3)2+AgCl.\nC2H5OH+O2->CO2+H2O.\nC4H10+O2->CO2+H2O.\nA12B23+C34D45+ABCD->A6D7+B8C9.\nA98B+B98C+C98->A98B99C99.\nA2+B3+C5+D7+E11+F13->ABCDEF.\n.\n output: 1 3 2\n2 1 2\n1 1 1 1\n1 2 1 2\n1 3 2 3\n2 13 8 10\n2 123 33042 5511 4136\n1 1 1 1\n15015 10010 6006 4290 2730 2310 30030\n\n" }, { "title": "Problem G: Malfatti Circles", "content": "The configuration of three circles packed inside a triangle such that each circle is tangent to the\nother two circles and to two of the edges of the triangle has been studied by many mathematicians\nfor more than two centuries. Existence and uniqueness of such circles for an arbitrary triangle\nare easy to prove. Many methods of numerical calculation or geometric construction of such\ncircles from an arbitrarily given triangle have been discovered. Today, such circles are called the\nMalfatti circles.\n\nFigure 7 illustrates an example. The Malfatti circles of the triangle with the vertices (20,80),\n(-40, -20) and (120, -20) are approximately\n\n the circle with the center (24.281677,45.219486) and the radius 21.565935,\n\n the circle with the center (3.110950,4.409005) and the radius 24.409005, and\n\n the circle with the center (54.556724,7.107493) and the radius 27.107493.\nFigure 8 illustrates another example. The Malfatti circles of the triangle with the vertices\n(20, -20), (120, -20) and (-40,80) are approximately\n\n the circle with the center (25.629089, -10.057956) and the radius 9.942044,\n\n the circle with the center (53.225883, -0.849435) and the radius 19.150565, and\n\n the circle with the center (19.701191,19.203466) and the radius 19.913790.\nYour mission is to write a program to calculate the radii of the Malfatti circles of the given\ntriangles.", "constraint": "", "input": "The input is a sequence of datasets. A dataset is a line containing six integers x_1, y_1 , x_2 , y_2, x_3\nand y_3 in this order, separated by a space. The coordinates of the vertices of the given triangle\nare (x_1 , y_1 ), (x_2 , y_2 ) and (x_3 , y_3 ), respectively. You can assume that the vertices form a triangle\ncounterclockwise. You can also assume that the following two conditions hold.\n\n All of the coordinate values are greater than -1000 and less than 1000.\n\n None of the Malfatti circles of the triangle has a radius less than 0.1.\nThe end of the input is indicated by a line containing six zeros separated by a space.", "output": "For each input dataset, three decimal fractions r_1 , r_2 and r_3 should be printed in a line in this\norder separated by a space. The radii of the Malfatti circles nearest to the vertices with the\ncoordinates (x_1 , y_1 ), (x_2 , y_2 ) and (x_3 , y_3 ) should be r_1 , r_2 and r_3 , respectively.\n\nNone of the output values may have an error greater than 0.0001. No extra character should\nappear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 20 80 -40 -20 120 -20\n20 -20 120 -20 -40 80\n0 0 1 0 0 1\n0 0 999 1 -999 1\n897 -916 847 -972 890 -925\n999 999 -999 -998 -998 -999\n-999 -999 999 -999 0 731\n-999 -999 999 -464 -464 999\n979 -436 -955 -337 157 -439\n0 0 0 0 0 0\n output: 21.565935 24.409005 27.107493\n9.942044 19.150565 19.913790\n0.148847 0.207107 0.207107\n0.125125 0.499750 0.499750\n0.373458 0.383897 0.100456\n0.706768 0.353509 0.353509\n365.638023 365.638023 365.601038\n378.524085 378.605339 378.605339\n21.895803 22.052921 5.895714"], "Pid": "p00880", "ProblemText": "Task Description: The configuration of three circles packed inside a triangle such that each circle is tangent to the\nother two circles and to two of the edges of the triangle has been studied by many mathematicians\nfor more than two centuries. Existence and uniqueness of such circles for an arbitrary triangle\nare easy to prove. Many methods of numerical calculation or geometric construction of such\ncircles from an arbitrarily given triangle have been discovered. Today, such circles are called the\nMalfatti circles.\n\nFigure 7 illustrates an example. The Malfatti circles of the triangle with the vertices (20,80),\n(-40, -20) and (120, -20) are approximately\n\n the circle with the center (24.281677,45.219486) and the radius 21.565935,\n\n the circle with the center (3.110950,4.409005) and the radius 24.409005, and\n\n the circle with the center (54.556724,7.107493) and the radius 27.107493.\nFigure 8 illustrates another example. The Malfatti circles of the triangle with the vertices\n(20, -20), (120, -20) and (-40,80) are approximately\n\n the circle with the center (25.629089, -10.057956) and the radius 9.942044,\n\n the circle with the center (53.225883, -0.849435) and the radius 19.150565, and\n\n the circle with the center (19.701191,19.203466) and the radius 19.913790.\nYour mission is to write a program to calculate the radii of the Malfatti circles of the given\ntriangles.\nTask Input: The input is a sequence of datasets. A dataset is a line containing six integers x_1, y_1 , x_2 , y_2, x_3\nand y_3 in this order, separated by a space. The coordinates of the vertices of the given triangle\nare (x_1 , y_1 ), (x_2 , y_2 ) and (x_3 , y_3 ), respectively. You can assume that the vertices form a triangle\ncounterclockwise. You can also assume that the following two conditions hold.\n\n All of the coordinate values are greater than -1000 and less than 1000.\n\n None of the Malfatti circles of the triangle has a radius less than 0.1.\nThe end of the input is indicated by a line containing six zeros separated by a space.\nTask Output: For each input dataset, three decimal fractions r_1 , r_2 and r_3 should be printed in a line in this\norder separated by a space. The radii of the Malfatti circles nearest to the vertices with the\ncoordinates (x_1 , y_1 ), (x_2 , y_2 ) and (x_3 , y_3 ) should be r_1 , r_2 and r_3 , respectively.\n\nNone of the output values may have an error greater than 0.0001. No extra character should\nappear in the output.\nTask Samples: input: 20 80 -40 -20 120 -20\n20 -20 120 -20 -40 80\n0 0 1 0 0 1\n0 0 999 1 -999 1\n897 -916 847 -972 890 -925\n999 999 -999 -998 -998 -999\n-999 -999 999 -999 0 731\n-999 -999 999 -464 -464 999\n979 -436 -955 -337 157 -439\n0 0 0 0 0 0\n output: 21.565935 24.409005 27.107493\n9.942044 19.150565 19.913790\n0.148847 0.207107 0.207107\n0.125125 0.499750 0.499750\n0.373458 0.383897 0.100456\n0.706768 0.353509 0.353509\n365.638023 365.638023 365.601038\n378.524085 378.605339 378.605339\n21.895803 22.052921 5.895714\n\n" }, { "title": "Problem H: Twenty Questions", "content": "Consider a closed world and a set of features that are defined for all the objects in the world.\nEach feature can be answered with \"yes\" or \"no\". Using those features, we can identify any\nobject from the rest of the objects in the world. In other words, each object can be represented\nas a fixed-length sequence of booleans. Any object is different from other objects by at least\none feature.\n\nYou would like to identify an object from others. For this purpose, you can ask a series of\nquestions to someone who knows what the object is. Every question you can ask is about one\nof the features. He/she immediately answers each question with \"yes\" or \"no\" correctly. You\ncan choose the next question after you get the answer to the previous question.\n\nYou kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus\nmoney, it is necessary to minimize the number of questions in the worst case. You don 't know\nwhat is the correct answer, but fortunately know all the objects in the world. Therefore, you\ncan plan an optimal strategy before you start questioning.\n\nThe problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum\nnumber of questions by which every object in the set is identifiable.", "constraint": "", "input": "The input is a sequence of multiple datasets. Each dataset begins with a line which consists of\ntwo integers, m and n: the number of features, and the number of objects, respectively. You\ncan assume 0 < m <= 11 and 0 < n <= 128. It is followed by n lines, each of which corresponds\nto an object. Each line includes a binary string of length m which represent the value (\"yes\" or\n\"no\") of features. There are no two identical objects.\n\nThe end of the input is indicated by a line containing two zeros. There are at most 100 datasets.", "output": "For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 1\n11010101\n11 4\n00111001100\n01001101011\n01010000011\n01100110001\n11 16\n01000101111\n01011000000\n01011111001\n01101101001\n01110010111\n01110100111\n10000001010\n10010001000\n10010110100\n10100010100\n10101010110\n10110100010\n11001010011\n11011001001\n11111000111\n11111011101\n11 12\n10000000000\n01000000000\n00100000000\n00010000000\n00001000000\n00000100000\n00000010000\n00000001000\n00000000100\n00000000010\n00000000001\n00000000000\n9 32\n001000000\n000100000\n000010000\n000001000\n000000100\n000000010\n000000001\n000000000\n011000000\n010100000\n010010000\n010001000\n010000100\n010000010\n010000001\n010000000\n101000000\n100100000\n100010000\n100001000\n100000100\n100000010\n100000001\n100000000\n111000000\n110100000\n110010000\n110001000\n110000100\n110000010\n110000001\n110000000\n0 0\n output: 0\n2\n4\n11\n9"], "Pid": "p00881", "ProblemText": "Task Description: Consider a closed world and a set of features that are defined for all the objects in the world.\nEach feature can be answered with \"yes\" or \"no\". Using those features, we can identify any\nobject from the rest of the objects in the world. In other words, each object can be represented\nas a fixed-length sequence of booleans. Any object is different from other objects by at least\none feature.\n\nYou would like to identify an object from others. For this purpose, you can ask a series of\nquestions to someone who knows what the object is. Every question you can ask is about one\nof the features. He/she immediately answers each question with \"yes\" or \"no\" correctly. You\ncan choose the next question after you get the answer to the previous question.\n\nYou kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus\nmoney, it is necessary to minimize the number of questions in the worst case. You don 't know\nwhat is the correct answer, but fortunately know all the objects in the world. Therefore, you\ncan plan an optimal strategy before you start questioning.\n\nThe problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum\nnumber of questions by which every object in the set is identifiable.\nTask Input: The input is a sequence of multiple datasets. Each dataset begins with a line which consists of\ntwo integers, m and n: the number of features, and the number of objects, respectively. You\ncan assume 0 < m <= 11 and 0 < n <= 128. It is followed by n lines, each of which corresponds\nto an object. Each line includes a binary string of length m which represent the value (\"yes\" or\n\"no\") of features. There are no two identical objects.\n\nThe end of the input is indicated by a line containing two zeros. There are at most 100 datasets.\nTask Output: For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.\nTask Samples: input: 8 1\n11010101\n11 4\n00111001100\n01001101011\n01010000011\n01100110001\n11 16\n01000101111\n01011000000\n01011111001\n01101101001\n01110010111\n01110100111\n10000001010\n10010001000\n10010110100\n10100010100\n10101010110\n10110100010\n11001010011\n11011001001\n11111000111\n11111011101\n11 12\n10000000000\n01000000000\n00100000000\n00010000000\n00001000000\n00000100000\n00000010000\n00000001000\n00000000100\n00000000010\n00000000001\n00000000000\n9 32\n001000000\n000100000\n000010000\n000001000\n000000100\n000000010\n000000001\n000000000\n011000000\n010100000\n010010000\n010001000\n010000100\n010000010\n010000001\n010000000\n101000000\n100100000\n100010000\n100001000\n100000100\n100000010\n100000001\n100000000\n111000000\n110100000\n110010000\n110001000\n110000100\n110000010\n110000001\n110000000\n0 0\n output: 0\n2\n4\n11\n9\n\n" }, { "title": "Problem I: Hobby on Rails", "content": "ICPC (International Connecting Points Company) starts to sell a new railway toy. It consists\nof a toy tramcar and many rail units on square frames of the same size. There are four types\nof rail units, namely, straight (S), curve (C), left-switch (L) and right-switch (R) as shown in\nFigure 9. A switch has three ends, namely, branch/merge-end (B/M-end), straight-end (S-end)\nand curve-end (C-end).\n\nA switch is either in \"through\" or \"branching\" state. When the tramcar comes from B/M-end,\nand if the switch is in the through-state, the tramcar goes through to S-end and the state changes\nto branching; if the switch is in the branching-state, it branches toward C-end and the state\nchanges to through. When the tramcar comes from S-end or C-end, it goes out from B/M-end\nregardless of the state. The state does not change in this case.\n\nKids are given rail units of various types that fill a rectangle area of w * h, as shown in Fig-\nure 10(a). Rail units meeting at an edge of adjacent two frames are automatically connected.\nEach rail unit may be independently rotated around the center of its frame by multiples of 90\ndegrees in order to change the connection of rail units, but its position cannot be changed.\n\nKids should make \"valid\" layouts by rotating each rail unit, such as getting Figure 10(b) from\nFigure 10(a). A layout is valid when all rails at three ends of every switch are directly or\nindirectly connected to an end of another switch or itself. A layout in Figure 10(c) is invalid as\nwell as Figure 10(a). Invalid layouts are frowned upon.\n\nWhen a tramcar runs in a valid layout, it will eventually begin to repeat the same route forever.\nThat is, we will eventually find the tramcar periodically comes to the same running condition,\nwhich is a triple of the tramcar position in the rectangle area, its direction, and the set of the\nstates of all the switches.\n\nA periodical route is a sequence of rail units on which the tramcar starts from a rail unit with\na running condition and returns to the same rail unit with the same running condition for the first time. A periodical route through a switch or switches is called the \"fun route\", since kids\nlike the rattling sound the tramcar makes when it passes through a switch. The tramcar takes\nthe same unit time to go through a rail unit, not depending on the types of the unit or the\ntramcar directions. After the tramcar starts on a rail unit on a “fun route”, it will come back to\nthe same unit with the same running condition, sooner or later. The fun time T of a fun route\nis the number of time units that the tramcar takes for going around the route.\n\nOf course, kids better enjoy layouts with longer fun time. Given a variety of rail units placed\non a rectangular area, your job is to rotate the given rail units appropriately and to find the fun\nroute with the longest fun time in the valid layouts.\n\nFor example, there is a fun route in Figure 10(b). Its fun time is 24. Let the toy tramcar start\nfrom B/M-end at (1,2) toward (1,3) and the states of all the switches are the through-states. It\ngoes through (1,3), (1,4), (1,5), (2,5), (2,4), (1,4), (1,3), (1,2), (1,1), (2,1), (2,2) and (1,2).\nHere, the tramcar goes through (1,2) with the same position and the same direction, but with\nthe different states of the switches. Then the tramcar goes through (1,3), (1,4), (2,4), (2,5),\n(1,5), (1,4), (1,3), (1,2), (2,2), (2,1), (1,1) and (1,2). Here, the tramcar goes through (1,2)\nagain, but with the same switch states as the initial ones. Counting the rail units the tramcar\nvisited, the tramcar should have run 24 units of time after its start, and thus the fun time is 24.\n\nThere may be many valid layouts with the given rail units. For example, a valid layout containing\na fun route with the fun time 120 is shown in Figure 11(a). Another valid layout containing a\nfun route with the fun time 148 derived from that in Figure 11(a) is shown in Figure 11(b). The\nfour rail units whose rotations are changed from Figure 11(a) are indicated by the thick lines.\n\nA valid layout depicted in Figure 12(a) contains two fun routes, where one consists of the rail\nunits (1,1), (2,1), (3,1), (4,1), (4,2), (3,2), (2,2), (1,2) with T = 8, and the other consists of\nall the remaining rail units with T = 18.\n\nAnother valid layout depicted in Figure 12(b) has two fun routes whose fun times are T = 12\nand T = 20. The layout in Figure 12(a) is different from that in Figure 12(b) at the eight rail\nunits rotated by multiples of 90 degrees. There are other valid layouts with some rotations of\nrail units but there is no fun route with the fun time longer than 20, so that the longest fun\ntime for this example (Figure 12) is 20.\nNote that there may be simple cyclic routes that do not go through any switches in a valid\nlayout, which are not counted as the fun routes. In Figure 13, there are two fun routes and one\nsimple cyclic route. Their fun times are 12 and 14, respectively. The required time for going\naround the simple cyclic route is 20 that is greater than fun times of the fun routes. However,\nthe longest fun time is still 14.", "constraint": "", "input": "The input consists of multiple datasets, followed by a line containing two zeros separated by a\nspace. Each dataset has the following format.\n\nw h\na_11 . . . a_1w\n. . . \na_h1 . . . a_hw\n\nw is the number of the rail units in a row, and h is the number of those in a column. a_ij\n(1 <= i <= h, 1 <= j <= w) is one of uppercase letters 'S', 'C', 'L' and 'R', which indicate the types\nof the rail unit at (i, j) position, i. e. , straight, curve, left-switch and right-switch, respectively.\nItems in a line are separated by a space. You can assume that 2 <= w <= 6,2 <= h <= 6 and the\nsum of the numbers of left-switches and right-switches is greater than or equal to 2 and less\nthan or equal to 6.", "output": "For each dataset, an integer should be printed that indicates the longest fun time of all the fun\nroutes in all the valid layouts with the given rail units. When there is no valid layout according\nto the given rail units, a zero should be printed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 2\nC L S R C\nC C S C C\n6 4\nC C C C C C\nS L R R C S\nS S S L C S\nC C C C C C\n6 6\nC L S S S C\nC C C S S C\nC C C S S C\nC L C S S C\nC C L S S C\nC S L S S C\n6 6\nC S S S S C\nS C S L C S\nS C S R C S\nS C L S C S\nS C R S C S\nC S S S S C\n4 4\nS C C S\nS C L S\nS L C S\nC C C C\n6 4\nC R S S L C\nC R L R L C\nC S C C S C\nC S S S S C\n0 0\n output: 24\n20\n148\n14\n0\n178"], "Pid": "p00882", "ProblemText": "Task Description: ICPC (International Connecting Points Company) starts to sell a new railway toy. It consists\nof a toy tramcar and many rail units on square frames of the same size. There are four types\nof rail units, namely, straight (S), curve (C), left-switch (L) and right-switch (R) as shown in\nFigure 9. A switch has three ends, namely, branch/merge-end (B/M-end), straight-end (S-end)\nand curve-end (C-end).\n\nA switch is either in \"through\" or \"branching\" state. When the tramcar comes from B/M-end,\nand if the switch is in the through-state, the tramcar goes through to S-end and the state changes\nto branching; if the switch is in the branching-state, it branches toward C-end and the state\nchanges to through. When the tramcar comes from S-end or C-end, it goes out from B/M-end\nregardless of the state. The state does not change in this case.\n\nKids are given rail units of various types that fill a rectangle area of w * h, as shown in Fig-\nure 10(a). Rail units meeting at an edge of adjacent two frames are automatically connected.\nEach rail unit may be independently rotated around the center of its frame by multiples of 90\ndegrees in order to change the connection of rail units, but its position cannot be changed.\n\nKids should make \"valid\" layouts by rotating each rail unit, such as getting Figure 10(b) from\nFigure 10(a). A layout is valid when all rails at three ends of every switch are directly or\nindirectly connected to an end of another switch or itself. A layout in Figure 10(c) is invalid as\nwell as Figure 10(a). Invalid layouts are frowned upon.\n\nWhen a tramcar runs in a valid layout, it will eventually begin to repeat the same route forever.\nThat is, we will eventually find the tramcar periodically comes to the same running condition,\nwhich is a triple of the tramcar position in the rectangle area, its direction, and the set of the\nstates of all the switches.\n\nA periodical route is a sequence of rail units on which the tramcar starts from a rail unit with\na running condition and returns to the same rail unit with the same running condition for the first time. A periodical route through a switch or switches is called the \"fun route\", since kids\nlike the rattling sound the tramcar makes when it passes through a switch. The tramcar takes\nthe same unit time to go through a rail unit, not depending on the types of the unit or the\ntramcar directions. After the tramcar starts on a rail unit on a “fun route”, it will come back to\nthe same unit with the same running condition, sooner or later. The fun time T of a fun route\nis the number of time units that the tramcar takes for going around the route.\n\nOf course, kids better enjoy layouts with longer fun time. Given a variety of rail units placed\non a rectangular area, your job is to rotate the given rail units appropriately and to find the fun\nroute with the longest fun time in the valid layouts.\n\nFor example, there is a fun route in Figure 10(b). Its fun time is 24. Let the toy tramcar start\nfrom B/M-end at (1,2) toward (1,3) and the states of all the switches are the through-states. It\ngoes through (1,3), (1,4), (1,5), (2,5), (2,4), (1,4), (1,3), (1,2), (1,1), (2,1), (2,2) and (1,2).\nHere, the tramcar goes through (1,2) with the same position and the same direction, but with\nthe different states of the switches. Then the tramcar goes through (1,3), (1,4), (2,4), (2,5),\n(1,5), (1,4), (1,3), (1,2), (2,2), (2,1), (1,1) and (1,2). Here, the tramcar goes through (1,2)\nagain, but with the same switch states as the initial ones. Counting the rail units the tramcar\nvisited, the tramcar should have run 24 units of time after its start, and thus the fun time is 24.\n\nThere may be many valid layouts with the given rail units. For example, a valid layout containing\na fun route with the fun time 120 is shown in Figure 11(a). Another valid layout containing a\nfun route with the fun time 148 derived from that in Figure 11(a) is shown in Figure 11(b). The\nfour rail units whose rotations are changed from Figure 11(a) are indicated by the thick lines.\n\nA valid layout depicted in Figure 12(a) contains two fun routes, where one consists of the rail\nunits (1,1), (2,1), (3,1), (4,1), (4,2), (3,2), (2,2), (1,2) with T = 8, and the other consists of\nall the remaining rail units with T = 18.\n\nAnother valid layout depicted in Figure 12(b) has two fun routes whose fun times are T = 12\nand T = 20. The layout in Figure 12(a) is different from that in Figure 12(b) at the eight rail\nunits rotated by multiples of 90 degrees. There are other valid layouts with some rotations of\nrail units but there is no fun route with the fun time longer than 20, so that the longest fun\ntime for this example (Figure 12) is 20.\nNote that there may be simple cyclic routes that do not go through any switches in a valid\nlayout, which are not counted as the fun routes. In Figure 13, there are two fun routes and one\nsimple cyclic route. Their fun times are 12 and 14, respectively. The required time for going\naround the simple cyclic route is 20 that is greater than fun times of the fun routes. However,\nthe longest fun time is still 14.\nTask Input: The input consists of multiple datasets, followed by a line containing two zeros separated by a\nspace. Each dataset has the following format.\n\nw h\na_11 . . . a_1w\n. . . \na_h1 . . . a_hw\n\nw is the number of the rail units in a row, and h is the number of those in a column. a_ij\n(1 <= i <= h, 1 <= j <= w) is one of uppercase letters 'S', 'C', 'L' and 'R', which indicate the types\nof the rail unit at (i, j) position, i. e. , straight, curve, left-switch and right-switch, respectively.\nItems in a line are separated by a space. You can assume that 2 <= w <= 6,2 <= h <= 6 and the\nsum of the numbers of left-switches and right-switches is greater than or equal to 2 and less\nthan or equal to 6.\nTask Output: For each dataset, an integer should be printed that indicates the longest fun time of all the fun\nroutes in all the valid layouts with the given rail units. When there is no valid layout according\nto the given rail units, a zero should be printed.\nTask Samples: input: 5 2\nC L S R C\nC C S C C\n6 4\nC C C C C C\nS L R R C S\nS S S L C S\nC C C C C C\n6 6\nC L S S S C\nC C C S S C\nC C C S S C\nC L C S S C\nC C L S S C\nC S L S S C\n6 6\nC S S S S C\nS C S L C S\nS C S R C S\nS C L S C S\nS C R S C S\nC S S S S C\n4 4\nS C C S\nS C L S\nS L C S\nC C C C\n6 4\nC R S S L C\nC R L R L C\nC S C C S C\nC S S S S C\n0 0\n output: 24\n20\n148\n14\n0\n178\n\n" }, { "title": "Problem J: Infected Land", "content": "The earth is under an attack of a deadly virus. Luckily, prompt actions of the Ministry of\nHealth against this emergency successfully confined the spread of the infection within a square\ngrid of areas. Recently, public health specialists found an interesting pattern with regard to the\ntransition of infected areas. At each step in time, every area in the grid changes its infection\nstate according to infection states of its directly (horizontally, vertically, and diagonally) adjacent\nareas.\n\n An infected area continues to be infected if it has two or three adjacent infected areas.\n\n An uninfected area becomes infected if it has exactly three adjacent infected areas.\n\n An area becomes free of the virus, otherwise.\nYour mission is to fight against the virus and disinfect all the areas. The Ministry of Health\nlets an anti-virus vehicle prototype under your command. The functionality of the vehicle is\nsummarized as follows.\n\n At the beginning of each time step, you move the vehicle to one of the eight adjacent areas.\n The vehicle is not allowed to move to an infected area (to protect its operators from the\n virus). It is not allowed to stay in the same area.\n\n Following vehicle motion, all the areas, except for the area where the vehicle is in, change\n their infection states according to the transition rules described above. \n Special functionality of the vehicle protects its area from virus infection even if the area\n is adjacent to exactly three infected areas. Unfortunately, this virus-protection capability\n of the vehicle does not last. Once the vehicle leaves the area, depending on the infection\n states of the adjacent areas, the area can be infected. \n The area where the vehicle is in, which is uninfected, has the same effect to its adjacent\n areas as an infected area as far as the transition rules are concerned.\nThe following series of figures illustrate a sample scenario that successfully achieves the goal.\n\nInitially, your vehicle denoted by @ is found at (1,5) in a 5 * 5-grid of areas, and you see some\ninfected areas which are denoted by #'s.\n\nFirstly, at the beginning of time step 1, you move your vehicle diagonally to the southwest,\nthat is, to the area (2,4). Note that this vehicle motion was possible because this area was not\ninfected at the start of time step 1.\n\nFollowing this vehicle motion, infection state of each area changes according to the transition\nrules. The column \"1-end\" of the figure illustrates the result of such changes at the end of time\nstep 1. Note that the area (3,3) becomes infected because there were two adjacent infected areas\nand the vehicle was also in an adjacent area, three areas in total.\n\nIn time step 2, you move your vehicle to the west and position it at (2,3).\n\nThen infection states of other areas change. Note that even if your vehicle had exactly three\ninfected adjacent areas (west, southwest, and south), the area that is being visited by the vehicle\nis not infected. The result of such changes at the end of time step 2 is as depicted in \"2-end\".\n\nFinally, in time step 3, you move your vehicle to the east. After the change of the infection\nstates, you see that all the areas have become virus free! This completely disinfected situation\nis the goal. In the scenario we have seen, you have successfully disinfected all the areas in three\ntime steps by commanding the vehicle to move (1) southwest, (2) west, and (3) east.\n\nYour mission is to find the length of the shortest sequence(s) of vehicle motion commands that\ncan successfully disinfect all the areas.", "constraint": "", "input": "The input is a sequence of datasets. The end of the input is indicated by a line containing a\nsingle zero. Each dataset is formatted as follows.\n\nn\na_11 a_12 . . . a_1n\na_21 a_22 . . . a_2n\n. . . \na_n1 a_n2 . . . a_nn\n\nHere, n is the size of the grid. That means that the grid is comprised of n * n areas. You\nmay assume 1 <= n <= 5. The rest of the dataset consists of n lines of n letters. Each letter a_ij\nspecifies the state of the area at the beginning: '#' for infection, '. ' for free of virus, and '@' for\nthe initial location of the vehicle. The only character that can appear in a line is '#', '. ', or '@'.\nAmong n * n areas, there exists exactly one area which has '@'.", "output": "For each dataset, output the minimum number of time steps that is required to disinfect all the\nareas. If there exists no motion command sequence that leads to complete disinfection, output\n-1. The output should not contain any other extra character.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n...\n.@.\n...\n3\n.##\n.#.\n@##\n3\n##.\n#..\n@..\n5\n....@\n##...\n#....\n...#.\n##.##\n5\n#...#\n...#.\n#....\n...##\n..@..\n5\n#....\n.....\n.....\n.....\n..@..\n5\n#..#.\n#.#.#\n.#.#.\n....#\n.#@##\n5\n..##.\n..#..\n#....\n#....\n.#@..\n0\n output: 0\n10\n-1\n3\n2\n1\n6\n4"], "Pid": "p00883", "ProblemText": "Task Description: The earth is under an attack of a deadly virus. Luckily, prompt actions of the Ministry of\nHealth against this emergency successfully confined the spread of the infection within a square\ngrid of areas. Recently, public health specialists found an interesting pattern with regard to the\ntransition of infected areas. At each step in time, every area in the grid changes its infection\nstate according to infection states of its directly (horizontally, vertically, and diagonally) adjacent\nareas.\n\n An infected area continues to be infected if it has two or three adjacent infected areas.\n\n An uninfected area becomes infected if it has exactly three adjacent infected areas.\n\n An area becomes free of the virus, otherwise.\nYour mission is to fight against the virus and disinfect all the areas. The Ministry of Health\nlets an anti-virus vehicle prototype under your command. The functionality of the vehicle is\nsummarized as follows.\n\n At the beginning of each time step, you move the vehicle to one of the eight adjacent areas.\n The vehicle is not allowed to move to an infected area (to protect its operators from the\n virus). It is not allowed to stay in the same area.\n\n Following vehicle motion, all the areas, except for the area where the vehicle is in, change\n their infection states according to the transition rules described above. \n Special functionality of the vehicle protects its area from virus infection even if the area\n is adjacent to exactly three infected areas. Unfortunately, this virus-protection capability\n of the vehicle does not last. Once the vehicle leaves the area, depending on the infection\n states of the adjacent areas, the area can be infected. \n The area where the vehicle is in, which is uninfected, has the same effect to its adjacent\n areas as an infected area as far as the transition rules are concerned.\nThe following series of figures illustrate a sample scenario that successfully achieves the goal.\n\nInitially, your vehicle denoted by @ is found at (1,5) in a 5 * 5-grid of areas, and you see some\ninfected areas which are denoted by #'s.\n\nFirstly, at the beginning of time step 1, you move your vehicle diagonally to the southwest,\nthat is, to the area (2,4). Note that this vehicle motion was possible because this area was not\ninfected at the start of time step 1.\n\nFollowing this vehicle motion, infection state of each area changes according to the transition\nrules. The column \"1-end\" of the figure illustrates the result of such changes at the end of time\nstep 1. Note that the area (3,3) becomes infected because there were two adjacent infected areas\nand the vehicle was also in an adjacent area, three areas in total.\n\nIn time step 2, you move your vehicle to the west and position it at (2,3).\n\nThen infection states of other areas change. Note that even if your vehicle had exactly three\ninfected adjacent areas (west, southwest, and south), the area that is being visited by the vehicle\nis not infected. The result of such changes at the end of time step 2 is as depicted in \"2-end\".\n\nFinally, in time step 3, you move your vehicle to the east. After the change of the infection\nstates, you see that all the areas have become virus free! This completely disinfected situation\nis the goal. In the scenario we have seen, you have successfully disinfected all the areas in three\ntime steps by commanding the vehicle to move (1) southwest, (2) west, and (3) east.\n\nYour mission is to find the length of the shortest sequence(s) of vehicle motion commands that\ncan successfully disinfect all the areas.\nTask Input: The input is a sequence of datasets. The end of the input is indicated by a line containing a\nsingle zero. Each dataset is formatted as follows.\n\nn\na_11 a_12 . . . a_1n\na_21 a_22 . . . a_2n\n. . . \na_n1 a_n2 . . . a_nn\n\nHere, n is the size of the grid. That means that the grid is comprised of n * n areas. You\nmay assume 1 <= n <= 5. The rest of the dataset consists of n lines of n letters. Each letter a_ij\nspecifies the state of the area at the beginning: '#' for infection, '. ' for free of virus, and '@' for\nthe initial location of the vehicle. The only character that can appear in a line is '#', '. ', or '@'.\nAmong n * n areas, there exists exactly one area which has '@'.\nTask Output: For each dataset, output the minimum number of time steps that is required to disinfect all the\nareas. If there exists no motion command sequence that leads to complete disinfection, output\n-1. The output should not contain any other extra character.\nTask Samples: input: 3\n...\n.@.\n...\n3\n.##\n.#.\n@##\n3\n##.\n#..\n@..\n5\n....@\n##...\n#....\n...#.\n##.##\n5\n#...#\n...#.\n#....\n...##\n..@..\n5\n#....\n.....\n.....\n.....\n..@..\n5\n#..#.\n#.#.#\n.#.#.\n....#\n.#@##\n5\n..##.\n..#..\n#....\n#....\n.#@..\n0\n output: 0\n10\n-1\n3\n2\n1\n6\n4\n\n" }, { "title": "Problem A: Membership Management", "content": "Peter is a senior manager of Agile Change Management (ACM) Inc. , where each employee is a member of one or more task groups. Since ACM is agile, task groups are often reorganized and their members frequently change, so membership management is his constant headache.\n\nPeter updates the membership information whenever any changes occur: for instance, the following line written by him means that Carol and Alice are the members of the Design Group.\n\ndesign: carol, alice.\n\nThe name preceding the colon is the group name and the names following it specify its members.\n\nA smaller task group may be included in a larger one. So, a group name can appear as a member of another group, for instance, as follows. \n\ndevelopment: alice, bob, design, eve.\n\nSimply unfolding the design above gives the following membership specification, which is equivalent to the original.\n\ndevelopment: alice, bob, carol, alice, eve.\n\nIn this case, however, alice occurs twice. After removing one of the duplicates, we have the following more concise specification.\n\ndevelopment: alice, bob, carol, eve.\n\nYour mission in this problem is to write a program that, given group specifications, identifies group members.\n\nNote that Peter's specifications can include deeply nested groups. In the following, for instance, the group one contains a single member dave.\n\none: another.\nanother: yetanother.\nyetanother: dave.", "constraint": "", "input": "The input is a sequence of datasets, each being in the following format.\n\nn\ngroup_1: member_1,1, . . . , member_1, m1. \n. \n. \n. \ngroup_i: member_i, 1, . . . , member_i, mi. \n. \n. \n. \ngroup_n: member_n, 1, . . . , member_n, mn. \n\nThe first line contains n, which represents the number of groups and is a positive integer no more than 100. Each of the following n lines contains the membership information of a group: group_i (1 <= i <= n) is the name of the i-th task group and is followed by a colon (: ) and then the list of its m_i member s that are delimited by a comma (, ) and terminated by a period (. ).\n\nThose group names are mutually different. Each m_i (1 <= i <= n) is between 1 and 10, inclusive. A member is another group name if it is one of group_1, group_2, . . . , or groupn. Otherwise it is an employee name.\n\nThere are no circular (or recursive) definitions of group(s). You may assume that m_i member names of a group are mutually different.\n\nEach group or employee name is a non-empty character string of length between 1 and 15, inclusive, and consists of lowercase letters.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output the number of employees included in the first group of the dataset, that is group_1, in a line. No extra characters should occur in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0\n output: 4\n1\n6\n4\n2"], "Pid": "p00884", "ProblemText": "Task Description: Peter is a senior manager of Agile Change Management (ACM) Inc. , where each employee is a member of one or more task groups. Since ACM is agile, task groups are often reorganized and their members frequently change, so membership management is his constant headache.\n\nPeter updates the membership information whenever any changes occur: for instance, the following line written by him means that Carol and Alice are the members of the Design Group.\n\ndesign: carol, alice.\n\nThe name preceding the colon is the group name and the names following it specify its members.\n\nA smaller task group may be included in a larger one. So, a group name can appear as a member of another group, for instance, as follows. \n\ndevelopment: alice, bob, design, eve.\n\nSimply unfolding the design above gives the following membership specification, which is equivalent to the original.\n\ndevelopment: alice, bob, carol, alice, eve.\n\nIn this case, however, alice occurs twice. After removing one of the duplicates, we have the following more concise specification.\n\ndevelopment: alice, bob, carol, eve.\n\nYour mission in this problem is to write a program that, given group specifications, identifies group members.\n\nNote that Peter's specifications can include deeply nested groups. In the following, for instance, the group one contains a single member dave.\n\none: another.\nanother: yetanother.\nyetanother: dave.\nTask Input: The input is a sequence of datasets, each being in the following format.\n\nn\ngroup_1: member_1,1, . . . , member_1, m1. \n. \n. \n. \ngroup_i: member_i, 1, . . . , member_i, mi. \n. \n. \n. \ngroup_n: member_n, 1, . . . , member_n, mn. \n\nThe first line contains n, which represents the number of groups and is a positive integer no more than 100. Each of the following n lines contains the membership information of a group: group_i (1 <= i <= n) is the name of the i-th task group and is followed by a colon (: ) and then the list of its m_i member s that are delimited by a comma (, ) and terminated by a period (. ).\n\nThose group names are mutually different. Each m_i (1 <= i <= n) is between 1 and 10, inclusive. A member is another group name if it is one of group_1, group_2, . . . , or groupn. Otherwise it is an employee name.\n\nThere are no circular (or recursive) definitions of group(s). You may assume that m_i member names of a group are mutually different.\n\nEach group or employee name is a non-empty character string of length between 1 and 15, inclusive, and consists of lowercase letters.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output the number of employees included in the first group of the dataset, that is group_1, in a line. No extra characters should occur in the output.\nTask Samples: input: 2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0\n output: 4\n1\n6\n4\n2\n\n" }, { "title": "Problem B: Balloon Collecting", "content": "\"Balloons should be captured efficiently\", the game designer says. He is designing an oldfashioned game with two dimensional graphics. In the game, balloons fall onto the ground one after another, and the player manipulates a robot vehicle on the ground to capture the balloons. The player can control the vehicle to move left or right, or simply stay. When one of the balloons reaches the ground, the vehicle and the balloon must reside at the same position, otherwise the balloon will burst and the game ends.\n\nFigure B. 1: Robot vehicle and falling balloons\nThe goal of the game is to store all the balloons into the house at the left end on the game field. The vehicle can carry at most three balloons at a time, but its speed changes according to the number of the carrying balloons. When the vehicle carries k balloons (k = 0,1,2,3), it takes k+1 units of time to move one unit distance. The player will get higher score when the total moving distance of the vehicle is shorter.\n\nYour mission is to help the game designer check game data consisting of a set of balloons. Given a landing position (as the distance from the house) and a landing time of each balloon, you must judge whether a player can capture all the balloons, and answer the minimum moving distance needed to capture and store all the balloons. The vehicle starts from the house. If the player cannot capture all the balloons, you must identify the first balloon that the player cannot capture.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nn\np_1 t_1\n. \n. \n. \np_n t_n\n\nThe first line contains an integer n, which represents the number of balloons (0 < n <= 40). Each of the following n lines contains two integers p_i and t_i (1 <= i <= n) separated by a space. p_i and t_i represent the position and the time when the i-th balloon reaches the ground (0 < p_i <= 100,0 < t_i <= 50000). You can assume t_i < t_j for i < j. The position of the house is 0, and the game starts from the time 0.\n\nThe sizes of the vehicle, the house, and the balloons are small enough, and should be ignored. The vehicle needs 0 time for catching the balloons or storing them into the house. The vehicle can start moving immediately after these operations. \n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output one word and one integer in a line separated by a space. No extra characters should occur in the output.\n\n If the player can capture all the balloons, output \"OK\" and an integer that represents the minimum moving distance of the vehicle to capture and store all the balloons.\n If it is impossible for the player to capture all the balloons, output \"NG\" and an integer k such that the k-th balloon in the dataset is the first balloon that the player cannot capture.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n10 100\n100 270\n2\n10 100\n100 280\n3\n100 150\n10 360\n40 450\n3\n100 150\n10 360\n40 440\n2\n100 10\n50 200\n2\n100 100\n50 110\n1\n15 10\n4\n1 10\n2 20\n3 100\n90 200\n0\n output: OK 220\nOK 200\nOK 260\nOK 280\nNG 1\nNG 2\nNG 1\nOK 188"], "Pid": "p00885", "ProblemText": "Task Description: \"Balloons should be captured efficiently\", the game designer says. He is designing an oldfashioned game with two dimensional graphics. In the game, balloons fall onto the ground one after another, and the player manipulates a robot vehicle on the ground to capture the balloons. The player can control the vehicle to move left or right, or simply stay. When one of the balloons reaches the ground, the vehicle and the balloon must reside at the same position, otherwise the balloon will burst and the game ends.\n\nFigure B. 1: Robot vehicle and falling balloons\nThe goal of the game is to store all the balloons into the house at the left end on the game field. The vehicle can carry at most three balloons at a time, but its speed changes according to the number of the carrying balloons. When the vehicle carries k balloons (k = 0,1,2,3), it takes k+1 units of time to move one unit distance. The player will get higher score when the total moving distance of the vehicle is shorter.\n\nYour mission is to help the game designer check game data consisting of a set of balloons. Given a landing position (as the distance from the house) and a landing time of each balloon, you must judge whether a player can capture all the balloons, and answer the minimum moving distance needed to capture and store all the balloons. The vehicle starts from the house. If the player cannot capture all the balloons, you must identify the first balloon that the player cannot capture.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nn\np_1 t_1\n. \n. \n. \np_n t_n\n\nThe first line contains an integer n, which represents the number of balloons (0 < n <= 40). Each of the following n lines contains two integers p_i and t_i (1 <= i <= n) separated by a space. p_i and t_i represent the position and the time when the i-th balloon reaches the ground (0 < p_i <= 100,0 < t_i <= 50000). You can assume t_i < t_j for i < j. The position of the house is 0, and the game starts from the time 0.\n\nThe sizes of the vehicle, the house, and the balloons are small enough, and should be ignored. The vehicle needs 0 time for catching the balloons or storing them into the house. The vehicle can start moving immediately after these operations. \n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output one word and one integer in a line separated by a space. No extra characters should occur in the output.\n\n If the player can capture all the balloons, output \"OK\" and an integer that represents the minimum moving distance of the vehicle to capture and store all the balloons.\n If it is impossible for the player to capture all the balloons, output \"NG\" and an integer k such that the k-th balloon in the dataset is the first balloon that the player cannot capture.\nTask Samples: input: 2\n10 100\n100 270\n2\n10 100\n100 280\n3\n100 150\n10 360\n40 450\n3\n100 150\n10 360\n40 440\n2\n100 10\n50 200\n2\n100 100\n50 110\n1\n15 10\n4\n1 10\n2 20\n3 100\n90 200\n0\n output: OK 220\nOK 200\nOK 260\nOK 280\nNG 1\nNG 2\nNG 1\nOK 188\n\n" }, { "title": "Problem C: Towns along a Highway", "content": "There are several towns on a highway. The highway has no forks. Given the distances between the neighboring towns, we can calculate all distances from any town to others. For example, given five towns (A, B, C, D and E) and the distances between neighboring towns like in Figure C. 1, we can calculate the distance matrix as an upper triangular matrix containing the distances between all pairs of the towns, as shown in Figure C. 2.\nFigure C. 1: An example of towns\n\nFigure C. 2: The distance matrix for Figure C. 1\n\nIn this problem, you must solve the inverse problem. You know only the distances between all pairs of the towns, that is, N(N - 1)/2 numbers in the above matrix. Then, you should recover the order of the towns and the distances from each town to the next.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN\nd_1 d_2 . . . d_N(N-1)/2\n\nThe first line contains an integer N (2 <= N <= 20), which is the number of the towns on the highway. The following lines contain N(N-1)/2 integers separated by a single space or a newline, which are the distances between all pairs of the towns. Numbers are given in descending order without any information where they appear in the matrix. You can assume that each distance is between 1 and 400, inclusive. Notice that the longest distance is the distance from the leftmost town to the rightmost.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output N - 1 integers in a line, each of which is the distance from a town to the next in the order of the towns. Numbers in a line must be separated by a single space. If the answer is not unique, output multiple lines ordered by the lexicographical order as a sequence of integers, each of which corresponds to an answer. For example, '2 10' should precede '10 2'. If no answer exists, output nothing. At the end of the output for each dataset, a line containing five minus symbols '-----' should be printed for human readability. No extra characters should occur in the output. For example, extra spaces at the end of a line are not allowed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n1\n3\n5 3 2\n3\n6 3 2\n5\n9 8 7 6 6 4 3 2 2 1\n6\n9 8 8 7 6 6 5 5 3 3 3 2 2 1 1\n6\n11 10 9 8 7 6 6 5 5 4 3 2 2 1 1\n7\n72 65 55 51 48 45 40 38 34 32 27 25 24 23 21 17 14 13 11 10 7\n20\n190 189 188 187 186 185 184 183 182 181 180 179 178 177 176 175 174 173 172 171\n170 169 168 167 166 165 164 163 162 161 160 159 158 157 156 155 154 153 152 151\n150 149 148 147 146 145 144 143 142 141 140 139 138 137 136 135 134 133 132 131\n130 129 128 127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112 111\n110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91\n90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71\n70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51\n50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31\n30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11\n10 9 8 7 6 5 4 3 2 1\n19\n60 59 58 56 53 52 51 50 48 48 47 46 45 45 44 43 43 42 42 41 41 40 40 40\n40 40 40 40 39 39 39 38 38 38 37 37 36 36 35 35 34 33 33 32 32 32 31 31\n30 30 30 29 28 28 28 28 27 27 26 26 25 25 25 25 24 24 23 23 23 23 22 22\n22 22 21 21 21 21 20 20 20 20 20 20 20 20 20 20 20 20 20 19 19 19 19 19\n18 18 18 18 18 17 17 17 17 16 16 16 15 15 15 15 14 14 13 13 13 12 12 12\n12 12 11 11 11 10 10 10 10 10 9 9 8 8 8 8 8 8 7 7 7 6 6 6 5 5 5 5 5 5 4\n4 4 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1\n0\n output: 1\n-----\n2 3\n3 2\n-----\n-----\n1 2 4 2\n2 4 2 1\n-----\n1 2 3 2 1\n-----\n1 1 4 2 3\n1 5 1 2 2\n2 2 1 5 1\n3 2 4 1 1\n-----\n7 14 11 13 10 17\n17 10 13 11 14 7\n-----\n-----\n1 1 2 3 5 8 1 1 2 3 5 8 1 1 2 3 5 8\n8 5 3 2 1 1 8 5 3 2 1 1 8 5 3 2 1 1\n-----"], "Pid": "p00886", "ProblemText": "Task Description: There are several towns on a highway. The highway has no forks. Given the distances between the neighboring towns, we can calculate all distances from any town to others. For example, given five towns (A, B, C, D and E) and the distances between neighboring towns like in Figure C. 1, we can calculate the distance matrix as an upper triangular matrix containing the distances between all pairs of the towns, as shown in Figure C. 2.\nFigure C. 1: An example of towns\n\nFigure C. 2: The distance matrix for Figure C. 1\n\nIn this problem, you must solve the inverse problem. You know only the distances between all pairs of the towns, that is, N(N - 1)/2 numbers in the above matrix. Then, you should recover the order of the towns and the distances from each town to the next.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN\nd_1 d_2 . . . d_N(N-1)/2\n\nThe first line contains an integer N (2 <= N <= 20), which is the number of the towns on the highway. The following lines contain N(N-1)/2 integers separated by a single space or a newline, which are the distances between all pairs of the towns. Numbers are given in descending order without any information where they appear in the matrix. You can assume that each distance is between 1 and 400, inclusive. Notice that the longest distance is the distance from the leftmost town to the rightmost.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output N - 1 integers in a line, each of which is the distance from a town to the next in the order of the towns. Numbers in a line must be separated by a single space. If the answer is not unique, output multiple lines ordered by the lexicographical order as a sequence of integers, each of which corresponds to an answer. For example, '2 10' should precede '10 2'. If no answer exists, output nothing. At the end of the output for each dataset, a line containing five minus symbols '-----' should be printed for human readability. No extra characters should occur in the output. For example, extra spaces at the end of a line are not allowed.\nTask Samples: input: 2\n1\n3\n5 3 2\n3\n6 3 2\n5\n9 8 7 6 6 4 3 2 2 1\n6\n9 8 8 7 6 6 5 5 3 3 3 2 2 1 1\n6\n11 10 9 8 7 6 6 5 5 4 3 2 2 1 1\n7\n72 65 55 51 48 45 40 38 34 32 27 25 24 23 21 17 14 13 11 10 7\n20\n190 189 188 187 186 185 184 183 182 181 180 179 178 177 176 175 174 173 172 171\n170 169 168 167 166 165 164 163 162 161 160 159 158 157 156 155 154 153 152 151\n150 149 148 147 146 145 144 143 142 141 140 139 138 137 136 135 134 133 132 131\n130 129 128 127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112 111\n110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91\n90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71\n70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51\n50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31\n30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11\n10 9 8 7 6 5 4 3 2 1\n19\n60 59 58 56 53 52 51 50 48 48 47 46 45 45 44 43 43 42 42 41 41 40 40 40\n40 40 40 40 39 39 39 38 38 38 37 37 36 36 35 35 34 33 33 32 32 32 31 31\n30 30 30 29 28 28 28 28 27 27 26 26 25 25 25 25 24 24 23 23 23 23 22 22\n22 22 21 21 21 21 20 20 20 20 20 20 20 20 20 20 20 20 20 19 19 19 19 19\n18 18 18 18 18 17 17 17 17 16 16 16 15 15 15 15 14 14 13 13 13 12 12 12\n12 12 11 11 11 10 10 10 10 10 9 9 8 8 8 8 8 8 7 7 7 6 6 6 5 5 5 5 5 5 4\n4 4 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1\n0\n output: 1\n-----\n2 3\n3 2\n-----\n-----\n1 2 4 2\n2 4 2 1\n-----\n1 2 3 2 1\n-----\n1 1 4 2 3\n1 5 1 2 2\n2 2 1 5 1\n3 2 4 1 1\n-----\n7 14 11 13 10 17\n17 10 13 11 14 7\n-----\n-----\n1 1 2 3 5 8 1 1 2 3 5 8 1 1 2 3 5 8\n8 5 3 2 1 1 8 5 3 2 1 1 8 5 3 2 1 1\n-----\n\n" }, { "title": "Problem D: Awkward Lights", "content": "You are working as a night watchman in an office building. Your task is to check whether all the lights in the building are turned off after all the office workers in the building have left the office. If there are lights that are turned on, you must turn off those lights. This task is not as easy as it sounds to be because of the strange behavior of the lighting system of the building as described below. Although an electrical engineer checked the lighting system carefully, he could not determine the cause of this behavior. So you have no option but to continue to rely on this system for the time being.\n\nEach floor in the building consists of a grid of square rooms. Every room is equipped with one light and one toggle switch. A toggle switch has two positions but they do not mean fixed ON/OFF. When the position of the toggle switch of a room is changed to the other position, in addition to that room, the ON/OFF states of the lights of the rooms at a certain Manhattan distance from that room are reversed. The Manhattan distance between the room at (x_1, y_1) of a grid of rooms and the room at (x_2, y_2) is given by |x_1 - x_2| + |y_1 - y_2|. For example, if the position of the toggle switch of the room at (2,2) of a 4 * 4 grid of rooms is changed and the given Manhattan distance is two, the ON/OFF states of the lights of the rooms at (1,1), (1,3), (2,4), (3,1), (3,3), and (4,2) as well as at (2,2) are reversed as shown in Figure D. 1, where black and white squares represent the ON/OFF states of the lights.\n\nFigure D. 1: An example behavior of the lighting system\nYour mission is to write a program that answer whether all the lights on a floor can be turned off.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nm n d\nS_11 S_12 S_13 . . . S_1m\nS_21 S_22 S_23 . . . S_2m\n. . . \nS_n1 S_n2 S_n3 . . . S_nm\n\nThe first line of a dataset contains three integers. m and n (1 <= m <= 25,1 <= n <= 25) are the numbers of columns and rows of the grid, respectively. d (1 <= d <= m + n) indicates the Manhattan distance. Subsequent n lines of m integers are the initial ON/OFF states. Each S_ij (1 <= i <= n, 1 <= j <= m) indicates the initial ON/OFF state of the light of the room at (i, j): '0' for OFF and '1' for ON.\n\nThe end of the input is indicated by a line containing three zeros.", "output": "For each dataset, output '1' if all the lights can be turned off. If not, output '0'. In either case,\nprint it in one line for each input dataset.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0\n output: 1\n1\n0\n1\n0\n0\n1\n1\n0\n1"], "Pid": "p00887", "ProblemText": "Task Description: You are working as a night watchman in an office building. Your task is to check whether all the lights in the building are turned off after all the office workers in the building have left the office. If there are lights that are turned on, you must turn off those lights. This task is not as easy as it sounds to be because of the strange behavior of the lighting system of the building as described below. Although an electrical engineer checked the lighting system carefully, he could not determine the cause of this behavior. So you have no option but to continue to rely on this system for the time being.\n\nEach floor in the building consists of a grid of square rooms. Every room is equipped with one light and one toggle switch. A toggle switch has two positions but they do not mean fixed ON/OFF. When the position of the toggle switch of a room is changed to the other position, in addition to that room, the ON/OFF states of the lights of the rooms at a certain Manhattan distance from that room are reversed. The Manhattan distance between the room at (x_1, y_1) of a grid of rooms and the room at (x_2, y_2) is given by |x_1 - x_2| + |y_1 - y_2|. For example, if the position of the toggle switch of the room at (2,2) of a 4 * 4 grid of rooms is changed and the given Manhattan distance is two, the ON/OFF states of the lights of the rooms at (1,1), (1,3), (2,4), (3,1), (3,3), and (4,2) as well as at (2,2) are reversed as shown in Figure D. 1, where black and white squares represent the ON/OFF states of the lights.\n\nFigure D. 1: An example behavior of the lighting system\nYour mission is to write a program that answer whether all the lights on a floor can be turned off.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nm n d\nS_11 S_12 S_13 . . . S_1m\nS_21 S_22 S_23 . . . S_2m\n. . . \nS_n1 S_n2 S_n3 . . . S_nm\n\nThe first line of a dataset contains three integers. m and n (1 <= m <= 25,1 <= n <= 25) are the numbers of columns and rows of the grid, respectively. d (1 <= d <= m + n) indicates the Manhattan distance. Subsequent n lines of m integers are the initial ON/OFF states. Each S_ij (1 <= i <= n, 1 <= j <= m) indicates the initial ON/OFF state of the light of the room at (i, j): '0' for OFF and '1' for ON.\n\nThe end of the input is indicated by a line containing three zeros.\nTask Output: For each dataset, output '1' if all the lights can be turned off. If not, output '0'. In either case,\nprint it in one line for each input dataset.\nTask Samples: input: 1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0\n output: 1\n1\n0\n1\n0\n0\n1\n1\n0\n1\n\n" }, { "title": "Problem E: The Two Men of the Japanese Alps", "content": "Two experienced climbers are planning a first-ever attempt: they start at two points of the equal altitudes on a mountain range, move back and forth on a single route keeping their altitudes equal, and finally meet with each other at a point on the route. A wise man told them that if a route has no point lower than the start points (of the equal altitudes) there is at least a way to achieve the attempt. This is the reason why the two climbers dare to start planning this fancy attempt.\n\nThe two climbers already obtained altimeters (devices that indicate altitude) and communication devices that are needed for keeping their altitudes equal. They also picked up a candidate route for the attempt: the route consists of consequent line segments without branches; the two starting points are at the two ends of the route; there is no point lower than the two starting points of the equal altitudes. An illustration of the route is given in Figure E. 1 (this figure corresponds to the first dataset of the sample input).\n\nFigure E. 1: An illustration of a route\nThe attempt should be possible for the route as the wise man said. The two climbers, however, could not find a pair of move sequences to achieve the attempt, because they cannot keep their altitudes equal without a complex combination of both forward and backward moves. For example, for the route illustrated above: a climber starting at p_1 (say A) moves to s, and the other climber (say B) moves from p_6 to p_5; then A moves back to t while B moves to p_4; finally A arrives at p_3 and at the same time B also arrives at p_3. Things can be much more complicated and thus they asked you to write a program to find a pair of move sequences for them.\n\nThere may exist more than one possible pair of move sequences, and thus you are requested to find the pair of move sequences with the shortest length sum. Here, we measure the length along the route surface, i. e. , an uphill path from (0,0) to (3,4) has the length of 5.", "constraint": "", "input": "The input is a sequence of datasets.\n\nThe first line of each dataset has an integer indicating the number of points N (2 <= N <= 100) on the route. Each of the following N lines has the coordinates (x_i, y_i) (i = 1,2, . . . , N) of the points: the two start points are (x_1, y_1) and (x_N, y_N); the line segments of the route connect (x_i, y_i) and (x_i+1, y_i+1) for i = 1,2, . . . , N - 1. Here, x_i is the horizontal distance along the route from the start point x_1, and y_i is the altitude relative to the start point y_1. All the coordinates are non-negative integers smaller than 1000, and inequality x_i < x_i+1 holds for i = 1,2, . . , N - 1, and 0 = y_1 = y_N <= y_i for i = 2,3, . . . , N - 1.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output the minimum sum of lengths (along the route) of move sequences until the two climbers meet with each other at a point on the route. Each output value may not have an error greater than 0.01.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6\n0 0\n3 4\n9 12\n17 6\n21 9\n33 0\n5\n0 0\n10 0\n20 0\n30 0\n40 0\n10\n0 0\n1 2\n3 0\n6 3\n9 0\n11 2\n13 0\n15 2\n16 2\n18 0\n7\n0 0\n150 997\n300 1\n450 999\n600 2\n750 998\n900 0\n0\n output: 52.5\n40.0\n30.3356209304689\n10078.072814085803"], "Pid": "p00888", "ProblemText": "Task Description: Two experienced climbers are planning a first-ever attempt: they start at two points of the equal altitudes on a mountain range, move back and forth on a single route keeping their altitudes equal, and finally meet with each other at a point on the route. A wise man told them that if a route has no point lower than the start points (of the equal altitudes) there is at least a way to achieve the attempt. This is the reason why the two climbers dare to start planning this fancy attempt.\n\nThe two climbers already obtained altimeters (devices that indicate altitude) and communication devices that are needed for keeping their altitudes equal. They also picked up a candidate route for the attempt: the route consists of consequent line segments without branches; the two starting points are at the two ends of the route; there is no point lower than the two starting points of the equal altitudes. An illustration of the route is given in Figure E. 1 (this figure corresponds to the first dataset of the sample input).\n\nFigure E. 1: An illustration of a route\nThe attempt should be possible for the route as the wise man said. The two climbers, however, could not find a pair of move sequences to achieve the attempt, because they cannot keep their altitudes equal without a complex combination of both forward and backward moves. For example, for the route illustrated above: a climber starting at p_1 (say A) moves to s, and the other climber (say B) moves from p_6 to p_5; then A moves back to t while B moves to p_4; finally A arrives at p_3 and at the same time B also arrives at p_3. Things can be much more complicated and thus they asked you to write a program to find a pair of move sequences for them.\n\nThere may exist more than one possible pair of move sequences, and thus you are requested to find the pair of move sequences with the shortest length sum. Here, we measure the length along the route surface, i. e. , an uphill path from (0,0) to (3,4) has the length of 5.\nTask Input: The input is a sequence of datasets.\n\nThe first line of each dataset has an integer indicating the number of points N (2 <= N <= 100) on the route. Each of the following N lines has the coordinates (x_i, y_i) (i = 1,2, . . . , N) of the points: the two start points are (x_1, y_1) and (x_N, y_N); the line segments of the route connect (x_i, y_i) and (x_i+1, y_i+1) for i = 1,2, . . . , N - 1. Here, x_i is the horizontal distance along the route from the start point x_1, and y_i is the altitude relative to the start point y_1. All the coordinates are non-negative integers smaller than 1000, and inequality x_i < x_i+1 holds for i = 1,2, . . , N - 1, and 0 = y_1 = y_N <= y_i for i = 2,3, . . . , N - 1.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output the minimum sum of lengths (along the route) of move sequences until the two climbers meet with each other at a point on the route. Each output value may not have an error greater than 0.01.\nTask Samples: input: 6\n0 0\n3 4\n9 12\n17 6\n21 9\n33 0\n5\n0 0\n10 0\n20 0\n30 0\n40 0\n10\n0 0\n1 2\n3 0\n6 3\n9 0\n11 2\n13 0\n15 2\n16 2\n18 0\n7\n0 0\n150 997\n300 1\n450 999\n600 2\n750 998\n900 0\n0\n output: 52.5\n40.0\n30.3356209304689\n10078.072814085803\n\n" }, { "title": "Problem F: Find the Multiples", "content": "You are given a sequence a_0a_1. . . a_N-1 digits and a prime number Q. For each i <= j with a_i ! = 0, the subsequence a_ia_i+1. . . a_j can be read as a decimal representation of a positive integer. Subsequences with leading zeros are not considered. Your task is to count the number of pairs (i, j) such that the corresponding subsequence is a multiple of Q.", "constraint": "", "input": "The input consists of at most 50 datasets. Each dataset is represented by a line containing four integers N, S, W, and Q, separated by spaces, where 1 <= N <= 10^5,1 <= S <= 10^9,1 <= W <= 10^9, and Q is a prime number less than 10^8. The sequence a_0. . . a_N-1 of length N is generated by the following code, in which ai is written as a[i].\n\n int g = S;\n for(int i=0; ii (1 <= i <= m) are the originating node, the destination node and the associated cost of the i-th edge, each separated by a single space. They satisfy 1 <= f_i, t_i <= n and 0 <= c_i <= 10000. You can assume that f_i ! = t_i and (f_i, t_i) ! = (f_j, t_j) when i ! = j.\n\nYou can assume that, for each dataset, there is at least one path from node 1 to node n, and that the cost of the minimum cost path from node 1 to node n of the given graph is greater than c.\n\nThe end of the input is indicated by a line containing three zeros separated by single spaces.", "output": "For each dataset, output a line containing the minimum number of edges whose cost(s) should be changed in order to make the cost of the minimum cost path from node 1 to node n equal to the target cost c. Costs of edges cannot be made negative. The output should not contain any other extra characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3 3\n1 2 3\n2 3 3\n1 3 8\n12 12 2010\n1 2 0\n2 3 3000\n3 4 0\n4 5 3000\n5 6 3000\n6 12 2010\n2 7 100\n7 8 200\n8 9 300\n9 10 400\n10 11 500\n11 6 512\n10 18 1\n1 2 9\n1 3 2\n1 4 6\n2 5 0\n2 6 10\n2 7 2\n3 5 10\n3 6 3\n3 7 10\n4 7 6\n5 8 10\n6 8 2\n6 9 11\n7 9 3\n8 9 9\n8 10 8\n9 10 1\n8 2 1\n0 0 0\n output: 1\n2\n3"], "Pid": "p00890", "ProblemText": "Task Description: You are a judge of a programming contest. You are preparing a dataset for a graph problem to seek for the cost of the minimum cost path. You've generated some random cases, but they are not interesting. You want to produce a dataset whose answer is a desired value such as the number representing this year 2010. So you will tweak (which means 'adjust') the cost of the minimum cost path to a given value by changing the costs of some edges. The number of changes should be made as few as possible.\n\nA non-negative integer c and a directed graph G are given. Each edge of G is associated with a cost of a non-negative integer. Given a path from one node of G to another, we can define the cost of the path as the sum of the costs of edges constituting the path. Given a pair of nodes in G, we can associate it with a non-negative cost which is the minimum of the costs of paths connecting them.\n\nGiven a graph and a pair of nodes in it, you are asked to adjust the costs of edges so that the minimum cost path from one node to the other will be the given target cost c. You can assume that c is smaller than the cost of the minimum cost path between the given nodes in the original graph.\n\nFor example, in Figure G. 1, the minimum cost of the path from node 1 to node 3 in the given graph is 6. In order to adjust this minimum cost to 2, we can change the cost of the edge from node 1 to node 3 to 2. This direct edge becomes the minimum cost path after the change. \n\nFor another example, in Figure G. 2, the minimum cost of the path from node 1 to node 12 in the given graph is 4022. In order to adjust this minimum cost to 2010, we can change the cost of the edge from node 6 to node 12 and one of the six edges in the right half of the graph. There are many possibilities of edge modification, but the minimum number of modified edges is 2.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nn m c\nf_1 t_1 c_1\nf_2 t_2 c_2\n. \n. \n. \nf_m t_m c_m\n \n Figure G. 1: Example 1 of graph \n Figure G. 2: Example 2 of graph \n \n\nThe integers n, m and c are the number of the nodes, the number of the edges, and the target cost, respectively, each separated by a single space, where 2 <= n <= 100,1 <= m <= 1000 and 0 <= c <= 100000.\n\nEach node in the graph is represented by an integer 1 through n.\n\nThe following m lines represent edges: the integers f_i, t_i and ci (1 <= i <= m) are the originating node, the destination node and the associated cost of the i-th edge, each separated by a single space. They satisfy 1 <= f_i, t_i <= n and 0 <= c_i <= 10000. You can assume that f_i ! = t_i and (f_i, t_i) ! = (f_j, t_j) when i ! = j.\n\nYou can assume that, for each dataset, there is at least one path from node 1 to node n, and that the cost of the minimum cost path from node 1 to node n of the given graph is greater than c.\n\nThe end of the input is indicated by a line containing three zeros separated by single spaces.\nTask Output: For each dataset, output a line containing the minimum number of edges whose cost(s) should be changed in order to make the cost of the minimum cost path from node 1 to node n equal to the target cost c. Costs of edges cannot be made negative. The output should not contain any other extra characters.\nTask Samples: input: 3 3 3\n1 2 3\n2 3 3\n1 3 8\n12 12 2010\n1 2 0\n2 3 3000\n3 4 0\n4 5 3000\n5 6 3000\n6 12 2010\n2 7 100\n7 8 200\n8 9 300\n9 10 400\n10 11 500\n11 6 512\n10 18 1\n1 2 9\n1 3 2\n1 4 6\n2 5 0\n2 6 10\n2 7 2\n3 5 10\n3 6 3\n3 7 10\n4 7 6\n5 8 10\n6 8 2\n6 9 11\n7 9 3\n8 9 9\n8 10 8\n9 10 1\n8 2 1\n0 0 0\n output: 1\n2\n3\n\n" }, { "title": "Problem H: Where's Wally", "content": "Do you know the famous series of children's books named \"Where's Wally\"? Each of the books contains a variety of pictures of hundreds of people. Readers are challenged to find a person called Wally in the crowd.\n\nWe can consider \"Where's Wally\" as a kind of pattern matching of two-dimensional graphical images. Wally's figure is to be looked for in the picture. It would be interesting to write a computer program to solve \"Where's Wally\", but this is not an easy task since Wally in the pictures may be slightly different in his appearances. We give up the idea, and make the problem much easier to solve. You are requested to solve an easier version of the graphical pattern matching problem.\n\nAn image and a pattern are given. Both are rectangular matrices of bits (in fact, the pattern is always square-shaped). 0 means white, and 1 black. The problem here is to count the number of occurrences of the pattern in the image, i. e. the number of squares in the image exactly matching the pattern. Patterns appearing rotated by any multiples of 90 degrees and/or turned over forming a mirror image should also be taken into account.", "constraint": "", "input": "The input is a sequence of datasets each in the following format.\n\nw h p\nimage data\npattern data\n\nThe first line of a dataset consists of three positive integers w, h and p. w is the width of the image and h is the height of the image. Both are counted in numbers of bits. p is the width and height of the pattern. The pattern is always square-shaped. You may assume 1 <= w <= 1000,1 <= h <= 1000, and 1 <= p <= 100.\n\nThe following h lines give the image. Each line consists of ⌈w/6⌉ (which is equal to &⌊(w+5)/6⌋) characters, and corresponds to a horizontal line of the image. Each of these characters represents six bits on the image line, from left to right, in a variant of the BASE64 encoding format. The encoding rule is given in the following table. The most significant bit of the value in the table corresponds to the leftmost bit in the image. The last character may also represent a few bits beyond the width of the image; these bits should be ignored.\n \n \n character value (six bits) \n A-Z 0-25 \n\n a-z 26-51 \n\n 0-9 52-61 \n\n + 62 \n\n / 63 \n\n \nThe last p lines give the pattern. Each line consists of ⌈p/6⌉ characters, and is encoded in the same way as the image.\n\nA line containing three zeros indicates the end of the input. The total size of the input does not\nexceed two megabytes.", "output": "For each dataset in the input, one line containing the number of matched squares in the image should be output. An output line should not contain extra characters.\n\nTwo or more matching squares may be mutually overlapping. In such a case, they are counted separately. On the other hand, a single square is never counted twice or more, even if it matches both the original pattern and its rotation, for example.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 48 3 3\ngAY4I4wA\ngIIgIIgg\nw4IAYAg4\ng\ng\nw\n153 3 3\nkkkkkkkkkkkkkkkkkkkkkkkkkg\nSSSSSSSSSSSSSSSSSSSSSSSSSQ\nJJJJJJJJJJJJJJJJJJJJJJJJJI\ng\nQ\nI\n1 1 2\nA\nA\nA\n384 3 2\nABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/\nBCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/A\nCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/AB\nA\nA\n0 0 0\n output: 8\n51\n0\n98"], "Pid": "p00891", "ProblemText": "Task Description: Do you know the famous series of children's books named \"Where's Wally\"? Each of the books contains a variety of pictures of hundreds of people. Readers are challenged to find a person called Wally in the crowd.\n\nWe can consider \"Where's Wally\" as a kind of pattern matching of two-dimensional graphical images. Wally's figure is to be looked for in the picture. It would be interesting to write a computer program to solve \"Where's Wally\", but this is not an easy task since Wally in the pictures may be slightly different in his appearances. We give up the idea, and make the problem much easier to solve. You are requested to solve an easier version of the graphical pattern matching problem.\n\nAn image and a pattern are given. Both are rectangular matrices of bits (in fact, the pattern is always square-shaped). 0 means white, and 1 black. The problem here is to count the number of occurrences of the pattern in the image, i. e. the number of squares in the image exactly matching the pattern. Patterns appearing rotated by any multiples of 90 degrees and/or turned over forming a mirror image should also be taken into account.\nTask Input: The input is a sequence of datasets each in the following format.\n\nw h p\nimage data\npattern data\n\nThe first line of a dataset consists of three positive integers w, h and p. w is the width of the image and h is the height of the image. Both are counted in numbers of bits. p is the width and height of the pattern. The pattern is always square-shaped. You may assume 1 <= w <= 1000,1 <= h <= 1000, and 1 <= p <= 100.\n\nThe following h lines give the image. Each line consists of ⌈w/6⌉ (which is equal to &⌊(w+5)/6⌋) characters, and corresponds to a horizontal line of the image. Each of these characters represents six bits on the image line, from left to right, in a variant of the BASE64 encoding format. The encoding rule is given in the following table. The most significant bit of the value in the table corresponds to the leftmost bit in the image. The last character may also represent a few bits beyond the width of the image; these bits should be ignored.\n \n \n character value (six bits) \n A-Z 0-25 \n\n a-z 26-51 \n\n 0-9 52-61 \n\n + 62 \n\n / 63 \n\n \nThe last p lines give the pattern. Each line consists of ⌈p/6⌉ characters, and is encoded in the same way as the image.\n\nA line containing three zeros indicates the end of the input. The total size of the input does not\nexceed two megabytes.\nTask Output: For each dataset in the input, one line containing the number of matched squares in the image should be output. An output line should not contain extra characters.\n\nTwo or more matching squares may be mutually overlapping. In such a case, they are counted separately. On the other hand, a single square is never counted twice or more, even if it matches both the original pattern and its rotation, for example.\nTask Samples: input: 48 3 3\ngAY4I4wA\ngIIgIIgg\nw4IAYAg4\ng\ng\nw\n153 3 3\nkkkkkkkkkkkkkkkkkkkkkkkkkg\nSSSSSSSSSSSSSSSSSSSSSSSSSQ\nJJJJJJJJJJJJJJJJJJJJJJJJJI\ng\nQ\nI\n1 1 2\nA\nA\nA\n384 3 2\nABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/\nBCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/A\nCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/AB\nA\nA\n0 0 0\n output: 8\n51\n0\n98\n\n" }, { "title": "Problem I: Intersection of Two Prisms", "content": "Suppose that P_1 is an infinite-height prism whose axis is parallel to the z-axis, and P_2 is also an infinite-height prism whose axis is parallel to the y-axis. P_1 is defined by the polygon C_1 which is the cross section of P_1 and the xy-plane, and P_2 is also defined by the polygon C_2 which is the cross section of P_2 and the xz-plane.\n\nFigure I. 1 shows two cross sections which appear as the first dataset in the sample input, and\nFigure I. 2 shows the relationship between the prisms and their cross sections.\nFigure I. 1: Cross sections of Prisms\n\nFigure I. 2: Prisms and their cross sections\n\nFigure I. 3: Intersection of two prisms\n\nFigure I. 3 shows the intersection of two prisms in Figure I. 2, namely, P_1 and P_2.\n\nWrite a program which calculates the volume of the intersection of two prisms.", "constraint": "", "input": "The input is a sequence of datasets. The number of datasets is less than 200.\n\nEach dataset is formatted as follows.\n\nm n\nx_11 y_11\nx_12 y_12 \n. \n. \n. \nx_1m y_1m \nx_21 z_21\nx_22 z_22\n. \n. \n. \nx_2n z_2n\n\nm and n are integers (3 <= m <= 100,3 <= n <= 100) which represent the numbers of the vertices of the polygons, C_1 and C_2, respectively.\n\nx_1i, y1i, x_2j and z_2j are integers between -100 and 100, inclusive. (x_1i, y_1i) and (x_2j , z_2j) mean the i-th and j-th vertices' positions of C_1 and C_2 respectively.\n\nThe sequences of these vertex positions are given in the counterclockwise order either on the xy-plane or the xz-plane as in Figure I. 1.\n\nYou may assume that all the polygons are convex, that is, all the interior angles of the polygons are less than 180 degrees. You may also assume that all the polygons are simple, that is, each polygon's boundary does not cross nor touch itself.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output the volume of the intersection of the two prisms, P_1 and P_2, with a decimal representation in a line.\n\nNone of the output values may have an error greater than 0.001. The output should not contain any other extra characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 3\n7 2\n3 3\n0 2\n3 1\n4 2\n0 1\n8 1\n4 4\n30 2\n30 12\n2 12\n2 2\n15 2\n30 8\n13 14\n2 8\n8 5\n13 5\n21 7\n21 9\n18 15\n11 15\n6 10\n6 8\n8 5\n10 12\n5 9\n15 6\n20 10\n18 12\n3 3\n5 5\n10 3\n10 10\n20 8\n10 15\n10 8\n4 4\n-98 99\n-99 -99\n99 -98\n99 97\n-99 99\n-98 -98\n99 -99\n96 99\n0 0\n output: 4.708333333333333\n1680.0000000000005\n491.1500000000007\n0.0\n7600258.4847715655"], "Pid": "p00892", "ProblemText": "Task Description: Suppose that P_1 is an infinite-height prism whose axis is parallel to the z-axis, and P_2 is also an infinite-height prism whose axis is parallel to the y-axis. P_1 is defined by the polygon C_1 which is the cross section of P_1 and the xy-plane, and P_2 is also defined by the polygon C_2 which is the cross section of P_2 and the xz-plane.\n\nFigure I. 1 shows two cross sections which appear as the first dataset in the sample input, and\nFigure I. 2 shows the relationship between the prisms and their cross sections.\nFigure I. 1: Cross sections of Prisms\n\nFigure I. 2: Prisms and their cross sections\n\nFigure I. 3: Intersection of two prisms\n\nFigure I. 3 shows the intersection of two prisms in Figure I. 2, namely, P_1 and P_2.\n\nWrite a program which calculates the volume of the intersection of two prisms.\nTask Input: The input is a sequence of datasets. The number of datasets is less than 200.\n\nEach dataset is formatted as follows.\n\nm n\nx_11 y_11\nx_12 y_12 \n. \n. \n. \nx_1m y_1m \nx_21 z_21\nx_22 z_22\n. \n. \n. \nx_2n z_2n\n\nm and n are integers (3 <= m <= 100,3 <= n <= 100) which represent the numbers of the vertices of the polygons, C_1 and C_2, respectively.\n\nx_1i, y1i, x_2j and z_2j are integers between -100 and 100, inclusive. (x_1i, y_1i) and (x_2j , z_2j) mean the i-th and j-th vertices' positions of C_1 and C_2 respectively.\n\nThe sequences of these vertex positions are given in the counterclockwise order either on the xy-plane or the xz-plane as in Figure I. 1.\n\nYou may assume that all the polygons are convex, that is, all the interior angles of the polygons are less than 180 degrees. You may also assume that all the polygons are simple, that is, each polygon's boundary does not cross nor touch itself.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output the volume of the intersection of the two prisms, P_1 and P_2, with a decimal representation in a line.\n\nNone of the output values may have an error greater than 0.001. The output should not contain any other extra characters.\nTask Samples: input: 4 3\n7 2\n3 3\n0 2\n3 1\n4 2\n0 1\n8 1\n4 4\n30 2\n30 12\n2 12\n2 2\n15 2\n30 8\n13 14\n2 8\n8 5\n13 5\n21 7\n21 9\n18 15\n11 15\n6 10\n6 8\n8 5\n10 12\n5 9\n15 6\n20 10\n18 12\n3 3\n5 5\n10 3\n10 10\n20 8\n10 15\n10 8\n4 4\n-98 99\n-99 -99\n99 -98\n99 97\n-99 99\n-98 -98\n99 -99\n96 99\n0 0\n output: 4.708333333333333\n1680.0000000000005\n491.1500000000007\n0.0\n7600258.4847715655\n\n" }, { "title": "Problem J: Matrix Calculator", "content": "Dr. Jimbo, an applied mathematician, needs to calculate matrices all day for solving his own problems. In his laboratory, he uses an excellent application program for manipulating matrix expressions, however, he cannot use it outside his laboratory because the software consumes much of resources. He wants to manipulate matrices outside, so he needs a small program similar to the excellent application for his handheld computer. \n\nYour job is to provide him a program that computes expressions of matrices.\n\nExpressions of matrices are described in a simple language. Its syntax is shown in Table J. 1. Note that even a space and a newline have meaningful roles in the syntax.\n\nThe start symbol of this syntax is program that is defined as a sequence of assignments in Table J. 1. Each assignment has a variable on the left hand side of an equal symbol (\"=\") and an expression of matrices on the right hand side followed by a period and a newline (NL). It denotes an assignment of the value of the expression to the variable. The variable (var in Table J. 1) is indicated by an uppercase Roman letter. The value of the expression (expr) is a matrix or a scalar, whose elements are integers. Here, a scalar integer and a 1 * 1 matrix whose only element is the same integer can be used interchangeably.\n\nAn expression is one or more terms connected by \"+\" or \"-\" symbols. A term is one or more factors connected by \"*\" symbol. These operators (\"+\", \"-\", \"*\") are left associative.\n\nA factor is either a primary expression (primary) or a \"-\" symbol followed by a factor. This unary operator \"-\" is right associative.\n\nThe meaning of operators are the same as those in the ordinary arithmetic on matrices: Denoting matrices by A and B, A + B, A - B, A * B, and -A are defined as the matrix sum, difference, product, and negation. The sizes of A and B should be the same for addition and subtraction. The number of columns of A and the number of rows of B should be the same for multiplication.\n\nNote that all the operators +, -, * and unary - represent computations of addition, subtraction, multiplication and negation modulo M = 2^15 = 32768, respectively. Thus all the values are nonnegative integers between 0 and 32767, inclusive. For example, the result of an expression 2 - 3 should be 32767, instead of -1.\n\ninum is a non-negative decimal integer less than M.\n\nvar represents the matrix that is assigned to the variable var in the most recent preceding assignment statement of the same variable.\n\nmatrix represents a mathematical matrix similar to a 2-dimensional array whose elements are integers. It is denoted by a row-seq with a pair of enclosing square brackets. row-seq represents a sequence of rows, adjacent two of which are separated by a semicolon. row represents a sequence of expressions, adjacent two of which are separated by a space character.\n\nFor example, [1 2 3; 4 5 6] represents a matrix . The first row has three integers separated by two space characters, i. e. \"1 2 3\". The second row has three integers, i. e. \"4 5 6\". Here, the row-seq consists of the two rows separated by a semicolon. The matrix is denoted by the row-seq with a pair of square brackets.\n\nNote that elements of a row may be matrices again. Thus the nested representation of a matrix may appear. The number of rows of the value of each expression of a row should be the same, and the number of columns of the value of each row of a row-seq should be the same.\n\nFor example, a matrix represented by\n\n [[1 2 3; 4 5 6] [7 8; 9 10] [11; 12]; 13 14 15 16 17 18]\n\nis The sizes of matrices should be consistent, as mentioned above, in order to form a well-formed matrix as the result. For example, [[1 2; 3 4] [5; 6; 7]; 6 7 8] is not consistent since the first row \"[1 2; 3 4] [5; 6; 7]\" has two matrices (2 * 2 and 3 * 1) whose numbers of rows are different. [1 2; 3 4 5] is not consistent since the number of columns of two rows are different.\n\nThe multiplication of 1 * 1 matrix and m * n matrix is well-defined for arbitrary m > 0 and n > 0, since a 1 * 1 matrices can be regarded as a scalar integer. For example, 2*[1 2; 3 4] and [1 2; 3 4]*3 represent the products of a scalar and a matrix and . [2]*[1 2; 3 4] and [1 2; 3 4]*[3] are also well-defined similarly.\n\nAn indexed-primary is a primary expression followed by two expressions as indices. The first index is 1 * k integer matrix denoted by (i_1 i_2 . . . i_k), and the second index is 1 * l integer matrix denoted by (j_1 j_2 . . . j_l). The two indices specify the submatrix extracted from the matrix which is the value of the preceding primary expression. The size of the submatrix is k * l and whose (a, b)-element is the (i_a, j_b)-element of the value of the preceding primary expression. The way of indexing is one-origin, i. e. , the first element is indexed by 1.\n\nFor example, the value of ([1 2; 3 4]+[3 0; 0 2])([1], [2]) is equal to 2, since the value of its primary expression is a matrix [4 2; 3 6], and the first index [1] and the second [2] indicate the (1,2)-element of the matrix. The same integer may appear twice or more in an index matrix, e. g. , the first index matrix of an expression [1 2; 3 4]([2 1 1], [2 1]) is [2 1 1], which has two 1's. Its value is .\n\nA transposed-primary is a primary expression followed by a single quote symbol (\"'\"), which indicates the transpose operation. The transposed matrix of an m * n matrix A = (a_ij) (i = 1, . . . , m and j = 1, . . . , n) is the n * m matrix B = (b_ij) (i = 1, . . . , n and j = 1, . . . , m), where b_ij = a_ji. For example, the value of [1 2; 3 4]' is .", "constraint": "", "input": "The input consists of multiple datasets, followed by a line containing a zero. Each dataset has the following format.\n\nn\nprogram\n\nn is a positive integer, which is followed by a program that is a sequence of single or multiple \nlines each of which is an assignment statement whose syntax is defined in Table J. 1. n indicates \nthe number of the assignment statements in the program. All the values of vars are undefined at the beginning of a program.\n\nYou can assume the following:\n\n 1 <= n <= 10,\n\n the number of characters in a line does not exceed 80 (excluding a newline),\n\nthere are no syntax errors and semantic errors (e. g. , reference of undefined var),\n\n the number of rows of matrices appearing in the computations does not exceed 100, and\n\n the number of columns of matrices appearing in the computations does not exceed 100.", "output": "For each dataset, the value of the expression of each assignment statement of the program should be printed in the same order. All the values should be printed as non-negative integers less than M.\n\nWhen the value is an m * n matrix A = (a_ij) (i = 1, . . . , m and j = 1, . . . , n), m lines should be printed. In the k-th line (1 <= k <= m), integers of the k-th row, i. e. , a_k1, . . . , a_kn, should be printed separated by a space.\n\nAfter the last value of a dataset is printed, a line containing five minus symbols '-----' should be printed for human readability.\n\nThe output should not contain any other extra characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\nA=[1 2 3;4 5 6].\n1\nA=[[1 2 3;4 5 6] [7 8;9 10] [11;12];13 14 15 16 17 18].\n3\nB=[3 -2 1;-9 8 7].\nC=([1 2 3;4 5 6]+B)(2,3).\nD=([1 2 3;4 5 6]+B)([1 2],[2 3]).\n5\nA=2*[1 2;-3 4]'.\nB=A([2 1 2],[2 1]).\nA=[1 2;3 4]*3.\nA=[2]*[1 2;3 4].\nA=[1 2;3 4]*[3].\n2\nA=[11 12 13;0 22 23;0 0 33].\nA=[A A';--A''' A].\n2\nA=[1 -1 1;1 1 -1;-1 1 1]*3.\nA=[A -A+-A;-A'([3 2 1],[3 2 1]) -A'].\n1\nA=1([1 1 1],[1 1 1 1]).\n3\nA=[1 2 -3;4 -5 6;-7 8 9].\nB=A([3 1 2],[2 1 3]).\nC=A*B-B*A+-A*-B-B*-A.\n3\nA=[1 2 3 4 5].\nB=A'*A.\nC=B([1 5],[5 1]).\n3\nA=[-11 12 13;21 -22 23;31 32 -33].\nB=[1 0 0;0 1 0;0 0 1].\nC=[(A-B) (A+B)*B (A+B)*(B-A)([1 1 1],[3 2 1]) [1 2 3;2 1 1;-1 2 1]*(A-B)].\n3\nA=[11 12 13;0 22 23;0 0 33].\nB=[1 2].\nC=------A((((B))),B)(B,B)''''''.\n2\nA=1+[2]+[[3]]+[[[4]]]+2*[[[[5]]]]*3.\nB=[(-[([(-A)]+-A)])].\n8\nA=[1 2;3 4].\nB=[A A+[1 1;0 1]*4;A+[1 1;0 1]'*8 A+[1 1;0 1]''*12].\nC=B([1],[1]).\nC=B([1],[1 2 3 4]).\nC=B([1 2 3 4],[1]).\nC=B([2 3],[2 3]).\nA=[1 2;1 2].\nD=(A*-A+-A)'(A'(1,[1 2]),A'(2,[1 2])).\n0\n output: 1 2 3\n4 5 6\n-----\n1 2 3 7 8 11\n4 5 6 9 10 12\n13 14 15 16 17 18\n-----\n3 32766 1\n32759 8 7\n13\n0 4\n13 13\n-----\n2 32762\n4 8\n8 4\n32762 2\n8 4\n3 6\n9 12\n2 4\n6 8\n3 6\n9 12\n-----\n11 12 13\n0 22 23\n0 0 33\n11 12 13 11 0 0\n0 22 23 12 22 0\n0 0 33 13 23 33\n11 0 0 11 12 13\n12 22 0 0 22 23\n13 23 33 0 0 33\n-----\n3 32765 3\n3 3 32765\n32765 3 3\n3 32765 3 32762 6 32762\n3 3 32765 32762 32762 6\n32765 3 3 6 32762 32762\n32765 3 32765 32765 32765 3\n32765 32765 3 3 32765 32765\n3 32765 32765 32765 3 32765\n-----\n1 1 1 1\n1 1 1 1\n1 1 1 1\n-----\n1 2 32765\n4 32763 6\n32761 8 9\n8 32761 9\n2 1 32765\n32763 4 6\n54 32734 32738\n32752 32750 174\n32598 186 32702\n-----\n1 2 3 4 5\n1 2 3 4 5\n2 4 6 8 10\n3 6 9 12 15\n4 8 12 16 20\n5 10 15 20 25\n5 1\n25 5\n-----\n32757 12 13\n21 32746 23\n31 32 32735\n1 0 0\n0 1 0\n0 0 1\n32756 12 13 32758 12 13 32573 32588 180 123 62 32725\n21 32745 23 21 32747 23 32469 32492 276 28 33 15\n31 32 32734 31 32 32736 32365 32396 372 85 32742 32767\n-----\n11 12 13\n0 22 23\n0 0 33\n1 2\n11 12\n0 22\n-----\n40\n80\n-----\n1 2\n3 4\n1 2 5 6\n3 4 3 8\n9 2 13 14\n11 12 3 16\n1\n1 2 5 6\n1\n3\n9\n11\n4 3\n2 13\n1 2\n1 2\n32764 32764\n32764 32764\n-----"], "Pid": "p00893", "ProblemText": "Task Description: Dr. Jimbo, an applied mathematician, needs to calculate matrices all day for solving his own problems. In his laboratory, he uses an excellent application program for manipulating matrix expressions, however, he cannot use it outside his laboratory because the software consumes much of resources. He wants to manipulate matrices outside, so he needs a small program similar to the excellent application for his handheld computer. \n\nYour job is to provide him a program that computes expressions of matrices.\n\nExpressions of matrices are described in a simple language. Its syntax is shown in Table J. 1. Note that even a space and a newline have meaningful roles in the syntax.\n\nThe start symbol of this syntax is program that is defined as a sequence of assignments in Table J. 1. Each assignment has a variable on the left hand side of an equal symbol (\"=\") and an expression of matrices on the right hand side followed by a period and a newline (NL). It denotes an assignment of the value of the expression to the variable. The variable (var in Table J. 1) is indicated by an uppercase Roman letter. The value of the expression (expr) is a matrix or a scalar, whose elements are integers. Here, a scalar integer and a 1 * 1 matrix whose only element is the same integer can be used interchangeably.\n\nAn expression is one or more terms connected by \"+\" or \"-\" symbols. A term is one or more factors connected by \"*\" symbol. These operators (\"+\", \"-\", \"*\") are left associative.\n\nA factor is either a primary expression (primary) or a \"-\" symbol followed by a factor. This unary operator \"-\" is right associative.\n\nThe meaning of operators are the same as those in the ordinary arithmetic on matrices: Denoting matrices by A and B, A + B, A - B, A * B, and -A are defined as the matrix sum, difference, product, and negation. The sizes of A and B should be the same for addition and subtraction. The number of columns of A and the number of rows of B should be the same for multiplication.\n\nNote that all the operators +, -, * and unary - represent computations of addition, subtraction, multiplication and negation modulo M = 2^15 = 32768, respectively. Thus all the values are nonnegative integers between 0 and 32767, inclusive. For example, the result of an expression 2 - 3 should be 32767, instead of -1.\n\ninum is a non-negative decimal integer less than M.\n\nvar represents the matrix that is assigned to the variable var in the most recent preceding assignment statement of the same variable.\n\nmatrix represents a mathematical matrix similar to a 2-dimensional array whose elements are integers. It is denoted by a row-seq with a pair of enclosing square brackets. row-seq represents a sequence of rows, adjacent two of which are separated by a semicolon. row represents a sequence of expressions, adjacent two of which are separated by a space character.\n\nFor example, [1 2 3; 4 5 6] represents a matrix . The first row has three integers separated by two space characters, i. e. \"1 2 3\". The second row has three integers, i. e. \"4 5 6\". Here, the row-seq consists of the two rows separated by a semicolon. The matrix is denoted by the row-seq with a pair of square brackets.\n\nNote that elements of a row may be matrices again. Thus the nested representation of a matrix may appear. The number of rows of the value of each expression of a row should be the same, and the number of columns of the value of each row of a row-seq should be the same.\n\nFor example, a matrix represented by\n\n [[1 2 3; 4 5 6] [7 8; 9 10] [11; 12]; 13 14 15 16 17 18]\n\nis The sizes of matrices should be consistent, as mentioned above, in order to form a well-formed matrix as the result. For example, [[1 2; 3 4] [5; 6; 7]; 6 7 8] is not consistent since the first row \"[1 2; 3 4] [5; 6; 7]\" has two matrices (2 * 2 and 3 * 1) whose numbers of rows are different. [1 2; 3 4 5] is not consistent since the number of columns of two rows are different.\n\nThe multiplication of 1 * 1 matrix and m * n matrix is well-defined for arbitrary m > 0 and n > 0, since a 1 * 1 matrices can be regarded as a scalar integer. For example, 2*[1 2; 3 4] and [1 2; 3 4]*3 represent the products of a scalar and a matrix and . [2]*[1 2; 3 4] and [1 2; 3 4]*[3] are also well-defined similarly.\n\nAn indexed-primary is a primary expression followed by two expressions as indices. The first index is 1 * k integer matrix denoted by (i_1 i_2 . . . i_k), and the second index is 1 * l integer matrix denoted by (j_1 j_2 . . . j_l). The two indices specify the submatrix extracted from the matrix which is the value of the preceding primary expression. The size of the submatrix is k * l and whose (a, b)-element is the (i_a, j_b)-element of the value of the preceding primary expression. The way of indexing is one-origin, i. e. , the first element is indexed by 1.\n\nFor example, the value of ([1 2; 3 4]+[3 0; 0 2])([1], [2]) is equal to 2, since the value of its primary expression is a matrix [4 2; 3 6], and the first index [1] and the second [2] indicate the (1,2)-element of the matrix. The same integer may appear twice or more in an index matrix, e. g. , the first index matrix of an expression [1 2; 3 4]([2 1 1], [2 1]) is [2 1 1], which has two 1's. Its value is .\n\nA transposed-primary is a primary expression followed by a single quote symbol (\"'\"), which indicates the transpose operation. The transposed matrix of an m * n matrix A = (a_ij) (i = 1, . . . , m and j = 1, . . . , n) is the n * m matrix B = (b_ij) (i = 1, . . . , n and j = 1, . . . , m), where b_ij = a_ji. For example, the value of [1 2; 3 4]' is .\nTask Input: The input consists of multiple datasets, followed by a line containing a zero. Each dataset has the following format.\n\nn\nprogram\n\nn is a positive integer, which is followed by a program that is a sequence of single or multiple \nlines each of which is an assignment statement whose syntax is defined in Table J. 1. n indicates \nthe number of the assignment statements in the program. All the values of vars are undefined at the beginning of a program.\n\nYou can assume the following:\n\n 1 <= n <= 10,\n\n the number of characters in a line does not exceed 80 (excluding a newline),\n\nthere are no syntax errors and semantic errors (e. g. , reference of undefined var),\n\n the number of rows of matrices appearing in the computations does not exceed 100, and\n\n the number of columns of matrices appearing in the computations does not exceed 100.\nTask Output: For each dataset, the value of the expression of each assignment statement of the program should be printed in the same order. All the values should be printed as non-negative integers less than M.\n\nWhen the value is an m * n matrix A = (a_ij) (i = 1, . . . , m and j = 1, . . . , n), m lines should be printed. In the k-th line (1 <= k <= m), integers of the k-th row, i. e. , a_k1, . . . , a_kn, should be printed separated by a space.\n\nAfter the last value of a dataset is printed, a line containing five minus symbols '-----' should be printed for human readability.\n\nThe output should not contain any other extra characters.\nTask Samples: input: 1\nA=[1 2 3;4 5 6].\n1\nA=[[1 2 3;4 5 6] [7 8;9 10] [11;12];13 14 15 16 17 18].\n3\nB=[3 -2 1;-9 8 7].\nC=([1 2 3;4 5 6]+B)(2,3).\nD=([1 2 3;4 5 6]+B)([1 2],[2 3]).\n5\nA=2*[1 2;-3 4]'.\nB=A([2 1 2],[2 1]).\nA=[1 2;3 4]*3.\nA=[2]*[1 2;3 4].\nA=[1 2;3 4]*[3].\n2\nA=[11 12 13;0 22 23;0 0 33].\nA=[A A';--A''' A].\n2\nA=[1 -1 1;1 1 -1;-1 1 1]*3.\nA=[A -A+-A;-A'([3 2 1],[3 2 1]) -A'].\n1\nA=1([1 1 1],[1 1 1 1]).\n3\nA=[1 2 -3;4 -5 6;-7 8 9].\nB=A([3 1 2],[2 1 3]).\nC=A*B-B*A+-A*-B-B*-A.\n3\nA=[1 2 3 4 5].\nB=A'*A.\nC=B([1 5],[5 1]).\n3\nA=[-11 12 13;21 -22 23;31 32 -33].\nB=[1 0 0;0 1 0;0 0 1].\nC=[(A-B) (A+B)*B (A+B)*(B-A)([1 1 1],[3 2 1]) [1 2 3;2 1 1;-1 2 1]*(A-B)].\n3\nA=[11 12 13;0 22 23;0 0 33].\nB=[1 2].\nC=------A((((B))),B)(B,B)''''''.\n2\nA=1+[2]+[[3]]+[[[4]]]+2*[[[[5]]]]*3.\nB=[(-[([(-A)]+-A)])].\n8\nA=[1 2;3 4].\nB=[A A+[1 1;0 1]*4;A+[1 1;0 1]'*8 A+[1 1;0 1]''*12].\nC=B([1],[1]).\nC=B([1],[1 2 3 4]).\nC=B([1 2 3 4],[1]).\nC=B([2 3],[2 3]).\nA=[1 2;1 2].\nD=(A*-A+-A)'(A'(1,[1 2]),A'(2,[1 2])).\n0\n output: 1 2 3\n4 5 6\n-----\n1 2 3 7 8 11\n4 5 6 9 10 12\n13 14 15 16 17 18\n-----\n3 32766 1\n32759 8 7\n13\n0 4\n13 13\n-----\n2 32762\n4 8\n8 4\n32762 2\n8 4\n3 6\n9 12\n2 4\n6 8\n3 6\n9 12\n-----\n11 12 13\n0 22 23\n0 0 33\n11 12 13 11 0 0\n0 22 23 12 22 0\n0 0 33 13 23 33\n11 0 0 11 12 13\n12 22 0 0 22 23\n13 23 33 0 0 33\n-----\n3 32765 3\n3 3 32765\n32765 3 3\n3 32765 3 32762 6 32762\n3 3 32765 32762 32762 6\n32765 3 3 6 32762 32762\n32765 3 32765 32765 32765 3\n32765 32765 3 3 32765 32765\n3 32765 32765 32765 3 32765\n-----\n1 1 1 1\n1 1 1 1\n1 1 1 1\n-----\n1 2 32765\n4 32763 6\n32761 8 9\n8 32761 9\n2 1 32765\n32763 4 6\n54 32734 32738\n32752 32750 174\n32598 186 32702\n-----\n1 2 3 4 5\n1 2 3 4 5\n2 4 6 8 10\n3 6 9 12 15\n4 8 12 16 20\n5 10 15 20 25\n5 1\n25 5\n-----\n32757 12 13\n21 32746 23\n31 32 32735\n1 0 0\n0 1 0\n0 0 1\n32756 12 13 32758 12 13 32573 32588 180 123 62 32725\n21 32745 23 21 32747 23 32469 32492 276 28 33 15\n31 32 32734 31 32 32736 32365 32396 372 85 32742 32767\n-----\n11 12 13\n0 22 23\n0 0 33\n1 2\n11 12\n0 22\n-----\n40\n80\n-----\n1 2\n3 4\n1 2 5 6\n3 4 3 8\n9 2 13 14\n11 12 3 16\n1\n1 2 5 6\n1\n3\n9\n11\n4 3\n2 13\n1 2\n1 2\n32764 32764\n32764 32764\n-----\n\n" }, { "title": "Problem A: Gift from the Goddess of Programming", "content": "The goddess of programming is reviewing a thick logbook, which is a yearly record of visitors\nto her holy altar of programming. The logbook also records her visits at the altar.\n\nThe altar attracts programmers from all over the world because one visitor is chosen every\nyear and endowed with a gift of miracle programming power by the goddess. The endowed\nprogrammer is chosen from those programmers who spent the longest time at the altar during\nthe goddess's presence. There have been enthusiastic visitors who spent very long time at the\naltar but failed to receive the gift because the goddess was absent during their visits.\n\nNow, your mission is to write a program that finds how long the programmer to be endowed\nstayed at the altar during the goddess's presence.", "constraint": "", "input": "The input is a sequence of datasets. The number of datasets is less than 100. Each dataset is\nformatted as follows.\n\nn\nM_1/D_1 h_1: m_1e_1 p_1\nM_2/D_2 h_2: m_2e_2 p_2\n. \n. \n. \nM_n/D_n h_n: m_ne_n p_n\n\nThe first line of a dataset contains a positive even integer, n <= 1000, which denotes the number\nof lines of the logbook. This line is followed by n lines of space-separated data, where M_i/D_i\nidentifies the month and the day of the visit, h_i: m_i represents the time of either the entrance\nto or exit from the altar, e_i is either I for entrance, or O for exit, and p_i identifies the visitor.\n\nAll the lines in the logbook are formatted in a fixed-column format. Both the month and the\nday in the month are represented by two digits. Therefore April 1 is represented by 04/01 and\nnot by 4/1. The time is described in the 24-hour system, taking two digits for the hour, followed\nby a colon and two digits for minutes, 09: 13 for instance and not like 9: 13. A programmer is\nidentified by an ID, a unique number using three digits. The same format is used to indicate\nentrance and exit of the goddess, whose ID is 000.\n\nAll the lines in the logbook are sorted in ascending order with respect to date and time. Because\nthe altar is closed at midnight, the altar is emptied at 00: 00. You may assume that each time\nin the input is between 00: 01 and 23: 59, inclusive.\n\nA programmer may leave the altar just after entering it. In this case, the entrance and exit\ntime are the same and the length of such a visit is considered 0 minute. You may assume for\nsuch entrance and exit records, the line that corresponds to the entrance appears earlier in the\ninput than the line that corresponds to the exit. You may assume that at least one programmer\nappears in the logbook.\n\nThe end of the input is indicated by a line containing a single zero.", "output": "For each dataset, output the total sum of the blessed time of the endowed programmer. The\nblessed time of a programmer is the length of his/her stay at the altar during the presence of\nthe goddess. The endowed programmer is the one whose total blessed time is the longest among\nall the programmers. The output should be represented in minutes. Note that the goddess of\nprogramming is not a programmer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 14\n04/21 09:00 I 000\n04/21 09:00 I 001\n04/21 09:15 I 002\n04/21 09:30 O 001\n04/21 09:45 O 000\n04/21 10:00 O 002\n04/28 09:00 I 003\n04/28 09:15 I 000\n04/28 09:30 I 004\n04/28 09:45 O 004\n04/28 10:00 O 000\n04/28 10:15 O 003\n04/29 20:00 I 002\n04/29 21:30 O 002\n20\n06/01 09:00 I 001\n06/01 09:15 I 002\n06/01 09:15 I 003\n06/01 09:30 O 002\n06/01 10:00 I 000\n06/01 10:15 O 001\n06/01 10:30 I 002\n06/01 10:45 O 002\n06/01 11:00 I 001\n06/01 11:15 O 000\n06/01 11:30 I 002\n06/01 11:45 O 001\n06/01 12:00 O 002\n06/01 12:15 I 000\n06/01 12:30 I 002\n06/01 12:45 O 000\n06/01 13:00 I 000\n06/01 13:15 O 000\n06/01 13:30 O 002\n06/01 13:45 O 003\n0\n output: 45\n120"], "Pid": "p00894", "ProblemText": "Task Description: The goddess of programming is reviewing a thick logbook, which is a yearly record of visitors\nto her holy altar of programming. The logbook also records her visits at the altar.\n\nThe altar attracts programmers from all over the world because one visitor is chosen every\nyear and endowed with a gift of miracle programming power by the goddess. The endowed\nprogrammer is chosen from those programmers who spent the longest time at the altar during\nthe goddess's presence. There have been enthusiastic visitors who spent very long time at the\naltar but failed to receive the gift because the goddess was absent during their visits.\n\nNow, your mission is to write a program that finds how long the programmer to be endowed\nstayed at the altar during the goddess's presence.\nTask Input: The input is a sequence of datasets. The number of datasets is less than 100. Each dataset is\nformatted as follows.\n\nn\nM_1/D_1 h_1: m_1e_1 p_1\nM_2/D_2 h_2: m_2e_2 p_2\n. \n. \n. \nM_n/D_n h_n: m_ne_n p_n\n\nThe first line of a dataset contains a positive even integer, n <= 1000, which denotes the number\nof lines of the logbook. This line is followed by n lines of space-separated data, where M_i/D_i\nidentifies the month and the day of the visit, h_i: m_i represents the time of either the entrance\nto or exit from the altar, e_i is either I for entrance, or O for exit, and p_i identifies the visitor.\n\nAll the lines in the logbook are formatted in a fixed-column format. Both the month and the\nday in the month are represented by two digits. Therefore April 1 is represented by 04/01 and\nnot by 4/1. The time is described in the 24-hour system, taking two digits for the hour, followed\nby a colon and two digits for minutes, 09: 13 for instance and not like 9: 13. A programmer is\nidentified by an ID, a unique number using three digits. The same format is used to indicate\nentrance and exit of the goddess, whose ID is 000.\n\nAll the lines in the logbook are sorted in ascending order with respect to date and time. Because\nthe altar is closed at midnight, the altar is emptied at 00: 00. You may assume that each time\nin the input is between 00: 01 and 23: 59, inclusive.\n\nA programmer may leave the altar just after entering it. In this case, the entrance and exit\ntime are the same and the length of such a visit is considered 0 minute. You may assume for\nsuch entrance and exit records, the line that corresponds to the entrance appears earlier in the\ninput than the line that corresponds to the exit. You may assume that at least one programmer\nappears in the logbook.\n\nThe end of the input is indicated by a line containing a single zero.\nTask Output: For each dataset, output the total sum of the blessed time of the endowed programmer. The\nblessed time of a programmer is the length of his/her stay at the altar during the presence of\nthe goddess. The endowed programmer is the one whose total blessed time is the longest among\nall the programmers. The output should be represented in minutes. Note that the goddess of\nprogramming is not a programmer.\nTask Samples: input: 14\n04/21 09:00 I 000\n04/21 09:00 I 001\n04/21 09:15 I 002\n04/21 09:30 O 001\n04/21 09:45 O 000\n04/21 10:00 O 002\n04/28 09:00 I 003\n04/28 09:15 I 000\n04/28 09:30 I 004\n04/28 09:45 O 004\n04/28 10:00 O 000\n04/28 10:15 O 003\n04/29 20:00 I 002\n04/29 21:30 O 002\n20\n06/01 09:00 I 001\n06/01 09:15 I 002\n06/01 09:15 I 003\n06/01 09:30 O 002\n06/01 10:00 I 000\n06/01 10:15 O 001\n06/01 10:30 I 002\n06/01 10:45 O 002\n06/01 11:00 I 001\n06/01 11:15 O 000\n06/01 11:30 I 002\n06/01 11:45 O 001\n06/01 12:00 O 002\n06/01 12:15 I 000\n06/01 12:30 I 002\n06/01 12:45 O 000\n06/01 13:00 I 000\n06/01 13:15 O 000\n06/01 13:30 O 002\n06/01 13:45 O 003\n0\n output: 45\n120\n\n" }, { "title": "Problem B: The Sorcerer's Donut", "content": "Your master went to the town for a day. You could have a relaxed day without hearing his\nscolding. But he ordered you to make donuts dough by the evening. Loving donuts so much, he\ncan't live without eating tens of donuts everyday. What a chore for such a beautiful day.\n\nBut last week, you overheard a magic spell that your master was using. It was the time to\ntry. You casted the spell on a broomstick sitting on a corner of the kitchen. With a flash of\nlights, the broom sprouted two arms and two legs, and became alive. You ordered him, then he\nbrought flour from the storage, and started kneading dough. The spell worked, and how fast he\nkneaded it!\n\nA few minutes later, there was a tall pile of dough on the kitchen table. That was enough for\nthe next week. \\OK, stop now. \" You ordered. But he didn't stop. Help! You didn't know the\nspell to stop him! Soon the kitchen table was filled with hundreds of pieces of dough, and he\nstill worked as fast as he could. If you could not stop him now, you would be choked in the\nkitchen filled with pieces of dough.\n\nWait, didn't your master write his spells on his notebooks? You went to his den, and found the\nnotebook that recorded the spell of cessation.\n\nBut it was not the end of the story. The spell written in the notebook is not easily read by\nothers. He used a plastic model of a donut as a notebook for recording the spell. He split the\nsurface of the donut-shaped model into square mesh (Figure B. 1), and filled with the letters\n(Figure B. 2). He hid the spell so carefully that the pattern on the surface looked meaningless.\nBut you knew that he wrote the pattern so that the spell \"appears\" more than once (see the next\nparagraph for the precise conditions). The spell was not necessarily written in the left-to-right\ndirection, but any of the 8 directions, namely left-to-right, right-to-left, top-down, bottom-up,\nand the 4 diagonal directions.\n\nYou should be able to find the spell as the longest string that appears more than once. Here,\na string is considered to appear more than once if there are square sequences having the string\non the donut that satisfy the following conditions. \nEach square sequence does not overlap itself. (Two square sequences can share some squares. )\n\nThe square sequences start from different squares, and/or go to different directions.\n\n \n \n\n \n \n\n \n \n \nFigure B. 1: The Sorcerer's Donut Before\nFilled with Letters, Showing the Mesh and 8\nPossible Spell Directions \n \n
    \n\nFigure B. 2: The Sorcerer's Donut After Filled\nwith Letters\n\n \n\n \n\nNote that a palindrome (i. e. , a string that is the same whether you read it backwards or forwards)\nthat satisfies the first condition \"appears\" twice.\n\nThe pattern on the donut is given as a matrix of letters as follows.\n\nABCD\nEFGH\nIJKL\n\nNote that the surface of the donut has no ends; the top and bottom sides, and the left and right\nsides of the pattern are respectively connected. There can be square sequences longer than both\nthe vertical and horizontal lengths of the pattern. For example, from the letter F in the above\npattern, the strings in the longest non-self-overlapping sequences towards the 8 directions are\nas follows.\n\nFGHE\nFKDEJCHIBGLA\nFJB\nFIDGJAHKBELC\nFEHG\nFALGBIHCJEDK\nFBJ\nFCLEBKHAJGDI\n\nPlease write a program that finds the magic spell before you will be choked with pieces of donuts\ndough.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset begins with a line of two integers h and w,\nwhich denote the size of the pattern, followed by h lines of w uppercase letters from A to Z,\ninclusive, which denote the pattern on the donut. You may assume 3 <= h <= 10 and 3 <= w <= 20.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output the magic spell. If there is more than one longest string of the same\nlength, the first one in the dictionary order must be the spell. The spell is known to be at least\ntwo letters long. When no spell is found, output 0 (zero).", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 7\nRRCABXT\nAABMFAB\nRROMJAC\nAPTADAB\nYABADAO\n3 13\nABCDEFGHIJKLM\nXMADAMIMADAMY\nACEGIKMOQSUWY\n3 4\nDEFG\nACAB\nHIJK\n3 6\nABCDEF\nGHIAKL\nMNOPQR\n10 19\nJFZODYDXMZZPEYTRNCW\nXVGHPOKEYNZTQFZJKOD\nEYEHHQKHFZOVNRGOOLP\nQFZOIHRQMGHPNISHXOC\nDRGILJHSQEHHQLYTILL\nNCSHQMKHTZZIHRPAUJA\nNCCTINCLAUTFJHSZBVK\nLPBAUJIUMBVQYKHTZCW\nXMYHBVKUGNCWTLLAUID\nEYNDCCWLEOODXYUMBVN\n0 0\n output: ABRACADABRA\nMADAMIMADAM\nABAC\n0\nABCDEFGHIJKLMNOPQRSTUVWXYZHHHHHABCDEFGHIJKLMNOPQRSTUVWXYZ"], "Pid": "p00895", "ProblemText": "Task Description: Your master went to the town for a day. You could have a relaxed day without hearing his\nscolding. But he ordered you to make donuts dough by the evening. Loving donuts so much, he\ncan't live without eating tens of donuts everyday. What a chore for such a beautiful day.\n\nBut last week, you overheard a magic spell that your master was using. It was the time to\ntry. You casted the spell on a broomstick sitting on a corner of the kitchen. With a flash of\nlights, the broom sprouted two arms and two legs, and became alive. You ordered him, then he\nbrought flour from the storage, and started kneading dough. The spell worked, and how fast he\nkneaded it!\n\nA few minutes later, there was a tall pile of dough on the kitchen table. That was enough for\nthe next week. \\OK, stop now. \" You ordered. But he didn't stop. Help! You didn't know the\nspell to stop him! Soon the kitchen table was filled with hundreds of pieces of dough, and he\nstill worked as fast as he could. If you could not stop him now, you would be choked in the\nkitchen filled with pieces of dough.\n\nWait, didn't your master write his spells on his notebooks? You went to his den, and found the\nnotebook that recorded the spell of cessation.\n\nBut it was not the end of the story. The spell written in the notebook is not easily read by\nothers. He used a plastic model of a donut as a notebook for recording the spell. He split the\nsurface of the donut-shaped model into square mesh (Figure B. 1), and filled with the letters\n(Figure B. 2). He hid the spell so carefully that the pattern on the surface looked meaningless.\nBut you knew that he wrote the pattern so that the spell \"appears\" more than once (see the next\nparagraph for the precise conditions). The spell was not necessarily written in the left-to-right\ndirection, but any of the 8 directions, namely left-to-right, right-to-left, top-down, bottom-up,\nand the 4 diagonal directions.\n\nYou should be able to find the spell as the longest string that appears more than once. Here,\na string is considered to appear more than once if there are square sequences having the string\non the donut that satisfy the following conditions. \nEach square sequence does not overlap itself. (Two square sequences can share some squares. )\n\nThe square sequences start from different squares, and/or go to different directions.\n\n \n \n\n \n \n\n \n \n \nFigure B. 1: The Sorcerer's Donut Before\nFilled with Letters, Showing the Mesh and 8\nPossible Spell Directions \n \n
    \n\nFigure B. 2: The Sorcerer's Donut After Filled\nwith Letters\n\n \n\n \n\nNote that a palindrome (i. e. , a string that is the same whether you read it backwards or forwards)\nthat satisfies the first condition \"appears\" twice.\n\nThe pattern on the donut is given as a matrix of letters as follows.\n\nABCD\nEFGH\nIJKL\n\nNote that the surface of the donut has no ends; the top and bottom sides, and the left and right\nsides of the pattern are respectively connected. There can be square sequences longer than both\nthe vertical and horizontal lengths of the pattern. For example, from the letter F in the above\npattern, the strings in the longest non-self-overlapping sequences towards the 8 directions are\nas follows.\n\nFGHE\nFKDEJCHIBGLA\nFJB\nFIDGJAHKBELC\nFEHG\nFALGBIHCJEDK\nFBJ\nFCLEBKHAJGDI\n\nPlease write a program that finds the magic spell before you will be choked with pieces of donuts\ndough.\nTask Input: The input is a sequence of datasets. Each dataset begins with a line of two integers h and w,\nwhich denote the size of the pattern, followed by h lines of w uppercase letters from A to Z,\ninclusive, which denote the pattern on the donut. You may assume 3 <= h <= 10 and 3 <= w <= 20.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output the magic spell. If there is more than one longest string of the same\nlength, the first one in the dictionary order must be the spell. The spell is known to be at least\ntwo letters long. When no spell is found, output 0 (zero).\nTask Samples: input: 5 7\nRRCABXT\nAABMFAB\nRROMJAC\nAPTADAB\nYABADAO\n3 13\nABCDEFGHIJKLM\nXMADAMIMADAMY\nACEGIKMOQSUWY\n3 4\nDEFG\nACAB\nHIJK\n3 6\nABCDEF\nGHIAKL\nMNOPQR\n10 19\nJFZODYDXMZZPEYTRNCW\nXVGHPOKEYNZTQFZJKOD\nEYEHHQKHFZOVNRGOOLP\nQFZOIHRQMGHPNISHXOC\nDRGILJHSQEHHQLYTILL\nNCSHQMKHTZZIHRPAUJA\nNCCTINCLAUTFJHSZBVK\nLPBAUJIUMBVQYKHTZCW\nXMYHBVKUGNCWTLLAUID\nEYNDCCWLEOODXYUMBVN\n0 0\n output: ABRACADABRA\nMADAMIMADAM\nABAC\n0\nABCDEFGHIJKLMNOPQRSTUVWXYZHHHHHABCDEFGHIJKLMNOPQRSTUVWXYZ\n\n" }, { "title": "Problem C: Weaker than Planned", "content": "The committee members of the Kitoshima programming contest had decided to use crypto-graphic software for their secret communication. They had asked a company, Kodai Software,\nto develop cryptographic software that employed a cipher based on highly sophisticated mathematics.\n\nAccording to reports on IT projects, many projects are not delivered on time, on budget, with\nrequired features and functions. This applied to this case. Kodai Software failed to implement\nthe cipher by the appointed date of delivery, and asked to use a simpler version that employed\na type of substitution cipher for the moment. The committee members got angry and strongly\nrequested to deliver the full specification product, but they unwillingly decided to use this inferior\nproduct for the moment.\n\nIn what follows, we call the text before encryption, plaintext, and the text after encryption, \nciphertext.\n\nThis simple cipher substitutes letters in the plaintext, and its substitution rule is specified with\na set of pairs. A pair consists of two letters and is unordered, that is, the order of the letters\nin the pair does not matter. A pair (A, B) and a pair (B, A) have the same meaning. In one\nsubstitution rule, one letter can appear in at most one single pair. When a letter in a pair\nappears in the plaintext, the letter is replaced with the other letter in the pair. Letters not\nspecified in any pairs are left as they are.\n\nFor example, by substituting the plaintext\n\nABCDEFGHIJKLMNOPQRSTUVWXYZ\n\nwith the substitution rule {(A, Z), (B, Y)} results in the following ciphertext.\n\nZYCDEFGHIJKLMNOPQRSTUVWXBA\n\nThis may be a big chance for us, because the substitution rule seems weak against cracking.\nWe may be able to know communications between committee members. The mission here is to\ndevelop a deciphering program that finds the plaintext messages from given ciphertext messages.\n\nA ciphertext message is composed of one or more ciphertext words. A ciphertext word is\ngenerated from a plaintext word with a substitution rule. You have a list of candidate words \ncontaining the words that can appear in the plaintext; no other words may appear. Some words\nin the list may not actually be used in the plaintext.\n\nThere always exists at least one sequence of candidate words from which the given ciphertext\nis obtained by some substitution rule. There may be cases where it is impossible to uniquely\nidentify the plaintext from a given ciphertext and the list of candidate words.", "constraint": "", "input": "The input consists of multiple datasets, each of which contains a ciphertext message and a list\nof candidate words in the following format.\n\nn\nword_1\n. \n. \n. \nword_n\nsequence\n\nn in the first line is a positive integer, representing the number of candidate words. Each of the\nnext n lines represents one of the candidate words. The last line, sequence, is a sequence of one\nor more ciphertext words separated by a single space and terminated with a period.\n\nYou may assume the number of characters in each sequence is more than 1 and less than or\nequal to 80 including spaces and the period. The number of candidate words in the list, n, does\nnot exceed 20. Only 26 uppercase letters, A to Z, are used in the words and the length of each\nword is from 1 to 20, inclusive.\n\nA line of a single zero indicates the end of the input.", "output": "For each dataset, your program should print the deciphered message in a line. Two adjacent\nwords in an output line should be separated by a single space and the last word should be\nfollowed by a single period. When it is impossible to uniquely identify the plaintext, the output\nline should be a single hyphen followed by a single period.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nA\nAND\nCAT\nDOG\nZ XUW ZVX Z YZT.\n2\nAZ\nAY\nZA.\n2\nAA\nBB\nCC.\n16\nA\nB\nC\nD\nE\nF\nG\nH\nI\nJ\nK\nL\nM\nN\nO\nABCDEFGHIJKLMNO\nA B C D E F G H I J K L M N O ABCDEFGHIJKLMNO.\n0\n output: A DOG AND A CAT.\nAZ.\n-.\nA B C D E F G H I J K L M N O ABCDEFGHIJKLMNO."], "Pid": "p00896", "ProblemText": "Task Description: The committee members of the Kitoshima programming contest had decided to use crypto-graphic software for their secret communication. They had asked a company, Kodai Software,\nto develop cryptographic software that employed a cipher based on highly sophisticated mathematics.\n\nAccording to reports on IT projects, many projects are not delivered on time, on budget, with\nrequired features and functions. This applied to this case. Kodai Software failed to implement\nthe cipher by the appointed date of delivery, and asked to use a simpler version that employed\na type of substitution cipher for the moment. The committee members got angry and strongly\nrequested to deliver the full specification product, but they unwillingly decided to use this inferior\nproduct for the moment.\n\nIn what follows, we call the text before encryption, plaintext, and the text after encryption, \nciphertext.\n\nThis simple cipher substitutes letters in the plaintext, and its substitution rule is specified with\na set of pairs. A pair consists of two letters and is unordered, that is, the order of the letters\nin the pair does not matter. A pair (A, B) and a pair (B, A) have the same meaning. In one\nsubstitution rule, one letter can appear in at most one single pair. When a letter in a pair\nappears in the plaintext, the letter is replaced with the other letter in the pair. Letters not\nspecified in any pairs are left as they are.\n\nFor example, by substituting the plaintext\n\nABCDEFGHIJKLMNOPQRSTUVWXYZ\n\nwith the substitution rule {(A, Z), (B, Y)} results in the following ciphertext.\n\nZYCDEFGHIJKLMNOPQRSTUVWXBA\n\nThis may be a big chance for us, because the substitution rule seems weak against cracking.\nWe may be able to know communications between committee members. The mission here is to\ndevelop a deciphering program that finds the plaintext messages from given ciphertext messages.\n\nA ciphertext message is composed of one or more ciphertext words. A ciphertext word is\ngenerated from a plaintext word with a substitution rule. You have a list of candidate words \ncontaining the words that can appear in the plaintext; no other words may appear. Some words\nin the list may not actually be used in the plaintext.\n\nThere always exists at least one sequence of candidate words from which the given ciphertext\nis obtained by some substitution rule. There may be cases where it is impossible to uniquely\nidentify the plaintext from a given ciphertext and the list of candidate words.\nTask Input: The input consists of multiple datasets, each of which contains a ciphertext message and a list\nof candidate words in the following format.\n\nn\nword_1\n. \n. \n. \nword_n\nsequence\n\nn in the first line is a positive integer, representing the number of candidate words. Each of the\nnext n lines represents one of the candidate words. The last line, sequence, is a sequence of one\nor more ciphertext words separated by a single space and terminated with a period.\n\nYou may assume the number of characters in each sequence is more than 1 and less than or\nequal to 80 including spaces and the period. The number of candidate words in the list, n, does\nnot exceed 20. Only 26 uppercase letters, A to Z, are used in the words and the length of each\nword is from 1 to 20, inclusive.\n\nA line of a single zero indicates the end of the input.\nTask Output: For each dataset, your program should print the deciphered message in a line. Two adjacent\nwords in an output line should be separated by a single space and the last word should be\nfollowed by a single period. When it is impossible to uniquely identify the plaintext, the output\nline should be a single hyphen followed by a single period.\nTask Samples: input: 4\nA\nAND\nCAT\nDOG\nZ XUW ZVX Z YZT.\n2\nAZ\nAY\nZA.\n2\nAA\nBB\nCC.\n16\nA\nB\nC\nD\nE\nF\nG\nH\nI\nJ\nK\nL\nM\nN\nO\nABCDEFGHIJKLMNO\nA B C D E F G H I J K L M N O ABCDEFGHIJKLMNO.\n0\n output: A DOG AND A CAT.\nAZ.\n-.\nA B C D E F G H I J K L M N O ABCDEFGHIJKLMNO.\n\n" }, { "title": "Problem D: Long Distance Taxi", "content": "A taxi driver, Nakamura, was so delighted because he got a passenger who wanted to go to a\ncity thousands of kilometers away. However, he had a problem. As you may know, most taxis in\nJapan run on liquefied petroleum gas (LPG) because it is cheaper than gasoline. There are more\nthan 50,000 gas stations in the country, but less than one percent of them sell LPG. Although\nthe LPG tank of his car was full, the tank capacity is limited and his car runs 10 kilometer per\nliter, so he may not be able to get to the destination without filling the tank on the way. He\nknew all the locations of LPG stations.\nYour task is to write a program that finds the best way from the current location to the destination without running out of gas.", "constraint": "", "input": "The input consists of several datasets, and each dataset is in the following format.\n\nN M cap\nsrc dest\nc_1,1 c_1,2 d_1\nc_2,1 c_2,2 d_2\n. \n. \n. \nc_N, 1 c_N, 2 d_N\ns_1\ns_2\n. \n. \n. \ns_M\n

    \nThe first line of a dataset contains three integers (N, M, cap), where N is the number of roads\n(1 <= N <= 3000), M is the number of LPG stations (1<= M <= 300), and cap is the tank capacity\n(1 <= cap <= 200) in liter. The next line contains the name of the current city (src) and the name\nof the destination city (dest). The destination city is always different from the current city.\nThe following N lines describe roads that connect cities. The road i (1 <= i <= N) connects two\ndifferent cities c_i, 1 and c_i, 2 with an integer distance d_i (0 < d_i <= 2000) in kilometer, and he can\ngo from either city to the other. You can assume that no two different roads connect the same\npair of cities. The columns are separated by a single space. The next M lines (s_1, s_2, . . . , s_M) indicate the names of the cities with LPG station. \nYou can assume that a city with LPG station has at least one road.\nThe name of a city has no more than 15 characters. Only English alphabet ('A' to 'Z' and 'a'\nto 'z', case sensitive) is allowed for the name.\nA line with three zeros terminates the input.", "output": "For each dataset, output a line containing the length (in kilometer) of the shortest possible\njourney from the current city to the destination city. If Nakamura cannot reach the destination,\noutput \"-1\" (without quotation marks). You must not output any other characters.\nThe actual tank capacity is usually a little bit larger than that on the specification sheet, so\nyou can assume that he can reach a city even when the remaining amount of the gas becomes\nexactly zero. In addition, you can always fill the tank at the destination so you do not have to\nworry about the return trip.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3 34\nTokyo Kyoto\nTokyo Niigata 335\nTokyo Shizuoka 174\nShizuoka Nagoya 176\nNagoya Kyoto 195\nToyama Niigata 215\nToyama Kyoto 296\nNagoya\nNiigata\nToyama\n6 3 30\nTokyo Kyoto\nTokyo Niigata 335\nTokyo Shizuoka 174\nShizuoka Nagoya 176\nNagoya Kyoto 195\nToyama Niigata 215\nToyama Kyoto 296\nNagoya\nNiigata\nToyama\n0 0 0\n output: 846\n-1"], "Pid": "p00897", "ProblemText": "Task Description: A taxi driver, Nakamura, was so delighted because he got a passenger who wanted to go to a\ncity thousands of kilometers away. However, he had a problem. As you may know, most taxis in\nJapan run on liquefied petroleum gas (LPG) because it is cheaper than gasoline. There are more\nthan 50,000 gas stations in the country, but less than one percent of them sell LPG. Although\nthe LPG tank of his car was full, the tank capacity is limited and his car runs 10 kilometer per\nliter, so he may not be able to get to the destination without filling the tank on the way. He\nknew all the locations of LPG stations.\nYour task is to write a program that finds the best way from the current location to the destination without running out of gas.\nTask Input: The input consists of several datasets, and each dataset is in the following format.\n\nN M cap\nsrc dest\nc_1,1 c_1,2 d_1\nc_2,1 c_2,2 d_2\n. \n. \n. \nc_N, 1 c_N, 2 d_N\ns_1\ns_2\n. \n. \n. \ns_M\n

    \nThe first line of a dataset contains three integers (N, M, cap), where N is the number of roads\n(1 <= N <= 3000), M is the number of LPG stations (1<= M <= 300), and cap is the tank capacity\n(1 <= cap <= 200) in liter. The next line contains the name of the current city (src) and the name\nof the destination city (dest). The destination city is always different from the current city.\nThe following N lines describe roads that connect cities. The road i (1 <= i <= N) connects two\ndifferent cities c_i, 1 and c_i, 2 with an integer distance d_i (0 < d_i <= 2000) in kilometer, and he can\ngo from either city to the other. You can assume that no two different roads connect the same\npair of cities. The columns are separated by a single space. The next M lines (s_1, s_2, . . . , s_M) indicate the names of the cities with LPG station. \nYou can assume that a city with LPG station has at least one road.\nThe name of a city has no more than 15 characters. Only English alphabet ('A' to 'Z' and 'a'\nto 'z', case sensitive) is allowed for the name.\nA line with three zeros terminates the input.\nTask Output: For each dataset, output a line containing the length (in kilometer) of the shortest possible\njourney from the current city to the destination city. If Nakamura cannot reach the destination,\noutput \"-1\" (without quotation marks). You must not output any other characters.\nThe actual tank capacity is usually a little bit larger than that on the specification sheet, so\nyou can assume that he can reach a city even when the remaining amount of the gas becomes\nexactly zero. In addition, you can always fill the tank at the destination so you do not have to\nworry about the return trip.\nTask Samples: input: 6 3 34\nTokyo Kyoto\nTokyo Niigata 335\nTokyo Shizuoka 174\nShizuoka Nagoya 176\nNagoya Kyoto 195\nToyama Niigata 215\nToyama Kyoto 296\nNagoya\nNiigata\nToyama\n6 3 30\nTokyo Kyoto\nTokyo Niigata 335\nTokyo Shizuoka 174\nShizuoka Nagoya 176\nNagoya Kyoto 195\nToyama Niigata 215\nToyama Kyoto 296\nNagoya\nNiigata\nToyama\n0 0 0\n output: 846\n-1\n\n" }, { "title": "Problem E: Driving an Icosahedral Rover", "content": "After decades of fruitless efforts, one of the expedition teams of ITO (Intersolar Tourism Organization) finally found a planet that would surely provide one of the best tourist attractions\nwithin a ten light-year radius from our solar system. The most attractive feature of the planet,\nbesides its comfortable gravity and calm weather, is the area called Mare Triangularis. Despite\nthe name, the area is not covered with water but is a great plane. Its unique feature is that it is\ndivided into equilateral triangular sections of the same size, called trigons. The trigons provide\na unique impressive landscape, a must for tourism. It is no wonder the board of ITO decided\nto invest a vast amount on the planet.\n\nDespite the expected secrecy of the staff, the Society of Astrogeology caught this information\nin no time, as always. They immediately sent their president's letter to the Institute of Science\nand Education of the Commonwealth Galactica claiming that authoritative academic inspections\nwere to be completed before any commercial exploitation might damage the nature.\n\nFortunately, astrogeologists do not plan to practice all the possible inspections on all of the\ntrigons; there are far too many of them. Inspections are planned only on some characteristic\ntrigons and, for each of them, in one of twenty different scientific aspects.\n\nTo accelerate building this new tourist resort, ITO's construction machinery team has already succeeded in putting their brand-new\ninvention in practical use. It is a rover vehicle of the shape of an icosahedron, a regular polyhedron with twenty faces of equilateral triangles. \nThe machine is customized\nso that each of the twenty faces exactly fits each of the trigons. \nControlling the high-tech gyromotor installed inside its body, the rover can roll onto one of the three trigons neighboring the one its bottom is\non.\n\n\n \n \n\n \n \n \nFigure E. 1: The Rover on Mare Triangularis\n \n\n \n\nEach of the twenty faces has its own function. The set of equipments installed on the bottom\nface touching the ground can be applied to the trigon it is on. Of course, the rover was meant to accelerate construction of the luxury hotels to host rich interstellar travelers, but, changing\nthe installed equipment sets, it can also be used to accelerate academic inspections.\n\nYou are the driver of this rover and are asked to move the vehicle onto the trigon specified by\nthe leader of the scientific commission with the smallest possible steps. What makes your task\nmore difficult is that the designated face installed with the appropriate set of equipments has to\nbe the bottom. The direction of the rover does not matter.\n\n
    \n \n
    \n\n \n \n\n \n \n \nFigure E. 2: The Coordinate System \n \n \n\nFigure E. 3: Face Numbering\n \n\n \n\nThe trigons of Mare Triangularis are given two-dimensional coordinates as shown in Figure E. 2.\nLike maps used for the Earth, the x axis is from the west to the east, and the y axis is from the\nsouth to the north. Note that all the trigons with its coordinates (x , y) has neighboring trigons\nwith coordinates (x - 1 , y) and (x + 1 , y). In addition to these, when x + y is even, it has a\nneighbor (x , y + 1); otherwise, that is, when x + y is odd, it has a neighbor (x , y - 1).\n\nFigure E. 3 shows a development of the skin of the rover. The top face of the development\nmakes the exterior. That is, if the numbers on faces of the development were actually marked\non the faces of the rover, they should been readable from its outside. These numbers are used\nto identify the faces.\n\nWhen you start the rover, it is on the trigon (0,0) and the face 0 is touching the ground. The\nrover is placed so that rolling towards north onto the trigon (0,1) makes the face numbered 5\nto be at the bottom.\n\nAs your first step, you can choose one of the three adjacent trigons, namely those with coordinates (-1,0), (1,0), \nand (0,1), to visit. The bottom will be the face numbered 4,1, and 5,\nrespectively. If you choose to go to (1,0) in the first rolling step, the second step can bring\nthe rover to either of (0,0), (2,0), or (1, -1). The bottom face will be either of 0,6, or 2,\ncorrespondingly. The rover may visit any of the trigons twice or more, including the start and the goal trigons, when appropriate.\n\nThe theoretical design section of ITO showed that the rover can reach any goal trigon on the\nspecified bottom face within a finite number of steps.", "constraint": "", "input": "The input consists of a number of datasets. The number of datasets does not exceed 50.\n\nEach of the datasets has three integers x, y, and n in one line, separated by a space. Here, (x, y)\nspecifies the coordinates of the trigon to which you have to move the rover, and n specifies the\nface that should be at the bottom.\n\nThe end of the input is indicated by a line containing three zeros.", "output": "The output for each dataset should be a line containing a single integer that gives the minimum\nnumber of steps required to set the rover on the specified trigon with the specified face touching\nthe ground. No other characters should appear in the output.\n\nYou can assume that the maximum number of required steps does not exceed 100. Mare Triangularis\n is broad enough so that any of its edges cannot be reached within that number of\nsteps.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 0 1\n3 5 2\n-4 1 3\n13 -13 2\n-32 15 9\n-50 50 0\n0 0 0\n output: 6\n10\n9\n30\n47\n100"], "Pid": "p00898", "ProblemText": "Task Description: After decades of fruitless efforts, one of the expedition teams of ITO (Intersolar Tourism Organization) finally found a planet that would surely provide one of the best tourist attractions\nwithin a ten light-year radius from our solar system. The most attractive feature of the planet,\nbesides its comfortable gravity and calm weather, is the area called Mare Triangularis. Despite\nthe name, the area is not covered with water but is a great plane. Its unique feature is that it is\ndivided into equilateral triangular sections of the same size, called trigons. The trigons provide\na unique impressive landscape, a must for tourism. It is no wonder the board of ITO decided\nto invest a vast amount on the planet.\n\nDespite the expected secrecy of the staff, the Society of Astrogeology caught this information\nin no time, as always. They immediately sent their president's letter to the Institute of Science\nand Education of the Commonwealth Galactica claiming that authoritative academic inspections\nwere to be completed before any commercial exploitation might damage the nature.\n\nFortunately, astrogeologists do not plan to practice all the possible inspections on all of the\ntrigons; there are far too many of them. Inspections are planned only on some characteristic\ntrigons and, for each of them, in one of twenty different scientific aspects.\n\nTo accelerate building this new tourist resort, ITO's construction machinery team has already succeeded in putting their brand-new\ninvention in practical use. It is a rover vehicle of the shape of an icosahedron, a regular polyhedron with twenty faces of equilateral triangles. \nThe machine is customized\nso that each of the twenty faces exactly fits each of the trigons. \nControlling the high-tech gyromotor installed inside its body, the rover can roll onto one of the three trigons neighboring the one its bottom is\non.\n\n\n \n \n\n \n \n \nFigure E. 1: The Rover on Mare Triangularis\n \n\n \n\nEach of the twenty faces has its own function. The set of equipments installed on the bottom\nface touching the ground can be applied to the trigon it is on. Of course, the rover was meant to accelerate construction of the luxury hotels to host rich interstellar travelers, but, changing\nthe installed equipment sets, it can also be used to accelerate academic inspections.\n\nYou are the driver of this rover and are asked to move the vehicle onto the trigon specified by\nthe leader of the scientific commission with the smallest possible steps. What makes your task\nmore difficult is that the designated face installed with the appropriate set of equipments has to\nbe the bottom. The direction of the rover does not matter.\n\n
    \n \n
    \n\n \n \n\n \n \n \nFigure E. 2: The Coordinate System \n \n \n\nFigure E. 3: Face Numbering\n \n\n \n\nThe trigons of Mare Triangularis are given two-dimensional coordinates as shown in Figure E. 2.\nLike maps used for the Earth, the x axis is from the west to the east, and the y axis is from the\nsouth to the north. Note that all the trigons with its coordinates (x , y) has neighboring trigons\nwith coordinates (x - 1 , y) and (x + 1 , y). In addition to these, when x + y is even, it has a\nneighbor (x , y + 1); otherwise, that is, when x + y is odd, it has a neighbor (x , y - 1).\n\nFigure E. 3 shows a development of the skin of the rover. The top face of the development\nmakes the exterior. That is, if the numbers on faces of the development were actually marked\non the faces of the rover, they should been readable from its outside. These numbers are used\nto identify the faces.\n\nWhen you start the rover, it is on the trigon (0,0) and the face 0 is touching the ground. The\nrover is placed so that rolling towards north onto the trigon (0,1) makes the face numbered 5\nto be at the bottom.\n\nAs your first step, you can choose one of the three adjacent trigons, namely those with coordinates (-1,0), (1,0), \nand (0,1), to visit. The bottom will be the face numbered 4,1, and 5,\nrespectively. If you choose to go to (1,0) in the first rolling step, the second step can bring\nthe rover to either of (0,0), (2,0), or (1, -1). The bottom face will be either of 0,6, or 2,\ncorrespondingly. The rover may visit any of the trigons twice or more, including the start and the goal trigons, when appropriate.\n\nThe theoretical design section of ITO showed that the rover can reach any goal trigon on the\nspecified bottom face within a finite number of steps.\nTask Input: The input consists of a number of datasets. The number of datasets does not exceed 50.\n\nEach of the datasets has three integers x, y, and n in one line, separated by a space. Here, (x, y)\nspecifies the coordinates of the trigon to which you have to move the rover, and n specifies the\nface that should be at the bottom.\n\nThe end of the input is indicated by a line containing three zeros.\nTask Output: The output for each dataset should be a line containing a single integer that gives the minimum\nnumber of steps required to set the rover on the specified trigon with the specified face touching\nthe ground. No other characters should appear in the output.\n\nYou can assume that the maximum number of required steps does not exceed 100. Mare Triangularis\n is broad enough so that any of its edges cannot be reached within that number of\nsteps.\nTask Samples: input: 0 0 1\n3 5 2\n-4 1 3\n13 -13 2\n-32 15 9\n-50 50 0\n0 0 0\n output: 6\n10\n9\n30\n47\n100\n\n" }, { "title": "Problem F: City Merger", "content": "Recent improvements in information and communication technology have made it possible to provide municipal service to a wider area more quickly and with less costs. Stimulated by this, and probably for saving their not sufficient funds, mayors of many cities started to discuss on mergers of their cities.\n\nThere are, of course, many obstacles to actually put the planned mergers in practice. Each city has its own culture of which citizens are proud. One of the largest sources of friction is with the name of the new city. All citizens would insist that the name of the new city should have the original name of their own city at least as a part of it. Simply concatenating all the original names would, however, make the name too long for everyday use.\n\nYou are asked by a group of mayors to write a program that finds the shortest possible name for the new city that includes all the original names of the merged cities. If two or more cities have common parts, they can be overlapped. For example, if \"FUKUOKA\", \"OKAYAMA\", and \"YAMAGUCHI\" cities are to be merged, \"FUKUOKAYAMAGUCHI\" is such a name that include all three of the original city names. Although this includes all the characters of the city name \"FUKUYAMA\" in this order, it does not appear as a consecutive substring, and thus \"FUKUYAMA\" is not considered to be included in the name.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset begins with a line containing a positive integer n (n <= 14), which denotes the number of cities to be merged. The following n lines contain the names of the cities in uppercase alphabetical letters, one in each line. You may assume that none of the original city names has more than 20 characters. Of course, no two cities have the same name.\n\nThe end of the input is indicated by a line consisting of a zero.", "output": "For each dataset, output the length of the shortest possible name of the new city in one line. The output should not contain any other characters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nFUKUOKA\nOKAYAMA\nYAMAGUCHI\n3\nFUKUOKA\nFUKUYAMA\nOKAYAMA\n2\nABCDE\nEDCBA\n4\nGA\nDEFG\nCDDE\nABCD\n2\nABCDE\nC\n14\nAAAAA\nBBBBB\nCCCCC\nDDDDD\nEEEEE\nFFFFF\nGGGGG\nHHHHH\nIIIII\nJJJJJ\nKKKKK\nLLLLL\nMMMMM\nNNNNN\n0\n output: 16\n19\n9\n9\n5\n70"], "Pid": "p00899", "ProblemText": "Task Description: Recent improvements in information and communication technology have made it possible to provide municipal service to a wider area more quickly and with less costs. Stimulated by this, and probably for saving their not sufficient funds, mayors of many cities started to discuss on mergers of their cities.\n\nThere are, of course, many obstacles to actually put the planned mergers in practice. Each city has its own culture of which citizens are proud. One of the largest sources of friction is with the name of the new city. All citizens would insist that the name of the new city should have the original name of their own city at least as a part of it. Simply concatenating all the original names would, however, make the name too long for everyday use.\n\nYou are asked by a group of mayors to write a program that finds the shortest possible name for the new city that includes all the original names of the merged cities. If two or more cities have common parts, they can be overlapped. For example, if \"FUKUOKA\", \"OKAYAMA\", and \"YAMAGUCHI\" cities are to be merged, \"FUKUOKAYAMAGUCHI\" is such a name that include all three of the original city names. Although this includes all the characters of the city name \"FUKUYAMA\" in this order, it does not appear as a consecutive substring, and thus \"FUKUYAMA\" is not considered to be included in the name.\nTask Input: The input is a sequence of datasets. Each dataset begins with a line containing a positive integer n (n <= 14), which denotes the number of cities to be merged. The following n lines contain the names of the cities in uppercase alphabetical letters, one in each line. You may assume that none of the original city names has more than 20 characters. Of course, no two cities have the same name.\n\nThe end of the input is indicated by a line consisting of a zero.\nTask Output: For each dataset, output the length of the shortest possible name of the new city in one line. The output should not contain any other characters.\nTask Samples: input: 3\nFUKUOKA\nOKAYAMA\nYAMAGUCHI\n3\nFUKUOKA\nFUKUYAMA\nOKAYAMA\n2\nABCDE\nEDCBA\n4\nGA\nDEFG\nCDDE\nABCD\n2\nABCDE\nC\n14\nAAAAA\nBBBBB\nCCCCC\nDDDDD\nEEEEE\nFFFFF\nGGGGG\nHHHHH\nIIIII\nJJJJJ\nKKKKK\nLLLLL\nMMMMM\nNNNNN\n0\n output: 16\n19\n9\n9\n5\n70\n\n" }, { "title": "Problem G: Captain Q's Treasure", "content": "You got an old map, which turned out to be drawn by the infamous pirate “Captain Q”. It shows the locations of a lot of treasure chests buried in an island.\n\nThe map is divided into square sections, each of which has a digit on it or has no digit. The digit represents the number of chests in its 9 neighboring sections (the section itself and its 8 neighbors). You may assume that there is at most one chest in each section.\n\nAlthough you have the map, you can't determine the sections where the chests are buried. Even the total number of chests buried in the island is unknown. However, it is possible to calculate the minimum number of chests buried in the island. Your mission in this problem is to write a program that calculates it.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nh w\nmap\n\nThe first line of a dataset consists of two positive integers h and w. h is the height of the map and w is the width of the map. You may assume 1<=h<=15 and 1<=w<=15.\n\nThe following h lines give the map. Each line consists of w characters and corresponds to a horizontal strip of the map. Each of the characters in the line represents the state of a section as follows.\n\n‘. ': The section is not a part of the island (water). No chest is here.\n\n‘* ': The section is a part of the island, and the number of chests in its 9 neighbors is not known.\n\n‘0 '-‘9 ': The section is a part of the island, and the digit represents the number of chests in its 9 neighbors.\n\nYou may assume that the map is not self-contradicting, i. e. , there is at least one arrangement of chests. You may also assume the number of sections with digits is at least one and at most 15.\n\nA line containing two zeros indicates the end of the input.", "output": "For each dataset, output a line that contains the minimum number of chests. The output should not contain any other character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 6\n*2.2**\n..*...\n..2...\n..*...\n*2.2**\n6 5\n.*2*.\n..*..\n..*..\n..2..\n..*..\n.*2*.\n5 6\n.1111.\n**...*\n33....\n**...0\n.*2**.\n6 9\n....1....\n...1.1...\n....1....\n.1..*..1.\n1.1***1.1\n.1..*..1.\n9 9\n*********\n*4*4*4*4*\n*********\n*4*4*4*4*\n*********\n*4*4*4*4*\n*********\n*4*4*4***\n*********\n0 0\n output: 6\n5\n5\n6\n23"], "Pid": "p00900", "ProblemText": "Task Description: You got an old map, which turned out to be drawn by the infamous pirate “Captain Q”. It shows the locations of a lot of treasure chests buried in an island.\n\nThe map is divided into square sections, each of which has a digit on it or has no digit. The digit represents the number of chests in its 9 neighboring sections (the section itself and its 8 neighbors). You may assume that there is at most one chest in each section.\n\nAlthough you have the map, you can't determine the sections where the chests are buried. Even the total number of chests buried in the island is unknown. However, it is possible to calculate the minimum number of chests buried in the island. Your mission in this problem is to write a program that calculates it.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nh w\nmap\n\nThe first line of a dataset consists of two positive integers h and w. h is the height of the map and w is the width of the map. You may assume 1<=h<=15 and 1<=w<=15.\n\nThe following h lines give the map. Each line consists of w characters and corresponds to a horizontal strip of the map. Each of the characters in the line represents the state of a section as follows.\n\n‘. ': The section is not a part of the island (water). No chest is here.\n\n‘* ': The section is a part of the island, and the number of chests in its 9 neighbors is not known.\n\n‘0 '-‘9 ': The section is a part of the island, and the digit represents the number of chests in its 9 neighbors.\n\nYou may assume that the map is not self-contradicting, i. e. , there is at least one arrangement of chests. You may also assume the number of sections with digits is at least one and at most 15.\n\nA line containing two zeros indicates the end of the input.\nTask Output: For each dataset, output a line that contains the minimum number of chests. The output should not contain any other character.\nTask Samples: input: 5 6\n*2.2**\n..*...\n..2...\n..*...\n*2.2**\n6 5\n.*2*.\n..*..\n..*..\n..2..\n..*..\n.*2*.\n5 6\n.1111.\n**...*\n33....\n**...0\n.*2**.\n6 9\n....1....\n...1.1...\n....1....\n.1..*..1.\n1.1***1.1\n.1..*..1.\n9 9\n*********\n*4*4*4*4*\n*********\n*4*4*4*4*\n*********\n*4*4*4*4*\n*********\n*4*4*4***\n*********\n0 0\n output: 6\n5\n5\n6\n23\n\n" }, { "title": "Problem H: ASCII Expression", "content": "Mathematical expressions appearing in old papers and old technical articles are printed with typewriter in several lines, where a fixed-width or monospaced font is required to print characters (digits, symbols and spaces). Let us consider the following mathematical expression.\n\nIt is printed in the following four lines:\n\n 4 2\n( 1 - ---- ) * - 5 + 6\n 2\n 3\n\nwhere “- 5” indicates unary minus followed by 5. We call such an expression of lines “ASCII expression”.\n\nFor helping those who want to evaluate ASCII expressions obtained through optical character recognition (OCR) from old papers, your job is to write a program that recognizes the structure of ASCII expressions and computes their values.\n\nFor the sake of simplicity, you may assume that ASCII expressions are constructed by the following rules. Its syntax is shown in Table H. 1.\n \n \n(1) \n Terminal symbols are ‘0 ', ‘1 ', ‘2 ', ‘3 ', ‘4 ', ‘5 ', ‘6 ', ‘7 ', ‘8 ', ‘9 ', ‘+ ', ‘- ', ‘* ', ‘( ', ‘) ', and ‘  '. \n \n(2) \n Nonterminal symbols are expr, term, factor, powexpr, primary, fraction and digit. The start symbol is expr. \n \n(3) \n A “cell” is a rectangular region of characters that corresponds to a terminal or nonterminal symbol (Figure H. 1). In the cell, there are no redundant rows and columns that consist only of space characters. A cell corresponding to a terminal symbol consists of a single character. A cell corresponding to a nonterminal symbol contains cell(s) corresponding to its descendant(s) but never partially overlaps others. \n \n(4) \n Each cell has a base-line, a top-line, and a bottom-line. The base-lines of child cells of the right-hand side of rules I, II, III, and V should be aligned. Their vertical position defines the base-line position of their left-hand side cell. \nTable H. 1: Rules for constructing ASCII expressions (similar to Backus-Naur Form) The box indicates the cell of the terminal or nonterminal symbol that corresponds to a rectan- gular region of characters. Note that each syntactically-needed space character is explicitly\nindicated by the period character denoted by, here. \n \n\n \n \n(5) \n powexpr consists of a primary and an optional digit. The digit is placed one line above the base-line of the primary cell. They are horizontally adjacent to each other. The base-line of a powexpr is that of the primary. \n \n(6) \n fraction is indicated by three or more consecutive hyphens called “vinculum”. Its dividend expr is placed just above the vinculum, and its divisor expr is placed just beneath it. The number of the hyphens of the vinculum, denoted by w_h, is equal to 2 + max(w_1, w_2), where w_1 and w_2 indicate the width of the cell of the dividend and that of the divisor, respectively. These cells are centered, where there are ⌈(w_h-w_k)/2⌉ space characters to the left and ⌊(w_h-w_k)/2⌋ space characters to the right, (k = 1,2). The base-line of a fraction is at the position of the vinculum. \n \n(7) \n digit consists of one character. \n\n \nFor example, the negative fraction is represented in three lines:\n 3\n- ---\n 4where the left-most hyphen means a unary minus operator. One space character is required between the unary minus and the vinculum of the fraction. The fraction is represented in four lines:\n 3 + 4 * - 2\n-------------\n 2\n - 1 - 2\n\nwhere the widths of the cells of the dividend and divisor are 11 and 8 respectively. Hence the number of hyphens of the vinculum is 2 + max(11,8) = 13. The divisor is centered by ⌈(13-8)/2⌉ = 3 space characters (hyphens) to the left and ⌊(13-8)/2⌋ = 2 to the right.\n\nThe powexpr (4^2)^3 is represented in two lines:\n\n 2 3\n( 4 )\n\nwhere the cell for 2 is placed one line above the base-line of the cell for 4, and the cell for 3 is placed one line above the base-line of the cell for a primary (4^2).", "constraint": "", "input": "The input consists of multiple datasets, followed by a line containing a zero. Each dataset has the following format.\n\nn\nstr_1\nstr_2\n.\n.\n.\nstr_n\n\nn is a positive integer, which indicates the number of the following lines with the same length that represent the cell of an ASCII expression. str_k is the k-th line of the cell where each space character is replaced with a period.\n\nYou may assume that n <= 20 and that the length of the lines is no more than 80.", "output": "For each dataset, one line containing a non-negative integer less than 2011 should be output. The integer indicates the value of the ASCII expression in modular arithmetic under modulo 2011. The output should not contain any other characters.\n\nThere is no fraction with the divisor that is equal to zero or a multiple of 2011.\n\nNote that powexpr x^0 is defined as 1, and x^y (y is a positive integer) is defined as the product x*x*. . . *x where the number of x's is equal to y.\n\nA fractionis computed as the multiplication of x and the inverse of y, i. e. , x* inv(y), under y modulo 2011. The inverse of y (1 <= y < 2011) is uniquely defined as the integer z (1 <= z < 2011) that satisfies z * y ≡ 1 (mod 2011), since 2011 is a prime number.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n........4...2..........\n(.1.-.----.)..*.-.5.+.6\n........2..............\n.......3...............\n3\n...3.\n-.---\n...4.\n4\n.3.+.4.*.-.2.\n-------------\n..........2..\n...-.1.-.2...\n2\n...2..3\n(.4..).\n1\n2.+.3.*.5.-.7.+.9\n1\n(.2.+.3.).*.(.5.-.7.).+.9\n3\n.2....3.\n4..+.---\n......5.\n3\n.2......-.-.3.\n4..-.-.-------\n..........5...\n9\n............1............\n-------------------------\n..............1..........\n.1.+.-------------------.\n................1........\n......1.+.-------------..\n..................1......\n...........1.+.-------...\n................1.+.2....\n15\n.................2......\n................---.....\n.......2.........5....3.\n.(.---------.+.-----.)..\n.....7...........3......\n....---.+.1.............\n.....4..................\n------------------------\n.......2................\n......---...............\n.......5.......2....2...\n...(.-----.+.-----.)....\n.......3.......3........\n..............---.......\n...............4........\n2\n.0....2....\n3..+.4..*.5\n20\n............2............................2......................................\n...........3............................3.......................................\n..........----.........................----.....................................\n............4............................4......................................\n.....2.+.------.+.1...............2.+.------.+.1................................\n............2............................2......................................\n...........2............................2........................2..............\n..........----.........................----.....................3...............\n............2............................2.....................----.............\n...........3............................3........................4..............\n(.(.----------------.+.2.+.3.).*.----------------.+.2.).*.2.+.------.+.1.+.2.*.5\n............2............................2.......................2..............\n...........5............................5.......................2...............\n..........----.........................----....................----.............\n............6............................6.......................2..............\n.........------.......................------....................3...............\n............3............................3......................................\n..........----.........................----.....................................\n............2............................2......................................\n...........7............................7.......................................\n0\n output: 501\n502\n1\n74\n19\n2010\n821\n821\n1646\n148\n81\n1933"], "Pid": "p00901", "ProblemText": "Task Description: Mathematical expressions appearing in old papers and old technical articles are printed with typewriter in several lines, where a fixed-width or monospaced font is required to print characters (digits, symbols and spaces). Let us consider the following mathematical expression.\n\nIt is printed in the following four lines:\n\n 4 2\n( 1 - ---- ) * - 5 + 6\n 2\n 3\n\nwhere “- 5” indicates unary minus followed by 5. We call such an expression of lines “ASCII expression”.\n\nFor helping those who want to evaluate ASCII expressions obtained through optical character recognition (OCR) from old papers, your job is to write a program that recognizes the structure of ASCII expressions and computes their values.\n\nFor the sake of simplicity, you may assume that ASCII expressions are constructed by the following rules. Its syntax is shown in Table H. 1.\n \n \n(1) \n Terminal symbols are ‘0 ', ‘1 ', ‘2 ', ‘3 ', ‘4 ', ‘5 ', ‘6 ', ‘7 ', ‘8 ', ‘9 ', ‘+ ', ‘- ', ‘* ', ‘( ', ‘) ', and ‘  '. \n \n(2) \n Nonterminal symbols are expr, term, factor, powexpr, primary, fraction and digit. The start symbol is expr. \n \n(3) \n A “cell” is a rectangular region of characters that corresponds to a terminal or nonterminal symbol (Figure H. 1). In the cell, there are no redundant rows and columns that consist only of space characters. A cell corresponding to a terminal symbol consists of a single character. A cell corresponding to a nonterminal symbol contains cell(s) corresponding to its descendant(s) but never partially overlaps others. \n \n(4) \n Each cell has a base-line, a top-line, and a bottom-line. The base-lines of child cells of the right-hand side of rules I, II, III, and V should be aligned. Their vertical position defines the base-line position of their left-hand side cell. \nTable H. 1: Rules for constructing ASCII expressions (similar to Backus-Naur Form) The box indicates the cell of the terminal or nonterminal symbol that corresponds to a rectan- gular region of characters. Note that each syntactically-needed space character is explicitly\nindicated by the period character denoted by, here. \n \n\n \n \n(5) \n powexpr consists of a primary and an optional digit. The digit is placed one line above the base-line of the primary cell. They are horizontally adjacent to each other. The base-line of a powexpr is that of the primary. \n \n(6) \n fraction is indicated by three or more consecutive hyphens called “vinculum”. Its dividend expr is placed just above the vinculum, and its divisor expr is placed just beneath it. The number of the hyphens of the vinculum, denoted by w_h, is equal to 2 + max(w_1, w_2), where w_1 and w_2 indicate the width of the cell of the dividend and that of the divisor, respectively. These cells are centered, where there are ⌈(w_h-w_k)/2⌉ space characters to the left and ⌊(w_h-w_k)/2⌋ space characters to the right, (k = 1,2). The base-line of a fraction is at the position of the vinculum. \n \n(7) \n digit consists of one character. \n\n \nFor example, the negative fraction is represented in three lines:\n 3\n- ---\n 4where the left-most hyphen means a unary minus operator. One space character is required between the unary minus and the vinculum of the fraction. The fraction is represented in four lines:\n 3 + 4 * - 2\n-------------\n 2\n - 1 - 2\n\nwhere the widths of the cells of the dividend and divisor are 11 and 8 respectively. Hence the number of hyphens of the vinculum is 2 + max(11,8) = 13. The divisor is centered by ⌈(13-8)/2⌉ = 3 space characters (hyphens) to the left and ⌊(13-8)/2⌋ = 2 to the right.\n\nThe powexpr (4^2)^3 is represented in two lines:\n\n 2 3\n( 4 )\n\nwhere the cell for 2 is placed one line above the base-line of the cell for 4, and the cell for 3 is placed one line above the base-line of the cell for a primary (4^2).\nTask Input: The input consists of multiple datasets, followed by a line containing a zero. Each dataset has the following format.\n\nn\nstr_1\nstr_2\n.\n.\n.\nstr_n\n\nn is a positive integer, which indicates the number of the following lines with the same length that represent the cell of an ASCII expression. str_k is the k-th line of the cell where each space character is replaced with a period.\n\nYou may assume that n <= 20 and that the length of the lines is no more than 80.\nTask Output: For each dataset, one line containing a non-negative integer less than 2011 should be output. The integer indicates the value of the ASCII expression in modular arithmetic under modulo 2011. The output should not contain any other characters.\n\nThere is no fraction with the divisor that is equal to zero or a multiple of 2011.\n\nNote that powexpr x^0 is defined as 1, and x^y (y is a positive integer) is defined as the product x*x*. . . *x where the number of x's is equal to y.\n\nA fractionis computed as the multiplication of x and the inverse of y, i. e. , x* inv(y), under y modulo 2011. The inverse of y (1 <= y < 2011) is uniquely defined as the integer z (1 <= z < 2011) that satisfies z * y ≡ 1 (mod 2011), since 2011 is a prime number.\nTask Samples: input: 4\n........4...2..........\n(.1.-.----.)..*.-.5.+.6\n........2..............\n.......3...............\n3\n...3.\n-.---\n...4.\n4\n.3.+.4.*.-.2.\n-------------\n..........2..\n...-.1.-.2...\n2\n...2..3\n(.4..).\n1\n2.+.3.*.5.-.7.+.9\n1\n(.2.+.3.).*.(.5.-.7.).+.9\n3\n.2....3.\n4..+.---\n......5.\n3\n.2......-.-.3.\n4..-.-.-------\n..........5...\n9\n............1............\n-------------------------\n..............1..........\n.1.+.-------------------.\n................1........\n......1.+.-------------..\n..................1......\n...........1.+.-------...\n................1.+.2....\n15\n.................2......\n................---.....\n.......2.........5....3.\n.(.---------.+.-----.)..\n.....7...........3......\n....---.+.1.............\n.....4..................\n------------------------\n.......2................\n......---...............\n.......5.......2....2...\n...(.-----.+.-----.)....\n.......3.......3........\n..............---.......\n...............4........\n2\n.0....2....\n3..+.4..*.5\n20\n............2............................2......................................\n...........3............................3.......................................\n..........----.........................----.....................................\n............4............................4......................................\n.....2.+.------.+.1...............2.+.------.+.1................................\n............2............................2......................................\n...........2............................2........................2..............\n..........----.........................----.....................3...............\n............2............................2.....................----.............\n...........3............................3........................4..............\n(.(.----------------.+.2.+.3.).*.----------------.+.2.).*.2.+.------.+.1.+.2.*.5\n............2............................2.......................2..............\n...........5............................5.......................2...............\n..........----.........................----....................----.............\n............6............................6.......................2..............\n.........------.......................------....................3...............\n............3............................3......................................\n..........----.........................----.....................................\n............2............................2......................................\n...........7............................7.......................................\n0\n output: 501\n502\n1\n74\n19\n2010\n821\n821\n1646\n148\n81\n1933\n\n" }, { "title": "Problem I: Encircling Circles", "content": "You are given a set of circles C of a variety of radii (radiuses) placed at a variety of positions, possibly overlapping one another. Given a circle with radius r, that circle may be placed so that it encircles all of the circles in the set C if r is large enough.\n\nThere may be more than one possible position of the circle of radius r to encircle all the member circles of C. We define the region U as the union of the areas of encircling circles at all such positions. In other words, for each point in U, there exists a circle of radius r that encircles that point and all the members of C. Your task is to calculate the length of the periphery of that region U.\n\nFigure I. 1 shows an example of the set of circles C and the region U. In the figure, three circles contained in C are expressed by circles of solid circumference, some possible positions of the encircling circles are expressed by circles of dashed circumference, and the area U is expressed by a thick dashed closed curve.", "constraint": "", "input": "The input is a sequence of datasets. The number of datasets is less than 100.\n\nEach dataset is formatted as follows.\n\nn r\nx_1 y_1 r_1\nx_2 y_2 r_2\n. \n. \n. \nx_n y_n r_n\n\nThe first line of a dataset contains two positive integers, n and r, separated by a single space. n means the number of the circles in the set C and does not exceed 100. r means the radius of the encircling circle and does not exceed 1000.\n\nEach of the n lines following the first line contains three integers separated by a single space. (x_i, y_i) means the center position of the i-th circle of the set C and r_i means its radius.\n\nYou may assume -500<=x_i <=500, -500<=y_i <=500, and 1<=r_i <=500.\n\nThe end of the input is indicated by a line containing two zeros separated by a single space.", "output": "For each dataset, output a line containing a decimal fraction which means the length of the periphery (circumferential length) of the region U.\n\nThe output should not contain an error greater than 0.01. You can assume that, when r changes by ε (|ε| < 0.0000001), the length of the periphery of the region U will not change more than 0.001.\n\nIf r is too small to cover all of the circles in C, output a line containing only 0.0.\n\nNo other characters should be contained in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 10\n5 5 7\n2 12\n5 5 7\n8 6 3\n3 10\n3 11 2\n2 1 1\n2 16 3\n3 15\n-5 2 5\n9 2 9\n5 8 6\n3 38\n-25 -10 8\n30 5 7\n-3 35 11\n3 39\n-25 -10 8\n30 5 7\n-3 35 11\n3 800\n-400 400 2\n300 300 1\n300 302 1\n3 800\n400 -400 2\n300 300 1\n307 300 3\n8 147\n130 80 12\n130 -40 12\n-110 80 12\n-110 -40 12\n70 140 12\n70 -100 12\n-50 140 12\n-50 -100 12\n3 493\n345 154 10\n291 111 75\n-275 -301 46\n4 55\n54 0 1\n40 30 5\n27 36 10\n0 48 7\n3 30\n0 3 3\n-3 0 4\n400 0 3\n3 7\n2 3 2\n-5 -4 2\n-4 3 2\n3 10\n-5 -4 5\n2 3 5\n-4 3 5\n4 6\n4 6 1\n5 5 1\n1 7 1\n0 1 1\n3 493\n345 154 10\n291 111 75\n-275 -301 46\n5 20\n-9 12 5\n0 15 5\n3 -3 3\n12 9 5\n-12 9 5\n0 0\n output: 81.68140899333463\n106.81415022205297\n74.11215318612639\n108.92086846105579\n0.0\n254.85616536128433\n8576.936716409238\n8569.462129048667\n929.1977057481128\n4181.124698202453\n505.09134735536804\n0.0\n46.82023824234038\n65.66979416387915\n50.990642291793506\n4181.124698202453\n158.87951420768937\n\n"], "Pid": "p00902", "ProblemText": "Task Description: You are given a set of circles C of a variety of radii (radiuses) placed at a variety of positions, possibly overlapping one another. Given a circle with radius r, that circle may be placed so that it encircles all of the circles in the set C if r is large enough.\n\nThere may be more than one possible position of the circle of radius r to encircle all the member circles of C. We define the region U as the union of the areas of encircling circles at all such positions. In other words, for each point in U, there exists a circle of radius r that encircles that point and all the members of C. Your task is to calculate the length of the periphery of that region U.\n\nFigure I. 1 shows an example of the set of circles C and the region U. In the figure, three circles contained in C are expressed by circles of solid circumference, some possible positions of the encircling circles are expressed by circles of dashed circumference, and the area U is expressed by a thick dashed closed curve.\nTask Input: The input is a sequence of datasets. The number of datasets is less than 100.\n\nEach dataset is formatted as follows.\n\nn r\nx_1 y_1 r_1\nx_2 y_2 r_2\n. \n. \n. \nx_n y_n r_n\n\nThe first line of a dataset contains two positive integers, n and r, separated by a single space. n means the number of the circles in the set C and does not exceed 100. r means the radius of the encircling circle and does not exceed 1000.\n\nEach of the n lines following the first line contains three integers separated by a single space. (x_i, y_i) means the center position of the i-th circle of the set C and r_i means its radius.\n\nYou may assume -500<=x_i <=500, -500<=y_i <=500, and 1<=r_i <=500.\n\nThe end of the input is indicated by a line containing two zeros separated by a single space.\nTask Output: For each dataset, output a line containing a decimal fraction which means the length of the periphery (circumferential length) of the region U.\n\nThe output should not contain an error greater than 0.01. You can assume that, when r changes by ε (|ε| < 0.0000001), the length of the periphery of the region U will not change more than 0.001.\n\nIf r is too small to cover all of the circles in C, output a line containing only 0.0.\n\nNo other characters should be contained in the output.\nTask Samples: input: 1 10\n5 5 7\n2 12\n5 5 7\n8 6 3\n3 10\n3 11 2\n2 1 1\n2 16 3\n3 15\n-5 2 5\n9 2 9\n5 8 6\n3 38\n-25 -10 8\n30 5 7\n-3 35 11\n3 39\n-25 -10 8\n30 5 7\n-3 35 11\n3 800\n-400 400 2\n300 300 1\n300 302 1\n3 800\n400 -400 2\n300 300 1\n307 300 3\n8 147\n130 80 12\n130 -40 12\n-110 80 12\n-110 -40 12\n70 140 12\n70 -100 12\n-50 140 12\n-50 -100 12\n3 493\n345 154 10\n291 111 75\n-275 -301 46\n4 55\n54 0 1\n40 30 5\n27 36 10\n0 48 7\n3 30\n0 3 3\n-3 0 4\n400 0 3\n3 7\n2 3 2\n-5 -4 2\n-4 3 2\n3 10\n-5 -4 5\n2 3 5\n-4 3 5\n4 6\n4 6 1\n5 5 1\n1 7 1\n0 1 1\n3 493\n345 154 10\n291 111 75\n-275 -301 46\n5 20\n-9 12 5\n0 15 5\n3 -3 3\n12 9 5\n-12 9 5\n0 0\n output: 81.68140899333463\n106.81415022205297\n74.11215318612639\n108.92086846105579\n0.0\n254.85616536128433\n8576.936716409238\n8569.462129048667\n929.1977057481128\n4181.124698202453\n505.09134735536804\n0.0\n46.82023824234038\n65.66979416387915\n50.990642291793506\n4181.124698202453\n158.87951420768937\n\n\n\n" }, { "title": "Problem J: Round Trip", "content": "Jim is planning to visit one of his best friends in a town in the mountain area. First, he leaves his hometown and goes to the destination town. This is called the go phase. Then, he comes back to his hometown. This is called the return phase. You are expected to write a program to find the minimum total cost of this trip, which is the sum of the costs of the go phase and the return phase.\n\nThere is a network of towns including these two towns. Every road in this network is one-way, i. e. , can only be used towards the specified direction. Each road requires a certain cost to travel.\n\nIn addition to the cost of roads, it is necessary to pay a specified fee to go through each town on the way. However, since this is the visa fee for the town, it is not necessary to pay the fee on the second or later visit to the same town.\n\nThe altitude (height) of each town is given. On the go phase, the use of descending roads is inhibited. That is, when going from town a to b, the altitude of a should not be greater than that of b. On the return phase, the use of ascending roads is inhibited in a similar manner. If the altitudes of a and b are equal, the road from a to b can be used on both phases.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn m\nd_2 e_2\nd_3 e_3\n. \n. \n. \nd_n-1\te_n-1\na_1 b_1 c_1\na_2 b_2 c_2\n. \n. \n. \na_m b_m c_m\n\nEvery input item in a dataset is a non-negative integer. Input items in a line are separated by a space.\n\nn is the number of towns in the network. m is the number of (one-way) roads. You can assume the inequalities 2 <= n <= 50 and 0 <= m <= n(n-1) hold. Towns are numbered from 1 to n, inclusive. The town 1 is Jim's hometown, and the town n is the destination town.\n\nd_i is the visa fee of the town i, and e_i is its altitude. You can assume 1 <= d_i <= 1000 and 1<=e_i <= 999 for 2<=i<=n-1. The towns 1 and n do not impose visa fee. The altitude of the town 1 is 0, and that of the town n is 1000. Multiple towns may have the same altitude, but you can assume that there are no more than 10 towns with the same altitude.\n\nThe j-th road is from the town a_j to b_j with the cost c_j (1 <= j <= m). You can assume 1 <= a_j <= n, 1 <= b_j <= n, and 1 <= c_j <= 1000. You can directly go from a_j to b_j, but not from b_j to a_j unless a road from b_j to a_j is separately given. There are no two roads connecting the same pair of towns towards the same direction, that is, for any i and j such that i ! = j, a_i ! = a_j or b_i ! = b_j. There are no roads connecting a town to itself, that is, for any j, a_j ! = b_j.\n\nThe last dataset is followed by a line containing two zeros (separated by a space).", "output": "For each dataset in the input, a line containing the minimum total cost, including the visa fees, of the trip should be output. If such a trip is not possible, output “-1”.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 6\n3 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n3 6\n5 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n4 5\n3 1\n3 1\n1 2 5\n2 3 5\n3 4 5\n4 2 5\n3 1 5\n2 1\n2 1 1\n0 0\n output: 7\n8\n36\n-1"], "Pid": "p00903", "ProblemText": "Task Description: Jim is planning to visit one of his best friends in a town in the mountain area. First, he leaves his hometown and goes to the destination town. This is called the go phase. Then, he comes back to his hometown. This is called the return phase. You are expected to write a program to find the minimum total cost of this trip, which is the sum of the costs of the go phase and the return phase.\n\nThere is a network of towns including these two towns. Every road in this network is one-way, i. e. , can only be used towards the specified direction. Each road requires a certain cost to travel.\n\nIn addition to the cost of roads, it is necessary to pay a specified fee to go through each town on the way. However, since this is the visa fee for the town, it is not necessary to pay the fee on the second or later visit to the same town.\n\nThe altitude (height) of each town is given. On the go phase, the use of descending roads is inhibited. That is, when going from town a to b, the altitude of a should not be greater than that of b. On the return phase, the use of ascending roads is inhibited in a similar manner. If the altitudes of a and b are equal, the road from a to b can be used on both phases.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn m\nd_2 e_2\nd_3 e_3\n. \n. \n. \nd_n-1\te_n-1\na_1 b_1 c_1\na_2 b_2 c_2\n. \n. \n. \na_m b_m c_m\n\nEvery input item in a dataset is a non-negative integer. Input items in a line are separated by a space.\n\nn is the number of towns in the network. m is the number of (one-way) roads. You can assume the inequalities 2 <= n <= 50 and 0 <= m <= n(n-1) hold. Towns are numbered from 1 to n, inclusive. The town 1 is Jim's hometown, and the town n is the destination town.\n\nd_i is the visa fee of the town i, and e_i is its altitude. You can assume 1 <= d_i <= 1000 and 1<=e_i <= 999 for 2<=i<=n-1. The towns 1 and n do not impose visa fee. The altitude of the town 1 is 0, and that of the town n is 1000. Multiple towns may have the same altitude, but you can assume that there are no more than 10 towns with the same altitude.\n\nThe j-th road is from the town a_j to b_j with the cost c_j (1 <= j <= m). You can assume 1 <= a_j <= n, 1 <= b_j <= n, and 1 <= c_j <= 1000. You can directly go from a_j to b_j, but not from b_j to a_j unless a road from b_j to a_j is separately given. There are no two roads connecting the same pair of towns towards the same direction, that is, for any i and j such that i ! = j, a_i ! = a_j or b_i ! = b_j. There are no roads connecting a town to itself, that is, for any j, a_j ! = b_j.\n\nThe last dataset is followed by a line containing two zeros (separated by a space).\nTask Output: For each dataset in the input, a line containing the minimum total cost, including the visa fees, of the trip should be output. If such a trip is not possible, output “-1”.\nTask Samples: input: 3 6\n3 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n3 6\n5 1\n1 2 1\n2 3 1\n3 2 1\n2 1 1\n1 3 4\n3 1 4\n4 5\n3 1\n3 1\n1 2 5\n2 3 5\n3 4 5\n4 2 5\n3 1 5\n2 1\n2 1 1\n0 0\n output: 7\n8\n36\n-1\n\n" }, { "title": "Problem B: Stylish", "content": "Stylish is a programming language whose syntax comprises names, that are sequences of Latin alphabet letters, three types of grouping symbols, periods ('. '), and newlines. Grouping symbols, namely round brackets ('(' and ')'), curly brackets ('{' and '}'), and square brackets ('[' and ']'), must match and be nested properly. Unlike most other programming languages, Stylish uses periods instead of whitespaces for the purpose of term separation. The following is an example of a Stylish program.\n\n1 ( Welcome . to\n2 . . . . . . . . . Stylish )\n3 { Stylish . is\n4 . . . . . [. ( a. programming . language . fun . to. learn )\n5 . . . . . . . ]\n6 . . . . . Maybe . [\n7 . . . . . . . It. will . be. an. official . ICPC . language\n8 . . . . . . . ]\n9 . . . . . }\n\nAs you see in the example, a Stylish program is indented by periods. The amount of indentation of a line is the number of leading periods of it.\n\nYour mission is to visit Stylish masters, learn their indentation styles, and become the youngest Stylish master. An indentation style for well-indented Stylish programs is defined by a triple of integers, (R, C, S), satisfying 1 <= R, C, S <= 20. R, C and S are amounts of indentation introduced by an open round bracket, an open curly bracket, and an open square bracket, respectively.\n\nIn a well-indented program, the amount of indentation of a line is given by R(r_o - r_c) + C(c_o - c_c) + S(s_o - s_c), where r_o, c_o, and s_o are the numbers of occurrences of open round, curly, and square brackets in all preceding lines, respectively, and r_c, c_c, and s_c are those of close brackets. The first line has no indentation in any well-indented program.\n\nThe above example is formatted in the indentation style (R, C, S) = (9,5,2). The only grouping symbol occurring in the first line of the above program is an open round bracket. Therefore the amount of indentation for the second line is 9 · (1 - 0) + 5 · (0 - 0) + 2 ·(0 - 0) = 9. The first four lines contain two open round brackets, one open curly bracket, one open square bracket, two close round brackets, but no close curly nor square bracket. Therefore the amount of indentation for the fifth line is 9 · (2 - 2) + 5 · (1 - 0) + 2 · (1 - 0) = 7.\n\nStylish masters write only well-indented Stylish programs. Every master has his/her own indentation style.\n\nWrite a program that imitates indentation styles of Stylish masters.", "constraint": "", "input": "The input consists of multiple datasets. The first line of a dataset contains two integers p (1 <= p <= 10) and q (1 <= q <= 10). The next p lines form a well-indented program P written by a\nStylish master and the following q lines form another program Q. You may assume that every line of both programs has at least one character and at most 80 characters. Also, you may assume that no line of Q starts with a period.\n\nThe last dataset is followed by a line containing two zeros.", "output": "Apply the indentation style of P to Q and output the appropriate amount of indentation for each line of Q. The amounts must be output in a line in the order of corresponding lines of Q and they must be separated by a single space. The last one should not be followed by trailing spaces. If the appropriate amount of indentation of a line of Q cannot be determined uniquely through analysis of P, then output -1 for that line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n(Follow.my.style\n.........starting.from.round.brackets)\n{then.curly.brackets\n.....[.and.finally\n.......square.brackets.]}\n(Thank.you\n{for.showing.me\n[all\nthe.secrets]})\n4 2\n(This.time.I.will.show.you\n.........(how.to.use.round.brackets)\n.........[but.not.about.square.brackets]\n.........{nor.curly.brackets})\n(I.learned\nhow.to.use.round.brackets)\n4 2\n(This.time.I.will.show.you\n.........(how.to.use.round.brackets)\n.........[but.not.about.square.brackets]\n.........{nor.curly.brackets})\n[I.have.not.learned\nhow.to.use.square.brackets]\n2 2\n(Be.smart.and.let.fear.of\n..(closed.brackets).go)\n(A.pair.of.round.brackets.enclosing\n[A.line.enclosed.in.square.brackets])\n1 2\nTelling.you.nothing.but.you.can.make.it\n[One.liner.(is).(never.indented)]\n[One.liner.(is).(never.indented)]\n2 4\n([{Learn.from.my.KungFu\n...}])\n((\n{{\n[[\n]]}}))\n1 2\nDo.not.waste.your.time.trying.to.read.from.emptiness\n(\n)\n2 3\n({Quite.interesting.art.of.ambiguity\n....})\n{\n(\n)}\n2 4\n({[\n............................................................]})\n(\n{\n[\n]})\n0 0\n output: 0 9 14 16\n0 9\n0 -1\n0 2\n0 0\n0 2 4 6\n0 -1\n0 -1 4\n0 20 40 60"], "Pid": "p00905", "ProblemText": "Task Description: Stylish is a programming language whose syntax comprises names, that are sequences of Latin alphabet letters, three types of grouping symbols, periods ('. '), and newlines. Grouping symbols, namely round brackets ('(' and ')'), curly brackets ('{' and '}'), and square brackets ('[' and ']'), must match and be nested properly. Unlike most other programming languages, Stylish uses periods instead of whitespaces for the purpose of term separation. The following is an example of a Stylish program.\n\n1 ( Welcome . to\n2 . . . . . . . . . Stylish )\n3 { Stylish . is\n4 . . . . . [. ( a. programming . language . fun . to. learn )\n5 . . . . . . . ]\n6 . . . . . Maybe . [\n7 . . . . . . . It. will . be. an. official . ICPC . language\n8 . . . . . . . ]\n9 . . . . . }\n\nAs you see in the example, a Stylish program is indented by periods. The amount of indentation of a line is the number of leading periods of it.\n\nYour mission is to visit Stylish masters, learn their indentation styles, and become the youngest Stylish master. An indentation style for well-indented Stylish programs is defined by a triple of integers, (R, C, S), satisfying 1 <= R, C, S <= 20. R, C and S are amounts of indentation introduced by an open round bracket, an open curly bracket, and an open square bracket, respectively.\n\nIn a well-indented program, the amount of indentation of a line is given by R(r_o - r_c) + C(c_o - c_c) + S(s_o - s_c), where r_o, c_o, and s_o are the numbers of occurrences of open round, curly, and square brackets in all preceding lines, respectively, and r_c, c_c, and s_c are those of close brackets. The first line has no indentation in any well-indented program.\n\nThe above example is formatted in the indentation style (R, C, S) = (9,5,2). The only grouping symbol occurring in the first line of the above program is an open round bracket. Therefore the amount of indentation for the second line is 9 · (1 - 0) + 5 · (0 - 0) + 2 ·(0 - 0) = 9. The first four lines contain two open round brackets, one open curly bracket, one open square bracket, two close round brackets, but no close curly nor square bracket. Therefore the amount of indentation for the fifth line is 9 · (2 - 2) + 5 · (1 - 0) + 2 · (1 - 0) = 7.\n\nStylish masters write only well-indented Stylish programs. Every master has his/her own indentation style.\n\nWrite a program that imitates indentation styles of Stylish masters.\nTask Input: The input consists of multiple datasets. The first line of a dataset contains two integers p (1 <= p <= 10) and q (1 <= q <= 10). The next p lines form a well-indented program P written by a\nStylish master and the following q lines form another program Q. You may assume that every line of both programs has at least one character and at most 80 characters. Also, you may assume that no line of Q starts with a period.\n\nThe last dataset is followed by a line containing two zeros.\nTask Output: Apply the indentation style of P to Q and output the appropriate amount of indentation for each line of Q. The amounts must be output in a line in the order of corresponding lines of Q and they must be separated by a single space. The last one should not be followed by trailing spaces. If the appropriate amount of indentation of a line of Q cannot be determined uniquely through analysis of P, then output -1 for that line.\nTask Samples: input: 5 4\n(Follow.my.style\n.........starting.from.round.brackets)\n{then.curly.brackets\n.....[.and.finally\n.......square.brackets.]}\n(Thank.you\n{for.showing.me\n[all\nthe.secrets]})\n4 2\n(This.time.I.will.show.you\n.........(how.to.use.round.brackets)\n.........[but.not.about.square.brackets]\n.........{nor.curly.brackets})\n(I.learned\nhow.to.use.round.brackets)\n4 2\n(This.time.I.will.show.you\n.........(how.to.use.round.brackets)\n.........[but.not.about.square.brackets]\n.........{nor.curly.brackets})\n[I.have.not.learned\nhow.to.use.square.brackets]\n2 2\n(Be.smart.and.let.fear.of\n..(closed.brackets).go)\n(A.pair.of.round.brackets.enclosing\n[A.line.enclosed.in.square.brackets])\n1 2\nTelling.you.nothing.but.you.can.make.it\n[One.liner.(is).(never.indented)]\n[One.liner.(is).(never.indented)]\n2 4\n([{Learn.from.my.KungFu\n...}])\n((\n{{\n[[\n]]}}))\n1 2\nDo.not.waste.your.time.trying.to.read.from.emptiness\n(\n)\n2 3\n({Quite.interesting.art.of.ambiguity\n....})\n{\n(\n)}\n2 4\n({[\n............................................................]})\n(\n{\n[\n]})\n0 0\n output: 0 9 14 16\n0 9\n0 -1\n0 2\n0 0\n0 2 4 6\n0 -1\n0 -1 4\n0 20 40 60\n\n" }, { "title": "Problem C: One-Dimensional Cellular Automaton", "content": "There is a one-dimensional cellular automaton consisting of N cells. Cells are numbered from 0 to N - 1.\n\nEach cell has a state represented as a non-negative integer less than M. The states of cells evolve through discrete time steps. We denote the state of the i-th cell at time t as S(i, t). The state at time t + 1 is defined by the equation \n\nS(i, t + 1) = (A * S(i - 1, t) + B * S(i, t) + C * S(i + 1, t)) mod M,         (1)\n\nwhere A, B and C are non-negative integer constants. For i < 0 or N <= i, we define S(i, t) = 0.\n\nGiven an automaton definition and initial states of cells, your mission is to write a program that computes the states of the cells at a specified time T.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN M A B C T\nS(0,0) S(1,0) . . . S(N - 1,0)\n\nThe first line of a dataset consists of six integers, namely N, M, A, B, C and T. N is the number of cells. M is the modulus in the equation (1). A, B and C are coefficients in the equation (1). Finally, T is the time for which you should compute the states.\n\nYou may assume that 0 < N <= 50,0 < M <= 1000,0 <= A, B, C < M and 0 <= T <= 10^9.\n\nThe second line consists of N integers, each of which is non-negative and less than M. They represent the states of the cells at time zero.\n\nA line containing six zeros indicates the end of the input.", "output": "For each dataset, output a line that contains the states of the cells at time T. The format of the output is as follows.\n\nS(0, T) S(1, T) . . . S(N - 1, T)\n\nEach state must be represented as an integer and the integers must be separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 1 3 2 0\n0 1 2 0 1\n5 7 1 3 2 1\n0 1 2 0 1\n5 13 1 3 2 11\n0 1 2 0 1\n5 5 2 0 1 100\n0 1 2 0 1\n6 6 0 2 3 1000\n0 1 2 0 1 4\n20 1000 0 2 3 1000000000\n0 1 2 0 1 0 1 2 0 1 0 1 2 0 1 0 1 2 0 1\n30 2 1 0 1 1000000000\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0\n30 2 1 1 1 1000000000\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n30 5 2 3 1 1000000000\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0\n output: 0 1 2 0 1\n2 0 0 4 3\n2 12 10 9 11\n3 0 4 2 1\n0 4 2 0 4 4\n0 376 752 0 376 0 376 752 0 376 0 376 752 0 376 0 376 752 0 376\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0\n1 1 3 2 2 2 3 3 1 4 3 1 2 3 0 4 3 3 0 4 2 2 2 2 1 1 2 1 3 0"], "Pid": "p00906", "ProblemText": "Task Description: There is a one-dimensional cellular automaton consisting of N cells. Cells are numbered from 0 to N - 1.\n\nEach cell has a state represented as a non-negative integer less than M. The states of cells evolve through discrete time steps. We denote the state of the i-th cell at time t as S(i, t). The state at time t + 1 is defined by the equation \n\nS(i, t + 1) = (A * S(i - 1, t) + B * S(i, t) + C * S(i + 1, t)) mod M,         (1)\n\nwhere A, B and C are non-negative integer constants. For i < 0 or N <= i, we define S(i, t) = 0.\n\nGiven an automaton definition and initial states of cells, your mission is to write a program that computes the states of the cells at a specified time T.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN M A B C T\nS(0,0) S(1,0) . . . S(N - 1,0)\n\nThe first line of a dataset consists of six integers, namely N, M, A, B, C and T. N is the number of cells. M is the modulus in the equation (1). A, B and C are coefficients in the equation (1). Finally, T is the time for which you should compute the states.\n\nYou may assume that 0 < N <= 50,0 < M <= 1000,0 <= A, B, C < M and 0 <= T <= 10^9.\n\nThe second line consists of N integers, each of which is non-negative and less than M. They represent the states of the cells at time zero.\n\nA line containing six zeros indicates the end of the input.\nTask Output: For each dataset, output a line that contains the states of the cells at time T. The format of the output is as follows.\n\nS(0, T) S(1, T) . . . S(N - 1, T)\n\nEach state must be represented as an integer and the integers must be separated by a space.\nTask Samples: input: 5 4 1 3 2 0\n0 1 2 0 1\n5 7 1 3 2 1\n0 1 2 0 1\n5 13 1 3 2 11\n0 1 2 0 1\n5 5 2 0 1 100\n0 1 2 0 1\n6 6 0 2 3 1000\n0 1 2 0 1 4\n20 1000 0 2 3 1000000000\n0 1 2 0 1 0 1 2 0 1 0 1 2 0 1 0 1 2 0 1\n30 2 1 0 1 1000000000\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0\n30 2 1 1 1 1000000000\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n30 5 2 3 1 1000000000\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0\n output: 0 1 2 0 1\n2 0 0 4 3\n2 12 10 9 11\n3 0 4 2 1\n0 4 2 0 4 4\n0 376 752 0 376 0 376 752 0 376 0 376 752 0 376 0 376 752 0 376\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0\n1 1 3 2 2 2 3 3 1 4 3 1 2 3 0 4 3 3 0 4 2 2 2 2 1 1 2 1 3 0\n\n" }, { "title": "Problem D: Find the Outlier", "content": "Professor Abacus has just built a new computing engine for making numerical tables. It was designed to calculate the values of a polynomial function in one variable at several points at a time. With the polynomial function f(x) = x^2 + 2x + 1, for instance, a possible expected calculation result is 1 (= f(0)), 4 (= f(1)), 9 (= f(2)), 16 (= f(3)), and 25 (= f(4)).\n\nIt is a pity, however, the engine seemingly has faulty components and exactly one value among those calculated simultaneously is always wrong. With the same polynomial function as above, it can, for instance, output 1,4,12,16, and 25 instead of 1,4,9,16, and 25.\n\nYou are requested to help the professor identify the faulty components. As the first step, you should write a program that scans calculation results of the engine and finds the wrong values.", "constraint": "", "input": "The input is a sequence of datasets, each representing a calculation result in the following format.\n\nd\nv_0\nv_1\n. . . \nv_d+2\n\nHere, d in the first line is a positive integer that represents the degree of the polynomial, namely, the highest exponent of the variable. For instance, the degree of 4x^5 + 3x + 0.5 is five and that of 2.4x + 3.8 is one. d is at most five.\n\nThe following d + 3 lines contain the calculation result of f(0), f(1), . . . , and f(d + 2) in this order, where f is the polynomial function. Each of the lines contains a decimal fraction between -100.0 and 100.0, exclusive.\n\nYou can assume that the wrong value, which is exactly one of f(0), f(1), . . . , and f(d+2), has an error greater than 1.0. Since rounding errors are inevitable, the other values may also have errors but they are small and never exceed 10^-6.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output i in a line when v_i is wrong.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1.0\n4.0\n12.0\n16.0\n25.0\n1\n-30.5893962764\n5.76397083962\n39.3853798058\n74.3727663177\n4\n42.4715310246\n79.5420238202\n28.0282396675\n-30.3627807522\n-49.8363481393\n-25.5101480106\n7.58575761381\n5\n-21.9161699038\n-48.469304271\n-24.3188578417\n-2.35085940324\n-9.70239202086\n-47.2709510623\n-93.5066246072\n-82.5073836498\n0\n output: 2\n1\n1\n6"], "Pid": "p00907", "ProblemText": "Task Description: Professor Abacus has just built a new computing engine for making numerical tables. It was designed to calculate the values of a polynomial function in one variable at several points at a time. With the polynomial function f(x) = x^2 + 2x + 1, for instance, a possible expected calculation result is 1 (= f(0)), 4 (= f(1)), 9 (= f(2)), 16 (= f(3)), and 25 (= f(4)).\n\nIt is a pity, however, the engine seemingly has faulty components and exactly one value among those calculated simultaneously is always wrong. With the same polynomial function as above, it can, for instance, output 1,4,12,16, and 25 instead of 1,4,9,16, and 25.\n\nYou are requested to help the professor identify the faulty components. As the first step, you should write a program that scans calculation results of the engine and finds the wrong values.\nTask Input: The input is a sequence of datasets, each representing a calculation result in the following format.\n\nd\nv_0\nv_1\n. . . \nv_d+2\n\nHere, d in the first line is a positive integer that represents the degree of the polynomial, namely, the highest exponent of the variable. For instance, the degree of 4x^5 + 3x + 0.5 is five and that of 2.4x + 3.8 is one. d is at most five.\n\nThe following d + 3 lines contain the calculation result of f(0), f(1), . . . , and f(d + 2) in this order, where f is the polynomial function. Each of the lines contains a decimal fraction between -100.0 and 100.0, exclusive.\n\nYou can assume that the wrong value, which is exactly one of f(0), f(1), . . . , and f(d+2), has an error greater than 1.0. Since rounding errors are inevitable, the other values may also have errors but they are small and never exceed 10^-6.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output i in a line when v_i is wrong.\nTask Samples: input: 2\n1.0\n4.0\n12.0\n16.0\n25.0\n1\n-30.5893962764\n5.76397083962\n39.3853798058\n74.3727663177\n4\n42.4715310246\n79.5420238202\n28.0282396675\n-30.3627807522\n-49.8363481393\n-25.5101480106\n7.58575761381\n5\n-21.9161699038\n-48.469304271\n-24.3188578417\n-2.35085940324\n-9.70239202086\n-47.2709510623\n-93.5066246072\n-82.5073836498\n0\n output: 2\n1\n1\n6\n\n" }, { "title": "Problem E: Sliding Block Puzzle", "content": "In sliding block puzzles, we repeatedly slide pieces (blocks) to open spaces within a frame to establish a goal placement of pieces.\n\nA puzzle creator has designed a new puzzle by combining the ideas of sliding block puzzles and mazes. The puzzle is played in a rectangular frame segmented into unit squares. Some squares are pre-occupied by obstacles. There are a number of pieces placed in the frame, one 2 * 2 king piece and some number of 1 * 1 pawn pieces. Exactly two 1 * 1 squares are left open. If a pawn piece is adjacent to an open square, we can slide the piece there. If a whole edge of the king piece is adjacent to two open squares, we can slide the king piece. We cannot move the obstacles. Starting from a given initial placement, the objective of the puzzle is to move the king piece to the upper-left corner of the frame. \n\nThe following figure illustrates the initial placement of the fourth dataset of the sample input.\n\nFigure E. 1: The fourth dataset of the sample input.\nYour task is to write a program that computes the minimum number of moves to solve the puzzle from a given placement of pieces. Here, one move means sliding either king or pawn piece to an adjacent position.", "constraint": "", "input": "The input is a sequence of datasets. The first line of a dataset consists of two integers H and W separated by a space, where H and W are the height and the width of the frame. The following H lines, each consisting of W characters, denote the initial placement of pieces. In those H lines, 'X', 'o', '*', and '. ' denote a part of the king piece, a pawn piece, an obstacle, and an open square, respectively. There are no other characters in those H lines. You may assume that 3 <= H <= 50 and 3 <= W <= 50.\n\nA line containing two zeros separated by a space indicates the end of the input.", "output": "For each dataset, output a line containing the minimum number of moves required to move the king piece to the upper-left corner. If there is no way to do so, output -1.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3\noo.\noXX\n.XX\n3 3\nXXo\nXX.\no.o\n3 5\n.o*XX\noooXX\noooo.\n7 12\noooooooooooo\nooooo*****oo\noooooo****oo\no**ooo***ooo\no***ooooo..o\no**ooooooXXo\nooooo****XXo\n5 30\noooooooooooooooooooooooooooooo\noooooooooooooooooooooooooooooo\no***************************oo\nXX.ooooooooooooooooooooooooooo\nXX.ooooooooooooooooooooooooooo\n0 0\n output: 11\n0\n-1\n382\n6807"], "Pid": "p00908", "ProblemText": "Task Description: In sliding block puzzles, we repeatedly slide pieces (blocks) to open spaces within a frame to establish a goal placement of pieces.\n\nA puzzle creator has designed a new puzzle by combining the ideas of sliding block puzzles and mazes. The puzzle is played in a rectangular frame segmented into unit squares. Some squares are pre-occupied by obstacles. There are a number of pieces placed in the frame, one 2 * 2 king piece and some number of 1 * 1 pawn pieces. Exactly two 1 * 1 squares are left open. If a pawn piece is adjacent to an open square, we can slide the piece there. If a whole edge of the king piece is adjacent to two open squares, we can slide the king piece. We cannot move the obstacles. Starting from a given initial placement, the objective of the puzzle is to move the king piece to the upper-left corner of the frame. \n\nThe following figure illustrates the initial placement of the fourth dataset of the sample input.\n\nFigure E. 1: The fourth dataset of the sample input.\nYour task is to write a program that computes the minimum number of moves to solve the puzzle from a given placement of pieces. Here, one move means sliding either king or pawn piece to an adjacent position.\nTask Input: The input is a sequence of datasets. The first line of a dataset consists of two integers H and W separated by a space, where H and W are the height and the width of the frame. The following H lines, each consisting of W characters, denote the initial placement of pieces. In those H lines, 'X', 'o', '*', and '. ' denote a part of the king piece, a pawn piece, an obstacle, and an open square, respectively. There are no other characters in those H lines. You may assume that 3 <= H <= 50 and 3 <= W <= 50.\n\nA line containing two zeros separated by a space indicates the end of the input.\nTask Output: For each dataset, output a line containing the minimum number of moves required to move the king piece to the upper-left corner. If there is no way to do so, output -1.\nTask Samples: input: 3 3\noo.\noXX\n.XX\n3 3\nXXo\nXX.\no.o\n3 5\n.o*XX\noooXX\noooo.\n7 12\noooooooooooo\nooooo*****oo\noooooo****oo\no**ooo***ooo\no***ooooo..o\no**ooooooXXo\nooooo****XXo\n5 30\noooooooooooooooooooooooooooooo\noooooooooooooooooooooooooooooo\no***************************oo\nXX.ooooooooooooooooooooooooooo\nXX.ooooooooooooooooooooooooooo\n0 0\n output: 11\n0\n-1\n382\n6807\n\n" }, { "title": "Problem F: Never Wait for Weights", "content": "In a laboratory, an assistant, Nathan Wada, is measuring weight differences between sample pieces pair by pair. He is using a balance because it can more precisely measure the weight difference between two samples than a spring scale when the samples have nearly the same weight.\n\nHe is occasionally asked the weight differences between pairs of samples. He can or cannot answer based on measurement results already obtained.\n\nSince he is accumulating a massive amount of measurement data, it is now not easy for him to promptly tell the weight differences. Nathan asks you to develop a program that records measurement results and automatically tells the weight differences.", "constraint": "", "input": "The input consists of multiple datasets. The first line of a dataset contains two integers N and M. N denotes the number of sample pieces (2 <= N <= 100,000). Each sample is assigned a unique number from 1 to N as an identifier. The rest of the dataset consists of M lines (1 <= M <= 100,000), each of which corresponds to either a measurement result or an inquiry. They are given in chronological order.\n\nA measurement result has the format,\n\n    ! a b w\n\nwhich represents the sample piece numbered b is heavier than one numbered a by w micrograms (a ! = b). That is, w = w_b - w_a, where w_a and w_b are the weights of a and b, respectively. Here, w is a non-negative integer not exceeding 1,000,000.\n\nYou may assume that all measurements are exact and consistent. \n\nAn inquiry has the format,\n\n    ? a b\n\nwhich asks the weight difference between the sample pieces numbered a and b (a ! = b).\n\nThe last dataset is followed by a line consisting of two zeros separated by a space.", "output": "For each inquiry, ? a b, print the weight difference in micrograms between the sample pieces numbered a and b, w_b - w_a, followed by a newline if the weight difference can be computed based on the measurement results prior to the inquiry. The difference can be zero, or negative as well as positive. You can assume that its absolute value is at most 1,000,000. If the difference cannot be computed based on the measurement results prior to the inquiry, print UNKNOWN followed by a newline.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n! 1 2 1\n? 1 2\n2 2\n! 1 2 1\n? 2 1\n4 7\n! 1 2 100\n? 2 3\n! 2 3 100\n? 2 3\n? 1 3\n! 4 3 150\n? 4 1\n0 0\n output: 1\n-1\nUNKNOWN\n100\n200\n-50"], "Pid": "p00909", "ProblemText": "Task Description: In a laboratory, an assistant, Nathan Wada, is measuring weight differences between sample pieces pair by pair. He is using a balance because it can more precisely measure the weight difference between two samples than a spring scale when the samples have nearly the same weight.\n\nHe is occasionally asked the weight differences between pairs of samples. He can or cannot answer based on measurement results already obtained.\n\nSince he is accumulating a massive amount of measurement data, it is now not easy for him to promptly tell the weight differences. Nathan asks you to develop a program that records measurement results and automatically tells the weight differences.\nTask Input: The input consists of multiple datasets. The first line of a dataset contains two integers N and M. N denotes the number of sample pieces (2 <= N <= 100,000). Each sample is assigned a unique number from 1 to N as an identifier. The rest of the dataset consists of M lines (1 <= M <= 100,000), each of which corresponds to either a measurement result or an inquiry. They are given in chronological order.\n\nA measurement result has the format,\n\n    ! a b w\n\nwhich represents the sample piece numbered b is heavier than one numbered a by w micrograms (a ! = b). That is, w = w_b - w_a, where w_a and w_b are the weights of a and b, respectively. Here, w is a non-negative integer not exceeding 1,000,000.\n\nYou may assume that all measurements are exact and consistent. \n\nAn inquiry has the format,\n\n    ? a b\n\nwhich asks the weight difference between the sample pieces numbered a and b (a ! = b).\n\nThe last dataset is followed by a line consisting of two zeros separated by a space.\nTask Output: For each inquiry, ? a b, print the weight difference in micrograms between the sample pieces numbered a and b, w_b - w_a, followed by a newline if the weight difference can be computed based on the measurement results prior to the inquiry. The difference can be zero, or negative as well as positive. You can assume that its absolute value is at most 1,000,000. If the difference cannot be computed based on the measurement results prior to the inquiry, print UNKNOWN followed by a newline.\nTask Samples: input: 2 2\n! 1 2 1\n? 1 2\n2 2\n! 1 2 1\n? 2 1\n4 7\n! 1 2 100\n? 2 3\n! 2 3 100\n? 2 3\n? 1 3\n! 4 3 150\n? 4 1\n0 0\n output: 1\n-1\nUNKNOWN\n100\n200\n-50\n\n" }, { "title": "Problem G: Let There Be Light", "content": "Suppose that there are some light sources and many spherical balloons. All light sources have sizes small enough to be modeled as point light sources, and they emit light in all directions. The surfaces of the balloons absorb light and do not reflect light. Surprisingly in this world, balloons may overlap.\n\nYou want the total illumination intensity at an objective point as high as possible. For this purpose, some of the balloons obstructing lights can be removed. Because of the removal costs, however, there is a certain limit on the number of balloons to be removed. Thus, you would like to remove an appropriate set of balloons so as to maximize the illumination intensity at the objective point.\n\nThe following figure illustrates the configuration specified in the first dataset of the sample input given below. The figure shows the xy-plane, which is enough because, in this dataset, the z-coordinates of all the light sources, balloon centers, and the objective point are zero. In the figure, light sources are shown as stars and balloons as circles. The objective point is at the origin, and you may remove up to 4 balloons. In this case, the dashed circles in the figure correspond to the balloons to be removed.\n\nFigure G. 1: First dataset of the sample input.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN M R\nS_1x S_1y S_1z S_1r\n. . . \nS_Nx S_Ny S_Nz S_Nr\nT_1x T_1y T_1z T_1b\n. . . \nT_Mx T_My T_Mz T_Mb\nE_x E_y E_z\n\nThe first line of a dataset contains three positive integers, N, M and R, separated by a single space. N means the number of balloons that does not exceed 2000. M means the number of light sources that does not exceed 15. R means the number of balloons that may be removed, which does not exceed N.\n\nEach of the N lines following the first line contains four integers separated by a single space. (S_ix, S_iy, S_iz) means the center position of the i-th balloon and S_ir means its radius.\n\nEach of the following M lines contains four integers separated by a single space. (T_jx, T_jy, T_jz) means the position of the j-th light source and T_jb means its brightness.\n\nThe last line of a dataset contains three integers separated by a single space. (E_x, E_y, E_z) means the position of the objective point.\n\nS_ix, S_iy, S_iz, T_jx, T_jy, T_jz, E_x, E_y and E_z are greater than -500, and less than 500. S_ir is greater than 0, and less than 500. T_jb is greater than 0, and less than 80000.\n\nAt the objective point, the intensity of the light from the j-th light source is in inverse proportion to the square of the distance, namely\n\nT_jb / { (T_jx - E_x)^2 + (T_jy - E_y)^2 + (T_jz - E_z)^2 }, \n\nif there is no balloon interrupting the light. The total illumination intensity is the sum of the above.\n\nYou may assume the following.\n\n The distance between the objective point and any light source is not less than 1.\n\n For every i and j, even if S_ir changes by ε (|ε| < 0.01), whether the i-th balloon hides the j-th light or not does not change.\nThe end of the input is indicated by a line of three zeros.", "output": "For each dataset, output a line containing a decimal fraction which means the highest possible illumination intensity at the objective point after removing R balloons. The output should not contain an error greater than 0.0001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 12 5 4\n0 10 0 1\n1 5 0 2\n1 4 0 2\n0 0 0 2\n10 0 0 1\n3 -1 0 2\n5 -1 0 2\n10 10 0 15\n0 -10 0 1\n10 -10 0 1\n-10 -10 0 1\n10 10 0 1\n0 10 0 240\n10 0 0 200\n10 -2 0 52\n-10 0 0 100\n1 1 0 2\n0 0 0\n12 5 4\n0 10 0 1\n1 5 0 2\n1 4 0 2\n0 0 0 2\n10 0 0 1\n3 -1 0 2\n5 -1 0 2\n10 10 0 15\n0 -10 0 1\n10 -10 0 1\n-10 -10 0 1\n10 10 0 1\n0 10 0 260\n10 0 0 200\n10 -2 0 52\n-10 0 0 100\n1 1 0 2\n0 0 0\n5 1 3\n1 2 0 2\n-1 8 -1 8\n-2 -3 5 6\n-2 1 3 3\n-4 2 3 5\n1 1 2 7\n0 0 0\n5 1 2\n1 2 0 2\n-1 8 -1 8\n-2 -3 5 6\n-2 1 3 3\n-4 2 3 5\n1 1 2 7\n0 0 0\n0 0 0\n output: 3.5\n3.6\n1.1666666666666667\n0.0"], "Pid": "p00910", "ProblemText": "Task Description: Suppose that there are some light sources and many spherical balloons. All light sources have sizes small enough to be modeled as point light sources, and they emit light in all directions. The surfaces of the balloons absorb light and do not reflect light. Surprisingly in this world, balloons may overlap.\n\nYou want the total illumination intensity at an objective point as high as possible. For this purpose, some of the balloons obstructing lights can be removed. Because of the removal costs, however, there is a certain limit on the number of balloons to be removed. Thus, you would like to remove an appropriate set of balloons so as to maximize the illumination intensity at the objective point.\n\nThe following figure illustrates the configuration specified in the first dataset of the sample input given below. The figure shows the xy-plane, which is enough because, in this dataset, the z-coordinates of all the light sources, balloon centers, and the objective point are zero. In the figure, light sources are shown as stars and balloons as circles. The objective point is at the origin, and you may remove up to 4 balloons. In this case, the dashed circles in the figure correspond to the balloons to be removed.\n\nFigure G. 1: First dataset of the sample input.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nN M R\nS_1x S_1y S_1z S_1r\n. . . \nS_Nx S_Ny S_Nz S_Nr\nT_1x T_1y T_1z T_1b\n. . . \nT_Mx T_My T_Mz T_Mb\nE_x E_y E_z\n\nThe first line of a dataset contains three positive integers, N, M and R, separated by a single space. N means the number of balloons that does not exceed 2000. M means the number of light sources that does not exceed 15. R means the number of balloons that may be removed, which does not exceed N.\n\nEach of the N lines following the first line contains four integers separated by a single space. (S_ix, S_iy, S_iz) means the center position of the i-th balloon and S_ir means its radius.\n\nEach of the following M lines contains four integers separated by a single space. (T_jx, T_jy, T_jz) means the position of the j-th light source and T_jb means its brightness.\n\nThe last line of a dataset contains three integers separated by a single space. (E_x, E_y, E_z) means the position of the objective point.\n\nS_ix, S_iy, S_iz, T_jx, T_jy, T_jz, E_x, E_y and E_z are greater than -500, and less than 500. S_ir is greater than 0, and less than 500. T_jb is greater than 0, and less than 80000.\n\nAt the objective point, the intensity of the light from the j-th light source is in inverse proportion to the square of the distance, namely\n\nT_jb / { (T_jx - E_x)^2 + (T_jy - E_y)^2 + (T_jz - E_z)^2 }, \n\nif there is no balloon interrupting the light. The total illumination intensity is the sum of the above.\n\nYou may assume the following.\n\n The distance between the objective point and any light source is not less than 1.\n\n For every i and j, even if S_ir changes by ε (|ε| < 0.01), whether the i-th balloon hides the j-th light or not does not change.\nThe end of the input is indicated by a line of three zeros.\nTask Output: For each dataset, output a line containing a decimal fraction which means the highest possible illumination intensity at the objective point after removing R balloons. The output should not contain an error greater than 0.0001.\nTask Samples: input: 12 5 4\n0 10 0 1\n1 5 0 2\n1 4 0 2\n0 0 0 2\n10 0 0 1\n3 -1 0 2\n5 -1 0 2\n10 10 0 15\n0 -10 0 1\n10 -10 0 1\n-10 -10 0 1\n10 10 0 1\n0 10 0 240\n10 0 0 200\n10 -2 0 52\n-10 0 0 100\n1 1 0 2\n0 0 0\n12 5 4\n0 10 0 1\n1 5 0 2\n1 4 0 2\n0 0 0 2\n10 0 0 1\n3 -1 0 2\n5 -1 0 2\n10 10 0 15\n0 -10 0 1\n10 -10 0 1\n-10 -10 0 1\n10 10 0 1\n0 10 0 260\n10 0 0 200\n10 -2 0 52\n-10 0 0 100\n1 1 0 2\n0 0 0\n5 1 3\n1 2 0 2\n-1 8 -1 8\n-2 -3 5 6\n-2 1 3 3\n-4 2 3 5\n1 1 2 7\n0 0 0\n5 1 2\n1 2 0 2\n-1 8 -1 8\n-2 -3 5 6\n-2 1 3 3\n-4 2 3 5\n1 1 2 7\n0 0 0\n0 0 0\n output: 3.5\n3.6\n1.1666666666666667\n0.0\n\n" }, { "title": "Problem H: Company Organization", "content": "You started a company a few years ago and fortunately it has been highly successful. As the growth of the company, you noticed that you need to manage employees in a more organized way, and decided to form several groups and assign employees to them.\n\nNow, you are planning to form n groups, each of which corresponds to a project in the company. Sometimes you have constraints on members in groups. For example, a group must be a subset of another group because the former group will consist of senior members of the latter group, the members in two groups must be the same because current activities of the two projects are closely related, the members in two groups must not be exactly the same to avoid corruption, two groups cannot have a common employee because of a security reason, and two groups must have a common employee to facilitate collaboration.\n\nIn summary, by letting X_i (i = 1, . . . , n) be the set of employees assigned to the i-th group, we have five types of constraints as follows.\n\n X_i ⊆ X_j\n\n X_i = X_j\n\n X_i ! = X_j\n\n X_i ∩ X_j = ∅\n\n X_i ∩ X_j ! = ∅\nSince you have listed up constraints without considering consistency, it might be the case that you cannot satisfy all the constraints. Constraints are thus ordered according to their priorities, and you now want to know how many constraints of the highest priority can be satisfied.\n\nYou do not have to take ability of employees into consideration. That is, you can assign anyone to any group. Also, you can form groups with no employee. Furthermore, you can hire or fire as many employees as you want if you can satisfy more constraints by doing so.\n\nFor example, suppose that we have the following five constraints on three groups in the order of their priorities, corresponding to the first dataset in the sample input.\n\nX_2 ⊆ X_1\n\nX_3 ⊆ X_2\n\nX_1 ⊆ X_3\n\nX_1 ! = X_3\n\nX_3 ⊆ X_1\nBy assigning the same set of employees to X_1, X_2, and X_3, we can satisfy the first three constraints. However, no matter how we assign employees to X_1, X_2, and X_3, we cannot satisfy the first four highest priority constraints at the same time. Though we can satisfy the first three constraints and the fifth constraint at the same time, the answer should be three.", "constraint": "", "input": "The input consists of several datasets. The first line of a dataset consists of two integers n (2 <= n <= 100) and m (1 <= m <= 10000), which indicate the number of groups and the number of constraints, respectively. Then, description of m constraints follows. The description of each constraint consists of three integers s (1 <= s <= 5), i (1 <= i <= n), and j (1 <= j <= n, j ! == i), meaning a constraint of the s-th type imposed on the i-th group and the j-th group. The type number of a constraint is as listed above. The constraints are given in the descending order of priority.\n\nThe input ends with a line containing two zeros.", "output": "For each dataset, output the number of constraints of the highest priority satisfiable at the same time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n1 2 1\n1 3 2\n1 1 3\n3 1 3\n1 3 1\n4 4\n1 2 1\n1 3 2\n1 1 3\n4 1 3\n4 5\n1 2 1\n1 3 2\n1 1 3\n4 1 3\n5 1 3\n2 3\n1 1 2\n2 1 2\n3 1 2\n0 0\n output: 3\n4\n4\n2"], "Pid": "p00911", "ProblemText": "Task Description: You started a company a few years ago and fortunately it has been highly successful. As the growth of the company, you noticed that you need to manage employees in a more organized way, and decided to form several groups and assign employees to them.\n\nNow, you are planning to form n groups, each of which corresponds to a project in the company. Sometimes you have constraints on members in groups. For example, a group must be a subset of another group because the former group will consist of senior members of the latter group, the members in two groups must be the same because current activities of the two projects are closely related, the members in two groups must not be exactly the same to avoid corruption, two groups cannot have a common employee because of a security reason, and two groups must have a common employee to facilitate collaboration.\n\nIn summary, by letting X_i (i = 1, . . . , n) be the set of employees assigned to the i-th group, we have five types of constraints as follows.\n\n X_i ⊆ X_j\n\n X_i = X_j\n\n X_i ! = X_j\n\n X_i ∩ X_j = ∅\n\n X_i ∩ X_j ! = ∅\nSince you have listed up constraints without considering consistency, it might be the case that you cannot satisfy all the constraints. Constraints are thus ordered according to their priorities, and you now want to know how many constraints of the highest priority can be satisfied.\n\nYou do not have to take ability of employees into consideration. That is, you can assign anyone to any group. Also, you can form groups with no employee. Furthermore, you can hire or fire as many employees as you want if you can satisfy more constraints by doing so.\n\nFor example, suppose that we have the following five constraints on three groups in the order of their priorities, corresponding to the first dataset in the sample input.\n\nX_2 ⊆ X_1\n\nX_3 ⊆ X_2\n\nX_1 ⊆ X_3\n\nX_1 ! = X_3\n\nX_3 ⊆ X_1\nBy assigning the same set of employees to X_1, X_2, and X_3, we can satisfy the first three constraints. However, no matter how we assign employees to X_1, X_2, and X_3, we cannot satisfy the first four highest priority constraints at the same time. Though we can satisfy the first three constraints and the fifth constraint at the same time, the answer should be three.\nTask Input: The input consists of several datasets. The first line of a dataset consists of two integers n (2 <= n <= 100) and m (1 <= m <= 10000), which indicate the number of groups and the number of constraints, respectively. Then, description of m constraints follows. The description of each constraint consists of three integers s (1 <= s <= 5), i (1 <= i <= n), and j (1 <= j <= n, j ! == i), meaning a constraint of the s-th type imposed on the i-th group and the j-th group. The type number of a constraint is as listed above. The constraints are given in the descending order of priority.\n\nThe input ends with a line containing two zeros.\nTask Output: For each dataset, output the number of constraints of the highest priority satisfiable at the same time.\nTask Samples: input: 4 5\n1 2 1\n1 3 2\n1 1 3\n3 1 3\n1 3 1\n4 4\n1 2 1\n1 3 2\n1 1 3\n4 1 3\n4 5\n1 2 1\n1 3 2\n1 1 3\n4 1 3\n5 1 3\n2 3\n1 1 2\n2 1 2\n3 1 2\n0 0\n output: 3\n4\n4\n2\n\n" }, { "title": "Problem I: Beautiful Spacing", "content": "Text is a sequence of words, and a word consists of characters. Your task is to put words into a grid with W columns and sufficiently many lines. For the beauty of the layout, the following conditions have to be satisfied.\n\nThe words in the text must be placed keeping their original order. The following figures show correct and incorrect layout examples for a 4 word text \"This is a pen\" into 11 columns. \n \n Figure I. 1: A good layout. \n Figure I. 2: BAD | Do not reorder words. \n \nBetween two words adjacent in the same line, you must place at least one space character. You sometimes have to put more than one space in order to meet other conditions. \n\nFigure I. 3: BAD | Words must be separated by spaces.\nA word must occupy the same number of consecutive columns as the number of characters in it. You cannot break a single word into two or more by breaking it into lines or by inserting spaces. \n\nFigure I. 4: BAD | Characters in a single word must be contiguous.\nThe text must be justified to the both sides. That is, the first word of a line must startfrom the first column of the line, and except the last line, the last word of a line must end at the last column. \n\nFigure I. 5: BAD | Lines must be justi\fed to both the left and the right sides.\n\nThe text is the most beautifully laid out when there is no unnecessarily long spaces. For instance, the layout in Figure I. 6 has at most 2 contiguous spaces, which is more beautiful than that in Figure I. 1, having 3 contiguous spaces. Given an input text and the number of columns, please find a layout such that the length of the longest contiguous spaces between words is minimum.\nFigure I. 6: A good and the most beautiful layout.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\n    W N\n    x_1 x_2 . . . x_N\n\nW, N, and x_i are all integers. W is the number of columns (3 <= W <= 80,000). N is the number of words (2 <= N <= 50,000). x_i is the number of characters in the i-th word (1 <= x_i <= (W-1)/2 ). Note that the upper bound on x_i assures that there always exists a layout satisfying the conditions.\n\nThe last dataset is followed by a line containing two zeros.", "output": "For each dataset, print the smallest possible number of the longest contiguous spaces between words.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 11 4\n4 2 1 3\n5 7\n1 1 1 2 2 1 2\n11 7\n3 1 3 1 3 3 4\n100 3\n30 30 39\n30 3\n2 5 3\n0 0\n output: 2\n1\n2\n40\n1"], "Pid": "p00912", "ProblemText": "Task Description: Text is a sequence of words, and a word consists of characters. Your task is to put words into a grid with W columns and sufficiently many lines. For the beauty of the layout, the following conditions have to be satisfied.\n\nThe words in the text must be placed keeping their original order. The following figures show correct and incorrect layout examples for a 4 word text \"This is a pen\" into 11 columns. \n \n Figure I. 1: A good layout. \n Figure I. 2: BAD | Do not reorder words. \n \nBetween two words adjacent in the same line, you must place at least one space character. You sometimes have to put more than one space in order to meet other conditions. \n\nFigure I. 3: BAD | Words must be separated by spaces.\nA word must occupy the same number of consecutive columns as the number of characters in it. You cannot break a single word into two or more by breaking it into lines or by inserting spaces. \n\nFigure I. 4: BAD | Characters in a single word must be contiguous.\nThe text must be justified to the both sides. That is, the first word of a line must startfrom the first column of the line, and except the last line, the last word of a line must end at the last column. \n\nFigure I. 5: BAD | Lines must be justi\fed to both the left and the right sides.\n\nThe text is the most beautifully laid out when there is no unnecessarily long spaces. For instance, the layout in Figure I. 6 has at most 2 contiguous spaces, which is more beautiful than that in Figure I. 1, having 3 contiguous spaces. Given an input text and the number of columns, please find a layout such that the length of the longest contiguous spaces between words is minimum.\nFigure I. 6: A good and the most beautiful layout.\nTask Input: The input consists of multiple datasets, each in the following format.\n\n    W N\n    x_1 x_2 . . . x_N\n\nW, N, and x_i are all integers. W is the number of columns (3 <= W <= 80,000). N is the number of words (2 <= N <= 50,000). x_i is the number of characters in the i-th word (1 <= x_i <= (W-1)/2 ). Note that the upper bound on x_i assures that there always exists a layout satisfying the conditions.\n\nThe last dataset is followed by a line containing two zeros.\nTask Output: For each dataset, print the smallest possible number of the longest contiguous spaces between words.\nTask Samples: input: 11 4\n4 2 1 3\n5 7\n1 1 1 2 2 1 2\n11 7\n3 1 3 1 3 3 4\n100 3\n30 30 39\n30 3\n2 5 3\n0 0\n output: 2\n1\n2\n40\n1\n\n" }, { "title": "Problem J: Cubic Colonies", "content": "In AD 3456, the earth is too small for hundreds of billions of people to live in peace. Interstellar Colonization Project with Cubes (ICPC) is a project that tries to move people on the earth to space colonies to ameliorate the problem. ICPC obtained funding from governments and manufactured space colonies very quickly and at low cost using prefabricated cubic blocks.\n\nThe largest colony looks like a Rubik's cube. It consists of 3 * 3 * 3 cubic blocks (Figure J. 1A). Smaller colonies miss some of the blocks in the largest colony.\n\nWhen we manufacture a colony with multiple cubic blocks, we begin with a single block. Then we iteratively glue a next block to existing blocks in a way that faces of them match exactly. Every pair of touched faces is glued.\n\nFigure J. 1: Example of the largest colony and a smaller colony\nHowever, just before the first launch, we found a design flaw with the colonies. We need to add a cable to connect two points on the surface of each colony, but we cannot change the inside of the prefabricated blocks in a short time. Therefore we decided to attach a cable on the surface of each colony. If a part of the cable is not on the surface, it would be sheared off during the launch, so we have to put the whole cable on the surface. We would like to minimize the lengths of the cables due to budget constraints. The dashed line in Figure J. 1B is such an example.\n\nWrite a program that, given the shape of a colony and a pair of points on its surface, calculates the length of the shortest possible cable for that colony.", "constraint": "", "input": "The input contains a series of datasets. Each dataset describes a single colony and the pair of the points for the colony in the following format.\n\nx_1 y_1 z_1 x_2 y_2 z_2\nb_0,0,0b_1,0,0b_2,0,0\nb_0,1,0b_1,1,0b_2,1,0\nb_0,2,0b_1,2,0b_2,2,0\nb_0,0,1b_1,0,1b_2,0,1\nb_0,1,1b_1,1,1b_2,1,1\nb_0,2,1b_1,2,1b_2,2,1\nb_0,0,2b_1,0,2b_2,0,2\nb_0,1,2b_1,1,2b_2,1,2\nb_0,2,2b_1,2,2b_2,2,2\n\n(x_1, y_1, z_1) and (x_2, y_2, z_2) are the two distinct points on the surface of the colony, where x_1, x_2, y_1, y_2, z_1, z_2 are integers that satisfy 0 <= x_1, x_2, y_1, y_2, z_1, z_2 <= 3. b_i, j, k is '#' when there is a cubic block whose two diagonal vertices are (i, j, k) and (i + 1, j + 1, k + 1), and b_i, j, k is '. ' if there is no block. Figure J. 1A corresponds to the first dataset in the sample input, whereas Figure J. 1B corresponds to the second. A cable can pass through a zero-width gap between two blocks if they are touching only on their vertices or edges. In Figure J. 2A, which is the third dataset in the sample input, the shortest cable goes from the point A (0,0,2) to the point B (2,2,2), passing through (1,1,2), which is shared by six blocks. Similarly, in Figure J. 2B (the fourth dataset in the sample input), the shortest cable goes through the gap between two blocks not glued directly. When two blocks share only a single vertex, you can put a cable through the vertex (Figure J. 2C; the fifth dataset in the sample input).\n\nYou can assume that there is no colony consisting of all 3 * 3 * 3 cubes but the center cube.\n\nSix zeros terminate the input.\n\nFigure J. 2: Dashed lines are the shortest cables. Some blocks are shown partially transparent\nfor illustration.", "output": "For each dataset, output a line containing the length of the shortest cable that connects the two given points. We accept errors less than 0.0001. You can assume that given two points can be connected by a cable.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 0 0 3 3 3\n###\n###\n###\n###\n###\n###\n###\n###\n###\n3 3 0 0 0 3\n#..\n###\n###\n###\n###\n###\n#.#\n###\n###\n0 0 2 2 2 2\n...\n...\n...\n.#.\n#..\n...\n##.\n##.\n...\n0 1 2 2 1 1\n...\n...\n...\n.#.\n#..\n...\n##.\n##.\n...\n3 2 0 2 3 2\n###\n..#\n...\n..#\n...\n.#.\n..#\n..#\n.##\n0 0 0 0 0 0\n output: 6.70820393249936941515\n6.47870866461907457534\n2.82842712474619029095\n2.23606797749978980505\n2.82842712474619029095"], "Pid": "p00913", "ProblemText": "Task Description: In AD 3456, the earth is too small for hundreds of billions of people to live in peace. Interstellar Colonization Project with Cubes (ICPC) is a project that tries to move people on the earth to space colonies to ameliorate the problem. ICPC obtained funding from governments and manufactured space colonies very quickly and at low cost using prefabricated cubic blocks.\n\nThe largest colony looks like a Rubik's cube. It consists of 3 * 3 * 3 cubic blocks (Figure J. 1A). Smaller colonies miss some of the blocks in the largest colony.\n\nWhen we manufacture a colony with multiple cubic blocks, we begin with a single block. Then we iteratively glue a next block to existing blocks in a way that faces of them match exactly. Every pair of touched faces is glued.\n\nFigure J. 1: Example of the largest colony and a smaller colony\nHowever, just before the first launch, we found a design flaw with the colonies. We need to add a cable to connect two points on the surface of each colony, but we cannot change the inside of the prefabricated blocks in a short time. Therefore we decided to attach a cable on the surface of each colony. If a part of the cable is not on the surface, it would be sheared off during the launch, so we have to put the whole cable on the surface. We would like to minimize the lengths of the cables due to budget constraints. The dashed line in Figure J. 1B is such an example.\n\nWrite a program that, given the shape of a colony and a pair of points on its surface, calculates the length of the shortest possible cable for that colony.\nTask Input: The input contains a series of datasets. Each dataset describes a single colony and the pair of the points for the colony in the following format.\n\nx_1 y_1 z_1 x_2 y_2 z_2\nb_0,0,0b_1,0,0b_2,0,0\nb_0,1,0b_1,1,0b_2,1,0\nb_0,2,0b_1,2,0b_2,2,0\nb_0,0,1b_1,0,1b_2,0,1\nb_0,1,1b_1,1,1b_2,1,1\nb_0,2,1b_1,2,1b_2,2,1\nb_0,0,2b_1,0,2b_2,0,2\nb_0,1,2b_1,1,2b_2,1,2\nb_0,2,2b_1,2,2b_2,2,2\n\n(x_1, y_1, z_1) and (x_2, y_2, z_2) are the two distinct points on the surface of the colony, where x_1, x_2, y_1, y_2, z_1, z_2 are integers that satisfy 0 <= x_1, x_2, y_1, y_2, z_1, z_2 <= 3. b_i, j, k is '#' when there is a cubic block whose two diagonal vertices are (i, j, k) and (i + 1, j + 1, k + 1), and b_i, j, k is '. ' if there is no block. Figure J. 1A corresponds to the first dataset in the sample input, whereas Figure J. 1B corresponds to the second. A cable can pass through a zero-width gap between two blocks if they are touching only on their vertices or edges. In Figure J. 2A, which is the third dataset in the sample input, the shortest cable goes from the point A (0,0,2) to the point B (2,2,2), passing through (1,1,2), which is shared by six blocks. Similarly, in Figure J. 2B (the fourth dataset in the sample input), the shortest cable goes through the gap between two blocks not glued directly. When two blocks share only a single vertex, you can put a cable through the vertex (Figure J. 2C; the fifth dataset in the sample input).\n\nYou can assume that there is no colony consisting of all 3 * 3 * 3 cubes but the center cube.\n\nSix zeros terminate the input.\n\nFigure J. 2: Dashed lines are the shortest cables. Some blocks are shown partially transparent\nfor illustration.\nTask Output: For each dataset, output a line containing the length of the shortest cable that connects the two given points. We accept errors less than 0.0001. You can assume that given two points can be connected by a cable.\nTask Samples: input: 0 0 0 3 3 3\n###\n###\n###\n###\n###\n###\n###\n###\n###\n3 3 0 0 0 3\n#..\n###\n###\n###\n###\n###\n#.#\n###\n###\n0 0 2 2 2 2\n...\n...\n...\n.#.\n#..\n...\n##.\n##.\n...\n0 1 2 2 1 1\n...\n...\n...\n.#.\n#..\n...\n##.\n##.\n...\n3 2 0 2 3 2\n###\n..#\n...\n..#\n...\n.#.\n..#\n..#\n.##\n0 0 0 0 0 0\n output: 6.70820393249936941515\n6.47870866461907457534\n2.82842712474619029095\n2.23606797749978980505\n2.82842712474619029095\n\n" }, { "title": "Problem A: Equal Sum Sets", "content": "Let us consider sets of positive integers less than or equal to n. Note that all elements of a set are different. Also note that the order of elements doesn't matter, that is, both {3,5,9} and {5,9,3} mean the same set.\n\nSpecifying the number of set elements and their sum to be k and s, respectively, sets satisfying the conditions are limited. When n = 9, k = 3 and s = 23, {6,8,9} is the only such set. There may be more than one such set, in general, however. When n = 9, k = 3 and s = 22, both {5,8,9} and {6,7,9} are possible.\n\nYou have to write a program that calculates the number of the sets that satisfy the given conditions.", "constraint": "", "input": "The input consists of multiple datasets. The number of datasets does not exceed 100.\n\nEach of the datasets has three integers n, k and s in one line, separated by a space. You may assume 1 <= n <= 20,1 <= k <= 10 and 1 <= s <= 155.\n\nThe end of the input is indicated by a line containing three zeros.", "output": "The output for each dataset should be a line containing a single integer that gives the number of the sets that satisfy the conditions. No other characters should appear in the output.\n\nYou can assume that the number of sets does not exceed 2^31 - 1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 3 23\n9 3 22\n10 3 28\n16 10 107\n20 8 102\n20 10 105\n20 10 155\n3 4 3\n4 2 11\n0 0 0\n output: 1\n2\n0\n20\n1542\n5448\n1\n0\n0"], "Pid": "p00914", "ProblemText": "Task Description: Let us consider sets of positive integers less than or equal to n. Note that all elements of a set are different. Also note that the order of elements doesn't matter, that is, both {3,5,9} and {5,9,3} mean the same set.\n\nSpecifying the number of set elements and their sum to be k and s, respectively, sets satisfying the conditions are limited. When n = 9, k = 3 and s = 23, {6,8,9} is the only such set. There may be more than one such set, in general, however. When n = 9, k = 3 and s = 22, both {5,8,9} and {6,7,9} are possible.\n\nYou have to write a program that calculates the number of the sets that satisfy the given conditions.\nTask Input: The input consists of multiple datasets. The number of datasets does not exceed 100.\n\nEach of the datasets has three integers n, k and s in one line, separated by a space. You may assume 1 <= n <= 20,1 <= k <= 10 and 1 <= s <= 155.\n\nThe end of the input is indicated by a line containing three zeros.\nTask Output: The output for each dataset should be a line containing a single integer that gives the number of the sets that satisfy the conditions. No other characters should appear in the output.\n\nYou can assume that the number of sets does not exceed 2^31 - 1.\nTask Samples: input: 9 3 23\n9 3 22\n10 3 28\n16 10 107\n20 8 102\n20 10 105\n20 10 155\n3 4 3\n4 2 11\n0 0 0\n output: 1\n2\n0\n20\n1542\n5448\n1\n0\n0\n\n" }, { "title": "Problem B: The Last Ant", "content": "A straight tunnel without branches is crowded with busy ants coming and going. Some ants walk left to right and others right to left. All ants walk at a constant speed of 1 cm/s. When two ants meet, they try to pass each other. However, some sections of the tunnel are narrow and two ants cannot pass each other. When two ants meet at a narrow section, they turn around and start walking in the opposite directions. When an ant reaches either end of the tunnel, it leaves the tunnel.\n\nThe tunnel has an integer length in centimeters. Every narrow section of the tunnel is integer centimeters distant from the both ends. Except for these sections, the tunnel is wide enough for ants to pass each other. All ants start walking at distinct narrow sections. No ants will newly enter the tunnel. Consequently, all the ants in the tunnel will eventually leave it. Your task is to write a program that tells which is the last ant to leave the tunnel and when it will.\n\nFigure B. 1 shows the movements of the ants during the first two seconds in a tunnel 6 centimeters long. Initially, three ants, numbered 1,2, and 3, start walking at narrow sections, 1,2, and 5 centimeters distant from the left end, respectively. After 0.5 seconds, the ants 1 and 2 meet at a wide section, and they pass each other. Two seconds after the start, the ants 1 and 3 meet at a narrow section, and they turn around.\n\nFigure B. 1 corresponds to the first dataset of the sample input.\nFigure B. 1. Movements of ants", "constraint": "", "input": "The input consists of one or more datasets. Each dataset is formatted as follows.\n\nn l\nd_1 p_1\nd_2 p_2\n. . .\nd_n p_n\n\nThe first line of a dataset contains two integers separated by a space. n (1 <= n <= 20) represents the number of ants, and l (n + 1 <= l <= 100) represents the length of the tunnel in centimeters. The following n lines describe the initial states of ants. Each of the lines has two items, d_i and p_i, separated by a space. Ants are given numbers 1 through n. The ant numbered i has the initial direction d_i and the initial position p_i. The initial direction d_i (1 <= i <= n) is L (to the\nleft) or R (to the right). The initial position p_i (1 <= i <= n) is an integer specifying the distance from the left end of the tunnel in centimeters. Ants are listed in the left to right order, that is, 1 <= p_1 < p_2 < . . . < p_n <= l - 1.\n\nThe last dataset is followed by a line containing two zeros separated by a space.", "output": "For each dataset, output how many seconds it will take before all the ants leave the tunnel, and which of the ants will be the last. The last ant is identified by its number. If two ants will leave at the same time, output the number indicating the ant that will leave through the left end of the tunnel.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 6\nR 1\nL 2\nL 5\n1 10\nR 1\n2 10\nR 5\nL 7\n2 10\nR 3\nL 8\n2 99\nR 1\nL 98\n4 10\nL 1\nR 2\nL 8\nR 9\n6 10\nR 2\nR 3\nL 4\nR 6\nL 7\nL 8\n0 0\n output: 5 1\n9 1\n7 1\n8 2\n98 2\n8 2\n8 3"], "Pid": "p00915", "ProblemText": "Task Description: A straight tunnel without branches is crowded with busy ants coming and going. Some ants walk left to right and others right to left. All ants walk at a constant speed of 1 cm/s. When two ants meet, they try to pass each other. However, some sections of the tunnel are narrow and two ants cannot pass each other. When two ants meet at a narrow section, they turn around and start walking in the opposite directions. When an ant reaches either end of the tunnel, it leaves the tunnel.\n\nThe tunnel has an integer length in centimeters. Every narrow section of the tunnel is integer centimeters distant from the both ends. Except for these sections, the tunnel is wide enough for ants to pass each other. All ants start walking at distinct narrow sections. No ants will newly enter the tunnel. Consequently, all the ants in the tunnel will eventually leave it. Your task is to write a program that tells which is the last ant to leave the tunnel and when it will.\n\nFigure B. 1 shows the movements of the ants during the first two seconds in a tunnel 6 centimeters long. Initially, three ants, numbered 1,2, and 3, start walking at narrow sections, 1,2, and 5 centimeters distant from the left end, respectively. After 0.5 seconds, the ants 1 and 2 meet at a wide section, and they pass each other. Two seconds after the start, the ants 1 and 3 meet at a narrow section, and they turn around.\n\nFigure B. 1 corresponds to the first dataset of the sample input.\nFigure B. 1. Movements of ants\nTask Input: The input consists of one or more datasets. Each dataset is formatted as follows.\n\nn l\nd_1 p_1\nd_2 p_2\n. . .\nd_n p_n\n\nThe first line of a dataset contains two integers separated by a space. n (1 <= n <= 20) represents the number of ants, and l (n + 1 <= l <= 100) represents the length of the tunnel in centimeters. The following n lines describe the initial states of ants. Each of the lines has two items, d_i and p_i, separated by a space. Ants are given numbers 1 through n. The ant numbered i has the initial direction d_i and the initial position p_i. The initial direction d_i (1 <= i <= n) is L (to the\nleft) or R (to the right). The initial position p_i (1 <= i <= n) is an integer specifying the distance from the left end of the tunnel in centimeters. Ants are listed in the left to right order, that is, 1 <= p_1 < p_2 < . . . < p_n <= l - 1.\n\nThe last dataset is followed by a line containing two zeros separated by a space.\nTask Output: For each dataset, output how many seconds it will take before all the ants leave the tunnel, and which of the ants will be the last. The last ant is identified by its number. If two ants will leave at the same time, output the number indicating the ant that will leave through the left end of the tunnel.\nTask Samples: input: 3 6\nR 1\nL 2\nL 5\n1 10\nR 1\n2 10\nR 5\nL 7\n2 10\nR 3\nL 8\n2 99\nR 1\nL 98\n4 10\nL 1\nR 2\nL 8\nR 9\n6 10\nR 2\nR 3\nL 4\nR 6\nL 7\nL 8\n0 0\n output: 5 1\n9 1\n7 1\n8 2\n98 2\n8 2\n8 3\n\n" }, { "title": "Problem C: Count the Regions", "content": "There are a number of rectangles on the x-y plane. The four sides of the rectangles are parallel to either the x-axis or the y-axis, and all of the rectangles reside within a range specified later. There are no other constraints on the coordinates of the rectangles.\n\nThe plane is partitioned into regions surrounded by the sides of one or more rectangles. In an example shown in Figure C. 1, three rectangles overlap one another, and the plane is partitioned into eight regions.\n\nRectangles may overlap in more complex ways. For example, two rectangles may have overlapped sides, they may share their corner points, and/or they may be nested. Figure C. 2 illustrates such cases.\n\nYour job is to write a program that counts the number of the regions on the plane partitioned\nby the rectangles.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is formatted as follows.\n\nn\nl_1 t_1 r_1 b_1\nl_2 t_2 r_2 b_2\n:\nl_n t_n r_n b_n\n\nA dataset starts with n (1 <= n <= 50), the number of rectangles on the plane. Each of the\nfollowing n lines describes a rectangle. The i-th line contains four integers, l_i, t_i, r_i, and b_i, which are the coordinates of the i-th rectangle; (l_i, t_i) gives the x-y coordinates of the top left corner, and (r_i, b_i) gives that of the bottom right corner of the rectangle (0 <= l_i < r_i <= 10^6,0 <= b_i < t_i <= 10^6, for 1 <= i <= n). The four integers are separated by a space.\n\nThe input is terminated by a single zero.", "output": "For each dataset, output a line containing the number of regions on the plane partitioned by the sides of the rectangles.\n\nFigure C. 1. Three rectangles partition the plane into eight regions. This corresponds to the first dataset of the sample input. The x- and y-axes are shown for illustration purposes only, and therefore they do not partition the plane.\nFigure C. 2. Rectangles overlapping in more complex ways. This corresponds to the\nsecond dataset.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0\n output: 8\n6\n6"], "Pid": "p00916", "ProblemText": "Task Description: There are a number of rectangles on the x-y plane. The four sides of the rectangles are parallel to either the x-axis or the y-axis, and all of the rectangles reside within a range specified later. There are no other constraints on the coordinates of the rectangles.\n\nThe plane is partitioned into regions surrounded by the sides of one or more rectangles. In an example shown in Figure C. 1, three rectangles overlap one another, and the plane is partitioned into eight regions.\n\nRectangles may overlap in more complex ways. For example, two rectangles may have overlapped sides, they may share their corner points, and/or they may be nested. Figure C. 2 illustrates such cases.\n\nYour job is to write a program that counts the number of the regions on the plane partitioned\nby the rectangles.\nTask Input: The input consists of multiple datasets. Each dataset is formatted as follows.\n\nn\nl_1 t_1 r_1 b_1\nl_2 t_2 r_2 b_2\n:\nl_n t_n r_n b_n\n\nA dataset starts with n (1 <= n <= 50), the number of rectangles on the plane. Each of the\nfollowing n lines describes a rectangle. The i-th line contains four integers, l_i, t_i, r_i, and b_i, which are the coordinates of the i-th rectangle; (l_i, t_i) gives the x-y coordinates of the top left corner, and (r_i, b_i) gives that of the bottom right corner of the rectangle (0 <= l_i < r_i <= 10^6,0 <= b_i < t_i <= 10^6, for 1 <= i <= n). The four integers are separated by a space.\n\nThe input is terminated by a single zero.\nTask Output: For each dataset, output a line containing the number of regions on the plane partitioned by the sides of the rectangles.\n\nFigure C. 1. Three rectangles partition the plane into eight regions. This corresponds to the first dataset of the sample input. The x- and y-axes are shown for illustration purposes only, and therefore they do not partition the plane.\nFigure C. 2. Rectangles overlapping in more complex ways. This corresponds to the\nsecond dataset.\nTask Samples: input: 3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0\n output: 8\n6\n6\n\n" }, { "title": "Problem D: Clock Hands", "content": "We have an analog clock whose three hands (the second hand, the minute hand and the hour hand) rotate quite smoothly. You can measure two angles between the second hand and two other hands.\n\nWrite a program to find the time at which \"No two hands overlap each other\" and \"Two angles between the second hand and two other hands are equal\" for the first time on or after a given time.\n\nFigure D. 1. Angles between the second hand and two other hands\nClocks are not limited to 12-hour clocks. The hour hand of an H-hour clock goes around once in H hours. The minute hand still goes around once every hour, and the second hand goes around once every minute. At 0: 0: 0 (midnight), all the hands are at the upright position.", "constraint": "", "input": "The input consists of multiple datasets. Each of the dataset has four integers H, h, m and s in one line, separated by a space. H means that the clock is an H-hour clock. h, m and s mean hour, minute and second of the specified time, respectively.\n\nYou may assume 2 <= H <= 100,0 <= h < H, 0 <= m < 60, and 0 <= s < 60.\n\nThe end of the input is indicated by a line containing four zeros.\n\nFigure D. 2. Examples of H-hour clock (6-hour clock and 15-hour clock)", "output": "Output the time T at which \"No two hands overlap each other\" and \"Two angles between the second hand and two other hands are equal\" for the first time on and after the specified time.\n\nFor T being h_o: m_o: s_o (s_o seconds past m_o minutes past h_o o'clock), output four non-negative integers h_o, m_o, n, and d in one line, separated by a space, where n/d is the irreducible fraction representing s_o. For integer s_o including 0, let d be 1.\n\nThe time should be expressed in the remainder of H hours. In other words, one second after\n(H - 1): 59: 59 is 0: 0: 0, not H: 0: 0.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 12 0 0 0\n12 11 59 59\n12 1 56 0\n12 1 56 3\n12 1 56 34\n12 3 9 43\n12 3 10 14\n12 7 17 58\n12 7 18 28\n12 7 23 0\n12 7 23 31\n2 0 38 29\n2 0 39 0\n2 0 39 30\n2 1 6 20\n2 1 20 1\n2 1 20 31\n3 2 15 0\n3 2 59 30\n4 0 28 48\n5 1 5 40\n5 1 6 10\n5 1 7 41\n11 0 55 0\n0 0 0 0\n output: 0 0 43200 1427\n0 0 43200 1427\n1 56 4080 1427\n1 56 47280 1427\n1 57 4860 1427\n3 10 18600 1427\n3 10 61800 1427\n7 18 39240 1427\n7 18 82440 1427\n7 23 43140 1427\n7 24 720 1427\n0 38 4680 79\n0 39 2340 79\n0 40 0 1\n1 6 3960 79\n1 20 2400 79\n1 21 60 79\n2 15 0 1\n0 0 2700 89\n0 28 48 1\n1 6 320 33\n1 6 40 1\n1 8 120 11\n0 55 0 1"], "Pid": "p00917", "ProblemText": "Task Description: We have an analog clock whose three hands (the second hand, the minute hand and the hour hand) rotate quite smoothly. You can measure two angles between the second hand and two other hands.\n\nWrite a program to find the time at which \"No two hands overlap each other\" and \"Two angles between the second hand and two other hands are equal\" for the first time on or after a given time.\n\nFigure D. 1. Angles between the second hand and two other hands\nClocks are not limited to 12-hour clocks. The hour hand of an H-hour clock goes around once in H hours. The minute hand still goes around once every hour, and the second hand goes around once every minute. At 0: 0: 0 (midnight), all the hands are at the upright position.\nTask Input: The input consists of multiple datasets. Each of the dataset has four integers H, h, m and s in one line, separated by a space. H means that the clock is an H-hour clock. h, m and s mean hour, minute and second of the specified time, respectively.\n\nYou may assume 2 <= H <= 100,0 <= h < H, 0 <= m < 60, and 0 <= s < 60.\n\nThe end of the input is indicated by a line containing four zeros.\n\nFigure D. 2. Examples of H-hour clock (6-hour clock and 15-hour clock)\nTask Output: Output the time T at which \"No two hands overlap each other\" and \"Two angles between the second hand and two other hands are equal\" for the first time on and after the specified time.\n\nFor T being h_o: m_o: s_o (s_o seconds past m_o minutes past h_o o'clock), output four non-negative integers h_o, m_o, n, and d in one line, separated by a space, where n/d is the irreducible fraction representing s_o. For integer s_o including 0, let d be 1.\n\nThe time should be expressed in the remainder of H hours. In other words, one second after\n(H - 1): 59: 59 is 0: 0: 0, not H: 0: 0.\nTask Samples: input: 12 0 0 0\n12 11 59 59\n12 1 56 0\n12 1 56 3\n12 1 56 34\n12 3 9 43\n12 3 10 14\n12 7 17 58\n12 7 18 28\n12 7 23 0\n12 7 23 31\n2 0 38 29\n2 0 39 0\n2 0 39 30\n2 1 6 20\n2 1 20 1\n2 1 20 31\n3 2 15 0\n3 2 59 30\n4 0 28 48\n5 1 5 40\n5 1 6 10\n5 1 7 41\n11 0 55 0\n0 0 0 0\n output: 0 0 43200 1427\n0 0 43200 1427\n1 56 4080 1427\n1 56 47280 1427\n1 57 4860 1427\n3 10 18600 1427\n3 10 61800 1427\n7 18 39240 1427\n7 18 82440 1427\n7 23 43140 1427\n7 24 720 1427\n0 38 4680 79\n0 39 2340 79\n0 40 0 1\n1 6 3960 79\n1 20 2400 79\n1 21 60 79\n2 15 0 1\n0 0 2700 89\n0 28 48 1\n1 6 320 33\n1 6 40 1\n1 8 120 11\n0 55 0 1\n\n" }, { "title": "Problem E: Dragon's Cruller", "content": "Dragon's Cruller is a sliding puzzle on a torus. The torus surface is partitioned into nine squares as shown in its development in Figure E. 1. Here, two squares with one of the sides on the development labeled with the same letter are adjacent to each other, actually sharing the side. Figure E. 2 shows which squares are adjacent to which and in which way. Pieces numbered from 1 through 8 are placed on eight out of the nine squares, leaving the remaining one empty.\n\nFigure E. 1. A 3 * 3 Dragon 's Cruller torus\nA piece can be slid to an empty square from one of its adjacent squares. The goal of the puzzle is, by sliding pieces a number of times, to reposition the pieces from the given starting arrangement into the given goal arrangement. Figure E. 3 illustrates arrangements directly reached from the arrangement shown in the center after four possible slides. The cost to slide a piece depends on the direction but is independent of the position nor the piece.\n\nYour mission is to find the minimum cost required to reposition the pieces from the given starting\narrangement into the given goal arrangement.\n\nFigure E. 2. Adjacency\nFigure E. 3. Examples of sliding steps\nUnlike some sliding puzzles on a flat square, it is known that any goal arrangement can be reached from any starting arrangements on this torus.", "constraint": "", "input": "The input is a sequence of at most 30 datasets.\n\nA dataset consists of seven lines. The first line contains two positive integers c_h and c_v, which represent the respective costs to move a piece horizontally and vertically. You can assume that\nboth c_h and c_v are less than 100. The next three lines specify the starting arrangement and the last three the goal arrangement, each in the following format.\n\nd_A d_B d_C\nd_D d_E d_F\nd_G d_H d_I\n\nEach line consists of three digits separated by a space. The digit d_X (X is one of A through I) indicates the state of the square X as shown in Figure E. 2. Digits 1, . . . , 8 indicate that the piece of that number is on the square. The digit 0 indicates that the square is empty.\n\nThe end of the input is indicated by two zeros separated by a space.", "output": "For each dataset, output the minimum total cost to achieve the goal, in a line. The total cost is the sum of the costs of moves from the starting arrangement to the goal arrangement. No other characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 9\n6 3 0\n8 1 2\n4 5 7\n6 3 0\n8 1 2\n4 5 7\n31 31\n4 3 6\n0 1 5\n8 2 7\n0 3 6\n4 1 5\n8 2 7\n92 4\n1 5 3\n4 0 7\n8 2 6\n1 5 0\n4 7 3\n8 2 6\n12 28\n3 4 5\n0 2 6\n7 1 8\n5 7 1\n8 6 2\n0 3 4\n0 0\n output: 0\n31\n96\n312"], "Pid": "p00918", "ProblemText": "Task Description: Dragon's Cruller is a sliding puzzle on a torus. The torus surface is partitioned into nine squares as shown in its development in Figure E. 1. Here, two squares with one of the sides on the development labeled with the same letter are adjacent to each other, actually sharing the side. Figure E. 2 shows which squares are adjacent to which and in which way. Pieces numbered from 1 through 8 are placed on eight out of the nine squares, leaving the remaining one empty.\n\nFigure E. 1. A 3 * 3 Dragon 's Cruller torus\nA piece can be slid to an empty square from one of its adjacent squares. The goal of the puzzle is, by sliding pieces a number of times, to reposition the pieces from the given starting arrangement into the given goal arrangement. Figure E. 3 illustrates arrangements directly reached from the arrangement shown in the center after four possible slides. The cost to slide a piece depends on the direction but is independent of the position nor the piece.\n\nYour mission is to find the minimum cost required to reposition the pieces from the given starting\narrangement into the given goal arrangement.\n\nFigure E. 2. Adjacency\nFigure E. 3. Examples of sliding steps\nUnlike some sliding puzzles on a flat square, it is known that any goal arrangement can be reached from any starting arrangements on this torus.\nTask Input: The input is a sequence of at most 30 datasets.\n\nA dataset consists of seven lines. The first line contains two positive integers c_h and c_v, which represent the respective costs to move a piece horizontally and vertically. You can assume that\nboth c_h and c_v are less than 100. The next three lines specify the starting arrangement and the last three the goal arrangement, each in the following format.\n\nd_A d_B d_C\nd_D d_E d_F\nd_G d_H d_I\n\nEach line consists of three digits separated by a space. The digit d_X (X is one of A through I) indicates the state of the square X as shown in Figure E. 2. Digits 1, . . . , 8 indicate that the piece of that number is on the square. The digit 0 indicates that the square is empty.\n\nThe end of the input is indicated by two zeros separated by a space.\nTask Output: For each dataset, output the minimum total cost to achieve the goal, in a line. The total cost is the sum of the costs of moves from the starting arrangement to the goal arrangement. No other characters should appear in the output.\nTask Samples: input: 4 9\n6 3 0\n8 1 2\n4 5 7\n6 3 0\n8 1 2\n4 5 7\n31 31\n4 3 6\n0 1 5\n8 2 7\n0 3 6\n4 1 5\n8 2 7\n92 4\n1 5 3\n4 0 7\n8 2 6\n1 5 0\n4 7 3\n8 2 6\n12 28\n3 4 5\n0 2 6\n7 1 8\n5 7 1\n8 6 2\n0 3 4\n0 0\n output: 0\n31\n96\n312\n\n" }, { "title": "Problem F: Directional Resemblance", "content": "Vectors have their directions and two vectors make an angle between them. Given a set of three-dimensional vectors, your task is to find the pair among them that makes the smallest angle.", "constraint": "", "input": "The input is a sequence of datasets. A dataset specifies a set of three-dimensional vectors, some of which are directly given in the dataset and the others are generated by the procedure described below.\n\nEach dataset is formatted as follows.\n\nm n S W\nx_1 y_1 z_1\nx_2 y_2 z_2\n:\nx_m y_m z_m\n\nThe first line contains four integers m, n, S, and W.\n\nThe integer m is the number of vectors whose three components are directly specified in the\ndataset. Starting from the second line, m lines have the three components of m vectors. The i-th line of which indicates the vector v_i = (x_i, y_i, z_i). All the vector components are positive integers less than or equal to 100.\n\nThe integer n is the number of vectors generated by the following procedure.\n\nint g = S;\nfor(int i=m+1; i<=m+n; i++) {\n x[i] = (g/7) %100 + 1;\n y[i] = (g/700) %100 + 1;\n z[i] = (g/70000)%100 + 1;\n if( g%2 == 0 ) { g = (g/2); }\n else { g = (g/2) ^ W; }\n}\n\nFor i = m + 1, . . . , m + n, the i-th vector v_i of the set has three components x[i], y[i], and z[i] generated by this procedure.\n\nHere, values of S and W are the parameters S and W given in the first line of the dataset. You may assume 1 <= S <= 10^9 and 1 <= W <= 10^9.\n\nThe total number of vectors satisfies 2 <= m + n <= 12 * 10^4. Note that exactly the same vector may be specified twice or more in a single dataset.\n\nA line containing four zeros indicates the end of the input. The total of m+n for all the datasets in the input never exceeds 16 * 10^5.", "output": "For each dataset, output the pair of vectors among the specified set with the smallest non-zero angle in between. It is assured that there are at least two vectors having different directions.\n\nVectors should be indicated by their three components. The output for a pair of vectors v_a and v_b should be formatted in a line as follows.\n\nx_a y_a z_a x_b y_b z_b\n\nTwo vectors (x_a, y_a, z_a) and (x_b, y_b, z_b) are ordered in the dictionary order, that is, v_a < v_b if x_a < x_b, or if x_a = x_b and y_a < y_b, or if x_a = x_b, y_a = y_b and z_a < z_b. When a vector pair is output, the smaller vector in this order should be output first.\n\nIf more than one pair makes the equal smallest angle, the pair that is the smallest among them in the dictionary order between vector pairs should be output. The pair (v_i, v_j) is smaller than the pair (v_k, v_l) if v_i < v_k, or if v_i = v_k and v_j < v_l.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 0 2013 1124\n1 1 1\n2 2 2\n2 1 1\n1 2 1\n2 100 131832453 129800231\n42 40 46\n42 40 46\n0 100000 7004674 484521438\n0 0 0 0\n output: 1 1 1 1 2 1\n42 40 46 83 79 91\n92 92 79 99 99 85"], "Pid": "p00919", "ProblemText": "Task Description: Vectors have their directions and two vectors make an angle between them. Given a set of three-dimensional vectors, your task is to find the pair among them that makes the smallest angle.\nTask Input: The input is a sequence of datasets. A dataset specifies a set of three-dimensional vectors, some of which are directly given in the dataset and the others are generated by the procedure described below.\n\nEach dataset is formatted as follows.\n\nm n S W\nx_1 y_1 z_1\nx_2 y_2 z_2\n:\nx_m y_m z_m\n\nThe first line contains four integers m, n, S, and W.\n\nThe integer m is the number of vectors whose three components are directly specified in the\ndataset. Starting from the second line, m lines have the three components of m vectors. The i-th line of which indicates the vector v_i = (x_i, y_i, z_i). All the vector components are positive integers less than or equal to 100.\n\nThe integer n is the number of vectors generated by the following procedure.\n\nint g = S;\nfor(int i=m+1; i<=m+n; i++) {\n x[i] = (g/7) %100 + 1;\n y[i] = (g/700) %100 + 1;\n z[i] = (g/70000)%100 + 1;\n if( g%2 == 0 ) { g = (g/2); }\n else { g = (g/2) ^ W; }\n}\n\nFor i = m + 1, . . . , m + n, the i-th vector v_i of the set has three components x[i], y[i], and z[i] generated by this procedure.\n\nHere, values of S and W are the parameters S and W given in the first line of the dataset. You may assume 1 <= S <= 10^9 and 1 <= W <= 10^9.\n\nThe total number of vectors satisfies 2 <= m + n <= 12 * 10^4. Note that exactly the same vector may be specified twice or more in a single dataset.\n\nA line containing four zeros indicates the end of the input. The total of m+n for all the datasets in the input never exceeds 16 * 10^5.\nTask Output: For each dataset, output the pair of vectors among the specified set with the smallest non-zero angle in between. It is assured that there are at least two vectors having different directions.\n\nVectors should be indicated by their three components. The output for a pair of vectors v_a and v_b should be formatted in a line as follows.\n\nx_a y_a z_a x_b y_b z_b\n\nTwo vectors (x_a, y_a, z_a) and (x_b, y_b, z_b) are ordered in the dictionary order, that is, v_a < v_b if x_a < x_b, or if x_a = x_b and y_a < y_b, or if x_a = x_b, y_a = y_b and z_a < z_b. When a vector pair is output, the smaller vector in this order should be output first.\n\nIf more than one pair makes the equal smallest angle, the pair that is the smallest among them in the dictionary order between vector pairs should be output. The pair (v_i, v_j) is smaller than the pair (v_k, v_l) if v_i < v_k, or if v_i = v_k and v_j < v_l.\nTask Samples: input: 4 0 2013 1124\n1 1 1\n2 2 2\n2 1 1\n1 2 1\n2 100 131832453 129800231\n42 40 46\n42 40 46\n0 100000 7004674 484521438\n0 0 0 0\n output: 1 1 1 1 2 1\n42 40 46 83 79 91\n92 92 79 99 99 85\n\n" }, { "title": "Problem G: Longest Chain", "content": "Let us compare two triples a = (x_a, y_a, z_a) and b = (x_b, y_b, z_b) by a partial order ∠ defined as follows.\na ∠ b &h Arr; x_a < x_b and y_a < y_b and z_a < z_b \nYour mission is to find, in the given set of triples, the longest ascending series a_1 ∠ a_2 ∠ . . . ∠ a_k.", "constraint": "", "input": "The input is a sequence of datasets, each specifying a set of triples formatted as follows.\n\nm n A B\nx_1 y_1 z_1\nx_2 y_2 z_2\n. . .\nx_m y_m z_m\n\nHere, m, n, A and B in the first line, and all of x_i, y_i and z_i (i = 1, . . . , m) in the following lines are non-negative integers.\n\nEach dataset specifies a set of m + n triples. The triples p_1 through p_m are explicitly specified in the dataset, the i-th triple p_i being (x_i, y_i, z_i). The remaining n triples are specified by parameters A and B given to the following generator routine.\n\nint a = A, b = B, C = ~(1<<31), M = (1<<16)-1;\nint r() {\n a = 36969 * (a & M) + (a >> 16);\n b = 18000 * (b & M) + (b >> 16);\n return (C & ((a << 16) + b)) % 1000000;\n}\n\nRepeated 3n calls of r() defined as above yield values of x_m+1, y_m+1, z_m+1, x_m+2, y_m+2, z_m+2, . . . , x_m+n, y_m+n, and z_m+n, in this order.\n\nYou can assume that 1 <= m + n <= 3 * 10^5,1 <= A, B <= 2^16, and 0 <= x_k, y_k, z_k < 10^6 for 1 <= k <= m + n.\n\nThe input ends with a line containing four zeros. The total of m + n for all the datasets does not exceed 2 * 10^6.", "output": "For each dataset, output the length of the longest ascending series of triples in the specified set. If p_i_1 ∠ p_i_2 ∠ . . . ∠ p_i_k is the longest, the answer should be k.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 0 1 1\n0 0 0\n0 2 2\n1 1 1\n2 0 2\n2 2 0\n2 2 2\n5 0 1 1\n0 0 0\n1 1 1\n2 2 2\n3 3 3\n4 4 4\n10 0 1 1\n3 0 0\n2 1 0\n2 0 1\n1 2 0\n1 1 1\n1 0 2\n0 3 0\n0 2 1\n0 1 2\n0 0 3\n0 10 1 1\n0 0 0 0\n output: 3\n5\n1\n3"], "Pid": "p00920", "ProblemText": "Task Description: Let us compare two triples a = (x_a, y_a, z_a) and b = (x_b, y_b, z_b) by a partial order ∠ defined as follows.\na ∠ b &h Arr; x_a < x_b and y_a < y_b and z_a < z_b \nYour mission is to find, in the given set of triples, the longest ascending series a_1 ∠ a_2 ∠ . . . ∠ a_k.\nTask Input: The input is a sequence of datasets, each specifying a set of triples formatted as follows.\n\nm n A B\nx_1 y_1 z_1\nx_2 y_2 z_2\n. . .\nx_m y_m z_m\n\nHere, m, n, A and B in the first line, and all of x_i, y_i and z_i (i = 1, . . . , m) in the following lines are non-negative integers.\n\nEach dataset specifies a set of m + n triples. The triples p_1 through p_m are explicitly specified in the dataset, the i-th triple p_i being (x_i, y_i, z_i). The remaining n triples are specified by parameters A and B given to the following generator routine.\n\nint a = A, b = B, C = ~(1<<31), M = (1<<16)-1;\nint r() {\n a = 36969 * (a & M) + (a >> 16);\n b = 18000 * (b & M) + (b >> 16);\n return (C & ((a << 16) + b)) % 1000000;\n}\n\nRepeated 3n calls of r() defined as above yield values of x_m+1, y_m+1, z_m+1, x_m+2, y_m+2, z_m+2, . . . , x_m+n, y_m+n, and z_m+n, in this order.\n\nYou can assume that 1 <= m + n <= 3 * 10^5,1 <= A, B <= 2^16, and 0 <= x_k, y_k, z_k < 10^6 for 1 <= k <= m + n.\n\nThe input ends with a line containing four zeros. The total of m + n for all the datasets does not exceed 2 * 10^6.\nTask Output: For each dataset, output the length of the longest ascending series of triples in the specified set. If p_i_1 ∠ p_i_2 ∠ . . . ∠ p_i_k is the longest, the answer should be k.\nTask Samples: input: 6 0 1 1\n0 0 0\n0 2 2\n1 1 1\n2 0 2\n2 2 0\n2 2 2\n5 0 1 1\n0 0 0\n1 1 1\n2 2 2\n3 3 3\n4 4 4\n10 0 1 1\n3 0 0\n2 1 0\n2 0 1\n1 2 0\n1 1 1\n1 0 2\n0 3 0\n0 2 1\n0 1 2\n0 0 3\n0 10 1 1\n0 0 0 0\n output: 3\n5\n1\n3\n\n" }, { "title": "Problem H: Don't Burst the Balloon", "content": "An open-top box having a square bottom is placed on the floor. You see a number of needles vertically planted on its bottom.\n\nYou want to place a largest possible spheric balloon touching the box bottom, interfering with none of the side walls nor the needles.\n\nJava Specific: Submitted Java programs may not use \"java. awt. geom. Area\". You may use it for your debugging purposes.\n\nFigure H. 1 shows an example of a box with needles and the corresponding largest spheric balloon. It corresponds to the first dataset of the sample input below.\n\nFigure H. 1. The upper shows an example layout and the lower shows the largest spheric balloon that can be placed.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is formatted as follows.\n\nn w\nx_1 y_1 h_1\n:\nx_n y_n h_n\n\nThe first line of a dataset contains two positive integers, n and w, separated by a space. n represents the number of needles, and w represents the height of the side walls.\n\nThe bottom of the box is a 100 * 100 square. The corners of the bottom face are placed at positions (0,0,0), (0,100,0), (100,100,0), and (100,0,0).\n\nEach of the n lines following the first line contains three integers, x_i, y_i, and h_i. (x_i, y_i, 0) and h_i represent the base position and the height of the i-th needle. No two needles stand at the same position.\n\nYou can assume that 1 <= n <= 10,10 <= w <= 200,0 < x_i < 100,0 < y_i < 100 and 1 <= h_i <= 200. You can ignore the thicknesses of the needles and the walls.\n\nThe end of the input is indicated by a line of two zeros. The number of datasets does not exceed 1000.", "output": "For each dataset, output a single line containing the maximum radius of a balloon that can touch the bottom of the box without interfering with the side walls or the needles. The output should not contain an error greater than 0.0001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 16\n70 66 40\n38 52 20\n40 35 10\n70 30 10\n20 60 10\n1 100\n54 75 200\n1 10\n90 10 1\n1 11\n54 75 200\n3 10\n53 60 1\n61 38 1\n45 48 1\n4 10\n20 20 10\n20 80 10\n80 20 10\n80 80 10\n0 0\n output: 26.00000\n39.00000\n130.00000\n49.49777\n85.00000\n95.00000"], "Pid": "p00921", "ProblemText": "Task Description: An open-top box having a square bottom is placed on the floor. You see a number of needles vertically planted on its bottom.\n\nYou want to place a largest possible spheric balloon touching the box bottom, interfering with none of the side walls nor the needles.\n\nJava Specific: Submitted Java programs may not use \"java. awt. geom. Area\". You may use it for your debugging purposes.\n\nFigure H. 1 shows an example of a box with needles and the corresponding largest spheric balloon. It corresponds to the first dataset of the sample input below.\n\nFigure H. 1. The upper shows an example layout and the lower shows the largest spheric balloon that can be placed.\nTask Input: The input is a sequence of datasets. Each dataset is formatted as follows.\n\nn w\nx_1 y_1 h_1\n:\nx_n y_n h_n\n\nThe first line of a dataset contains two positive integers, n and w, separated by a space. n represents the number of needles, and w represents the height of the side walls.\n\nThe bottom of the box is a 100 * 100 square. The corners of the bottom face are placed at positions (0,0,0), (0,100,0), (100,100,0), and (100,0,0).\n\nEach of the n lines following the first line contains three integers, x_i, y_i, and h_i. (x_i, y_i, 0) and h_i represent the base position and the height of the i-th needle. No two needles stand at the same position.\n\nYou can assume that 1 <= n <= 10,10 <= w <= 200,0 < x_i < 100,0 < y_i < 100 and 1 <= h_i <= 200. You can ignore the thicknesses of the needles and the walls.\n\nThe end of the input is indicated by a line of two zeros. The number of datasets does not exceed 1000.\nTask Output: For each dataset, output a single line containing the maximum radius of a balloon that can touch the bottom of the box without interfering with the side walls or the needles. The output should not contain an error greater than 0.0001.\nTask Samples: input: 5 16\n70 66 40\n38 52 20\n40 35 10\n70 30 10\n20 60 10\n1 100\n54 75 200\n1 10\n90 10 1\n1 11\n54 75 200\n3 10\n53 60 1\n61 38 1\n45 48 1\n4 10\n20 20 10\n20 80 10\n80 20 10\n80 80 10\n0 0\n output: 26.00000\n39.00000\n130.00000\n49.49777\n85.00000\n95.00000\n\n" }, { "title": "Problem I: Hidden Tree", "content": "Consider a binary tree whose leaves are assigned integer weights. Such a tree is called balanced if, for every non-leaf node, the sum of the weights in its left subtree is equal to that in the right subtree. For instance, the tree in the following figure is balanced.\n\nFigure I. 1. A balanced tree\nA balanced tree is said to be hidden in a sequence A, if the integers obtained by listing the weights of all leaves of the tree from left to right form a subsequence of A. Here, a subsequence is a sequence that can be derived by deleting zero or more elements from the original sequence without changing the order of the remaining elements.\n\nFor instance, the balanced tree in the figure above is hidden in the sequence 3 4 1 3 1 2 4 4 6, because 4 1 1 2 4 4 is a subsequence of it.\n\nNow, your task is to find, in a given sequence of integers, the balanced tree with the largest number of leaves hidden in it. In fact, the tree shown in Figure I. 1 has the largest number of leaves among the balanced trees hidden in the sequence mentioned above.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset represents a sequence A of integers in the format\n\nN\nA_1 A_2 . . . A_N\n\nwhere 1 <= N <= 1000 and 1 <= A_i <= 500 for 1 <= i <= N. N is the length of the input sequence, and A_i is the i-th element of the sequence.\n\nThe input ends with a line consisting of a single zero. The number of datasets does not exceed 50.", "output": "For each dataset, find the balanced tree with the largest number of leaves among those hidden in A, and output, in a line, the number of its leaves.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 9\n3 4 1 3 1 2 4 4 6\n4\n3 12 6 3\n10\n10 9 8 7 6 5 4 3 2 1\n11\n10 9 8 7 6 5 4 3 2 1 1\n8\n1 1 1 1 1 1 1 1\n0\n output: 6\n2\n1\n5\n8"], "Pid": "p00922", "ProblemText": "Task Description: Consider a binary tree whose leaves are assigned integer weights. Such a tree is called balanced if, for every non-leaf node, the sum of the weights in its left subtree is equal to that in the right subtree. For instance, the tree in the following figure is balanced.\n\nFigure I. 1. A balanced tree\nA balanced tree is said to be hidden in a sequence A, if the integers obtained by listing the weights of all leaves of the tree from left to right form a subsequence of A. Here, a subsequence is a sequence that can be derived by deleting zero or more elements from the original sequence without changing the order of the remaining elements.\n\nFor instance, the balanced tree in the figure above is hidden in the sequence 3 4 1 3 1 2 4 4 6, because 4 1 1 2 4 4 is a subsequence of it.\n\nNow, your task is to find, in a given sequence of integers, the balanced tree with the largest number of leaves hidden in it. In fact, the tree shown in Figure I. 1 has the largest number of leaves among the balanced trees hidden in the sequence mentioned above.\nTask Input: The input consists of multiple datasets. Each dataset represents a sequence A of integers in the format\n\nN\nA_1 A_2 . . . A_N\n\nwhere 1 <= N <= 1000 and 1 <= A_i <= 500 for 1 <= i <= N. N is the length of the input sequence, and A_i is the i-th element of the sequence.\n\nThe input ends with a line consisting of a single zero. The number of datasets does not exceed 50.\nTask Output: For each dataset, find the balanced tree with the largest number of leaves among those hidden in A, and output, in a line, the number of its leaves.\nTask Samples: input: 9\n3 4 1 3 1 2 4 4 6\n4\n3 12 6 3\n10\n10 9 8 7 6 5 4 3 2 1\n11\n10 9 8 7 6 5 4 3 2 1 1\n8\n1 1 1 1 1 1 1 1\n0\n output: 6\n2\n1\n5\n8\n\n" }, { "title": "Problem J: C(O|W|A*RD*|S)* CROSSWORD Puzzle", "content": "The first crossword puzzle was published on December 21,1913 by Arthur Wynne. To celebrate the centennial of his great-great-grandfather's invention, John \"Coward\" Wynne^1 was struggling to make crossword puzzles. He was such a coward that whenever he thought of a tricky clue for a word, he couldn 't stop worrying if people would blame him for choosing a bad clue that could never mean that word. At the end of the day, he cowardly chose boring clues, which made his puzzles less interesting.\n\nOne day, he came up with a brilliant idea: puzzles in which word meanings do not matter, and yet interesting. He told his idea to his colleagues, who admitted that the idea was intriguing. They even named his puzzles \"Coward's Crossword Puzzles\" after his nickname. \n\nHowever, making a Coward's crossword puzzle was not easy. Even though he did not have to think about word meanings, it was not easy to check if a puzzle has one and only one set of answers. As the day of the centennial anniversary was approaching, John started worrying if he would not be able to make interesting ones in time. Let's help John by writing a program that solves Coward's crossword puzzles.\n\nEach puzzle consists of h * w cells along with h across clues and w down clues. The clues are regular expressions written in a pattern language whose BNF syntax is given as in the table below.\n\nclue : : = \"^\" pattern \"$\"\npattern : : = simple | pattern \"|\" simple\nsimple : : = basic | simple basic\nbasic : : = elementary | elementary \"*\"\nelementary : : = \". \" | \"A\" | \"B\" | . . . | \"Z\" | \"(\" pattern \")\"\nTable J. 1. BNF syntax of the pattern language.\nThe clues (as denoted by p and q below) match words (as denoted by s below) according to the\nfollowing rules.\n\n^p$ matches s if p matches s.\n\np|q matches a string s if p and/or q matches s.\n\npq matches a string s if there exist s_1 and s_2 such that s_1s_2 = s, p matches s_1, and q matches s_2.\n\np* matches a string s if s is empty, or there exist s_1 and s_2 such that s_1s_2 = s, p matches\n\ns_1, and p* matches s_2.\n\nEach of A, B, . . . , Z matches the respective letter itself.\n\n(p) matches s if p matches s.\n\n. is the shorthand of (A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z).\nBelow is an example of a Coward 's crossword puzzle with the answers filled in the cells.\n\nJava Specific: Submitted Java programs may not use classes in the java. util. regex package.\nC++ Specific: Submitted C++ programs may not use the std: : regex class.\n note:\n^1 All characters appearing in this problem, except for Arthur Wynne, are fictitious. Any resemblance to real persons, living or dead, is purely coincidental.", "constraint": "", "input": "The input consists of multiple datasets, each of which represents a puzzle given in the following format.\n\nh w\np_1\np_2\n. . .\np_h\nq_1\nq_2\n. . .\nq_2\n\nHere, h and w represent the vertical and horizontal numbers of cells, respectively, where 2 <= h, w <= 4. The p_i and q_j are the across and down clues for the i-th row and j-th column, respectively. Any clue has no more than 512 characters.\n\nThe last dataset is followed by a line of two zeros. You may assume that there are no more than 30 datasets in the input.", "output": "For each dataset, when the puzzle has a unique set of answers, output it as h lines of w characters. When the puzzle has no set of answers, or more than one set of answers, output \"none\" or \"ambiguous\" without double quotations, respectively.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 2\n^(C|I|T|Y)*$\n\n^(C|O|P|S)*$\n\n^(F|L|I|P)*$\n\n^(B|A|C|K)*$\n\n2 2\n^HE|LL|O*$\n\n^(P|L|E|A|S|E)*$\n\n^(H|L)*$\n\n^EP|IP|EF$\n\n4 4\n^LONG|TALL|S*ALLY$\n\n^(R*EV*|OL*U(TIO)*N)*$\n\n^(STRAWBERRY|F*I*E*L*D*S*|FOREVER)*$\n\n^P.S.|I|LOVE|YOU$\n\n^(RE|A|L)((L|OV*E)*)$\n\n^(LUC*Y*|IN.THE.SKY)(WITH|DI*A*M*ON*D*S*)$\n\n^(IVE*|GOT|A|F*E*E*L*I*N*G*)*$\n\n^YEST*E*R*D*A*Y*$\n\n2 3\n^(C|P)(OL|AS)$\n\n^(LU|TO)(X|R)$\n\n^CT|PL$\n\n^OU|AO$\n\n^SR|LX$\n\n2 2\n^T*|(HI)|S*$\n\n^SE|NT|EN|CE$\n\n^IS$\n\n^(F|A|L|S|E)*$\n\n2 4\n^ARKA|BARB|COLU$\n\n^NSAS|ADOS|MBIA$\n\n^..$\n\n^..$\n\n^KA|RO|LI$\n\n^AS|BA|US$\n\n0 0\n output: IC\nPC\nHE\nLP\nALLY\nOUNE\nEDIS\nLOVE\nambiguous\nnone\nARKA\nNSAS"], "Pid": "p00923", "ProblemText": "Task Description: The first crossword puzzle was published on December 21,1913 by Arthur Wynne. To celebrate the centennial of his great-great-grandfather's invention, John \"Coward\" Wynne^1 was struggling to make crossword puzzles. He was such a coward that whenever he thought of a tricky clue for a word, he couldn 't stop worrying if people would blame him for choosing a bad clue that could never mean that word. At the end of the day, he cowardly chose boring clues, which made his puzzles less interesting.\n\nOne day, he came up with a brilliant idea: puzzles in which word meanings do not matter, and yet interesting. He told his idea to his colleagues, who admitted that the idea was intriguing. They even named his puzzles \"Coward's Crossword Puzzles\" after his nickname. \n\nHowever, making a Coward's crossword puzzle was not easy. Even though he did not have to think about word meanings, it was not easy to check if a puzzle has one and only one set of answers. As the day of the centennial anniversary was approaching, John started worrying if he would not be able to make interesting ones in time. Let's help John by writing a program that solves Coward's crossword puzzles.\n\nEach puzzle consists of h * w cells along with h across clues and w down clues. The clues are regular expressions written in a pattern language whose BNF syntax is given as in the table below.\n\nclue : : = \"^\" pattern \"$\"\npattern : : = simple | pattern \"|\" simple\nsimple : : = basic | simple basic\nbasic : : = elementary | elementary \"*\"\nelementary : : = \". \" | \"A\" | \"B\" | . . . | \"Z\" | \"(\" pattern \")\"\nTable J. 1. BNF syntax of the pattern language.\nThe clues (as denoted by p and q below) match words (as denoted by s below) according to the\nfollowing rules.\n\n^p$ matches s if p matches s.\n\np|q matches a string s if p and/or q matches s.\n\npq matches a string s if there exist s_1 and s_2 such that s_1s_2 = s, p matches s_1, and q matches s_2.\n\np* matches a string s if s is empty, or there exist s_1 and s_2 such that s_1s_2 = s, p matches\n\ns_1, and p* matches s_2.\n\nEach of A, B, . . . , Z matches the respective letter itself.\n\n(p) matches s if p matches s.\n\n. is the shorthand of (A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z).\nBelow is an example of a Coward 's crossword puzzle with the answers filled in the cells.\n\nJava Specific: Submitted Java programs may not use classes in the java. util. regex package.\nC++ Specific: Submitted C++ programs may not use the std: : regex class.\n note:\n^1 All characters appearing in this problem, except for Arthur Wynne, are fictitious. Any resemblance to real persons, living or dead, is purely coincidental.\nTask Input: The input consists of multiple datasets, each of which represents a puzzle given in the following format.\n\nh w\np_1\np_2\n. . .\np_h\nq_1\nq_2\n. . .\nq_2\n\nHere, h and w represent the vertical and horizontal numbers of cells, respectively, where 2 <= h, w <= 4. The p_i and q_j are the across and down clues for the i-th row and j-th column, respectively. Any clue has no more than 512 characters.\n\nThe last dataset is followed by a line of two zeros. You may assume that there are no more than 30 datasets in the input.\nTask Output: For each dataset, when the puzzle has a unique set of answers, output it as h lines of w characters. When the puzzle has no set of answers, or more than one set of answers, output \"none\" or \"ambiguous\" without double quotations, respectively.\nTask Samples: input: 2 2\n^(C|I|T|Y)*$\n\n^(C|O|P|S)*$\n\n^(F|L|I|P)*$\n\n^(B|A|C|K)*$\n\n2 2\n^HE|LL|O*$\n\n^(P|L|E|A|S|E)*$\n\n^(H|L)*$\n\n^EP|IP|EF$\n\n4 4\n^LONG|TALL|S*ALLY$\n\n^(R*EV*|OL*U(TIO)*N)*$\n\n^(STRAWBERRY|F*I*E*L*D*S*|FOREVER)*$\n\n^P.S.|I|LOVE|YOU$\n\n^(RE|A|L)((L|OV*E)*)$\n\n^(LUC*Y*|IN.THE.SKY)(WITH|DI*A*M*ON*D*S*)$\n\n^(IVE*|GOT|A|F*E*E*L*I*N*G*)*$\n\n^YEST*E*R*D*A*Y*$\n\n2 3\n^(C|P)(OL|AS)$\n\n^(LU|TO)(X|R)$\n\n^CT|PL$\n\n^OU|AO$\n\n^SR|LX$\n\n2 2\n^T*|(HI)|S*$\n\n^SE|NT|EN|CE$\n\n^IS$\n\n^(F|A|L|S|E)*$\n\n2 4\n^ARKA|BARB|COLU$\n\n^NSAS|ADOS|MBIA$\n\n^..$\n\n^..$\n\n^KA|RO|LI$\n\n^AS|BA|US$\n\n0 0\n output: IC\nPC\nHE\nLP\nALLY\nOUNE\nEDIS\nLOVE\nambiguous\nnone\nARKA\nNSAS\n\n" }, { "title": "Problem A:\nBit String Reordering", "content": "You have to reorder a given bit string as specified. The only operation allowed is swapping adjacent bit pairs. Please write a program that calculates the minimum number of swaps required.\n\n The initial bit string is simply represented by a sequence of bits, while the target is specified by a run-length code. The run-length code of a bit string is a sequence of the lengths of maximal consecutive sequences of zeros or ones in the bit string. For example, the run-length code of \"011100\" is \"1 3 2\". Note that there are two different bit strings with the same run-length code, one starting with zero and the other starting with one. The target is either of these two.\n\n In Sample Input 1, bit string \"100101\" should be reordered so that its run-length code is \"1 3 2\", which means either \"100011\" or \"011100\". At least four swaps are required to obtain \"011100\". On the other hand, only one swap is required to make \"100011\". Thus, in this example, 1 is the answer.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows. \n\n$N$ $M$\n$b_1$ $b_2$ . . . $b_N$\n$p_1$ $p_2$ . . . $p_M$\n\nThe first line contains two integers $N$ ($1 <= N <= 15$) and $M$ ($1 <= M <= N$). The second line\nspecifies the initial bit string by $N$ integers. Each integer $b_i$ is either 0 or 1. The third line contains the run-length code, consisting of $M$ integers. Integers $p_1$ through $p_M$ represent the lengths of consecutive sequences of zeros or ones in the bit string, from left to right. Here, $1 <= p_j$ for $1 <= j <= M$ and $\\sum^{M}_{j=1} p_j = N$ hold. It is guaranteed that the initial bit string can be reordered into a bit string with its run-length code $p_1, . . . , p_M$.", "output": "Output the minimum number of swaps required", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3\n1 0 0 1 0 1\n1 3 2\n output: 1", "input: 7 2\n1 1 1 0 0 0 0\n4 3\n output: 12", "input: 15 14\n1 0 1 0 1 0 1 0 1 0 1 0 1 0 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 2\n output: 7", "input: 1 1\n0\n1\n output: 0"], "Pid": "p00924", "ProblemText": "Task Description: You have to reorder a given bit string as specified. The only operation allowed is swapping adjacent bit pairs. Please write a program that calculates the minimum number of swaps required.\n\n The initial bit string is simply represented by a sequence of bits, while the target is specified by a run-length code. The run-length code of a bit string is a sequence of the lengths of maximal consecutive sequences of zeros or ones in the bit string. For example, the run-length code of \"011100\" is \"1 3 2\". Note that there are two different bit strings with the same run-length code, one starting with zero and the other starting with one. The target is either of these two.\n\n In Sample Input 1, bit string \"100101\" should be reordered so that its run-length code is \"1 3 2\", which means either \"100011\" or \"011100\". At least four swaps are required to obtain \"011100\". On the other hand, only one swap is required to make \"100011\". Thus, in this example, 1 is the answer.\nTask Input: The input consists of a single test case. The test case is formatted as follows. \n\n$N$ $M$\n$b_1$ $b_2$ . . . $b_N$\n$p_1$ $p_2$ . . . $p_M$\n\nThe first line contains two integers $N$ ($1 <= N <= 15$) and $M$ ($1 <= M <= N$). The second line\nspecifies the initial bit string by $N$ integers. Each integer $b_i$ is either 0 or 1. The third line contains the run-length code, consisting of $M$ integers. Integers $p_1$ through $p_M$ represent the lengths of consecutive sequences of zeros or ones in the bit string, from left to right. Here, $1 <= p_j$ for $1 <= j <= M$ and $\\sum^{M}_{j=1} p_j = N$ hold. It is guaranteed that the initial bit string can be reordered into a bit string with its run-length code $p_1, . . . , p_M$.\nTask Output: Output the minimum number of swaps required\nTask Samples: input: 6 3\n1 0 0 1 0 1\n1 3 2\n output: 1\ninput: 7 2\n1 1 1 0 0 0 0\n4 3\n output: 12\ninput: 15 14\n1 0 1 0 1 0 1 0 1 0 1 0 1 0 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 2\n output: 7\ninput: 1 1\n0\n1\n output: 0\n\n" }, { "title": "Problem B:\nMiscalculation", "content": "Bob is an elementary schoolboy, not so good at mathematics. He found Father's calculator and tried cheating on his homework using it. His homework was calculating given expressions containing multiplications and additions. Multiplications should be done prior to additions, of course, but the calculator evaluates the expression from left to right, neglecting the operator precedence. So his answers may be the result of either of the following two calculation rules.\n\n Doing multiplication before addition\n\n Doing calculation from left to right neglecting the operator precedence\n Write a program that tells which of the rules is applied from an expression and his answer.\n\n An expression consists of integers and operators. All the integers have only one digit, from 0 to 9. There are two kinds of operators + and *, which represent addition and multiplication, respectively.\n\n The following is an example expression.\n\n1+2*3+4\n\n Calculating this expression with the multiplication-first rule, the answer is 11, as in Sample Input 1. With the left-to-right rule, however, the answer will be 13 as shown in Sample Input 2.\n\n There may be cases in which both rules lead to the same result and you cannot tell which of the rules is applied. Moreover, Bob sometimes commits miscalculations. When neither rules would result in Bob 's answer, it is clear that he actually did.", "constraint": "", "input": "The input consists of a single test case specified with two lines. The first line contains the expression to be calculated. The number of characters of the expression is always odd and less than or equal to 17. Each of the odd-numbered characters in the expression is a digit from '0' to '9'. Each of the even-numbered characters is an operator '+' or '*'. The second line contains an integer which ranges from 0 to 999999999, inclusive. This integer represents Bob's answer for the expression given in the first line.", "output": "Output one of the following four characters: \n\nM     When only the multiplication-first rule results Bob's answer. \nL     When only the left-to-right rule results Bob's answer. \nU     When both of the rules result Bob's answer. \nI     When neither of the rules results Bob's answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1+2*3+4\n11\n output: M", "input: 1+2*3+4\n13\n output: L", "input: 3\n3\n output: U", "input: 1+2*3+4\n9\n output: I"], "Pid": "p00925", "ProblemText": "Task Description: Bob is an elementary schoolboy, not so good at mathematics. He found Father's calculator and tried cheating on his homework using it. His homework was calculating given expressions containing multiplications and additions. Multiplications should be done prior to additions, of course, but the calculator evaluates the expression from left to right, neglecting the operator precedence. So his answers may be the result of either of the following two calculation rules.\n\n Doing multiplication before addition\n\n Doing calculation from left to right neglecting the operator precedence\n Write a program that tells which of the rules is applied from an expression and his answer.\n\n An expression consists of integers and operators. All the integers have only one digit, from 0 to 9. There are two kinds of operators + and *, which represent addition and multiplication, respectively.\n\n The following is an example expression.\n\n1+2*3+4\n\n Calculating this expression with the multiplication-first rule, the answer is 11, as in Sample Input 1. With the left-to-right rule, however, the answer will be 13 as shown in Sample Input 2.\n\n There may be cases in which both rules lead to the same result and you cannot tell which of the rules is applied. Moreover, Bob sometimes commits miscalculations. When neither rules would result in Bob 's answer, it is clear that he actually did.\nTask Input: The input consists of a single test case specified with two lines. The first line contains the expression to be calculated. The number of characters of the expression is always odd and less than or equal to 17. Each of the odd-numbered characters in the expression is a digit from '0' to '9'. Each of the even-numbered characters is an operator '+' or '*'. The second line contains an integer which ranges from 0 to 999999999, inclusive. This integer represents Bob's answer for the expression given in the first line.\nTask Output: Output one of the following four characters: \n\nM     When only the multiplication-first rule results Bob's answer. \nL     When only the left-to-right rule results Bob's answer. \nU     When both of the rules result Bob's answer. \nI     When neither of the rules results Bob's answer.\nTask Samples: input: 1+2*3+4\n11\n output: M\ninput: 1+2*3+4\n13\n output: L\ninput: 3\n3\n output: U\ninput: 1+2*3+4\n9\n output: I\n\n" }, { "title": "Problem C:\nShopping", "content": "Your friend will enjoy shopping. She will walk through a mall along a straight street, where $N$ individual shops (numbered from 1 to $N$) are aligned at regular intervals. Each shop has one door and is located at the one side of the street. The distances between the doors of the adjacent shops are the same length, i. e. a unit length. Starting shopping at the entrance of the mall, she visits shops in order to purchase goods. She has to go to the exit of the mall after shopping.\n\n She requires some restrictions on visiting order of shops. Each of the restrictions indicates that she shall visit a shop before visiting another shop. For example, when she wants to buy a nice dress before choosing heels, she shall visit a boutique before visiting a shoe store. When the boutique is farther than the shoe store, she must pass the shoe store before visiting the boutique, and go back to the shoe store after visiting the boutique.\n\n If only the order of the visiting shops satisfies all the restrictions, she can visit other shops in any order she likes.\n\n Write a program to determine the minimum required walking length for her to move from the entrance to the exit.\n\n Assume that the position of the door of the shop numbered $k$ is $k$ units far from the entrance, where the position of the exit is $N + 1$ units far from the entrance.", "constraint": "", "input": "The input consists of a single test case. \n\n$N$ $m$\n$c_1$ $d_1$\n. \n. \n. \n$c_m$ $d_m$\n\n \n The first line contains two integers $N$ and $m$, where $N$ ($1 <= N <= 1000$) is the number of shops, and $m$ ($0 <= m <= 500$) is the number of restrictions. Each of the next $m$ lines contains two integers $c_i$ and $d_i$ ($1 <= c_i < d_i <= N$) indicating the $i$-th restriction on the visiting order, where she must visit the shop numbered $c_i$ after she visits the shop numbered $d_i$ ($i = 1, . . . , m$).\n\t \n There are no pair of $j$ and $k$ that satisfy $c_j = c_k$ and $d_j = d_k$.", "output": "Output the minimum required walking length for her to move from the entrance to the exit. You should omit the length of her walk in the insides of shops.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 3\n3 7\n8 9\n2 5\n output: 23", "input: 10 3\n8 9\n6 7\n2 4\n output: 19", "input: 10 0\n output: 11", "input: 10 6\n6 7\n4 5\n2 5\n6 9\n3 5\n6 8\n output: 23", "input: 1000 8\n3 4\n6 1000\n5 1000\n7 1000\n8 1000\n4 1000\n9 1000\n1 2\n output: 2997"], "Pid": "p00926", "ProblemText": "Task Description: Your friend will enjoy shopping. She will walk through a mall along a straight street, where $N$ individual shops (numbered from 1 to $N$) are aligned at regular intervals. Each shop has one door and is located at the one side of the street. The distances between the doors of the adjacent shops are the same length, i. e. a unit length. Starting shopping at the entrance of the mall, she visits shops in order to purchase goods. She has to go to the exit of the mall after shopping.\n\n She requires some restrictions on visiting order of shops. Each of the restrictions indicates that she shall visit a shop before visiting another shop. For example, when she wants to buy a nice dress before choosing heels, she shall visit a boutique before visiting a shoe store. When the boutique is farther than the shoe store, she must pass the shoe store before visiting the boutique, and go back to the shoe store after visiting the boutique.\n\n If only the order of the visiting shops satisfies all the restrictions, she can visit other shops in any order she likes.\n\n Write a program to determine the minimum required walking length for her to move from the entrance to the exit.\n\n Assume that the position of the door of the shop numbered $k$ is $k$ units far from the entrance, where the position of the exit is $N + 1$ units far from the entrance.\nTask Input: The input consists of a single test case. \n\n$N$ $m$\n$c_1$ $d_1$\n. \n. \n. \n$c_m$ $d_m$\n\n \n The first line contains two integers $N$ and $m$, where $N$ ($1 <= N <= 1000$) is the number of shops, and $m$ ($0 <= m <= 500$) is the number of restrictions. Each of the next $m$ lines contains two integers $c_i$ and $d_i$ ($1 <= c_i < d_i <= N$) indicating the $i$-th restriction on the visiting order, where she must visit the shop numbered $c_i$ after she visits the shop numbered $d_i$ ($i = 1, . . . , m$).\n\t \n There are no pair of $j$ and $k$ that satisfy $c_j = c_k$ and $d_j = d_k$.\nTask Output: Output the minimum required walking length for her to move from the entrance to the exit. You should omit the length of her walk in the insides of shops.\nTask Samples: input: 10 3\n3 7\n8 9\n2 5\n output: 23\ninput: 10 3\n8 9\n6 7\n2 4\n output: 19\ninput: 10 0\n output: 11\ninput: 10 6\n6 7\n4 5\n2 5\n6 9\n3 5\n6 8\n output: 23\ninput: 1000 8\n3 4\n6 1000\n5 1000\n7 1000\n8 1000\n4 1000\n9 1000\n1 2\n output: 2997\n\n" }, { "title": "Problem D:\nSpace Golf", "content": "You surely have never heard of this new planet surface exploration scheme, as it is being carried out in a project with utmost secrecy. The scheme is expected to cut costs of conventional rovertype mobile explorers considerably, using projected-type equipment nicknamed \"observation bullets\".\n\n Bullets do not have any active mobile abilities of their own, which is the main reason of their cost-efficiency. Each of the bullets, after being shot out on a launcher given its initial velocity, makes a parabolic trajectory until it touches down. It bounces on the surface and makes another parabolic trajectory. This will be repeated virtually infinitely.\n\n We want each of the bullets to bounce precisely at the respective spot of interest on the planet surface, adjusting its initial velocity. A variety of sensors in the bullet can gather valuable data at this instant of bounce, and send them to the observation base. Although this may sound like a conventional target shooting practice, there are several issues that make the problem more difficult.\n\n There may be some obstacles between the launcher and the target spot. The obstacles stand upright and are very thin that we can ignore their widths. Once the bullet touches any of the obstacles, we cannot be sure of its trajectory thereafter. So we have to plan launches to avoid these obstacles.\n\n Launching the bullet almost vertically in a speed high enough, we can easily make it hit the target without touching any of the obstacles, but giving a high initial speed is energyconsuming. Energy is extremely precious in space exploration, and the initial speed of the bullet should be minimized. Making the bullet bounce a number of times may make the bullet reach the target with lower initial speed.\n\n The bullet should bounce, however, no more than a given number of times. Although the body of the bullet is made strong enough, some of the sensors inside may not stand repetitive shocks. The allowed numbers of bounces vary on the type of the observation bullets.\n You are summoned engineering assistance to this project to author a smart program that tells the minimum required initial speed of the bullet to accomplish the mission.\n\nFigure D. 1 gives a sketch of a situation, roughly corresponding to the situation of the Sample\nInput 4 given below.\nFigure D. 1. A sample situation\n\n You can assume the following.\n\n The atmosphere of the planet is so thin that atmospheric resistance can be ignored.\n\n The planet is large enough so that its surface can be approximated to be a completely flat plane.\n\n The gravity acceleration can be approximated to be constant up to the highest points a bullet can reach.\n These mean that the bullets fly along a perfect parabolic trajectory.\n\n You can also assume the following.\n\n The surface of the planet and the bullets are made so hard that bounces can be approximated as elastic collisions. In other words, loss of kinetic energy on bounces can be ignored. As we can also ignore the atmospheric resistance, the velocity of a bullet immediately after a bounce is equal to the velocity immediately after its launch.\n\n The bullets are made compact enough to ignore their sizes.\n\n The launcher is also built compact enough to ignore its height.\n You, a programming genius, may not be an expert in physics. Let us review basics of rigid-body dynamics.\n\nWe will describe here the velocity of the bullet $v$ with its horizontal and vertical components $v_x$ and $v_y$ (positive meaning upward). The initial velocity has the components $v_{ix}$ and $v_{iy}$, that is, immediately after the launch of the bullet, $v_x = v_{ix}$ and $v_y = v_{iy}$ hold. We denote the horizontal distance of the bullet from the launcher as $x$ and its altitude as $y$ at time $t$.\n The horizontal velocity component of the bullet is kept constant during its flight when atmospheric resistance is ignored. Thus the horizontal distance from the launcher is proportional to the time elapsed.\n \n \\[\n x = v_{ix}t\n\\tag{1}\n \\]\n \n The vertical velocity component $v_y$ is gradually decelerated by the gravity. With the gravity acceleration of $g$, the following differential equation holds during the flight.\n\n \\[\n \\frac{dv_y}{dt} = -g\n \\tag{2}\n\\]\n \nSolving this with the initial conditions of $v_y = v_{iy}$ and $y = 0$ when $t = 0$, we obtain the\n following.\n \\[\n y = -\\frac{1}{2} gt^2 + v_{iy}t\n \\tag{3}\n \\]\n \\[\n= -(\\frac{1}{2}gt - v_{iy})t\n \\tag{4}\n \\]\n \n The equation (4) tells that the bullet reaches the ground again when $t = 2v_{iy}/g$. Thus, the distance of the point of the bounce from the launcher is $2v_{ix}v_{iy}/g$. In other words, to make the bullet fly the distance of $l$, the two components of the initial velocity should satisfy $2v_{ix}v_{iy} = lg$.\n \n Eliminating the parameter $t$ from the simultaneous equations above, we obtain the following equation that describes the parabolic trajectory of the bullet.\n \\[\n y = -(\\frac{g}{2v^2_{ix}})x^2 + (\\frac{v_{iy}}{v_{ix}})x\n \\tag{5}\n \\]\n \nFor ease of computation, a special unit system is used in this project, according to which the gravity acceleration $g$ of the planet is exactly 1.0.", "constraint": "", "input": "The input consists of a single test case with the following format. \n\n$d$ $n$ $b$\n$p_1$ $h_1$\n$p_2$ $h_2$\n. \n. \n. \n $p_n$ $h_n$\n\n \nThe first line contains three integers, $d$, $n$, and $b$. Here, $d$ is the distance from the launcher\n to the target spot ($1 <= d <= 10000$), $n$ is the number of obstacles ($1 <= n <= 10$), and $b$ is the maximum number of bounces allowed, not including the bounce at the target spot ($0 <= b <= 15$).\n\nEach of the following $n$ lines has two integers. In the $k$-th line, $p_k$ is the position of the $k$-th obstacle, its distance from the launcher, and $h_k$ is its height from the ground level. You can assume that $0 < p_1$, $p_k < p_{k+1}$ for $k = 1, . . . , n - 1$, and $p_n < d$. You can also assume that\n$1 <= h_k <= 10000$ for $k = 1, . . . , n$.", "output": "Output the smallest possible initial speed $v_i$ that makes the bullet reach the target. The initial speed $v_i$ of the bullet is defined as follows.\n\n \\[\nv_i = \\sqrt{v_{ix}^2 + v_{iy}^2}\n \\]\n\nThe output should not contain an error greater than 0.0001", "content_img": true, "lang": "en", "error": false, "samples": ["input: 100 1 0\n50 100\n output: 14.57738", "input: 10 1 0\n4 2\n output: 3.16228", "input: 100 4 3\n20 10\n30 10\n40 10\n50 10\n output: 7.78175", "input: 343 3 2\n56 42\n190 27\n286 34\n output: 11.08710"], "Pid": "p00927", "ProblemText": "Task Description: You surely have never heard of this new planet surface exploration scheme, as it is being carried out in a project with utmost secrecy. The scheme is expected to cut costs of conventional rovertype mobile explorers considerably, using projected-type equipment nicknamed \"observation bullets\".\n\n Bullets do not have any active mobile abilities of their own, which is the main reason of their cost-efficiency. Each of the bullets, after being shot out on a launcher given its initial velocity, makes a parabolic trajectory until it touches down. It bounces on the surface and makes another parabolic trajectory. This will be repeated virtually infinitely.\n\n We want each of the bullets to bounce precisely at the respective spot of interest on the planet surface, adjusting its initial velocity. A variety of sensors in the bullet can gather valuable data at this instant of bounce, and send them to the observation base. Although this may sound like a conventional target shooting practice, there are several issues that make the problem more difficult.\n\n There may be some obstacles between the launcher and the target spot. The obstacles stand upright and are very thin that we can ignore their widths. Once the bullet touches any of the obstacles, we cannot be sure of its trajectory thereafter. So we have to plan launches to avoid these obstacles.\n\n Launching the bullet almost vertically in a speed high enough, we can easily make it hit the target without touching any of the obstacles, but giving a high initial speed is energyconsuming. Energy is extremely precious in space exploration, and the initial speed of the bullet should be minimized. Making the bullet bounce a number of times may make the bullet reach the target with lower initial speed.\n\n The bullet should bounce, however, no more than a given number of times. Although the body of the bullet is made strong enough, some of the sensors inside may not stand repetitive shocks. The allowed numbers of bounces vary on the type of the observation bullets.\n You are summoned engineering assistance to this project to author a smart program that tells the minimum required initial speed of the bullet to accomplish the mission.\n\nFigure D. 1 gives a sketch of a situation, roughly corresponding to the situation of the Sample\nInput 4 given below.\nFigure D. 1. A sample situation\n\n You can assume the following.\n\n The atmosphere of the planet is so thin that atmospheric resistance can be ignored.\n\n The planet is large enough so that its surface can be approximated to be a completely flat plane.\n\n The gravity acceleration can be approximated to be constant up to the highest points a bullet can reach.\n These mean that the bullets fly along a perfect parabolic trajectory.\n\n You can also assume the following.\n\n The surface of the planet and the bullets are made so hard that bounces can be approximated as elastic collisions. In other words, loss of kinetic energy on bounces can be ignored. As we can also ignore the atmospheric resistance, the velocity of a bullet immediately after a bounce is equal to the velocity immediately after its launch.\n\n The bullets are made compact enough to ignore their sizes.\n\n The launcher is also built compact enough to ignore its height.\n You, a programming genius, may not be an expert in physics. Let us review basics of rigid-body dynamics.\n\nWe will describe here the velocity of the bullet $v$ with its horizontal and vertical components $v_x$ and $v_y$ (positive meaning upward). The initial velocity has the components $v_{ix}$ and $v_{iy}$, that is, immediately after the launch of the bullet, $v_x = v_{ix}$ and $v_y = v_{iy}$ hold. We denote the horizontal distance of the bullet from the launcher as $x$ and its altitude as $y$ at time $t$.\n The horizontal velocity component of the bullet is kept constant during its flight when atmospheric resistance is ignored. Thus the horizontal distance from the launcher is proportional to the time elapsed.\n \n \\[\n x = v_{ix}t\n\\tag{1}\n \\]\n \n The vertical velocity component $v_y$ is gradually decelerated by the gravity. With the gravity acceleration of $g$, the following differential equation holds during the flight.\n\n \\[\n \\frac{dv_y}{dt} = -g\n \\tag{2}\n\\]\n \nSolving this with the initial conditions of $v_y = v_{iy}$ and $y = 0$ when $t = 0$, we obtain the\n following.\n \\[\n y = -\\frac{1}{2} gt^2 + v_{iy}t\n \\tag{3}\n \\]\n \\[\n= -(\\frac{1}{2}gt - v_{iy})t\n \\tag{4}\n \\]\n \n The equation (4) tells that the bullet reaches the ground again when $t = 2v_{iy}/g$. Thus, the distance of the point of the bounce from the launcher is $2v_{ix}v_{iy}/g$. In other words, to make the bullet fly the distance of $l$, the two components of the initial velocity should satisfy $2v_{ix}v_{iy} = lg$.\n \n Eliminating the parameter $t$ from the simultaneous equations above, we obtain the following equation that describes the parabolic trajectory of the bullet.\n \\[\n y = -(\\frac{g}{2v^2_{ix}})x^2 + (\\frac{v_{iy}}{v_{ix}})x\n \\tag{5}\n \\]\n \nFor ease of computation, a special unit system is used in this project, according to which the gravity acceleration $g$ of the planet is exactly 1.0.\nTask Input: The input consists of a single test case with the following format. \n\n$d$ $n$ $b$\n$p_1$ $h_1$\n$p_2$ $h_2$\n. \n. \n. \n $p_n$ $h_n$\n\n \nThe first line contains three integers, $d$, $n$, and $b$. Here, $d$ is the distance from the launcher\n to the target spot ($1 <= d <= 10000$), $n$ is the number of obstacles ($1 <= n <= 10$), and $b$ is the maximum number of bounces allowed, not including the bounce at the target spot ($0 <= b <= 15$).\n\nEach of the following $n$ lines has two integers. In the $k$-th line, $p_k$ is the position of the $k$-th obstacle, its distance from the launcher, and $h_k$ is its height from the ground level. You can assume that $0 < p_1$, $p_k < p_{k+1}$ for $k = 1, . . . , n - 1$, and $p_n < d$. You can also assume that\n$1 <= h_k <= 10000$ for $k = 1, . . . , n$.\nTask Output: Output the smallest possible initial speed $v_i$ that makes the bullet reach the target. The initial speed $v_i$ of the bullet is defined as follows.\n\n \\[\nv_i = \\sqrt{v_{ix}^2 + v_{iy}^2}\n \\]\n\nThe output should not contain an error greater than 0.0001\nTask Samples: input: 100 1 0\n50 100\n output: 14.57738\ninput: 10 1 0\n4 2\n output: 3.16228\ninput: 100 4 3\n20 10\n30 10\n40 10\n50 10\n output: 7.78175\ninput: 343 3 2\n56 42\n190 27\n286 34\n output: 11.08710\n\n" }, { "title": "Problem E:\nAutomotive Navigation", "content": "The International Commission for Perfect Cars (ICPC) has constructed a city scale test course for advanced driver assistance systems. Your company, namely the Automotive Control Machines (ACM), is appointed by ICPC to make test runs on the course.\n\n The test course consists of streets, each running straight either east-west or north-south. No streets of the test course have dead ends, that is, at each end of a street, it meets another one. There are no grade separated streets either, and so if a pair of orthogonal streets run through the same geographical location, they always meet at a crossing or a junction, where a car can turn from one to the other. No U-turns are allowed on the test course and a car never moves outside of the streets.\n\n Oops! You have just received an error report telling that the GPS (Global Positioning System) unit of a car running on the test course was broken and the driver got lost. Fortunately, however, the odometer and the electronic compass of the car are still alive.\n\n You are requested to write a program to estimate the current location of the car from available information. You have the car's location just before its GPS unit was broken. Also, you can remotely measure the running distance and the direction of the car once every time unit. The measured direction of the car is one of north, east, south, and west. If you measure the direction of the car while it is making a turn, the measurement result can be the direction either before or after the turn. You can assume that the width of each street is zero.\n\n The car's direction when the GPS unit was broken is not known. You should consider every possible direction consistent with the street on which the car was running at that time.", "constraint": "", "input": "The input consists of a single test case. The first line contains four integers $n$, $x_0$, $y_0$, $t$, which are the number of streets ($4 <= n <= 50$), $x$- and $y$-coordinates of the car at time zero, when the GPS unit was broken, and the current time ($1 <= t <= 100$), respectively. $(x_0, y_0)$ is of course on some street. This is followed by $n$ lines, each containing four integers $x_s$, $y_s$, $x_e$, $y_e$ describing a street from $(x_s, y_s)$ to $(x_e, y_e)$ where $(x_s, y_s) \\ne (x_e, y_e)$. Since each street runs either east-west or north-south, $x_s = x_e$ or $y_s = y_e$ is also satisfied. You can assume that no two parallel streets overlap or meet. In this coordinate system, the $x$- and $y$-axes point east and north, respectively. Each input coordinate is non-negative and at most 50. Each of the remaining $t$ lines contains an integer $d_i$ ($1 <= d_i <= 10$), specifying the measured running distance from time $i - 1$ to $i$, and a letter $c_i$, denoting the measured direction of the car at time $i$ and being either N for north, E for east, W for west, or S for south.", "output": "Output all the possible current locations of the car that are consistent with the measurements. If they are $(x_1, y_1), (x_2, y_2), . . . , (x_p, y_p)$ in the lexicographic order, that is, $x_i < x_j$ or $x_i = x_j$ and $y_i < y_j$ if $1 <= i < j <= p$, output the following: \n\n$x_1$ $y_1$\n$x_2$ $y_2$\n. \n. \n. \n\t$x_p$ $y_p$\n\n\t\n\tEach output line should consist of two integers separated by a space.\n\nYou can assume that at least one location on a street is consistent with the measurements", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 1 1\n1 1 1 2\n2 2 2 1\n2 2 1 2\n1 1 2 1\n9 N\n output: 1 1\n2 2", "input: 6 0 0 2\n0 0 2 0\n0 1 2 1\n0 2 2 2\n0 0 0 2\n1 0 1 2\n2 0 2 2\n2 E\n7 N\n output: 0 1\n1 0\n1 2\n2 1", "input: 7 10 0 1\n5 0 10 0\n8 5 15 5\n5 10 15 10\n5 0 5 10\n8 5 8 10\n10 0 10 10\n15 5 15 10\n10 N\n output: 5 5\n8 8\n10 10\n15 5"], "Pid": "p00928", "ProblemText": "Task Description: The International Commission for Perfect Cars (ICPC) has constructed a city scale test course for advanced driver assistance systems. Your company, namely the Automotive Control Machines (ACM), is appointed by ICPC to make test runs on the course.\n\n The test course consists of streets, each running straight either east-west or north-south. No streets of the test course have dead ends, that is, at each end of a street, it meets another one. There are no grade separated streets either, and so if a pair of orthogonal streets run through the same geographical location, they always meet at a crossing or a junction, where a car can turn from one to the other. No U-turns are allowed on the test course and a car never moves outside of the streets.\n\n Oops! You have just received an error report telling that the GPS (Global Positioning System) unit of a car running on the test course was broken and the driver got lost. Fortunately, however, the odometer and the electronic compass of the car are still alive.\n\n You are requested to write a program to estimate the current location of the car from available information. You have the car's location just before its GPS unit was broken. Also, you can remotely measure the running distance and the direction of the car once every time unit. The measured direction of the car is one of north, east, south, and west. If you measure the direction of the car while it is making a turn, the measurement result can be the direction either before or after the turn. You can assume that the width of each street is zero.\n\n The car's direction when the GPS unit was broken is not known. You should consider every possible direction consistent with the street on which the car was running at that time.\nTask Input: The input consists of a single test case. The first line contains four integers $n$, $x_0$, $y_0$, $t$, which are the number of streets ($4 <= n <= 50$), $x$- and $y$-coordinates of the car at time zero, when the GPS unit was broken, and the current time ($1 <= t <= 100$), respectively. $(x_0, y_0)$ is of course on some street. This is followed by $n$ lines, each containing four integers $x_s$, $y_s$, $x_e$, $y_e$ describing a street from $(x_s, y_s)$ to $(x_e, y_e)$ where $(x_s, y_s) \\ne (x_e, y_e)$. Since each street runs either east-west or north-south, $x_s = x_e$ or $y_s = y_e$ is also satisfied. You can assume that no two parallel streets overlap or meet. In this coordinate system, the $x$- and $y$-axes point east and north, respectively. Each input coordinate is non-negative and at most 50. Each of the remaining $t$ lines contains an integer $d_i$ ($1 <= d_i <= 10$), specifying the measured running distance from time $i - 1$ to $i$, and a letter $c_i$, denoting the measured direction of the car at time $i$ and being either N for north, E for east, W for west, or S for south.\nTask Output: Output all the possible current locations of the car that are consistent with the measurements. If they are $(x_1, y_1), (x_2, y_2), . . . , (x_p, y_p)$ in the lexicographic order, that is, $x_i < x_j$ or $x_i = x_j$ and $y_i < y_j$ if $1 <= i < j <= p$, output the following: \n\n$x_1$ $y_1$\n$x_2$ $y_2$\n. \n. \n. \n\t$x_p$ $y_p$\n\n\t\n\tEach output line should consist of two integers separated by a space.\n\nYou can assume that at least one location on a street is consistent with the measurements\nTask Samples: input: 4 2 1 1\n1 1 1 2\n2 2 2 1\n2 2 1 2\n1 1 2 1\n9 N\n output: 1 1\n2 2\ninput: 6 0 0 2\n0 0 2 0\n0 1 2 1\n0 2 2 2\n0 0 0 2\n1 0 1 2\n2 0 2 2\n2 E\n7 N\n output: 0 1\n1 0\n1 2\n2 1\ninput: 7 10 0 1\n5 0 10 0\n8 5 15 5\n5 10 15 10\n5 0 5 10\n8 5 8 10\n10 0 10 10\n15 5 15 10\n10 N\n output: 5 5\n8 8\n10 10\n15 5\n\n" }, { "title": "Problem F:\nThere is No Alternative", "content": "ICPC (Isles of Coral Park City) consist of several beautiful islands.\n\n The citizens requested construction of bridges between islands to resolve inconveniences of using boats between islands, and they demand that all the islands should be reachable from any other islands via one or more bridges.\n\n The city mayor selected a number of pairs of islands, and ordered a building company to estimate the costs to build bridges between the pairs. With this estimate, the mayor has to decide the set of bridges to build, minimizing the total construction cost.\n\n However, it is difficult for him to select the most cost-efficient set of bridges among those connecting all the islands. For example, three sets of bridges connect all the islands for the Sample Input 1. The bridges in each set are expressed by bold edges in Figure F. 1.\nFigure F. 1. Three sets of bridges connecting all the islands for Sample Input 1\n\n As the first step, he decided to build only those bridges which are contained in all the sets of bridges to connect all the islands and minimize the cost. We refer to such bridges as no alternative bridges. In Figure F. 2, no alternative bridges are drawn as thick edges for the Sample Input 1,2 and 3.\nFigure F. 2. No alternative bridges for Sample Input 1,2 and 3\n\nWrite a program that advises the mayor which bridges are no alternative bridges for the given input.", "constraint": "", "input": "The input consists of a single test case.\n \n\n$N$ $M$\n$S_1$ $D_1$ $C_1$\n. \n. \n. \n$S_M$ $D_M$ $C_M$\nThe first line contains two positive integers $N$ and $M$. $N$ represents the number of islands and each island is identified by an integer 1 through $N$. $M$ represents the number of the pairs of islands between which a bridge may be built.\n\nEach line of the next $M$ lines contains three integers $S_i$, $D_i$ and $C_i$ ($1 <= i <= M$) which represent that it will cost $C_i$ to build the bridge between islands $S_i$ and $D_i$. You may assume $3 <= N <= 500$, $N - 1 <= M <= min(50000, N(N - 1)/2)$, $1 <= S_i < D_i <= N$, and $1 <= C_i <= 10000$. No two bridges connect the same pair of two islands, that is, if $i \\ne j$ and $S_i = S_j$, then $D_i \\ne D_j$ . If all the candidate bridges are built, all the islands are reachable from any other islands via one or more bridges.", "output": "Output two integers, which mean the number of no alternative bridges and the sum of their construction cost, separated by a space.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 4\n1 2 3\n1 3 3\n2 3 3\n2 4 3\n output: 1 3", "input: 4 4\n1 2 3\n1 3 5\n2 3 3\n2 4 3\n output: 3 9", "input: 4 4\n1 2 3\n1 3 1\n2 3 3\n2 4 3\n output: 2 4", "input: 3 3\n1 2 1\n2 3 1\n1 3 1\n output: 0 0"], "Pid": "p00929", "ProblemText": "Task Description: ICPC (Isles of Coral Park City) consist of several beautiful islands.\n\n The citizens requested construction of bridges between islands to resolve inconveniences of using boats between islands, and they demand that all the islands should be reachable from any other islands via one or more bridges.\n\n The city mayor selected a number of pairs of islands, and ordered a building company to estimate the costs to build bridges between the pairs. With this estimate, the mayor has to decide the set of bridges to build, minimizing the total construction cost.\n\n However, it is difficult for him to select the most cost-efficient set of bridges among those connecting all the islands. For example, three sets of bridges connect all the islands for the Sample Input 1. The bridges in each set are expressed by bold edges in Figure F. 1.\nFigure F. 1. Three sets of bridges connecting all the islands for Sample Input 1\n\n As the first step, he decided to build only those bridges which are contained in all the sets of bridges to connect all the islands and minimize the cost. We refer to such bridges as no alternative bridges. In Figure F. 2, no alternative bridges are drawn as thick edges for the Sample Input 1,2 and 3.\nFigure F. 2. No alternative bridges for Sample Input 1,2 and 3\n\nWrite a program that advises the mayor which bridges are no alternative bridges for the given input.\nTask Input: The input consists of a single test case.\n \n\n$N$ $M$\n$S_1$ $D_1$ $C_1$\n. \n. \n. \n$S_M$ $D_M$ $C_M$\nThe first line contains two positive integers $N$ and $M$. $N$ represents the number of islands and each island is identified by an integer 1 through $N$. $M$ represents the number of the pairs of islands between which a bridge may be built.\n\nEach line of the next $M$ lines contains three integers $S_i$, $D_i$ and $C_i$ ($1 <= i <= M$) which represent that it will cost $C_i$ to build the bridge between islands $S_i$ and $D_i$. You may assume $3 <= N <= 500$, $N - 1 <= M <= min(50000, N(N - 1)/2)$, $1 <= S_i < D_i <= N$, and $1 <= C_i <= 10000$. No two bridges connect the same pair of two islands, that is, if $i \\ne j$ and $S_i = S_j$, then $D_i \\ne D_j$ . If all the candidate bridges are built, all the islands are reachable from any other islands via one or more bridges.\nTask Output: Output two integers, which mean the number of no alternative bridges and the sum of their construction cost, separated by a space.\nTask Samples: input: 4 4\n1 2 3\n1 3 3\n2 3 3\n2 4 3\n output: 1 3\ninput: 4 4\n1 2 3\n1 3 5\n2 3 3\n2 4 3\n output: 3 9\ninput: 4 4\n1 2 3\n1 3 1\n2 3 3\n2 4 3\n output: 2 4\ninput: 3 3\n1 2 1\n2 3 1\n1 3 1\n output: 0 0\n\n" }, { "title": "Problem G:\nFlipping Parentheses", "content": "A string consisting only of parentheses '(' and ')' is called balanced if it is one of the following.\n\n A string \"()\" is balanced.\n\n Concatenation of two balanced strings are balanced.\n\n When a string $s$ is balanced, so is the concatenation of three strings \"(\", $s$, and \")\" in this order.\n Note that the condition is stronger than merely the numbers of '(' and ')' are equal. For instance, \"())(()\" is not balanced.\n\n Your task is to keep a string in a balanced state, under a severe condition in which a cosmic ray may flip the direction of parentheses.\n\n You are initially given a balanced string. Each time the direction of a single parenthesis is flipped, your program is notified the position of the changed character in the string. Then, calculate and output the leftmost position that, if the parenthesis there is flipped, the whole string gets back to the balanced state. After the string is balanced by changing the parenthesis indicated by your program, next cosmic ray flips another parenthesis, and the steps are repeated several times.", "constraint": "", "input": "The input consists of a single test case formatted as follows. \n\n$N$ $Q$\n$s$\n$q_1$\n. \n. \n. \n$q_Q$\n\n \nThe first line consists of two integers $N$ and $Q$ ($2 <= N <= 300000$, $1 <= Q <= 150000$). The second line is a string $s$ of balanced parentheses with length $N$. Each of the following $Q$ lines is an integer $q_i$ ($1 <= q_i <= N$) that indicates that the direction of the $q_i$-th parenthesis is flipped.", "output": "For each event $q_i$, output the position of the leftmost parenthesis you need to flip in order to get back to the balanced state.\n\nNote that each input flipping event $q_i$ is applied to the string after the previous flip $q_{i-1}$ and its fix.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3\n((()))\n4\n3\n1\n output: 2\n2\n1", "input: 20 9\n()((((()))))()()()()\n15\n20\n13\n5\n3\n10\n3\n17\n18\n output: 2\n20\n8\n5\n3\n2\n2\n3\n18\n\n In the first sample, the initial state is \"((()))\". The 4th parenthesis is flipped and the string becomes \"(((())\". Then, to keep the balance you should flip the 2nd parenthesis and get \"()(())\". The next flip of the 3rd parenthesis is applied to the last state and yields \"())())\". To rebalance it, you have to change the 2nd parenthesis again yielding \"(()())\"."], "Pid": "p00930", "ProblemText": "Task Description: A string consisting only of parentheses '(' and ')' is called balanced if it is one of the following.\n\n A string \"()\" is balanced.\n\n Concatenation of two balanced strings are balanced.\n\n When a string $s$ is balanced, so is the concatenation of three strings \"(\", $s$, and \")\" in this order.\n Note that the condition is stronger than merely the numbers of '(' and ')' are equal. For instance, \"())(()\" is not balanced.\n\n Your task is to keep a string in a balanced state, under a severe condition in which a cosmic ray may flip the direction of parentheses.\n\n You are initially given a balanced string. Each time the direction of a single parenthesis is flipped, your program is notified the position of the changed character in the string. Then, calculate and output the leftmost position that, if the parenthesis there is flipped, the whole string gets back to the balanced state. After the string is balanced by changing the parenthesis indicated by your program, next cosmic ray flips another parenthesis, and the steps are repeated several times.\nTask Input: The input consists of a single test case formatted as follows. \n\n$N$ $Q$\n$s$\n$q_1$\n. \n. \n. \n$q_Q$\n\n \nThe first line consists of two integers $N$ and $Q$ ($2 <= N <= 300000$, $1 <= Q <= 150000$). The second line is a string $s$ of balanced parentheses with length $N$. Each of the following $Q$ lines is an integer $q_i$ ($1 <= q_i <= N$) that indicates that the direction of the $q_i$-th parenthesis is flipped.\nTask Output: For each event $q_i$, output the position of the leftmost parenthesis you need to flip in order to get back to the balanced state.\n\nNote that each input flipping event $q_i$ is applied to the string after the previous flip $q_{i-1}$ and its fix.\nTask Samples: input: 6 3\n((()))\n4\n3\n1\n output: 2\n2\n1\ninput: 20 9\n()((((()))))()()()()\n15\n20\n13\n5\n3\n10\n3\n17\n18\n output: 2\n20\n8\n5\n3\n2\n2\n3\n18\n\n In the first sample, the initial state is \"((()))\". The 4th parenthesis is flipped and the string becomes \"(((())\". Then, to keep the balance you should flip the 2nd parenthesis and get \"()(())\". The next flip of the 3rd parenthesis is applied to the last state and yields \"())())\". To rebalance it, you have to change the 2nd parenthesis again yielding \"(()())\".\n\n" }, { "title": "Problem H:\nCornering at Poles", "content": "You are invited to a robot contest. In the contest, you are given a disc-shaped robot that is placed on a flat field. A set of poles are standing on the ground. The robot can move in all directions, but must avoid the poles. However, the robot can make turns around the poles touching them.\n\n Your mission is to find the shortest path of the robot to reach the given goal position. The length of the path is defined by the moving distance of the center of the robot. Figure H. 1 shows the shortest path for a sample layout. In this figure, a red line connecting a pole pair means that the distance between the poles is shorter than the diameter of the robot and the robot cannot go through between them.\nFigure H. 1. The shortest path for a sample layout", "constraint": "", "input": "The input consists of a single test case. \n\n$N$ $G_x$ $G_y$\n$x_1$ $y_1$\n. \n. \n. \n$x_N$ $y_N$\nThe first line contains three integers. $N$ represents the number of the poles ($1 <= N <= 8$). $(G_x, G_y)$ represents the goal position. The robot starts with its center at $(0,0)$, and the robot accomplishes its task when the center of the robot reaches the position $(G_x, G_y)$. You can assume that the starting and goal positions are not the same.\n\n Each of the following $N$ lines contains two integers. $(x_i, y_i)$ represents the standing position of the $i$-th pole. Each input coordinate of $(G_x, G_y)$ and $(x_i, y_i)$ is between $-1000$ and $1000$, inclusive. The radius of the robot is $100$, and you can ignore the thickness of the poles. No pole is standing within a $100.01$ radius from the starting or goal positions. For the distance $d_{i, j}$ between the $i$-th and $j$-th poles $(i \\ne j)$, you can assume $1 <= d_{i, j} < 199.99$ or $200.01 < d_{i, j}$.\n\t \nFigure H. 1 shows the shortest path for Sample Input 1 below, and Figure H. 2 shows the shortest paths for the remaining Sample Inputs.\nFigure H. 2. The shortest paths for the sample layouts", "output": "Output the length of the shortest path to reach the goal. If the robot cannot reach the goal, output 0.0. The output should not contain an error greater than 0.0001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8 900 0\n40 100\n70 -80\n350 30\n680 -20\n230 230\n300 400\n530 130\n75 -275\n output: 1210.99416", "input: 1 0 200\n120 0\n output: 200.0", "input: 3 110 110\n0 110\n110 0\n200 10\n output: 476.95048", "input: 4 0 200\n90 90\n-90 90\n-90 -90\n90 -90\n output: 0.0", "input: 2 0 -210\n20 -105\n-5 -105\n output: 325.81116", "input: 8 680 -50\n80 80\n80 -100\n480 -120\n-80 -110\n240 -90\n-80 100\n-270 100\n-420 -20\n output: 1223.53071"], "Pid": "p00931", "ProblemText": "Task Description: You are invited to a robot contest. In the contest, you are given a disc-shaped robot that is placed on a flat field. A set of poles are standing on the ground. The robot can move in all directions, but must avoid the poles. However, the robot can make turns around the poles touching them.\n\n Your mission is to find the shortest path of the robot to reach the given goal position. The length of the path is defined by the moving distance of the center of the robot. Figure H. 1 shows the shortest path for a sample layout. In this figure, a red line connecting a pole pair means that the distance between the poles is shorter than the diameter of the robot and the robot cannot go through between them.\nFigure H. 1. The shortest path for a sample layout\nTask Input: The input consists of a single test case. \n\n$N$ $G_x$ $G_y$\n$x_1$ $y_1$\n. \n. \n. \n$x_N$ $y_N$\nThe first line contains three integers. $N$ represents the number of the poles ($1 <= N <= 8$). $(G_x, G_y)$ represents the goal position. The robot starts with its center at $(0,0)$, and the robot accomplishes its task when the center of the robot reaches the position $(G_x, G_y)$. You can assume that the starting and goal positions are not the same.\n\n Each of the following $N$ lines contains two integers. $(x_i, y_i)$ represents the standing position of the $i$-th pole. Each input coordinate of $(G_x, G_y)$ and $(x_i, y_i)$ is between $-1000$ and $1000$, inclusive. The radius of the robot is $100$, and you can ignore the thickness of the poles. No pole is standing within a $100.01$ radius from the starting or goal positions. For the distance $d_{i, j}$ between the $i$-th and $j$-th poles $(i \\ne j)$, you can assume $1 <= d_{i, j} < 199.99$ or $200.01 < d_{i, j}$.\n\t \nFigure H. 1 shows the shortest path for Sample Input 1 below, and Figure H. 2 shows the shortest paths for the remaining Sample Inputs.\nFigure H. 2. The shortest paths for the sample layouts\nTask Output: Output the length of the shortest path to reach the goal. If the robot cannot reach the goal, output 0.0. The output should not contain an error greater than 0.0001.\nTask Samples: input: 8 900 0\n40 100\n70 -80\n350 30\n680 -20\n230 230\n300 400\n530 130\n75 -275\n output: 1210.99416\ninput: 1 0 200\n120 0\n output: 200.0\ninput: 3 110 110\n0 110\n110 0\n200 10\n output: 476.95048\ninput: 4 0 200\n90 90\n-90 90\n-90 -90\n90 -90\n output: 0.0\ninput: 2 0 -210\n20 -105\n-5 -105\n output: 325.81116\ninput: 8 680 -50\n80 80\n80 -100\n480 -120\n-80 -110\n240 -90\n-80 100\n-270 100\n-420 -20\n output: 1223.53071\n\n" }, { "title": "Problem I:\nSweet War", "content": "There are two countries, Imperial Cacao and Principality of Cocoa. Two girls, Alice (the Empress of Cacao) and Brianna (the Princess of Cocoa) are friends and both of them love chocolate very much.\n\nOne day, Alice found a transparent tube filled with chocolate balls (Figure I. 1). The tube has only one opening at its top end. The tube is narrow, and the chocolate balls are put in a line. Chocolate balls are identified by integers 1,2, . . . , $N$ where $N$ is the number of chocolate balls. Chocolate ball 1 is at the top and is next to the opening of the tube. Chocolate ball 2 is next to chocolate ball 1, . . . , and chocolate ball $N$ is at the bottom end of the tube. The chocolate balls can be only taken out from the opening, and therefore the chocolate balls must be taken out in the increasing order of their numbers.\nFigure I. 1. Transparent tube filled with chocolate balls\n\nAlice visited Brianna to share the tube and eat the chocolate balls together. They looked at the chocolate balls carefully, and estimated that the $nutrition value$ and the $deliciousness$ of chocolate ball $i$ are $r_i$ and $s_i$, respectively. Here, each of the girls wants to maximize the sum of the deliciousness of chocolate balls that she would eat. They are sufficiently wise to resolve this\nconflict peacefully, so they have decided to play a game, and eat the chocolate balls according to the rule of the game as follows:\n\n Alice and Brianna have initial energy levels, denoted by nonnegative integers $A$ and $B$, respectively.\n\n Alice and Brianna takes one of the following two actions in turn:\n \n Pass: she does not eat any chocolate balls. She gets a little hungry $-$ specifically, her energy level is decreased by 1. She cannot pass when her energy level is 0.\n\nEat: she eats the topmost chocolate ball $-$ let this chocolate ball $i$ (that is, the chocolate ball with the smallest number at that time). Her energy level is increased by $r_i$, the nutrition value of chocolate ball $i$ (and NOT decreased by 1). Of course, chocolate ball $i$ is removed from the tube.\n \n Alice takes her turn first.\n\n The game ends when all chocolate balls are eaten.\n\n You are a member of the staff serving for Empress Alice. Your task is to calculate the sums of deliciousness that each of Alice and Brianna can gain, when both of them play optimally.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows.\n \n$N$ $A$ $B$\n$r_1$ $s_1$\n$r_2$ $s_2$\n. \n. \n. \n$r_N$ $s_N$\n\n The first line contains three integers, $N$, $A$ and $B$. $N$ represents the number of chocolate balls. $A$ and $B$ represent the initial energy levels of Alice and Brianna, respectively. The following $N$ lines describe the chocolate balls in the tube. The chocolate balls are numbered from 1 to $N$, and each of the lines contains two integers, $r_i$ and $s_i$ for $1 <= i <= N$. $r_i$ and $s_i$ represent the nutrition value and the deliciousness of chocolate ball $i$, respectively. The input satisfies\n\n $1 <= N <= 150$,\n\n $0 <= A, B, r_i <= 10^9$,\n\n $0 <= s_i$, and\n\n $\\sum^N_{i=1} s_i <= 150$", "output": "Output two integers that represent the total deliciousness that Alice and Brianna can obtain when they play optimally", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 5 4\n5 7\n4 8\n output: 8 7", "input: 3 50 1\n49 1\n0 10\n0 1\n output: 10 2", "input: 4 3 2\n1 5\n2 46\n92 40\n1 31\n output: 77 45", "input: 5 2 5\n56 2\n22 73\n2 2\n1 55\n14 18\n output: 57 93"], "Pid": "p00932", "ProblemText": "Task Description: There are two countries, Imperial Cacao and Principality of Cocoa. Two girls, Alice (the Empress of Cacao) and Brianna (the Princess of Cocoa) are friends and both of them love chocolate very much.\n\nOne day, Alice found a transparent tube filled with chocolate balls (Figure I. 1). The tube has only one opening at its top end. The tube is narrow, and the chocolate balls are put in a line. Chocolate balls are identified by integers 1,2, . . . , $N$ where $N$ is the number of chocolate balls. Chocolate ball 1 is at the top and is next to the opening of the tube. Chocolate ball 2 is next to chocolate ball 1, . . . , and chocolate ball $N$ is at the bottom end of the tube. The chocolate balls can be only taken out from the opening, and therefore the chocolate balls must be taken out in the increasing order of their numbers.\nFigure I. 1. Transparent tube filled with chocolate balls\n\nAlice visited Brianna to share the tube and eat the chocolate balls together. They looked at the chocolate balls carefully, and estimated that the $nutrition value$ and the $deliciousness$ of chocolate ball $i$ are $r_i$ and $s_i$, respectively. Here, each of the girls wants to maximize the sum of the deliciousness of chocolate balls that she would eat. They are sufficiently wise to resolve this\nconflict peacefully, so they have decided to play a game, and eat the chocolate balls according to the rule of the game as follows:\n\n Alice and Brianna have initial energy levels, denoted by nonnegative integers $A$ and $B$, respectively.\n\n Alice and Brianna takes one of the following two actions in turn:\n \n Pass: she does not eat any chocolate balls. She gets a little hungry $-$ specifically, her energy level is decreased by 1. She cannot pass when her energy level is 0.\n\nEat: she eats the topmost chocolate ball $-$ let this chocolate ball $i$ (that is, the chocolate ball with the smallest number at that time). Her energy level is increased by $r_i$, the nutrition value of chocolate ball $i$ (and NOT decreased by 1). Of course, chocolate ball $i$ is removed from the tube.\n \n Alice takes her turn first.\n\n The game ends when all chocolate balls are eaten.\n\n You are a member of the staff serving for Empress Alice. Your task is to calculate the sums of deliciousness that each of Alice and Brianna can gain, when both of them play optimally.\nTask Input: The input consists of a single test case. The test case is formatted as follows.\n \n$N$ $A$ $B$\n$r_1$ $s_1$\n$r_2$ $s_2$\n. \n. \n. \n$r_N$ $s_N$\n\n The first line contains three integers, $N$, $A$ and $B$. $N$ represents the number of chocolate balls. $A$ and $B$ represent the initial energy levels of Alice and Brianna, respectively. The following $N$ lines describe the chocolate balls in the tube. The chocolate balls are numbered from 1 to $N$, and each of the lines contains two integers, $r_i$ and $s_i$ for $1 <= i <= N$. $r_i$ and $s_i$ represent the nutrition value and the deliciousness of chocolate ball $i$, respectively. The input satisfies\n\n $1 <= N <= 150$,\n\n $0 <= A, B, r_i <= 10^9$,\n\n $0 <= s_i$, and\n\n $\\sum^N_{i=1} s_i <= 150$\nTask Output: Output two integers that represent the total deliciousness that Alice and Brianna can obtain when they play optimally\nTask Samples: input: 2 5 4\n5 7\n4 8\n output: 8 7\ninput: 3 50 1\n49 1\n0 10\n0 1\n output: 10 2\ninput: 4 3 2\n1 5\n2 46\n92 40\n1 31\n output: 77 45\ninput: 5 2 5\n56 2\n22 73\n2 2\n1 55\n14 18\n output: 57 93\n\n" }, { "title": "Problem J:\nExhibition", "content": "The city government is planning an exhibition and collecting industrial products. There are $n$ candidates of industrial products for the exhibition, and the city government decided to choose $k$ of them. They want to minimize the total price of the $k$ products. However, other criteria such as their sizes and weights should be also taken into account. To address this issue, the city government decided to use the following strategy: The $i$-th product has three parameters, price, size, and weight, denoted by $x_i$, $y_i$, and $z_i$, respectively. Then, the city government chooses $k$ items $i_1, . . . , i_k$ ($1 <= i_j <= n$) that minimizes the evaluation measure\n\n \\[\ne = (\\sum^k_{j=1}x_{ij}) (\\sum^k_{j=1}y_{ij}) (\\sum^k_{j=1}z_{ij}),\n \\]\n\n which incorporates the prices, the sizes, and the weights of products. If there are two or more choices that minimize $e$, the government chooses one of them uniformly at random.\n\nYou are working for the company that makes the product 1. The company has decided to cut the price, reduce the size, and/or reduce the weight of the product so that the city government may choose the product of your company, that is, to make the probability of choosing the product positive. We have three parameters $A$, $B$, and $C$. If we want to reduce the price, size, and weight to $(1 - \\alpha)x_1$, $(1 - \\beta)y_1$, and $(1 - \\gamma)z_1$ ($0 <= \\alpha, \\beta, \\gamma <= 1$), respectively, then we have to invest $\\alpha A + \\beta B + \\gamma C$ million yen. We note that the resulting price, size, and weight do not have to be integers. Your task is to compute the minimum investment required to make the city government possibly choose the product of your company. You may assume that employees of all the other companies are too lazy to make such an effort.", "constraint": "", "input": "The input consists of a single test case with the following format. \n\n \n$n$ $k$ $A$ $B$ $C$\n$x_1$ $y_1$ $z_1$\n$x_2$ $y_2$ $z_2$\n. \n. \n. \n$x_n$ $y_n$ $z_n$\n\n \n The first line contains five integers. The integer $n$ ($1 <= n <= 50$) is the number of industrial products, and the integer $k$ ($1 <= k <= n$) is the number of products that will be chosen by the city government. The integers $A$, $B$, $C$ ($1 <= A, B, C <= 100$) are the parameters that determine the cost of changing the price, the size, and the weight, respectively, of the product 1.\n\nEach of the following $n$ lines contains three integers, $x_i$, $y_i$, and $z_i$ ($1 <= x_i, y_i, z_i <= 100$), which are the price, the size, and the weight, respectively, of the $i$-th product.", "output": "Output the minimum cost (in million yen) in order to make the city government possibly choose the product of your company. The output should not contain an absolute error greater than $10^{-4}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 5 1 2 3\n5 5 5\n1 5 5\n2 5 4\n3 5 3\n4 5 2\n5 5 1\n output: 0.631579", "input: 6 1 1 2 3\n10 20 30\n1 2 3\n2 4 6\n3 6 9\n4 8 12\n5 10 15\n output: 0.999000"], "Pid": "p00933", "ProblemText": "Task Description: The city government is planning an exhibition and collecting industrial products. There are $n$ candidates of industrial products for the exhibition, and the city government decided to choose $k$ of them. They want to minimize the total price of the $k$ products. However, other criteria such as their sizes and weights should be also taken into account. To address this issue, the city government decided to use the following strategy: The $i$-th product has three parameters, price, size, and weight, denoted by $x_i$, $y_i$, and $z_i$, respectively. Then, the city government chooses $k$ items $i_1, . . . , i_k$ ($1 <= i_j <= n$) that minimizes the evaluation measure\n\n \\[\ne = (\\sum^k_{j=1}x_{ij}) (\\sum^k_{j=1}y_{ij}) (\\sum^k_{j=1}z_{ij}),\n \\]\n\n which incorporates the prices, the sizes, and the weights of products. If there are two or more choices that minimize $e$, the government chooses one of them uniformly at random.\n\nYou are working for the company that makes the product 1. The company has decided to cut the price, reduce the size, and/or reduce the weight of the product so that the city government may choose the product of your company, that is, to make the probability of choosing the product positive. We have three parameters $A$, $B$, and $C$. If we want to reduce the price, size, and weight to $(1 - \\alpha)x_1$, $(1 - \\beta)y_1$, and $(1 - \\gamma)z_1$ ($0 <= \\alpha, \\beta, \\gamma <= 1$), respectively, then we have to invest $\\alpha A + \\beta B + \\gamma C$ million yen. We note that the resulting price, size, and weight do not have to be integers. Your task is to compute the minimum investment required to make the city government possibly choose the product of your company. You may assume that employees of all the other companies are too lazy to make such an effort.\nTask Input: The input consists of a single test case with the following format. \n\n \n$n$ $k$ $A$ $B$ $C$\n$x_1$ $y_1$ $z_1$\n$x_2$ $y_2$ $z_2$\n. \n. \n. \n$x_n$ $y_n$ $z_n$\n\n \n The first line contains five integers. The integer $n$ ($1 <= n <= 50$) is the number of industrial products, and the integer $k$ ($1 <= k <= n$) is the number of products that will be chosen by the city government. The integers $A$, $B$, $C$ ($1 <= A, B, C <= 100$) are the parameters that determine the cost of changing the price, the size, and the weight, respectively, of the product 1.\n\nEach of the following $n$ lines contains three integers, $x_i$, $y_i$, and $z_i$ ($1 <= x_i, y_i, z_i <= 100$), which are the price, the size, and the weight, respectively, of the $i$-th product.\nTask Output: Output the minimum cost (in million yen) in order to make the city government possibly choose the product of your company. The output should not contain an absolute error greater than $10^{-4}$.\nTask Samples: input: 6 5 1 2 3\n5 5 5\n1 5 5\n2 5 4\n3 5 3\n4 5 2\n5 5 1\n output: 0.631579\ninput: 6 1 1 2 3\n10 20 30\n1 2 3\n2 4 6\n3 6 9\n4 8 12\n5 10 15\n output: 0.999000\n\n" }, { "title": "Problem K:\n$L_{\\infty}$ Jumps", "content": "Given two points $(p, q)$ and $(p', q')$ in the XY-plane, the $L_{\\infty}$ distance between them is defined as $max(|p - p'|, |q - q'|)$. In this problem, you are given four integers $n$, $d$, $s$, $t$. Suppose that you are initially standing at point $(0,0)$ and you need to move to point $(s, t)$. For this purpose, you perform jumps exactly $n$ times. In each jump, you must move exactly $d$ in the $L_{\\infty}$ distance measure. In addition, the point you reach by a jump must be a lattice point in the XY-plane. That is, when you are standing at point $(p, q)$, you can move to a new point $(p', q')$ by a single jump if $p'$ and $q'$ are integers and $max(|p - p'|, |q - q'|) = d$ holds.\n\n Note that you cannot stop jumping even if you reach the destination point $(s, t)$ before you perform the jumps $n$ times.\n\n To make the problem more interesting, suppose that some cost occurs for each jump. You are given $2n$ additional integers $x_1$, $y_1$, $x_2$, $y_2$, . . . , $x_n$, $y_n$ such that $max(|x_i|, |y_i|) = d$ holds for each $1 <= i <= n$. The cost of the $i$-th (1-indexed) jump is defined as follows: Let $(p, q)$ be a point at which you are standing before the $i$-th jump. Consider a set of lattice points that you can jump to. Note that this set consists of all the lattice points on the edge of a certain square. We assign integer 1 to point $(p + x_i, q + y_i)$. Then, we assign integers $2,3, . . . , 8d$ to the remaining points in the set in the counter-clockwise order. (Here, assume that the right direction is positive in the $x$-axis and the upper direction is positive in the $y$-axis. ) These integers represent the costs when you perform a jump to these points.\n\n For example, Figure K. 1 illustrates the points reachable by your $i$-th jump when $d = 2$ and you are at $(3,1)$. The numbers represent the costs for $x_i = -1$ and $y_i = -2$.\nFigure K. 1. Reachable points and their costs\n\n Compute and output the minimum required sum of the costs for the objective.", "constraint": "", "input": "The input consists of a single test case. \n\n$n$ $d$ $s$ $t$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. \n. \n. \n$x_n$ $y_n$\nThe first line contains four integers. $n$ ($1 <= n <= 40$) is the number of jumps to perform. $d$ ($1 <= d <= 10^{10}$) is the $L_{\\infty}$ distance which you must move by a single jump. $s$ and $t$ ($|s|, |t| <= nd$) are the $x$ and $y$ coordinates of the destination point. It is guaranteed that there is at least one way to reach the destination point by performing $n$ jumps.\n\nEach of the following $n$ lines contains two integers, $x_i$ and $y_i$ with $max(|x_i|, |y_i|) = d$.", "output": "Output the minimum required cost to reach the destination point.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 2 4 0\n2 2\n-2 -2\n-2 2\n output: 15", "input: 4 1 2 -2\n1 -1\n1 0\n1 1\n-1 0\n output: 10", "input: 6 5 0 2\n5 2\n-5 2\n5 0\n-3 5\n-5 4\n5 5\n output: 24", "input: 5 91 -218 -351\n91 91\n91 91\n91 91\n91 91\n91 91\n output: 1958", "input: 1 10000000000 -10000000000 -2527532346\n8198855077 10000000000\n output: 30726387424"], "Pid": "p00934", "ProblemText": "Task Description: Given two points $(p, q)$ and $(p', q')$ in the XY-plane, the $L_{\\infty}$ distance between them is defined as $max(|p - p'|, |q - q'|)$. In this problem, you are given four integers $n$, $d$, $s$, $t$. Suppose that you are initially standing at point $(0,0)$ and you need to move to point $(s, t)$. For this purpose, you perform jumps exactly $n$ times. In each jump, you must move exactly $d$ in the $L_{\\infty}$ distance measure. In addition, the point you reach by a jump must be a lattice point in the XY-plane. That is, when you are standing at point $(p, q)$, you can move to a new point $(p', q')$ by a single jump if $p'$ and $q'$ are integers and $max(|p - p'|, |q - q'|) = d$ holds.\n\n Note that you cannot stop jumping even if you reach the destination point $(s, t)$ before you perform the jumps $n$ times.\n\n To make the problem more interesting, suppose that some cost occurs for each jump. You are given $2n$ additional integers $x_1$, $y_1$, $x_2$, $y_2$, . . . , $x_n$, $y_n$ such that $max(|x_i|, |y_i|) = d$ holds for each $1 <= i <= n$. The cost of the $i$-th (1-indexed) jump is defined as follows: Let $(p, q)$ be a point at which you are standing before the $i$-th jump. Consider a set of lattice points that you can jump to. Note that this set consists of all the lattice points on the edge of a certain square. We assign integer 1 to point $(p + x_i, q + y_i)$. Then, we assign integers $2,3, . . . , 8d$ to the remaining points in the set in the counter-clockwise order. (Here, assume that the right direction is positive in the $x$-axis and the upper direction is positive in the $y$-axis. ) These integers represent the costs when you perform a jump to these points.\n\n For example, Figure K. 1 illustrates the points reachable by your $i$-th jump when $d = 2$ and you are at $(3,1)$. The numbers represent the costs for $x_i = -1$ and $y_i = -2$.\nFigure K. 1. Reachable points and their costs\n\n Compute and output the minimum required sum of the costs for the objective.\nTask Input: The input consists of a single test case. \n\n$n$ $d$ $s$ $t$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. \n. \n. \n$x_n$ $y_n$\nThe first line contains four integers. $n$ ($1 <= n <= 40$) is the number of jumps to perform. $d$ ($1 <= d <= 10^{10}$) is the $L_{\\infty}$ distance which you must move by a single jump. $s$ and $t$ ($|s|, |t| <= nd$) are the $x$ and $y$ coordinates of the destination point. It is guaranteed that there is at least one way to reach the destination point by performing $n$ jumps.\n\nEach of the following $n$ lines contains two integers, $x_i$ and $y_i$ with $max(|x_i|, |y_i|) = d$.\nTask Output: Output the minimum required cost to reach the destination point.\nTask Samples: input: 3 2 4 0\n2 2\n-2 -2\n-2 2\n output: 15\ninput: 4 1 2 -2\n1 -1\n1 0\n1 1\n-1 0\n output: 10\ninput: 6 5 0 2\n5 2\n-5 2\n5 0\n-3 5\n-5 4\n5 5\n output: 24\ninput: 5 91 -218 -351\n91 91\n91 91\n91 91\n91 91\n91 91\n output: 1958\ninput: 1 10000000000 -10000000000 -2527532346\n8198855077 10000000000\n output: 30726387424\n\n" }, { "title": "Problem A\nDecimal Sequences", "content": "Hanako learned the conjecture that all the non-negative integers appear in the infinite digit sequence of the decimal representation of $\\pi$ = 3.14159265. . . , the ratio of a circle's circumference to its diameter. After that, whenever she watches a sequence of digits, she tries to count up non-negative integers whose decimal representations appear as its subsequences.\n\nFor example, given a sequence \"3 0 1\", she finds representations of five non-negative integers 3,0,1,30 and 301 that appear as its subsequences.\n\nYour job is to write a program that, given a finite sequence of digits, outputs the smallest non-negative integer not appearing in the sequence. In the above example, 0 and 1 appear, but 2 does not. So, 2 should be the answer.", "constraint": "", "input": "The input consists of a single test case. \n$n$\n$d_1$ $d_2$ . . . $d_n$\n$n$ is a positive integer that indicates the number of digits. Each of $d_k$'s $(k = 1, . . . , n)$ is a digit. There is a space or a newline between $d_k$ and $d_{k+1}$ $(k = 1, . . . , n - 1)$.\n\nYou can assume that $1 <= n <= 1000$.", "output": "Print the smallest non-negative integer not appearing in the sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 0 1\n output: 2", "input: 11\n9 8 7 6 5 4 3 2 1 1 0\n output: 12", "input: 10\n9 0 8 7 6 5 4 3 2 1\n output: 10", "input: 100\n3 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2\n6 1 8 7 9 2 0 2 3 7 5 9 2 2 8 9 7 3 6\n1 2 9 3 1 9 4 7 8 4 5 0 3 6 1 0 6 3 2\n0 6 1 5 5 4 7 6 5 6 9 3 7 4 5 2 5 4 7\n4 4 3 0 7 8 6 8 8 4 3 1 4 9 2 0 6 8 9\n2 6 6 4 9\n output: 11", "input: 100\n7 2 7 5 4 7 4 4 5 8 1 5 7 7 0 5 6 2 0\n4 3 4 1 1 0 6 1 6 6 2 1 7 9 2 4 6 9 3\n6 2 8 0 5 9 7 6 3 1 4 9 1 9 1 2 6 4 2\n9 7 8 3 9 5 5 2 3 3 8 4 0 6 8 2 5 5 0\n6 7 1 8 5 1 4 8 1 3 7 3 3 5 3 0 6 0 6\n5 3 2 2 2\n output: 86", "input: 1\n3\n output: 0"], "Pid": "p00935", "ProblemText": "Task Description: Hanako learned the conjecture that all the non-negative integers appear in the infinite digit sequence of the decimal representation of $\\pi$ = 3.14159265. . . , the ratio of a circle's circumference to its diameter. After that, whenever she watches a sequence of digits, she tries to count up non-negative integers whose decimal representations appear as its subsequences.\n\nFor example, given a sequence \"3 0 1\", she finds representations of five non-negative integers 3,0,1,30 and 301 that appear as its subsequences.\n\nYour job is to write a program that, given a finite sequence of digits, outputs the smallest non-negative integer not appearing in the sequence. In the above example, 0 and 1 appear, but 2 does not. So, 2 should be the answer.\nTask Input: The input consists of a single test case. \n$n$\n$d_1$ $d_2$ . . . $d_n$\n$n$ is a positive integer that indicates the number of digits. Each of $d_k$'s $(k = 1, . . . , n)$ is a digit. There is a space or a newline between $d_k$ and $d_{k+1}$ $(k = 1, . . . , n - 1)$.\n\nYou can assume that $1 <= n <= 1000$.\nTask Output: Print the smallest non-negative integer not appearing in the sequence.\nTask Samples: input: 3\n3 0 1\n output: 2\ninput: 11\n9 8 7 6 5 4 3 2 1 1 0\n output: 12\ninput: 10\n9 0 8 7 6 5 4 3 2 1\n output: 10\ninput: 100\n3 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2\n6 1 8 7 9 2 0 2 3 7 5 9 2 2 8 9 7 3 6\n1 2 9 3 1 9 4 7 8 4 5 0 3 6 1 0 6 3 2\n0 6 1 5 5 4 7 6 5 6 9 3 7 4 5 2 5 4 7\n4 4 3 0 7 8 6 8 8 4 3 1 4 9 2 0 6 8 9\n2 6 6 4 9\n output: 11\ninput: 100\n7 2 7 5 4 7 4 4 5 8 1 5 7 7 0 5 6 2 0\n4 3 4 1 1 0 6 1 6 6 2 1 7 9 2 4 6 9 3\n6 2 8 0 5 9 7 6 3 1 4 9 1 9 1 2 6 4 2\n9 7 8 3 9 5 5 2 3 3 8 4 0 6 8 2 5 5 0\n6 7 1 8 5 1 4 8 1 3 7 3 3 5 3 0 6 0 6\n5 3 2 2 2\n output: 86\ninput: 1\n3\n output: 0\n\n" }, { "title": "Problem B\nSqueeze the Cylinders", "content": "Laid on the flat ground in the stockyard are a number of heavy metal cylinders with (possibly) different diameters but with the same length. Their ends are aligned and their axes are oriented to exactly the same direction.\n\nWe'd like to minimize the area occupied. The cylinders are too heavy to lift up, although rolling them is not too difficult. So, we decided to push the cylinders with two high walls from both sides.\n\nYour task is to compute the minimum possible distance between the two walls when cylinders are squeezed as much as possible. Cylinders and walls may touch one another. They cannot be lifted up from the ground, and thus their order cannot be altered.\n\nFigure B. 1. Cylinders between two walls", "constraint": "", "input": "The input consists of a single test case. The first line has an integer $N$ $(1 <= N <= 500)$, which is the number of cylinders. The second line has $N$ positive integers at most 10,000. They are the radii of cylinders from one side to the other.", "output": "Print the distance between the two walls when they fully squeeze up the cylinders. The number should not contain an error greater than 0.0001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n10 10\n output: 40.00000000", "input: 2\n4 12\n output: 29.85640646", "input: 5\n1 10 1 10 1\n output: 40.00000000", "input: 3\n1 1 1\n output: 6.00000000", "input: 2\n5000 10000\n output: 29142.13562373\n\nThe following figures correspond to the Sample 1,2, and 3."], "Pid": "p00936", "ProblemText": "Task Description: Laid on the flat ground in the stockyard are a number of heavy metal cylinders with (possibly) different diameters but with the same length. Their ends are aligned and their axes are oriented to exactly the same direction.\n\nWe'd like to minimize the area occupied. The cylinders are too heavy to lift up, although rolling them is not too difficult. So, we decided to push the cylinders with two high walls from both sides.\n\nYour task is to compute the minimum possible distance between the two walls when cylinders are squeezed as much as possible. Cylinders and walls may touch one another. They cannot be lifted up from the ground, and thus their order cannot be altered.\n\nFigure B. 1. Cylinders between two walls\nTask Input: The input consists of a single test case. The first line has an integer $N$ $(1 <= N <= 500)$, which is the number of cylinders. The second line has $N$ positive integers at most 10,000. They are the radii of cylinders from one side to the other.\nTask Output: Print the distance between the two walls when they fully squeeze up the cylinders. The number should not contain an error greater than 0.0001.\nTask Samples: input: 2\n10 10\n output: 40.00000000\ninput: 2\n4 12\n output: 29.85640646\ninput: 5\n1 10 1 10 1\n output: 40.00000000\ninput: 3\n1 1 1\n output: 6.00000000\ninput: 2\n5000 10000\n output: 29142.13562373\n\nThe following figures correspond to the Sample 1,2, and 3.\n\n" }, { "title": "Problem C\nSibling Rivalry", "content": "You are playing a game with your elder brother.\n\nFirst, a number of circles and arrows connecting some pairs of the circles are drawn on the ground. Two of the circles are marked as the start circle and the goal circle.\n\nAt the start of the game, you are on the start circle. In each turn of the game, your brother tells you a number, and you have to take that number of steps. At each step, you choose one of the arrows outgoing from the circle you are on, and move to the circle the arrow is heading to. You can visit the same circle or use the same arrow any number of times.\n\nYour aim is to stop on the goal circle after the fewest possible turns, while your brother's aim is to prevent it as long as possible. Note that, in each single turn, you must take the exact number of steps your brother tells you. Even when you visit the goal circle during a turn, you have to leave it if more steps are to be taken.\n\nIf you reach a circle with no outgoing arrows before completing all the steps, then you lose the game. You also have to note that, your brother may be able to repeat turns forever, not allowing you to stop after any of them.\n\nYour brother, mean but not too selfish, thought that being allowed to choose arbitrary numbers is not fair. So, he decided to declare three numbers at the start of the game and to use only those numbers.\n\nYour task now is, given the configuration of circles and arrows, and the three numbers declared, to compute the smallest possible number of turns within which you can always \fnish the game, no matter how your brother chooses the numbers.", "constraint": "", "input": "The input consists of a single test case, formatted as follows. \n$n$ $m$ $a$ $b$ $c$\n$u_1$ $v_1$\n. . . \n$u_m$ $v_m$\n\nAll numbers in a test case are integers. $n$ is the number of circles $(2 <= n <= 50)$. Circles are numbered 1 through $n$. The start and goal circles are numbered 1 and $n$, respectively. $m$ is the number of arrows $(0 <= m <= n(n - 1))$. $a$, $b$, and $c$ are the three numbers your brother declared $(1 <= a, b, c <= 100)$. The pair, $u_i$ and $v_i$, means that there is an arrow from the circle $u_i$ to the circle $v_i$. It is ensured that $u_i \\ne v_i$ for all $i$, and $u_i \\ne u_j$ or $v_i \\ne v_j$ if $i \\ne j$.", "output": "Print the smallest possible number of turns within which you can always finish the game. Print IMPOSSIBLE if your brother can prevent you from reaching the goal, by either making you repeat the turns forever or leading you to a circle without outgoing arrows.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3 1 2 4\n1 2\n2 3\n3 1\n output: IMPOSSIBLE", "input: 8 12 1 2 3\n1 2\n2 3\n1 4\n2 4\n3 4\n1 5\n5 8\n4 6\n6 7\n4 8\n6 8\n7 8\n output: 2\n\nFor Sample Input 1, your brother may choose 1 first, then 2, and repeat these forever. Then you can never finish.\nFor Sample Input 2 (Figure C.1), if your brother chooses 2 or 3, you can finish with a single turn. If he chooses 1, you will have three options.\n\n Move to the circle 5. This is a bad idea: Your brother may then choose 2 or 3 and make you lose.\n Move to the circle 4. This is the best choice: From the circle 4, no matter any of 1,2, or 3 your brother chooses in the next turn, you can finish immediately.\nMove to the circle 2. This is not optimal for you. If your brother chooses 1 in the next turn, you cannot finish yet. It will take three or more turns in total.\n\nIn summary, no matter how your brother acts, you can finish within two turns. Thus the answer is 2.\nFigure C.1. Sample Input 2"], "Pid": "p00937", "ProblemText": "Task Description: You are playing a game with your elder brother.\n\nFirst, a number of circles and arrows connecting some pairs of the circles are drawn on the ground. Two of the circles are marked as the start circle and the goal circle.\n\nAt the start of the game, you are on the start circle. In each turn of the game, your brother tells you a number, and you have to take that number of steps. At each step, you choose one of the arrows outgoing from the circle you are on, and move to the circle the arrow is heading to. You can visit the same circle or use the same arrow any number of times.\n\nYour aim is to stop on the goal circle after the fewest possible turns, while your brother's aim is to prevent it as long as possible. Note that, in each single turn, you must take the exact number of steps your brother tells you. Even when you visit the goal circle during a turn, you have to leave it if more steps are to be taken.\n\nIf you reach a circle with no outgoing arrows before completing all the steps, then you lose the game. You also have to note that, your brother may be able to repeat turns forever, not allowing you to stop after any of them.\n\nYour brother, mean but not too selfish, thought that being allowed to choose arbitrary numbers is not fair. So, he decided to declare three numbers at the start of the game and to use only those numbers.\n\nYour task now is, given the configuration of circles and arrows, and the three numbers declared, to compute the smallest possible number of turns within which you can always \fnish the game, no matter how your brother chooses the numbers.\nTask Input: The input consists of a single test case, formatted as follows. \n$n$ $m$ $a$ $b$ $c$\n$u_1$ $v_1$\n. . . \n$u_m$ $v_m$\n\nAll numbers in a test case are integers. $n$ is the number of circles $(2 <= n <= 50)$. Circles are numbered 1 through $n$. The start and goal circles are numbered 1 and $n$, respectively. $m$ is the number of arrows $(0 <= m <= n(n - 1))$. $a$, $b$, and $c$ are the three numbers your brother declared $(1 <= a, b, c <= 100)$. The pair, $u_i$ and $v_i$, means that there is an arrow from the circle $u_i$ to the circle $v_i$. It is ensured that $u_i \\ne v_i$ for all $i$, and $u_i \\ne u_j$ or $v_i \\ne v_j$ if $i \\ne j$.\nTask Output: Print the smallest possible number of turns within which you can always finish the game. Print IMPOSSIBLE if your brother can prevent you from reaching the goal, by either making you repeat the turns forever or leading you to a circle without outgoing arrows.\nTask Samples: input: 3 3 1 2 4\n1 2\n2 3\n3 1\n output: IMPOSSIBLE\ninput: 8 12 1 2 3\n1 2\n2 3\n1 4\n2 4\n3 4\n1 5\n5 8\n4 6\n6 7\n4 8\n6 8\n7 8\n output: 2\n\nFor Sample Input 1, your brother may choose 1 first, then 2, and repeat these forever. Then you can never finish.\nFor Sample Input 2 (Figure C.1), if your brother chooses 2 or 3, you can finish with a single turn. If he chooses 1, you will have three options.\n\n Move to the circle 5. This is a bad idea: Your brother may then choose 2 or 3 and make you lose.\n Move to the circle 4. This is the best choice: From the circle 4, no matter any of 1,2, or 3 your brother chooses in the next turn, you can finish immediately.\nMove to the circle 2. This is not optimal for you. If your brother chooses 1 in the next turn, you cannot finish yet. It will take three or more turns in total.\n\nIn summary, no matter how your brother acts, you can finish within two turns. Thus the answer is 2.\nFigure C.1. Sample Input 2\n\n" }, { "title": "Problem D\nWall Clocks", "content": "You are the manager of a chocolate sales team. Your team customarily takes tea breaks every two hours, during which varieties of new chocolate products of your company are served. Everyone looks forward to the tea breaks so much that they frequently give a glance at a wall clock.\n\nRecently, your team has moved to a new office. You have just arranged desks in the office. One team member asked you to hang a clock on the wall in front of her desk so that she will not be late for tea breaks. Naturally, everyone seconded her.\n\nYou decided to provide an enough number of clocks to be hung in the field of view of everyone. Your team members will be satisfied if they have at least one clock (regardless of the orientation of the clock) in their view, or, more precisely, within 45 degrees left and 45 degrees right (both ends inclusive) from the facing directions of their seats. In order to buy as few clocks as possible, you should write a program that calculates the minimum number of clocks needed to\nmeet everyone's demand.\n\nThe office room is rectangular aligned to north-south and east-west directions. As the walls are tall enough, you can hang clocks even above the door and can assume one's eyesight is not blocked by other members or furniture. You can also assume that each clock is a point (of size zero), and so you can hang a clock even on a corner of the room.\n\nFor example, assume that there are two members. If they are sitting facing each other at positions shown in Figure D. 1(A), you need to provide two clocks as they see distinct sections of the wall. If their seats are arranged as shown in Figure D. 1(B), their fields of view have a common point on the wall. Thus, you can meet their demands by hanging a single clock at the point. In Figure D. 1(C), their fields of view have a common wall section. You can meet their demands with a single clock by hanging it anywhere in the section. Arrangements (A), (B), and (C) in Figure D. 1 correspond to Sample Input 1,2, and 3, respectively.", "constraint": "", "input": "The input consists of a single test case, formatted as follows. \n$n$ $w$ $d$\n$x_1$ $y_1$ $f_1$\n. . . \n$x_n$ $y_n$ $f_n$\n\nFigure D. 1. Arrangements of seats and clocks. Gray area indicates field of view.\n\nAll numbers in the test case are integers. The first line contains the number of team members $n$ $(1 <= n <= 1,000)$ and the size of the office room $w$ and $d$ $(2 <= w, d <= 100,000)$. The office room has its width $w$ east-west, and depth $d$ north-south. Each of the following $n$ lines indicates the position and the orientation of the seat of a team member. Each member has a seat at a distinct position $(x_i, y_i)$ facing the direction $f_i$, for $i = 1, . . . , n$. Here $1 <= x_i <= w - 1,1 <= y_i <= d - 1$, and $f_i$ is one of N, E, W, and S, meaning north, east, west, and south, respectively. The position $(x, y)$ means $x$ distant from the west wall and $y$ distant from the south wall.", "output": "Print the minimum number of clocks needed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 10 6\n4 4 E\n6 4 W\n output: 2", "input: 2 10 6\n2 4 E\n6 4 W\n output: 1", "input: 2 10 6\n3 2 S\n6 4 W\n output: 1", "input: 6 10 6\n1 5 N\n7 1 N\n8 2 E\n9 1 S\n4 4 S\n3 3 W\n output: 3", "input: 4 10 6\n4 3 W\n2 4 N\n4 4 W\n3 3 S\n output: 2", "input: 4 100000 40000\n25000 25000 S\n20000 30000 S\n75000 25000 S\n80000 30000 S\n output: 1"], "Pid": "p00938", "ProblemText": "Task Description: You are the manager of a chocolate sales team. Your team customarily takes tea breaks every two hours, during which varieties of new chocolate products of your company are served. Everyone looks forward to the tea breaks so much that they frequently give a glance at a wall clock.\n\nRecently, your team has moved to a new office. You have just arranged desks in the office. One team member asked you to hang a clock on the wall in front of her desk so that she will not be late for tea breaks. Naturally, everyone seconded her.\n\nYou decided to provide an enough number of clocks to be hung in the field of view of everyone. Your team members will be satisfied if they have at least one clock (regardless of the orientation of the clock) in their view, or, more precisely, within 45 degrees left and 45 degrees right (both ends inclusive) from the facing directions of their seats. In order to buy as few clocks as possible, you should write a program that calculates the minimum number of clocks needed to\nmeet everyone's demand.\n\nThe office room is rectangular aligned to north-south and east-west directions. As the walls are tall enough, you can hang clocks even above the door and can assume one's eyesight is not blocked by other members or furniture. You can also assume that each clock is a point (of size zero), and so you can hang a clock even on a corner of the room.\n\nFor example, assume that there are two members. If they are sitting facing each other at positions shown in Figure D. 1(A), you need to provide two clocks as they see distinct sections of the wall. If their seats are arranged as shown in Figure D. 1(B), their fields of view have a common point on the wall. Thus, you can meet their demands by hanging a single clock at the point. In Figure D. 1(C), their fields of view have a common wall section. You can meet their demands with a single clock by hanging it anywhere in the section. Arrangements (A), (B), and (C) in Figure D. 1 correspond to Sample Input 1,2, and 3, respectively.\nTask Input: The input consists of a single test case, formatted as follows. \n$n$ $w$ $d$\n$x_1$ $y_1$ $f_1$\n. . . \n$x_n$ $y_n$ $f_n$\n\nFigure D. 1. Arrangements of seats and clocks. Gray area indicates field of view.\n\nAll numbers in the test case are integers. The first line contains the number of team members $n$ $(1 <= n <= 1,000)$ and the size of the office room $w$ and $d$ $(2 <= w, d <= 100,000)$. The office room has its width $w$ east-west, and depth $d$ north-south. Each of the following $n$ lines indicates the position and the orientation of the seat of a team member. Each member has a seat at a distinct position $(x_i, y_i)$ facing the direction $f_i$, for $i = 1, . . . , n$. Here $1 <= x_i <= w - 1,1 <= y_i <= d - 1$, and $f_i$ is one of N, E, W, and S, meaning north, east, west, and south, respectively. The position $(x, y)$ means $x$ distant from the west wall and $y$ distant from the south wall.\nTask Output: Print the minimum number of clocks needed.\nTask Samples: input: 2 10 6\n4 4 E\n6 4 W\n output: 2\ninput: 2 10 6\n2 4 E\n6 4 W\n output: 1\ninput: 2 10 6\n3 2 S\n6 4 W\n output: 1\ninput: 6 10 6\n1 5 N\n7 1 N\n8 2 E\n9 1 S\n4 4 S\n3 3 W\n output: 3\ninput: 4 10 6\n4 3 W\n2 4 N\n4 4 W\n3 3 S\n output: 2\ninput: 4 100000 40000\n25000 25000 S\n20000 30000 S\n75000 25000 S\n80000 30000 S\n output: 1\n\n" }, { "title": "Problem E\nBringing Order to Disorder", "content": "A sequence of digits usually represents a number, but we may define an alternative interpretation. In this problem we define a new interpretation with the order relation $\\prec$ among the digit sequences of the same length defined below.\n\nLet $s$ be a sequence of $n$ digits, $d_1d_2 . . . d_n$, where each $d_i$ $(1 <= i <= n)$ is one of 0,1, . . . , and 9. Let sum($s$), prod($s$), and int($s$) be as follows: \n\nsum($s$) = $d_1 + d_2 + . . . + d_n$\nprod($s$) = $(d_1 + 1) * (d_2 + 1) * . . . * (d_n + 1)$\nint($s$) = $d_1 * 10^{n-1} + d_2 * 10^{n-2} + . . . + d_n * 10^0$\nint($s$) is the integer the digit sequence $s$ represents with normal decimal interpretation.\n\nLet $s_1$ and $s_2$ be sequences of the same number of digits. Then $s_1 \\prec s_2$ ($s_1$ is less than $s_2$) is satisfied if and only if one of the following conditions is satisfied.\n\n sum($s_1$) $<$ sum($s_2$)\n\n sum($s_1$) $=$ sum($s_2$) and prod($s_1$) $<$ prod($s_2$)\n\n sum($s_1$) $=$ sum($s_2$), prod($s_1$) $=$ prod($s_2$), and int($s_1$) $<$ int($s_2$)\nFor 2-digit sequences, for instance, the following relations are satisfied. \n$00 \\prec 01 \\prec 10 \\prec 02 \\prec 20 \\prec 11 \\prec 03 \\prec 30 \\prec 12 \\prec 21 \\prec . . . \\prec 89 \\prec 98 \\prec 99$\n\nYour task is, given an $n$-digit sequence $s$, to count up the number of $n$-digit sequences that are less than $s$ in the order $\\prec$ defined above.", "constraint": "", "input": "The input consists of a single test case in a line. \n\n$d_1d_2 . . . d_n$\n$n$ is a positive integer at most 14. Each of $d_1, d_2, . . . , $ and $d_n$ is a digit.", "output": "Print the number of the $n$-digit sequences less than $d_1d_2 . . . d_n$ in the order defined above.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 20\n output: 4", "input: 020\n output: 5", "input: 118\n output: 245", "input: 11111111111111\n output: 40073759", "input: 99777222222211\n output: 23733362467675"], "Pid": "p00939", "ProblemText": "Task Description: A sequence of digits usually represents a number, but we may define an alternative interpretation. In this problem we define a new interpretation with the order relation $\\prec$ among the digit sequences of the same length defined below.\n\nLet $s$ be a sequence of $n$ digits, $d_1d_2 . . . d_n$, where each $d_i$ $(1 <= i <= n)$ is one of 0,1, . . . , and 9. Let sum($s$), prod($s$), and int($s$) be as follows: \n\nsum($s$) = $d_1 + d_2 + . . . + d_n$\nprod($s$) = $(d_1 + 1) * (d_2 + 1) * . . . * (d_n + 1)$\nint($s$) = $d_1 * 10^{n-1} + d_2 * 10^{n-2} + . . . + d_n * 10^0$\nint($s$) is the integer the digit sequence $s$ represents with normal decimal interpretation.\n\nLet $s_1$ and $s_2$ be sequences of the same number of digits. Then $s_1 \\prec s_2$ ($s_1$ is less than $s_2$) is satisfied if and only if one of the following conditions is satisfied.\n\n sum($s_1$) $<$ sum($s_2$)\n\n sum($s_1$) $=$ sum($s_2$) and prod($s_1$) $<$ prod($s_2$)\n\n sum($s_1$) $=$ sum($s_2$), prod($s_1$) $=$ prod($s_2$), and int($s_1$) $<$ int($s_2$)\nFor 2-digit sequences, for instance, the following relations are satisfied. \n$00 \\prec 01 \\prec 10 \\prec 02 \\prec 20 \\prec 11 \\prec 03 \\prec 30 \\prec 12 \\prec 21 \\prec . . . \\prec 89 \\prec 98 \\prec 99$\n\nYour task is, given an $n$-digit sequence $s$, to count up the number of $n$-digit sequences that are less than $s$ in the order $\\prec$ defined above.\nTask Input: The input consists of a single test case in a line. \n\n$d_1d_2 . . . d_n$\n$n$ is a positive integer at most 14. Each of $d_1, d_2, . . . , $ and $d_n$ is a digit.\nTask Output: Print the number of the $n$-digit sequences less than $d_1d_2 . . . d_n$ in the order defined above.\nTask Samples: input: 20\n output: 4\ninput: 020\n output: 5\ninput: 118\n output: 245\ninput: 11111111111111\n output: 40073759\ninput: 99777222222211\n output: 23733362467675\n\n" }, { "title": "Problem F\nDeadlock Detection", "content": "You are working on an analysis of a system with multiple processes and some kinds of resource (such as memory pages, DMA channels, and I/O ports). Each kind of resource has a certain number of instances. A process has to acquire resource instances for its execution. The number of required instances of a resource kind depends on a process. A process finishes its execution and terminates eventually after all the resource in need are acquired. These resource instances are released then so that other processes can use them. No process releases instances before its termination. Processes keep trying to acquire resource instances in need, one by one, without taking account of behavior of other processes. Since processes run independently of others, they may sometimes become unable to finish their execution because of deadlock.\n\nA process has to wait when no more resource instances in need are available until some other processes release ones on their termination. Deadlock is a situation in which two or more processes wait for termination of each other, and, regrettably, forever. This happens with the following scenario: One process A acquires the sole instance of resource X, and another process B acquires the sole instance of another resource Y; after that, A tries to acquire an instance of Y, and B tries to acquire an instance of X. As there are no instances of Y other than one acquired by B, A will never acquire Y before B finishes its execution, while B will never acquire X before A finishes. There may be more complicated deadlock situations involving three or more processes.\n\nYour task is, receiving the system's resource allocation time log (from the system's start to a certain time), to determine when the system fell into a deadlock-unavoidable state. Deadlock may usually be avoided by an appropriate allocation order, but deadlock-unavoidable states are those in which some resource allocation has already been made and no allocation order from then on can ever avoid deadlock.\n\n Let us consider an example corresponding to Sample Input 1 below. The system has two kinds of resource $R_1$ and $R_2$, and two processes $P_1$ and $P_2$. The system has three instances of $R_1$ and four instances of $R_2$. Process $P_1$ needs three instances of $R_1$ and two instances of $R_2$ to finish its execution, while process $P_2$ needs a single instance of $R_1$ and three instances of $R_2$. The resource allocation time log is given as follows.\n\nAt time 4, $P_2$ acquired $R_1$ and the number of available instances of $R_1$ became less than $P_1$'s need of $R_1$. Therefore, it became necessary for $P_1$ to wait $P_2$ to terminate and release the instance. However, at time 5, $P_1$ acquired $R_2$ necessary for $P_2$ to finish its execution, and thus it became necessary also for $P_2$ to wait $P_1$; the deadlock became unavoidable at this time.\n\nNote that the deadlock was still avoidable at time 4 by finishing $P_2$ first (Sample Input 2).", "constraint": "", "input": "The input consists of a single test case formatted as follows. \n$p$ $r$ $t$\n$l_1$ . . . $l_r$\n$n_{1,1}$ . . . $n_{1, r}$\n. . . \n$n_{p, 1}$ . . . $n_{p, r}$\n$P_1$ $R_1$\n. . . \n$P_t$ $R_t$\n$p$ is the number of processes, and is an integer between 2 and 300, inclusive. The processes are numbered 1 through $p$. $r$ is the number of resource kinds, and is an integer between 1 and 300, inclusive. The resource kinds are numbered 1 through $r$. $t$ is the length of the time log, and is an integer between 1 and 200,000, inclusive. $l_j$ $(1 <= j <= r)$ is the number of initially available instances of the resource kind $j$, and is an integer between 1 and 100, inclusive. $n_{i, j}$ $(1 <= i <= p, 1 <= j <= r)$ is the number of resource instances of the resource kind $j$ that the process $i$ needs, and is an integer between 0 and $l_j$ , inclusive. For every $i$, at least one of $n_{i, j}$ is non-zero. Each pair of $P_k$ and $R_k$ $(1 <= k <= t)$ is a resource allocation log at time $k$ meaning that process $P_k$ acquired an instance of resource $R_k$.\n\nYou may assume that the time log is consistent: no process acquires unnecessary resource instances; no process acquires instances after its termination; and a process does not acquire any instance of a resource kind when no instance is available.", "output": "Print the time when the system fell into a deadlock-unavoidable state. If the system could still avoid deadlock at time $t$, print -1.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 2 7\n3 4\n3 2\n1 3\n1 1\n2 2\n1 2\n2 1\n1 2\n2 2\n1 1\n output: 5", "input: 2 2 5\n3 4\n3 2\n1 3\n1 1\n2 2\n1 2\n2 1\n2 2\n output: -1"], "Pid": "p00940", "ProblemText": "Task Description: You are working on an analysis of a system with multiple processes and some kinds of resource (such as memory pages, DMA channels, and I/O ports). Each kind of resource has a certain number of instances. A process has to acquire resource instances for its execution. The number of required instances of a resource kind depends on a process. A process finishes its execution and terminates eventually after all the resource in need are acquired. These resource instances are released then so that other processes can use them. No process releases instances before its termination. Processes keep trying to acquire resource instances in need, one by one, without taking account of behavior of other processes. Since processes run independently of others, they may sometimes become unable to finish their execution because of deadlock.\n\nA process has to wait when no more resource instances in need are available until some other processes release ones on their termination. Deadlock is a situation in which two or more processes wait for termination of each other, and, regrettably, forever. This happens with the following scenario: One process A acquires the sole instance of resource X, and another process B acquires the sole instance of another resource Y; after that, A tries to acquire an instance of Y, and B tries to acquire an instance of X. As there are no instances of Y other than one acquired by B, A will never acquire Y before B finishes its execution, while B will never acquire X before A finishes. There may be more complicated deadlock situations involving three or more processes.\n\nYour task is, receiving the system's resource allocation time log (from the system's start to a certain time), to determine when the system fell into a deadlock-unavoidable state. Deadlock may usually be avoided by an appropriate allocation order, but deadlock-unavoidable states are those in which some resource allocation has already been made and no allocation order from then on can ever avoid deadlock.\n\n Let us consider an example corresponding to Sample Input 1 below. The system has two kinds of resource $R_1$ and $R_2$, and two processes $P_1$ and $P_2$. The system has three instances of $R_1$ and four instances of $R_2$. Process $P_1$ needs three instances of $R_1$ and two instances of $R_2$ to finish its execution, while process $P_2$ needs a single instance of $R_1$ and three instances of $R_2$. The resource allocation time log is given as follows.\n\nAt time 4, $P_2$ acquired $R_1$ and the number of available instances of $R_1$ became less than $P_1$'s need of $R_1$. Therefore, it became necessary for $P_1$ to wait $P_2$ to terminate and release the instance. However, at time 5, $P_1$ acquired $R_2$ necessary for $P_2$ to finish its execution, and thus it became necessary also for $P_2$ to wait $P_1$; the deadlock became unavoidable at this time.\n\nNote that the deadlock was still avoidable at time 4 by finishing $P_2$ first (Sample Input 2).\nTask Input: The input consists of a single test case formatted as follows. \n$p$ $r$ $t$\n$l_1$ . . . $l_r$\n$n_{1,1}$ . . . $n_{1, r}$\n. . . \n$n_{p, 1}$ . . . $n_{p, r}$\n$P_1$ $R_1$\n. . . \n$P_t$ $R_t$\n$p$ is the number of processes, and is an integer between 2 and 300, inclusive. The processes are numbered 1 through $p$. $r$ is the number of resource kinds, and is an integer between 1 and 300, inclusive. The resource kinds are numbered 1 through $r$. $t$ is the length of the time log, and is an integer between 1 and 200,000, inclusive. $l_j$ $(1 <= j <= r)$ is the number of initially available instances of the resource kind $j$, and is an integer between 1 and 100, inclusive. $n_{i, j}$ $(1 <= i <= p, 1 <= j <= r)$ is the number of resource instances of the resource kind $j$ that the process $i$ needs, and is an integer between 0 and $l_j$ , inclusive. For every $i$, at least one of $n_{i, j}$ is non-zero. Each pair of $P_k$ and $R_k$ $(1 <= k <= t)$ is a resource allocation log at time $k$ meaning that process $P_k$ acquired an instance of resource $R_k$.\n\nYou may assume that the time log is consistent: no process acquires unnecessary resource instances; no process acquires instances after its termination; and a process does not acquire any instance of a resource kind when no instance is available.\nTask Output: Print the time when the system fell into a deadlock-unavoidable state. If the system could still avoid deadlock at time $t$, print -1.\nTask Samples: input: 2 2 7\n3 4\n3 2\n1 3\n1 1\n2 2\n1 2\n2 1\n1 2\n2 2\n1 1\n output: 5\ninput: 2 2 5\n3 4\n3 2\n1 3\n1 1\n2 2\n1 2\n2 1\n2 2\n output: -1\n\n" }, { "title": "Problem G\nDo Geese See God?", "content": "A palindrome is a sequence of characters which reads the same backward or forward. Famous ones include \"dogeeseseegod\" (\"Do geese see God? \"), \"amoreroma\" (\"Amore, Roma. \") and \"risetovotesir\" (\"Rise to vote, sir. \").\n\nAn ancient sutra has been handed down through generations at a temple on Tsukuba foothills. They say the sutra was a palindrome, but some of the characters have been dropped through transcription.\n\nA famous scholar in the field of religious studies was asked to recover the original. After long repeated deliberations, he concluded that no information to recover the original has been lost, and that the original can be reconstructed as the shortest palindrome including all the characters of the current sutra in the same order. That is to say, the original sutra is obtained by adding some characters before, between, and/or behind the characters of the current.\n\nGiven a character sequence, your program should output one of the shortest palindromes containing the characters of the current sutra preserving their order. One of the shortest? Yes, more than one shortest palindromes may exist. Which of them to output is also specified as its rank among the candidates in the lexicographical order.\n\nFor example, if the current sutra is cdba and 7th is specified, your program should output cdabadc among the 8 candidates, abcdcba, abdcdba, acbdbca, acdbdca, cabdbac, cadbdac, cdabadc and cdbabdc.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows. \n$S$\n$k$\nThe first line contains a string $S$ composed of lowercase letters from 'a' to 'z'. The length of $S$ is greater than 0, and less than or equal to 2000. The second line contains an integer $k$ which represents the rank in the lexicographical order among the candidates of the original sutra. $1 <= k <= 10^{18}$.", "output": "Output the $k$-th string in the lexicographical order among the candidates of the original sutra. If the number of the candidates is less than $k$, output NONE.\n\nThough the first lines of the Sample Input/Output 7 are folded at the right margin, they are actually single lines.", "content_img": false, "lang": "en", "error": false, "samples": ["input: crc\n1\n output: crc", "input: icpc\n1\n output: icpci", "input: hello\n1\n output: heolloeh", "input: hoge\n8\n output: hogegoh", "input: hoge\n9\n output: NONE", "input: bbaaab\n2\n output: NONE", "input: thdstodxtksrnfacdsohnlfuivqvqsozdstwa\nszmkboehgcerwxawuojpfuvlxxdfkezprodne\nttawsyqazekcftgqbrrtkzngaxzlnphynkmsd\nsdleqaxnhehwzgzwtldwaacfczqkfpvxnalnn\nhfzbagzhqhstcymdeijlbkbbubdnptolrmemf\nxlmmzhfpshykxvzbjmcnsusllpyqghzhdvljd\nxrrebeef\n11469362357953500\n output: feeberrthdstodxtksrnfacdjsohnlfuivdhq\nvqsozhgdqypllstwausnzcmjkboehgcerzvwx\nakyhswuojpfhzumvmlxxdfkmezmprlotpndbu\nbbkblnjiedttmawsyqazekcftgshqbrhrtkzn\ngaxbzfhnnlanxvphyfnkqmzcsdfscaawdleqa\nxtnhehwzgzwhehntxaqeldwaacsfdsczmqknf\nyhpvxnalnnhfzbxagnzktrhrbqhsgtfckezaq\nyswamttdeijnlbkbbubdnptolrpmzemkfdxxl\nmvmuzhfpjouwshykaxwvzrecgheobkjmcznsu\nawtsllpyqdghzosqvqhdviuflnhosjdcafnrs\nktxdotsdhtrrebeef"], "Pid": "p00941", "ProblemText": "Task Description: A palindrome is a sequence of characters which reads the same backward or forward. Famous ones include \"dogeeseseegod\" (\"Do geese see God? \"), \"amoreroma\" (\"Amore, Roma. \") and \"risetovotesir\" (\"Rise to vote, sir. \").\n\nAn ancient sutra has been handed down through generations at a temple on Tsukuba foothills. They say the sutra was a palindrome, but some of the characters have been dropped through transcription.\n\nA famous scholar in the field of religious studies was asked to recover the original. After long repeated deliberations, he concluded that no information to recover the original has been lost, and that the original can be reconstructed as the shortest palindrome including all the characters of the current sutra in the same order. That is to say, the original sutra is obtained by adding some characters before, between, and/or behind the characters of the current.\n\nGiven a character sequence, your program should output one of the shortest palindromes containing the characters of the current sutra preserving their order. One of the shortest? Yes, more than one shortest palindromes may exist. Which of them to output is also specified as its rank among the candidates in the lexicographical order.\n\nFor example, if the current sutra is cdba and 7th is specified, your program should output cdabadc among the 8 candidates, abcdcba, abdcdba, acbdbca, acdbdca, cabdbac, cadbdac, cdabadc and cdbabdc.\nTask Input: The input consists of a single test case. The test case is formatted as follows. \n$S$\n$k$\nThe first line contains a string $S$ composed of lowercase letters from 'a' to 'z'. The length of $S$ is greater than 0, and less than or equal to 2000. The second line contains an integer $k$ which represents the rank in the lexicographical order among the candidates of the original sutra. $1 <= k <= 10^{18}$.\nTask Output: Output the $k$-th string in the lexicographical order among the candidates of the original sutra. If the number of the candidates is less than $k$, output NONE.\n\nThough the first lines of the Sample Input/Output 7 are folded at the right margin, they are actually single lines.\nTask Samples: input: crc\n1\n output: crc\ninput: icpc\n1\n output: icpci\ninput: hello\n1\n output: heolloeh\ninput: hoge\n8\n output: hogegoh\ninput: hoge\n9\n output: NONE\ninput: bbaaab\n2\n output: NONE\ninput: thdstodxtksrnfacdsohnlfuivqvqsozdstwa\nszmkboehgcerwxawuojpfuvlxxdfkezprodne\nttawsyqazekcftgqbrrtkzngaxzlnphynkmsd\nsdleqaxnhehwzgzwtldwaacfczqkfpvxnalnn\nhfzbagzhqhstcymdeijlbkbbubdnptolrmemf\nxlmmzhfpshykxvzbjmcnsusllpyqghzhdvljd\nxrrebeef\n11469362357953500\n output: feeberrthdstodxtksrnfacdjsohnlfuivdhq\nvqsozhgdqypllstwausnzcmjkboehgcerzvwx\nakyhswuojpfhzumvmlxxdfkmezmprlotpndbu\nbbkblnjiedttmawsyqazekcftgshqbrhrtkzn\ngaxbzfhnnlanxvphyfnkqmzcsdfscaawdleqa\nxtnhehwzgzwhehntxaqeldwaacsfdsczmqknf\nyhpvxnalnnhfzbxagnzktrhrbqhsgtfckezaq\nyswamttdeijnlbkbbubdnptolrpmzemkfdxxl\nmvmuzhfpjouwshykaxwvzrecgheobkjmcznsu\nawtsllpyqdghzosqvqhdviuflnhosjdcafnrs\nktxdotsdhtrrebeef\n\n" }, { "title": "Problem H\nRotating Cutter Bits", "content": "The machine tool technology never stops its development. One of the recent proposals is more flexible lathes in which not only the workpiece but also the cutter bit rotate around parallel axles in synchronization. When the lathe is switched on, the workpiece and the cutter bit start rotating at the same angular velocity, that is, to the same direction and at the same rotational speed. On collision with the cutter bit, parts of the workpiece that intersect with the cutter bit are cut out.\n\nTo show the usefulness of the mechanism, you are asked to simulate the cutting process by such a lathe.\n\nAlthough the workpiece and the cutter bit may have complex shapes, focusing on cross sections of them on a plane perpendicular to the spinning axles would suffice. We introduce an $xy$-coordinate system on a plane perpendicular to the two axles, in which the center of rotation of the workpiece is at the origin $(0,0)$, while that of the cutter bit is at $(L, 0)$. You can assume both the workpiece and the cutter bit have polygonal cross sections, not necessarily convex.\n\nNote that, even when this cross section of the workpiece is divided into two or more parts, the workpiece remain undivided on other cross sections. \n\nWe refer to the lattice points (points with both $x$ and $y$ coordinates being integers) strictly inside, that is, inside and not on an edge, of the workpiece before the rotation as points of interest, or POI in short.\n\nOur interest is in how many POI will remain after one full rotation of 360 degrees of both the workpiece and the cutter bit. POI are said to remain if they are strictly inside the resultant workpiece. Write a program that counts them for the given workpiece and cutter bit configuration.\n\nFigure H. 1(a) illustrates the workpiece (in black line) and the cutter bit (in blue line) given in Sample Input 1. Two circles indicate positions of the rotation centers of the workpiece and the cutter bit. The red cross-shaped marks indicate the POI.\n\nFigure H. 1(b) illustrates the workpiece and the cutter bit in progress in case that the rotation direction is clockwise. The light blue area indicates the area cut-off.\n\nFigure H. 1(c) illustrates the result of this sample. Note that one of POI is on the edge of the resulting shape. You should not count this point. There are eight POI remained.\n\nFigure H. 1. The workpiece and the cutter bit in Sample 1", "constraint": "", "input": "The input consists of a single test case with the following format. \n$M$ $N$ $L$\n$x_{w1}$ $y_{w1}$\n. . . \n$x_{w M}$ $y_{w M}$\n$x_{c1}$ $y_{c1}$\n. . . \n$x_{c N}$ $y_{c N}$\nThe first line contains three integers. $M$ is the number of vertices of the workpiece $(4 <= M <= 20)$\nand $N$ is the number of vertices of the cutter bit $(4 <= N <= 20)$. $L$ specifies the position of the\nrotation center of the cutter bit $(1 <= L <= 10000)$.\n\nEach of the following $M$ lines contains two integers. The $i$-th line has $x_{wi}$ and $y_{wi}$, telling that the position of the $i$-th vertex of the workpiece has the coordinates $(x_{wi}, y_{wi})$. The vertices are given in the counter-clockwise order.\n\n$N$ more following lines are positions of the vertices of the cutter bit, in the same manner, but the coordinates are given as offsets from its center of rotation, $(L, 0)$. That is, the position of the $j$-th vertex of the cutter bit has the coordinates $(L + x_{cj} , y_{cj} )$.\n\nYou may assume $-10000 <= x_{wi}, y_{wi}, x_{cj} , y_{cj} <= 10000$ for $1 <= i <= M$ and $1 <= j <= N$.\n\nAll the edges of the workpiece and the cutter bit at initial rotation positions are parallel to the $x$-axis or the $y$-axis. In other words, for each $i$ $(1 <= i <= M), x_{wi} = x_{wi'}$ or $y_{wi} = y_{wi'}$ holds, where $i' = (i $ mod$ M) + 1$. Edges are parallel to the $x$- and the $y$-axes alternately. These can also be said about the cutter bit.\n\nYou may assume that the cross section of the workpiece forms a simple polygon, that is, no two edges have common points except for adjacent edges. The same can be said about the cutter bit. The workpiece and the cutter bit do not touch or overlap before starting the rotation.\n\nNote that $(0,0)$ is not always inside the workpiece and $(L, 0)$ is not always inside the cutter bit.", "output": "Output the number of POI remaining strictly inside the workpiece.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 6 5\n-2 5\n-2 -1\n2 -1\n2 5\n-2 1\n-2 0\n0 0\n0 -2\n2 -2\n2 1\n output: 8", "input: 14 14 6000\n-3000 3000\n-3000 -3000\n3000 -3000\n3000 -2000\n2000 -2000\n2000 -1000\n1000 -1000\n1000 0\n0 0\n0 1000\n-1000 1000\n-1000 2000\n-2000 2000\n-2000 3000\n3000 3000\n-3000 3000\n-3000 2000\n-2000 2000\n-2000 1000\n-1000 1000\n-1000 0\n0 0\n0 -1000\n1000 -1000\n1000 -2000\n2000 -2000\n2000 -3000\n3000 -3000\n output: 6785772", "input: 12 12 11\n-50 45\n-50 -45\n40 -45\n40 25\n-10 25\n-10 -5\n0 -5\n0 15\n30 15\n30 -35\n-40 -35\n-40 45\n50 -45\n50 45\n-40 45\n-40 -25\n10 -25\n10 5\n0 5\n0 -15\n-30 -15\n-30 35\n40 35\n40 -45\n output: 966", "input: 20 4 11\n-5 5\n-5 -10\n-4 -10\n-4 -1\n-3 -1\n-3 -10\n1 -10\n1 -4\n0 -4\n0 -1\n1 -1\n1 0\n4 0\n4 -1\n10 -1\n10 3\n1 3\n1 4\n10 4\n10 5\n0 0\n3 0\n3 3\n0 3\n output: 64"], "Pid": "p00942", "ProblemText": "Task Description: The machine tool technology never stops its development. One of the recent proposals is more flexible lathes in which not only the workpiece but also the cutter bit rotate around parallel axles in synchronization. When the lathe is switched on, the workpiece and the cutter bit start rotating at the same angular velocity, that is, to the same direction and at the same rotational speed. On collision with the cutter bit, parts of the workpiece that intersect with the cutter bit are cut out.\n\nTo show the usefulness of the mechanism, you are asked to simulate the cutting process by such a lathe.\n\nAlthough the workpiece and the cutter bit may have complex shapes, focusing on cross sections of them on a plane perpendicular to the spinning axles would suffice. We introduce an $xy$-coordinate system on a plane perpendicular to the two axles, in which the center of rotation of the workpiece is at the origin $(0,0)$, while that of the cutter bit is at $(L, 0)$. You can assume both the workpiece and the cutter bit have polygonal cross sections, not necessarily convex.\n\nNote that, even when this cross section of the workpiece is divided into two or more parts, the workpiece remain undivided on other cross sections. \n\nWe refer to the lattice points (points with both $x$ and $y$ coordinates being integers) strictly inside, that is, inside and not on an edge, of the workpiece before the rotation as points of interest, or POI in short.\n\nOur interest is in how many POI will remain after one full rotation of 360 degrees of both the workpiece and the cutter bit. POI are said to remain if they are strictly inside the resultant workpiece. Write a program that counts them for the given workpiece and cutter bit configuration.\n\nFigure H. 1(a) illustrates the workpiece (in black line) and the cutter bit (in blue line) given in Sample Input 1. Two circles indicate positions of the rotation centers of the workpiece and the cutter bit. The red cross-shaped marks indicate the POI.\n\nFigure H. 1(b) illustrates the workpiece and the cutter bit in progress in case that the rotation direction is clockwise. The light blue area indicates the area cut-off.\n\nFigure H. 1(c) illustrates the result of this sample. Note that one of POI is on the edge of the resulting shape. You should not count this point. There are eight POI remained.\n\nFigure H. 1. The workpiece and the cutter bit in Sample 1\nTask Input: The input consists of a single test case with the following format. \n$M$ $N$ $L$\n$x_{w1}$ $y_{w1}$\n. . . \n$x_{w M}$ $y_{w M}$\n$x_{c1}$ $y_{c1}$\n. . . \n$x_{c N}$ $y_{c N}$\nThe first line contains three integers. $M$ is the number of vertices of the workpiece $(4 <= M <= 20)$\nand $N$ is the number of vertices of the cutter bit $(4 <= N <= 20)$. $L$ specifies the position of the\nrotation center of the cutter bit $(1 <= L <= 10000)$.\n\nEach of the following $M$ lines contains two integers. The $i$-th line has $x_{wi}$ and $y_{wi}$, telling that the position of the $i$-th vertex of the workpiece has the coordinates $(x_{wi}, y_{wi})$. The vertices are given in the counter-clockwise order.\n\n$N$ more following lines are positions of the vertices of the cutter bit, in the same manner, but the coordinates are given as offsets from its center of rotation, $(L, 0)$. That is, the position of the $j$-th vertex of the cutter bit has the coordinates $(L + x_{cj} , y_{cj} )$.\n\nYou may assume $-10000 <= x_{wi}, y_{wi}, x_{cj} , y_{cj} <= 10000$ for $1 <= i <= M$ and $1 <= j <= N$.\n\nAll the edges of the workpiece and the cutter bit at initial rotation positions are parallel to the $x$-axis or the $y$-axis. In other words, for each $i$ $(1 <= i <= M), x_{wi} = x_{wi'}$ or $y_{wi} = y_{wi'}$ holds, where $i' = (i $ mod$ M) + 1$. Edges are parallel to the $x$- and the $y$-axes alternately. These can also be said about the cutter bit.\n\nYou may assume that the cross section of the workpiece forms a simple polygon, that is, no two edges have common points except for adjacent edges. The same can be said about the cutter bit. The workpiece and the cutter bit do not touch or overlap before starting the rotation.\n\nNote that $(0,0)$ is not always inside the workpiece and $(L, 0)$ is not always inside the cutter bit.\nTask Output: Output the number of POI remaining strictly inside the workpiece.\nTask Samples: input: 4 6 5\n-2 5\n-2 -1\n2 -1\n2 5\n-2 1\n-2 0\n0 0\n0 -2\n2 -2\n2 1\n output: 8\ninput: 14 14 6000\n-3000 3000\n-3000 -3000\n3000 -3000\n3000 -2000\n2000 -2000\n2000 -1000\n1000 -1000\n1000 0\n0 0\n0 1000\n-1000 1000\n-1000 2000\n-2000 2000\n-2000 3000\n3000 3000\n-3000 3000\n-3000 2000\n-2000 2000\n-2000 1000\n-1000 1000\n-1000 0\n0 0\n0 -1000\n1000 -1000\n1000 -2000\n2000 -2000\n2000 -3000\n3000 -3000\n output: 6785772\ninput: 12 12 11\n-50 45\n-50 -45\n40 -45\n40 25\n-10 25\n-10 -5\n0 -5\n0 15\n30 15\n30 -35\n-40 -35\n-40 45\n50 -45\n50 45\n-40 45\n-40 -25\n10 -25\n10 5\n0 5\n0 -15\n-30 -15\n-30 35\n40 35\n40 -45\n output: 966\ninput: 20 4 11\n-5 5\n-5 -10\n-4 -10\n-4 -1\n-3 -1\n-3 -10\n1 -10\n1 -4\n0 -4\n0 -1\n1 -1\n1 0\n4 0\n4 -1\n10 -1\n10 3\n1 3\n1 4\n10 4\n10 5\n0 0\n3 0\n3 3\n0 3\n output: 64\n\n" }, { "title": "Problem I\nRouting a Marathon Race", "content": "As a member of the ICPC (Ibaraki Committee of Physical Competitions), you are responsible for planning the route of a marathon event held in the City of Tsukuba. A great number of runners, from beginners to experts, are expected to take part.\n\nYou have at hand a city map that lists all the street segments suited for the event and all the junctions on them. The race is to start at the junction in front of Tsukuba High, and the goal is at the junction in front of City Hall, both of which are marked on the map.\n\nTo avoid congestion and confusion of runners of divergent skills, the route should not visit the same junction twice. Consequently, although the street segments can be used in either direction, they can be included at most once in the route. As the main objective of the event is in recreation and health promotion of citizens, time records are not important and the route distance can be arbitrarily decided.\n\nA number of personnel have to be stationed at every junction on the route. Junctions adjacent to them, i. e. , junctions connected directly by a street segment to the junctions on the route, also need personnel staffing to keep casual traffic from interfering the race. The same number of personnel is required when a junction is on the route and when it is adjacent to one, but different junctions require different numbers of personnel depending on their sizes and shapes, which are also indicated on the map.\n\nThe municipal authorities are eager in reducing the costs including the personnel expense for\nevents of this kind. Your task is to write a program that plans a route with the minimum\npossible number of personnel required and outputs that number.", "constraint": "", "input": "The input consists of a single test case representing a summary city map, formatted as follows. \n$n$ $m$\n$c_1$\n. . . \n$c_n$\n$i_1$ $j_1$\n. . . \n$i_m$ $j_m$\nThe first line of a test case has two positive integers, $n$ and $m$. Here, $n$ indicates the number of junctions in the map $(2 <= n <= 40)$, and $m$ is the number of street segments connecting adjacent junctions. Junctions are identified by integers 1 through $n$.\n\nThen comes $n$ lines indicating numbers of personnel required. The $k$-th line of which, an integer $c_k$ $(1 <= c_k <= 100)$, is the number of personnel required for the junction $k$.\n\nThe remaining $m$ lines list street segments between junctions. Each of these lines has two integers $i_k$ and $j_k$, representing a segment connecting junctions $i_k$ and $j_k$ $(i_k \\ne j_k)$. There is at most one street segment connecting the same pair of junctions.\n\nThe race starts at junction 1 and the goal is at junction $n$. It is guaranteed that there is at least one route connecting the start and the goal junctions.", "output": "Output an integer indicating the minimum possible number of personnel required.\n\nFigure I. 1. The Lowest-Cost Route for Sample Input 1\nFigure I. 1 shows the lowest-cost route for Sample Input 1. The arrows indicate the route and the circles painted gray are junctions requiring personnel assignment. The minimum number of required personnel is 17 in this case.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 6\n3\n1\n9\n4\n3\n6\n1 2\n1 4\n2 6\n5 4\n6 5\n3 2\n output: 17"], "Pid": "p00943", "ProblemText": "Task Description: As a member of the ICPC (Ibaraki Committee of Physical Competitions), you are responsible for planning the route of a marathon event held in the City of Tsukuba. A great number of runners, from beginners to experts, are expected to take part.\n\nYou have at hand a city map that lists all the street segments suited for the event and all the junctions on them. The race is to start at the junction in front of Tsukuba High, and the goal is at the junction in front of City Hall, both of which are marked on the map.\n\nTo avoid congestion and confusion of runners of divergent skills, the route should not visit the same junction twice. Consequently, although the street segments can be used in either direction, they can be included at most once in the route. As the main objective of the event is in recreation and health promotion of citizens, time records are not important and the route distance can be arbitrarily decided.\n\nA number of personnel have to be stationed at every junction on the route. Junctions adjacent to them, i. e. , junctions connected directly by a street segment to the junctions on the route, also need personnel staffing to keep casual traffic from interfering the race. The same number of personnel is required when a junction is on the route and when it is adjacent to one, but different junctions require different numbers of personnel depending on their sizes and shapes, which are also indicated on the map.\n\nThe municipal authorities are eager in reducing the costs including the personnel expense for\nevents of this kind. Your task is to write a program that plans a route with the minimum\npossible number of personnel required and outputs that number.\nTask Input: The input consists of a single test case representing a summary city map, formatted as follows. \n$n$ $m$\n$c_1$\n. . . \n$c_n$\n$i_1$ $j_1$\n. . . \n$i_m$ $j_m$\nThe first line of a test case has two positive integers, $n$ and $m$. Here, $n$ indicates the number of junctions in the map $(2 <= n <= 40)$, and $m$ is the number of street segments connecting adjacent junctions. Junctions are identified by integers 1 through $n$.\n\nThen comes $n$ lines indicating numbers of personnel required. The $k$-th line of which, an integer $c_k$ $(1 <= c_k <= 100)$, is the number of personnel required for the junction $k$.\n\nThe remaining $m$ lines list street segments between junctions. Each of these lines has two integers $i_k$ and $j_k$, representing a segment connecting junctions $i_k$ and $j_k$ $(i_k \\ne j_k)$. There is at most one street segment connecting the same pair of junctions.\n\nThe race starts at junction 1 and the goal is at junction $n$. It is guaranteed that there is at least one route connecting the start and the goal junctions.\nTask Output: Output an integer indicating the minimum possible number of personnel required.\n\nFigure I. 1. The Lowest-Cost Route for Sample Input 1\nFigure I. 1 shows the lowest-cost route for Sample Input 1. The arrows indicate the route and the circles painted gray are junctions requiring personnel assignment. The minimum number of required personnel is 17 in this case.\nTask Samples: input: 6 6\n3\n1\n9\n4\n3\n6\n1 2\n1 4\n2 6\n5 4\n6 5\n3 2\n output: 17\n\n" }, { "title": "Problem J\nPost Office Investigation", "content": "In this country, all international mails from abroad are first gathered to the central post office, and then delivered to each destination post office relaying some post offices on the way. The delivery routes between post offices are described by a directed graph $G = (V, E)$, where $V$ is the set of post offices and $E$ is the set of possible mail forwarding steps. Due to the inefficient operations, you cannot expect that the mails are delivered along the shortest route.\n\nThe set of post offices can be divided into a certain number of groups. Here, a group is defined as a set of post offices where mails can be forwarded from any member of the group to any other member, directly or indirectly. The number of post offices in such a group does not exceed 10.\n\nThe post offices frequently receive complaints from customers that some mails are not delivered yet. Such a problem is usually due to system trouble in a single post office, but identifying which is not easy. Thus, when such complaints are received, the customer support sends staff to check the system of each candidate post office. Here, the investigation cost to check the system of the post office $u$ is given by $c_u$, which depends on the scale of the post office.\n\nSince there are many post offices in the country, and such complaints are frequently received, reducing the investigation cost is an important issue. To reduce the cost, the post service administration determined to use the following scheduling rule: When complaints on undelivered mails are received by the post offices $w_1, . . . , w_k$ one day, staff is sent on the next day to investigate a single post office $v$ with the lowest investigation cost among candidates. Here, the post office $v$ is a candidate if all mails from the central post office to the post offices $w_1, . . . , w_k$ must go through $v$. If no problem is found in the post office $v$, we have to decide the order of investigating other post offices, but the problem is left to some future days.\n\nYour job is to write a program that finds the cost of the lowest-cost candidate when the list of complained post offices in a day, described by $w_1, . . . , w_k$, is given as a query.", "constraint": "", "input": "The input consists of a single test case, formatted as follows. \n$n$ $m$\n$u_1$ $v_1$\n. . . \n$u_m$ $v_m$\n$c_1$\n. . . \n$c_n$\n$q$\n$k_1$ $w_{11}$ . . . $w_{1k_1}$\n. . . \n$k_q$ $w_{q1}$ . . . $w_{qk_q}$\n$n$ is the number of post offices $(2 <= n <= 50,000)$, which are numbered from 1 to $n$. Here, post office 1 corresponds to the central post office. $m$ is the number of forwarding pairs of post offices $(1 <= m <= 100,000)$. The pair, $u_i$ and $v_i$, means that some of the mails received at post office $u_i$ are forwarded to post office $v_i$ $(i = 1, . . . , m)$. $c_j$ is the investigation cost for the post office $j$ $(j = 1, . . . , n, 1 <= c_j <= 10^9)$. $q$ $(q >= 1)$ is the number of queries, and each query is specified by a list of post offices which received undelivered mail complaints. $k_i$ $(k_i >= 1)$ is the length of the list and $w_{i1}, . . . , w_{ik_i}$ are the distinct post offices in the list. $\\sum_{i=1}^{q} k_i <= 50,000$.\n\nYou can assume that there is at least one delivery route from the central post office to all the post offices.", "output": "For each query, you should output a single integer that is the lowest cost of the candidate of troubled post office.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 8\n1 2\n1 3\n2 4\n2 5\n2 8\n3 5\n3 6\n4 7\n1000\n100\n100\n10\n10\n10\n1\n1\n3\n2 8 6\n2 4 7\n2 7 8\n output: 1000\n10\n100", "input: 10 12\n1 2\n2 3\n3 4\n4 2\n4 5\n5 6\n6 7\n7 5\n7 8\n8 9\n9 10\n10 8\n10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n3\n2 3 4\n3 6 7 8\n3 9 6 3\n output: 8\n5\n8"], "Pid": "p00944", "ProblemText": "Task Description: In this country, all international mails from abroad are first gathered to the central post office, and then delivered to each destination post office relaying some post offices on the way. The delivery routes between post offices are described by a directed graph $G = (V, E)$, where $V$ is the set of post offices and $E$ is the set of possible mail forwarding steps. Due to the inefficient operations, you cannot expect that the mails are delivered along the shortest route.\n\nThe set of post offices can be divided into a certain number of groups. Here, a group is defined as a set of post offices where mails can be forwarded from any member of the group to any other member, directly or indirectly. The number of post offices in such a group does not exceed 10.\n\nThe post offices frequently receive complaints from customers that some mails are not delivered yet. Such a problem is usually due to system trouble in a single post office, but identifying which is not easy. Thus, when such complaints are received, the customer support sends staff to check the system of each candidate post office. Here, the investigation cost to check the system of the post office $u$ is given by $c_u$, which depends on the scale of the post office.\n\nSince there are many post offices in the country, and such complaints are frequently received, reducing the investigation cost is an important issue. To reduce the cost, the post service administration determined to use the following scheduling rule: When complaints on undelivered mails are received by the post offices $w_1, . . . , w_k$ one day, staff is sent on the next day to investigate a single post office $v$ with the lowest investigation cost among candidates. Here, the post office $v$ is a candidate if all mails from the central post office to the post offices $w_1, . . . , w_k$ must go through $v$. If no problem is found in the post office $v$, we have to decide the order of investigating other post offices, but the problem is left to some future days.\n\nYour job is to write a program that finds the cost of the lowest-cost candidate when the list of complained post offices in a day, described by $w_1, . . . , w_k$, is given as a query.\nTask Input: The input consists of a single test case, formatted as follows. \n$n$ $m$\n$u_1$ $v_1$\n. . . \n$u_m$ $v_m$\n$c_1$\n. . . \n$c_n$\n$q$\n$k_1$ $w_{11}$ . . . $w_{1k_1}$\n. . . \n$k_q$ $w_{q1}$ . . . $w_{qk_q}$\n$n$ is the number of post offices $(2 <= n <= 50,000)$, which are numbered from 1 to $n$. Here, post office 1 corresponds to the central post office. $m$ is the number of forwarding pairs of post offices $(1 <= m <= 100,000)$. The pair, $u_i$ and $v_i$, means that some of the mails received at post office $u_i$ are forwarded to post office $v_i$ $(i = 1, . . . , m)$. $c_j$ is the investigation cost for the post office $j$ $(j = 1, . . . , n, 1 <= c_j <= 10^9)$. $q$ $(q >= 1)$ is the number of queries, and each query is specified by a list of post offices which received undelivered mail complaints. $k_i$ $(k_i >= 1)$ is the length of the list and $w_{i1}, . . . , w_{ik_i}$ are the distinct post offices in the list. $\\sum_{i=1}^{q} k_i <= 50,000$.\n\nYou can assume that there is at least one delivery route from the central post office to all the post offices.\nTask Output: For each query, you should output a single integer that is the lowest cost of the candidate of troubled post office.\nTask Samples: input: 8 8\n1 2\n1 3\n2 4\n2 5\n2 8\n3 5\n3 6\n4 7\n1000\n100\n100\n10\n10\n10\n1\n1\n3\n2 8 6\n2 4 7\n2 7 8\n output: 1000\n10\n100\ninput: 10 12\n1 2\n2 3\n3 4\n4 2\n4 5\n5 6\n6 7\n7 5\n7 8\n8 9\n9 10\n10 8\n10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n3\n2 3 4\n3 6 7 8\n3 9 6 3\n output: 8\n5\n8\n\n" }, { "title": "Problem K\nMin-Max Distance Game", "content": "Alice and Bob are playing the following game. Initially, $n$ stones are placed in a straight line on a table. Alice and Bob take turns alternately. In each turn, the player picks one of the stones and removes it. The game continues until the number of stones on the straight line becomes two. The two stones are called result stones. Alice's objective is to make the result stones as distant as possible, while Bob's is to make them closer.\n\nYou are given the coordinates of the stones and the player's name who takes the first turn. Assuming that both Alice and Bob do their best, compute and output the distance between the result stones at the end of the game.", "constraint": "", "input": "The input consists of a single test case with the following format. \n$n$ $f$\n$x_1$ $x_2$ . . . $x_n$\n$n$ is the number of stones $(3 <= n <= 10^5)$. $f$ is the name of the first player, either Alice or Bob. For each $i$, $x_i$ is an integer that represents the distance of the $i$-th stone from the edge of the table. It is guaranteed that $0 <= x_1 < x_2 < . . . < x_n <= 10^9$ holds.", "output": "Output the distance between the result stones in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 Alice\n10 20 30 40 50\n output: 30", "input: 5 Bob\n2 3 5 7 11\n output: 2"], "Pid": "p00945", "ProblemText": "Task Description: Alice and Bob are playing the following game. Initially, $n$ stones are placed in a straight line on a table. Alice and Bob take turns alternately. In each turn, the player picks one of the stones and removes it. The game continues until the number of stones on the straight line becomes two. The two stones are called result stones. Alice's objective is to make the result stones as distant as possible, while Bob's is to make them closer.\n\nYou are given the coordinates of the stones and the player's name who takes the first turn. Assuming that both Alice and Bob do their best, compute and output the distance between the result stones at the end of the game.\nTask Input: The input consists of a single test case with the following format. \n$n$ $f$\n$x_1$ $x_2$ . . . $x_n$\n$n$ is the number of stones $(3 <= n <= 10^5)$. $f$ is the name of the first player, either Alice or Bob. For each $i$, $x_i$ is an integer that represents the distance of the $i$-th stone from the edge of the table. It is guaranteed that $0 <= x_1 < x_2 < . . . < x_n <= 10^9$ holds.\nTask Output: Output the distance between the result stones in one line.\nTask Samples: input: 5 Alice\n10 20 30 40 50\n output: 30\ninput: 5 Bob\n2 3 5 7 11\n output: 2\n\n" }, { "title": "Problem A\nRearranging a Sequence", "content": "You are given an ordered sequence of integers, ($1,2,3, . . . , n$). Then, a number of requests will be given. Each request specifies an integer in the sequence. You need to move the specified integer to the head of the sequence, leaving the order of the rest untouched. Your task is to find the order of the elements in the sequence after following all the requests successively.", "constraint": "", "input": "The input consists of a single test case of the following form. \n\n$n$ $m$\n$e_1$\n. . . \n$e_m$\n\nThe integer $n$ is the length of the sequence ($1 <= n <= 200000$). The integer $m$ is the number of requests ($1 <= m <= 100000$). The following $m$ lines are the requests, namely $e_1, . . . , e_m$, one per line. Each request $e_i$ ($1 <= i <= m$) is an integer between 1 and $n$, inclusive, designating the element to move. Note that, the integers designate the integers themselves to move, not their positions in the sequence.", "output": "Output the sequence after processing all the requests. Its elements are to be output, one per line, in the order in the sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n4\n2\n5\n output: 5\n2\n4\n1\n3", "input: 10 8\n1\n4\n7\n3\n4\n10\n1\n3\n output: 3\n1\n10\n4\n7\n2\n5\n6\n8\n9\n\nIn Sample Input 1, the initial sequence is (1,2,3,4,5). The first request is to move the integer 4 to the head, that is, to change the sequence to (4,1,2,3,5). The next request to move the integer 2 to the head makes the sequence (2,4,1,3,5). Finally, 5 is moved to the head, resulting in (5,2,4,1,3)."], "Pid": "p00946", "ProblemText": "Task Description: You are given an ordered sequence of integers, ($1,2,3, . . . , n$). Then, a number of requests will be given. Each request specifies an integer in the sequence. You need to move the specified integer to the head of the sequence, leaving the order of the rest untouched. Your task is to find the order of the elements in the sequence after following all the requests successively.\nTask Input: The input consists of a single test case of the following form. \n\n$n$ $m$\n$e_1$\n. . . \n$e_m$\n\nThe integer $n$ is the length of the sequence ($1 <= n <= 200000$). The integer $m$ is the number of requests ($1 <= m <= 100000$). The following $m$ lines are the requests, namely $e_1, . . . , e_m$, one per line. Each request $e_i$ ($1 <= i <= m$) is an integer between 1 and $n$, inclusive, designating the element to move. Note that, the integers designate the integers themselves to move, not their positions in the sequence.\nTask Output: Output the sequence after processing all the requests. Its elements are to be output, one per line, in the order in the sequence.\nTask Samples: input: 5 3\n4\n2\n5\n output: 5\n2\n4\n1\n3\ninput: 10 8\n1\n4\n7\n3\n4\n10\n1\n3\n output: 3\n1\n10\n4\n7\n2\n5\n6\n8\n9\n\nIn Sample Input 1, the initial sequence is (1,2,3,4,5). The first request is to move the integer 4 to the head, that is, to change the sequence to (4,1,2,3,5). The next request to move the integer 2 to the head makes the sequence (2,4,1,3,5). Finally, 5 is moved to the head, resulting in (5,2,4,1,3).\n\n" }, { "title": "Problem B\nQuality of Check Digits", "content": "The small city where you live plans to introduce a new social security number (SSN) system. Each citizen will be identified by a five-digit SSN. Its first four digits indicate the basic ID number (0000 - 9999) and the last one digit is a check digit for detecting errors.\n\nFor computing check digits, the city has decided to use an operation table. An operation table is a 10 $*$ 10 table of decimal digits whose diagonal elements are all 0. Below are two example operation tables.\n\n \n \n \nOperation Table 1\n \n      \n \nOperation Table 2\n \n \n \n\n \n      \n \n\n \n \n\nUsing an operation table, the check digit $e$ for a four-digit basic ID number $abcd$ is computed by using the following formula. Here, $i \\otimes\n j$ denotes the table element at row $i$ and column $j$. \n$e = (((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d$\n\nFor example, by using Operation Table 1 the check digit $e$ for a basic ID number $abcd = $ 2016 is computed in the following way. \n$e = (((0 \\otimes 2) \\otimes 0) \\otimes 1) \\otimes 6$\n$\\; \\; \\; = (( \\; \\; \\; \\; \\; \\; \\; \\; \\; 1 \\otimes 0) \\otimes 1) \\otimes 6$\n$\\; \\; \\; = ( \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; 7 \\otimes 1) \\otimes 6$\n$\\; \\; \\; = \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; 9 \\otimes 6$\n$\\; \\; \\; = \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; 6$\nThus, the SSN is 20166.\n\nNote that the check digit depends on the operation table used. With Operation Table 2, we have $e = $ 3 for the same basic ID number 2016, and the whole SSN will be 20163.\nFigure B. 1. Two kinds of common human errors\n\nThe purpose of adding the check digit is to detect human errors in writing/typing SSNs. The following check function can detect certain human errors. For a five-digit number $abcde$, the check function is defined as follows.\n\ncheck($abcde$) $ = ((((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d) \\otimes e$\n\nThis function returns 0 for a correct SSN. This is because every diagonal element in an operation table is 0 and for a correct SSN we have $e = (((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d$: \n\ncheck($abcde$) $ = ((((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d) \\otimes e = e \\otimes e = 0$\n\nOn the other hand, a non-zero value returned by check indicates that the given number cannot be a correct SSN. Note that, depending on the operation table used, check function may return 0 for an incorrect SSN. Kinds of errors detected depends on the operation table used; the table decides the quality of error detection.\n\nThe city authority wants to detect two kinds of common human errors on digit sequences: altering one single digit and transposing two adjacent digits, as shown in Figure B. 1. \n\nAn operation table is good if it can detect all the common errors of the two kinds on all SSNs made from four-digit basic ID numbers 0000{9999. Note that errors with the check digit, as well as with four basic ID digits, should be detected. For example, Operation Table 1 is good. Operation Table 2 is not good because, for 20613, which is a number obtained by transposing the 3rd and the 4th digits of a correct SSN 20163, check(20613) is 0. Actually, among 10000 basic ID numbers, Operation Table 2 cannot detect one or more common errors for as many as 3439 basic ID numbers.\n\nGiven an operation table, decide how good it is by counting the number of basic ID numbers for which the given table cannot detect one or more common errors.", "constraint": "", "input": "The input consists of a single test case of the following format. \n\n$x_{00}$ $x_{01}$ . . . $x_{09}$\n. . . \n$x_{90}$ $x_{91}$ . . . $x_{99}$\n\nThe input describes an operation table with $x_{ij}$ being the decimal digit at row $i$ and column $j$. Each line corresponds to a row of the table, in which elements are separated by a single space. The diagonal elements $x_{ii}$ ($i = 0, . . . , 9$) are always 0.", "output": "Output the number of basic ID numbers for which the given table cannot detect one or more common human errors.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 3 1 7 5 9 8 6 4 2\n7 0 9 2 1 5 4 8 6 3\n4 2 0 6 8 7 1 3 5 9\n1 7 5 0 9 8 3 4 2 6\n6 1 2 3 0 4 5 9 7 8\n3 6 7 4 2 0 9 5 8 1\n5 8 6 9 7 2 0 1 3 4\n8 9 4 5 3 6 2 0 1 7\n9 4 3 8 6 1 7 2 0 5\n2 5 8 1 4 3 6 7 9 0\n output: 0", "input: 0 1 2 3 4 5 6 7 8 9\n9 0 1 2 3 4 5 6 7 8\n8 9 0 1 2 3 4 5 6 7\n7 8 9 0 1 2 3 4 5 6\n6 7 8 9 0 1 2 3 4 5\n5 6 7 8 9 0 1 2 3 4\n4 5 6 7 8 9 0 1 2 3\n3 4 5 6 7 8 9 0 1 2\n2 3 4 5 6 7 8 9 0 1\n1 2 3 4 5 6 7 8 9 0\n output: 3439", "input: 0 9 8 7 6 5 4 3 2 1\n1 0 9 8 7 6 5 4 3 2\n2 1 0 9 8 7 6 5 4 3\n3 2 1 0 9 8 7 6 5 4\n4 3 2 1 0 9 8 7 6 5\n5 4 3 2 1 0 9 8 7 6\n6 5 4 3 2 1 0 9 8 7\n7 6 5 4 3 2 1 0 9 8\n8 7 6 5 4 3 2 1 0 9\n9 8 7 6 5 4 3 2 1 0\n output: 9995", "input: 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 10000"], "Pid": "p00947", "ProblemText": "Task Description: The small city where you live plans to introduce a new social security number (SSN) system. Each citizen will be identified by a five-digit SSN. Its first four digits indicate the basic ID number (0000 - 9999) and the last one digit is a check digit for detecting errors.\n\nFor computing check digits, the city has decided to use an operation table. An operation table is a 10 $*$ 10 table of decimal digits whose diagonal elements are all 0. Below are two example operation tables.\n\n \n \n \nOperation Table 1\n \n      \n \nOperation Table 2\n \n \n \n\n \n      \n \n\n \n \n\nUsing an operation table, the check digit $e$ for a four-digit basic ID number $abcd$ is computed by using the following formula. Here, $i \\otimes\n j$ denotes the table element at row $i$ and column $j$. \n$e = (((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d$\n\nFor example, by using Operation Table 1 the check digit $e$ for a basic ID number $abcd = $ 2016 is computed in the following way. \n$e = (((0 \\otimes 2) \\otimes 0) \\otimes 1) \\otimes 6$\n$\\; \\; \\; = (( \\; \\; \\; \\; \\; \\; \\; \\; \\; 1 \\otimes 0) \\otimes 1) \\otimes 6$\n$\\; \\; \\; = ( \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; 7 \\otimes 1) \\otimes 6$\n$\\; \\; \\; = \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; 9 \\otimes 6$\n$\\; \\; \\; = \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; \\; 6$\nThus, the SSN is 20166.\n\nNote that the check digit depends on the operation table used. With Operation Table 2, we have $e = $ 3 for the same basic ID number 2016, and the whole SSN will be 20163.\nFigure B. 1. Two kinds of common human errors\n\nThe purpose of adding the check digit is to detect human errors in writing/typing SSNs. The following check function can detect certain human errors. For a five-digit number $abcde$, the check function is defined as follows.\n\ncheck($abcde$) $ = ((((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d) \\otimes e$\n\nThis function returns 0 for a correct SSN. This is because every diagonal element in an operation table is 0 and for a correct SSN we have $e = (((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d$: \n\ncheck($abcde$) $ = ((((0 \\otimes a) \\otimes b) \\otimes c) \\otimes d) \\otimes e = e \\otimes e = 0$\n\nOn the other hand, a non-zero value returned by check indicates that the given number cannot be a correct SSN. Note that, depending on the operation table used, check function may return 0 for an incorrect SSN. Kinds of errors detected depends on the operation table used; the table decides the quality of error detection.\n\nThe city authority wants to detect two kinds of common human errors on digit sequences: altering one single digit and transposing two adjacent digits, as shown in Figure B. 1. \n\nAn operation table is good if it can detect all the common errors of the two kinds on all SSNs made from four-digit basic ID numbers 0000{9999. Note that errors with the check digit, as well as with four basic ID digits, should be detected. For example, Operation Table 1 is good. Operation Table 2 is not good because, for 20613, which is a number obtained by transposing the 3rd and the 4th digits of a correct SSN 20163, check(20613) is 0. Actually, among 10000 basic ID numbers, Operation Table 2 cannot detect one or more common errors for as many as 3439 basic ID numbers.\n\nGiven an operation table, decide how good it is by counting the number of basic ID numbers for which the given table cannot detect one or more common errors.\nTask Input: The input consists of a single test case of the following format. \n\n$x_{00}$ $x_{01}$ . . . $x_{09}$\n. . . \n$x_{90}$ $x_{91}$ . . . $x_{99}$\n\nThe input describes an operation table with $x_{ij}$ being the decimal digit at row $i$ and column $j$. Each line corresponds to a row of the table, in which elements are separated by a single space. The diagonal elements $x_{ii}$ ($i = 0, . . . , 9$) are always 0.\nTask Output: Output the number of basic ID numbers for which the given table cannot detect one or more common human errors.\nTask Samples: input: 0 3 1 7 5 9 8 6 4 2\n7 0 9 2 1 5 4 8 6 3\n4 2 0 6 8 7 1 3 5 9\n1 7 5 0 9 8 3 4 2 6\n6 1 2 3 0 4 5 9 7 8\n3 6 7 4 2 0 9 5 8 1\n5 8 6 9 7 2 0 1 3 4\n8 9 4 5 3 6 2 0 1 7\n9 4 3 8 6 1 7 2 0 5\n2 5 8 1 4 3 6 7 9 0\n output: 0\ninput: 0 1 2 3 4 5 6 7 8 9\n9 0 1 2 3 4 5 6 7 8\n8 9 0 1 2 3 4 5 6 7\n7 8 9 0 1 2 3 4 5 6\n6 7 8 9 0 1 2 3 4 5\n5 6 7 8 9 0 1 2 3 4\n4 5 6 7 8 9 0 1 2 3\n3 4 5 6 7 8 9 0 1 2\n2 3 4 5 6 7 8 9 0 1\n1 2 3 4 5 6 7 8 9 0\n output: 3439\ninput: 0 9 8 7 6 5 4 3 2 1\n1 0 9 8 7 6 5 4 3 2\n2 1 0 9 8 7 6 5 4 3\n3 2 1 0 9 8 7 6 5 4\n4 3 2 1 0 9 8 7 6 5\n5 4 3 2 1 0 9 8 7 6\n6 5 4 3 2 1 0 9 8 7\n7 6 5 4 3 2 1 0 9 8\n8 7 6 5 4 3 2 1 0 9\n9 8 7 6 5 4 3 2 1 0\n output: 9995\ninput: 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n output: 10000\n\n" }, { "title": "Problem C\nDistribution Center", "content": "The factory of the Impractically Complicated Products Corporation has many manufacturing lines and the same number of corresponding storage rooms. The same number of conveyor lanes are laid out in parallel to transfer goods from manufacturing lines directly to the corresponding storage rooms. Now, they plan to install a number of robot arms here and there between pairs of adjacent conveyor lanes so that goods in one of the lanes can be picked up and released down on the other, and also in the opposite way. This should allow mixing up goods from different manufacturing lines to the storage rooms.\n\nDepending on the positions of robot arms, the goods from each of the manufacturing lines can only be delivered to some of the storage rooms. Your task is to find the number of manufacturing lines from which goods can be transferred to each of the storage rooms, given the number of conveyor lanes and positions of robot arms.", "constraint": "", "input": "The input consists of a single test case, formatted as follows. \n\n$n$ $m$\n$x_1$ $y_1$\n. . . \n$x_m$ $y_m$\n\nAn integer $n$ ($2 <= n <= 200000$) in the first line is the number of conveyor lanes. The lanes are numbered from 1 to $n$, and two lanes with their numbers differing with 1 are adjacent. All of them start from the position $x = 0$ and end at $x = 100000$. The other integer $m$ ($1 <= m < 100000$) is the number of robot arms.\n\nThe following $m$ lines indicate the positions of the robot arms by two integers $x_i$ ($0 < x_i < 100000$) and $y_i$ ($1 <= y_i < n$). Here, $x_i$ is the x-coordinate of the $i$-th robot arm, which can pick goods on either the lane $y_i$ or the lane $y_i + 1$ at position $x = x_i$, and then release them on the other at the same x-coordinate.\n\nYou can assume that positions of no two robot arms have the same $x$-coordinate, that is, $x_i \\ne x_j$ for any $i \\ne j$.\nFigure C. 1. Illustration of Sample Input 1", "output": "Output $n$ integers separated by a space in one line. The $i$-th integer is the number of the manufacturing lines from which the storage room connected to the conveyor lane $i$ can accept goods.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 3\n1000 1\n2000 2\n3000 3\n output: 2 3 4 4", "input: 4 3\n1 1\n3 2\n2 3\n output: 2 4 4 2"], "Pid": "p00948", "ProblemText": "Task Description: The factory of the Impractically Complicated Products Corporation has many manufacturing lines and the same number of corresponding storage rooms. The same number of conveyor lanes are laid out in parallel to transfer goods from manufacturing lines directly to the corresponding storage rooms. Now, they plan to install a number of robot arms here and there between pairs of adjacent conveyor lanes so that goods in one of the lanes can be picked up and released down on the other, and also in the opposite way. This should allow mixing up goods from different manufacturing lines to the storage rooms.\n\nDepending on the positions of robot arms, the goods from each of the manufacturing lines can only be delivered to some of the storage rooms. Your task is to find the number of manufacturing lines from which goods can be transferred to each of the storage rooms, given the number of conveyor lanes and positions of robot arms.\nTask Input: The input consists of a single test case, formatted as follows. \n\n$n$ $m$\n$x_1$ $y_1$\n. . . \n$x_m$ $y_m$\n\nAn integer $n$ ($2 <= n <= 200000$) in the first line is the number of conveyor lanes. The lanes are numbered from 1 to $n$, and two lanes with their numbers differing with 1 are adjacent. All of them start from the position $x = 0$ and end at $x = 100000$. The other integer $m$ ($1 <= m < 100000$) is the number of robot arms.\n\nThe following $m$ lines indicate the positions of the robot arms by two integers $x_i$ ($0 < x_i < 100000$) and $y_i$ ($1 <= y_i < n$). Here, $x_i$ is the x-coordinate of the $i$-th robot arm, which can pick goods on either the lane $y_i$ or the lane $y_i + 1$ at position $x = x_i$, and then release them on the other at the same x-coordinate.\n\nYou can assume that positions of no two robot arms have the same $x$-coordinate, that is, $x_i \\ne x_j$ for any $i \\ne j$.\nFigure C. 1. Illustration of Sample Input 1\nTask Output: Output $n$ integers separated by a space in one line. The $i$-th integer is the number of the manufacturing lines from which the storage room connected to the conveyor lane $i$ can accept goods.\nTask Samples: input: 4 3\n1000 1\n2000 2\n3000 3\n output: 2 3 4 4\ninput: 4 3\n1 1\n3 2\n2 3\n output: 2 4 4 2\n\n" }, { "title": "Problem D\nHidden Anagrams", "content": "An anagram is a word or a phrase that is formed by rearranging the letters of another. For instance, by rearranging the letters of \"William Shakespeare, \" we can have its anagrams \"I am a weakish speller, \" \"I'll make a wise phrase, \" and so on. Note that when $A$ is an anagram of $B$, $B$ is an anagram of $A$.\n\nIn the above examples, differences in letter cases are ignored, and word spaces and punctuation symbols are freely inserted and/or removed. These rules are common but not applied here; only exact matching of the letters is considered.\n\nFor two strings $s_1$ and $s_2$ of letters, if a substring $s'_1$ of $s_1$ is an anagram of a substring $s'_2$ of $s_2$, we call $s'_1$ a hidden anagram of the two strings, $s_1$ and $s_2$. Of course, $s'_2$ is also a hidden anagram of them.\n\nYour task is to write a program that, for given two strings, computes the length of the longest hidden anagrams of them.\n\nSuppose, for instance, that \"anagram\" and \"grandmother\" are given. Their substrings \"nagr\" and \"gran\" are hidden anagrams since by moving letters you can have one from the other. They are the longest since any substrings of \"grandmother\" of lengths five or more must contain \"d\" or \"o\" that \"anagram\" does not. In this case, therefore, the length of the longest hidden anagrams is four. Note that a substring must be a sequence of letters occurring consecutively in the original string and so \"nagrm\" and \"granm\" are not hidden anagrams.", "constraint": "", "input": "The input consists of a single test case in two lines. \n\n$s_1$\n$s_2$\n\n$s_1$ and $s_2$ are strings consisting of lowercase letters (a through z) and their lengths are between 1 and 4000, inclusive.", "output": "Output the length of the longest hidden anagrams of $s_1$ and $s_2$. If there are no hidden anagrams, print a zero.", "content_img": false, "lang": "en", "error": false, "samples": ["input: anagram\ngrandmother\n output: 4", "input: williamshakespeare\niamaweakishspeller\n output: 18", "input: aaaaaaaabbbbbbbb\nxxxxxabababxxxxxabab\n output: 6", "input: abababacdcdcd\nefefefghghghghgh\n output: 0"], "Pid": "p00949", "ProblemText": "Task Description: An anagram is a word or a phrase that is formed by rearranging the letters of another. For instance, by rearranging the letters of \"William Shakespeare, \" we can have its anagrams \"I am a weakish speller, \" \"I'll make a wise phrase, \" and so on. Note that when $A$ is an anagram of $B$, $B$ is an anagram of $A$.\n\nIn the above examples, differences in letter cases are ignored, and word spaces and punctuation symbols are freely inserted and/or removed. These rules are common but not applied here; only exact matching of the letters is considered.\n\nFor two strings $s_1$ and $s_2$ of letters, if a substring $s'_1$ of $s_1$ is an anagram of a substring $s'_2$ of $s_2$, we call $s'_1$ a hidden anagram of the two strings, $s_1$ and $s_2$. Of course, $s'_2$ is also a hidden anagram of them.\n\nYour task is to write a program that, for given two strings, computes the length of the longest hidden anagrams of them.\n\nSuppose, for instance, that \"anagram\" and \"grandmother\" are given. Their substrings \"nagr\" and \"gran\" are hidden anagrams since by moving letters you can have one from the other. They are the longest since any substrings of \"grandmother\" of lengths five or more must contain \"d\" or \"o\" that \"anagram\" does not. In this case, therefore, the length of the longest hidden anagrams is four. Note that a substring must be a sequence of letters occurring consecutively in the original string and so \"nagrm\" and \"granm\" are not hidden anagrams.\nTask Input: The input consists of a single test case in two lines. \n\n$s_1$\n$s_2$\n\n$s_1$ and $s_2$ are strings consisting of lowercase letters (a through z) and their lengths are between 1 and 4000, inclusive.\nTask Output: Output the length of the longest hidden anagrams of $s_1$ and $s_2$. If there are no hidden anagrams, print a zero.\nTask Samples: input: anagram\ngrandmother\n output: 4\ninput: williamshakespeare\niamaweakishspeller\n output: 18\ninput: aaaaaaaabbbbbbbb\nxxxxxabababxxxxxabab\n output: 6\ninput: abababacdcdcd\nefefefghghghghgh\n output: 0\n\n" }, { "title": "Problem E\nInfallibly Crack Perplexing Cryptarithm", "content": "You are asked to crack an encrypted equation over binary numbers.\n\n The original equation consists only of binary digits (\"0\" and \"1\"), operator symbols (\"+\", \"-\", and \"*\"), parentheses (\"(\" and \")\"), and an equal sign (\"=\"). The encryption replaces some occurrences of characters in an original arithmetic equation by letters. Occurrences of one character are replaced, if ever, by the same letter. Occurrences of two different characters are never replaced by the same letter. Note that the encryption does not always replace all the occurrences of the same character; some of its occurrences may be replaced while others may be left as they are. Some characters may be left unreplaced. Any character in the Roman alphabet, in either lowercase or uppercase, may be used as a replacement letter. Note that cases are significant, that is, \"a\" and \"A\" are different letters. Note that not only digits but also operator symbols, parentheses and even the equal sign are possibly replaced.\n\n The arithmetic equation is derived from the start symbol of $Q$ of the following context-free grammar. \n $Q : : = E=E$\n $E : : = T | E+T | E-T$\n $T : : = F | T*F $\n $F : : = N | -F | (E) $\n $N : : = 0 | 1B $\n $B : : = \\epsilon | 0B | 1B$\n\nHere, $\\epsilon$ means empty.\n\n As shown in this grammar, the arithmetic equation should have one equal sign. Each side of the equation is an expression consisting of numbers, additions, subtractions, multiplications, and negations. Multiplication has precedence over both addition and subtraction, while negation precedes multiplication. Multiplication, addition and subtraction are left associative. For example, x-y+z means (x-y)+z, not x-(y+z). Numbers are in binary notation, represented by a sequence of binary digits, 0 and 1. Multi-digit numbers always start with 1. Parentheses and negations may appear redundantly in the equation, as in ((--x+y))+z.\n\nWrite a program that, for a given encrypted equation, counts the number of different possible original correct equations. Here, an equation should conform to the grammar and it is correct when the computed values of the both sides are equal.\n\n For Sample Input 1, C must be = because any equation has one = between two expressions. Then, because A and M should be different, although there are equations conforming to the grammar, none of them can be correct.\n\n For Sample Input 2, the only possible correct equation is -0=0.\n\nFor Sample Input 3 (B-A-Y-L-zero-R), there are three different correct equations, 0=-(0), 0=(-0), and -0=(0). Note that one of the two occurrences of zero is not replaced with a letter in the encrypted equation.", "constraint": "", "input": "The input consists of a single test case which is a string of Roman alphabet characters, binary digits, operator symbols, parentheses and equal signs. The input string has at most 31 characters.", "output": "Print in a line the number of correct equations that can be encrypted into the input string.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ACM\n output: 0", "input: icpc\n output: 1", "input: BAYL0R\n output: 3", "input: -AB+AC-A\n output: 1", "input: abcdefghi\n output: 0", "input: 111-10=1+10*10\n output: 1", "input: 0=10-1\n output: 0"], "Pid": "p00950", "ProblemText": "Task Description: You are asked to crack an encrypted equation over binary numbers.\n\n The original equation consists only of binary digits (\"0\" and \"1\"), operator symbols (\"+\", \"-\", and \"*\"), parentheses (\"(\" and \")\"), and an equal sign (\"=\"). The encryption replaces some occurrences of characters in an original arithmetic equation by letters. Occurrences of one character are replaced, if ever, by the same letter. Occurrences of two different characters are never replaced by the same letter. Note that the encryption does not always replace all the occurrences of the same character; some of its occurrences may be replaced while others may be left as they are. Some characters may be left unreplaced. Any character in the Roman alphabet, in either lowercase or uppercase, may be used as a replacement letter. Note that cases are significant, that is, \"a\" and \"A\" are different letters. Note that not only digits but also operator symbols, parentheses and even the equal sign are possibly replaced.\n\n The arithmetic equation is derived from the start symbol of $Q$ of the following context-free grammar. \n $Q : : = E=E$\n $E : : = T | E+T | E-T$\n $T : : = F | T*F $\n $F : : = N | -F | (E) $\n $N : : = 0 | 1B $\n $B : : = \\epsilon | 0B | 1B$\n\nHere, $\\epsilon$ means empty.\n\n As shown in this grammar, the arithmetic equation should have one equal sign. Each side of the equation is an expression consisting of numbers, additions, subtractions, multiplications, and negations. Multiplication has precedence over both addition and subtraction, while negation precedes multiplication. Multiplication, addition and subtraction are left associative. For example, x-y+z means (x-y)+z, not x-(y+z). Numbers are in binary notation, represented by a sequence of binary digits, 0 and 1. Multi-digit numbers always start with 1. Parentheses and negations may appear redundantly in the equation, as in ((--x+y))+z.\n\nWrite a program that, for a given encrypted equation, counts the number of different possible original correct equations. Here, an equation should conform to the grammar and it is correct when the computed values of the both sides are equal.\n\n For Sample Input 1, C must be = because any equation has one = between two expressions. Then, because A and M should be different, although there are equations conforming to the grammar, none of them can be correct.\n\n For Sample Input 2, the only possible correct equation is -0=0.\n\nFor Sample Input 3 (B-A-Y-L-zero-R), there are three different correct equations, 0=-(0), 0=(-0), and -0=(0). Note that one of the two occurrences of zero is not replaced with a letter in the encrypted equation.\nTask Input: The input consists of a single test case which is a string of Roman alphabet characters, binary digits, operator symbols, parentheses and equal signs. The input string has at most 31 characters.\nTask Output: Print in a line the number of correct equations that can be encrypted into the input string.\nTask Samples: input: ACM\n output: 0\ninput: icpc\n output: 1\ninput: BAYL0R\n output: 3\ninput: -AB+AC-A\n output: 1\ninput: abcdefghi\n output: 0\ninput: 111-10=1+10*10\n output: 1\ninput: 0=10-1\n output: 0\n\n" }, { "title": "Problem F\nThree Kingdoms of Bourdelot", "content": "You are an archaeologist at the Institute for Cryptic Pedigree Charts, specialized in the study of the ancient Three Kingdoms of Bourdelot. One day, you found a number of documents on the dynasties of the Three Kingdoms of Bourdelot during excavation of an ancient ruin. Since the early days of the Kingdoms of Bourdelot are veiled in mystery and even the names of many kings and queens are lost in history, the documents are expected to reveal the blood relationship of the ancient dynasties.\n\n The documents have lines, each of which consists of a pair of names, presumably of ancient royal family members. An example of a document with two lines follows.\n\nAlice Bob\nBob Clare\n\n Lines should have been complete sentences, but the documents are heavily damaged and therefore you can read only two names per line. At first, you thought that all of those lines described the true ancestor relations, but you found that would lead to contradiction. Later, you found that some documents should be interpreted negatively in order to understand the ancestor relations without contradiction. Formally, a document should be interpreted either as a positive document or as a negative document.\n\n In a positive document, the person on the left in each line is an ancestor of the person on the right in the line. If the document above is a positive document, it should be interpreted as \"Alice is an ancestor of Bob, and Bob is an ancestor of Clare\".\n \n\n In a negative document, the person on the left in each line is NOT an ancestor of the person on the right in the line. If the document above is a negative document, it should be interpreted as \"Alice is NOT an ancestor of Bob, and Bob is NOT an ancestor of Clare\".\n \n A single document can never be a mixture of positive and negative parts. The document above can never read \"Alice is an ancestor of Bob, and Bob is NOT an ancestor of Clare\".\n\n You also found that there can be ancestor-descendant pairs that didn't directly appear in the documents but can be inferred by the following rule: For any persons $x$, $y$ and $z$, if $x$ is an ancestor of $y$ and $y$ is an ancestor of $z$, then $x$ is an ancestor of $z$. For example, if the document above is a positive document, then the ancestor-descendant pair of \"Alice Clare\" is inferred.\n\n You are interested in the ancestry relationship of two royal family members. Unfortunately, the interpretation of the documents, that is, which are positive and which are negative, is unknown. Given a set of documents and two distinct names $p$ and $q$, your task is to find an interpretation of the documents that does not contradict with the hypothesis that $p$ is an ancestor of $q$. An interpretation of the documents contradicts with the hypothesis if and only if there exist persons $x$ and $y$ such that we can infer from the interpretation of the documents and the hypothesis that\n\n $x$ is an ancestor of $y$ and $y$ is an ancestor of $x$, or\n\n $x$ is an ancestor of $y$ and $x$ is not an ancestor of $y$.\n We are sure that every person mentioned in the documents had a unique single name, i. e. , no two persons have the same name and one person is never mentioned with different names.\n\n When a person A is an ancestor of another person B, the person A can be a parent, a grandparent, a great-grandparent, or so on, of the person B. Also, there can be persons or ancestor-descendant pairs that do not appear in the documents. For example, for a family tree shown in Figure F. 1, there can be a positive document:\n\nA H\nB H\nD H\nF H\nE I\n\n where persons C and G do not appear, and the ancestor-descendant pairs such as \"A E\", \"D F\", and \"C I\" do not appear.\nFigure F. 1. A Family Tree", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$p$ $q$\n$n$\n$c_1$\n. \n. \n. \n$c_n$\n\n The first line of a test case consists of two distinct names, $p$ and $q$, separated by a space. The second line of a test case consists of a single integer $n$ that indicates the number of documents. Then the descriptions of $n$ documents follow.\n\n The description of the $i$-th document $c_i$ is formatted as follows: \n\n $m_i$\n $x_{i, 1}$ $y_{i, 1}$\n . \n . \n . \n $x_{i, m_i}$ $y_{i, m_i}$\n\n The first line consists of a single integer $m_i$ that indicates the number of pairs of names in the document. Each of the following $m_i$ lines consists of a pair of distinct names $x_{i, j}$ and $y_{i, j}$ ($1 <= j <= m_i$), separated by a space.\n\n Each name consists of lowercase or uppercase letters and its length is between 1 and 5, inclusive.\n\n A test case satisfies the following constraints.\n\n $1 <= n <= 1000$.\n\n $1 <= m_i$.\n\n $\\sum^{n}_{i=1} m_i <= 100000$, that is, the total number of pairs of names in the documents does not exceed 100000.\n\n The number of distinct names that appear in a test case does not exceed 300.", "output": "Output \"Yes\" (without quotes) in a single line if there exists an interpretation of the documents that does not contradict with the hypothesis that $p$ is an ancestor of $q$. Output \"No\", otherwise.", "content_img": true, "lang": "en", "error": false, "samples": ["input: Alice Bob\n3\n2\nAlice Bob\nBob Clare\n2\nBob Clare\nClare David\n2\nClare David\nDavid Alice\n output: No", "input: Alice David\n3\n2\nAlice Bob\nBob Clare\n2\nBob Clare\nClare David\n2\nClare David\nDavid Alice\n output: Yes", "input: Alice Bob\n1\n2\nClare David\nDavid Clare\n output: Yes"], "Pid": "p00951", "ProblemText": "Task Description: You are an archaeologist at the Institute for Cryptic Pedigree Charts, specialized in the study of the ancient Three Kingdoms of Bourdelot. One day, you found a number of documents on the dynasties of the Three Kingdoms of Bourdelot during excavation of an ancient ruin. Since the early days of the Kingdoms of Bourdelot are veiled in mystery and even the names of many kings and queens are lost in history, the documents are expected to reveal the blood relationship of the ancient dynasties.\n\n The documents have lines, each of which consists of a pair of names, presumably of ancient royal family members. An example of a document with two lines follows.\n\nAlice Bob\nBob Clare\n\n Lines should have been complete sentences, but the documents are heavily damaged and therefore you can read only two names per line. At first, you thought that all of those lines described the true ancestor relations, but you found that would lead to contradiction. Later, you found that some documents should be interpreted negatively in order to understand the ancestor relations without contradiction. Formally, a document should be interpreted either as a positive document or as a negative document.\n\n In a positive document, the person on the left in each line is an ancestor of the person on the right in the line. If the document above is a positive document, it should be interpreted as \"Alice is an ancestor of Bob, and Bob is an ancestor of Clare\".\n \n\n In a negative document, the person on the left in each line is NOT an ancestor of the person on the right in the line. If the document above is a negative document, it should be interpreted as \"Alice is NOT an ancestor of Bob, and Bob is NOT an ancestor of Clare\".\n \n A single document can never be a mixture of positive and negative parts. The document above can never read \"Alice is an ancestor of Bob, and Bob is NOT an ancestor of Clare\".\n\n You also found that there can be ancestor-descendant pairs that didn't directly appear in the documents but can be inferred by the following rule: For any persons $x$, $y$ and $z$, if $x$ is an ancestor of $y$ and $y$ is an ancestor of $z$, then $x$ is an ancestor of $z$. For example, if the document above is a positive document, then the ancestor-descendant pair of \"Alice Clare\" is inferred.\n\n You are interested in the ancestry relationship of two royal family members. Unfortunately, the interpretation of the documents, that is, which are positive and which are negative, is unknown. Given a set of documents and two distinct names $p$ and $q$, your task is to find an interpretation of the documents that does not contradict with the hypothesis that $p$ is an ancestor of $q$. An interpretation of the documents contradicts with the hypothesis if and only if there exist persons $x$ and $y$ such that we can infer from the interpretation of the documents and the hypothesis that\n\n $x$ is an ancestor of $y$ and $y$ is an ancestor of $x$, or\n\n $x$ is an ancestor of $y$ and $x$ is not an ancestor of $y$.\n We are sure that every person mentioned in the documents had a unique single name, i. e. , no two persons have the same name and one person is never mentioned with different names.\n\n When a person A is an ancestor of another person B, the person A can be a parent, a grandparent, a great-grandparent, or so on, of the person B. Also, there can be persons or ancestor-descendant pairs that do not appear in the documents. For example, for a family tree shown in Figure F. 1, there can be a positive document:\n\nA H\nB H\nD H\nF H\nE I\n\n where persons C and G do not appear, and the ancestor-descendant pairs such as \"A E\", \"D F\", and \"C I\" do not appear.\nFigure F. 1. A Family Tree\nTask Input: The input consists of a single test case of the following format.\n\n$p$ $q$\n$n$\n$c_1$\n. \n. \n. \n$c_n$\n\n The first line of a test case consists of two distinct names, $p$ and $q$, separated by a space. The second line of a test case consists of a single integer $n$ that indicates the number of documents. Then the descriptions of $n$ documents follow.\n\n The description of the $i$-th document $c_i$ is formatted as follows: \n\n $m_i$\n $x_{i, 1}$ $y_{i, 1}$\n . \n . \n . \n $x_{i, m_i}$ $y_{i, m_i}$\n\n The first line consists of a single integer $m_i$ that indicates the number of pairs of names in the document. Each of the following $m_i$ lines consists of a pair of distinct names $x_{i, j}$ and $y_{i, j}$ ($1 <= j <= m_i$), separated by a space.\n\n Each name consists of lowercase or uppercase letters and its length is between 1 and 5, inclusive.\n\n A test case satisfies the following constraints.\n\n $1 <= n <= 1000$.\n\n $1 <= m_i$.\n\n $\\sum^{n}_{i=1} m_i <= 100000$, that is, the total number of pairs of names in the documents does not exceed 100000.\n\n The number of distinct names that appear in a test case does not exceed 300.\nTask Output: Output \"Yes\" (without quotes) in a single line if there exists an interpretation of the documents that does not contradict with the hypothesis that $p$ is an ancestor of $q$. Output \"No\", otherwise.\nTask Samples: input: Alice Bob\n3\n2\nAlice Bob\nBob Clare\n2\nBob Clare\nClare David\n2\nClare David\nDavid Alice\n output: No\ninput: Alice David\n3\n2\nAlice Bob\nBob Clare\n2\nBob Clare\nClare David\n2\nClare David\nDavid Alice\n output: Yes\ninput: Alice Bob\n1\n2\nClare David\nDavid Clare\n output: Yes\n\n" }, { "title": "Problem G\n Placing Medals on a Binary Tree", "content": "You have drawn a chart of a perfect binary tree, like one shown in Figure G. 1. The figure shows a finite tree, but, if needed, you can add more nodes beneath the leaves, making the tree arbitrarily deeper.\n Figure G. 1. A Perfect Binary Tree Chart\n\n Tree nodes are associated with their depths, defined recursively. The root has the depth of zero, and the child nodes of a node of depth d have their depths $d + 1$.\nYou also have a pile of a certain number of medals, each engraved with some number. You want to know whether the medals can be placed on the tree chart satisfying the following conditions.\n\n A medal engraved with $d$ should be on a node of depth $d$.\n\n One tree node can accommodate at most one medal.\n\n The path to the root from a node with a medal should not pass through another node with a medal.\n You have to place medals satisfying the above conditions, one by one, starting from the top of the pile down to its bottom. If there exists no placement of a medal satisfying the conditions, you have to throw it away and simply proceed to the next medal.\n\n You may have choices to place medals on different nodes. You want to find the best placement. When there are two or more placements satisfying the rule, one that places a medal upper in the pile is better. For example, when there are two placements of four medal, one that places only the top and the 2nd medal, and the other that places the top, the 3rd, and the 4th medal, the former is better.\n\nIn Sample Input 1, you have a pile of six medals engraved with 2,3,1,1,4, and 2 again respectively, from top to bottom.\n\n The first medal engraved with 2 can be placed, as shown in Figure G. 2 (A).\n\n Then the second medal engraved with 3 may be placed , as shown in Figure G. 2 (B).\n\n The third medal engraved with 1 cannot be placed if the second medal were placed as stated above, because both of the two nodes of depth 1 are along the path to the root from nodes already with a medal. Replacing the second medal satisfying the placement conditions, however, enables a placement shown in Figure G. 2 (C).\n\n The fourth medal, again engraved with 1, cannot be placed with any replacements of the three medals already placed satisfying the conditions. This medal is thus thrown away.\n\n The fifth medal engraved with 4 can be placed as shown in of Figure G. 2 (D). \n\n The last medal engraved with 2 cannot be placed on any of the nodes with whatever replacements.\n\nFigure G. 2. Medal Placements", "constraint": "", "input": "The input consists of a single test case in the format below. \n\n$n$ \n$x_1$ \n. \n. \n. \n$x_n$ \n\nThe first line has $n$, an integer representing the number of medals ($1 <= n <= 5 * 10^5$). The following $n$ lines represent the positive integers engraved on the medals. The $i$-th line of which has an integer $x_i$ ($1 <= x_i <= 10^9$) engraved on the $i$-th medal of the pile from the top.", "output": "When the best placement is chosen, for each i from 1 through n, output Yes in a line if the i-th medal is placed; otherwise, output No in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6\n2\n3\n1\n1\n4\n2\n output: Yes\nYes\nYes\nNo\nYes\nNo", "input: 10\n4\n4\n4\n4\n4\n4\n4\n4\n1\n4\n output: Yes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo"], "Pid": "p00952", "ProblemText": "Task Description: You have drawn a chart of a perfect binary tree, like one shown in Figure G. 1. The figure shows a finite tree, but, if needed, you can add more nodes beneath the leaves, making the tree arbitrarily deeper.\n Figure G. 1. A Perfect Binary Tree Chart\n\n Tree nodes are associated with their depths, defined recursively. The root has the depth of zero, and the child nodes of a node of depth d have their depths $d + 1$.\nYou also have a pile of a certain number of medals, each engraved with some number. You want to know whether the medals can be placed on the tree chart satisfying the following conditions.\n\n A medal engraved with $d$ should be on a node of depth $d$.\n\n One tree node can accommodate at most one medal.\n\n The path to the root from a node with a medal should not pass through another node with a medal.\n You have to place medals satisfying the above conditions, one by one, starting from the top of the pile down to its bottom. If there exists no placement of a medal satisfying the conditions, you have to throw it away and simply proceed to the next medal.\n\n You may have choices to place medals on different nodes. You want to find the best placement. When there are two or more placements satisfying the rule, one that places a medal upper in the pile is better. For example, when there are two placements of four medal, one that places only the top and the 2nd medal, and the other that places the top, the 3rd, and the 4th medal, the former is better.\n\nIn Sample Input 1, you have a pile of six medals engraved with 2,3,1,1,4, and 2 again respectively, from top to bottom.\n\n The first medal engraved with 2 can be placed, as shown in Figure G. 2 (A).\n\n Then the second medal engraved with 3 may be placed , as shown in Figure G. 2 (B).\n\n The third medal engraved with 1 cannot be placed if the second medal were placed as stated above, because both of the two nodes of depth 1 are along the path to the root from nodes already with a medal. Replacing the second medal satisfying the placement conditions, however, enables a placement shown in Figure G. 2 (C).\n\n The fourth medal, again engraved with 1, cannot be placed with any replacements of the three medals already placed satisfying the conditions. This medal is thus thrown away.\n\n The fifth medal engraved with 4 can be placed as shown in of Figure G. 2 (D). \n\n The last medal engraved with 2 cannot be placed on any of the nodes with whatever replacements.\n\nFigure G. 2. Medal Placements\nTask Input: The input consists of a single test case in the format below. \n\n$n$ \n$x_1$ \n. \n. \n. \n$x_n$ \n\nThe first line has $n$, an integer representing the number of medals ($1 <= n <= 5 * 10^5$). The following $n$ lines represent the positive integers engraved on the medals. The $i$-th line of which has an integer $x_i$ ($1 <= x_i <= 10^9$) engraved on the $i$-th medal of the pile from the top.\nTask Output: When the best placement is chosen, for each i from 1 through n, output Yes in a line if the i-th medal is placed; otherwise, output No in a line.\nTask Samples: input: 6\n2\n3\n1\n1\n4\n2\n output: Yes\nYes\nYes\nNo\nYes\nNo\ninput: 10\n4\n4\n4\n4\n4\n4\n4\n4\n1\n4\n output: Yes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\n\n" }, { "title": "Problem H\n Animal Companion in Maze", "content": "George, your pet monkey, has escaped, slipping the leash!\n\n George is hopping around in a maze-like building with many rooms. The doors of the rooms, if any, lead directly to an adjacent room, not through corridors. Some of the doors, however, are one-way: they can be opened only from one of their two sides.\n\n He repeats randomly picking a door he can open and moving to the room through it. You are chasing him but he is so quick that you cannot catch him easily. He never returns immediately to the room he just has come from through the same door, believing that you are behind him. If any other doors lead to the room he has just left, however, he may pick that door and go back.\n\n If he cannot open any doors except one through which he came from, voila, you can catch him there eventually.\n\n You know how rooms of the building are connected with doors, but you don't know in which room George currently is.\n\nIt takes one unit of time for George to move to an adjacent room through a door.\n\nWrite a program that computes how long it may take before George will be confined in a room. You have to find the longest time, considering all the possibilities of the room George is in initially, and all the possibilities of his choices of doors to go through.\n\n Note that, depending on the room organization, George may have possibilities to continue hopping around forever without being caught.\n\nDoors may be on the ceilings or the floors of rooms; the connection of the rooms may not be drawn as a planar graph.", "constraint": "", "input": "The input consists of a single test case, in the following format. \n\n$n$ $m$\n$x_1$ $y_1$ $w_1$\n. \n. \n. \n$x_m$ $y_m$ $w_m$\n\n The first line contains two integers $n$ ($2 <= n <= 100000$) and $m$ ($1 <= m <= 100000$), the number of rooms and doors, respectively. Next $m$ lines contain the information of doors. The $i$-th line of these contains three integers $x_i$, $y_i$ and $w_i$ ($1 <= x_i <= n, 1 <= y_i <= n, x_i \\ne y_i, w_i = 1$ or $2$), meaning that the $i$-th door connects two rooms numbered $x_i$ and $y_i$, and it is one-way from $x_i$ to $y_i$ if $w_i = 1$, two-way if $w_i = 2$.", "output": "Output the maximum number of time units after which George will be confined in a room. If George has possibilities to continue hopping around forever, output \"Infinite\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n1 2 2\n output: 1", "input: 2 2\n1 2 1\n2 1 1\n output: Infinite", "input: 6 7\n1 3 2\n3 2 1\n3 5 1\n3 6 2\n4 3 1\n4 6 1\n5 2 1\n output: 4", "input: 3 2\n1 3 1\n1 3 1\n output: 1"], "Pid": "p00953", "ProblemText": "Task Description: George, your pet monkey, has escaped, slipping the leash!\n\n George is hopping around in a maze-like building with many rooms. The doors of the rooms, if any, lead directly to an adjacent room, not through corridors. Some of the doors, however, are one-way: they can be opened only from one of their two sides.\n\n He repeats randomly picking a door he can open and moving to the room through it. You are chasing him but he is so quick that you cannot catch him easily. He never returns immediately to the room he just has come from through the same door, believing that you are behind him. If any other doors lead to the room he has just left, however, he may pick that door and go back.\n\n If he cannot open any doors except one through which he came from, voila, you can catch him there eventually.\n\n You know how rooms of the building are connected with doors, but you don't know in which room George currently is.\n\nIt takes one unit of time for George to move to an adjacent room through a door.\n\nWrite a program that computes how long it may take before George will be confined in a room. You have to find the longest time, considering all the possibilities of the room George is in initially, and all the possibilities of his choices of doors to go through.\n\n Note that, depending on the room organization, George may have possibilities to continue hopping around forever without being caught.\n\nDoors may be on the ceilings or the floors of rooms; the connection of the rooms may not be drawn as a planar graph.\nTask Input: The input consists of a single test case, in the following format. \n\n$n$ $m$\n$x_1$ $y_1$ $w_1$\n. \n. \n. \n$x_m$ $y_m$ $w_m$\n\n The first line contains two integers $n$ ($2 <= n <= 100000$) and $m$ ($1 <= m <= 100000$), the number of rooms and doors, respectively. Next $m$ lines contain the information of doors. The $i$-th line of these contains three integers $x_i$, $y_i$ and $w_i$ ($1 <= x_i <= n, 1 <= y_i <= n, x_i \\ne y_i, w_i = 1$ or $2$), meaning that the $i$-th door connects two rooms numbered $x_i$ and $y_i$, and it is one-way from $x_i$ to $y_i$ if $w_i = 1$, two-way if $w_i = 2$.\nTask Output: Output the maximum number of time units after which George will be confined in a room. If George has possibilities to continue hopping around forever, output \"Infinite\".\nTask Samples: input: 2 1\n1 2 2\n output: 1\ninput: 2 2\n1 2 1\n2 1 1\n output: Infinite\ninput: 6 7\n1 3 2\n3 2 1\n3 5 1\n3 6 2\n4 3 1\n4 6 1\n5 2 1\n output: 4\ninput: 3 2\n1 3 1\n1 3 1\n output: 1\n\n" }, { "title": "Problem I\n Skinny Polygon", "content": "You are asked to find a polygon that satisfies all the following conditions, given two integers, $x_{bb}$ and $y_{bb}$.\n\n The number of vertices is either 3 or 4.\n\n Edges of the polygon do not intersect nor overlap with other edges, i. e. , they do not share any points with other edges except for their endpoints.\n\n The $x$- and $y$-coordinates of each vertex are integers. \n\n The $x$-coordinate of each vertex is between 0 and $x_{bb}$, inclusive. Similarly, the $y$-coordinate is between 0 and $y_{bb}$, inclusive.\n\n At least one vertex has its $x$-coordinate 0.\n\n At least one vertex has its $x$-coordinate $x_{bb}$.\n\n At least one vertex has its $y$-coordinate 0.\n\n At least one vertex has its $y$-coordinate $y_{bb}$.\n\n The area of the polygon does not exceed 25000.\n The polygon may be non-convex.", "constraint": "", "input": "The input consists of multiple test cases. The first line of the input contains an integer $n$, which is the number of the test cases ($1 <= n <= 10^5$). Each of the following $n$ lines contains a test case formatted as follows. \n\n $x_{bb}$ $y_{bb}$\n\n $x_{bb}$ and $y_{bb}$ ($2 <= x_{bb} <= 10^9,2 <= y_{bb} <= 10^9$) are integers stated above.", "output": "For each test case, output description of one polygon satisfying the conditions stated above, in the following format. \n\n$v$\n$x_1$ $y_1$\n. \n. \n. \n$x_v$ $y_v$\n\nHere, $v$ is the number of vertices, and each pair of $x_i$ and $y_i$ gives the coordinates of the $i$-th vertex, $(x_i, y_i)$. The first vertex $(x_1, y_1)$ can be chosen arbitrarily, and the rest should be listed either in clockwise or in counterclockwise order.\n\nWhen more than one polygon satisfies the conditions, any one of them is acceptable. You can prove that, with the input values ranging as stated above, there is at least one polygon satisfying the conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n5 6\n1000000000 2\n output: 4\n5 6\n0 6\n0 0\n5 0\n3\n1000000000 0\n0 2\n999999999 0"], "Pid": "p00954", "ProblemText": "Task Description: You are asked to find a polygon that satisfies all the following conditions, given two integers, $x_{bb}$ and $y_{bb}$.\n\n The number of vertices is either 3 or 4.\n\n Edges of the polygon do not intersect nor overlap with other edges, i. e. , they do not share any points with other edges except for their endpoints.\n\n The $x$- and $y$-coordinates of each vertex are integers. \n\n The $x$-coordinate of each vertex is between 0 and $x_{bb}$, inclusive. Similarly, the $y$-coordinate is between 0 and $y_{bb}$, inclusive.\n\n At least one vertex has its $x$-coordinate 0.\n\n At least one vertex has its $x$-coordinate $x_{bb}$.\n\n At least one vertex has its $y$-coordinate 0.\n\n At least one vertex has its $y$-coordinate $y_{bb}$.\n\n The area of the polygon does not exceed 25000.\n The polygon may be non-convex.\nTask Input: The input consists of multiple test cases. The first line of the input contains an integer $n$, which is the number of the test cases ($1 <= n <= 10^5$). Each of the following $n$ lines contains a test case formatted as follows. \n\n $x_{bb}$ $y_{bb}$\n\n $x_{bb}$ and $y_{bb}$ ($2 <= x_{bb} <= 10^9,2 <= y_{bb} <= 10^9$) are integers stated above.\nTask Output: For each test case, output description of one polygon satisfying the conditions stated above, in the following format. \n\n$v$\n$x_1$ $y_1$\n. \n. \n. \n$x_v$ $y_v$\n\nHere, $v$ is the number of vertices, and each pair of $x_i$ and $y_i$ gives the coordinates of the $i$-th vertex, $(x_i, y_i)$. The first vertex $(x_1, y_1)$ can be chosen arbitrarily, and the rest should be listed either in clockwise or in counterclockwise order.\n\nWhen more than one polygon satisfies the conditions, any one of them is acceptable. You can prove that, with the input values ranging as stated above, there is at least one polygon satisfying the conditions.\nTask Samples: input: 2\n5 6\n1000000000 2\n output: 4\n5 6\n0 6\n0 0\n5 0\n3\n1000000000 0\n0 2\n999999999 0\n\n" }, { "title": "Problem J\nCover the Polygon with Your Disk", "content": "A convex polygon is drawn on a flat paper sheet. You are trying to place a disk in your hands to cover as large area of the polygon as possible. In other words, the intersection area of the polygon and the disk should be maximized.", "constraint": "", "input": "The input consists of a single test case, formatted as follows. All input items are integers. \n\n$n$ $r$\n$x_1$ $y_1$\n. \n. \n. \n$x_n$ $y_n$\n\n$n$ is the number of vertices of the polygon ($3 <= n <= 10$). $r$ is the radius of the disk ($1 <= r <= 100$).\n$x_i$ and $y_i$ give the coordinate values of the $i$-th vertex of the polygon ($1 <= i <= n$). Coordinate values satisfy $0 <= x_i <= 100$ and $0 <= y_i <= 100$.\n\nThe vertices are given in counterclockwise order. As stated above, the given polygon is convex. In other words, interior angles at all of its vertices are less than 180$^{\\circ}$. Note that the border of a convex polygon never crosses or touches itself.", "output": "Output the largest possible intersection area of the polygon and the disk. The answer should not have an error greater than 0.0001 ($10^{-4}$).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n0 0\n6 0\n6 6\n0 6\n output: 35.759506", "input: 3 1\n0 0\n2 1\n1 3\n output: 2.113100", "input: 3 1\n0 0\n100 1\n99 1\n output: 0.019798", "input: 4 1\n0 0\n100 10\n100 12\n0 1\n output: 3.137569", "input: 10 10\n0 0\n10 0\n20 1\n30 3\n40 6\n50 10\n60 15\n70 21\n80 28\n90 36\n output: 177.728187", "input: 10 49\n50 0\n79 10\n96 32\n96 68\n79 90\n50 100\n21 90\n4 68\n4 32\n21 10\n output: 7181.603297"], "Pid": "p00955", "ProblemText": "Task Description: A convex polygon is drawn on a flat paper sheet. You are trying to place a disk in your hands to cover as large area of the polygon as possible. In other words, the intersection area of the polygon and the disk should be maximized.\nTask Input: The input consists of a single test case, formatted as follows. All input items are integers. \n\n$n$ $r$\n$x_1$ $y_1$\n. \n. \n. \n$x_n$ $y_n$\n\n$n$ is the number of vertices of the polygon ($3 <= n <= 10$). $r$ is the radius of the disk ($1 <= r <= 100$).\n$x_i$ and $y_i$ give the coordinate values of the $i$-th vertex of the polygon ($1 <= i <= n$). Coordinate values satisfy $0 <= x_i <= 100$ and $0 <= y_i <= 100$.\n\nThe vertices are given in counterclockwise order. As stated above, the given polygon is convex. In other words, interior angles at all of its vertices are less than 180$^{\\circ}$. Note that the border of a convex polygon never crosses or touches itself.\nTask Output: Output the largest possible intersection area of the polygon and the disk. The answer should not have an error greater than 0.0001 ($10^{-4}$).\nTask Samples: input: 4 4\n0 0\n6 0\n6 6\n0 6\n output: 35.759506\ninput: 3 1\n0 0\n2 1\n1 3\n output: 2.113100\ninput: 3 1\n0 0\n100 1\n99 1\n output: 0.019798\ninput: 4 1\n0 0\n100 10\n100 12\n0 1\n output: 3.137569\ninput: 10 10\n0 0\n10 0\n20 1\n30 3\n40 6\n50 10\n60 15\n70 21\n80 28\n90 36\n output: 177.728187\ninput: 10 49\n50 0\n79 10\n96 32\n96 68\n79 90\n50 100\n21 90\n4 68\n4 32\n21 10\n output: 7181.603297\n\n" }, { "title": "Problem K\nBlack and White Boxes", "content": "Alice and Bob play the following game.\n\n There are a number of straight piles of boxes. The boxes have the same size and are painted either black or white.\n Two players, namely Alice and Bob, take their turns alternately. Who to play first is decided by a fair random draw.\n In Alice's turn, she selects a black box in one of the piles, and removes the box together with all the boxes above it, if any. If no black box to remove is left, she loses the game.\n In Bob's turn, he selects a white box in one of the piles, and removes the box together with all the boxes above it, if any. If no white box to remove is left, he loses the game. \n\nGiven an initial configuration of piles and who plays first, the game is a definite perfect information game. In such a game, one of the players has sure win provided he or she plays best. The draw for the first player, thus, essentially decides the winner.\n\nIn fact, this seemingly boring property is common with many popular games, such as chess. The chess game, however, is complicated enough to prevent thorough analyses, even by supercomputers, which leaves us rooms to enjoy playing.\n\nThis game of box piles, however, is not as complicated. The best plays may be more easily found. Thus, initial configurations should be fair, that is, giving both players chances to win. A configuration in which one player can always win, regardless of who plays first, is undesirable.\n\nYou are asked to arrange an initial configuration for this game by picking a number of piles from the given candidate set. As more complicated configuration makes the game more enjoyable, you are expected to find the configuration with the maximum number of boxes among fair ones.", "constraint": "", "input": "The input consists of a single test case, formatted as follows. \n\n$n$\n$p_1$\n. \n. \n. \n$p_n$\n\nA positive integer $n$ ($<= 40$) is the number of candidate piles. Each $p_i$ is a string of characters B and W, representing the $i$-th candidate pile. B and W mean black and white boxes, respectively. They appear in the order in the pile, from bottom to top. The number of boxes in a candidate pile does not exceed 40.", "output": "In a line the maximum possible number of boxes in a fair initial configuration consisting of some of the candidate piles. If only the empty configuration is fair, output a zero.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nB\nW\nWB\nWB\n output: 5", "input: 6\nB\nW\nWB\nWB\nBWW\nBWW\n output: 10"], "Pid": "p00956", "ProblemText": "Task Description: Alice and Bob play the following game.\n\n There are a number of straight piles of boxes. The boxes have the same size and are painted either black or white.\n Two players, namely Alice and Bob, take their turns alternately. Who to play first is decided by a fair random draw.\n In Alice's turn, she selects a black box in one of the piles, and removes the box together with all the boxes above it, if any. If no black box to remove is left, she loses the game.\n In Bob's turn, he selects a white box in one of the piles, and removes the box together with all the boxes above it, if any. If no white box to remove is left, he loses the game. \n\nGiven an initial configuration of piles and who plays first, the game is a definite perfect information game. In such a game, one of the players has sure win provided he or she plays best. The draw for the first player, thus, essentially decides the winner.\n\nIn fact, this seemingly boring property is common with many popular games, such as chess. The chess game, however, is complicated enough to prevent thorough analyses, even by supercomputers, which leaves us rooms to enjoy playing.\n\nThis game of box piles, however, is not as complicated. The best plays may be more easily found. Thus, initial configurations should be fair, that is, giving both players chances to win. A configuration in which one player can always win, regardless of who plays first, is undesirable.\n\nYou are asked to arrange an initial configuration for this game by picking a number of piles from the given candidate set. As more complicated configuration makes the game more enjoyable, you are expected to find the configuration with the maximum number of boxes among fair ones.\nTask Input: The input consists of a single test case, formatted as follows. \n\n$n$\n$p_1$\n. \n. \n. \n$p_n$\n\nA positive integer $n$ ($<= 40$) is the number of candidate piles. Each $p_i$ is a string of characters B and W, representing the $i$-th candidate pile. B and W mean black and white boxes, respectively. They appear in the order in the pile, from bottom to top. The number of boxes in a candidate pile does not exceed 40.\nTask Output: In a line the maximum possible number of boxes in a fair initial configuration consisting of some of the candidate piles. If only the empty configuration is fair, output a zero.\nTask Samples: input: 4\nB\nW\nWB\nWB\n output: 5\ninput: 6\nB\nW\nWB\nWB\nBWW\nBWW\n output: 10\n\n" }, { "title": "Problem A\n Secret of Chocolate Poles", "content": "Wendy, the master of a chocolate shop, is thinking of displaying poles of chocolate disks in the showcase. She can use three kinds of chocolate disks: white thin disks, dark thin disks, and dark thick disks. The thin disks are $1$ cm thick, and the thick disks are $k$ cm thick. Disks will be piled in glass cylinders.\n\n Each pole should satisfy the following conditions for her secret mission, which we cannot tell.\n\n A pole should consist of at least one disk.\n\n The total thickness of disks in a pole should be less than or equal to $l$ cm.\n\n The top disk and the bottom disk of a pole should be dark.\n\n A disk directly upon a white disk should be dark and vice versa.\n As examples, six side views of poles are drawn in Figure A. 1. These are the only possible side views she can make when $l = 5$ and $k = 3$.\n\n Figure A. 1. Six chocolate poles corresponding to Sample Input 1\n \n\n Your task is to count the number of distinct side views she can make for given $l$ and $k$ to help her accomplish her secret mission.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$l$ $k$\n\n Here, the maximum possible total thickness of disks in a pole is $l$ cm, and the thickness of the thick disks is $k$ cm. $l$ and $k$ are integers satisfying $1 <= l <= 100$ and $2 <= k <= 10$.", "output": "Output the number of possible distinct patterns.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 3\n output: 6", "input: 9 10\n output: 5", "input: 10 10\n output: 6", "input: 20 5\n output: 86", "input: 100 2\n output: 3626169232670"], "Pid": "p00957", "ProblemText": "Task Description: Wendy, the master of a chocolate shop, is thinking of displaying poles of chocolate disks in the showcase. She can use three kinds of chocolate disks: white thin disks, dark thin disks, and dark thick disks. The thin disks are $1$ cm thick, and the thick disks are $k$ cm thick. Disks will be piled in glass cylinders.\n\n Each pole should satisfy the following conditions for her secret mission, which we cannot tell.\n\n A pole should consist of at least one disk.\n\n The total thickness of disks in a pole should be less than or equal to $l$ cm.\n\n The top disk and the bottom disk of a pole should be dark.\n\n A disk directly upon a white disk should be dark and vice versa.\n As examples, six side views of poles are drawn in Figure A. 1. These are the only possible side views she can make when $l = 5$ and $k = 3$.\n\n Figure A. 1. Six chocolate poles corresponding to Sample Input 1\n \n\n Your task is to count the number of distinct side views she can make for given $l$ and $k$ to help her accomplish her secret mission.\nTask Input: The input consists of a single test case in the following format.\n\n$l$ $k$\n\n Here, the maximum possible total thickness of disks in a pole is $l$ cm, and the thickness of the thick disks is $k$ cm. $l$ and $k$ are integers satisfying $1 <= l <= 100$ and $2 <= k <= 10$.\nTask Output: Output the number of possible distinct patterns.\nTask Samples: input: 5 3\n output: 6\ninput: 9 10\n output: 5\ninput: 10 10\n output: 6\ninput: 20 5\n output: 86\ninput: 100 2\n output: 3626169232670\n\n" }, { "title": "Problem B\n Parallel Lines", "content": "Given an even number of distinct planar points, consider coupling all of the points into pairs. All the possible couplings are to be considered as long as all the given points are coupled to one and only one other point.\n\n When lines are drawn connecting the two points of all the coupled point pairs, some of the drawn lines can be parallel to some others. Your task is to find the maximum number of parallel line pairs considering all the possible couplings of the points.\n\n For the case given in the first sample input with four points, there are three patterns of point couplings as shown in Figure B. 1. The numbers of parallel line pairs are 0,0, and 1, from the left. So the maximum is 1.\nFigure B. 1. All three possible couplings for Sample Input 1\n\n For the case given in the second sample input with eight points, the points can be coupled as shown in Figure B. 2. With such a point pairing, all four lines are parallel to one another. In other words, the six line pairs $(L_1, L_2)$, $(L_1, L_3)$, $(L_1, L_4)$, $(L_2, L_3)$, $(L_2, L_4)$ and $(L_3, L_4)$ are parallel. So the maximum number of parallel line pairs, in this case, is 6.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$m$\n$x_1$ $y_1$\n. . .\n$x_m$ $y_m$\n Figure B. 2. Maximizing the number of parallel line pairs for Sample Input 2\n\n The first line contains an even integer $m$, which is the number of points ($2 <= m <= 16$). Each of the following $m$ lines gives the coordinates of a point. Integers $x_i$ and $y_i$ ($-1000 <= x_i <= 1000, -1000 <= y_i <= 1000$) in the $i$-th line of them give the $x$- and $y$-coordinates, respectively, of the $i$-th point.\n\n The positions of points are all different, that is, $x_i \\ne x_j$ or $y_i \\ne y_j$ holds for all $i \\ne j$. Furthermore, No three points lie on a single line.", "output": "Output the maximum possible number of parallel line pairs stated above, in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n1 1\n0 2\n2 4\n output: 1", "input: 8\n0 0\n0 5\n2 2\n2 7\n3 -2\n5 0\n4 -2\n8 2\n output: 6", "input: 6\n0 0\n0 5\n3 -2\n3 5\n5 0\n5 7\n output: 3", "input: 2\n-1000 1000\n1000 -1000\n output: 0", "input: 16\n327 449\n-509 761\n-553 515\n360 948\n147 877\n-694 468\n241 320\n463 -753\n-206 -991\n473 -738\n-156 -916\n-215 54\n-112 -476\n-452 780\n-18 -335\n-146 77\n output: 12"], "Pid": "p00958", "ProblemText": "Task Description: Given an even number of distinct planar points, consider coupling all of the points into pairs. All the possible couplings are to be considered as long as all the given points are coupled to one and only one other point.\n\n When lines are drawn connecting the two points of all the coupled point pairs, some of the drawn lines can be parallel to some others. Your task is to find the maximum number of parallel line pairs considering all the possible couplings of the points.\n\n For the case given in the first sample input with four points, there are three patterns of point couplings as shown in Figure B. 1. The numbers of parallel line pairs are 0,0, and 1, from the left. So the maximum is 1.\nFigure B. 1. All three possible couplings for Sample Input 1\n\n For the case given in the second sample input with eight points, the points can be coupled as shown in Figure B. 2. With such a point pairing, all four lines are parallel to one another. In other words, the six line pairs $(L_1, L_2)$, $(L_1, L_3)$, $(L_1, L_4)$, $(L_2, L_3)$, $(L_2, L_4)$ and $(L_3, L_4)$ are parallel. So the maximum number of parallel line pairs, in this case, is 6.\nTask Input: The input consists of a single test case of the following format.\n\n$m$\n$x_1$ $y_1$\n. . .\n$x_m$ $y_m$\n Figure B. 2. Maximizing the number of parallel line pairs for Sample Input 2\n\n The first line contains an even integer $m$, which is the number of points ($2 <= m <= 16$). Each of the following $m$ lines gives the coordinates of a point. Integers $x_i$ and $y_i$ ($-1000 <= x_i <= 1000, -1000 <= y_i <= 1000$) in the $i$-th line of them give the $x$- and $y$-coordinates, respectively, of the $i$-th point.\n\n The positions of points are all different, that is, $x_i \\ne x_j$ or $y_i \\ne y_j$ holds for all $i \\ne j$. Furthermore, No three points lie on a single line.\nTask Output: Output the maximum possible number of parallel line pairs stated above, in one line.\nTask Samples: input: 4\n0 0\n1 1\n0 2\n2 4\n output: 1\ninput: 8\n0 0\n0 5\n2 2\n2 7\n3 -2\n5 0\n4 -2\n8 2\n output: 6\ninput: 6\n0 0\n0 5\n3 -2\n3 5\n5 0\n5 7\n output: 3\ninput: 2\n-1000 1000\n1000 -1000\n output: 0\ninput: 16\n327 449\n-509 761\n-553 515\n360 948\n147 877\n-694 468\n241 320\n463 -753\n-206 -991\n473 -738\n-156 -916\n-215 54\n-112 -476\n-452 780\n-18 -335\n-146 77\n output: 12\n\n" }, { "title": "Problem C\n Medical Checkup", "content": "Students of the university have to go for a medical checkup, consisting of lots of checkup items, numbered 1,2,3, and so on.\n\n Students are now forming a long queue, waiting for the checkup to start. Students are also numbered 1,2,3, and so on, from the top of the queue. They have to undergo checkup items in the order of the item numbers, not skipping any of them nor changing the order. The order of students should not be changed either.\n\n Multiple checkup items can be carried out in parallel, but each item can be carried out for only one student at a time. Students have to wait in queues of their next checkup items until all the others before them finish.\n\n Each of the students is associated with an integer value called health condition. For a student with the health condition $h$, it takes $h$ minutes to finish each of the checkup items. You may assume that no interval is needed between two students on the same checkup item or two checkup items for a single student.\n\n Your task is to find the items students are being checked up or waiting for at a specified time $t$.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$n$ $t$\n$h_1$\n. . .\n$h_n$\n\n $n$ and $t$ are integers. $n$ is the number of the students ($1 <= n <= 10^5$). $t$ specifies the time of our concern ($0 <= t <= 10^9$). For each $i$, the integer $h_i$ is the health condition of student $i$ ($1 <= h_ <= 10^9$).", "output": "Output $n$ lines each containing a single integer. The $i$-th line should contain the checkup item number of the item which the student $i$ is being checked up or is waiting for, at ($t+0.5$) minutes after the checkup starts. You may assume that all the students are yet to finish some of the checkup items at that moment.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 20\n5\n7\n3\n output: 5\n3\n2", "input: 5 1000000000\n5553\n2186\n3472\n2605\n1790\n output: 180083\n180083\n180082\n180082\n180082"], "Pid": "p00959", "ProblemText": "Task Description: Students of the university have to go for a medical checkup, consisting of lots of checkup items, numbered 1,2,3, and so on.\n\n Students are now forming a long queue, waiting for the checkup to start. Students are also numbered 1,2,3, and so on, from the top of the queue. They have to undergo checkup items in the order of the item numbers, not skipping any of them nor changing the order. The order of students should not be changed either.\n\n Multiple checkup items can be carried out in parallel, but each item can be carried out for only one student at a time. Students have to wait in queues of their next checkup items until all the others before them finish.\n\n Each of the students is associated with an integer value called health condition. For a student with the health condition $h$, it takes $h$ minutes to finish each of the checkup items. You may assume that no interval is needed between two students on the same checkup item or two checkup items for a single student.\n\n Your task is to find the items students are being checked up or waiting for at a specified time $t$.\nTask Input: The input consists of a single test case in the following format.\n\n$n$ $t$\n$h_1$\n. . .\n$h_n$\n\n $n$ and $t$ are integers. $n$ is the number of the students ($1 <= n <= 10^5$). $t$ specifies the time of our concern ($0 <= t <= 10^9$). For each $i$, the integer $h_i$ is the health condition of student $i$ ($1 <= h_ <= 10^9$).\nTask Output: Output $n$ lines each containing a single integer. The $i$-th line should contain the checkup item number of the item which the student $i$ is being checked up or is waiting for, at ($t+0.5$) minutes after the checkup starts. You may assume that all the students are yet to finish some of the checkup items at that moment.\nTask Samples: input: 3 20\n5\n7\n3\n output: 5\n3\n2\ninput: 5 1000000000\n5553\n2186\n3472\n2605\n1790\n output: 180083\n180083\n180082\n180082\n180082\n\n" }, { "title": "Problem D\n Making Perimeter of the Convex Hull Shortest", "content": "The convex hull of a set of three or more planar points is, when not all of them are on one line, the convex polygon with the smallest area that has all the points of the set on its boundary or in its inside. Your task is, given positions of the points of a set, to find how much shorter the perimeter of the convex hull can be made by excluding two points from the set.\n\n The figures below correspond to the three cases given as Sample Input 1 to 3. Encircled points are excluded to make the shortest convex hull depicted as thick dashed lines.\n \n \n \n \n \n \nSample Input 1 \nSample Input 2 \nSample Input 3", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$n$\n$x_1$ $y_1$\n. . .\n$x_n$ $y_n$\n\n Here, $n$ is the number of points in the set satisfying $5 <= n <= 10^5$. For each $i$, ($x_i, y_i$) gives the coordinates of the position of the $i$-th point in the set. $x_i$ and $y_i$ are integers between $-10^6$ and $10^6$, inclusive. All the points in the set are distinct, that is, $x_j \\ne x_k$ or $y_j \\ne y_k$ holds when $j \\ne k$. It is guaranteed that no single line goes through $n - 2$ or more points in the set.", "output": "Output the difference of the perimeter of the convex hull of the original set and the shortest of the perimeters of the convex hulls of the subsets with two points excluded from the original set. The output should not have an error greater than $10^{-4}$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10\n-53 62\n-19 58\n-11 11\n-9 -22\n45 -7\n37 -39\n47 -58\n-2 41\n-37 10\n13 42\n output: 72.96316928", "input: 10\n-53 62\n-19 58\n-11 11\n-9 -22\n45 -7\n43 -47\n47 -58\n-2 41\n-37 10\n13 42\n output: 62.62947992", "input: 10\n-53 62\n-35 47\n-11 11\n-9 -22\n45 -7\n43 -47\n47 -58\n-2 41\n-37 10\n13 42\n output: 61.58166534"], "Pid": "p00960", "ProblemText": "Task Description: The convex hull of a set of three or more planar points is, when not all of them are on one line, the convex polygon with the smallest area that has all the points of the set on its boundary or in its inside. Your task is, given positions of the points of a set, to find how much shorter the perimeter of the convex hull can be made by excluding two points from the set.\n\n The figures below correspond to the three cases given as Sample Input 1 to 3. Encircled points are excluded to make the shortest convex hull depicted as thick dashed lines.\n \n \n \n \n \n \nSample Input 1 \nSample Input 2 \nSample Input 3\nTask Input: The input consists of a single test case in the following format.\n\n$n$\n$x_1$ $y_1$\n. . .\n$x_n$ $y_n$\n\n Here, $n$ is the number of points in the set satisfying $5 <= n <= 10^5$. For each $i$, ($x_i, y_i$) gives the coordinates of the position of the $i$-th point in the set. $x_i$ and $y_i$ are integers between $-10^6$ and $10^6$, inclusive. All the points in the set are distinct, that is, $x_j \\ne x_k$ or $y_j \\ne y_k$ holds when $j \\ne k$. It is guaranteed that no single line goes through $n - 2$ or more points in the set.\nTask Output: Output the difference of the perimeter of the convex hull of the original set and the shortest of the perimeters of the convex hulls of the subsets with two points excluded from the original set. The output should not have an error greater than $10^{-4}$.\nTask Samples: input: 10\n-53 62\n-19 58\n-11 11\n-9 -22\n45 -7\n37 -39\n47 -58\n-2 41\n-37 10\n13 42\n output: 72.96316928\ninput: 10\n-53 62\n-19 58\n-11 11\n-9 -22\n45 -7\n43 -47\n47 -58\n-2 41\n-37 10\n13 42\n output: 62.62947992\ninput: 10\n-53 62\n-35 47\n-11 11\n-9 -22\n45 -7\n43 -47\n47 -58\n-2 41\n-37 10\n13 42\n output: 61.58166534\n\n" }, { "title": "Problem E\n Black or White", "content": "Here lies a row of a number of bricks each painted either black or white. With a single stroke of your brush, you can overpaint a part of the row of bricks at once with either black or white paint. Using white paint, all the black bricks in the painted part become white while originally white bricks remain white; with black paint, white bricks become black and black ones remain black. The number of bricks painted in one stroke, however, is limited because your brush cannot hold too much paint at a time. For each brush stroke, you can paint any part of the row with any number of bricks up to the limit.\n\n In the first case of the sample input, the initial colors of four bricks are black, white, white, and black. You can repaint them to white, black, black, and white with two strokes: the first stroke paints all four bricks white and the second stroke paints two bricks in the middle black.\n\n Your task is to calculate the minimum number of brush strokes needed to change the brick colors as specified. Never mind the cost of the paints.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n \n$n$ $k$\n$s$\n$t$\n\n The first line contains two integers $n$ and $k$ ($1 <= k <= n <= 500 000$). $n$ is the number of bricks in the row and $k$ is the maximum number of bricks painted in a single stroke. The second line contains a string $s$ of $n$ characters, which indicates the initial colors of the bricks. The third line contains another string $t$ of $n$ characters, which indicates the desired colors of the bricks. All the characters in both s and t are either B or W meaning black and white, respectively.", "output": "Output the minimum number of brush strokes required to repaint the bricks into the desired colors.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\nBWWB\nWBBW\n output: 2", "input: 4 3\nBWWB\nWBBW\n output: 3", "input: 4 3\nBWWW\nBWWW\n output: 0", "input: 7 1\nBBWBWBW\nWBBWWBB\n output: 4"], "Pid": "p00961", "ProblemText": "Task Description: Here lies a row of a number of bricks each painted either black or white. With a single stroke of your brush, you can overpaint a part of the row of bricks at once with either black or white paint. Using white paint, all the black bricks in the painted part become white while originally white bricks remain white; with black paint, white bricks become black and black ones remain black. The number of bricks painted in one stroke, however, is limited because your brush cannot hold too much paint at a time. For each brush stroke, you can paint any part of the row with any number of bricks up to the limit.\n\n In the first case of the sample input, the initial colors of four bricks are black, white, white, and black. You can repaint them to white, black, black, and white with two strokes: the first stroke paints all four bricks white and the second stroke paints two bricks in the middle black.\n\n Your task is to calculate the minimum number of brush strokes needed to change the brick colors as specified. Never mind the cost of the paints.\nTask Input: The input consists of a single test case formatted as follows.\n \n$n$ $k$\n$s$\n$t$\n\n The first line contains two integers $n$ and $k$ ($1 <= k <= n <= 500 000$). $n$ is the number of bricks in the row and $k$ is the maximum number of bricks painted in a single stroke. The second line contains a string $s$ of $n$ characters, which indicates the initial colors of the bricks. The third line contains another string $t$ of $n$ characters, which indicates the desired colors of the bricks. All the characters in both s and t are either B or W meaning black and white, respectively.\nTask Output: Output the minimum number of brush strokes required to repaint the bricks into the desired colors.\nTask Samples: input: 4 4\nBWWB\nWBBW\n output: 2\ninput: 4 3\nBWWB\nWBBW\n output: 3\ninput: 4 3\nBWWW\nBWWW\n output: 0\ninput: 7 1\nBBWBWBW\nWBBWWBB\n output: 4\n\n" }, { "title": "Problem F\n Pizza Delivery", "content": "Alyssa is a college student, living in New Tsukuba City. All the streets in the city are one-way. A new social experiment starting tomorrow is on alternative traffic regulation reversing the one-way directions of street sections. Reversals will be on one single street section between two adjacent intersections for each day; the directions of all the other sections will not change, and the reversal will be canceled on the next day.\n\nAlyssa orders a piece of pizza everyday from the same pizzeria. The pizza is delivered along the shortest route from the intersection with the pizzeria to the intersection with Alyssa's house.\n\n Altering the traffic regulation may change the shortest route. Please tell Alyssa how the social experiment will affect the pizza delivery route.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$n$ $m$\n$a_1$ $b_1$ $c_1$\n. . .\n$a_m$ $b_m$ $c_m$\n\n The first line contains two integers, $n$, the number of intersections, and $m$, the number of street sections in New Tsukuba City ($2 <= n <= 100 000,1 <= m <= 100 000$). The intersections are numbered $1$ through $n$ and the street sections are numbered $1$ through $m$.\n\n The following $m$ lines contain the information about the street sections, each with three integers $a_i$, $b_i$, and $c_i$ ($1 <= a_i n, 1 <= b_i <= n, a_i \\ne b_i, 1 <= c_i <= 100 000$). They mean that the street section numbered $i$ connects two intersections with the one-way direction from $a_i$ to $b_i$, which will be reversed on the $i$-th day. The street section has the length of $c_i$. Note that there may be more than one street section connecting the same pair of intersections.\n\n The pizzeria is on the intersection 1 and Alyssa's house is on the intersection 2. It is guaranteed that at least one route exists from the pizzeria to Alyssa's before the social experiment starts.", "output": "The output should contain $m$ lines. The $i$-th line should be\n\n HAPPY if the shortest route on the $i$-th day will become shorter,\n\n SOSO if the length of the shortest route on the $i$-th day will not change, and\n\n SAD if the shortest route on the $i$-th day will be longer or if there will be no route from the pizzeria to Alyssa's house.\n Alyssa doesn't mind whether the delivery bike can go back to the pizzeria or not.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n1 3 5\n3 4 6\n4 2 7\n2 1 18\n2 3 12\n output: SAD\nSAD\nSAD\nSOSO\nHAPPY", "input: 7 5\n1 3 2\n1 6 3\n4 2 4\n6 2 5\n7 5 6\n output: SOSO\nSAD\nSOSO\nSAD\nSOSO", "input: 10 14\n1 7 9\n1 8 3\n2 8 4\n2 6 11\n3 7 8\n3 4 4\n3 2 1\n3 2 7\n4 8 4\n5 6 11\n5 8 12\n6 10 6\n7 10 8\n8 3 6\n output: SOSO\nSAD\nHAPPY\nSOSO\nSOSO\nSOSO\nSAD\nSOSO\nSOSO\nSOSO\nSOSO\nSOSO\nSOSO\nSAD"], "Pid": "p00962", "ProblemText": "Task Description: Alyssa is a college student, living in New Tsukuba City. All the streets in the city are one-way. A new social experiment starting tomorrow is on alternative traffic regulation reversing the one-way directions of street sections. Reversals will be on one single street section between two adjacent intersections for each day; the directions of all the other sections will not change, and the reversal will be canceled on the next day.\n\nAlyssa orders a piece of pizza everyday from the same pizzeria. The pizza is delivered along the shortest route from the intersection with the pizzeria to the intersection with Alyssa's house.\n\n Altering the traffic regulation may change the shortest route. Please tell Alyssa how the social experiment will affect the pizza delivery route.\nTask Input: The input consists of a single test case in the following format.\n\n$n$ $m$\n$a_1$ $b_1$ $c_1$\n. . .\n$a_m$ $b_m$ $c_m$\n\n The first line contains two integers, $n$, the number of intersections, and $m$, the number of street sections in New Tsukuba City ($2 <= n <= 100 000,1 <= m <= 100 000$). The intersections are numbered $1$ through $n$ and the street sections are numbered $1$ through $m$.\n\n The following $m$ lines contain the information about the street sections, each with three integers $a_i$, $b_i$, and $c_i$ ($1 <= a_i n, 1 <= b_i <= n, a_i \\ne b_i, 1 <= c_i <= 100 000$). They mean that the street section numbered $i$ connects two intersections with the one-way direction from $a_i$ to $b_i$, which will be reversed on the $i$-th day. The street section has the length of $c_i$. Note that there may be more than one street section connecting the same pair of intersections.\n\n The pizzeria is on the intersection 1 and Alyssa's house is on the intersection 2. It is guaranteed that at least one route exists from the pizzeria to Alyssa's before the social experiment starts.\nTask Output: The output should contain $m$ lines. The $i$-th line should be\n\n HAPPY if the shortest route on the $i$-th day will become shorter,\n\n SOSO if the length of the shortest route on the $i$-th day will not change, and\n\n SAD if the shortest route on the $i$-th day will be longer or if there will be no route from the pizzeria to Alyssa's house.\n Alyssa doesn't mind whether the delivery bike can go back to the pizzeria or not.\nTask Samples: input: 4 5\n1 3 5\n3 4 6\n4 2 7\n2 1 18\n2 3 12\n output: SAD\nSAD\nSAD\nSOSO\nHAPPY\ninput: 7 5\n1 3 2\n1 6 3\n4 2 4\n6 2 5\n7 5 6\n output: SOSO\nSAD\nSOSO\nSAD\nSOSO\ninput: 10 14\n1 7 9\n1 8 3\n2 8 4\n2 6 11\n3 7 8\n3 4 4\n3 2 1\n3 2 7\n4 8 4\n5 6 11\n5 8 12\n6 10 6\n7 10 8\n8 3 6\n output: SOSO\nSAD\nHAPPY\nSOSO\nSOSO\nSOSO\nSAD\nSOSO\nSOSO\nSOSO\nSOSO\nSOSO\nSOSO\nSAD\n\n" }, { "title": "Problem G\n Rendezvous on a Tetrahedron", "content": "One day, you found two worms $P$ and $Q$ crawling on the surface of a regular tetrahedron with four vertices $A$, $B$, $C$ and $D$. Both worms started from the vertex $A$, went straight ahead, and stopped crawling after a while.\n\n When a worm reached one of the edges of the tetrahedron, it moved on to the adjacent face and kept going without changing the angle to the crossed edge (Figure G. 1).\n\n Write a program which tells whether or not $P$ and $Q$ were on the same face of the tetrahedron when they stopped crawling.\n\n You may assume that each of the worms is a point without length, area, or volume.\n Figure G. 1. Crossing an edge\n\n Incidentally, lengths of the two trails the worms left on the tetrahedron were exact integral multiples of the unit length. Here, the unit length is the edge length of the tetrahedron. Each trail is more than 0: 001 unit distant from any vertices, except for its start point and its neighborhood.\n This means that worms have crossed at least one edge. Both worms stopped at positions more than 0: 001 unit distant from any of the edges.\n\n The initial crawling direction of a worm is specified by two items: the edge $XY$ which is the first edge the worm encountered after its start, and the angle $d$ between the edge $AX$ and the direction of the worm, in degrees.\nFigure G. 2. Trails of the worms corresponding to Sample Input 1\n\n Figure G. 2 shows the case of Sample Input 1. In this case, $P$ went over the edge $CD$ and stopped on the face opposite to the vertex $A$, while $Q$ went over the edge $DB$ and also stopped on the same face.", "constraint": "", "input": "The input consists of a single test case, formatted as follows.\n\n$X_PY_P$ $d_P$ $l_P$\n$X_QY_Q$ $d_Q$ $l_Q$\n\n $X_WY_W$ ($W = P, Q$) is the first edge the worm $W$ crossed after its start. $X_WY_W$ is one of BC, CD or DB.\n\n An integer $d_W$ ($1 <= d_W <= 59$) is the angle in degrees between edge $AX_W$ and the initial direction of the worm $W$ on the face $\\triangle AX_WY_W$.\n\n An integer $l_W$ ($1 <= l_W <= 20$) is the length of the trail of worm $W$ left on the surface, in unit lengths.", "output": "Output YES when and only when the two worms stopped on the same face of the tetrahedron. Otherwise, output NO.", "content_img": true, "lang": "en", "error": false, "samples": ["input: CD 30 1\nDB 30 1\n output: YES", "input: BC 1 1\nDB 59 1\n output: YES", "input: BC 29 20\nBC 32 20\n output: NO"], "Pid": "p00963", "ProblemText": "Task Description: One day, you found two worms $P$ and $Q$ crawling on the surface of a regular tetrahedron with four vertices $A$, $B$, $C$ and $D$. Both worms started from the vertex $A$, went straight ahead, and stopped crawling after a while.\n\n When a worm reached one of the edges of the tetrahedron, it moved on to the adjacent face and kept going without changing the angle to the crossed edge (Figure G. 1).\n\n Write a program which tells whether or not $P$ and $Q$ were on the same face of the tetrahedron when they stopped crawling.\n\n You may assume that each of the worms is a point without length, area, or volume.\n Figure G. 1. Crossing an edge\n\n Incidentally, lengths of the two trails the worms left on the tetrahedron were exact integral multiples of the unit length. Here, the unit length is the edge length of the tetrahedron. Each trail is more than 0: 001 unit distant from any vertices, except for its start point and its neighborhood.\n This means that worms have crossed at least one edge. Both worms stopped at positions more than 0: 001 unit distant from any of the edges.\n\n The initial crawling direction of a worm is specified by two items: the edge $XY$ which is the first edge the worm encountered after its start, and the angle $d$ between the edge $AX$ and the direction of the worm, in degrees.\nFigure G. 2. Trails of the worms corresponding to Sample Input 1\n\n Figure G. 2 shows the case of Sample Input 1. In this case, $P$ went over the edge $CD$ and stopped on the face opposite to the vertex $A$, while $Q$ went over the edge $DB$ and also stopped on the same face.\nTask Input: The input consists of a single test case, formatted as follows.\n\n$X_PY_P$ $d_P$ $l_P$\n$X_QY_Q$ $d_Q$ $l_Q$\n\n $X_WY_W$ ($W = P, Q$) is the first edge the worm $W$ crossed after its start. $X_WY_W$ is one of BC, CD or DB.\n\n An integer $d_W$ ($1 <= d_W <= 59$) is the angle in degrees between edge $AX_W$ and the initial direction of the worm $W$ on the face $\\triangle AX_WY_W$.\n\n An integer $l_W$ ($1 <= l_W <= 20$) is the length of the trail of worm $W$ left on the surface, in unit lengths.\nTask Output: Output YES when and only when the two worms stopped on the same face of the tetrahedron. Otherwise, output NO.\nTask Samples: input: CD 30 1\nDB 30 1\n output: YES\ninput: BC 1 1\nDB 59 1\n output: YES\ninput: BC 29 20\nBC 32 20\n output: NO\n\n" }, { "title": "Problem H\n Homework", "content": "Taro is a student of Ibaraki College of Prominent Computing. In this semester, he takes two courses, mathematics and informatics. After each class, the teacher may assign homework. Taro may be given multiple assignments in a single class, and each assignment may have a different deadline. Each assignment has a unique ID number.\n\n Everyday after school, Taro completes at most one assignment as follows. First, he decides which course's homework to do at random by ipping a coin. Let $S$ be the set of all the unfinished assignments of the chosen course whose deadline has not yet passed. If $S$ is empty, he plays a video game without doing any homework on that day even if there are unfinished assignments of the other course. Otherwise, with $T \\subseteq S$ being the set of assignments with the nearest deadline among $S$, he completes the one with the smallest assignment ID among $T$.\n\n The number of assignments Taro will complete until the end of the semester depends on the result of coin ips. Given the schedule of homework assignments, your task is to compute the maximum and the minimum numbers of assignments Taro will complete.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$n$ $m$\n$s_1$ $t_1$\n. . .\n$s_n$ $t_n$\n\n The first line contains two integers $n$ and $m$ satisfying $1 <= m < n <= 400$. $n$ denotes the total number of assignments in this semester, and $m$ denotes the number of assignments of the mathematics course (so the number of assignments of the informatics course is $n - m$). Each assignment has a unique ID from $1$ to $n$; assignments with IDs $1$ through $m$ are those of the mathematics course, and the rest are of the informatics course. The next $n$ lines show the schedule of assignments. The $i$-th line of them contains two integers $s_i$ and $t_i$ satisfying $1 <= s_i <= t_i <= 400$, which means that the assignment of ID $i$ is given to Taro on the $s_i$-th day of the semester, and its deadline is the end of the $t_i$-th day.", "output": "In the first line, print the maximum number of assignments Taro will complete. In the second line, print the minimum number of assignments Taro will complete.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3\n1 2\n1 5\n2 3\n2 6\n4 5\n4 6\n output: 6\n2", "input: 6 3\n1 1\n2 3\n4 4\n1 1\n2 4\n3 3\n output: 4\n3"], "Pid": "p00964", "ProblemText": "Task Description: Taro is a student of Ibaraki College of Prominent Computing. In this semester, he takes two courses, mathematics and informatics. After each class, the teacher may assign homework. Taro may be given multiple assignments in a single class, and each assignment may have a different deadline. Each assignment has a unique ID number.\n\n Everyday after school, Taro completes at most one assignment as follows. First, he decides which course's homework to do at random by ipping a coin. Let $S$ be the set of all the unfinished assignments of the chosen course whose deadline has not yet passed. If $S$ is empty, he plays a video game without doing any homework on that day even if there are unfinished assignments of the other course. Otherwise, with $T \\subseteq S$ being the set of assignments with the nearest deadline among $S$, he completes the one with the smallest assignment ID among $T$.\n\n The number of assignments Taro will complete until the end of the semester depends on the result of coin ips. Given the schedule of homework assignments, your task is to compute the maximum and the minimum numbers of assignments Taro will complete.\nTask Input: The input consists of a single test case in the following format.\n\n$n$ $m$\n$s_1$ $t_1$\n. . .\n$s_n$ $t_n$\n\n The first line contains two integers $n$ and $m$ satisfying $1 <= m < n <= 400$. $n$ denotes the total number of assignments in this semester, and $m$ denotes the number of assignments of the mathematics course (so the number of assignments of the informatics course is $n - m$). Each assignment has a unique ID from $1$ to $n$; assignments with IDs $1$ through $m$ are those of the mathematics course, and the rest are of the informatics course. The next $n$ lines show the schedule of assignments. The $i$-th line of them contains two integers $s_i$ and $t_i$ satisfying $1 <= s_i <= t_i <= 400$, which means that the assignment of ID $i$ is given to Taro on the $s_i$-th day of the semester, and its deadline is the end of the $t_i$-th day.\nTask Output: In the first line, print the maximum number of assignments Taro will complete. In the second line, print the minimum number of assignments Taro will complete.\nTask Samples: input: 6 3\n1 2\n1 5\n2 3\n2 6\n4 5\n4 6\n output: 6\n2\ninput: 6 3\n1 1\n2 3\n4 4\n1 1\n2 4\n3 3\n output: 4\n3\n\n" }, { "title": "Problem I\n Starting a Scenic Railroad Service", "content": "Jim, working for a railroad company, is responsible for planning a new tourist train service. He is sure that the train route along a scenic valley will arise a big boom, but not quite sure how big the boom will be.\n\n A market survey was ordered and Jim has just received an estimated list of passengers' travel sections. Based on the list, he'd like to estimate the minimum number of train seats that meets the demand.\n\n Providing as many seats as all of the passengers may cost unreasonably high. Assigning the same seat to more than one passenger without overlapping travel sections may lead to a great cost cutback.\n\n Two different policies are considered on seat assignments. As the views from the train windows depend on the seat positions, it would be better if passengers can choose a seat. One possible policy (named `policy-1') is to allow the passengers to choose an arbitrary seat among all the remaining seats when they make their reservations. As the order of reservations is unknown, all the possible orders must be considered on counting the required number of seats.\n\n The other policy (named `policy-2') does not allow the passengers to choose their seats; the seat assignments are decided by the railroad operator, not by the passengers, after all the reservations are completed. This policy may reduce the number of the required seats considerably.\n\n Your task is to let Jim know how di\u000berent these two policies are by providing him a program that computes the numbers of seats required under the two seat reservation policies. Let us consider a case where there are four stations, S1, S2, S3, and S4, and four expected passengers $p_1$, $p_2$, $p_3$, and $p_4$ with the travel list below.\n\n \n \npassenger \nfrom \nto \n \n $p_1$ \n S1 \n S2 \n \n $p_2$ \n S2 \n S3 \n \n $p_3$ \n S1 \n S3 \n \n $p_4$ \n S3 \n S4 \n \n\n The travel sections of $p_1$ and $p_2$ do not overlap, that of $p_3$ overlaps those of $p_1$ and $p_2$, and that of $p_4$ does not overlap those of any others.\n\n Let's check if two seats would suffice under the policy-1. If $p_1$ books a seat first, either of the two seats can be chosen. If $p_2$ books second, as the travel section does not overlap that of $p_1$, the same seat can be booked, but the other seat may look more attractive to $p_2$. If $p_2$ reserves a seat different from that of $p_1$, there will remain no available seats for $p_3$ between S1 and S3 (Figure I. 1).\nFigure I. 1. With two seats\n\n With three seats, $p_3$ can find a seat with any seat reservation combinations by $p_1$ and $p_2$. $p_4$ can also book a seat for there are no other passengers between S3 and S4 (Figure I. 2).\nFigure I. 2. With three seats\n\n For this travel list, only three seats suffice considering all the possible reservation orders and seat preferences under the policy-1.\n\n On the other hand, deciding the seat assignments after all the reservations are completed enables a tight assignment with only two seats under the policy-2 (Figure I. 3).\nFigure I. 3. Tight assignment to two seats", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$a_1$ $b_1$\n. . .\n$a_n$ $b_n$\n\n Here, the first line has an integer $n$, the number of the passengers in the estimated list of passengers' travel sections ($1 <= n <= 200 000$). The stations are numbered starting from 1 in their order along the route. Each of the following $n$ lines describes the travel for each passenger by two integers, the boarding and the alighting station numbers, $a_i$ and $b_i$, respectively ($1 <= a_i < b_i <= 100 000$). Note that more than one passenger in the list may have the same boarding and alighting stations.", "output": "Two integers $s_1$ and $s_2$ should be output in a line in this order, separated by a space. $s_1$ and $s_2$ are the numbers of seats required under the policy-1 and -2, respectively.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1 3\n1 3\n3 6\n3 6\n output: 2 2", "input: 4\n1 2\n2 3\n1 3\n3 4\n output: 3 2", "input: 10\n84 302\n275 327\n364 538\n26 364\n29 386\n545 955\n715 965\n404 415\n903 942\n150 402\n output: 6 5"], "Pid": "p00965", "ProblemText": "Task Description: Jim, working for a railroad company, is responsible for planning a new tourist train service. He is sure that the train route along a scenic valley will arise a big boom, but not quite sure how big the boom will be.\n\n A market survey was ordered and Jim has just received an estimated list of passengers' travel sections. Based on the list, he'd like to estimate the minimum number of train seats that meets the demand.\n\n Providing as many seats as all of the passengers may cost unreasonably high. Assigning the same seat to more than one passenger without overlapping travel sections may lead to a great cost cutback.\n\n Two different policies are considered on seat assignments. As the views from the train windows depend on the seat positions, it would be better if passengers can choose a seat. One possible policy (named `policy-1') is to allow the passengers to choose an arbitrary seat among all the remaining seats when they make their reservations. As the order of reservations is unknown, all the possible orders must be considered on counting the required number of seats.\n\n The other policy (named `policy-2') does not allow the passengers to choose their seats; the seat assignments are decided by the railroad operator, not by the passengers, after all the reservations are completed. This policy may reduce the number of the required seats considerably.\n\n Your task is to let Jim know how di\u000berent these two policies are by providing him a program that computes the numbers of seats required under the two seat reservation policies. Let us consider a case where there are four stations, S1, S2, S3, and S4, and four expected passengers $p_1$, $p_2$, $p_3$, and $p_4$ with the travel list below.\n\n \n \npassenger \nfrom \nto \n \n $p_1$ \n S1 \n S2 \n \n $p_2$ \n S2 \n S3 \n \n $p_3$ \n S1 \n S3 \n \n $p_4$ \n S3 \n S4 \n \n\n The travel sections of $p_1$ and $p_2$ do not overlap, that of $p_3$ overlaps those of $p_1$ and $p_2$, and that of $p_4$ does not overlap those of any others.\n\n Let's check if two seats would suffice under the policy-1. If $p_1$ books a seat first, either of the two seats can be chosen. If $p_2$ books second, as the travel section does not overlap that of $p_1$, the same seat can be booked, but the other seat may look more attractive to $p_2$. If $p_2$ reserves a seat different from that of $p_1$, there will remain no available seats for $p_3$ between S1 and S3 (Figure I. 1).\nFigure I. 1. With two seats\n\n With three seats, $p_3$ can find a seat with any seat reservation combinations by $p_1$ and $p_2$. $p_4$ can also book a seat for there are no other passengers between S3 and S4 (Figure I. 2).\nFigure I. 2. With three seats\n\n For this travel list, only three seats suffice considering all the possible reservation orders and seat preferences under the policy-1.\n\n On the other hand, deciding the seat assignments after all the reservations are completed enables a tight assignment with only two seats under the policy-2 (Figure I. 3).\nFigure I. 3. Tight assignment to two seats\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$a_1$ $b_1$\n. . .\n$a_n$ $b_n$\n\n Here, the first line has an integer $n$, the number of the passengers in the estimated list of passengers' travel sections ($1 <= n <= 200 000$). The stations are numbered starting from 1 in their order along the route. Each of the following $n$ lines describes the travel for each passenger by two integers, the boarding and the alighting station numbers, $a_i$ and $b_i$, respectively ($1 <= a_i < b_i <= 100 000$). Note that more than one passenger in the list may have the same boarding and alighting stations.\nTask Output: Two integers $s_1$ and $s_2$ should be output in a line in this order, separated by a space. $s_1$ and $s_2$ are the numbers of seats required under the policy-1 and -2, respectively.\nTask Samples: input: 4\n1 3\n1 3\n3 6\n3 6\n output: 2 2\ninput: 4\n1 2\n2 3\n1 3\n3 4\n output: 3 2\ninput: 10\n84 302\n275 327\n364 538\n26 364\n29 386\n545 955\n715 965\n404 415\n903 942\n150 402\n output: 6 5\n\n" }, { "title": "Problem J String Puzzle", "content": "The input consists of a single test case in the following format.\n\n$n$ $a$ $b$ $q$\n$x_1$ $c_1$\n. . .\n$x_a$ $c_a$\n$y_1$ $h_1$\n. . .\n$y_b$ $h_b$\n$z_1$\n. . .\n$z_q$\n\n The first line contains four integers $n$, $a$, $b$, and $q$. $n$ ($1 <= n <= 10^9$) is the length of the secret string, $a$ ($0 <= a <= 1000$) is the number of the hints on letters in specified positions, $b$ ($0 <= b <= 1000$) is the number of the hints on duplicated substrings, and $q$ ($1 <= q <= 1000$) is the number of positions asked.\n\n The $i$-th line of the following a lines contains an integer $x_i$ and an uppercase letter $c_i$ meaning that the letter at the position $x_i$ of the secret string is $c_i$. These hints are ordered in their positions, i. e. , $1 <= x_1 < . . . < x_a <= n$.\n\t \n The $i$-th line of the following $b$ lines contains two integers, $y_i$ and $h_i$. It is guaranteed that they satisfy $2 <= y_1 < . . . < y_b <= n$ and $0 <= h_i < y_i$. When $h_i$ is not 0, the substring of the secret string starting from the position $y_i$ with the length $y_{i+1} - y_i$ (or $n+1-y_i$ when $i = b$) is identical to the substring with the same length starting from the position $h_i$. Lines with $h_i = 0$ does not tell any hints except that $y_i$ in the line indicates the end of the substring specified in the line immediately above.\n\t \n Each of the following $q$ lines has an integer $z_i$ ($1 <= z_i <= n$), specifying the position of the letter in the secret string to output.\n\n It is ensured that there exists at least one secret string that matches all the given information. In other words, the given hints have no contradiction.", "constraint": "", "input": "the input consists of a single test case in the following format.\n \n$n$ $a$ $b$ $q$\n$x_1$ $c_1$\n. . .\n$x_a$ $c_a$\n$y_1$ $h_1$\n. . .\n$y_b$ $h_b$\n$z_1$\n. . .\n$z_q$\n \n the first line contains four integers $n$, $a$, $b$, and $q$. $n$ ($1 <= n <= 10^9$) is the length of the secret string, $a$ ($0 <= a <= 1000$) is the number of the hints on letters in specified positions, $b$ ($0 <= b <= 1000$) is the number of the hints on duplicated substrings, and $q$ ($1 <= q <= 1000$) is the number of positions asked.\n \n the $i$-th line of the following a lines contains an integer $x_i$ and an uppercase letter $c_i$ meaning that the letter at the position $x_i$ of the secret string is $c_i$. these hints are ordered in their positions, i. e. , $1 <= x_1 < . . . < x_a <= n$.\n\t \n the $i$-th line of the following $b$ lines contains two integers, $y_i$ and $h_i$. it is guaranteed that they satisfy $2 <= y_1 < . . . < y_b <= n$ and $0 <= h_i < y_i$. when $h_i$ is not 0, the substring of the secret string starting from the position $y_i$ with the length $y_{i+1} - y_i$ (or $n+1-y_i$ when $i = b$) is identical to the substring with the same length starting from the position $h_i$. lines with $h_i = 0$ does not tell any hints except that $y_i$ in the line indicates the end of the substring specified in the line immediately above.\n\t \n each of the following $q$ lines has an integer $z_i$ ($1 <= z_i <= n$), specifying the position of the letter in the secret string to output.\n \n it is ensured that there exists at least one secret string that matches all the given information. in other words, the given hints have no contradiction.", "output": "The output should be a single line consisting only of $q$ characters. The character at position $i$ of the output should be the letter at position $z_i$ of the the secret string if it is uniquely determined from the hints, or ? otherwise.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 9 4 5 4\n3 C\n4 I\n7 C\n9 P\n2 1\n4 0\n6 2\n7 0\n8 4\n8\n1\n9\n6\n output: ICPC", "input: 1000000000 1 1 2\n20171217 A\n3 1\n42\n987654321\n output: ?A"], "Pid": "p00966", "ProblemText": "Task Description: The input consists of a single test case in the following format.\n\n$n$ $a$ $b$ $q$\n$x_1$ $c_1$\n. . .\n$x_a$ $c_a$\n$y_1$ $h_1$\n. . .\n$y_b$ $h_b$\n$z_1$\n. . .\n$z_q$\n\n The first line contains four integers $n$, $a$, $b$, and $q$. $n$ ($1 <= n <= 10^9$) is the length of the secret string, $a$ ($0 <= a <= 1000$) is the number of the hints on letters in specified positions, $b$ ($0 <= b <= 1000$) is the number of the hints on duplicated substrings, and $q$ ($1 <= q <= 1000$) is the number of positions asked.\n\n The $i$-th line of the following a lines contains an integer $x_i$ and an uppercase letter $c_i$ meaning that the letter at the position $x_i$ of the secret string is $c_i$. These hints are ordered in their positions, i. e. , $1 <= x_1 < . . . < x_a <= n$.\n\t \n The $i$-th line of the following $b$ lines contains two integers, $y_i$ and $h_i$. It is guaranteed that they satisfy $2 <= y_1 < . . . < y_b <= n$ and $0 <= h_i < y_i$. When $h_i$ is not 0, the substring of the secret string starting from the position $y_i$ with the length $y_{i+1} - y_i$ (or $n+1-y_i$ when $i = b$) is identical to the substring with the same length starting from the position $h_i$. Lines with $h_i = 0$ does not tell any hints except that $y_i$ in the line indicates the end of the substring specified in the line immediately above.\n\t \n Each of the following $q$ lines has an integer $z_i$ ($1 <= z_i <= n$), specifying the position of the letter in the secret string to output.\n\n It is ensured that there exists at least one secret string that matches all the given information. In other words, the given hints have no contradiction.\nTask Input: the input consists of a single test case in the following format.\n \n$n$ $a$ $b$ $q$\n$x_1$ $c_1$\n. . .\n$x_a$ $c_a$\n$y_1$ $h_1$\n. . .\n$y_b$ $h_b$\n$z_1$\n. . .\n$z_q$\n \n the first line contains four integers $n$, $a$, $b$, and $q$. $n$ ($1 <= n <= 10^9$) is the length of the secret string, $a$ ($0 <= a <= 1000$) is the number of the hints on letters in specified positions, $b$ ($0 <= b <= 1000$) is the number of the hints on duplicated substrings, and $q$ ($1 <= q <= 1000$) is the number of positions asked.\n \n the $i$-th line of the following a lines contains an integer $x_i$ and an uppercase letter $c_i$ meaning that the letter at the position $x_i$ of the secret string is $c_i$. these hints are ordered in their positions, i. e. , $1 <= x_1 < . . . < x_a <= n$.\n\t \n the $i$-th line of the following $b$ lines contains two integers, $y_i$ and $h_i$. it is guaranteed that they satisfy $2 <= y_1 < . . . < y_b <= n$ and $0 <= h_i < y_i$. when $h_i$ is not 0, the substring of the secret string starting from the position $y_i$ with the length $y_{i+1} - y_i$ (or $n+1-y_i$ when $i = b$) is identical to the substring with the same length starting from the position $h_i$. lines with $h_i = 0$ does not tell any hints except that $y_i$ in the line indicates the end of the substring specified in the line immediately above.\n\t \n each of the following $q$ lines has an integer $z_i$ ($1 <= z_i <= n$), specifying the position of the letter in the secret string to output.\n \n it is ensured that there exists at least one secret string that matches all the given information. in other words, the given hints have no contradiction.\nTask Output: The output should be a single line consisting only of $q$ characters. The character at position $i$ of the output should be the letter at position $z_i$ of the the secret string if it is uniquely determined from the hints, or ? otherwise.\nTask Samples: input: 9 4 5 4\n3 C\n4 I\n7 C\n9 P\n2 1\n4 0\n6 2\n7 0\n8 4\n8\n1\n9\n6\n output: ICPC\ninput: 1000000000 1 1 2\n20171217 A\n3 1\n42\n987654321\n output: ?A\n\n" }, { "title": "Problem K\n Counting Cycles", "content": "Given an undirected graph, count the number of simple cycles in the graph. Here, a simple cycle is a connected subgraph all of whose vertices have degree exactly two.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$ $m$\n$u_1$ $v_1$\n. . .\n$u_m$ $v_m$\n\n A test case represents an undirected graph $G$.\n\n The first line shows the number of vertices $n$ ($3 <= n <= 100 000$) and the number of edges $m$ ($n - 1 <= m <= n + 15$). The vertices of the graph are numbered from $1$ to $n$.\n\nThe edges of the graph are specified in the following $m$ lines. Two integers $u_i$ and $v_i$ in the\n$i$-th line of these m lines mean that there is an edge between vertices $u_i$ and $v_i$. Here, you can assume that $u_i < v_i$ and thus there are no self loops.\n\t \n For all pairs of $i$ and $j$ ($i \\ne j$), either $u_i \\ne u_j$ or $v_i \\ne v_j$ holds. In other words, there are no parallel edges.\n\n You can assume that $G$ is connected.", "output": "The output should be a line containing a single number that is the number of simple cycles in the graph.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n1 2\n1 3\n1 4\n2 3\n3 4\n output: 3", "input: 7 9\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7\n2 3\n4 5\n6 7\n output: 3", "input: 4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n output: 7"], "Pid": "p00967", "ProblemText": "Task Description: Given an undirected graph, count the number of simple cycles in the graph. Here, a simple cycle is a connected subgraph all of whose vertices have degree exactly two.\nTask Input: The input consists of a single test case of the following format.\n\n$n$ $m$\n$u_1$ $v_1$\n. . .\n$u_m$ $v_m$\n\n A test case represents an undirected graph $G$.\n\n The first line shows the number of vertices $n$ ($3 <= n <= 100 000$) and the number of edges $m$ ($n - 1 <= m <= n + 15$). The vertices of the graph are numbered from $1$ to $n$.\n\nThe edges of the graph are specified in the following $m$ lines. Two integers $u_i$ and $v_i$ in the\n$i$-th line of these m lines mean that there is an edge between vertices $u_i$ and $v_i$. Here, you can assume that $u_i < v_i$ and thus there are no self loops.\n\t \n For all pairs of $i$ and $j$ ($i \\ne j$), either $u_i \\ne u_j$ or $v_i \\ne v_j$ holds. In other words, there are no parallel edges.\n\n You can assume that $G$ is connected.\nTask Output: The output should be a line containing a single number that is the number of simple cycles in the graph.\nTask Samples: input: 4 5\n1 2\n1 3\n1 4\n2 3\n3 4\n output: 3\ninput: 7 9\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7\n2 3\n4 5\n6 7\n output: 3\ninput: 4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n output: 7\n\n" }, { "title": "Digits Are Not Just Characters", "content": "Mr. Manuel Majorana Minore made a number of files with numbers in their names. He wants to have a list of the files, but the file listing command commonly used lists them in an order different from what he prefers, interpreting digit sequences in them as ASCII code sequences, not as numbers. For example, the files file10, file20 and file3 are listed in this order.\n\nWrite a program which decides the orders of file names interpreting digit sequences as numeric\nvalues.\n\n Each file name consists of uppercase letters (from 'A' to 'Z'), lowercase letters (from 'a' to 'z'), and digits (from '0' to '9').\n\nA file name is looked upon as a sequence of items, each being either a letter or a number. Each\nsingle uppercase or lowercase letter forms a letter item. Each consecutive sequence of digits forms a number item.\n\n Two item are ordered as follows.\n\n Number items come before letter items.\n\n Two letter items are ordered by their ASCII codes.\n\n Two number items are ordered by their values when interpreted as decimal numbers.\n Two file names are compared item by item, starting from the top, and the order of the first different corresponding items decides the order of the file names. If one of them, say $A$, has more items than the other, $B$, and all the items of $B$ are the same as the corresponding items of $A$, $B$ should come before.\n\n For example, three file names in Sample Input 1, file10, file20, and file3 all start with the same sequence of four letter items f, i, l, and e, followed by a number item, 10,20, and 3, respectively. Comparing numeric values of these number items, they are ordered as file3 $<$ file10 $<$ file20.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$s_0$\n$s_1$\n:\n$s_n$\n\n The integer $n$ in the first line gives the number of file names ($s_1$ through $s_n$) to be compared with the file name given in the next line ($s_0$). Here, $n$ satisfies $1 <= n <= 1000$.\n\n The following $n + 1$ lines are file names, $s_0$ through $s_n$, one in each line. They have at least one and no more than nine characters. Each of the characters is either an uppercase letter, a lowercase letter, or a digit.\n\n Sequences of digits in the file names never start with a digit zero (0).", "output": "For each of the file names, $s_1$ through $s_n$, output one line with a character indicating whether it should come before $s_0$ or not. The character should be \"-\" if it is to be listed before $s_0$; otherwise, it should be \"+\", including cases where two names are identical.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\nfile10\nfile20\nfile3\n output: +\n-", "input: 11\nX52Y\nX\nX5\nX52\nX52Y\nX52Y6\n32\nABC\nXYZ\nx51y\nX8Y\nX222\n output: -\n-\n-\n+\n+\n-\n-\n+\n+\n-\n+"], "Pid": "p00968", "ProblemText": "Task Description: Mr. Manuel Majorana Minore made a number of files with numbers in their names. He wants to have a list of the files, but the file listing command commonly used lists them in an order different from what he prefers, interpreting digit sequences in them as ASCII code sequences, not as numbers. For example, the files file10, file20 and file3 are listed in this order.\n\nWrite a program which decides the orders of file names interpreting digit sequences as numeric\nvalues.\n\n Each file name consists of uppercase letters (from 'A' to 'Z'), lowercase letters (from 'a' to 'z'), and digits (from '0' to '9').\n\nA file name is looked upon as a sequence of items, each being either a letter or a number. Each\nsingle uppercase or lowercase letter forms a letter item. Each consecutive sequence of digits forms a number item.\n\n Two item are ordered as follows.\n\n Number items come before letter items.\n\n Two letter items are ordered by their ASCII codes.\n\n Two number items are ordered by their values when interpreted as decimal numbers.\n Two file names are compared item by item, starting from the top, and the order of the first different corresponding items decides the order of the file names. If one of them, say $A$, has more items than the other, $B$, and all the items of $B$ are the same as the corresponding items of $A$, $B$ should come before.\n\n For example, three file names in Sample Input 1, file10, file20, and file3 all start with the same sequence of four letter items f, i, l, and e, followed by a number item, 10,20, and 3, respectively. Comparing numeric values of these number items, they are ordered as file3 $<$ file10 $<$ file20.\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$s_0$\n$s_1$\n:\n$s_n$\n\n The integer $n$ in the first line gives the number of file names ($s_1$ through $s_n$) to be compared with the file name given in the next line ($s_0$). Here, $n$ satisfies $1 <= n <= 1000$.\n\n The following $n + 1$ lines are file names, $s_0$ through $s_n$, one in each line. They have at least one and no more than nine characters. Each of the characters is either an uppercase letter, a lowercase letter, or a digit.\n\n Sequences of digits in the file names never start with a digit zero (0).\nTask Output: For each of the file names, $s_1$ through $s_n$, output one line with a character indicating whether it should come before $s_0$ or not. The character should be \"-\" if it is to be listed before $s_0$; otherwise, it should be \"+\", including cases where two names are identical.\nTask Samples: input: 2\nfile10\nfile20\nfile3\n output: +\n-\ninput: 11\nX52Y\nX\nX5\nX52\nX52Y\nX52Y6\n32\nABC\nXYZ\nx51y\nX8Y\nX222\n output: -\n-\n-\n+\n+\n-\n-\n+\n+\n-\n+\n\n" }, { "title": "Arithmetic Progressions", "content": "An arithmetic progression is a sequence of numbers $a_1, a_2, . . . , a_k$ where the difference of consecutive members $a_{i+1} - a_i$ is a constant ($1 <= i <= k-1$). For example, the sequence 5,8,11,14,17 is an arithmetic progression of length 5 with the common difference 3.\n\nIn this problem, you are requested to find the longest arithmetic progression which can be formed selecting some numbers from a given set of numbers. For example, if the given set of numbers is {0,1,3,5,6,9}, you can form arithmetic progressions such as 0,3,6,9 with the common difference 3, or 9,5,1 with the common difference -4. In this case, the progressions 0,3,6,9\nand 9,6,3,0 are the longest.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$v_1$ $v_2$ . . . $v_n$\n\n $n$ is the number of elements of the set, which is an integer satisfying $2 <= n <= 5000$. Each $v_i$ ($1 <= i <= n$) is an element of the set, which is an integer satisfying $0 <= v_i <= 10^9$. $v_i$'s are all different, i. e. , $v_i \\ne v_j$ if $i \\ne j$.", "output": "Output the length of the longest arithmetic progressions which can be formed selecting some numbers from the given set of numbers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n0 1 3 5 6 9\n output: 4", "input: 7\n1 4 7 3 2 6 5\n \n7\n output: 7", "input: 5\n1 2 4 8 16\n output: 2"], "Pid": "p00969", "ProblemText": "Task Description: An arithmetic progression is a sequence of numbers $a_1, a_2, . . . , a_k$ where the difference of consecutive members $a_{i+1} - a_i$ is a constant ($1 <= i <= k-1$). For example, the sequence 5,8,11,14,17 is an arithmetic progression of length 5 with the common difference 3.\n\nIn this problem, you are requested to find the longest arithmetic progression which can be formed selecting some numbers from a given set of numbers. For example, if the given set of numbers is {0,1,3,5,6,9}, you can form arithmetic progressions such as 0,3,6,9 with the common difference 3, or 9,5,1 with the common difference -4. In this case, the progressions 0,3,6,9\nand 9,6,3,0 are the longest.\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$v_1$ $v_2$ . . . $v_n$\n\n $n$ is the number of elements of the set, which is an integer satisfying $2 <= n <= 5000$. Each $v_i$ ($1 <= i <= n$) is an element of the set, which is an integer satisfying $0 <= v_i <= 10^9$. $v_i$'s are all different, i. e. , $v_i \\ne v_j$ if $i \\ne j$.\nTask Output: Output the length of the longest arithmetic progressions which can be formed selecting some numbers from the given set of numbers.\nTask Samples: input: 6\n0 1 3 5 6 9\n output: 4\ninput: 7\n1 4 7 3 2 6 5\n \n7\n output: 7\ninput: 5\n1 2 4 8 16\n output: 2\n\n" }, { "title": "Emergency Evacuation", "content": "The Japanese government plans to increase the number of inbound tourists to forty million in the year 2020, and sixty million in 2030. Not only increasing touristic appeal but also developing tourism infrastructure further is indispensable to accomplish such numbers.\n\n One possible enhancement on transport is providing cars extremely long and/or wide, carrying many passengers at a time. Too large a car, however, may require too long to evacuate all passengers in an emergency. You are requested to help estimating the time required.\n\n The car is assumed to have the following seat arrangement.\n\n A center aisle goes straight through the car, directly connecting to the emergency exit door at the rear center of the car.\n\n The rows of the same number of passenger seats are on both sides of the aisle.\n A rough estimation requested is based on a simple step-wise model. All passengers are initially on a distinct seat, and they can make one of the following moves in each step.\n\n Passengers on a seat can move to an adjacent seat toward the aisle. Passengers on a seat adjacent to the aisle can move sideways directly to the aisle.\n\n Passengers on the aisle can move backward by one row of seats. If the passenger is in front of the emergency exit, that is, by the rear-most seat rows, he/she can get off the car.\n The seat or the aisle position to move to must be empty; either no other passenger is there before the step, or the passenger there empties the seat by moving to another position in the same step. When two or more passengers satisfy the condition for the same position, only one of them can move, keeping the others wait in their original positions.\n\n The leftmost figure of Figure C. 1 depicts the seat arrangement of a small car given in Sample Input 1. The car have five rows of seats, two seats each on both sides of the aisle, totaling twenty. The initial positions of seven passengers on board are also shown.\n\n The two other figures of Figure C. 1 show possible positions of passengers after the first and the second steps. Passenger movements are indicated by fat arrows. Note that, two of the passengers in the front seat had to wait for a vacancy in the first step, and one in the second row had to wait in the next step.\n\n Your task is to write a program that gives the smallest possible number of steps for all the passengers to get off the car, given the seat arrangement and passengers' initial positions.\n Figure C. 1", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$r$ $s$ $p$\n$i_1$ $j_1$\n. . .\n$i_p$ $j_p$\n\n Here, $r$ is the number of passenger seat rows, $s$ is the number of seats on each side of the aisle, and $p$ is the number of passengers. They are integers satisfying $1 <= r <= 500$, $1 <= s <= 500$, and $1 <= p <= 2rs$.\n\n The following $p$ lines give initial seat positions of the passengers. The $k$-th line with $i_k$ and $j_k$ means that the $k$-th passenger's seat is in the $i_k$-th seat row and it is the $j_k$-th seat on that row. Here, rows and seats are counted from front to rear and left to right, both starting from one. They satisfy $1 <= i_k <= r$ and $1 <= j_k <= 2s$. Passengers are on distinct seats, that is, $i_k \\ne= i_l$ or $j_k \\ne j_l$ holds if $k \\ne l$.", "output": "The output should be one line containing a single integer, the minimum number of steps required\nfor all the passengers to get off the car.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 2 7\n1 1\n1 2\n1 3\n2 3\n2 4\n4 4\n5 2\n output: 9", "input: 500 500 16\n1 1\n1 2\n1 999\n1 1000\n2 1\n2 2\n2 999\n2 1000\n3 1\n3 2\n3 999\n3 1000\n499 500\n499 501\n499 999\n499 1000\n output: 1008"], "Pid": "p00970", "ProblemText": "Task Description: The Japanese government plans to increase the number of inbound tourists to forty million in the year 2020, and sixty million in 2030. Not only increasing touristic appeal but also developing tourism infrastructure further is indispensable to accomplish such numbers.\n\n One possible enhancement on transport is providing cars extremely long and/or wide, carrying many passengers at a time. Too large a car, however, may require too long to evacuate all passengers in an emergency. You are requested to help estimating the time required.\n\n The car is assumed to have the following seat arrangement.\n\n A center aisle goes straight through the car, directly connecting to the emergency exit door at the rear center of the car.\n\n The rows of the same number of passenger seats are on both sides of the aisle.\n A rough estimation requested is based on a simple step-wise model. All passengers are initially on a distinct seat, and they can make one of the following moves in each step.\n\n Passengers on a seat can move to an adjacent seat toward the aisle. Passengers on a seat adjacent to the aisle can move sideways directly to the aisle.\n\n Passengers on the aisle can move backward by one row of seats. If the passenger is in front of the emergency exit, that is, by the rear-most seat rows, he/she can get off the car.\n The seat or the aisle position to move to must be empty; either no other passenger is there before the step, or the passenger there empties the seat by moving to another position in the same step. When two or more passengers satisfy the condition for the same position, only one of them can move, keeping the others wait in their original positions.\n\n The leftmost figure of Figure C. 1 depicts the seat arrangement of a small car given in Sample Input 1. The car have five rows of seats, two seats each on both sides of the aisle, totaling twenty. The initial positions of seven passengers on board are also shown.\n\n The two other figures of Figure C. 1 show possible positions of passengers after the first and the second steps. Passenger movements are indicated by fat arrows. Note that, two of the passengers in the front seat had to wait for a vacancy in the first step, and one in the second row had to wait in the next step.\n\n Your task is to write a program that gives the smallest possible number of steps for all the passengers to get off the car, given the seat arrangement and passengers' initial positions.\n Figure C. 1\nTask Input: The input consists of a single test case of the following format.\n\n$r$ $s$ $p$\n$i_1$ $j_1$\n. . .\n$i_p$ $j_p$\n\n Here, $r$ is the number of passenger seat rows, $s$ is the number of seats on each side of the aisle, and $p$ is the number of passengers. They are integers satisfying $1 <= r <= 500$, $1 <= s <= 500$, and $1 <= p <= 2rs$.\n\n The following $p$ lines give initial seat positions of the passengers. The $k$-th line with $i_k$ and $j_k$ means that the $k$-th passenger's seat is in the $i_k$-th seat row and it is the $j_k$-th seat on that row. Here, rows and seats are counted from front to rear and left to right, both starting from one. They satisfy $1 <= i_k <= r$ and $1 <= j_k <= 2s$. Passengers are on distinct seats, that is, $i_k \\ne= i_l$ or $j_k \\ne j_l$ holds if $k \\ne l$.\nTask Output: The output should be one line containing a single integer, the minimum number of steps required\nfor all the passengers to get off the car.\nTask Samples: input: 5 2 7\n1 1\n1 2\n1 3\n2 3\n2 4\n4 4\n5 2\n output: 9\ninput: 500 500 16\n1 1\n1 2\n1 999\n1 1000\n2 1\n2 2\n2 999\n2 1000\n3 1\n3 2\n3 999\n3 1000\n499 500\n499 501\n499 999\n499 1000\n output: 1008\n\n" }, { "title": "Shortest Common Non-Subsequence", "content": "A subsequence of a sequence $P$ is a sequence that can be derived from the original sequence $P$ by picking up some or no elements of $P$ preserving the order. For example, \"ICPC\" is a subsequence of \"MICROPROCESSOR\".\n\n A common subsequence of two sequences is a subsequence of both sequences. The famous longest common subsequence problem is finding the longest of common subsequences of two given sequences.\n\n In this problem, conversely, we consider the shortest common non-subsequence problem: Given two sequences consisting of 0 and 1, your task is to find the shortest sequence also consisting of 0 and 1 that is a subsequence of neither of the two sequences.", "constraint": "", "input": "The input consists of a single test case with two lines. Both lines are sequences consisting only of 0 and 1. Their lengths are between 1 and 4000, inclusive.", "output": "In one line the shortest common non-subsequence of two given sequences. If there are two or more such sequences, you should output the lexicographically smallest one. Here, a sequence $P$ is lexicographically smaller than another sequence $Q$ of the same length if there exists $k$ such that $P_1 = Q_1, . . . , P_{k-1} = Q_{k-1}$, and $P_k < Q_k$, where $S_i$ is the $i$-th character of a sequence $S$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0101\n1100001\n output: 0010", "input: 101010101\n010101010\n output: 000000", "input: 11111111\n00000000\n output: 01"], "Pid": "p00971", "ProblemText": "Task Description: A subsequence of a sequence $P$ is a sequence that can be derived from the original sequence $P$ by picking up some or no elements of $P$ preserving the order. For example, \"ICPC\" is a subsequence of \"MICROPROCESSOR\".\n\n A common subsequence of two sequences is a subsequence of both sequences. The famous longest common subsequence problem is finding the longest of common subsequences of two given sequences.\n\n In this problem, conversely, we consider the shortest common non-subsequence problem: Given two sequences consisting of 0 and 1, your task is to find the shortest sequence also consisting of 0 and 1 that is a subsequence of neither of the two sequences.\nTask Input: The input consists of a single test case with two lines. Both lines are sequences consisting only of 0 and 1. Their lengths are between 1 and 4000, inclusive.\nTask Output: In one line the shortest common non-subsequence of two given sequences. If there are two or more such sequences, you should output the lexicographically smallest one. Here, a sequence $P$ is lexicographically smaller than another sequence $Q$ of the same length if there exists $k$ such that $P_1 = Q_1, . . . , P_{k-1} = Q_{k-1}$, and $P_k < Q_k$, where $S_i$ is the $i$-th character of a sequence $S$.\nTask Samples: input: 0101\n1100001\n output: 0010\ninput: 101010101\n010101010\n output: 000000\ninput: 11111111\n00000000\n output: 01\n\n" }, { "title": "Eulerian Flight Tour", "content": "You have an airline route map of a certain region. All the airports in the region and all the non-stop routes between them are on the map. Here, a non-stop route is a flight route that provides non-stop flights in both ways.\n\n Named after the great mathematician Leonhard Euler, an Eulerian tour is an itinerary visiting all the airports in the region taking a single flight of every non-stop route available in the region. To be precise, it is a list of airports, satisfying all of the following.\n\n The list begins and ends with the same airport.\n\n There are non-stop routes between pairs of airports adjacent in the list.\n\n All the airports in the region appear at least once in the list. Note that it is allowed to have some airports appearing multiple times.\n\n For all the airport pairs with non-stop routes in between, there should be one and only one adjacent appearance of two airports of the pair in the list in either order.\n It may not always be possible to find an Eulerian tour only with the non-stop routes listed in the map. Adding more routes, however, may enable Eulerian tours. Your task is to find a set of additional routes that enables Eulerian tours.", "constraint": "", "input": "The input consists of a single test case.\n\n$n$ $m$\n$a_1$ $b_1$\n. . .\n$a_m$ $b_m$\n\n $n$ ($3 <= n <= 100$) is the number of airports. The airports are numbered from 1 to $n$. $m$ ($0 <= m <= \\frac{n(n-1)}{2}$) is the number of pairs of airports that have non-stop routes. Among the $m$ lines following it, integers $a_i$ and $b_i$ on the $i$-th line of them ($1 <= i <= m$) are airport numbers between which a non-stop route is operated. You can assume $1 <= a_i < b_i <= n$, and for any $i \\ne j$, either $a_i \\ne a_j$ or $b_i \\ne b_j$ holds.", "output": "Output a set of additional non-stop routes that enables Eulerian tours. If two or more different sets will do, any one of them is acceptable. The output should be in the following format.\n\n$k$\n$c_1$ $d_1$\n. . .\n$c_k$ $d_k$\n\n $k$ is the number of non-stop routes to add, possibly zero. Each of the following $k$ lines should have a pair of integers, separated by a space. Integers $c_i$ and $d_i$ in the $i$-th line ($c_i < d_i$) are airport numbers specifying that a non-stop route is to be added between them. These pairs, ($c_i, d_i$) for $1 <= i <= k$, should be distinct and should not appear in the input.\n\n If adding new non-stop routes can never enable Eulerian tours, output -1 in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n1 2\n3 4\n output: 2\n1 4\n2 3", "input: 6 9\n1 4\n1 5\n1 6\n2 4\n2 5\n2 6\n3 4\n3 5\n3 6\n output: -1", "input: 6 7\n1 2\n1 3\n1 4\n2 3\n4 5\n4 6\n5 6\n output: 3\n1 5\n2 4\n2 5", "input: 4 3\n2 3\n2 4\n3 4\n output: -1", "input: 5 5\n1 3\n1 4\n2 4\n2 5\n3 5\n output: 0"], "Pid": "p00972", "ProblemText": "Task Description: You have an airline route map of a certain region. All the airports in the region and all the non-stop routes between them are on the map. Here, a non-stop route is a flight route that provides non-stop flights in both ways.\n\n Named after the great mathematician Leonhard Euler, an Eulerian tour is an itinerary visiting all the airports in the region taking a single flight of every non-stop route available in the region. To be precise, it is a list of airports, satisfying all of the following.\n\n The list begins and ends with the same airport.\n\n There are non-stop routes between pairs of airports adjacent in the list.\n\n All the airports in the region appear at least once in the list. Note that it is allowed to have some airports appearing multiple times.\n\n For all the airport pairs with non-stop routes in between, there should be one and only one adjacent appearance of two airports of the pair in the list in either order.\n It may not always be possible to find an Eulerian tour only with the non-stop routes listed in the map. Adding more routes, however, may enable Eulerian tours. Your task is to find a set of additional routes that enables Eulerian tours.\nTask Input: The input consists of a single test case.\n\n$n$ $m$\n$a_1$ $b_1$\n. . .\n$a_m$ $b_m$\n\n $n$ ($3 <= n <= 100$) is the number of airports. The airports are numbered from 1 to $n$. $m$ ($0 <= m <= \\frac{n(n-1)}{2}$) is the number of pairs of airports that have non-stop routes. Among the $m$ lines following it, integers $a_i$ and $b_i$ on the $i$-th line of them ($1 <= i <= m$) are airport numbers between which a non-stop route is operated. You can assume $1 <= a_i < b_i <= n$, and for any $i \\ne j$, either $a_i \\ne a_j$ or $b_i \\ne b_j$ holds.\nTask Output: Output a set of additional non-stop routes that enables Eulerian tours. If two or more different sets will do, any one of them is acceptable. The output should be in the following format.\n\n$k$\n$c_1$ $d_1$\n. . .\n$c_k$ $d_k$\n\n $k$ is the number of non-stop routes to add, possibly zero. Each of the following $k$ lines should have a pair of integers, separated by a space. Integers $c_i$ and $d_i$ in the $i$-th line ($c_i < d_i$) are airport numbers specifying that a non-stop route is to be added between them. These pairs, ($c_i, d_i$) for $1 <= i <= k$, should be distinct and should not appear in the input.\n\n If adding new non-stop routes can never enable Eulerian tours, output -1 in a line.\nTask Samples: input: 4 2\n1 2\n3 4\n output: 2\n1 4\n2 3\ninput: 6 9\n1 4\n1 5\n1 6\n2 4\n2 5\n2 6\n3 4\n3 5\n3 6\n output: -1\ninput: 6 7\n1 2\n1 3\n1 4\n2 3\n4 5\n4 6\n5 6\n output: 3\n1 5\n2 4\n2 5\ninput: 4 3\n2 3\n2 4\n3 4\n output: -1\ninput: 5 5\n1 3\n1 4\n2 4\n2 5\n3 5\n output: 0\n\n" }, { "title": "Fair Chocolate-Cutting", "content": "You are given a flat piece of chocolate of convex polygon shape. You are to cut it into two pieces of precisely the same amount with a straight knife.\n\n Write a program that computes, for a given convex polygon, the maximum and minimum lengths of the line segments that divide the polygon into two equal areas.\n\n The figures below correspond to first two sample inputs. Two dashed lines in each of them correspond to the equal-area cuts of minimum and maximum lengths.\n Figure F. 1. Sample Chocolate Pieces and Cut Lines", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$x_1$ $y_1$\n. . .\n$x_n$ $y_n$\n\n The first line has an integer $n$, which is the number of vertices of the given polygon. Here, $n$ is between 3 and 5000, inclusive. Each of the following $n$ lines has two integers $x_i$ and $y_i$, which give the coordinates ($x_i, y_i$) of the $i$-th vertex of the polygon, in counterclockwise order. Both $x_i$ and $y_i$ are between 0 and 100 000, inclusive.\n\n The polygon is guaranteed to be simple and convex. In other words, no two edges of the polygon intersect each other and interior angles at all of its vertices are less than $180^\\circ$.", "output": "Two lines should be output. The first line should have the minimum length of a straight line segment that partitions the polygon into two parts of the equal area. The second line should have the maximum length of such a line segment. The answer will be considered as correct if the values output have an absolute or relative error less than $10^{-6}$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n10 0\n10 10\n0 10\n output: 10\n14.142135623730950488", "input: 3\n0 0\n6 0\n3 10\n output: 4.2426406871192851464\n10.0", "input: 5\n0 0\n99999 20000\n100000 70000\n33344 63344\n1 50000\n output: 54475.580091580027976\n120182.57592539864775", "input: 6\n100 350\n101 349\n6400 3440\n6400 3441\n1200 7250\n1199 7249\n output: 4559.2050019027964982\n6216.7174287968524227"], "Pid": "p00973", "ProblemText": "Task Description: You are given a flat piece of chocolate of convex polygon shape. You are to cut it into two pieces of precisely the same amount with a straight knife.\n\n Write a program that computes, for a given convex polygon, the maximum and minimum lengths of the line segments that divide the polygon into two equal areas.\n\n The figures below correspond to first two sample inputs. Two dashed lines in each of them correspond to the equal-area cuts of minimum and maximum lengths.\n Figure F. 1. Sample Chocolate Pieces and Cut Lines\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$x_1$ $y_1$\n. . .\n$x_n$ $y_n$\n\n The first line has an integer $n$, which is the number of vertices of the given polygon. Here, $n$ is between 3 and 5000, inclusive. Each of the following $n$ lines has two integers $x_i$ and $y_i$, which give the coordinates ($x_i, y_i$) of the $i$-th vertex of the polygon, in counterclockwise order. Both $x_i$ and $y_i$ are between 0 and 100 000, inclusive.\n\n The polygon is guaranteed to be simple and convex. In other words, no two edges of the polygon intersect each other and interior angles at all of its vertices are less than $180^\\circ$.\nTask Output: Two lines should be output. The first line should have the minimum length of a straight line segment that partitions the polygon into two parts of the equal area. The second line should have the maximum length of such a line segment. The answer will be considered as correct if the values output have an absolute or relative error less than $10^{-6}$.\nTask Samples: input: 4\n0 0\n10 0\n10 10\n0 10\n output: 10\n14.142135623730950488\ninput: 3\n0 0\n6 0\n3 10\n output: 4.2426406871192851464\n10.0\ninput: 5\n0 0\n99999 20000\n100000 70000\n33344 63344\n1 50000\n output: 54475.580091580027976\n120182.57592539864775\ninput: 6\n100 350\n101 349\n6400 3440\n6400 3441\n1200 7250\n1199 7249\n output: 4559.2050019027964982\n6216.7174287968524227\n\n" }, { "title": "Four-Coloring", "content": "You are given a planar embedding of a connected graph. Each vertex of the graph corresponds to a distinct point with integer coordinates. Each edge between two vertices corresponds to a straight line segment connecting the two points corresponding to the vertices. As the given embedding is planar, the line segments corresponding to edges do not share any points other than their common endpoints. The given embedding is organized so that inclinations of all the line segments are multiples of 45 degrees. In other words, for two points with coordinates ($x_u, y_u$) and ($x_v, y_v$) corresponding to vertices $u$ and $v$ with an edge between them, one of $x_u = x_v$, $y_u = y_v$, or $|x_u - x_v| = |y_u - y_v|$ holds.\nFigure H. 1. Sample Input 1 and 2\n\n Your task is to color each vertex in one of the four colors, {1,2,3,4}, so that no two vertices connected by an edge are of the same color. According to the famous four color theorem, such a coloring is always possible. Please find one.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$ $m$\n$x_1$ $y_1$\n. . .\n$x_n$ $y_n$\n$u_1$ $v_1$\n. . .\n$u_m$ $v_m$\n\n The first line contains two integers, $n$ and $m$. $n$ is the number of vertices and $m$ is the number of edges satisfying $3 <= n <= m <= 10 000$. The vertices are numbered 1 through $n$. Each of the next $n$ lines contains two integers. Integers on the $v$-th line, $x_v$ ($0 <= x_v <= 1000$) and $y_v$ ($0 <= y_v <= 1000$), denote the coordinates of the point corresponding to the vertex $v$. Vertices correspond to distinct points, i. e. , ($x_u, y_u$) $\\ne$ ($x_v, y_v$) holds for $u \\ne v$. Each of the next $m$ lines contains two integers. Integers on the $i$-th line, $u_i$ and $v_i$, with $1 <= u_i < v_i <= n$, mean that there is an edge connecting two vertices $u_i$ and $v_i$.", "output": "The output should consist of $n$ lines. The $v$-th line of the output should contain one integer $c_v \\in \\{1,2,3,4\\}$ which means that the vertex $v$ is to be colored $c_v$. The output must satisfy $c_u \\ne c_v$ for every edge connecting $u$ and $v$ in the graph. If there are multiple solutions, you may output any one of them.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 8\n0 0\n2 0\n0 2\n2 2\n1 1\n1 2\n1 3\n1 5\n2 4\n2 5\n3 4\n3 5\n4 5\n output: 1\n2\n2\n1\n3", "input: 6 10\n0 0\n1 0\n1 1\n2 1\n0 2\n1 2\n1 2\n1 3\n1 5\n2 3\n2 4\n3 4\n3 5\n3 6\n4 6\n5 6\n output: 1\n2\n3\n4\n2\n1"], "Pid": "p00975", "ProblemText": "Task Description: You are given a planar embedding of a connected graph. Each vertex of the graph corresponds to a distinct point with integer coordinates. Each edge between two vertices corresponds to a straight line segment connecting the two points corresponding to the vertices. As the given embedding is planar, the line segments corresponding to edges do not share any points other than their common endpoints. The given embedding is organized so that inclinations of all the line segments are multiples of 45 degrees. In other words, for two points with coordinates ($x_u, y_u$) and ($x_v, y_v$) corresponding to vertices $u$ and $v$ with an edge between them, one of $x_u = x_v$, $y_u = y_v$, or $|x_u - x_v| = |y_u - y_v|$ holds.\nFigure H. 1. Sample Input 1 and 2\n\n Your task is to color each vertex in one of the four colors, {1,2,3,4}, so that no two vertices connected by an edge are of the same color. According to the famous four color theorem, such a coloring is always possible. Please find one.\nTask Input: The input consists of a single test case of the following format.\n\n$n$ $m$\n$x_1$ $y_1$\n. . .\n$x_n$ $y_n$\n$u_1$ $v_1$\n. . .\n$u_m$ $v_m$\n\n The first line contains two integers, $n$ and $m$. $n$ is the number of vertices and $m$ is the number of edges satisfying $3 <= n <= m <= 10 000$. The vertices are numbered 1 through $n$. Each of the next $n$ lines contains two integers. Integers on the $v$-th line, $x_v$ ($0 <= x_v <= 1000$) and $y_v$ ($0 <= y_v <= 1000$), denote the coordinates of the point corresponding to the vertex $v$. Vertices correspond to distinct points, i. e. , ($x_u, y_u$) $\\ne$ ($x_v, y_v$) holds for $u \\ne v$. Each of the next $m$ lines contains two integers. Integers on the $i$-th line, $u_i$ and $v_i$, with $1 <= u_i < v_i <= n$, mean that there is an edge connecting two vertices $u_i$ and $v_i$.\nTask Output: The output should consist of $n$ lines. The $v$-th line of the output should contain one integer $c_v \\in \\{1,2,3,4\\}$ which means that the vertex $v$ is to be colored $c_v$. The output must satisfy $c_u \\ne c_v$ for every edge connecting $u$ and $v$ in the graph. If there are multiple solutions, you may output any one of them.\nTask Samples: input: 5 8\n0 0\n2 0\n0 2\n2 2\n1 1\n1 2\n1 3\n1 5\n2 4\n2 5\n3 4\n3 5\n4 5\n output: 1\n2\n2\n1\n3\ninput: 6 10\n0 0\n1 0\n1 1\n2 1\n0 2\n1 2\n1 2\n1 3\n1 5\n2 3\n2 4\n3 4\n3 5\n3 6\n4 6\n5 6\n output: 1\n2\n3\n4\n2\n1\n\n" }, { "title": "Ranks", "content": "A finite field F_2 consists of two elements: 0 and 1. Addition and multiplication on F_2 are those on integers modulo two, as defined below.\n\n \n \n \n \n
    + \n0 \n1 \n 0 0 1 \n\n 1 1 0 \n\n \n \n \n     \n \n \n \n \n$*$ \n0 \n1 \n 0 0 0 \n\n 1 0 1 \n\n \n \n \n A set of vectors $v_1, . . . , v_k$ over F_2 with the same dimension is said to be linearly independent when, for $c_1, . . . , c_k \\in $ F_2, $c_1v_1 + . . . + c_kv_k = 0$ is equivalent to $c_1 = . . . = c_k = 0$, where $0$ is the zero vector, the vector with all its elements being zero.\n\n The rank of a matrix is the maximum cardinality of its linearly independent sets of column vectors. For example, the rank of the matrix\n\n$\n <=ft[\n \\begin{array}{rrr}\n 0 & 0 & 1 \\\\\n 1 & 0 & 1\n \\end{array}\n \\right]\n$\n \n is two; the column vectors\n\n $\n <=ft[\n \\begin{array}{rrr}\n 0 \\\\\n 1 \n \\end{array}\n \\right]\n$ \n \nand\n\n $\n <=ft[\n \\begin{array}{rrr}\n 1 \\\\\n 1 \n \\end{array}\n \\right]\n$ \n\n \n (the first and the third columns) are linearly independent while the set of all three column vectors is not linearly independent. Note that the rank is zero for the zero matrix.\n\n Given the above definition of the rank of matrices, the following may be an intriguing question. How does a modification of an entry in a matrix change the rank of the matrix? To investigate this question, let us suppose that we are given a matrix $A$ over F_2. For any indices $i$ and $j$, let $A^{(ij)}$ be a matrix equivalent to $A$ except that the $(i, j)$ entry is flipped.\n\n In this problem, we are interested in the rank of the matrix $A^{(ij)}$. Let us denote the rank of $A$ by $r$, and that of $A^{(ij)}$ by $r^{(ij)}$. Your task is to determine, for all $(i, j)$ entries, the relation of ranks before and after flipping the entry out of the following possibilities: $(i) r^{(ij)} < r, (ii) r^{(ij)} = r$, or $(iii) r^{(ij)} > r$.", "constraint": "", "input": "The input consists of a single test case of the following format.\n \n$n$ $m$\n$A_{11}$ . . . $A_{1m}$\n.\n.\n.\n$A_{n1}$ . . . $A_{nm}$\n\n $n$ and $m$ are the numbers of rows and columns in the matrix $A$, respectively ($1 <= n <= 1000,1 <= m <= 1000$). In the next $n$ lines, the entries of $A$ are listed without spaces in between. $A_{ij}$ is the entry in the $i$-th row and $j$-th column, which is either 0 or 1.", "output": "Output $n$ lines, each consisting of $m$ characters. The character in the $i$-th line at the $j$-th position must be either - (minus), 0 (zero), or + (plus). They correspond to the possibilities (i), (ii), and (iii) in the problem statement respectively.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n001\n101\n output: -0-\n-00", "input: 5 4\n1111\n1000\n1000\n1000\n1000\n output: 0000\n0+++\n0+++\n0+++\n0+++", "input: 10 10\n1000001001\n0000010100\n0000100010\n0001000001\n0010000010\n0100000100\n1000001000\n0000010000\n0000100000\n0001000001\n output: 000-00000-\n0-00000-00\n00-00000-0\n+00000+000\n00-0000000\n0-00000000\n000-00000-\n0-000-0-00\n00-0-000-0\n+00000+000", "input: 1 1\n0\n output: +"], "Pid": "p00976", "ProblemText": "Task Description: A finite field F_2 consists of two elements: 0 and 1. Addition and multiplication on F_2 are those on integers modulo two, as defined below.\n\n \n \n \n \n
    + \n0 \n1 \n 0 0 1 \n\n 1 1 0 \n\n \n \n \n     \n \n \n \n \n$*$ \n0 \n1 \n 0 0 0 \n\n 1 0 1 \n\n \n \n \n A set of vectors $v_1, . . . , v_k$ over F_2 with the same dimension is said to be linearly independent when, for $c_1, . . . , c_k \\in $ F_2, $c_1v_1 + . . . + c_kv_k = 0$ is equivalent to $c_1 = . . . = c_k = 0$, where $0$ is the zero vector, the vector with all its elements being zero.\n\n The rank of a matrix is the maximum cardinality of its linearly independent sets of column vectors. For example, the rank of the matrix\n\n$\n <=ft[\n \\begin{array}{rrr}\n 0 & 0 & 1 \\\\\n 1 & 0 & 1\n \\end{array}\n \\right]\n$\n \n is two; the column vectors\n\n $\n <=ft[\n \\begin{array}{rrr}\n 0 \\\\\n 1 \n \\end{array}\n \\right]\n$ \n \nand\n\n $\n <=ft[\n \\begin{array}{rrr}\n 1 \\\\\n 1 \n \\end{array}\n \\right]\n$ \n\n \n (the first and the third columns) are linearly independent while the set of all three column vectors is not linearly independent. Note that the rank is zero for the zero matrix.\n\n Given the above definition of the rank of matrices, the following may be an intriguing question. How does a modification of an entry in a matrix change the rank of the matrix? To investigate this question, let us suppose that we are given a matrix $A$ over F_2. For any indices $i$ and $j$, let $A^{(ij)}$ be a matrix equivalent to $A$ except that the $(i, j)$ entry is flipped.\n\n In this problem, we are interested in the rank of the matrix $A^{(ij)}$. Let us denote the rank of $A$ by $r$, and that of $A^{(ij)}$ by $r^{(ij)}$. Your task is to determine, for all $(i, j)$ entries, the relation of ranks before and after flipping the entry out of the following possibilities: $(i) r^{(ij)} < r, (ii) r^{(ij)} = r$, or $(iii) r^{(ij)} > r$.\nTask Input: The input consists of a single test case of the following format.\n \n$n$ $m$\n$A_{11}$ . . . $A_{1m}$\n.\n.\n.\n$A_{n1}$ . . . $A_{nm}$\n\n $n$ and $m$ are the numbers of rows and columns in the matrix $A$, respectively ($1 <= n <= 1000,1 <= m <= 1000$). In the next $n$ lines, the entries of $A$ are listed without spaces in between. $A_{ij}$ is the entry in the $i$-th row and $j$-th column, which is either 0 or 1.\nTask Output: Output $n$ lines, each consisting of $m$ characters. The character in the $i$-th line at the $j$-th position must be either - (minus), 0 (zero), or + (plus). They correspond to the possibilities (i), (ii), and (iii) in the problem statement respectively.\nTask Samples: input: 2 3\n001\n101\n output: -0-\n-00\ninput: 5 4\n1111\n1000\n1000\n1000\n1000\n output: 0000\n0+++\n0+++\n0+++\n0+++\ninput: 10 10\n1000001001\n0000010100\n0000100010\n0001000001\n0010000010\n0100000100\n1000001000\n0000010000\n0000100000\n0001000001\n output: 000-00000-\n0-00000-00\n00-00000-0\n+00000+000\n00-0000000\n0-00000000\n000-00000-\n0-000-0-00\n00-0-000-0\n+00000+000\ninput: 1 1\n0\n output: +\n\n" }, { "title": "Colorful Tree", "content": "A tree structure with some colors associated with its vertices and a sequence of commands on it are given. A command is either an update operation or a query on the tree. Each of the update operations changes the color of a specified vertex, without changing the tree structure. Each of the queries asks the number of edges in the minimum connected subgraph of the tree that contains all the vertices of the specified color.\n \n Your task is to find answers of each of the queries, assuming that the commands are performed in the given order.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$a_1$ $b_1$\n. . .\n$a_{n-1}$ $b_{n-1}$\n$c_1 . . . c_n$\n$m$\n$command_1$\n. . .\n$command_m$\n\n The first line contains an integer $n$ ($2 <= n <= 100 000$), the number of vertices of the tree. The vertices are numbered 1 through $n$. Each of the following $n - 1$ lines contains two integers $a_i$ ($1 <= a_i <= n$) and $b_i$ ($1 <= b_i <= n$), meaning that the $i$-th edge connects vertices $a_i$ and $b_i$. It is ensured that all the vertices are connected, that is, the given graph is a tree. The next line contains $n$ integers, $c_1$ through $c_n$, where $c_j$ ($1 <= c_j <= 100 000$) is the initial color of vertex $j$. The next line contains an integer $m$ ($1 <= m <= 100 000$), which indicates the number of commands. Each of the following $m$ lines contains a command in the following format.\n\n$U$ $x_k$ $y_k$\nor\n$Q$ $y_k$\n\n When the $k$-th command starts with U, it means an update operation changing the color of vertex $x_k$ ($1 <= x_k <= n$) to $y_k$ ($1 <= y_k <= 100 000$). When the $k$-th command starts with Q, it means a query asking the number of edges in the minimum connected subgraph of the tree that contains all the vertices of color $y_k$ ($1 <= y_k <= 100 000$).", "output": "For each query, output the number of edges in the minimum connected subgraph of the tree containing all the vertices of the specified color. If the tree doesn't contain any vertex of the specified color, output -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n2 3\n3 4\n2 5\n1 2 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 1\n output: 2\n2\n0\n-1\n3\n2\n2\n0"], "Pid": "p00977", "ProblemText": "Task Description: A tree structure with some colors associated with its vertices and a sequence of commands on it are given. A command is either an update operation or a query on the tree. Each of the update operations changes the color of a specified vertex, without changing the tree structure. Each of the queries asks the number of edges in the minimum connected subgraph of the tree that contains all the vertices of the specified color.\n \n Your task is to find answers of each of the queries, assuming that the commands are performed in the given order.\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$a_1$ $b_1$\n. . .\n$a_{n-1}$ $b_{n-1}$\n$c_1 . . . c_n$\n$m$\n$command_1$\n. . .\n$command_m$\n\n The first line contains an integer $n$ ($2 <= n <= 100 000$), the number of vertices of the tree. The vertices are numbered 1 through $n$. Each of the following $n - 1$ lines contains two integers $a_i$ ($1 <= a_i <= n$) and $b_i$ ($1 <= b_i <= n$), meaning that the $i$-th edge connects vertices $a_i$ and $b_i$. It is ensured that all the vertices are connected, that is, the given graph is a tree. The next line contains $n$ integers, $c_1$ through $c_n$, where $c_j$ ($1 <= c_j <= 100 000$) is the initial color of vertex $j$. The next line contains an integer $m$ ($1 <= m <= 100 000$), which indicates the number of commands. Each of the following $m$ lines contains a command in the following format.\n\n$U$ $x_k$ $y_k$\nor\n$Q$ $y_k$\n\n When the $k$-th command starts with U, it means an update operation changing the color of vertex $x_k$ ($1 <= x_k <= n$) to $y_k$ ($1 <= y_k <= 100 000$). When the $k$-th command starts with Q, it means a query asking the number of edges in the minimum connected subgraph of the tree that contains all the vertices of color $y_k$ ($1 <= y_k <= 100 000$).\nTask Output: For each query, output the number of edges in the minimum connected subgraph of the tree containing all the vertices of the specified color. If the tree doesn't contain any vertex of the specified color, output -1 instead.\nTask Samples: input: 5\n1 2\n2 3\n3 4\n2 5\n1 2 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 1\n output: 2\n2\n0\n-1\n3\n2\n2\n0\n\n" }, { "title": "Sixth Sense", "content": "Ms. Future is gifted with precognition. Naturally, she is excellent at some card games since she can correctly foresee every player's actions, except her own. Today, she accepted a challenge from a reckless gambler Mr. Past. They agreed to play a simple two-player trick-taking card game.\n\n Cards for the game have a number printed on one side, leaving the other side blank making indistinguishable from other cards.\n\n A game starts with the same number, say $n$, of cards being handed out to both players, without revealing the printed number to the opponent.\n\n A game consists of $n$ tricks. In each trick, both players pull one card out of her/his hand. The player pulling out the card with the larger number takes this trick. Because Ms. Future is extremely good at this game, they have agreed to give tricks to Mr. Past when both pull out cards with the same number. Once a card is used, it can never be used later in the same game. The game continues until all the cards in the hands are used up. The objective of the game is to take as many tricks as possible.\n\n Your mission of this problem is to help Ms. Future by providing a computer program to determine the best playing order of the cards in her hand. Since she has the sixth sense, your program can utilize information that is not available to ordinary people before the game.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$p_1$ . . . $p_n$\n$f_1$ . . . $f_n$\n\n $n$ in the first line is the number of tricks, which is an integer between 2 and 5000, inclusive. The second line represents the Mr. Past's playing order of the cards in his hand. In the $i$-th trick, he will pull out a card with the number $p_i$ ($1 <= i <= n$). The third line represents the Ms. Future's hand. $f_i$ ($1 <= i <= n$) is the number that she will see on the $i$-th received card from the dealer. Every number in the second or third line is an integer between 1 and 10 000, inclusive. These lines may have duplicate numbers.", "output": "The output should be a single line containing $n$ integers $a_1 . . . a_n$ separated by a space, where $a_i$ ($1 <= i <= n$) is the number on the card she should play at the $i$-th trick for maximizing the number of taken tricks. If there are two or more such sequences of numbers, output the lexicographically greatest one among them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 4 5\n1 2 3 4 5\n output: 2 3 4 5 1", "input: 5\n3 4 5 6 7\n1 3 5 7 9\n output: 9 5 7 3 1", "input: 5\n3 2 2 1 1\n1 1 2 2 3\n output: 1 3 1 2 2", "input: 5\n3 4 10 4 9\n2 7 3 6 9\n output: 9 7 3 6 2"], "Pid": "p00978", "ProblemText": "Task Description: Ms. Future is gifted with precognition. Naturally, she is excellent at some card games since she can correctly foresee every player's actions, except her own. Today, she accepted a challenge from a reckless gambler Mr. Past. They agreed to play a simple two-player trick-taking card game.\n\n Cards for the game have a number printed on one side, leaving the other side blank making indistinguishable from other cards.\n\n A game starts with the same number, say $n$, of cards being handed out to both players, without revealing the printed number to the opponent.\n\n A game consists of $n$ tricks. In each trick, both players pull one card out of her/his hand. The player pulling out the card with the larger number takes this trick. Because Ms. Future is extremely good at this game, they have agreed to give tricks to Mr. Past when both pull out cards with the same number. Once a card is used, it can never be used later in the same game. The game continues until all the cards in the hands are used up. The objective of the game is to take as many tricks as possible.\n\n Your mission of this problem is to help Ms. Future by providing a computer program to determine the best playing order of the cards in her hand. Since she has the sixth sense, your program can utilize information that is not available to ordinary people before the game.\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$p_1$ . . . $p_n$\n$f_1$ . . . $f_n$\n\n $n$ in the first line is the number of tricks, which is an integer between 2 and 5000, inclusive. The second line represents the Mr. Past's playing order of the cards in his hand. In the $i$-th trick, he will pull out a card with the number $p_i$ ($1 <= i <= n$). The third line represents the Ms. Future's hand. $f_i$ ($1 <= i <= n$) is the number that she will see on the $i$-th received card from the dealer. Every number in the second or third line is an integer between 1 and 10 000, inclusive. These lines may have duplicate numbers.\nTask Output: The output should be a single line containing $n$ integers $a_1 . . . a_n$ separated by a space, where $a_i$ ($1 <= i <= n$) is the number on the card she should play at the $i$-th trick for maximizing the number of taken tricks. If there are two or more such sequences of numbers, output the lexicographically greatest one among them.\nTask Samples: input: 5\n1 2 3 4 5\n1 2 3 4 5\n output: 2 3 4 5 1\ninput: 5\n3 4 5 6 7\n1 3 5 7 9\n output: 9 5 7 3 1\ninput: 5\n3 2 2 1 1\n1 1 2 2 3\n output: 1 3 1 2 2\ninput: 5\n3 4 10 4 9\n2 7 3 6 9\n output: 9 7 3 6 2\n\n" }, { "title": "Fast Forwarding", "content": "Mr. Anderson frequently rents video tapes of his favorite classic films. Watching the films so many times, he has learned the precise start times of his favorite scenes in all such films. He now wants to find how to wind the tape to watch his favorite scene as quickly as possible on his video player.\n\n When the [play] button is pressed, the film starts at the normal playback speed. The video player has two buttons to control the playback speed: The [3x] button triples the speed, while the [1/3x] button reduces the speed to one third. These speed control buttons, however, do not take effect on the instance they are pressed. Exactly one second after playback starts and every second thereafter, the states of these speed control buttons are checked. If the [3x] button is pressed on the timing of the check, the playback speed becomes three times the current speed. If the [1/3x] button is pressed, the playback speed becomes one third of the current speed, unless it is already the normal speed.\n\n For instance, assume that his favorite scene starts at 19 seconds from the start of the film. When the [3x] button is on at one second and at two seconds after the playback starts, and the [1/3x] button is on at three seconds and at five seconds after the start, the desired scene can be watched in the normal speed five seconds after starting the playback, as depicted in the following chart.\n\n Your task is to compute the shortest possible time period after the playback starts until the desired scene starts. The playback of the scene, of course, should be in the normal speed.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$t$\n\n The given single integer $t$ ($0 <= t < 2^{50}$) is the start time of the target scene.", "output": "Print an integer that is the minimum possible time in seconds before he can start watching the target scene in the normal speed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 19\n output: 5", "input: 13\n output: 5", "input: 123456789098765\n output: 85", "input: 51\n output: 11", "input: 0\n output: 0", "input: 3\n output: 3", "input: 4\n output: 2"], "Pid": "p00979", "ProblemText": "Task Description: Mr. Anderson frequently rents video tapes of his favorite classic films. Watching the films so many times, he has learned the precise start times of his favorite scenes in all such films. He now wants to find how to wind the tape to watch his favorite scene as quickly as possible on his video player.\n\n When the [play] button is pressed, the film starts at the normal playback speed. The video player has two buttons to control the playback speed: The [3x] button triples the speed, while the [1/3x] button reduces the speed to one third. These speed control buttons, however, do not take effect on the instance they are pressed. Exactly one second after playback starts and every second thereafter, the states of these speed control buttons are checked. If the [3x] button is pressed on the timing of the check, the playback speed becomes three times the current speed. If the [1/3x] button is pressed, the playback speed becomes one third of the current speed, unless it is already the normal speed.\n\n For instance, assume that his favorite scene starts at 19 seconds from the start of the film. When the [3x] button is on at one second and at two seconds after the playback starts, and the [1/3x] button is on at three seconds and at five seconds after the start, the desired scene can be watched in the normal speed five seconds after starting the playback, as depicted in the following chart.\n\n Your task is to compute the shortest possible time period after the playback starts until the desired scene starts. The playback of the scene, of course, should be in the normal speed.\nTask Input: The input consists of a single test case of the following format.\n\n$t$\n\n The given single integer $t$ ($0 <= t < 2^{50}$) is the start time of the target scene.\nTask Output: Print an integer that is the minimum possible time in seconds before he can start watching the target scene in the normal speed.\nTask Samples: input: 19\n output: 5\ninput: 13\n output: 5\ninput: 123456789098765\n output: 85\ninput: 51\n output: 11\ninput: 0\n output: 0\ninput: 3\n output: 3\ninput: 4\n output: 2\n\n" }, { "title": "Estimating the Flood Risk", "content": "Mr. Boat is the owner of a vast extent of land. As many typhoons have struck Japan this year, he became concerned of flood risk of his estate and he wants to know the average altitude of his land. The land is too vast to measure the altitude at many spots. As no steep slopes are in the estate, he thought that it would be enough to measure the altitudes at only a limited number of sites and then approximate the altitudes of the rest based on them.\n\n Multiple approximations might be possible based on the same measurement results, in which case he wants to know the worst case, that is, one giving the lowest average altitude.\n\n Mr. Boat 's estate, which has a rectangular shape, is divided into grid-aligned rectangular areas of the same size. Altitude measurements have been carried out in some of these areas, and the measurement results are now at hand. The altitudes of the remaining areas are to be approximated on the assumption that altitudes of two adjoining areas sharing an edge differ at most 1.\n\n In the first sample given below, the land is divided into 5 * 4 areas. The altitudes of the areas at (1,1) and (5,4) are measured 10 and 3, respectively. In this case, the altitudes of all the areas are uniquely determined on the assumption that altitudes of adjoining areas differ at most 1.\n\n In the second sample, there are multiple possibilities, among which one that gives the lowest average altitude should be considered.\n\nIn the third sample, no altitude assignments satisfy the assumption on altitude differences.\n\n Your job is to write a program that approximates the average altitude of his estate. To be precise, the program should compute the total of approximated and measured altitudes of all the mesh-divided areas. If two or more different approximations are possible, the program should compute the total with the severest approximation, that is, one giving the lowest total of the altitudes.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$w$ $d$ $n$\n$x_1$ $y_1$ $z_1$\n.\n.\n.\n$x_n$ $y_n$ $z_n$\n\nHere, $w$, $d$, and $n$ are integers between $1$ and $50$, inclusive. $w$ and $d$ are the numbers of areas in the two sides of the land. $n$ is the number of areas where altitudes are measured. The $i$-th line of the following $n$ lines contains three integers, $x_i$, $y_i$, and $z_i$ satisfying $1 <= x_i <= w$, $1 <= y_i <= d$, and $-100 <= z_i <= 100$. They mean that the altitude of the area at $(x_i\n, y_i)$ was measured to be $z_i$. At most one measurement result is given for the same area, i. e. , for $i \\ne j$, $(x_i, y_i) \\ne (x_j , y_j)$.", "output": "If all the unmeasured areas can be assigned their altitudes without any conflicts with the measured altitudes assuming that two adjoining areas have the altitude difference of at most 1, output an integer that is the total of the measured or approximated altitudes of all the areas. If more than one such altitude assignment is possible, output the minimum altitude total among the possible assignments.\n\n If no altitude assignments satisfy the altitude difference assumption, output No.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 4 2\n1 1 10\n5 4 3\n output: 130", "input: 5 4 3\n2 2 0\n4 3 0\n5 1 2\n output: -14", "input: 3 3 2\n1 1 8\n3 3 3\n output: No", "input: 2 2 1\n1 1 -100\n output: -404"], "Pid": "p00980", "ProblemText": "Task Description: Mr. Boat is the owner of a vast extent of land. As many typhoons have struck Japan this year, he became concerned of flood risk of his estate and he wants to know the average altitude of his land. The land is too vast to measure the altitude at many spots. As no steep slopes are in the estate, he thought that it would be enough to measure the altitudes at only a limited number of sites and then approximate the altitudes of the rest based on them.\n\n Multiple approximations might be possible based on the same measurement results, in which case he wants to know the worst case, that is, one giving the lowest average altitude.\n\n Mr. Boat 's estate, which has a rectangular shape, is divided into grid-aligned rectangular areas of the same size. Altitude measurements have been carried out in some of these areas, and the measurement results are now at hand. The altitudes of the remaining areas are to be approximated on the assumption that altitudes of two adjoining areas sharing an edge differ at most 1.\n\n In the first sample given below, the land is divided into 5 * 4 areas. The altitudes of the areas at (1,1) and (5,4) are measured 10 and 3, respectively. In this case, the altitudes of all the areas are uniquely determined on the assumption that altitudes of adjoining areas differ at most 1.\n\n In the second sample, there are multiple possibilities, among which one that gives the lowest average altitude should be considered.\n\nIn the third sample, no altitude assignments satisfy the assumption on altitude differences.\n\n Your job is to write a program that approximates the average altitude of his estate. To be precise, the program should compute the total of approximated and measured altitudes of all the mesh-divided areas. If two or more different approximations are possible, the program should compute the total with the severest approximation, that is, one giving the lowest total of the altitudes.\nTask Input: The input consists of a single test case of the following format.\n\n$w$ $d$ $n$\n$x_1$ $y_1$ $z_1$\n.\n.\n.\n$x_n$ $y_n$ $z_n$\n\nHere, $w$, $d$, and $n$ are integers between $1$ and $50$, inclusive. $w$ and $d$ are the numbers of areas in the two sides of the land. $n$ is the number of areas where altitudes are measured. The $i$-th line of the following $n$ lines contains three integers, $x_i$, $y_i$, and $z_i$ satisfying $1 <= x_i <= w$, $1 <= y_i <= d$, and $-100 <= z_i <= 100$. They mean that the altitude of the area at $(x_i\n, y_i)$ was measured to be $z_i$. At most one measurement result is given for the same area, i. e. , for $i \\ne j$, $(x_i, y_i) \\ne (x_j , y_j)$.\nTask Output: If all the unmeasured areas can be assigned their altitudes without any conflicts with the measured altitudes assuming that two adjoining areas have the altitude difference of at most 1, output an integer that is the total of the measured or approximated altitudes of all the areas. If more than one such altitude assignment is possible, output the minimum altitude total among the possible assignments.\n\n If no altitude assignments satisfy the altitude difference assumption, output No.\nTask Samples: input: 5 4 2\n1 1 10\n5 4 3\n output: 130\ninput: 5 4 3\n2 2 0\n4 3 0\n5 1 2\n output: -14\ninput: 3 3 2\n1 1 8\n3 3 3\n output: No\ninput: 2 2 1\n1 1 -100\n output: -404\n\n" }, { "title": "Wall Painting", "content": "Here stands a wall made of a number of vertical panels. The panels are not painted yet.\n\n You have a number of robots each of which can paint panels in a single color, either red, green, or blue. Each of the robots, when activated, paints panels between a certain position and another certain position in a certain color. The panels painted and the color to paint them are fixed for each of the robots, but which of them are to be activated and the order of their activation can be arbitrarily decided.\n\n You 'd like to have the wall painted to have a high aesthetic value. Here, the aesthetic value of the wall is defined simply as the sum of aesthetic values of the panels of the wall, and the aesthetic value of a panel is defined to be:\n\n 0, if the panel is left unpainted.\n\n The bonus value specified, if it is painted only in a single color, no matter how many times it is painted.\n\n The penalty value specified, if it is once painted in a color and then overpainted in one or more different colors.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$ $m$ $x$ $y$\n$c_1$ $l_1$ $r_1$\n.\n.\n.\n$c_m$ $l_m$ $r_m$\n\n Here, $n$ is the number of the panels ($1 <= n <= 10^9$) and $m$ is the number of robots ($1 <= m <= 2 * 10^5$). $x$ and $y$ are integers between $1$ and $10^5$, inclusive. $x$ is the bonus value and $-y$ is the penalty value. The panels of the wall are consecutively numbered $1$ through $n$. The $i$-th robot, when activated, paints all the panels of numbers $l_i$ through $r_i$ ($1 <= l_i <= r_i <= n$) in color with color number $c_i$ ($c_i \\in \\{1,2,3\\}$). Color numbers 1,2, and 3 correspond to red, green, and blue, respectively.", "output": "Output a single integer in a line which is the maximum achievable aesthetic value of the wall.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 5 10 5\n1 1 7\n3 1 2\n1 5 6\n3 1 4\n3 6 8\n output: 70", "input: 26 3 9 7\n1 11 13\n3 1 11\n3 18 26\n output: 182", "input: 21 10 10 5\n1 10 21\n3 4 16\n1 1 7\n3 11 21\n3 1 16\n3 3 3\n2 1 17\n3 5 18\n1 7 11\n2 3 14\n output: 210", "input: 21 15 8 7\n2 12 21\n2 1 2\n3 6 13\n2 13 17\n1 11 19\n3 3 5\n1 12 13\n3 2 2\n1 12 15\n1 5 17\n1 2 3\n1 1 9\n1 8 12\n3 8 9\n3 2 9\n output: 153"], "Pid": "p00981", "ProblemText": "Task Description: Here stands a wall made of a number of vertical panels. The panels are not painted yet.\n\n You have a number of robots each of which can paint panels in a single color, either red, green, or blue. Each of the robots, when activated, paints panels between a certain position and another certain position in a certain color. The panels painted and the color to paint them are fixed for each of the robots, but which of them are to be activated and the order of their activation can be arbitrarily decided.\n\n You 'd like to have the wall painted to have a high aesthetic value. Here, the aesthetic value of the wall is defined simply as the sum of aesthetic values of the panels of the wall, and the aesthetic value of a panel is defined to be:\n\n 0, if the panel is left unpainted.\n\n The bonus value specified, if it is painted only in a single color, no matter how many times it is painted.\n\n The penalty value specified, if it is once painted in a color and then overpainted in one or more different colors.\nTask Input: The input consists of a single test case of the following format.\n\n$n$ $m$ $x$ $y$\n$c_1$ $l_1$ $r_1$\n.\n.\n.\n$c_m$ $l_m$ $r_m$\n\n Here, $n$ is the number of the panels ($1 <= n <= 10^9$) and $m$ is the number of robots ($1 <= m <= 2 * 10^5$). $x$ and $y$ are integers between $1$ and $10^5$, inclusive. $x$ is the bonus value and $-y$ is the penalty value. The panels of the wall are consecutively numbered $1$ through $n$. The $i$-th robot, when activated, paints all the panels of numbers $l_i$ through $r_i$ ($1 <= l_i <= r_i <= n$) in color with color number $c_i$ ($c_i \\in \\{1,2,3\\}$). Color numbers 1,2, and 3 correspond to red, green, and blue, respectively.\nTask Output: Output a single integer in a line which is the maximum achievable aesthetic value of the wall.\nTask Samples: input: 8 5 10 5\n1 1 7\n3 1 2\n1 5 6\n3 1 4\n3 6 8\n output: 70\ninput: 26 3 9 7\n1 11 13\n3 1 11\n3 18 26\n output: 182\ninput: 21 10 10 5\n1 10 21\n3 4 16\n1 1 7\n3 11 21\n3 1 16\n3 3 3\n2 1 17\n3 5 18\n1 7 11\n2 3 14\n output: 210\ninput: 21 15 8 7\n2 12 21\n2 1 2\n3 6 13\n2 13 17\n1 11 19\n3 3 5\n1 12 13\n3 2 2\n1 12 15\n1 5 17\n1 2 3\n1 1 9\n1 8 12\n3 8 9\n3 2 9\n output: 153\n\n" }, { "title": "Twin Trees Bros.", "content": "To meet the demand of ICPC (International Cacao Plantation Consortium), you have to check whether two given trees are twins or not.\nThe term tree in the graph theory means a connected graph where the number of edges is one less than the number of nodes. ICPC, in addition, gives three-dimensional grid points as the locations of the tree nodes. Their definition of two trees being twins is that, there exists a geometric transformation function which gives a one-to-one mapping of all the nodes of one tree to the nodes of the other such that for each edge of one tree, there exists an edge in the other tree connecting the corresponding nodes. The geometric transformation should be a combination of the following transformations:\n translations, in which coordinate values are added with some constants,\n uniform scaling with positive scale factors, in which all three coordinate values are multiplied by the same positive constant, and \n rotations of any amounts around either $x$-, $y$-, and $z$-axes.\n Note that two trees can be twins in more than one way, that is, with different correspondences of nodes.\n Write a program that decides whether two trees are twins or not and outputs the number of different node correspondences.\n Hereinafter, transformations will be described in the right-handed $xyz$-coordinate system.\n Trees in the sample inputs 1 through 4 are shown in the following figures. The numbers in the figures are the node numbers defined below.\n For the sample input 1, each node of the red tree is mapped to the corresponding node of the blue tree by the transformation that translates $(-3,0,0)$, rotates $-\\pi / 2$ around the $z$-axis, rotates $\\pi / 4$ around the $x$-axis, and finally scales by $\\sqrt{2}$. By this mapping, nodes #1, #2, and #3 of the red tree at $(0,0,0)$, $(1,0,0)$, and $(3,0,0)$ correspond to nodes #6, #5, and #4 of the blue tree at $(0,3,3)$, $(0,2,2)$, and $(0,0,0)$, respectively. This is the only possible correspondence of the twin trees.\n For the sample input 2, red nodes #1, #2, #3, and #4 can be mapped to blue nodes #6, #5, #7, and #8. Another node correspondence exists that maps nodes #1, #2, #3, and #4 to #6, #5, #8, and #7.\n For the sample input 3, the two trees are not twins. There exist transformations that map nodes of one tree to distinct nodes of the other, but the edge connections do not agree.\n For the sample input 4, there is no transformation that maps nodes of one tree to those of the other.", "constraint": "", "input": "The input consists of a single test case of the following format.\n$n$\n$x_1$ $y_1$ $z_1$\n.\n.\n.\n$x_n$ $y_n$ $z_n$\n$u_1$ $v_1$\n.\n.\n.\n$u_{n-1}$ $v_{n-1}$\n$x_{n+1}$ $y_{n+1}$ $z_{n+1}$\n.\n.\n.\n$x_{2n}$ $y_{2n}$ $z_{2n}$\n$u_n$ $v_n$\n.\n.\n.\n$u_{2n-2}$ $v_{2n-2}$\n The input describes two trees. The first line contains an integer $n$ representing the number of nodes of each tree ($3 <= n <= 200$). Descriptions of two trees follow.\n Description of a tree consists of $n$ lines that give the vertex positions and $n - 1$ lines that show the connection relation of the vertices.\n Nodes are numbered $1$ through $n$ for the first tree, and $n + 1$ through $2n$ for the second tree.\n The triplet $(x_i, y_i, z_i)$ gives the coordinates of the node numbered $i$. $x_i$, $y_i$, and $z_i$ are integers in the range between $-1000$ and $1000$, inclusive. Nodes of a single tree have distinct coordinates.\n The pair of integers $(u_j , v_j )$ means that an edge exists between nodes numbered $u_j$ and $v_j$ ($u_j \ne v_j$). $1 <= u_j <= n$ and $1 <= v_j <= n$ hold for $1 <= j <= n - 1$, and $n + 1 <= u_j <= 2n$ and $n + 1 <= v_j <= 2n$ hold for $n <= j <= 2n - 2$.", "output": "Output the number of different node correspondences if two trees are twins. Output a zero, otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 0\n1 0 0\n3 0 0\n1 2\n2 3\n0 0 0\n0 2 2\n0 3 3\n4 5\n5 6\n output: 1", "input: 4\n1 0 0\n2 0 0\n2 1 0\n2 -1 0\n1 2\n2 3\n2 4\n0 1 1\n0 0 0\n0 2 0\n0 0 2\n5 6\n5 7\n5 8\n output: 2"], "Pid": "p00982", "ProblemText": "Task Description: To meet the demand of ICPC (International Cacao Plantation Consortium), you have to check whether two given trees are twins or not.\nThe term tree in the graph theory means a connected graph where the number of edges is one less than the number of nodes. ICPC, in addition, gives three-dimensional grid points as the locations of the tree nodes. Their definition of two trees being twins is that, there exists a geometric transformation function which gives a one-to-one mapping of all the nodes of one tree to the nodes of the other such that for each edge of one tree, there exists an edge in the other tree connecting the corresponding nodes. The geometric transformation should be a combination of the following transformations:\n translations, in which coordinate values are added with some constants,\n uniform scaling with positive scale factors, in which all three coordinate values are multiplied by the same positive constant, and \n rotations of any amounts around either $x$-, $y$-, and $z$-axes.\n Note that two trees can be twins in more than one way, that is, with different correspondences of nodes.\n Write a program that decides whether two trees are twins or not and outputs the number of different node correspondences.\n Hereinafter, transformations will be described in the right-handed $xyz$-coordinate system.\n Trees in the sample inputs 1 through 4 are shown in the following figures. The numbers in the figures are the node numbers defined below.\n For the sample input 1, each node of the red tree is mapped to the corresponding node of the blue tree by the transformation that translates $(-3,0,0)$, rotates $-\\pi / 2$ around the $z$-axis, rotates $\\pi / 4$ around the $x$-axis, and finally scales by $\\sqrt{2}$. By this mapping, nodes #1, #2, and #3 of the red tree at $(0,0,0)$, $(1,0,0)$, and $(3,0,0)$ correspond to nodes #6, #5, and #4 of the blue tree at $(0,3,3)$, $(0,2,2)$, and $(0,0,0)$, respectively. This is the only possible correspondence of the twin trees.\n For the sample input 2, red nodes #1, #2, #3, and #4 can be mapped to blue nodes #6, #5, #7, and #8. Another node correspondence exists that maps nodes #1, #2, #3, and #4 to #6, #5, #8, and #7.\n For the sample input 3, the two trees are not twins. There exist transformations that map nodes of one tree to distinct nodes of the other, but the edge connections do not agree.\n For the sample input 4, there is no transformation that maps nodes of one tree to those of the other.\nTask Input: The input consists of a single test case of the following format.\n$n$\n$x_1$ $y_1$ $z_1$\n.\n.\n.\n$x_n$ $y_n$ $z_n$\n$u_1$ $v_1$\n.\n.\n.\n$u_{n-1}$ $v_{n-1}$\n$x_{n+1}$ $y_{n+1}$ $z_{n+1}$\n.\n.\n.\n$x_{2n}$ $y_{2n}$ $z_{2n}$\n$u_n$ $v_n$\n.\n.\n.\n$u_{2n-2}$ $v_{2n-2}$\n The input describes two trees. The first line contains an integer $n$ representing the number of nodes of each tree ($3 <= n <= 200$). Descriptions of two trees follow.\n Description of a tree consists of $n$ lines that give the vertex positions and $n - 1$ lines that show the connection relation of the vertices.\n Nodes are numbered $1$ through $n$ for the first tree, and $n + 1$ through $2n$ for the second tree.\n The triplet $(x_i, y_i, z_i)$ gives the coordinates of the node numbered $i$. $x_i$, $y_i$, and $z_i$ are integers in the range between $-1000$ and $1000$, inclusive. Nodes of a single tree have distinct coordinates.\n The pair of integers $(u_j , v_j )$ means that an edge exists between nodes numbered $u_j$ and $v_j$ ($u_j \ne v_j$). $1 <= u_j <= n$ and $1 <= v_j <= n$ hold for $1 <= j <= n - 1$, and $n + 1 <= u_j <= 2n$ and $n + 1 <= v_j <= 2n$ hold for $n <= j <= 2n - 2$.\nTask Output: Output the number of different node correspondences if two trees are twins. Output a zero, otherwise.\nTask Samples: input: 3\n0 0 0\n1 0 0\n3 0 0\n1 2\n2 3\n0 0 0\n0 2 2\n0 3 3\n4 5\n5 6\n output: 1\ninput: 4\n1 0 0\n2 0 0\n2 1 0\n2 -1 0\n1 2\n2 3\n2 4\n0 1 1\n0 0 0\n0 2 0\n0 0 2\n5 6\n5 7\n5 8\n output: 2\n\n" }, { "title": "Reordering the Documents", "content": "Susan is good at arranging her dining table for convenience, but not her office desk.\n\n Susan has just finished the paperwork on a set of documents, which are still piled on her desk. They have serial numbers and were stacked in order when her boss brought them in. The ordering, however, is not perfect now, as she has been too lazy to put the documents slid out of the pile back to their proper positions. Hearing that she has finished, the boss wants her to return the documents immediately in the document box he is sending her. The documents should be stowed in the box, of course, in the order of their serial numbers.\n\n The desk has room just enough for two more document piles where Susan plans to make two temporary piles. All the documents in the current pile are to be moved one by one from the top to either of the two temporary piles. As making these piles too tall in haste would make them tumble, not too many documents should be placed on them. After moving all the documents to the temporary piles and receiving the document box, documents in the two piles will be moved from their tops, one by one, into the box. Documents should be in reverse order of their serial numbers in the two piles to allow moving them to the box in order.\n\n For example, assume that the pile has six documents #1, #3, #4, #2, #6, and #5, in this order from the top, and that the temporary piles can have no more than three documents. Then, she can form two temporary piles, one with documents #6, #4, and #3, from the top, and the other with #5, #2, and #1 (Figure E. 1). Both of the temporary piles are reversely ordered. Then, comparing the serial numbers of documents on top of the two temporary piles, one with the larger number (#6, in this case) is to be removed and stowed into the document box first. Repeating this, all the documents will be perfectly ordered in the document box.\n Figure E. 1. Making two temporary piles\n\n Susan is wondering whether the plan is actually feasible with the documents in the current pile and, if so, how many different ways of stacking them to two temporary piles would do. You are asked to help Susan by writing a program to compute the number of different ways, which should be zero if the plan is not feasible.\n\n As each of the documents in the pile can be moved to either of the two temporary piles, for $n$ documents, there are $2^n$ different choice combinations in total, but some of them may disturb the reverse order of the temporary piles and are thus inappropriate.\n\n The example described above corresponds to the first case of the sample input. In this case, the last two documents, #5 and #6, can be swapped their destinations. Also, exchanging the roles of two temporary piles totally will be OK. As any other move sequences would make one of the piles higher than three and/or make them out of order, the total number of different ways of stacking documents to temporary piles in this example is $2 * 2 = 4$.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$ $m$\n$s_1$ . . . $s_n$\n \n Here, $n$ is the number of documents in the pile ($1 <= n <= 5000$), and $m$ is the number of documents that can be stacked in one temporary pile without committing risks of making it tumble down ($n/2 <= m <= n$). Numbers $s_1$ through $s_n$ are the serial numbers of the documents in the document pile, from its top to its bottom. It is guaranteed that all the numbers $1$ through $n$ appear exactly once.", "output": "Output a single integer in a line which is the number of ways to form two temporary piles suited for the objective. When no choice will do, the number of ways is $0$, of course.\n\n If the number of possible ways is greater than or equal to $10^9 + 7$, output the number of ways modulo $10^9 + 7$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 3\n1 3 4 2 6 5\n output: 4", "input: 6 6\n1 3 4 2 6 5\n output: 8", "input: 4 4\n4 3 1 2\n output: 0"], "Pid": "p00983", "ProblemText": "Task Description: Susan is good at arranging her dining table for convenience, but not her office desk.\n\n Susan has just finished the paperwork on a set of documents, which are still piled on her desk. They have serial numbers and were stacked in order when her boss brought them in. The ordering, however, is not perfect now, as she has been too lazy to put the documents slid out of the pile back to their proper positions. Hearing that she has finished, the boss wants her to return the documents immediately in the document box he is sending her. The documents should be stowed in the box, of course, in the order of their serial numbers.\n\n The desk has room just enough for two more document piles where Susan plans to make two temporary piles. All the documents in the current pile are to be moved one by one from the top to either of the two temporary piles. As making these piles too tall in haste would make them tumble, not too many documents should be placed on them. After moving all the documents to the temporary piles and receiving the document box, documents in the two piles will be moved from their tops, one by one, into the box. Documents should be in reverse order of their serial numbers in the two piles to allow moving them to the box in order.\n\n For example, assume that the pile has six documents #1, #3, #4, #2, #6, and #5, in this order from the top, and that the temporary piles can have no more than three documents. Then, she can form two temporary piles, one with documents #6, #4, and #3, from the top, and the other with #5, #2, and #1 (Figure E. 1). Both of the temporary piles are reversely ordered. Then, comparing the serial numbers of documents on top of the two temporary piles, one with the larger number (#6, in this case) is to be removed and stowed into the document box first. Repeating this, all the documents will be perfectly ordered in the document box.\n Figure E. 1. Making two temporary piles\n\n Susan is wondering whether the plan is actually feasible with the documents in the current pile and, if so, how many different ways of stacking them to two temporary piles would do. You are asked to help Susan by writing a program to compute the number of different ways, which should be zero if the plan is not feasible.\n\n As each of the documents in the pile can be moved to either of the two temporary piles, for $n$ documents, there are $2^n$ different choice combinations in total, but some of them may disturb the reverse order of the temporary piles and are thus inappropriate.\n\n The example described above corresponds to the first case of the sample input. In this case, the last two documents, #5 and #6, can be swapped their destinations. Also, exchanging the roles of two temporary piles totally will be OK. As any other move sequences would make one of the piles higher than three and/or make them out of order, the total number of different ways of stacking documents to temporary piles in this example is $2 * 2 = 4$.\nTask Input: The input consists of a single test case of the following format.\n\n$n$ $m$\n$s_1$ . . . $s_n$\n \n Here, $n$ is the number of documents in the pile ($1 <= n <= 5000$), and $m$ is the number of documents that can be stacked in one temporary pile without committing risks of making it tumble down ($n/2 <= m <= n$). Numbers $s_1$ through $s_n$ are the serial numbers of the documents in the document pile, from its top to its bottom. It is guaranteed that all the numbers $1$ through $n$ appear exactly once.\nTask Output: Output a single integer in a line which is the number of ways to form two temporary piles suited for the objective. When no choice will do, the number of ways is $0$, of course.\n\n If the number of possible ways is greater than or equal to $10^9 + 7$, output the number of ways modulo $10^9 + 7$.\nTask Samples: input: 6 3\n1 3 4 2 6 5\n output: 4\ninput: 6 6\n1 3 4 2 6 5\n output: 8\ninput: 4 4\n4 3 1 2\n output: 0\n\n" }, { "title": "Halting Problem", "content": "A unique law is enforced in the Republic of Finite Loop. Under the law, programs that never halt are regarded as viruses. Releasing such a program is a cybercrime. So, you want to make sure that your software products always halt under their normal use.\n\n It is widely known that there exists no algorithm that can determine whether an arbitrary given program halts or not for a given arbitrary input. Fortunately, your products are based on a simple computation model given below. So, you can write a program that can tell whether a given program based on the model will eventually halt for a given input.\n\n The computation model for the products has only one variable $x$ and $N + 1$ states, numbered $1$ through $N + 1$. The variable $x$ can store any integer value. The state $N + 1$ means that the program has terminated. For each integer $i$ ($1 <= i <= N$), the behavior of the program in the state $i$ is described by five integers $a_i$, $b_i$, $c_i$, $d_i$ and $e_i$ ($c_i$ and $e_i$ are indices of states).\n\n On start of a program, its state is initialized to $1$, and the value of $x$ is initialized by $x_0$, the input to the program. When the program is in the state $i$ ($1 <= i <= N$), either of the following takes place in one execution step:\n\n if $x$ is equal to $a_i$, the value of $x$ changes to $x + b_i$ and the program state becomes $c_i$;\n\n otherwise, the value of $x$ changes to $x + d_i$ and the program state becomes $e_i$.\n The program terminates when the program state becomes $N + 1$.\n\n Your task is to write a program to determine whether a given program eventually halts or not for a given input, and, if it halts, to compute how many steps are executed. The initialization is not counted as a step.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$N$ $x_0$\n$a_1$ $b_1$ $c_1$ $d_1$ $e_1$\n.\n.\n.\n$a_N$ $b_N$ $c_N$ $d_N$ $e_N$\n\n The first line contains two integers $N$ ($1 <= N <= 10^5$) and $x_0$ ($-10^{13} <= x_0 <= 10^{13}$). The number of the states of the program is $N + 1$. $x_0$ is the initial value of the variable $x$. Each of the next $N$ lines contains five integers $a_i$, $b_i$, $c_i$, $d_i$ and $e_i$ that determine the behavior of the program when it is in the state $i$. $a_i$, $b_i$ and $d_i$ are integers between $-10^{13}$ and $10^{13}$, inclusive. $c_i$ and $e_i$ are integers between $1$ and $N + 1$, inclusive.", "output": "If the given program eventually halts with the given input, output a single integer in a line which is the number of steps executed until the program terminates. Since the number may be very large, output the number modulo $10^9 + 7$.\n\n Output $-1$ if the program will never halt.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 0\n5 1 2 1 1\n10 1 3 2 2\n output: 9", "input: 3 1\n0 1 4 2 3\n1 0 1 1 3\n3 -2 2 1 4\n output: -1", "input: 3 3\n1 -1 2 2 2\n1 1 1 -1 3\n1 1 4 -2 1\n output: -1"], "Pid": "p00984", "ProblemText": "Task Description: A unique law is enforced in the Republic of Finite Loop. Under the law, programs that never halt are regarded as viruses. Releasing such a program is a cybercrime. So, you want to make sure that your software products always halt under their normal use.\n\n It is widely known that there exists no algorithm that can determine whether an arbitrary given program halts or not for a given arbitrary input. Fortunately, your products are based on a simple computation model given below. So, you can write a program that can tell whether a given program based on the model will eventually halt for a given input.\n\n The computation model for the products has only one variable $x$ and $N + 1$ states, numbered $1$ through $N + 1$. The variable $x$ can store any integer value. The state $N + 1$ means that the program has terminated. For each integer $i$ ($1 <= i <= N$), the behavior of the program in the state $i$ is described by five integers $a_i$, $b_i$, $c_i$, $d_i$ and $e_i$ ($c_i$ and $e_i$ are indices of states).\n\n On start of a program, its state is initialized to $1$, and the value of $x$ is initialized by $x_0$, the input to the program. When the program is in the state $i$ ($1 <= i <= N$), either of the following takes place in one execution step:\n\n if $x$ is equal to $a_i$, the value of $x$ changes to $x + b_i$ and the program state becomes $c_i$;\n\n otherwise, the value of $x$ changes to $x + d_i$ and the program state becomes $e_i$.\n The program terminates when the program state becomes $N + 1$.\n\n Your task is to write a program to determine whether a given program eventually halts or not for a given input, and, if it halts, to compute how many steps are executed. The initialization is not counted as a step.\nTask Input: The input consists of a single test case of the following format.\n\n$N$ $x_0$\n$a_1$ $b_1$ $c_1$ $d_1$ $e_1$\n.\n.\n.\n$a_N$ $b_N$ $c_N$ $d_N$ $e_N$\n\n The first line contains two integers $N$ ($1 <= N <= 10^5$) and $x_0$ ($-10^{13} <= x_0 <= 10^{13}$). The number of the states of the program is $N + 1$. $x_0$ is the initial value of the variable $x$. Each of the next $N$ lines contains five integers $a_i$, $b_i$, $c_i$, $d_i$ and $e_i$ that determine the behavior of the program when it is in the state $i$. $a_i$, $b_i$ and $d_i$ are integers between $-10^{13}$ and $10^{13}$, inclusive. $c_i$ and $e_i$ are integers between $1$ and $N + 1$, inclusive.\nTask Output: If the given program eventually halts with the given input, output a single integer in a line which is the number of steps executed until the program terminates. Since the number may be very large, output the number modulo $10^9 + 7$.\n\n Output $-1$ if the program will never halt.\nTask Samples: input: 2 0\n5 1 2 1 1\n10 1 3 2 2\n output: 9\ninput: 3 1\n0 1 4 2 3\n1 0 1 1 3\n3 -2 2 1 4\n output: -1\ninput: 3 3\n1 -1 2 2 2\n1 1 1 -1 3\n1 1 4 -2 1\n output: -1\n\n" }, { "title": "Ambiguous Encoding", "content": "A friend of yours is designing an encoding scheme of a set of characters into a set of variable length bit sequences. You are asked to check whether the encoding is ambiguous or not. In an encoding scheme, characters are given distinct bit sequences of possibly different lengths as their codes. A character sequence is encoded into a bit sequence which is the concatenation of the codes of the characters in the string in the order of their appearances. An encoding scheme is said to be ambiguous if there exist two different character sequences encoded into exactly the same bit sequence. Such a bit sequence is called an “ambiguous binary sequence”.\n\n For example, encoding characters “A”, “B”, and “C” to 0,01 and 10, respectively, is ambiguous. This scheme encodes two different character strings “AC” and “BA” into the same bit sequence 010.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$w_1$\n.\n.\n.\n$w_n$\n\n Here, $n$ is the size of the set of characters to encode ($1 <= n <= 1000$). The $i$-th line of the following $n$ lines, $w_i$, gives the bit sequence for the $i$-th character as a non-empty sequence of at most 16 binary digits, 0 or 1. Note that different characters are given different codes, that is, $w_i \\ne w_j$ for $i \\ne j$.", "output": "If the given encoding is ambiguous, print in a line the number of bits in the shortest ambiguous binary sequence. Output zero, otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0\n01\n10\n output: 3", "input: 3\n00\n01\n1\n output: 0", "input: 3\n00\n10\n1\n output: 0", "input: 10\n1001\n1011\n01000\n00011\n01011\n1010\n00100\n10011\n11110\n0110\n output: 13", "input: 3\n1101\n1\n10\n output: 4"], "Pid": "p00985", "ProblemText": "Task Description: A friend of yours is designing an encoding scheme of a set of characters into a set of variable length bit sequences. You are asked to check whether the encoding is ambiguous or not. In an encoding scheme, characters are given distinct bit sequences of possibly different lengths as their codes. A character sequence is encoded into a bit sequence which is the concatenation of the codes of the characters in the string in the order of their appearances. An encoding scheme is said to be ambiguous if there exist two different character sequences encoded into exactly the same bit sequence. Such a bit sequence is called an “ambiguous binary sequence”.\n\n For example, encoding characters “A”, “B”, and “C” to 0,01 and 10, respectively, is ambiguous. This scheme encodes two different character strings “AC” and “BA” into the same bit sequence 010.\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$w_1$\n.\n.\n.\n$w_n$\n\n Here, $n$ is the size of the set of characters to encode ($1 <= n <= 1000$). The $i$-th line of the following $n$ lines, $w_i$, gives the bit sequence for the $i$-th character as a non-empty sequence of at most 16 binary digits, 0 or 1. Note that different characters are given different codes, that is, $w_i \\ne w_j$ for $i \\ne j$.\nTask Output: If the given encoding is ambiguous, print in a line the number of bits in the shortest ambiguous binary sequence. Output zero, otherwise.\nTask Samples: input: 3\n0\n01\n10\n output: 3\ninput: 3\n00\n01\n1\n output: 0\ninput: 3\n00\n10\n1\n output: 0\ninput: 10\n1001\n1011\n01000\n00011\n01011\n1010\n00100\n10011\n11110\n0110\n output: 13\ninput: 3\n1101\n1\n10\n output: 4\n\n" }, { "title": "Parentheses Editor", "content": "You are working with a strange text editor for texts consisting only of open and close parentheses. The editor accepts the following three keys as editing commands to modify the text kept in it.\n\n ‘( ' appends an open parenthesis (‘( ') to the end of the text.\n\n ‘) ' appends a close parenthesis (‘) ') to the end of the text.\n\n ‘- ' removes the last character of the text.\n A balanced string is one of the following.\n\n “()”\n\n “($X$)” where $X$ is a balanced string\n\n “$XY$” where both $X$ and $Y$ are balanced strings\n Initially, the editor keeps an empty text. You are interested in the number of balanced substrings in the text kept in the editor after each of your key command inputs. Note that, for the same balanced substring occurring twice or more, their occurrences should be counted separately. Also note that, when some balanced substrings are inside a balanced substring, both the inner and outer balanced substrings should be counted.", "constraint": "", "input": "The input consists of a single test case given in a line containing a number of characters, each of which is a command key to the editor, that is, either ‘( ', ‘) ', or ‘- '. The number of characters does not exceed 200 000. They represent a key input sequence to the editor.\n\nIt is guaranteed that no ‘- ' command comes when the text is empty.", "output": "Print the numbers of balanced substrings in the text kept in the editor after each of the key command inputs are applied, each in one line. Thus, the number of output lines should be the same as the number of characters in the input line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: (()())---)\n output: 0\n0\n1\n1\n3\n4\n3\n1\n1\n2", "input: ()--()()----)(()()))\n output: 0\n1\n0\n0\n0\n1\n1\n3\n1\n1\n0\n0\n0\n0\n0\n1\n1\n3\n4\n4"], "Pid": "p00986", "ProblemText": "Task Description: You are working with a strange text editor for texts consisting only of open and close parentheses. The editor accepts the following three keys as editing commands to modify the text kept in it.\n\n ‘( ' appends an open parenthesis (‘( ') to the end of the text.\n\n ‘) ' appends a close parenthesis (‘) ') to the end of the text.\n\n ‘- ' removes the last character of the text.\n A balanced string is one of the following.\n\n “()”\n\n “($X$)” where $X$ is a balanced string\n\n “$XY$” where both $X$ and $Y$ are balanced strings\n Initially, the editor keeps an empty text. You are interested in the number of balanced substrings in the text kept in the editor after each of your key command inputs. Note that, for the same balanced substring occurring twice or more, their occurrences should be counted separately. Also note that, when some balanced substrings are inside a balanced substring, both the inner and outer balanced substrings should be counted.\nTask Input: The input consists of a single test case given in a line containing a number of characters, each of which is a command key to the editor, that is, either ‘( ', ‘) ', or ‘- '. The number of characters does not exceed 200 000. They represent a key input sequence to the editor.\n\nIt is guaranteed that no ‘- ' command comes when the text is empty.\nTask Output: Print the numbers of balanced substrings in the text kept in the editor after each of the key command inputs are applied, each in one line. Thus, the number of output lines should be the same as the number of characters in the input line.\nTask Samples: input: (()())---)\n output: 0\n0\n1\n1\n3\n4\n3\n1\n1\n2\ninput: ()--()()----)(()()))\n output: 0\n1\n0\n0\n0\n1\n1\n3\n1\n1\n0\n0\n0\n0\n0\n1\n1\n3\n4\n4\n\n" }, { "title": "One-Way Conveyors", "content": "You are working at a factory manufacturing many different products. Products have to be processed on a number of different machine tools. Machine shops with these machines are connected with conveyor lines to exchange unfinished products. Each unfinished product is transferred from a machine shop to another through one or more of these conveyors.\n\n As the orders of the processes required are not the same for different types of products, the conveyor lines are currently operated in two-way. This may induce inefficiency as conveyors have to be completely emptied before switching their directions. Kaizen (efficiency improvements) may be found here!\n\n Adding more conveyors is too costly. If all the required transfers are possible with currently installed conveyors operating in fixed directions, no additional costs are required. All the required transfers, from which machine shop to which, are listed at hand. You want to know whether all the required transfers can be enabled with all the conveyors operated in one-way, and if yes, directions of the conveyor lines enabling it.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$ $m$\n$x_1$ $y_1$\n.\n.\n.\n$x_m$ $y_m$\n$k$\n$a_1$ $b_1$\n.\n.\n.\n$a_k$ $b_k$\n\nThe first line contains two integers $n$ ($2 <= n <= 10 000$) and $m$ ($1 <= m <= 100 000$), the number of machine shops and the number of conveyors, respectively. Machine shops are numbered $1$ through $n$. Each of the following $m$ lines contains two integers $x_i$ and $y_i$ ($1 <= x_i < y_i <= n$), meaning that the $i$-th conveyor connects machine shops $x_i$ and $y_i$. At most one conveyor is installed between any two machine shops. It is guaranteed that any two machine shops are connected through one or more conveyors. The next line contains an integer $k$ ($1 <= k <= 100 000$), which indicates the number of required transfers from a machine shop to another. Each of the following $k$ lines contains two integers $a_i$ and $b_i$ ($1 <= a_i <= n$, $1 <= b_i <= n$, $a_i \\ne b_i$), meaning that transfer from the machine shop $a_i$ to the machine shop $b_i$ is required. Either $a_i \\ne a_j$ or $b_i \\ne b_j$ holds for $i \\ne j$.", "output": "Output “No” if it is impossible to enable all the required transfers when all the conveyors are operated in one-way. Otherwise, output “Yes” in a line first, followed by $m$ lines each of which describes the directions of the conveyors. All the required transfers should be possible with the conveyor lines operated in these directions. Each direction should be described as a pair of the machine shop numbers separated by a space, with the start shop number on the left and the end shop number on the right. The order of these $m$ lines do not matter as far as all the conveyors are specified without duplicates or omissions. If there are multiple feasible direction assignments, whichever is fine.\n", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n2 3\n3\n1 2\n1 3\n2 3\n output: Yes\n1 2\n2 3", "input: 3 2\n1 2\n2 3\n3\n1 2\n1 3\n3 2\n output: No", "input: 4 4\n1 2\n1 3\n1 4\n2 3\n7\n1 2\n1 3\n1 4\n2 1\n2 3\n3 1\n3 2\n output: Yes\n1 2\n2 3\n3 1\n1 4"], "Pid": "p00987", "ProblemText": "Task Description: You are working at a factory manufacturing many different products. Products have to be processed on a number of different machine tools. Machine shops with these machines are connected with conveyor lines to exchange unfinished products. Each unfinished product is transferred from a machine shop to another through one or more of these conveyors.\n\n As the orders of the processes required are not the same for different types of products, the conveyor lines are currently operated in two-way. This may induce inefficiency as conveyors have to be completely emptied before switching their directions. Kaizen (efficiency improvements) may be found here!\n\n Adding more conveyors is too costly. If all the required transfers are possible with currently installed conveyors operating in fixed directions, no additional costs are required. All the required transfers, from which machine shop to which, are listed at hand. You want to know whether all the required transfers can be enabled with all the conveyors operated in one-way, and if yes, directions of the conveyor lines enabling it.\nTask Input: The input consists of a single test case of the following format.\n\n$n$ $m$\n$x_1$ $y_1$\n.\n.\n.\n$x_m$ $y_m$\n$k$\n$a_1$ $b_1$\n.\n.\n.\n$a_k$ $b_k$\n\nThe first line contains two integers $n$ ($2 <= n <= 10 000$) and $m$ ($1 <= m <= 100 000$), the number of machine shops and the number of conveyors, respectively. Machine shops are numbered $1$ through $n$. Each of the following $m$ lines contains two integers $x_i$ and $y_i$ ($1 <= x_i < y_i <= n$), meaning that the $i$-th conveyor connects machine shops $x_i$ and $y_i$. At most one conveyor is installed between any two machine shops. It is guaranteed that any two machine shops are connected through one or more conveyors. The next line contains an integer $k$ ($1 <= k <= 100 000$), which indicates the number of required transfers from a machine shop to another. Each of the following $k$ lines contains two integers $a_i$ and $b_i$ ($1 <= a_i <= n$, $1 <= b_i <= n$, $a_i \\ne b_i$), meaning that transfer from the machine shop $a_i$ to the machine shop $b_i$ is required. Either $a_i \\ne a_j$ or $b_i \\ne b_j$ holds for $i \\ne j$.\nTask Output: Output “No” if it is impossible to enable all the required transfers when all the conveyors are operated in one-way. Otherwise, output “Yes” in a line first, followed by $m$ lines each of which describes the directions of the conveyors. All the required transfers should be possible with the conveyor lines operated in these directions. Each direction should be described as a pair of the machine shop numbers separated by a space, with the start shop number on the left and the end shop number on the right. The order of these $m$ lines do not matter as far as all the conveyors are specified without duplicates or omissions. If there are multiple feasible direction assignments, whichever is fine.\n\nTask Samples: input: 3 2\n1 2\n2 3\n3\n1 2\n1 3\n2 3\n output: Yes\n1 2\n2 3\ninput: 3 2\n1 2\n2 3\n3\n1 2\n1 3\n3 2\n output: No\ninput: 4 4\n1 2\n1 3\n1 4\n2 3\n7\n1 2\n1 3\n1 4\n2 1\n2 3\n3 1\n3 2\n output: Yes\n1 2\n2 3\n3 1\n1 4\n\n" }, { "title": "Fun Region", "content": "Dr. Ciel lives in a planar island with a polygonal coastline. She loves strolling on the island along spiral paths. Here, a path is called spiral if both of the following are satisfied.\n\n The path is a simple planar polyline with no self-intersections.\n\n At all of its vertices, the line segment directions turn clockwise.\n Four paths are depicted below. Circle markers represent the departure points, and arrow heads represent the destinations of paths. Among the paths, only the leftmost is spiral.\n\n Dr. Ciel finds a point fun if, for all of the vertices of the island 's coastline, there exists a spiral path that starts from the point, ends at the vertex, and does not cross the coastline. Here, the spiral path may touch or overlap the coastline.\n\nIn the following figure, the outer polygon represents a coastline. The point ★ is fun, while the point ✖ is not fun. Dotted polylines starting from ★ are valid spiral paths that end at coastline vertices.\n Figure J. 1. Samples 1,2, and 3.\n\n We can prove that the set of all the fun points forms a (possibly empty) connected region, which we call the fun region. Given the coastline, your task is to write a program that computes the area size of the fun region.\n\n Figure J. 1 visualizes the three samples given below. The outer polygons correspond to the island 's coastlines. The fun regions are shown as the gray areas.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$n$\n$x_1$ $y_1$\n.\n.\n.\n$x_n$ $y_n$\n\n $n$ is the number of vertices of the polygon that represents the coastline ($3 <= n <= 2000$). Each of the following $n$ lines has two integers $x_i$ and $y_i$ , which give the coordinates ($x_i, y_i$) of the $i$-th vertex of the polygon, in counterclockwise order. $x_i$ and $y_i$ are between $0$ and $10 000$, inclusive. Here, the $x$-axis of the coordinate system directs right and the $y$-axis directs up. The polygon is simple, that is, it does not intersect nor touch itself. Note that the polygon may be non-convex. It is guaranteed that the inner angle of each vertex is not exactly $180$ degrees.", "output": "Output the area of the fun region in one line. Absolute or relative errors less than $10^{-7}$ are permissible.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n10 0\n20 10\n10 30\n0 10\n output: 300.00", "input: 10\n145 269\n299 271\n343 193\n183 139\n408 181\n356 324\n176 327\n147 404\n334 434\n102 424\n output: 12658.3130191", "input: 6\n144 401\n297 322\n114 282\n372 178\n197 271\n368 305\n output: 0.0"], "Pid": "p00988", "ProblemText": "Task Description: Dr. Ciel lives in a planar island with a polygonal coastline. She loves strolling on the island along spiral paths. Here, a path is called spiral if both of the following are satisfied.\n\n The path is a simple planar polyline with no self-intersections.\n\n At all of its vertices, the line segment directions turn clockwise.\n Four paths are depicted below. Circle markers represent the departure points, and arrow heads represent the destinations of paths. Among the paths, only the leftmost is spiral.\n\n Dr. Ciel finds a point fun if, for all of the vertices of the island 's coastline, there exists a spiral path that starts from the point, ends at the vertex, and does not cross the coastline. Here, the spiral path may touch or overlap the coastline.\n\nIn the following figure, the outer polygon represents a coastline. The point ★ is fun, while the point ✖ is not fun. Dotted polylines starting from ★ are valid spiral paths that end at coastline vertices.\n Figure J. 1. Samples 1,2, and 3.\n\n We can prove that the set of all the fun points forms a (possibly empty) connected region, which we call the fun region. Given the coastline, your task is to write a program that computes the area size of the fun region.\n\n Figure J. 1 visualizes the three samples given below. The outer polygons correspond to the island 's coastlines. The fun regions are shown as the gray areas.\nTask Input: The input consists of a single test case of the following format.\n\n$n$\n$x_1$ $y_1$\n.\n.\n.\n$x_n$ $y_n$\n\n $n$ is the number of vertices of the polygon that represents the coastline ($3 <= n <= 2000$). Each of the following $n$ lines has two integers $x_i$ and $y_i$ , which give the coordinates ($x_i, y_i$) of the $i$-th vertex of the polygon, in counterclockwise order. $x_i$ and $y_i$ are between $0$ and $10 000$, inclusive. Here, the $x$-axis of the coordinate system directs right and the $y$-axis directs up. The polygon is simple, that is, it does not intersect nor touch itself. Note that the polygon may be non-convex. It is guaranteed that the inner angle of each vertex is not exactly $180$ degrees.\nTask Output: Output the area of the fun region in one line. Absolute or relative errors less than $10^{-7}$ are permissible.\nTask Samples: input: 4\n10 0\n20 10\n10 30\n0 10\n output: 300.00\ninput: 10\n145 269\n299 271\n343 193\n183 139\n408 181\n356 324\n176 327\n147 404\n334 434\n102 424\n output: 12658.3130191\ninput: 6\n144 401\n297 322\n114 282\n372 178\n197 271\n368 305\n output: 0.0\n\n" }, { "title": "Draw in Straight Lines", "content": "You plan to draw a black-and-white painting on a rectangular canvas. The painting will be a grid array of pixels, either black or white. You can paint black or white lines or dots on the initially white canvas.\n\n You can apply a sequence of the following two operations in any order.\n\n Painting pixels on a horizontal or vertical line segment, single pixel wide and two or more pixel long, either black or white. This operation has a cost proportional to the length (the number of pixels) of the line segment multiplied by a specified coefficient in addition to a specified constant cost.\n \n\n Painting a single pixel, either black or white. This operation has a specified constant cost.\n \n You can overpaint already painted pixels as long as the following conditions are satisfied.\n\n The pixel has been painted at most once before. Overpainting a pixel too many times results in too thick layers of inks, making the picture look ugly. Note that painting a pixel with the same color is also counted as overpainting. For instance, if you have painted a pixel with black twice, you can paint it neither black nor white anymore.\n The pixel once painted white should not be overpainted with the black ink. As the white ink takes very long to dry, overpainting the same pixel black would make the pixel gray, rather than black. The reverse, that is, painting white over a pixel already painted black, has no problem.\n \n Your task is to compute the minimum total cost to draw the specified image.", "constraint": "", "input": "The input consists of a single test case. The first line contains five integers $n$, $m$, $a$, $b$, and $c$, where $n$ ($1 <= n <= 40$) and $m$ ($1 <= m <= 40$) are the height and the width of the canvas in the number of pixels, and $a$ ($0 <= a <= 40$), $b$ ($0 <= b <= 40$), and $c$ ($0 <= c <= 40$) are constants defining painting costs as follows. Painting a line segment of length $l$ costs $al + b$ and painting a single pixel costs $c$. These three constants satisfy $c <= a + b$.\n\nThe next $n$ lines show the black-and-white image you want to draw. Each of the lines contains a string of length $m$. The $j$-th character of the $i$-th string is ‘# ' if the color of the pixel in the $i$-th row and the $j$-th column is to be black, and it is ‘. ' if the color is to be white.", "output": "Output the minimum cost.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 1 2 3\n.#.\n###\n.#.\n output: 10", "input: 2 7 0 1 1\n###.###\n###.###\n output: 3", "input: 5 5 1 4 4\n..#..\n..#..\n##.##\n..#..\n..#..\n output: 24", "input: 7 24 1 10 10\n###...###..#####....###.\n.#...#...#.#....#..#...#\n.#..#......#....#.#.....\n.#..#......#####..#.....\n.#..#......#......#.....\n.#...#...#.#.......#...#\n###...###..#........###.\n output: 256"], "Pid": "p00989", "ProblemText": "Task Description: You plan to draw a black-and-white painting on a rectangular canvas. The painting will be a grid array of pixels, either black or white. You can paint black or white lines or dots on the initially white canvas.\n\n You can apply a sequence of the following two operations in any order.\n\n Painting pixels on a horizontal or vertical line segment, single pixel wide and two or more pixel long, either black or white. This operation has a cost proportional to the length (the number of pixels) of the line segment multiplied by a specified coefficient in addition to a specified constant cost.\n \n\n Painting a single pixel, either black or white. This operation has a specified constant cost.\n \n You can overpaint already painted pixels as long as the following conditions are satisfied.\n\n The pixel has been painted at most once before. Overpainting a pixel too many times results in too thick layers of inks, making the picture look ugly. Note that painting a pixel with the same color is also counted as overpainting. For instance, if you have painted a pixel with black twice, you can paint it neither black nor white anymore.\n The pixel once painted white should not be overpainted with the black ink. As the white ink takes very long to dry, overpainting the same pixel black would make the pixel gray, rather than black. The reverse, that is, painting white over a pixel already painted black, has no problem.\n \n Your task is to compute the minimum total cost to draw the specified image.\nTask Input: The input consists of a single test case. The first line contains five integers $n$, $m$, $a$, $b$, and $c$, where $n$ ($1 <= n <= 40$) and $m$ ($1 <= m <= 40$) are the height and the width of the canvas in the number of pixels, and $a$ ($0 <= a <= 40$), $b$ ($0 <= b <= 40$), and $c$ ($0 <= c <= 40$) are constants defining painting costs as follows. Painting a line segment of length $l$ costs $al + b$ and painting a single pixel costs $c$. These three constants satisfy $c <= a + b$.\n\nThe next $n$ lines show the black-and-white image you want to draw. Each of the lines contains a string of length $m$. The $j$-th character of the $i$-th string is ‘# ' if the color of the pixel in the $i$-th row and the $j$-th column is to be black, and it is ‘. ' if the color is to be white.\nTask Output: Output the minimum cost.\nTask Samples: input: 3 3 1 2 3\n.#.\n###\n.#.\n output: 10\ninput: 2 7 0 1 1\n###.###\n###.###\n output: 3\ninput: 5 5 1 4 4\n..#..\n..#..\n##.##\n..#..\n..#..\n output: 24\ninput: 7 24 1 10 10\n###...###..#####....###.\n.#...#...#.#....#..#...#\n.#..#......#....#.#.....\n.#..#......#####..#.....\n.#..#......#......#.....\n.#...#...#.#.......#...#\n###...###..#........###.\n output: 256\n\n" }, { "title": "Entrance Examination", "content": "The International Competitive Programming College (ICPC) is famous\nfor its research on competitive programming.\nApplicants to the college are required to take its entrance examination.\n\nThe successful applicants of the examination are chosen as follows.\n\nThe score of any successful applicant is higher than that of any unsuccessful applicant.\n\nThe number of successful applicants n must be between n_min and n_max, inclusive.\nWe choose n within the specified range that maximizes the gap. \nHere, the gap means the difference between the lowest score of\nsuccessful applicants and the highest score of unsuccessful applicants.\n When two or more candidates for n make exactly the same gap, \nuse the greatest n among them.\nLet's see the first couple of examples given in Sample Input below.\nIn the first example, n_min and n_max are two and four, respectively, and there are five applicants whose scores are 100,90,82,70, and 65.\nFor n of two, three and four, the gaps will be 8,12, and 5, respectively.\nWe must choose three as n, because it maximizes the gap.\n\nIn the second example, n_min and n_max are two and four, respectively, and there are five applicants whose scores are 100,90,80,75, and 65.\nFor n of two, three and four, the gap will be 10,5, and 10, \nrespectively. Both two and four maximize the gap, and we must choose the\n greatest number, four.\n\nYou are requested to write a program that computes the number of successful applicants that satisfies the conditions.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is formatted as follows.\n\nm n_min n_max\nP_1\nP_2\n. . . \nP_m\n\nThe first line of a dataset contains three integers separated by single spaces.\nm represents the number of applicants, n_min represents the minimum number of successful applicants, and n_max represents the maximum number of successful applicants.\nEach of the following m lines contains an integer\nP_i, which represents the score of each applicant.\nThe scores are listed in descending order.\nThese numbers satisfy 0 < n_min < n_max < m <= 200,0 <= P_i <= 10000 (1 <= i <= m) and P_nmin > P_nmax+1. These ensure that there always exists an n satisfying the conditions.\n\nThe end of the input is represented by a line containing three zeros separated by single spaces.", "output": "For each dataset, output the number of successful applicants in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 4\n100\n90\n82\n70\n65\n5 2 4\n100\n90\n80\n75\n65\n3 1 2\n5000\n4000\n3000\n4 2 3\n10000\n10000\n8000\n8000\n4 2 3\n10000\n10000\n10000\n8000\n5 2 3\n100\n80\n68\n60\n45\n0 0 0\n output: 3\n4\n2\n2\n3\n2"], "Pid": "p01085", "ProblemText": "Task Description: The International Competitive Programming College (ICPC) is famous\nfor its research on competitive programming.\nApplicants to the college are required to take its entrance examination.\n\nThe successful applicants of the examination are chosen as follows.\n\nThe score of any successful applicant is higher than that of any unsuccessful applicant.\n\nThe number of successful applicants n must be between n_min and n_max, inclusive.\nWe choose n within the specified range that maximizes the gap. \nHere, the gap means the difference between the lowest score of\nsuccessful applicants and the highest score of unsuccessful applicants.\n When two or more candidates for n make exactly the same gap, \nuse the greatest n among them.\nLet's see the first couple of examples given in Sample Input below.\nIn the first example, n_min and n_max are two and four, respectively, and there are five applicants whose scores are 100,90,82,70, and 65.\nFor n of two, three and four, the gaps will be 8,12, and 5, respectively.\nWe must choose three as n, because it maximizes the gap.\n\nIn the second example, n_min and n_max are two and four, respectively, and there are five applicants whose scores are 100,90,80,75, and 65.\nFor n of two, three and four, the gap will be 10,5, and 10, \nrespectively. Both two and four maximize the gap, and we must choose the\n greatest number, four.\n\nYou are requested to write a program that computes the number of successful applicants that satisfies the conditions.\nTask Input: The input consists of multiple datasets. Each dataset is formatted as follows.\n\nm n_min n_max\nP_1\nP_2\n. . . \nP_m\n\nThe first line of a dataset contains three integers separated by single spaces.\nm represents the number of applicants, n_min represents the minimum number of successful applicants, and n_max represents the maximum number of successful applicants.\nEach of the following m lines contains an integer\nP_i, which represents the score of each applicant.\nThe scores are listed in descending order.\nThese numbers satisfy 0 < n_min < n_max < m <= 200,0 <= P_i <= 10000 (1 <= i <= m) and P_nmin > P_nmax+1. These ensure that there always exists an n satisfying the conditions.\n\nThe end of the input is represented by a line containing three zeros separated by single spaces.\nTask Output: For each dataset, output the number of successful applicants in a line.\nTask Samples: input: 5 2 4\n100\n90\n82\n70\n65\n5 2 4\n100\n90\n80\n75\n65\n3 1 2\n5000\n4000\n3000\n4 2 3\n10000\n10000\n8000\n8000\n4 2 3\n10000\n10000\n10000\n8000\n5 2 3\n100\n80\n68\n60\n45\n0 0 0\n output: 3\n4\n2\n2\n3\n2\n\n" }, { "title": "Short Phrase", "content": "A Short Phrase (aka. Tanku) is a fixed verse, inspired by Japanese poetry Tanka and Haiku.\nIt is a sequence of words, each consisting of lowercase letters 'a' to 'z', and must satisfy the following condition:\n\n(The Condition for a Short Phrase)\nThe sequence of words can be divided into five sections such that the \ntotal number of the letters in the word(s) of the first section is five,\n that of the second is seven, and those of the rest are five, seven, and\n seven, respectively.\n\nThe following is an example of a Short Phrase.\n\ndo the best\nand enjoy today\nat acm icpc\n\nIn this example, the sequence of the nine words can be divided into five\n sections (1) \"do\" and \"the\", (2) \"best\" and \"and\", (3) \"enjoy\", (4) \n\"today\" and \"at\", and (5) \"acm\" and \"icpc\" such that they have 5,7,5, \n7, and 7 letters in this order, respectively.\nThis surely satisfies the condition of a Short Phrase.\n\nNow, Short Phrase Parnassus published by your company has \nreceived a lot of contributions.\nBy an unfortunate accident, however, some irrelevant texts seem to be \nadded at beginnings and ends of contributed Short Phrases.\nYour mission is to write a program that finds the Short Phrase from a \nsequence of words that may have an irrelevant prefix and/or a suffix.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn\nw_1\n. . . \nw_n\n\nHere, n is the number of words, which is a positive integer not exceeding 40;\nw_i is the i-th word, consisting solely of lowercase letters from 'a' to 'z'.\nThe length of each word is between 1 and 10, inclusive.\nYou can assume that every dataset includes a Short Phrase.\n\nThe end of the input is indicated by a line with a single zero.", "output": "For each dataset, output a single line containing i where\nthe first word of the Short Phrase is w_i.\nWhen multiple Short Phrases occur in the dataset, you should output the first one.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\ndo\nthe\nbest\nand\nenjoy\ntoday\nat\nacm\nicpc\n14\noh\nyes\nby\nfar\nit\nis\nwow\nso\nbad\nto\nme\nyou\nknow\nhey\n15\nabcde\nfghijkl\nmnopq\nrstuvwx\nyzz\nabcde\nfghijkl\nmnopq\nrstuvwx\nyz\nabcde\nfghijkl\nmnopq\nrstuvwx\nyz\n0\n output: 1\n2\n6"], "Pid": "p01086", "ProblemText": "Task Description: A Short Phrase (aka. Tanku) is a fixed verse, inspired by Japanese poetry Tanka and Haiku.\nIt is a sequence of words, each consisting of lowercase letters 'a' to 'z', and must satisfy the following condition:\n\n(The Condition for a Short Phrase)\nThe sequence of words can be divided into five sections such that the \ntotal number of the letters in the word(s) of the first section is five,\n that of the second is seven, and those of the rest are five, seven, and\n seven, respectively.\n\nThe following is an example of a Short Phrase.\n\ndo the best\nand enjoy today\nat acm icpc\n\nIn this example, the sequence of the nine words can be divided into five\n sections (1) \"do\" and \"the\", (2) \"best\" and \"and\", (3) \"enjoy\", (4) \n\"today\" and \"at\", and (5) \"acm\" and \"icpc\" such that they have 5,7,5, \n7, and 7 letters in this order, respectively.\nThis surely satisfies the condition of a Short Phrase.\n\nNow, Short Phrase Parnassus published by your company has \nreceived a lot of contributions.\nBy an unfortunate accident, however, some irrelevant texts seem to be \nadded at beginnings and ends of contributed Short Phrases.\nYour mission is to write a program that finds the Short Phrase from a \nsequence of words that may have an irrelevant prefix and/or a suffix.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn\nw_1\n. . . \nw_n\n\nHere, n is the number of words, which is a positive integer not exceeding 40;\nw_i is the i-th word, consisting solely of lowercase letters from 'a' to 'z'.\nThe length of each word is between 1 and 10, inclusive.\nYou can assume that every dataset includes a Short Phrase.\n\nThe end of the input is indicated by a line with a single zero.\nTask Output: For each dataset, output a single line containing i where\nthe first word of the Short Phrase is w_i.\nWhen multiple Short Phrases occur in the dataset, you should output the first one.\nTask Samples: input: 9\ndo\nthe\nbest\nand\nenjoy\ntoday\nat\nacm\nicpc\n14\noh\nyes\nby\nfar\nit\nis\nwow\nso\nbad\nto\nme\nyou\nknow\nhey\n15\nabcde\nfghijkl\nmnopq\nrstuvwx\nyzz\nabcde\nfghijkl\nmnopq\nrstuvwx\nyz\nabcde\nfghijkl\nmnopq\nrstuvwx\nyz\n0\n output: 1\n2\n6\n\n" }, { "title": "ICPC Calculator", "content": "In mathematics, we usually specify the order of operations by using\nparentheses.\nFor example, 7 * (3 + 2) always means multiplying 7 by the result of 3 + 2 and never means adding 2 to the result of 7 * 3.\n\nHowever, there are people who do not like parentheses.\nInternational Counter of Parentheses Council (ICPC) is attempting\nto make a notation without parentheses the world standard.\nThey are always making studies of such no-parentheses notations.\n\nDr. Tsukuba, a member of ICPC, invented a new parenthesis-free notation.\nIn his notation, a single expression is represented by multiple\nlines, each of which contains an addition operator ( + ), a\nmultiplication operator ( * ) or an integer.\nAn expression is either a single integer or an operator application to operands. \nIntegers are denoted in decimal notation in one line.\nAn operator application is denoted by a line of its operator immediately\nfollowed by lines denoting its two or more operands,\neach of which is an expression, recursively.\nNote that when an operand is an operator application,\nit comprises multiple lines.\n\nAs expressions may be arbitrarily nested,\nwe have to make it clear which operator is applied to which operands.\nFor that purpose, each of the expressions is given its nesting level. \nThe top level expression has the nesting level of 0.\nWhen an expression of level n is an operator application,\nits operands are expressions of level n + 1.\nThe first line of an expression starts with a sequence of periods ( . ),\nthe number of which indicates the level of the expression.\n\nFor example, 2 + 3 in the regular mathematics is denoted as in Figure 1.\nAn operator can be applied to two or more operands.\nOperators + and * represent operations\nof summation of all operands and multiplication of all operands,\nrespectively. For example, Figure 2 shows an expression multiplying\n2,3, and 4.\nFor a more complicated example, an expression (2 + 3 + 4) * 5 in\nthe regular mathematics can be expressed as in Figure 3 while (2 + 3) * 4 * 5\ncan be expressed as in Figure 4.\n+\n. 2\n. 3\n*\n. 2\n. 3\n. 4\n*\n. +\n. . 2\n. . 3\n. . 4\n. 5\n*\n. +\n. . 2\n. . 3\n. 4\n. 5\n\n Your job is to write a program that computes the value of expressions\n written in Dr. Tsukuba's notation to help him.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset\n starts with a line containing a positive integer n, followed by\n n lines denoting a single expression in Dr. Tsukuba's notation.\n\n You may assume that, in the expressions given in the input,\n every integer comprises a single digit and that\n every expression has no more than nine integers.\n You may also assume that all the input expressions are valid\n in the Dr. Tsukuba's notation.\n The input contains no extra characters, such as spaces or empty lines.\n\n The last dataset is immediately followed by a line with a single zero.", "output": "For each dataset, output a single line containing an integer\nwhich is the value of the given expression.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n9\n4\n+\n.1\n.2\n.3\n9\n+\n.0\n.+\n..*\n...1\n...*\n....1\n....2\n..0\n10\n+\n.+\n..6\n..2\n.+\n..1\n..*\n...7\n...6\n.3\n0\n output: 9\n6\n2\n54"], "Pid": "p01087", "ProblemText": "Task Description: In mathematics, we usually specify the order of operations by using\nparentheses.\nFor example, 7 * (3 + 2) always means multiplying 7 by the result of 3 + 2 and never means adding 2 to the result of 7 * 3.\n\nHowever, there are people who do not like parentheses.\nInternational Counter of Parentheses Council (ICPC) is attempting\nto make a notation without parentheses the world standard.\nThey are always making studies of such no-parentheses notations.\n\nDr. Tsukuba, a member of ICPC, invented a new parenthesis-free notation.\nIn his notation, a single expression is represented by multiple\nlines, each of which contains an addition operator ( + ), a\nmultiplication operator ( * ) or an integer.\nAn expression is either a single integer or an operator application to operands. \nIntegers are denoted in decimal notation in one line.\nAn operator application is denoted by a line of its operator immediately\nfollowed by lines denoting its two or more operands,\neach of which is an expression, recursively.\nNote that when an operand is an operator application,\nit comprises multiple lines.\n\nAs expressions may be arbitrarily nested,\nwe have to make it clear which operator is applied to which operands.\nFor that purpose, each of the expressions is given its nesting level. \nThe top level expression has the nesting level of 0.\nWhen an expression of level n is an operator application,\nits operands are expressions of level n + 1.\nThe first line of an expression starts with a sequence of periods ( . ),\nthe number of which indicates the level of the expression.\n\nFor example, 2 + 3 in the regular mathematics is denoted as in Figure 1.\nAn operator can be applied to two or more operands.\nOperators + and * represent operations\nof summation of all operands and multiplication of all operands,\nrespectively. For example, Figure 2 shows an expression multiplying\n2,3, and 4.\nFor a more complicated example, an expression (2 + 3 + 4) * 5 in\nthe regular mathematics can be expressed as in Figure 3 while (2 + 3) * 4 * 5\ncan be expressed as in Figure 4.\n+\n. 2\n. 3\n*\n. 2\n. 3\n. 4\n*\n. +\n. . 2\n. . 3\n. . 4\n. 5\n*\n. +\n. . 2\n. . 3\n. 4\n. 5\n\n Your job is to write a program that computes the value of expressions\n written in Dr. Tsukuba's notation to help him.\nTask Input: The input consists of multiple datasets. Each dataset\n starts with a line containing a positive integer n, followed by\n n lines denoting a single expression in Dr. Tsukuba's notation.\n\n You may assume that, in the expressions given in the input,\n every integer comprises a single digit and that\n every expression has no more than nine integers.\n You may also assume that all the input expressions are valid\n in the Dr. Tsukuba's notation.\n The input contains no extra characters, such as spaces or empty lines.\n\n The last dataset is immediately followed by a line with a single zero.\nTask Output: For each dataset, output a single line containing an integer\nwhich is the value of the given expression.\nTask Samples: input: 1\n9\n4\n+\n.1\n.2\n.3\n9\n+\n.0\n.+\n..*\n...1\n...*\n....1\n....2\n..0\n10\n+\n.+\n..6\n..2\n.+\n..1\n..*\n...7\n...6\n.3\n0\n output: 9\n6\n2\n54\n\n" }, { "title": "500-yen Saving", "content": "\"500-yen Saving\" is one of Japanese famous methods to save money. The\nmethod is quite simple; whenever you receive a 500-yen coin in your\nchange of shopping, put the coin to your 500-yen saving box.\nTypically, you will find more than one million yen in your saving box\nin ten years.\nSome Japanese people are addicted to the 500-yen saving. They try\ntheir best to collect 500-yen coins efficiently by using 1000-yen bills\nand some coins effectively in their purchasing. For example, you will give\n1320 yen (one 1000-yen bill, three 100-yen coins and two 10-yen coins)\nto pay 817 yen, to receive one 500-yen coin (and three 1-yen coins)\nin the change.\n\nA friend of yours is one of these 500-yen saving addicts. He is\nplanning a sightseeing trip and wants to visit a number of souvenir\nshops along his way. He will visit souvenir shops one by one\naccording to the trip plan. Every souvenir shop sells only one kind of\nsouvenir goods, and he has the complete list of their prices. He\nwants to collect as many 500-yen coins as possible through buying\nat most one souvenir from a shop. On his departure,\nhe will start with sufficiently many 1000-yen bills and no coins at\nall. The order of shops to visit cannot be changed. As far as he can\ncollect the same number of 500-yen coins, he wants to cut his expenses\nas much as possible.\n\nLet's say that he is visiting shops with their souvenir prices of 800\nyen, 700 yen, 1600 yen, and 600 yen, in this order. He can collect at\nmost two 500-yen coins spending 2900 yen, the least expenses to collect\ntwo 500-yen coins, in this case. After skipping the first shop, the\nway of spending 700-yen at the second shop is by handing over a\n1000-yen bill and receiving three 100-yen coins. In the next shop,\nhanding over one of these 100-yen coins and two 1000-yen bills for\nbuying a 1600-yen souvenir will make him receive one 500-yen coin. In\nalmost the same way, he can obtain another 500-yen coin at the last\nshop. He can also collect two 500-yen coins buying at the first shop,\nbut his total expenditure will be at least 3000 yen because he needs\nto buy both the 1600-yen and 600-yen souvenirs in this case.\n\nYou are asked to make a program to help his collecting 500-yen coins\nduring the trip. Receiving souvenirs' prices listed in the order\nof visiting the shops, your program is to find the maximum number of\n500-yen coins that he can collect during his trip, and the minimum\nexpenses needed for that number of 500-yen coins.\n\nFor shopping, he can use an arbitrary number of 1-yen, 5-yen, 10-yen,\n50-yen, and 100-yen coins he has, and arbitrarily many 1000-yen bills.\nThe shop always returns the exact change, i. e. , the difference between\nthe amount he hands over and the price of the souvenir. The shop has\nsufficient stock of coins and the change is always composed of the\nsmallest possible number of 1-yen, 5-yen, 10-yen, 50-yen, 100-yen, and\n500-yen coins and 1000-yen bills. He may use more money than the\nprice of the souvenir, even if he can put the exact money, to obtain\ndesired coins as change; buying a souvenir of 1000 yen, he can hand\nover one 1000-yen bill and five 100-yen coins and receive a 500-yen\ncoin. Note that using too many coins does no good; handing over ten\n100-yen coins and a 1000-yen bill for a souvenir of 1000 yen, he will\nreceive a 1000-yen bill as the change, not two 500-yen coins.", "constraint": "", "input": "The input consists of at most 50 datasets, each in the following format.\n\nn \np_1\n. . . \np_n \n\nn is the number of souvenir shops, which is a positive integer not\ngreater than 100.\n\np_i is the price of the souvenir of the i-th souvenir shop.\n\np_i is a positive integer not greater than 5000.\n\nThe end of the input is indicated by a line with a single zero.", "output": "For each dataset, print a line containing two integers c and s separated by a space.\n\nHere, c is the maximum number of 500-yen coins that he can get during his\ntrip, and s is the minimum expenses that he need to pay to get c\n500-yen coins.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n800\n700\n1600\n600\n4\n300\n700\n1600\n600\n4\n300\n700\n1600\n650\n3\n1000\n2000\n500\n3\n250\n250\n1000\n4\n1251\n667\n876\n299\n0\n output: 2 2900\n3 2500\n3 3250\n1 500\n3 1500\n3 2217"], "Pid": "p01088", "ProblemText": "Task Description: \"500-yen Saving\" is one of Japanese famous methods to save money. The\nmethod is quite simple; whenever you receive a 500-yen coin in your\nchange of shopping, put the coin to your 500-yen saving box.\nTypically, you will find more than one million yen in your saving box\nin ten years.\nSome Japanese people are addicted to the 500-yen saving. They try\ntheir best to collect 500-yen coins efficiently by using 1000-yen bills\nand some coins effectively in their purchasing. For example, you will give\n1320 yen (one 1000-yen bill, three 100-yen coins and two 10-yen coins)\nto pay 817 yen, to receive one 500-yen coin (and three 1-yen coins)\nin the change.\n\nA friend of yours is one of these 500-yen saving addicts. He is\nplanning a sightseeing trip and wants to visit a number of souvenir\nshops along his way. He will visit souvenir shops one by one\naccording to the trip plan. Every souvenir shop sells only one kind of\nsouvenir goods, and he has the complete list of their prices. He\nwants to collect as many 500-yen coins as possible through buying\nat most one souvenir from a shop. On his departure,\nhe will start with sufficiently many 1000-yen bills and no coins at\nall. The order of shops to visit cannot be changed. As far as he can\ncollect the same number of 500-yen coins, he wants to cut his expenses\nas much as possible.\n\nLet's say that he is visiting shops with their souvenir prices of 800\nyen, 700 yen, 1600 yen, and 600 yen, in this order. He can collect at\nmost two 500-yen coins spending 2900 yen, the least expenses to collect\ntwo 500-yen coins, in this case. After skipping the first shop, the\nway of spending 700-yen at the second shop is by handing over a\n1000-yen bill and receiving three 100-yen coins. In the next shop,\nhanding over one of these 100-yen coins and two 1000-yen bills for\nbuying a 1600-yen souvenir will make him receive one 500-yen coin. In\nalmost the same way, he can obtain another 500-yen coin at the last\nshop. He can also collect two 500-yen coins buying at the first shop,\nbut his total expenditure will be at least 3000 yen because he needs\nto buy both the 1600-yen and 600-yen souvenirs in this case.\n\nYou are asked to make a program to help his collecting 500-yen coins\nduring the trip. Receiving souvenirs' prices listed in the order\nof visiting the shops, your program is to find the maximum number of\n500-yen coins that he can collect during his trip, and the minimum\nexpenses needed for that number of 500-yen coins.\n\nFor shopping, he can use an arbitrary number of 1-yen, 5-yen, 10-yen,\n50-yen, and 100-yen coins he has, and arbitrarily many 1000-yen bills.\nThe shop always returns the exact change, i. e. , the difference between\nthe amount he hands over and the price of the souvenir. The shop has\nsufficient stock of coins and the change is always composed of the\nsmallest possible number of 1-yen, 5-yen, 10-yen, 50-yen, 100-yen, and\n500-yen coins and 1000-yen bills. He may use more money than the\nprice of the souvenir, even if he can put the exact money, to obtain\ndesired coins as change; buying a souvenir of 1000 yen, he can hand\nover one 1000-yen bill and five 100-yen coins and receive a 500-yen\ncoin. Note that using too many coins does no good; handing over ten\n100-yen coins and a 1000-yen bill for a souvenir of 1000 yen, he will\nreceive a 1000-yen bill as the change, not two 500-yen coins.\nTask Input: The input consists of at most 50 datasets, each in the following format.\n\nn \np_1\n. . . \np_n \n\nn is the number of souvenir shops, which is a positive integer not\ngreater than 100.\n\np_i is the price of the souvenir of the i-th souvenir shop.\n\np_i is a positive integer not greater than 5000.\n\nThe end of the input is indicated by a line with a single zero.\nTask Output: For each dataset, print a line containing two integers c and s separated by a space.\n\nHere, c is the maximum number of 500-yen coins that he can get during his\ntrip, and s is the minimum expenses that he need to pay to get c\n500-yen coins.\nTask Samples: input: 4\n800\n700\n1600\n600\n4\n300\n700\n1600\n600\n4\n300\n700\n1600\n650\n3\n1000\n2000\n500\n3\n250\n250\n1000\n4\n1251\n667\n876\n299\n0\n output: 2 2900\n3 2500\n3 3250\n1 500\n3 1500\n3 2217\n\n" }, { "title": "Deadlock Detection", "content": "In concurrent processing environments, a deadlock is an undesirable\nsituation where two or more threads are mutually waiting for others to\nfinish using some resources and cannot proceed further.\n\nYour task is to detect whether there is any possibility of deadlocks\nwhen multiple threads try to execute a given instruction sequence concurrently.\n\nThe instruction sequence consists of characters ' u ' or digits from\n' 0 ' to ' 9 ', and each of them represents one instruction.\n10 threads are trying to execute the same single instruction sequence.\nEach thread starts its execution from the beginning of the sequence and\ncontinues in the given order, until all the instructions are\nexecuted.\n\nThere are 10 shared resources called locks from L_0 to L_9.\nA digit k is the instruction for acquiring the lock L_k.\nAfter one of the threads acquires a lock L_k,\nit is kept by the thread until it is released by the instruction ' u '.\nWhile a lock is kept, none of the threads, including one already acquired it,\ncannot newly acquire the same lock L_k.\n\nPrecisely speaking, the following steps are repeated until all threads\nfinish.\n\nOne thread that has not finished yet is chosen arbitrarily.\n\nThe chosen thread tries to execute the next instruction that is not executed yet.\nIf the next instruction is a digit k and\n\t\tthe lock L_k is not kept by any thread,\n\t\tthe thread executes the instruction k and acquires L_k.\n\nIf the next instruction is a digit k and\n\t\tthe lock L_k is already kept by some thread,\n\t\tthe instruction k is not executed.\n\nIf the next instruction is ' u ',\n\t\tthe instruction is executed and all the locks currently kept by the thread\n\t\tare released.\n\nAfter executing several steps, sometimes, it falls into the situation \nthat the next instructions\nof all unfinished threads are for acquiring already kept locks.\nOnce such a situation happens, no instruction will ever be executed no \nmatter which thread is chosen. This situation is called a deadlock.\n\nThere are instruction sequences for which threads can never reach a\ndeadlock regardless of the execution order.\nSuch instruction sequences are called safe.\nOtherwise, in other words, if there exists one or more execution orders\nthat lead to a deadlock, the execution sequence is called unsafe.\n\nYour task is to write a program that tells whether the given instruction sequence is safe or unsafe.", "constraint": "", "input": "The input consists of at most 50 datasets, each in the following format.\n\nn\ns\n\nn is the length of the instruction sequence and s is a string representing the sequence.\nn is a positive integer not exceeding 10,000.\nEach character of s is either a digit (' 0 ' to ' 9 ') or ' u ',\nand s always ends with ' u '.\n\nThe end of the input is indicated by a line with a zero.", "output": "For each dataset, if the given instruction sequence is safe, then print \"SAFE\" in a line.\nIf it is unsafe, then print \"UNSAFE\" in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 11\n01u12u0123u\n6\n01u10u\n8\n201u210u\n9\n01u12u20u\n3\n77u\n12\n9u8u845u954u\n0\n output: SAFE\nUNSAFE\nSAFE\nUNSAFE\nUNSAFE\nUNSAFE\nThe second input \"01u10u\" may possibly cause a deadlock. After one\nthread has executed the initial four instructions \"01u1\", the\nthread keeps only one lock L_1. If another thread executes the first\ninstruction '0' at this time, this thread acquires L_0. Then, the\nfirst thread tries to acquire L_0, already kept by the second\nthread, while the second thread tries to acquire L_1, kept by the\nfirst thread; This leads to a deadlock.\n →\n →\n\nFigure 1: Why the Sample Input 2 \"01u10u\" is unsafe.\nContrarily, the third input \"201u210u\" is safe.\nIf one thread had executed up to \"201u21\" and another to \"20\", then\none may think it would lead to a deadlock, but this\ncan never happen because no two threads can simultaneously keep L_2."], "Pid": "p01089", "ProblemText": "Task Description: In concurrent processing environments, a deadlock is an undesirable\nsituation where two or more threads are mutually waiting for others to\nfinish using some resources and cannot proceed further.\n\nYour task is to detect whether there is any possibility of deadlocks\nwhen multiple threads try to execute a given instruction sequence concurrently.\n\nThe instruction sequence consists of characters ' u ' or digits from\n' 0 ' to ' 9 ', and each of them represents one instruction.\n10 threads are trying to execute the same single instruction sequence.\nEach thread starts its execution from the beginning of the sequence and\ncontinues in the given order, until all the instructions are\nexecuted.\n\nThere are 10 shared resources called locks from L_0 to L_9.\nA digit k is the instruction for acquiring the lock L_k.\nAfter one of the threads acquires a lock L_k,\nit is kept by the thread until it is released by the instruction ' u '.\nWhile a lock is kept, none of the threads, including one already acquired it,\ncannot newly acquire the same lock L_k.\n\nPrecisely speaking, the following steps are repeated until all threads\nfinish.\n\nOne thread that has not finished yet is chosen arbitrarily.\n\nThe chosen thread tries to execute the next instruction that is not executed yet.\nIf the next instruction is a digit k and\n\t\tthe lock L_k is not kept by any thread,\n\t\tthe thread executes the instruction k and acquires L_k.\n\nIf the next instruction is a digit k and\n\t\tthe lock L_k is already kept by some thread,\n\t\tthe instruction k is not executed.\n\nIf the next instruction is ' u ',\n\t\tthe instruction is executed and all the locks currently kept by the thread\n\t\tare released.\n\nAfter executing several steps, sometimes, it falls into the situation \nthat the next instructions\nof all unfinished threads are for acquiring already kept locks.\nOnce such a situation happens, no instruction will ever be executed no \nmatter which thread is chosen. This situation is called a deadlock.\n\nThere are instruction sequences for which threads can never reach a\ndeadlock regardless of the execution order.\nSuch instruction sequences are called safe.\nOtherwise, in other words, if there exists one or more execution orders\nthat lead to a deadlock, the execution sequence is called unsafe.\n\nYour task is to write a program that tells whether the given instruction sequence is safe or unsafe.\nTask Input: The input consists of at most 50 datasets, each in the following format.\n\nn\ns\n\nn is the length of the instruction sequence and s is a string representing the sequence.\nn is a positive integer not exceeding 10,000.\nEach character of s is either a digit (' 0 ' to ' 9 ') or ' u ',\nand s always ends with ' u '.\n\nThe end of the input is indicated by a line with a zero.\nTask Output: For each dataset, if the given instruction sequence is safe, then print \"SAFE\" in a line.\nIf it is unsafe, then print \"UNSAFE\" in a line.\nTask Samples: input: 11\n01u12u0123u\n6\n01u10u\n8\n201u210u\n9\n01u12u20u\n3\n77u\n12\n9u8u845u954u\n0\n output: SAFE\nUNSAFE\nSAFE\nUNSAFE\nUNSAFE\nUNSAFE\nThe second input \"01u10u\" may possibly cause a deadlock. After one\nthread has executed the initial four instructions \"01u1\", the\nthread keeps only one lock L_1. If another thread executes the first\ninstruction '0' at this time, this thread acquires L_0. Then, the\nfirst thread tries to acquire L_0, already kept by the second\nthread, while the second thread tries to acquire L_1, kept by the\nfirst thread; This leads to a deadlock.\n →\n →\n\nFigure 1: Why the Sample Input 2 \"01u10u\" is unsafe.\nContrarily, the third input \"201u210u\" is safe.\nIf one thread had executed up to \"201u21\" and another to \"20\", then\none may think it would lead to a deadlock, but this\ncan never happen because no two threads can simultaneously keep L_2.\n\n" }, { "title": "Bridge Construction Planning", "content": "There is a city consisting of many small islands, and the citizens live in these islands.\nCitizens feel inconvenience in requiring ferry rides between these islands.\nThe city mayor decided to build bridges connecting all the islands.\n\nThe city has two construction companies, A and B.\nThe mayor requested these companies for proposals, and obtained proposals in the form:\n\"Company A (or B) can build a bridge between islands u and v in w hundred million yen. \"\n\nThe mayor wants to accept some of these proposals to make a plan with the lowest budget.\nHowever, if the mayor accepts too many proposals of one company,\nthe other may go bankrupt, which is not desirable for the city with only two construction companies.\nHowever, on the other hand, to avoid criticism on wasteful construction,\nthe mayor can only accept the minimum number (i. e. , n - 1) of bridges for connecting all the islands.\nThus, the mayor made a decision that exactly k proposals by the company A\nand exactly n - 1 - k proposals by the company B should be accepted.\n\nYour task is to write a program that computes the cost of the plan with the lowest budget that satisfies the constraints.\nHere, the cost of a plan means the sum of all the costs mentioned in the accepted proposals.", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of datasets is at most 30.\nEach dataset is in the following format.\n\nn m k\nu_1 v_1 w_1 l_1\n. . . \nu_m v_m w_m l_m\n\nThe first line contains three integers n, m, and k, where\nn is the number of islands, m is the total number of proposals,\n and k is the number of proposals that are to be ordered to company A\n(2 <= n <= 200,1 <= m <= 600, and 0 <= k <= n-1).\nIslands are identified by integers, 1 through n.\nThe following m lines denote the proposals each of which is described with three integers\nu_i, v_i, w_i and one character l_i,\nwhere\nu_i and v_i denote two bridged islands,\n w_i is the cost of the bridge (in hundred million yen),\nand l_i is the name of the company that submits this proposal\n(1 <= u_i <= n, 1 <= v_i <= n, 1 <= w_i <= 100, and l_i = 'A' or 'B').\nYou can assume that each bridge connects distinct islands, i. e. , u_i ! = v_i,\nand each company gives at most one proposal for each pair of islands, i. e. , {u_i, v_i} ! = {u_j, v_j} if i ! = j and l_i = l_j.\n\nThe end of the input is indicated by a line with three zeros separated by single spaces.", "output": "For each dataset, output a single line containing a single integer that \ndenotes the cost (in hundred million yen) of the plan with the lowest \nbudget.\nIf there are no plans that satisfy the constraints, output -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 2\n1 2 2 A\n1 3 2 A\n1 4 2 A\n2 3 1 B\n3 4 1 B\n5 8 2\n1 2 1 A\n2 3 1 A\n3 4 3 A\n4 5 3 A\n1 2 5 B\n2 3 5 B\n3 4 8 B\n4 5 8 B\n5 5 1\n1 2 1 A\n2 3 1 A\n3 4 1 A\n4 5 1 B\n3 5 1 B\n4 5 3\n1 2 2 A\n2 4 3 B\n3 4 4 B\n2 3 5 A\n3 1 6 A\n0 0 0\n output: 5\n16\n-1\n-1"], "Pid": "p01090", "ProblemText": "Task Description: There is a city consisting of many small islands, and the citizens live in these islands.\nCitizens feel inconvenience in requiring ferry rides between these islands.\nThe city mayor decided to build bridges connecting all the islands.\n\nThe city has two construction companies, A and B.\nThe mayor requested these companies for proposals, and obtained proposals in the form:\n\"Company A (or B) can build a bridge between islands u and v in w hundred million yen. \"\n\nThe mayor wants to accept some of these proposals to make a plan with the lowest budget.\nHowever, if the mayor accepts too many proposals of one company,\nthe other may go bankrupt, which is not desirable for the city with only two construction companies.\nHowever, on the other hand, to avoid criticism on wasteful construction,\nthe mayor can only accept the minimum number (i. e. , n - 1) of bridges for connecting all the islands.\nThus, the mayor made a decision that exactly k proposals by the company A\nand exactly n - 1 - k proposals by the company B should be accepted.\n\nYour task is to write a program that computes the cost of the plan with the lowest budget that satisfies the constraints.\nHere, the cost of a plan means the sum of all the costs mentioned in the accepted proposals.\nTask Input: The input consists of multiple datasets.\nThe number of datasets is at most 30.\nEach dataset is in the following format.\n\nn m k\nu_1 v_1 w_1 l_1\n. . . \nu_m v_m w_m l_m\n\nThe first line contains three integers n, m, and k, where\nn is the number of islands, m is the total number of proposals,\n and k is the number of proposals that are to be ordered to company A\n(2 <= n <= 200,1 <= m <= 600, and 0 <= k <= n-1).\nIslands are identified by integers, 1 through n.\nThe following m lines denote the proposals each of which is described with three integers\nu_i, v_i, w_i and one character l_i,\nwhere\nu_i and v_i denote two bridged islands,\n w_i is the cost of the bridge (in hundred million yen),\nand l_i is the name of the company that submits this proposal\n(1 <= u_i <= n, 1 <= v_i <= n, 1 <= w_i <= 100, and l_i = 'A' or 'B').\nYou can assume that each bridge connects distinct islands, i. e. , u_i ! = v_i,\nand each company gives at most one proposal for each pair of islands, i. e. , {u_i, v_i} ! = {u_j, v_j} if i ! = j and l_i = l_j.\n\nThe end of the input is indicated by a line with three zeros separated by single spaces.\nTask Output: For each dataset, output a single line containing a single integer that \ndenotes the cost (in hundred million yen) of the plan with the lowest \nbudget.\nIf there are no plans that satisfy the constraints, output -1.\nTask Samples: input: 4 5 2\n1 2 2 A\n1 3 2 A\n1 4 2 A\n2 3 1 B\n3 4 1 B\n5 8 2\n1 2 1 A\n2 3 1 A\n3 4 3 A\n4 5 3 A\n1 2 5 B\n2 3 5 B\n3 4 8 B\n4 5 8 B\n5 5 1\n1 2 1 A\n2 3 1 A\n3 4 1 A\n4 5 1 B\n3 5 1 B\n4 5 3\n1 2 2 A\n2 4 3 B\n3 4 4 B\n2 3 5 A\n3 1 6 A\n0 0 0\n output: 5\n16\n-1\n-1\n\n" }, { "title": "Complex Paper Folding", "content": "Dr. G, an authority in paper folding and one of the directors of\nIntercultural Consortium on Paper Crafts,\nbelieves complexity gives figures beauty.\nAs one of his assistants, your job is to find the way to fold a paper\nto obtain the most complex figure.\nDr. G defines the complexity of a figure by the number of vertices.\nWith the same number of vertices, one with longer perimeter is more\ncomplex.\nTo simplify the problem, we consider papers with convex polygon in\ntheir shapes and folding them only once.\nEach paper should be folded so that one of its vertices exactly lies\non top of another vertex.\n\nWrite a program that, for each given convex polygon, outputs the\nperimeter of the most complex polygon obtained by folding it once.\n\nFigure 1 (left) illustrates the polygon given in the first dataset of\nSample Input. This happens to be a rectangle.\n\nFolding this rectangle can yield three different polygons illustrated in the Figures 1-a to c by solid\nlines.\nFor this dataset, you should answer the perimeter of the pentagon\nshown in Figure 1-a. Though the rectangle in Figure 1-b has longer\nperimeter, the number of vertices takes priority.\n\n\n \n \n \n \n\n \n (a) \n (b) \n (c) \n\n \nFigure 1: The case of the first sample input\nFigure 2 (left) illustrates the polygon given in the second\ndataset of Sample Input, which is a triangle. Whichever pair of its vertices are\nchosen, quadrangles are obtained as shown in Figures 2-a to c. Among\nthese, you should answer the longest perimeter, which is that of the\nquadrangle shown in Figure 2-a.\n\n
    \n \n \n \n \n\n \n (a) \n (b) \n (c) \n\n \nFigure 2: The case of the second sample input\nAlthough we start with a convex polygon, folding it may result a\nconcave polygon.\nFigure 3 (left) illustrates the polygon given in the third dataset in Sample Input.\nA concave hexagon shown in Figure 3 (right) can be obtained\nby folding it, which has the largest number of vertices.\n\nFigure 3: The case of the third sample input\nFigure 4 (left) illustrates the polygon given in the fifth dataset in \nSample\nInput.\nAlthough the perimeter of the polygon in Figure 4-b is longer than that \nof the polygon in Figure 4-a, because the polygon in Figure 4-b is a \nquadrangle, the answer should be the perimeter of the pentagon in Figure\n 4-a.\n\n
    \n \n \n \n\n \n (a) \n (b) \n\n \nFigure 4: The case of the fifth sample input", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn \nx_1 y_1 \n. . . \nx_n y_n \n\nn is the number of vertices of the given polygon.\nn is a positive integer satisfying 3 <= n <= 20.\n(x_i, y_i) gives the coordinates of\nthe i-th vertex.\nx_i and y_i are integers\nsatisfying 0 <= x_i, y_i < 1000.\nThe vertices (x_1, y_1), . . . , (x_n, y_n)\nare given in the counterclockwise order on the xy-plane with y axis oriented upwards.\nYou can assume that all the given polygons are convex.\n\nAll the possible polygons obtained by folding the given polygon\nsatisfy the following conditions.\n\nDistance between any two vertices is greater than or equal to 0.00001. \n\nFor any three consecutive vertices P, Q, and R, the distance between the\npoint Q and the line passing through the points P and R is greater than or equal to 0.00001. \nThe end of the input is indicated by a line with a zero.", "output": "For each dataset, output the perimeter of the most complex polygon\nobtained through folding the given polygon.\n\nThe output value should not have an error greater than 0.00001.\nAny extra characters should not appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n10 0\n10 5\n0 5\n3\n5 0\n17 3\n7 10\n4\n0 5\n5 0\n10 0\n7 8\n4\n0 0\n40 0\n50 5\n0 5\n4\n0 0\n10 0\n20 5\n10 5\n7\n4 0\n20 0\n24 1\n22 10\n2 10\n0 6\n0 4\n18\n728 997\n117 996\n14 988\n1 908\n0 428\n2 98\n6 54\n30 28\n106 2\n746 1\n979 17\n997 25\n998 185\n999 573\n999 938\n995 973\n970 993\n910 995\n6\n0 40\n0 30\n10 0\n20 0\n40 70\n30 70\n0\n output: 23.090170\n28.528295\n23.553450\n97.135255\n34.270510\n57.124116\n3327.900180\n142.111776"], "Pid": "p01091", "ProblemText": "Task Description: Dr. G, an authority in paper folding and one of the directors of\nIntercultural Consortium on Paper Crafts,\nbelieves complexity gives figures beauty.\nAs one of his assistants, your job is to find the way to fold a paper\nto obtain the most complex figure.\nDr. G defines the complexity of a figure by the number of vertices.\nWith the same number of vertices, one with longer perimeter is more\ncomplex.\nTo simplify the problem, we consider papers with convex polygon in\ntheir shapes and folding them only once.\nEach paper should be folded so that one of its vertices exactly lies\non top of another vertex.\n\nWrite a program that, for each given convex polygon, outputs the\nperimeter of the most complex polygon obtained by folding it once.\n\nFigure 1 (left) illustrates the polygon given in the first dataset of\nSample Input. This happens to be a rectangle.\n\nFolding this rectangle can yield three different polygons illustrated in the Figures 1-a to c by solid\nlines.\nFor this dataset, you should answer the perimeter of the pentagon\nshown in Figure 1-a. Though the rectangle in Figure 1-b has longer\nperimeter, the number of vertices takes priority.\n\n
    \n \n \n \n \n\n \n (a) \n (b) \n (c) \n\n \nFigure 1: The case of the first sample input\nFigure 2 (left) illustrates the polygon given in the second\ndataset of Sample Input, which is a triangle. Whichever pair of its vertices are\nchosen, quadrangles are obtained as shown in Figures 2-a to c. Among\nthese, you should answer the longest perimeter, which is that of the\nquadrangle shown in Figure 2-a.\n\n
    \n \n \n \n \n\n \n (a) \n (b) \n (c) \n\n \nFigure 2: The case of the second sample input\nAlthough we start with a convex polygon, folding it may result a\nconcave polygon.\nFigure 3 (left) illustrates the polygon given in the third dataset in Sample Input.\nA concave hexagon shown in Figure 3 (right) can be obtained\nby folding it, which has the largest number of vertices.\n\nFigure 3: The case of the third sample input\nFigure 4 (left) illustrates the polygon given in the fifth dataset in \nSample\nInput.\nAlthough the perimeter of the polygon in Figure 4-b is longer than that \nof the polygon in Figure 4-a, because the polygon in Figure 4-b is a \nquadrangle, the answer should be the perimeter of the pentagon in Figure\n 4-a.\n\n
    \n \n \n \n\n \n (a) \n (b) \n\n \nFigure 4: The case of the fifth sample input\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn \nx_1 y_1 \n. . . \nx_n y_n \n\nn is the number of vertices of the given polygon.\nn is a positive integer satisfying 3 <= n <= 20.\n(x_i, y_i) gives the coordinates of\nthe i-th vertex.\nx_i and y_i are integers\nsatisfying 0 <= x_i, y_i < 1000.\nThe vertices (x_1, y_1), . . . , (x_n, y_n)\nare given in the counterclockwise order on the xy-plane with y axis oriented upwards.\nYou can assume that all the given polygons are convex.\n\nAll the possible polygons obtained by folding the given polygon\nsatisfy the following conditions.\n\nDistance between any two vertices is greater than or equal to 0.00001. \n\nFor any three consecutive vertices P, Q, and R, the distance between the\npoint Q and the line passing through the points P and R is greater than or equal to 0.00001. \nThe end of the input is indicated by a line with a zero.\nTask Output: For each dataset, output the perimeter of the most complex polygon\nobtained through folding the given polygon.\n\nThe output value should not have an error greater than 0.00001.\nAny extra characters should not appear in the output.\nTask Samples: input: 4\n0 0\n10 0\n10 5\n0 5\n3\n5 0\n17 3\n7 10\n4\n0 5\n5 0\n10 0\n7 8\n4\n0 0\n40 0\n50 5\n0 5\n4\n0 0\n10 0\n20 5\n10 5\n7\n4 0\n20 0\n24 1\n22 10\n2 10\n0 6\n0 4\n18\n728 997\n117 996\n14 988\n1 908\n0 428\n2 98\n6 54\n30 28\n106 2\n746 1\n979 17\n997 25\n998 185\n999 573\n999 938\n995 973\n970 993\n910 995\n6\n0 40\n0 30\n10 0\n20 0\n40 70\n30 70\n0\n output: 23.090170\n28.528295\n23.553450\n97.135255\n34.270510\n57.124116\n3327.900180\n142.111776\n\n" }, { "title": "Development of Small Flying Robots", "content": "You are developing small flying robots in your laboratory.\n\nThe laboratory is a box-shaped building with K levels, each numbered 1 through K from bottom to top.\nThe floors of all levels are square-shaped with their edges precisely aligned east-west and north-south.\nEach floor is divided into R * R cells.\nWe denote the cell on the z-th level in the x-th column from the west and the y-th row from the south as (x, y, z).\n(Here, x and y are one-based. )\nFor each x, y, and z (z > 1),\nthe cell (x, y, z) is located immediately above the cell (x, y, z - 1).\n\nThere are N robots flying in the laboratory,\neach numbered from 1 through N.\nInitially, the i-th robot is located at the cell (x_i, y_i, z_i).\n\nBy your effort so far,\nyou successfully implemented the feature to move each flying robot to any place that you planned.\nAs the next step, you want to implement a new feature that gathers all\nthe robots in some single cell with the lowest energy consumption,\nbased on their current locations and the surrounding environment.\n\nFloors of the level two and above have several holes.\nHoles are rectangular and their edges align with edges of the\ncells on the floors.\nThere are M holes in the laboratory building, each numbered 1 through M.\nThe j-th hole can be described by five integers\nu_1j, v_1j, u_2j, v_2j, and w_j.\nThe j-th hole extends over the cells (x, y, w_j)\nwhere\n u_1j <= x <= u_2j and\n v_1j <= y <= v_2j.\n\nPossible movements of robots and energy consumption involved are as follows.\n\nYou can move a robot from one cell to an adjacent cell, toward one of north, south, east, or west.\n The robot consumes its energy by 1 for this move.\n\n If there is a hole to go through immediately above,\n you can move the robot upward by a single level.\n The robot consumes its energy by 100 for this move.\nThe robots never fall down even if there is a hole below.\nNote that you can move two or more robots to the same cell.\n\nNow, you want to gather all the flying robots at a single cell in the\nK-th level where there is no hole on the floor, with the least energy consumption.\nCompute and output the minimum total energy required by the robots.", "constraint": "", "input": "The input consists of at most 32 datasets, each in the following format.\nEvery value in the input is an integer.\n\nN \nM K R \nx_1 y_1 z_1 \n . . . \nx_N y_N z_N \nu_11 v_11 u_21 v_21 w_1 \n . . . \nu_1M v_1M u_2M v_2M w_M \n\nN is the number of robots in the laboratory (1 <= N <= 100).\nM is the number of holes (1 <= M <= 50),\nK is the number of levels (2 <= K <= 10),\nand R is the number of cells in one row and also one column on a single floor (3 <= R <= 1,000,000).\nFor each i,\nintegers x_i, y_i, and z_i\nrepresent the cell that the i-th robot initially located at\n(1 <= x_i <= R,\n 1 <= y_i <= R,\n 1 <= z_i <= K).\nFurther,\nfor each j,\nintegers\nu_1j, v_1j, u_2j, v_2j, and w_j\ndescribe the position and the extent of the j-th hole\n(1 <= u_1j <= u_2j <= R,\n 1 <= v_1j <= v_2j <= R,\n 2 <= w_j <= K).\n\nThe following are guaranteed.\n\nIn each level higher than or equal to two, there exists at least one hole.\n\nIn each level, there exists at least one cell not belonging to any holes.\n\nNo two holes overlap. That is, each cell belongs to at most one hole.\nTwo or more robots can initially be located at the same cell.\nAlso note that two neighboring cells may belong to different holes.\n\nThe end of the input is indicated by a line with a single zero.", "output": "For each dataset, print the minimum total energy consumption in a single line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n1 2 8\n1 1 1\n8 8 1\n3 3 3 3 2\n3\n3 2 3\n1 1 2\n1 1 2\n1 1 2\n1 1 1 1 2\n1 2 1 2 2\n2 1 2 1 2\n2\n2 3 100\n100 50 1\n1 50 3\n100 1 100 100 3\n1 1 1 100 2\n5\n6 7 60\n11 11 1\n11 51 1\n51 11 1\n51 51 1\n31 31 1\n11 11 51 51 2\n11 11 51 51 3\n11 11 51 51 4\n11 11 51 51 5\n18 1 54 42 6\n1 43 59 60 7\n5\n6 4 9\n5 5 3\n1 1 1\n1 9 1\n9 1 1\n9 9 1\n3 3 7 7 4\n4 4 6 6 2\n1 1 2 2 3\n1 8 2 9 3\n8 1 9 2 3\n8 8 9 9 3\n5\n10 5 50\n3 40 1\n29 13 2\n39 28 1\n50 50 1\n25 30 5\n3 5 10 10 2\n11 11 14 14 2\n15 15 20 23 2\n40 40 41 50 2\n1 49 3 50 2\n30 30 50 50 3\n1 1 10 10 4\n1 30 1 50 5\n20 30 20 50 5\n40 30 40 50 5\n15\n2 2 1000000\n514898 704203 1\n743530 769450 1\n202298 424059 1\n803485 898125 1\n271735 512227 1\n442644 980009 1\n444735 799591 1\n474132 623298 1\n67459 184056 1\n467347 302466 1\n477265 160425 2\n425470 102631 2\n547058 210758 2\n52246 779950 2\n291896 907904 2\n480318 350180 768473 486661 2\n776214 135749 872708 799857 2\n0\n output: 216\n6\n497\n3181\n1365\n1930\n6485356"], "Pid": "p01092", "ProblemText": "Task Description: You are developing small flying robots in your laboratory.\n\nThe laboratory is a box-shaped building with K levels, each numbered 1 through K from bottom to top.\nThe floors of all levels are square-shaped with their edges precisely aligned east-west and north-south.\nEach floor is divided into R * R cells.\nWe denote the cell on the z-th level in the x-th column from the west and the y-th row from the south as (x, y, z).\n(Here, x and y are one-based. )\nFor each x, y, and z (z > 1),\nthe cell (x, y, z) is located immediately above the cell (x, y, z - 1).\n\nThere are N robots flying in the laboratory,\neach numbered from 1 through N.\nInitially, the i-th robot is located at the cell (x_i, y_i, z_i).\n\nBy your effort so far,\nyou successfully implemented the feature to move each flying robot to any place that you planned.\nAs the next step, you want to implement a new feature that gathers all\nthe robots in some single cell with the lowest energy consumption,\nbased on their current locations and the surrounding environment.\n\nFloors of the level two and above have several holes.\nHoles are rectangular and their edges align with edges of the\ncells on the floors.\nThere are M holes in the laboratory building, each numbered 1 through M.\nThe j-th hole can be described by five integers\nu_1j, v_1j, u_2j, v_2j, and w_j.\nThe j-th hole extends over the cells (x, y, w_j)\nwhere\n u_1j <= x <= u_2j and\n v_1j <= y <= v_2j.\n\nPossible movements of robots and energy consumption involved are as follows.\n\nYou can move a robot from one cell to an adjacent cell, toward one of north, south, east, or west.\n The robot consumes its energy by 1 for this move.\n\n If there is a hole to go through immediately above,\n you can move the robot upward by a single level.\n The robot consumes its energy by 100 for this move.\nThe robots never fall down even if there is a hole below.\nNote that you can move two or more robots to the same cell.\n\nNow, you want to gather all the flying robots at a single cell in the\nK-th level where there is no hole on the floor, with the least energy consumption.\nCompute and output the minimum total energy required by the robots.\nTask Input: The input consists of at most 32 datasets, each in the following format.\nEvery value in the input is an integer.\n\nN \nM K R \nx_1 y_1 z_1 \n . . . \nx_N y_N z_N \nu_11 v_11 u_21 v_21 w_1 \n . . . \nu_1M v_1M u_2M v_2M w_M \n\nN is the number of robots in the laboratory (1 <= N <= 100).\nM is the number of holes (1 <= M <= 50),\nK is the number of levels (2 <= K <= 10),\nand R is the number of cells in one row and also one column on a single floor (3 <= R <= 1,000,000).\nFor each i,\nintegers x_i, y_i, and z_i\nrepresent the cell that the i-th robot initially located at\n(1 <= x_i <= R,\n 1 <= y_i <= R,\n 1 <= z_i <= K).\nFurther,\nfor each j,\nintegers\nu_1j, v_1j, u_2j, v_2j, and w_j\ndescribe the position and the extent of the j-th hole\n(1 <= u_1j <= u_2j <= R,\n 1 <= v_1j <= v_2j <= R,\n 2 <= w_j <= K).\n\nThe following are guaranteed.\n\nIn each level higher than or equal to two, there exists at least one hole.\n\nIn each level, there exists at least one cell not belonging to any holes.\n\nNo two holes overlap. That is, each cell belongs to at most one hole.\nTwo or more robots can initially be located at the same cell.\nAlso note that two neighboring cells may belong to different holes.\n\nThe end of the input is indicated by a line with a single zero.\nTask Output: For each dataset, print the minimum total energy consumption in a single line.\nTask Samples: input: 2\n1 2 8\n1 1 1\n8 8 1\n3 3 3 3 2\n3\n3 2 3\n1 1 2\n1 1 2\n1 1 2\n1 1 1 1 2\n1 2 1 2 2\n2 1 2 1 2\n2\n2 3 100\n100 50 1\n1 50 3\n100 1 100 100 3\n1 1 1 100 2\n5\n6 7 60\n11 11 1\n11 51 1\n51 11 1\n51 51 1\n31 31 1\n11 11 51 51 2\n11 11 51 51 3\n11 11 51 51 4\n11 11 51 51 5\n18 1 54 42 6\n1 43 59 60 7\n5\n6 4 9\n5 5 3\n1 1 1\n1 9 1\n9 1 1\n9 9 1\n3 3 7 7 4\n4 4 6 6 2\n1 1 2 2 3\n1 8 2 9 3\n8 1 9 2 3\n8 8 9 9 3\n5\n10 5 50\n3 40 1\n29 13 2\n39 28 1\n50 50 1\n25 30 5\n3 5 10 10 2\n11 11 14 14 2\n15 15 20 23 2\n40 40 41 50 2\n1 49 3 50 2\n30 30 50 50 3\n1 1 10 10 4\n1 30 1 50 5\n20 30 20 50 5\n40 30 40 50 5\n15\n2 2 1000000\n514898 704203 1\n743530 769450 1\n202298 424059 1\n803485 898125 1\n271735 512227 1\n442644 980009 1\n444735 799591 1\n474132 623298 1\n67459 184056 1\n467347 302466 1\n477265 160425 2\n425470 102631 2\n547058 210758 2\n52246 779950 2\n291896 907904 2\n480318 350180 768473 486661 2\n776214 135749 872708 799857 2\n0\n output: 216\n6\n497\n3181\n1365\n1930\n6485356\n\n" }, { "title": "Selection of Participants of an Experiment", "content": "Dr. Tsukuba has devised a new method of programming training.\nIn order to evaluate the effectiveness of this method,\nhe plans to carry out a control experiment.\nHaving two students as the participants of the experiment,\none of them will be trained under the conventional method\nand the other under his new method.\nComparing the final scores of these two,\nhe will be able to judge the effectiveness of his method.\n\nIt is important to select two students having the closest possible scores,\nfor making the comparison fair.\nHe has a list of the scores of all students\nwho can participate in the experiment.\nYou are asked to write a program which selects two of them\nhaving the smallest difference in their scores.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn\na_1 a_2 … a_n\n\nA dataset consists of two lines.\nThe number of students n is given in the first line.\nn is an integer satisfying 2 <= n <= 1000.\nThe second line gives scores of n students.\na_i (1 <= i <= n) is the score of the i-th student, which is a non-negative integer not greater than 1,000,000.\n\nThe end of the input is indicated by a line containing a zero.\nThe sum of n's of all the datasets does not exceed 50,000.", "output": "For each dataset, select two students with the smallest difference in their scores,\nand output in a line (the absolute value of) the difference.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n10 10 10 10 10\n5\n1 5 8 9 11\n7\n11 34 83 47 59 29 70\n0\n output: 0\n1\n5"], "Pid": "p01093", "ProblemText": "Task Description: Dr. Tsukuba has devised a new method of programming training.\nIn order to evaluate the effectiveness of this method,\nhe plans to carry out a control experiment.\nHaving two students as the participants of the experiment,\none of them will be trained under the conventional method\nand the other under his new method.\nComparing the final scores of these two,\nhe will be able to judge the effectiveness of his method.\n\nIt is important to select two students having the closest possible scores,\nfor making the comparison fair.\nHe has a list of the scores of all students\nwho can participate in the experiment.\nYou are asked to write a program which selects two of them\nhaving the smallest difference in their scores.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn\na_1 a_2 … a_n\n\nA dataset consists of two lines.\nThe number of students n is given in the first line.\nn is an integer satisfying 2 <= n <= 1000.\nThe second line gives scores of n students.\na_i (1 <= i <= n) is the score of the i-th student, which is a non-negative integer not greater than 1,000,000.\n\nThe end of the input is indicated by a line containing a zero.\nThe sum of n's of all the datasets does not exceed 50,000.\nTask Output: For each dataset, select two students with the smallest difference in their scores,\nand output in a line (the absolute value of) the difference.\nTask Samples: input: 5\n10 10 10 10 10\n5\n1 5 8 9 11\n7\n11 34 83 47 59 29 70\n0\n output: 0\n1\n5\n\n" }, { "title": "Look for the Winner!", "content": "The citizens of TKB City are famous for their deep love in elections and vote counting.\nToday they hold an election for the next chairperson of the electoral commission.\nNow the voting has just been closed and the counting is going to start.\nThe TKB citizens have strong desire to know the winner as early as possible during vote counting.\n\nThe election candidate receiving the most votes shall be the next chairperson.\nSuppose for instance that we have three candidates A, B, and C and ten votes.\nSuppose also that we have already counted six of the ten votes and the vote counts of A, B, and C are four, one, and one, respectively.\nAt this moment, every candidate has a chance to receive four more votes and so everyone can still be the winner.\nHowever, if the next vote counted is cast for A, A is ensured to be the winner since A already has five votes and B or C can have at most four votes at the end.\nIn this example, therefore, the TKB citizens can know the winner just when the seventh vote is counted. \n\nYour mission is to write a program that receives every vote counted, one by one, identifies the winner, and determines when the winner gets ensured.", "constraint": "", "input": "The input consists of at most 1500 datasets, each consisting of two lines in the following format.\n\nn\nc_1 c_2 … c_n\n\nn in the first line represents the number of votes, and is a positive integer no greater than 100.\nThe second line represents the n votes, separated by a space.\nEach c_i (1 <= i <= n) is a single uppercase letter, i. e. one of 'A' through 'Z'.\nThis represents the election candidate for which the i-th vote was cast.\nCounting shall be done in the given order from c_1 to c_n.\n\nYou should assume that at least two stand as candidates even when all the votes are cast for one candidate.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, unless the election ends in a tie, output a single line containing an uppercase letter c and an integer d separated by a space:\nc should represent the election winner and d should represent after counting how many votes the winner is identified.\nOtherwise, that is, if the election ends in a tie, output a single line containing `TIE'.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\nA\n4\nA A B B\n5\nL M N L N\n6\nK K K K K K\n6\nX X X Y Z X\n10\nA A A B A C A C C B\n10\nU U U U U V V W W W\n0\n output: A 1\nTIE\nTIE\nK 4\nX 5\nA 7\nU 8"], "Pid": "p01094", "ProblemText": "Task Description: The citizens of TKB City are famous for their deep love in elections and vote counting.\nToday they hold an election for the next chairperson of the electoral commission.\nNow the voting has just been closed and the counting is going to start.\nThe TKB citizens have strong desire to know the winner as early as possible during vote counting.\n\nThe election candidate receiving the most votes shall be the next chairperson.\nSuppose for instance that we have three candidates A, B, and C and ten votes.\nSuppose also that we have already counted six of the ten votes and the vote counts of A, B, and C are four, one, and one, respectively.\nAt this moment, every candidate has a chance to receive four more votes and so everyone can still be the winner.\nHowever, if the next vote counted is cast for A, A is ensured to be the winner since A already has five votes and B or C can have at most four votes at the end.\nIn this example, therefore, the TKB citizens can know the winner just when the seventh vote is counted. \n\nYour mission is to write a program that receives every vote counted, one by one, identifies the winner, and determines when the winner gets ensured.\nTask Input: The input consists of at most 1500 datasets, each consisting of two lines in the following format.\n\nn\nc_1 c_2 … c_n\n\nn in the first line represents the number of votes, and is a positive integer no greater than 100.\nThe second line represents the n votes, separated by a space.\nEach c_i (1 <= i <= n) is a single uppercase letter, i. e. one of 'A' through 'Z'.\nThis represents the election candidate for which the i-th vote was cast.\nCounting shall be done in the given order from c_1 to c_n.\n\nYou should assume that at least two stand as candidates even when all the votes are cast for one candidate.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, unless the election ends in a tie, output a single line containing an uppercase letter c and an integer d separated by a space:\nc should represent the election winner and d should represent after counting how many votes the winner is identified.\nOtherwise, that is, if the election ends in a tie, output a single line containing `TIE'.\nTask Samples: input: 1\nA\n4\nA A B B\n5\nL M N L N\n6\nK K K K K K\n6\nX X X Y Z X\n10\nA A A B A C A C C B\n10\nU U U U U V V W W W\n0\n output: A 1\nTIE\nTIE\nK 4\nX 5\nA 7\nU 8\n\n" }, { "title": "Bamboo Blossoms", "content": "The bamboos live for decades, and at the end of their lives,\n they flower to make their seeds. Dr. ACM, a biologist, was fascinated\n by the bamboos in blossom in his travel to Tsukuba. He liked\n the flower so much that he was tempted to make a garden where\n the bamboos bloom annually. Dr. ACM started research of\n improving breed of the bamboos, and finally, he established\n a method to develop bamboo breeds with controlled lifetimes.\n With this method, he can develop bamboo breeds that flower\n after arbitrarily specified years.\n\n Let us call bamboos that flower k years after sowing\n \"k-year-bamboos. \"\n k years after being sowed, k-year-bamboos make\n their seeds and then die,\n hence their next generation flowers after another k years.\n In this way, if he sows seeds of k-year-bamboos, he can\n see bamboo blossoms every k years. For example,\n assuming that he sows seeds of 15-year-bamboos,\n he can see bamboo blossoms every 15 years;\n 15 years, 30 years, 45 years, and so on, after sowing.\n\n Dr. ACM asked you for designing his garden. His garden is partitioned\n into blocks, in each of which only a single breed of bamboo can grow.\n Dr. ACM requested you to decide which breeds of bamboos\n should he sow in the blocks in order to see bamboo blossoms\n in at least one block for as many years as possible.\n\n You immediately suggested to sow seeds of one-year-bamboos in all blocks.\n Dr. ACM, however, said that it was difficult to develop a bamboo breed\n with short lifetime, and would like a plan using only those breeds with\n long lifetimes. He also said that, although he could wait for some years\n until he would see the first bloom, he would like to see it in\n every following year.\n Then, you suggested a plan\n to sow seeds of 10-year-bamboos, for example, in different blocks each year,\n that is, to sow in a block this year and in another block next year, and so on,\n for 10 years. Following this plan, he could see\n bamboo blossoms in one block every year except for the first 10 years.\n Dr. ACM objected again saying he had determined to sow in all\n blocks this year.\n\n After all, you made up your mind to make a sowing plan where the bamboos\n bloom in at least one block for as many consecutive years as possible\n after the first m years (including this year)\n under the following conditions:\n \nthe plan should use only those bamboo breeds whose\n lifetimes are m years or longer, and\n Dr. ACM should sow the seeds in all the blocks only this year.", "constraint": "", "input": "The input consists of at most 50 datasets, each in the following format.\n\nm n\n\n An integer m (2 <= m <= 100) represents the lifetime\n (in years)\n of the bamboos with the shortest lifetime that Dr. ACM can use for\n gardening.\n An integer n (1 <= n <= 500,000) represents the number of blocks.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "No matter how good your plan is, a \"dull-year\" would\n eventually come, in which the bamboos do not flower in any block.\n For each dataset, output in a line an integer meaning how many\n years from now the first dull-year comes after the first m years.\n\n Note that the input of m = 2 and n = 500,000\n (the last dataset of the Sample Input) gives the largest answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n3 4\n10 20\n100 50\n2 500000\n0 0\n output: 4\n11\n47\n150\n7368791"], "Pid": "p01095", "ProblemText": "Task Description: The bamboos live for decades, and at the end of their lives,\n they flower to make their seeds. Dr. ACM, a biologist, was fascinated\n by the bamboos in blossom in his travel to Tsukuba. He liked\n the flower so much that he was tempted to make a garden where\n the bamboos bloom annually. Dr. ACM started research of\n improving breed of the bamboos, and finally, he established\n a method to develop bamboo breeds with controlled lifetimes.\n With this method, he can develop bamboo breeds that flower\n after arbitrarily specified years.\n\n Let us call bamboos that flower k years after sowing\n \"k-year-bamboos. \"\n k years after being sowed, k-year-bamboos make\n their seeds and then die,\n hence their next generation flowers after another k years.\n In this way, if he sows seeds of k-year-bamboos, he can\n see bamboo blossoms every k years. For example,\n assuming that he sows seeds of 15-year-bamboos,\n he can see bamboo blossoms every 15 years;\n 15 years, 30 years, 45 years, and so on, after sowing.\n\n Dr. ACM asked you for designing his garden. His garden is partitioned\n into blocks, in each of which only a single breed of bamboo can grow.\n Dr. ACM requested you to decide which breeds of bamboos\n should he sow in the blocks in order to see bamboo blossoms\n in at least one block for as many years as possible.\n\n You immediately suggested to sow seeds of one-year-bamboos in all blocks.\n Dr. ACM, however, said that it was difficult to develop a bamboo breed\n with short lifetime, and would like a plan using only those breeds with\n long lifetimes. He also said that, although he could wait for some years\n until he would see the first bloom, he would like to see it in\n every following year.\n Then, you suggested a plan\n to sow seeds of 10-year-bamboos, for example, in different blocks each year,\n that is, to sow in a block this year and in another block next year, and so on,\n for 10 years. Following this plan, he could see\n bamboo blossoms in one block every year except for the first 10 years.\n Dr. ACM objected again saying he had determined to sow in all\n blocks this year.\n\n After all, you made up your mind to make a sowing plan where the bamboos\n bloom in at least one block for as many consecutive years as possible\n after the first m years (including this year)\n under the following conditions:\n \nthe plan should use only those bamboo breeds whose\n lifetimes are m years or longer, and\n Dr. ACM should sow the seeds in all the blocks only this year.\nTask Input: The input consists of at most 50 datasets, each in the following format.\n\nm n\n\n An integer m (2 <= m <= 100) represents the lifetime\n (in years)\n of the bamboos with the shortest lifetime that Dr. ACM can use for\n gardening.\n An integer n (1 <= n <= 500,000) represents the number of blocks.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: No matter how good your plan is, a \"dull-year\" would\n eventually come, in which the bamboos do not flower in any block.\n For each dataset, output in a line an integer meaning how many\n years from now the first dull-year comes after the first m years.\n\n Note that the input of m = 2 and n = 500,000\n (the last dataset of the Sample Input) gives the largest answer.\nTask Samples: input: 3 1\n3 4\n10 20\n100 50\n2 500000\n0 0\n output: 4\n11\n47\n150\n7368791\n\n" }, { "title": "Daruma Otoshi", "content": "You are playing a variant of a game called \"Daruma Otoshi (Dharma Block Striking)\".\n\nAt the start of a game, several wooden blocks of the same size but with varying weights\nare stacked on top of each other, forming a tower.\nAnother block symbolizing Dharma is placed atop.\nYou have a wooden hammer with its head thicker than the height of a block,\nbut not twice that.\n\nYou can choose any two adjacent blocks, except Dharma on the top,\ndiffering at most 1 in their weight,\nand push both of them out of the stack with a single blow of your hammer.\nThe blocks above the removed ones then fall straight down,\nwithout collapsing the tower.\n\nYou cannot hit a block pair with weight difference of 2 or more,\nfor that makes too hard to push out blocks while keeping the balance of the tower.\nThere is no chance in hitting three blocks out at a time,\nfor that would require superhuman accuracy.\n\nThe goal of the game is to remove as many blocks as you can.\nYour task is to decide the number of blocks that can be removed\nby repeating the blows in an optimal order.\n\nFigure D1. Striking out two blocks at a time\nIn the above figure, with a stack of four blocks weighing 1,2,3, and\n1, in this order from the bottom, you can hit middle\ntwo blocks, weighing 2 and 3, out from the stack. The blocks above will\nthen fall down, and two blocks weighing 1 and the Dharma block will remain.\nYou can then push out the remaining pair of weight-1 blocks after that.", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of datasets is at most 50.\nEach dataset is in the following format.\n\nn \nw_1 w_2 … w_n \n\nn is the number of blocks, except Dharma on the top.\nn is a positive integer not exceeding 300.\nw_i gives the weight of the i-th block counted from the bottom.\nw_i is an integer between 1 and 1000, inclusive.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output in a line the maximum number of blocks you can remove.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1 2 3 4\n4\n1 2 3 1\n5\n5 1 2 3 6\n14\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\n5\n1 3 5 1 3\n0\n output: 4\n4\n2\n12\n0"], "Pid": "p01096", "ProblemText": "Task Description: You are playing a variant of a game called \"Daruma Otoshi (Dharma Block Striking)\".\n\nAt the start of a game, several wooden blocks of the same size but with varying weights\nare stacked on top of each other, forming a tower.\nAnother block symbolizing Dharma is placed atop.\nYou have a wooden hammer with its head thicker than the height of a block,\nbut not twice that.\n\nYou can choose any two adjacent blocks, except Dharma on the top,\ndiffering at most 1 in their weight,\nand push both of them out of the stack with a single blow of your hammer.\nThe blocks above the removed ones then fall straight down,\nwithout collapsing the tower.\n\nYou cannot hit a block pair with weight difference of 2 or more,\nfor that makes too hard to push out blocks while keeping the balance of the tower.\nThere is no chance in hitting three blocks out at a time,\nfor that would require superhuman accuracy.\n\nThe goal of the game is to remove as many blocks as you can.\nYour task is to decide the number of blocks that can be removed\nby repeating the blows in an optimal order.\n\nFigure D1. Striking out two blocks at a time\nIn the above figure, with a stack of four blocks weighing 1,2,3, and\n1, in this order from the bottom, you can hit middle\ntwo blocks, weighing 2 and 3, out from the stack. The blocks above will\nthen fall down, and two blocks weighing 1 and the Dharma block will remain.\nYou can then push out the remaining pair of weight-1 blocks after that.\nTask Input: The input consists of multiple datasets.\nThe number of datasets is at most 50.\nEach dataset is in the following format.\n\nn \nw_1 w_2 … w_n \n\nn is the number of blocks, except Dharma on the top.\nn is a positive integer not exceeding 300.\nw_i gives the weight of the i-th block counted from the bottom.\nw_i is an integer between 1 and 1000, inclusive.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output in a line the maximum number of blocks you can remove.\nTask Samples: input: 4\n1 2 3 4\n4\n1 2 3 1\n5\n5 1 2 3 6\n14\n8 7 1 4 3 5 4 1 6 8 10 4 6 5\n5\n1 3 5 1 3\n0\n output: 4\n4\n2\n12\n0\n\n" }, { "title": "3D Printing", "content": "We are designing an installation art piece consisting of \na number of cubes with 3D printing technology for submitting one to\nInstallation art Contest with Printed Cubes (ICPC).\nAt this time, we are trying to model a piece consisting of exactly k cubes \nof the same size facing the same direction.\n\nFirst, using a CAD system, \nwe prepare n (n >= k) positions as candidates\nin the 3D space where cubes can be placed.\n\nWhen cubes would be placed at all the candidate positions, \nthe following three conditions are satisfied.\nEach cube may overlap zero, one or two other cubes, but not three or more.\n\nWhen a cube overlap two other cubes, those two cubes do not overlap.\n\nTwo non-overlapping cubes do not touch at their surfaces, edges or corners.\n\nSecond, choosing appropriate k different positions from n candidates\nand placing cubes there, \nwe obtain a connected polyhedron as a union of the k cubes. \n\nWhen we use a 3D printer,\nwe usually print only the thin surface of a 3D object.\n\nIn order to save the amount of filament material for the 3D printer, \nwe want to find the polyhedron with the minimal surface area.\n\nYour job is to find the polyhedron with the minimal surface area\nconsisting of k connected\ncubes placed at k selected positions among n given ones. \n\nFigure E1. A polyhedron formed with connected identical cubes.", "constraint": "", "input": "The input consists of multiple datasets. \nThe number of datasets is at most 100.\nEach dataset is in the following format.\n\nn k s\nx_1 y_1 z_1\n. . . \nx_n y_n z_n\n\nIn the first line of a dataset,\nn is the number of the candidate positions,\nk is the number of the cubes to form the connected polyhedron,\nand s is the edge length of cubes. \nn, k and s are integers separated by a space. \nThe following n lines specify the n candidate positions.\nIn the i-th line, there are three integers \nx_i,\ny_i and \nz_i\nthat specify the coordinates of a position, \nwhere the corner of the cube with the smallest coordinate values\nmay be placed.\nEdges of the cubes are to be aligned with either of three axes.\nAll the values of coordinates are integers separated by a space.\n\nThe three conditions on the candidate positions mentioned above are satisfied.\n\nThe parameters satisfy the following conditions:\n1 <= k <= n <= 2000,3 <= s <= 100, and\n-4*10^7 <= x_i, y_i, z_i <= 4*10^7. \n\nThe end of the input is indicated by a line containing three zeros\nseparated by a space.", "output": "For each dataset, output a single line containing one integer\nindicating the surface area of the connected polyhedron with \nthe minimal surface area.\n\nWhen no k cubes form a connected polyhedron, output -1.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 1 100\n100 100 100\n6 4 10\n100 100 100\n106 102 102\n112 110 104\n104 116 102\n100 114 104\n92 107 100\n10 4 10\n-100 101 100\n-108 102 120\n-116 103 100\n-124 100 100\n-132 99 100\n-92 98 100\n-84 100 140\n-76 103 100\n-68 102 100\n-60 101 100\n10 4 10\n100 100 100\n108 101 100\n116 102 100\n124 100 100\n132 102 100\n200 100 103\n192 100 102\n184 100 101\n176 100 100\n168 100 103\n4 4 10\n100 100 100\n108 94 100\n116 100 100\n108 106 100\n23 6 10\n100 100 100\n96 109 100\n100 118 100\n109 126 100\n118 126 100\n127 118 98\n127 109 104\n127 100 97\n118 91 102\n109 91 100\n111 102 100\n111 102 109\n111 102 118\n111 102 91\n111 102 82\n111 114 96\n111 114 105\n102 114 114\n93 114 114\n84 114 105\n84 114 96\n93 114 87\n102 114 87\n10 3 10\n100 100 100\n116 116 102\n132 132 104\n148 148 106\n164 164 108\n108 108 108\n124 124 106\n140 140 104\n156 156 102\n172 172 100\n0 0 0\n output: 60000\n1856\n-1\n1632\n1856\n2796\n1640"], "Pid": "p01097", "ProblemText": "Task Description: We are designing an installation art piece consisting of \na number of cubes with 3D printing technology for submitting one to\nInstallation art Contest with Printed Cubes (ICPC).\nAt this time, we are trying to model a piece consisting of exactly k cubes \nof the same size facing the same direction.\n\nFirst, using a CAD system, \nwe prepare n (n >= k) positions as candidates\nin the 3D space where cubes can be placed.\n\nWhen cubes would be placed at all the candidate positions, \nthe following three conditions are satisfied.\nEach cube may overlap zero, one or two other cubes, but not three or more.\n\nWhen a cube overlap two other cubes, those two cubes do not overlap.\n\nTwo non-overlapping cubes do not touch at their surfaces, edges or corners.\n\nSecond, choosing appropriate k different positions from n candidates\nand placing cubes there, \nwe obtain a connected polyhedron as a union of the k cubes. \n\nWhen we use a 3D printer,\nwe usually print only the thin surface of a 3D object.\n\nIn order to save the amount of filament material for the 3D printer, \nwe want to find the polyhedron with the minimal surface area.\n\nYour job is to find the polyhedron with the minimal surface area\nconsisting of k connected\ncubes placed at k selected positions among n given ones. \n\nFigure E1. A polyhedron formed with connected identical cubes.\nTask Input: The input consists of multiple datasets. \nThe number of datasets is at most 100.\nEach dataset is in the following format.\n\nn k s\nx_1 y_1 z_1\n. . . \nx_n y_n z_n\n\nIn the first line of a dataset,\nn is the number of the candidate positions,\nk is the number of the cubes to form the connected polyhedron,\nand s is the edge length of cubes. \nn, k and s are integers separated by a space. \nThe following n lines specify the n candidate positions.\nIn the i-th line, there are three integers \nx_i,\ny_i and \nz_i\nthat specify the coordinates of a position, \nwhere the corner of the cube with the smallest coordinate values\nmay be placed.\nEdges of the cubes are to be aligned with either of three axes.\nAll the values of coordinates are integers separated by a space.\n\nThe three conditions on the candidate positions mentioned above are satisfied.\n\nThe parameters satisfy the following conditions:\n1 <= k <= n <= 2000,3 <= s <= 100, and\n-4*10^7 <= x_i, y_i, z_i <= 4*10^7. \n\nThe end of the input is indicated by a line containing three zeros\nseparated by a space.\nTask Output: For each dataset, output a single line containing one integer\nindicating the surface area of the connected polyhedron with \nthe minimal surface area.\n\nWhen no k cubes form a connected polyhedron, output -1.\nTask Samples: input: 1 1 100\n100 100 100\n6 4 10\n100 100 100\n106 102 102\n112 110 104\n104 116 102\n100 114 104\n92 107 100\n10 4 10\n-100 101 100\n-108 102 120\n-116 103 100\n-124 100 100\n-132 99 100\n-92 98 100\n-84 100 140\n-76 103 100\n-68 102 100\n-60 101 100\n10 4 10\n100 100 100\n108 101 100\n116 102 100\n124 100 100\n132 102 100\n200 100 103\n192 100 102\n184 100 101\n176 100 100\n168 100 103\n4 4 10\n100 100 100\n108 94 100\n116 100 100\n108 106 100\n23 6 10\n100 100 100\n96 109 100\n100 118 100\n109 126 100\n118 126 100\n127 118 98\n127 109 104\n127 100 97\n118 91 102\n109 91 100\n111 102 100\n111 102 109\n111 102 118\n111 102 91\n111 102 82\n111 114 96\n111 114 105\n102 114 114\n93 114 114\n84 114 105\n84 114 96\n93 114 87\n102 114 87\n10 3 10\n100 100 100\n116 116 102\n132 132 104\n148 148 106\n164 164 108\n108 108 108\n124 124 106\n140 140 104\n156 156 102\n172 172 100\n0 0 0\n output: 60000\n1856\n-1\n1632\n1856\n2796\n1640\n\n" }, { "title": "Deciphering Characters", "content": "Image data which are left by a mysterious syndicate were discovered. \nYou are requested to analyze the data.\nThe syndicate members used characters invented independently. \nA binary image corresponds to one character written in black ink on white paper.\n\nAlthough you found many variant images that represent the same character, \nyou discovered that you can judge whether or not two images represent the same character with the surrounding relation of connected components. We present some definitions as follows. Here, we assume that white pixels fill outside of the given image.\n\n White connected component : A set of white pixels connected to each other horizontally or vertically (see below).\n\n Black connected component : A set of black pixels connected to each other horizontally, vertically, or diagonally (see below).\n\n Connected component : A white or a black connected component.\n\n Background component : The connected component including pixels outside of the image. Any white pixels on the periphery of the image are thus included in the background component.\n\n \n \n \n \n \n \n \n connected \n disconnected \n connected \n connected \n \n
    Connectedness of white pixels      \nConnectedness of black pixels \n \n\nLet C_1 be a connected component in an image and C_2 be another connected component in the same image with the opposite color.\nLet's think of a modified image in which colors of all pixels not included in C_1 nor C_2 are changed to that of C_2. If neither C_1 nor C_2 is the background component, the color of the background component is changed to that of C_2. We say that C_1 surrounds C_2 in the original image when pixels in C_2 are not included in the background component in the modified image. (see below)\n\nTwo images represent the same character if both of the following conditions are satisfied.\n\n The two images have the same number of connected components.\n\n Let S and S' be the sets of connected components of the two images. A bijective function f : S → S' satisfying the following conditions exists.\n For each connected component C that belongs to S, f (C) has the same color as C. \n\n For each of C_1 and C_2 belonging to S, f (C_1) surrounds f (C_2) if and only if C_1 surrounds C_2.\nLet's see an example. Connected components in the images of the figure below has the following surrounding relations.\n\n C_1 surrounds C_2.\n\n C_2 surrounds C_3.\n\n C_2 surrounds C_4.\n\n C'_1 surrounds C'_2.\n\n C'_2 surrounds C'_3.\n\n C'_2 surrounds C'_4.\nA bijective function defined as f (C_i) = C'_i for each connected component satisfies the conditions stated above. Therefore, we can conclude that the two images represent the same character.\n \n\nMake a program judging whether given two images represent the same character.", "constraint": "", "input": "The input consists of at most 200 datasets. The end of the input is represented by a line containing two zeros. Each dataset is formatted as follows.\n\nimage 1\nimage 2\n\nEach image has the following format.\n\nh w\np_(1,1) . . . p_(1, w)\n. . . \np_(h, 1) . . . p_(h, w)\n\nh and w are the height and the width of the image in numbers of pixels.\nYou may assume that 1 <= h <= 100 and 1 <= w <= 100.\n\nEach of the following h lines consists of w characters. \np_(y, x) is a character representing the color\nof the pixel in the y-th row from the top and the x-th column from the left.\nCharacters are either a period (\". \") meaning white or a sharp sign (\"#\") meaning black.", "output": "For each dataset, output \"yes\" if the two images represent the same character, or output \"no\", otherwise, in a line. The output should not contain extra characters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 6\n.#..#.\n#.##.#\n.#..#.\n8 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#..#..#\n.#####.\n...#...\n3 3\n#..\n...\n#..\n3 3\n#..\n.#.\n#..\n3 3\n...\n...\n...\n3 3\n...\n.#.\n...\n3 3\n.#.\n#.#\n.#.\n3 3\n.#.\n###\n.#.\n7 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#.....#\n.#####.\n7 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#..#..#\n.#####.\n7 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#.....#\n.#####.\n7 11\n.#####.....\n#.....#....\n#..#..#..#.\n#.#.#.#.#.#\n#..#..#..#.\n#.....#....\n.#####.....\n7 3\n.#.\n#.#\n.#.\n#.#\n.#.\n#.#\n.#.\n7 7\n.#####.\n#..#..#\n#..#..#\n#.#.#.#\n#..#..#\n#..#..#\n.#####.\n3 1\n#\n#\n.\n1 2\n#.\n0 0\n output: yes\nno\nno\nno\nno\nno\nyes\nyes"], "Pid": "p01098", "ProblemText": "Task Description: Image data which are left by a mysterious syndicate were discovered. \nYou are requested to analyze the data.\nThe syndicate members used characters invented independently. \nA binary image corresponds to one character written in black ink on white paper.\n\nAlthough you found many variant images that represent the same character, \nyou discovered that you can judge whether or not two images represent the same character with the surrounding relation of connected components. We present some definitions as follows. Here, we assume that white pixels fill outside of the given image.\n\n White connected component : A set of white pixels connected to each other horizontally or vertically (see below).\n\n Black connected component : A set of black pixels connected to each other horizontally, vertically, or diagonally (see below).\n\n Connected component : A white or a black connected component.\n\n Background component : The connected component including pixels outside of the image. Any white pixels on the periphery of the image are thus included in the background component.\n\n \n \n \n \n \n \n \n connected \n disconnected \n connected \n connected \n \nConnectedness of white pixels      \nConnectedness of black pixels \n \n\nLet C_1 be a connected component in an image and C_2 be another connected component in the same image with the opposite color.\nLet's think of a modified image in which colors of all pixels not included in C_1 nor C_2 are changed to that of C_2. If neither C_1 nor C_2 is the background component, the color of the background component is changed to that of C_2. We say that C_1 surrounds C_2 in the original image when pixels in C_2 are not included in the background component in the modified image. (see below)\n\nTwo images represent the same character if both of the following conditions are satisfied.\n\n The two images have the same number of connected components.\n\n Let S and S' be the sets of connected components of the two images. A bijective function f : S → S' satisfying the following conditions exists.\n For each connected component C that belongs to S, f (C) has the same color as C. \n\n For each of C_1 and C_2 belonging to S, f (C_1) surrounds f (C_2) if and only if C_1 surrounds C_2.\nLet's see an example. Connected components in the images of the figure below has the following surrounding relations.\n\n C_1 surrounds C_2.\n\n C_2 surrounds C_3.\n\n C_2 surrounds C_4.\n\n C'_1 surrounds C'_2.\n\n C'_2 surrounds C'_3.\n\n C'_2 surrounds C'_4.\nA bijective function defined as f (C_i) = C'_i for each connected component satisfies the conditions stated above. Therefore, we can conclude that the two images represent the same character.\n \n\nMake a program judging whether given two images represent the same character.\nTask Input: The input consists of at most 200 datasets. The end of the input is represented by a line containing two zeros. Each dataset is formatted as follows.\n\nimage 1\nimage 2\n\nEach image has the following format.\n\nh w\np_(1,1) . . . p_(1, w)\n. . . \np_(h, 1) . . . p_(h, w)\n\nh and w are the height and the width of the image in numbers of pixels.\nYou may assume that 1 <= h <= 100 and 1 <= w <= 100.\n\nEach of the following h lines consists of w characters. \np_(y, x) is a character representing the color\nof the pixel in the y-th row from the top and the x-th column from the left.\nCharacters are either a period (\". \") meaning white or a sharp sign (\"#\") meaning black.\nTask Output: For each dataset, output \"yes\" if the two images represent the same character, or output \"no\", otherwise, in a line. The output should not contain extra characters.\nTask Samples: input: 3 6\n.#..#.\n#.##.#\n.#..#.\n8 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#..#..#\n.#####.\n...#...\n3 3\n#..\n...\n#..\n3 3\n#..\n.#.\n#..\n3 3\n...\n...\n...\n3 3\n...\n.#.\n...\n3 3\n.#.\n#.#\n.#.\n3 3\n.#.\n###\n.#.\n7 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#.....#\n.#####.\n7 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#..#..#\n.#####.\n7 7\n.#####.\n#.....#\n#..#..#\n#.#.#.#\n#..#..#\n#.....#\n.#####.\n7 11\n.#####.....\n#.....#....\n#..#..#..#.\n#.#.#.#.#.#\n#..#..#..#.\n#.....#....\n.#####.....\n7 3\n.#.\n#.#\n.#.\n#.#\n.#.\n#.#\n.#.\n7 7\n.#####.\n#..#..#\n#..#..#\n#.#.#.#\n#..#..#\n#..#..#\n.#####.\n3 1\n#\n#\n.\n1 2\n#.\n0 0\n output: yes\nno\nno\nno\nno\nno\nyes\nyes\n\n" }, { "title": "Warp Drive", "content": "The warp drive technology is reforming air travel, making the travel times drastically shorter.\nAircraft reaching above the warp fields built on the ground surface can be transferred to any desired destination in a twinkling.\n\nWith the current immature technology, however, building warp fields is quite expensive.\nOur budget allows building only two of them.\nFortunately, the cost does not depend on the locations of the warp fields,\nand we can build them anywhere on the ground surface, even at an airport.\n\nYour task is, given locations of airports and a list of one way flights among them, find the best locations to build the two warp fields that give the minimal average cost.\nThe average cost is the root mean square of travel times of all the flights, defined as follows.\n\nHere, m is the number of flights and t_j is the shortest possible travel time of the j-th flight.\nNote that the value of t_j depends on the locations of the warp fields.\n\nFor simplicity, we approximate the surface of the ground by a flat two dimensional plane, and approximate airports, aircraft, and warp fields by points on the plane.\nDifferent flights use different aircraft with possibly different cruising speeds.\nTimes required for climb, acceleration, deceleration and descent are negligible.\nFurther, when an aircraft reaches above a warp field, time required after that to its destination is zero.\nAs is explained below, the airports have integral coordinates. Note, however, that the warp fields can have non-integer coordinates.", "constraint": "", "input": "The input consists of at most 35 datasets, each in the following format.\n\nn m \nx_1 y_1 \n. . . \nx_n y_n \na_1 b_1 v_1 \n. . . \na_m b_m v_m \n\nn is the number of airports, and m is the number of flights (2 <= n <= 20,2 <= m <= 40).\nFor each i, x_i and y_i are the coordinates of the i-th airport.\nx_i and y_i are integers with absolute values at most 1000.\nFor each j, a_j and b_j are integers between 1 and n inclusive, and are the indices of the departure and arrival airports for the j-th flight, respectively.\nv_j is the cruising speed for the j-th flight, that is, the distance that the aircraft of the flight moves in one time unit.\nv_j is a decimal fraction with two digits after the decimal point (1 <= v_j <= 10).\n\nThe following are guaranteed.\n\nTwo different airports have different coordinates.\n\nThe departure and arrival airports of any of the flights are different.\n\nTwo different flights have different departure airport and/or arrival airport.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output the average cost when you place the two warp fields optimally.\nThe output should not contain an absolute error greater than 10^-6.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 4\n100 4\n100 0\n0 0\n1 2 1.00\n2 1 1.00\n3 1 9.99\n3 2 9.99\n7 6\n0 0\n1 0\n2 0\n0 10\n1 10\n2 10\n20 5\n1 7 1.00\n2 7 1.00\n3 7 1.00\n4 7 1.00\n5 7 1.00\n6 7 1.00\n4 4\n-1 -1\n1 -1\n-1 1\n1 1\n1 4 1.10\n4 2 2.10\n2 3 3.10\n3 1 4.10\n8 12\n-91 0\n-62 0\n-18 0\n2 0\n23 0\n55 0\n63 0\n80 0\n2 7 3.96\n3 2 2.25\n2 4 5.48\n8 7 9.74\n5 6 6.70\n7 6 1.51\n4 1 7.41\n5 8 1.11\n6 3 2.98\n3 4 2.75\n1 8 5.89\n4 5 5.37\n0 0\n output: 1.414214\n0.816497\n0.356001\n5.854704"], "Pid": "p01099", "ProblemText": "Task Description: The warp drive technology is reforming air travel, making the travel times drastically shorter.\nAircraft reaching above the warp fields built on the ground surface can be transferred to any desired destination in a twinkling.\n\nWith the current immature technology, however, building warp fields is quite expensive.\nOur budget allows building only two of them.\nFortunately, the cost does not depend on the locations of the warp fields,\nand we can build them anywhere on the ground surface, even at an airport.\n\nYour task is, given locations of airports and a list of one way flights among them, find the best locations to build the two warp fields that give the minimal average cost.\nThe average cost is the root mean square of travel times of all the flights, defined as follows.\n\nHere, m is the number of flights and t_j is the shortest possible travel time of the j-th flight.\nNote that the value of t_j depends on the locations of the warp fields.\n\nFor simplicity, we approximate the surface of the ground by a flat two dimensional plane, and approximate airports, aircraft, and warp fields by points on the plane.\nDifferent flights use different aircraft with possibly different cruising speeds.\nTimes required for climb, acceleration, deceleration and descent are negligible.\nFurther, when an aircraft reaches above a warp field, time required after that to its destination is zero.\nAs is explained below, the airports have integral coordinates. Note, however, that the warp fields can have non-integer coordinates.\nTask Input: The input consists of at most 35 datasets, each in the following format.\n\nn m \nx_1 y_1 \n. . . \nx_n y_n \na_1 b_1 v_1 \n. . . \na_m b_m v_m \n\nn is the number of airports, and m is the number of flights (2 <= n <= 20,2 <= m <= 40).\nFor each i, x_i and y_i are the coordinates of the i-th airport.\nx_i and y_i are integers with absolute values at most 1000.\nFor each j, a_j and b_j are integers between 1 and n inclusive, and are the indices of the departure and arrival airports for the j-th flight, respectively.\nv_j is the cruising speed for the j-th flight, that is, the distance that the aircraft of the flight moves in one time unit.\nv_j is a decimal fraction with two digits after the decimal point (1 <= v_j <= 10).\n\nThe following are guaranteed.\n\nTwo different airports have different coordinates.\n\nThe departure and arrival airports of any of the flights are different.\n\nTwo different flights have different departure airport and/or arrival airport.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output the average cost when you place the two warp fields optimally.\nThe output should not contain an absolute error greater than 10^-6.\nTask Samples: input: 3 4\n100 4\n100 0\n0 0\n1 2 1.00\n2 1 1.00\n3 1 9.99\n3 2 9.99\n7 6\n0 0\n1 0\n2 0\n0 10\n1 10\n2 10\n20 5\n1 7 1.00\n2 7 1.00\n3 7 1.00\n4 7 1.00\n5 7 1.00\n6 7 1.00\n4 4\n-1 -1\n1 -1\n-1 1\n1 1\n1 4 1.10\n4 2 2.10\n2 3 3.10\n3 1 4.10\n8 12\n-91 0\n-62 0\n-18 0\n2 0\n23 0\n55 0\n63 0\n80 0\n2 7 3.96\n3 2 2.25\n2 4 5.48\n8 7 9.74\n5 6 6.70\n7 6 1.51\n4 1 7.41\n5 8 1.11\n6 3 2.98\n3 4 2.75\n1 8 5.89\n4 5 5.37\n0 0\n output: 1.414214\n0.816497\n0.356001\n5.854704\n\n" }, { "title": "Gift Exchange Party", "content": "A gift exchange party will be held at a school in TKB City.\n\nFor every pair of students who are close friends, one gift must be given from one to the other at this party, but not the other way around.\nIt is decided in advance the gift directions, that is, which student of each pair receives a gift.\nNo other gift exchanges are made.\n\nIf each pair randomly decided the gift direction,\nsome might receive countless gifts, while some might receive only few or even none.\n\nYou'd like to decide the gift directions for all the friend pairs\nthat minimize the difference between the smallest and the largest numbers of gifts received by a student.\nFind the smallest and the largest numbers of gifts received\nwhen the difference between them is minimized.\nWhen there is more than one way to realize that, \nfind the way that maximizes the smallest number of received gifts.", "constraint": "", "input": "The input consists of at most 10 datasets, each in the following format.\n\nn m\nu_1 v_1\n. . . \nu_m v_m\n\nn is the number of students, and m is the number of friendship relations (2 <= n <= 100,1 <= m <= n (n-1)/2). \nStudents are denoted by integers between 1 and n, inclusive.\nThe following m lines describe the friendship relations: for each i, student u_i and v_i are close friends (u_i < v_i).\nThe same friendship relations do not appear more than once.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output a single line containing two integers l and h separated by a single space.\nHere, l and h are the smallest and the largest numbers, respectively, of gifts received by a student.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2\n2 3\n1 3\n4 3\n1 2\n1 3\n1 4\n4 6\n1 2\n1 3\n1 4\n2 3\n3 4\n2 4\n0 0\n output: 1 1\n0 1\n1 2"], "Pid": "p01100", "ProblemText": "Task Description: A gift exchange party will be held at a school in TKB City.\n\nFor every pair of students who are close friends, one gift must be given from one to the other at this party, but not the other way around.\nIt is decided in advance the gift directions, that is, which student of each pair receives a gift.\nNo other gift exchanges are made.\n\nIf each pair randomly decided the gift direction,\nsome might receive countless gifts, while some might receive only few or even none.\n\nYou'd like to decide the gift directions for all the friend pairs\nthat minimize the difference between the smallest and the largest numbers of gifts received by a student.\nFind the smallest and the largest numbers of gifts received\nwhen the difference between them is minimized.\nWhen there is more than one way to realize that, \nfind the way that maximizes the smallest number of received gifts.\nTask Input: The input consists of at most 10 datasets, each in the following format.\n\nn m\nu_1 v_1\n. . . \nu_m v_m\n\nn is the number of students, and m is the number of friendship relations (2 <= n <= 100,1 <= m <= n (n-1)/2). \nStudents are denoted by integers between 1 and n, inclusive.\nThe following m lines describe the friendship relations: for each i, student u_i and v_i are close friends (u_i < v_i).\nThe same friendship relations do not appear more than once.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output a single line containing two integers l and h separated by a single space.\nHere, l and h are the smallest and the largest numbers, respectively, of gifts received by a student.\nTask Samples: input: 3 3\n1 2\n2 3\n1 3\n4 3\n1 2\n1 3\n1 4\n4 6\n1 2\n1 3\n1 4\n2 3\n3 4\n2 4\n0 0\n output: 1 1\n0 1\n1 2\n\n" }, { "title": "Taro's Shopping", "content": "Mammy decided to give Taro his first shopping experience.\nMammy tells him to choose any two items he wants from those\nlisted in the shopping catalogue,\nbut Taro cannot decide which two, as all the items look attractive.\nThus he plans to buy the pair of two items with\nthe highest price sum, not exceeding the amount Mammy allows.\nAs getting two of the same item is boring, he wants two different items.\n\nYou are asked to help Taro select the two items.\nThe price list for all of the items is given.\nAmong pairs of two items in the list,\nfind the pair with the highest price sum\nnot exceeding the allowed amount,\nand report the sum.\nTaro is buying two items, not one, nor three, nor more.\nNote that, two or more items in the list may be priced equally.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn m\na_1 a_2 . . . a_n\n\nA dataset consists of two lines.\nIn the first line, the number of items n and the maximum\npayment allowed m are given.\nn is an integer satisfying 2 <= n <= 1000.\nm is an integer satisfying 2 <= m <= 2,000,000.\nIn the second line, prices of n items are given.\na_i (1 <= i <= n) is the price\nof the i-th item.\nThis value is an integer greater than or equal to 1 and\nless than or equal to 1,000,000.\n\nThe end of the input is indicated by a line containing two zeros.\nThe sum of n's of all the datasets does not exceed 50,000.", "output": "For each dataset, find the pair with the highest price sum\nnot exceeding the allowed amount m\nand output the sum in a line.\nIf the price sum of every pair of items exceeds m,\noutput NONE instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 45\n10 20 30\n6 10\n1 2 5 8 9 11\n7 100\n11 34 83 47 59 29 70\n4 100\n80 70 60 50\n4 20\n10 5 10 16\n0 0\n output: 40\n10\n99\nNONE\n20"], "Pid": "p01101", "ProblemText": "Task Description: Mammy decided to give Taro his first shopping experience.\nMammy tells him to choose any two items he wants from those\nlisted in the shopping catalogue,\nbut Taro cannot decide which two, as all the items look attractive.\nThus he plans to buy the pair of two items with\nthe highest price sum, not exceeding the amount Mammy allows.\nAs getting two of the same item is boring, he wants two different items.\n\nYou are asked to help Taro select the two items.\nThe price list for all of the items is given.\nAmong pairs of two items in the list,\nfind the pair with the highest price sum\nnot exceeding the allowed amount,\nand report the sum.\nTaro is buying two items, not one, nor three, nor more.\nNote that, two or more items in the list may be priced equally.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn m\na_1 a_2 . . . a_n\n\nA dataset consists of two lines.\nIn the first line, the number of items n and the maximum\npayment allowed m are given.\nn is an integer satisfying 2 <= n <= 1000.\nm is an integer satisfying 2 <= m <= 2,000,000.\nIn the second line, prices of n items are given.\na_i (1 <= i <= n) is the price\nof the i-th item.\nThis value is an integer greater than or equal to 1 and\nless than or equal to 1,000,000.\n\nThe end of the input is indicated by a line containing two zeros.\nThe sum of n's of all the datasets does not exceed 50,000.\nTask Output: For each dataset, find the pair with the highest price sum\nnot exceeding the allowed amount m\nand output the sum in a line.\nIf the price sum of every pair of items exceeds m,\noutput NONE instead.\nTask Samples: input: 3 45\n10 20 30\n6 10\n1 2 5 8 9 11\n7 100\n11 34 83 47 59 29 70\n4 100\n80 70 60 50\n4 20\n10 5 10 16\n0 0\n output: 40\n10\n99\nNONE\n20\n\n" }, { "title": "Almost Identical Programs", "content": "The programming contest named\nConcours de Programmation Comtemporaine Interuniversitaire (CPCI)\nhas a judging system similar to that of ICPC;\ncontestants have to submit correct outputs for two different inputs\nto be accepted as a correct solution.\n\nEach of the submissions should include the program that generated\nthe output. A pair of submissions is judged to be a correct\nsolution when, in addition to the correctness of the outputs, they\ninclude an identical program.\n\nMany contestants, however, do not stop including a different version\nof their programs in their second submissions, after modifying a\nsingle string literal in their programs representing \nthe input file name, attempting to process different input.\n\nThe organizers of CPCI are exploring the possibility of showing a\nspecial error message for such close submissions, \nindicating contestants what's wrong with such submissions.\n\nYour task is to detect such close submissions.", "constraint": "", "input": "The input consists of at most 100 datasets, each in the following format.\n\ns_1\ns_2\n\nEach of s_1 and s_2 is\na string written in a line, with the length between 1 and 200, inclusive.\nThey are the first and the second submitted programs respectively.\n\nA program consists of lowercase letters (a, b, . . . , z), uppercase letters (A, B, . . . , Z),\ndigits (0,1, . . . , 9), double quotes (\"), and semicolons (; ).\nWhen double quotes occur in a program, there are always even number of them.\n\nThe end of the input is indicated by a line containing one '. ' (period).", "output": "For each dataset, print the judge result in a line.\n\nIf the given two programs are identical, print IDENTICAL.\nIf two programs differ with only one corresponding string literal, print CLOSE.\nOtherwise, print DIFFERENT.\n\nA string literal is a possibly empty sequence of characters between an\nodd-numbered occurrence of a double quote and the next occurrence of\na double quote.", "content_img": false, "lang": "en", "error": false, "samples": ["input: print\"hello\";print123\nprint\"hello\";print123\nread\"B1input\";solve;output;\nread\"B2\";solve;output;\nread\"C1\";solve;output\"C1ans\";\nread\"C2\";solve;output\"C2ans\";\n\"\"\"\"\"\"\"\"\n\"\"\"42\"\"\"\"\"\nslow\"program\"\nfast\"code\"\n\"super\"fast\"program\"\n\"super\"faster\"program\"\nX\"\"\nX\nI\"S\"\"CREAM\"\nI\"CE\"\"CREAM\"\n11\"22\"11\n1\"33\"111\n.\n output: IDENTICAL\nCLOSE\nDIFFERENT\nCLOSE\nDIFFERENT\nDIFFERENT\nDIFFERENT\nCLOSE\nDIFFERENT"], "Pid": "p01102", "ProblemText": "Task Description: The programming contest named\nConcours de Programmation Comtemporaine Interuniversitaire (CPCI)\nhas a judging system similar to that of ICPC;\ncontestants have to submit correct outputs for two different inputs\nto be accepted as a correct solution.\n\nEach of the submissions should include the program that generated\nthe output. A pair of submissions is judged to be a correct\nsolution when, in addition to the correctness of the outputs, they\ninclude an identical program.\n\nMany contestants, however, do not stop including a different version\nof their programs in their second submissions, after modifying a\nsingle string literal in their programs representing \nthe input file name, attempting to process different input.\n\nThe organizers of CPCI are exploring the possibility of showing a\nspecial error message for such close submissions, \nindicating contestants what's wrong with such submissions.\n\nYour task is to detect such close submissions.\nTask Input: The input consists of at most 100 datasets, each in the following format.\n\ns_1\ns_2\n\nEach of s_1 and s_2 is\na string written in a line, with the length between 1 and 200, inclusive.\nThey are the first and the second submitted programs respectively.\n\nA program consists of lowercase letters (a, b, . . . , z), uppercase letters (A, B, . . . , Z),\ndigits (0,1, . . . , 9), double quotes (\"), and semicolons (; ).\nWhen double quotes occur in a program, there are always even number of them.\n\nThe end of the input is indicated by a line containing one '. ' (period).\nTask Output: For each dataset, print the judge result in a line.\n\nIf the given two programs are identical, print IDENTICAL.\nIf two programs differ with only one corresponding string literal, print CLOSE.\nOtherwise, print DIFFERENT.\n\nA string literal is a possibly empty sequence of characters between an\nodd-numbered occurrence of a double quote and the next occurrence of\na double quote.\nTask Samples: input: print\"hello\";print123\nprint\"hello\";print123\nread\"B1input\";solve;output;\nread\"B2\";solve;output;\nread\"C1\";solve;output\"C1ans\";\nread\"C2\";solve;output\"C2ans\";\n\"\"\"\"\"\"\"\"\n\"\"\"42\"\"\"\"\"\nslow\"program\"\nfast\"code\"\n\"super\"fast\"program\"\n\"super\"faster\"program\"\nX\"\"\nX\nI\"S\"\"CREAM\"\nI\"CE\"\"CREAM\"\n11\"22\"11\n1\"33\"111\n.\n output: IDENTICAL\nCLOSE\nDIFFERENT\nCLOSE\nDIFFERENT\nDIFFERENT\nDIFFERENT\nCLOSE\nDIFFERENT\n\n" }, { "title": "A Garden with Ponds", "content": "Mr. Gardiner is a modern garden designer who is excellent at utilizing the terrain features.\n His design method is unique: he first decides the location of ponds and design them with the terrain features intact.\n\n According to his unique design procedure, all of his ponds are rectangular with simple aspect ratios.\n First, Mr. Gardiner draws a regular grid on the map of the garden site so that the land is divided into cells of unit square, and annotates every cell with its elevation.\n In his design method, a pond occupies a rectangular area consisting of a number of cells.\n Each of its outermost cells has to be higher than all of its inner cells.\n For instance, in the following grid map, in which numbers are elevations of cells, a pond can occupy the shaded area, where the outermost cells are shaded darker and the inner cells are shaded lighter.\n You can easily see that the elevations of the outermost cells are at least three and those of the inner ones are at most two.\n\n A rectangular area on which a pond is built must have at least one inner cell.\n Therefore, both its width and depth are at least three.\n\n When you pour water at an inner cell of a pond, the water can be kept in the pond until its level reaches that of the lowest outermost cells.\n If you continue pouring, the water inevitably spills over. \n Mr. Gardiner considers the larger capacity the pond has, the better it is.\n Here, the capacity of a pond is the maximum amount of water it can keep.\n For instance, when a pond is built on the shaded area in the above map, its capacity is (3 - 1) + (3 - 0) + (3 - 2) = 6, where 3 is the lowest elevation of the outermost cells and 1,0,2 are the elevations of the inner cells.\n Your mission is to write a computer program that, given a grid map describing the elevation of each unit square cell, calculates the largest possible capacity of a pond built in the site.\n\n Note that neither of the following rectangular areas can be a pond.\n In the left one, the cell at the bottom right corner is not higher than the inner cell.\n In the right one, the central cell is as high as the outermost cells.", "constraint": "", "input": "The input consists of at most 100 datasets, each in the following format.\n\nd w\ne_1,1 . . . e_1, w\n. . .\ne_d, 1 . . . e_d, w\n\nThe first line contains d and w, representing the depth and the width, respectively, of the garden site described in the map. \nThey are positive integers between 3 and 10, inclusive.\nEach of the following d lines contains w integers between 0 and 9, inclusive, separated by a space.\nThe x-th integer in the y-th line of the d lines is the elevation of the unit square cell with coordinates (x, y).\n\nThe end of the input is indicated by a line containing two zeros separated by a space.", "output": "For each dataset, output a single line containing the largest possible capacity of a pond that can be built in the garden site described in the dataset.\n If no ponds can be built, output a single line containing a zero.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3\n2 3 2\n2 1 2\n2 3 1\n3 5\n3 3 4 3 3\n3 1 0 2 3\n3 3 4 3 2\n7 7\n1 1 1 1 1 0 0\n1 0 0 0 1 0 0\n1 0 1 1 1 1 1\n1 0 1 0 1 0 1\n1 1 1 1 1 0 1\n0 0 1 0 0 0 1\n0 0 1 1 1 1 1\n6 6\n1 1 1 1 2 2\n1 0 0 2 0 2\n1 0 0 2 0 2\n3 3 3 9 9 9\n3 0 0 9 0 9\n3 3 3 9 9 9\n0 0\n output: 0\n3\n1\n9"], "Pid": "p01103", "ProblemText": "Task Description: Mr. Gardiner is a modern garden designer who is excellent at utilizing the terrain features.\n His design method is unique: he first decides the location of ponds and design them with the terrain features intact.\n\n According to his unique design procedure, all of his ponds are rectangular with simple aspect ratios.\n First, Mr. Gardiner draws a regular grid on the map of the garden site so that the land is divided into cells of unit square, and annotates every cell with its elevation.\n In his design method, a pond occupies a rectangular area consisting of a number of cells.\n Each of its outermost cells has to be higher than all of its inner cells.\n For instance, in the following grid map, in which numbers are elevations of cells, a pond can occupy the shaded area, where the outermost cells are shaded darker and the inner cells are shaded lighter.\n You can easily see that the elevations of the outermost cells are at least three and those of the inner ones are at most two.\n\n A rectangular area on which a pond is built must have at least one inner cell.\n Therefore, both its width and depth are at least three.\n\n When you pour water at an inner cell of a pond, the water can be kept in the pond until its level reaches that of the lowest outermost cells.\n If you continue pouring, the water inevitably spills over. \n Mr. Gardiner considers the larger capacity the pond has, the better it is.\n Here, the capacity of a pond is the maximum amount of water it can keep.\n For instance, when a pond is built on the shaded area in the above map, its capacity is (3 - 1) + (3 - 0) + (3 - 2) = 6, where 3 is the lowest elevation of the outermost cells and 1,0,2 are the elevations of the inner cells.\n Your mission is to write a computer program that, given a grid map describing the elevation of each unit square cell, calculates the largest possible capacity of a pond built in the site.\n\n Note that neither of the following rectangular areas can be a pond.\n In the left one, the cell at the bottom right corner is not higher than the inner cell.\n In the right one, the central cell is as high as the outermost cells.\nTask Input: The input consists of at most 100 datasets, each in the following format.\n\nd w\ne_1,1 . . . e_1, w\n. . .\ne_d, 1 . . . e_d, w\n\nThe first line contains d and w, representing the depth and the width, respectively, of the garden site described in the map. \nThey are positive integers between 3 and 10, inclusive.\nEach of the following d lines contains w integers between 0 and 9, inclusive, separated by a space.\nThe x-th integer in the y-th line of the d lines is the elevation of the unit square cell with coordinates (x, y).\n\nThe end of the input is indicated by a line containing two zeros separated by a space.\nTask Output: For each dataset, output a single line containing the largest possible capacity of a pond that can be built in the garden site described in the dataset.\n If no ponds can be built, output a single line containing a zero.\nTask Samples: input: 3 3\n2 3 2\n2 1 2\n2 3 1\n3 5\n3 3 4 3 3\n3 1 0 2 3\n3 3 4 3 2\n7 7\n1 1 1 1 1 0 0\n1 0 0 0 1 0 0\n1 0 1 1 1 1 1\n1 0 1 0 1 0 1\n1 1 1 1 1 0 1\n0 0 1 0 0 0 1\n0 0 1 1 1 1 1\n6 6\n1 1 1 1 2 2\n1 0 0 2 0 2\n1 0 0 2 0 2\n3 3 3 9 9 9\n3 0 0 9 0 9\n3 3 3 9 9 9\n0 0\n output: 0\n3\n1\n9\n\n" }, { "title": "Making Lunch Boxes", "content": "Taro has been hooked on making lunch boxes recently.\nTaro has obtained a new lunch box recipe book today, and wants to try as many of the recipes listed in the book as possible.\n\nEnough of the ingredients for all the recipes are at hand, but they all are in vacuum packs of two.\nIf only one of them is used leaving the other, the leftover will be rotten easily, but making two of the same recipe is not interesting.\nThus he decided to make a set of lunch boxes, each with different recipe, that wouldn't leave any unused ingredients.\n\nNote that the book may include recipes for different lunch boxes made of the same set of ingredients.\n\nHow many lunch box recipes can Taro try today at most following his dogma?", "constraint": "", "input": "The input consists of at most 50 datasets, each in the following format.\n\nn m\nb_1,1. . . b_1, m\n. . .\nb_n, 1. . . b_n, m\n\nThe first line contains n, which is the number of recipes listed in the book, and m, which is the number of ingredients.\nBoth n and m are positive integers and satisfy 1 <= n <= 500,1 <= m <= 500 and 1 <= n * m <= 500.\nThe following n lines contain the information for each recipe with the string of length m consisting of 0 or 1.\nb_i, j implies whether the i-th recipe needs the j-th ingredient.\n1 means the ingredient is needed for the recipe and 0 means not.\nEach line contains at least one 1.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output the maximum number of recipes Taro can try.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n110\n101\n011\n110\n7 1\n1\n1\n1\n1\n1\n1\n1\n4 5\n10000\n01000\n00100\n00010\n6 6\n111111\n011000\n100000\n000010\n100001\n100100\n0 0\n output: 3\n6\n0\n6"], "Pid": "p01104", "ProblemText": "Task Description: Taro has been hooked on making lunch boxes recently.\nTaro has obtained a new lunch box recipe book today, and wants to try as many of the recipes listed in the book as possible.\n\nEnough of the ingredients for all the recipes are at hand, but they all are in vacuum packs of two.\nIf only one of them is used leaving the other, the leftover will be rotten easily, but making two of the same recipe is not interesting.\nThus he decided to make a set of lunch boxes, each with different recipe, that wouldn't leave any unused ingredients.\n\nNote that the book may include recipes for different lunch boxes made of the same set of ingredients.\n\nHow many lunch box recipes can Taro try today at most following his dogma?\nTask Input: The input consists of at most 50 datasets, each in the following format.\n\nn m\nb_1,1. . . b_1, m\n. . .\nb_n, 1. . . b_n, m\n\nThe first line contains n, which is the number of recipes listed in the book, and m, which is the number of ingredients.\nBoth n and m are positive integers and satisfy 1 <= n <= 500,1 <= m <= 500 and 1 <= n * m <= 500.\nThe following n lines contain the information for each recipe with the string of length m consisting of 0 or 1.\nb_i, j implies whether the i-th recipe needs the j-th ingredient.\n1 means the ingredient is needed for the recipe and 0 means not.\nEach line contains at least one 1.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output the maximum number of recipes Taro can try.\nTask Samples: input: 4 3\n110\n101\n011\n110\n7 1\n1\n1\n1\n1\n1\n1\n1\n4 5\n10000\n01000\n00100\n00010\n6 6\n111111\n011000\n100000\n000010\n100001\n100100\n0 0\n output: 3\n6\n0\n6\n\n" }, { "title": "Boolean Expression Compressor", "content": "You are asked to build a compressor for Boolean expressions\nthat transforms expressions to the shortest form keeping their meaning. \n\nThe grammar of the Boolean expressions has terminals \n0 1 a b c d - ^ * ( ), start symbol and the following production rule: \n\n  : : =  0  |  1  |  a  |  b  |  c  |  d  |  -  |  (^)  |  (*)\n\nLetters a, b, c and d represent Boolean\nvariables that have values of either 0 or 1.\nOperators are evaluated as shown in the Table below.\nIn other words, - means negation (NOT),\n^ means exclusive disjunction (XOR), and \n* means logical conjunction (AND). \n\nTable: Evaluations of operators\nWrite a program that calculates the length of the shortest expression that\nevaluates equal to the given expression with whatever values of the four variables.\n\nFor example, 0, that is the first expression in the sample input,\ncannot be shortened further.\nTherefore the shortest length for this expression is 1.\n\nFor another example, (a*(1*b)), the second in the sample input,\nalways evaluates equal to (a*b) and (b*a),\nwhich are the shortest. The output for this expression, thus, should be 5.", "constraint": "", "input": "The input consists of multiple datasets.\nA dataset consists of one line, containing an expression\nconforming to the grammar described above.\nThe length of the expression is less than or equal to 16 characters.\n\nThe end of the input is indicated by a line containing one\n‘. ’ (period).\nThe number of datasets in the input is at most 200.", "output": "For each dataset, \noutput a single line containing an integer which is the length of the\nshortest expression that has the same value as the given expression for \nall combinations of values in the variables.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0\n(a*(1*b))\n(1^a)\n(-(-a*-b)*a)\n(a^(b^(c^d)))\n.\n output: 1\n5\n2\n1\n13"], "Pid": "p01105", "ProblemText": "Task Description: You are asked to build a compressor for Boolean expressions\nthat transforms expressions to the shortest form keeping their meaning. \n\nThe grammar of the Boolean expressions has terminals \n0 1 a b c d - ^ * ( ), start symbol and the following production rule: \n\n  : : =  0  |  1  |  a  |  b  |  c  |  d  |  -  |  (^)  |  (*)\n\nLetters a, b, c and d represent Boolean\nvariables that have values of either 0 or 1.\nOperators are evaluated as shown in the Table below.\nIn other words, - means negation (NOT),\n^ means exclusive disjunction (XOR), and \n* means logical conjunction (AND). \n\nTable: Evaluations of operators\nWrite a program that calculates the length of the shortest expression that\nevaluates equal to the given expression with whatever values of the four variables.\n\nFor example, 0, that is the first expression in the sample input,\ncannot be shortened further.\nTherefore the shortest length for this expression is 1.\n\nFor another example, (a*(1*b)), the second in the sample input,\nalways evaluates equal to (a*b) and (b*a),\nwhich are the shortest. The output for this expression, thus, should be 5.\nTask Input: The input consists of multiple datasets.\nA dataset consists of one line, containing an expression\nconforming to the grammar described above.\nThe length of the expression is less than or equal to 16 characters.\n\nThe end of the input is indicated by a line containing one\n‘. ’ (period).\nThe number of datasets in the input is at most 200.\nTask Output: For each dataset, \noutput a single line containing an integer which is the length of the\nshortest expression that has the same value as the given expression for \nall combinations of values in the variables.\nTask Samples: input: 0\n(a*(1*b))\n(1^a)\n(-(-a*-b)*a)\n(a^(b^(c^d)))\n.\n output: 1\n5\n2\n1\n13\n\n" }, { "title": "Folding a Ribbon", "content": "Think of repetitively folding a very long and thin ribbon. First,\n the ribbon is spread out from left to right, then it is creased at\n its center, and one half of the ribbon is laid over the other. You\n can either fold it from the left to the right, picking up the left\n end of the ribbon and laying it over the right end, or from the\n right to the left, doing the same in the reverse direction. To fold\n the already folded ribbon, the whole layers of the ribbon are\n treated as one thicker ribbon, again from the left to the right or\n the reverse.\n\n After folding the ribbon a number of times, one of the layers of the\n ribbon is marked, and then the ribbon is completely unfolded\n restoring the original state. Many creases remain on the\n unfolded ribbon, and one certain part of the ribbon between two\n creases or a ribbon end should be found marked. Knowing which\n layer is marked and the position of the marked part when the ribbon\n is spread out, can you tell all the directions of the repeated\n folding, from the left or from the right?\n\n The figure below depicts the case of the first dataset of the sample input.", "constraint": "", "input": "The input consists of at most 100 datasets, each being a line\n containing three integers.\n\nn i j\n\n The three integers mean the following: The ribbon is folded n\n times in a certain order; then, the i-th layer of the folded\n ribbon, counted from the top, is marked; when the ribbon is unfolded\n completely restoring the original state, the marked part is\n the j-th part of the ribbon separated by creases, counted\n from the left. Both i and j are one-based, that is,\n the topmost layer is the layer 1 and the leftmost part is numbered\n 1. These integers satisfy 1 <= n <= 60,1 <= i\n <= 2^n, and 1 <= j <=\n 2^n.\n\n The end of the input is indicated by a line with three zeros.", "output": "For each dataset, output one of the possible folding sequences that\n bring about the result specified in the dataset.\n\n The folding sequence should be given in one line consisting\n of n characters, each being either L\n or R. L means a folding from the left to the\n right, and R means from the right to the left. The folding\n operations are to be carried out in the order specified in the\n sequence.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3 2\n12 578 2214\n59 471605241352156968 431565444592236940\n0 0 0\n output: LRR\nRLLLRRRLRRLL\nLRRRLRRLLRRRRLLLLRLLRRRLRRLLRLLLLLLRLRLLRLRLLLRLRLLRLLRRRLL"], "Pid": "p01106", "ProblemText": "Task Description: Think of repetitively folding a very long and thin ribbon. First,\n the ribbon is spread out from left to right, then it is creased at\n its center, and one half of the ribbon is laid over the other. You\n can either fold it from the left to the right, picking up the left\n end of the ribbon and laying it over the right end, or from the\n right to the left, doing the same in the reverse direction. To fold\n the already folded ribbon, the whole layers of the ribbon are\n treated as one thicker ribbon, again from the left to the right or\n the reverse.\n\n After folding the ribbon a number of times, one of the layers of the\n ribbon is marked, and then the ribbon is completely unfolded\n restoring the original state. Many creases remain on the\n unfolded ribbon, and one certain part of the ribbon between two\n creases or a ribbon end should be found marked. Knowing which\n layer is marked and the position of the marked part when the ribbon\n is spread out, can you tell all the directions of the repeated\n folding, from the left or from the right?\n\n The figure below depicts the case of the first dataset of the sample input.\nTask Input: The input consists of at most 100 datasets, each being a line\n containing three integers.\n\nn i j\n\n The three integers mean the following: The ribbon is folded n\n times in a certain order; then, the i-th layer of the folded\n ribbon, counted from the top, is marked; when the ribbon is unfolded\n completely restoring the original state, the marked part is\n the j-th part of the ribbon separated by creases, counted\n from the left. Both i and j are one-based, that is,\n the topmost layer is the layer 1 and the leftmost part is numbered\n 1. These integers satisfy 1 <= n <= 60,1 <= i\n <= 2^n, and 1 <= j <=\n 2^n.\n\n The end of the input is indicated by a line with three zeros.\nTask Output: For each dataset, output one of the possible folding sequences that\n bring about the result specified in the dataset.\n\n The folding sequence should be given in one line consisting\n of n characters, each being either L\n or R. L means a folding from the left to the\n right, and R means from the right to the left. The folding\n operations are to be carried out in the order specified in the\n sequence.\nTask Samples: input: 3 3 2\n12 578 2214\n59 471605241352156968 431565444592236940\n0 0 0\n output: LRR\nRLLLRRRLRRLL\nLRRRLRRLLRRRRLLLLRLLRRRLRRLLRLLLLLLRLRLLRLRLLLRLRLLRLLRRRLL\n\n" }, { "title": "Go around the Labyrinth", "content": "Explorer Taro got a floor plan of a labyrinth.\nThe floor of this labyrinth is in the form of a two-dimensional grid.\nEach of the cells on the floor plan corresponds to a room and is indicated whether it can be entered or not.\nThe labyrinth has only one entrance located at the northwest corner, which is upper left on the floor plan.\nThere is a treasure chest in each of the rooms at other three corners, southwest, southeast, and northeast.\nTo get a treasure chest, Taro must move onto the room where the treasure chest is placed.\n\nTaro starts from the entrance room and repeats moving to one of the enterable adjacent rooms in the four directions, north, south, east, or west.\nHe wants to collect all the three treasure chests and come back to the entrance room.\nA bad news for Taro is that, the labyrinth is quite dilapidated and even for its enterable rooms except for the entrance room, floors are so fragile that, once passed over, it will collapse and the room becomes not enterable.\nDetermine whether it is possible to collect all the treasure chests and return to the entrance.", "constraint": "", "input": "The input consists of at most 100 datasets, each in the following format.\n\nN M\nc_1,1. . . c_1, M\n. . .\nc_N, 1. . . c_N, M\n\nThe first line contains N, which is the number of rooms in the north-south direction, and M, which is the number of rooms in the east-west direction.\nN and M are integers satisfying 2 <= N <= 50 and 2 <= M <= 50.\nEach of the following N lines contains a string of length M.\nThe j-th character c_i, j of the i-th string represents the state of the room (i, j), i-th from the northernmost and j-th from the westernmost;\nthe character is the period ('. ') if the room is enterable and the number sign ('#') if the room is not enterable.\nThe entrance is located at (1,1), and the treasure chests are placed at (N, 1), (N, M) and (1, M).\nAll of these four rooms are enterable.\nTaro cannot go outside the given N * M rooms.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output YES if it is possible to collect all the treasure chests and return to the entrance room, and otherwise, output NO in a single line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0\n output: YES\nNO\nYES\nNO\nNO"], "Pid": "p01107", "ProblemText": "Task Description: Explorer Taro got a floor plan of a labyrinth.\nThe floor of this labyrinth is in the form of a two-dimensional grid.\nEach of the cells on the floor plan corresponds to a room and is indicated whether it can be entered or not.\nThe labyrinth has only one entrance located at the northwest corner, which is upper left on the floor plan.\nThere is a treasure chest in each of the rooms at other three corners, southwest, southeast, and northeast.\nTo get a treasure chest, Taro must move onto the room where the treasure chest is placed.\n\nTaro starts from the entrance room and repeats moving to one of the enterable adjacent rooms in the four directions, north, south, east, or west.\nHe wants to collect all the three treasure chests and come back to the entrance room.\nA bad news for Taro is that, the labyrinth is quite dilapidated and even for its enterable rooms except for the entrance room, floors are so fragile that, once passed over, it will collapse and the room becomes not enterable.\nDetermine whether it is possible to collect all the treasure chests and return to the entrance.\nTask Input: The input consists of at most 100 datasets, each in the following format.\n\nN M\nc_1,1. . . c_1, M\n. . .\nc_N, 1. . . c_N, M\n\nThe first line contains N, which is the number of rooms in the north-south direction, and M, which is the number of rooms in the east-west direction.\nN and M are integers satisfying 2 <= N <= 50 and 2 <= M <= 50.\nEach of the following N lines contains a string of length M.\nThe j-th character c_i, j of the i-th string represents the state of the room (i, j), i-th from the northernmost and j-th from the westernmost;\nthe character is the period ('. ') if the room is enterable and the number sign ('#') if the room is not enterable.\nThe entrance is located at (1,1), and the treasure chests are placed at (N, 1), (N, M) and (1, M).\nAll of these four rooms are enterable.\nTaro cannot go outside the given N * M rooms.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output YES if it is possible to collect all the treasure chests and return to the entrance room, and otherwise, output NO in a single line.\nTask Samples: input: 3 3\n...\n.#.\n...\n5 5\n..#..\n.....\n#....\n.....\n.....\n3 8\n..#.....\n........\n.....#..\n3 5\n..#..\n.....\n..#..\n4 4\n....\n....\n..##\n..#.\n0 0\n output: YES\nNO\nYES\nNO\nNO\n\n" }, { "title": "Equivalent Deformation", "content": "Two triangles T_1 and T_2 with the same area are on a plane.\nYour task is to perform the following operation to T_1 several times so that it is exactly superposed on T_2.\nHere, vertices of T_1 can be on any of the vertices of T_2.\nCompute the minimum number of operations required to superpose T_1 on T_2.\n\n(Operation): Choose one vertex of the triangle and move it to an arbitrary point on a line passing through the vertex and parallel to the opposite side.\n\nAn operation example\nThe following figure shows a possible sequence of the operations for the first dataset of the sample input.", "constraint": "", "input": "The input consists of at most 2000 datasets, each in the following format.\n\nx_11 y_11\nx_12 y_12\nx_13 y_13\nx_21 y_21\nx_22 y_22\nx_23 y_23\n\nx_ij and y_ij are the x- and y-coordinate of the j-th vertex of T_i.\n\nThe following holds for the dataset.\n\nAll the coordinate values are integers with at most 1000 of absolute values.\n\nT_1 and T_2 have the same positive area size.\n\nThe given six vertices are all distinct points.\nAn empty line is placed between datasets.\n\nThe end of the input is indicated by EOF.", "output": "For each dataset, output the minimum number of operations required in one line.\nIf five or more operations are required, output Many instead.\n\nNote that, vertices may have non-integral values after they are moved.\n\nYou can prove that, for any input satisfying the above constraints, the number of operations required is bounded by some constant.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 1\n2 2\n1 0\n1 3\n5 2\n4 3\n\n0 0\n0 1\n1 0\n0 3\n0 2\n1 -1\n\n-5 -4\n0 1\n0 15\n-10 14\n-5 10\n0 -8\n\n-110 221\n-731 525\n-555 -258\n511 -83\n-1000 -737\n66 -562\n\n533 -45\n-525 -450\n-282 -667\n-439 823\n-196 606\n-768 -233\n\n0 0\n0 1\n1 0\n99 1\n100 1\n55 2\n\n354 -289\n89 -79\n256 -166\n131 -196\n-774 -809\n-519 -623\n\n-990 688\n-38 601\n-360 712\n384 759\n-241 140\n-59 196\n\n629 -591\n360 -847\n936 -265\n109 -990\n-456 -913\n-787 -884\n\n-1000 -1000\n-999 -999\n-1000 -998\n1000 1000\n999 999\n1000 998\n\n-386 -83\n404 -83\n-408 -117\n-162 -348\n128 -88\n296 -30\n\n-521 -245\n-613 -250\n797 451\n-642 239\n646 309\n-907 180\n\n-909 -544\n-394 10\n-296 260\n-833 268\n-875 882\n-907 -423\n output: 4\n3\n3\n3\n3\n4\n4\n4\n4\nMany\nMany\nMany\nMany"], "Pid": "p01108", "ProblemText": "Task Description: Two triangles T_1 and T_2 with the same area are on a plane.\nYour task is to perform the following operation to T_1 several times so that it is exactly superposed on T_2.\nHere, vertices of T_1 can be on any of the vertices of T_2.\nCompute the minimum number of operations required to superpose T_1 on T_2.\n\n(Operation): Choose one vertex of the triangle and move it to an arbitrary point on a line passing through the vertex and parallel to the opposite side.\n\nAn operation example\nThe following figure shows a possible sequence of the operations for the first dataset of the sample input.\nTask Input: The input consists of at most 2000 datasets, each in the following format.\n\nx_11 y_11\nx_12 y_12\nx_13 y_13\nx_21 y_21\nx_22 y_22\nx_23 y_23\n\nx_ij and y_ij are the x- and y-coordinate of the j-th vertex of T_i.\n\nThe following holds for the dataset.\n\nAll the coordinate values are integers with at most 1000 of absolute values.\n\nT_1 and T_2 have the same positive area size.\n\nThe given six vertices are all distinct points.\nAn empty line is placed between datasets.\n\nThe end of the input is indicated by EOF.\nTask Output: For each dataset, output the minimum number of operations required in one line.\nIf five or more operations are required, output Many instead.\n\nNote that, vertices may have non-integral values after they are moved.\n\nYou can prove that, for any input satisfying the above constraints, the number of operations required is bounded by some constant.\nTask Samples: input: 0 1\n2 2\n1 0\n1 3\n5 2\n4 3\n\n0 0\n0 1\n1 0\n0 3\n0 2\n1 -1\n\n-5 -4\n0 1\n0 15\n-10 14\n-5 10\n0 -8\n\n-110 221\n-731 525\n-555 -258\n511 -83\n-1000 -737\n66 -562\n\n533 -45\n-525 -450\n-282 -667\n-439 823\n-196 606\n-768 -233\n\n0 0\n0 1\n1 0\n99 1\n100 1\n55 2\n\n354 -289\n89 -79\n256 -166\n131 -196\n-774 -809\n-519 -623\n\n-990 688\n-38 601\n-360 712\n384 759\n-241 140\n-59 196\n\n629 -591\n360 -847\n936 -265\n109 -990\n-456 -913\n-787 -884\n\n-1000 -1000\n-999 -999\n-1000 -998\n1000 1000\n999 999\n1000 998\n\n-386 -83\n404 -83\n-408 -117\n-162 -348\n128 -88\n296 -30\n\n-521 -245\n-613 -250\n797 451\n-642 239\n646 309\n-907 180\n\n-909 -544\n-394 10\n-296 260\n-833 268\n-875 882\n-907 -423\n output: 4\n3\n3\n3\n3\n4\n4\n4\n4\nMany\nMany\nMany\nMany\n\n" }, { "title": "Income Inequality", "content": "We often compute the average as the first step\nin processing statistical data.\nYes, the average is a good tendency measure of data,\nbut it is not always the best.\nIn some cases, the average may hinder the understanding\nof the data.\n\nFor example, consider the national income of a country.\nAs the term income inequality suggests,\na small number of people earn a good portion of the gross national income\nin many countries.\nIn such cases, the average income computes much higher than the\nincome of the vast majority.\nIt is not appropriate to regard the average as the income of typical people.\n\nLet us observe the above-mentioned phenomenon in some concrete data.\nIncomes of n people, a_1, . . . ,\na_n, are given.\nYou are asked to write a program that reports the number of people\nwhose incomes are less than or equal to the average\n(a_1 + . . . + a_n) / n.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn\na_1 a_2 . . . a_n\n\nA dataset consists of two lines.\nIn the first line, the number of people n is given.\nn is an integer satisfying 2 <= n <= 10 000.\nIn the second line, incomes of n people are given.\na_i (1 <= i <= n) is the income\nof the i-th person.\nThis value is an integer greater than or equal to 1 and\nless than or equal to 100 000.\n\nThe end of the input is indicated by a line containing a zero.\nThe sum of n's of all the datasets does not exceed 50 000.", "output": "For each dataset, output the number of people whose incomes are\nless than or equal to the average.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n15 15 15 15 15 15 15\n4\n10 20 30 60\n10\n1 1 1 1 1 1 1 1 1 100\n7\n90 90 90 90 90 90 10\n7\n2 7 1 8 2 8 4\n0\n output: 7\n3\n9\n1\n4"], "Pid": "p01109", "ProblemText": "Task Description: We often compute the average as the first step\nin processing statistical data.\nYes, the average is a good tendency measure of data,\nbut it is not always the best.\nIn some cases, the average may hinder the understanding\nof the data.\n\nFor example, consider the national income of a country.\nAs the term income inequality suggests,\na small number of people earn a good portion of the gross national income\nin many countries.\nIn such cases, the average income computes much higher than the\nincome of the vast majority.\nIt is not appropriate to regard the average as the income of typical people.\n\nLet us observe the above-mentioned phenomenon in some concrete data.\nIncomes of n people, a_1, . . . ,\na_n, are given.\nYou are asked to write a program that reports the number of people\nwhose incomes are less than or equal to the average\n(a_1 + . . . + a_n) / n.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn\na_1 a_2 . . . a_n\n\nA dataset consists of two lines.\nIn the first line, the number of people n is given.\nn is an integer satisfying 2 <= n <= 10 000.\nIn the second line, incomes of n people are given.\na_i (1 <= i <= n) is the income\nof the i-th person.\nThis value is an integer greater than or equal to 1 and\nless than or equal to 100 000.\n\nThe end of the input is indicated by a line containing a zero.\nThe sum of n's of all the datasets does not exceed 50 000.\nTask Output: For each dataset, output the number of people whose incomes are\nless than or equal to the average.\nTask Samples: input: 7\n15 15 15 15 15 15 15\n4\n10 20 30 60\n10\n1 1 1 1 1 1 1 1 1 100\n7\n90 90 90 90 90 90 10\n7\n2 7 1 8 2 8 4\n0\n output: 7\n3\n9\n1\n4\n\n" }, { "title": "Origami, or the art of folding paper", "content": "Master Grus is a famous origami (paper folding) artist, who is\nenthusiastic about exploring the possibility of origami art.\nFor future creation, he is now planning fundamental\nexperiments to establish the general theory of origami.\n\nOne rectangular piece of paper is used in each of his experiments.\nHe folds it horizontally and/or vertically several times and then\npunches through holes in the folded paper.\n\nThe following figure illustrates the folding process of a simple experiment,\nwhich corresponds to the third dataset of the Sample Input below.\nFolding the 10 * 8 rectangular piece of paper shown at top left\nthree times results in the 6 * 6 square shape shown at\nbottom left.\nIn the figure, dashed lines indicate the locations to fold the paper\nand round arrows indicate the directions of folding.\nGrid lines are shown as solid lines to tell the sizes of rectangular\nshapes and the exact locations of folding.\nColor densities represent the numbers of overlapping layers.\nPunching through holes at A and B in the folded paper makes\nnine holes in the paper, eight at A and another at B.\n\nYour mission in this problem is to write a computer program to count\nthe number of holes in the paper, given the information on a rectangular\npiece of paper and folding and punching instructions.", "constraint": "", "input": "The input consists of at most 1000 datasets, each in the following format.\n\nn m t p\nd_1 c_1 \n. . . \nd_t c_t \nx_1 y_1 \n. . . \nx_p y_p \n\nn and m are the width and the height, respectively, of\na rectangular piece of paper.\nThey are positive integers at most 32.\nt and p are the numbers of folding and punching\ninstructions, respectively.\nThey are positive integers at most 20.\nThe pair of d_i and c_i gives the\ni-th folding instruction as follows:\n\nd_i is either 1 or 2.\n\nc_i is a positive integer.\n\nIf d_i is 1, the left-hand side of the vertical folding line that passes at c_i right to the left boundary is folded onto the right-hand side. \n\nIf d_i is 2, the lower side of the horizontal folding line that passes at c_i above the lower boundary is folded onto the upper side. \n\nid_ic_ic_ix_iy_iix_iy_i\nThe end of the input is indicated by a line containing four zeros.", "output": "For each dataset, output p lines, the i-th of which contains\nthe number of holes punched in the paper by the i-th punching instruction.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 1 1 1\n1 1\n0 0\n1 3 2 1\n2 1\n2 1\n0 0\n10 8 3 2\n2 2\n1 3\n1 1\n0 1\n3 4\n3 3 3 2\n1 2\n2 1\n1 1\n0 1\n0 0\n0 0 0 0\n output: 2\n3\n8\n1\n3\n6"], "Pid": "p01110", "ProblemText": "Task Description: Master Grus is a famous origami (paper folding) artist, who is\nenthusiastic about exploring the possibility of origami art.\nFor future creation, he is now planning fundamental\nexperiments to establish the general theory of origami.\n\nOne rectangular piece of paper is used in each of his experiments.\nHe folds it horizontally and/or vertically several times and then\npunches through holes in the folded paper.\n\nThe following figure illustrates the folding process of a simple experiment,\nwhich corresponds to the third dataset of the Sample Input below.\nFolding the 10 * 8 rectangular piece of paper shown at top left\nthree times results in the 6 * 6 square shape shown at\nbottom left.\nIn the figure, dashed lines indicate the locations to fold the paper\nand round arrows indicate the directions of folding.\nGrid lines are shown as solid lines to tell the sizes of rectangular\nshapes and the exact locations of folding.\nColor densities represent the numbers of overlapping layers.\nPunching through holes at A and B in the folded paper makes\nnine holes in the paper, eight at A and another at B.\n\nYour mission in this problem is to write a computer program to count\nthe number of holes in the paper, given the information on a rectangular\npiece of paper and folding and punching instructions.\nTask Input: The input consists of at most 1000 datasets, each in the following format.\n\nn m t p\nd_1 c_1 \n. . . \nd_t c_t \nx_1 y_1 \n. . . \nx_p y_p \n\nn and m are the width and the height, respectively, of\na rectangular piece of paper.\nThey are positive integers at most 32.\nt and p are the numbers of folding and punching\ninstructions, respectively.\nThey are positive integers at most 20.\nThe pair of d_i and c_i gives the\ni-th folding instruction as follows:\n\nd_i is either 1 or 2.\n\nc_i is a positive integer.\n\nIf d_i is 1, the left-hand side of the vertical folding line that passes at c_i right to the left boundary is folded onto the right-hand side. \n\nIf d_i is 2, the lower side of the horizontal folding line that passes at c_i above the lower boundary is folded onto the upper side. \n\nid_ic_ic_ix_iy_iix_iy_i\nThe end of the input is indicated by a line containing four zeros.\nTask Output: For each dataset, output p lines, the i-th of which contains\nthe number of holes punched in the paper by the i-th punching instruction.\nTask Samples: input: 2 1 1 1\n1 1\n0 0\n1 3 2 1\n2 1\n2 1\n0 0\n10 8 3 2\n2 2\n1 3\n1 1\n0 1\n3 4\n3 3 3 2\n1 2\n2 1\n1 1\n0 1\n0 0\n0 0 0 0\n output: 2\n3\n8\n1\n3\n6\n\n" }, { "title": "Skyscraper \"Minato Harukas\"", "content": "Mr. Port plans to start a new business renting one or more floors\nof the new skyscraper with one giga floors, Minato Harukas.\n \nHe wants to rent as many vertically adjacent floors as possible, \nbecause he wants to show advertisement on as many vertically\nadjacent windows as possible.\n\nThe rent for one floor is proportional to the floor number,\nthat is, the rent per month for the n-th floor is n times\nthat of the first floor.\nHere, the ground floor is called the first floor in the American style,\nand basement floors are out of consideration for the renting.\n\nIn order to help Mr. Port, you should write a program that computes\nthe vertically adjacent floors satisfying his requirement and\nwhose total rental cost per month is \nexactly equal to his budget.\n\nFor example, when his budget is 15 units, \nwith one unit being the rent of the first floor,\nthere are four possible rent plans,\n1+2+3+4+5,4+5+6,7+8, and 15. \nFor all of them, the sums are equal to 15.\nOf course in this example the rent of maximal number of the floors \nis that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.", "constraint": "", "input": "The input consists of multiple datasets,\neach in the following format.\n\nb \n\nA dataset consists of one line,\nthe budget of Mr. Port b as multiples of the rent of the first floor.\nb  is a positive integer satisfying 1 < b < 10^9.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets does not exceed 1000.", "output": "For each dataset, output a single line containing two positive integers\nrepresenting the plan with the maximal number of vertically adjacent floors\nwith its rent price exactly equal to the budget of Mr. Port.\nThe first should be the lowest floor number and\nthe second should be the number of floors.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15\n16\n2\n3\n9699690\n223092870\n847288609\n900660121\n987698769\n999999999\n0\n output: 1 5\n16 1\n2 1\n1 2\n16 4389\n129 20995\n4112949 206\n15006 30011\n46887 17718\n163837 5994"], "Pid": "p01111", "ProblemText": "Task Description: Mr. Port plans to start a new business renting one or more floors\nof the new skyscraper with one giga floors, Minato Harukas.\n \nHe wants to rent as many vertically adjacent floors as possible, \nbecause he wants to show advertisement on as many vertically\nadjacent windows as possible.\n\nThe rent for one floor is proportional to the floor number,\nthat is, the rent per month for the n-th floor is n times\nthat of the first floor.\nHere, the ground floor is called the first floor in the American style,\nand basement floors are out of consideration for the renting.\n\nIn order to help Mr. Port, you should write a program that computes\nthe vertically adjacent floors satisfying his requirement and\nwhose total rental cost per month is \nexactly equal to his budget.\n\nFor example, when his budget is 15 units, \nwith one unit being the rent of the first floor,\nthere are four possible rent plans,\n1+2+3+4+5,4+5+6,7+8, and 15. \nFor all of them, the sums are equal to 15.\nOf course in this example the rent of maximal number of the floors \nis that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.\nTask Input: The input consists of multiple datasets,\neach in the following format.\n\nb \n\nA dataset consists of one line,\nthe budget of Mr. Port b as multiples of the rent of the first floor.\nb  is a positive integer satisfying 1 < b < 10^9.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets does not exceed 1000.\nTask Output: For each dataset, output a single line containing two positive integers\nrepresenting the plan with the maximal number of vertically adjacent floors\nwith its rent price exactly equal to the budget of Mr. Port.\nThe first should be the lowest floor number and\nthe second should be the number of floors.\nTask Samples: input: 15\n16\n2\n3\n9699690\n223092870\n847288609\n900660121\n987698769\n999999999\n0\n output: 1 5\n16 1\n2 1\n1 2\n16 4389\n129 20995\n4112949 206\n15006 30011\n46887 17718\n163837 5994\n\n" }, { "title": "Playoff by all the teams", "content": "The Minato Mirai Football Association hosts its annual championship\nas a single round-robin tournament,\nin which each team plays a single match against all the others.\nUnlike many other round-robin tournaments of football,\nmatches never result in a draw in this tournament.\nWhen the regular time match is a tie,\novertime is played, and, when it is a tie again,\na penalty shootout is played to decide the winner.\n\nIf two or more teams won the most number of matches in the round-robin,\na playoff is conducted among them to decide the champion.\nHowever, if the number of teams is an odd number,\nit is possible that all the teams may have\nthe same number of wins and losses,\nin which case all the teams participate in the playoff,\ncalled a \"full playoff\" here.\n\nNow, some of the tournament matches have already been played and we know\ntheir results.\nWhether or not a full playoff will be required may\ndepend on the results of the remaining matches.\n\nWrite a program that computes the number of win/loss combination patterns\nof the remaining matches that lead to a full playoff.\n\nThe first datatset of the Sample Input represents the results of the\nfirst three matches in a round-robin tournament of five teams, shown\nin the following table.\nIn the table, gray cells indicate the matches not played yet.\n\n Team_1 Team_2 Team_3 Team_4 Team_5 \n\n Team_1
        lost lost \n\n Team_2   lost     \n\n Team_3   won     \n\n Team_4 won       \n\n Team_5 won       \n\n \nIn this case,\nall the teams win the same number of matches\nwith only two win/loss combination patterns\nof the remaining matches,\nwhich lead to a full playoff,\nas shown below.\n\nIn the two tables, the differences are indicated in light yellow.\n\n Team_1 Team_2 Team_3 Team_4 Team_5 \n\n Team_1 won won lost lost \n\n Team_2 lost lost won won \n\n Team_3 lost won
    won lost \n\n Team_4 won lost lost won \n\n Team_5 won lost won lost \n\n \n Team_1 Team_2 Team_3 Team_4 Team_5 \n\n Team_1 won won lost lost \n\n Team_2 lost lost won won \n\n Team_3 lost won
    lost won \n\n Team_4 won lost won lost \n\n Team_5 won lost lost won", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn\nm\nx_1 y_1 \n. . . \nx_m y_m \n\nn is an odd integer, 3,5,7, or 9,\nindicating the number of teams participating in the tournament.\n\nm is a positive integer less than n(n-1)/2,\nwhich is the number of matches already finished.\n\nx_i and y_i give\nthe result of the i-th match that has already taken place,\nindicating that team x_i defeated team\ny_i.\nEach of x_i and y_i is an integer 1 through n\nwhich indicates the team number. \nNo team plays against itself, that is, for any i,\nx_i ! = y_i.\nThe match result of the same team pair appears at most once.\nThat is, if i ! = j,\nthen\n(x_i, y_i) ! =\n(x_j, y_j) and\n(x_i, y_i) ! =\n(y_j, x_j) hold.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets does not exceed 100.", "output": "For each dataset, output a single line containing one integer\nwhich indicates the number of possible future win/loss patterns\nthat a full playoff will be required.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n3\n3 2\n4 1\n5 1\n3\n1\n1 2\n3\n2\n1 2\n3 2\n5\n4\n4 1\n4 2\n5 1\n5 2\n5\n3\n4 1\n4 2\n5 1\n5\n4\n3 2\n4 1\n5 1\n5 2\n9\n11\n6 1\n6 4\n7 2\n7 3\n7 4\n8 2\n8 3\n8 4\n9 1\n9 3\n9 5\n9\n10\n6 1\n6 4\n7 2\n7 3\n7 4\n8 2\n8 3\n8 4\n9 1\n9 3\n5\n6\n4 3\n2 1\n5 1\n2 4\n1 3\n2 3\n9\n1\n1 2\n0\n output: 2\n1\n0\n0\n1\n0\n0\n16\n0\n1615040"], "Pid": "p01112", "ProblemText": "Task Description: The Minato Mirai Football Association hosts its annual championship\nas a single round-robin tournament,\nin which each team plays a single match against all the others.\nUnlike many other round-robin tournaments of football,\nmatches never result in a draw in this tournament.\nWhen the regular time match is a tie,\novertime is played, and, when it is a tie again,\na penalty shootout is played to decide the winner.\n\nIf two or more teams won the most number of matches in the round-robin,\na playoff is conducted among them to decide the champion.\nHowever, if the number of teams is an odd number,\nit is possible that all the teams may have\nthe same number of wins and losses,\nin which case all the teams participate in the playoff,\ncalled a \"full playoff\" here.\n\nNow, some of the tournament matches have already been played and we know\ntheir results.\nWhether or not a full playoff will be required may\ndepend on the results of the remaining matches.\n\nWrite a program that computes the number of win/loss combination patterns\nof the remaining matches that lead to a full playoff.\n\nThe first datatset of the Sample Input represents the results of the\nfirst three matches in a round-robin tournament of five teams, shown\nin the following table.\nIn the table, gray cells indicate the matches not played yet.\n\n Team_1 Team_2 Team_3 Team_4 Team_5 \n\n Team_1
        lost lost \n\n Team_2   lost     \n\n Team_3   won     \n\n Team_4 won       \n\n Team_5 won       \n\n \nIn this case,\nall the teams win the same number of matches\nwith only two win/loss combination patterns\nof the remaining matches,\nwhich lead to a full playoff,\nas shown below.\n\nIn the two tables, the differences are indicated in light yellow.\n\n Team_1 Team_2 Team_3 Team_4 Team_5 \n\n Team_1 won won lost lost \n\n Team_2 lost lost won won \n\n Team_3 lost won
    won lost \n\n Team_4 won lost lost won \n\n Team_5 won lost won lost \n\n \n Team_1 Team_2 Team_3 Team_4 Team_5 \n\n Team_1 won won lost lost \n\n Team_2 lost lost won won \n\n Team_3 lost won
    lost won \n\n Team_4 won lost won lost \n\n Team_5 won lost lost won\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn\nm\nx_1 y_1 \n. . . \nx_m y_m \n\nn is an odd integer, 3,5,7, or 9,\nindicating the number of teams participating in the tournament.\n\nm is a positive integer less than n(n-1)/2,\nwhich is the number of matches already finished.\n\nx_i and y_i give\nthe result of the i-th match that has already taken place,\nindicating that team x_i defeated team\ny_i.\nEach of x_i and y_i is an integer 1 through n\nwhich indicates the team number. \nNo team plays against itself, that is, for any i,\nx_i ! = y_i.\nThe match result of the same team pair appears at most once.\nThat is, if i ! = j,\nthen\n(x_i, y_i) ! =\n(x_j, y_j) and\n(x_i, y_i) ! =\n(y_j, x_j) hold.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets does not exceed 100.\nTask Output: For each dataset, output a single line containing one integer\nwhich indicates the number of possible future win/loss patterns\nthat a full playoff will be required.\nTask Samples: input: 5\n3\n3 2\n4 1\n5 1\n3\n1\n1 2\n3\n2\n1 2\n3 2\n5\n4\n4 1\n4 2\n5 1\n5 2\n5\n3\n4 1\n4 2\n5 1\n5\n4\n3 2\n4 1\n5 1\n5 2\n9\n11\n6 1\n6 4\n7 2\n7 3\n7 4\n8 2\n8 3\n8 4\n9 1\n9 3\n9 5\n9\n10\n6 1\n6 4\n7 2\n7 3\n7 4\n8 2\n8 3\n8 4\n9 1\n9 3\n5\n6\n4 3\n2 1\n5 1\n2 4\n1 3\n2 3\n9\n1\n1 2\n0\n output: 2\n1\n0\n0\n1\n0\n0\n16\n0\n1615040\n\n" }, { "title": "Floating-Point Numbers", "content": "In this problem, we consider floating-point number formats, data representation formats to approximate real numbers on computers.\n\nScientific notation is a method to express a number, frequently used for\nnumbers too large or too small to be written tersely in usual decimal form.\nIn scientific notation, all numbers are written in the form\nm * 10^e.\nHere, m (called significand) is a number\ngreater than or equal to 1 and less than 10,\nand e (called exponent) is an integer.\nFor example, a number 13.5 is equal to 1.35 * 10^1,\nso we can express it in scientific notation with significand 1.35 and exponent 1.\n\nAs binary number representation is convenient on computers,\nlet's consider binary scientific notation with base two, instead of ten.\nIn binary scientific notation, all numbers are written in the form\nm * 2^e.\nSince the base is two, m is limited to be less than 2.\nFor example, 13.5 is equal to 1.6875 * 2^3,\nso we can express it in binary scientific notation\nwith significand 1.6875 and exponent 3.\nThe significand 1.6875 is equal to 1 + 1/2 + 1/8 + 1/16,\nwhich is 1.1011_2 in binary notation.\nSimilarly, the exponent 3 can be expressed as 11_2 in binary notation.\n\nA floating-point number expresses a number in binary scientific notation in finite number of bits.\nAlthough the accuracy of the significand and the range of the exponent are limited by the number of bits, we can express numbers in a wide range with reasonably high accuracy.\n\nIn this problem, we consider a 64-bit floating-point number format,\nsimplified from one actually used widely,\nin which only those numbers greater than or equal to 1 can be expressed.\nHere, the first 12 bits are used for the exponent and the remaining 52 bits for the significand.\n\nLet's denote the 64 bits of a floating-point number by\nb_64. . . b_1.\nWith e an unsigned binary integer\n(b_64. . . b_53)_2,\nand with m a binary fraction represented by the remaining 52 bits\nplus one (1. b_52. . . b_1)_2,\nthe floating-point number represents the number\nm * 2^e.\n\nWe show below the bit string of the representation of 13.5 in the format described above.\n\nIn floating-point addition operations, the results have to be approximated by numbers representable in floating-point format.\nHere, we assume that the approximation is by truncation.\nWhen the sum of two floating-point numbers a and b is expressed in binary scientific notation as\na + b = m * 2^e (1 <= m < 2,0 <= e < 2^12),\nthe result of addition operation on them will be a floating-point number with its first 12 bits representing e as an unsigned integer\nand the remaining 52 bits representing the first 52 bits of the binary fraction of m.\n\nA disadvantage of this approximation method is that the approximation error accumulates easily.\nTo verify this, let's make an experiment of adding a floating-point number many times, as in the pseudocode shown below.\nHere, s and a are floating-point numbers, and the results of individual addition are approximated as described above.\ns : = a\nfor n times {\n s : = s + a\n}\n\nFor a given floating-point number a and a number of repetitions n,\ncompute the bits of the floating-point number s when the above pseudocode finishes.", "constraint": "", "input": "The input consists of at most 1000 datasets, each in the following format.\n\nn \nb_52. . . b_1 \n\nn is the number of repetitions. (1 <= n <= 10^18)\nFor each i, b_i is either 0 or 1.\nAs for the floating-point number a in the pseudocode, the exponent is 0 and the significand is b_52. . . b_1.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, the 64 bits of the floating-point number s after finishing the pseudocode should be output as a sequence of 64 digits, each being 0 or 1 in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n0000000000000000000000000000000000000000000000000000\n2\n0000000000000000000000000000000000000000000000000000\n3\n0000000000000000000000000000000000000000000000000000\n4\n0000000000000000000000000000000000000000000000000000\n7\n1101000000000000000000000000000000000000000000000000\n100\n1100011010100001100111100101000111001001111100101011\n123456789\n1010101010101010101010101010101010101010101010101010\n1000000000000000000\n1111111111111111111111111111111111111111111111111111\n0\n output: 0000000000010000000000000000000000000000000000000000000000000000\n0000000000011000000000000000000000000000000000000000000000000000\n0000000000100000000000000000000000000000000000000000000000000000\n0000000000100100000000000000000000000000000000000000000000000000\n0000000000111101000000000000000000000000000000000000000000000000\n0000000001110110011010111011100001101110110010001001010101111111\n0000000110111000100001110101011001000111100001010011110101011000\n0000001101010000000000000000000000000000000000000000000000000000"], "Pid": "p01113", "ProblemText": "Task Description: In this problem, we consider floating-point number formats, data representation formats to approximate real numbers on computers.\n\nScientific notation is a method to express a number, frequently used for\nnumbers too large or too small to be written tersely in usual decimal form.\nIn scientific notation, all numbers are written in the form\nm * 10^e.\nHere, m (called significand) is a number\ngreater than or equal to 1 and less than 10,\nand e (called exponent) is an integer.\nFor example, a number 13.5 is equal to 1.35 * 10^1,\nso we can express it in scientific notation with significand 1.35 and exponent 1.\n\nAs binary number representation is convenient on computers,\nlet's consider binary scientific notation with base two, instead of ten.\nIn binary scientific notation, all numbers are written in the form\nm * 2^e.\nSince the base is two, m is limited to be less than 2.\nFor example, 13.5 is equal to 1.6875 * 2^3,\nso we can express it in binary scientific notation\nwith significand 1.6875 and exponent 3.\nThe significand 1.6875 is equal to 1 + 1/2 + 1/8 + 1/16,\nwhich is 1.1011_2 in binary notation.\nSimilarly, the exponent 3 can be expressed as 11_2 in binary notation.\n\nA floating-point number expresses a number in binary scientific notation in finite number of bits.\nAlthough the accuracy of the significand and the range of the exponent are limited by the number of bits, we can express numbers in a wide range with reasonably high accuracy.\n\nIn this problem, we consider a 64-bit floating-point number format,\nsimplified from one actually used widely,\nin which only those numbers greater than or equal to 1 can be expressed.\nHere, the first 12 bits are used for the exponent and the remaining 52 bits for the significand.\n\nLet's denote the 64 bits of a floating-point number by\nb_64. . . b_1.\nWith e an unsigned binary integer\n(b_64. . . b_53)_2,\nand with m a binary fraction represented by the remaining 52 bits\nplus one (1. b_52. . . b_1)_2,\nthe floating-point number represents the number\nm * 2^e.\n\nWe show below the bit string of the representation of 13.5 in the format described above.\n\nIn floating-point addition operations, the results have to be approximated by numbers representable in floating-point format.\nHere, we assume that the approximation is by truncation.\nWhen the sum of two floating-point numbers a and b is expressed in binary scientific notation as\na + b = m * 2^e (1 <= m < 2,0 <= e < 2^12),\nthe result of addition operation on them will be a floating-point number with its first 12 bits representing e as an unsigned integer\nand the remaining 52 bits representing the first 52 bits of the binary fraction of m.\n\nA disadvantage of this approximation method is that the approximation error accumulates easily.\nTo verify this, let's make an experiment of adding a floating-point number many times, as in the pseudocode shown below.\nHere, s and a are floating-point numbers, and the results of individual addition are approximated as described above.\ns : = a\nfor n times {\n s : = s + a\n}\n\nFor a given floating-point number a and a number of repetitions n,\ncompute the bits of the floating-point number s when the above pseudocode finishes.\nTask Input: The input consists of at most 1000 datasets, each in the following format.\n\nn \nb_52. . . b_1 \n\nn is the number of repetitions. (1 <= n <= 10^18)\nFor each i, b_i is either 0 or 1.\nAs for the floating-point number a in the pseudocode, the exponent is 0 and the significand is b_52. . . b_1.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, the 64 bits of the floating-point number s after finishing the pseudocode should be output as a sequence of 64 digits, each being 0 or 1 in one line.\nTask Samples: input: 1\n0000000000000000000000000000000000000000000000000000\n2\n0000000000000000000000000000000000000000000000000000\n3\n0000000000000000000000000000000000000000000000000000\n4\n0000000000000000000000000000000000000000000000000000\n7\n1101000000000000000000000000000000000000000000000000\n100\n1100011010100001100111100101000111001001111100101011\n123456789\n1010101010101010101010101010101010101010101010101010\n1000000000000000000\n1111111111111111111111111111111111111111111111111111\n0\n output: 0000000000010000000000000000000000000000000000000000000000000000\n0000000000011000000000000000000000000000000000000000000000000000\n0000000000100000000000000000000000000000000000000000000000000000\n0000000000100100000000000000000000000000000000000000000000000000\n0000000000111101000000000000000000000000000000000000000000000000\n0000000001110110011010111011100001101110110010001001010101111111\n0000000110111000100001110101011001000111100001010011110101011000\n0000001101010000000000000000000000000000000000000000000000000000\n\n" }, { "title": "Equilateral Triangular Fence", "content": "Ms. Misumi owns an orchard along a straight road.\nRecently, wild boars have been witnessed strolling around the orchard aiming at pears, and she plans to construct a fence around many of the pear trees.\nThe orchard contains n pear trees, whose locations are given by the two-dimensional Euclidean coordinates (x_1, y_1), . . . , (x_n, y_n). For simplicity, we neglect the thickness of pear trees.\nMs. Misumi's aesthetic tells that the fence has to form a equilateral triangle with one of its edges parallel to the road.\nIts opposite apex, of course, should be apart from the road.\nThe coordinate system for the positions of the pear trees is chosen so that the road is expressed as y = 0, and the pear trees are located at y >= 1.\n\nDue to budget constraints, Ms. Misumi decided to allow at most k trees to be left outside of the fence.\nYou are to find the shortest possible perimeter of the fence on this condition.\n\nThe following figure shows the first dataset of the Sample Input.\nThere are four pear trees at (-1,2), (0,1), (1,2), and (2,1). \nBy excluding (-1,2) from the fence, we obtain the equilateral triangle with perimeter 6.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn \nk \nx_1 y_1 \n. . . \nx_n y_n \n\nEach of the datasets consists of n+2 lines.\nn in the first line is the integer representing the number of pear trees; it satisfies 3 <= n <= 10 000.\nk in the second line is the integer representing the number of pear trees that may be left outside of the fence; it satisfies 1 <= k <= min(n-2,5 000).\nThe following n lines have two integers each representing the x- and y- coordinates, in this order, of the locations of pear trees; it satisfies -10 000 <= x_i <= 10 000,1 <= y_i <= 10 000.\nNo two pear trees are at the same location, i. e. , (x_i, y_i)=(x_j, y_j) only if i=j.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets is at most 100.", "output": "For each dataset, output a single number that represents the shortest possible perimeter of the fence.\nThe output must not contain an error greater than 10^-6.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1\n0 1\n1 2\n-1 2\n2 1\n4\n1\n1 1\n2 2\n1 3\n1 4\n4\n1\n1 1\n2 2\n3 1\n4 1\n4\n1\n1 2\n2 1\n3 2\n4 2\n5\n2\n0 1\n0 2\n0 3\n0 4\n0 5\n6\n3\n0 2\n2 2\n1 1\n0 3\n2 3\n1 4\n0\n output: 6.000000000000\n6.928203230276\n6.000000000000\n7.732050807569\n6.928203230276\n6.000000000000"], "Pid": "p01114", "ProblemText": "Task Description: Ms. Misumi owns an orchard along a straight road.\nRecently, wild boars have been witnessed strolling around the orchard aiming at pears, and she plans to construct a fence around many of the pear trees.\nThe orchard contains n pear trees, whose locations are given by the two-dimensional Euclidean coordinates (x_1, y_1), . . . , (x_n, y_n). For simplicity, we neglect the thickness of pear trees.\nMs. Misumi's aesthetic tells that the fence has to form a equilateral triangle with one of its edges parallel to the road.\nIts opposite apex, of course, should be apart from the road.\nThe coordinate system for the positions of the pear trees is chosen so that the road is expressed as y = 0, and the pear trees are located at y >= 1.\n\nDue to budget constraints, Ms. Misumi decided to allow at most k trees to be left outside of the fence.\nYou are to find the shortest possible perimeter of the fence on this condition.\n\nThe following figure shows the first dataset of the Sample Input.\nThere are four pear trees at (-1,2), (0,1), (1,2), and (2,1). \nBy excluding (-1,2) from the fence, we obtain the equilateral triangle with perimeter 6.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn \nk \nx_1 y_1 \n. . . \nx_n y_n \n\nEach of the datasets consists of n+2 lines.\nn in the first line is the integer representing the number of pear trees; it satisfies 3 <= n <= 10 000.\nk in the second line is the integer representing the number of pear trees that may be left outside of the fence; it satisfies 1 <= k <= min(n-2,5 000).\nThe following n lines have two integers each representing the x- and y- coordinates, in this order, of the locations of pear trees; it satisfies -10 000 <= x_i <= 10 000,1 <= y_i <= 10 000.\nNo two pear trees are at the same location, i. e. , (x_i, y_i)=(x_j, y_j) only if i=j.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets is at most 100.\nTask Output: For each dataset, output a single number that represents the shortest possible perimeter of the fence.\nThe output must not contain an error greater than 10^-6.\nTask Samples: input: 4\n1\n0 1\n1 2\n-1 2\n2 1\n4\n1\n1 1\n2 2\n1 3\n1 4\n4\n1\n1 1\n2 2\n3 1\n4 1\n4\n1\n1 2\n2 1\n3 2\n4 2\n5\n2\n0 1\n0 2\n0 3\n0 4\n0 5\n6\n3\n0 2\n2 2\n1 1\n0 3\n2 3\n1 4\n0\n output: 6.000000000000\n6.928203230276\n6.000000000000\n7.732050807569\n6.928203230276\n6.000000000000\n\n" }, { "title": "Expression Mining", "content": "Consider an arithmetic expression built by combining single-digit positive integers\nwith addition symbols +, multiplication symbols *,\nand parentheses ( ),\ndefined by the following grammar rules with the start symbol E.\n E : : = T | E '+' T\n T : : = F | T '*' F\n F : : = '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' | '(' E ')'\n\nWhen such an arithmetic expression is viewed as a string,\nits substring, that is, a contiguous sequence of characters within the string,\nmay again form an arithmetic expression.\n\nGiven an integer n and a string s representing an arithmetic expression,\nlet us count the number of its substrings that can be read as arithmetic expressions\nwith values computed equal to n.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn\ns\n\nA dataset consists of two lines.\nIn the first line, the target value n is given.\nn is an integer satisfying 1 <= n <= 10^9.\n\nThe string s given in the second line\nis an arithmetic expression conforming to the grammar defined above.\nThe length of s does not exceed 2*10^6.\nThe nesting depth of the parentheses in the string is at most 1000.\n\nThe end of the input is indicated by a line containing a single zero.\nThe sum of the lengths of s\nin all the datasets does not exceed 5*10^6.", "output": "For each dataset, output in one line the number of substrings of s that\nconform to the above grammar and have the value n.\nThe same sequence of characters appearing at different positions should be counted separately.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n(1+2)*3+3\n2\n1*1*1+1*1*1\n587\n1*(2*3*4)+5+((6+7*8))*(9)\n0\n output: 4\n9\n2"], "Pid": "p01115", "ProblemText": "Task Description: Consider an arithmetic expression built by combining single-digit positive integers\nwith addition symbols +, multiplication symbols *,\nand parentheses ( ),\ndefined by the following grammar rules with the start symbol E.\n E : : = T | E '+' T\n T : : = F | T '*' F\n F : : = '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' | '(' E ')'\n\nWhen such an arithmetic expression is viewed as a string,\nits substring, that is, a contiguous sequence of characters within the string,\nmay again form an arithmetic expression.\n\nGiven an integer n and a string s representing an arithmetic expression,\nlet us count the number of its substrings that can be read as arithmetic expressions\nwith values computed equal to n.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn\ns\n\nA dataset consists of two lines.\nIn the first line, the target value n is given.\nn is an integer satisfying 1 <= n <= 10^9.\n\nThe string s given in the second line\nis an arithmetic expression conforming to the grammar defined above.\nThe length of s does not exceed 2*10^6.\nThe nesting depth of the parentheses in the string is at most 1000.\n\nThe end of the input is indicated by a line containing a single zero.\nThe sum of the lengths of s\nin all the datasets does not exceed 5*10^6.\nTask Output: For each dataset, output in one line the number of substrings of s that\nconform to the above grammar and have the value n.\nThe same sequence of characters appearing at different positions should be counted separately.\nTask Samples: input: 3\n(1+2)*3+3\n2\n1*1*1+1*1*1\n587\n1*(2*3*4)+5+((6+7*8))*(9)\n0\n output: 4\n9\n2\n\n" }, { "title": "For Programming Excellence", "content": "A countless number of skills are required to be an excellent programmer.\n Different skills have different importance degrees,\n and the total programming competence is measured by\n the sum of products of levels and importance degrees of his/her skills.\n\n In this summer season,\n you are planning to attend a summer programming school.\n The school offers courses for many of such skills.\n Attending a course for a skill,\n your level of the skill will be improved in proportion to the tuition paid,\n one level per one yen of tuition, however,\n each skill has its upper limit of the level\n and spending more money will never improve the skill level further.\n Skills are not independent: For taking a course for a skill,\n except for the most basic course,\n you have to have at least a certain level of its prerequisite skill.\n\n You want to realize the highest possible programming competence measure\n within your limited budget for tuition fees.", "constraint": "", "input": "The input consists of no more than 100 datasets, each in the following format.\n\nn k\nh_1 . . . h_n \ns_1 . . . s_n \np_2 . . . p_n \nl_2 . . . l_n \n\n The first line has two integers,\n n, the number of different skills between 2 and 100, inclusive, and\n k, the budget amount available between 1 and 10^5, inclusive.\n In what follows, skills are numbered 1 through n.\n \n The second line has n integers\n h_1. . . h_n,\n in which h_i is the maximum level of the skill i,\n between 1 and 10^5, inclusive.\n \n The third line has n integers\n s_1. . . s_n,\n in which s_i is the importance degree of the skill i,\n between 1 and 10^9, inclusive.\n \n The fourth line has n-1 integers\n p_2. . . p_n,\n in which p_i is the prerequisite skill of the skill i,\n between 1 and i-1, inclusive.\n The skill 1 has no prerequisites.\n \n The fifth line has n-1 integers\n l_2. . . l_n,\n in which l_i is the least level of prerequisite skill\n p_i required to learn the skill i,\n between 1 and h_pi , inclusive.\n \nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output a single line containing one integer,\n which is the highest programming competence measure achievable,\n that is,\n the maximum sum of the products of\n levels and importance degrees of the skills,\n within the given tuition budget,\n starting with level zero for all the skills.\n You do not have to use up all the budget.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 10\n5 4 3\n1 2 3\n1 2\n5 2\n5 40\n10 10 10 10 8\n1 2 3 4 5\n1 1 2 3\n10 10 10 10\n5 10\n2 2 2 5 2\n2 2 2 5 2\n1 1 2 2\n2 1 2 1\n0 0\n output: 18\n108\n35"], "Pid": "p01116", "ProblemText": "Task Description: A countless number of skills are required to be an excellent programmer.\n Different skills have different importance degrees,\n and the total programming competence is measured by\n the sum of products of levels and importance degrees of his/her skills.\n\n In this summer season,\n you are planning to attend a summer programming school.\n The school offers courses for many of such skills.\n Attending a course for a skill,\n your level of the skill will be improved in proportion to the tuition paid,\n one level per one yen of tuition, however,\n each skill has its upper limit of the level\n and spending more money will never improve the skill level further.\n Skills are not independent: For taking a course for a skill,\n except for the most basic course,\n you have to have at least a certain level of its prerequisite skill.\n\n You want to realize the highest possible programming competence measure\n within your limited budget for tuition fees.\nTask Input: The input consists of no more than 100 datasets, each in the following format.\n\nn k\nh_1 . . . h_n \ns_1 . . . s_n \np_2 . . . p_n \nl_2 . . . l_n \n\n The first line has two integers,\n n, the number of different skills between 2 and 100, inclusive, and\n k, the budget amount available between 1 and 10^5, inclusive.\n In what follows, skills are numbered 1 through n.\n \n The second line has n integers\n h_1. . . h_n,\n in which h_i is the maximum level of the skill i,\n between 1 and 10^5, inclusive.\n \n The third line has n integers\n s_1. . . s_n,\n in which s_i is the importance degree of the skill i,\n between 1 and 10^9, inclusive.\n \n The fourth line has n-1 integers\n p_2. . . p_n,\n in which p_i is the prerequisite skill of the skill i,\n between 1 and i-1, inclusive.\n The skill 1 has no prerequisites.\n \n The fifth line has n-1 integers\n l_2. . . l_n,\n in which l_i is the least level of prerequisite skill\n p_i required to learn the skill i,\n between 1 and h_pi , inclusive.\n \nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output a single line containing one integer,\n which is the highest programming competence measure achievable,\n that is,\n the maximum sum of the products of\n levels and importance degrees of the skills,\n within the given tuition budget,\n starting with level zero for all the skills.\n You do not have to use up all the budget.\nTask Samples: input: 3 10\n5 4 3\n1 2 3\n1 2\n5 2\n5 40\n10 10 10 10 8\n1 2 3 4 5\n1 1 2 3\n10 10 10 10\n5 10\n2 2 2 5 2\n2 2 2 5 2\n1 1 2 2\n2 1 2 1\n0 0\n output: 18\n108\n35\n\n" }, { "title": "Scores of Final Examination", "content": "I am a junior high school teacher.\nThe final examination has just finished, and I have\nall the students' scores of all the subjects.\nI want to know the highest total score among the students,\nbut it is not an easy task as the student scores are\nlisted separately for each subject.\nI would like to ask you, an excellent programmer, to help me\nby writing a program that finds the total score of a student\nwith the highest total score.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn m\np_1,1 p_1,2 … p_1, n\np_2,1 p_2,2 … p_2, n\n…\np_m, 1 p_m, 2 … p_m, n\n\nThe first line of a dataset has two integers n and m.\nn is the number of students (1 <= n <= 1000).\nm is the number of subjects (1 <= m <= 50).\nEach of the following m lines gives n students' scores\nof a subject.\np_j, k is an integer representing\nthe k-th student's\nscore of the subject j (1 <= j <= m\nand 1 <= k <= n).\nIt satisfies 0 <= p_j, k <= 1000.\n\nThe end of the input is indicated by a line containing two zeros.\nThe number of datasets does not exceed 100.", "output": "For each dataset, output the total score of a student with the highest\ntotal score.\nThe total score s_k\nof the student k is defined by\ns_k =\np_1, k + … + p_m, k.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n10 20 30 40 50\n15 25 35 45 55\n6 3\n10 20 30 15 25 35\n21 34 11 52 20 18\n31 15 42 10 21 19\n4 2\n0 0 0 0\n0 0 0 0\n0 0\n output: 105\n83\n0"], "Pid": "p01117", "ProblemText": "Task Description: I am a junior high school teacher.\nThe final examination has just finished, and I have\nall the students' scores of all the subjects.\nI want to know the highest total score among the students,\nbut it is not an easy task as the student scores are\nlisted separately for each subject.\nI would like to ask you, an excellent programmer, to help me\nby writing a program that finds the total score of a student\nwith the highest total score.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn m\np_1,1 p_1,2 … p_1, n\np_2,1 p_2,2 … p_2, n\n…\np_m, 1 p_m, 2 … p_m, n\n\nThe first line of a dataset has two integers n and m.\nn is the number of students (1 <= n <= 1000).\nm is the number of subjects (1 <= m <= 50).\nEach of the following m lines gives n students' scores\nof a subject.\np_j, k is an integer representing\nthe k-th student's\nscore of the subject j (1 <= j <= m\nand 1 <= k <= n).\nIt satisfies 0 <= p_j, k <= 1000.\n\nThe end of the input is indicated by a line containing two zeros.\nThe number of datasets does not exceed 100.\nTask Output: For each dataset, output the total score of a student with the highest\ntotal score.\nThe total score s_k\nof the student k is defined by\ns_k =\np_1, k + … + p_m, k.\nTask Samples: input: 5 2\n10 20 30 40 50\n15 25 35 45 55\n6 3\n10 20 30 15 25 35\n21 34 11 52 20 18\n31 15 42 10 21 19\n4 2\n0 0 0 0\n0 0 0 0\n0 0\n output: 105\n83\n0\n\n" }, { "title": "On-Screen Keyboard", "content": "You are to input a string with an OSK (on-screen keyboard).\n A remote control with five buttons, four arrows and an OK (Fig. B-1),\n is used for the OSK.\n Find the minimum number of button presses required\n to input a given string with the given OSK.\n
    \n\n Fig. B-1 Remote control \n \n
    \n
    \n\n Fig. B-2 An on-screen keyboard \n \n
    \n\n \n Character to input Move of highlighted cells Button presses \n\n \n\n I →, →, →, →, →, →, →, →, OK (9 presses) \n\n C ←, ←, ←, ←, ←, ←, OK (7 presses) \n\n P ↓, →, →, →, →, OK (6 presses) \n\n C ↑, ←, ←, ←, ←, OK (6 presses) \n\n \n \n\n
    \n\n Fig. B-3 The minimum steps to input “ICPC” with the OSK in Fig. B-2\n \n
    \n\n The OSK has cells arranged in a grid, each of which has a\n character in it or is empty.\n No two of the cells have the same character.\n \n One of the cells of the OSK is highlighted, and\n pressing the OK button will input the character in that cell,\n if the cell is not empty.\n \n Initially, the cell at the top-left corner is highlighted.\n Pressing one of the arrow buttons will change the highlighted cell\n to one of the adjacent cells in the direction of the arrow.\n When the highlighted cell is on an edge of the OSK,\n pushing the arrow button with the direction to go out of the edge\n will have no effect.\n \n For example, using the OSK with its arrangement shown in Fig. B-2,\n a string “ICPC” can be input with 28 button presses\n as shown in Fig. B-3, which is the minimum number of presses.\n\n \n Characters in cells of the OSKs are any of a lowercase letter\n (‘a ', ‘b ', . . . , ‘z '),\n an uppercase letter\n (‘A ', ‘B ', . . . , ‘Z '),\n a digit\n (‘0 ', ‘1 ', . . . , ‘9 '),\n a comma (‘, '),\n a hyphen (‘- '),\n a dot (‘. '),\n a slash (‘/ '),\n a colon (‘: '),\n a semicolon (‘; '),\n or an at sign (‘@ ').", "constraint": "", "input": "The input consists of at most 100 datasets, each in the following format.\n\n

    \nh w\nr_1\n . . . \nr_h\ns\n\nThe two integers h and w in the first line are\nthe height and the width of the OSK, respectively.\nThey are separated by a space, and satisfy 1 <= h <= 50 and 1 <= w <= 50. \n\n Each of the next h lines gives a row of the OSK.\nThe i-th row, r_i is a string of length w.\n The characters in the string corresponds to the characters\nin the cells of the i-th row of the OSK\nor an underscore (‘_ ') indicating an empty cell,\n from left to right.\n\n The given OSK satisfies the conditions stated above.\n\n The next line is a string s to be input. Its length is between 1 and 1000, inclusive.\n All the characters in s appear in the given OSK.\n Note that s does not contain underscores.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output a single line containing an integer indicating the minimum number of button presses required to input the given string with the given OSK.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 9\nABCDEFGHI\nJKLMNOPQR\nSTUVWXYZ_\nICPC\n5 11\n___________\n____A______\n________M__\n___________\n_C_________\nACM\n4 21\n1_2_3_4_5_6_7_8_9_0_-\nQqWwEeRrTtYyUuIiOoPp@\nAaSsDdFfGgHhJjKkLl;_:\nZzXxCcVvBbNnMm,_._/__\nICPC2019,AsiaYokohamaRegional,QualificationRound\n0 0\n output: 28\n23\n493"], "Pid": "p01118", "ProblemText": "Task Description: You are to input a string with an OSK (on-screen keyboard).\n A remote control with five buttons, four arrows and an OK (Fig. B-1),\n is used for the OSK.\n Find the minimum number of button presses required\n to input a given string with the given OSK.\n

    \n\n Fig. B-1 Remote control \n \n
    \n
    \n\n Fig. B-2 An on-screen keyboard \n \n
    \n
    \n \n Character to input Move of highlighted cells Button presses \n\n \n\n I →, →, →, →, →, →, →, →, OK (9 presses) \n\n C ←, ←, ←, ←, ←, ←, OK (7 presses) \n\n P ↓, →, →, →, →, OK (6 presses) \n\n C ↑, ←, ←, ←, ←, OK (6 presses) \n\n \n \n\n
    \n\n Fig. B-3 The minimum steps to input “ICPC” with the OSK in Fig. B-2\n \n
    \n\n The OSK has cells arranged in a grid, each of which has a\n character in it or is empty.\n No two of the cells have the same character.\n \n One of the cells of the OSK is highlighted, and\n pressing the OK button will input the character in that cell,\n if the cell is not empty.\n \n Initially, the cell at the top-left corner is highlighted.\n Pressing one of the arrow buttons will change the highlighted cell\n to one of the adjacent cells in the direction of the arrow.\n When the highlighted cell is on an edge of the OSK,\n pushing the arrow button with the direction to go out of the edge\n will have no effect.\n \n For example, using the OSK with its arrangement shown in Fig. B-2,\n a string “ICPC” can be input with 28 button presses\n as shown in Fig. B-3, which is the minimum number of presses.\n\n \n Characters in cells of the OSKs are any of a lowercase letter\n (‘a ', ‘b ', . . . , ‘z '),\n an uppercase letter\n (‘A ', ‘B ', . . . , ‘Z '),\n a digit\n (‘0 ', ‘1 ', . . . , ‘9 '),\n a comma (‘, '),\n a hyphen (‘- '),\n a dot (‘. '),\n a slash (‘/ '),\n a colon (‘: '),\n a semicolon (‘; '),\n or an at sign (‘@ ').\nTask Input: The input consists of at most 100 datasets, each in the following format.\n\n

    \nh w\nr_1\n . . . \nr_h\ns\n\nThe two integers h and w in the first line are\nthe height and the width of the OSK, respectively.\nThey are separated by a space, and satisfy 1 <= h <= 50 and 1 <= w <= 50. \n\n Each of the next h lines gives a row of the OSK.\nThe i-th row, r_i is a string of length w.\n The characters in the string corresponds to the characters\nin the cells of the i-th row of the OSK\nor an underscore (‘_ ') indicating an empty cell,\n from left to right.\n\n The given OSK satisfies the conditions stated above.\n\n The next line is a string s to be input. Its length is between 1 and 1000, inclusive.\n All the characters in s appear in the given OSK.\n Note that s does not contain underscores.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output a single line containing an integer indicating the minimum number of button presses required to input the given string with the given OSK.\nTask Samples: input: 3 9\nABCDEFGHI\nJKLMNOPQR\nSTUVWXYZ_\nICPC\n5 11\n___________\n____A______\n________M__\n___________\n_C_________\nACM\n4 21\n1_2_3_4_5_6_7_8_9_0_-\nQqWwEeRrTtYyUuIiOoPp@\nAaSsDdFfGgHhJjKkLl;_:\nZzXxCcVvBbNnMm,_._/__\nICPC2019,AsiaYokohamaRegional,QualificationRound\n0 0\n output: 28\n23\n493\n\n" }, { "title": "Balance Scale", "content": "You, an experimental chemist, have a balance scale and a kit of\n weights for measuring weights of powder chemicals.\n \n For work efficiency, a single use of the balance scale should be\n enough for measurement of each amount. You can use any number of\n weights at a time, placing them either on the balance plate\n opposite to the chemical or on the same plate with the chemical.\n For example, if you have two weights of 2 and 9 units, you can\n measure out not only 2 and 9 units of the chemical, but also 11 units\n by placing both on the plate opposite to the chemical (Fig. C-1\n left), and 7 units by placing one of them on the plate with the\n chemical (Fig. C-1 right). These are the only amounts that can be\n measured out efficiently.\n \n\n

    \n\n Fig. C-1 Measuring 11 and 7 units of chemical\n \n
    \n\n You have at hand a list of amounts of chemicals to measure today.\n The weight kit already at hand, however, may not be enough to\n efficiently measure all the amounts in the measurement list. If\n not, you can purchase one single new weight to supplement the kit,\n but, as heavier weights are more expensive, you'd like to do with\n the lightest possible.\n \n Note that, although weights of arbitrary positive masses are in\n the market, none with negative masses can be found.", "constraint": "", "input": "The input consists of at most 100 datasets, each in the following format.\n \n\nn m\na_1 a_2 . . . a_n\nw_1 w_2 . . . w_m\n\n The first line of a dataset has n and m,\n the number of amounts in the measurement list and\n the number of weights in the weight kit at hand, respectively.\n They are integers separated by a space\n satisfying 1 <= n <= 100 and 1 <= m <= 10.\n \n The next line has the n amounts in the measurement list,\n a_1 through a_n, \n separated by spaces.\n Each of a_i is an integer\n satisfying 1 <= a_i <= 10^9,\n and a_i ! = a_j holds for\n i ! = j.\n \n The third and final line of a dataset has the list of the masses\n of the m weights at hand,\n w_1 through w_m, \n separated by spaces.\n Each of w_j is an integer,\n satisfying 1 <= w_j <= 10^8.\n Two or more weights may have the same mass.\n \n The end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output a single line containing an integer\n specified as follows.\n \n\n\tIf all the amounts in the measurement list can be measured out\n\twithout any additional weights, 0.\n \n\tIf adding one more weight will make all the amounts in the\n\tmeasurement list measurable, the mass of the lightest among\n\tsuch weights. The weight added may be heavier than\n\t10^8 units.\n \n\tIf adding one more weight is never enough to measure out all\n\tthe amounts in the measurement list, -1.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 2\n9 2 7 11\n2 9\n6 2\n7 3 6 12 16 9\n2 9\n5 2\n7 3 6 12 17\n2 9\n7 5\n15 21 33 48 51 75 111\n36 54 57 93 113\n0 0\n output: 0\n5\n-1\n5"], "Pid": "p01119", "ProblemText": "Task Description: You, an experimental chemist, have a balance scale and a kit of\n weights for measuring weights of powder chemicals.\n \n For work efficiency, a single use of the balance scale should be\n enough for measurement of each amount. You can use any number of\n weights at a time, placing them either on the balance plate\n opposite to the chemical or on the same plate with the chemical.\n For example, if you have two weights of 2 and 9 units, you can\n measure out not only 2 and 9 units of the chemical, but also 11 units\n by placing both on the plate opposite to the chemical (Fig. C-1\n left), and 7 units by placing one of them on the plate with the\n chemical (Fig. C-1 right). These are the only amounts that can be\n measured out efficiently.\n \n\n
    \n\n Fig. C-1 Measuring 11 and 7 units of chemical\n \n
    \n\n You have at hand a list of amounts of chemicals to measure today.\n The weight kit already at hand, however, may not be enough to\n efficiently measure all the amounts in the measurement list. If\n not, you can purchase one single new weight to supplement the kit,\n but, as heavier weights are more expensive, you'd like to do with\n the lightest possible.\n \n Note that, although weights of arbitrary positive masses are in\n the market, none with negative masses can be found.\nTask Input: The input consists of at most 100 datasets, each in the following format.\n \n\nn m\na_1 a_2 . . . a_n\nw_1 w_2 . . . w_m\n\n The first line of a dataset has n and m,\n the number of amounts in the measurement list and\n the number of weights in the weight kit at hand, respectively.\n They are integers separated by a space\n satisfying 1 <= n <= 100 and 1 <= m <= 10.\n \n The next line has the n amounts in the measurement list,\n a_1 through a_n, \n separated by spaces.\n Each of a_i is an integer\n satisfying 1 <= a_i <= 10^9,\n and a_i ! = a_j holds for\n i ! = j.\n \n The third and final line of a dataset has the list of the masses\n of the m weights at hand,\n w_1 through w_m, \n separated by spaces.\n Each of w_j is an integer,\n satisfying 1 <= w_j <= 10^8.\n Two or more weights may have the same mass.\n \n The end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output a single line containing an integer\n specified as follows.\n \n\n\tIf all the amounts in the measurement list can be measured out\n\twithout any additional weights, 0.\n \n\tIf adding one more weight will make all the amounts in the\n\tmeasurement list measurable, the mass of the lightest among\n\tsuch weights. The weight added may be heavier than\n\t10^8 units.\n \n\tIf adding one more weight is never enough to measure out all\n\tthe amounts in the measurement list, -1.\nTask Samples: input: 4 2\n9 2 7 11\n2 9\n6 2\n7 3 6 12 16 9\n2 9\n5 2\n7 3 6 12 17\n2 9\n7 5\n15 21 33 48 51 75 111\n36 54 57 93 113\n0 0\n output: 0\n5\n-1\n5\n\n" }, { "title": "Tally Counters", "content": "A number of tally counters are placed in a row.\nPushing the button on a counter will increment the displayed value by one, or, when the value is already the maximum, it goes down to one.\nAll the counters are of the same model with the same maximum value.\n
    \n\nFig. D-1 Tally Counters\n\n
    \n\nStarting from the values initially displayed on each of the counters, you want to change all the displayed values to target values specified for each.\nAs you don't want the hassle, however, of pushing buttons of many counters one be one, you devised a special tool.\nUsing the tool, you can push buttons of one or more\nadjacent counters, one push for each, in a single operation.\nYou can choose an arbitrary number of counters at any position in\neach operation, as far as they are consecutively lined up.\n\nHow many operations are required at least to change the displayed values on counters to the target values?", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn m \na_1 a_2 . . . a_n \nb_1 b_2 . . . b_n \n\nEach dataset consists of 3 lines.\nThe first line contains n (1 <= n <= 1000) and m (1 <= m <= 10000), the number of counters and the maximum value displayed on counters, respectively.\nThe second line contains the initial values on counters, a_i (1 <= a_i <= m), separated by spaces.\nThe third line contains the target values on counters, b_i (1 <= b_i <= m), separated by spaces.\n\nThe end of the input is indicated by a line containing two zeros.\nThe number of datasets does not exceed 100.", "output": "For each dataset, print in a line the minimum number of operations required to make all of the counters display the target values.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 5\n2 3 1 4\n2 5 5 2\n3 100\n1 10 100\n1 10 100\n5 10000\n4971 7482 1238 8523 1823\n3287 9013 9812 297 1809\n0 0\n output: 4\n0\n14731"], "Pid": "p01120", "ProblemText": "Task Description: A number of tally counters are placed in a row.\nPushing the button on a counter will increment the displayed value by one, or, when the value is already the maximum, it goes down to one.\nAll the counters are of the same model with the same maximum value.\n
    \n\nFig. D-1 Tally Counters\n\n
    \n\nStarting from the values initially displayed on each of the counters, you want to change all the displayed values to target values specified for each.\nAs you don't want the hassle, however, of pushing buttons of many counters one be one, you devised a special tool.\nUsing the tool, you can push buttons of one or more\nadjacent counters, one push for each, in a single operation.\nYou can choose an arbitrary number of counters at any position in\neach operation, as far as they are consecutively lined up.\n\nHow many operations are required at least to change the displayed values on counters to the target values?\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn m \na_1 a_2 . . . a_n \nb_1 b_2 . . . b_n \n\nEach dataset consists of 3 lines.\nThe first line contains n (1 <= n <= 1000) and m (1 <= m <= 10000), the number of counters and the maximum value displayed on counters, respectively.\nThe second line contains the initial values on counters, a_i (1 <= a_i <= m), separated by spaces.\nThe third line contains the target values on counters, b_i (1 <= b_i <= m), separated by spaces.\n\nThe end of the input is indicated by a line containing two zeros.\nThe number of datasets does not exceed 100.\nTask Output: For each dataset, print in a line the minimum number of operations required to make all of the counters display the target values.\nTask Samples: input: 4 5\n2 3 1 4\n2 5 5 2\n3 100\n1 10 100\n1 10 100\n5 10000\n4971 7482 1238 8523 1823\n3287 9013 9812 297 1809\n0 0\n output: 4\n0\n14731\n\n" }, { "title": "Cube Surface Puzzle", "content": "Given a set of six pieces, “Cube Surface Puzzle” is to construct a hollow cube with filled surface.\nPieces of a puzzle is made of a number of small unit cubes laid grid-aligned on a plane.\nFor a puzzle constructing a cube of its side length n,\nunit cubes are on either of the following two areas.\n Core (blue): A square area with its side length n-2.\n Unit cubes fill up this area.\n\nFringe (red): The area of width 1 unit forming the outer fringe of the core.\n Each unit square in this area may be empty or with a unit cube on it.\nEach piece is connected with faces of its unit cubes.\nPieces can be arbitrarily rotated and either side of the pieces can\nbe inside or outside of the constructed cube.\nThe unit cubes on the core area should come in the centers of the\nfaces of the constructed cube.\n\nConsider that we have six pieces in Fig. E-1 (The first dataset of Sample Input).\nThen, we can construct a cube as shown in Fig. E-2.\n
    \n\n Fig. E-1 Pieces from the first dataset of Sample Input\n\n
    \n
    \n\n Fig. E-2 Constructing a cube\n\n
    \n\nMr. Hadrian Hex has collected a number of cube surface puzzles.\nOne day, those pieces were mixed together and he\ncannot find yet from which six pieces he can construct a cube.\nYour task is to write a program to help Mr. Hex, which judges whether we can construct a cube for a given set of pieces.", "constraint": "", "input": "The input consists of at most 200 datasets, each in the following format.\n\nn\nx_1,1x_1,2 … x_1, n\nx_2,1x_2,2 … x_2, n\n…\nx_6n, 1x_6n, 2 … x_6n, n\n\n The first line contains an integer n denoting the length of one side of the cube to be constructed (3 <= n <= 9, n is odd).\nThe following 6n lines give the six pieces.\nEach piece is described in n lines.\nEach of the lines corresponds to one grid row and each of the characters in\nthe line, either ‘X ' or ‘. ', indicates whether or not a unit cube is on\nthe corresponding unit square: ‘X ' means a unit cube is on the column and ‘. ' means none is there.\n\n The core area of each piece is centered in the data for the piece.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output “Yes” if we can construct a cube, or “No” if we cannot.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n..XX.\n.XXX.\nXXXXX\nXXXXX\nX....\n....X\nXXXXX\n.XXX.\n.XXX.\n.....\n..XXX\nXXXX.\n.XXXX\n.XXXX\n...X.\n...X.\n.XXXX\nXXXX.\nXXXX.\n.X.X.\nXXX.X\n.XXXX\nXXXXX\n.XXXX\n.XXXX\nXX...\n.XXXX\nXXXXX\nXXXXX\nXX...\n5\n..XX.\n.XXX.\nXXXXX\nXXXX.\nX....\n....X\nXXXXX\n.XXX.\n.XXX.\n.....\n.XXXX\nXXXX.\n.XXXX\n.XXXX\n...X.\n...X.\n.XXXX\nXXXX.\nXXXX.\n.X.X.\nXXX.X\n.XXXX\nXXXXX\n.XXXX\n.XXXX\nXX...\nXXXXX\nXXXXX\n.XXXX\nXX...\n0\n output: Yes\nNo"], "Pid": "p01121", "ProblemText": "Task Description: Given a set of six pieces, “Cube Surface Puzzle” is to construct a hollow cube with filled surface.\nPieces of a puzzle is made of a number of small unit cubes laid grid-aligned on a plane.\nFor a puzzle constructing a cube of its side length n,\nunit cubes are on either of the following two areas.\n Core (blue): A square area with its side length n-2.\n Unit cubes fill up this area.\n\nFringe (red): The area of width 1 unit forming the outer fringe of the core.\n Each unit square in this area may be empty or with a unit cube on it.\nEach piece is connected with faces of its unit cubes.\nPieces can be arbitrarily rotated and either side of the pieces can\nbe inside or outside of the constructed cube.\nThe unit cubes on the core area should come in the centers of the\nfaces of the constructed cube.\n\nConsider that we have six pieces in Fig. E-1 (The first dataset of Sample Input).\nThen, we can construct a cube as shown in Fig. E-2.\n
    \n\n Fig. E-1 Pieces from the first dataset of Sample Input\n\n
    \n
    \n\n Fig. E-2 Constructing a cube\n\n
    \n\nMr. Hadrian Hex has collected a number of cube surface puzzles.\nOne day, those pieces were mixed together and he\ncannot find yet from which six pieces he can construct a cube.\nYour task is to write a program to help Mr. Hex, which judges whether we can construct a cube for a given set of pieces.\nTask Input: The input consists of at most 200 datasets, each in the following format.\n\nn\nx_1,1x_1,2 … x_1, n\nx_2,1x_2,2 … x_2, n\n…\nx_6n, 1x_6n, 2 … x_6n, n\n\n The first line contains an integer n denoting the length of one side of the cube to be constructed (3 <= n <= 9, n is odd).\nThe following 6n lines give the six pieces.\nEach piece is described in n lines.\nEach of the lines corresponds to one grid row and each of the characters in\nthe line, either ‘X ' or ‘. ', indicates whether or not a unit cube is on\nthe corresponding unit square: ‘X ' means a unit cube is on the column and ‘. ' means none is there.\n\n The core area of each piece is centered in the data for the piece.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output “Yes” if we can construct a cube, or “No” if we cannot.\nTask Samples: input: 5\n..XX.\n.XXX.\nXXXXX\nXXXXX\nX....\n....X\nXXXXX\n.XXX.\n.XXX.\n.....\n..XXX\nXXXX.\n.XXXX\n.XXXX\n...X.\n...X.\n.XXXX\nXXXX.\nXXXX.\n.X.X.\nXXX.X\n.XXXX\nXXXXX\n.XXXX\n.XXXX\nXX...\n.XXXX\nXXXXX\nXXXXX\nXX...\n5\n..XX.\n.XXX.\nXXXXX\nXXXX.\nX....\n....X\nXXXXX\n.XXX.\n.XXX.\n.....\n.XXXX\nXXXX.\n.XXXX\n.XXXX\n...X.\n...X.\n.XXXX\nXXXX.\nXXXX.\n.X.X.\nXXX.X\n.XXXX\nXXXXX\n.XXXX\n.XXXX\nXX...\nXXXXX\nXXXXX\n.XXXX\nXX...\n0\n output: Yes\nNo\n\n" }, { "title": "Flipping Colors", "content": "You are given an undirected complete graph.\nEvery pair of the nodes in the graph is connected by an edge,\ncolored either red or black.\nEach edge is associated with an integer value called penalty.\n\nBy repeating certain operations on the given graph,\na “spanning tree” should be formed with only the red edges.\nThat is, the number of red edges should be made exactly one less than\nthe number of nodes, and all the nodes should be made connected\nonly via red edges, directly or indirectly.\nIf two or more such trees can be formed,\none with the least sum of penalties of red edges should be chosen.\n\nIn a single operation step, you choose one of the nodes and flip the colors\nof all the edges connected to it:\nRed ones will turn to black, and black ones to red.\n
    \n\n Fig. F-1 The first dataset of Sample Input and its solution\n \n
    \n\nFor example, the leftmost graph of Fig. F-1 illustrates the first\ndataset of Sample Input.\nBy flipping the colors of all the edges connected to the node 3, and\nthen flipping all the edges connected to the node 2,\nyou can form a spanning tree made of red edges as shown in the\nrightmost graph of the figure.", "constraint": "", "input": "The input consists of multiple datasets, each in the following format.\n\nn \ne_1,2 e_1,3 . . . e_1, n-1 e_1, n\ne_2,3 e_2,4 . . . e_2, n\n. . . \ne_n-1, n\n\nThe integer n (2 <= n <= 300) is the number of nodes.\nThe nodes are numbered from 1 to n.\nThe integer e_i, k (1 <= |e_i, k| <= 10^5)\ndenotes the penalty and the initial color of the edge between the node i and the node k.\nIts absolute value |e_i, k| represents the penalty of the edge.\ne_i, k > 0 means that the edge is initially red,\nand e_i, k < 0 means it is black.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets does not exceed 50.", "output": "For each dataset, print the sum of edge penalties of the red spanning tree\nwith the least sum of edge penalties obtained by the above-described operations.\nIf a red spanning tree can never be made by such operations, print -1.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n3 3 1\n2 6\n-4\n3\n1 -10\n100\n5\n-2 -2 -2 -2\n-1 -1 -1\n-1 -1\n1\n4\n-4 7 6\n2 3\n-1\n0\n output: 7\n11\n-1\n9"], "Pid": "p01122", "ProblemText": "Task Description: You are given an undirected complete graph.\nEvery pair of the nodes in the graph is connected by an edge,\ncolored either red or black.\nEach edge is associated with an integer value called penalty.\n\nBy repeating certain operations on the given graph,\na “spanning tree” should be formed with only the red edges.\nThat is, the number of red edges should be made exactly one less than\nthe number of nodes, and all the nodes should be made connected\nonly via red edges, directly or indirectly.\nIf two or more such trees can be formed,\none with the least sum of penalties of red edges should be chosen.\n\nIn a single operation step, you choose one of the nodes and flip the colors\nof all the edges connected to it:\nRed ones will turn to black, and black ones to red.\n
    \n\n Fig. F-1 The first dataset of Sample Input and its solution\n \n
    \n\nFor example, the leftmost graph of Fig. F-1 illustrates the first\ndataset of Sample Input.\nBy flipping the colors of all the edges connected to the node 3, and\nthen flipping all the edges connected to the node 2,\nyou can form a spanning tree made of red edges as shown in the\nrightmost graph of the figure.\nTask Input: The input consists of multiple datasets, each in the following format.\n\nn \ne_1,2 e_1,3 . . . e_1, n-1 e_1, n\ne_2,3 e_2,4 . . . e_2, n\n. . . \ne_n-1, n\n\nThe integer n (2 <= n <= 300) is the number of nodes.\nThe nodes are numbered from 1 to n.\nThe integer e_i, k (1 <= |e_i, k| <= 10^5)\ndenotes the penalty and the initial color of the edge between the node i and the node k.\nIts absolute value |e_i, k| represents the penalty of the edge.\ne_i, k > 0 means that the edge is initially red,\nand e_i, k < 0 means it is black.\n\nThe end of the input is indicated by a line containing a zero.\nThe number of datasets does not exceed 50.\nTask Output: For each dataset, print the sum of edge penalties of the red spanning tree\nwith the least sum of edge penalties obtained by the above-described operations.\nIf a red spanning tree can never be made by such operations, print -1.\nTask Samples: input: 4\n3 3 1\n2 6\n-4\n3\n1 -10\n100\n5\n-2 -2 -2 -2\n-1 -1 -1\n-1 -1\n1\n4\n-4 7 6\n2 3\n-1\n0\n output: 7\n11\n-1\n9\n\n" }, { "title": "Let's Move Tiles!", "content": "You have a framed square board forming a grid of square cells.\nEach of the cells is either empty or with a square tile fitting in the cell engraved with a Roman character.\nYou can tilt the board to one of four directions, away from you, toward you, to the left, or to the right,\nmaking all the tiles slide up, down, left, or right, respectively, until they are squeezed to an edge frame of the board.\n\nThe figure below shows an example of how the positions of the tiles change by tilting the board toward you.\n\nLet the characters U, D, L, and R represent the operations of tilting the board away from you, toward you, to the left, and to the right, respectively.\nFurther, let strings consisting of these characters represent the sequences of corresponding operations.\nFor example, the string DRU means a sequence of tilting toward you first, then to the right, and, finally, away from you.\nThis will move tiles down first, then to the right, and finally, up.\n\nTo deal with very long operational sequences, we introduce a notation for repeated sequences.\nFor a non-empty sequence seq, the notation (seq)k means that the sequence seq is repeated k times.\nHere, k is an integer.\nFor example, (LR)3 means the same operational sequence as LRLRLR.\nThis notation for repetition can be nested.\nFor example, ((URD)3L)2R means URDURDURDLURDURDURDLR.\n\nYour task is to write a program that,\ngiven an initial positions of tiles on the board and an operational sequence,\ncomputes the tile positions after the given operations are finished.", "constraint": "", "input": "The input consists of at most 100 datasets, each in the following format.\n\nn \ns_11 . . . s_1n \n. . . \ns_n1 . . . s_nn \nseq\n\nIn the first line, n is the number of cells in one row (and also in one column) of the board (2 <= n <= 50).\nThe following n lines contain the initial states of the board cells.\ns_ij is a character indicating the initial state of the cell in the i-th row from the top and in the j-th column from the left (both starting with one).\nIt is either ‘. ' (a period), meaning the cell is empty, or an uppercase letter ‘A '-‘Z ', meaning a tile engraved with that character is there.\n\nseq is a string that represents an operational sequence.\nThe length of seq is between 1 and 1000, inclusive.\nIt is guaranteed that seq denotes an operational sequence as described above.\nThe numbers in seq denoting repetitions are between 2 and 10^18, inclusive, and are without leading zeros.\nFurthermore, the length of the operational sequence after unrolling all the nested repetitions is guaranteed to be at most 10^18.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output the states of the board cells, after performing the given operational sequence starting from the given initial states.\nThe output should be formatted in n lines, in the same format as the initial board cell states are given in the input.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n..E.\n.AD.\nB...\n..C.\nD\n4\n..E.\n.AD.\nB...\n..C.\nDR\n3\n...\n.A.\nBC.\n((URD)3L)2R\n5\n...P.\nPPPPP\nPPP..\nPPPPP\n..P..\nLRLR(LR)12RLLR\n20\n....................\n....................\n.III..CC..PPP...CC..\n..I..C..C.P..P.C..C.\n..I..C....P..P.C....\n..I..C....PPP..C....\n..I..C....P....C....\n..I..C..C.P....C..C.\n.III..CC..P.....CC..\n....................\n..XX...XX...X...XX..\n.X..X.X..X..X..X..X.\n....X.X..X..X..X..X.\n...X..X..X..X..X..X.\n...X..X..X..X...XXX.\n..X...X..X..X.....X.\n..X...X..X..X.....X.\n.XXXX..XX...X...XX..\n....................\n....................\n((LDRU)1000(DLUR)2000(RULD)3000(URDL)4000)123456789012\n6\n...NE.\nMFJ..G\n...E..\n.FBN.K\n....MN\nRA.I..\n((((((((((((((((((((((((URD)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L\n0\n output: ....\n..E.\n..D.\nBAC.\n....\n...E\n...D\n.BAC\n...\n..C\n.AB\n....P\nPPPPP\n..PPP\nPPPPP\n....P\n....................\n....................\n....................\n....................\n....................\nXXXX................\nPXXXX...............\nCXXXX...............\nXXXXX...............\nXXPCXX..............\nCCXXCX..............\nCXXXXX..............\nCXXXXX..............\nCPCIXXX.............\nCXPPCXX.............\nPCXXXIC.............\nCPPCCXI.............\nCXCIPXXX............\nXCPCICIXX...........\nPIPPICIXII..........\n......\n......\nN.....\nJNG...\nRMMKFE\nBEAIFN"], "Pid": "p01123", "ProblemText": "Task Description: You have a framed square board forming a grid of square cells.\nEach of the cells is either empty or with a square tile fitting in the cell engraved with a Roman character.\nYou can tilt the board to one of four directions, away from you, toward you, to the left, or to the right,\nmaking all the tiles slide up, down, left, or right, respectively, until they are squeezed to an edge frame of the board.\n\nThe figure below shows an example of how the positions of the tiles change by tilting the board toward you.\n\nLet the characters U, D, L, and R represent the operations of tilting the board away from you, toward you, to the left, and to the right, respectively.\nFurther, let strings consisting of these characters represent the sequences of corresponding operations.\nFor example, the string DRU means a sequence of tilting toward you first, then to the right, and, finally, away from you.\nThis will move tiles down first, then to the right, and finally, up.\n\nTo deal with very long operational sequences, we introduce a notation for repeated sequences.\nFor a non-empty sequence seq, the notation (seq)k means that the sequence seq is repeated k times.\nHere, k is an integer.\nFor example, (LR)3 means the same operational sequence as LRLRLR.\nThis notation for repetition can be nested.\nFor example, ((URD)3L)2R means URDURDURDLURDURDURDLR.\n\nYour task is to write a program that,\ngiven an initial positions of tiles on the board and an operational sequence,\ncomputes the tile positions after the given operations are finished.\nTask Input: The input consists of at most 100 datasets, each in the following format.\n\nn \ns_11 . . . s_1n \n. . . \ns_n1 . . . s_nn \nseq\n\nIn the first line, n is the number of cells in one row (and also in one column) of the board (2 <= n <= 50).\nThe following n lines contain the initial states of the board cells.\ns_ij is a character indicating the initial state of the cell in the i-th row from the top and in the j-th column from the left (both starting with one).\nIt is either ‘. ' (a period), meaning the cell is empty, or an uppercase letter ‘A '-‘Z ', meaning a tile engraved with that character is there.\n\nseq is a string that represents an operational sequence.\nThe length of seq is between 1 and 1000, inclusive.\nIt is guaranteed that seq denotes an operational sequence as described above.\nThe numbers in seq denoting repetitions are between 2 and 10^18, inclusive, and are without leading zeros.\nFurthermore, the length of the operational sequence after unrolling all the nested repetitions is guaranteed to be at most 10^18.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output the states of the board cells, after performing the given operational sequence starting from the given initial states.\nThe output should be formatted in n lines, in the same format as the initial board cell states are given in the input.\nTask Samples: input: 4\n..E.\n.AD.\nB...\n..C.\nD\n4\n..E.\n.AD.\nB...\n..C.\nDR\n3\n...\n.A.\nBC.\n((URD)3L)2R\n5\n...P.\nPPPPP\nPPP..\nPPPPP\n..P..\nLRLR(LR)12RLLR\n20\n....................\n....................\n.III..CC..PPP...CC..\n..I..C..C.P..P.C..C.\n..I..C....P..P.C....\n..I..C....PPP..C....\n..I..C....P....C....\n..I..C..C.P....C..C.\n.III..CC..P.....CC..\n....................\n..XX...XX...X...XX..\n.X..X.X..X..X..X..X.\n....X.X..X..X..X..X.\n...X..X..X..X..X..X.\n...X..X..X..X...XXX.\n..X...X..X..X.....X.\n..X...X..X..X.....X.\n.XXXX..XX...X...XX..\n....................\n....................\n((LDRU)1000(DLUR)2000(RULD)3000(URDL)4000)123456789012\n6\n...NE.\nMFJ..G\n...E..\n.FBN.K\n....MN\nRA.I..\n((((((((((((((((((((((((URD)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L\n0\n output: ....\n..E.\n..D.\nBAC.\n....\n...E\n...D\n.BAC\n...\n..C\n.AB\n....P\nPPPPP\n..PPP\nPPPPP\n....P\n....................\n....................\n....................\n....................\n....................\nXXXX................\nPXXXX...............\nCXXXX...............\nXXXXX...............\nXXPCXX..............\nCCXXCX..............\nCXXXXX..............\nCXXXXX..............\nCPCIXXX.............\nCXPPCXX.............\nPCXXXIC.............\nCPPCCXI.............\nCXCIPXXX............\nXCPCICIXX...........\nPIPPICIXII..........\n......\n......\nN.....\nJNG...\nRMMKFE\nBEAIFN\n\n" }, { "title": "Addition on Convex Polygons", "content": "Mr. Convexman likes convex polygons very much.\nDuring his study on convex polygons, he has come up with the following elegant addition on convex polygons.\n The sum of two points in the xy-plane,\n(x_1, y_1) and\n(x_2, y_2)\nis defined as\n(x_1 + x_2, y_1 + y_2).\n\nA polygon is treated as the set of all the points on its\nboundary and in its inside.\nHere, the sum of two polygons S_1 and S_2,\nS_1 + S_2, is defined as\nthe set of all the points v_1 + v_2\nsatisfying v_1 ∈ S_1 and\nv_2 ∈ S_2.\nSums of two convex polygons, thus defined, are always convex polygons!\nThe multiplication of a non-negative integer and a polygon is defined inductively by\n0S = {(0,0)} and, for a positive integer k,\nk S = (k - 1)S + S.\nIn this problem, line segments and points are also considered as convex polygons.\n\nMr. Convexman made many convex polygons based on two convex polygons\nP and Q to study properties of the addition, but one\nday, he threw away by mistake the piece of paper on which he had written\ndown the vertex positions of the two polygons and the calculation process.\nWhat remains at hand are only the vertex positions of two\nconvex polygons R and S that are represented as\nlinear combinations of P and Q with non-negative integer coefficients:\n\nR = a P + b Q, and\nS = c P + d Q.\n\nFortunately, he remembers that the coordinates of all vertices of P and Q are integers\nand the coefficients a, b, c and d satisfy ad - bc = 1.\n\nMr. Convexman has requested you, a programmer and his friend, to make a program to recover P and Q from R and S,\nthat is, he wants you to, for given convex polygons R and S, compute non-negative integers a, b, c, d (ad - bc = 1)\nand two convex polygons P and Q with vertices on integer points satisfying the above equation.\nThe equation may have many solutions.\nMake a program to compute the minimum possible sum of the areas of P and Q satisfying the equation.", "constraint": "", "input": "The input consists of at most 40 datasets, each in the following format.\n\nn m \nx_1 y_1 \n. . . \nx_n y_n \nx'_1 y'_1 \n. . . \nx'_m y'_m \n\nn is the number of vertices of the convex polygon R, and m is that of S.\nn and m are integers and satisfy 3 <= n <= 1000 and 3 <= m <= 1000.\n(x_i, y_i) represents the coordinates of the i-th vertex of the convex polygon R\nand (x'_i, y'_i) represents that of S.\nx_i, y_i, x'_i and y'_i are integers between -10^6 and 10^6, inclusive.\nThe vertices of each convex polygon are given in counterclockwise order.\nThree different vertices of one convex polygon do not lie on a single line.\n\nThe end of the input is indicated by a line containing two zeros.", "output": "For each dataset, output a single line containing an integer representing the double of the sum of the areas of P and Q.\nNote that the areas are always integers when doubled because the coordinates of each vertex of P and Q are integers.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 3\n0 0\n2 0\n2 1\n1 2\n0 2\n0 0\n1 0\n0 1\n4 4\n0 0\n5 0\n5 5\n0 5\n0 0\n2 0\n2 2\n0 2\n3 3\n0 0\n1 0\n0 1\n0 1\n0 0\n1 1\n3 3\n0 0\n1 0\n1 1\n0 0\n1 0\n1 1\n4 4\n0 0\n2 0\n2 2\n0 2\n0 0\n1 0\n1 2\n0 2\n4 4\n0 0\n3 0\n3 1\n0 1\n0 0\n1 0\n1 1\n0 1\n0 0\n output: 3\n2\n2\n1\n0\n2"], "Pid": "p01124", "ProblemText": "Task Description: Mr. Convexman likes convex polygons very much.\nDuring his study on convex polygons, he has come up with the following elegant addition on convex polygons.\n The sum of two points in the xy-plane,\n(x_1, y_1) and\n(x_2, y_2)\nis defined as\n(x_1 + x_2, y_1 + y_2).\n\nA polygon is treated as the set of all the points on its\nboundary and in its inside.\nHere, the sum of two polygons S_1 and S_2,\nS_1 + S_2, is defined as\nthe set of all the points v_1 + v_2\nsatisfying v_1 ∈ S_1 and\nv_2 ∈ S_2.\nSums of two convex polygons, thus defined, are always convex polygons!\nThe multiplication of a non-negative integer and a polygon is defined inductively by\n0S = {(0,0)} and, for a positive integer k,\nk S = (k - 1)S + S.\nIn this problem, line segments and points are also considered as convex polygons.\n\nMr. Convexman made many convex polygons based on two convex polygons\nP and Q to study properties of the addition, but one\nday, he threw away by mistake the piece of paper on which he had written\ndown the vertex positions of the two polygons and the calculation process.\nWhat remains at hand are only the vertex positions of two\nconvex polygons R and S that are represented as\nlinear combinations of P and Q with non-negative integer coefficients:\n\nR = a P + b Q, and\nS = c P + d Q.\n\nFortunately, he remembers that the coordinates of all vertices of P and Q are integers\nand the coefficients a, b, c and d satisfy ad - bc = 1.\n\nMr. Convexman has requested you, a programmer and his friend, to make a program to recover P and Q from R and S,\nthat is, he wants you to, for given convex polygons R and S, compute non-negative integers a, b, c, d (ad - bc = 1)\nand two convex polygons P and Q with vertices on integer points satisfying the above equation.\nThe equation may have many solutions.\nMake a program to compute the minimum possible sum of the areas of P and Q satisfying the equation.\nTask Input: The input consists of at most 40 datasets, each in the following format.\n\nn m \nx_1 y_1 \n. . . \nx_n y_n \nx'_1 y'_1 \n. . . \nx'_m y'_m \n\nn is the number of vertices of the convex polygon R, and m is that of S.\nn and m are integers and satisfy 3 <= n <= 1000 and 3 <= m <= 1000.\n(x_i, y_i) represents the coordinates of the i-th vertex of the convex polygon R\nand (x'_i, y'_i) represents that of S.\nx_i, y_i, x'_i and y'_i are integers between -10^6 and 10^6, inclusive.\nThe vertices of each convex polygon are given in counterclockwise order.\nThree different vertices of one convex polygon do not lie on a single line.\n\nThe end of the input is indicated by a line containing two zeros.\nTask Output: For each dataset, output a single line containing an integer representing the double of the sum of the areas of P and Q.\nNote that the areas are always integers when doubled because the coordinates of each vertex of P and Q are integers.\nTask Samples: input: 5 3\n0 0\n2 0\n2 1\n1 2\n0 2\n0 0\n1 0\n0 1\n4 4\n0 0\n5 0\n5 5\n0 5\n0 0\n2 0\n2 2\n0 2\n3 3\n0 0\n1 0\n0 1\n0 1\n0 0\n1 1\n3 3\n0 0\n1 0\n1 1\n0 0\n1 0\n1 1\n4 4\n0 0\n2 0\n2 2\n0 2\n0 0\n1 0\n1 2\n0 2\n4 4\n0 0\n3 0\n3 1\n0 1\n0 0\n1 0\n1 1\n0 1\n0 0\n output: 3\n2\n2\n1\n0\n2\n\n" }, { "title": "Problem A: Blackjack", "content": "Brian Jones is an undergraduate student at Advanced College of Metropolitan. Recently he was\ngiven an assignment in his class of Computer Science to write a program that plays a dealer of\nblackjack.\n\nBlackjack is a game played with one or more decks of playing cards. The objective of each player\nis to have the score of the hand close to 21 without going over 21. The score is the total points\nof the cards in the hand. Cards from 2 to 10 are worth their face value. Face cards (jack, queen\nand king) are worth 10 points. An ace counts as 11 or 1 such a way the score gets closer to\nbut does not exceed 21. A hand of more than 21 points is called bust, which makes a player\nautomatically lose. A hand of 21 points with exactly two cards, that is, a pair of an ace and a\nten-point card (a face card or a ten) is called a blackjack and treated as a special hand.\n\nThe game is played as follows. The dealer first deals two cards each to all players and the dealer\nhimself. In case the dealer gets a blackjack, the dealer wins and the game ends immediately. In\nother cases, players that have blackjacks win automatically. The remaining players make their\nturns one by one. Each player decides to take another card (hit) or to stop taking (stand) in\nhis turn. He may repeatedly hit until he chooses to stand or he busts, in which case his turn\nis over and the next player begins his play. After all players finish their plays, the dealer plays\naccording to the following rules:\n\nHits if the score of the hand is 16 or less.\n\nAlso hits if the score of the hand is 17 and one of aces is counted as 11.\n\nStands otherwise.\nPlayers that have unbusted hands of higher points than that of the dealer win. All players that\ndo not bust win in case the dealer busts. It does not matter, however, whether players win or\nlose, since the subject of the assignment is just to simulate a dealer.\n\nBy the way, Brian is not good at programming, thus the assignment is a very hard task for him.\n\nSo he calls you for help, as you are a good programmer.\nYour task is to write a program that counts the score of the dealer 's hand after his play for each\ngiven sequence of cards.", "constraint": "", "input": "The first line of the input contains a single positive integer N , which represents the number of\ntest cases. Then N test cases follow.\n\nEach case consists of two lines. The first line contains two characters, which indicate the cards\nin the dealer 's initial hand. The second line contains eight characters, which indicate the top\neight cards in the pile after all players finish their plays.\n\nA character that represents a card is one of A, 2,3,4,5,6,7,8,9, T, J, Q and K, where A is\nan ace, T a ten, J a jack, Q a queen and K a king.\n\nCharacters in a line are delimited by a single space.\n\nThe same cards may appear up to four times in one test case. Note that, under this condition,\nthe dealer never needs to hit more than eight times as long as he or she plays according to the\nrule described above.", "output": "For each case, print on a line “blackjack” if the dealer has a blackjack; “bust” if the dealer\nbusts; the score of the dealer 's hand otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n5 4\n9 2 8 3 7 4 6 5\nA J\nK Q J T 9 8 7 6\nT 4\n7 J A 6 Q T K 7\n2 2\n2 3 4 K 2 3 4 K\n output: 18\nblackjack\n21\nbust"], "Pid": "p01149", "ProblemText": "Task Description: Brian Jones is an undergraduate student at Advanced College of Metropolitan. Recently he was\ngiven an assignment in his class of Computer Science to write a program that plays a dealer of\nblackjack.\n\nBlackjack is a game played with one or more decks of playing cards. The objective of each player\nis to have the score of the hand close to 21 without going over 21. The score is the total points\nof the cards in the hand. Cards from 2 to 10 are worth their face value. Face cards (jack, queen\nand king) are worth 10 points. An ace counts as 11 or 1 such a way the score gets closer to\nbut does not exceed 21. A hand of more than 21 points is called bust, which makes a player\nautomatically lose. A hand of 21 points with exactly two cards, that is, a pair of an ace and a\nten-point card (a face card or a ten) is called a blackjack and treated as a special hand.\n\nThe game is played as follows. The dealer first deals two cards each to all players and the dealer\nhimself. In case the dealer gets a blackjack, the dealer wins and the game ends immediately. In\nother cases, players that have blackjacks win automatically. The remaining players make their\nturns one by one. Each player decides to take another card (hit) or to stop taking (stand) in\nhis turn. He may repeatedly hit until he chooses to stand or he busts, in which case his turn\nis over and the next player begins his play. After all players finish their plays, the dealer plays\naccording to the following rules:\n\nHits if the score of the hand is 16 or less.\n\nAlso hits if the score of the hand is 17 and one of aces is counted as 11.\n\nStands otherwise.\nPlayers that have unbusted hands of higher points than that of the dealer win. All players that\ndo not bust win in case the dealer busts. It does not matter, however, whether players win or\nlose, since the subject of the assignment is just to simulate a dealer.\n\nBy the way, Brian is not good at programming, thus the assignment is a very hard task for him.\n\nSo he calls you for help, as you are a good programmer.\nYour task is to write a program that counts the score of the dealer 's hand after his play for each\ngiven sequence of cards.\nTask Input: The first line of the input contains a single positive integer N , which represents the number of\ntest cases. Then N test cases follow.\n\nEach case consists of two lines. The first line contains two characters, which indicate the cards\nin the dealer 's initial hand. The second line contains eight characters, which indicate the top\neight cards in the pile after all players finish their plays.\n\nA character that represents a card is one of A, 2,3,4,5,6,7,8,9, T, J, Q and K, where A is\nan ace, T a ten, J a jack, Q a queen and K a king.\n\nCharacters in a line are delimited by a single space.\n\nThe same cards may appear up to four times in one test case. Note that, under this condition,\nthe dealer never needs to hit more than eight times as long as he or she plays according to the\nrule described above.\nTask Output: For each case, print on a line “blackjack” if the dealer has a blackjack; “bust” if the dealer\nbusts; the score of the dealer 's hand otherwise.\nTask Samples: input: 4\n5 4\n9 2 8 3 7 4 6 5\nA J\nK Q J T 9 8 7 6\nT 4\n7 J A 6 Q T K 7\n2 2\n2 3 4 K 2 3 4 K\n output: 18\nblackjack\n21\nbust\n\n" }, { "title": "Problem B: Eight Princes", "content": "Once upon a time in a kingdom far, far away, there lived eight princes. Sadly they were on very\nbad terms so they began to quarrel every time they met.\n\nOne day, the princes needed to seat at the same round table as a party was held. Since they\nwere always in bad mood, a quarrel would begin whenever:\n\nA prince took the seat next to another prince.\n\nA prince took the seat opposite to that of another prince (this happens only when the\n table has an even number of seats), since they would give malignant looks each other.\n\nTherefore the seat each prince would seat was needed to be carefully determined in order to\navoid their quarrels. You are required to, given the number of the seats, count the number of\nways to have all eight princes seat in peace.", "constraint": "", "input": "Each line in the input contains single integer value N , which represents the number of seats on\nthe round table. A single zero terminates the input.", "output": "For each input N , output the number of possible ways to have all princes take their seat without\ncausing any quarrels. Mirrored or rotated placements must be counted as different.\n\nYou may assume that the output value does not exceed 10^14.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n16\n17\n0\n output: 0\n0\n685440"], "Pid": "p01150", "ProblemText": "Task Description: Once upon a time in a kingdom far, far away, there lived eight princes. Sadly they were on very\nbad terms so they began to quarrel every time they met.\n\nOne day, the princes needed to seat at the same round table as a party was held. Since they\nwere always in bad mood, a quarrel would begin whenever:\n\nA prince took the seat next to another prince.\n\nA prince took the seat opposite to that of another prince (this happens only when the\n table has an even number of seats), since they would give malignant looks each other.\n\nTherefore the seat each prince would seat was needed to be carefully determined in order to\navoid their quarrels. You are required to, given the number of the seats, count the number of\nways to have all eight princes seat in peace.\nTask Input: Each line in the input contains single integer value N , which represents the number of seats on\nthe round table. A single zero terminates the input.\nTask Output: For each input N , output the number of possible ways to have all princes take their seat without\ncausing any quarrels. Mirrored or rotated placements must be counted as different.\n\nYou may assume that the output value does not exceed 10^14.\nTask Samples: input: 8\n16\n17\n0\n output: 0\n0\n685440\n\n" }, { "title": "Problem D: Divisor is the Conqueror", "content": "Divisor is the Conquerer is a solitaire card game. Although this simple game itself is a great\nway to pass one 's time, you, a programmer, always kill your time by programming. Your task\nis to write a computer program that automatically solves Divisor is the Conquerer games. Here\nis the rule of this game:\n\nFirst, you randomly draw N cards (1 <= N <= 52) from your deck of playing cards. The game is\nplayed only with those cards; the other cards will not be used.\n\nThen you repeatedly pick one card to play among those in your hand. You are allowed to choose\nany card in the initial turn. After that, you are only allowed to pick a card that conquers the\ncards you have already played. A card is said to conquer a set of cards when the rank of the card\ndivides the sum of the ranks in the set. For example, the card 7 conquers the set {5,11,12},\nwhile the card 11 does not conquer the set {5,7,12}.\n\nYou win the game if you successfully play all N cards you have drawn. You lose if you fails,\nthat is, you faces a situation in which no card in your hand conquers the set of cards you have\nplayed.", "constraint": "", "input": "The input consists of multiple test cases.\n\nEach test case consists of two lines. The first line contains an integer N (1 <= N <= 52), which represents the number of the cards. The second line contains N integers c_1 , . . . , c_N (1 <= c_i <= 13),\neach of which represents the rank of the card. You may assume that there are at most four cards\nwith the same rank in one list.\n\nThe input is terminated by a line with a single zero.", "output": "For each test case, you should output one line. If there are any winning strategies for the cards\nof the input, print any one of them as a list of N integers separated by a space.\n\nIf there is no winning strategy, print “No”.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 3 7\n4\n2 3 3 3\n0\n output: 3 3 1 7 2\nNo"], "Pid": "p01151", "ProblemText": "Task Description: Divisor is the Conquerer is a solitaire card game. Although this simple game itself is a great\nway to pass one 's time, you, a programmer, always kill your time by programming. Your task\nis to write a computer program that automatically solves Divisor is the Conquerer games. Here\nis the rule of this game:\n\nFirst, you randomly draw N cards (1 <= N <= 52) from your deck of playing cards. The game is\nplayed only with those cards; the other cards will not be used.\n\nThen you repeatedly pick one card to play among those in your hand. You are allowed to choose\nany card in the initial turn. After that, you are only allowed to pick a card that conquers the\ncards you have already played. A card is said to conquer a set of cards when the rank of the card\ndivides the sum of the ranks in the set. For example, the card 7 conquers the set {5,11,12},\nwhile the card 11 does not conquer the set {5,7,12}.\n\nYou win the game if you successfully play all N cards you have drawn. You lose if you fails,\nthat is, you faces a situation in which no card in your hand conquers the set of cards you have\nplayed.\nTask Input: The input consists of multiple test cases.\n\nEach test case consists of two lines. The first line contains an integer N (1 <= N <= 52), which represents the number of the cards. The second line contains N integers c_1 , . . . , c_N (1 <= c_i <= 13),\neach of which represents the rank of the card. You may assume that there are at most four cards\nwith the same rank in one list.\n\nThe input is terminated by a line with a single zero.\nTask Output: For each test case, you should output one line. If there are any winning strategies for the cards\nof the input, print any one of them as a list of N integers separated by a space.\n\nIf there is no winning strategy, print “No”.\nTask Samples: input: 5\n1 2 3 3 7\n4\n2 3 3 3\n0\n output: 3 3 1 7 2\nNo\n\n" }, { "title": "Problem E: Reading a Chord", "content": "In this problem, you are required to write a program that enumerates all chord names for given\ntones.\n\nWe suppose an ordinary scale that consists of the following 12 tones:\n\nC, C^# , D, D^# , E, F, F^# , G, G^# , A, A^# , B\n\nTwo adjacent tones are different by a half step; the right one is higher. Hence, for example, the\ntone G is higher than the tone E by three half steps. In addition, the tone C is higher than the\ntone B by a half step. Strictly speaking, the tone C of the next octave follows the tone B, but\noctaves do not matter in this problem.\n\nA chord consists of two or more different tones, and is called by its chord name. A chord may be\nrepresented by multiple chord names, but each chord name represents exactly one set of tones.\n\nIn general, a chord is represented by a basic chord pattern (base chord) and additional tones\n(tension) as needed. In this problem, we consider five basic patterns as listed below, and up to\none additional tone.\nFigure 1: Base chords (only shown those built on C)\n\nThe chords listed above are built on the tone C, and thus their names begin with C. The tone\nthat a chord is built on (the tone C for these chords) is called the root of the chord.\n\nA chord specifies its root by an absolute tone, and its other components by tones relative to its\nroot. Thus we can obtain another chord by shifting all components of a chord. For example, the\nchord name D represents a chord consisting of the tones D, F^# and A, which are the shifted-up\ntones of C, E and G (which are components of the chord C) by two half steps.\n\nAn additional tone, a tension, is represented by a number that may be preceding a plus or\nminus sign, and designated parentheses after the basic pattern. The figure below denotes which\nnumber is used to indicate each tone.\n\nFigure 2: Tensions for C chords\n\nFor example, C(9) represents the chord C with the additional tone D, that is, a chord that\nconsists of C, D, E and G. Similarly, C(+11) represents the chord C plus the tone F^#.\n\nThe numbers that specify tensions denote relative tones to the roots of chords like the compo-\nnents of the chords. Thus change of the root also changes the tones specified by the number, as\nillustrated below.\nFigure 3: Tensions for E chords\n\n+5 and -5 are the special tensions. They do not indicate to add another tone to the chords,\nbut to sharp (shift half-step up) or flat (shift half-step down) the fifth tone (the tone seven half\nsteps higher than the root). Therefore, for example, C(+5) represents a chord that consists of\nC, E and G^# , not C, E, G and G^#.\n\nFigure 4 describes the syntax of chords in Backus-Naur Form.\n\nNow suppose we find chord names for the tones C, E and G. First, we easily find the chord C\nconsists of the tones C, E and G by looking up the base chord table shown above. Therefore\n‘C ' should be printed. We have one more chord name for those tones. The chord Em obviously\nrepresents the set of tones E, G and B. Here, if you sharp the tone B, we have the set of tones\nE, G and C. Such modification can be specified by a tension, +5 in this case. Thus ‘Em(+5) '\nshould also be printed.\nFigure 4: Syntax of chords in BNF", "constraint": "", "input": "The first line of input contains an integer N, which indicates the number of test cases.\n\nEach line after that contains one test case. A test case consists of an integer m (3 <= m <= 5)\nfollowed by m tones. There is exactly one space character between each tones. The same tone\ndoes not appear more than once in one test case.\n\nTones are given as described above.", "output": "Your program should output one line for each test case.\n\nIt should enumerate all chord names that completely match the set of tones given as input (i. e.\nthe set of tones represented by each chord name must be equal to that of input) in any order.\n\nNo chord name should be output more than once. Chord names must be separated by exactly\none space character. No extra space is allowed.\n\nIf no chord name matches the set of tones, your program should just print ‘UNKNOWN ' (note that\nthis word must be written in capital letters).", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n3 C E G\n3 C E G#\n4 C A G E\n5 F A C E D\n3 C D E\n output: C Em(+5)\nC(+5) E(+5) G#(+5)\nC(13) Am7 Am(+13)\nDm7(9) FM7(13)\nUNKNOWN"], "Pid": "p01152", "ProblemText": "Task Description: In this problem, you are required to write a program that enumerates all chord names for given\ntones.\n\nWe suppose an ordinary scale that consists of the following 12 tones:\n\nC, C^# , D, D^# , E, F, F^# , G, G^# , A, A^# , B\n\nTwo adjacent tones are different by a half step; the right one is higher. Hence, for example, the\ntone G is higher than the tone E by three half steps. In addition, the tone C is higher than the\ntone B by a half step. Strictly speaking, the tone C of the next octave follows the tone B, but\noctaves do not matter in this problem.\n\nA chord consists of two or more different tones, and is called by its chord name. A chord may be\nrepresented by multiple chord names, but each chord name represents exactly one set of tones.\n\nIn general, a chord is represented by a basic chord pattern (base chord) and additional tones\n(tension) as needed. In this problem, we consider five basic patterns as listed below, and up to\none additional tone.\nFigure 1: Base chords (only shown those built on C)\n\nThe chords listed above are built on the tone C, and thus their names begin with C. The tone\nthat a chord is built on (the tone C for these chords) is called the root of the chord.\n\nA chord specifies its root by an absolute tone, and its other components by tones relative to its\nroot. Thus we can obtain another chord by shifting all components of a chord. For example, the\nchord name D represents a chord consisting of the tones D, F^# and A, which are the shifted-up\ntones of C, E and G (which are components of the chord C) by two half steps.\n\nAn additional tone, a tension, is represented by a number that may be preceding a plus or\nminus sign, and designated parentheses after the basic pattern. The figure below denotes which\nnumber is used to indicate each tone.\n\nFigure 2: Tensions for C chords\n\nFor example, C(9) represents the chord C with the additional tone D, that is, a chord that\nconsists of C, D, E and G. Similarly, C(+11) represents the chord C plus the tone F^#.\n\nThe numbers that specify tensions denote relative tones to the roots of chords like the compo-\nnents of the chords. Thus change of the root also changes the tones specified by the number, as\nillustrated below.\nFigure 3: Tensions for E chords\n\n+5 and -5 are the special tensions. They do not indicate to add another tone to the chords,\nbut to sharp (shift half-step up) or flat (shift half-step down) the fifth tone (the tone seven half\nsteps higher than the root). Therefore, for example, C(+5) represents a chord that consists of\nC, E and G^# , not C, E, G and G^#.\n\nFigure 4 describes the syntax of chords in Backus-Naur Form.\n\nNow suppose we find chord names for the tones C, E and G. First, we easily find the chord C\nconsists of the tones C, E and G by looking up the base chord table shown above. Therefore\n‘C ' should be printed. We have one more chord name for those tones. The chord Em obviously\nrepresents the set of tones E, G and B. Here, if you sharp the tone B, we have the set of tones\nE, G and C. Such modification can be specified by a tension, +5 in this case. Thus ‘Em(+5) '\nshould also be printed.\nFigure 4: Syntax of chords in BNF\nTask Input: The first line of input contains an integer N, which indicates the number of test cases.\n\nEach line after that contains one test case. A test case consists of an integer m (3 <= m <= 5)\nfollowed by m tones. There is exactly one space character between each tones. The same tone\ndoes not appear more than once in one test case.\n\nTones are given as described above.\nTask Output: Your program should output one line for each test case.\n\nIt should enumerate all chord names that completely match the set of tones given as input (i. e.\nthe set of tones represented by each chord name must be equal to that of input) in any order.\n\nNo chord name should be output more than once. Chord names must be separated by exactly\none space character. No extra space is allowed.\n\nIf no chord name matches the set of tones, your program should just print ‘UNKNOWN ' (note that\nthis word must be written in capital letters).\nTask Samples: input: 5\n3 C E G\n3 C E G#\n4 C A G E\n5 F A C E D\n3 C D E\n output: C Em(+5)\nC(+5) E(+5) G#(+5)\nC(13) Am7 Am(+13)\nDm7(9) FM7(13)\nUNKNOWN\n\n" }, { "title": "Problem G: Gather on the Clock", "content": "There is a self-playing game called Gather on the Clock.\n\nAt the beginning of a game, a number of cards are placed on a ring. Each card is labeled by a\nvalue.\n\nIn each step of a game, you pick up any one of the cards on the ring and put it on the next one\nin clockwise order. You will gain the score by the difference of the two values. You should deal\nwith the two cards as one card in the later steps. You repeat this step until only one card is left\non the ring, and the score of the game is the sum of the gained scores.\n\nYour task is to write a program that calculates the maximum score for the given initial state,\nwhich specifies the values of cards and their placements on the ring.\n\nThe figure shown below is an example, in which the initial state is illustrated on the left, and\nthe subsequent states to the right. The picked cards are 1,3 and 3, respectively, and the score\nof this game is 6.\nFigure 6: An illustrative play of Gather on the Clock", "constraint": "", "input": "The input consists of multiple test cases. The first line contains the number of cases. For each\ncase, a line describing a state follows. The line begins with an integer n (2 <= n <= 100), the\nnumber of cards on the ring, and then n numbers describing the values of the cards follow. Note\nthat the values are given in clockwise order. You can assume all these numbers are non-negative\nand do not exceed 100. They are separated by a single space character.", "output": "For each case, output the maximum score in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n4 0 1 2 3\n6 1 8 0 3 5 9\n output: 6\n34"], "Pid": "p01153", "ProblemText": "Task Description: There is a self-playing game called Gather on the Clock.\n\nAt the beginning of a game, a number of cards are placed on a ring. Each card is labeled by a\nvalue.\n\nIn each step of a game, you pick up any one of the cards on the ring and put it on the next one\nin clockwise order. You will gain the score by the difference of the two values. You should deal\nwith the two cards as one card in the later steps. You repeat this step until only one card is left\non the ring, and the score of the game is the sum of the gained scores.\n\nYour task is to write a program that calculates the maximum score for the given initial state,\nwhich specifies the values of cards and their placements on the ring.\n\nThe figure shown below is an example, in which the initial state is illustrated on the left, and\nthe subsequent states to the right. The picked cards are 1,3 and 3, respectively, and the score\nof this game is 6.\nFigure 6: An illustrative play of Gather on the Clock\nTask Input: The input consists of multiple test cases. The first line contains the number of cases. For each\ncase, a line describing a state follows. The line begins with an integer n (2 <= n <= 100), the\nnumber of cards on the ring, and then n numbers describing the values of the cards follow. Note\nthat the values are given in clockwise order. You can assume all these numbers are non-negative\nand do not exceed 100. They are separated by a single space character.\nTask Output: For each case, output the maximum score in a line.\nTask Samples: input: 2\n4 0 1 2 3\n6 1 8 0 3 5 9\n output: 6\n34\n\n" }, { "title": "Problem I: Light The Room", "content": "You are given plans of rooms of polygonal shapes. The walls of the rooms on the plans are\nplaced parallel to either x-axis or y-axis. In addition, the walls are made of special materials so\nthey reflect light from sources as mirrors do, but only once. In other words, the walls do not\nreflect light already reflected at another point of the walls.\n\nNow we have each room furnished with one lamp. Walls will be illuminated by the lamp directly\nor indirectly. However, since the walls reflect the light only once, some part of the walls may\nnot be illuminated.\n\nYou are requested to write a program that calculates the total length of unilluminated part of\nthe walls.\nFigure 10: The room given as the second case in Sample Input", "constraint": "", "input": "The input consists of multiple test cases.\n\nThe first line of each case contains a single positive even integer N (4 <= N <= 20), which indicates\nthe number of the corners. The following N lines describe the corners counterclockwise. The\ni-th line contains two integers x_i and y_i , where (x_i , y_i ) indicates the coordinates of the i-th\ncorner. The last line of the case contains x' and y' , where (x' , y' ) indicates the coordinates of\nthe lamp.\n\nTo make the problem simple, you may assume that the input meets the following conditions:\n\nAll coordinate values are integers not greater than 100 in their absolute values.\n\nNo two walls intersect or touch except for their ends.\n\nThe walls do not intersect nor touch each other.\n\nThe walls turn each corner by a right angle.\n\nThe lamp exists strictly inside the room off the wall.\n\nThe x-coordinate of the lamp does not coincide with that of any wall; neither does the\n y-coordinate.\nThe input is terminated by a line containing a single zero.", "output": "For each case, output the length of the unilluminated part in one line. The output value may\nhave an arbitrary number of decimal digits, but may not contain an error greater than 10^-3 .", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n2 0\n2 2\n0 2\n1 1\n6\n2 2\n2 5\n0 5\n0 0\n5 0\n5 2\n1 4\n0\n output: 0.000\n3.000"], "Pid": "p01154", "ProblemText": "Task Description: You are given plans of rooms of polygonal shapes. The walls of the rooms on the plans are\nplaced parallel to either x-axis or y-axis. In addition, the walls are made of special materials so\nthey reflect light from sources as mirrors do, but only once. In other words, the walls do not\nreflect light already reflected at another point of the walls.\n\nNow we have each room furnished with one lamp. Walls will be illuminated by the lamp directly\nor indirectly. However, since the walls reflect the light only once, some part of the walls may\nnot be illuminated.\n\nYou are requested to write a program that calculates the total length of unilluminated part of\nthe walls.\nFigure 10: The room given as the second case in Sample Input\nTask Input: The input consists of multiple test cases.\n\nThe first line of each case contains a single positive even integer N (4 <= N <= 20), which indicates\nthe number of the corners. The following N lines describe the corners counterclockwise. The\ni-th line contains two integers x_i and y_i , where (x_i , y_i ) indicates the coordinates of the i-th\ncorner. The last line of the case contains x' and y' , where (x' , y' ) indicates the coordinates of\nthe lamp.\n\nTo make the problem simple, you may assume that the input meets the following conditions:\n\nAll coordinate values are integers not greater than 100 in their absolute values.\n\nNo two walls intersect or touch except for their ends.\n\nThe walls do not intersect nor touch each other.\n\nThe walls turn each corner by a right angle.\n\nThe lamp exists strictly inside the room off the wall.\n\nThe x-coordinate of the lamp does not coincide with that of any wall; neither does the\n y-coordinate.\nThe input is terminated by a line containing a single zero.\nTask Output: For each case, output the length of the unilluminated part in one line. The output value may\nhave an arbitrary number of decimal digits, but may not contain an error greater than 10^-3 .\nTask Samples: input: 4\n0 0\n2 0\n2 2\n0 2\n1 1\n6\n2 2\n2 5\n0 5\n0 0\n5 0\n5 2\n1 4\n0\n output: 0.000\n3.000\n\n" }, { "title": "Problem A: Ruins", "content": "In 1936, a dictator Hiedler who aimed at world domination had a deep obsession with the Lost Ark. A\nperson with this ark would gain mystic power according to legend. To break the ambition of the dictator,\nACM (the Alliance of Crusaders against Mazis) entrusted a secret task to an archeologist Indiana Johns.\nIndiana stepped into a vast and harsh desert to find the ark.\n\nIndiana finally found an underground treasure house at a ruin in the desert. The treasure house seems\nstoring the ark. However, the door to the treasure house has a special lock, and it is not easy to open\nthe door.\n\nTo open the door, he should solve a problem raised by two positive integers a and b inscribed on the door.\nThe problem requires him to find the minimum sum of squares of differences for all pairs of two integers\nadjacent in a sorted sequence that contains four positive integers a_1, a_2 , b_1 and b_2 such that a = a_1a_2\nand b = b_1b_2. Note that these four integers does not need to be different. For instance, suppose 33 and\n40 are inscribed on the door, he would have a sequence 3,5,8,11 as 33 and 40 can be decomposed into\n3 * 11 and 5 * 8 respectively. This sequence gives the sum (5 - 3)^2 + (8 - 5)^2 + (11 - 8)^2 = 22, which is\nthe smallest sum among all possible sorted sequences. This example is included as the first data set in\nthe sample input.\n\nOnce Indiana fails to give the correct solution, he will suffer a calamity by a curse. On the other hand,\nhe needs to solve the problem as soon as possible, since many pawns under Hiedler are also searching\nfor the ark, and they might find the same treasure house. He will be immediately killed if this situation\nhappens. So he decided to solve the problem by your computer program.\n\nYour task is to write a program to solve the problem presented above.", "constraint": "", "input": "The input consists of a series of data sets. Each data set is given by a line that contains two positive\nintegers not greater than 10,000.\n\nThe end of the input is represented by a pair of zeros, which should not be processed.", "output": "For each data set, print a single integer that represents the minimum square sum in a line. No extra\nspace or text should appear.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 33 40\n57 144\n0 0\n output: 22\n94"], "Pid": "p01155", "ProblemText": "Task Description: In 1936, a dictator Hiedler who aimed at world domination had a deep obsession with the Lost Ark. A\nperson with this ark would gain mystic power according to legend. To break the ambition of the dictator,\nACM (the Alliance of Crusaders against Mazis) entrusted a secret task to an archeologist Indiana Johns.\nIndiana stepped into a vast and harsh desert to find the ark.\n\nIndiana finally found an underground treasure house at a ruin in the desert. The treasure house seems\nstoring the ark. However, the door to the treasure house has a special lock, and it is not easy to open\nthe door.\n\nTo open the door, he should solve a problem raised by two positive integers a and b inscribed on the door.\nThe problem requires him to find the minimum sum of squares of differences for all pairs of two integers\nadjacent in a sorted sequence that contains four positive integers a_1, a_2 , b_1 and b_2 such that a = a_1a_2\nand b = b_1b_2. Note that these four integers does not need to be different. For instance, suppose 33 and\n40 are inscribed on the door, he would have a sequence 3,5,8,11 as 33 and 40 can be decomposed into\n3 * 11 and 5 * 8 respectively. This sequence gives the sum (5 - 3)^2 + (8 - 5)^2 + (11 - 8)^2 = 22, which is\nthe smallest sum among all possible sorted sequences. This example is included as the first data set in\nthe sample input.\n\nOnce Indiana fails to give the correct solution, he will suffer a calamity by a curse. On the other hand,\nhe needs to solve the problem as soon as possible, since many pawns under Hiedler are also searching\nfor the ark, and they might find the same treasure house. He will be immediately killed if this situation\nhappens. So he decided to solve the problem by your computer program.\n\nYour task is to write a program to solve the problem presented above.\nTask Input: The input consists of a series of data sets. Each data set is given by a line that contains two positive\nintegers not greater than 10,000.\n\nThe end of the input is represented by a pair of zeros, which should not be processed.\nTask Output: For each data set, print a single integer that represents the minimum square sum in a line. No extra\nspace or text should appear.\nTask Samples: input: 33 40\n57 144\n0 0\n output: 22\n94\n\n" }, { "title": "Problem B: Hyper Rock-Scissors-Paper", "content": "Rock-Scissors-Paper is a game played with hands and often used for random choice of a person for some\npurpose. Today, we have got an extended version, namely, Hyper Rock-Scissors-Paper (or Hyper RSP\nfor short).\n\nIn a game of Hyper RSP, the players simultaneously presents their hands forming any one of the following\n15 gestures: Rock, Fire, Scissors, Snake, Human, Tree, Wolf, Sponge, Paper, Air, Water, Dragon, Devil,\nLightning, and Gun.\nFigure 1: Hyper Rock-Scissors-Paper\n\nThe arrows in the figure above show the defeating relation. For example, Rock defeats Fire, Scissors,\nSnake, Human, Tree, Wolf, and Sponge. Fire defeats Scissors, Snake, Human, Tree, Wolf, Sponge, and\nPaper. Generally speaking, each hand defeats other seven hands located after in anti-clockwise order in\nthe figure. A player is said to win the game if the player 's hand defeats at least one of the other hands,\nand is not defeated by any of the other hands.\n\nYour task is to determine the winning hand, given multiple hands presented by the players.", "constraint": "", "input": "The input consists of a series of data sets. The first line of each data set is the number N of the players\n(N < 1000). The next N lines are the hands presented by the players.\n\nThe end of the input is indicated by a line containing single zero.", "output": "For each data set, output the winning hand in a single line. When there are no winners in the game,\noutput “Draw” (without quotes).", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8\nLightning\nGun\nPaper\nSponge\nWater\nDragon\nDevil\nAir\n3\nRock\nScissors\nPaper\n0\n output: Sponge\nDraw"], "Pid": "p01156", "ProblemText": "Task Description: Rock-Scissors-Paper is a game played with hands and often used for random choice of a person for some\npurpose. Today, we have got an extended version, namely, Hyper Rock-Scissors-Paper (or Hyper RSP\nfor short).\n\nIn a game of Hyper RSP, the players simultaneously presents their hands forming any one of the following\n15 gestures: Rock, Fire, Scissors, Snake, Human, Tree, Wolf, Sponge, Paper, Air, Water, Dragon, Devil,\nLightning, and Gun.\nFigure 1: Hyper Rock-Scissors-Paper\n\nThe arrows in the figure above show the defeating relation. For example, Rock defeats Fire, Scissors,\nSnake, Human, Tree, Wolf, and Sponge. Fire defeats Scissors, Snake, Human, Tree, Wolf, Sponge, and\nPaper. Generally speaking, each hand defeats other seven hands located after in anti-clockwise order in\nthe figure. A player is said to win the game if the player 's hand defeats at least one of the other hands,\nand is not defeated by any of the other hands.\n\nYour task is to determine the winning hand, given multiple hands presented by the players.\nTask Input: The input consists of a series of data sets. The first line of each data set is the number N of the players\n(N < 1000). The next N lines are the hands presented by the players.\n\nThe end of the input is indicated by a line containing single zero.\nTask Output: For each data set, output the winning hand in a single line. When there are no winners in the game,\noutput “Draw” (without quotes).\nTask Samples: input: 8\nLightning\nGun\nPaper\nSponge\nWater\nDragon\nDevil\nAir\n3\nRock\nScissors\nPaper\n0\n output: Sponge\nDraw\n\n" }, { "title": "Problem C: Online Quizu System", "content": "ICPC (Internet Contents Providing Company) is working on a killer game named Quiz Millionaire Attack.\nIt is a quiz system played over the Internet. You are joining ICPC as an engineer, and you are responsible\nfor designing a protocol between clients and the game server for this system. As bandwidth assigned for\nthe server is quite limited, data size exchanged between clients and the server should be reduced as much\nas possible. In addition, all clients should be well synchronized during the quiz session for a simultaneous\nplay. In particular, much attention should be paid to the delay on receiving packets.\n\nTo verify that your protocol meets the above demands, you have decided to simulate the communication\nbetween clients and the server and calculate the data size exchanged during one game.\n\nA game has the following process. First, players participating and problems to be used are fixed. All\nplayers are using the same client program and already have the problem statements downloaded, so you\ndon 't need to simulate this part. Then the game begins. The first problem is presented to the players,\nand the players answer it within a fixed amount of time. After that, the second problem is presented,\nand so forth. When all problems have been completed, the game ends. During each problem phase,\nthe players are notified of what other players have done. Before you submit your answer, you can know\nwho have already submitted their answers. After you have submitted your answer, you can know what\nanswers are submitted by other players.\n\nWhen each problem phase starts, the server sends a synchronization packet for problem-start to all the\nplayers, and begins a polling process. Every 1,000 milliseconds after the beginning of polling, the server\nchecks whether it received new answers from the players strictly before that moment, and if there are\nany, sends a notification to all the players:\n\n If a player hasn 't submitted an answer yet, the server sends it a notification packet type A describing\n others ' answers about the newly received answers.\n\n If a player is one of those who submitted the newly received answers, the server sends it a notification\n packet type B describing others ' answers about all the answers submitted by other players (i. e.\n excluding the player him/herself 's answer) strictly before that moment.\n\n If a player has already submitted an answer, the server sends it a notification packet type B describing\n others ' answers about the newly received answers.\n\n Note that, in all above cases, notification packets (both types A and B) must contain information\n about at least one player, and otherwise a notification packet will not be sent.\n\nWhen 20,000 milliseconds have passed after sending the synchronization packet for problem-start, the\nserver sends notification packets of type A or B if needed, and then sends a synchronization packet for\nproblem-end to all the players, to terminate the problem.\n\nOn the other hand, players will be able to answer the problem after receiving the synchronization packet\nfor problem-start and before receiving the synchronization packet for problem-end. Answers will be sent\nusing an answer packet.\n\nThe packets referred above have the formats shown by the following tables.", "constraint": "", "input": "The input consists of multiple test cases. Each test case begins with a line consisting of two integers\nM and N (1 <= M, N <= 100), denoting the number of players and problems, respectively. The next\nline contains M non-negative integers D_0 , D_1 , . . . , D_M - 1 , denoting the communication delay between\neach players and the server (players are assigned ID 's ranging from 0 to M - 1, inclusive). Then follow\nN blocks describing the submissions for each problem. Each block begins with a line containing an\ninteger L, denoting the number of players that submitted an answer for that problem. Each of the\nfollowing L lines gives the answer from one player, described by three fields P, T, and A separated by a\nwhitespace. Here P is an integer denoting the player ID, T is an integer denoting the time elapsed from the reception of synchronization packet for problem-start and the submission on the player 's side, and A\nis an alphanumeric string denoting the player 's answer, whose length is between 1 and 9, inclusive. Those\nL lines may be given in an arbitrary order. You may assume that all answer packets will be received by\nthe server within 19,999 milliseconds (inclusive) after sending synchronization packet for problem-start.\n\nThe input is terminated by a line containing two zeros.", "output": "For each test case, you are to print M + 1 lines. In the first line, print the data size sent and received\nby the server, separated by a whitespace. In the next M lines, print the data size sent and received by\neach player, separated by a whitespace, in ascending order of player ID. Print a blank line between two\nconsecutive test cases.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2 10\n3\n0 3420 o\n1 4589 o\n2 4638 x\n3\n1 6577 SUZUMIYA\n2 7644 SUZUMIYA\n0 19979 YASUZUMI\n4 2\n150 150 150 150\n4\n0 1344 HOGEHOGE\n1 1466 HOGEHOGE\n2 1789 HOGEHOGE\n3 19100 GEHO\n2\n2 1200 SETTEN\n3 700 SETTEN\n0 0\n output: 177 57\n19 58\n19 57\n19 62\n\n253 70\n13 58\n13 58\n24 66\n20 71"], "Pid": "p01157", "ProblemText": "Task Description: ICPC (Internet Contents Providing Company) is working on a killer game named Quiz Millionaire Attack.\nIt is a quiz system played over the Internet. You are joining ICPC as an engineer, and you are responsible\nfor designing a protocol between clients and the game server for this system. As bandwidth assigned for\nthe server is quite limited, data size exchanged between clients and the server should be reduced as much\nas possible. In addition, all clients should be well synchronized during the quiz session for a simultaneous\nplay. In particular, much attention should be paid to the delay on receiving packets.\n\nTo verify that your protocol meets the above demands, you have decided to simulate the communication\nbetween clients and the server and calculate the data size exchanged during one game.\n\nA game has the following process. First, players participating and problems to be used are fixed. All\nplayers are using the same client program and already have the problem statements downloaded, so you\ndon 't need to simulate this part. Then the game begins. The first problem is presented to the players,\nand the players answer it within a fixed amount of time. After that, the second problem is presented,\nand so forth. When all problems have been completed, the game ends. During each problem phase,\nthe players are notified of what other players have done. Before you submit your answer, you can know\nwho have already submitted their answers. After you have submitted your answer, you can know what\nanswers are submitted by other players.\n\nWhen each problem phase starts, the server sends a synchronization packet for problem-start to all the\nplayers, and begins a polling process. Every 1,000 milliseconds after the beginning of polling, the server\nchecks whether it received new answers from the players strictly before that moment, and if there are\nany, sends a notification to all the players:\n\n If a player hasn 't submitted an answer yet, the server sends it a notification packet type A describing\n others ' answers about the newly received answers.\n\n If a player is one of those who submitted the newly received answers, the server sends it a notification\n packet type B describing others ' answers about all the answers submitted by other players (i. e.\n excluding the player him/herself 's answer) strictly before that moment.\n\n If a player has already submitted an answer, the server sends it a notification packet type B describing\n others ' answers about the newly received answers.\n\n Note that, in all above cases, notification packets (both types A and B) must contain information\n about at least one player, and otherwise a notification packet will not be sent.\n\nWhen 20,000 milliseconds have passed after sending the synchronization packet for problem-start, the\nserver sends notification packets of type A or B if needed, and then sends a synchronization packet for\nproblem-end to all the players, to terminate the problem.\n\nOn the other hand, players will be able to answer the problem after receiving the synchronization packet\nfor problem-start and before receiving the synchronization packet for problem-end. Answers will be sent\nusing an answer packet.\n\nThe packets referred above have the formats shown by the following tables.\nTask Input: The input consists of multiple test cases. Each test case begins with a line consisting of two integers\nM and N (1 <= M, N <= 100), denoting the number of players and problems, respectively. The next\nline contains M non-negative integers D_0 , D_1 , . . . , D_M - 1 , denoting the communication delay between\neach players and the server (players are assigned ID 's ranging from 0 to M - 1, inclusive). Then follow\nN blocks describing the submissions for each problem. Each block begins with a line containing an\ninteger L, denoting the number of players that submitted an answer for that problem. Each of the\nfollowing L lines gives the answer from one player, described by three fields P, T, and A separated by a\nwhitespace. Here P is an integer denoting the player ID, T is an integer denoting the time elapsed from the reception of synchronization packet for problem-start and the submission on the player 's side, and A\nis an alphanumeric string denoting the player 's answer, whose length is between 1 and 9, inclusive. Those\nL lines may be given in an arbitrary order. You may assume that all answer packets will be received by\nthe server within 19,999 milliseconds (inclusive) after sending synchronization packet for problem-start.\n\nThe input is terminated by a line containing two zeros.\nTask Output: For each test case, you are to print M + 1 lines. In the first line, print the data size sent and received\nby the server, separated by a whitespace. In the next M lines, print the data size sent and received by\neach player, separated by a whitespace, in ascending order of player ID. Print a blank line between two\nconsecutive test cases.\nTask Samples: input: 3 2\n1 2 10\n3\n0 3420 o\n1 4589 o\n2 4638 x\n3\n1 6577 SUZUMIYA\n2 7644 SUZUMIYA\n0 19979 YASUZUMI\n4 2\n150 150 150 150\n4\n0 1344 HOGEHOGE\n1 1466 HOGEHOGE\n2 1789 HOGEHOGE\n3 19100 GEHO\n2\n2 1200 SETTEN\n3 700 SETTEN\n0 0\n output: 177 57\n19 58\n19 57\n19 62\n\n253 70\n13 58\n13 58\n24 66\n20 71\n\n" }, { "title": "Problem D: Rock Man", "content": "You were the master craftsman in the stone age, and you devoted your life to carving many varieties of\ntools out of natural stones. Your works have ever been displayed respectfully in many museums, even in\n2006 A. D. However, most people visiting the museums do not spend so much time to look at your works.\nSeeing the situation from the Heaven, you brought back memories of those days you had frantically lived.\n\nOne day in your busiest days, you got a number of orders for making tools. Each order requested one\ntool which was different from the other orders. It often took some days to fill one order without special\ntools. But you could use tools which you had already made completely, in order to carve new tools more\nquickly. For each tool in the list of the orders, there was exactly one tool which could support carving it.\n\nIn those days, your schedule to fill the orders was not so efficient. You are now thinking of making the\nmost efficient schedule, i. e. the schedule for all orders being filled in the shortest days, using the program\nyou are going to write.", "constraint": "", "input": "The input consists of a series of test cases. Each case begins with a line containing a single integer N\nwhich represents the number of ordered tools.\n\nThen N lines follow, each specifying an order by four elements separated by one or more space: name,\nday_1, sup and day_2. name is the name of the tool in the corresponding order. day_1 is the number of\nrequired days to make the tool without any support tool. sup is the name of the tool that can support\ncarving the target tool. day_2 is the number of required days make the tool with the corresponding support\ntool.\n\nThe input terminates with the case where N = 0. You should not process this case.\n\nYou can assume that the input follows the constraints below:\n\n N <= 1000;\n\n name consists of no longer than 32 non-space characters, and is unique in each case;\n\n sup is one of all names given in the same case; and\n\n 0 < day_2 < day_1 < 20000.", "output": "For each test case, output a single line containing an integer which represents the minimum number of\ndays required to fill all N orders.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\ngu 20 pa 10\nci 20 gu 10\npa 20 ci 10\n2\ntool 20 tool 10\nproduct 1000 tool 10\n8\nfishhook 21 disk 3\nmill 14 axe 7\nboomerang 56 sundial 28\nflint 35 fishhook 5\naxe 35 flint 14\ndisk 42 disk 2\nsundial 14 disk 7\nhammer 28 mill 7\n0\n output: 40\n30\n113"], "Pid": "p01158", "ProblemText": "Task Description: You were the master craftsman in the stone age, and you devoted your life to carving many varieties of\ntools out of natural stones. Your works have ever been displayed respectfully in many museums, even in\n2006 A. D. However, most people visiting the museums do not spend so much time to look at your works.\nSeeing the situation from the Heaven, you brought back memories of those days you had frantically lived.\n\nOne day in your busiest days, you got a number of orders for making tools. Each order requested one\ntool which was different from the other orders. It often took some days to fill one order without special\ntools. But you could use tools which you had already made completely, in order to carve new tools more\nquickly. For each tool in the list of the orders, there was exactly one tool which could support carving it.\n\nIn those days, your schedule to fill the orders was not so efficient. You are now thinking of making the\nmost efficient schedule, i. e. the schedule for all orders being filled in the shortest days, using the program\nyou are going to write.\nTask Input: The input consists of a series of test cases. Each case begins with a line containing a single integer N\nwhich represents the number of ordered tools.\n\nThen N lines follow, each specifying an order by four elements separated by one or more space: name,\nday_1, sup and day_2. name is the name of the tool in the corresponding order. day_1 is the number of\nrequired days to make the tool without any support tool. sup is the name of the tool that can support\ncarving the target tool. day_2 is the number of required days make the tool with the corresponding support\ntool.\n\nThe input terminates with the case where N = 0. You should not process this case.\n\nYou can assume that the input follows the constraints below:\n\n N <= 1000;\n\n name consists of no longer than 32 non-space characters, and is unique in each case;\n\n sup is one of all names given in the same case; and\n\n 0 < day_2 < day_1 < 20000.\nTask Output: For each test case, output a single line containing an integer which represents the minimum number of\ndays required to fill all N orders.\nTask Samples: input: 3\ngu 20 pa 10\nci 20 gu 10\npa 20 ci 10\n2\ntool 20 tool 10\nproduct 1000 tool 10\n8\nfishhook 21 disk 3\nmill 14 axe 7\nboomerang 56 sundial 28\nflint 35 fishhook 5\naxe 35 flint 14\ndisk 42 disk 2\nsundial 14 disk 7\nhammer 28 mill 7\n0\n output: 40\n30\n113\n\n" }, { "title": "Problem E: Autocorrelation Function", "content": "Nathan O. Davis is taking a class of signal processing as a student in engineering. Today 's topic of the\nclass was autocorrelation. It is a mathematical tool for analysis of signals represented by functions or\nseries of values. Autocorrelation gives correlation of a signal with itself. For a continuous real function\nf(x), the autocorrelation function R_f (r) is given by\n\nwhere r is a real number.\n\nThe professor teaching in the class presented an assignment today. This assignment requires students\nto make plots of the autocorrelation functions for given functions. Each function is piecewise linear and\ncontinuous for all real numbers. The figure below depicts one of those functions.\n\nFigure 1: An Example of Given Functions\nThe professor suggested use of computer programs, but unfortunately Nathan hates programming. So he\ncalls you for help, as he knows you are a great programmer. You are requested to write a program that\ncomputes the value of the autocorrelation function where a function f(x) and a parameter r are given as\nthe input. Since he is good at utilization of existing software, he could finish his assignment with your\nprogram.", "constraint": "", "input": "The input consists of a series of data sets.\n\nThe first line of each data set contains an integer n (3 <= n <= 100) and a real number r (-100 <= r <= 100),\nwhere n denotes the number of endpoints forming sub-intervals in the function f(x), and r gives the\nparameter of the autocorrelation function R_f(r). The i-th of the following n lines contains two integers\nx_i (-100 <= x_i <= 100) and y_i (-50 <= y_i <= 50), where (x_i , y_i ) is the coordinates of the i-th endpoint.\nThe endpoints are given in increasing order of their x-coordinates, and no couple of endpoints shares the\nsame x-coordinate value. The y-coordinates of the first and last endpoints are always zero.\n\nThe end of input is indicated by n = r = 0. This is not part of data sets, and hence should not be\nprocessed.", "output": "For each data set, your program should print the value of the autocorrelation function in a line. Each\nvalue may be printed with an arbitrary number of digits after the decimal point, but should not contain\nan error greater than 10^-4 .", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 1\n0 0\n1 1\n2 0\n11 1.5\n0 0\n2 7\n5 3\n7 8\n10 -5\n13 4\n15 -1\n17 3\n20 -7\n23 9\n24 0\n0 0\n output: 0.166666666666667\n165.213541666667"], "Pid": "p01159", "ProblemText": "Task Description: Nathan O. Davis is taking a class of signal processing as a student in engineering. Today 's topic of the\nclass was autocorrelation. It is a mathematical tool for analysis of signals represented by functions or\nseries of values. Autocorrelation gives correlation of a signal with itself. For a continuous real function\nf(x), the autocorrelation function R_f (r) is given by\n\nwhere r is a real number.\n\nThe professor teaching in the class presented an assignment today. This assignment requires students\nto make plots of the autocorrelation functions for given functions. Each function is piecewise linear and\ncontinuous for all real numbers. The figure below depicts one of those functions.\n\nFigure 1: An Example of Given Functions\nThe professor suggested use of computer programs, but unfortunately Nathan hates programming. So he\ncalls you for help, as he knows you are a great programmer. You are requested to write a program that\ncomputes the value of the autocorrelation function where a function f(x) and a parameter r are given as\nthe input. Since he is good at utilization of existing software, he could finish his assignment with your\nprogram.\nTask Input: The input consists of a series of data sets.\n\nThe first line of each data set contains an integer n (3 <= n <= 100) and a real number r (-100 <= r <= 100),\nwhere n denotes the number of endpoints forming sub-intervals in the function f(x), and r gives the\nparameter of the autocorrelation function R_f(r). The i-th of the following n lines contains two integers\nx_i (-100 <= x_i <= 100) and y_i (-50 <= y_i <= 50), where (x_i , y_i ) is the coordinates of the i-th endpoint.\nThe endpoints are given in increasing order of their x-coordinates, and no couple of endpoints shares the\nsame x-coordinate value. The y-coordinates of the first and last endpoints are always zero.\n\nThe end of input is indicated by n = r = 0. This is not part of data sets, and hence should not be\nprocessed.\nTask Output: For each data set, your program should print the value of the autocorrelation function in a line. Each\nvalue may be printed with an arbitrary number of digits after the decimal point, but should not contain\nan error greater than 10^-4 .\nTask Samples: input: 3 1\n0 0\n1 1\n2 0\n11 1.5\n0 0\n2 7\n5 3\n7 8\n10 -5\n13 4\n15 -1\n17 3\n20 -7\n23 9\n24 0\n0 0\n output: 0.166666666666667\n165.213541666667\n\n" }, { "title": "Problem F: It Prefokery Pio", "content": "You are a member of a secret society named Japanese Abekobe Group, which is called J. A. G. for short.\nThose who belong to this society often exchange encrypted messages. You received lots of encrypted\nmessages this morning, and you tried to decrypt them as usual. However, because you received so many\nand long messages today, you had to give up decrypting them by yourself. So you decided to decrypt\nthem with the help of a computer program that you are going to write.\n\nThe encryption scheme in J. A. G. utilizes palindromes. A palindrome is a word or phrase that reads\nthe same in either direction. For example, “MADAM”, “REVIVER” and “SUCCUS” are palindromes,\nwhile “ADAM”, “REVENGE” and “SOCCER” are not.\n\nSpecifically to this scheme, words and phrases made of only one or two letters are not regarded as\npalindromes. For example, “A” and “MM” are not regarded as palindromes.\n\nThe encryption scheme is quite simple: each message is encrypted by inserting extra letters in such a\nway that the longest one among all subsequences forming palindromes gives the original message. In\nother words, you can decrypt the message by extracting the longest palindrome subsequence. Here, a\nsubsequence means a new string obtained by picking up some letters from a string without altering the\nrelative positions of the remaining letters. For example, the longest palindrome subsequence of a string\n“YMAOKDOAMIMHAADAMMA” is “MADAMIMADAM” as indicated below by underline.\n\nNow you are ready for writing a program.", "constraint": "", "input": "The input consists of a series of data sets. Each data set contains a line made of up to 2,000 capital\nletters which represents an encrypted string.\n\nThe end of the input is indicated by EOF (end-of-file marker).", "output": "For each data set, write a decrypted message in a separate line. If there is more than one decrypted\nmessage possible (i. e. if there is more than one palindrome subsequence not shorter than any other ones),\nyou may write any of the possible messages.\n\nYou can assume that the length of the longest palindrome subsequence of each data set is always longer\nthan two letters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: YMAOKDOAMIMHAADAMMA\nLELVEEL\n output: MADAMIMADAM\nLEVEL"], "Pid": "p01160", "ProblemText": "Task Description: You are a member of a secret society named Japanese Abekobe Group, which is called J. A. G. for short.\nThose who belong to this society often exchange encrypted messages. You received lots of encrypted\nmessages this morning, and you tried to decrypt them as usual. However, because you received so many\nand long messages today, you had to give up decrypting them by yourself. So you decided to decrypt\nthem with the help of a computer program that you are going to write.\n\nThe encryption scheme in J. A. G. utilizes palindromes. A palindrome is a word or phrase that reads\nthe same in either direction. For example, “MADAM”, “REVIVER” and “SUCCUS” are palindromes,\nwhile “ADAM”, “REVENGE” and “SOCCER” are not.\n\nSpecifically to this scheme, words and phrases made of only one or two letters are not regarded as\npalindromes. For example, “A” and “MM” are not regarded as palindromes.\n\nThe encryption scheme is quite simple: each message is encrypted by inserting extra letters in such a\nway that the longest one among all subsequences forming palindromes gives the original message. In\nother words, you can decrypt the message by extracting the longest palindrome subsequence. Here, a\nsubsequence means a new string obtained by picking up some letters from a string without altering the\nrelative positions of the remaining letters. For example, the longest palindrome subsequence of a string\n“YMAOKDOAMIMHAADAMMA” is “MADAMIMADAM” as indicated below by underline.\n\nNow you are ready for writing a program.\nTask Input: The input consists of a series of data sets. Each data set contains a line made of up to 2,000 capital\nletters which represents an encrypted string.\n\nThe end of the input is indicated by EOF (end-of-file marker).\nTask Output: For each data set, write a decrypted message in a separate line. If there is more than one decrypted\nmessage possible (i. e. if there is more than one palindrome subsequence not shorter than any other ones),\nyou may write any of the possible messages.\n\nYou can assume that the length of the longest palindrome subsequence of each data set is always longer\nthan two letters.\nTask Samples: input: YMAOKDOAMIMHAADAMMA\nLELVEEL\n output: MADAMIMADAM\nLEVEL\n\n" }, { "title": "Problem G: Traffic", "content": "You are a resident of Kyoot (oh, well, it 's not a misspelling! ) city. All streets there are neatly built on a\ngrid; some streets run in a meridional (north-south) direction and others in a zonal (east-west) direction.\nThe streets that run from north to south are called avenues, whereas those which run from east to west\nare called drives.\n\nEvery avenue and drive in the city is numbered to distinguish one from another. The westernmost avenue\nis called the 1st avenue. The avenue which lies next to the 1st avenue is the 2nd avenue, and so forth.\nSimilarly, drives are numbered from south to north. The figure below illustrates this situation.\nFigure 1: The Road Map of the Kyoot City\n\nThere is an intersection with traffic signals to regulate traffic on each crossing point of an avenue and a\ndrive. Each traffic signal in this city has two lights. One of these lights is colored green, and means “you\nmay go”. The other is red, and means “you must stop here”. If you reached an intersection during the\nred light (including the case where the light turns to red on your arrival), you must stop and wait there\nuntil the light turns to green again. However, you do not have to wait in the case where the light has\njust turned to green when you arrived there.\n\nTraffic signals are controlled by a computer so that the lights for two different directions always show\ndifferent colors. Thus if the light for an avenue is green, then the light for a drive must be red, and vice\nversa. In order to avoid car crashes, they will never be green together. Nor will they be red together, for efficiency. So all the signals at one intersection turn simultaneously; no sooner does one signal turn to\nred than the other turns to green. Each signal has a prescribed time interval and permanently repeats\nthe cycle.\nFigure 2: Signal and Intersection\n\nBy the way, you are planning to visit your friend by car tomorrow. You want to see her as early as\npossible, so you are going to drive through the shortest route. However, due to existence of the traffic\nsignals, you cannot easily figure out which way to take (the city also has a very sophisticated camera\nnetwork to prevent crime or violation: the police would surely arrest you if you didn 't stop on the red\nlight! ). So you decided to write a program to calculate the shortest possible time to her house, given the\ntown map and the configuration of all traffic signals.\n\nYour car runs one unit distance in one unit time. Time needed to turn left or right, to begin moving,\nand to stop your car is negligible. You do not need to take other cars into consideration.", "constraint": "", "input": "The input consists of multiple test cases. Each test case is given in the format below:\n\nw h\nd_A, 1 d_A, 2 . . . d_A, w-1\nd_D, 1 d_D, 2 . . . d_D, h-1\nns_1,1 ew_1,1 s_1,1\n.\n.\n.\nns_w, 1 ew_w, 1 s_w, 1\nns_1,2 ew_1,2 s_1,2\n.\n.\n.\nns_w, h ew_w, h s_w, h\nx_s y_s\nx_d y_d\n\nTwo integers w and h (2 <= w, h <= 100) in the first line indicate the number of avenues and drives in the\ncity, respectively. The next two lines contain (w - 1) and (h - 1) integers, each of which specifies the\ndistance between two adjacent avenues and drives. It is guaranteed that 2 <= d_A, i , d_D, j <= 1,000.\n\nThe next (w * h) lines are the configuration of traffic signals. Three parameters ns_i, j, ew_i, j and s_i, j\ndescribe the traffic signal (i, j) which stands at the crossing point of the i-th avenue and the j-th drive.\nns_i, j and ew_i, j (1 <= ns_i, j, ew_i, j < 100) are time intervals for which the light for a meridional direction\nand a zonal direction is green, respectively. s_i, j is the initial state of the light: 0 indicates the light is\ngreen for a meridional direction, 1 for a zonal direction. All the traffic signal have just switched the state\nto s_i, j at your departure time.\n\nThe last two lines of a case specify the position of your house (x_s, y_s ) and your friend 's house (x_d, y_d ),\nrespectively. These coordinates are relative to the traffic signal (0,0). x-axis is parallel to the drives,\nand y-axis is parallel to the avenues. x-coordinate increases as you go east, and y-coordinate increases\nas you go north. You may assume that these positions are on streets and will never coincide with any\nintersection.\n\nAll parameters are integers and separated by a blank character.\n\nThe end of input is identified by a line containing two zeros. This is not a part of the input and should\nnot be processed.", "output": "For each test case, output a line containing the shortest possible time from your house to your friend 's\nhouse.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 4\n2 2 2\n2 2 2\n99 1 0\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n99 1 0\n99 1 0\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n99 1 0\n1 0\n1 6\n2 2\n10\n10\n5 5 0\n5 5 0\n5 5 0\n5 5 0\n5 0\n5 10\n0 0\n output: 28\n25"], "Pid": "p01161", "ProblemText": "Task Description: You are a resident of Kyoot (oh, well, it 's not a misspelling! ) city. All streets there are neatly built on a\ngrid; some streets run in a meridional (north-south) direction and others in a zonal (east-west) direction.\nThe streets that run from north to south are called avenues, whereas those which run from east to west\nare called drives.\n\nEvery avenue and drive in the city is numbered to distinguish one from another. The westernmost avenue\nis called the 1st avenue. The avenue which lies next to the 1st avenue is the 2nd avenue, and so forth.\nSimilarly, drives are numbered from south to north. The figure below illustrates this situation.\nFigure 1: The Road Map of the Kyoot City\n\nThere is an intersection with traffic signals to regulate traffic on each crossing point of an avenue and a\ndrive. Each traffic signal in this city has two lights. One of these lights is colored green, and means “you\nmay go”. The other is red, and means “you must stop here”. If you reached an intersection during the\nred light (including the case where the light turns to red on your arrival), you must stop and wait there\nuntil the light turns to green again. However, you do not have to wait in the case where the light has\njust turned to green when you arrived there.\n\nTraffic signals are controlled by a computer so that the lights for two different directions always show\ndifferent colors. Thus if the light for an avenue is green, then the light for a drive must be red, and vice\nversa. In order to avoid car crashes, they will never be green together. Nor will they be red together, for efficiency. So all the signals at one intersection turn simultaneously; no sooner does one signal turn to\nred than the other turns to green. Each signal has a prescribed time interval and permanently repeats\nthe cycle.\nFigure 2: Signal and Intersection\n\nBy the way, you are planning to visit your friend by car tomorrow. You want to see her as early as\npossible, so you are going to drive through the shortest route. However, due to existence of the traffic\nsignals, you cannot easily figure out which way to take (the city also has a very sophisticated camera\nnetwork to prevent crime or violation: the police would surely arrest you if you didn 't stop on the red\nlight! ). So you decided to write a program to calculate the shortest possible time to her house, given the\ntown map and the configuration of all traffic signals.\n\nYour car runs one unit distance in one unit time. Time needed to turn left or right, to begin moving,\nand to stop your car is negligible. You do not need to take other cars into consideration.\nTask Input: The input consists of multiple test cases. Each test case is given in the format below:\n\nw h\nd_A, 1 d_A, 2 . . . d_A, w-1\nd_D, 1 d_D, 2 . . . d_D, h-1\nns_1,1 ew_1,1 s_1,1\n.\n.\n.\nns_w, 1 ew_w, 1 s_w, 1\nns_1,2 ew_1,2 s_1,2\n.\n.\n.\nns_w, h ew_w, h s_w, h\nx_s y_s\nx_d y_d\n\nTwo integers w and h (2 <= w, h <= 100) in the first line indicate the number of avenues and drives in the\ncity, respectively. The next two lines contain (w - 1) and (h - 1) integers, each of which specifies the\ndistance between two adjacent avenues and drives. It is guaranteed that 2 <= d_A, i , d_D, j <= 1,000.\n\nThe next (w * h) lines are the configuration of traffic signals. Three parameters ns_i, j, ew_i, j and s_i, j\ndescribe the traffic signal (i, j) which stands at the crossing point of the i-th avenue and the j-th drive.\nns_i, j and ew_i, j (1 <= ns_i, j, ew_i, j < 100) are time intervals for which the light for a meridional direction\nand a zonal direction is green, respectively. s_i, j is the initial state of the light: 0 indicates the light is\ngreen for a meridional direction, 1 for a zonal direction. All the traffic signal have just switched the state\nto s_i, j at your departure time.\n\nThe last two lines of a case specify the position of your house (x_s, y_s ) and your friend 's house (x_d, y_d ),\nrespectively. These coordinates are relative to the traffic signal (0,0). x-axis is parallel to the drives,\nand y-axis is parallel to the avenues. x-coordinate increases as you go east, and y-coordinate increases\nas you go north. You may assume that these positions are on streets and will never coincide with any\nintersection.\n\nAll parameters are integers and separated by a blank character.\n\nThe end of input is identified by a line containing two zeros. This is not a part of the input and should\nnot be processed.\nTask Output: For each test case, output a line containing the shortest possible time from your house to your friend 's\nhouse.\nTask Samples: input: 4 4\n2 2 2\n2 2 2\n99 1 0\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n99 1 0\n99 1 0\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n1 99 1\n99 1 0\n1 0\n1 6\n2 2\n10\n10\n5 5 0\n5 5 0\n5 5 0\n5 5 0\n5 0\n5 10\n0 0\n output: 28\n25\n\n" }, { "title": "Problem I: The Extreme Slalom", "content": "Automobile Company Moving has developed a new ride for switchbacks. The most impressive feature of\nthis machine is its mobility that we can move and turn to any direction at the same speed.\n\nAs the promotion of the ride, the company started a new competition named the extreme slalom. A\ncourse of the extreme slalom consists of some gates numbered from 1. Each gate is represented by a line\nsegment. A rider starts at the first gate and runs to the last gate by going through or touching the gates\nin the order of their numbers. Going through or touching gates other than the target one is allowed but\nnot counted.\n\nYour team is going to participate at the next competition. To win the competition, it is quite important\nto run on the shortest path. Your task is to write a program that computes the shortest length to support\nyour colleagues.\nFigure 1: An Example Course for the Extreme Slalom", "constraint": "", "input": "The input consists of a number of courses.\n\nThe first line of a course is an integer indicating the number n (2 <= n <= 12) of gates. The following\nn lines specify the gates in the order of traversals. A line contains four integers x_1 , y_1 , x_2 , and y_2\n(0 <= x_1 , y_1 , x_2 , y_2 <= 100) specifying the two endpoints of the gate. You may assume that no couple of\ngates touch or intersect each other.\n\nThe end of the input is indicated by a line containing a single zero.", "output": "Print the shortest length out in one line for each course. You may print an arbitrary number of digits\nafter the decimal points provided that difference from the exact answer is not greater than 0.0001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n0 4 2 4\n0 2 2 0\n3 0 4 2\n6 2 6 0\n0\n output: 8.0000"], "Pid": "p01162", "ProblemText": "Task Description: Automobile Company Moving has developed a new ride for switchbacks. The most impressive feature of\nthis machine is its mobility that we can move and turn to any direction at the same speed.\n\nAs the promotion of the ride, the company started a new competition named the extreme slalom. A\ncourse of the extreme slalom consists of some gates numbered from 1. Each gate is represented by a line\nsegment. A rider starts at the first gate and runs to the last gate by going through or touching the gates\nin the order of their numbers. Going through or touching gates other than the target one is allowed but\nnot counted.\n\nYour team is going to participate at the next competition. To win the competition, it is quite important\nto run on the shortest path. Your task is to write a program that computes the shortest length to support\nyour colleagues.\nFigure 1: An Example Course for the Extreme Slalom\nTask Input: The input consists of a number of courses.\n\nThe first line of a course is an integer indicating the number n (2 <= n <= 12) of gates. The following\nn lines specify the gates in the order of traversals. A line contains four integers x_1 , y_1 , x_2 , and y_2\n(0 <= x_1 , y_1 , x_2 , y_2 <= 100) specifying the two endpoints of the gate. You may assume that no couple of\ngates touch or intersect each other.\n\nThe end of the input is indicated by a line containing a single zero.\nTask Output: Print the shortest length out in one line for each course. You may print an arbitrary number of digits\nafter the decimal points provided that difference from the exact answer is not greater than 0.0001.\nTask Samples: input: 4\n0 4 2 4\n0 2 2 0\n3 0 4 2\n6 2 6 0\n0\n output: 8.0000\n\n" }, { "title": "Problem A: Space Coconut Crab II", "content": "A space hunter, Ken Marineblue traveled the universe, looking for the space coconut crab. The\nspace coconut crab was a crustacean known to be the largest in the universe. It was said that\nthe space coconut crab had a body of more than 400 meters long and a leg span of no shorter\nthan 1000 meters long. Although there were numerous reports by people who saw the space\ncoconut crab, nobody have yet succeeded in capturing it.\n\nAfter years of his intensive research, Ken discovered an interesting habit of the space coconut\ncrab. Surprisingly, the space coconut crab went back and forth between the space and the\nhyperspace by phase drive, which was the latest warp technology. As we, human beings, was\nnot able to move to the hyperspace, he had to work out an elaborate plan to capture them.\nFortunately, he found that the coconut crab took a long time to move between the hyperspace\nand the space because it had to keep still in order to charge a sufficient amount of energy for\nphase drive. He thought that he could capture them immediately after the warp-out, as they\nmoved so slowly in the space.\n\nHe decided to predict from the amount of the charged energy the coordinates in the space\nwhere the space coconut crab would appear, as he could only observe the amount of the charged\nenergy by measuring the time spent for charging in the hyperspace. His recent spaceship,\nWeapon Breaker, was installed with an artificial intelligence system, CANEL. She analyzed the\naccumulated data and found another surprising fact; the space coconut crab always warped out\nnear to the center of a triangle that satisfied the following conditions:\n\neach vertex of the triangle was one of the planets in the universe;\n\nthe length of every side of the triangle was a prime number; and\n\nthe total length of the three sides of the triangle was equal to T, the time duration the\n space coconut crab had spent in charging energy in the hyperspace before moving to the\n space.\nCANEL also devised the method to determine the three planets comprising the triangle from\nthe amount of energy that the space coconut crab charged and the lengths of the triangle sides.\nHowever, the number of the candidate triangles might be more than one.\n\nKen decided to begin with calculating how many different triangles were possible, analyzing\nthe data he had obtained in the past research. Your job is to calculate the number of different\ntriangles which satisfies the conditions mentioned above, for each given T.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset comes with a line that contains a single\npositive integer T (1 <= T <= 30000).\n\nThe end of input is indicated by a line that contains a zero. This should not be processed.", "output": "For each dataset, print the number of different possible triangles in a line. Two triangles are\ndifferent if and only if they are not congruent.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\n12\n15\n777\n4999\n5000\n0\n output: 0\n1\n2\n110\n2780\n0"], "Pid": "p01163", "ProblemText": "Task Description: A space hunter, Ken Marineblue traveled the universe, looking for the space coconut crab. The\nspace coconut crab was a crustacean known to be the largest in the universe. It was said that\nthe space coconut crab had a body of more than 400 meters long and a leg span of no shorter\nthan 1000 meters long. Although there were numerous reports by people who saw the space\ncoconut crab, nobody have yet succeeded in capturing it.\n\nAfter years of his intensive research, Ken discovered an interesting habit of the space coconut\ncrab. Surprisingly, the space coconut crab went back and forth between the space and the\nhyperspace by phase drive, which was the latest warp technology. As we, human beings, was\nnot able to move to the hyperspace, he had to work out an elaborate plan to capture them.\nFortunately, he found that the coconut crab took a long time to move between the hyperspace\nand the space because it had to keep still in order to charge a sufficient amount of energy for\nphase drive. He thought that he could capture them immediately after the warp-out, as they\nmoved so slowly in the space.\n\nHe decided to predict from the amount of the charged energy the coordinates in the space\nwhere the space coconut crab would appear, as he could only observe the amount of the charged\nenergy by measuring the time spent for charging in the hyperspace. His recent spaceship,\nWeapon Breaker, was installed with an artificial intelligence system, CANEL. She analyzed the\naccumulated data and found another surprising fact; the space coconut crab always warped out\nnear to the center of a triangle that satisfied the following conditions:\n\neach vertex of the triangle was one of the planets in the universe;\n\nthe length of every side of the triangle was a prime number; and\n\nthe total length of the three sides of the triangle was equal to T, the time duration the\n space coconut crab had spent in charging energy in the hyperspace before moving to the\n space.\nCANEL also devised the method to determine the three planets comprising the triangle from\nthe amount of energy that the space coconut crab charged and the lengths of the triangle sides.\nHowever, the number of the candidate triangles might be more than one.\n\nKen decided to begin with calculating how many different triangles were possible, analyzing\nthe data he had obtained in the past research. Your job is to calculate the number of different\ntriangles which satisfies the conditions mentioned above, for each given T.\nTask Input: The input consists of multiple datasets. Each dataset comes with a line that contains a single\npositive integer T (1 <= T <= 30000).\n\nThe end of input is indicated by a line that contains a zero. This should not be processed.\nTask Output: For each dataset, print the number of different possible triangles in a line. Two triangles are\ndifferent if and only if they are not congruent.\nTask Samples: input: 10\n12\n15\n777\n4999\n5000\n0\n output: 0\n1\n2\n110\n2780\n0\n\n" }, { "title": "Problem B: Sort the Panels", "content": "There was an explorer Henry Nelson traveling all over the world. One day he reached an ancient\nbuilding. He decided to enter this building for his interest, but its entrance seemed to be locked\nby a strange security system.\n\nThere were some black and white panels placed on a line at equal intervals in front of the\nentrance, and a strange machine with a cryptogram attached. After a while, he managed to\nread this cryptogram: this entrance would be unlocked when the panels were rearranged in a\ncertain order, and he needed to use this special machine to change the order of panels.\n\nAll he could do with this machine was to swap arbitrary pairs of panels. Each swap could be\nperformed by the following steps:\n\nmove the machine to one panel and mark it;\n\nmove the machine to another panel and again mark it; then\n\nturn on a special switch of the machine to have the two marked panels swapped.\nIt was impossible to have more than two panels marked simultaneously. The marks would be\nerased every time the panels are swapped.\n\nHe had to change the order of panels by a number of swaps to enter the building. Unfortunately,\nhowever, the machine was so heavy that he didn 't want to move it more than needed. Then\nwhich steps could be the best?\n\nYour task is to write a program that finds the minimum cost needed to rearrange the panels,\nwhere moving the machine between adjacent panels is defined to require the cost of one. You\ncan arbitrarily choose the initial position of the machine, and don 't have to count the cost for\nmoving the machine to that position.", "constraint": "", "input": "The input consists of multiple datasets.\n\nEach dataset consists of three lines. The first line contains an integer N, which indicates the\nnumber of panels (2 <= N <= 16). The second and third lines contain N characters each,\nand describe the initial and final orders of the panels respectively. Each character in these descriptions is either ‘B ' (for black) or ‘W ' (for white) and denotes the color of the panel. The\npanels of the same color should not be distinguished.\n\nThe input is terminated by a line with a single zero.", "output": "For each dataset, output the minimum cost on a line. You can assume that there is at least one\nway to change the order of the panels from the initial one to the final one.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nWBWB\nBWBW\n8\nWWWWBWBB\nWWBBWBWW\n0\n output: 3\n9"], "Pid": "p01164", "ProblemText": "Task Description: There was an explorer Henry Nelson traveling all over the world. One day he reached an ancient\nbuilding. He decided to enter this building for his interest, but its entrance seemed to be locked\nby a strange security system.\n\nThere were some black and white panels placed on a line at equal intervals in front of the\nentrance, and a strange machine with a cryptogram attached. After a while, he managed to\nread this cryptogram: this entrance would be unlocked when the panels were rearranged in a\ncertain order, and he needed to use this special machine to change the order of panels.\n\nAll he could do with this machine was to swap arbitrary pairs of panels. Each swap could be\nperformed by the following steps:\n\nmove the machine to one panel and mark it;\n\nmove the machine to another panel and again mark it; then\n\nturn on a special switch of the machine to have the two marked panels swapped.\nIt was impossible to have more than two panels marked simultaneously. The marks would be\nerased every time the panels are swapped.\n\nHe had to change the order of panels by a number of swaps to enter the building. Unfortunately,\nhowever, the machine was so heavy that he didn 't want to move it more than needed. Then\nwhich steps could be the best?\n\nYour task is to write a program that finds the minimum cost needed to rearrange the panels,\nwhere moving the machine between adjacent panels is defined to require the cost of one. You\ncan arbitrarily choose the initial position of the machine, and don 't have to count the cost for\nmoving the machine to that position.\nTask Input: The input consists of multiple datasets.\n\nEach dataset consists of three lines. The first line contains an integer N, which indicates the\nnumber of panels (2 <= N <= 16). The second and third lines contain N characters each,\nand describe the initial and final orders of the panels respectively. Each character in these descriptions is either ‘B ' (for black) or ‘W ' (for white) and denotes the color of the panel. The\npanels of the same color should not be distinguished.\n\nThe input is terminated by a line with a single zero.\nTask Output: For each dataset, output the minimum cost on a line. You can assume that there is at least one\nway to change the order of the panels from the initial one to the final one.\nTask Samples: input: 4\nWBWB\nBWBW\n8\nWWWWBWBB\nWWBBWBWW\n0\n output: 3\n9\n\n" }, { "title": "Problem C: Disarmament of the Units", "content": "This is a story in a country far away. In this country, two armed groups, ACM and ICPC, have\nfought in the civil war for many years. However, today October 21, reconciliation was approved\nbetween them; they have marked a turning point in their histories.\n\nIn this country, there are a number of roads either horizontal or vertical, and a town is built on\nevery endpoint and every intersection of those roads (although only one town is built at each\nplace). Some towns have units of either ACM or ICPC. These units have become unneeded\nby the reconciliation. So, we should make them disarm in a verifiable way simultaneously. All\ndisarmament must be carried out at the towns designated for each group, and only one unit can\nbe disarmed at each town. Therefore, we need to move the units.\n\nThe command of this mission is entrusted to you. You can have only one unit moved by a\nsingle order, where the unit must move to another town directly connected by a single road.\nYou cannot make the next order to any unit until movement of the unit is completed. The unit\ncannot pass nor stay at any town another unit stays at. In addition, even though reconciliation\nwas approved, members of those units are still irritable enough to start battles. For these\nreasons, two units belonging to different groups may not stay at towns on the same road. You\nfurther have to order to the two groups alternatively, because ordering only to one group may\ncause their dissatisfaction. In spite of this restriction, you can order to either group first.\n\nYour job is to write a program to find the minimum number of orders required to complete the\nmission of disarmament.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nn m_A m_I\nrx_1,1 ry_1,1 rx_1,2 ry_1,2\n. . .\nrx_n, 1 ry_n, 1 rx_n, 2 ry_n, 2\nsx_A, 1 sy_A, 1\n. . .\nsx_A, mA sy_A, mA\nsx_I, 1 sy_I, 1\n. . .\nsx_I, mI sy_I, mI\ntx_A, 1 ty_A, 1\n. . .\ntx_A, mA ty_A, mA\ntx_I, 1 ty_I, 1\n. . .\ntx_I, mI ty_I, mI\n\nn is the number of roads. m_A and m_I are the number of units in ACM and ICPC respectively\n(m_A > 0, m_I > 0, m_A + m_B < 8). (rx_i, 1, ry_i, 1 ) and (rx_i, 2, ry_i, 2 ) indicate the two endpoints of the\ni-th road, which is always parallel to either x-axis or y-axis. A series of (sx_A, i, sy_A, i ) indicates\nthe coordinates of the towns where the ACM units initially stay, and a series of (sx_I, i, sy_I, i )\nindicates where the ICPC units initially stay. A series of (tx_A, i, ty_A, i ) indicates the coordinates\nof the towns where the ACM units can be disarmed, and a series of (tx_I, i , ty_I, i ) indicates where\nthe ICPC units can be disarmed.\n\nYou may assume the following:\n\n the number of towns, that is, the total number of coordinates where endpoints and/or\n intersections of the roads exist does not exceed 18;\n\n no two horizontal roads are connected nor ovarlapped; no two vertical roads, either;\n\n all the towns are connected by roads; and\n\n no pair of ACM and ICPC units initially stay in the towns on the same road.\nThe input is terminated by a line with triple zeros, which should not be processed.", "output": "For each dataset, print the minimum required number of orders in a line. It is guaranteed that\nthere is at least one way to complete the mission.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1 1\n0 0 2 0\n1 1 2 1\n1 2 3 2\n1 0 1 2\n2 0 2 2\n0 0\n3 2\n2 1\n1 2\n2 1 1\n1 0 1 2\n0 1 2 1\n1 0\n0 1\n1 0\n2 1\n2 1 1\n1 0 1 2\n0 1 2 1\n1 0\n0 1\n1 2\n2 1\n4 1 1\n0 0 2 0\n1 1 3 1\n1 0 1 1\n2 0 2 1\n0 0\n3 1\n1 0\n2 1\n5 1 1\n0 0 2 0\n1 1 2 1\n1 2 3 2\n1 0 1 2\n2 0 2 2\n0 0\n3 2\n3 2\n0 0\n8 3 3\n1 1 3 1\n0 2 4 2\n1 3 5 3\n2 4 4 4\n1 1 1 3\n2 0 2 4\n3 1 3 5\n4 2 4 4\n0 2\n1 1\n2 0\n3 5\n4 4\n5 3\n3 5\n4 4\n5 3\n0 2\n1 1\n2 0\n0 0 0\n output: 3\n1\n2\n2\n7\n18"], "Pid": "p01165", "ProblemText": "Task Description: This is a story in a country far away. In this country, two armed groups, ACM and ICPC, have\nfought in the civil war for many years. However, today October 21, reconciliation was approved\nbetween them; they have marked a turning point in their histories.\n\nIn this country, there are a number of roads either horizontal or vertical, and a town is built on\nevery endpoint and every intersection of those roads (although only one town is built at each\nplace). Some towns have units of either ACM or ICPC. These units have become unneeded\nby the reconciliation. So, we should make them disarm in a verifiable way simultaneously. All\ndisarmament must be carried out at the towns designated for each group, and only one unit can\nbe disarmed at each town. Therefore, we need to move the units.\n\nThe command of this mission is entrusted to you. You can have only one unit moved by a\nsingle order, where the unit must move to another town directly connected by a single road.\nYou cannot make the next order to any unit until movement of the unit is completed. The unit\ncannot pass nor stay at any town another unit stays at. In addition, even though reconciliation\nwas approved, members of those units are still irritable enough to start battles. For these\nreasons, two units belonging to different groups may not stay at towns on the same road. You\nfurther have to order to the two groups alternatively, because ordering only to one group may\ncause their dissatisfaction. In spite of this restriction, you can order to either group first.\n\nYour job is to write a program to find the minimum number of orders required to complete the\nmission of disarmament.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nn m_A m_I\nrx_1,1 ry_1,1 rx_1,2 ry_1,2\n. . .\nrx_n, 1 ry_n, 1 rx_n, 2 ry_n, 2\nsx_A, 1 sy_A, 1\n. . .\nsx_A, mA sy_A, mA\nsx_I, 1 sy_I, 1\n. . .\nsx_I, mI sy_I, mI\ntx_A, 1 ty_A, 1\n. . .\ntx_A, mA ty_A, mA\ntx_I, 1 ty_I, 1\n. . .\ntx_I, mI ty_I, mI\n\nn is the number of roads. m_A and m_I are the number of units in ACM and ICPC respectively\n(m_A > 0, m_I > 0, m_A + m_B < 8). (rx_i, 1, ry_i, 1 ) and (rx_i, 2, ry_i, 2 ) indicate the two endpoints of the\ni-th road, which is always parallel to either x-axis or y-axis. A series of (sx_A, i, sy_A, i ) indicates\nthe coordinates of the towns where the ACM units initially stay, and a series of (sx_I, i, sy_I, i )\nindicates where the ICPC units initially stay. A series of (tx_A, i, ty_A, i ) indicates the coordinates\nof the towns where the ACM units can be disarmed, and a series of (tx_I, i , ty_I, i ) indicates where\nthe ICPC units can be disarmed.\n\nYou may assume the following:\n\n the number of towns, that is, the total number of coordinates where endpoints and/or\n intersections of the roads exist does not exceed 18;\n\n no two horizontal roads are connected nor ovarlapped; no two vertical roads, either;\n\n all the towns are connected by roads; and\n\n no pair of ACM and ICPC units initially stay in the towns on the same road.\nThe input is terminated by a line with triple zeros, which should not be processed.\nTask Output: For each dataset, print the minimum required number of orders in a line. It is guaranteed that\nthere is at least one way to complete the mission.\nTask Samples: input: 5 1 1\n0 0 2 0\n1 1 2 1\n1 2 3 2\n1 0 1 2\n2 0 2 2\n0 0\n3 2\n2 1\n1 2\n2 1 1\n1 0 1 2\n0 1 2 1\n1 0\n0 1\n1 0\n2 1\n2 1 1\n1 0 1 2\n0 1 2 1\n1 0\n0 1\n1 2\n2 1\n4 1 1\n0 0 2 0\n1 1 3 1\n1 0 1 1\n2 0 2 1\n0 0\n3 1\n1 0\n2 1\n5 1 1\n0 0 2 0\n1 1 2 1\n1 2 3 2\n1 0 1 2\n2 0 2 2\n0 0\n3 2\n3 2\n0 0\n8 3 3\n1 1 3 1\n0 2 4 2\n1 3 5 3\n2 4 4 4\n1 1 1 3\n2 0 2 4\n3 1 3 5\n4 2 4 4\n0 2\n1 1\n2 0\n3 5\n4 4\n5 3\n3 5\n4 4\n5 3\n0 2\n1 1\n2 0\n0 0 0\n output: 3\n1\n2\n2\n7\n18\n\n" }, { "title": "Problem D: So Sleepy", "content": "You have an appointment to meet a friend of yours today, but you are so sleepy because you\ndidn 't sleep well last night.\n\nAs you will go by trains to the station for the rendezvous, you can have a sleep on a train. You\ncan start to sleep as soon as you get on a train and keep asleep just until you get off. However,\nbecause of your habitude, you can sleep only on one train on your way to the destination.\n\nGiven the time schedule of trains as well as your departure time and your appointed time, your\ntask is to write a program which outputs the longest possible time duration of your sleep in a\ntrain, under the condition that you can reach the destination by the appointed time.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset looks like below:\n\nS T\nD Time_D A Time_A\nN1\nK_1,1 Time_1,1\n. . .\nK_1, N1 Time_1, N1\nN_2\nK_2,1 Time_2,1\n. . .\nK_2, N2 Time_2, N2\n. . .\nN_T\nK_T, 1 Time_T, 1\n. . .\nK_T, NT Time_T, NT\n\nThe first line of each dataset contains S (1 <= S <= 1000) and T (0 <= T <= 100), which denote\nthe numbers of stations and trains respectively. The second line contains the departure station\n(D), the departure time (Time_D ), the appointed station (A), and the appointed time (Time_A ), in this order. Then T sets of time schedule for trains follow. On the first line of the i-th set,\nthere will be N_i which indicates the number of stations the i-th train stops at. Then N_i lines\nfollow, each of which contains the station identifier (K_i, j ) followed by the time when the train\nstops at (i. e. arrives at and/or departs from) that station (Time_i, j ).\n\nEach station has a unique identifier, which is an integer between 1 and S. Each time is given\nin the format hh: mm, where hh represents the two-digit hour ranging from “00” to “23”, and\nmm represents the two-digit minute from “00” to “59”.\nThe input is terminated by a line that contains two zeros.\n\nYou may assume the following:\n\n each train stops at two stations or more; \n\n each train never stops at the same station more than once;\n\n a train takes at least one minute from one station to the next;\n\n all the times that appear in each dataset are those of the same day; and\n\n as being an expert in transfer, you can catch other trains that depart at the time just you\n arrive the station.", "output": "For each dataset, your program must output the maximum time in minutes you can sleep if you\ncan reach to the destination station in time, or “impossible” (without the quotes) otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1 09:00 3 10:00\n3\n1 09:10\n2 09:30\n3 09:40\n3 2\n1 09:00 1 10:00\n3\n1 09:10\n2 09:30\n3 09:40\n3\n3 09:20\n2 09:30\n1 10:00\n1 0\n1 09:00 1 10:00\n1 0\n1 10:00 1 09:00\n3 1\n1 09:00 3 09:35\n3\n1 09:10\n2 09:30\n3 09:40\n4 3\n1 09:00 4 11:00\n3\n1 09:10\n2 09:20\n4 09:40\n3\n1 10:30\n3 10:40\n4 10:50\n4\n1 08:50\n2 09:30\n3 10:30\n4 11:10\n0 0\n output: 30\n30\n0\nimpossible\nimpossible\n60"], "Pid": "p01166", "ProblemText": "Task Description: You have an appointment to meet a friend of yours today, but you are so sleepy because you\ndidn 't sleep well last night.\n\nAs you will go by trains to the station for the rendezvous, you can have a sleep on a train. You\ncan start to sleep as soon as you get on a train and keep asleep just until you get off. However,\nbecause of your habitude, you can sleep only on one train on your way to the destination.\n\nGiven the time schedule of trains as well as your departure time and your appointed time, your\ntask is to write a program which outputs the longest possible time duration of your sleep in a\ntrain, under the condition that you can reach the destination by the appointed time.\nTask Input: The input consists of multiple datasets. Each dataset looks like below:\n\nS T\nD Time_D A Time_A\nN1\nK_1,1 Time_1,1\n. . .\nK_1, N1 Time_1, N1\nN_2\nK_2,1 Time_2,1\n. . .\nK_2, N2 Time_2, N2\n. . .\nN_T\nK_T, 1 Time_T, 1\n. . .\nK_T, NT Time_T, NT\n\nThe first line of each dataset contains S (1 <= S <= 1000) and T (0 <= T <= 100), which denote\nthe numbers of stations and trains respectively. The second line contains the departure station\n(D), the departure time (Time_D ), the appointed station (A), and the appointed time (Time_A ), in this order. Then T sets of time schedule for trains follow. On the first line of the i-th set,\nthere will be N_i which indicates the number of stations the i-th train stops at. Then N_i lines\nfollow, each of which contains the station identifier (K_i, j ) followed by the time when the train\nstops at (i. e. arrives at and/or departs from) that station (Time_i, j ).\n\nEach station has a unique identifier, which is an integer between 1 and S. Each time is given\nin the format hh: mm, where hh represents the two-digit hour ranging from “00” to “23”, and\nmm represents the two-digit minute from “00” to “59”.\nThe input is terminated by a line that contains two zeros.\n\nYou may assume the following:\n\n each train stops at two stations or more; \n\n each train never stops at the same station more than once;\n\n a train takes at least one minute from one station to the next;\n\n all the times that appear in each dataset are those of the same day; and\n\n as being an expert in transfer, you can catch other trains that depart at the time just you\n arrive the station.\nTask Output: For each dataset, your program must output the maximum time in minutes you can sleep if you\ncan reach to the destination station in time, or “impossible” (without the quotes) otherwise.\nTask Samples: input: 3 1\n1 09:00 3 10:00\n3\n1 09:10\n2 09:30\n3 09:40\n3 2\n1 09:00 1 10:00\n3\n1 09:10\n2 09:30\n3 09:40\n3\n3 09:20\n2 09:30\n1 10:00\n1 0\n1 09:00 1 10:00\n1 0\n1 10:00 1 09:00\n3 1\n1 09:00 3 09:35\n3\n1 09:10\n2 09:30\n3 09:40\n4 3\n1 09:00 4 11:00\n3\n1 09:10\n2 09:20\n4 09:40\n3\n1 10:30\n3 10:40\n4 10:50\n4\n1 08:50\n2 09:30\n3 10:30\n4 11:10\n0 0\n output: 30\n30\n0\nimpossible\nimpossible\n60\n\n" }, { "title": "Problem E: Alice in Foxland", "content": "- The world is made of foxes; people with watchful eyes will find foxes in every\nfragment of the world.\n\nDefoxyrenardnucleic Acids (or DNAs for short) and Renardnucleic Acids (or RNAs) are similar\norganic molecules contained in organisms. Each of those molecules consists of a sequence of 26\nkinds of nucleobases. We can represent such sequences as strings by having each lowercase letter\nfrom ‘a ' to ‘z ' denote one kind of nucleobase. The only difference between DNAs and RNAs is\nthe way of those nucleobases being bonded.\n\nIn the year of 2323, Prof. Fuchs discovered that DNAs including particular substrings act as\ncatalysts, that is, accelerate some chemical reactions. He further discovered that the reactions\nare accelerated as the DNAs have longer sequences. For example, DNAs including the sequence\n“fox” act as catalysts that accelerate dissolution of nitrogen oxides (NOx ). The DNAs “redfox”\nand “cutefoxes” are two of the instances, and the latter provides more acceleration than the\nformer. On the other hand, the DNA “foooox” will not be such a catalyst, since it does not\ninclude “fox” as a substring.\n\nDNAs can be easily obtained by extraction from some plants such as glory lilies. However,\nalmost all of extracted molecules have different sequences each other, and we can obtain very\nfew molecules that act as catalysts. From this background, many scientists have worked for\nfinding a way to obtain the demanded molecules.\n\nIn the year of 2369, Prof. Hu finally discovered the following process:\n\n Prepare two DNAs X and Y .\n\n Generate RNAs X' and Y' with their sequences copied from the DNAs X and Y respectively.\n\n Delete zero or more bases from X' using some chemicals to obtain an RNA X''.\n\n Also delete zero or more bases from Y' to obtain an RNA Y'' , which has the same sequence\n as X'' .\n\n Obtain a resulting DNA Z from the two RNAs X'' and Y''\n same sequence as X'' and Y''.\n\nFigure 1: New Method for Generation of DNAs\n\nThe point is use of RNAs. It is difficult to delete specific bases on DNAs but relatively easy on\nRNAs. On the other hand, since RNAs are less stable than DNAs, there is no known way to\nobtain RNAs directly from some organisms. This is why we obtain RNAs from DNAs.\n\nAlice is a researcher in Tail Environmental Natural Catalyst Organization. She is now requested\nto generate DNAs with particular substrings, applying Hu 's method to some pairs of DNAs.\nSince longer DNAs are preferred, she wants a means of knowing the longest possible DNAs. So\nshe asked you for help.\n\nYour task is to write a program that outputs the sequence of the longest possible DNA which\ncan be generated from the given pair of DNAs X and Y and contains the given substring C.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset consists of three lines. The first and\nsecond lines contain the sequences X and Y respectively. The third line contains the substring\nC. Each of the sequences and the substrings contains only lowercase letters (‘a '–‘z ') and has\nthe length between 1 and 1600 inclusive.\n\nThe input is terminated by a line with “*”.", "output": "For each dataset, output the longest sequence in a line. If DNAs with the substring C cannot\nbe obtained in any way, output “Impossible” instead. Any of them is acceptable in case there\nare two or more longest DNAs possible.", "content_img": true, "lang": "en", "error": false, "samples": ["input: czujthebdgfoliskax\nbdgchuptzefliskaox\nfox\nfennec\noinarisama\nxiaorong\ncustomizedrevisedfoooox\naccurateredundantfooooooooox\nfox\n*\n output: cutefox\nImpossible\ncuteredfox"], "Pid": "p01167", "ProblemText": "Task Description: - The world is made of foxes; people with watchful eyes will find foxes in every\nfragment of the world.\n\nDefoxyrenardnucleic Acids (or DNAs for short) and Renardnucleic Acids (or RNAs) are similar\norganic molecules contained in organisms. Each of those molecules consists of a sequence of 26\nkinds of nucleobases. We can represent such sequences as strings by having each lowercase letter\nfrom ‘a ' to ‘z ' denote one kind of nucleobase. The only difference between DNAs and RNAs is\nthe way of those nucleobases being bonded.\n\nIn the year of 2323, Prof. Fuchs discovered that DNAs including particular substrings act as\ncatalysts, that is, accelerate some chemical reactions. He further discovered that the reactions\nare accelerated as the DNAs have longer sequences. For example, DNAs including the sequence\n“fox” act as catalysts that accelerate dissolution of nitrogen oxides (NOx ). The DNAs “redfox”\nand “cutefoxes” are two of the instances, and the latter provides more acceleration than the\nformer. On the other hand, the DNA “foooox” will not be such a catalyst, since it does not\ninclude “fox” as a substring.\n\nDNAs can be easily obtained by extraction from some plants such as glory lilies. However,\nalmost all of extracted molecules have different sequences each other, and we can obtain very\nfew molecules that act as catalysts. From this background, many scientists have worked for\nfinding a way to obtain the demanded molecules.\n\nIn the year of 2369, Prof. Hu finally discovered the following process:\n\n Prepare two DNAs X and Y .\n\n Generate RNAs X' and Y' with their sequences copied from the DNAs X and Y respectively.\n\n Delete zero or more bases from X' using some chemicals to obtain an RNA X''.\n\n Also delete zero or more bases from Y' to obtain an RNA Y'' , which has the same sequence\n as X'' .\n\n Obtain a resulting DNA Z from the two RNAs X'' and Y''\n same sequence as X'' and Y''.\n\nFigure 1: New Method for Generation of DNAs\n\nThe point is use of RNAs. It is difficult to delete specific bases on DNAs but relatively easy on\nRNAs. On the other hand, since RNAs are less stable than DNAs, there is no known way to\nobtain RNAs directly from some organisms. This is why we obtain RNAs from DNAs.\n\nAlice is a researcher in Tail Environmental Natural Catalyst Organization. She is now requested\nto generate DNAs with particular substrings, applying Hu 's method to some pairs of DNAs.\nSince longer DNAs are preferred, she wants a means of knowing the longest possible DNAs. So\nshe asked you for help.\n\nYour task is to write a program that outputs the sequence of the longest possible DNA which\ncan be generated from the given pair of DNAs X and Y and contains the given substring C.\nTask Input: The input consists of multiple datasets. Each dataset consists of three lines. The first and\nsecond lines contain the sequences X and Y respectively. The third line contains the substring\nC. Each of the sequences and the substrings contains only lowercase letters (‘a '–‘z ') and has\nthe length between 1 and 1600 inclusive.\n\nThe input is terminated by a line with “*”.\nTask Output: For each dataset, output the longest sequence in a line. If DNAs with the substring C cannot\nbe obtained in any way, output “Impossible” instead. Any of them is acceptable in case there\nare two or more longest DNAs possible.\nTask Samples: input: czujthebdgfoliskax\nbdgchuptzefliskaox\nfox\nfennec\noinarisama\nxiaorong\ncustomizedrevisedfoooox\naccurateredundantfooooooooox\nfox\n*\n output: cutefox\nImpossible\ncuteredfox\n\n" }, { "title": "Problem F: Lying about Your Age", "content": "You have moved to a new town. As starting a new life, you have made up your mind to do\none thing: lying about your age. Since no person in this town knows your history, you don 't\nhave to worry about immediate exposure. Also, in order to ease your conscience somewhat,\nyou have decided to claim ages that represent your real ages when interpreted as the base-M\nnumbers (2 <= M <= 16). People will misunderstand your age as they interpret the claimed age\nas a decimal number (i. e. of the base 10).\n\nNeedless to say, you don 't want to have your real age revealed to the people in the future. So\nyou should claim only one age each year, it should contain digits of decimal numbers (i. e. ‘0 '\nthrough ‘9 '), and it should always be equal to or greater than that of the previous year (when\ninterpreted as decimal).\n\nHow old can you claim you are, after some years?", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is a single line that contains three integers\nA, B, and C, where A is the present real age (in decimal), B is the age you presently claim\n(which can be a non-decimal number), and C is the real age at which you are to find the age\nyou will claim (in decimal). It is guaranteed that 0 <= A < C <= 200, while B may contain up to\neight digits. No digits other than ‘0 ' through ‘9 ' appear in those numbers.\n\nThe end of input is indicated by A = B = C = -1, which should not be processed.", "output": "For each dataset, print in a line the minimum age you can claim when you become C years old.\nIn case the age you presently claim cannot be interpreted as your real age with the base from 2\nthrough 16, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 23 18 53\n46 30 47\n-1 -1 -1\n output: 49\n-1"], "Pid": "p01168", "ProblemText": "Task Description: You have moved to a new town. As starting a new life, you have made up your mind to do\none thing: lying about your age. Since no person in this town knows your history, you don 't\nhave to worry about immediate exposure. Also, in order to ease your conscience somewhat,\nyou have decided to claim ages that represent your real ages when interpreted as the base-M\nnumbers (2 <= M <= 16). People will misunderstand your age as they interpret the claimed age\nas a decimal number (i. e. of the base 10).\n\nNeedless to say, you don 't want to have your real age revealed to the people in the future. So\nyou should claim only one age each year, it should contain digits of decimal numbers (i. e. ‘0 '\nthrough ‘9 '), and it should always be equal to or greater than that of the previous year (when\ninterpreted as decimal).\n\nHow old can you claim you are, after some years?\nTask Input: The input consists of multiple datasets. Each dataset is a single line that contains three integers\nA, B, and C, where A is the present real age (in decimal), B is the age you presently claim\n(which can be a non-decimal number), and C is the real age at which you are to find the age\nyou will claim (in decimal). It is guaranteed that 0 <= A < C <= 200, while B may contain up to\neight digits. No digits other than ‘0 ' through ‘9 ' appear in those numbers.\n\nThe end of input is indicated by A = B = C = -1, which should not be processed.\nTask Output: For each dataset, print in a line the minimum age you can claim when you become C years old.\nIn case the age you presently claim cannot be interpreted as your real age with the base from 2\nthrough 16, print -1 instead.\nTask Samples: input: 23 18 53\n46 30 47\n-1 -1 -1\n output: 49\n-1\n\n" }, { "title": "Problem G: Turn Polygons", "content": "HCII, the health committee for interstellar intelligence, aims to take care of the health of every\ninterstellar intelligence.\n\nStaff of HCII uses a special equipment for health checks of patients. This equipment looks like a\npolygon-shaped room with plenty of instruments. The staff puts a patient into the equipment,\nthen the equipment rotates clockwise to diagnose the patient from various angles. It fits many\nspecies without considering the variety of shapes, but not suitable for big patients. Furthermore,\neven if it fits the patient, it can hit the patient during rotation.\nFigure 1: The Equipment used by HCII\n\nThe interior shape of the equipment is a polygon with M vertices, and the shape of patients\nis a convex polygon with N vertices. Your job is to calculate how much you can rotate the\nequipment clockwise without touching the patient, and output the angle in degrees.", "constraint": "", "input": "The input consists of multiple data sets, followed by a line containing “0 0”. Each data set is\ngiven as follows:\n\nM N\npx_1 py_1 px_2 py_2 . . . px_M py_M\nqx_1 qy_1 qx_2 qy_2 . . . qx_N qy_N\ncx cy\n\nThe first line contains two integers M and N (3 <= M, N <= 10). The second line contains 2M\nintegers, where (px_j , py_j ) are the coordinates of the j-th vertex of the equipment. The third\nline contains 2N integers, where (qx_j , qy_j ) are the coordinates of the j-th vertex of the patient.\nThe fourth line contains two integers cx and cy, which indicate the coordinates of the center of\nrotation.\n\nAll the coordinates are between -1000 and 1000, inclusive. The vertices of each polygon are\ngiven in counterclockwise order.\n\nAt the initial state, the patient is inside the equipment, and they don 't intersect each other.\nYou may assume that the equipment doesn 't approach patients closer than 10^-6 without hitting\npatients, and that the equipment gets the patient to stick out by the length greater than 10^-6\nwhenever the equipment keeps its rotation after hitting the patient.", "output": "For each data set, print the angle in degrees in a line. Each angle should be given as a decimal\nwith an arbitrary number of fractional digits, and with an absolute error of at most 10^-7 .\n\nIf the equipment never hit the patient during the rotation, print 360 as the angle.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 4\n0 0 20 0 20 10 0 10 1 5\n10 3 12 5 10 7 8 5\n10 5\n4 3\n0 0 10 0 10 5 0 5\n3 1 6 1 5 4\n0 0\n5 3\n0 0 10 0 10 10 0 10 3 5\n1 1 4 1 4 6\n0 0\n0 0\n output: 360.0000000\n12.6803835\n3.3722867"], "Pid": "p01169", "ProblemText": "Task Description: HCII, the health committee for interstellar intelligence, aims to take care of the health of every\ninterstellar intelligence.\n\nStaff of HCII uses a special equipment for health checks of patients. This equipment looks like a\npolygon-shaped room with plenty of instruments. The staff puts a patient into the equipment,\nthen the equipment rotates clockwise to diagnose the patient from various angles. It fits many\nspecies without considering the variety of shapes, but not suitable for big patients. Furthermore,\neven if it fits the patient, it can hit the patient during rotation.\nFigure 1: The Equipment used by HCII\n\nThe interior shape of the equipment is a polygon with M vertices, and the shape of patients\nis a convex polygon with N vertices. Your job is to calculate how much you can rotate the\nequipment clockwise without touching the patient, and output the angle in degrees.\nTask Input: The input consists of multiple data sets, followed by a line containing “0 0”. Each data set is\ngiven as follows:\n\nM N\npx_1 py_1 px_2 py_2 . . . px_M py_M\nqx_1 qy_1 qx_2 qy_2 . . . qx_N qy_N\ncx cy\n\nThe first line contains two integers M and N (3 <= M, N <= 10). The second line contains 2M\nintegers, where (px_j , py_j ) are the coordinates of the j-th vertex of the equipment. The third\nline contains 2N integers, where (qx_j , qy_j ) are the coordinates of the j-th vertex of the patient.\nThe fourth line contains two integers cx and cy, which indicate the coordinates of the center of\nrotation.\n\nAll the coordinates are between -1000 and 1000, inclusive. The vertices of each polygon are\ngiven in counterclockwise order.\n\nAt the initial state, the patient is inside the equipment, and they don 't intersect each other.\nYou may assume that the equipment doesn 't approach patients closer than 10^-6 without hitting\npatients, and that the equipment gets the patient to stick out by the length greater than 10^-6\nwhenever the equipment keeps its rotation after hitting the patient.\nTask Output: For each data set, print the angle in degrees in a line. Each angle should be given as a decimal\nwith an arbitrary number of fractional digits, and with an absolute error of at most 10^-7 .\n\nIf the equipment never hit the patient during the rotation, print 360 as the angle.\nTask Samples: input: 5 4\n0 0 20 0 20 10 0 10 1 5\n10 3 12 5 10 7 8 5\n10 5\n4 3\n0 0 10 0 10 5 0 5\n3 1 6 1 5 4\n0 0\n5 3\n0 0 10 0 10 10 0 10 3 5\n1 1 4 1 4 6\n0 0\n0 0\n output: 360.0000000\n12.6803835\n3.3722867\n\n" }, { "title": "Problem H: Robot's Crash", "content": "Prof. Jenifer A. Gibson is carrying out experiments with many robots. Since those robots are\nexpensive, she wants to avoid their crashes during her experiments at her all effort. So she asked\nyou, her assistant, as follows.\n\n“Suppose that we have n (2 <= n <= 100000) robots of the circular shape with the radius of r,\nand that they are placed on the xy-plane without overlaps. Each robot starts to move straight\nwith a velocity of either v or -v simultaneously, say, at the time of zero. The robots keep their\nmoving infinitely unless I stop them. I 'd like to know in advance if some robots will crash each\nother. The robots crash when their centers get closer than the distance of 2r. I 'd also like to\nknow the time of the first crash, if any, so I can stop the robots before the crash. Well, could\nyou please write a program for this purpose? ”", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nn\nvx vy\nr\nrx_1 ry_1 u_1\nrx_2 ry_2 u_2\n. . .\nrx_n ry_n u_n\n\nn is the number of robots. (vx, vy) denotes the vector of the velocity v. r is the radius of the\nrobots. (rx_i , ry_i ) denotes the coordinates of the center of the i-th robot. u_i denotes the moving\ndirection of the i-th robot, where 1 indicates the i-th robot moves with the velocity (vx , vy),\nand -1 indicates (-vx , -vy).\n\nAll the coordinates range from -1200 to 1200. Both vx and vy range from -1 to 1.\n\nYou may assume all the following hold for any pair of robots:\n\nthey must not be placed closer than the distance of (2r + 10^-8 ) at the initial state;\n\n they must get closer than the distance of (2r - 10^-8 ) if they crash each other at some\n point of time; and\n\n they must not get closer than the distance of (2r + 10^-8 ) if they don 't crash.\nThe input is terminated by a line that contains a zero. This should not be processed.", "output": "For each dataset, print the first crash time in a line, or “SAFE” if no pair of robots crashes each\nother. Each crash time should be given as a decimal with an arbitrary number of fractional\ndigits, and with an absolute error of at most 10^-4.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1.0 0.0\n0.5\n0.0 0.0 1\n2.0 0.0 -1\n2\n1.0 0.0\n0.5\n0.0 0.0 -1\n2.0 0.0 1\n0\n output: 0.500000\nSAFE"], "Pid": "p01170", "ProblemText": "Task Description: Prof. Jenifer A. Gibson is carrying out experiments with many robots. Since those robots are\nexpensive, she wants to avoid their crashes during her experiments at her all effort. So she asked\nyou, her assistant, as follows.\n\n“Suppose that we have n (2 <= n <= 100000) robots of the circular shape with the radius of r,\nand that they are placed on the xy-plane without overlaps. Each robot starts to move straight\nwith a velocity of either v or -v simultaneously, say, at the time of zero. The robots keep their\nmoving infinitely unless I stop them. I 'd like to know in advance if some robots will crash each\nother. The robots crash when their centers get closer than the distance of 2r. I 'd also like to\nknow the time of the first crash, if any, so I can stop the robots before the crash. Well, could\nyou please write a program for this purpose? ”\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nn\nvx vy\nr\nrx_1 ry_1 u_1\nrx_2 ry_2 u_2\n. . .\nrx_n ry_n u_n\n\nn is the number of robots. (vx, vy) denotes the vector of the velocity v. r is the radius of the\nrobots. (rx_i , ry_i ) denotes the coordinates of the center of the i-th robot. u_i denotes the moving\ndirection of the i-th robot, where 1 indicates the i-th robot moves with the velocity (vx , vy),\nand -1 indicates (-vx , -vy).\n\nAll the coordinates range from -1200 to 1200. Both vx and vy range from -1 to 1.\n\nYou may assume all the following hold for any pair of robots:\n\nthey must not be placed closer than the distance of (2r + 10^-8 ) at the initial state;\n\n they must get closer than the distance of (2r - 10^-8 ) if they crash each other at some\n point of time; and\n\n they must not get closer than the distance of (2r + 10^-8 ) if they don 't crash.\nThe input is terminated by a line that contains a zero. This should not be processed.\nTask Output: For each dataset, print the first crash time in a line, or “SAFE” if no pair of robots crashes each\nother. Each crash time should be given as a decimal with an arbitrary number of fractional\ndigits, and with an absolute error of at most 10^-4.\nTask Samples: input: 2\n1.0 0.0\n0.5\n0.0 0.0 1\n2.0 0.0 -1\n2\n1.0 0.0\n0.5\n0.0 0.0 -1\n2.0 0.0 1\n0\n output: 0.500000\nSAFE\n\n" }, { "title": "Problem A: Everlasting. . . ?", "content": "Everlasting Sa-Ga, a new, hot and very popular role-playing game, is out on October 19,2008.\nFans have been looking forward to a new title of Everlasting Sa-Ga.\n\nLittle Jimmy is in trouble. He is a seven-year-old boy, and he obtained the Everlasting Sa-Ga\nand is attempting to reach the end of the game before his friends. However, he is facing difficulty\nsolving the riddle of the first maze in this game -- Everlasting Sa-Ga is notorious in extremely\nhard riddles like Neverending Fantasy and Forever Quest.\n\nThe riddle is as follows. There are two doors on the last floor of the maze: the door to the\ntreasure repository and the gate to the hell. If he wrongly opens the door to the hell, the game\nis over and his save data will be deleted. Therefore, he should never open the wrong door.\n\nSo now, how can he find the door to the next stage? There is a positive integer given for each\ndoor -- it is a great hint to this riddle. The door to the treasure repository has the integer that\ngives the larger key number. The key number of a positive integer n is the largest prime factor\nminus the total sum of any other prime factors, where the prime factors are the prime numbers\nthat divide into n without leaving a remainder. Note that each prime factor should be counted\nonly once.\n\nAs an example, suppose there are doors with integers 30 and 20 respectively. Since 30 has three\nprime factors 2,3 and 5, its key number is 5 - (2 + 3) = 0. Similarly, since 20 has two prime\nfactors 2 and 5, its key number 20 is 5 - 2 = 3. Jimmy therefore should open the door with 20.\n\nYour job is to write a program to help Jimmy by solving this riddle.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset consists of a line that contains two integers a\nand b separated by a space (2 <= a, b <= 10^6 ). It is guaranteed that key numbers of these integers\nare always different.\n\nThe input is terminated by a line with two zeros. This line is not part of any datasets and thus\nshould not be processed.", "output": "For each dataset, print in a line ‘a ' (without quotes) if the door with the integer a is connected\nto the treasure repository; print ‘b ' otherwise. No extra space or character is allowed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 15\n30 20\n0 0\n output: a\nb"], "Pid": "p01171", "ProblemText": "Task Description: Everlasting Sa-Ga, a new, hot and very popular role-playing game, is out on October 19,2008.\nFans have been looking forward to a new title of Everlasting Sa-Ga.\n\nLittle Jimmy is in trouble. He is a seven-year-old boy, and he obtained the Everlasting Sa-Ga\nand is attempting to reach the end of the game before his friends. However, he is facing difficulty\nsolving the riddle of the first maze in this game -- Everlasting Sa-Ga is notorious in extremely\nhard riddles like Neverending Fantasy and Forever Quest.\n\nThe riddle is as follows. There are two doors on the last floor of the maze: the door to the\ntreasure repository and the gate to the hell. If he wrongly opens the door to the hell, the game\nis over and his save data will be deleted. Therefore, he should never open the wrong door.\n\nSo now, how can he find the door to the next stage? There is a positive integer given for each\ndoor -- it is a great hint to this riddle. The door to the treasure repository has the integer that\ngives the larger key number. The key number of a positive integer n is the largest prime factor\nminus the total sum of any other prime factors, where the prime factors are the prime numbers\nthat divide into n without leaving a remainder. Note that each prime factor should be counted\nonly once.\n\nAs an example, suppose there are doors with integers 30 and 20 respectively. Since 30 has three\nprime factors 2,3 and 5, its key number is 5 - (2 + 3) = 0. Similarly, since 20 has two prime\nfactors 2 and 5, its key number 20 is 5 - 2 = 3. Jimmy therefore should open the door with 20.\n\nYour job is to write a program to help Jimmy by solving this riddle.\nTask Input: The input is a sequence of datasets. Each dataset consists of a line that contains two integers a\nand b separated by a space (2 <= a, b <= 10^6 ). It is guaranteed that key numbers of these integers\nare always different.\n\nThe input is terminated by a line with two zeros. This line is not part of any datasets and thus\nshould not be processed.\nTask Output: For each dataset, print in a line ‘a ' (without quotes) if the door with the integer a is connected\nto the treasure repository; print ‘b ' otherwise. No extra space or character is allowed.\nTask Samples: input: 10 15\n30 20\n0 0\n output: a\nb\n\n" }, { "title": "Problem B: Headstrong Student", "content": "You are a teacher at a cram school for elementary school pupils.\n\nOne day, you showed your students how to calculate division of fraction in a class of mathematics.\nYour lesson was kind and fluent, and it seemed everything was going so well - except for one\nthing. After some experiences, a student Max got so curious about how precise he could compute\nthe quotient. He tried many divisions asking you for a help, and finally found a case where\nthe answer became an infinite fraction. He was fascinated with such a case, so he continued\ncomputing the answer. But it was clear for you the answer was an infinite fraction - no matter\nhow many digits he computed, he wouldn 't reach the end.\n\nSince you have many other things to tell in today 's class, you can 't leave this as it is. So you\ndecided to use a computer to calculate the answer in turn of him. Actually you succeeded to\npersuade him that he was going into a loop, so it was enough for him to know how long he could\ncompute before entering a loop.\n\nYour task now is to write a program which computes where the recurring part starts and the\nlength of the recurring part, for given dividend/divisor pairs. All computation should be done\nin decimal numbers. If the specified dividend/divisor pair gives a finite fraction, your program\nshould treat the length of the recurring part as 0.", "constraint": "", "input": "The input consists of multiple datasets. Each line of the input describes a dataset. A dataset\nconsists of two positive integers x and y, which specifies the dividend and the divisor, respectively.\nYou may assume that 1 <= x < y <= 1,000,000.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of datasets\nand should not be processed.", "output": "For each dataset, your program should output a line containing two integers separated by exactly\none blank character.\n\nThe former describes the number of digits after the decimal point before the recurring part\nstarts. And the latter describes the length of the recurring part.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3\n1 6\n3 5\n2 200\n25 99\n0 0\n output: 0 1\n1 1\n1 0\n2 0\n0 2"], "Pid": "p01172", "ProblemText": "Task Description: You are a teacher at a cram school for elementary school pupils.\n\nOne day, you showed your students how to calculate division of fraction in a class of mathematics.\nYour lesson was kind and fluent, and it seemed everything was going so well - except for one\nthing. After some experiences, a student Max got so curious about how precise he could compute\nthe quotient. He tried many divisions asking you for a help, and finally found a case where\nthe answer became an infinite fraction. He was fascinated with such a case, so he continued\ncomputing the answer. But it was clear for you the answer was an infinite fraction - no matter\nhow many digits he computed, he wouldn 't reach the end.\n\nSince you have many other things to tell in today 's class, you can 't leave this as it is. So you\ndecided to use a computer to calculate the answer in turn of him. Actually you succeeded to\npersuade him that he was going into a loop, so it was enough for him to know how long he could\ncompute before entering a loop.\n\nYour task now is to write a program which computes where the recurring part starts and the\nlength of the recurring part, for given dividend/divisor pairs. All computation should be done\nin decimal numbers. If the specified dividend/divisor pair gives a finite fraction, your program\nshould treat the length of the recurring part as 0.\nTask Input: The input consists of multiple datasets. Each line of the input describes a dataset. A dataset\nconsists of two positive integers x and y, which specifies the dividend and the divisor, respectively.\nYou may assume that 1 <= x < y <= 1,000,000.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of datasets\nand should not be processed.\nTask Output: For each dataset, your program should output a line containing two integers separated by exactly\none blank character.\n\nThe former describes the number of digits after the decimal point before the recurring part\nstarts. And the latter describes the length of the recurring part.\nTask Samples: input: 1 3\n1 6\n3 5\n2 200\n25 99\n0 0\n output: 0 1\n1 1\n1 0\n2 0\n0 2\n\n" }, { "title": "Problem C: Dig or Climb", "content": "Benjamin Forest VIII is a king of a country. One of his best friends Nod lives in a village far from\nhis castle. Nod gets seriously sick and is on the verge of death. Benjamin orders his subordinate\nRed to bring good medicine for him as soon as possible. However, there is no road from the\ncastle to the village. Therefore, Red needs to climb over mountains and across canyons to reach\nthe village. He has decided to get to the village on the shortest path on a map, that is, he will\nmove on the straight line between the castle and the village. Then his way can be considered as\npolyline with n points (x_1, y_1) . . . (x_n , y_n ) as illustlated in the following figure.\nFigure 1: An example route from the castle to the village\n\nHere, x_i indicates the distance between the castle and the point i, as the crow flies, and y_i\nindicates the height of the point i. The castle is located on the point (x_1 , y_1 ), and the village is\nlocated on the point (x_n , y_n).\n\nRed can walk in speed v_w . Also, since he has a skill to cut a tunnel through a mountain\nhorizontally, he can move inside the mountain in speed v_c.\n\nYour job is to write a program to the minimum time to get to the village.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nv_w v_c\nx_1 y_1\n. . .\nx_n y_n\n\nYou may assume all the following: n <= 1,000,1 <= v_w, v_c <= 10, -10,000 <= x_i, y_i <= 10,000, and\nx_i < x_j for all i < j.\n\nThe input is terminated in case of n = 0. This is not part of any datasets and thus should not\nbe processed.", "output": "For each dataset, you should print the minimum time required to get to the village in a line.\nEach minimum time should be given as a decimal with an arbitrary number of fractional digits\nand with an absolute error of at most 10^-6 . No extra space or character is allowed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n2 1\n0 0\n50 50\n100 0\n3\n1 1\n0 0\n50 50\n100 0\n3\n1 2\n0 0\n50 50\n100 0\n3\n2 1\n0 0\n100 100\n150 50\n6\n1 2\n0 0\n50 50\n100 0\n150 0\n200 50\n250 0\n0\n output: 70.710678\n100.000000\n50.000000\n106.066017\n150.000000"], "Pid": "p01173", "ProblemText": "Task Description: Benjamin Forest VIII is a king of a country. One of his best friends Nod lives in a village far from\nhis castle. Nod gets seriously sick and is on the verge of death. Benjamin orders his subordinate\nRed to bring good medicine for him as soon as possible. However, there is no road from the\ncastle to the village. Therefore, Red needs to climb over mountains and across canyons to reach\nthe village. He has decided to get to the village on the shortest path on a map, that is, he will\nmove on the straight line between the castle and the village. Then his way can be considered as\npolyline with n points (x_1, y_1) . . . (x_n , y_n ) as illustlated in the following figure.\nFigure 1: An example route from the castle to the village\n\nHere, x_i indicates the distance between the castle and the point i, as the crow flies, and y_i\nindicates the height of the point i. The castle is located on the point (x_1 , y_1 ), and the village is\nlocated on the point (x_n , y_n).\n\nRed can walk in speed v_w . Also, since he has a skill to cut a tunnel through a mountain\nhorizontally, he can move inside the mountain in speed v_c.\n\nYour job is to write a program to the minimum time to get to the village.\nTask Input: The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nv_w v_c\nx_1 y_1\n. . .\nx_n y_n\n\nYou may assume all the following: n <= 1,000,1 <= v_w, v_c <= 10, -10,000 <= x_i, y_i <= 10,000, and\nx_i < x_j for all i < j.\n\nThe input is terminated in case of n = 0. This is not part of any datasets and thus should not\nbe processed.\nTask Output: For each dataset, you should print the minimum time required to get to the village in a line.\nEach minimum time should be given as a decimal with an arbitrary number of fractional digits\nand with an absolute error of at most 10^-6 . No extra space or character is allowed.\nTask Samples: input: 3\n2 1\n0 0\n50 50\n100 0\n3\n1 1\n0 0\n50 50\n100 0\n3\n1 2\n0 0\n50 50\n100 0\n3\n2 1\n0 0\n100 100\n150 50\n6\n1 2\n0 0\n50 50\n100 0\n150 0\n200 50\n250 0\n0\n output: 70.710678\n100.000000\n50.000000\n106.066017\n150.000000\n\n" }, { "title": "Problem D: Rotation Estimation", "content": "Mr. Nod is an astrologist and has defined a new constellation. He took two photos of the\nconstellation to foretell a future of his friend. The constellation consists of n stars. The shape\nof the constellation in these photos are the same, but the angle of them are different because\nthese photos were taken on a different day. He foretells a future by the difference of the angle\nof them.\n\nYour job is to write a program to calculate the difference of the angle of two constellation.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nx_1,1 y_1,1\n. . .\nx_1, n y_1, n\nx_2,1 y_2,1\n. . .\nx_2, n y_2, n\n\nThe first line of each dataset contains a positive integers n (n <= 1,000). The next n lines contain\ntwo real numbers x_1, i and y_1, i (|x_1, i|, |y_1, i| <= 100), where (x_1, i , y_1, i) denotes the coordinates of\nthe i-th star of the constellation in the first photo. The next n lines contain two real numbers\nx_2, i and y_2, i (|x_2, i|, |y_2, i| <= 100), where (x_2, i , y_2, i ) denotes the coordinates of the i-th star of the\nconstellation in the second photo.\n\nNote that the ordering of the stars does not matter for the sameness. It is guaranteed that\ndistance between every pair of stars in each photo is larger than 10^-5.\n\nThe input is terminated in case of n = 0. This is not part of any datasets and thus should not\nbe processed.", "output": "For each dataset, you should print a non-negative real number which is the difference of the\nangle of the constellation in the first photo and in the second photo. The difference should be in radian, and should not be negative. If there are two or more solutions, you should print\nthe smallest one. The difference may be printed with any number of digits after decimal point,\nprovided the absolute error does not exceed 10^-7. No extra space or character is allowed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0.0 0.0\n1.0 1.0\n0.0 1.0\n3.0 3.0\n2.0 2.0\n3.0 2.0\n0\n output: 3.14159265359"], "Pid": "p01174", "ProblemText": "Task Description: Mr. Nod is an astrologist and has defined a new constellation. He took two photos of the\nconstellation to foretell a future of his friend. The constellation consists of n stars. The shape\nof the constellation in these photos are the same, but the angle of them are different because\nthese photos were taken on a different day. He foretells a future by the difference of the angle\nof them.\n\nYour job is to write a program to calculate the difference of the angle of two constellation.\nTask Input: The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nx_1,1 y_1,1\n. . .\nx_1, n y_1, n\nx_2,1 y_2,1\n. . .\nx_2, n y_2, n\n\nThe first line of each dataset contains a positive integers n (n <= 1,000). The next n lines contain\ntwo real numbers x_1, i and y_1, i (|x_1, i|, |y_1, i| <= 100), where (x_1, i , y_1, i) denotes the coordinates of\nthe i-th star of the constellation in the first photo. The next n lines contain two real numbers\nx_2, i and y_2, i (|x_2, i|, |y_2, i| <= 100), where (x_2, i , y_2, i ) denotes the coordinates of the i-th star of the\nconstellation in the second photo.\n\nNote that the ordering of the stars does not matter for the sameness. It is guaranteed that\ndistance between every pair of stars in each photo is larger than 10^-5.\n\nThe input is terminated in case of n = 0. This is not part of any datasets and thus should not\nbe processed.\nTask Output: For each dataset, you should print a non-negative real number which is the difference of the\nangle of the constellation in the first photo and in the second photo. The difference should be in radian, and should not be negative. If there are two or more solutions, you should print\nthe smallest one. The difference may be printed with any number of digits after decimal point,\nprovided the absolute error does not exceed 10^-7. No extra space or character is allowed.\nTask Samples: input: 3\n0.0 0.0\n1.0 1.0\n0.0 1.0\n3.0 3.0\n2.0 2.0\n3.0 2.0\n0\n output: 3.14159265359\n\n" }, { "title": "Problem E: Optimal Rest", "content": "Music Macro Language (MML) is a language for textual representation of musical scores. Although there are various dialects of MML, all of them provide a set of commands to describe\nscores, such as commands for notes, rests, octaves, volumes, and so forth.\n\nIn this problem, we focus on rests, i. e. intervals of silence. Each rest command consists of a\ncommand specifier ‘R ' followed by a duration specifier. Each duration specifier is basically one\nof the following numbers: ‘1 ', ‘2 ', ‘4 ', ‘8 ', ‘16 ', ‘32 ', and ‘64 ', where ‘1 ' denotes a whole (1), ‘2 '\na half (1/2), ‘4 ' a quarter (1/4), ‘8 ' an eighth (1/8), and so on. This number is called the base\nduration, and optionally followed by one or more dots. The first dot adds the duration by the\nhalf of the base duration. For example, ‘4. ' denotes the duration of ‘4 ' (a quarter) plus ‘8 ' (an\neighth, i. e. the half of a quarter), or simply 1.5 times as long as ‘4 '. In other words, ‘R4. ' is\nequivalent to ‘R4R8 '. In case with two or more dots, each extra dot extends the duration by the\nhalf of the previous one. Thus ‘4. . ' denotes the duration of ‘4 ' plus ‘8 ' plus ‘16 ', ‘4. . . ' denotes\nthe duration of ‘4 ' plus ‘8 ' plus ‘16 ' plus ‘32 ', and so on. The duration extended by dots cannot\nbe shorter than ‘64 '. For exapmle, neither ‘64. ' nor ‘16. . . ' will be accepted since both of the\nlast dots indicate the half of ‘64 ' (i. e. the duration of 1/128).\n\nIn this problem, you are required to write a program that finds the shortest expressions equivalent\nto given sequences of rest commands.", "constraint": "", "input": "The input consists of multiple datasets. The first line of the input contains the number of\ndatasets N. Then, N datasets follow, each containing a sequence of valid rest commands in one\nline. You may assume that no sequence contains more than 100,000 characters.", "output": "For each dataset, your program should output the shortest expression in one line. If there are\nmultiple expressions of the shortest length, output the lexicographically smallest one.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nR2R2\nR1R2R4R8R16R32R64\nR1R4R16\n output: R1\nR1......\nR16R1R4"], "Pid": "p01175", "ProblemText": "Task Description: Music Macro Language (MML) is a language for textual representation of musical scores. Although there are various dialects of MML, all of them provide a set of commands to describe\nscores, such as commands for notes, rests, octaves, volumes, and so forth.\n\nIn this problem, we focus on rests, i. e. intervals of silence. Each rest command consists of a\ncommand specifier ‘R ' followed by a duration specifier. Each duration specifier is basically one\nof the following numbers: ‘1 ', ‘2 ', ‘4 ', ‘8 ', ‘16 ', ‘32 ', and ‘64 ', where ‘1 ' denotes a whole (1), ‘2 '\na half (1/2), ‘4 ' a quarter (1/4), ‘8 ' an eighth (1/8), and so on. This number is called the base\nduration, and optionally followed by one or more dots. The first dot adds the duration by the\nhalf of the base duration. For example, ‘4. ' denotes the duration of ‘4 ' (a quarter) plus ‘8 ' (an\neighth, i. e. the half of a quarter), or simply 1.5 times as long as ‘4 '. In other words, ‘R4. ' is\nequivalent to ‘R4R8 '. In case with two or more dots, each extra dot extends the duration by the\nhalf of the previous one. Thus ‘4. . ' denotes the duration of ‘4 ' plus ‘8 ' plus ‘16 ', ‘4. . . ' denotes\nthe duration of ‘4 ' plus ‘8 ' plus ‘16 ' plus ‘32 ', and so on. The duration extended by dots cannot\nbe shorter than ‘64 '. For exapmle, neither ‘64. ' nor ‘16. . . ' will be accepted since both of the\nlast dots indicate the half of ‘64 ' (i. e. the duration of 1/128).\n\nIn this problem, you are required to write a program that finds the shortest expressions equivalent\nto given sequences of rest commands.\nTask Input: The input consists of multiple datasets. The first line of the input contains the number of\ndatasets N. Then, N datasets follow, each containing a sequence of valid rest commands in one\nline. You may assume that no sequence contains more than 100,000 characters.\nTask Output: For each dataset, your program should output the shortest expression in one line. If there are\nmultiple expressions of the shortest length, output the lexicographically smallest one.\nTask Samples: input: 3\nR2R2\nR1R2R4R8R16R32R64\nR1R4R16\n output: R1\nR1......\nR16R1R4\n\n" }, { "title": "Problem F: Controlled Tournament", "content": "National Association of Tennis is planning to hold a tennis competition among professional\nplayers. The competition is going to be a knockout tournament, and you are assigned the task\nto make the arrangement of players in the tournament.\n\nYou are given the detailed report about all participants of the competition. The report contains\nthe results of recent matches between all pairs of the participants. Examining the data, you 've\nnoticed that it is only up to the opponent whether one player wins or not.\n\nSince one of your special friends are attending the competition, you want him to get the best\nprize. So you want to know the possibility where he wins the gold medal. However it is not so\neasy to figure out because there are many participants. You have decided to write a program\nwhich calculates the number of possible arrangements of tournament in which your friend wins\nthe gold medal.\n\nIn order to make your trick hidden from everyone, you need to avoid making a factitive tourna-\nment tree. So you have to minimize the height of your tournament tree.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the format as described below.\n\nN M\nR_11 R_12 . . . R_1N\nR_21 R_22 . . . R_2N\n. . .\nR_N1 R_N2 . . . R_NN\n\nN (2 <= N <= 16) is the number of player, and M (1 <= M <= N) is your friend 's ID (numbered\nfrom 1). R_ij is the result of a match between the i-th player and the j-th player. When i-th\nplayer always wins, R_ij = 1. Otherwise, R_ij = 0. It is guaranteed that the matrix is consistent:\nfor all i ! = j, R_ij = 0 if and only if R_ji = 1. The diagonal elements R_ii are just given for\nconvenience and are always 0.\n\nThe end of input is indicated by a line containing two zeros. This line is not a part of any\ndatasets and should not be processed.", "output": "For each dataset, your program should output in a line the number of possible tournaments in\nwhich your friend wins the first prize.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n0 1\n0 0\n2 1\n0 0\n1 0\n3 3\n0 1 1\n0 0 1\n0 0 0\n3 3\n0 1 0\n0 0 0\n1 1 0\n3 1\n0 1 0\n0 0 0\n1 1 0\n3 3\n0 1 0\n0 0 1\n1 0 0\n6 4\n0 0 0 0 0 1\n1 0 1 0 1 0\n1 0 0 1 1 0\n1 1 0 0 1 0\n1 0 0 0 0 0\n0 1 1 1 1 0\n7 2\n0 1 0 0 0 1 0\n0 0 1 0 1 1 1\n1 0 0 1 1 0 0\n1 1 0 0 0 1 0\n1 0 0 1 0 0 1\n0 0 1 0 1 0 0\n1 0 1 1 0 1 0\n8 6\n0 0 0 0 1 0 0 0\n1 0 1 1 0 0 0 0\n1 0 0 0 1 0 0 0\n1 0 1 0 0 1 0 1\n0 1 0 1 0 0 1 0\n1 1 1 0 1 0 0 1\n1 1 1 1 0 1 0 0\n1 1 1 0 1 0 1 0\n0 0\n output: 1\n0\n0\n3\n0\n1\n11\n139\n78"], "Pid": "p01176", "ProblemText": "Task Description: National Association of Tennis is planning to hold a tennis competition among professional\nplayers. The competition is going to be a knockout tournament, and you are assigned the task\nto make the arrangement of players in the tournament.\n\nYou are given the detailed report about all participants of the competition. The report contains\nthe results of recent matches between all pairs of the participants. Examining the data, you 've\nnoticed that it is only up to the opponent whether one player wins or not.\n\nSince one of your special friends are attending the competition, you want him to get the best\nprize. So you want to know the possibility where he wins the gold medal. However it is not so\neasy to figure out because there are many participants. You have decided to write a program\nwhich calculates the number of possible arrangements of tournament in which your friend wins\nthe gold medal.\n\nIn order to make your trick hidden from everyone, you need to avoid making a factitive tourna-\nment tree. So you have to minimize the height of your tournament tree.\nTask Input: The input consists of multiple datasets. Each dataset has the format as described below.\n\nN M\nR_11 R_12 . . . R_1N\nR_21 R_22 . . . R_2N\n. . .\nR_N1 R_N2 . . . R_NN\n\nN (2 <= N <= 16) is the number of player, and M (1 <= M <= N) is your friend 's ID (numbered\nfrom 1). R_ij is the result of a match between the i-th player and the j-th player. When i-th\nplayer always wins, R_ij = 1. Otherwise, R_ij = 0. It is guaranteed that the matrix is consistent:\nfor all i ! = j, R_ij = 0 if and only if R_ji = 1. The diagonal elements R_ii are just given for\nconvenience and are always 0.\n\nThe end of input is indicated by a line containing two zeros. This line is not a part of any\ndatasets and should not be processed.\nTask Output: For each dataset, your program should output in a line the number of possible tournaments in\nwhich your friend wins the first prize.\nTask Samples: input: 2 1\n0 1\n0 0\n2 1\n0 0\n1 0\n3 3\n0 1 1\n0 0 1\n0 0 0\n3 3\n0 1 0\n0 0 0\n1 1 0\n3 1\n0 1 0\n0 0 0\n1 1 0\n3 3\n0 1 0\n0 0 1\n1 0 0\n6 4\n0 0 0 0 0 1\n1 0 1 0 1 0\n1 0 0 1 1 0\n1 1 0 0 1 0\n1 0 0 0 0 0\n0 1 1 1 1 0\n7 2\n0 1 0 0 0 1 0\n0 0 1 0 1 1 1\n1 0 0 1 1 0 0\n1 1 0 0 0 1 0\n1 0 0 1 0 0 1\n0 0 1 0 1 0 0\n1 0 1 1 0 1 0\n8 6\n0 0 0 0 1 0 0 0\n1 0 1 1 0 0 0 0\n1 0 0 0 1 0 0 0\n1 0 1 0 0 1 0 1\n0 1 0 1 0 0 1 0\n1 1 1 0 1 0 0 1\n1 1 1 1 0 1 0 0\n1 1 1 0 1 0 1 0\n0 0\n output: 1\n0\n0\n3\n0\n1\n11\n139\n78\n\n" }, { "title": "Problem G: Entangled Tree", "content": "The electronics division in Ishimatsu Company consists of various development departments\nfor electronic devices including disks and storages, network devices, mobile phones, and many\nothers. Each department covers a wide range of products. For example, the department of disks\nand storages develops internal and external hard disk drives, USB thumb drives, solid-state\ndrives, and so on. This situation brings staff in the product management division difficulty\ncategorizing these numerous products because of their poor understanding of computer devices.\n\nOne day, a staff member suggested a tree-based diagram named a category diagram in order to\nmake their tasks easier. A category diagram is depicted as follows. Firstly, they prepare one\nlarge sheet of paper. Secondly, they write down the names of the development departments\non the upper side of the sheet. These names represent the start nodes of the diagram. Each\nstart node is connected to either a single split node or a single end node (these nodes will be\nmentioned soon later). Then they write down a number of questions that distinguish features\nof products in the middle, and these questions represent the split nodes of the diagram. Each\nsplit node is connected with other split nodes and end nodes, and each line from a split node\nis labeled with the answer to the question. Finally, they write down all category names on the\nlower side, which represents the end nodes.\n\nThe classification of each product is done like the following. They begin with the start node that\ncorresponds to the department developing the product. Visiting some split nodes, they traces\nthe lines down until they reach one of the end nodes labeled with a category name. Then they\nfind the product classified into the resultant category.\n\nThe visual appearance of a category diagram makes the diagram quite understandable even for\nnon-geek persons. However, product managers are not good at drawing the figures by hand, so\nmost of the diagrams were often messy due to many line crossings. For this reason, they hired\nyou, a talented programmer, to obtain the clean diagrams equivalent to their diagrams. Here,\nwe mean the clean diagrams as those with no line crossings.\n\nYour task is to write a program that finds the clean diagrams. For simplicity, we simply ignore\nthe questions of the split nodes, and use integers from 1 to N instead of the category names.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset follows the format below:\n\n N M Q\n split node info_1\n split node info_2\n . . .\n split node info_M\n query_1\n query_2\n . . .\n query_Q\n\nThe first line of each dataset contains three integers N (1 <= N <= 100000), M (0 <= M <= N - 1),\nand Q (1 <= Q <= 1000, Q <= N), representing the number of end nodes and split nodes, and the\nnumber of queries respectively. Then M lines describing the split nodes follow. Each split node\nis described in the format below:\n\n Y L label_1 label_2 . . .\n\nThe first two integers, Y (0 <= Y <= 10^9 ) and L, which indicates the y-coordinate where the\nsplit node locates (the smaller is the higher) and the size of a label list. After that, L integer\nnumbers of end node labels which directly or indirectly connected to the split node follow. This\nis a key information for node connections. A split node A is connected to another split node B\nif and only if both A and B refer (at least) one identical end node in their label lists, and the\ny-coordinate of B is the lowest of all split nodes referring identical end nodes and located below\nA. The split node is connected to the end node if and only if that is the lowest node among all\nnodes which contain the same label as the end node 's label. The start node is directly connected\nto the end node, if and only if the end node is connected to none of the split nodes.\n\nAfter the information of the category diagram, Q lines of integers follow. These integers indicate\nthe horizontal positions of the end nodes in the diagram. The leftmost position is numbered 1.\n\nThe input is terminated by the dataset with N = M = Q = 0, and this dataset should not be\nprocessed.", "output": "Your program must print the Q lines, each of which denotes the label of the end node at the\nposition indicated by the queries in the clean diagram. One blank line must follow after the\noutput for each dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 3\n10 2 1 2\n20 2 3 2\n1\n2\n3\n5 2 5\n10 3 1 2 4\n20 3 2 3 5\n1\n2\n3\n4\n5\n4 1 4\n10 2 1 4\n1\n2\n3\n4\n4 3 4\n30 2 1 4\n20 2 2 4\n10 2 3 4\n1\n2\n3\n4\n4 3 4\n10 2 1 4\n20 2 2 4\n30 2 3 4\n1\n2\n3\n4\n4 3 4\n10 2 1 2\n15 2 1 4\n20 2 2 3\n1\n2\n3\n4\n3 2 3\n10 2 2 3\n20 2 1 2\n1\n2\n3\n1 0 1\n1\n0 0 0\n output: 1\n2\n3\n\n1\n2\n3\n5\n4\n\n1\n4\n2\n3\n\n1\n4\n2\n3\n\n1\n2\n3\n4\n\n1\n4\n2\n3\n\n1\n2\n3\n\n1"], "Pid": "p01177", "ProblemText": "Task Description: The electronics division in Ishimatsu Company consists of various development departments\nfor electronic devices including disks and storages, network devices, mobile phones, and many\nothers. Each department covers a wide range of products. For example, the department of disks\nand storages develops internal and external hard disk drives, USB thumb drives, solid-state\ndrives, and so on. This situation brings staff in the product management division difficulty\ncategorizing these numerous products because of their poor understanding of computer devices.\n\nOne day, a staff member suggested a tree-based diagram named a category diagram in order to\nmake their tasks easier. A category diagram is depicted as follows. Firstly, they prepare one\nlarge sheet of paper. Secondly, they write down the names of the development departments\non the upper side of the sheet. These names represent the start nodes of the diagram. Each\nstart node is connected to either a single split node or a single end node (these nodes will be\nmentioned soon later). Then they write down a number of questions that distinguish features\nof products in the middle, and these questions represent the split nodes of the diagram. Each\nsplit node is connected with other split nodes and end nodes, and each line from a split node\nis labeled with the answer to the question. Finally, they write down all category names on the\nlower side, which represents the end nodes.\n\nThe classification of each product is done like the following. They begin with the start node that\ncorresponds to the department developing the product. Visiting some split nodes, they traces\nthe lines down until they reach one of the end nodes labeled with a category name. Then they\nfind the product classified into the resultant category.\n\nThe visual appearance of a category diagram makes the diagram quite understandable even for\nnon-geek persons. However, product managers are not good at drawing the figures by hand, so\nmost of the diagrams were often messy due to many line crossings. For this reason, they hired\nyou, a talented programmer, to obtain the clean diagrams equivalent to their diagrams. Here,\nwe mean the clean diagrams as those with no line crossings.\n\nYour task is to write a program that finds the clean diagrams. For simplicity, we simply ignore\nthe questions of the split nodes, and use integers from 1 to N instead of the category names.\nTask Input: The input consists of multiple datasets. Each dataset follows the format below:\n\n N M Q\n split node info_1\n split node info_2\n . . .\n split node info_M\n query_1\n query_2\n . . .\n query_Q\n\nThe first line of each dataset contains three integers N (1 <= N <= 100000), M (0 <= M <= N - 1),\nand Q (1 <= Q <= 1000, Q <= N), representing the number of end nodes and split nodes, and the\nnumber of queries respectively. Then M lines describing the split nodes follow. Each split node\nis described in the format below:\n\n Y L label_1 label_2 . . .\n\nThe first two integers, Y (0 <= Y <= 10^9 ) and L, which indicates the y-coordinate where the\nsplit node locates (the smaller is the higher) and the size of a label list. After that, L integer\nnumbers of end node labels which directly or indirectly connected to the split node follow. This\nis a key information for node connections. A split node A is connected to another split node B\nif and only if both A and B refer (at least) one identical end node in their label lists, and the\ny-coordinate of B is the lowest of all split nodes referring identical end nodes and located below\nA. The split node is connected to the end node if and only if that is the lowest node among all\nnodes which contain the same label as the end node 's label. The start node is directly connected\nto the end node, if and only if the end node is connected to none of the split nodes.\n\nAfter the information of the category diagram, Q lines of integers follow. These integers indicate\nthe horizontal positions of the end nodes in the diagram. The leftmost position is numbered 1.\n\nThe input is terminated by the dataset with N = M = Q = 0, and this dataset should not be\nprocessed.\nTask Output: Your program must print the Q lines, each of which denotes the label of the end node at the\nposition indicated by the queries in the clean diagram. One blank line must follow after the\noutput for each dataset.\nTask Samples: input: 3 2 3\n10 2 1 2\n20 2 3 2\n1\n2\n3\n5 2 5\n10 3 1 2 4\n20 3 2 3 5\n1\n2\n3\n4\n5\n4 1 4\n10 2 1 4\n1\n2\n3\n4\n4 3 4\n30 2 1 4\n20 2 2 4\n10 2 3 4\n1\n2\n3\n4\n4 3 4\n10 2 1 4\n20 2 2 4\n30 2 3 4\n1\n2\n3\n4\n4 3 4\n10 2 1 2\n15 2 1 4\n20 2 2 3\n1\n2\n3\n4\n3 2 3\n10 2 2 3\n20 2 1 2\n1\n2\n3\n1 0 1\n1\n0 0 0\n output: 1\n2\n3\n\n1\n2\n3\n5\n4\n\n1\n4\n2\n3\n\n1\n4\n2\n3\n\n1\n2\n3\n4\n\n1\n4\n2\n3\n\n1\n2\n3\n\n1\n\n" }, { "title": "Problem H: Ramen Shop", "content": "Ron is a master of a ramen shop.\n\nRecently, he has noticed some customers wait for a long time. This has been caused by lack of\nseats during lunch time. Customers loses their satisfaction if they waits for a long time, and\neven some of them will give up waiting and go away. For this reason, he has decided to increase\nseats in his shop. To determine how many seats are appropriate, he has asked you, an excellent\nprogrammer, to write a simulator of customer behavior.\n\nCustomers come to his shop in groups, each of which is associated with the following four\nparameters:\n\n T_i : when the group comes to the shop\n\n P_i : number of customers\n\n W_i : how long the group can wait for their seats\n\n E_i : how long the group takes for eating\nThe i-th group comes to the shop with P_i customers together at the time T_i . If P_i successive\nseats are available at that time, the group takes their seats immediately. Otherwise, they waits\nfor such seats being available. When the group fails to take their seats within the time W_i\n(inclusive) from their coming and strictly before the closing time, they give up waiting and go\naway. In addition, if there are other groups waiting, the new group cannot take their seats until\nthe earlier groups are taking seats or going away.\n\nThe shop has N counters numbered uniquely from 1 to N. The i-th counter has C_i seats. The\ngroup prefers “seats with a greater distance to the nearest group. ” Precisely, the group takes\ntheir seats according to the criteria listed below. Here, S_L denotes the number of successive\nempty seats on the left side of the group after their seating, and S_R the number on the right\nside. S_L and S_R are considered to be infinity if there are no other customers on the left side\nand on the right side respectively.\n\n Prefers seats maximizing min{S_L, S_R}.\n\n If there are multiple alternatives meeting the first criterion, prefers seats maximizing\n max{S_L, S_R}.\n\n If there are still multiple alternatives, prefers the counter of the smallest number.\n\n If there are still multiple alternatives, prefers the leftmost seats.\nWhen multiple groups are leaving the shop at the same time and some other group is waiting\nfor available seats, seat assignment for the waiting group should be made after all the finished\ngroups leave the shop.\n\nYour task is to calculate the average satisfaction over customers. The satisfaction of a customer\nin the i-th group is given as follows:\n\n If the group goes away without eating, -1.\n\n Otherwise, (W_i - t_i )/W_i where t_i is the actual waiting time for the i-th group (the value ranges between 0 to 1 inclusive).", "constraint": "", "input": "The input consists of multiple datasets.\n\nEach dataset has the following format:\n\n N M T\n C_1 C_2 . . . C_N\n T_1 P_1 W_1 E_1\n T_2 P_2 W_2 E_2\n . . .\n T_M P_M W_M E_M\n\nN indicates the number of counters, M indicates the number of groups and T indicates the\nclosing time. The shop always opens at the time 0. All input values are integers.\n\nYou can assume that 1 <= N <= 100,1 <= M <= 10000,1 <= T <= 10^9,1 <= C_i <= 100,0 <= T_1 < T_2 < . . . < T_M < T, 1 <= P_i <= max C_i, 1 <= W_i <= 10^9 and 1 <= E_i <= 10^9.\n\nThe input is terminated by a line with three zeros. This is not part of any datasets.", "output": "For each dataset, output the average satisfaction over all customers in a line. Each output value\nmay be printed with an arbitrary number of fractional digits, but may not contain an absolute\nerror greater than 10^-9.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 4 100\n7\n10 1 50 50\n15 2 50 50\n25 1 50 50\n35 3 50 50\n1 2 100\n5\n30 3 20 50\n40 4 40 50\n1 2 100\n5\n49 3 20 50\n60 4 50 30\n1 2 100\n5\n50 3 20 50\n60 4 50 30\n2 3 100\n4 2\n10 4 20 20\n30 2 20 20\n40 4 20 20\n0 0 0\n output: 0.7428571428571429\n0.4285714285714285\n0.5542857142857143\n-0.1428571428571428\n0.8000000000000000"], "Pid": "p01178", "ProblemText": "Task Description: Ron is a master of a ramen shop.\n\nRecently, he has noticed some customers wait for a long time. This has been caused by lack of\nseats during lunch time. Customers loses their satisfaction if they waits for a long time, and\neven some of them will give up waiting and go away. For this reason, he has decided to increase\nseats in his shop. To determine how many seats are appropriate, he has asked you, an excellent\nprogrammer, to write a simulator of customer behavior.\n\nCustomers come to his shop in groups, each of which is associated with the following four\nparameters:\n\n T_i : when the group comes to the shop\n\n P_i : number of customers\n\n W_i : how long the group can wait for their seats\n\n E_i : how long the group takes for eating\nThe i-th group comes to the shop with P_i customers together at the time T_i . If P_i successive\nseats are available at that time, the group takes their seats immediately. Otherwise, they waits\nfor such seats being available. When the group fails to take their seats within the time W_i\n(inclusive) from their coming and strictly before the closing time, they give up waiting and go\naway. In addition, if there are other groups waiting, the new group cannot take their seats until\nthe earlier groups are taking seats or going away.\n\nThe shop has N counters numbered uniquely from 1 to N. The i-th counter has C_i seats. The\ngroup prefers “seats with a greater distance to the nearest group. ” Precisely, the group takes\ntheir seats according to the criteria listed below. Here, S_L denotes the number of successive\nempty seats on the left side of the group after their seating, and S_R the number on the right\nside. S_L and S_R are considered to be infinity if there are no other customers on the left side\nand on the right side respectively.\n\n Prefers seats maximizing min{S_L, S_R}.\n\n If there are multiple alternatives meeting the first criterion, prefers seats maximizing\n max{S_L, S_R}.\n\n If there are still multiple alternatives, prefers the counter of the smallest number.\n\n If there are still multiple alternatives, prefers the leftmost seats.\nWhen multiple groups are leaving the shop at the same time and some other group is waiting\nfor available seats, seat assignment for the waiting group should be made after all the finished\ngroups leave the shop.\n\nYour task is to calculate the average satisfaction over customers. The satisfaction of a customer\nin the i-th group is given as follows:\n\n If the group goes away without eating, -1.\n\n Otherwise, (W_i - t_i )/W_i where t_i is the actual waiting time for the i-th group (the value ranges between 0 to 1 inclusive).\nTask Input: The input consists of multiple datasets.\n\nEach dataset has the following format:\n\n N M T\n C_1 C_2 . . . C_N\n T_1 P_1 W_1 E_1\n T_2 P_2 W_2 E_2\n . . .\n T_M P_M W_M E_M\n\nN indicates the number of counters, M indicates the number of groups and T indicates the\nclosing time. The shop always opens at the time 0. All input values are integers.\n\nYou can assume that 1 <= N <= 100,1 <= M <= 10000,1 <= T <= 10^9,1 <= C_i <= 100,0 <= T_1 < T_2 < . . . < T_M < T, 1 <= P_i <= max C_i, 1 <= W_i <= 10^9 and 1 <= E_i <= 10^9.\n\nThe input is terminated by a line with three zeros. This is not part of any datasets.\nTask Output: For each dataset, output the average satisfaction over all customers in a line. Each output value\nmay be printed with an arbitrary number of fractional digits, but may not contain an absolute\nerror greater than 10^-9.\nTask Samples: input: 1 4 100\n7\n10 1 50 50\n15 2 50 50\n25 1 50 50\n35 3 50 50\n1 2 100\n5\n30 3 20 50\n40 4 40 50\n1 2 100\n5\n49 3 20 50\n60 4 50 30\n1 2 100\n5\n50 3 20 50\n60 4 50 30\n2 3 100\n4 2\n10 4 20 20\n30 2 20 20\n40 4 20 20\n0 0 0\n output: 0.7428571428571429\n0.4285714285714285\n0.5542857142857143\n-0.1428571428571428\n0.8000000000000000\n\n" }, { "title": "Problem I: Cousin's Aunt", "content": "Sarah is a girl who likes reading books.\n\nOne day, she wondered about the relationship of a family in a mystery novel. The story said,\n\nB is A 's father 's brother 's son, and\n\nC is B 's aunt.\nThen she asked herself, “So how many degrees of kinship are there between A and C? ”\n\nThere are two possible relationships between B and C, that is, C is either B 's father 's sister or\nB 's mother 's sister in the story. If C is B 's father 's sister, C is in the third degree of kinship to\nA (A 's father 's sister). On the other hand, if C is B 's mother 's sister, C is in the fifth degree of\nkinship to A (A 's father 's brother 's wife 's sister).\n\nYou are a friend of Sarah 's and good at programming. You can help her by writing a general\nprogram to calculate the maximum and minimum degrees of kinship between A and C under\ngiven relationship.\n\nThe relationship of A and C is represented by a sequence of the following basic relations: father,\nmother, son, daughter, husband, wife, brother, sister, grandfather, grandmother, grandson,\ngranddaughter, uncle, aunt, nephew, and niece. Here are some descriptions about these relations:\n\nX 's brother is equivalent to X 's father 's or mother 's son not identical to X.\n\nX 's grandfather is equivalent to X 's father 's or mother 's father.\n\nX 's grandson is equivalent to X 's son 's or daughter 's son.\n\nX 's uncle is equivalent to X 's father 's or mother 's brother.\n\nX 's nephew is equivalent to X 's brother 's or sister 's son.\n\nSimilar rules apply to sister, grandmother, granddaughter, aunt and niece.\nIn this problem, you can assume there are none of the following relations in the family: adoptions,\nmarriages between relatives (i. e. the family tree has no cycles), divorces, remarriages, bigamous\nmarriages and same-sex marriages.\n\nThe degree of kinship is defined as follows:\n\n The distance from X to X 's father, X 's mother, X 's son or X 's daughter is one.\n\n The distance from X to X 's husband or X 's wife is zero.\n\n The degree of kinship between X and Y is equal to the shortest distance from X to Y\n deduced from the above rules.", "constraint": "", "input": "The input contains multiple datasets. The first line consists of a positive integer that indicates\nthe number of datasets.\n\nEach dataset is given by one line in the following format:\n\n C is A( 's relation)*\n\nHere, relation is one of the following:\n\nfather, mother, son, daughter, husband, wife, brother,\nsister, grandfather, grandmother, grandson, granddaughter, uncle, aunt, nephew, niece.\n\nAn asterisk denotes zero or more occurance of portion surrounded by the parentheses. The\nnumber of relations in each dataset is at most ten.", "output": "For each dataset, print a line containing the maximum and minimum degrees of kinship separated\nby exact one space. No extra characters are allowed of the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\nC is A's father's brother's son's aunt\nC is A's mother's brother's son's aunt\nC is A's son's mother's mother's son\nC is A's aunt's niece's aunt's niece\nC is A's father's son's brother\nC is A's son's son's mother\nC is A\n output: 5 3\n5 1\n2 2\n6 0\n2 0\n1 1\n0 0"], "Pid": "p01179", "ProblemText": "Task Description: Sarah is a girl who likes reading books.\n\nOne day, she wondered about the relationship of a family in a mystery novel. The story said,\n\nB is A 's father 's brother 's son, and\n\nC is B 's aunt.\nThen she asked herself, “So how many degrees of kinship are there between A and C? ”\n\nThere are two possible relationships between B and C, that is, C is either B 's father 's sister or\nB 's mother 's sister in the story. If C is B 's father 's sister, C is in the third degree of kinship to\nA (A 's father 's sister). On the other hand, if C is B 's mother 's sister, C is in the fifth degree of\nkinship to A (A 's father 's brother 's wife 's sister).\n\nYou are a friend of Sarah 's and good at programming. You can help her by writing a general\nprogram to calculate the maximum and minimum degrees of kinship between A and C under\ngiven relationship.\n\nThe relationship of A and C is represented by a sequence of the following basic relations: father,\nmother, son, daughter, husband, wife, brother, sister, grandfather, grandmother, grandson,\ngranddaughter, uncle, aunt, nephew, and niece. Here are some descriptions about these relations:\n\nX 's brother is equivalent to X 's father 's or mother 's son not identical to X.\n\nX 's grandfather is equivalent to X 's father 's or mother 's father.\n\nX 's grandson is equivalent to X 's son 's or daughter 's son.\n\nX 's uncle is equivalent to X 's father 's or mother 's brother.\n\nX 's nephew is equivalent to X 's brother 's or sister 's son.\n\nSimilar rules apply to sister, grandmother, granddaughter, aunt and niece.\nIn this problem, you can assume there are none of the following relations in the family: adoptions,\nmarriages between relatives (i. e. the family tree has no cycles), divorces, remarriages, bigamous\nmarriages and same-sex marriages.\n\nThe degree of kinship is defined as follows:\n\n The distance from X to X 's father, X 's mother, X 's son or X 's daughter is one.\n\n The distance from X to X 's husband or X 's wife is zero.\n\n The degree of kinship between X and Y is equal to the shortest distance from X to Y\n deduced from the above rules.\nTask Input: The input contains multiple datasets. The first line consists of a positive integer that indicates\nthe number of datasets.\n\nEach dataset is given by one line in the following format:\n\n C is A( 's relation)*\n\nHere, relation is one of the following:\n\nfather, mother, son, daughter, husband, wife, brother,\nsister, grandfather, grandmother, grandson, granddaughter, uncle, aunt, nephew, niece.\n\nAn asterisk denotes zero or more occurance of portion surrounded by the parentheses. The\nnumber of relations in each dataset is at most ten.\nTask Output: For each dataset, print a line containing the maximum and minimum degrees of kinship separated\nby exact one space. No extra characters are allowed of the output.\nTask Samples: input: 7\nC is A's father's brother's son's aunt\nC is A's mother's brother's son's aunt\nC is A's son's mother's mother's son\nC is A's aunt's niece's aunt's niece\nC is A's father's son's brother\nC is A's son's son's mother\nC is A\n output: 5 3\n5 1\n2 2\n6 0\n2 0\n1 1\n0 0\n\n" }, { "title": "The Closest Circle", "content": "You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of\nthe largest circle is not double longer than that of the smallest.\nFigure 1: The Sample Input\n\nThe distance between two circles C_1 and C_2 is given by the usual formula\n\nwhere (x_i, y_i ) is the coordinates of the center of the circle C_i, and r_i is the radius of C_i, for i = 1,2.\n\nYour task is to write a program that finds the closest pair of circles and print their distance.", "constraint": "", "input": "The input consists of a series of test cases, followed by a single line only containing a single zero, which\nindicates the end of input.\n\nEach test case begins with a line containing an integer N (2 <= N <= 100000), which indicates the number\nof circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal\nnumbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of\nthe center of the circle, respectively.", "output": "For each test case, print the distance between the closest circles. You may print any number of digits\nafter the decimal point, but the error must not exceed 0.00001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1.0 0.0 0.0\n1.5 0.0 3.0\n2.0 4.0 0.0\n1.0 3.0 4.0\n0\n output: 0.5"], "Pid": "p01180", "ProblemText": "Task Description: You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of\nthe largest circle is not double longer than that of the smallest.\nFigure 1: The Sample Input\n\nThe distance between two circles C_1 and C_2 is given by the usual formula\n\nwhere (x_i, y_i ) is the coordinates of the center of the circle C_i, and r_i is the radius of C_i, for i = 1,2.\n\nYour task is to write a program that finds the closest pair of circles and print their distance.\nTask Input: The input consists of a series of test cases, followed by a single line only containing a single zero, which\nindicates the end of input.\n\nEach test case begins with a line containing an integer N (2 <= N <= 100000), which indicates the number\nof circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal\nnumbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of\nthe center of the circle, respectively.\nTask Output: For each test case, print the distance between the closest circles. You may print any number of digits\nafter the decimal point, but the error must not exceed 0.00001.\nTask Samples: input: 4\n1.0 0.0 0.0\n1.5 0.0 3.0\n2.0 4.0 0.0\n1.0 3.0 4.0\n0\n output: 0.5\n\n" }, { "title": "Problem A: Moduic Squares", "content": "Have you ever heard of Moduic Squares? They are like 3 * 3 Magic Squares, but each of them has one\nextra cell called a moduic cell. Hence a Moduic Square has the following form.\nFigure 1: A Moduic Square\n\nEach of cells labeled from A to J contains one number from 1 to 10, where no two cells contain the same\nnumber. The sums of three numbers in the same rows, in the same columns, and in the diagonals in the\n3 * 3 cells must be congruent modulo the number in the moduic cell. Here is an example Moduic Square:\nFigure 2: An example Moduic Square\n\nYou can easily see that all the sums are congruent to 0 modulo 5.\n\nNow, we can consider interesting puzzles in which we complete Moduic Squares with partially filled cells.\nFor example, we can complete the following square by filling 4 into the empty cell on the left and 9 on\nthe right. Alternatively, we can also complete the square by filling 9 on the left and 4 on the right. So\nthis puzzle has two possible solutions.\n\nFigure 3: A Moduic Square as a puzzle\n\nYour task is to write a program that determines the number of solutions for each given puzzle.", "constraint": "", "input": "The input contains multiple test cases. Each test case is specified on a single line made of 10 integers\nthat represent cells A, B, C, D, E, F, G, H, I, and J as shown in the first figure of the problem statement.\nPositive integer means that the corresponding cell is already filled with the integer. Zero means that the\ncorresponding cell is left empty.\n\nThe end of input is identified with a line containing ten of -1 's. This is not part of test cases.", "output": "For each test case, output a single integer indicating the number of solutions on a line. There may be\ncases with no solutions, in which you should output 0 as the number.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 1 6 8 10 7 0 0 2 5\n0 0 0 0 0 0 0 0 0 1\n-1 -1 -1 -1 -1 -1 -1 -1 -1 -1\n output: 2\n362880"], "Pid": "p01181", "ProblemText": "Task Description: Have you ever heard of Moduic Squares? They are like 3 * 3 Magic Squares, but each of them has one\nextra cell called a moduic cell. Hence a Moduic Square has the following form.\nFigure 1: A Moduic Square\n\nEach of cells labeled from A to J contains one number from 1 to 10, where no two cells contain the same\nnumber. The sums of three numbers in the same rows, in the same columns, and in the diagonals in the\n3 * 3 cells must be congruent modulo the number in the moduic cell. Here is an example Moduic Square:\nFigure 2: An example Moduic Square\n\nYou can easily see that all the sums are congruent to 0 modulo 5.\n\nNow, we can consider interesting puzzles in which we complete Moduic Squares with partially filled cells.\nFor example, we can complete the following square by filling 4 into the empty cell on the left and 9 on\nthe right. Alternatively, we can also complete the square by filling 9 on the left and 4 on the right. So\nthis puzzle has two possible solutions.\n\nFigure 3: A Moduic Square as a puzzle\n\nYour task is to write a program that determines the number of solutions for each given puzzle.\nTask Input: The input contains multiple test cases. Each test case is specified on a single line made of 10 integers\nthat represent cells A, B, C, D, E, F, G, H, I, and J as shown in the first figure of the problem statement.\nPositive integer means that the corresponding cell is already filled with the integer. Zero means that the\ncorresponding cell is left empty.\n\nThe end of input is identified with a line containing ten of -1 's. This is not part of test cases.\nTask Output: For each test case, output a single integer indicating the number of solutions on a line. There may be\ncases with no solutions, in which you should output 0 as the number.\nTask Samples: input: 3 1 6 8 10 7 0 0 2 5\n0 0 0 0 0 0 0 0 0 1\n-1 -1 -1 -1 -1 -1 -1 -1 -1 -1\n output: 2\n362880\n\n" }, { "title": "Problem B: Restaurant", "content": "Steve runs a small restaurant in a city. Also, as he is the only cook in his restaurant, he cooks everything\nordered by customers.\n\nBasically he attends to orders by first-come-first-served principle. He takes some prescribed time to\nprepare each dish. As a customer can order more than one dish at a time, Steve starts his cooking with\nthe dish that takes the longest time to prepare. In case that there are two or more dishes that take\nthe same amount of time to prepare, he makes these dishes in the sequence as listed in the menu card\nof his restaurant. Note that he does not care in which order these dishes have been ordered. When he\ncompletes all dishes ordered by a customer, he immediately passes these dishes to the waitress and has\nthem served to the customer. Time for serving is negligible.\n\nOn the other hand, during his cooking for someone 's order, another customer may come and order dishes.\nFor his efficiency, he decided to prepare together multiple dishes of the same if possible. When he starts\ncooking for new dishes, he looks over the orders accepted by that time (including the order accepted\nexactly at that time if any), and counts the number of the same dishes he is going to cook next. Time\nrequired for cooking is the same no matter how many dishes he prepare at once. Unfortunately, he has\nonly limited capacity in the kitchen, and hence it is sometimes impossible that the requested number of\ndishes are prepared at once. In such cases, he just prepares as many dishes as possible.\n\nYour task is to write a program that simulates the restaurant. Given a list of dishes in the menu card\nand orders from customers with their accepted times, your program should output a list of times when\neach customer is served.", "constraint": "", "input": "The input contains multiple data sets. Each data set is in the format below:\n\nN M\nName_1 Limit_1 Time_1\n. . .\nName_N Limit_N Time_N\nT_1 K_1 Dish_1,1 . . . Dish_1, K1\n. . .\nT_M K_M Dish_M, 1 . . . Dish_M, KM\n\nHere, N (1 <= N <= 20) and M (1 <= M <= 100) specify the number of entries in the menu card and the\nnumber of orders that Steve will receive, respectively; each Name_i is the name of a dish of the i-th entry\nin the menu card, which consists of up to 20 alphabetical letters; Limit_i (1 <= Limit_i <= 10) is the number of dishes he can prepare at the same time; Time_i (1 <= Time_i <= 1000) is time required to prepare a dish\n(or dishes) of the i-th entry; T_j (1 <= T_j <= 10000000) is the time when the j-th order is accepted; K_j\n(1 <= K_j <= 10) is the number of dishes in the j-th order; and each Dish_j, k represents a dish in the j-th\norder.\n\nYou may assume that every dish in the orders is listed in the menu card, but you should note that each\norder may contain multiple occurrences of the same dishes. The orders are given in ascending order by\nT_j , and no two orders are accepted at the same time.\n\nThe input is terminated with a line that contains two zeros. This is not part of data sets and hence\nshould not be processed.", "output": "Your program should produce the output of M -lines for each data set. The i-th line of the output should\ncontain a single integer that indicates the time when the i-th order will be completed and served to the\ncustomer.\n\nPrint a blank line between two successive data sets.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\nRamen 3 10\nChahan 5 5\nGyoza 5 10\nRice 1 1\nSoup 1 1\n5 2 Ramen Gyoza\n10 6 Chahan Gyoza Soup Ramen Gyoza Rice\n20 1 Chahan\n25 1 Ramen\n0 0\n output: 25\n42\n40\n35"], "Pid": "p01182", "ProblemText": "Task Description: Steve runs a small restaurant in a city. Also, as he is the only cook in his restaurant, he cooks everything\nordered by customers.\n\nBasically he attends to orders by first-come-first-served principle. He takes some prescribed time to\nprepare each dish. As a customer can order more than one dish at a time, Steve starts his cooking with\nthe dish that takes the longest time to prepare. In case that there are two or more dishes that take\nthe same amount of time to prepare, he makes these dishes in the sequence as listed in the menu card\nof his restaurant. Note that he does not care in which order these dishes have been ordered. When he\ncompletes all dishes ordered by a customer, he immediately passes these dishes to the waitress and has\nthem served to the customer. Time for serving is negligible.\n\nOn the other hand, during his cooking for someone 's order, another customer may come and order dishes.\nFor his efficiency, he decided to prepare together multiple dishes of the same if possible. When he starts\ncooking for new dishes, he looks over the orders accepted by that time (including the order accepted\nexactly at that time if any), and counts the number of the same dishes he is going to cook next. Time\nrequired for cooking is the same no matter how many dishes he prepare at once. Unfortunately, he has\nonly limited capacity in the kitchen, and hence it is sometimes impossible that the requested number of\ndishes are prepared at once. In such cases, he just prepares as many dishes as possible.\n\nYour task is to write a program that simulates the restaurant. Given a list of dishes in the menu card\nand orders from customers with their accepted times, your program should output a list of times when\neach customer is served.\nTask Input: The input contains multiple data sets. Each data set is in the format below:\n\nN M\nName_1 Limit_1 Time_1\n. . .\nName_N Limit_N Time_N\nT_1 K_1 Dish_1,1 . . . Dish_1, K1\n. . .\nT_M K_M Dish_M, 1 . . . Dish_M, KM\n\nHere, N (1 <= N <= 20) and M (1 <= M <= 100) specify the number of entries in the menu card and the\nnumber of orders that Steve will receive, respectively; each Name_i is the name of a dish of the i-th entry\nin the menu card, which consists of up to 20 alphabetical letters; Limit_i (1 <= Limit_i <= 10) is the number of dishes he can prepare at the same time; Time_i (1 <= Time_i <= 1000) is time required to prepare a dish\n(or dishes) of the i-th entry; T_j (1 <= T_j <= 10000000) is the time when the j-th order is accepted; K_j\n(1 <= K_j <= 10) is the number of dishes in the j-th order; and each Dish_j, k represents a dish in the j-th\norder.\n\nYou may assume that every dish in the orders is listed in the menu card, but you should note that each\norder may contain multiple occurrences of the same dishes. The orders are given in ascending order by\nT_j , and no two orders are accepted at the same time.\n\nThe input is terminated with a line that contains two zeros. This is not part of data sets and hence\nshould not be processed.\nTask Output: Your program should produce the output of M -lines for each data set. The i-th line of the output should\ncontain a single integer that indicates the time when the i-th order will be completed and served to the\ncustomer.\n\nPrint a blank line between two successive data sets.\nTask Samples: input: 5 4\nRamen 3 10\nChahan 5 5\nGyoza 5 10\nRice 1 1\nSoup 1 1\n5 2 Ramen Gyoza\n10 6 Chahan Gyoza Soup Ramen Gyoza Rice\n20 1 Chahan\n25 1 Ramen\n0 0\n output: 25\n42\n40\n35\n\n" }, { "title": "Problem C: Tetrahedra", "content": "Peter P. Pepper is facing a difficulty.\n\nAfter fierce battles with the Principality of Croode, the Aaronbarc Kingdom, for which he serves, had\nthe last laugh in the end. Peter had done great service in the war, and the king decided to give him a\nbig reward. But alas, the mean king gave him a hard question to try his intelligence. Peter is given a\nnumber of sticks, and he is requested to form a tetrahedral vessel with these sticks. Then he will be, said\nthe king, given as much patas (currency in this kingdom) as the volume of the vessel. In the situation,\nhe has only to form a frame of a vessel.\nFigure 1: An example tetrahedron vessel\n\nThe king posed two rules to him in forming a vessel: (1) he need not use all of the given sticks, and (2)\nhe must not glue two or more sticks together in order to make a longer stick.\n\nNeedless to say, he wants to obtain as much patas as possible. Thus he wants to know the maximum\npatas he can be given. So he called you, a friend of him, and asked to write a program to solve the\nproblem.", "constraint": "", "input": "The input consists of multiple test cases. Each test case is given in a line in the format below:\n\n N a_1 a_2 . . . a_N\n\nwhere N indicates the number of sticks Peter is given, and a_i indicates the length (in centimeters) of\neach stick. You may assume 6 <= N <= 15 and 1 <= a_i <= 100.\n\nThe input terminates with the line containing a single zero.", "output": "For each test case, print the maximum possible volume (in cubic centimeters) of a tetrahedral vessel\nwhich can be formed with the given sticks. You may print an arbitrary number of digits after the decimal\npoint, provided that the printed value does not contain an error greater than 10^-6.\n\nIt is guaranteed that for each test case, at least one tetrahedral vessel can be formed.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 7 1 2 2 2 2 2 2\n0\n output: 0.942809"], "Pid": "p01183", "ProblemText": "Task Description: Peter P. Pepper is facing a difficulty.\n\nAfter fierce battles with the Principality of Croode, the Aaronbarc Kingdom, for which he serves, had\nthe last laugh in the end. Peter had done great service in the war, and the king decided to give him a\nbig reward. But alas, the mean king gave him a hard question to try his intelligence. Peter is given a\nnumber of sticks, and he is requested to form a tetrahedral vessel with these sticks. Then he will be, said\nthe king, given as much patas (currency in this kingdom) as the volume of the vessel. In the situation,\nhe has only to form a frame of a vessel.\nFigure 1: An example tetrahedron vessel\n\nThe king posed two rules to him in forming a vessel: (1) he need not use all of the given sticks, and (2)\nhe must not glue two or more sticks together in order to make a longer stick.\n\nNeedless to say, he wants to obtain as much patas as possible. Thus he wants to know the maximum\npatas he can be given. So he called you, a friend of him, and asked to write a program to solve the\nproblem.\nTask Input: The input consists of multiple test cases. Each test case is given in a line in the format below:\n\n N a_1 a_2 . . . a_N\n\nwhere N indicates the number of sticks Peter is given, and a_i indicates the length (in centimeters) of\neach stick. You may assume 6 <= N <= 15 and 1 <= a_i <= 100.\n\nThe input terminates with the line containing a single zero.\nTask Output: For each test case, print the maximum possible volume (in cubic centimeters) of a tetrahedral vessel\nwhich can be formed with the given sticks. You may print an arbitrary number of digits after the decimal\npoint, provided that the printed value does not contain an error greater than 10^-6.\n\nIt is guaranteed that for each test case, at least one tetrahedral vessel can be formed.\nTask Samples: input: 7 1 2 2 2 2 2 2\n0\n output: 0.942809\n\n" }, { "title": "Problem D: International Party", "content": "Isaac H. Ives is attending an international student party (maybe for girl-hunting). Students there enjoy\ntalking in groups with excellent foods and drinks. However, since students come to the party from all\nover the world, groups may not have a language spoken by all students of the group. In such groups,\nsome student(s) need to work as interpreters, but intervals caused by interpretation make their talking\nless exciting.\n\nNeedless to say, students want exciting talks. To have talking exciting as much as possible, Isaac proposed\nthe following rule: the number of languages used in talking should be as little as possible, and not exceed\nfive. Many students agreed with his proposal, but it is not easy for them to find languages each student\nshould speak. So he calls you for help.\n\nYour task is to write a program that shows the minimum set of languages to make talking possible, given\nlists of languages each student speaks.", "constraint": "", "input": "The input consists of a series of data sets.\n\nThe first line of each data set contains two integers N (1 <= N <= 30) and M (2 <= M <= 20) separated\nby a blank, which represent the numbers of languages and students respectively. The following N lines\ncontain language names, one name per line. The following M lines describe students in the group. The\ni-th line consists of an integer K_i that indicates the number of languages the i-th student speaks, and\nK_i language names separated by a single space. Each language name consists of up to twenty alphabetic\nletters.\n\nA line that contains two zeros indicates the end of input and is not part of a data set.", "output": "Print a line that contains the minimum number L of languages to be spoken, followed by L language\nnames in any order. Each language name should be printed in a separate line. In case two or more sets of\nthe same size is possible, you may print any one of them. If it is impossible for the group to enjoy talking\nwith not more than five languages, you should print a single line that contains “Impossible” (without\nquotes).\n\nPrint an empty line between data sets.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\nEnglish\nFrench\nJapanese\n1 English\n2 French English\n2 Japanese English\n1 Japanese\n2 2\nEnglish\nJapanese\n1 English\n1 Japanese\n6 7\nEnglish\nDutch\nGerman\nFrench\nItalian\nSpanish\n1 English\n2 English Dutch\n2 Dutch German\n2 German French\n2 French Italian\n2 Italian Spanish\n1 Spanish\n0 0\n output: 2\nEnglish\nJapanese\n\nImpossible\n\nImpossible"], "Pid": "p01184", "ProblemText": "Task Description: Isaac H. Ives is attending an international student party (maybe for girl-hunting). Students there enjoy\ntalking in groups with excellent foods and drinks. However, since students come to the party from all\nover the world, groups may not have a language spoken by all students of the group. In such groups,\nsome student(s) need to work as interpreters, but intervals caused by interpretation make their talking\nless exciting.\n\nNeedless to say, students want exciting talks. To have talking exciting as much as possible, Isaac proposed\nthe following rule: the number of languages used in talking should be as little as possible, and not exceed\nfive. Many students agreed with his proposal, but it is not easy for them to find languages each student\nshould speak. So he calls you for help.\n\nYour task is to write a program that shows the minimum set of languages to make talking possible, given\nlists of languages each student speaks.\nTask Input: The input consists of a series of data sets.\n\nThe first line of each data set contains two integers N (1 <= N <= 30) and M (2 <= M <= 20) separated\nby a blank, which represent the numbers of languages and students respectively. The following N lines\ncontain language names, one name per line. The following M lines describe students in the group. The\ni-th line consists of an integer K_i that indicates the number of languages the i-th student speaks, and\nK_i language names separated by a single space. Each language name consists of up to twenty alphabetic\nletters.\n\nA line that contains two zeros indicates the end of input and is not part of a data set.\nTask Output: Print a line that contains the minimum number L of languages to be spoken, followed by L language\nnames in any order. Each language name should be printed in a separate line. In case two or more sets of\nthe same size is possible, you may print any one of them. If it is impossible for the group to enjoy talking\nwith not more than five languages, you should print a single line that contains “Impossible” (without\nquotes).\n\nPrint an empty line between data sets.\nTask Samples: input: 3 4\nEnglish\nFrench\nJapanese\n1 English\n2 French English\n2 Japanese English\n1 Japanese\n2 2\nEnglish\nJapanese\n1 English\n1 Japanese\n6 7\nEnglish\nDutch\nGerman\nFrench\nItalian\nSpanish\n1 English\n2 English Dutch\n2 Dutch German\n2 German French\n2 French Italian\n2 Italian Spanish\n1 Spanish\n0 0\n output: 2\nEnglish\nJapanese\n\nImpossible\n\nImpossible\n\n" }, { "title": "Problem E: Hide-and-seek", "content": "Hide-and-seek is a children 's game. Players hide here and there, and one player called it tries to find all\nthe other players.\n\nNow you played it and found all the players, so it 's turn to hide from it. Since you have got tired of\nrunning around for finding players, you don 't want to play it again. So you are going to hide yourself at\nthe place as far as possible from it. But where is that?\n\nYour task is to find the place and calculate the maximum possible distance from it to the place to hide.", "constraint": "", "input": "The input contains a number of test cases.\n\nThe first line of each test case contains a positive integer N (N <= 1000). The following N lines give\nthe map where hide-and-seek is played. The map consists of N corridors. Each line contains four real\nnumbers x_1, y_1, x_2, and y_2, where (x_1, y_1 ) and (x_2, y_2 ) indicate the two end points of the corridor. All\ncorridors are straight, and their widths are negligible. After these N lines, there is a line containing two\nreal numbers sx and sy, indicating the position of it. You can hide at an arbitrary place of any corridor,\nand it always walks along corridors. Numbers in the same line are separated by a single space.\n\nIt is guaranteed that its starting position (sx, sy) is located on some corridor and linked to all corridors\ndirectly or indirectly.\n\nThe end of the input is indicated by a line containing a single zero.", "output": "For each test case, output a line containing the distance along the corridors from ‘it”s starting position\nto the farthest position. The value may contain an error less than or equal to 0.001. You may print any\nnumber of digits below the decimal point.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0 3 3\n0 4 3 1\n1 1\n0\n output: 4.243"], "Pid": "p01185", "ProblemText": "Task Description: Hide-and-seek is a children 's game. Players hide here and there, and one player called it tries to find all\nthe other players.\n\nNow you played it and found all the players, so it 's turn to hide from it. Since you have got tired of\nrunning around for finding players, you don 't want to play it again. So you are going to hide yourself at\nthe place as far as possible from it. But where is that?\n\nYour task is to find the place and calculate the maximum possible distance from it to the place to hide.\nTask Input: The input contains a number of test cases.\n\nThe first line of each test case contains a positive integer N (N <= 1000). The following N lines give\nthe map where hide-and-seek is played. The map consists of N corridors. Each line contains four real\nnumbers x_1, y_1, x_2, and y_2, where (x_1, y_1 ) and (x_2, y_2 ) indicate the two end points of the corridor. All\ncorridors are straight, and their widths are negligible. After these N lines, there is a line containing two\nreal numbers sx and sy, indicating the position of it. You can hide at an arbitrary place of any corridor,\nand it always walks along corridors. Numbers in the same line are separated by a single space.\n\nIt is guaranteed that its starting position (sx, sy) is located on some corridor and linked to all corridors\ndirectly or indirectly.\n\nThe end of the input is indicated by a line containing a single zero.\nTask Output: For each test case, output a line containing the distance along the corridors from ‘it”s starting position\nto the farthest position. The value may contain an error less than or equal to 0.001. You may print any\nnumber of digits below the decimal point.\nTask Samples: input: 2\n0 0 3 3\n0 4 3 1\n1 1\n0\n output: 4.243\n\n" }, { "title": "Problem F: TV Watching", "content": "You are addicted to watching TV, and you watch so many TV programs every day. You have been in\ntrouble recently: the airtimes of your favorite TV programs overlap.\n\nFortunately, you have both a TV and a video recorder at your home. You can therefore watch a program\non air while another program (on a different channel) is recorded to a video at the same time. However,\nit is not easy to decide which programs should be watched on air or recorded to a video. As you are a\ntalented computer programmer, you have decided to write a program to find the way of watching TV\nprograms which gives you the greatest possible satisfaction.\n\nYour program (for a computer) will be given TV listing of a day along with your score for each TV\nprogram. Each score represents how much you will be satisfied if you watch the corresponding TV\nprogram on air or with a video. Your program should compute the maximum possible sum of the scores\nof the TV programs that you can watch.", "constraint": "", "input": "The input consists of several scenarios.\n\nThe first line of each scenario contains an integer N (1 <= N <= 1000) that represents the number of\nprograms. Each of the following N lines contains program information in the format below:\nTT_bT_eR_1R_2\nT is the title of the program and is composed by up to 32 alphabetical letters. T_b and T_e specify the\nstart time and the end time of broadcasting, respectively. R_1 and R_2 indicate the score when you watch\nthe program on air and when you have the program recorded, respectively.\n\nAll times given in the input have the form of “hh: mm” and range from 00: 00 to 23: 59. You may assume\nthat no program is broadcast across the twelve midnight.\n\nThe end of the input is indicated by a line containing only a single zero. This is not part of scenarios.", "output": "For each scenario, output the maximum possible score in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nOmoikkiriTV 12:00 13:00 5 1\nWaratteIitomo 12:00 13:00 10 2\nWatarusekennhaOnibakari 20:00 21:00 10 3\nSuzumiyaharuhiNoYuuutsu 23:00 23:30 100 40\n5\na 0:00 1:00 100 100\nb 0:00 1:00 101 101\nc 0:00 1:00 102 102\nd 0:00 1:00 103 103\ne 0:00 1:00 104 104\n0\n output: 121\n207"], "Pid": "p01186", "ProblemText": "Task Description: You are addicted to watching TV, and you watch so many TV programs every day. You have been in\ntrouble recently: the airtimes of your favorite TV programs overlap.\n\nFortunately, you have both a TV and a video recorder at your home. You can therefore watch a program\non air while another program (on a different channel) is recorded to a video at the same time. However,\nit is not easy to decide which programs should be watched on air or recorded to a video. As you are a\ntalented computer programmer, you have decided to write a program to find the way of watching TV\nprograms which gives you the greatest possible satisfaction.\n\nYour program (for a computer) will be given TV listing of a day along with your score for each TV\nprogram. Each score represents how much you will be satisfied if you watch the corresponding TV\nprogram on air or with a video. Your program should compute the maximum possible sum of the scores\nof the TV programs that you can watch.\nTask Input: The input consists of several scenarios.\n\nThe first line of each scenario contains an integer N (1 <= N <= 1000) that represents the number of\nprograms. Each of the following N lines contains program information in the format below:\nTT_bT_eR_1R_2\nT is the title of the program and is composed by up to 32 alphabetical letters. T_b and T_e specify the\nstart time and the end time of broadcasting, respectively. R_1 and R_2 indicate the score when you watch\nthe program on air and when you have the program recorded, respectively.\n\nAll times given in the input have the form of “hh: mm” and range from 00: 00 to 23: 59. You may assume\nthat no program is broadcast across the twelve midnight.\n\nThe end of the input is indicated by a line containing only a single zero. This is not part of scenarios.\nTask Output: For each scenario, output the maximum possible score in a line.\nTask Samples: input: 4\nOmoikkiriTV 12:00 13:00 5 1\nWaratteIitomo 12:00 13:00 10 2\nWatarusekennhaOnibakari 20:00 21:00 10 3\nSuzumiyaharuhiNoYuuutsu 23:00 23:30 100 40\n5\na 0:00 1:00 100 100\nb 0:00 1:00 101 101\nc 0:00 1:00 102 102\nd 0:00 1:00 103 103\ne 0:00 1:00 104 104\n0\n output: 121\n207\n\n" }, { "title": "Problem G: Make Friendships", "content": "Isaac H. Ives attended an international student party and made a lot of girl friends (as many other persons\nexpected). To strike up a good friendship with them, he decided to have dates with them. However, it\nis hard for him to schedule dates because he made so many friends. Thus he decided to find the best\nschedule using a computer program. The most important criterion in scheduling is how many different\ngirl friends he will date. Of course, the more friends he will date, the better the schedule is. However,\nthough he has the ability to write a program finding the best schedule, he doesn 't have enough time to\nwrite it.\n\nYour task is to write a program to find the best schedule instead of him.", "constraint": "", "input": "The input consists of a series of data sets. The first line of each data set contains a single positive integer\nN (N <= 1,000) that represents the number of persons Isaac made friends with in the party. The next line\ngives Isaac 's schedule, followed by N lines that give his new friends ' schedules. Each schedule consists of\na positive integer M that represents the number of available days followed by M positive integers each\nof which represents an available day.\n\nThe input is terminated by a line that contains a single zero. This is not part of data sets and should\nnot be processed.", "output": "For each data set, print a line that contains the maximum number of girl friends Isaac can have dates\nwith.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 1 3 5\n2 1 4\n4 1 2 3 6\n1 3\n0\n output: 2"], "Pid": "p01187", "ProblemText": "Task Description: Isaac H. Ives attended an international student party and made a lot of girl friends (as many other persons\nexpected). To strike up a good friendship with them, he decided to have dates with them. However, it\nis hard for him to schedule dates because he made so many friends. Thus he decided to find the best\nschedule using a computer program. The most important criterion in scheduling is how many different\ngirl friends he will date. Of course, the more friends he will date, the better the schedule is. However,\nthough he has the ability to write a program finding the best schedule, he doesn 't have enough time to\nwrite it.\n\nYour task is to write a program to find the best schedule instead of him.\nTask Input: The input consists of a series of data sets. The first line of each data set contains a single positive integer\nN (N <= 1,000) that represents the number of persons Isaac made friends with in the party. The next line\ngives Isaac 's schedule, followed by N lines that give his new friends ' schedules. Each schedule consists of\na positive integer M that represents the number of available days followed by M positive integers each\nof which represents an available day.\n\nThe input is terminated by a line that contains a single zero. This is not part of data sets and should\nnot be processed.\nTask Output: For each data set, print a line that contains the maximum number of girl friends Isaac can have dates\nwith.\nTask Samples: input: 3\n3 1 3 5\n2 1 4\n4 1 2 3 6\n1 3\n0\n output: 2\n\n" }, { "title": "Problem H: Slippy Floors", "content": "The princess of the Fancy Kingdom has been loved by many people for her lovely face. However the\nwitch of the Snow World has been jealous of the princess being loved. For her jealousy, the witch has\nshut the princess into the Ice Tower built by the witch 's extreme magical power.\n\nAs the Ice Tower is made of cubic ice blocks that stick hardly, the tower can be regarded to be composed\nof levels each of which is represented by a 2D grid map. The only way for the princess to escape from the\ntower is to reach downward stairs on every level. However, many magical traps set by the witch obstruct\nher moving ways. In addition, because of being made of ice, the floor is so slippy that movement of the\nprincess is very restricted. To be precise, the princess can only press on one adjacent wall to move against\nthe wall as the reaction. She is only allowed to move in the vertical or horizontal direction, not in the\ndiagonal direction. Moreover, she is forced to keep moving without changing the direction until she is\nprevented from further moving by the wall, or she reaches a stairway or a magical trap. She must avoid\nthe traps by any means because her being caught by any of these traps implies her immediate death by\nits magic. These restriction on her movement makes her escape from the tower impossible, so she would\nbe frozen to death without any help.\n\nYou are a servant of the witch of the Snow World, but unlike the witch you love the princess as many other\npeople do. So you decided to help her with her escape. However, if you would go help her directly in the\nIce Tower, the witch would notice your act to cause your immediate death along with her. Considering\nthis matter and your ability, all you can do for her is to generate snowmans at arbitrary places (grid\ncells) neither occupied by the traps nor specified as the cell where the princess is initially placed. These\nsnowmans are equivalent to walls, thus the princess may utilize them for her escape. On the other hand,\nyour magical power is limited, so you should generate the least number of snowmans needed for her\nescape.\n\nYou are required to write a program that solves placement of snowmans for given a map on each level,\nsuch that the number of generated snowmans are minimized.", "constraint": "", "input": "The first line of the input contains a single integer that represents the number of levels in the Ice Tower.\nEach level is given by a line containing two integers NY (3 <= NY <= 30) and NX (3 <= NX <= 30) that\nindicate the vertical and horizontal sizes of the grid map respectively, and following NY lines that specify\nthe grid map. Each of the NY lines contain NX characters, where ‘A ' represents the initial place of the\nprincess, ‘> ' the downward stairs, ‘. ' a place outside the tower, ‘_ ' an ordinary floor, ‘# ' a wall, and ‘^ ' a\nmagical trap. Every map has exactly one ‘A ' and one ‘> '.\n\nYou may assume that there is no way of the princess moving to places outside the tower or beyond the\nmaps, and every case can be solved with not more than ten snowmans. The judge also guarantees that\nthis problem can be solved without extraordinary optimizations.", "output": "For each level, print on a line the least number of snowmans required to be generated for letting the\nprincess get to the downward stairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10 30\n......#############...........\n....##_____________#..........\n...#________________####......\n..#________####_________#.....\n.#________#....##________#....\n#_________#......#________#...\n#__________###...#_____^^_#...\n.#__________A_#...#____^^_#...\n..#___________#...#_>__###....\n...###########.....####.......\n7 17\n......#..........\n.....#_##........\n.#...#_A_#.......\n#^####___#.......\n#_______#........\n#>_____#.........\n########.........\n6 5\n#####\n#_A_#\n#___#\n#_>_#\n#___#\n#####\n output: 2\n1\n0"], "Pid": "p01188", "ProblemText": "Task Description: The princess of the Fancy Kingdom has been loved by many people for her lovely face. However the\nwitch of the Snow World has been jealous of the princess being loved. For her jealousy, the witch has\nshut the princess into the Ice Tower built by the witch 's extreme magical power.\n\nAs the Ice Tower is made of cubic ice blocks that stick hardly, the tower can be regarded to be composed\nof levels each of which is represented by a 2D grid map. The only way for the princess to escape from the\ntower is to reach downward stairs on every level. However, many magical traps set by the witch obstruct\nher moving ways. In addition, because of being made of ice, the floor is so slippy that movement of the\nprincess is very restricted. To be precise, the princess can only press on one adjacent wall to move against\nthe wall as the reaction. She is only allowed to move in the vertical or horizontal direction, not in the\ndiagonal direction. Moreover, she is forced to keep moving without changing the direction until she is\nprevented from further moving by the wall, or she reaches a stairway or a magical trap. She must avoid\nthe traps by any means because her being caught by any of these traps implies her immediate death by\nits magic. These restriction on her movement makes her escape from the tower impossible, so she would\nbe frozen to death without any help.\n\nYou are a servant of the witch of the Snow World, but unlike the witch you love the princess as many other\npeople do. So you decided to help her with her escape. However, if you would go help her directly in the\nIce Tower, the witch would notice your act to cause your immediate death along with her. Considering\nthis matter and your ability, all you can do for her is to generate snowmans at arbitrary places (grid\ncells) neither occupied by the traps nor specified as the cell where the princess is initially placed. These\nsnowmans are equivalent to walls, thus the princess may utilize them for her escape. On the other hand,\nyour magical power is limited, so you should generate the least number of snowmans needed for her\nescape.\n\nYou are required to write a program that solves placement of snowmans for given a map on each level,\nsuch that the number of generated snowmans are minimized.\nTask Input: The first line of the input contains a single integer that represents the number of levels in the Ice Tower.\nEach level is given by a line containing two integers NY (3 <= NY <= 30) and NX (3 <= NX <= 30) that\nindicate the vertical and horizontal sizes of the grid map respectively, and following NY lines that specify\nthe grid map. Each of the NY lines contain NX characters, where ‘A ' represents the initial place of the\nprincess, ‘> ' the downward stairs, ‘. ' a place outside the tower, ‘_ ' an ordinary floor, ‘# ' a wall, and ‘^ ' a\nmagical trap. Every map has exactly one ‘A ' and one ‘> '.\n\nYou may assume that there is no way of the princess moving to places outside the tower or beyond the\nmaps, and every case can be solved with not more than ten snowmans. The judge also guarantees that\nthis problem can be solved without extraordinary optimizations.\nTask Output: For each level, print on a line the least number of snowmans required to be generated for letting the\nprincess get to the downward stairs.\nTask Samples: input: 3\n10 30\n......#############...........\n....##_____________#..........\n...#________________####......\n..#________####_________#.....\n.#________#....##________#....\n#_________#......#________#...\n#__________###...#_____^^_#...\n.#__________A_#...#____^^_#...\n..#___________#...#_>__###....\n...###########.....####.......\n7 17\n......#..........\n.....#_##........\n.#...#_A_#.......\n#^####___#.......\n#_______#........\n#>_____#.........\n########.........\n6 5\n#####\n#_A_#\n#___#\n#_>_#\n#___#\n#####\n output: 2\n1\n0\n\n" }, { "title": "Problem I: Roads in a City", "content": "Roads in a city play important roles in development of the city. Once a road is built, people start their\nliving around the road. A broader road has a bigger capacity, that is, people can live on a wider area\naround the road.\n\nInterstellar Conglomerate of Plantation and Colonization (ICPC) is now planning to develop roads on\na new territory. The new territory is a square and is completely clear. ICPC has already made several\nplans, but there are some difficulties in judging which plan is the best.\n\nTherefore, ICPC has collected several great programmers including you, and asked them to write programs\nthat compute several metrics for each plan. Fortunately your task is a rather simple one. You are asked to\ncompute the area where people can live from the given information about the locations and the capacities\nof the roads.\n\nThe following figure shows the first plan given as the sample input.\nFigure 1: The first plan given as the sample input", "constraint": "", "input": "The input consists of a number of plans. The first line of each plan denotes the number n of roads\n(n <= 50), and the following n lines provide five integers x_1, y_1, x_2, y_2, and r, separated by a space.\n(x_1, y_1 ) and (x_2, y_2) denote the two endpoints of a road (-15 <= x_1, y_1, x_2, y_2 <= 15), and the value r\ndenotes the capacity that is represented by the maximum distance from the road where people can live\n(r <= 10).\n\nThe end of the input is indicated by a line that contains only a single zero.\n\nThe territory is located at -5 <= x, y <= 5. You may assume that each road forms a straight line segment\nand that any lines do not degenerate.", "output": "Print the area where people can live in one line for each plan. You may print an arbitrary number of\ndigits after the decimal points, provided that difference from the exact answer is not greater than 0.01.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n0 -12 0 0 2\n0 0 12 0 2\n0\n output: 39.14159"], "Pid": "p01189", "ProblemText": "Task Description: Roads in a city play important roles in development of the city. Once a road is built, people start their\nliving around the road. A broader road has a bigger capacity, that is, people can live on a wider area\naround the road.\n\nInterstellar Conglomerate of Plantation and Colonization (ICPC) is now planning to develop roads on\na new territory. The new territory is a square and is completely clear. ICPC has already made several\nplans, but there are some difficulties in judging which plan is the best.\n\nTherefore, ICPC has collected several great programmers including you, and asked them to write programs\nthat compute several metrics for each plan. Fortunately your task is a rather simple one. You are asked to\ncompute the area where people can live from the given information about the locations and the capacities\nof the roads.\n\nThe following figure shows the first plan given as the sample input.\nFigure 1: The first plan given as the sample input\nTask Input: The input consists of a number of plans. The first line of each plan denotes the number n of roads\n(n <= 50), and the following n lines provide five integers x_1, y_1, x_2, y_2, and r, separated by a space.\n(x_1, y_1 ) and (x_2, y_2) denote the two endpoints of a road (-15 <= x_1, y_1, x_2, y_2 <= 15), and the value r\ndenotes the capacity that is represented by the maximum distance from the road where people can live\n(r <= 10).\n\nThe end of the input is indicated by a line that contains only a single zero.\n\nThe territory is located at -5 <= x, y <= 5. You may assume that each road forms a straight line segment\nand that any lines do not degenerate.\nTask Output: Print the area where people can live in one line for each plan. You may print an arbitrary number of\ndigits after the decimal points, provided that difference from the exact answer is not greater than 0.01.\nTask Samples: input: 2\n0 -12 0 0 2\n0 0 12 0 2\n0\n output: 39.14159\n\n" }, { "title": "Reading Brackets in English", "content": "Shun and his professor are studying Lisp and S-expressions. Shun is in Tokyo in order to make a presen-\ntation of their research. His professor cannot go with him because of another work today.\n\nHe was making final checks for his slides an hour ago. Then, unfortunately, he found some serious\nmistakes! He called his professor immediately since he did not have enough data in his hand to fix the\nmistakes.\n\nTheir discussion is still going on now. The discussion looks proceeding with difficulty. Most of their data\nare written in S-expressions, so they have to exchange S-expressions via telephone.\n\nYour task is to write a program that outputs S-expressions represented by a given English phrase.", "constraint": "", "input": "The first line of the input contains a single positive integer N, which represents the number of test cases.\nThen N test cases follow.\n\nEach case consists of a line. The line contains an English phrase that represents an S-expression. The\nlength of the phrase is up to 1000 characters.\n\nThe rules to translate an S-expression are as follows.\n\n An S-expression which has one element is translated into “a list of ”. (e. g. “(A)” will be “a list of A”)\n\n An S-expression which has two elements is translated into “a list of and ”. (e. g. “(A B)” will be “a list of A and B”)\n\n An S-expression which has more than three elements is translated into “a list of , , . . . and ”. (e. g. “(A B C D)” will be “a list of A, B, C and D”)\n\n The above rules are applied recursively. (e. g. “(A (P Q) B (X Y Z) C)” will be “a list of\n A, a list of P and Q, B, a list of X, Y and Z and C”)\nEach atomic element of an S-expression is a string made of less than 10 capital letters. All words (“a”,\n“list”, “of” and “and”) and atomic elements of S-expressions are separated by a single space character,\nbut no space character is inserted before comma (”, ”). No phrases for empty S-expressions occur in the\ninput. You can assume that all test cases can be translated into S-expressions, but the possible expressions\nmay not be unique.", "output": "For each test case, output the corresponding S-expression in a separate line. If the given phrase involves\ntwo or more different S-expressions, output “AMBIGUOUS” (without quotes).\n\nA single space character should be inserted between the elements of the S-expression, while no space\ncharacter should be inserted after open brackets (“(”) and before closing brackets (“)”).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\na list of A, B, C and D\na list of A, a list of P and Q, B, a list of X, Y and Z and C\na list of A\na list of a list of A and B\n output: (A B C D)\n(A (P Q) B (X Y Z) C)\n(A)\nAMBIGUOUS"], "Pid": "p01190", "ProblemText": "Task Description: Shun and his professor are studying Lisp and S-expressions. Shun is in Tokyo in order to make a presen-\ntation of their research. His professor cannot go with him because of another work today.\n\nHe was making final checks for his slides an hour ago. Then, unfortunately, he found some serious\nmistakes! He called his professor immediately since he did not have enough data in his hand to fix the\nmistakes.\n\nTheir discussion is still going on now. The discussion looks proceeding with difficulty. Most of their data\nare written in S-expressions, so they have to exchange S-expressions via telephone.\n\nYour task is to write a program that outputs S-expressions represented by a given English phrase.\nTask Input: The first line of the input contains a single positive integer N, which represents the number of test cases.\nThen N test cases follow.\n\nEach case consists of a line. The line contains an English phrase that represents an S-expression. The\nlength of the phrase is up to 1000 characters.\n\nThe rules to translate an S-expression are as follows.\n\n An S-expression which has one element is translated into “a list of ”. (e. g. “(A)” will be “a list of A”)\n\n An S-expression which has two elements is translated into “a list of and ”. (e. g. “(A B)” will be “a list of A and B”)\n\n An S-expression which has more than three elements is translated into “a list of , , . . . and ”. (e. g. “(A B C D)” will be “a list of A, B, C and D”)\n\n The above rules are applied recursively. (e. g. “(A (P Q) B (X Y Z) C)” will be “a list of\n A, a list of P and Q, B, a list of X, Y and Z and C”)\nEach atomic element of an S-expression is a string made of less than 10 capital letters. All words (“a”,\n“list”, “of” and “and”) and atomic elements of S-expressions are separated by a single space character,\nbut no space character is inserted before comma (”, ”). No phrases for empty S-expressions occur in the\ninput. You can assume that all test cases can be translated into S-expressions, but the possible expressions\nmay not be unique.\nTask Output: For each test case, output the corresponding S-expression in a separate line. If the given phrase involves\ntwo or more different S-expressions, output “AMBIGUOUS” (without quotes).\n\nA single space character should be inserted between the elements of the S-expression, while no space\ncharacter should be inserted after open brackets (“(”) and before closing brackets (“)”).\nTask Samples: input: 4\na list of A, B, C and D\na list of A, a list of P and Q, B, a list of X, Y and Z and C\na list of A\na list of a list of A and B\n output: (A B C D)\n(A (P Q) B (X Y Z) C)\n(A)\nAMBIGUOUS\n\n" }, { "title": "Grated Radish", "content": "Grated radish (daikon-oroshi) is one of the essential spices in Japanese cuisine. As the name shows, it 's\nmade by grating white radish.\n\nYou are developing an automated robot for grating radish. You have finally finished developing mechan-\nical modules that grates radish according to given instructions from the microcomputer. So you need to\ndevelop the software in the microcomputer that controls the mechanical modules. As the first step, you\nhave decided to write a program that simulates the given instructions and predicts the resulting shape of\nthe radish.", "constraint": "", "input": "The input consists of a number of test cases. The first line on each case contains two floating numbers R\nand L (in centimeters), representing the radius and the length of the cylinder-shaped radish, respectively.\nThe white radish is placed in the xyz-coordinate system in such a way that cylinder 's axis of rotational\nsymmetry lies on the z axis.\nFigure 1: The placement of the white radish\n\nThe next line contains a single integer N, the number of instructions. The following N lines specify\ninstructions given to the grating robot. Each instruction consists of two floating numbers θ and V, where\nθ is the angle of grating plane in degrees, and V (in cubic centimeters) is the volume of the grated part of\nthe radish.\n\nYou may assume the following conditions:\n\n the direction is measured from positive x axis (0 degree) to positive y axis (90 degrees),\n\n 1 <= R <= 5 (in centimeters),\n\n 1 <= L <= 40 (in centimeters),\n\n 0 <= θ < 360, and\n\n the sum of V 's is the smaller than the volume of the given white radish.\n\nFigure 2: An example of grating", "output": "For each test case, print out in one line two numbers that indicate the shape of the base side (the side\nparallel to xy-plane) of the remaining radish after the entire grating procedure is finished, where the first\nnumber of the total length is the linear (straight) part and the second is the total length of the curved part.\n\nYou may output an arbitrary number of digits after the decimal points, provided that difference from the\ntrue answer is smaller than 10^-6 centimeters.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n1 2\n1\n42 3.141592653589793\n5 20\n3\n0 307.09242465218927\n180 307.09242465218927\n90 728.30573874452591\n output: 2.0 3.141592653589793\n8.660254038 5.235987756"], "Pid": "p01191", "ProblemText": "Task Description: Grated radish (daikon-oroshi) is one of the essential spices in Japanese cuisine. As the name shows, it 's\nmade by grating white radish.\n\nYou are developing an automated robot for grating radish. You have finally finished developing mechan-\nical modules that grates radish according to given instructions from the microcomputer. So you need to\ndevelop the software in the microcomputer that controls the mechanical modules. As the first step, you\nhave decided to write a program that simulates the given instructions and predicts the resulting shape of\nthe radish.\nTask Input: The input consists of a number of test cases. The first line on each case contains two floating numbers R\nand L (in centimeters), representing the radius and the length of the cylinder-shaped radish, respectively.\nThe white radish is placed in the xyz-coordinate system in such a way that cylinder 's axis of rotational\nsymmetry lies on the z axis.\nFigure 1: The placement of the white radish\n\nThe next line contains a single integer N, the number of instructions. The following N lines specify\ninstructions given to the grating robot. Each instruction consists of two floating numbers θ and V, where\nθ is the angle of grating plane in degrees, and V (in cubic centimeters) is the volume of the grated part of\nthe radish.\n\nYou may assume the following conditions:\n\n the direction is measured from positive x axis (0 degree) to positive y axis (90 degrees),\n\n 1 <= R <= 5 (in centimeters),\n\n 1 <= L <= 40 (in centimeters),\n\n 0 <= θ < 360, and\n\n the sum of V 's is the smaller than the volume of the given white radish.\n\nFigure 2: An example of grating\nTask Output: For each test case, print out in one line two numbers that indicate the shape of the base side (the side\nparallel to xy-plane) of the remaining radish after the entire grating procedure is finished, where the first\nnumber of the total length is the linear (straight) part and the second is the total length of the curved part.\n\nYou may output an arbitrary number of digits after the decimal points, provided that difference from the\ntrue answer is smaller than 10^-6 centimeters.\nTask Samples: input: 2\n1 2\n1\n42 3.141592653589793\n5 20\n3\n0 307.09242465218927\n180 307.09242465218927\n90 728.30573874452591\n output: 2.0 3.141592653589793\n8.660254038 5.235987756\n\n" }, { "title": "Greedy, Greedy.", "content": "Once upon a time, there lived a dumb king. He always messes things up based on his whimsical ideas.\nThis time, he decided to renew the kingdom 's coin system. Currently the kingdom has three types of\ncoins of values 1,5, and 25. He is thinking of replacing these with another set of coins.\n\nYesterday, he suggested a coin set of values 7,77, and 777. “They look so fortunate, don 't they? ” said\nhe. But obviously you can 't pay, for example, 10, using this coin set. Thus his suggestion was rejected.\n\nToday, he suggested a coin set of values 1,8,27, and 64. “They are all cubic numbers. How beautiful! ”\nBut another problem arises: using this coin set, you have to be quite careful in order to make changes\nefficiently. Suppose you are to make changes for a value of 40. If you use a greedy algorithm, i. e.\ncontinuously take the coin with the largest value until you reach an end, you will end up with seven\ncoins: one coin of value 27, one coin of value 8, and five coins of value 1. However, you can make\nchanges for 40 using five coins of value 8, which is fewer. This kind of inefficiency is undesirable, and\nthus his suggestion was rejected again.\n\nTomorrow, he would probably make another suggestion. It 's quite a waste of time dealing with him, so\nlet 's write a program that automatically examines whether the above two conditions are satisfied.", "constraint": "", "input": "The input consists of multiple test cases. Each test case is given in a line with the format\n\n n c_1 c_2 . . . c_n\n\nwhere n is the number of kinds of coins in the suggestion of the king, and each c_i is the coin value.\n\nYou may assume 1 <= n <= 50 and 0 < c_1 < c_2 < . . . < c_n < 1000.\n\nThe input is terminated by a single zero.", "output": "For each test case, print the answer in a line. The answer should begin with “Case #i: ”, where i is the\ntest case number starting from 1, followed by\n\n “Cannot pay some amount” if some (positive integer) amount of money cannot be paid using\n the given coin set,\n\n “Cannot use greedy algorithm” if any amount can be paid, though not necessarily with the\n least possible number of coins using the greedy algorithm,\n\n “OK” otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 5 25\n3 7 77 777\n4 1 8 27 64\n0\n output: Case #1: OK\nCase #2: Cannot pay some amount\nCase #3: Cannot use greedy algorithm"], "Pid": "p01192", "ProblemText": "Task Description: Once upon a time, there lived a dumb king. He always messes things up based on his whimsical ideas.\nThis time, he decided to renew the kingdom 's coin system. Currently the kingdom has three types of\ncoins of values 1,5, and 25. He is thinking of replacing these with another set of coins.\n\nYesterday, he suggested a coin set of values 7,77, and 777. “They look so fortunate, don 't they? ” said\nhe. But obviously you can 't pay, for example, 10, using this coin set. Thus his suggestion was rejected.\n\nToday, he suggested a coin set of values 1,8,27, and 64. “They are all cubic numbers. How beautiful! ”\nBut another problem arises: using this coin set, you have to be quite careful in order to make changes\nefficiently. Suppose you are to make changes for a value of 40. If you use a greedy algorithm, i. e.\ncontinuously take the coin with the largest value until you reach an end, you will end up with seven\ncoins: one coin of value 27, one coin of value 8, and five coins of value 1. However, you can make\nchanges for 40 using five coins of value 8, which is fewer. This kind of inefficiency is undesirable, and\nthus his suggestion was rejected again.\n\nTomorrow, he would probably make another suggestion. It 's quite a waste of time dealing with him, so\nlet 's write a program that automatically examines whether the above two conditions are satisfied.\nTask Input: The input consists of multiple test cases. Each test case is given in a line with the format\n\n n c_1 c_2 . . . c_n\n\nwhere n is the number of kinds of coins in the suggestion of the king, and each c_i is the coin value.\n\nYou may assume 1 <= n <= 50 and 0 < c_1 < c_2 < . . . < c_n < 1000.\n\nThe input is terminated by a single zero.\nTask Output: For each test case, print the answer in a line. The answer should begin with “Case #i: ”, where i is the\ntest case number starting from 1, followed by\n\n “Cannot pay some amount” if some (positive integer) amount of money cannot be paid using\n the given coin set,\n\n “Cannot use greedy algorithm” if any amount can be paid, though not necessarily with the\n least possible number of coins using the greedy algorithm,\n\n “OK” otherwise.\nTask Samples: input: 3 1 5 25\n3 7 77 777\n4 1 8 27 64\n0\n output: Case #1: OK\nCase #2: Cannot pay some amount\nCase #3: Cannot use greedy algorithm\n\n" }, { "title": "First Experience", "content": "After spending long long time, you had gotten tired of computer programming. Instead you were inter-\nested in electronic construction. As your first work, you built a simple calculator. It can handle positive\nintegers of up to four decimal digits, and perform addition, subtraction and multiplication of numbers.\nYou didn 't implement division just because it was so complicated. Although the calculator almost worked\nwell, you noticed that it displays unexpected results in several cases. So, you decided to try its simulation\nby a computer program in order to figure out the cause of unexpected behaviors.\n\nThe specification of the calculator you built is as follows. There are three registers on the calculator. The\nregister R1 stores the value of the operation result of the latest operation; the register R2 stores the new\ninput value; and the register R3 stores the input operator. At the beginning, both R1 and R2 hold zero,\nand R3 holds a null operator. The calculator has keys for decimal digits from ‘0 ' to ‘9 ' and operators\n‘+ ', ‘- ', ‘* ' and ‘= '. The four operators indicate addition, subtraction, multiplication and conclusion,\nrespectively. When a digit key is pressed, R2 is multiplied by ten, and then added by the pressed digit\n(as a number). When ‘+ ', ‘- ' or ‘* ' is pressed, the calculator first applies the binary operator held in R3\nto the values in R1 and R2 and updates R1 with the result of the operation. Suppose R1 has 10, R2 has\n3, and R3 has ‘- ' (subtraction operator), R1 is updated with 7 ( = 10 - 3). If R3 holds a null operator,\nthe result will be equal to the value of R2. After R1 is updated, R2 is cleared to zero and R3 is set to the\noperator which the user entered. ‘= ' indicates termination of a computation. So, when ‘= ' is pressed,\nthe calculator applies the operator held in R3 in the same manner as the other operators, and displays the\nfinal result to the user. After the final result is displayed, R3 is reinitialized with a null operator.\n\nThe calculator cannot handle numbers with five or more decimal digits. Because of that, if the intermediate computation produces a value less than 0 (i. e. , a negative number) or greater than 9999, the calculator\ndisplays “E” that stands for error, and ignores the rest of the user input until ‘= ' is pressed.\n\nYour task is to write a program to simulate the simple calculator.", "constraint": "", "input": "The input consists of multiple test cases.\n\nEach line of the input specifies one test case, indicating the order of key strokes which a user entered.\nThe input consists only decimal digits (from ‘0 ' to ‘9 ') and valid operators ‘+ ', ‘- ', ‘* ' and ‘= ' where ‘* '\nstands for ‘* '.\n\nYou may assume that ‘= ' occurs only at the end of each line, and no case contains more than 80 key\nstrokes.\n\nThe end of input is indicated by EOF.", "output": "For each test case, output one line which contains the result of simulation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1+2+3+4+5+6+7+8+9+10=\n1000-500-250-125=\n1*2*3*4*5*6=\n5000*5000=\n10-100=\n100*100=\n10000=\n output: 55\n125\n720\nE\nE\nE\nE"], "Pid": "p01193", "ProblemText": "Task Description: After spending long long time, you had gotten tired of computer programming. Instead you were inter-\nested in electronic construction. As your first work, you built a simple calculator. It can handle positive\nintegers of up to four decimal digits, and perform addition, subtraction and multiplication of numbers.\nYou didn 't implement division just because it was so complicated. Although the calculator almost worked\nwell, you noticed that it displays unexpected results in several cases. So, you decided to try its simulation\nby a computer program in order to figure out the cause of unexpected behaviors.\n\nThe specification of the calculator you built is as follows. There are three registers on the calculator. The\nregister R1 stores the value of the operation result of the latest operation; the register R2 stores the new\ninput value; and the register R3 stores the input operator. At the beginning, both R1 and R2 hold zero,\nand R3 holds a null operator. The calculator has keys for decimal digits from ‘0 ' to ‘9 ' and operators\n‘+ ', ‘- ', ‘* ' and ‘= '. The four operators indicate addition, subtraction, multiplication and conclusion,\nrespectively. When a digit key is pressed, R2 is multiplied by ten, and then added by the pressed digit\n(as a number). When ‘+ ', ‘- ' or ‘* ' is pressed, the calculator first applies the binary operator held in R3\nto the values in R1 and R2 and updates R1 with the result of the operation. Suppose R1 has 10, R2 has\n3, and R3 has ‘- ' (subtraction operator), R1 is updated with 7 ( = 10 - 3). If R3 holds a null operator,\nthe result will be equal to the value of R2. After R1 is updated, R2 is cleared to zero and R3 is set to the\noperator which the user entered. ‘= ' indicates termination of a computation. So, when ‘= ' is pressed,\nthe calculator applies the operator held in R3 in the same manner as the other operators, and displays the\nfinal result to the user. After the final result is displayed, R3 is reinitialized with a null operator.\n\nThe calculator cannot handle numbers with five or more decimal digits. Because of that, if the intermediate computation produces a value less than 0 (i. e. , a negative number) or greater than 9999, the calculator\ndisplays “E” that stands for error, and ignores the rest of the user input until ‘= ' is pressed.\n\nYour task is to write a program to simulate the simple calculator.\nTask Input: The input consists of multiple test cases.\n\nEach line of the input specifies one test case, indicating the order of key strokes which a user entered.\nThe input consists only decimal digits (from ‘0 ' to ‘9 ') and valid operators ‘+ ', ‘- ', ‘* ' and ‘= ' where ‘* '\nstands for ‘* '.\n\nYou may assume that ‘= ' occurs only at the end of each line, and no case contains more than 80 key\nstrokes.\n\nThe end of input is indicated by EOF.\nTask Output: For each test case, output one line which contains the result of simulation.\nTask Samples: input: 1+2+3+4+5+6+7+8+9+10=\n1000-500-250-125=\n1*2*3*4*5*6=\n5000*5000=\n10-100=\n100*100=\n10000=\n output: 55\n125\n720\nE\nE\nE\nE\n\n" }, { "title": "Web 0.5", "content": "In a forest, there lived a spider named Tim. Tim was so smart that he created a huge, well-structured web.\nSurprisingly, his web forms a set of equilateral and concentric N-sided polygons whose edge lengths\nform an arithmetic sequence.\nFigure 1: An example web of Tim\n\nCorresponding vertices of the N-sided polygons lie on a straight line, each apart from neighboring ver-\ntices by distance 1. Neighboring vertices are connected by a thread (shown in the figure as solid lines),\non which Tim can walk (you may regard Tim as a point). Radial axes are numbered from 1 to N in a\nrotational order, so you can denote by (r, i) the vertex on axis i and apart from the center of the web by\ndistance r. You may consider the web as infinitely large, i. e. consisting of infinite number of N-sided\npolygons, since the web is so gigantic.\n\nTim 's web is thus marvelous, but currently has one problem: due to rainstorms, some of the threads are\ndamaged and Tim can 't walk on those parts.\n\nNow, a bug has been caught on the web. Thanks to the web having so organized a structure, Tim accu-\nrately figures out where the bug is, and heads out for that position. You, as a biologist, are interested in\nwhether Tim is smart enough to move through the shortest possible route. To judge that, however, you\nneed to know the length of the shortest route yourself, and thereby decided to write a program which\ncalculates that length.", "constraint": "", "input": "The input consists of multiple test cases. Each test case begins with a line containing two integers N\n(3 <= N <= 100) and X (0 <= X <= 100), where N is as described above and X denotes the number of\ndamaged threads. Next line contains four integers r_S, i_S, r_T, and i_T, meaning that Tim is starting at (r_S, i_S) and the bug is at (r_T, i_T). This line is followed by X lines, each containing four integers r_A, i_A, r_B, and\ni_B, meaning that a thread connecting (r_A, i_A) and (r_B, i_B) is damaged. Here (r_A, i_A) and (r_B, i_B) will be\nalways neighboring to each other. Also, for all vertices (r, i) given above, you may assume 1 <= r <= 10^7\nand 1 <= i <= N.\n\nThere will be at most 200 test cases. You may also assume that Tim is always able to reach where the\nbug is.\n\nThe input is terminated by a line containing two zeros.", "output": "For each test case, print the length of the shortest route in a line. You may print any number of digits\nafter the decimal point, but the error must not be greater than 0.01.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 1\n2 1 3 2\n2 1 2 2\n0 0\n output: 4.18"], "Pid": "p01194", "ProblemText": "Task Description: In a forest, there lived a spider named Tim. Tim was so smart that he created a huge, well-structured web.\nSurprisingly, his web forms a set of equilateral and concentric N-sided polygons whose edge lengths\nform an arithmetic sequence.\nFigure 1: An example web of Tim\n\nCorresponding vertices of the N-sided polygons lie on a straight line, each apart from neighboring ver-\ntices by distance 1. Neighboring vertices are connected by a thread (shown in the figure as solid lines),\non which Tim can walk (you may regard Tim as a point). Radial axes are numbered from 1 to N in a\nrotational order, so you can denote by (r, i) the vertex on axis i and apart from the center of the web by\ndistance r. You may consider the web as infinitely large, i. e. consisting of infinite number of N-sided\npolygons, since the web is so gigantic.\n\nTim 's web is thus marvelous, but currently has one problem: due to rainstorms, some of the threads are\ndamaged and Tim can 't walk on those parts.\n\nNow, a bug has been caught on the web. Thanks to the web having so organized a structure, Tim accu-\nrately figures out where the bug is, and heads out for that position. You, as a biologist, are interested in\nwhether Tim is smart enough to move through the shortest possible route. To judge that, however, you\nneed to know the length of the shortest route yourself, and thereby decided to write a program which\ncalculates that length.\nTask Input: The input consists of multiple test cases. Each test case begins with a line containing two integers N\n(3 <= N <= 100) and X (0 <= X <= 100), where N is as described above and X denotes the number of\ndamaged threads. Next line contains four integers r_S, i_S, r_T, and i_T, meaning that Tim is starting at (r_S, i_S) and the bug is at (r_T, i_T). This line is followed by X lines, each containing four integers r_A, i_A, r_B, and\ni_B, meaning that a thread connecting (r_A, i_A) and (r_B, i_B) is damaged. Here (r_A, i_A) and (r_B, i_B) will be\nalways neighboring to each other. Also, for all vertices (r, i) given above, you may assume 1 <= r <= 10^7\nand 1 <= i <= N.\n\nThere will be at most 200 test cases. You may also assume that Tim is always able to reach where the\nbug is.\n\nThe input is terminated by a line containing two zeros.\nTask Output: For each test case, print the length of the shortest route in a line. You may print any number of digits\nafter the decimal point, but the error must not be greater than 0.01.\nTask Samples: input: 5 1\n2 1 3 2\n2 1 2 2\n0 0\n output: 4.18\n\n" }, { "title": "Philosopher's Stone", "content": "In search for wisdom and wealth, Alchemy, the art of transmutation, has long been pursued by people.\nThe crucial point of Alchemy was considered to find the recipe for philosopher 's stone, which will be a\ncatalyst to produce gold and silver from common metals, and even medicine giving eternal life.\n\nAlchemists owned Alchemical Reactors, symbols of their profession. Each recipe of Alchemy went like\nthis: gather appropriate materials; melt then mix them in your Reactor for an appropriate period; then\nyou will get the desired material along with some waste.\n\nA long experience presented two natural laws, which are widely accepted among Alchemists. One is the\nlaw of conservation of mass, that is, no reaction can change the total mass of things taking part. Because\nof this law, in any Alchemical reaction, mass of product is not greater than the sum of mass of materials.\nThe other is the law of the directionality in Alchemical reactions. This law implies, if the matter A\nproduces the matter B, then the matter A can never be produced using the matter B.\n\nOne night, Demiurge, the Master of Alchemists, revealed the recipe of philosopher 's stone to have every\nAlchemist 's dream realized. Since this night, this ultimate recipe, which had been sought for centuries,\nhas been an open secret.\n\nAlice and Betty were also Alchemists who had been seeking the philosopher 's stone and who were told\nthe ultimate recipe in that night. In addition, they deeply had wanted to complete the philosopher 's stone\nearlier than any other Alchemists, so they began to solve the way to complete the recipe in the shortest\ntime.\n\nYour task is write a program that computes the smallest number of days needed to complete the philoso-\npher 's stone, given the recipe of philosopher 's stone and materials in their hands.", "constraint": "", "input": "The input consists of a number of test cases.\n\nEach test case starts with a line containing a single integer n, then n recipes follow.\n\nEach recipe starts with a line containing a string, the name of the product. Then a line with two integers\nm and d is given, where m is the number of materials and d is the number of days needed to finish the\nreaction. Each of the following m lines specify the name and amount of a material needed for reaction.\n\nThose n recipes are followed by a list of materials the two Alchemists initially have. The first line\nindicates the size of the list. Then pairs of the material name and the amount are given, each pair in one\nline.\n\nEvery name contains printable characters of the ASCII code, i. e. no whitespace or control characters.\nNo two recipe will produce the item of the same name. Each test case always include one recipe for\n“philosopher 's-stone, ” which is wanted to be produced. Some empty lines may occur in the input\nfor human-readability.", "output": "For each case, output a single line containing the shortest day needed to complete producing the philoso-\npher 's stone, or “impossible” in case production of philosopher 's stone is impossible.\n\nAs there are two Alchemists, they can control two reaction in parallel. A reaction can start whenever the\nmaterials in recipe and at least one Alchemist is available. Time spent in any acts other than reaction,\nsuch as rests, meals, cleaning reactors, or exchanging items, can be regarded as negligibly small.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nphilosopher's-stone\n4 10\ntongue 1\ntear 1\ndunkelheit 1\naroma-materia 1\n\naroma-materia\n4 5\nsolt 1\nholy-water 1\ngolden-rock 1\nneutralizer 2\n\nneutralizer\n1 1\nred-rock 5\n\n7\ntongue 1\ntear 1\ndunkelheit 1\nsolt 2\nholy-water 3\ngolden-rock 2\nred-rock 10\n\n2\nphilosopher's-stone\n5 3\nninjin 1\njagaimo 3\ntamanegi 1\nbarmont 12\n\nbarmont\n3 1\ncurry 5\nkomugiko 20\nbatar 10\n\n7\nninjin 3\njagaimo 2\ntamanegi 5\ncurry 150\nkomugiko 750\nbatar 200\n\n0\n output: 16\nimpossible"], "Pid": "p01195", "ProblemText": "Task Description: In search for wisdom and wealth, Alchemy, the art of transmutation, has long been pursued by people.\nThe crucial point of Alchemy was considered to find the recipe for philosopher 's stone, which will be a\ncatalyst to produce gold and silver from common metals, and even medicine giving eternal life.\n\nAlchemists owned Alchemical Reactors, symbols of their profession. Each recipe of Alchemy went like\nthis: gather appropriate materials; melt then mix them in your Reactor for an appropriate period; then\nyou will get the desired material along with some waste.\n\nA long experience presented two natural laws, which are widely accepted among Alchemists. One is the\nlaw of conservation of mass, that is, no reaction can change the total mass of things taking part. Because\nof this law, in any Alchemical reaction, mass of product is not greater than the sum of mass of materials.\nThe other is the law of the directionality in Alchemical reactions. This law implies, if the matter A\nproduces the matter B, then the matter A can never be produced using the matter B.\n\nOne night, Demiurge, the Master of Alchemists, revealed the recipe of philosopher 's stone to have every\nAlchemist 's dream realized. Since this night, this ultimate recipe, which had been sought for centuries,\nhas been an open secret.\n\nAlice and Betty were also Alchemists who had been seeking the philosopher 's stone and who were told\nthe ultimate recipe in that night. In addition, they deeply had wanted to complete the philosopher 's stone\nearlier than any other Alchemists, so they began to solve the way to complete the recipe in the shortest\ntime.\n\nYour task is write a program that computes the smallest number of days needed to complete the philoso-\npher 's stone, given the recipe of philosopher 's stone and materials in their hands.\nTask Input: The input consists of a number of test cases.\n\nEach test case starts with a line containing a single integer n, then n recipes follow.\n\nEach recipe starts with a line containing a string, the name of the product. Then a line with two integers\nm and d is given, where m is the number of materials and d is the number of days needed to finish the\nreaction. Each of the following m lines specify the name and amount of a material needed for reaction.\n\nThose n recipes are followed by a list of materials the two Alchemists initially have. The first line\nindicates the size of the list. Then pairs of the material name and the amount are given, each pair in one\nline.\n\nEvery name contains printable characters of the ASCII code, i. e. no whitespace or control characters.\nNo two recipe will produce the item of the same name. Each test case always include one recipe for\n“philosopher 's-stone, ” which is wanted to be produced. Some empty lines may occur in the input\nfor human-readability.\nTask Output: For each case, output a single line containing the shortest day needed to complete producing the philoso-\npher 's stone, or “impossible” in case production of philosopher 's stone is impossible.\n\nAs there are two Alchemists, they can control two reaction in parallel. A reaction can start whenever the\nmaterials in recipe and at least one Alchemist is available. Time spent in any acts other than reaction,\nsuch as rests, meals, cleaning reactors, or exchanging items, can be regarded as negligibly small.\nTask Samples: input: 3\nphilosopher's-stone\n4 10\ntongue 1\ntear 1\ndunkelheit 1\naroma-materia 1\n\naroma-materia\n4 5\nsolt 1\nholy-water 1\ngolden-rock 1\nneutralizer 2\n\nneutralizer\n1 1\nred-rock 5\n\n7\ntongue 1\ntear 1\ndunkelheit 1\nsolt 2\nholy-water 3\ngolden-rock 2\nred-rock 10\n\n2\nphilosopher's-stone\n5 3\nninjin 1\njagaimo 3\ntamanegi 1\nbarmont 12\n\nbarmont\n3 1\ncurry 5\nkomugiko 20\nbatar 10\n\n7\nninjin 3\njagaimo 2\ntamanegi 5\ncurry 150\nkomugiko 750\nbatar 200\n\n0\n output: 16\nimpossible\n\n" }, { "title": "The Phantom", "content": "Mr. Hoge is in trouble. He just bought a new mansion, but it 's haunted by a phantom. He asked a famous conjurer\nDr. Huga to get rid of the phantom. Dr. Huga went to see the mansion, and found that the phantom is scared by\nits own mirror images. Dr. Huga set two flat mirrors in order to get rid of the phantom.\n\nAs you may know, you can make many mirror images even with only two mirrors. You are to count up the\nnumber of the images as his assistant. Given the coordinates of the mirrors and the phantom, show the number\nof images of the phantom which can be seen through the mirrors.", "constraint": "", "input": "The input consists of multiple test cases. Each test cases starts with a line which contains two positive integers,\np_x and p_y (1 <= p_x, p_y <= 50), which are the x- and y-coordinate of the phantom. In the next two lines, each line\ncontains four positive integers u_x, u_y, v_x and v_y (1 <= u_x, u_y, v_x, v_y <= 50), which are the coordinates of the mirror.\n\nEach mirror can be seen as a line segment, and its thickness is negligible. No mirror touches or crosses with\nanother mirror. Also, you can assume that no images will appear within the distance of 10^-5 from the endpoints\nof the mirrors.\n\nThe input ends with a line which contains two zeros.", "output": "For each case, your program should output one line to the standard output, which contains the number of images\nrecognized by the phantom. If the number is equal to or greater than 100, print “TOO MANY” instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n3 3 5 3\n3 5 5 6\n4 4\n3 3 5 3\n3 5 5 5\n0 0\n output: 4\nTOO MANY"], "Pid": "p01196", "ProblemText": "Task Description: Mr. Hoge is in trouble. He just bought a new mansion, but it 's haunted by a phantom. He asked a famous conjurer\nDr. Huga to get rid of the phantom. Dr. Huga went to see the mansion, and found that the phantom is scared by\nits own mirror images. Dr. Huga set two flat mirrors in order to get rid of the phantom.\n\nAs you may know, you can make many mirror images even with only two mirrors. You are to count up the\nnumber of the images as his assistant. Given the coordinates of the mirrors and the phantom, show the number\nof images of the phantom which can be seen through the mirrors.\nTask Input: The input consists of multiple test cases. Each test cases starts with a line which contains two positive integers,\np_x and p_y (1 <= p_x, p_y <= 50), which are the x- and y-coordinate of the phantom. In the next two lines, each line\ncontains four positive integers u_x, u_y, v_x and v_y (1 <= u_x, u_y, v_x, v_y <= 50), which are the coordinates of the mirror.\n\nEach mirror can be seen as a line segment, and its thickness is negligible. No mirror touches or crosses with\nanother mirror. Also, you can assume that no images will appear within the distance of 10^-5 from the endpoints\nof the mirrors.\n\nThe input ends with a line which contains two zeros.\nTask Output: For each case, your program should output one line to the standard output, which contains the number of images\nrecognized by the phantom. If the number is equal to or greater than 100, print “TOO MANY” instead.\nTask Samples: input: 4 4\n3 3 5 3\n3 5 5 6\n4 4\n3 3 5 3\n3 5 5 5\n0 0\n output: 4\nTOO MANY\n\n" }, { "title": "Rakunarok", "content": "You are deeply disappointed with the real world, so you have decided to live the rest of your life in the world of\nMMORPG (Massively Multi-Player Online Role Playing Game). You are no more concerned about the time you\nspend in the game: all you need is efficiency.\n\nOne day, you have to move from one town to another. In this game, some pairs of towns are connected by roads\nwhere players can travel. Various monsters will raid players on roads. However, since you are a high-level player,\nthey are nothing but the source of experience points. Every road is bi-directional. A path is represented by a\nsequence of towns, where consecutive towns are connected by roads.\n\nYou are now planning to move to the destination town through the most efficient path. Here, the efficiency of a\npath is measured by the total experience points you will earn in the path divided by the time needed to travel the\npath.\n\nSince your object is moving, not training, you choose only a straightforward path. A path is said straightforward\nif, for any two consecutive towns in the path, the latter is closer to the destination than the former. The distance\nof two towns is measured by the shortest time needed to move from one town to another.\n\nWrite a program to find a path that gives the highest efficiency.", "constraint": "", "input": "The first line contains a single integer c that indicates the number of cases.\n\nThe first line of each test case contains two integers n and m that represent the numbers of towns and roads\nrespectively. The next line contains two integers s and t that denote the starting and destination towns respectively.\nThen m lines follow. The i-th line contains four integers u_i, v_i, e_i, and t_i, where u_i and v_i are two towns connected\nby the i-th road, e_i is the experience points to be earned, and t_i is the time needed to pass the road.\n\nEach town is indicated by the town index number from 0 to (n - 1). The starting and destination towns never\ncoincide. n, m, e_i's and t_i's are positive and not greater than 1000.", "output": "For each case output in a single line, the highest possible efficiency. Print the answer with four decimal digits.\nThe answer may not contain an error greater than 10^-4.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n\n3 3\n0 2\n0 2 240 80\n0 1 130 60\n1 2 260 60\n\n3 3\n0 2\n0 2 180 60\n0 1 130 60\n1 2 260 60\n output: 3.2500\n3.0000"], "Pid": "p01197", "ProblemText": "Task Description: You are deeply disappointed with the real world, so you have decided to live the rest of your life in the world of\nMMORPG (Massively Multi-Player Online Role Playing Game). You are no more concerned about the time you\nspend in the game: all you need is efficiency.\n\nOne day, you have to move from one town to another. In this game, some pairs of towns are connected by roads\nwhere players can travel. Various monsters will raid players on roads. However, since you are a high-level player,\nthey are nothing but the source of experience points. Every road is bi-directional. A path is represented by a\nsequence of towns, where consecutive towns are connected by roads.\n\nYou are now planning to move to the destination town through the most efficient path. Here, the efficiency of a\npath is measured by the total experience points you will earn in the path divided by the time needed to travel the\npath.\n\nSince your object is moving, not training, you choose only a straightforward path. A path is said straightforward\nif, for any two consecutive towns in the path, the latter is closer to the destination than the former. The distance\nof two towns is measured by the shortest time needed to move from one town to another.\n\nWrite a program to find a path that gives the highest efficiency.\nTask Input: The first line contains a single integer c that indicates the number of cases.\n\nThe first line of each test case contains two integers n and m that represent the numbers of towns and roads\nrespectively. The next line contains two integers s and t that denote the starting and destination towns respectively.\nThen m lines follow. The i-th line contains four integers u_i, v_i, e_i, and t_i, where u_i and v_i are two towns connected\nby the i-th road, e_i is the experience points to be earned, and t_i is the time needed to pass the road.\n\nEach town is indicated by the town index number from 0 to (n - 1). The starting and destination towns never\ncoincide. n, m, e_i's and t_i's are positive and not greater than 1000.\nTask Output: For each case output in a single line, the highest possible efficiency. Print the answer with four decimal digits.\nThe answer may not contain an error greater than 10^-4.\nTask Samples: input: 2\n\n3 3\n0 2\n0 2 240 80\n0 1 130 60\n1 2 260 60\n\n3 3\n0 2\n0 2 180 60\n0 1 130 60\n1 2 260 60\n output: 3.2500\n3.0000\n\n" }, { "title": "Dock to the Future", "content": "You had long wanted a spaceship, and finally you bought a used one yesterday! You have heard that the most\ndifficult thing on spaceship driving is to stop your ship at the right position in the dock. Of course you are no\nexception. After a dozen of failures, you gave up doing all the docking process manually. You began to write a\nsimple program that helps you to stop a spaceship.\n\nFirst, you somehow put the spaceship on the straight course to the dock manually. Let the distance to the limit\nline be x[m], and the speed against the dock be v[m/s]. Now you turn on the decelerating rocket. Then, your\nprogram will control the rocket to stop the spaceship at the best position.\n\nYour spaceship is equipped with a decelerating rocket with n modes. When the spaceship is in mode-i (0 <= i < n),\nthe deceleration rate is a_i[m/s^2]. You cannot re-accelerate the spaceship. The accelerating rocket is too powerful\nto be used during docking. Also, you cannot turn off-and-on the decelerating rocket, because your spaceship is a\nused and old one, once you stopped the rocket, it is less certain whether you can turn it on again. In other words,\nthe time you turn off the rocket is the time you stop your spaceship at the right position.\n\nAfter turning on the deceleration rocket, your program can change the mode or stop the rocket at every sec-\nond, starting at the very moment the deceleration began. Given x and v, your program have to make a plan of\ndeceleration. The purpose and the priority of your program is as follows:\n\n Stop the spaceship exactly at the limit line. If this is possible, print “perfect”.\n\n If it is impossible, then stop the spaceship at the position nearest possible to the limit line, but before the\n line. In this case, print “good d”, where d is the distance between the limit line and the stopped position.\n Print three digits after the decimal point.\n\n If it is impossible again, decelerate the spaceship to have negative speed, and print “try again”.\n\n If all of these three cases are impossible, then the spaceship cannot avoid overrunning the limit line. In this\n case, print “crash”.", "constraint": "", "input": "The first line of the input consists of a single integer c, the number of test cases.\n\nEach test case begins with a single integer n (1 <= n <= 10), the number of deceleration modes. The following line\ncontains n positive integers a_0, . . . , a_n-1 (1 <= a_i <= 100), each denoting the deceleration rate of each mode.\n\nThe next line contains a single integer q (1 <= q <= 20), and then q lines follow. Each of them contains two positive\nintegers x and v (1 <= x, v <= 100) defined in the problem statement.", "output": "For each pair of x and v, print the result in one line. A blank line should be inserted between the test cases.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n3\n2 4 6\n4\n10 100\n2 3\n10 6\n7 6\n output: crash\ntry again\ngood 1.000\nperfect"], "Pid": "p01198", "ProblemText": "Task Description: You had long wanted a spaceship, and finally you bought a used one yesterday! You have heard that the most\ndifficult thing on spaceship driving is to stop your ship at the right position in the dock. Of course you are no\nexception. After a dozen of failures, you gave up doing all the docking process manually. You began to write a\nsimple program that helps you to stop a spaceship.\n\nFirst, you somehow put the spaceship on the straight course to the dock manually. Let the distance to the limit\nline be x[m], and the speed against the dock be v[m/s]. Now you turn on the decelerating rocket. Then, your\nprogram will control the rocket to stop the spaceship at the best position.\n\nYour spaceship is equipped with a decelerating rocket with n modes. When the spaceship is in mode-i (0 <= i < n),\nthe deceleration rate is a_i[m/s^2]. You cannot re-accelerate the spaceship. The accelerating rocket is too powerful\nto be used during docking. Also, you cannot turn off-and-on the decelerating rocket, because your spaceship is a\nused and old one, once you stopped the rocket, it is less certain whether you can turn it on again. In other words,\nthe time you turn off the rocket is the time you stop your spaceship at the right position.\n\nAfter turning on the deceleration rocket, your program can change the mode or stop the rocket at every sec-\nond, starting at the very moment the deceleration began. Given x and v, your program have to make a plan of\ndeceleration. The purpose and the priority of your program is as follows:\n\n Stop the spaceship exactly at the limit line. If this is possible, print “perfect”.\n\n If it is impossible, then stop the spaceship at the position nearest possible to the limit line, but before the\n line. In this case, print “good d”, where d is the distance between the limit line and the stopped position.\n Print three digits after the decimal point.\n\n If it is impossible again, decelerate the spaceship to have negative speed, and print “try again”.\n\n If all of these three cases are impossible, then the spaceship cannot avoid overrunning the limit line. In this\n case, print “crash”.\nTask Input: The first line of the input consists of a single integer c, the number of test cases.\n\nEach test case begins with a single integer n (1 <= n <= 10), the number of deceleration modes. The following line\ncontains n positive integers a_0, . . . , a_n-1 (1 <= a_i <= 100), each denoting the deceleration rate of each mode.\n\nThe next line contains a single integer q (1 <= q <= 20), and then q lines follow. Each of them contains two positive\nintegers x and v (1 <= x, v <= 100) defined in the problem statement.\nTask Output: For each pair of x and v, print the result in one line. A blank line should be inserted between the test cases.\nTask Samples: input: 1\n3\n2 4 6\n4\n10 100\n2 3\n10 6\n7 6\n output: crash\ntry again\ngood 1.000\nperfect\n\n" }, { "title": "Flame of Nucleus", "content": "Year 20XX — a nuclear explosion has burned the world. Half the people on the planet have died. Fearful.\n\nOne city, fortunately, was not directly damaged by the explosion. This city consists of N domes (numbered 1\nthrough N inclusive) and M bidirectional transportation pipelines connecting the domes. In dome i, P_i citizens\nreside currently and there is a nuclear shelter capable of protecting K_i citizens. Also, it takes D_i days to travel\nfrom one end to the other end of pipeline i.\n\nIt has been turned out that this city will be polluted by nuclear radiation in L days after today. So each citizen\nshould take refuge in some shelter, possibly traveling through the pipelines. Citizens will be dead if they reach\ntheir shelters in exactly or more than L days.\n\nHow many citizens can survive at most in this situation?", "constraint": "", "input": "The input consists of multiple test cases. Each test case begins with a line consisting of three integers N, M\nand L (1 <= N <= 100, M >= 0,1 <= L <= 10000). This is followed by M lines describing the configuration of\ntransportation pipelines connecting the domes. The i-th line contains three integers A_i, B_i and D_i (1 <= A_i < B_i <=\nN, 1 <= D_i <= 10000), denoting that the i-th pipeline connects dome A_i and B_i. There is at most one pipeline\nbetween any pair of domes. Finally, there come two lines, each consisting of N integers. The first gives P_1 , . . . ,\nP_N (0 <= P_i <= 10^6) and the second gives K_1 , . . . , K_N (0 <= K_i <= 10^6).\n\nThe input is terminated by EOF. All integers in each line are separated by a whitespace.", "output": "For each test case, print in a line the maximum number of people who can survive.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 0 1\n51\n50\n2 1 1\n1 2 1\n1000 0\n0 1000\n4 3 5\n1 2 4\n1 3 1\n3 4 2\n0 1000 1000 1000\n3000 0 0 0\n output: 50\n0\n3000"], "Pid": "p01199", "ProblemText": "Task Description: Year 20XX — a nuclear explosion has burned the world. Half the people on the planet have died. Fearful.\n\nOne city, fortunately, was not directly damaged by the explosion. This city consists of N domes (numbered 1\nthrough N inclusive) and M bidirectional transportation pipelines connecting the domes. In dome i, P_i citizens\nreside currently and there is a nuclear shelter capable of protecting K_i citizens. Also, it takes D_i days to travel\nfrom one end to the other end of pipeline i.\n\nIt has been turned out that this city will be polluted by nuclear radiation in L days after today. So each citizen\nshould take refuge in some shelter, possibly traveling through the pipelines. Citizens will be dead if they reach\ntheir shelters in exactly or more than L days.\n\nHow many citizens can survive at most in this situation?\nTask Input: The input consists of multiple test cases. Each test case begins with a line consisting of three integers N, M\nand L (1 <= N <= 100, M >= 0,1 <= L <= 10000). This is followed by M lines describing the configuration of\ntransportation pipelines connecting the domes. The i-th line contains three integers A_i, B_i and D_i (1 <= A_i < B_i <=\nN, 1 <= D_i <= 10000), denoting that the i-th pipeline connects dome A_i and B_i. There is at most one pipeline\nbetween any pair of domes. Finally, there come two lines, each consisting of N integers. The first gives P_1 , . . . ,\nP_N (0 <= P_i <= 10^6) and the second gives K_1 , . . . , K_N (0 <= K_i <= 10^6).\n\nThe input is terminated by EOF. All integers in each line are separated by a whitespace.\nTask Output: For each test case, print in a line the maximum number of people who can survive.\nTask Samples: input: 1 0 1\n51\n50\n2 1 1\n1 2 1\n1000 0\n0 1000\n4 3 5\n1 2 4\n1 3 1\n3 4 2\n0 1000 1000 1000\n3000 0 0 0\n output: 50\n0\n3000\n\n" }, { "title": "Resource", "content": "Dr. Keith Miller is a researcher who studies the history of Island of Constitutional People 's Country (ICPC).\nMany studies by him and his colleagues have revealed various facts about ICPC. Although it is a single large\nisland today, it was divided in several smaller islands in some ancient period, and each island was ruled by a\nking. In addition to the islands, there were several resource regions on the sea, and people living in the islands\nused energy resource obtained in those regions.\n\nRecently Dr. Miller discovered some ancient documents that described the agreements made among the kings.\nSome of them focused on resource regions, and can be summarized as follows: each island was allowed to mine\nresource only in its exclusive resource zone (ERZ). The ERZ of each island was defined as a sea area within an\nagreed distance d from the boundary of the island. In case areas occur where more than one ERZ overwrapped,\nsuch areas were divided by equidistant curves, and each divided area belonged to the ERZ of the nearest island.\n\nNow Dr. Miller wants to know how much resource allocated to each island, which will help him to grasp the\npower balance among the islands. For that purpose, he called you as a talented programmer. Your task is to write\na program that makes rough estimation about the amount of resource available for each island. For simplicity,\nthe world map is represented on a two-dimensional plane, where each of the islands and the resource regions\nis represented as a convex polygon. Because of the difference in the resource deposit among the regions, the\namount of resource per unit area is also given for each region. In this settings, the amount of resource available\nin a (partial) area of a region is given by * . The total amount of resource\nfor each island is given by the sum of the amount of resource available in all (partial) areas of the regions included\nin the ERZ.", "constraint": "", "input": "The input consists of no more than five test cases.\n\nThe first line of each test case contains two integers M and N (1 <= M, N <= 5) that indicate the numbers of islands\nand resource regions, respectively. The next line contains a single real number d (0 < d <= 10) that represents the\nagreed distance for the ERZs. After that M lines appear to describe the islands: the i-th line specifies the shape\nof the i-th island as stated below. Then N lines appear to describe the resource regions: the j-th line contains\na single real number a_j (0 < a_j <= 1), the amount of resource per unit area in the j-th region, followed by the\nspecification for the shape of the j-th region.\n\nEach of the (polygonal) shapes is specified by a single integer n (3 <= n <= 6), the number of vertices in the\nshape, followed by n pairs of integers where the k-th pair x_k and y_k gives the coordinates of the k-th vertex. Each\ncoordinate value ranges from 0 to 50 inclusive. The vertices are given in the counterclockwise order. No shape\nhas vertices other than the endpoints of edges. No pair of shapes overwrap.\n\nEach real number in the input is given with up to two fractional digits.\n\nThe input is terminated by a line that contains two zeros.", "output": "For each test case, print M lines where the i-th line represents the total amount of resource for the i-th island.\nEach amount should be printed with one fractional digit, and should not contain an error greater than 0.1.\n\nPrint an empty line between two consecutive cases.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n10.00\n3 10 10 20 10 10 20\n4 30 10 40 10 40 20 30 20\n1.00 3 0 0 10 0 0 10\n0.50 4 20 15 25 15 25 20 20 20\n0.75 6 40 35 50 40 40 50 30 50 25 45 30 40\n4 1\n5.00\n3 0 0 24 0 0 24\n3 50 0 50 24 26 0\n3 0 50 0 26 24 50\n3 50 50 26 50 50 26\n1.00 4 25 0 50 25 25 50 0 25\n0 0\n output: 35.4\n5.6\n\n133.3\n133.3\n133.3\n133.3"], "Pid": "p01200", "ProblemText": "Task Description: Dr. Keith Miller is a researcher who studies the history of Island of Constitutional People 's Country (ICPC).\nMany studies by him and his colleagues have revealed various facts about ICPC. Although it is a single large\nisland today, it was divided in several smaller islands in some ancient period, and each island was ruled by a\nking. In addition to the islands, there were several resource regions on the sea, and people living in the islands\nused energy resource obtained in those regions.\n\nRecently Dr. Miller discovered some ancient documents that described the agreements made among the kings.\nSome of them focused on resource regions, and can be summarized as follows: each island was allowed to mine\nresource only in its exclusive resource zone (ERZ). The ERZ of each island was defined as a sea area within an\nagreed distance d from the boundary of the island. In case areas occur where more than one ERZ overwrapped,\nsuch areas were divided by equidistant curves, and each divided area belonged to the ERZ of the nearest island.\n\nNow Dr. Miller wants to know how much resource allocated to each island, which will help him to grasp the\npower balance among the islands. For that purpose, he called you as a talented programmer. Your task is to write\na program that makes rough estimation about the amount of resource available for each island. For simplicity,\nthe world map is represented on a two-dimensional plane, where each of the islands and the resource regions\nis represented as a convex polygon. Because of the difference in the resource deposit among the regions, the\namount of resource per unit area is also given for each region. In this settings, the amount of resource available\nin a (partial) area of a region is given by * . The total amount of resource\nfor each island is given by the sum of the amount of resource available in all (partial) areas of the regions included\nin the ERZ.\nTask Input: The input consists of no more than five test cases.\n\nThe first line of each test case contains two integers M and N (1 <= M, N <= 5) that indicate the numbers of islands\nand resource regions, respectively. The next line contains a single real number d (0 < d <= 10) that represents the\nagreed distance for the ERZs. After that M lines appear to describe the islands: the i-th line specifies the shape\nof the i-th island as stated below. Then N lines appear to describe the resource regions: the j-th line contains\na single real number a_j (0 < a_j <= 1), the amount of resource per unit area in the j-th region, followed by the\nspecification for the shape of the j-th region.\n\nEach of the (polygonal) shapes is specified by a single integer n (3 <= n <= 6), the number of vertices in the\nshape, followed by n pairs of integers where the k-th pair x_k and y_k gives the coordinates of the k-th vertex. Each\ncoordinate value ranges from 0 to 50 inclusive. The vertices are given in the counterclockwise order. No shape\nhas vertices other than the endpoints of edges. No pair of shapes overwrap.\n\nEach real number in the input is given with up to two fractional digits.\n\nThe input is terminated by a line that contains two zeros.\nTask Output: For each test case, print M lines where the i-th line represents the total amount of resource for the i-th island.\nEach amount should be printed with one fractional digit, and should not contain an error greater than 0.1.\n\nPrint an empty line between two consecutive cases.\nTask Samples: input: 2 3\n10.00\n3 10 10 20 10 10 20\n4 30 10 40 10 40 20 30 20\n1.00 3 0 0 10 0 0 10\n0.50 4 20 15 25 15 25 20 20 20\n0.75 6 40 35 50 40 40 50 30 50 25 45 30 40\n4 1\n5.00\n3 0 0 24 0 0 24\n3 50 0 50 24 26 0\n3 0 50 0 26 24 50\n3 50 50 26 50 50 26\n1.00 4 25 0 50 25 25 50 0 25\n0 0\n output: 35.4\n5.6\n\n133.3\n133.3\n133.3\n133.3\n\n" }, { "title": "Exact Arithmetic", "content": "Let X be a set of all rational numbers and all numbers of form q√r, where q is a non-zero rational number and r\nis an integer greater than 1. Here r must not have a quadratic number except for 1 as its divisor. Also, let X^* be a\nset of all numbers which can be expressed as a sum of one or more elements in X.\n\nA machine Y is a stack-based calculator which operates on the values in X^* and has the instructions shown in the table below.\n\n
    \n \n push n \n Pushes an integer specified in the operand onto the stack. \n \n add \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 + x_1). \n \n sub \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 - x_1 ). \n \n mul \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 * x_1 ).\n \n \n div \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 ÷ x_1).\nx_1 must be a non-zero value in X (not X^*).\n \n \n sqrt \n Pops one value x from the stack and pushes the square root of x. x must be a non-negative rational number.\n \n \n disp \n Pops one value x from the stack, and outputs the string representation of the value x to the display. The representation rules are stated later.\n \n \n stop \n Terminates calculation. The stack must be empty when this instruction is called.\n \n \nTable 1: Instruction Set for the Machine Y\n\nA sufficient number of values must exist in the stack on execution of every instruction. In addition, due to the\nlimitation of the machine Y, no more values can be pushed when the stack already stores as many as 256 values.\nAlso, there exist several restrictions on values to be pushed onto the stack:\n\n For rational numbers, neither numerator nor denominator in the irreducible form may exceed 32,768 in its absolute value.\n\n For any element in X of the form q√r = (a/b)√r, |a√r| <= 32,768 and |b| <= 32,768.\n\n For any element in X^*, each term in the sum must satisfy the above conditions.\nThe rules for the string representations of the values (on the machine Y) are as follows:\n\n A rational number is represented as either an integer or an irreducible fraction with a denominator greater\n than 1. A fraction is represented as \"/\". A sign symbol - precedes in case of a negative number.\n\n A number of the form q√r is represented as \"^*sqrt(r)\" except for the case\n with q = ±1, in which the number is represented as \"sqrt(r)\" (q = 1) or \"-sqrt(r)\" (q = -1).\n\n For the sum of two or more elements of X, string representations of all the (non-zero) elements are con-\n nected using the binary operator +. In this case, all terms with the same rooted number are merged into a\n single term, and the terms must be shown in the ascending order of its root component. For the purpose of\n this rule, all rational numbers are regarded to accompany √1.\n\n There is exactly one space character before and after each of the binary operator +. No space character appears at any other place.\nThe followings are a few examples of valid string representations:\n\n0\n1\n-1/10\n2*sqrt(2) + 1/2*sqrt(3) + -1/2*sqrt(5)\n1/2 + sqrt(10) + -sqrt(30)\n\nYour task is to write a program that simulates the machine Y.", "constraint": "", "input": "The input is a sequence of instructions. Each line contains a single instruction. You may assume that every\ninstruction is called in a legal way. The instruction stop appears only once, at the end of the entire input.", "output": "Output the strings which the machine Y will display. Write each string in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: push 1\npush 2\nsqrt\ndiv\npush 1\npush 3\nsqrt\ndiv\nadd\ndisp\npush 8\nsqrt\npush 3\npush 2\nsqrt\nmul\nadd\ndisp\nstop\n output: 1/2*sqrt(2) + 1/3*sqrt(3)\n5*sqrt(2)"], "Pid": "p01201", "ProblemText": "Task Description: Let X be a set of all rational numbers and all numbers of form q√r, where q is a non-zero rational number and r\nis an integer greater than 1. Here r must not have a quadratic number except for 1 as its divisor. Also, let X^* be a\nset of all numbers which can be expressed as a sum of one or more elements in X.\n\nA machine Y is a stack-based calculator which operates on the values in X^* and has the instructions shown in the table below.\n\n
    \n \n push n \n Pushes an integer specified in the operand onto the stack. \n \n add \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 + x_1). \n \n sub \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 - x_1 ). \n \n mul \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 * x_1 ).\n \n \n div \n Pops two values x_1 and x_2 from the top of the stack in this order, then pushes (x_2 ÷ x_1).\nx_1 must be a non-zero value in X (not X^*).\n \n \n sqrt \n Pops one value x from the stack and pushes the square root of x. x must be a non-negative rational number.\n \n \n disp \n Pops one value x from the stack, and outputs the string representation of the value x to the display. The representation rules are stated later.\n \n \n stop \n Terminates calculation. The stack must be empty when this instruction is called.\n \n \nTable 1: Instruction Set for the Machine Y\n\nA sufficient number of values must exist in the stack on execution of every instruction. In addition, due to the\nlimitation of the machine Y, no more values can be pushed when the stack already stores as many as 256 values.\nAlso, there exist several restrictions on values to be pushed onto the stack:\n\n For rational numbers, neither numerator nor denominator in the irreducible form may exceed 32,768 in its absolute value.\n\n For any element in X of the form q√r = (a/b)√r, |a√r| <= 32,768 and |b| <= 32,768.\n\n For any element in X^*, each term in the sum must satisfy the above conditions.\nThe rules for the string representations of the values (on the machine Y) are as follows:\n\n A rational number is represented as either an integer or an irreducible fraction with a denominator greater\n than 1. A fraction is represented as \"/\". A sign symbol - precedes in case of a negative number.\n\n A number of the form q√r is represented as \"^*sqrt(r)\" except for the case\n with q = ±1, in which the number is represented as \"sqrt(r)\" (q = 1) or \"-sqrt(r)\" (q = -1).\n\n For the sum of two or more elements of X, string representations of all the (non-zero) elements are con-\n nected using the binary operator +. In this case, all terms with the same rooted number are merged into a\n single term, and the terms must be shown in the ascending order of its root component. For the purpose of\n this rule, all rational numbers are regarded to accompany √1.\n\n There is exactly one space character before and after each of the binary operator +. No space character appears at any other place.\nThe followings are a few examples of valid string representations:\n\n0\n1\n-1/10\n2*sqrt(2) + 1/2*sqrt(3) + -1/2*sqrt(5)\n1/2 + sqrt(10) + -sqrt(30)\n\nYour task is to write a program that simulates the machine Y.\nTask Input: The input is a sequence of instructions. Each line contains a single instruction. You may assume that every\ninstruction is called in a legal way. The instruction stop appears only once, at the end of the entire input.\nTask Output: Output the strings which the machine Y will display. Write each string in a line.\nTask Samples: input: push 1\npush 2\nsqrt\ndiv\npush 1\npush 3\nsqrt\ndiv\nadd\ndisp\npush 8\nsqrt\npush 3\npush 2\nsqrt\nmul\nadd\ndisp\nstop\n output: 1/2*sqrt(2) + 1/3*sqrt(3)\n5*sqrt(2)\n\n" }, { "title": "Problem A: Dance Dance Revolution", "content": "Dance Dance Revolution is one of the most popular arcade games in Japan. The rule of this game is very\nsimple. A series of four arrow symbols, up, down, left and right, flows downwards on the screen in time\nto music. The machine has four panels under your foot, each of which corresponds to one of the four\narrows, and you have to make steps on these panels according to the arrows displayed on the screen. The\nmore accurate in timing, the higher score you will mark.\nFigure 1: Layout of Arrow Panels and Screen\n\nEach series of arrows is commonly called a score. Difficult scores usually have hundreds of arrows, and\nnewbies will often be scared when seeing those arrows fill up the monitor screen. Conversely, scores\nwith fewer arrows are considered to be easy ones.\n\nOne day, a friend of yours, who is an enthusiast of this game, asked you a favor. What he wanted is an\nautomated method to see if given scores are natural. A score is considered as natural when there is a\nsequence of steps that meets all the following conditions:\n\n left-foot steps and right-foot steps appear in turn;\n\n the same panel is not stepped on any two consecutive arrows;\n\n a player can keep his or her upper body facing forward during a play; and\n his or her legs never cross each other.\n\nYour task is to write a program that determines whether scores are natural ones.", "constraint": "", "input": "The first line of the input contains a positive integer. This indicates the number of data sets.\n\nEach data set consists of a string written in a line. Each string is made of four letters, “U” for up, “D”\nfor down, “L” for left and “R” for right, and specifies arrows in a score. No string contains more than\n100,000 characters.", "output": "For each data set, output in a line “Yes” if the score is natural, or “No” otherwise.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\nUU\nRDUL\nULDURDULDURDULDURDULDURD\n output: No\nYes\nYes"], "Pid": "p01202", "ProblemText": "Task Description: Dance Dance Revolution is one of the most popular arcade games in Japan. The rule of this game is very\nsimple. A series of four arrow symbols, up, down, left and right, flows downwards on the screen in time\nto music. The machine has four panels under your foot, each of which corresponds to one of the four\narrows, and you have to make steps on these panels according to the arrows displayed on the screen. The\nmore accurate in timing, the higher score you will mark.\nFigure 1: Layout of Arrow Panels and Screen\n\nEach series of arrows is commonly called a score. Difficult scores usually have hundreds of arrows, and\nnewbies will often be scared when seeing those arrows fill up the monitor screen. Conversely, scores\nwith fewer arrows are considered to be easy ones.\n\nOne day, a friend of yours, who is an enthusiast of this game, asked you a favor. What he wanted is an\nautomated method to see if given scores are natural. A score is considered as natural when there is a\nsequence of steps that meets all the following conditions:\n\n left-foot steps and right-foot steps appear in turn;\n\n the same panel is not stepped on any two consecutive arrows;\n\n a player can keep his or her upper body facing forward during a play; and\n his or her legs never cross each other.\n\nYour task is to write a program that determines whether scores are natural ones.\nTask Input: The first line of the input contains a positive integer. This indicates the number of data sets.\n\nEach data set consists of a string written in a line. Each string is made of four letters, “U” for up, “D”\nfor down, “L” for left and “R” for right, and specifies arrows in a score. No string contains more than\n100,000 characters.\nTask Output: For each data set, output in a line “Yes” if the score is natural, or “No” otherwise.\nTask Samples: input: 3\nUU\nRDUL\nULDURDULDURDULDURDULDURD\n output: No\nYes\nYes\n\n" }, { "title": "Problem B: Compress Files", "content": "Your computer is a little old-fashioned. Its CPU is slow, its memory is not enough, and its hard drive is\nnear to running out of space. It is natural for you to hunger for a new computer, but sadly you are not so\nrich. You have to live with the aged computer for a while.\n\nAt present, you have a trouble that requires a temporary measure immediately. You downloaded a new\nsoftware from the Internet, but failed to install due to the lack of space. For this reason, you have decided\nto compress all the existing files into archives and remove all the original uncompressed files, so more\nspace becomes available in your hard drive.\n\nIt is a little complicated task to do this within the limited space of your hard drive. You are planning to\nmake free space by repeating the following three-step procedure:\n\n Choose a set of files that have not been compressed yet.\n\n Compress the chosen files into one new archive and save it in your hard drive. Note that this step\n needs space enough to store both of the original files and the archive in your hard drive.\n\n Remove all the files that have been compressed.\nFor simplicity, you don 't take into account extraction of any archives, but you would like to reduce the\nnumber of archives as much as possible under this condition. Your task is to write a program to find the\nminimum number of archives for each given set of uncompressed files.", "constraint": "", "input": "The input consists of multiple data sets.\n\nEach data set starts with a line containing two integers n (1 <= n <= 14) and m (1 <= m <= 1000), where\nn indicates the number of files and m indicates the available space of your hard drive before the task of\ncompression. This line is followed by n lines, each of which contains two integers b_i and a_i. b_i indicates\nthe size of the i-th file without compression, and a_i indicates the size when compressed. The size of each\narchive is the sum of the compressed sizes of its contents. It is guaranteed that b_i >= a_i holds for any\n1 <= i <= n.\n\nA line containing two zeros indicates the end of input.", "output": "For each test case, print the minimum number of compressed files in a line. If you cannot compress all\nthe files in any way, print “Impossible” instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 1\n2 1\n2 1\n2 1\n2 1\n2 1\n5 1\n1 1\n4 2\n0 0\n output: 2\nImpossible"], "Pid": "p01203", "ProblemText": "Task Description: Your computer is a little old-fashioned. Its CPU is slow, its memory is not enough, and its hard drive is\nnear to running out of space. It is natural for you to hunger for a new computer, but sadly you are not so\nrich. You have to live with the aged computer for a while.\n\nAt present, you have a trouble that requires a temporary measure immediately. You downloaded a new\nsoftware from the Internet, but failed to install due to the lack of space. For this reason, you have decided\nto compress all the existing files into archives and remove all the original uncompressed files, so more\nspace becomes available in your hard drive.\n\nIt is a little complicated task to do this within the limited space of your hard drive. You are planning to\nmake free space by repeating the following three-step procedure:\n\n Choose a set of files that have not been compressed yet.\n\n Compress the chosen files into one new archive and save it in your hard drive. Note that this step\n needs space enough to store both of the original files and the archive in your hard drive.\n\n Remove all the files that have been compressed.\nFor simplicity, you don 't take into account extraction of any archives, but you would like to reduce the\nnumber of archives as much as possible under this condition. Your task is to write a program to find the\nminimum number of archives for each given set of uncompressed files.\nTask Input: The input consists of multiple data sets.\n\nEach data set starts with a line containing two integers n (1 <= n <= 14) and m (1 <= m <= 1000), where\nn indicates the number of files and m indicates the available space of your hard drive before the task of\ncompression. This line is followed by n lines, each of which contains two integers b_i and a_i. b_i indicates\nthe size of the i-th file without compression, and a_i indicates the size when compressed. The size of each\narchive is the sum of the compressed sizes of its contents. It is guaranteed that b_i >= a_i holds for any\n1 <= i <= n.\n\nA line containing two zeros indicates the end of input.\nTask Output: For each test case, print the minimum number of compressed files in a line. If you cannot compress all\nthe files in any way, print “Impossible” instead.\nTask Samples: input: 6 1\n2 1\n2 1\n2 1\n2 1\n2 1\n5 1\n1 1\n4 2\n0 0\n output: 2\nImpossible\n\n" }, { "title": "Problem C: Save the Energy", "content": "You were caught in a magical trap and transferred to a strange field due to its cause. This field is three-\ndimensional and has many straight paths of infinite length. With your special ability, you found where\nyou can exit the field, but moving there is not so easy. You can move along the paths easily without your\nenergy, but you need to spend your energy when moving outside the paths. One unit of energy is required\nper distance unit. As you want to save your energy, you have decided to find the best route to the exit\nwith the assistance of your computer.\n\nYour task is to write a program that computes the minimum amount of energy required to move between\nthe given source and destination. The width of each path is small enough to be negligible, and so is your\nsize.", "constraint": "", "input": "The input consists of multiple data sets. Each data set has the following format:\nN\nx_s y_s z_s x_t y_t z_t\nx_1,1 y_1,1 z_1,1 x_1,2 y_1,2 z_1,2\n .\n .\n .\nx_N, 1 y_N, 1 z_N, 1 x_N, 2 y_N, 2 z_N, 2\n\nN is an integer that indicates the number of the straight paths (2 <= N <= 100). (x_s, y_s, z_s) and (x_t, y_t, z_t)\ndenote the coordinates of the source and the destination respectively. (x_i, 1, y_i, 1, z_i, 1) and (x_i, 2, y_i, 2, z_i, 2)\ndenote the coordinates of the two points that the i-th straight path passes. All coordinates do not exceed 30,000 in their absolute values.\n\nThe distance units between two points (x_u, y_u, z_u) and (x_v, y_v, z_v) is given by the Euclidean distance as follows:\n\nIt is guaranteed that the source and the destination both lie on paths. Also, each data set contains no\nstraight paths that are almost but not actually parallel, although may contain some straight paths that are\nstrictly parallel.\n\nThe end of input is indicated by a line with a single zero. This is not part of any data set.", "output": "For each data set, print the required energy on a line. Each value may be printed with an arbitrary number\nof decimal digits, but should not contain the error greater than 0.001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n0 0 0 0 2 0\n0 0 1 0 0 -1\n2 0 0 0 2 0\n3\n0 5 0 3 1 4\n0 1 0 0 -1 0\n1 0 1 -1 0 1\n3 1 -1 3 1 1\n2\n0 0 0 3 0 0\n0 0 0 0 1 0\n3 0 0 3 1 0\n0\n output: 1.414\n2.000\n3.000"], "Pid": "p01204", "ProblemText": "Task Description: You were caught in a magical trap and transferred to a strange field due to its cause. This field is three-\ndimensional and has many straight paths of infinite length. With your special ability, you found where\nyou can exit the field, but moving there is not so easy. You can move along the paths easily without your\nenergy, but you need to spend your energy when moving outside the paths. One unit of energy is required\nper distance unit. As you want to save your energy, you have decided to find the best route to the exit\nwith the assistance of your computer.\n\nYour task is to write a program that computes the minimum amount of energy required to move between\nthe given source and destination. The width of each path is small enough to be negligible, and so is your\nsize.\nTask Input: The input consists of multiple data sets. Each data set has the following format:\nN\nx_s y_s z_s x_t y_t z_t\nx_1,1 y_1,1 z_1,1 x_1,2 y_1,2 z_1,2\n .\n .\n .\nx_N, 1 y_N, 1 z_N, 1 x_N, 2 y_N, 2 z_N, 2\n\nN is an integer that indicates the number of the straight paths (2 <= N <= 100). (x_s, y_s, z_s) and (x_t, y_t, z_t)\ndenote the coordinates of the source and the destination respectively. (x_i, 1, y_i, 1, z_i, 1) and (x_i, 2, y_i, 2, z_i, 2)\ndenote the coordinates of the two points that the i-th straight path passes. All coordinates do not exceed 30,000 in their absolute values.\n\nThe distance units between two points (x_u, y_u, z_u) and (x_v, y_v, z_v) is given by the Euclidean distance as follows:\n\nIt is guaranteed that the source and the destination both lie on paths. Also, each data set contains no\nstraight paths that are almost but not actually parallel, although may contain some straight paths that are\nstrictly parallel.\n\nThe end of input is indicated by a line with a single zero. This is not part of any data set.\nTask Output: For each data set, print the required energy on a line. Each value may be printed with an arbitrary number\nof decimal digits, but should not contain the error greater than 0.001.\nTask Samples: input: 2\n0 0 0 0 2 0\n0 0 1 0 0 -1\n2 0 0 0 2 0\n3\n0 5 0 3 1 4\n0 1 0 0 -1 0\n1 0 1 -1 0 1\n3 1 -1 3 1 1\n2\n0 0 0 3 0 0\n0 0 0 0 1 0\n3 0 0 3 1 0\n0\n output: 1.414\n2.000\n3.000\n\n" }, { "title": "Problem D: Goofy Converter", "content": "Nathan O. Davis is a student at the department of integrated systems. He is now taking a class in in-\ntegrated curcuits. He is an idiot. One day, he got an assignment as follows: design a logic circuit that\ntakes a sequence of positive integers as input, and that outputs a sequence of 1-bit integers from which\nthe original input sequence can be restored uniquely.\n\nNathan has no idea. So he searched for hints on the Internet, and found several pages that describe the\n1-bit DAC. This is a type of digital-analog converter which takes a sequence of positive integers as input,\nand outputs a sequence of 1-bit integers.\n\nSeeing how 1-bit DAC works on these pages, Nathan came up with a new idea for the desired converter.\nHis converter takes a sequence L of positive integers, and a positive integer M aside from the sequence,\nand outputs a sequence K of 1-bit integers such that:\n\nHe is not so smart, however. It is clear that his converter does not work for some sequences. Your task is\nto write a program in order to show the new converter cannot satisfy the requirements of his assignment,\neven though it would make Nathan in despair.", "constraint": "", "input": "The input consists of a series of data sets. Each data set is given in the following format:\n\n N M\n L_0 L_1 . . . L_N-1\n\nN is the length of the sequence L. M and L are the input to Nathan 's converter as described above. You\nmay assume the followings: 1 <= N <= 1000,1 <= M <= 12, and 0 <= L_j <= M for j = 0, . . . , N - 1.\n\nThe input is terminated by N = M = 0.", "output": "For each data set, output a binary sequence K of the length (N + M - 1) if there exists a sequence which\nholds the equation mentioned above, or “Goofy” (without quotes) otherwise. If more than one sequence\nis possible, output any one of them.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 4\n4 3 2 2\n4 4\n4 3 2 3\n0 0\n output: 1111001\nGoofy"], "Pid": "p01205", "ProblemText": "Task Description: Nathan O. Davis is a student at the department of integrated systems. He is now taking a class in in-\ntegrated curcuits. He is an idiot. One day, he got an assignment as follows: design a logic circuit that\ntakes a sequence of positive integers as input, and that outputs a sequence of 1-bit integers from which\nthe original input sequence can be restored uniquely.\n\nNathan has no idea. So he searched for hints on the Internet, and found several pages that describe the\n1-bit DAC. This is a type of digital-analog converter which takes a sequence of positive integers as input,\nand outputs a sequence of 1-bit integers.\n\nSeeing how 1-bit DAC works on these pages, Nathan came up with a new idea for the desired converter.\nHis converter takes a sequence L of positive integers, and a positive integer M aside from the sequence,\nand outputs a sequence K of 1-bit integers such that:\n\nHe is not so smart, however. It is clear that his converter does not work for some sequences. Your task is\nto write a program in order to show the new converter cannot satisfy the requirements of his assignment,\neven though it would make Nathan in despair.\nTask Input: The input consists of a series of data sets. Each data set is given in the following format:\n\n N M\n L_0 L_1 . . . L_N-1\n\nN is the length of the sequence L. M and L are the input to Nathan 's converter as described above. You\nmay assume the followings: 1 <= N <= 1000,1 <= M <= 12, and 0 <= L_j <= M for j = 0, . . . , N - 1.\n\nThe input is terminated by N = M = 0.\nTask Output: For each data set, output a binary sequence K of the length (N + M - 1) if there exists a sequence which\nholds the equation mentioned above, or “Goofy” (without quotes) otherwise. If more than one sequence\nis possible, output any one of them.\nTask Samples: input: 4 4\n4 3 2 2\n4 4\n4 3 2 3\n0 0\n output: 1111001\nGoofy\n\n" }, { "title": "Problem E: Black Force", "content": "A dam construction project was designed around an area called Black Force. The area is surrounded by\nmountains and its rugged terrain is said to be very suitable for constructing a dam.\n\nHowever, the project is now almost pushed into cancellation by a strong protest campaign started by the\nlocal residents. Your task is to plan out a compromise proposal. In other words, you must find a way to\nbuild a dam with sufficient capacity, without destroying the inhabited area of the residents.\n\nThe map of Black Force is given as H * W cells (0 < H, W <= 20). Each cell h_i, j is a positive integer\nrepresenting the height of the place. The dam can be constructed at a connected region surrounded\nby higher cells, as long as the region contains neither the outermost cells nor the inhabited area of the\nresidents. Here, a region is said to be connected if one can go between any pair of cells in the region\nby following a sequence of left-, right-, top-, or bottom-adjacent cells without leaving the region. The\nconstructed dam can store water up to the height of the lowest surrounding cell. The capacity of the dam\nis the maximum volume of water it can store. Water of the depth of 1 poured to a single cell has the\nvolume of 1.\n\nThe important thing is that, in the case it is difficult to build a sufficient large dam, it is allowed to\nchoose (at most) one cell and do groundwork to increase the height of the cell by 1 unit. Unfortunately,\nconsidering the protest campaign, groundwork of larger scale is impossible. Needless to say, you cannot\ndo the groundwork at the inhabited cell.\n\nGiven the map, the required capacity, and the list of cells inhabited, please determine whether it is possible\nto construct a dam.", "constraint": "", "input": "The input consists of multiple data sets. Each data set is given in the following format:\n\n H W C R\n h_1,1 h_1,2 . . . h_1, W\n . . .\n h_H, 1 h_H, 2 . . . h_H, W\n y_1 x_1\n . . .\n y_R x_R\n\nH and W is the size of the map. is the required capacity. R (0 < R < H * W) is the number of cells\ninhabited. The following H lines represent the map, where each line contains W numbers separated by\nspace. Then, the R lines containing the coordinates of inhabited cells follow. The line “y x” means that\nthe cell h_y, x is inhabited.\n\nThe end of input is indicated by a line “0 0 0 0”. This line should not be processed.", "output": "For each data set, print “Yes” if it is possible to construct a dam with capacity equal to or more than C.\nOtherwise, print “No”.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4 1 1\n2 2 2 2\n2 1 1 2\n2 1 1 2\n2 1 2 2\n1 1\n4 4 1 1\n2 2 2 2\n2 1 1 2\n2 1 1 2\n2 1 2 2\n2 2\n4 4 1 1\n2 2 2 2\n2 1 1 2\n2 1 1 2\n2 1 1 2\n1 1\n3 6 6 1\n1 6 7 1 7 1\n5 1 2 8 1 6\n1 4 3 1 5 1\n1 4\n5 6 21 1\n1 3 3 3 3 1\n3 1 1 1 1 3\n3 1 1 3 2 2\n3 1 1 1 1 3\n1 3 3 3 3 1\n3 4\n0 0 0 0\n output: Yes\nNo\nNo\nNo\nYes"], "Pid": "p01206", "ProblemText": "Task Description: A dam construction project was designed around an area called Black Force. The area is surrounded by\nmountains and its rugged terrain is said to be very suitable for constructing a dam.\n\nHowever, the project is now almost pushed into cancellation by a strong protest campaign started by the\nlocal residents. Your task is to plan out a compromise proposal. In other words, you must find a way to\nbuild a dam with sufficient capacity, without destroying the inhabited area of the residents.\n\nThe map of Black Force is given as H * W cells (0 < H, W <= 20). Each cell h_i, j is a positive integer\nrepresenting the height of the place. The dam can be constructed at a connected region surrounded\nby higher cells, as long as the region contains neither the outermost cells nor the inhabited area of the\nresidents. Here, a region is said to be connected if one can go between any pair of cells in the region\nby following a sequence of left-, right-, top-, or bottom-adjacent cells without leaving the region. The\nconstructed dam can store water up to the height of the lowest surrounding cell. The capacity of the dam\nis the maximum volume of water it can store. Water of the depth of 1 poured to a single cell has the\nvolume of 1.\n\nThe important thing is that, in the case it is difficult to build a sufficient large dam, it is allowed to\nchoose (at most) one cell and do groundwork to increase the height of the cell by 1 unit. Unfortunately,\nconsidering the protest campaign, groundwork of larger scale is impossible. Needless to say, you cannot\ndo the groundwork at the inhabited cell.\n\nGiven the map, the required capacity, and the list of cells inhabited, please determine whether it is possible\nto construct a dam.\nTask Input: The input consists of multiple data sets. Each data set is given in the following format:\n\n H W C R\n h_1,1 h_1,2 . . . h_1, W\n . . .\n h_H, 1 h_H, 2 . . . h_H, W\n y_1 x_1\n . . .\n y_R x_R\n\nH and W is the size of the map. is the required capacity. R (0 < R < H * W) is the number of cells\ninhabited. The following H lines represent the map, where each line contains W numbers separated by\nspace. Then, the R lines containing the coordinates of inhabited cells follow. The line “y x” means that\nthe cell h_y, x is inhabited.\n\nThe end of input is indicated by a line “0 0 0 0”. This line should not be processed.\nTask Output: For each data set, print “Yes” if it is possible to construct a dam with capacity equal to or more than C.\nOtherwise, print “No”.\nTask Samples: input: 4 4 1 1\n2 2 2 2\n2 1 1 2\n2 1 1 2\n2 1 2 2\n1 1\n4 4 1 1\n2 2 2 2\n2 1 1 2\n2 1 1 2\n2 1 2 2\n2 2\n4 4 1 1\n2 2 2 2\n2 1 1 2\n2 1 1 2\n2 1 1 2\n1 1\n3 6 6 1\n1 6 7 1 7 1\n5 1 2 8 1 6\n1 4 3 1 5 1\n1 4\n5 6 21 1\n1 3 3 3 3 1\n3 1 1 1 1 3\n3 1 1 3 2 2\n3 1 1 1 1 3\n1 3 3 3 3 1\n3 4\n0 0 0 0\n output: Yes\nNo\nNo\nNo\nYes\n\n" }, { "title": "Problem A: Hit and Blow", "content": "Hit and blow is a popular code-breaking game played by two people, one codemaker and one\ncodebreaker. The objective of this game is that the codebreaker guesses correctly a secret\nnumber the codemaker makes in his or her mind.\n\nThe game is played as follows. The codemaker first chooses a secret number that consists of\nfour different digits, which may contain a leading zero. Next, the codebreaker makes the first\nattempt to guess the secret number. The guessed number needs to be legal (i. e. consist of four\ndifferent digits). The codemaker then tells the numbers of hits and blows to the codebreaker.\nHits are the matching digits on their right positions, and blows are those on different positions.\nFor example, if the secret number is 4321 and the guessed is 2401, there is one hit and two blows\nwhere 1 is a hit and 2 and 4 are blows. After being told, the codebreaker makes the second\nattempt, then the codemaker tells the numbers of hits and blows, then the codebreaker makes\nthe third attempt, and so forth. The game ends when the codebreaker gives the correct number.\n\nYour task in this problem is to write a program that determines, given the situation, whether\nthe codebreaker can logically guess the secret number within the next two attempts. Your\nprogram will be given the four-digit numbers the codebreaker has guessed, and the responses\nthe codemaker has made to those numbers, and then should make output according to the\nfollowing rules:\n\n if only one secret number is possible, print the secret number;\n\n if more than one secret number is possible, but there are one or more critical numbers,\n print the smallest one;\n\n otherwise, print “? ? ? ? ” (four question symbols).\nHere, critical numbers mean those such that, after being given the number of hits and blows for\nthem on the next attempt, the codebreaker can determine the secret number uniquely.", "constraint": "", "input": "The input consists of multiple data sets. Each data set is given in the following format:\n\nN\nfour-digit-number_1 n-hits_1 n-blows_1\n. . .\nfour-digit-number_N n-hits_N n-blows_N\n\nN is the number of attempts that has been made. four-digit-number_i is the four-digit number\nguessed on the i-th attempt, and n-hits_i and n-blows_i are the numbers of hits and blows for that\nnumber, respectively. It is guaranteed that there is at least one possible secret number in each\ndata set.\n\nThe end of input is indicated by a line that contains a zero. This line should not be processed.", "output": "For each data set, print a four-digit number or “? ? ? ? ” on a line, according to the rules stated\nabove.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1234 3 0\n1245 3 0\n1\n1234 0 0\n2\n0123 0 4\n1230 0 4\n0\n output: 1235\n????\n0132"], "Pid": "p01207", "ProblemText": "Task Description: Hit and blow is a popular code-breaking game played by two people, one codemaker and one\ncodebreaker. The objective of this game is that the codebreaker guesses correctly a secret\nnumber the codemaker makes in his or her mind.\n\nThe game is played as follows. The codemaker first chooses a secret number that consists of\nfour different digits, which may contain a leading zero. Next, the codebreaker makes the first\nattempt to guess the secret number. The guessed number needs to be legal (i. e. consist of four\ndifferent digits). The codemaker then tells the numbers of hits and blows to the codebreaker.\nHits are the matching digits on their right positions, and blows are those on different positions.\nFor example, if the secret number is 4321 and the guessed is 2401, there is one hit and two blows\nwhere 1 is a hit and 2 and 4 are blows. After being told, the codebreaker makes the second\nattempt, then the codemaker tells the numbers of hits and blows, then the codebreaker makes\nthe third attempt, and so forth. The game ends when the codebreaker gives the correct number.\n\nYour task in this problem is to write a program that determines, given the situation, whether\nthe codebreaker can logically guess the secret number within the next two attempts. Your\nprogram will be given the four-digit numbers the codebreaker has guessed, and the responses\nthe codemaker has made to those numbers, and then should make output according to the\nfollowing rules:\n\n if only one secret number is possible, print the secret number;\n\n if more than one secret number is possible, but there are one or more critical numbers,\n print the smallest one;\n\n otherwise, print “? ? ? ? ” (four question symbols).\nHere, critical numbers mean those such that, after being given the number of hits and blows for\nthem on the next attempt, the codebreaker can determine the secret number uniquely.\nTask Input: The input consists of multiple data sets. Each data set is given in the following format:\n\nN\nfour-digit-number_1 n-hits_1 n-blows_1\n. . .\nfour-digit-number_N n-hits_N n-blows_N\n\nN is the number of attempts that has been made. four-digit-number_i is the four-digit number\nguessed on the i-th attempt, and n-hits_i and n-blows_i are the numbers of hits and blows for that\nnumber, respectively. It is guaranteed that there is at least one possible secret number in each\ndata set.\n\nThe end of input is indicated by a line that contains a zero. This line should not be processed.\nTask Output: For each data set, print a four-digit number or “? ? ? ? ” on a line, according to the rules stated\nabove.\nTask Samples: input: 2\n1234 3 0\n1245 3 0\n1\n1234 0 0\n2\n0123 0 4\n1230 0 4\n0\n output: 1235\n????\n0132\n\n" }, { "title": "Problem B: Turn Left", "content": "Taro got a driver 's license with a great effort in his campus days, but unfortunately there had\nbeen no opportunities for him to drive. He ended up obtaining a gold license.\n\nOne day, he and his friends made a plan to go on a trip to Kyoto with you. At the end of their\nmeeting, they agreed to go around by car, but there was a big problem; none of his friends was\nable to drive a car. Thus he had no choice but to become the driver.\n\nThe day of our departure has come. He is going to drive but would never turn to the right for\nfear of crossing an opposite lane (note that cars keep left in Japan). Furthermore, he cannot\nU-turn for the lack of his technique. The car is equipped with a car navigation system, but the\nsystem cannot search for a route without right turns. So he asked to you: “I hate right turns,\nso, could you write a program to find the shortest left-turn-only route to the destination, using\nthe road map taken from this navigation system? ”", "constraint": "", "input": "The input consists of multiple data sets. The first line of the input contains the number of data\nsets. Each data set is described in the format below:\n\nm n\nname_1 x_1 y_1\n. . .\nname_m x_m y_m\np_1 q_1\n. . .\np_n q_n\nsrc dst\n\nm is the number of intersections. n is the number of roads. name_i is the name of the i-th\nintersection. (x_i, y_i) are the integer coordinates of the i-th intersection, where the positive x\ngoes to the east, and the positive y goes to the north. p_j and q_j are the intersection names\nthat represent the endpoints of the j-th road. All roads are bidirectional and either vertical or\nhorizontal. src and dst are the names of the source and destination intersections, respectively.\n\nYou may assume all of the followings:\n\n 2 <= m <= 1000,0 <= x_i <= 10000, and 0 <= y_i <= 10000;\n\n each intersection name is a sequence of one or more alphabetical characters at most 25\n character long;\n\n no intersections share the same coordinates;\n\n no pair of roads have common points other than their endpoints;\n\n no road has intersections in the middle;\n\n no pair of intersections has more than one road;\n\n Taro can start the car in any direction; and\n\n the source and destination intersections are different.\nNote that there may be a case that an intersection is connected to less than three roads in\nthe input data; the rode map may not include smaller roads which are not appropriate for the\nnon-local people. In such a case, you still have to consider them as intersections when you go\nthem through.", "output": "For each data set, print how many times at least Taro needs to pass intersections when he drive\nthe route of the shortest distance without right turns. The source and destination intersections\nmust be considered as “passed” (thus should be counted) when Taro starts from the source or\narrives at the destination. Also note that there may be more than one shortest route possible.\n\nPrint “impossible” if there is no route to the destination without right turns.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\nKarasumaKitaoji 0 6150\nKarasumaNanajo 0 0\nKarasumaNanajo KarasumaKitaoji\nKarasumaKitaoji KarasumaNanajo\n3 2\nKujoOmiya 0 0\nKujoAburanokoji 400 0\nOmiyaNanajo 0 1150\nKujoOmiya KujoAburanokoji\nKujoOmiya OmiyaNanajo\nKujoAburanokoji OmiyaNanajo\n10 12\nKarasumaGojo 745 0\nHorikawaShijo 0 870\nShijoKarasuma 745 870\nShijoKawaramachi 1645 870\nHorikawaOike 0 1700\nKarasumaOike 745 1700\nKawaramachiOike 1645 1700\nKawabataOike 1945 1700\nKarasumaMarutamachi 745 2445\nKawaramachiMarutamachi 1645 2445\nKarasumaGojo ShijoKarasuma\nHorikawaShijo ShijoKarasuma\nShijoKarasuma ShijoKawaramachi\nHorikawaShijo HorikawaOike\nShijoKarasuma KarasumaOike\nShijoKawaramachi KawaramachiOike\nHorikawaOike KarasumaOike\nKarasumaOike KawaramachiOike\nKawaramachiOike KawabataOike\nKarasumaOike KarasumaMarutamachi\nKawaramachiOike KawaramachiMarutamachi\nKarasumaMarutamachi KawaramachiMarutamachi\nKarasumaGojo KawabataOike\n8 9\nNishikojiNanajo 0 0\nNishiojiNanajo 750 0\nNishikojiGojo 0 800\nNishiojiGojo 750 800\nHorikawaGojo 2550 800\nNishiojiShijo 750 1700\nEnmachi 750 3250\nHorikawaMarutamachi 2550 3250\nNishikojiNanajo NishiojiNanajo\nNishikojiNanajo NishikojiGojo\nNishiojiNanajo NishiojiGojo\nNishikojiGojo NishiojiGojo\nNishiojiGojo HorikawaGojo\nNishiojiGojo NishiojiShijo\nHorikawaGojo HorikawaMarutamachi\nNishiojiShijo Enmachi\nEnmachi HorikawaMarutamachi\nHorikawaGojo NishiojiShijo\n0 0\n output: 2\nimpossible\n13\n4"], "Pid": "p01208", "ProblemText": "Task Description: Taro got a driver 's license with a great effort in his campus days, but unfortunately there had\nbeen no opportunities for him to drive. He ended up obtaining a gold license.\n\nOne day, he and his friends made a plan to go on a trip to Kyoto with you. At the end of their\nmeeting, they agreed to go around by car, but there was a big problem; none of his friends was\nable to drive a car. Thus he had no choice but to become the driver.\n\nThe day of our departure has come. He is going to drive but would never turn to the right for\nfear of crossing an opposite lane (note that cars keep left in Japan). Furthermore, he cannot\nU-turn for the lack of his technique. The car is equipped with a car navigation system, but the\nsystem cannot search for a route without right turns. So he asked to you: “I hate right turns,\nso, could you write a program to find the shortest left-turn-only route to the destination, using\nthe road map taken from this navigation system? ”\nTask Input: The input consists of multiple data sets. The first line of the input contains the number of data\nsets. Each data set is described in the format below:\n\nm n\nname_1 x_1 y_1\n. . .\nname_m x_m y_m\np_1 q_1\n. . .\np_n q_n\nsrc dst\n\nm is the number of intersections. n is the number of roads. name_i is the name of the i-th\nintersection. (x_i, y_i) are the integer coordinates of the i-th intersection, where the positive x\ngoes to the east, and the positive y goes to the north. p_j and q_j are the intersection names\nthat represent the endpoints of the j-th road. All roads are bidirectional and either vertical or\nhorizontal. src and dst are the names of the source and destination intersections, respectively.\n\nYou may assume all of the followings:\n\n 2 <= m <= 1000,0 <= x_i <= 10000, and 0 <= y_i <= 10000;\n\n each intersection name is a sequence of one or more alphabetical characters at most 25\n character long;\n\n no intersections share the same coordinates;\n\n no pair of roads have common points other than their endpoints;\n\n no road has intersections in the middle;\n\n no pair of intersections has more than one road;\n\n Taro can start the car in any direction; and\n\n the source and destination intersections are different.\nNote that there may be a case that an intersection is connected to less than three roads in\nthe input data; the rode map may not include smaller roads which are not appropriate for the\nnon-local people. In such a case, you still have to consider them as intersections when you go\nthem through.\nTask Output: For each data set, print how many times at least Taro needs to pass intersections when he drive\nthe route of the shortest distance without right turns. The source and destination intersections\nmust be considered as “passed” (thus should be counted) when Taro starts from the source or\narrives at the destination. Also note that there may be more than one shortest route possible.\n\nPrint “impossible” if there is no route to the destination without right turns.\nTask Samples: input: 2 1\nKarasumaKitaoji 0 6150\nKarasumaNanajo 0 0\nKarasumaNanajo KarasumaKitaoji\nKarasumaKitaoji KarasumaNanajo\n3 2\nKujoOmiya 0 0\nKujoAburanokoji 400 0\nOmiyaNanajo 0 1150\nKujoOmiya KujoAburanokoji\nKujoOmiya OmiyaNanajo\nKujoAburanokoji OmiyaNanajo\n10 12\nKarasumaGojo 745 0\nHorikawaShijo 0 870\nShijoKarasuma 745 870\nShijoKawaramachi 1645 870\nHorikawaOike 0 1700\nKarasumaOike 745 1700\nKawaramachiOike 1645 1700\nKawabataOike 1945 1700\nKarasumaMarutamachi 745 2445\nKawaramachiMarutamachi 1645 2445\nKarasumaGojo ShijoKarasuma\nHorikawaShijo ShijoKarasuma\nShijoKarasuma ShijoKawaramachi\nHorikawaShijo HorikawaOike\nShijoKarasuma KarasumaOike\nShijoKawaramachi KawaramachiOike\nHorikawaOike KarasumaOike\nKarasumaOike KawaramachiOike\nKawaramachiOike KawabataOike\nKarasumaOike KarasumaMarutamachi\nKawaramachiOike KawaramachiMarutamachi\nKarasumaMarutamachi KawaramachiMarutamachi\nKarasumaGojo KawabataOike\n8 9\nNishikojiNanajo 0 0\nNishiojiNanajo 750 0\nNishikojiGojo 0 800\nNishiojiGojo 750 800\nHorikawaGojo 2550 800\nNishiojiShijo 750 1700\nEnmachi 750 3250\nHorikawaMarutamachi 2550 3250\nNishikojiNanajo NishiojiNanajo\nNishikojiNanajo NishikojiGojo\nNishiojiNanajo NishiojiGojo\nNishikojiGojo NishiojiGojo\nNishiojiGojo HorikawaGojo\nNishiojiGojo NishiojiShijo\nHorikawaGojo HorikawaMarutamachi\nNishiojiShijo Enmachi\nEnmachi HorikawaMarutamachi\nHorikawaGojo NishiojiShijo\n0 0\n output: 2\nimpossible\n13\n4\n\n" }, { "title": "Problem C: !", "content": "You are one of ICPC participants and in charge of developing a library for multiprecision numbers\nand radix conversion. You have just finished writing the code, so next you have to test if it\nworks correctly. You decided to write a simple, well-known factorial function for this purpose:\n\nYour task is to write a program that shows the number of trailing zeros when you compute M!\nin base N, given N and M.", "constraint": "", "input": "The input contains multiple data sets. Each data set is described by one line in the format\nbelow:\n\n N M\n\nwhere N is a decimal number between 8 and 36 inclusive, and M is given in the string repre-\nsentation in base N. Exactly one white space character appears between them.\n\nThe string representation of M contains up to 12 characters in base N. In case N is greater\nthan 10, capital letters A, B, C, . . . may appear in the string representation, and they represent\n10,11,12, . . . , respectively.\n\nThe input is terminated by a line containing two zeros. You should not process this line.", "output": "For each data set, output a line containing a decimal integer, which is equal to the number of\ntrailing zeros in the string representation of M! in base N.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10 500\n16 A\n0 0\n output: 124\n2"], "Pid": "p01209", "ProblemText": "Task Description: You are one of ICPC participants and in charge of developing a library for multiprecision numbers\nand radix conversion. You have just finished writing the code, so next you have to test if it\nworks correctly. You decided to write a simple, well-known factorial function for this purpose:\n\nYour task is to write a program that shows the number of trailing zeros when you compute M!\nin base N, given N and M.\nTask Input: The input contains multiple data sets. Each data set is described by one line in the format\nbelow:\n\n N M\n\nwhere N is a decimal number between 8 and 36 inclusive, and M is given in the string repre-\nsentation in base N. Exactly one white space character appears between them.\n\nThe string representation of M contains up to 12 characters in base N. In case N is greater\nthan 10, capital letters A, B, C, . . . may appear in the string representation, and they represent\n10,11,12, . . . , respectively.\n\nThe input is terminated by a line containing two zeros. You should not process this line.\nTask Output: For each data set, output a line containing a decimal integer, which is equal to the number of\ntrailing zeros in the string representation of M! in base N.\nTask Samples: input: 10 500\n16 A\n0 0\n output: 124\n2\n\n" }, { "title": "Problem D: Speed", "content": "Do you know Speed? It is one of popular card games, in which two players compete how quick\nthey can move their cards to tables.\n\nTo play Speed, two players sit face-to-face first. Each player has a deck and a tableau assigned\nfor him, and between them are two tables to make a pile on, one in left and one in right. A\ntableau can afford up to only four cards.\n\nThere are some simple rules to carry on the game:\n\n A player is allowed to move a card from his own tableau onto a pile, only when the rank\n of the moved card is a neighbor of that of the card on top of the pile. For example A and\n 2,4 and 3 are neighbors. A and K are also neighbors in this game.\n\n He is also allowed to draw a card from the deck and put it on a vacant area of the tableau.\n\n If both players attempt to move cards on the same table at the same time, only the faster\n player can put a card on the table. The other player cannot move his card to the pile (as\n it is no longer a neighbor of the top card), and has to bring it back to his tableau.\nFirst each player draws four cards from his deck, and places them face on top on the tableau.\nIn case he does not have enough cards to fill out the tableau, simply draw as many as possible.\nThe game starts by drawing one more card from the deck and placing it on the tables on their\nright simultaneously. If the deck is already empty, he can move an arbitrary card on his tableau\nto the table.\n\nThen they continue performing their actions according to the rule described above until both\nof them come to a deadend, that is, have no way to move cards. Every time a deadend occurs,\nthey start over from each drawing a card (or taking a card from his or her tableau) and placing\non his or her right table, regardless of its face. The player who has run out of his card first is\nthe winner of the game.\n\nMr. James A. Games is so addicted in this simple game, and decided to develop robots that\nplays it. He has just completed designing the robots and their program, but is not sure if they\nwork well, as the design is so complicated. So he asked you, a friend of his, to write a program\nthat simulates the robots.\n\nThe algorithm for the robots is designed as follows:\nA robot draws cards in the order they are dealt.\n \n Each robot is always given one or more cards.\n\n In the real game of Speed, the players first classify cards by their colors to enable\n them to easily figure out which player put the card. But this step is skipped in this\n simulation.\n\n The game uses only one card set split into two. In other words, there appears at most\n one card with the same face in the two decks given to the robots.\n\n As a preparation, each robot draws four cards, and puts them to the tableau from right\n to left.\n \n If there are not enough cards in its deck, draw all cards in the deck.\n\n After this step has been completed on both robots, they synchronize to each other and\n start the game by putting the first cards onto the tables in the same moment.\n \n If there remains one or more cards in the deck, a robot draws the top one and puts it\n onto the right table. Otherwise, the robot takes the rightmost card from its tableau.\n\n Then two robots continue moving according to the basic rule of the game described above,\n until neither of them can move cards anymore.\n \n When a robot took a card from its tableau, it draws a card (if possible) from the deck\n to fill the vacant position after the card taken is put onto a table.\n\n It takes some amount of time to move cards. When a robot completes putting a card\n onto a table while another robot is moving to put a card onto the same table, the\n robot in motion has to give up the action immediately and returns the card to its\n original position.\n\n A robot can start moving to put a card on a pile at the same time when the neighbor\n is placed on the top of the pile.\n\n If two robots try to put cards onto the same table at the same moment, only the\n robot moving a card to the left can successfully put the card, due to the position\n settings.\n\n When a robot has multiple candidates in its tableau, it prefers the cards which can\n be placed on the right table to those which cannot. In case there still remain multiple\n choices, the robot prefers the weaker card.\n\n When it comes to a deadend situation, the robots start over from each putting a card to\n the table, then continue moving again according to the algorithm above.\n\n When one of the robots has run out the cards, i. e. , moved all dealt cards, the game ends.\n \n The robot which has run out the cards wins the game.\n\n When both robots run out the cards at the same moment, the robot which moved\n the stronger card in the last move wins.\n\nThe strength among the cards is determined by their ranks, then by the suits. The ranks are\nstrong in the following order: A > K > Q > J > X (10) > 9 > . . . > 3 > 2. The suits are strong\nin the following order: S (Spades) > H (Hearts) > D (Diamonds) > C (Cloves). In other words,\nSA is the strongest and C2 is the weakest.\n\nThe robots require the following amount of time to complete each action:\n\n 300 milliseconds to draw a card to the tableau,\n\n 500 milliseconds to move a card to the right table,\n\n 700 milliseconds to move a card to the left table, and\n\n 500 milliseconds to return a card to its original position.\nCancelling an action always takes the constant time of 500ms, regardless of the progress of\nthe action being cancelled. This time is counted from the exact moment when the action is\ninterrupted, not the beginning time of the action.\n\nYou may assume that these robots are well-synchronized, i. e. , there is no clock skew between\nthem.\n\nFor example, suppose Robot A is given the deck “S3 S5 S8 S9 S2” and Robot B is given the deck\n“H7 H3 H4”, then the playing will be like the description below. Note that, in the description,\n“the table A” (resp. “the table B”) denotes the right table for Robot A (resp. Robot B).\n\n Robot A draws four cards S3, S5, S8, and S9 to its tableau from right to left. Robot B\n draws all the three cards H7, H3, and H4.\n\n Then the two robots synchronize for the game start. Let this moment be 0ms.\n\n At the same moment, Robot A starts moving S2 to the table A from the deck, and Robot\n B starts moving H7 to the table B from the tableau.\n\n At 500ms, the both robots complete their moving cards. Then Robot A starts moving S3\n to the table A 1(which requires 500ms), and Robot B starts moving H3 also to the table\n A (which requires 700ms).\n\n At 1000ms, Robot A completes putting S3 on the table A. Robot B is interrupted its move\n and starts returning H3 to the tableau (which requires 500ms). At the same time Robot\n A starts moving S8 to the table B (which requires 700ms).\n\n At 1500ms, Robot B completes returning H3 and starts moving H4 to the table A (which\n requires 700ms).\n\n At 1700ms, Robot A completes putting S8 and starts moving S9 to the table B.\n\n At 2200ms, Robot B completes putting H4 and starts moving H3 to the table A.\n\n At 2400ms, Robot A completes putting S9 and starts moving S5 to the table A.\n\n At 2900ms, The both robots are to complete putting the cards on the table A. Since Robot\n B is moving the card to the table left to it, Robot B completes putting H3. Robot A is\n interrupted.\n\n Now Robot B has finished moving all the dealt cards, so Robot B wins this game.", "constraint": "", "input": "The input consists of multiple data sets, each of which is described by four lines. The first line\nof each data set contains an integer N_A , which specifies the number of cards to be dealt as a\ndeck to Robot A. The next line contains a card sequences of length N_A . Then the number N_B\nand card sequences of length N_B for Robot B follows, specified in the same manner.\n\nIn a card sequence, card specifications are separated with one space character between them.\nEach card specification is a string of 2 characters. The first character is one of ‘S ' (spades), ‘H '\n(hearts), ‘D ' (diamonds) or ‘C ' (cloves) and specifies the suit. The second is one of ‘A ', ‘K ', ‘Q ',\n‘J ', ‘X ' (for 10) or a digit between ‘9 ' and ‘2 ', and specifies the rank. As this game is played with\nonly one card set, there is no more than one card of the same face in each data set.\n\nThe end of the input is indicated by a single line containing a zero.", "output": "For each data set, output the result of a game in one line. Output “A wins. ” if Robot A wins,\nor output “B wins. ” if Robot B wins. No extra characters are allowed in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\nSA\n1\nC2\n2\nSA HA\n2\nC2 C3\n5\nS3 S5 S8 S9 S2\n3\nH7 H3 H4\n10\nH7 CJ C5 CA C6 S2 D8 DA S6 HK\n10\nC2 D6 D4 H5 DJ CX S8 S9 D3 D5\n0\n output: A wins.\nB wins.\nB wins.\nA wins."], "Pid": "p01210", "ProblemText": "Task Description: Do you know Speed? It is one of popular card games, in which two players compete how quick\nthey can move their cards to tables.\n\nTo play Speed, two players sit face-to-face first. Each player has a deck and a tableau assigned\nfor him, and between them are two tables to make a pile on, one in left and one in right. A\ntableau can afford up to only four cards.\n\nThere are some simple rules to carry on the game:\n\n A player is allowed to move a card from his own tableau onto a pile, only when the rank\n of the moved card is a neighbor of that of the card on top of the pile. For example A and\n 2,4 and 3 are neighbors. A and K are also neighbors in this game.\n\n He is also allowed to draw a card from the deck and put it on a vacant area of the tableau.\n\n If both players attempt to move cards on the same table at the same time, only the faster\n player can put a card on the table. The other player cannot move his card to the pile (as\n it is no longer a neighbor of the top card), and has to bring it back to his tableau.\nFirst each player draws four cards from his deck, and places them face on top on the tableau.\nIn case he does not have enough cards to fill out the tableau, simply draw as many as possible.\nThe game starts by drawing one more card from the deck and placing it on the tables on their\nright simultaneously. If the deck is already empty, he can move an arbitrary card on his tableau\nto the table.\n\nThen they continue performing their actions according to the rule described above until both\nof them come to a deadend, that is, have no way to move cards. Every time a deadend occurs,\nthey start over from each drawing a card (or taking a card from his or her tableau) and placing\non his or her right table, regardless of its face. The player who has run out of his card first is\nthe winner of the game.\n\nMr. James A. Games is so addicted in this simple game, and decided to develop robots that\nplays it. He has just completed designing the robots and their program, but is not sure if they\nwork well, as the design is so complicated. So he asked you, a friend of his, to write a program\nthat simulates the robots.\n\nThe algorithm for the robots is designed as follows:\nA robot draws cards in the order they are dealt.\n \n Each robot is always given one or more cards.\n\n In the real game of Speed, the players first classify cards by their colors to enable\n them to easily figure out which player put the card. But this step is skipped in this\n simulation.\n\n The game uses only one card set split into two. In other words, there appears at most\n one card with the same face in the two decks given to the robots.\n\n As a preparation, each robot draws four cards, and puts them to the tableau from right\n to left.\n \n If there are not enough cards in its deck, draw all cards in the deck.\n\n After this step has been completed on both robots, they synchronize to each other and\n start the game by putting the first cards onto the tables in the same moment.\n \n If there remains one or more cards in the deck, a robot draws the top one and puts it\n onto the right table. Otherwise, the robot takes the rightmost card from its tableau.\n\n Then two robots continue moving according to the basic rule of the game described above,\n until neither of them can move cards anymore.\n \n When a robot took a card from its tableau, it draws a card (if possible) from the deck\n to fill the vacant position after the card taken is put onto a table.\n\n It takes some amount of time to move cards. When a robot completes putting a card\n onto a table while another robot is moving to put a card onto the same table, the\n robot in motion has to give up the action immediately and returns the card to its\n original position.\n\n A robot can start moving to put a card on a pile at the same time when the neighbor\n is placed on the top of the pile.\n\n If two robots try to put cards onto the same table at the same moment, only the\n robot moving a card to the left can successfully put the card, due to the position\n settings.\n\n When a robot has multiple candidates in its tableau, it prefers the cards which can\n be placed on the right table to those which cannot. In case there still remain multiple\n choices, the robot prefers the weaker card.\n\n When it comes to a deadend situation, the robots start over from each putting a card to\n the table, then continue moving again according to the algorithm above.\n\n When one of the robots has run out the cards, i. e. , moved all dealt cards, the game ends.\n \n The robot which has run out the cards wins the game.\n\n When both robots run out the cards at the same moment, the robot which moved\n the stronger card in the last move wins.\n\nThe strength among the cards is determined by their ranks, then by the suits. The ranks are\nstrong in the following order: A > K > Q > J > X (10) > 9 > . . . > 3 > 2. The suits are strong\nin the following order: S (Spades) > H (Hearts) > D (Diamonds) > C (Cloves). In other words,\nSA is the strongest and C2 is the weakest.\n\nThe robots require the following amount of time to complete each action:\n\n 300 milliseconds to draw a card to the tableau,\n\n 500 milliseconds to move a card to the right table,\n\n 700 milliseconds to move a card to the left table, and\n\n 500 milliseconds to return a card to its original position.\nCancelling an action always takes the constant time of 500ms, regardless of the progress of\nthe action being cancelled. This time is counted from the exact moment when the action is\ninterrupted, not the beginning time of the action.\n\nYou may assume that these robots are well-synchronized, i. e. , there is no clock skew between\nthem.\n\nFor example, suppose Robot A is given the deck “S3 S5 S8 S9 S2” and Robot B is given the deck\n“H7 H3 H4”, then the playing will be like the description below. Note that, in the description,\n“the table A” (resp. “the table B”) denotes the right table for Robot A (resp. Robot B).\n\n Robot A draws four cards S3, S5, S8, and S9 to its tableau from right to left. Robot B\n draws all the three cards H7, H3, and H4.\n\n Then the two robots synchronize for the game start. Let this moment be 0ms.\n\n At the same moment, Robot A starts moving S2 to the table A from the deck, and Robot\n B starts moving H7 to the table B from the tableau.\n\n At 500ms, the both robots complete their moving cards. Then Robot A starts moving S3\n to the table A 1(which requires 500ms), and Robot B starts moving H3 also to the table\n A (which requires 700ms).\n\n At 1000ms, Robot A completes putting S3 on the table A. Robot B is interrupted its move\n and starts returning H3 to the tableau (which requires 500ms). At the same time Robot\n A starts moving S8 to the table B (which requires 700ms).\n\n At 1500ms, Robot B completes returning H3 and starts moving H4 to the table A (which\n requires 700ms).\n\n At 1700ms, Robot A completes putting S8 and starts moving S9 to the table B.\n\n At 2200ms, Robot B completes putting H4 and starts moving H3 to the table A.\n\n At 2400ms, Robot A completes putting S9 and starts moving S5 to the table A.\n\n At 2900ms, The both robots are to complete putting the cards on the table A. Since Robot\n B is moving the card to the table left to it, Robot B completes putting H3. Robot A is\n interrupted.\n\n Now Robot B has finished moving all the dealt cards, so Robot B wins this game.\nTask Input: The input consists of multiple data sets, each of which is described by four lines. The first line\nof each data set contains an integer N_A , which specifies the number of cards to be dealt as a\ndeck to Robot A. The next line contains a card sequences of length N_A . Then the number N_B\nand card sequences of length N_B for Robot B follows, specified in the same manner.\n\nIn a card sequence, card specifications are separated with one space character between them.\nEach card specification is a string of 2 characters. The first character is one of ‘S ' (spades), ‘H '\n(hearts), ‘D ' (diamonds) or ‘C ' (cloves) and specifies the suit. The second is one of ‘A ', ‘K ', ‘Q ',\n‘J ', ‘X ' (for 10) or a digit between ‘9 ' and ‘2 ', and specifies the rank. As this game is played with\nonly one card set, there is no more than one card of the same face in each data set.\n\nThe end of the input is indicated by a single line containing a zero.\nTask Output: For each data set, output the result of a game in one line. Output “A wins. ” if Robot A wins,\nor output “B wins. ” if Robot B wins. No extra characters are allowed in the output.\nTask Samples: input: 1\nSA\n1\nC2\n2\nSA HA\n2\nC2 C3\n5\nS3 S5 S8 S9 S2\n3\nH7 H3 H4\n10\nH7 CJ C5 CA C6 S2 D8 DA S6 HK\n10\nC2 D6 D4 H5 DJ CX S8 S9 D3 D5\n0\n output: A wins.\nB wins.\nB wins.\nA wins.\n\n" }, { "title": "Problem E: Spirograph", "content": "Some of you might have seen instruments like the figure below.\nFigure 1: Spirograph\n\nThere are a fixed circle (indicated by A in the figure) and a smaller interior circle with some\npinholes (indicated by B). By putting a pen point through one of the pinholes and then rolling\nthe circle B without slipping around the inside of the circle A, we can draw curves as illustrated\nbelow. Such curves are called hypotrochoids.\nFigure 2: An Example Hypotrochoid\n\nYour task is to write a program that calculates the length of hypotrochoid, given the radius of\nthe fixed circle A, the radius of the interior circle B, and the distance between the B 's centroid and the used pinhole.", "constraint": "", "input": "The input consists of multiple test cases. Each test case is described by a single line in which\nthree integers P, Q and R appear in this order, where P is the radius of the fixed circle A, Q\nis the radius of the interior circle B, and R is the distance between the centroid of the circle B\nand the pinhole. You can assume that 0 <= R < Q < P <= 1000. P, Q, and R are separated by\na single space, while no other spaces appear in the input.\n\nThe end of input is indicated by a line with P = Q = R = 0.", "output": "For each test case, output the length of the hypotrochoid curve. The error must be within\n10^-2 (= 0.01).", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 2 1\n3 2 0\n0 0 0\n output: 13.36\n6.28"], "Pid": "p01211", "ProblemText": "Task Description: Some of you might have seen instruments like the figure below.\nFigure 1: Spirograph\n\nThere are a fixed circle (indicated by A in the figure) and a smaller interior circle with some\npinholes (indicated by B). By putting a pen point through one of the pinholes and then rolling\nthe circle B without slipping around the inside of the circle A, we can draw curves as illustrated\nbelow. Such curves are called hypotrochoids.\nFigure 2: An Example Hypotrochoid\n\nYour task is to write a program that calculates the length of hypotrochoid, given the radius of\nthe fixed circle A, the radius of the interior circle B, and the distance between the B 's centroid and the used pinhole.\nTask Input: The input consists of multiple test cases. Each test case is described by a single line in which\nthree integers P, Q and R appear in this order, where P is the radius of the fixed circle A, Q\nis the radius of the interior circle B, and R is the distance between the centroid of the circle B\nand the pinhole. You can assume that 0 <= R < Q < P <= 1000. P, Q, and R are separated by\na single space, while no other spaces appear in the input.\n\nThe end of input is indicated by a line with P = Q = R = 0.\nTask Output: For each test case, output the length of the hypotrochoid curve. The error must be within\n10^-2 (= 0.01).\nTask Samples: input: 3 2 1\n3 2 0\n0 0 0\n output: 13.36\n6.28\n\n" }, { "title": "Problem F: Mysterious Dungeons", "content": "The Kingdom of Aqua Canora Mystica is a very affluent and peaceful country, but around the\nkingdom, there are many evil monsters that kill people. So the king gave an order to you to kill\nthe master monster.\n\nYou came to the dungeon where the monster lived. The dungeon consists of a grid of square\ncells. You explored the dungeon moving up, down, left and right. You finally found, fought\nagainst, and killed the monster.\n\nNow, you are going to get out of the dungeon and return home. However, you found strange\ncarpets and big rocks are placed in the dungeon, which were not there until you killed the\nmonster. They are caused by the final magic the monster cast just before its death! Every rock\noccupies one whole cell, and you cannot go through that cell. Also, each carpet covers exactly\none cell. Each rock is labeled by an uppercase letter and each carpet by a lowercase. Some of\nthe rocks and carpets may have the same label.\n\nWhile going around in the dungeon, you observed the following behaviors. When you enter\ninto the cell covered by a carpet, all the rocks labeled with the corresponding letter (e. g. , the\nrocks with ‘A ' for the carpets with ‘a ') disappear. After the disappearance, you can enter the\ncells where the rocks disappeared, but if you enter the same carpet cell again or another carpet\ncell with the same label, the rocks revive and prevent your entrance again. After the revival,\nyou have to move on the corresponding carpet cell again in order to have those rocks disappear\nagain.\n\nCan you exit from the dungeon? If you can, how quickly can you exit? Your task is to write\na program that determines whether you can exit the dungeon, and computes the minimum\nrequired time.", "constraint": "", "input": "The input consists of some data sets.\n\nEach data set begins with a line containing two integers, W and H (3 <= W, H <= 30). In each\nof the following H lines, there are W characters, describing the map of the dungeon as W * H\ngrid of square cells. Each character is one of the following:\n\n ‘@ ' denoting your current position,\n\n ‘< ' denoting the exit of the dungeon,\n\n A lowercase letter denoting a cell covered by a carpet with the label of that letter,\n\n An uppercase letter denoting a cell occupied by a rock with the label of that letter,\n\n ‘# ' denoting a wall, and\n\n ‘. ' denoting an empty cell.\nEvery dungeon is surrounded by wall cells (‘# '), and has exactly one ‘@ ' cell and one ‘< ' cell.\nThere can be up to eight distinct uppercase labels for the rocks and eight distinct lowercase\nlabels for the carpets.\n\nYou can move to one of adjacent cells (up, down, left, or right) in one second. You cannot move\nto wall cells or the rock cells.\n\nA line containing two zeros indicates the end of the input, and should not be processed.", "output": "For each data set, output the minimum time required to move from the ‘@ ' cell to the ‘< ' cell,\nin seconds, in one line. If you cannot exit, output -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 3\n########\n#
    \n \n \n \n \n Figure 2: Running on a Wall \n Figure 3: Non-consecutive Walls \n \n\nYou want to know the maximum number of gold blocks the ninja can get, and the minimum cost to get\nthose gold blocks. So you have decided to write a program for it as a programmer. Here, move of the\nninja from a cell to its adjacent cell is considered to take one unit of cost.\nTask Input: The input consists of multiple datasets.\n\nThe first line of each dataset contains two integers H (3 <= H <= 60) and W (3 <= W <= 80). H and W\nindicate the height and width of the mansion. The following H lines represent the map of the mansion.\nEach of these lines consists of W characters. Each character is one of the following: ‘% ' (entrance), ‘# '\n(wall), ‘. ' (floor), ‘^ ' (pitfall), ‘* ' (floor with a gold block).\n\nYou can assume that the number of gold blocks are less than or equal to 15 and every map is surrounded\nby wall cells.\n\nThe end of the input indicated with a line containing two zeros.\nTask Output: For each dataset, output the maximum number of gold blocks and the minimum cost in one line. Output\ntwo zeros instead if the ninja cannot get any gold blocks. No other characters should be contained in the\noutput.\nTask Samples: input: 6 23\n#######################\n#%.^.^#################\n#^^^^^######^^^^^^^^^^#\n#^^^...^^^^...^^*^^..*#\n#^^^^^^^^^^^^^^^^^^^^^#\n#######################\n5 16\n################\n#^^^^^^^^^^^^^^#\n#*..^^^.%.^^..*#\n#^^#####^^^^^^^#\n################\n0 0\n output: 1 44\n2 28\n\n" }, { "title": "Problem H: Robot Communication", "content": "In the year 21xx, human beings are proliferating across the galaxy. Since the end of the last century,\nthousands of pioneer spaceships have been launched in order to discover new habitation planets.\n\nThe Presitener is one of those spaceships, heading toward the Andromeda galaxy. After a long, long\ncruise in the hyperspace, the crew have finally found a very hopeful candidate planet. The next thing to\ndo is to investigate the planet whether it is really suitable for a new resident or not.\n\nFor that purpose, the ship is taking some unattended landers. The captain Juclean Dripac decided to\ndrop them to the planet and collect data about it. But unfortunately, these robots are a bit old and not so\nclever that the operator has to program what to do on the planet beforehand of the landing. Many staffs\nincluding you are called for making this important plan.\n\nThe most complicated phase in the mission is to gather and integrate all the data collected independently\nby many robots. The robots need to establish all-to-all communication channels to exchange the data,\nonce during the mission. That is, all the robots activate their communication channels all together at the\npredetermined time, and they exchange the data with each other at that time.\n\nThey use wireless channels to communicate with each other, so the distance between robots does not limit\nthe connectivity. But the farther two robots goes, the more power they have to use for communication.\nDue to the limitation of the battery capacity, you want to save the transmission power as much as possible.\n\nFor a good thing, communication units of the robots also have the routing functionality, each robot only\nhas to talk with the nearest robot. Suppose a graph whose vertices represent robots and edges represent\ncommunication channels established between them. If the graph is connected, all-to-all communication\ncan be established.\n\nYour task is to write the program to calculate the minimum total transmission power required for all-\nto-all communication among the robots. Each robot moves linearly on the planet surface. Each pair of\nrobots which communicate each other must occupy one channel, but you can assume enough number of\nchannels are available. The transmission power required for two robots is proportional to the distance\nbetween them, so the cost here is exactly the sum of the distances between each pair of robots which\nestablish a communication channel.\n\nYou may also regard the planet surface as a two-dimensional surface, as it is huge enough. The time\nrequired for communicating data among robots are also negligible.", "constraint": "", "input": "The input contains multiple datasets. Each dataset has the format below.\n\n N T\n x_1 y_1 vx_1 vy_1\n . . .\n x_N y_N vx_N vy_N\n\nThe first line of each dataset contains two integers; N is the number of robots used for gathering data\n(2 <= N <= 16), and T is the time limit of the mission (1 <= T < 1000).\n\nEach of the following N lines describes the motion of a robot. (x_i, y_i) and (vx_i, vy_i ) are the initial landing\nposition and the velocity of the i-th robot, respectively (|x_i|, |y_i| < 100000, |vx_i|, |vy_i| < 1000).\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and\nshould not be processed.", "output": "For each dataset, output in a line the minimum communication cost required for all-to-all communication.\nYour program may output an arbitrary number of digits after the decimal point. The absolute error should\nbe less than or equal to 0.001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n2 0 0 1\n0 4 1 0\n4 6 0 -1\n6 2 -1 0\n4 6\n2 0 0 1\n0 4 1 0\n4 6 0 -1\n6 2 -1 0\n0 0\n output: 6.00000000\n4.24264069"], "Pid": "p01266", "ProblemText": "Task Description: In the year 21xx, human beings are proliferating across the galaxy. Since the end of the last century,\nthousands of pioneer spaceships have been launched in order to discover new habitation planets.\n\nThe Presitener is one of those spaceships, heading toward the Andromeda galaxy. After a long, long\ncruise in the hyperspace, the crew have finally found a very hopeful candidate planet. The next thing to\ndo is to investigate the planet whether it is really suitable for a new resident or not.\n\nFor that purpose, the ship is taking some unattended landers. The captain Juclean Dripac decided to\ndrop them to the planet and collect data about it. But unfortunately, these robots are a bit old and not so\nclever that the operator has to program what to do on the planet beforehand of the landing. Many staffs\nincluding you are called for making this important plan.\n\nThe most complicated phase in the mission is to gather and integrate all the data collected independently\nby many robots. The robots need to establish all-to-all communication channels to exchange the data,\nonce during the mission. That is, all the robots activate their communication channels all together at the\npredetermined time, and they exchange the data with each other at that time.\n\nThey use wireless channels to communicate with each other, so the distance between robots does not limit\nthe connectivity. But the farther two robots goes, the more power they have to use for communication.\nDue to the limitation of the battery capacity, you want to save the transmission power as much as possible.\n\nFor a good thing, communication units of the robots also have the routing functionality, each robot only\nhas to talk with the nearest robot. Suppose a graph whose vertices represent robots and edges represent\ncommunication channels established between them. If the graph is connected, all-to-all communication\ncan be established.\n\nYour task is to write the program to calculate the minimum total transmission power required for all-\nto-all communication among the robots. Each robot moves linearly on the planet surface. Each pair of\nrobots which communicate each other must occupy one channel, but you can assume enough number of\nchannels are available. The transmission power required for two robots is proportional to the distance\nbetween them, so the cost here is exactly the sum of the distances between each pair of robots which\nestablish a communication channel.\n\nYou may also regard the planet surface as a two-dimensional surface, as it is huge enough. The time\nrequired for communicating data among robots are also negligible.\nTask Input: The input contains multiple datasets. Each dataset has the format below.\n\n N T\n x_1 y_1 vx_1 vy_1\n . . .\n x_N y_N vx_N vy_N\n\nThe first line of each dataset contains two integers; N is the number of robots used for gathering data\n(2 <= N <= 16), and T is the time limit of the mission (1 <= T < 1000).\n\nEach of the following N lines describes the motion of a robot. (x_i, y_i) and (vx_i, vy_i ) are the initial landing\nposition and the velocity of the i-th robot, respectively (|x_i|, |y_i| < 100000, |vx_i|, |vy_i| < 1000).\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and\nshould not be processed.\nTask Output: For each dataset, output in a line the minimum communication cost required for all-to-all communication.\nYour program may output an arbitrary number of digits after the decimal point. The absolute error should\nbe less than or equal to 0.001.\nTask Samples: input: 4 2\n2 0 0 1\n0 4 1 0\n4 6 0 -1\n6 2 -1 0\n4 6\n2 0 0 1\n0 4 1 0\n4 6 0 -1\n6 2 -1 0\n0 0\n output: 6.00000000\n4.24264069\n\n" }, { "title": "Problem A: Infected Computer", "content": "Adam Ivan is working as a system administrator at Soy Group, Inc. He is now facing at a big trouble:\na number of computers under his management have been infected by a computer virus. Unfortunately,\nanti-virus system in his company failed to detect this virus because it was very new.\n\nAdam has identified the first computer infected by the virus and collected the records of all data packets\nsent within his network. He is now trying to identify which computers have been infected. A computer\nis infected when receiving any data packet from any infected computer. The computer is not infected, on\nthe other hand, just by sending data packets to infected computers.\n\nIt seems almost impossible for him to list all infected computers by hand, because the size of the packet\nrecords is fairly large. So he asked you for help: write a program that can identify infected computers.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nN M\nt_1 s_1 d_1\nt_2 s_2 d_2\n. . . \nt_M s_M d_M\n\nN is the number of computers; M is the number of data packets; t_i (1 <= i <= M) is the time when the i-th\ndata packet is sent; s_i and d_i (1 <= i <= M) are the source and destination computers of the i-th data packet\nrespectively. The first infected computer is indicated by the number 1; the other computers are indicated\nby unique numbers between 2 and N.\n\nThe input meets the following constraints: 0 < N <= 20000,0 <= M <= 20000, and 0 <= t_i <= 10^9 for\n1 <= i <= N; all t_i 's are different; and the source and destination of each packet are always different.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the number of computers infected by the computer virus.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 1 2\n2 2 3\n3 2\n2 3 2\n1 2 1\n0 0\n output: 3\n1"], "Pid": "p01273", "ProblemText": "Task Description: Adam Ivan is working as a system administrator at Soy Group, Inc. He is now facing at a big trouble:\na number of computers under his management have been infected by a computer virus. Unfortunately,\nanti-virus system in his company failed to detect this virus because it was very new.\n\nAdam has identified the first computer infected by the virus and collected the records of all data packets\nsent within his network. He is now trying to identify which computers have been infected. A computer\nis infected when receiving any data packet from any infected computer. The computer is not infected, on\nthe other hand, just by sending data packets to infected computers.\n\nIt seems almost impossible for him to list all infected computers by hand, because the size of the packet\nrecords is fairly large. So he asked you for help: write a program that can identify infected computers.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nN M\nt_1 s_1 d_1\nt_2 s_2 d_2\n. . . \nt_M s_M d_M\n\nN is the number of computers; M is the number of data packets; t_i (1 <= i <= M) is the time when the i-th\ndata packet is sent; s_i and d_i (1 <= i <= M) are the source and destination computers of the i-th data packet\nrespectively. The first infected computer is indicated by the number 1; the other computers are indicated\nby unique numbers between 2 and N.\n\nThe input meets the following constraints: 0 < N <= 20000,0 <= M <= 20000, and 0 <= t_i <= 10^9 for\n1 <= i <= N; all t_i 's are different; and the source and destination of each packet are always different.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the number of computers infected by the computer virus.\nTask Samples: input: 3 2\n1 1 2\n2 2 3\n3 2\n2 3 2\n1 2 1\n0 0\n output: 3\n1\n\n" }, { "title": "Problem B: Magic Slayer", "content": "You are in a fantasy monster-ridden world. You are a slayer fighting against the monsters with magic\nspells.\n\nThe monsters have hit points for each, which represent their vitality. You can decrease their hit points\nby your magic spells: each spell gives certain points of damage, by which monsters lose their hit points,\nto either one monster or all monsters in front of you (depending on the spell). Monsters are defeated\nwhen their hit points decrease to less than or equal to zero. On the other hand, each spell may consume\na certain amount of your magic power. Since your magic power is limited, you want to defeat monsters\nusing the power as little as possible.\n\nWrite a program for this purpose.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nN\nHP_1\nHP_2\n. . . \nHP_N\nM\nName_1 MP_1 Target_1 Damage_1\nName_2 MP_2 Target_2 Damage_2\n. . . \nName_M MP_M Target_M Damage_M\n\nN is the number of monsters in front of you (1 <= N <= 100); HP_i is the hit points of the i-th monster\n(1 <= HP_i <= 100000); M is the number of available magic spells (1 <= M <= 100); Name_j is the name\nof the j-th spell, consisting of up to 16 uppercase and lowercase letters; MP_j is the amount of magic\npower consumed by the j-th spell (0 <= MP_j <= 99); Target_j is either \"Single\" or \"All\", where these\nindicate the j-th magic gives damage just to a single monster or to all monsters respectively; Damage_j is\nthe amount of damage (per monster in case of \"All\") made by the j-th magic (0 <= Damage_j <= 999999).\n\nAll the numbers in the input are integers. There is at least one spell that gives non-zero damage to\nmonsters.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, Print in a line the minimum amount of magic power consumed to defeat all the monsters in the input.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n8000 15000 30000\n3\nFlare 45 Single 8000\nMeteor 62 All 6000\nUltimate 80 All 9999\n0\n output: 232"], "Pid": "p01274", "ProblemText": "Task Description: You are in a fantasy monster-ridden world. You are a slayer fighting against the monsters with magic\nspells.\n\nThe monsters have hit points for each, which represent their vitality. You can decrease their hit points\nby your magic spells: each spell gives certain points of damage, by which monsters lose their hit points,\nto either one monster or all monsters in front of you (depending on the spell). Monsters are defeated\nwhen their hit points decrease to less than or equal to zero. On the other hand, each spell may consume\na certain amount of your magic power. Since your magic power is limited, you want to defeat monsters\nusing the power as little as possible.\n\nWrite a program for this purpose.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nN\nHP_1\nHP_2\n. . . \nHP_N\nM\nName_1 MP_1 Target_1 Damage_1\nName_2 MP_2 Target_2 Damage_2\n. . . \nName_M MP_M Target_M Damage_M\n\nN is the number of monsters in front of you (1 <= N <= 100); HP_i is the hit points of the i-th monster\n(1 <= HP_i <= 100000); M is the number of available magic spells (1 <= M <= 100); Name_j is the name\nof the j-th spell, consisting of up to 16 uppercase and lowercase letters; MP_j is the amount of magic\npower consumed by the j-th spell (0 <= MP_j <= 99); Target_j is either \"Single\" or \"All\", where these\nindicate the j-th magic gives damage just to a single monster or to all monsters respectively; Damage_j is\nthe amount of damage (per monster in case of \"All\") made by the j-th magic (0 <= Damage_j <= 999999).\n\nAll the numbers in the input are integers. There is at least one spell that gives non-zero damage to\nmonsters.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, Print in a line the minimum amount of magic power consumed to defeat all the monsters in the input.\nTask Samples: input: 3\n8000 15000 30000\n3\nFlare 45 Single 8000\nMeteor 62 All 6000\nUltimate 80 All 9999\n0\n output: 232\n\n" }, { "title": "Problem C: Dial Lock", "content": "A dial lock is a kind of lock which has some dials with printed numbers. It has a special sequence of\nnumbers, namely an unlocking sequence, to be opened.\n\nYou are working at a manufacturer of dial locks. Your job is to verify that every manufactured lock is\nunlocked by its unlocking sequence. In other words, you have to rotate many dials of many many locks.\n\nIt 's a very hard and boring task. You want to reduce time to open the locks.\nIt 's a good idea to rotate multiple dials at one time. It is, however, a difficult problem to find steps to open\na given lock with the fewest rotations. So you decided to write a program to find such steps for given\ninitial and unlocking sequences.\n\nYour company 's dial locks are composed of vertically stacked k (1 <= k <= 10) cylindrical dials. Every dial\nhas 10 numbers, from 0 to 9, along the side of the cylindrical shape from the left to the right in sequence.\nThe neighbor on the right of 9 is 0.\n\nA dial points one number at a certain position. If you rotate a dial to the left by i digits, the dial newly\npoints the i-th right number. In contrast, if you rotate a dial to the right by i digits, it points the i-th left\nnumber. For example, if you rotate a dial pointing 8 to the left by 3 digits, the dial newly points 1.\n\nYou can rotate more than one adjacent dial at one time. For example, consider a lock with 5 dials. You\ncan rotate just the 2nd dial. You can rotate the 3rd, 4th and 5th dials at the same time. But you cannot\nrotate the 1st and 3rd dials at one time without rotating the 2nd dial. When you rotate multiple dials, you\nhave to rotate them to the same direction by the same digits.\n\nYour program is to calculate the fewest number of rotations to unlock, for given initial and unlocking\nsequences. Rotating one or more adjacent dials to the same direction by the same digits is counted as one\nrotation.", "constraint": "", "input": "The input consists of multiple datasets. \n\nEach datset consists of two lines. The first line contains an integer k. The second lines contain two strings,\nseparated by a space, which indicate the initial and unlocking sequences.\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the minimum number of rotations in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1357 4680\n6\n777777 003330\n0\n output: 1\n2"], "Pid": "p01275", "ProblemText": "Task Description: A dial lock is a kind of lock which has some dials with printed numbers. It has a special sequence of\nnumbers, namely an unlocking sequence, to be opened.\n\nYou are working at a manufacturer of dial locks. Your job is to verify that every manufactured lock is\nunlocked by its unlocking sequence. In other words, you have to rotate many dials of many many locks.\n\nIt 's a very hard and boring task. You want to reduce time to open the locks.\nIt 's a good idea to rotate multiple dials at one time. It is, however, a difficult problem to find steps to open\na given lock with the fewest rotations. So you decided to write a program to find such steps for given\ninitial and unlocking sequences.\n\nYour company 's dial locks are composed of vertically stacked k (1 <= k <= 10) cylindrical dials. Every dial\nhas 10 numbers, from 0 to 9, along the side of the cylindrical shape from the left to the right in sequence.\nThe neighbor on the right of 9 is 0.\n\nA dial points one number at a certain position. If you rotate a dial to the left by i digits, the dial newly\npoints the i-th right number. In contrast, if you rotate a dial to the right by i digits, it points the i-th left\nnumber. For example, if you rotate a dial pointing 8 to the left by 3 digits, the dial newly points 1.\n\nYou can rotate more than one adjacent dial at one time. For example, consider a lock with 5 dials. You\ncan rotate just the 2nd dial. You can rotate the 3rd, 4th and 5th dials at the same time. But you cannot\nrotate the 1st and 3rd dials at one time without rotating the 2nd dial. When you rotate multiple dials, you\nhave to rotate them to the same direction by the same digits.\n\nYour program is to calculate the fewest number of rotations to unlock, for given initial and unlocking\nsequences. Rotating one or more adjacent dials to the same direction by the same digits is counted as one\nrotation.\nTask Input: The input consists of multiple datasets. \n\nEach datset consists of two lines. The first line contains an integer k. The second lines contain two strings,\nseparated by a space, which indicate the initial and unlocking sequences.\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the minimum number of rotations in one line.\nTask Samples: input: 4\n1357 4680\n6\n777777 003330\n0\n output: 1\n2\n\n" }, { "title": "Problem D: Double Sorting", "content": "Here we describe a typical problem. There are n balls and n boxes. Each ball is labeled by a unique\nnumber from 1 to n. Initially each box contains one of these balls. We can swap two balls in adjacent\nboxes. We are to sort these balls in increasing order by swaps, i. e. move the ball labeled by 1 to the first\nbox, labeled by 2 to the second box, and so forth. The question is how many swaps are needed.\n\nNow let us consider the situation where the balls are doubled, that is, there are 2n balls and n boxes,\nexactly two balls are labeled by k for each 1 <= k <= n, and the boxes contain two balls each. We can swap\ntwo balls in adjacent boxes, one ball from each box. We are to move the both balls labeled by 1 to the\nfirst box, labeled by 2 to the second box, and so forth. The question is again how many swaps are needed.\n\nHere is one interesting fact. We need 10 swaps to sort [5; 4; 3; 2; 1] (the state with 5 in the first box, 4 in\nthe second box, and so forth): swapping 5 and 4, then 5 and 3,5 and 2,5 and 1,4 and 3,4 and 2,4 and\n1,3 and 2,3 and 1, and finally 2 and 1. Then how many swaps we need to sort [5,5; 4,4; 3,3; 2,2; 1,1]\n(the state with two 5 's in the first box, two 4 's in the second box, and so forth)? Some of you might think\n20 swaps - this is not true, but the actual number is 15.\n\nWrite a program that calculates the number of swaps for the two-ball version and verify the above fact.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nn\nball_1,1 ball_1,2\nball_2,1 ball_2,2\n. . . \nball_n, 1 ball_n, 2\n\nn is the number of boxes (1 <= n <= 8). ball_i, 1 and ball_i, 2 , for 1 <= i <= n, are the labels of two balls initially\ncontained by the i-th box.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the minumum possible number of swaps.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n5 5\n4 4\n3 3\n2 2\n1 1\n5\n1 5\n3 4\n2 5\n2 3\n1 4\n8\n8 3\n4 2\n6 4\n3 5\n5 8\n7 1\n2 6\n1 7\n0\n output: 15\n9\n21"], "Pid": "p01276", "ProblemText": "Task Description: Here we describe a typical problem. There are n balls and n boxes. Each ball is labeled by a unique\nnumber from 1 to n. Initially each box contains one of these balls. We can swap two balls in adjacent\nboxes. We are to sort these balls in increasing order by swaps, i. e. move the ball labeled by 1 to the first\nbox, labeled by 2 to the second box, and so forth. The question is how many swaps are needed.\n\nNow let us consider the situation where the balls are doubled, that is, there are 2n balls and n boxes,\nexactly two balls are labeled by k for each 1 <= k <= n, and the boxes contain two balls each. We can swap\ntwo balls in adjacent boxes, one ball from each box. We are to move the both balls labeled by 1 to the\nfirst box, labeled by 2 to the second box, and so forth. The question is again how many swaps are needed.\n\nHere is one interesting fact. We need 10 swaps to sort [5; 4; 3; 2; 1] (the state with 5 in the first box, 4 in\nthe second box, and so forth): swapping 5 and 4, then 5 and 3,5 and 2,5 and 1,4 and 3,4 and 2,4 and\n1,3 and 2,3 and 1, and finally 2 and 1. Then how many swaps we need to sort [5,5; 4,4; 3,3; 2,2; 1,1]\n(the state with two 5 's in the first box, two 4 's in the second box, and so forth)? Some of you might think\n20 swaps - this is not true, but the actual number is 15.\n\nWrite a program that calculates the number of swaps for the two-ball version and verify the above fact.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nn\nball_1,1 ball_1,2\nball_2,1 ball_2,2\n. . . \nball_n, 1 ball_n, 2\n\nn is the number of boxes (1 <= n <= 8). ball_i, 1 and ball_i, 2 , for 1 <= i <= n, are the labels of two balls initially\ncontained by the i-th box.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the minumum possible number of swaps.\nTask Samples: input: 5\n5 5\n4 4\n3 3\n2 2\n1 1\n5\n1 5\n3 4\n2 5\n2 3\n1 4\n8\n8 3\n4 2\n6 4\n3 5\n5 8\n7 1\n2 6\n1 7\n0\n output: 15\n9\n21\n\n" }, { "title": "Problem E: Symmetry", "content": "Open Binary and Object Group organizes a programming contest every year. Mr. Hex belongs to this\ngroup and joins the judge team of the contest. This year, he created a geometric problem with its solution\nfor the contest. The problem required a set of points forming a line-symmetric polygon for the input.\nPreparing the input for this problem was also his task. The input was expected to cover all edge cases, so\nhe spent much time and attention to make them satisfactory.\n\nHowever, since he worked with lots of care and for a long time, he got tired before he finished. So He\nmight have made mistakes - there might be polygons not meeting the condition. It was not reasonable to\nprepare the input again from scratch. The judge team thus decided to find all line-asymmetric polygons\nin his input and fix them as soon as possible. They asked a programmer, just you, to write a program to\nfind incorrect polygons.\n\nYou can assume the following:\n\n Edges of the polygon must not cross or touch each other except for the end points of adjacent\n edges.\n\n It is acceptable for the polygon to have adjacent three vertexes on a line, but in such a case, there\n must be the vertex symmetric to each of them.", "constraint": "", "input": "The input consists of a set of points in the following format.\n\nN\nx_1 y_1\nx_2 y_2\n. . . \nx_N y_N\n\nThe first line of the input contains an integer N (3 <= N <= 1000), which denotes the number of points.\nThe following N lines describe each point. The i-th line contains two integers x_1, y_1 (-10000 <= x_i, y_i <= 10000), which denote the coordinates of the i-th point.\n\nNote that, although the points are the vertexes of a polygon, they are given in an artibrary order, not\nnecessarily clockwise or counterclockwise.", "output": "Output \"Yes\" in a line if the points can form a line-symmetric polygon, otherwise output \"No\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 1\n1 0\n0 0\n1 1\n output: Yes", "input: 4\n0 1\n1 -1\n0 0\n1 1\n output: No", "input: 9\n-1 1\n0 1\n1 1\n-1 0\n0 0\n1 0\n-1 -1\n0 -1\n1 -1\n output: No", "input: 3\n-1 -1\n0 0\n1 1\n output: No", "input: 4\n0 2\n0 0\n-1 0\n1 0\n output: Yes"], "Pid": "p01277", "ProblemText": "Task Description: Open Binary and Object Group organizes a programming contest every year. Mr. Hex belongs to this\ngroup and joins the judge team of the contest. This year, he created a geometric problem with its solution\nfor the contest. The problem required a set of points forming a line-symmetric polygon for the input.\nPreparing the input for this problem was also his task. The input was expected to cover all edge cases, so\nhe spent much time and attention to make them satisfactory.\n\nHowever, since he worked with lots of care and for a long time, he got tired before he finished. So He\nmight have made mistakes - there might be polygons not meeting the condition. It was not reasonable to\nprepare the input again from scratch. The judge team thus decided to find all line-asymmetric polygons\nin his input and fix them as soon as possible. They asked a programmer, just you, to write a program to\nfind incorrect polygons.\n\nYou can assume the following:\n\n Edges of the polygon must not cross or touch each other except for the end points of adjacent\n edges.\n\n It is acceptable for the polygon to have adjacent three vertexes on a line, but in such a case, there\n must be the vertex symmetric to each of them.\nTask Input: The input consists of a set of points in the following format.\n\nN\nx_1 y_1\nx_2 y_2\n. . . \nx_N y_N\n\nThe first line of the input contains an integer N (3 <= N <= 1000), which denotes the number of points.\nThe following N lines describe each point. The i-th line contains two integers x_1, y_1 (-10000 <= x_i, y_i <= 10000), which denote the coordinates of the i-th point.\n\nNote that, although the points are the vertexes of a polygon, they are given in an artibrary order, not\nnecessarily clockwise or counterclockwise.\nTask Output: Output \"Yes\" in a line if the points can form a line-symmetric polygon, otherwise output \"No\".\nTask Samples: input: 4\n0 1\n1 0\n0 0\n1 1\n output: Yes\ninput: 4\n0 1\n1 -1\n0 0\n1 1\n output: No\ninput: 9\n-1 1\n0 1\n1 1\n-1 0\n0 0\n1 0\n-1 -1\n0 -1\n1 -1\n output: No\ninput: 3\n-1 -1\n0 0\n1 1\n output: No\ninput: 4\n0 2\n0 0\n-1 0\n1 0\n output: Yes\n\n" }, { "title": "Problem F: Voronoi Island", "content": "Some of you know an old story of Voronoi Island. There were N liege lords and they are always involved\nin territorial disputes. The residents of the island were despaired of the disputes.\n\nOne day, a clever lord proposed to stop the disputes and divide the island fairly. His idea was to divide the\nisland such that any piece of area belongs to the load of the nearest castle. The method is called Voronoi\nDivision today.\n\nActually, there are many aspects of whether the method is fair. According to one historian, the clever\nlord suggested the method because he could gain broader area than other lords.\n\nYour task is to write a program to calculate the size of the area each lord can gain. You may assume that\nVoronoi Island has a convex shape.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nN M\nIx_1 Iy_1\nIx_2 Iy_2\n. . . \nIx_N Iy_N\nCx_1 Cy_1\nCx_2 Cy_2\n. . . \nCx_M Cy_M\n\nN is the number of the vertices of Voronoi Island; M is the number of the liege lords; (Ix_i, Iy_i) denotes\nthe coordinate of the i-th vertex; (Cx_i, Cy_i ) denotes the coordinate of the castle of the i-the lord.\n\nThe input meets the following constraints: 3 <= N <= 10,2 <= M <= 10, -100 <= Ix_i, Iy_i, Cx_i, Cy_i <= 100. The\nvertices are given counterclockwise. All the coordinates are integers.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the area gained by each liege lord with an absolute error of at most 10^-4 . You may output any\nnumber of digits after the decimal point. The order of the output areas must match that of the lords in the\ninput.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n0 0\n8 0\n0 8\n2 2\n4 2\n2 4\n0 0\n output: 9.0\n11.5\n11.5"], "Pid": "p01278", "ProblemText": "Task Description: Some of you know an old story of Voronoi Island. There were N liege lords and they are always involved\nin territorial disputes. The residents of the island were despaired of the disputes.\n\nOne day, a clever lord proposed to stop the disputes and divide the island fairly. His idea was to divide the\nisland such that any piece of area belongs to the load of the nearest castle. The method is called Voronoi\nDivision today.\n\nActually, there are many aspects of whether the method is fair. According to one historian, the clever\nlord suggested the method because he could gain broader area than other lords.\n\nYour task is to write a program to calculate the size of the area each lord can gain. You may assume that\nVoronoi Island has a convex shape.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nN M\nIx_1 Iy_1\nIx_2 Iy_2\n. . . \nIx_N Iy_N\nCx_1 Cy_1\nCx_2 Cy_2\n. . . \nCx_M Cy_M\n\nN is the number of the vertices of Voronoi Island; M is the number of the liege lords; (Ix_i, Iy_i) denotes\nthe coordinate of the i-th vertex; (Cx_i, Cy_i ) denotes the coordinate of the castle of the i-the lord.\n\nThe input meets the following constraints: 3 <= N <= 10,2 <= M <= 10, -100 <= Ix_i, Iy_i, Cx_i, Cy_i <= 100. The\nvertices are given counterclockwise. All the coordinates are integers.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the area gained by each liege lord with an absolute error of at most 10^-4 . You may output any\nnumber of digits after the decimal point. The order of the output areas must match that of the lords in the\ninput.\nTask Samples: input: 3 3\n0 0\n8 0\n0 8\n2 2\n4 2\n2 4\n0 0\n output: 9.0\n11.5\n11.5\n\n" }, { "title": "Problem G: Defend the Bases", "content": "A country Gizevom is being under a sneak and fierce attack by their foe. They have to deploy one or\nmore troops to every base immediately in order to defend their country. Otherwise their foe would take\nall the bases and declare \"All your base are belong to us. \"\n\nYou are asked to write a program that calculates the minimum time required for deployment, given the\npresent positions and marching speeds of troops and the positions of the bases.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nN M\nx_1 y_1 v_1\nx_2 y_2 v_2\n. . . \nx_N y_N v_N\nx'_1 y'_1\nx'_2 y'_2\n. . . \nx'_M y'_M\n\nN is the number of troops (1 <= N <= 100); M is the number of bases (1 <= M <= 100); (x_i, y_i ) denotes the present position of i-th troop; v_i is the speed of the i-th troop (1 <= v_i <= 100); (x'_j, y'_j) is the position of the j-th base.\n\nAll the coordinates are integers between 0 and 10000 inclusive.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the minimum required time in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n10 20 1\n0 10 1\n0 10\n10 0\n0 0\n output: 14.14213562"], "Pid": "p01279", "ProblemText": "Task Description: A country Gizevom is being under a sneak and fierce attack by their foe. They have to deploy one or\nmore troops to every base immediately in order to defend their country. Otherwise their foe would take\nall the bases and declare \"All your base are belong to us. \"\n\nYou are asked to write a program that calculates the minimum time required for deployment, given the\npresent positions and marching speeds of troops and the positions of the bases.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nN M\nx_1 y_1 v_1\nx_2 y_2 v_2\n. . . \nx_N y_N v_N\nx'_1 y'_1\nx'_2 y'_2\n. . . \nx'_M y'_M\n\nN is the number of troops (1 <= N <= 100); M is the number of bases (1 <= M <= 100); (x_i, y_i ) denotes the present position of i-th troop; v_i is the speed of the i-th troop (1 <= v_i <= 100); (x'_j, y'_j) is the position of the j-th base.\n\nAll the coordinates are integers between 0 and 10000 inclusive.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the minimum required time in a line.\nTask Samples: input: 2 2\n10 20 1\n0 10 1\n0 10\n10 0\n0 0\n output: 14.14213562\n\n" }, { "title": "Problem H: Galaxy Wide Web Service", "content": "The volume of access to a web service varies from time to time in a day. Also, the hours with the highest\nvolume of access varies from service to service. For example, a service popular in the United States\nmay receive more access in the daytime in the United States, while another service popular in Japan may\nreceive more access in the daytime in Japan. When you develop a web service, you have to design the\nsystem so it can handle all requests made during the busiest hours.\n\nYou are a lead engineer in charge of a web service in the 30th century. It 's the era of Galaxy Wide Web\n(GWW), thanks to the invention of faster-than-light communication. The service can be accessed from\nall over the galaxy. Thus many intelligent creatures, not limited to human beings, can use the service.\nSince the volume of access to your service is increasing these days, you have decided to reinforce the\nserver system. You want to design a new system that handles requests well even during the hours with the\nhighest volume of access. However, this is not a trivial task. Residents in each planet have their specific\nlength of a day, say, a cycle of life. The length of a day is not always 24 hours. Therefore, a cycle of the\nvolume of access are different by planets of users.\n\nYou have obtained hourly data of the volume of access for all planets where you provide the service.\nAssuming the volume of access follows a daily cycle for each planet, you want to know the highest\nvolume of access in one hour. It should be a quite easy task for you, a famous talented engineer in the\ngalaxy.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nN\nd_1 t_1 q_1,0 . . . q_1, d1-1\n. . . \nd_N t_N q_N, 0 . . . q_N, dN-1\n\nN is the number of planets. d_i (1 <= i <= N) is the length of a day in the planet i. \n\n\nt_i (0 <= t_i <= d_i - 1) is the current time of the planet i.\n\nq_i, j is the volume of access on the planet i during from the j-th hour to the (j+1)-th hour.\n\nYou may assume that N <= 100, d_i <= 24, q_i, j <= 1000000 (1 <= i <= N, 0 <= j <= d_i - 1).\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, output the maximum volume of access in one hour in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4 0 1 2 3 4\n2 0 2 1\n0\n output: 5"], "Pid": "p01280", "ProblemText": "Task Description: The volume of access to a web service varies from time to time in a day. Also, the hours with the highest\nvolume of access varies from service to service. For example, a service popular in the United States\nmay receive more access in the daytime in the United States, while another service popular in Japan may\nreceive more access in the daytime in Japan. When you develop a web service, you have to design the\nsystem so it can handle all requests made during the busiest hours.\n\nYou are a lead engineer in charge of a web service in the 30th century. It 's the era of Galaxy Wide Web\n(GWW), thanks to the invention of faster-than-light communication. The service can be accessed from\nall over the galaxy. Thus many intelligent creatures, not limited to human beings, can use the service.\nSince the volume of access to your service is increasing these days, you have decided to reinforce the\nserver system. You want to design a new system that handles requests well even during the hours with the\nhighest volume of access. However, this is not a trivial task. Residents in each planet have their specific\nlength of a day, say, a cycle of life. The length of a day is not always 24 hours. Therefore, a cycle of the\nvolume of access are different by planets of users.\n\nYou have obtained hourly data of the volume of access for all planets where you provide the service.\nAssuming the volume of access follows a daily cycle for each planet, you want to know the highest\nvolume of access in one hour. It should be a quite easy task for you, a famous talented engineer in the\ngalaxy.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nN\nd_1 t_1 q_1,0 . . . q_1, d1-1\n. . . \nd_N t_N q_N, 0 . . . q_N, dN-1\n\nN is the number of planets. d_i (1 <= i <= N) is the length of a day in the planet i. \n\n\nt_i (0 <= t_i <= d_i - 1) is the current time of the planet i.\n\nq_i, j is the volume of access on the planet i during from the j-th hour to the (j+1)-th hour.\n\nYou may assume that N <= 100, d_i <= 24, q_i, j <= 1000000 (1 <= i <= N, 0 <= j <= d_i - 1).\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, output the maximum volume of access in one hour in a line.\nTask Samples: input: 2\n4 0 1 2 3 4\n2 0 2 1\n0\n output: 5\n\n" }, { "title": "Problem I: Tatami", "content": "A tatami mat, a Japanese traditional floor cover, has a rectangular form with aspect ratio 1: 2. When\nspreading tatami mats on a floor, it is prohibited to make a cross with the border of the tatami mats,\nbecause it is believed to bring bad luck.\n\nYour task is to write a program that reports how many possible ways to spread tatami mats of the same\nsize on a floor of given height and width.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset cosists of a line which contains two integers H and W in this order, separated with a single\nspace. H and W are the height and the width of the floor respectively. The length of the shorter edge of a\ntatami mat is regarded as a unit length.\n\nYou may assume 0 < H, W <= 20.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the number of possible ways to spread tatami mats in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n4 4\n0 0\n output: 4\n2"], "Pid": "p01281", "ProblemText": "Task Description: A tatami mat, a Japanese traditional floor cover, has a rectangular form with aspect ratio 1: 2. When\nspreading tatami mats on a floor, it is prohibited to make a cross with the border of the tatami mats,\nbecause it is believed to bring bad luck.\n\nYour task is to write a program that reports how many possible ways to spread tatami mats of the same\nsize on a floor of given height and width.\nTask Input: The input consists of multiple datasets. Each dataset cosists of a line which contains two integers H and W in this order, separated with a single\nspace. H and W are the height and the width of the floor respectively. The length of the shorter edge of a\ntatami mat is regarded as a unit length.\n\nYou may assume 0 < H, W <= 20.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the number of possible ways to spread tatami mats in one line.\nTask Samples: input: 3 4\n4 4\n0 0\n output: 4\n2\n\n" }, { "title": "Problem J: Revenge of the Round Table", "content": "Two contries A and B have decided to make a meeting to get acquainted with each other. n ambassadors\nfrom A and B will attend the meeting in total.\n\nA round table is prepared for in the meeting. The ambassadors are getting seated at the round table, but\nthey have agreed that more than k ambassadors from the same country does not sit down at the round\ntable in a row for deeper exchange.\n\nYour task is to write a program that reports the number of possible arrangements when rotations are not\ncounted. Your program should report the number modulo M = 1000003.\n\nLet us provide an example. Suppose n = 4 and k = 2. When rotations are counted as different arrangements, the following six arrangements are possible.\n\n AABB\n ABBA\n BBAA\n BAAB\n ABAB\n BABA\n\nHowever, when rotations are regarded as same, the following two arrangements are possible.\n\n AABB\n ABAB\n\nTherefore the program should report 2.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset consists of two integers n (1 <= n <= 1000) and k (1 <= k <= 1000) in one line.\n\nIt does not always hold k < n. This means the program should consider cases in which the ambassadors\nfrom only one country attend the meeting.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the number of possible arrangements modulo M = 1000003 in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n3 2\n3 3\n4 2\n10 5\n1000 500\n0 0\n output: 0\n2\n4\n2\n90\n570682"], "Pid": "p01282", "ProblemText": "Task Description: Two contries A and B have decided to make a meeting to get acquainted with each other. n ambassadors\nfrom A and B will attend the meeting in total.\n\nA round table is prepared for in the meeting. The ambassadors are getting seated at the round table, but\nthey have agreed that more than k ambassadors from the same country does not sit down at the round\ntable in a row for deeper exchange.\n\nYour task is to write a program that reports the number of possible arrangements when rotations are not\ncounted. Your program should report the number modulo M = 1000003.\n\nLet us provide an example. Suppose n = 4 and k = 2. When rotations are counted as different arrangements, the following six arrangements are possible.\n\n AABB\n ABBA\n BBAA\n BAAB\n ABAB\n BABA\n\nHowever, when rotations are regarded as same, the following two arrangements are possible.\n\n AABB\n ABAB\n\nTherefore the program should report 2.\nTask Input: The input consists of multiple datasets. Each dataset consists of two integers n (1 <= n <= 1000) and k (1 <= k <= 1000) in one line.\n\nIt does not always hold k < n. This means the program should consider cases in which the ambassadors\nfrom only one country attend the meeting.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the number of possible arrangements modulo M = 1000003 in one line.\nTask Samples: input: 3 1\n3 2\n3 3\n4 2\n10 5\n1000 500\n0 0\n output: 0\n2\n4\n2\n90\n570682\n\n" }, { "title": "Problem A: Strange String Manipulation", "content": "A linear congruential generator produces a series R(⋅) of pseudo-random numbers by the following for-\nmulas:\n\nwhere S, A, C, and M are all parameters. In this problem, 0 <= S, A, C <= 15 and M = 256.\n\nNow suppose we have some input string I(⋅), where each character in the string is an integer between 0\nand (M - 1). Then, using the pseudo-random number series R(⋅), we obtain another string O(⋅) as the\noutput by the following formula:\n\nYour task is to write a program that shows the parameters S, A, and C such that the information entropy of the output string O(⋅) is minimized. Here, the information entropy H is given by the following formula:\n\nwhere N is the length of the string and #(x) is the number of occurences of the alphabet x.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nN\nI(1) I(2) . . . I(N)\n\nN does not exceed 256.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print in a line the values of the three parameters S, A, and C separated by a single space. If more than one solution gives the same minimum entropy, choose the solution with the smallest S, A, and then C.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n5 4 3 2 1\n5\n7 7 7 7 7\n10\n186 8 42 24 154 40 10 56 122 72\n0\n output: 0 1 1\n0 0 0\n8 7 14"], "Pid": "p01283", "ProblemText": "Task Description: A linear congruential generator produces a series R(⋅) of pseudo-random numbers by the following for-\nmulas:\n\nwhere S, A, C, and M are all parameters. In this problem, 0 <= S, A, C <= 15 and M = 256.\n\nNow suppose we have some input string I(⋅), where each character in the string is an integer between 0\nand (M - 1). Then, using the pseudo-random number series R(⋅), we obtain another string O(⋅) as the\noutput by the following formula:\n\nYour task is to write a program that shows the parameters S, A, and C such that the information entropy of the output string O(⋅) is minimized. Here, the information entropy H is given by the following formula:\n\nwhere N is the length of the string and #(x) is the number of occurences of the alphabet x.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nN\nI(1) I(2) . . . I(N)\n\nN does not exceed 256.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print in a line the values of the three parameters S, A, and C separated by a single space. If more than one solution gives the same minimum entropy, choose the solution with the smallest S, A, and then C.\nTask Samples: input: 5\n5 4 3 2 1\n5\n7 7 7 7 7\n10\n186 8 42 24 154 40 10 56 122 72\n0\n output: 0 1 1\n0 0 0\n8 7 14\n\n" }, { "title": "Problem B: Erratic Sleep Habits", "content": "Peter is a person with erratic sleep habits. He goes to sleep at twelve o'lock every midnight. He gets\nup just after one hour of sleep on some days; he may even sleep for twenty-three hours on other days.\nHis sleeping duration changes in a cycle, where he always sleeps for only one hour on the first day of the\ncycle.\n\nUnfortunately, he has some job interviews this month. No doubt he wants to be in time for them. He can\ntake anhydrous caffeine to reset his sleeping cycle to the beginning of the cycle anytime. Then he will\nwake up after one hour of sleep when he takes caffeine. But of course he wants to avoid taking caffeine\nas possible, since it may affect his health and accordingly his very important job interviews.\n\nYour task is to write a program that reports the minimum amount of caffeine required for Peter to attend\nall his interviews without being late, where the information about the cycle and the schedule of his\ninterviews are given. The time for move to the place of each interview should be considered negligible.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is given in the following format:\n\nT\nt_1 t_2 . . . t_T\nN\nD_1 M_1\nD_2 M_2\n . . . \nD_N M_N\n\nT is the length of the cycle (1 <= T <= 30); t_i (for 1 <= i <= T ) is the amount of sleep on the i-th day of the\ncycle, given in hours (1 <= t_i <= 23); N is the number of interviews (1 <= N <= 100); D_j (for 1 <= j <= N)\nis the day of the j-th interview (1 <= D_j <= 100); M_j (for 1 <= j <= N) is the hour when the j-th interview starts (1 <= M_j <= 23).\n\nThe numbers in the input are all integers. t_1 is always 1 as stated above. The day indicated by 1 is the\nfirst day in the cycle of Peter's sleep.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the minimum number of times Peter needs to take anhydrous caffeine.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 23\n3\n1 1\n2 1\n3 1\n0\n output: 2"], "Pid": "p01284", "ProblemText": "Task Description: Peter is a person with erratic sleep habits. He goes to sleep at twelve o'lock every midnight. He gets\nup just after one hour of sleep on some days; he may even sleep for twenty-three hours on other days.\nHis sleeping duration changes in a cycle, where he always sleeps for only one hour on the first day of the\ncycle.\n\nUnfortunately, he has some job interviews this month. No doubt he wants to be in time for them. He can\ntake anhydrous caffeine to reset his sleeping cycle to the beginning of the cycle anytime. Then he will\nwake up after one hour of sleep when he takes caffeine. But of course he wants to avoid taking caffeine\nas possible, since it may affect his health and accordingly his very important job interviews.\n\nYour task is to write a program that reports the minimum amount of caffeine required for Peter to attend\nall his interviews without being late, where the information about the cycle and the schedule of his\ninterviews are given. The time for move to the place of each interview should be considered negligible.\nTask Input: The input consists of multiple datasets. Each dataset is given in the following format:\n\nT\nt_1 t_2 . . . t_T\nN\nD_1 M_1\nD_2 M_2\n . . . \nD_N M_N\n\nT is the length of the cycle (1 <= T <= 30); t_i (for 1 <= i <= T ) is the amount of sleep on the i-th day of the\ncycle, given in hours (1 <= t_i <= 23); N is the number of interviews (1 <= N <= 100); D_j (for 1 <= j <= N)\nis the day of the j-th interview (1 <= D_j <= 100); M_j (for 1 <= j <= N) is the hour when the j-th interview starts (1 <= M_j <= 23).\n\nThe numbers in the input are all integers. t_1 is always 1 as stated above. The day indicated by 1 is the\nfirst day in the cycle of Peter's sleep.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the minimum number of times Peter needs to take anhydrous caffeine.\nTask Samples: input: 2\n1 23\n3\n1 1\n2 1\n3 1\n0\n output: 2\n\n" }, { "title": "Problem C: Find the Point", "content": "We understand that reading English is a great pain to many of you. So we 'll keep this problem statememt\nsimple. Write a program that reports the point equally distant from a set of lines given as the input. In\ncase of no solutions or multiple solutions, your program should report as such.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is given in the following format:\n\nn\nx_1,1 y_1,1 x_1,2 y_1,2\nx_2,1 y_2,1 x_2,2 y_2,2\n . . . \nx_n, 1 y_n, 1 x_n, 2 y_n, 2\n\nn is the number of lines (1 <= n <= 100); (x_i, 1, y_i, 1) and (x_i, 2, y_i, 2) denote the different points the i-th line passes through. The lines do not coincide each other. The coordinates are all integers between -10000\nand 10000.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print a line as follows. If there is exactly one point equally distant from all the given lines, print the x- and y-coordinates in this order with a single space between them. If there is more than one such point,\njust print \"Many\" (without quotes). If there is none, just print \"None\" (without quotes).\n\nThe coordinates may be printed with any number of digits after the decimal point, but should be accurate\nto 10^-4.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n-35 -35 100 100\n-49 49 2000 -2000\n4\n0 0 0 3\n0 0 3 0\n0 3 3 3\n3 0 3 3\n4\n0 3 -4 6\n3 0 6 -4\n2 3 6 6\n-1 2 -4 6\n0\n output: Many\n1.5000 1.5000\n1.000 1.000"], "Pid": "p01285", "ProblemText": "Task Description: We understand that reading English is a great pain to many of you. So we 'll keep this problem statememt\nsimple. Write a program that reports the point equally distant from a set of lines given as the input. In\ncase of no solutions or multiple solutions, your program should report as such.\nTask Input: The input consists of multiple datasets. Each dataset is given in the following format:\n\nn\nx_1,1 y_1,1 x_1,2 y_1,2\nx_2,1 y_2,1 x_2,2 y_2,2\n . . . \nx_n, 1 y_n, 1 x_n, 2 y_n, 2\n\nn is the number of lines (1 <= n <= 100); (x_i, 1, y_i, 1) and (x_i, 2, y_i, 2) denote the different points the i-th line passes through. The lines do not coincide each other. The coordinates are all integers between -10000\nand 10000.\n\nThe last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print a line as follows. If there is exactly one point equally distant from all the given lines, print the x- and y-coordinates in this order with a single space between them. If there is more than one such point,\njust print \"Many\" (without quotes). If there is none, just print \"None\" (without quotes).\n\nThe coordinates may be printed with any number of digits after the decimal point, but should be accurate\nto 10^-4.\nTask Samples: input: 2\n-35 -35 100 100\n-49 49 2000 -2000\n4\n0 0 0 3\n0 0 3 0\n0 3 3 3\n3 0 3 3\n4\n0 3 -4 6\n3 0 6 -4\n2 3 6 6\n-1 2 -4 6\n0\n output: Many\n1.5000 1.5000\n1.000 1.000\n\n" }, { "title": "Problem D: Luigi's Tavern", "content": "Luigi's Tavern is a thriving tavern in the Kingdom of Nahaila. The owner of the tavern Luigi supports to\norganize a party, because the main customers of the tavern are adventurers. Each adventurer has a job:\nhero, warrior, cleric or mage.\n\nAny party should meet the following conditions:\n\n A party should have a hero.\n\n The warrior and the hero in a party should get along with each other.\n\n The cleric and the warrior in a party should get along with each other.\n\n The mage and the cleric in a party should get along with each other.\n\n It is recommended that a party has a warrior, a cleric, and a mage, but it is allowed that at most\n N_W, N_C and N_m parties does not have a warrior, a cleric, and a mage respectively.\n\n A party without a cleric should have a warrior and a mage.\nNow, the tavern has H heroes, W warriors, C clerics and M mages. Your job is to write a program to find the maximum number of parties they can form.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nThe first line of the input contains 7 non-negative integers H, W, C, M, N_W, N_C, and N_M, each of which is less than or equals to 50. The i-th of the following W lines contains the list of heroes who will be getting along with the warrior i. The list begins with a non-negative integer n_i , less than or equals to H. Then the rest of the line should contain ni positive integers, each of which indicates the ID of a hero getting along with the warrior i.\n\nAfter these lists, the following C lines contain the lists of warriors getting along with the clerics in the same manner. The j-th line contains a list of warriors who will be getting along with the cleric j. Then the last M lines of the input contain the lists of clerics getting along with the mages, of course in the same\nmanner. The k-th line contains a list of clerics who will be getting along with the mage k.\n\nThe last dataset is followed by a line containing seven negative integers. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, you should output the maximum number of parties possible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 1 1 1 1 1\n1 1\n1 1\n1 1\n1 1 1 1 0 0 0\n1 1\n1 1\n1 1\n1 0 1 0 1 0 1\n0\n1 1 0 1 0 1 0\n0\n0\n1 1 0 1 0 1 0\n1 1\n0\n-1 -1 -1 -1 -1 -1 -1\n output: 2\n1\n1\n0\n1"], "Pid": "p01286", "ProblemText": "Task Description: Luigi's Tavern is a thriving tavern in the Kingdom of Nahaila. The owner of the tavern Luigi supports to\norganize a party, because the main customers of the tavern are adventurers. Each adventurer has a job:\nhero, warrior, cleric or mage.\n\nAny party should meet the following conditions:\n\n A party should have a hero.\n\n The warrior and the hero in a party should get along with each other.\n\n The cleric and the warrior in a party should get along with each other.\n\n The mage and the cleric in a party should get along with each other.\n\n It is recommended that a party has a warrior, a cleric, and a mage, but it is allowed that at most\n N_W, N_C and N_m parties does not have a warrior, a cleric, and a mage respectively.\n\n A party without a cleric should have a warrior and a mage.\nNow, the tavern has H heroes, W warriors, C clerics and M mages. Your job is to write a program to find the maximum number of parties they can form.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nThe first line of the input contains 7 non-negative integers H, W, C, M, N_W, N_C, and N_M, each of which is less than or equals to 50. The i-th of the following W lines contains the list of heroes who will be getting along with the warrior i. The list begins with a non-negative integer n_i , less than or equals to H. Then the rest of the line should contain ni positive integers, each of which indicates the ID of a hero getting along with the warrior i.\n\nAfter these lists, the following C lines contain the lists of warriors getting along with the clerics in the same manner. The j-th line contains a list of warriors who will be getting along with the cleric j. Then the last M lines of the input contain the lists of clerics getting along with the mages, of course in the same\nmanner. The k-th line contains a list of clerics who will be getting along with the mage k.\n\nThe last dataset is followed by a line containing seven negative integers. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, you should output the maximum number of parties possible.\nTask Samples: input: 2 1 1 1 1 1 1\n1 1\n1 1\n1 1\n1 1 1 1 0 0 0\n1 1\n1 1\n1 1\n1 0 1 0 1 0 1\n0\n1 1 0 1 0 1 0\n0\n0\n1 1 0 1 0 1 0\n1 1\n0\n-1 -1 -1 -1 -1 -1 -1\n output: 2\n1\n1\n0\n1\n\n" }, { "title": "Problem E: Colored Octahedra", "content": "A young boy John is playing with eight triangular panels. These panels are all regular triangles of the\nsame size, each painted in a single color; John is forming various octahedra with them.\n\nWhile he enjoys his playing, his father is wondering how many octahedra can be made of these panels\nsince he is a pseudo-mathematician. Your task is to help his father: write a program that reports the\nnumber of possible octahedra for given panels. Here, a pair of octahedra should be considered identical\nwhen they have the same combination of the colors allowing rotation.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nColor_1 Color_2 . . . Color_8\n\nEach Color_i (1 <= i <= 8) is a string of up to 20 lowercase alphabets and represents the color of the i-th\ntriangular panel.\n\nThe input ends with EOF.", "output": "For each dataset, output the number of different octahedra that can be made of given panels.", "content_img": false, "lang": "en", "error": false, "samples": ["input: blue blue blue blue blue blue blue blue\nred blue blue blue blue blue blue blue\nred red blue blue blue blue blue blue\n output: 1\n1\n3"], "Pid": "p01287", "ProblemText": "Task Description: A young boy John is playing with eight triangular panels. These panels are all regular triangles of the\nsame size, each painted in a single color; John is forming various octahedra with them.\n\nWhile he enjoys his playing, his father is wondering how many octahedra can be made of these panels\nsince he is a pseudo-mathematician. Your task is to help his father: write a program that reports the\nnumber of possible octahedra for given panels. Here, a pair of octahedra should be considered identical\nwhen they have the same combination of the colors allowing rotation.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nColor_1 Color_2 . . . Color_8\n\nEach Color_i (1 <= i <= 8) is a string of up to 20 lowercase alphabets and represents the color of the i-th\ntriangular panel.\n\nThe input ends with EOF.\nTask Output: For each dataset, output the number of different octahedra that can be made of given panels.\nTask Samples: input: blue blue blue blue blue blue blue blue\nred blue blue blue blue blue blue blue\nred red blue blue blue blue blue blue\n output: 1\n1\n3\n\n" }, { "title": "Problem F: Marked Ancestor", "content": "You are given a tree T that consists of N nodes. Each node is numbered from 1 to N, and node 1 is always the root node of T. Consider the following two operations on T:\n\nM v: (Mark) Mark node v.\n\nQ v: (Query) Print the index of the nearest marked ancestor of node v which is nearest to it. Initially, only the root node is marked. Note that a node is an ancestor of itself.\nYour job is to write a program that performs a sequence of these operations on a given tree and calculates\nthe value that each Q operation will print. To avoid too large output file, your program is requested to\nprint the sum of the outputs of all query operations. Note that the judges confirmed that it is possible to\ncalculate every output of query operations in a given sequence.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nThe first line of the input contains two integers N and Q, which denotes the number of nodes in the tree\nT and the number of operations, respectively. These numbers meet the following conditions: 1 <= N <= 100000 and 1 <= Q <= 100000.\n\nThe following N - 1 lines describe the configuration of the tree T. Each line contains a single integer p_i (i = 2, . . . , N), which represents the index of the parent of i-th node.\n\nThe next Q lines contain operations in order. Each operation is formatted as \"M v\" or \"Q v\", where v is the index of a node.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the sum of the outputs of all query operations in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3\n1\n1\n2\n3\n3\nQ 5\nM 3\nQ 5\n0 0\n output: 4"], "Pid": "p01288", "ProblemText": "Task Description: You are given a tree T that consists of N nodes. Each node is numbered from 1 to N, and node 1 is always the root node of T. Consider the following two operations on T:\n\nM v: (Mark) Mark node v.\n\nQ v: (Query) Print the index of the nearest marked ancestor of node v which is nearest to it. Initially, only the root node is marked. Note that a node is an ancestor of itself.\nYour job is to write a program that performs a sequence of these operations on a given tree and calculates\nthe value that each Q operation will print. To avoid too large output file, your program is requested to\nprint the sum of the outputs of all query operations. Note that the judges confirmed that it is possible to\ncalculate every output of query operations in a given sequence.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nThe first line of the input contains two integers N and Q, which denotes the number of nodes in the tree\nT and the number of operations, respectively. These numbers meet the following conditions: 1 <= N <= 100000 and 1 <= Q <= 100000.\n\nThe following N - 1 lines describe the configuration of the tree T. Each line contains a single integer p_i (i = 2, . . . , N), which represents the index of the parent of i-th node.\n\nThe next Q lines contain operations in order. Each operation is formatted as \"M v\" or \"Q v\", where v is the index of a node.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the sum of the outputs of all query operations in one line.\nTask Samples: input: 6 3\n1\n1\n2\n3\n3\nQ 5\nM 3\nQ 5\n0 0\n output: 4\n\n" }, { "title": "Problem G: Strange Couple", "content": "Alice and Bob are going to drive from their home to a theater for a date. They are very challenging - they have no maps with them even though they don 't know the route at all (since they have just moved to\ntheir new home). Yes, they will be going just by their feeling.\n\nThe town they drive can be considered as an undirected graph with a number of intersections (vertices)\nand roads (edges). Each intersection may or may not have a sign. On intersections with signs, Alice and\nBob will enter the road for the shortest route. When there is more than one such roads, they will go into\none of them at random.\n\nOn intersections without signs, they will just make a random choice. Each random selection is made with\nequal probabilities. They can even choose to go back to the road they have just come along, on a random\nselection.\n\nCalculate the expected distance Alice and Bob will drive before reaching the theater.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nn s t\nq_1 q_2 . . . q_n\na_11 a_12 . . . a_1n\na_21 a_22 . . . a_2n\n . \n . \n . \na_n1 a_n2 . . . a_nn\n\nn is the number of intersections (n <= 100). s and t are the intersections the home and the theater are\nlocated respectively (1 <= s, t <= n, s ! = t); q_i (for 1 <= i <= n) is either 1 or 0, where 1 denotes there is a\nsign at the i-th intersection and 0 denotes there is not; a_ij (for 1 <= i, j <= n) is a positive integer denoting\nthe distance of the road connecting the i-th and j-th intersections, or 0 indicating there is no road directly\nconnecting the intersections. The distance of each road does not exceed 10.\n\nSince the graph is undirectional, it holds a_ij = a_ji for any 1 <= i, j <= n. There can be roads connecting the\nsame intersection, that is, it does not always hold a_ii = 0. Also, note that the graph is not always planar.\n\nThe last dataset is followed by a line containing three zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the expected distance accurate to 10^-8 , or \"impossible\" (without quotes) if there is no route to get\nto the theater. The distance may be printed with any number of digits after the decimal point.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1 5\n1 0 1 0 0\n0 2 1 0 0\n2 0 0 1 0\n1 0 0 1 0\n0 1 1 0 1\n0 0 0 1 0\n0 0 0\n output: 8.50000000"], "Pid": "p01289", "ProblemText": "Task Description: Alice and Bob are going to drive from their home to a theater for a date. They are very challenging - they have no maps with them even though they don 't know the route at all (since they have just moved to\ntheir new home). Yes, they will be going just by their feeling.\n\nThe town they drive can be considered as an undirected graph with a number of intersections (vertices)\nand roads (edges). Each intersection may or may not have a sign. On intersections with signs, Alice and\nBob will enter the road for the shortest route. When there is more than one such roads, they will go into\none of them at random.\n\nOn intersections without signs, they will just make a random choice. Each random selection is made with\nequal probabilities. They can even choose to go back to the road they have just come along, on a random\nselection.\n\nCalculate the expected distance Alice and Bob will drive before reaching the theater.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nn s t\nq_1 q_2 . . . q_n\na_11 a_12 . . . a_1n\na_21 a_22 . . . a_2n\n . \n . \n . \na_n1 a_n2 . . . a_nn\n\nn is the number of intersections (n <= 100). s and t are the intersections the home and the theater are\nlocated respectively (1 <= s, t <= n, s ! = t); q_i (for 1 <= i <= n) is either 1 or 0, where 1 denotes there is a\nsign at the i-th intersection and 0 denotes there is not; a_ij (for 1 <= i, j <= n) is a positive integer denoting\nthe distance of the road connecting the i-th and j-th intersections, or 0 indicating there is no road directly\nconnecting the intersections. The distance of each road does not exceed 10.\n\nSince the graph is undirectional, it holds a_ij = a_ji for any 1 <= i, j <= n. There can be roads connecting the\nsame intersection, that is, it does not always hold a_ii = 0. Also, note that the graph is not always planar.\n\nThe last dataset is followed by a line containing three zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the expected distance accurate to 10^-8 , or \"impossible\" (without quotes) if there is no route to get\nto the theater. The distance may be printed with any number of digits after the decimal point.\nTask Samples: input: 5 1 5\n1 0 1 0 0\n0 2 1 0 0\n2 0 0 1 0\n1 0 0 1 0\n0 1 1 0 1\n0 0 0 1 0\n0 0 0\n output: 8.50000000\n\n" }, { "title": "Problem H: Queen's Case", "content": "A small country called Maltius was governed by a queen. The queen was known as an oppressive ruler.\nPeople in the country suffered from heavy taxes and forced labor. So some young people decided to form\na revolutionary army and fight against the queen. Now, they besieged the palace and have just rushed into\nthe entrance.\n\nYour task is to write a program to determine whether the queen can escape or will be caught by the army.\n\nHere is detailed description.\n\n The palace can be considered as grid squares.\n\n The queen and the army move alternately. The queen moves first.\n\n At each of their turns, they either move to an adjacent cell or stay at the same cell.\n\n Each of them must follow the optimal strategy.\n\n If the queen and the army are at the same cell, the queen will be caught by the army immediately.\n\n If the queen is at any of exit cells alone after the army 's turn, the queen can escape from the army.\n\n There may be cases in which the queen cannot escape but won 't be caught by the army forever,\n under their optimal strategies.\n\n hint:\nOn the first sample input, the queen can move to exit cells, but either way the queen will be caught at the\nnext army 's turn. So the optimal strategy for the queen is staying at the same cell. Then the army can\nmove to exit cells as well, but again either way the army will miss the queen from the other exit. So the\noptimal strategy for the army is also staying at the same cell. Thus the queen cannot escape but won 't be\ncaught.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset describes a map of the palace. The first line of the input contains two integers W (1 <= W <= 30) and H (1 <= H <= 30), which indicate the width and height of the palace. The following H lines, each of which contains W characters, denote the map of the palace. \"Q\" indicates the queen, \"A\" the army, \"E\" an exit, \"#\" a wall and \". \" a floor.\n\nThe map contains exactly one \"Q\", exactly one \"A\" and at least one \"E\". You can assume both the queen and the army can reach all the exits.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, output \"Queen can escape. \", \"Army can catch Queen. \" or \"Queen can not escape and Army can not catch Queen. \" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n####.\n..E..\n.####\n....Q\n0 0\n output: Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen."], "Pid": "p01290", "ProblemText": "Task Description: A small country called Maltius was governed by a queen. The queen was known as an oppressive ruler.\nPeople in the country suffered from heavy taxes and forced labor. So some young people decided to form\na revolutionary army and fight against the queen. Now, they besieged the palace and have just rushed into\nthe entrance.\n\nYour task is to write a program to determine whether the queen can escape or will be caught by the army.\n\nHere is detailed description.\n\n The palace can be considered as grid squares.\n\n The queen and the army move alternately. The queen moves first.\n\n At each of their turns, they either move to an adjacent cell or stay at the same cell.\n\n Each of them must follow the optimal strategy.\n\n If the queen and the army are at the same cell, the queen will be caught by the army immediately.\n\n If the queen is at any of exit cells alone after the army 's turn, the queen can escape from the army.\n\n There may be cases in which the queen cannot escape but won 't be caught by the army forever,\n under their optimal strategies.\n\n hint:\nOn the first sample input, the queen can move to exit cells, but either way the queen will be caught at the\nnext army 's turn. So the optimal strategy for the queen is staying at the same cell. Then the army can\nmove to exit cells as well, but again either way the army will miss the queen from the other exit. So the\noptimal strategy for the army is also staying at the same cell. Thus the queen cannot escape but won 't be\ncaught.\nTask Input: The input consists of multiple datasets. Each dataset describes a map of the palace. The first line of the input contains two integers W (1 <= W <= 30) and H (1 <= H <= 30), which indicate the width and height of the palace. The following H lines, each of which contains W characters, denote the map of the palace. \"Q\" indicates the queen, \"A\" the army, \"E\" an exit, \"#\" a wall and \". \" a floor.\n\nThe map contains exactly one \"Q\", exactly one \"A\" and at least one \"E\". You can assume both the queen and the army can reach all the exits.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, output \"Queen can escape. \", \"Army can catch Queen. \" or \"Queen can not escape and Army can not catch Queen. \" in a line.\nTask Samples: input: 2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n####.\n..E..\n.####\n....Q\n0 0\n output: Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n\n" }, { "title": "Problem I: Wind Passages", "content": "Wind Corridor is a covered passageway where strong wind is always blowing. It is a long corridor of\nwidth W, and there are several pillars in it. Each pillar is a right prism and its face is a polygon (not\nnecessarily convex).\n\nIn this problem, we consider two-dimensional space where the positive x-axis points the east and the\npositive y-axis points the north. The passageway spans from the south to the north, and its length is\ninfinity. Specifically, it covers the area 0 <= x <= W. The outside of the passageway is filled with walls.\nEach pillar is expressed as a polygon, and all the pillars are located within the corridor without conflicting\nor touching each other.\n\nWind blows from the south side of the corridor to the north. For each second, w unit volume of air can\nbe flowed at most if the minimum width of the path of the wind is w. Note that the path may fork and\nmerge, but never overlaps with pillars and walls.\n\nYour task in this problem is to write a program that calculates the maximum amount of air that can be\nflowed through the corridor per second.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nThe first line of the input contains two integers W and N. W is the width of the corridor, and N is the\nnumber of pillars. W and N satisfy the following condition: 1 <= W <= 10^4 and 0 <= N <= 200.\n\nThen, N specifications of each pillar follow. Each specification starts with a line that contains a single\ninteger M, which is the number of the vertices of a polygon (3 <= M <= 40). The following M lines describe the shape of the polygon. The i-th line (1 <= i <= M) contains two integers x_i and y_i that denote the coordinate of the i-th vertex (0 < x_i < W, 0 < y_i < 10^4).\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, your program should print a line that contains the maximum amount of air flow per second, in unit\nvolume. The output may contain arbitrary number of digits after the decimal point, but the absolute error\nmust not exceed 10^-6.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n4\n1 1\n1 2\n2 2\n2 1\n4\n3 3\n3 4\n4 4\n4 3\n0 0\n output: 3.41421356"], "Pid": "p01291", "ProblemText": "Task Description: Wind Corridor is a covered passageway where strong wind is always blowing. It is a long corridor of\nwidth W, and there are several pillars in it. Each pillar is a right prism and its face is a polygon (not\nnecessarily convex).\n\nIn this problem, we consider two-dimensional space where the positive x-axis points the east and the\npositive y-axis points the north. The passageway spans from the south to the north, and its length is\ninfinity. Specifically, it covers the area 0 <= x <= W. The outside of the passageway is filled with walls.\nEach pillar is expressed as a polygon, and all the pillars are located within the corridor without conflicting\nor touching each other.\n\nWind blows from the south side of the corridor to the north. For each second, w unit volume of air can\nbe flowed at most if the minimum width of the path of the wind is w. Note that the path may fork and\nmerge, but never overlaps with pillars and walls.\n\nYour task in this problem is to write a program that calculates the maximum amount of air that can be\nflowed through the corridor per second.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nThe first line of the input contains two integers W and N. W is the width of the corridor, and N is the\nnumber of pillars. W and N satisfy the following condition: 1 <= W <= 10^4 and 0 <= N <= 200.\n\nThen, N specifications of each pillar follow. Each specification starts with a line that contains a single\ninteger M, which is the number of the vertices of a polygon (3 <= M <= 40). The following M lines describe the shape of the polygon. The i-th line (1 <= i <= M) contains two integers x_i and y_i that denote the coordinate of the i-th vertex (0 < x_i < W, 0 < y_i < 10^4).\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, your program should print a line that contains the maximum amount of air flow per second, in unit\nvolume. The output may contain arbitrary number of digits after the decimal point, but the absolute error\nmust not exceed 10^-6.\nTask Samples: input: 5 2\n4\n1 1\n1 2\n2 2\n2 1\n4\n3 3\n3 4\n4 4\n4 3\n0 0\n output: 3.41421356\n\n" }, { "title": "Problem J: Secret Operation", "content": "Mary Ice is a member of a spy group. She is about to carry out a secret operation with her colleague.\n\nShe has got into a target place just now, but unfortunately the colleague has not reached there yet. She\nneeds to hide from her enemy George Water until the colleague comes. Mary may want to make herself\nappear in George 's sight as short as possible, so she will give less chance for George to find her.\n\nYou are requested to write a program that calculates the time Mary is in George 's sight before her colleague arrives, given the information about moves of Mary and George as well as obstacles blocking their\nsight.\n\nRead the Input section for the details of the situation.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset has the following format:\n\nTime R\nL\nMary X_1 Mary Y_1 Mary T_1\nMary X_2 Mary Y_2 Mary T_2\n. . . \nMary X_L Mary Y_L Mary T_L\nM\nGeorge X_1 George Y_1 George T_1\nGeorge X_2 George Y_2 George T_2\n. . . \nGeorge X_M George Y_M George T_M\nN\nBlock SX_1 Block SY_1 Block TX_1 Block TY_1\nBlock SX_2 Block SY_2 Block TX_2 Block TY_2\n. . . \nBlock SX_N Block SY_N Block TX_N Block TY_N\n\nThe first line contains two integers. Time (0 <= Time <= 100) is the time Mary's colleague reaches the\nplace. R (0 < R < 30000) is the distance George can see - he has a sight of this distance and of 45\ndegrees left and right from the direction he is moving. In other words, Mary is found by him if and only\nif she is within this distance from him and in the direction different by not greater than 45 degrees from\nhis moving direction and there is no obstacles between them.\n\nThe description of Mary's move follows. Mary moves from (Mary X_i, Mary Y_i) to (Mary X_i+1, Mary Y_i+1)\nstraight and at a constant speed during the time between Mary T_i and Mary T_i+1, for each 1 <= i <= L - 1.\nThe following constraints apply: 2 <= L <= 20, Mary T_1 = 0 and Mary T_L = Time, and Mary T_i < Mary T_i+1\nfor any 1 <= i <= L - 1.\n\nThe description of George's move is given in the same way with the same constraints, following Mary's.\nIn addition, (George X_j, George Y_j ) and (George X_j+1, George Y_j+1) do not coincide for any 1 <= j <= M - 1. In other words, George is always moving in some direction.\n\nFinally, there comes the information of the obstacles. Each obstacle has a rectangular shape occupying\n(Block SX_k, Block SY_k) to (Block TX_k, Block TY_k). No obstacle touches or crosses with another. The number of obstacles ranges from 0 to 20 inclusive.\n\nAll the coordinates are integers not greater than 10000 in their absolute values. You may assume that, if\nthe coordinates of Mary's and George's moves would be changed within the distance of 10^-6, the solution would be changed by not greater than 10^-6.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.", "output": "For each dataset, print the calculated time in a line. The time may be printed with any number of digits after the decimal\npoint, but should be accurate to 10^-4 .", "content_img": false, "lang": "en", "error": false, "samples": ["input: 50 100\n2\n50 50 0\n51 51 50\n2\n0 0 0\n1 1 50\n0\n0 0\n output: 50"], "Pid": "p01292", "ProblemText": "Task Description: Mary Ice is a member of a spy group. She is about to carry out a secret operation with her colleague.\n\nShe has got into a target place just now, but unfortunately the colleague has not reached there yet. She\nneeds to hide from her enemy George Water until the colleague comes. Mary may want to make herself\nappear in George 's sight as short as possible, so she will give less chance for George to find her.\n\nYou are requested to write a program that calculates the time Mary is in George 's sight before her colleague arrives, given the information about moves of Mary and George as well as obstacles blocking their\nsight.\n\nRead the Input section for the details of the situation.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nTime R\nL\nMary X_1 Mary Y_1 Mary T_1\nMary X_2 Mary Y_2 Mary T_2\n. . . \nMary X_L Mary Y_L Mary T_L\nM\nGeorge X_1 George Y_1 George T_1\nGeorge X_2 George Y_2 George T_2\n. . . \nGeorge X_M George Y_M George T_M\nN\nBlock SX_1 Block SY_1 Block TX_1 Block TY_1\nBlock SX_2 Block SY_2 Block TX_2 Block TY_2\n. . . \nBlock SX_N Block SY_N Block TX_N Block TY_N\n\nThe first line contains two integers. Time (0 <= Time <= 100) is the time Mary's colleague reaches the\nplace. R (0 < R < 30000) is the distance George can see - he has a sight of this distance and of 45\ndegrees left and right from the direction he is moving. In other words, Mary is found by him if and only\nif she is within this distance from him and in the direction different by not greater than 45 degrees from\nhis moving direction and there is no obstacles between them.\n\nThe description of Mary's move follows. Mary moves from (Mary X_i, Mary Y_i) to (Mary X_i+1, Mary Y_i+1)\nstraight and at a constant speed during the time between Mary T_i and Mary T_i+1, for each 1 <= i <= L - 1.\nThe following constraints apply: 2 <= L <= 20, Mary T_1 = 0 and Mary T_L = Time, and Mary T_i < Mary T_i+1\nfor any 1 <= i <= L - 1.\n\nThe description of George's move is given in the same way with the same constraints, following Mary's.\nIn addition, (George X_j, George Y_j ) and (George X_j+1, George Y_j+1) do not coincide for any 1 <= j <= M - 1. In other words, George is always moving in some direction.\n\nFinally, there comes the information of the obstacles. Each obstacle has a rectangular shape occupying\n(Block SX_k, Block SY_k) to (Block TX_k, Block TY_k). No obstacle touches or crosses with another. The number of obstacles ranges from 0 to 20 inclusive.\n\nAll the coordinates are integers not greater than 10000 in their absolute values. You may assume that, if\nthe coordinates of Mary's and George's moves would be changed within the distance of 10^-6, the solution would be changed by not greater than 10^-6.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\nTask Output: For each dataset, print the calculated time in a line. The time may be printed with any number of digits after the decimal\npoint, but should be accurate to 10^-4 .\nTask Samples: input: 50 100\n2\n50 50 0\n51 51 50\n2\n0 0 0\n1 1 50\n0\n0 0\n output: 50\n\n" }, { "title": "Problem A: Whist", "content": "Whist is a game played by four players with a standard deck of playing cards. The players seat\naround a table, namely, in north, east, south, and west. This game is played in a team-play\nbasis: the players seating opposite to each other become a team. In other words, they make two\nteams we could call the north-south team and the east-west team.\n\nRemember that the standard deck consists of 52 cards each of which has a rank and a suit. The\nrank indicates the strength of the card and is one of the following: 2,3,4,5,6,7,8,9,10, jack,\nqueen, king, and ace (from the lowest to the highest). The suit refers to the type of symbols\nprinted on the card, namely, spades, hearts, diamonds, and clubs. The deck contains exactly\none card for every possible pair of a rank and a suit, thus 52 cards.\n\nOne of the four players (called a dealer) shuffles the deck and deals out all the cards face down,\none by one, clockwise from the player left to him or her. Each player should have thirteen cards.\nThen the last dealt card, which belongs to the dealer, is turned face up. The suit of this card is\ncalled trumps and has a special meaning as mentioned below.\n\nA deal of this game consists of thirteen tricks. The objective for each team is winning more\ntricks than another team. The player left to the dealer leads the first trick by playing one of\nthe cards in his or her hand. Then the other players make their plays in the clockwise order.\nThey have to play a card of the suit led if they have one; they can play any card otherwise. The\ntrick is won by the player with the highest card of the suit led if no one plays a trump, or with\nthe highest trump otherwise. The winner of this trick leads the next trick, and the remaining\npart of the deal is played similarly. After the thirteen tricks have been played, the team winning\nmore tricks gains a score, one point per trick in excess of six.\n\nYour task is to write a program that determines the winning team and their score for given\nplays of a deal.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset corresponds to a single deal and has the\nfollowing format:\n\nTrump\nCard_N, 1 Card_N, 2 . . . Card_N, 13\nCard_E, 1 Card_E, 2 . . . Card_E, 13\nCard_S, 1 Card_S, 2 . . . Card_S, 13\nCard_W, 1 Card_W, 2 . . . Card_W, 13\n\nTrump indicates the trump suit. Card_N, i, Card_E, i, Card_S, i, and Card_W, i denote the card played in the i-th trick by the north, east, south, and west players respectively. Each card is represented\nby two characters; the first and second character indicates the rank and the suit respectively.\n\nThe rank is represented by one of the following characters: ‘2 ', ‘3 ', ‘4 ', ‘5 ', ‘6 ', ‘7 ', ‘8 ', ‘9 ', ‘T ' (10), ‘J ' (jack), ‘Q ' (queen), ‘K ' (king), and ‘A ' (ace). The suit is represented by one of the following characters: ‘S ' (spades), ‘H ' (hearts), ‘D ' (diamonds), and ‘C ' (clubs).\n\nYou should assume the cards have been dealt out by the west player. Thus the first trick is led\nby the north player. Also, the input does not contain any illegal plays.\n\nThe input is terminated by a line with “#”. This is not part of any dataset and thus should not\nbe processed.", "output": "For each dataset, print the winner and their score of the deal in a line, with a single space\nbetween them as a separator. The winner should be either “NS” (the north-south team) or “EW”\n(the east-west team). No extra character or whitespace should appear in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: H\n4C 8H QS 5D JD KS 8S AH 6H 7H 3S 7S 6D\nTC JC JS KD AC QC QD 2H QH 3H 3C 7C 4D\n6C 9C AS TD 5H 6S 5S KH TH AD 9S 8D 2D\n8C 5C 2S 7D KC 4S TS JH 4H 9H 2C 9D 3D\nD\n8D 9D 9S QS 4H 5H JD JS 9H 6S TH 6H QH\nQD 9C 5S 7S 7H AC 2D KD 6C 3D 8C TC 7C\n5D QC 3S 4S 3H 3C 6D KS JC AS 5C 8H TS\n4D 4C 8S 2S 2H KC TD JH 2C AH 7D AD KH\n#\n output: EW 1\nEW 2\nThe winners of the tricks in the first dataset are as follows (in the order of tricks): east, north,\nsouth, east, south, north, west, north, east, west, east, east, north."], "Pid": "p01293", "ProblemText": "Task Description: Whist is a game played by four players with a standard deck of playing cards. The players seat\naround a table, namely, in north, east, south, and west. This game is played in a team-play\nbasis: the players seating opposite to each other become a team. In other words, they make two\nteams we could call the north-south team and the east-west team.\n\nRemember that the standard deck consists of 52 cards each of which has a rank and a suit. The\nrank indicates the strength of the card and is one of the following: 2,3,4,5,6,7,8,9,10, jack,\nqueen, king, and ace (from the lowest to the highest). The suit refers to the type of symbols\nprinted on the card, namely, spades, hearts, diamonds, and clubs. The deck contains exactly\none card for every possible pair of a rank and a suit, thus 52 cards.\n\nOne of the four players (called a dealer) shuffles the deck and deals out all the cards face down,\none by one, clockwise from the player left to him or her. Each player should have thirteen cards.\nThen the last dealt card, which belongs to the dealer, is turned face up. The suit of this card is\ncalled trumps and has a special meaning as mentioned below.\n\nA deal of this game consists of thirteen tricks. The objective for each team is winning more\ntricks than another team. The player left to the dealer leads the first trick by playing one of\nthe cards in his or her hand. Then the other players make their plays in the clockwise order.\nThey have to play a card of the suit led if they have one; they can play any card otherwise. The\ntrick is won by the player with the highest card of the suit led if no one plays a trump, or with\nthe highest trump otherwise. The winner of this trick leads the next trick, and the remaining\npart of the deal is played similarly. After the thirteen tricks have been played, the team winning\nmore tricks gains a score, one point per trick in excess of six.\n\nYour task is to write a program that determines the winning team and their score for given\nplays of a deal.\nTask Input: The input is a sequence of datasets. Each dataset corresponds to a single deal and has the\nfollowing format:\n\nTrump\nCard_N, 1 Card_N, 2 . . . Card_N, 13\nCard_E, 1 Card_E, 2 . . . Card_E, 13\nCard_S, 1 Card_S, 2 . . . Card_S, 13\nCard_W, 1 Card_W, 2 . . . Card_W, 13\n\nTrump indicates the trump suit. Card_N, i, Card_E, i, Card_S, i, and Card_W, i denote the card played in the i-th trick by the north, east, south, and west players respectively. Each card is represented\nby two characters; the first and second character indicates the rank and the suit respectively.\n\nThe rank is represented by one of the following characters: ‘2 ', ‘3 ', ‘4 ', ‘5 ', ‘6 ', ‘7 ', ‘8 ', ‘9 ', ‘T ' (10), ‘J ' (jack), ‘Q ' (queen), ‘K ' (king), and ‘A ' (ace). The suit is represented by one of the following characters: ‘S ' (spades), ‘H ' (hearts), ‘D ' (diamonds), and ‘C ' (clubs).\n\nYou should assume the cards have been dealt out by the west player. Thus the first trick is led\nby the north player. Also, the input does not contain any illegal plays.\n\nThe input is terminated by a line with “#”. This is not part of any dataset and thus should not\nbe processed.\nTask Output: For each dataset, print the winner and their score of the deal in a line, with a single space\nbetween them as a separator. The winner should be either “NS” (the north-south team) or “EW”\n(the east-west team). No extra character or whitespace should appear in the output.\nTask Samples: input: H\n4C 8H QS 5D JD KS 8S AH 6H 7H 3S 7S 6D\nTC JC JS KD AC QC QD 2H QH 3H 3C 7C 4D\n6C 9C AS TD 5H 6S 5S KH TH AD 9S 8D 2D\n8C 5C 2S 7D KC 4S TS JH 4H 9H 2C 9D 3D\nD\n8D 9D 9S QS 4H 5H JD JS 9H 6S TH 6H QH\nQD 9C 5S 7S 7H AC 2D KD 6C 3D 8C TC 7C\n5D QC 3S 4S 3H 3C 6D KS JC AS 5C 8H TS\n4D 4C 8S 2S 2H KC TD JH 2C AH 7D AD KH\n#\n output: EW 1\nEW 2\nThe winners of the tricks in the first dataset are as follows (in the order of tricks): east, north,\nsouth, east, south, north, west, north, east, west, east, east, north.\n\n" }, { "title": "Problem B: For the Peace", "content": "This is a story of a world somewhere far from the earth. In this world, the land is parted into a\nnumber of countries ruled by empires. This world is not very peaceful: they have been involved\nin army race.\n\nThey are competing in production of missiles in particular. Nevertheless, no countries have\nstarted wars for years. Actually they have a reason they can 't get into wars - they have\nmissiles much more than enough to destroy the entire world. Once a war would begin among\ncountries, none of them could remain.\n\nThese missiles have given nothing but scare to people. The competition has caused big financial\nand psychological pressure to countries. People have been tired. Military have been tired. Even\nempires have been tired. No one wishes to keep on missile production.\n\nSo empires and diplomats of all countries held meetings quite a few times toward renouncement\nof missiles and abandon of further production. The meetings were quite difficult as they have\ndifferent matters. However, they overcame such difficulties and finally came to the agreement\nof a treaty. The points include:\n\n Each country will dispose all the missiles of their possession by a certain date.\n\n The war potential should not be different by greater than a certain amount d among all\n countries.\nLet us describe more details on the second point. Each missile has its capability, which represents\nhow much it can destroy the target. The war potential of each country is measured simply by\nthe sum of capability over missiles possessed by that country. The treaty requires the difference\nto be not greater than d between the maximum and minimum potential of all the countries.\n\nUnfortunately, it is not clear whether this treaty is feasible. Every country is going to dispose\ntheir missiles only in the order of time they were produced, from the oldest to the newest. Some\nmissiles have huge capability, and disposal of them may cause unbalance in potential.\n\nYour task is to write a program to see this feasibility.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is given in the following format:\n\nn d\nm_1 c_1,1 . . . c_1, m1\n. . . \nm_n c_n, 1 . . . c_n, mn\n\nThe first line contains two positive integers n and d, the number of countries and the tolerated\ndifference of potential (n <= 100, d <= 1000). Then n lines follow. The i-th line begins with a\nnon-negative integer m_i, the number of the missiles possessed by the i-th country. It is followed\nby a sequence of m_i positive integers. The j-th integer c_i, j represents the capability of the j-th\nnewest missile of the i-th country (c_i, j <= 1000). These integers are separated by a single space.\nNote that the country disposes their missiles in the reverse order of the given sequence.\n\nThe number of missiles is not greater than 10000. Also, you may assume the difference between\nthe maximum and minimum potential does not exceed d in any dataset.\n\nThe input is terminated by a line with two zeros. This line should not be processed.", "output": "For each dataset, print a single line. If they can dispose all their missiles according to the treaty,\nprint \"Yes\" (without quotes). Otherwise, print \"No\".\n\nNote that the judge is performed in a case-sensitive manner. No extra space or character is\nallowed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n3 4 1 1\n2 1 5\n2 3 3\n3 3\n3 2 3 1\n2 1 5\n2 3 3\n0 0\n output: Yes\nNo"], "Pid": "p01294", "ProblemText": "Task Description: This is a story of a world somewhere far from the earth. In this world, the land is parted into a\nnumber of countries ruled by empires. This world is not very peaceful: they have been involved\nin army race.\n\nThey are competing in production of missiles in particular. Nevertheless, no countries have\nstarted wars for years. Actually they have a reason they can 't get into wars - they have\nmissiles much more than enough to destroy the entire world. Once a war would begin among\ncountries, none of them could remain.\n\nThese missiles have given nothing but scare to people. The competition has caused big financial\nand psychological pressure to countries. People have been tired. Military have been tired. Even\nempires have been tired. No one wishes to keep on missile production.\n\nSo empires and diplomats of all countries held meetings quite a few times toward renouncement\nof missiles and abandon of further production. The meetings were quite difficult as they have\ndifferent matters. However, they overcame such difficulties and finally came to the agreement\nof a treaty. The points include:\n\n Each country will dispose all the missiles of their possession by a certain date.\n\n The war potential should not be different by greater than a certain amount d among all\n countries.\nLet us describe more details on the second point. Each missile has its capability, which represents\nhow much it can destroy the target. The war potential of each country is measured simply by\nthe sum of capability over missiles possessed by that country. The treaty requires the difference\nto be not greater than d between the maximum and minimum potential of all the countries.\n\nUnfortunately, it is not clear whether this treaty is feasible. Every country is going to dispose\ntheir missiles only in the order of time they were produced, from the oldest to the newest. Some\nmissiles have huge capability, and disposal of them may cause unbalance in potential.\n\nYour task is to write a program to see this feasibility.\nTask Input: The input is a sequence of datasets. Each dataset is given in the following format:\n\nn d\nm_1 c_1,1 . . . c_1, m1\n. . . \nm_n c_n, 1 . . . c_n, mn\n\nThe first line contains two positive integers n and d, the number of countries and the tolerated\ndifference of potential (n <= 100, d <= 1000). Then n lines follow. The i-th line begins with a\nnon-negative integer m_i, the number of the missiles possessed by the i-th country. It is followed\nby a sequence of m_i positive integers. The j-th integer c_i, j represents the capability of the j-th\nnewest missile of the i-th country (c_i, j <= 1000). These integers are separated by a single space.\nNote that the country disposes their missiles in the reverse order of the given sequence.\n\nThe number of missiles is not greater than 10000. Also, you may assume the difference between\nthe maximum and minimum potential does not exceed d in any dataset.\n\nThe input is terminated by a line with two zeros. This line should not be processed.\nTask Output: For each dataset, print a single line. If they can dispose all their missiles according to the treaty,\nprint \"Yes\" (without quotes). Otherwise, print \"No\".\n\nNote that the judge is performed in a case-sensitive manner. No extra space or character is\nallowed.\nTask Samples: input: 3 3\n3 4 1 1\n2 1 5\n2 3 3\n3 3\n3 2 3 1\n2 1 5\n2 3 3\n0 0\n output: Yes\nNo\n\n" }, { "title": "Problem C: Champernowne Constant", "content": "Champernown constant is an irrational number represented in decimal by \"0. \" followed by\nconcatenation of all positive integers in the increasing order. The first few digits of this constant\nare: 0.123456789101112. . .\n\nYour task is to write a program that outputs the K digits of Chapnernown constant starting at\nthe N-th place for given two natural numbers K and N.", "constraint": "", "input": "The input has multiple lines. Each line has two positive integers N and K (N <= 10^9, K <= 100)\nseparated by a space.\n\nThe end of input is indicated by a line with two zeros. This line should not be processed.", "output": "For each line, output a line that contains the K digits.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n6 7\n0 0\n output: 45678\n6789101"], "Pid": "p01295", "ProblemText": "Task Description: Champernown constant is an irrational number represented in decimal by \"0. \" followed by\nconcatenation of all positive integers in the increasing order. The first few digits of this constant\nare: 0.123456789101112. . .\n\nYour task is to write a program that outputs the K digits of Chapnernown constant starting at\nthe N-th place for given two natural numbers K and N.\nTask Input: The input has multiple lines. Each line has two positive integers N and K (N <= 10^9, K <= 100)\nseparated by a space.\n\nThe end of input is indicated by a line with two zeros. This line should not be processed.\nTask Output: For each line, output a line that contains the K digits.\nTask Samples: input: 4 5\n6 7\n0 0\n output: 45678\n6789101\n\n" }, { "title": "Problem D: Futon", "content": "The sales department of Japanese Ancient Giant Corp. is visiting a hot spring resort for their\nrecreational trip. For deepening their friendships, they are staying in one large room of a\nJapanese-style hotel called a ryokan.\n\nIn the ryokan, people sleep in Japanese-style beds called futons. They all have put their futons\non the floor just as they like. Now they are ready for sleeping but they have one concern: they\ndon 't like to go into their futons with their legs toward heads — this is regarded as a bad custom\nin Japanese tradition. However, it is not obvious whether they can follow a good custom. You\nare requested to write a program answering their question, as a talented programmer.\n\nHere let's model the situation. The room is considered to be a grid on an xy-plane. As usual,\nx-axis points toward right and y-axis points toward up. Each futon occupies two adjacent cells.\nPeople put their pillows on either of the two cells. Their heads come to the pillows; their foots\ncome to the other cells. If the cell of some person's foot becomes adjacent to the cell of another\nperson's head, regardless their directions, then it is considered as a bad case. Otherwise people\nare all right.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nx_1 y_1 dir_1\n . . . \nx_n y_n dir_n\n\nn is the number of futons (1 <= n <= 20,000); (x_i, y_i) denotes the coordinates of the left-bottom\ncorner of the i-th futon; dir_i is either 'x' or 'y' and denotes the direction of the i-th futon,\nwhere 'x' means the futon is put horizontally and 'y' means vertically. All coordinate values are\nnon-negative integers not greater than 10^9 .\n\nIt is guaranteed that no two futons in the input overlap each other.\n\nThe input is terminated by a line with a single zero. This is not part of any dataset and thus\nshould not be processed.", "output": "For each dataset, print \"Yes\" in a line if it is possible to avoid a bad case, or \"No\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0 x\n2 0 x\n0 1 x\n2 1 x\n4\n1 0 x\n0 1 x\n2 1 x\n1 2 x\n4\n0 0 x\n2 0 y\n0 1 y\n1 2 x\n0\n output: Yes\nNo\nYes"], "Pid": "p01296", "ProblemText": "Task Description: The sales department of Japanese Ancient Giant Corp. is visiting a hot spring resort for their\nrecreational trip. For deepening their friendships, they are staying in one large room of a\nJapanese-style hotel called a ryokan.\n\nIn the ryokan, people sleep in Japanese-style beds called futons. They all have put their futons\non the floor just as they like. Now they are ready for sleeping but they have one concern: they\ndon 't like to go into their futons with their legs toward heads — this is regarded as a bad custom\nin Japanese tradition. However, it is not obvious whether they can follow a good custom. You\nare requested to write a program answering their question, as a talented programmer.\n\nHere let's model the situation. The room is considered to be a grid on an xy-plane. As usual,\nx-axis points toward right and y-axis points toward up. Each futon occupies two adjacent cells.\nPeople put their pillows on either of the two cells. Their heads come to the pillows; their foots\ncome to the other cells. If the cell of some person's foot becomes adjacent to the cell of another\nperson's head, regardless their directions, then it is considered as a bad case. Otherwise people\nare all right.\nTask Input: The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nx_1 y_1 dir_1\n . . . \nx_n y_n dir_n\n\nn is the number of futons (1 <= n <= 20,000); (x_i, y_i) denotes the coordinates of the left-bottom\ncorner of the i-th futon; dir_i is either 'x' or 'y' and denotes the direction of the i-th futon,\nwhere 'x' means the futon is put horizontally and 'y' means vertically. All coordinate values are\nnon-negative integers not greater than 10^9 .\n\nIt is guaranteed that no two futons in the input overlap each other.\n\nThe input is terminated by a line with a single zero. This is not part of any dataset and thus\nshould not be processed.\nTask Output: For each dataset, print \"Yes\" in a line if it is possible to avoid a bad case, or \"No\" otherwise.\nTask Samples: input: 4\n0 0 x\n2 0 x\n0 1 x\n2 1 x\n4\n1 0 x\n0 1 x\n2 1 x\n1 2 x\n4\n0 0 x\n2 0 y\n0 1 y\n1 2 x\n0\n output: Yes\nNo\nYes\n\n" }, { "title": "Problem E: Safe Area", "content": "Nathan O. Davis is challenging a kind of shooter game. In this game, enemies emit laser beams\nfrom outside of the screen. A laser beam is a straight line with a certain thickness. Nathan\nmoves a circular-shaped machine within the screen, in such a way it does not overlap a laser\nbeam. As in many shooters, the machine is destroyed when the overlap happens.\n\nNathan is facing an uphill stage. Many enemies attack simultaneously in this stage, so eventually\nlaser beams fill out almost all of the screen. Surprisingly, it is even possible he has no \"safe area\" on the screen. In other words, the machine cannot survive wherever it is located in some\ncases.\n\nThe world is as kind as it is cruel! There is a special item that helps the machine to survive\nany dangerous situation, even if it is exposed in a shower of laser beams, for some seconds. In\naddition, another straight line (called \"a warning line\") is drawn on the screen for a few seconds\nbefore a laser beam is emit along that line.\n\nThe only problem is that Nathan has a little slow reflexes. He often messes up the timing to\nuse the special item. But he knows a good person who can write a program to make up his slow\nreflexes - it's you! So he asked you for help.\n\nYour task is to write a program to make judgement whether he should use the item or not, for\ngiven warning lines and the radius of the machine.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset corresponds to one situation with warning\nlines in the following format:\n\nW H N R\nx_1,1 y_1,1 x_1,2 y_1,2 t_1\nx_2,1 y_2,1 x_2,2 y_2,2 t_2\n . . . \nx_N, 1 y_N, 1 x_N, 2 y_N, 2 t_N\n\nThe first line of a dataset contains four integers W, H, N and R (2 < W <= 640,2 < H <= 480,\n0 <= N <= 100 and 0 < R < min{W, H}/2). The first two integers W and H indicate the width\nand height of the screen, respectively. The next integer N represents the number of laser beams.\nThe last integer R indicates the radius of the machine. It is guaranteed that the output would\nremain unchanged if the radius of the machine would become larger by 10^-5 than R.\n\nThe following N lines describe the N warning lines. The (i+1)-th line of the dataset corresponds\nto the i-th warning line, which is represented as a straight line which passes through two given\ndifferent coordinates (x_i, 1, y_i, 1 ) and (x_i, 2 , y_i, 2 ). The last integer t_i indicates the thickness of the\nlaser beam corresponding to the i-th warning line.\n\nAll given coordinates (x, y) on the screen are a pair of integers (0 <= x <= W, 0 <= y <= H). Note\nthat, however, the machine is allowed to be located at non-integer coordinates during the play.\n\nThe input is terminated by a line with four zeros. This line should not be processed.", "output": "For each case, print \"Yes\" in a line if there is a safe area, or print \"No\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100 100 1 1\n50 0 50 100 50\n640 480 1 1\n0 0 640 480 100\n0 0 0 0\n output: No\nYes"], "Pid": "p01297", "ProblemText": "Task Description: Nathan O. Davis is challenging a kind of shooter game. In this game, enemies emit laser beams\nfrom outside of the screen. A laser beam is a straight line with a certain thickness. Nathan\nmoves a circular-shaped machine within the screen, in such a way it does not overlap a laser\nbeam. As in many shooters, the machine is destroyed when the overlap happens.\n\nNathan is facing an uphill stage. Many enemies attack simultaneously in this stage, so eventually\nlaser beams fill out almost all of the screen. Surprisingly, it is even possible he has no \"safe area\" on the screen. In other words, the machine cannot survive wherever it is located in some\ncases.\n\nThe world is as kind as it is cruel! There is a special item that helps the machine to survive\nany dangerous situation, even if it is exposed in a shower of laser beams, for some seconds. In\naddition, another straight line (called \"a warning line\") is drawn on the screen for a few seconds\nbefore a laser beam is emit along that line.\n\nThe only problem is that Nathan has a little slow reflexes. He often messes up the timing to\nuse the special item. But he knows a good person who can write a program to make up his slow\nreflexes - it's you! So he asked you for help.\n\nYour task is to write a program to make judgement whether he should use the item or not, for\ngiven warning lines and the radius of the machine.\nTask Input: The input is a sequence of datasets. Each dataset corresponds to one situation with warning\nlines in the following format:\n\nW H N R\nx_1,1 y_1,1 x_1,2 y_1,2 t_1\nx_2,1 y_2,1 x_2,2 y_2,2 t_2\n . . . \nx_N, 1 y_N, 1 x_N, 2 y_N, 2 t_N\n\nThe first line of a dataset contains four integers W, H, N and R (2 < W <= 640,2 < H <= 480,\n0 <= N <= 100 and 0 < R < min{W, H}/2). The first two integers W and H indicate the width\nand height of the screen, respectively. The next integer N represents the number of laser beams.\nThe last integer R indicates the radius of the machine. It is guaranteed that the output would\nremain unchanged if the radius of the machine would become larger by 10^-5 than R.\n\nThe following N lines describe the N warning lines. The (i+1)-th line of the dataset corresponds\nto the i-th warning line, which is represented as a straight line which passes through two given\ndifferent coordinates (x_i, 1, y_i, 1 ) and (x_i, 2 , y_i, 2 ). The last integer t_i indicates the thickness of the\nlaser beam corresponding to the i-th warning line.\n\nAll given coordinates (x, y) on the screen are a pair of integers (0 <= x <= W, 0 <= y <= H). Note\nthat, however, the machine is allowed to be located at non-integer coordinates during the play.\n\nThe input is terminated by a line with four zeros. This line should not be processed.\nTask Output: For each case, print \"Yes\" in a line if there is a safe area, or print \"No\" otherwise.\nTask Samples: input: 100 100 1 1\n50 0 50 100 50\n640 480 1 1\n0 0 640 480 100\n0 0 0 0\n output: No\nYes\n\n" }, { "title": "Problem F: Water Tank", "content": "You built an apartment. The apartment has a water tank with a capacity of L in order to\nstore water for the residents. The tank works as a buffer between the water company and the\nresidents.\n\nIt is required to keep the tank \"not empty\" at least during use of water. A pump is used to\nprovide water into the tank. From the viewpoint of avoiding water shortage, a more powerful\npump is better, of course. But such powerful pumps are expensive. That 's the life.\n\nYou have a daily schedule table of water usage. It does not differ over days. The table is\ncomposed of some schedules. Each schedule is indicated by the starting time of usage, the\nending time and the used volume per unit of time during the given time span.\n\nAll right, you can find the minimum required speed of providing water for days from the schedule\ntable. You are to write a program to compute it.\n\nYou can assume the following conditions.\n\n A day consists of 86,400 units of time.\n\n No schedule starts before the time 0 (the beginning of the day).\n\n No schedule ends after the time 86,400 (the end of the day).\n\n No two schedules overlap.\n\n Water is not consumed without schedules.\n\n The tank is full of water when the tank starts its work.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset corresponds to a schedule table in the following\nformat:\n\nN L\ns_1 t_1 u_1\n . . . \ns_N t_N u_N\n\nThe first line of a dataset contains two integers N and L (1 <= N <= 86400,1 <= L <= 10^6), which\nrepresents the number of schedule in the table and the capacity of the tank, respectively.\n\nThe following N lines describe the N schedules. The (i + 1)-th line of the dataset corresponds to the i-th schedule, which consists of three integers s_i, t_i and u_i . The first two integers s_i and t_i indicate the starting time and the ending time of the schedule. The last integer u_i\n(1 <= u_i <= 10^6 ) indicates the consumed volume per unit of time during the schedule. It is\nguaranteed that 0 <= s_1 < t_1 <= s_2 < t_2 <= . . . <= s_n < t_n <= 86400.\n\nThe input is terminated by a line with two zeros. This line should not be processed.", "output": "For each case, print the minimum required amount of water per unit of time provided by the\npump in a line. The amount may be printed with an arbitrary number of digits after the decimal\npoint, but should not contain an absolute error greater than 10^-6.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 100\n0 86400 1\n1 100\n43200 86400 1\n0 0\n output: 1.000000\n0.997685"], "Pid": "p01298", "ProblemText": "Task Description: You built an apartment. The apartment has a water tank with a capacity of L in order to\nstore water for the residents. The tank works as a buffer between the water company and the\nresidents.\n\nIt is required to keep the tank \"not empty\" at least during use of water. A pump is used to\nprovide water into the tank. From the viewpoint of avoiding water shortage, a more powerful\npump is better, of course. But such powerful pumps are expensive. That 's the life.\n\nYou have a daily schedule table of water usage. It does not differ over days. The table is\ncomposed of some schedules. Each schedule is indicated by the starting time of usage, the\nending time and the used volume per unit of time during the given time span.\n\nAll right, you can find the minimum required speed of providing water for days from the schedule\ntable. You are to write a program to compute it.\n\nYou can assume the following conditions.\n\n A day consists of 86,400 units of time.\n\n No schedule starts before the time 0 (the beginning of the day).\n\n No schedule ends after the time 86,400 (the end of the day).\n\n No two schedules overlap.\n\n Water is not consumed without schedules.\n\n The tank is full of water when the tank starts its work.\nTask Input: The input is a sequence of datasets. Each dataset corresponds to a schedule table in the following\nformat:\n\nN L\ns_1 t_1 u_1\n . . . \ns_N t_N u_N\n\nThe first line of a dataset contains two integers N and L (1 <= N <= 86400,1 <= L <= 10^6), which\nrepresents the number of schedule in the table and the capacity of the tank, respectively.\n\nThe following N lines describe the N schedules. The (i + 1)-th line of the dataset corresponds to the i-th schedule, which consists of three integers s_i, t_i and u_i . The first two integers s_i and t_i indicate the starting time and the ending time of the schedule. The last integer u_i\n(1 <= u_i <= 10^6 ) indicates the consumed volume per unit of time during the schedule. It is\nguaranteed that 0 <= s_1 < t_1 <= s_2 < t_2 <= . . . <= s_n < t_n <= 86400.\n\nThe input is terminated by a line with two zeros. This line should not be processed.\nTask Output: For each case, print the minimum required amount of water per unit of time provided by the\npump in a line. The amount may be printed with an arbitrary number of digits after the decimal\npoint, but should not contain an absolute error greater than 10^-6.\nTask Samples: input: 1 100\n0 86400 1\n1 100\n43200 86400 1\n0 0\n output: 1.000000\n0.997685\n\n" }, { "title": "Problem G: Neko's Treasure", "content": "Maki is a house cat. One day she fortunately came at a wonderful-looking dried fish. Since she\nfelt not hungry on that day, she put it up in her bed. However there was a problem; a rat was\nliving in her house, and he was watching for a chance to steal her food. To secure the fish during\nthe time she is asleep, she decided to build some walls to prevent the rat from reaching her bed.\n\nMaki's house is represented as a two-dimensional plane. She has hidden the dried fish at (x_t, y_t).\nShe knows that the lair of the rat is located at (x_s, y_s ). She has some candidate locations to\nbuild walls. The i-th candidate is described by a circle of radius r_i centered at (x_i, y_i). She can\nbuild walls at as many candidate locations as she wants, unless they touch or cross each other.\nYou can assume that the size of the fish, the rat 's lair, and the thickness of walls are all very\nsmall and can be ignored.\n\nYour task is to write a program which determines the minimum number of walls the rat needs\nto climb over until he can get to Maki's bed from his lair, assuming that Maki made an optimal\nchoice of walls.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset corresponds to a single situation and has the following format:\n\nn\nx_s y_s x_t y_t\nx_1 y_1 r_1\n . . . \nx_n y_n r_n\n\nn is the number of candidate locations where to build walls (1 <= n <= 1000). (x_s, y_s ) and (x_t , y_t )\ndenote the coordinates of the rat's lair and Maki's bed, respectively. The i-th candidate location\nis a circle which has radius r_i (1 <= r_i <= 10000) and is centered at (x_i, y_i) (i = 1,2, . . . , n). All\ncoordinate values are integers between 0 and 10000 (inclusive).\n\nAll candidate locations are distinct and contain neither the rat's lair nor Maki's bed. The\npositions of the rat's lair and Maki's bed are also distinct.\n\nThe input is terminated by a line with \"0\". This is not part of any dataset and thus should not\nbe processed.", "output": "For each dataset, print a single line that contains the minimum number of walls the rat needs\nto climb over.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 100 100\n60 100 50\n100 100 10\n80 80 50\n4\n0 0 100 100\n50 50 50\n150 50 50\n50 150 50\n150 150 50\n0\n output: 2\n0"], "Pid": "p01299", "ProblemText": "Task Description: Maki is a house cat. One day she fortunately came at a wonderful-looking dried fish. Since she\nfelt not hungry on that day, she put it up in her bed. However there was a problem; a rat was\nliving in her house, and he was watching for a chance to steal her food. To secure the fish during\nthe time she is asleep, she decided to build some walls to prevent the rat from reaching her bed.\n\nMaki's house is represented as a two-dimensional plane. She has hidden the dried fish at (x_t, y_t).\nShe knows that the lair of the rat is located at (x_s, y_s ). She has some candidate locations to\nbuild walls. The i-th candidate is described by a circle of radius r_i centered at (x_i, y_i). She can\nbuild walls at as many candidate locations as she wants, unless they touch or cross each other.\nYou can assume that the size of the fish, the rat 's lair, and the thickness of walls are all very\nsmall and can be ignored.\n\nYour task is to write a program which determines the minimum number of walls the rat needs\nto climb over until he can get to Maki's bed from his lair, assuming that Maki made an optimal\nchoice of walls.\nTask Input: The input is a sequence of datasets. Each dataset corresponds to a single situation and has the following format:\n\nn\nx_s y_s x_t y_t\nx_1 y_1 r_1\n . . . \nx_n y_n r_n\n\nn is the number of candidate locations where to build walls (1 <= n <= 1000). (x_s, y_s ) and (x_t , y_t )\ndenote the coordinates of the rat's lair and Maki's bed, respectively. The i-th candidate location\nis a circle which has radius r_i (1 <= r_i <= 10000) and is centered at (x_i, y_i) (i = 1,2, . . . , n). All\ncoordinate values are integers between 0 and 10000 (inclusive).\n\nAll candidate locations are distinct and contain neither the rat's lair nor Maki's bed. The\npositions of the rat's lair and Maki's bed are also distinct.\n\nThe input is terminated by a line with \"0\". This is not part of any dataset and thus should not\nbe processed.\nTask Output: For each dataset, print a single line that contains the minimum number of walls the rat needs\nto climb over.\nTask Samples: input: 3\n0 0 100 100\n60 100 50\n100 100 10\n80 80 50\n4\n0 0 100 100\n50 50 50\n150 50 50\n50 150 50\n150 150 50\n0\n output: 2\n0\n\n" }, { "title": "Problem H: Eleven Lover", "content": "Edward Leven loves multiples of eleven very much. When he sees a number, he always tries\nto find consecutive subsequences (or substrings) forming multiples of eleven. He calls such\nsubsequences as 11-sequences. For example, he can find an 11-sequence 781 in a number 17819.\n\nHe thinks a number which has many 11-sequences is a good number. He would like to find out\na very good number. As the first step, he wants an easy way to count how many 11-sequences\nare there in a given number. Even for him, counting them from a big number is not easy.\nFortunately, one of his friends, you, is a brilliant programmer. He asks you to write a program\nto count the number of 11-sequences. Note that an 11-sequence must be a positive number\nwithout leading zeros.", "constraint": "", "input": "The input is a sequence of lines each of which contains a number consisting of less than or equal\nto 80000 digits.\n\nThe end of the input is indicated by a line containing a single zero, which should not be processed.", "output": "For each input number, output a line containing the number of 11-sequences.\n\nYou can assume the answer fits in a 32-bit signed integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 17819\n1111\n11011\n1234567891011121314151617181920\n0\n output: 1\n4\n4\n38"], "Pid": "p01300", "ProblemText": "Task Description: Edward Leven loves multiples of eleven very much. When he sees a number, he always tries\nto find consecutive subsequences (or substrings) forming multiples of eleven. He calls such\nsubsequences as 11-sequences. For example, he can find an 11-sequence 781 in a number 17819.\n\nHe thinks a number which has many 11-sequences is a good number. He would like to find out\na very good number. As the first step, he wants an easy way to count how many 11-sequences\nare there in a given number. Even for him, counting them from a big number is not easy.\nFortunately, one of his friends, you, is a brilliant programmer. He asks you to write a program\nto count the number of 11-sequences. Note that an 11-sequence must be a positive number\nwithout leading zeros.\nTask Input: The input is a sequence of lines each of which contains a number consisting of less than or equal\nto 80000 digits.\n\nThe end of the input is indicated by a line containing a single zero, which should not be processed.\nTask Output: For each input number, output a line containing the number of 11-sequences.\n\nYou can assume the answer fits in a 32-bit signed integer.\nTask Samples: input: 17819\n1111\n11011\n1234567891011121314151617181920\n0\n output: 1\n4\n4\n38\n\n" }, { "title": "Problem I: Crystal Jails", "content": "Artistic Crystal Manufacture developed products named Crystal Jails. They are cool ornaments\nforming a rectangular solid. They consist of colorful crystal cubes. There are bright cores on the\ncenter of cubes, which are the origin of the name. The combination of various colored reflections\nshows fantastic dance of lights.\n\nThe company wanted to make big sales with Crystal Jails. They thought nice-looking color\npatterns were the most important factor for attractive products. If they could provide several\nnice patterns, some customers would buy more than one products. However, they didn't have\nstaff who could design nice patterns. So they hired a temporary designer to decide the patterns.\n\nThe color pattern for mass production had a technical limitation: all cubes of the same color\nmust be connected. In addition, they needed to send the pattern to the factory as a set of blocks,\ni. e. shapes formed by cubes of the same color. They requested him to represent the design in\nthis form.\n\nAfter a week of work, he sent various ideas of the color patterns to them. At first, his designs\nlooked nice, but they noticed some patterns couldn 't form a rectangular solid. He was a good\ndesigner, but they had not noticed he lacked space geometrical sense.\n\nThey didn't have time to ask him to revise his design. Although it was acceptable to ignore bad\npatterns, it also took a lot of time to figure out all bad patterns manually. So the leader of this\nproject decided to ask you, a freelance programmer, for help.\n\nYour task is to write a program to judge whether a pattern can form a rectangular solid. Note\nthat blocks can be rotated.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is formatted as follows:\n\nW D H N\nBlock_1\nBlock_2\n . . . \nBlock_N\n\nThe first line of a dataset contains four positive integers W, D, H and N. W, D and H indicate\nthe width, depth and height of a Crystal Jail. N indicates the number of colors.\n\nThe remaining lines describe N colored blocks. Each description is formatted as follows:\n\nw d h\nc_111 c_211 . . . c_w11\nc_121 c_221 . . . c_w21\n. . . \nc_1d1 c_2d1 . . . c_wd1\nc_112 c_212 . . . c_w12\nc_122 c_222 . . . c_w22\n. . . \nc_1d2 c_2d2 . . . c_wd2\n. \n. \n. \nc_11h c_21h . . . c_w1h\nc_12h c_22h . . . c_w2h\n. . . \nc_1dh c_2dh . . . c_wdh\n\nThe first line of the description contains three positive integers w, d and h, which indicate the\nwidth, depth and height of the block. The following (d + 1) * h lines describe the shape of\nthe block. They show the cross-section layout of crystal cubes from bottom to top. On each\nheight, the layout is described as d lines of w characters. Each character c_xyz is either '*' or '. '.\n'*' indicates there is a crystal cube on that space, and '. ' indicates there is not. A blank line\nfollows after each (d * w)-matrix.\n\nThe input is terminated by a line containing four zeros.\n\nYou can assume the followings.\n\n 1 <= W, D, H, w, d, h <= 3.\n\n 1 <= N <= 27.\n\n Each block has at least one crystal cubes and they are connected.\n\n The total number of crystal cubes equals to W * D * H.", "output": "For each dataset, determine whether the given blocks can form a W * D * H rectangular solid\nand output \"Yes\" or \"No\" in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 3 5\n3 2 2\n***\n.*.\n\n.*.\n...\n\n3 2 1\n***\n**.\n\n3 1 3\n..*\n\n.**\n\n**.\n\n3 2 2\n..*\n...\n\n***\n..*\n\n3 1 3\n.**\n\n.**\n\n***\n\n3 3 3 2\n3 3 3\n***\n***\n***\n\n***\n*.*\n***\n\n***\n***\n***\n\n1 1 1\n*\n\n3 2 1 2\n3 1 1\n***\n\n2 2 1\n**\n*.\n\n0 0 0 0\n output: Yes\nYes\nNo"], "Pid": "p01301", "ProblemText": "Task Description: Artistic Crystal Manufacture developed products named Crystal Jails. They are cool ornaments\nforming a rectangular solid. They consist of colorful crystal cubes. There are bright cores on the\ncenter of cubes, which are the origin of the name. The combination of various colored reflections\nshows fantastic dance of lights.\n\nThe company wanted to make big sales with Crystal Jails. They thought nice-looking color\npatterns were the most important factor for attractive products. If they could provide several\nnice patterns, some customers would buy more than one products. However, they didn't have\nstaff who could design nice patterns. So they hired a temporary designer to decide the patterns.\n\nThe color pattern for mass production had a technical limitation: all cubes of the same color\nmust be connected. In addition, they needed to send the pattern to the factory as a set of blocks,\ni. e. shapes formed by cubes of the same color. They requested him to represent the design in\nthis form.\n\nAfter a week of work, he sent various ideas of the color patterns to them. At first, his designs\nlooked nice, but they noticed some patterns couldn 't form a rectangular solid. He was a good\ndesigner, but they had not noticed he lacked space geometrical sense.\n\nThey didn't have time to ask him to revise his design. Although it was acceptable to ignore bad\npatterns, it also took a lot of time to figure out all bad patterns manually. So the leader of this\nproject decided to ask you, a freelance programmer, for help.\n\nYour task is to write a program to judge whether a pattern can form a rectangular solid. Note\nthat blocks can be rotated.\nTask Input: The input consists of multiple datasets. Each dataset is formatted as follows:\n\nW D H N\nBlock_1\nBlock_2\n . . . \nBlock_N\n\nThe first line of a dataset contains four positive integers W, D, H and N. W, D and H indicate\nthe width, depth and height of a Crystal Jail. N indicates the number of colors.\n\nThe remaining lines describe N colored blocks. Each description is formatted as follows:\n\nw d h\nc_111 c_211 . . . c_w11\nc_121 c_221 . . . c_w21\n. . . \nc_1d1 c_2d1 . . . c_wd1\nc_112 c_212 . . . c_w12\nc_122 c_222 . . . c_w22\n. . . \nc_1d2 c_2d2 . . . c_wd2\n. \n. \n. \nc_11h c_21h . . . c_w1h\nc_12h c_22h . . . c_w2h\n. . . \nc_1dh c_2dh . . . c_wdh\n\nThe first line of the description contains three positive integers w, d and h, which indicate the\nwidth, depth and height of the block. The following (d + 1) * h lines describe the shape of\nthe block. They show the cross-section layout of crystal cubes from bottom to top. On each\nheight, the layout is described as d lines of w characters. Each character c_xyz is either '*' or '. '.\n'*' indicates there is a crystal cube on that space, and '. ' indicates there is not. A blank line\nfollows after each (d * w)-matrix.\n\nThe input is terminated by a line containing four zeros.\n\nYou can assume the followings.\n\n 1 <= W, D, H, w, d, h <= 3.\n\n 1 <= N <= 27.\n\n Each block has at least one crystal cubes and they are connected.\n\n The total number of crystal cubes equals to W * D * H.\nTask Output: For each dataset, determine whether the given blocks can form a W * D * H rectangular solid\nand output \"Yes\" or \"No\" in one line.\nTask Samples: input: 3 3 3 5\n3 2 2\n***\n.*.\n\n.*.\n...\n\n3 2 1\n***\n**.\n\n3 1 3\n..*\n\n.**\n\n**.\n\n3 2 2\n..*\n...\n\n***\n..*\n\n3 1 3\n.**\n\n.**\n\n***\n\n3 3 3 2\n3 3 3\n***\n***\n***\n\n***\n*.*\n***\n\n***\n***\n***\n\n1 1 1\n*\n\n3 2 1 2\n3 1 1\n***\n\n2 2 1\n**\n*.\n\n0 0 0 0\n output: Yes\nYes\nNo\n\n" }, { "title": "Problem J: Cave Explorer", "content": "Mike Smith is a man exploring caves all over the world.\n\nOne day, he faced a scaring creature blocking his way. He got scared, but in short time he took\nhis knife and then slashed it to attempt to kill it. Then they were split into parts, which soon\ndied out but the largest one. He slashed the creature a couple of times more to make it small\nenough, and finally became able to go forward.\n\nNow let us think of his situation in a mathematical way. The creature is considered to be a\npolygon, convex or concave. Mike slashes this creature straight with his knife in some direction.\nWe suppose here the direction is given for simpler settings, while the position is arbitrary. Then\nall split parts but the largest one disappears.\n\nYour task is to write a program that calculates the area of the remaining part when the creature\nis slashed in such a way that the area is minimized.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nv_x v_y\nx_1 y_1\n . . . \nx_n y_n\n\nThe first line contains an integer n, the number of vertices of the polygon that represents the\nshape of the creature (3 <= n <= 100). The next line contains two integers v_x and v_y, where\n(v_x, v_y) denote a vector that represents the direction of the knife (-10000 <= v_x, v_y <= 10000,\n\nv_x^2 + v_y^2 > 0). Then n lines follow. The i-th line contains two integers x_i and y_i, where (x_i, y_i)\ndenote the coordinates of the i-th vertex of the polygon (0 <= x_i, y_i <= 10000).\n\nThe vertices are given in the counterclockwise order. You may assume the polygon is always\nsimple, that is, the edges do not touch or cross each other except for end points.\n\nThe input is terminated by a line with a zero. This should not be processed.", "output": "For each dataset, print the minimum possible area in a line. The area may be printed with\nan arbitrary number of digits after the decimal point, but should not contain an absolute error\ngreater than 10^-2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 1\n0 0\n5 0\n1 1\n5 2\n0 2\n7\n9999 9998\n0 0\n2 0\n3 1\n1 1\n10000 9999\n2 2\n0 2\n0\n output: 2.00\n2.2500000"], "Pid": "p01302", "ProblemText": "Task Description: Mike Smith is a man exploring caves all over the world.\n\nOne day, he faced a scaring creature blocking his way. He got scared, but in short time he took\nhis knife and then slashed it to attempt to kill it. Then they were split into parts, which soon\ndied out but the largest one. He slashed the creature a couple of times more to make it small\nenough, and finally became able to go forward.\n\nNow let us think of his situation in a mathematical way. The creature is considered to be a\npolygon, convex or concave. Mike slashes this creature straight with his knife in some direction.\nWe suppose here the direction is given for simpler settings, while the position is arbitrary. Then\nall split parts but the largest one disappears.\n\nYour task is to write a program that calculates the area of the remaining part when the creature\nis slashed in such a way that the area is minimized.\nTask Input: The input is a sequence of datasets. Each dataset is given in the following format:\n\nn\nv_x v_y\nx_1 y_1\n . . . \nx_n y_n\n\nThe first line contains an integer n, the number of vertices of the polygon that represents the\nshape of the creature (3 <= n <= 100). The next line contains two integers v_x and v_y, where\n(v_x, v_y) denote a vector that represents the direction of the knife (-10000 <= v_x, v_y <= 10000,\n\nv_x^2 + v_y^2 > 0). Then n lines follow. The i-th line contains two integers x_i and y_i, where (x_i, y_i)\ndenote the coordinates of the i-th vertex of the polygon (0 <= x_i, y_i <= 10000).\n\nThe vertices are given in the counterclockwise order. You may assume the polygon is always\nsimple, that is, the edges do not touch or cross each other except for end points.\n\nThe input is terminated by a line with a zero. This should not be processed.\nTask Output: For each dataset, print the minimum possible area in a line. The area may be printed with\nan arbitrary number of digits after the decimal point, but should not contain an absolute error\ngreater than 10^-2.\nTask Samples: input: 5\n0 1\n0 0\n5 0\n1 1\n5 2\n0 2\n7\n9999 9998\n0 0\n2 0\n3 1\n1 1\n10000 9999\n2 2\n0 2\n0\n output: 2.00\n2.2500000\n\n" }, { "title": "Problem A: Alien's Counting", "content": "Natsuki and her friends were taken to the space by an alien and made friends with a lot of aliens. During the space travel, she discovered that aliens ' hands were often very different from humans '. Generally speaking, in a kind of aliens, there are N fingers and M bend rules on a hand. Each bend rule describes that a finger A always bends when a finger B bends. However, this rule does not always imply that the finger B bends when the finger A bends.\n\nWhen she were counting numbers with the fingers, she was anxious how many numbers her alien friends can count with the fingers. However, because some friends had too complicated rule sets, she could not calculate those. Would you write a program for her?", "constraint": "", "input": "N M\nS_1 D_1\nS_2 D_2\n. \n. \n. \nS_M D_M\n\nThe first line contains two integers N and M (1 <= N <= 1000,0 <= M <= 1000) in this order. The following M lines mean bend rules. Each line contains two integers S_i and D_i in this order, which mean that the finger D_i always bends when the finger S_i bends. Any finger appears at most once in S.", "output": "Calculate how many numbers her alien friends can count with the fingers. Print the answer modulo 1000000007 in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n2 3\n3 4\n4 3\n5 4\n output: 10", "input: 5 5\n1 2\n2 3\n3 4\n4 5\n5 1\n output: 2", "input: 5 0\n output: 32"], "Pid": "p01339", "ProblemText": "Task Description: Natsuki and her friends were taken to the space by an alien and made friends with a lot of aliens. During the space travel, she discovered that aliens ' hands were often very different from humans '. Generally speaking, in a kind of aliens, there are N fingers and M bend rules on a hand. Each bend rule describes that a finger A always bends when a finger B bends. However, this rule does not always imply that the finger B bends when the finger A bends.\n\nWhen she were counting numbers with the fingers, she was anxious how many numbers her alien friends can count with the fingers. However, because some friends had too complicated rule sets, she could not calculate those. Would you write a program for her?\nTask Input: N M\nS_1 D_1\nS_2 D_2\n. \n. \n. \nS_M D_M\n\nThe first line contains two integers N and M (1 <= N <= 1000,0 <= M <= 1000) in this order. The following M lines mean bend rules. Each line contains two integers S_i and D_i in this order, which mean that the finger D_i always bends when the finger S_i bends. Any finger appears at most once in S.\nTask Output: Calculate how many numbers her alien friends can count with the fingers. Print the answer modulo 1000000007 in a line.\nTask Samples: input: 5 4\n2 3\n3 4\n4 3\n5 4\n output: 10\ninput: 5 5\n1 2\n2 3\n3 4\n4 5\n5 1\n output: 2\ninput: 5 0\n output: 32\n\n" }, { "title": "Problem B: Kaeru Jump", "content": "There is a frog living in a big pond. He loves jumping between lotus leaves floating on the pond. Interestingly, these leaves have strange habits. First, a leaf will sink into the water after the frog jumps from it. Second, they are aligned regularly as if they are placed on the grid points as in the example below. \nFigure 1: Example of floating leaves\n\nRecently, He came up with a puzzle game using these habits. At the beginning of the game, he is on some leaf and faces to the upper, lower, left or right side. He can jump forward or to the left or right relative to his facing direction, but not backward or diagonally. For example, suppose he is facing to the left side, then he can jump to the left, upper and lower sides but not to the right side. In each jump, he will land on the nearest leaf on his jumping direction and face to that direction regardless of his previous state. The leaf he was on will vanish into the water after the jump. The goal of this puzzle is to jump from leaf to leaf until there is only one leaf remaining. \n\nSee the example shown in the figure below.\n\nIn this situation, he has three choices, namely, the leaves A, B and C. Note that he cannot jump to the leaf D since he cannot jump backward. Suppose that he choose the leaf B. After jumping there, the situation will change as shown in the following figure.\n\nHe can jump to either leaf E or F next.\n\nAfter some struggles, he found this puzzle difficult, since there are a lot of leaves on the pond. Can you help him to find out a solution?", "constraint": "", "input": "H W\nc_1,1 . . . c_1, W\n. \n. \n. \nc_H, 1 . . . c_H, W\n\nThe first line of the input contains two positive integers H and W (1 <= H, W <= 10). The following H lines, which contain W characters each, describe the initial configuration of the leaves and the frog using following characters:\n\n'. ' : water\n\n ‘o ' : a leaf\n\n ‘U ' : a frog facing upward (i. e. to the upper side) on a leaf\n\n ‘D ' : a frog facing downward (i. e. to the lower side) on a leaf\n\n ‘L ' : a frog facing leftward (i. e. to the left side) on a leaf\n\n ‘R ' : a frog facing rightward (i. e. to the right side) on a leaf\nYou can assume that there is only one frog in each input. You can also assume that the total number of leaves (including the leaf the frog is initially on) is at most 30.", "output": "Output a line consists of the characters ‘U ' (up), ‘D ' (down), ‘L ' (left) and ‘R ' (right) that describes a series of movements. The output should not contain any other characters, such as spaces. You can assume that there exists only one solution for each input.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 3\nUo.\n.oo\n output: RDR", "input: 10 10\n.o....o...\no.oo......\n..oo..oo..\n..o.......\n..oo..oo..\n..o...o.o.\no..U.o....\noo......oo\noo........\noo..oo....\n output: URRULULDDLUURDLLLURRDLDDDRRDR", "input: 10 1\nD\n.\n.\n.\n.\n.\n.\n.\n.\no\n output: D"], "Pid": "p01340", "ProblemText": "Task Description: There is a frog living in a big pond. He loves jumping between lotus leaves floating on the pond. Interestingly, these leaves have strange habits. First, a leaf will sink into the water after the frog jumps from it. Second, they are aligned regularly as if they are placed on the grid points as in the example below. \nFigure 1: Example of floating leaves\n\nRecently, He came up with a puzzle game using these habits. At the beginning of the game, he is on some leaf and faces to the upper, lower, left or right side. He can jump forward or to the left or right relative to his facing direction, but not backward or diagonally. For example, suppose he is facing to the left side, then he can jump to the left, upper and lower sides but not to the right side. In each jump, he will land on the nearest leaf on his jumping direction and face to that direction regardless of his previous state. The leaf he was on will vanish into the water after the jump. The goal of this puzzle is to jump from leaf to leaf until there is only one leaf remaining. \n\nSee the example shown in the figure below.\n\nIn this situation, he has three choices, namely, the leaves A, B and C. Note that he cannot jump to the leaf D since he cannot jump backward. Suppose that he choose the leaf B. After jumping there, the situation will change as shown in the following figure.\n\nHe can jump to either leaf E or F next.\n\nAfter some struggles, he found this puzzle difficult, since there are a lot of leaves on the pond. Can you help him to find out a solution?\nTask Input: H W\nc_1,1 . . . c_1, W\n. \n. \n. \nc_H, 1 . . . c_H, W\n\nThe first line of the input contains two positive integers H and W (1 <= H, W <= 10). The following H lines, which contain W characters each, describe the initial configuration of the leaves and the frog using following characters:\n\n'. ' : water\n\n ‘o ' : a leaf\n\n ‘U ' : a frog facing upward (i. e. to the upper side) on a leaf\n\n ‘D ' : a frog facing downward (i. e. to the lower side) on a leaf\n\n ‘L ' : a frog facing leftward (i. e. to the left side) on a leaf\n\n ‘R ' : a frog facing rightward (i. e. to the right side) on a leaf\nYou can assume that there is only one frog in each input. You can also assume that the total number of leaves (including the leaf the frog is initially on) is at most 30.\nTask Output: Output a line consists of the characters ‘U ' (up), ‘D ' (down), ‘L ' (left) and ‘R ' (right) that describes a series of movements. The output should not contain any other characters, such as spaces. You can assume that there exists only one solution for each input.\nTask Samples: input: 2 3\nUo.\n.oo\n output: RDR\ninput: 10 10\n.o....o...\no.oo......\n..oo..oo..\n..o.......\n..oo..oo..\n..o...o.o.\no..U.o....\noo......oo\noo........\noo..oo....\n output: URRULULDDLUURDLLLURRDLDDDRRDR\ninput: 10 1\nD\n.\n.\n.\n.\n.\n.\n.\n.\no\n output: D\n\n" }, { "title": "Problem C: Save your cats", "content": "Nicholas Y. Alford was a cat lover. He had a garden in a village and kept many cats in his garden. The cats were so cute that people in the village also loved them.\n\nOne day, an evil witch visited the village. She envied the cats for being loved by everyone. She drove magical piles in his garden and enclosed the cats with magical fences running between the piles. She said “Your cats are shut away in the fences until they become ugly old cats. ” like a curse and went away.\n\nNicholas tried to break the fences with a hummer, but the fences are impregnable against his effort. He went to a church and asked a priest help. The priest looked for how to destroy the magical fences in books and found they could be destroyed by holy water. The Required amount of the holy water to destroy a fence was proportional to the length of the fence. The holy water was, however, fairly expensive. So he decided to buy exactly the minimum amount of the holy water required to save all his cats. How much holy water would be required?", "constraint": "", "input": "The input has the following format:\n\nN M\nx_1 y_1\n. \n. \n. \nx_N y_N\np_1 q_1\n. \n. \n. \np_M q_M\n\nThe first line of the input contains two integers N (2 <= N <= 10000) and M (1 <= M). N indicates the number of magical piles and M indicates the number of magical fences. The following N lines describe the coordinates of the piles. Each line contains two integers x_i and y_i (-10000 <= x_i, y_i <= 10000). The following M lines describe the both ends of the fences. Each line contains two integers p_j and q_j (1 <= p_j, q_j <= N). It indicates a fence runs between the p_j-th pile and the q_j-th pile.\n\nYou can assume the following:\n\n No Piles have the same coordinates.\n\n A pile doesn 't lie on the middle of fence.\n\n No Fences cross each other.\n\n There is at least one cat in each enclosed area.\n\n It is impossible to destroy a fence partially.\n\n A unit of holy water is required to destroy a unit length of magical fence.", "output": "Output a line containing the minimum amount of the holy water required to save all his cats. Your program may output an arbitrary number of digits after the decimal point. However, the absolute error should be 0.001 or less.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n0 0\n3 0\n0 4\n1 2\n2 3\n3 1\n output: 3.000", "input: 4 3\n0 0\n-100 0\n100 0\n0 100\n1 2\n1 3\n1 4\n output: 0.000", "input: 6 7\n2 0\n6 0\n8 2\n6 3\n0 5\n1 7\n1 2\n2 3\n3 4\n4 1\n5 1\n5 4\n5 6\n output: 7.236", "input: 6 6\n0 0\n0 1\n1 0\n30 0\n0 40\n30 40\n1 2\n2 3\n3 1\n4 5\n5 6\n6 4\n output: 31.000"], "Pid": "p01341", "ProblemText": "Task Description: Nicholas Y. Alford was a cat lover. He had a garden in a village and kept many cats in his garden. The cats were so cute that people in the village also loved them.\n\nOne day, an evil witch visited the village. She envied the cats for being loved by everyone. She drove magical piles in his garden and enclosed the cats with magical fences running between the piles. She said “Your cats are shut away in the fences until they become ugly old cats. ” like a curse and went away.\n\nNicholas tried to break the fences with a hummer, but the fences are impregnable against his effort. He went to a church and asked a priest help. The priest looked for how to destroy the magical fences in books and found they could be destroyed by holy water. The Required amount of the holy water to destroy a fence was proportional to the length of the fence. The holy water was, however, fairly expensive. So he decided to buy exactly the minimum amount of the holy water required to save all his cats. How much holy water would be required?\nTask Input: The input has the following format:\n\nN M\nx_1 y_1\n. \n. \n. \nx_N y_N\np_1 q_1\n. \n. \n. \np_M q_M\n\nThe first line of the input contains two integers N (2 <= N <= 10000) and M (1 <= M). N indicates the number of magical piles and M indicates the number of magical fences. The following N lines describe the coordinates of the piles. Each line contains two integers x_i and y_i (-10000 <= x_i, y_i <= 10000). The following M lines describe the both ends of the fences. Each line contains two integers p_j and q_j (1 <= p_j, q_j <= N). It indicates a fence runs between the p_j-th pile and the q_j-th pile.\n\nYou can assume the following:\n\n No Piles have the same coordinates.\n\n A pile doesn 't lie on the middle of fence.\n\n No Fences cross each other.\n\n There is at least one cat in each enclosed area.\n\n It is impossible to destroy a fence partially.\n\n A unit of holy water is required to destroy a unit length of magical fence.\nTask Output: Output a line containing the minimum amount of the holy water required to save all his cats. Your program may output an arbitrary number of digits after the decimal point. However, the absolute error should be 0.001 or less.\nTask Samples: input: 3 3\n0 0\n3 0\n0 4\n1 2\n2 3\n3 1\n output: 3.000\ninput: 4 3\n0 0\n-100 0\n100 0\n0 100\n1 2\n1 3\n1 4\n output: 0.000\ninput: 6 7\n2 0\n6 0\n8 2\n6 3\n0 5\n1 7\n1 2\n2 3\n3 4\n4 1\n5 1\n5 4\n5 6\n output: 7.236\ninput: 6 6\n0 0\n0 1\n1 0\n30 0\n0 40\n30 40\n1 2\n2 3\n3 1\n4 5\n5 6\n6 4\n output: 31.000\n\n" }, { "title": "Problem D: Dungeon Wall", "content": "In 2337, people are bored at daily life and have crazy desire of having extraordinary experience. These days, “Dungeon Adventure” is one of the hottest attractions, where brave adventurers risk their lives to kill the evil monsters and save the world. \n\nYou are a manager of one of such dungeons. Recently you have been receiving a lot of complaints from soldiers who frequently enter your dungeon; they say your dungeon is too easy and they do not want to enter again. You are considering making your dungeon more difficult by increasing the distance between the entrance and the exit of your dungeon so that more monsters can approach the adventurers.\n\nThe shape of your dungeon is a rectangle whose width is W and whose height is H. The dungeon is a grid which consists of W * H square rooms of identical size 1 * 1. The southwest corner of the dungeon\nhas the coordinate (0; 0), and the northeast corner has (W, H). The outside of the dungeon is surrounded by walls, and there may be some more walls inside the dungeon in order to prevent adventurers from going directly to the exit. Each wall in the dungeon is parallel to either x-axis or y-axis, and both ends of each wall are at integer coordinates. An adventurer can move from one room to another room if they are adjacent vertically or horizontally and have no wall between.\n\nYou would like to add some walls to make the shortest path between the entrance and the exit longer. However, severe financial situation only allows you to build at most only one wall of a unit length. Note that a new wall must also follow the constraints stated above. Furthermore, you need to guarantee that there is at least one path from the entrance to the exit. \n\nYou are wondering where you should put a new wall to maximize the minimum number of steps between the entrance and the exit. Can you figure it out?", "constraint": "", "input": "W H N\nsx_0 sy_0 dx_0 dy_0\nsx_1 sy_1 dx_1 dy_1\n. \n. \n. \nix iy\nox oy\n-->\n\nThe first line contains three integers: W, H and N (1 <= W, H <= 50,0 <= N <= 1000). They are separated with a space.\n\nThe next N lines contain the specifications of N walls inside the dungeon. Each wall specification is a line containing four integers. The i-th specification contains sx_i, sy_i, dx_i and dy_i, separated with a space. These integers give the position of the i-th wall: it spans from (sx_i, sy_i) to (dx_i, dy_i).\n\nThe last two lines contain information about the locations of the entrance and the exit. The first line contains two integers ix and iy, and the second line contains two integers ox and oy. The entrance is located at the room whose south-west corner is (ix, iy), and the exit is located at the room whose southwest corner is (ox, oy).", "output": "Print the maximum possible increase in the minimum number of required steps between the entrance and the exit just by adding one wall. If there is no good place to build a new wall, print zero.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 4\n1 0 1 1\n1 3 1 4\n1 2 2 2\n2 1 2 3\n0 0\n1 0\n output: 6", "input: 50 2 0\n0 0\n49 0\n output: 2", "input: 50 2 0\n0 0\n49 1\n output: 0"], "Pid": "p01342", "ProblemText": "Task Description: In 2337, people are bored at daily life and have crazy desire of having extraordinary experience. These days, “Dungeon Adventure” is one of the hottest attractions, where brave adventurers risk their lives to kill the evil monsters and save the world. \n\nYou are a manager of one of such dungeons. Recently you have been receiving a lot of complaints from soldiers who frequently enter your dungeon; they say your dungeon is too easy and they do not want to enter again. You are considering making your dungeon more difficult by increasing the distance between the entrance and the exit of your dungeon so that more monsters can approach the adventurers.\n\nThe shape of your dungeon is a rectangle whose width is W and whose height is H. The dungeon is a grid which consists of W * H square rooms of identical size 1 * 1. The southwest corner of the dungeon\nhas the coordinate (0; 0), and the northeast corner has (W, H). The outside of the dungeon is surrounded by walls, and there may be some more walls inside the dungeon in order to prevent adventurers from going directly to the exit. Each wall in the dungeon is parallel to either x-axis or y-axis, and both ends of each wall are at integer coordinates. An adventurer can move from one room to another room if they are adjacent vertically or horizontally and have no wall between.\n\nYou would like to add some walls to make the shortest path between the entrance and the exit longer. However, severe financial situation only allows you to build at most only one wall of a unit length. Note that a new wall must also follow the constraints stated above. Furthermore, you need to guarantee that there is at least one path from the entrance to the exit. \n\nYou are wondering where you should put a new wall to maximize the minimum number of steps between the entrance and the exit. Can you figure it out?\nTask Input: W H N\nsx_0 sy_0 dx_0 dy_0\nsx_1 sy_1 dx_1 dy_1\n. \n. \n. \nix iy\nox oy\n-->\n\nThe first line contains three integers: W, H and N (1 <= W, H <= 50,0 <= N <= 1000). They are separated with a space.\n\nThe next N lines contain the specifications of N walls inside the dungeon. Each wall specification is a line containing four integers. The i-th specification contains sx_i, sy_i, dx_i and dy_i, separated with a space. These integers give the position of the i-th wall: it spans from (sx_i, sy_i) to (dx_i, dy_i).\n\nThe last two lines contain information about the locations of the entrance and the exit. The first line contains two integers ix and iy, and the second line contains two integers ox and oy. The entrance is located at the room whose south-west corner is (ix, iy), and the exit is located at the room whose southwest corner is (ox, oy).\nTask Output: Print the maximum possible increase in the minimum number of required steps between the entrance and the exit just by adding one wall. If there is no good place to build a new wall, print zero.\nTask Samples: input: 3 4 4\n1 0 1 1\n1 3 1 4\n1 2 2 2\n2 1 2 3\n0 0\n1 0\n output: 6\ninput: 50 2 0\n0 0\n49 0\n output: 2\ninput: 50 2 0\n0 0\n49 1\n output: 0\n\n" }, { "title": "Problem E: Psychic Accelerator", "content": "In the west of Tokyo, there is a city named “Academy City. ” There are many schools and laboratories to develop psychics in Academy City.\n\nYou are a psychic student of a school in Academy City. Your psychic ability is to give acceleration to a certain object.\n\nYou can use your psychic ability anytime and anywhere, but there are constraints. If the object remains stationary, you can give acceleration to the object in any direction. If the object is moving, you can give acceleration to the object only in 1) the direction the object is moving to, 2) the direction opposite to it, or 3) the direction perpendicular to it.\n\nToday 's training menu is to move the object along a given course. For simplicity you can regard the course as consisting of line segments and circular arcs in a 2-dimensional space. The course has no branching. All segments and arcs are connected smoothly, i. e. there are no sharp corners.\n\nIn the beginning, the object is placed at the starting point of the first line segment. You have to move the object to the ending point of the last line segment along the course and stop the object at that point by controlling its acceleration properly. Before the training, a coach ordered you to simulate the minimum time to move the object from the starting point to the ending point.\n\nYour task is to write a program which reads the shape of the course and the maximum acceleration a_max you can give to the object and calculates the minimum time to move the object from the starting point to the ending point.\n\nThe object follows basic physical laws. When the object is moving straight in some direction, with acceleration either forward or backward, the following equations hold:\nv = v_0 + at\nand\ns = v_0t + (1/2)at^2\nwhere v, s, v_0, a, and t are the velocity, the distance from the starting point, the initial velocity (i. e. the velocity at the starting point), the acceleration, and the time the object has been moving in that direction, respectively. Note that they can be simplified as follows:\nv^2 - v_0^2 = 2as\nWhen the object is moving along an arc, with acceleration to the centroid, the following equations hold:\na = v^2/r\nwher v, a, and r are the velocity, the acceleration, and the radius of the arc, respectively. Note that the object cannot change the velocity due to the criteria on your psychic ability.", "constraint": "", "input": "The input has the following format:\n\nN a_max\nx_a, 1 y_a, 1 x_b, 1 y_b, 1\nx_a, 2 y_a, 2 x_b, 2 y_b, 2\n. \n. \n. \n\nN is the number of line segments; a_max is the maximum acceleration you can give to the object; (x_a, i, y_a, i) and (x_b, i, y_b, i) are the starting point and the ending point of the i-th line segment, respectively. The given course may have crosses but you cannot change the direction there. \n\nThe input meets the following constraints: 0 < N <= 40000,1 <= a_max <= 100, and -100 <= x_ai, y_ai, x_bi, y_bi <= 100.", "output": "Print the minimum time to move the object from the starting point to the ending point with an relative or absolute error of at most 10^-6. You may output any number of digits after the decimal point.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n0 0 1 0\n1 1 0 1\n output: 5.2793638507", "input: 1 1\n0 0 2 0\n output: 2.8284271082", "input: 3 2\n0 0 2 0\n1 -1 1 2\n0 1 2 1\n output: 11.1364603512"], "Pid": "p01343", "ProblemText": "Task Description: In the west of Tokyo, there is a city named “Academy City. ” There are many schools and laboratories to develop psychics in Academy City.\n\nYou are a psychic student of a school in Academy City. Your psychic ability is to give acceleration to a certain object.\n\nYou can use your psychic ability anytime and anywhere, but there are constraints. If the object remains stationary, you can give acceleration to the object in any direction. If the object is moving, you can give acceleration to the object only in 1) the direction the object is moving to, 2) the direction opposite to it, or 3) the direction perpendicular to it.\n\nToday 's training menu is to move the object along a given course. For simplicity you can regard the course as consisting of line segments and circular arcs in a 2-dimensional space. The course has no branching. All segments and arcs are connected smoothly, i. e. there are no sharp corners.\n\nIn the beginning, the object is placed at the starting point of the first line segment. You have to move the object to the ending point of the last line segment along the course and stop the object at that point by controlling its acceleration properly. Before the training, a coach ordered you to simulate the minimum time to move the object from the starting point to the ending point.\n\nYour task is to write a program which reads the shape of the course and the maximum acceleration a_max you can give to the object and calculates the minimum time to move the object from the starting point to the ending point.\n\nThe object follows basic physical laws. When the object is moving straight in some direction, with acceleration either forward or backward, the following equations hold:\nv = v_0 + at\nand\ns = v_0t + (1/2)at^2\nwhere v, s, v_0, a, and t are the velocity, the distance from the starting point, the initial velocity (i. e. the velocity at the starting point), the acceleration, and the time the object has been moving in that direction, respectively. Note that they can be simplified as follows:\nv^2 - v_0^2 = 2as\nWhen the object is moving along an arc, with acceleration to the centroid, the following equations hold:\na = v^2/r\nwher v, a, and r are the velocity, the acceleration, and the radius of the arc, respectively. Note that the object cannot change the velocity due to the criteria on your psychic ability.\nTask Input: The input has the following format:\n\nN a_max\nx_a, 1 y_a, 1 x_b, 1 y_b, 1\nx_a, 2 y_a, 2 x_b, 2 y_b, 2\n. \n. \n. \n\nN is the number of line segments; a_max is the maximum acceleration you can give to the object; (x_a, i, y_a, i) and (x_b, i, y_b, i) are the starting point and the ending point of the i-th line segment, respectively. The given course may have crosses but you cannot change the direction there. \n\nThe input meets the following constraints: 0 < N <= 40000,1 <= a_max <= 100, and -100 <= x_ai, y_ai, x_bi, y_bi <= 100.\nTask Output: Print the minimum time to move the object from the starting point to the ending point with an relative or absolute error of at most 10^-6. You may output any number of digits after the decimal point.\nTask Samples: input: 2 1\n0 0 1 0\n1 1 0 1\n output: 5.2793638507\ninput: 1 1\n0 0 2 0\n output: 2.8284271082\ninput: 3 2\n0 0 2 0\n1 -1 1 2\n0 1 2 1\n output: 11.1364603512\n\n" }, { "title": "Problem F: Bouldering", "content": "Bouldering is a style of rock climbing. Boulderers are to climb up the rock with bare hands without supporting ropes. Your friend supposed that it should be interesting and exciting, so he decided to come to bouldering gymnasium to practice bouldering. Since your friend has not tried bouldering yet, he chose beginner 's course. However, in the beginner 's course, he found that some of two stones have too distant space between them, which might result his accidentally failure of grabbing certain stone and falling off to the ground and die! He gradually becomes anxious and wonders whether the course is actually for the beginners. So, he asked you to write the program which simulates the way he climbs up and checks whether he can climb up to the goal successfully.\n\nFor the sake of convenience, we assume that a boulderer consists of 5 line segments, representing his body, his right arm, his left arm, his right leg, and his left leg.\n\nOne of his end of the body is connected to his arms on their end points. And the other end of the body is connected to his legs on their end points, too. The maximum length of his body, his arms, and his legs are A, B and C respectively. He climbs up the wall by changing the length of his body parts from 0 to their maximum length, and by twisting them in any angle (in other word, 360 degrees). Refer the following figure representing the possible body arrangements.\nFigure 2: An example of possible body arrangements.\n\n5 line segments representing his body, arms and legs. The length of his body, arms and legs are 8,3 and 4 respectively. The picture describes his head as a filled circle for better understanding, which has no meaning in this problem.\n\nA boulderer climbs up the wall by grabbing at least three different rocks on the wall with his hands and feet. In the initial state, he holds 4 rocks with his hands and feet. Then he changes one of the holding rocks by moving his arms and/or legs. This is counted as one movement. His goal is to grab a rock named “destination rock” with one of his body parts. The rocks are considered as points with negligible size. You are to write a program which calculates the minimum number of movements required to grab the destination rock.", "constraint": "", "input": "The input data looks like the following lines:\n\nn\nA B C\nx_1 y_1\nx_2 y_2\nx_3 y_3\n. \n. \n. \nx_n y_n\n\nThe first line contains n (5 <= n <= 30), which represents the number of rocks.\n\nThe second line contains three integers A, B, C (1 <= A, B, C <= 50), which represent the length of body, arms, and legs of the climber respectively.\n\nThe last n lines describes the location of the rocks. The i-th contains two integers x_i and y_i (0 <= x_i, y_i <= 100), representing the x and y-coordinates of the i-th rock.\n\nIn the initial state, the boulderer is grabbing the 1st rock with his right hand, 2nd with his left hand, 3rd with his right foot, and 4th with left foot.\n\nYou may assume that the first 4 rocks are close to each other so that he can grab them all in the way described above.\n\nThe last rock is the destination rock.", "output": "Your program should output the minimum number of movements to reach the destination stone.\n\nIf it is impossible to grab the destination stone, output -1.\n\nYou may assume that, if A, B, C would be changed within 0.001, the answer would not change.\n\nFollowing figures represent just an example of how the boulderer climbs up to the destination in minimum number of movements. Note that the minimum number of movements can be obtained, by taking different way of climbing up, shortening the parts, rotating parts etc.\nFigure 3: An example of minimum movement for sample input 1.\n\nFigure 4: An example of minimum movement for sample input 2.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6\n4 3 3\n10 17\n15 14\n10 15\n11 12\n16 18\n15 22\n output: 3", "input: 7\n4 2 4\n11 18\n14 18\n10 14\n13 14\n14 17\n17 21\n16 26\n output: 3", "input: 6\n2 2 4\n12 22\n13 21\n14 15\n10 16\n16 24\n10 35\n output: -1", "input: 6\n2 3 3\n11 22\n12 20\n10 15\n11 17\n13 23\n16 22\n output: -1"], "Pid": "p01344", "ProblemText": "Task Description: Bouldering is a style of rock climbing. Boulderers are to climb up the rock with bare hands without supporting ropes. Your friend supposed that it should be interesting and exciting, so he decided to come to bouldering gymnasium to practice bouldering. Since your friend has not tried bouldering yet, he chose beginner 's course. However, in the beginner 's course, he found that some of two stones have too distant space between them, which might result his accidentally failure of grabbing certain stone and falling off to the ground and die! He gradually becomes anxious and wonders whether the course is actually for the beginners. So, he asked you to write the program which simulates the way he climbs up and checks whether he can climb up to the goal successfully.\n\nFor the sake of convenience, we assume that a boulderer consists of 5 line segments, representing his body, his right arm, his left arm, his right leg, and his left leg.\n\nOne of his end of the body is connected to his arms on their end points. And the other end of the body is connected to his legs on their end points, too. The maximum length of his body, his arms, and his legs are A, B and C respectively. He climbs up the wall by changing the length of his body parts from 0 to their maximum length, and by twisting them in any angle (in other word, 360 degrees). Refer the following figure representing the possible body arrangements.\nFigure 2: An example of possible body arrangements.\n\n5 line segments representing his body, arms and legs. The length of his body, arms and legs are 8,3 and 4 respectively. The picture describes his head as a filled circle for better understanding, which has no meaning in this problem.\n\nA boulderer climbs up the wall by grabbing at least three different rocks on the wall with his hands and feet. In the initial state, he holds 4 rocks with his hands and feet. Then he changes one of the holding rocks by moving his arms and/or legs. This is counted as one movement. His goal is to grab a rock named “destination rock” with one of his body parts. The rocks are considered as points with negligible size. You are to write a program which calculates the minimum number of movements required to grab the destination rock.\nTask Input: The input data looks like the following lines:\n\nn\nA B C\nx_1 y_1\nx_2 y_2\nx_3 y_3\n. \n. \n. \nx_n y_n\n\nThe first line contains n (5 <= n <= 30), which represents the number of rocks.\n\nThe second line contains three integers A, B, C (1 <= A, B, C <= 50), which represent the length of body, arms, and legs of the climber respectively.\n\nThe last n lines describes the location of the rocks. The i-th contains two integers x_i and y_i (0 <= x_i, y_i <= 100), representing the x and y-coordinates of the i-th rock.\n\nIn the initial state, the boulderer is grabbing the 1st rock with his right hand, 2nd with his left hand, 3rd with his right foot, and 4th with left foot.\n\nYou may assume that the first 4 rocks are close to each other so that he can grab them all in the way described above.\n\nThe last rock is the destination rock.\nTask Output: Your program should output the minimum number of movements to reach the destination stone.\n\nIf it is impossible to grab the destination stone, output -1.\n\nYou may assume that, if A, B, C would be changed within 0.001, the answer would not change.\n\nFollowing figures represent just an example of how the boulderer climbs up to the destination in minimum number of movements. Note that the minimum number of movements can be obtained, by taking different way of climbing up, shortening the parts, rotating parts etc.\nFigure 3: An example of minimum movement for sample input 1.\n\nFigure 4: An example of minimum movement for sample input 2.\nTask Samples: input: 6\n4 3 3\n10 17\n15 14\n10 15\n11 12\n16 18\n15 22\n output: 3\ninput: 7\n4 2 4\n11 18\n14 18\n10 14\n13 14\n14 17\n17 21\n16 26\n output: 3\ninput: 6\n2 2 4\n12 22\n13 21\n14 15\n10 16\n16 24\n10 35\n output: -1\ninput: 6\n2 3 3\n11 22\n12 20\n10 15\n11 17\n13 23\n16 22\n output: -1\n\n" }, { "title": "Problem G: DON'T PANIC!", "content": "Arthur is an innocent man who used to live on the Earth. He had lived a really commonplace life, until the day when the Earth was destroyed by aliens, who were not evil invaders but just contractors ordered to build a hyperspace bypass. In the moment when the demolition beams were shot at the Earth by them, Arthur was in front of his house and almost about to be decomposed into hydrogen, oxygen, carbon and some other atoms. However, fortunately, he survived; one of his friend Ford, who was actually an alien and had come to the Earth in the course of his trip around the universe, took him up to a spaceship just before the beam reached him.\n\nArthur and Ford successfully escaped, but it was only the beginning of their hardships. Soon it turned out that actually the spaceship was the contractor 's one itself, and as it can be easily imagined, they disliked humans. Therefore as soon as they found Arthur and Ford, they stopped at the nearest unexplored planet and dropped the two pity men out of the spaceship from 10 miles up above the land surface.\n\nAgain they 're in a pinch! Fortunately our hero Ford has a special item that let them safely land to the planet, known as a parachute, so they don 't worry about that. The problem is that they are just falling freely and can 't change the landing point, which may be on ground or sea. They want to know if they can land peacefully or need some swimming to the nearest coast.\n\nFord 's universal GPS gadget displays their expected position of landing by latitude/longitude. Also he has a guidebook that describes almost all the planets in the universe. According to it, the planet has the only one continent and hence only one sea. It has a description of the shape of the continent but, unfortunately, not in a intuitive way of graphical maps. So your task is to make a program to decide whether the point is on the land or not.", "constraint": "", "input": "N\nP_0 T_0\n. \n. \n. \nP_N T_N\n\nThe first line of the input contains an integer N (3 <= N <= 1000). The second line contains two integers P_0, T_0 which represents the latitude and the longitude of the point where Arthur and Ford are going to land. The following N lines describe the shape of the only continent on the planet. The k-th line contains two integers P_k and T_k, which represents the latitude and the longitude of a point V_k. The continent is described as a polygon with N vertices V_k on a sphere. The coastline of it is formed by cyclically connecting consecutive points with the shortest line.\n\n(P_k, T_k) (k = 0,1, . . . . , N) satisfies -90 <= P_k <= 90, -180 <= T_k <= 180. Positive latitude means north and negative means south. Positive longitude means east and negative means west. The border of the continent is given by counterclockwise order and you can assume there is always exactly one way to connect given two consecutive points by minimum distance, and the shape of the continent is not selfcrossing. The landing point will be never on the coastline.", "output": "If Arthur and Ford are going to land on the continent, print “Yes”. Otherwise “No”.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n10 10\n10 -10\n-10 -10\n-10 10\n output: Yes", "input: 4\n89 0\n0 0\n0 90\n0 180\n0 -90\n output: Yes", "input: 4\n89 0\n0 0\n0 -90\n0 180\n0 90\n output: No"], "Pid": "p01345", "ProblemText": "Task Description: Arthur is an innocent man who used to live on the Earth. He had lived a really commonplace life, until the day when the Earth was destroyed by aliens, who were not evil invaders but just contractors ordered to build a hyperspace bypass. In the moment when the demolition beams were shot at the Earth by them, Arthur was in front of his house and almost about to be decomposed into hydrogen, oxygen, carbon and some other atoms. However, fortunately, he survived; one of his friend Ford, who was actually an alien and had come to the Earth in the course of his trip around the universe, took him up to a spaceship just before the beam reached him.\n\nArthur and Ford successfully escaped, but it was only the beginning of their hardships. Soon it turned out that actually the spaceship was the contractor 's one itself, and as it can be easily imagined, they disliked humans. Therefore as soon as they found Arthur and Ford, they stopped at the nearest unexplored planet and dropped the two pity men out of the spaceship from 10 miles up above the land surface.\n\nAgain they 're in a pinch! Fortunately our hero Ford has a special item that let them safely land to the planet, known as a parachute, so they don 't worry about that. The problem is that they are just falling freely and can 't change the landing point, which may be on ground or sea. They want to know if they can land peacefully or need some swimming to the nearest coast.\n\nFord 's universal GPS gadget displays their expected position of landing by latitude/longitude. Also he has a guidebook that describes almost all the planets in the universe. According to it, the planet has the only one continent and hence only one sea. It has a description of the shape of the continent but, unfortunately, not in a intuitive way of graphical maps. So your task is to make a program to decide whether the point is on the land or not.\nTask Input: N\nP_0 T_0\n. \n. \n. \nP_N T_N\n\nThe first line of the input contains an integer N (3 <= N <= 1000). The second line contains two integers P_0, T_0 which represents the latitude and the longitude of the point where Arthur and Ford are going to land. The following N lines describe the shape of the only continent on the planet. The k-th line contains two integers P_k and T_k, which represents the latitude and the longitude of a point V_k. The continent is described as a polygon with N vertices V_k on a sphere. The coastline of it is formed by cyclically connecting consecutive points with the shortest line.\n\n(P_k, T_k) (k = 0,1, . . . . , N) satisfies -90 <= P_k <= 90, -180 <= T_k <= 180. Positive latitude means north and negative means south. Positive longitude means east and negative means west. The border of the continent is given by counterclockwise order and you can assume there is always exactly one way to connect given two consecutive points by minimum distance, and the shape of the continent is not selfcrossing. The landing point will be never on the coastline.\nTask Output: If Arthur and Ford are going to land on the continent, print “Yes”. Otherwise “No”.\nTask Samples: input: 4\n0 0\n10 10\n10 -10\n-10 -10\n-10 10\n output: Yes\ninput: 4\n89 0\n0 0\n0 90\n0 180\n0 -90\n output: Yes\ninput: 4\n89 0\n0 0\n0 -90\n0 180\n0 90\n output: No\n\n" }, { "title": "Problem H: Ropeway", "content": "On a small island, there are two towns Darkside and Sunnyside, with steep mountains between them. There 's a company Intertown Company of Package Conveyance; they own a ropeway car between Darkside and Sunnyside and are running a transportation business. They want maximize the revenue by loading as much package as possible on the ropeway car.\n\nThe ropeway car looks like the following. It 's L length long, and the center of it is hung from the rope. Let 's suppose the car to be a 1-dimensional line segment, and a package to be a point lying on the line. You can put packages at anywhere including the edge of the car, as long as the distance between the package and the center of the car is greater than or equal to R and the car doesn 't fall down.\n\nThe car will fall down when the following condition holds:\n\nHere N is the number of packages; m_i the weight of the i-th package; x_i is the position of the i-th package relative to the center of the car.\n\nYou, a Darkside programmer, are hired as an engineer of the company. Your task is to write a program which reads a list of package and checks if all the packages can be loaded in the listed order without the car falling down at any point.", "constraint": "", "input": "The input has two lines, describing one test case. The first line contains four integers N, L, M, R. The second line contains N integers m_0, m_1, . . . m_N-1. The integers are separated by a space.", "output": "If there is a way to load all the packages, output “Yes” in one line, without the quotes. Otherwise, output “No”.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3 2 1\n1 1 4\n output: Yes", "input: 3 3 2 1\n1 4 1\n output: No"], "Pid": "p01346", "ProblemText": "Task Description: On a small island, there are two towns Darkside and Sunnyside, with steep mountains between them. There 's a company Intertown Company of Package Conveyance; they own a ropeway car between Darkside and Sunnyside and are running a transportation business. They want maximize the revenue by loading as much package as possible on the ropeway car.\n\nThe ropeway car looks like the following. It 's L length long, and the center of it is hung from the rope. Let 's suppose the car to be a 1-dimensional line segment, and a package to be a point lying on the line. You can put packages at anywhere including the edge of the car, as long as the distance between the package and the center of the car is greater than or equal to R and the car doesn 't fall down.\n\nThe car will fall down when the following condition holds:\n\nHere N is the number of packages; m_i the weight of the i-th package; x_i is the position of the i-th package relative to the center of the car.\n\nYou, a Darkside programmer, are hired as an engineer of the company. Your task is to write a program which reads a list of package and checks if all the packages can be loaded in the listed order without the car falling down at any point.\nTask Input: The input has two lines, describing one test case. The first line contains four integers N, L, M, R. The second line contains N integers m_0, m_1, . . . m_N-1. The integers are separated by a space.\nTask Output: If there is a way to load all the packages, output “Yes” in one line, without the quotes. Otherwise, output “No”.\nTask Samples: input: 3 3 2 1\n1 1 4\n output: Yes\ninput: 3 3 2 1\n1 4 1\n output: No\n\n" }, { "title": "Problem I: How to Create a Good Game", "content": "A video game company called ICPC (International Company for Playing and Competing) is now developing a new arcade game. The new game features a lot of branches. This makes the game enjoyable for everyone, since players can choose their routes in the game depending on their skills. Rookie players can choose an easy route to enjoy the game, and talented players can choose their favorite routes to get high scores.\n\nIn the game, there are many checkpoints connected by paths. Each path consists of several stages, and completing stages on a path leads players to the next checkpoint. The game ends when players reach a particular checkpoint. At some checkpoints, players can choose which way to go, so routes diverge at that time. Sometimes different routes join together at a checkpoint. The paths between checkpoints are directed, and there is no loop (otherwise, players can play the game forever). In other words, the structure of the game can be viewed as a DAG (directed acyclic graph), when considering paths between checkpoints as directed edges.\n\nRecently, the development team completed the beta version of the game and received feedbacks from other teams. They were quite positive overall, but there are some comments that should be taken into consideration. Some testers pointed out that some routes were very short compared to the longest ones. Indeed, in the beta version, the number of stages in one play can vary drastically depending on the routes. Game designers complained many brilliant ideas of theirs were unused in the beta version because of the tight development schedule. They wanted to have more stages included in the final product. \n\nHowever, it 's not easy to add more stages. this is an arcade game – if the playing time was too long, it would bring down the income of the game and owners of arcades would complain. So, the longest route of the final product can 't be longer than that of the beta version. Moreover, the producer of the game didn 't want to change the structure of paths (i. e. , how the checkpoints connect to each other), since it would require rewriting the scenario, recording voices, creating new cutscenes, etc.\n\nConsidering all together, the producer decided to add as many new stages as possible, while keeping the maximum possible number of stages in one play and the structure of paths unchanged. How many new stages can be added to the game?", "constraint": "", "input": "N M\nx_1 y_1 s_1\n. \n. \n. \nx_M y_M s_M\n\nThe first line of the input contains two positive integers N and M (2 <= N <= 100,1 <= M <= 1000). N indicates the number of checkpoints, including the opening and ending of the game. M indicates the number of paths between checkpoints.\n\nThe following M lines describe the structure of paths in the beta version of the game. The i-th line contains three integers x_i , y_i and s_i (0 <= x_i < y_i <= N - 1,1 <= s_i <= 1000), which describe that there is a path from checkpoint x_i to y_i consists of si stages. As for indices of the checkpoints, note that 0 indicates the opening of the game and N - 1 indicates the ending of the game. You can assume that, for every checkpoint i, there exists a route from the opening to the ending which passes through checkpoint i. You can also assume that no two paths connect the same pair of checkpoints.", "output": "Output a line containing the maximum number of new stages that can be added to the game under the following constraints:\n\n You can 't increase the maximum possible number of stages in one play (i. e. , the length of the longest route to the ending).\n\n You can 't change the structure of paths (i. e. , how the checkpoints connect to each other).\n\n You can 't delete any stage that already exists in the beta version.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n0 1 5\n1 2 3\n0 2 2\n output: 6", "input: 2 1\n0 1 10\n output: 0", "input: 4 6\n0 1 5\n0 2 5\n0 3 5\n1 2 5\n1 3 5\n2 3 5\n output: 20"], "Pid": "p01347", "ProblemText": "Task Description: A video game company called ICPC (International Company for Playing and Competing) is now developing a new arcade game. The new game features a lot of branches. This makes the game enjoyable for everyone, since players can choose their routes in the game depending on their skills. Rookie players can choose an easy route to enjoy the game, and talented players can choose their favorite routes to get high scores.\n\nIn the game, there are many checkpoints connected by paths. Each path consists of several stages, and completing stages on a path leads players to the next checkpoint. The game ends when players reach a particular checkpoint. At some checkpoints, players can choose which way to go, so routes diverge at that time. Sometimes different routes join together at a checkpoint. The paths between checkpoints are directed, and there is no loop (otherwise, players can play the game forever). In other words, the structure of the game can be viewed as a DAG (directed acyclic graph), when considering paths between checkpoints as directed edges.\n\nRecently, the development team completed the beta version of the game and received feedbacks from other teams. They were quite positive overall, but there are some comments that should be taken into consideration. Some testers pointed out that some routes were very short compared to the longest ones. Indeed, in the beta version, the number of stages in one play can vary drastically depending on the routes. Game designers complained many brilliant ideas of theirs were unused in the beta version because of the tight development schedule. They wanted to have more stages included in the final product. \n\nHowever, it 's not easy to add more stages. this is an arcade game – if the playing time was too long, it would bring down the income of the game and owners of arcades would complain. So, the longest route of the final product can 't be longer than that of the beta version. Moreover, the producer of the game didn 't want to change the structure of paths (i. e. , how the checkpoints connect to each other), since it would require rewriting the scenario, recording voices, creating new cutscenes, etc.\n\nConsidering all together, the producer decided to add as many new stages as possible, while keeping the maximum possible number of stages in one play and the structure of paths unchanged. How many new stages can be added to the game?\nTask Input: N M\nx_1 y_1 s_1\n. \n. \n. \nx_M y_M s_M\n\nThe first line of the input contains two positive integers N and M (2 <= N <= 100,1 <= M <= 1000). N indicates the number of checkpoints, including the opening and ending of the game. M indicates the number of paths between checkpoints.\n\nThe following M lines describe the structure of paths in the beta version of the game. The i-th line contains three integers x_i , y_i and s_i (0 <= x_i < y_i <= N - 1,1 <= s_i <= 1000), which describe that there is a path from checkpoint x_i to y_i consists of si stages. As for indices of the checkpoints, note that 0 indicates the opening of the game and N - 1 indicates the ending of the game. You can assume that, for every checkpoint i, there exists a route from the opening to the ending which passes through checkpoint i. You can also assume that no two paths connect the same pair of checkpoints.\nTask Output: Output a line containing the maximum number of new stages that can be added to the game under the following constraints:\n\n You can 't increase the maximum possible number of stages in one play (i. e. , the length of the longest route to the ending).\n\n You can 't change the structure of paths (i. e. , how the checkpoints connect to each other).\n\n You can 't delete any stage that already exists in the beta version.\nTask Samples: input: 3 3\n0 1 5\n1 2 3\n0 2 2\n output: 6\ninput: 2 1\n0 1 10\n output: 0\ninput: 4 6\n0 1 5\n0 2 5\n0 3 5\n1 2 5\n1 3 5\n2 3 5\n output: 20\n\n" }, { "title": "Problem J: Cruel Bingo", "content": "Bingo is a party game played by many players and one game master. Each player is given a bingo card containing N^2 different numbers in a N * N grid (typically N = 5). The master draws numbers from a lottery one by one during the game. Each time a number is drawn, a player marks a square with that number if it exists. The player 's goal is to have N marked squares in a single vertical, horizontal, or diagonal line and then call “Bingo! ” The first player calling “Bingo! ” wins the game.\n\nIn ultimately unfortunate cases, a card can have exactly N unmarked squares, or N(N-1) marked squares, but not a bingo pattern. Your task in this problem is to write a program counting how many such patterns are possible from a given initial pattern, which contains zero or more marked squares.", "constraint": "", "input": "The input is given in the following format:\n\nN K\nx_1 y_1\n. \n. \n. \nx_K y_K\n\nThe input begins with a line containing two numbers N (1 <= N <= 32) and K (0 <= K <= 8), which represent the size of the bingo card and the number of marked squares in the initial pattern respectively.\nThen K lines follow, each containing two numbers x_i and y_i to indicate the square at (x_i, y_i) is marked. The coordinate values are zero-based (i. e. 0 <= x_i, y_i <= N - 1). No pair of marked squares coincides.", "output": "Count the number of possible non-bingo patterns with exactly N unmarked squares that can be made from the given initial pattern, and print the number in modulo 10007 in a line (since it is supposed to be huge). Rotated and mirrored patterns should be regarded as different and counted each.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n0 2\n3 1\n output: 6", "input: 4 2\n2 3\n3 2\n output: 6", "input: 10 3\n0 0\n4 4\n1 4\n output: 1127"], "Pid": "p01348", "ProblemText": "Task Description: Bingo is a party game played by many players and one game master. Each player is given a bingo card containing N^2 different numbers in a N * N grid (typically N = 5). The master draws numbers from a lottery one by one during the game. Each time a number is drawn, a player marks a square with that number if it exists. The player 's goal is to have N marked squares in a single vertical, horizontal, or diagonal line and then call “Bingo! ” The first player calling “Bingo! ” wins the game.\n\nIn ultimately unfortunate cases, a card can have exactly N unmarked squares, or N(N-1) marked squares, but not a bingo pattern. Your task in this problem is to write a program counting how many such patterns are possible from a given initial pattern, which contains zero or more marked squares.\nTask Input: The input is given in the following format:\n\nN K\nx_1 y_1\n. \n. \n. \nx_K y_K\n\nThe input begins with a line containing two numbers N (1 <= N <= 32) and K (0 <= K <= 8), which represent the size of the bingo card and the number of marked squares in the initial pattern respectively.\nThen K lines follow, each containing two numbers x_i and y_i to indicate the square at (x_i, y_i) is marked. The coordinate values are zero-based (i. e. 0 <= x_i, y_i <= N - 1). No pair of marked squares coincides.\nTask Output: Count the number of possible non-bingo patterns with exactly N unmarked squares that can be made from the given initial pattern, and print the number in modulo 10007 in a line (since it is supposed to be huge). Rotated and mirrored patterns should be regarded as different and counted each.\nTask Samples: input: 4 2\n0 2\n3 1\n output: 6\ninput: 4 2\n2 3\n3 2\n output: 6\ninput: 10 3\n0 0\n4 4\n1 4\n output: 1127\n\n" }, { "title": "Problem A: Era Name", "content": "As many of you know, we have two major calendar systems used in Japan today. One of them\nis Gregorian calendar which is widely used across the world. It is also known as “Western\ncalendar” in Japan.\n\nThe other calendar system is era-based calendar, or so-called “Japanese calendar. ” This system\ncomes from ancient Chinese systems. Recently in Japan it has been a common way to associate\ndates with the Emperors. In the era-based system, we represent a year with an era name given\nat the time a new Emperor assumes the throne. If the era name is “A”, the first regnal year\nwill be “A 1”, the second year will be “A 2”, and so forth.\n\nSince we have two different calendar systems, it is often needed to convert the date in one\ncalendar system to the other. In this problem, you are asked to write a program that converts\nwestern year to era-based year, given a database that contains association between several\nwestern years and era-based years.\n\nFor the simplicity, you can assume the following:\n\n A new era always begins on January 1st of the corresponding Gregorian year.\n\n The first year of an era is described as 1.\n\n There is no year in which more than one era switch takes place.\nPlease note that, however, the database you will see may be incomplete. In other words, some\nera that existed in the history may be missing from your data. So you will also have to detect\nthe cases where you cannot determine exactly which era the given year belongs to.", "constraint": "", "input": "The input contains multiple test cases. Each test case has the following format:\n\nN Q\nEra Name_1 Era Based Year_1 Western Year_1\n . \n . \n . \nEra Name_N Era Based Year_N Western Year_N\nQuery_1\n. \n. \n. \nQuery_Q\n\nThe first line of the input contains two positive integers N and Q (1 <= N <= 1000,1 <= Q <= 1000).\nN is the number of database entries, and Q is the number of queries.\n\nEach of the following N lines has three components: era name, era-based year number and the\ncorresponding western year (1 <= Era Based Year_i <= Western Year_i <= 10^9 ). Each of era names\nconsist of at most 16 Roman alphabet characters. Then the last Q lines of the input specifies\nqueries (1 <= Query_i <= 10^9 ), each of which is a western year to compute era-based representation.\n\nThe end of input is indicated by a line containing two zeros. This line is not part of any dataset\nand hence should not be processed.\n\nYou can assume that all the western year in the input is positive integers, and that there is no\ntwo entries that share the same era name.", "output": "For each query, output in a line the era name and the era-based year number corresponding to\nthe western year given, separated with a single whitespace. In case you cannot determine the\nera, output “Unknown” without quotes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\nmeiji 10 1877\ntaisho 6 1917\nshowa 62 1987\nheisei 22 2010\n1868\n1917\n1988\n1 1\nuniversalcentury 123 2168\n2010\n0 0\n output: meiji 1\ntaisho 6\nUnknown\nUnknown"], "Pid": "p01359", "ProblemText": "Task Description: As many of you know, we have two major calendar systems used in Japan today. One of them\nis Gregorian calendar which is widely used across the world. It is also known as “Western\ncalendar” in Japan.\n\nThe other calendar system is era-based calendar, or so-called “Japanese calendar. ” This system\ncomes from ancient Chinese systems. Recently in Japan it has been a common way to associate\ndates with the Emperors. In the era-based system, we represent a year with an era name given\nat the time a new Emperor assumes the throne. If the era name is “A”, the first regnal year\nwill be “A 1”, the second year will be “A 2”, and so forth.\n\nSince we have two different calendar systems, it is often needed to convert the date in one\ncalendar system to the other. In this problem, you are asked to write a program that converts\nwestern year to era-based year, given a database that contains association between several\nwestern years and era-based years.\n\nFor the simplicity, you can assume the following:\n\n A new era always begins on January 1st of the corresponding Gregorian year.\n\n The first year of an era is described as 1.\n\n There is no year in which more than one era switch takes place.\nPlease note that, however, the database you will see may be incomplete. In other words, some\nera that existed in the history may be missing from your data. So you will also have to detect\nthe cases where you cannot determine exactly which era the given year belongs to.\nTask Input: The input contains multiple test cases. Each test case has the following format:\n\nN Q\nEra Name_1 Era Based Year_1 Western Year_1\n . \n . \n . \nEra Name_N Era Based Year_N Western Year_N\nQuery_1\n. \n. \n. \nQuery_Q\n\nThe first line of the input contains two positive integers N and Q (1 <= N <= 1000,1 <= Q <= 1000).\nN is the number of database entries, and Q is the number of queries.\n\nEach of the following N lines has three components: era name, era-based year number and the\ncorresponding western year (1 <= Era Based Year_i <= Western Year_i <= 10^9 ). Each of era names\nconsist of at most 16 Roman alphabet characters. Then the last Q lines of the input specifies\nqueries (1 <= Query_i <= 10^9 ), each of which is a western year to compute era-based representation.\n\nThe end of input is indicated by a line containing two zeros. This line is not part of any dataset\nand hence should not be processed.\n\nYou can assume that all the western year in the input is positive integers, and that there is no\ntwo entries that share the same era name.\nTask Output: For each query, output in a line the era name and the era-based year number corresponding to\nthe western year given, separated with a single whitespace. In case you cannot determine the\nera, output “Unknown” without quotes.\nTask Samples: input: 4 3\nmeiji 10 1877\ntaisho 6 1917\nshowa 62 1987\nheisei 22 2010\n1868\n1917\n1988\n1 1\nuniversalcentury 123 2168\n2010\n0 0\n output: meiji 1\ntaisho 6\nUnknown\nUnknown\n\n" }, { "title": "Problem B: Step Step Evolution", "content": "Japanese video game company has developed the music video game called Step Step Evolution.\nThe gameplay of Step Step Evolution is very simple. Players stand on the dance platform, and\nstep on panels on it according to a sequence of arrows shown in the front screen.\n\nThere are eight types of direction arrows in the Step Step Evolution: UP, UPPER RIGHT,\nRIGHT, LOWER RIGHT, DOWN, LOWER LEFT, LEFT, and UPPER LEFT. These direction\narrows will scroll upward from the bottom of the screen. When the direction arrow overlaps the\nstationary arrow nearby the top, then the player must step on the corresponding arrow panel\non the dance platform. The figure below shows how the dance platform looks like.\n Figure 1: the dance platform for Step Step Evolution\nIn the game, you have to obey the following rule:\n\n Except for the beginning of the play, you must not press the arrow panel which is not\n correspond to the edit data.\n\n The foot must stay upon the panel where it presses last time, and will not be moved until\n it 's going to press the next arrow panel.\n\nThe left foot must not step on the panel which locates at right to the panel on which the\nright foot rests. Conversely, the right foot must not step on the panel which locates at left\nto the panel on which the left foot rests.\nAs for the third condition, the following figure shows the examples of the valid and invalid\nfootsteps.\nFigure 2: the examples of valid and invalid footsteps\nThe first one (left foot for LEFT, right foot for DOWN) and the second one (left foot for LOWER\nLEFT, right foot for UPPER LEFT) are valid footstep. The last one (left foot for RIGHT, right\nfoot for DOWN) is invalid footstep.\n\nNote that, at the beginning of the play, the left foot and right foot can be placed anywhere at\nthe arrow panel. Also, you can start first step with left foot or right foot, whichever you want.\n\nTo play this game in a beautiful way, the play style called “ Natural footstep style” is commonly\nknown among talented players. “Natural footstep style” is the style in which players make steps\nby the left foot and the right foot in turn. However, when a sequence of arrows is difficult,\nplayers are sometimes forced to violate this style.\n\nNow, your friend has created an edit data (the original sequence of direction arrows to be pushed)\nfor you. You are interested in how many times you have to violate “Natural footstep style” when\nyou optimally played with this edit data. In other words, what is the minimum number of times\nyou have to step on two consecutive arrows using the same foot?", "constraint": "", "input": "The input consists of several detasets. Each dataset is specified by one line containing a sequence\nof direction arrows. Directions are described by numbers from 1 to 9, except for 5. The figure\nbelow shows the correspondence between numbers and directions.\n\nYou may assume that the length of the sequence is between 1 and 100000, inclusive. Also, arrows\nof the same direction won 't appear consecutively in the line. The end of the input is indicated\nby a single “#”.\n\nFigure 3: the correspondence of the numbers to the direction arrows", "output": "For each dataset, output how many times you have to violate “Natural footstep style” when you\nplay optimally in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n12\n123\n369\n6748\n4247219123\n1232123212321232\n#\n output: 0\n0\n1\n0\n1\n2\n7"], "Pid": "p01360", "ProblemText": "Task Description: Japanese video game company has developed the music video game called Step Step Evolution.\nThe gameplay of Step Step Evolution is very simple. Players stand on the dance platform, and\nstep on panels on it according to a sequence of arrows shown in the front screen.\n\nThere are eight types of direction arrows in the Step Step Evolution: UP, UPPER RIGHT,\nRIGHT, LOWER RIGHT, DOWN, LOWER LEFT, LEFT, and UPPER LEFT. These direction\narrows will scroll upward from the bottom of the screen. When the direction arrow overlaps the\nstationary arrow nearby the top, then the player must step on the corresponding arrow panel\non the dance platform. The figure below shows how the dance platform looks like.\n Figure 1: the dance platform for Step Step Evolution\nIn the game, you have to obey the following rule:\n\n Except for the beginning of the play, you must not press the arrow panel which is not\n correspond to the edit data.\n\n The foot must stay upon the panel where it presses last time, and will not be moved until\n it 's going to press the next arrow panel.\n\nThe left foot must not step on the panel which locates at right to the panel on which the\nright foot rests. Conversely, the right foot must not step on the panel which locates at left\nto the panel on which the left foot rests.\nAs for the third condition, the following figure shows the examples of the valid and invalid\nfootsteps.\nFigure 2: the examples of valid and invalid footsteps\nThe first one (left foot for LEFT, right foot for DOWN) and the second one (left foot for LOWER\nLEFT, right foot for UPPER LEFT) are valid footstep. The last one (left foot for RIGHT, right\nfoot for DOWN) is invalid footstep.\n\nNote that, at the beginning of the play, the left foot and right foot can be placed anywhere at\nthe arrow panel. Also, you can start first step with left foot or right foot, whichever you want.\n\nTo play this game in a beautiful way, the play style called “ Natural footstep style” is commonly\nknown among talented players. “Natural footstep style” is the style in which players make steps\nby the left foot and the right foot in turn. However, when a sequence of arrows is difficult,\nplayers are sometimes forced to violate this style.\n\nNow, your friend has created an edit data (the original sequence of direction arrows to be pushed)\nfor you. You are interested in how many times you have to violate “Natural footstep style” when\nyou optimally played with this edit data. In other words, what is the minimum number of times\nyou have to step on two consecutive arrows using the same foot?\nTask Input: The input consists of several detasets. Each dataset is specified by one line containing a sequence\nof direction arrows. Directions are described by numbers from 1 to 9, except for 5. The figure\nbelow shows the correspondence between numbers and directions.\n\nYou may assume that the length of the sequence is between 1 and 100000, inclusive. Also, arrows\nof the same direction won 't appear consecutively in the line. The end of the input is indicated\nby a single “#”.\n\nFigure 3: the correspondence of the numbers to the direction arrows\nTask Output: For each dataset, output how many times you have to violate “Natural footstep style” when you\nplay optimally in one line.\nTask Samples: input: 1\n12\n123\n369\n6748\n4247219123\n1232123212321232\n#\n output: 0\n0\n1\n0\n1\n2\n7\n\n" }, { "title": "Problem C: Dungeon Quest II", "content": "The cave, called \"Mass of Darkness\", had been a agitating point of the evil, but the devil king\nand all of his soldiers were destroyed by the hero and the peace is there now.\n\nOne day, however, the hero was worrying about the rebirth of the devil king, so he decided to\nask security agency to patrol inside the cave.\n\nThe information of the cave is as follows:\n\n The cave is represented as a two-dimensional field which consists of rectangular grid of\n cells.\n\n The cave has R * C cells where R is the number of rows and C is the number of columns.\n\n Some of the cells in the cave contains a trap, and those who enter the trapping cell will\n lose his hit points.\n\n The type of traps varies widely: some of them reduce hit points seriously, and others give\n less damage.\nThe following is how the security agent patrols:\n\n The agent will start his patrol from upper left corner of the cave. \n - There are no traps at the upper left corner of the cave.\n\n The agent will patrol by tracing the steps which are specified by the hero. \n - The steps will be provided such that the agent never go outside of the cave during\n his patrol.\n\n The agent will bring potions to regain his hit point during his patrol.\n\n The agent can use potions just before entering the cell where he is going to step in.\n\n The type of potions also varies widely: some of them recover hit points so much, and\n others are less effective. \n - Note that agent 's hit point can be recovered up to HP_max which means his maximum\n hit point and is specified by the input data.\n\n The agent can use more than one type of potion at once.\n\n If the agent's hit point becomes less than or equal to 0, he will die.\nYour task is to write a program to check whether the agent can finish his patrol without dying.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is given in the following format:\n\nHP_init HP_max\nR C\na_1,1 a_1,2 . . . a_1, C\na_2,1 a_2,2 . . . a_2, C\n . \n . \n . \na_R, 1 a_R, 2 . . . a_R, C\nT\n [A-Z] d_1\n [A-Z] d_2\n . \n . \n . \n [A-Z] d_T\nS\n [UDLR] n_1\n [UDLR] n_2\n . \n . \n . \n [UDLR] n_S\nP\np_1\np_2\n . \n . \n . \np_P\n\nThe first line of a dataset contains two integers HP_init and HP_max (0 < HP_init <= HP_max <= 1000),\nmeaning the agent's initial hit point and the agent 's maximum hit point respectively.\n\nThe next line consists of R and C (1 <= R, C <= 100). Then, R lines which made of C characters\nrepresenting the information of the cave follow. The character a_i, j means there are the trap of\ntype a_i, j in i-th row and j-th column, and the type of trap is denoted as an uppercase alphabetic\ncharacter [A-Z].\n\nThe next line contains an integer T, which means how many type of traps to be described.\nThe following T lines contains a uppercase character [A-Z] and an integer d_i (0 <= d_i <= 1000),\nrepresenting the type of trap and the amount of damage it gives.\n\nThe next line contains an integer S (0 <= S <= 1000) representing the number of sequences which\nthe hero specified as the agent's patrol route. Then, S lines follows containing a character and\nan integer n_i ( ∑^S_i=1 n_i <= 1000), meaning the direction where the agent advances and the number\nof step he takes toward that direction. The direction character will be one of 'U', 'D', 'L', 'R' for\nUp, Down, Left, Right respectively and indicates the direction of the step.\n\nFinally, the line which contains an integer P (0 <= P <= 12) meaning how many type of potions\nthe agent has follows. The following P lines consists of an integer p_i (0 < p_i <= 1000) which\nindicated the amount of hit point it recovers.\nThe input is terminated by a line with two zeros. This line should not be processed.", "output": "For each dataset, print in a line \"YES\" if the agent finish his patrol successfully, or \"NO\" otherwise.\n\nIf the agent's hit point becomes less than or equal to 0 at the end of his patrol, the output\nshould be \"NO\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 10\n3 3\nAAA\nABA\nCCC\n3\nA 0\nB 5\nC 9\n3\nD 2\nR 1\nU 2\n5\n10\n10\n10\n10\n10\n100 100\n10 10\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\n8\nT 0\nH 1\nI 2\nS 3\nA 4\nP 5\nE 6\nN 7\n9\nR 1\nD 3\nR 8\nD 2\nL 9\nD 2\nR 9\nD 2\nL 9\n2\n20\n10\n0 0\n output: YES\nNO"], "Pid": "p01361", "ProblemText": "Task Description: The cave, called \"Mass of Darkness\", had been a agitating point of the evil, but the devil king\nand all of his soldiers were destroyed by the hero and the peace is there now.\n\nOne day, however, the hero was worrying about the rebirth of the devil king, so he decided to\nask security agency to patrol inside the cave.\n\nThe information of the cave is as follows:\n\n The cave is represented as a two-dimensional field which consists of rectangular grid of\n cells.\n\n The cave has R * C cells where R is the number of rows and C is the number of columns.\n\n Some of the cells in the cave contains a trap, and those who enter the trapping cell will\n lose his hit points.\n\n The type of traps varies widely: some of them reduce hit points seriously, and others give\n less damage.\nThe following is how the security agent patrols:\n\n The agent will start his patrol from upper left corner of the cave. \n - There are no traps at the upper left corner of the cave.\n\n The agent will patrol by tracing the steps which are specified by the hero. \n - The steps will be provided such that the agent never go outside of the cave during\n his patrol.\n\n The agent will bring potions to regain his hit point during his patrol.\n\n The agent can use potions just before entering the cell where he is going to step in.\n\n The type of potions also varies widely: some of them recover hit points so much, and\n others are less effective. \n - Note that agent 's hit point can be recovered up to HP_max which means his maximum\n hit point and is specified by the input data.\n\n The agent can use more than one type of potion at once.\n\n If the agent's hit point becomes less than or equal to 0, he will die.\nYour task is to write a program to check whether the agent can finish his patrol without dying.\nTask Input: The input is a sequence of datasets. Each dataset is given in the following format:\n\nHP_init HP_max\nR C\na_1,1 a_1,2 . . . a_1, C\na_2,1 a_2,2 . . . a_2, C\n . \n . \n . \na_R, 1 a_R, 2 . . . a_R, C\nT\n [A-Z] d_1\n [A-Z] d_2\n . \n . \n . \n [A-Z] d_T\nS\n [UDLR] n_1\n [UDLR] n_2\n . \n . \n . \n [UDLR] n_S\nP\np_1\np_2\n . \n . \n . \np_P\n\nThe first line of a dataset contains two integers HP_init and HP_max (0 < HP_init <= HP_max <= 1000),\nmeaning the agent's initial hit point and the agent 's maximum hit point respectively.\n\nThe next line consists of R and C (1 <= R, C <= 100). Then, R lines which made of C characters\nrepresenting the information of the cave follow. The character a_i, j means there are the trap of\ntype a_i, j in i-th row and j-th column, and the type of trap is denoted as an uppercase alphabetic\ncharacter [A-Z].\n\nThe next line contains an integer T, which means how many type of traps to be described.\nThe following T lines contains a uppercase character [A-Z] and an integer d_i (0 <= d_i <= 1000),\nrepresenting the type of trap and the amount of damage it gives.\n\nThe next line contains an integer S (0 <= S <= 1000) representing the number of sequences which\nthe hero specified as the agent's patrol route. Then, S lines follows containing a character and\nan integer n_i ( ∑^S_i=1 n_i <= 1000), meaning the direction where the agent advances and the number\nof step he takes toward that direction. The direction character will be one of 'U', 'D', 'L', 'R' for\nUp, Down, Left, Right respectively and indicates the direction of the step.\n\nFinally, the line which contains an integer P (0 <= P <= 12) meaning how many type of potions\nthe agent has follows. The following P lines consists of an integer p_i (0 < p_i <= 1000) which\nindicated the amount of hit point it recovers.\nThe input is terminated by a line with two zeros. This line should not be processed.\nTask Output: For each dataset, print in a line \"YES\" if the agent finish his patrol successfully, or \"NO\" otherwise.\n\nIf the agent's hit point becomes less than or equal to 0 at the end of his patrol, the output\nshould be \"NO\".\nTask Samples: input: 1 10\n3 3\nAAA\nABA\nCCC\n3\nA 0\nB 5\nC 9\n3\nD 2\nR 1\nU 2\n5\n10\n10\n10\n10\n10\n100 100\n10 10\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\nTHISISAPEN\n8\nT 0\nH 1\nI 2\nS 3\nA 4\nP 5\nE 6\nN 7\n9\nR 1\nD 3\nR 8\nD 2\nL 9\nD 2\nR 9\nD 2\nL 9\n2\n20\n10\n0 0\n output: YES\nNO\n\n" }, { "title": "Problem D: Dice Room", "content": "You are playing a popular video game which is famous for its depthful story and interesting\npuzzles. In the game you were locked in a mysterious house alone and there is no way to call for\nhelp, so you have to escape on yours own. However, almost every room in the house has some\nkind of puzzles and you cannot move to neighboring room without solving them.\n\nOne of the puzzles you encountered in the house is following. In a room, there was a device\nwhich looked just like a dice and laid on a table in the center of the room. Direction was written\non the wall. It read:\n\n \"This cube is a remote controller and you can manipulate a remote room, Dice\n Room, by it. The room has also a cubic shape whose surfaces are made up of 3x3\n unit squares and some squares have a hole on them large enough for you to go though\n it. You can rotate this cube so that in the middle of rotation at least one edge always\n touch the table, that is, to 4 directions. Rotating this cube affects the remote room\n in the same way and positions of holes on the room change. To get through the\n room, you should have holes on at least one of lower three squares on the front and\n back side of the room. \"\n\nYou can see current positions of holes by a monitor. Before going to Dice Room, you should\nrotate the cube so that you can go though the room. But you know rotating a room takes some\ntime and you don 't have much time, so you should minimize the number of rotation. How many\nrotations do you need to make it possible to get though Dice Room?", "constraint": "", "input": "The input consists of several datasets. Each dataset contains 6 tables of 3x3 characters which\ndescribe the initial position of holes on each side. Each character is either '*' or '. '. A hole is\nindicated by '*'. The order which six sides appears in is: front, right, back, left, top, bottom.\nThe order and orientation of them are described by this development view:\n\nFigure 4: Dice Room\nFigure 5: available dice rotations\n\nThere is a blank line after each dataset. The end of the input is indicated by a single '#'.", "output": "Print the minimum number of rotations needed in a line for each dataset. You may assume all\ndatasets have a solution.", "content_img": true, "lang": "en", "error": false, "samples": ["input: ...\n...\n.*.\n...\n...\n.*.\n...\n...\n...\n...\n...\n.*.\n...\n...\n.*.\n...\n...\n...\n\n...\n.*.\n...\n*..\n...\n..*\n*.*\n*.*\n*.*\n*.*\n.*.\n*.*\n*..\n.*.\n..*\n*.*\n...\n*.*\n\n...\n.*.\n.*.\n...\n.**\n*..\n...\n...\n.*.\n.*.\n...\n*..\n..*\n...\n.**\n...\n*..\n...\n\n#\n output: 3\n1\n0"], "Pid": "p01362", "ProblemText": "Task Description: You are playing a popular video game which is famous for its depthful story and interesting\npuzzles. In the game you were locked in a mysterious house alone and there is no way to call for\nhelp, so you have to escape on yours own. However, almost every room in the house has some\nkind of puzzles and you cannot move to neighboring room without solving them.\n\nOne of the puzzles you encountered in the house is following. In a room, there was a device\nwhich looked just like a dice and laid on a table in the center of the room. Direction was written\non the wall. It read:\n\n \"This cube is a remote controller and you can manipulate a remote room, Dice\n Room, by it. The room has also a cubic shape whose surfaces are made up of 3x3\n unit squares and some squares have a hole on them large enough for you to go though\n it. You can rotate this cube so that in the middle of rotation at least one edge always\n touch the table, that is, to 4 directions. Rotating this cube affects the remote room\n in the same way and positions of holes on the room change. To get through the\n room, you should have holes on at least one of lower three squares on the front and\n back side of the room. \"\n\nYou can see current positions of holes by a monitor. Before going to Dice Room, you should\nrotate the cube so that you can go though the room. But you know rotating a room takes some\ntime and you don 't have much time, so you should minimize the number of rotation. How many\nrotations do you need to make it possible to get though Dice Room?\nTask Input: The input consists of several datasets. Each dataset contains 6 tables of 3x3 characters which\ndescribe the initial position of holes on each side. Each character is either '*' or '. '. A hole is\nindicated by '*'. The order which six sides appears in is: front, right, back, left, top, bottom.\nThe order and orientation of them are described by this development view:\n\nFigure 4: Dice Room\nFigure 5: available dice rotations\n\nThere is a blank line after each dataset. The end of the input is indicated by a single '#'.\nTask Output: Print the minimum number of rotations needed in a line for each dataset. You may assume all\ndatasets have a solution.\nTask Samples: input: ...\n...\n.*.\n...\n...\n.*.\n...\n...\n...\n...\n...\n.*.\n...\n...\n.*.\n...\n...\n...\n\n...\n.*.\n...\n*..\n...\n..*\n*.*\n*.*\n*.*\n*.*\n.*.\n*.*\n*..\n.*.\n..*\n*.*\n...\n*.*\n\n...\n.*.\n.*.\n...\n.**\n*..\n...\n...\n.*.\n.*.\n...\n*..\n..*\n...\n.**\n...\n*..\n...\n\n#\n output: 3\n1\n0\n\n" }, { "title": "Problem E: Alice and Bomb", "content": "Alice and Bob were in love with each other, but they hate each other now.\n\nOne day, Alice found a bag. It looks like a bag that Bob had used when they go on a date.\nSuddenly Alice heard tick-tack sound. Alice intuitively thought that Bob is to kill her with a\nbomb. Fortunately, the bomb has not exploded yet, and there may be a little time remained to\nhide behind the buildings.\n\nThe appearance of the ACM city can be viewed as an infinite plane and each building forms a\npolygon. Alice is considered as a point and the bomb blast may reach Alice if the line segment\nwhich connects Alice and the bomb does not intersect an interior position of any building.\nAssume that the speed of bomb blast is infinite; when the bomb explodes, its blast wave will\nreach anywhere immediately, unless the bomb blast is interrupted by some buildings.\n\nThe figure below shows the example of the bomb explosion. Left figure shows the bomb and the\nbuildings(the polygons filled with black). Right figure shows the area(colored with gray) which\nis under the effect of blast wave after the bomb explosion.\n\nFigure 6: The example of the bomb explosion\nNote that even if the line segment connecting Alice and the bomb touches a border of a building,\nbomb blast still can blow off Alice. Since Alice wants to escape early, she wants to minimize the\nlength she runs in order to make herself hidden by the building.\n\nYour task is to write a program which reads the positions of Alice, the bomb and the buildings\nand calculate the minimum distance required for Alice to run and hide behind the building.", "constraint": "", "input": "The input contains multiple test cases. Each test case has the following format:\n\nN\nbx by\nm_1 x_1,1 y_1,1 . . . x_1, m1 y_1, m1\n. \n. \n. \nm_N x_N, 1 y_N, 1 . . . x_N, mN y_N, mN\n\nThe first line of each test case contains an integer N (1 <= N <= 100), which denotes the number\nof buildings. In the second line, there are two integers bx and by (-10000 <= bx, by <= 10000),\nwhich means the location of the bomb. Then, N lines follows, indicating the information of the\nbuildings.\n\nThe information of building is given as a polygon which consists of points. For each line, it has\nan integer m_i (3 <= m_i <= 100, ∑^N_i=1 m_i <= 500) meaning the number of points the polygon has,\nand then m_i pairs of integers x_i, j, y_i, j follow providing the x and y coordinate of the point.\n\nYou can assume that\n\n the polygon does not have self-intersections. \n\n any two polygons do not have a common point.\n\n the set of points is given in the counter-clockwise order.\n\n the initial positions of Alice and bomb will not by located inside the polygon.\n\n there are no bomb on the any extended lines of the given polygon 's segment.\nAlice is initially located at (0,0). It is possible that Alice is located at the boundary of a\npolygon.\n\nN = 0 denotes the end of the input. You may not process this as a test case.", "output": "For each test case, output one line which consists of the minimum distance required for Alice to\nrun and hide behind the building. An absolute error or relative error in your answer must be\nless than 10^-6.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n1 1\n4 -1 0 -2 -1 -1 -2 0 -1\n1\n0 3\n4 1 1 1 2 -1 2 -1 1\n1\n-6 -6\n6 1 -2 2 -2 2 3 -2 3 -2 1 1 1\n1\n-10 0\n4 0 -5 1 -5 1 5 0 5\n1\n10 1\n4 5 1 6 2 5 3 4 2\n2\n-47 -37\n4 14 3 20 13 9 12 15 9\n4 -38 -3 -34 -19 -34 -14 -24 -10\n0\n output: 1.00000000\n0.00000000\n3.23606798\n5.00000000\n1.00000000\n11.78517297"], "Pid": "p01363", "ProblemText": "Task Description: Alice and Bob were in love with each other, but they hate each other now.\n\nOne day, Alice found a bag. It looks like a bag that Bob had used when they go on a date.\nSuddenly Alice heard tick-tack sound. Alice intuitively thought that Bob is to kill her with a\nbomb. Fortunately, the bomb has not exploded yet, and there may be a little time remained to\nhide behind the buildings.\n\nThe appearance of the ACM city can be viewed as an infinite plane and each building forms a\npolygon. Alice is considered as a point and the bomb blast may reach Alice if the line segment\nwhich connects Alice and the bomb does not intersect an interior position of any building.\nAssume that the speed of bomb blast is infinite; when the bomb explodes, its blast wave will\nreach anywhere immediately, unless the bomb blast is interrupted by some buildings.\n\nThe figure below shows the example of the bomb explosion. Left figure shows the bomb and the\nbuildings(the polygons filled with black). Right figure shows the area(colored with gray) which\nis under the effect of blast wave after the bomb explosion.\n\nFigure 6: The example of the bomb explosion\nNote that even if the line segment connecting Alice and the bomb touches a border of a building,\nbomb blast still can blow off Alice. Since Alice wants to escape early, she wants to minimize the\nlength she runs in order to make herself hidden by the building.\n\nYour task is to write a program which reads the positions of Alice, the bomb and the buildings\nand calculate the minimum distance required for Alice to run and hide behind the building.\nTask Input: The input contains multiple test cases. Each test case has the following format:\n\nN\nbx by\nm_1 x_1,1 y_1,1 . . . x_1, m1 y_1, m1\n. \n. \n. \nm_N x_N, 1 y_N, 1 . . . x_N, mN y_N, mN\n\nThe first line of each test case contains an integer N (1 <= N <= 100), which denotes the number\nof buildings. In the second line, there are two integers bx and by (-10000 <= bx, by <= 10000),\nwhich means the location of the bomb. Then, N lines follows, indicating the information of the\nbuildings.\n\nThe information of building is given as a polygon which consists of points. For each line, it has\nan integer m_i (3 <= m_i <= 100, ∑^N_i=1 m_i <= 500) meaning the number of points the polygon has,\nand then m_i pairs of integers x_i, j, y_i, j follow providing the x and y coordinate of the point.\n\nYou can assume that\n\n the polygon does not have self-intersections. \n\n any two polygons do not have a common point.\n\n the set of points is given in the counter-clockwise order.\n\n the initial positions of Alice and bomb will not by located inside the polygon.\n\n there are no bomb on the any extended lines of the given polygon 's segment.\nAlice is initially located at (0,0). It is possible that Alice is located at the boundary of a\npolygon.\n\nN = 0 denotes the end of the input. You may not process this as a test case.\nTask Output: For each test case, output one line which consists of the minimum distance required for Alice to\nrun and hide behind the building. An absolute error or relative error in your answer must be\nless than 10^-6.\nTask Samples: input: 1\n1 1\n4 -1 0 -2 -1 -1 -2 0 -1\n1\n0 3\n4 1 1 1 2 -1 2 -1 1\n1\n-6 -6\n6 1 -2 2 -2 2 3 -2 3 -2 1 1 1\n1\n-10 0\n4 0 -5 1 -5 1 5 0 5\n1\n10 1\n4 5 1 6 2 5 3 4 2\n2\n-47 -37\n4 14 3 20 13 9 12 15 9\n4 -38 -3 -34 -19 -34 -14 -24 -10\n0\n output: 1.00000000\n0.00000000\n3.23606798\n5.00000000\n1.00000000\n11.78517297\n\n" }, { "title": "Problem F: Two-Wheel Buggy", "content": "International Car Production Company (ICPC), one of the largest automobile manufacturers in\nthe world, is now developing a new vehicle called \"Two-Wheel Buggy\". As its name suggests,\nthe vehicle has only two wheels. Quite simply, \"Two-Wheel Buggy\" is made up of two wheels\n(the left wheel and the right wheel) and a axle (a bar connecting two wheels). The figure below\nshows its basic structure.\n\nFigure 7: The basic structure of the buggy\nBefore making a prototype of this new vehicle, the company decided to run a computer simula-\ntion. The details of the simulation is as follows.\n\nIn the simulation, the buggy will move on the x-y plane. Let D be the distance from the center\nof the axle to the wheels. At the beginning of the simulation, the center of the axle is at (0,0),\nthe left wheel is at (-D, 0), and the right wheel is at (D, 0). The radii of two wheels are 1.\n\nFigure 8: The initial position of the buggy\nThe movement of the buggy in the simulation is controlled by a sequence of instructions. Each\ninstruction consists of three numbers, Lspeed, Rspeed and time. Lspeed and Rspeed indicate\nthe rotation speed of the left and right wheels, respectively, expressed in degree par second. time\nindicates how many seconds these two wheels keep their rotation speed. If a speed of a wheel\nis positive, it will rotate in the direction that causes the buggy to move forward. Conversely,\nif a speed is negative, it will rotate in the opposite direction. For example, if we set Lspeed as\n-360, the left wheel will rotate 360-degree in one second in the direction that makes the buggy\nmove backward. We can set Lspeed and Rspeed differently, and this makes the buggy turn left\nor right. Note that we can also set one of them positive and the other negative (in this case, the\nbuggy will spin around).\n\nFigure 9: Examples\nYour job is to write a program that calculates the final position of the buggy given a instruction\nsequence. For simplicity, you can can assume that wheels have no width, and that they would\nnever slip.", "constraint": "", "input": "The input consists of several datasets. Each dataset is formatted as follows.\n\nN D\nLspeed_1 Rspeed_1 time_1\n. \n. \n. \nLspeed_i Rspeed_i time_i\n. \n. \n. \nLspeed_N Rspeed_N time_N\n\nThe first line of a dataset contains two positive integers, N and D (1 <= N <= 100,1 <= D <= 10).\nN indicates the number of instructions in the dataset, and D indicates the distance between\nthe center of axle and the wheels. The following N lines describe the instruction sequence. The\ni-th line contains three integers, Lspeed_i, i (-360 <= Lspeed_i, Rspeed_i <= 360,1 <= time_i ), describing the i-th instruction to the buggy. You can assume that the sum of timei\nis at most 500.\n\nThe end of input is indicated by a line containing two zeros. This line is not part of any dataset\nand hence should not be processed.", "output": "For each dataset, output two lines indicating the final position of the center of the axle. The\nfirst line should contain the x-coordinate, and the second line should contain the y-coordinate.\nThe absolute error should be less than or equal to 10^-3 . No extra character should appear in\nthe output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 1\n180 90 2\n1 1\n180 180 20\n2 10\n360 -360 5\n-90 360 8\n3 2\n100 60 9\n-72 -72 10\n-45 -225 5\n0 0\n output: 3.00000\n3.00000\n0.00000\n62.83185\n12.00000\n0.00000\n-2.44505\n13.12132"], "Pid": "p01364", "ProblemText": "Task Description: International Car Production Company (ICPC), one of the largest automobile manufacturers in\nthe world, is now developing a new vehicle called \"Two-Wheel Buggy\". As its name suggests,\nthe vehicle has only two wheels. Quite simply, \"Two-Wheel Buggy\" is made up of two wheels\n(the left wheel and the right wheel) and a axle (a bar connecting two wheels). The figure below\nshows its basic structure.\n\nFigure 7: The basic structure of the buggy\nBefore making a prototype of this new vehicle, the company decided to run a computer simula-\ntion. The details of the simulation is as follows.\n\nIn the simulation, the buggy will move on the x-y plane. Let D be the distance from the center\nof the axle to the wheels. At the beginning of the simulation, the center of the axle is at (0,0),\nthe left wheel is at (-D, 0), and the right wheel is at (D, 0). The radii of two wheels are 1.\n\nFigure 8: The initial position of the buggy\nThe movement of the buggy in the simulation is controlled by a sequence of instructions. Each\ninstruction consists of three numbers, Lspeed, Rspeed and time. Lspeed and Rspeed indicate\nthe rotation speed of the left and right wheels, respectively, expressed in degree par second. time\nindicates how many seconds these two wheels keep their rotation speed. If a speed of a wheel\nis positive, it will rotate in the direction that causes the buggy to move forward. Conversely,\nif a speed is negative, it will rotate in the opposite direction. For example, if we set Lspeed as\n-360, the left wheel will rotate 360-degree in one second in the direction that makes the buggy\nmove backward. We can set Lspeed and Rspeed differently, and this makes the buggy turn left\nor right. Note that we can also set one of them positive and the other negative (in this case, the\nbuggy will spin around).\n\nFigure 9: Examples\nYour job is to write a program that calculates the final position of the buggy given a instruction\nsequence. For simplicity, you can can assume that wheels have no width, and that they would\nnever slip.\nTask Input: The input consists of several datasets. Each dataset is formatted as follows.\n\nN D\nLspeed_1 Rspeed_1 time_1\n. \n. \n. \nLspeed_i Rspeed_i time_i\n. \n. \n. \nLspeed_N Rspeed_N time_N\n\nThe first line of a dataset contains two positive integers, N and D (1 <= N <= 100,1 <= D <= 10).\nN indicates the number of instructions in the dataset, and D indicates the distance between\nthe center of axle and the wheels. The following N lines describe the instruction sequence. The\ni-th line contains three integers, Lspeed_i, i (-360 <= Lspeed_i, Rspeed_i <= 360,1 <= time_i ), describing the i-th instruction to the buggy. You can assume that the sum of timei\nis at most 500.\n\nThe end of input is indicated by a line containing two zeros. This line is not part of any dataset\nand hence should not be processed.\nTask Output: For each dataset, output two lines indicating the final position of the center of the axle. The\nfirst line should contain the x-coordinate, and the second line should contain the y-coordinate.\nThe absolute error should be less than or equal to 10^-3 . No extra character should appear in\nthe output.\nTask Samples: input: 1 1\n180 90 2\n1 1\n180 180 20\n2 10\n360 -360 5\n-90 360 8\n3 2\n100 60 9\n-72 -72 10\n-45 -225 5\n0 0\n output: 3.00000\n3.00000\n0.00000\n62.83185\n12.00000\n0.00000\n-2.44505\n13.12132\n\n" }, { "title": "Problem G: Camera Control", "content": "\"ACM48\" is one of the most popular dance vocal units in Japan. In this winter, ACM48 is\nplanning a world concert tour. You joined the tour as a camera engineer.\n\nYour role is to develop software which controls the camera on a stage. For simplicity you can\nregard the stage as 2-dimensional space. You can rotate the camera to an arbitrary direction\nby the software but cannot change its coordinate.\n\nDuring a stage performance, each member of ACM48 moves along her route and sings the part(s)\nassigned to her. Here, a route is given as a polygonal line.\n\nYou have to keep focusing the camera on a member during a stage performance. You can change\nthe member focused by the camera if and only if the current and next members are in the same\ndirection from the camera.\n\nYour task is to write a program which reads the stage performance plan and calculates the\nmaximum time that you can focus the camera on members that are singing.\n\nYou may assume the following are satisfied:\n\n You can focus the camera on an arbitrary member at the beginning time.\n\n Each route of the member does not touch the camera.\n\n Each member stays at the last coordinates after she reaches there.", "constraint": "", "input": "The input contains multiple test cases. Each test case has the following format:\n\nN\nc_x c_y\n The information of the 1-st member\n . \n . \n . \n The information of the N-th member\n\nN (1 <= N <= 50) is the number of the members. (c_x, c_y) is the coordinates of the camera. Then\nthe information of the N members follow.\n\nThe information of the i-th member has the following format:\n\nM_i\nx_i, 1 y_i, 1 t_i, 1\n . \n . \n . \nx_i, Mi y_i, Mi t_i, Mi \nL_i\nb_i, 1 e_i, 1\n . \n . \n . \nb_i, Li e_i, Li \n\nM_i (1 <= M_i <= 100) is the number of the points in the route. (x_i, j, y_i, j ) is the coordinates of the\nj-th in the route. t_i, j (0 = t_i, 0 < t_i, j < t_i, j+1 <= 10^3 for 0 < j) is the time that the i-th member\nreaches the j-th coordinates. L_i (0 <= L_i <= 100) is the number of the vocal part. b_i, k and e_i, k (0 <= b_i, k < e_i, k < b_i, k+1 < e_i, k+1 <= 10^3 ) are the beginning and the ending time of the k-th vocal\npart, respectively.\n\nAll the input values are integers. You may assume that the absolute of all the coordinates are\nnot more than 10^3 .\n\nN = 0 denotes the end of the input. You may not process this as a test case.", "output": "For each dataset, print the maximum time that you can focus the camera on singing members\nwith an absolute error of at most 10^-6. You may output any number of digits after the decimal\npoint.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0\n2\n-5 5 0\n5 5 10\n1\n0 6\n2\n5 5 0\n-5 5 10\n1\n6 10\n1\n7 -65\n2\n-65 10 0\n65 1 3\n2\n0 1\n23 24\n2\n0 0\n2\n100 10 0\n-10 10 10\n5\n0 1\n2 3\n4 5\n6 7\n8 9\n2\n10 0 0\n0 10 10\n5\n1 2\n3 4\n5 6\n7 8\n9 10\n0\n output: 9.00000000\n2.00000000\n5.98862017"], "Pid": "p01365", "ProblemText": "Task Description: \"ACM48\" is one of the most popular dance vocal units in Japan. In this winter, ACM48 is\nplanning a world concert tour. You joined the tour as a camera engineer.\n\nYour role is to develop software which controls the camera on a stage. For simplicity you can\nregard the stage as 2-dimensional space. You can rotate the camera to an arbitrary direction\nby the software but cannot change its coordinate.\n\nDuring a stage performance, each member of ACM48 moves along her route and sings the part(s)\nassigned to her. Here, a route is given as a polygonal line.\n\nYou have to keep focusing the camera on a member during a stage performance. You can change\nthe member focused by the camera if and only if the current and next members are in the same\ndirection from the camera.\n\nYour task is to write a program which reads the stage performance plan and calculates the\nmaximum time that you can focus the camera on members that are singing.\n\nYou may assume the following are satisfied:\n\n You can focus the camera on an arbitrary member at the beginning time.\n\n Each route of the member does not touch the camera.\n\n Each member stays at the last coordinates after she reaches there.\nTask Input: The input contains multiple test cases. Each test case has the following format:\n\nN\nc_x c_y\n The information of the 1-st member\n . \n . \n . \n The information of the N-th member\n\nN (1 <= N <= 50) is the number of the members. (c_x, c_y) is the coordinates of the camera. Then\nthe information of the N members follow.\n\nThe information of the i-th member has the following format:\n\nM_i\nx_i, 1 y_i, 1 t_i, 1\n . \n . \n . \nx_i, Mi y_i, Mi t_i, Mi \nL_i\nb_i, 1 e_i, 1\n . \n . \n . \nb_i, Li e_i, Li \n\nM_i (1 <= M_i <= 100) is the number of the points in the route. (x_i, j, y_i, j ) is the coordinates of the\nj-th in the route. t_i, j (0 = t_i, 0 < t_i, j < t_i, j+1 <= 10^3 for 0 < j) is the time that the i-th member\nreaches the j-th coordinates. L_i (0 <= L_i <= 100) is the number of the vocal part. b_i, k and e_i, k (0 <= b_i, k < e_i, k < b_i, k+1 < e_i, k+1 <= 10^3 ) are the beginning and the ending time of the k-th vocal\npart, respectively.\n\nAll the input values are integers. You may assume that the absolute of all the coordinates are\nnot more than 10^3 .\n\nN = 0 denotes the end of the input. You may not process this as a test case.\nTask Output: For each dataset, print the maximum time that you can focus the camera on singing members\nwith an absolute error of at most 10^-6. You may output any number of digits after the decimal\npoint.\nTask Samples: input: 2\n0 0\n2\n-5 5 0\n5 5 10\n1\n0 6\n2\n5 5 0\n-5 5 10\n1\n6 10\n1\n7 -65\n2\n-65 10 0\n65 1 3\n2\n0 1\n23 24\n2\n0 0\n2\n100 10 0\n-10 10 10\n5\n0 1\n2 3\n4 5\n6 7\n8 9\n2\n10 0 0\n0 10 10\n5\n1 2\n3 4\n5 6\n7 8\n9 10\n0\n output: 9.00000000\n2.00000000\n5.98862017\n\n" }, { "title": "Problem H: Road Construction", "content": "King Mercer is the king of ACM kingdom. There are one capital and some cities in his kingdom.\nAmazingly, there are no roads in the kingdom now. Recently, he planned to construct roads\nbetween the capital and the cities, but it turned out that the construction cost of his plan is\nmuch higher than expected.\n\nIn order to reduce the cost, he has decided to create a new construction plan by removing some\nroads from the original plan. However, he believes that a new plan should satisfy the following\nconditions:\n\n For every pair of cities, there is a route (a set of roads) connecting them.\n\n The minimum distance between the capital and each city does not change from his original\n plan.\nMany plans may meet the conditions above, but King Mercer wants to know the plan with\nminimum cost. Your task is to write a program which reads his original plan and calculates the\ncost of a new plan with the minimum cost.", "constraint": "", "input": "The input consists of several datasets. Each dataset is formatted as follows.\n\nN M\nu_1 v_1 d_1 c_1 \n . \n . \n . \nu_M v_M d_M c_M \n\nThe first line of each dataset begins with two integers, N and M (1 <= N <= 10000,0 <= M <=\n20000). N and M indicate the number of cities and the number of roads in the original plan,\nrespectively.\n\nThe following M lines describe the road information in the original plan. The i-th line contains\nfour integers, u_i, v_i, d_i and c_i (1 <= u_i, v_i <= N , u_i ! = v_i , 1 <= d_i <= 1000,1 <= c_i <= 1000). u_i , v_i, d_i\nand c_i indicate that there is a road which connects u_i-th city and v_i-th city, whose length is d_i and whose cost needed for construction is c_i.\n\nEach road is bidirectional. No two roads connect the same pair of cities. The 1-st city is the\ncapital in the kingdom.\n\nThe end of the input is indicated by a line containing two zeros separated by a space. You\nshould not process the line as a dataset.", "output": "For each dataset, print the minimum cost of a plan which satisfies the conditions in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 1 2\n2 3 2 1\n3 1 3 2\n5 5\n1 2 2 2\n2 3 1 1\n1 4 1 1\n4 5 1 1\n5 3 1 1\n5 10\n1 2 32 10\n1 3 43 43\n1 4 12 52\n1 5 84 23\n2 3 58 42\n2 4 86 99\n2 5 57 83\n3 4 11 32\n3 5 75 21\n4 5 23 43\n5 10\n1 2 1 53\n1 3 1 65\n1 4 1 24\n1 5 1 76\n2 3 1 19\n2 4 1 46\n2 5 1 25\n3 4 1 13\n3 5 1 65\n4 5 1 34\n0 0\n output: 3\n5\n137\n218"], "Pid": "p01366", "ProblemText": "Task Description: King Mercer is the king of ACM kingdom. There are one capital and some cities in his kingdom.\nAmazingly, there are no roads in the kingdom now. Recently, he planned to construct roads\nbetween the capital and the cities, but it turned out that the construction cost of his plan is\nmuch higher than expected.\n\nIn order to reduce the cost, he has decided to create a new construction plan by removing some\nroads from the original plan. However, he believes that a new plan should satisfy the following\nconditions:\n\n For every pair of cities, there is a route (a set of roads) connecting them.\n\n The minimum distance between the capital and each city does not change from his original\n plan.\nMany plans may meet the conditions above, but King Mercer wants to know the plan with\nminimum cost. Your task is to write a program which reads his original plan and calculates the\ncost of a new plan with the minimum cost.\nTask Input: The input consists of several datasets. Each dataset is formatted as follows.\n\nN M\nu_1 v_1 d_1 c_1 \n . \n . \n . \nu_M v_M d_M c_M \n\nThe first line of each dataset begins with two integers, N and M (1 <= N <= 10000,0 <= M <=\n20000). N and M indicate the number of cities and the number of roads in the original plan,\nrespectively.\n\nThe following M lines describe the road information in the original plan. The i-th line contains\nfour integers, u_i, v_i, d_i and c_i (1 <= u_i, v_i <= N , u_i ! = v_i , 1 <= d_i <= 1000,1 <= c_i <= 1000). u_i , v_i, d_i\nand c_i indicate that there is a road which connects u_i-th city and v_i-th city, whose length is d_i and whose cost needed for construction is c_i.\n\nEach road is bidirectional. No two roads connect the same pair of cities. The 1-st city is the\ncapital in the kingdom.\n\nThe end of the input is indicated by a line containing two zeros separated by a space. You\nshould not process the line as a dataset.\nTask Output: For each dataset, print the minimum cost of a plan which satisfies the conditions in a line.\nTask Samples: input: 3 3\n1 2 1 2\n2 3 2 1\n3 1 3 2\n5 5\n1 2 2 2\n2 3 1 1\n1 4 1 1\n4 5 1 1\n5 3 1 1\n5 10\n1 2 32 10\n1 3 43 43\n1 4 12 52\n1 5 84 23\n2 3 58 42\n2 4 86 99\n2 5 57 83\n3 4 11 32\n3 5 75 21\n4 5 23 43\n5 10\n1 2 1 53\n1 3 1 65\n1 4 1 24\n1 5 1 76\n2 3 1 19\n2 4 1 46\n2 5 1 25\n3 4 1 13\n3 5 1 65\n4 5 1 34\n0 0\n output: 3\n5\n137\n218\n\n" }, { "title": "Problem I: Operator", "content": "The customer telephone support center of the computer sales company called JAG is now in-\ncredibly confused. There are too many customers who request the support, and they call the\nsupport center all the time. So, the company wants to figure out how many operators needed\nto handle this situation.\n\nFor simplicity, let us focus on the following simple simulation.\n\nLet N be a number of customers. The i-th customer has id i, and is described by three numbers,\nM_i, L_i and K_i. M_i is the time required for phone support, L_i is the maximum stand by time\nuntil an operator answers the call, and K_i is the interval time from hanging up to calling back.\nLet us put these in other words: It takes M_i unit times for an operator to support i-th customer.\nIf the i-th customer is not answered by operators for L_i unit times, he hangs up the call. K_i\nunit times after hanging up, he calls back.\n\nOne operator can support only one customer simultaneously. When an operator finish a call, he\ncan immediately answer another call. If there are more than one customer waiting, an operator\nwill choose the customer with the smallest id.\n\nAt the beginning of the simulation, all customers call the support center at the same time. The\nsimulation succeeds if operators can finish answering all customers within T unit times.\n\nYour mission is to calculate the minimum number of operators needed to end this simulation\nsuccessfully.", "constraint": "", "input": "The input contains multiple datasets. Each dataset has the following format:\n\nN T\nM_1 L_1 K_1\n . \n . \n . \nM_N L_N K_N\n\nThe first line of a dataset contains two positive integers, N and T (1 <= N <= 1000,1 <= T <= 1000).\nN indicates the number of customers in the dataset, and T indicates the time limit of the\nsimulation.\n\nThe following N lines describe the information of customers. The i-th line contains three integers,\nM_i, L_i and K_i (1 <= M_i <= T , 1 <= L_i <= 1000,1 <= K_i <= 1000), describing i-th customer's\ninformation. M_i indicates the time required for phone support, Li indicates the maximum stand\nby time until an operator answers the call, and Ki indicates the is the interval time from hanging\nup to calling back.\n\nThe end of input is indicated by a line containing two zeros. This line is not part of any dataset\nand hence should not be processed.", "output": "For each dataset, print the minimum number of operators needed to end the simulation successfully in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 300\n100 50 150\n100 50 150\n100 50 150\n3 300\n100 50 150\n100 50 150\n200 50 150\n9 18\n3 1 1\n3 1 1\n3 1 1\n4 100 1\n5 100 1\n5 100 1\n10 5 3\n10 5 3\n1 7 1000\n10 18\n1 2 3\n2 3 4\n3 4 5\n4 5 6\n5 6 7\n6 7 8\n7 8 9\n8 9 10\n9 10 11\n10 11 12\n0 0\n output: 2\n3\n3\n4"], "Pid": "p01367", "ProblemText": "Task Description: The customer telephone support center of the computer sales company called JAG is now in-\ncredibly confused. There are too many customers who request the support, and they call the\nsupport center all the time. So, the company wants to figure out how many operators needed\nto handle this situation.\n\nFor simplicity, let us focus on the following simple simulation.\n\nLet N be a number of customers. The i-th customer has id i, and is described by three numbers,\nM_i, L_i and K_i. M_i is the time required for phone support, L_i is the maximum stand by time\nuntil an operator answers the call, and K_i is the interval time from hanging up to calling back.\nLet us put these in other words: It takes M_i unit times for an operator to support i-th customer.\nIf the i-th customer is not answered by operators for L_i unit times, he hangs up the call. K_i\nunit times after hanging up, he calls back.\n\nOne operator can support only one customer simultaneously. When an operator finish a call, he\ncan immediately answer another call. If there are more than one customer waiting, an operator\nwill choose the customer with the smallest id.\n\nAt the beginning of the simulation, all customers call the support center at the same time. The\nsimulation succeeds if operators can finish answering all customers within T unit times.\n\nYour mission is to calculate the minimum number of operators needed to end this simulation\nsuccessfully.\nTask Input: The input contains multiple datasets. Each dataset has the following format:\n\nN T\nM_1 L_1 K_1\n . \n . \n . \nM_N L_N K_N\n\nThe first line of a dataset contains two positive integers, N and T (1 <= N <= 1000,1 <= T <= 1000).\nN indicates the number of customers in the dataset, and T indicates the time limit of the\nsimulation.\n\nThe following N lines describe the information of customers. The i-th line contains three integers,\nM_i, L_i and K_i (1 <= M_i <= T , 1 <= L_i <= 1000,1 <= K_i <= 1000), describing i-th customer's\ninformation. M_i indicates the time required for phone support, Li indicates the maximum stand\nby time until an operator answers the call, and Ki indicates the is the interval time from hanging\nup to calling back.\n\nThe end of input is indicated by a line containing two zeros. This line is not part of any dataset\nand hence should not be processed.\nTask Output: For each dataset, print the minimum number of operators needed to end the simulation successfully in a line.\nTask Samples: input: 3 300\n100 50 150\n100 50 150\n100 50 150\n3 300\n100 50 150\n100 50 150\n200 50 150\n9 18\n3 1 1\n3 1 1\n3 1 1\n4 100 1\n5 100 1\n5 100 1\n10 5 3\n10 5 3\n1 7 1000\n10 18\n1 2 3\n2 3 4\n3 4 5\n4 5 6\n5 6 7\n6 7 8\n7 8 9\n8 9 10\n9 10 11\n10 11 12\n0 0\n output: 2\n3\n3\n4\n\n" }, { "title": "Problem J: Merry Christmas", "content": "International Christmas Present Company (ICPC) is a company to employ Santa and deliver\npresents on Christmas. Many parents request ICPC to deliver presents to their children at\nspecified time of December 24. Although same Santa can deliver two or more presents, because\nit takes time to move between houses, two or more Santa might be needed to finish all the\nrequests on time.\n\nEmploying Santa needs much money, so the president of ICPC employed you, a great program-\nmer, to optimize delivery schedule. Your task is to write a program to calculate the minimum\nnumber of Santa necessary to finish the given requests on time. Because each Santa has been\nwell trained and can conceal himself in the town, you can put the initial position of each Santa\nanywhere.", "constraint": "", "input": "The input consists of several datasets. Each dataset is formatted as follows.\n\nN M L\nu_1 v_1 d_1\nu_2 v_2 d_2\n . \n . \n . \nu_M v_M d_M\np_1 t_1\np_2 t_2\n . \n . \n . \np_L t_L\n\nThe first line of a dataset contains three integer, N , M and L (1 <= N <= 100,0 <= M <= 1000,\n1 <= L <= 1000) each indicates the number of houses, roads and requests respectively.\n\nThe following M lines describe the road network. The i-th line contains three integers, u_i , v_i ,\nand d_i (0 <= u_i < v_i <= N - 1,1 <= d_i <= 100) which means that there is a road connecting houses\nu_i and v_i with d_i length. Each road is bidirectional. There is at most one road between same\npair of houses. Whole network might be disconnected.\n\nThe next L lines describe the requests. The i-th line contains two integers, p_i and t_i (0 <= p_i <=\nN - 1,0 <= t_i <= 10^8 ) which means that there is a delivery request to house p_i on time t_i . There\nis at most one request for same place and time. You can assume that time taken other than\nmovement can be neglectable, and every Santa has the same speed, one unit distance per unit\ntime.\n\nThe end of the input is indicated by a line containing three zeros separated by a space, and you\nshould not process this as a test case.", "output": "Print the minimum number of Santa necessary to finish all the requests on time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 3\n0 1 10\n1 2 10\n0 0\n1 10\n2 0\n3 2 4\n0 1 10\n1 2 10\n0 0\n1 10\n2 20\n0 40\n10 10 10\n0 1 39\n2 3 48\n3 5 20\n4 8 43\n3 9 10\n8 9 40\n3 4 5\n5 7 20\n1 7 93\n1 3 20\n0 0\n1 100000000\n2 100\n3 543\n4 500\n5 400\n6 300\n7 200\n8 100\n9 100\n0 0 0\n output: 2\n1\n4"], "Pid": "p01368", "ProblemText": "Task Description: International Christmas Present Company (ICPC) is a company to employ Santa and deliver\npresents on Christmas. Many parents request ICPC to deliver presents to their children at\nspecified time of December 24. Although same Santa can deliver two or more presents, because\nit takes time to move between houses, two or more Santa might be needed to finish all the\nrequests on time.\n\nEmploying Santa needs much money, so the president of ICPC employed you, a great program-\nmer, to optimize delivery schedule. Your task is to write a program to calculate the minimum\nnumber of Santa necessary to finish the given requests on time. Because each Santa has been\nwell trained and can conceal himself in the town, you can put the initial position of each Santa\nanywhere.\nTask Input: The input consists of several datasets. Each dataset is formatted as follows.\n\nN M L\nu_1 v_1 d_1\nu_2 v_2 d_2\n . \n . \n . \nu_M v_M d_M\np_1 t_1\np_2 t_2\n . \n . \n . \np_L t_L\n\nThe first line of a dataset contains three integer, N , M and L (1 <= N <= 100,0 <= M <= 1000,\n1 <= L <= 1000) each indicates the number of houses, roads and requests respectively.\n\nThe following M lines describe the road network. The i-th line contains three integers, u_i , v_i ,\nand d_i (0 <= u_i < v_i <= N - 1,1 <= d_i <= 100) which means that there is a road connecting houses\nu_i and v_i with d_i length. Each road is bidirectional. There is at most one road between same\npair of houses. Whole network might be disconnected.\n\nThe next L lines describe the requests. The i-th line contains two integers, p_i and t_i (0 <= p_i <=\nN - 1,0 <= t_i <= 10^8 ) which means that there is a delivery request to house p_i on time t_i . There\nis at most one request for same place and time. You can assume that time taken other than\nmovement can be neglectable, and every Santa has the same speed, one unit distance per unit\ntime.\n\nThe end of the input is indicated by a line containing three zeros separated by a space, and you\nshould not process this as a test case.\nTask Output: Print the minimum number of Santa necessary to finish all the requests on time.\nTask Samples: input: 3 2 3\n0 1 10\n1 2 10\n0 0\n1 10\n2 0\n3 2 4\n0 1 10\n1 2 10\n0 0\n1 10\n2 20\n0 40\n10 10 10\n0 1 39\n2 3 48\n3 5 20\n4 8 43\n3 9 10\n8 9 40\n3 4 5\n5 7 20\n1 7 93\n1 3 20\n0 0\n1 100000000\n2 100\n3 543\n4 500\n5 400\n6 300\n7 200\n8 100\n9 100\n0 0 0\n output: 2\n1\n4\n\n" }, { "title": "Calender Colors", "content": "Taro is a member of a programming contest circle.\nIn this circle, the members manage their schedules in the system called Great Web Calender.\nTaro has just added some of his friends to his calendar so that he can browse their schedule on his calendar.\nThen he noticed that the system currently displays all the schedules in only one color, mixing the schedules for all his friends.\nThis is difficult to manage because it's hard to tell whose schedule each entry is.\n\nBut actually this calender system has the feature to change the color of schedule entries, based on the person who has the entries.\nSo Taro wants to use that feature to distinguish their plans by color.\n\nGiven the colors Taro can use and the number of members,\nyour task is to calculate the subset of colors to color all schedule entries.\nThe colors are given by \"Lab color space\".\n\nIn Lab color space,\nthe distance between two colors is defined by the square sum of the difference of each element.\nTaro has to pick up the subset of colors that maximizes the sum of distances of all color pairs in the set.", "constraint": "", "input": "The input is like the following style.\n\nN M\nL_{0} a_{0} b_{0}\nL_{1} a_{1} b_{1}\n. . . \nL_{N-1} a_{N-1} b_{N-1}\n\nThe first line contains two integers N and M (0 <= M <= N <= 20), where N is the number of colors in the input, and M is the number of friends Taro wants to select the colors for.\nEach of the following N lines contains three decimal integers L(0.0 <= L <= 100.0), a(-134.0 <= a <= 220.0) and b(-140.0 <= b <= 122.0) which represents a single color in Lab color space.", "output": "Output the maximal of the total distance.\nThe output should not contain an error greater than 10^{-5}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n0 0 0\n10 10 10\n100 100 100\n output: 30000.00000000000000000000", "input: 5 3\n12.0 15.0 9.0\n10.0 -3.0 2.2\n3.5 6.8 9.0\n2.1 4.4 5.9\n1.2 4.0 -5.4\n output: 1003.44000000000005456968", "input: 2 1\n1.0 1.0 1.0\n0.0 0.0 0.0\n output: 0.00000000000000000000"], "Pid": "p01417", "ProblemText": "Task Description: Taro is a member of a programming contest circle.\nIn this circle, the members manage their schedules in the system called Great Web Calender.\nTaro has just added some of his friends to his calendar so that he can browse their schedule on his calendar.\nThen he noticed that the system currently displays all the schedules in only one color, mixing the schedules for all his friends.\nThis is difficult to manage because it's hard to tell whose schedule each entry is.\n\nBut actually this calender system has the feature to change the color of schedule entries, based on the person who has the entries.\nSo Taro wants to use that feature to distinguish their plans by color.\n\nGiven the colors Taro can use and the number of members,\nyour task is to calculate the subset of colors to color all schedule entries.\nThe colors are given by \"Lab color space\".\n\nIn Lab color space,\nthe distance between two colors is defined by the square sum of the difference of each element.\nTaro has to pick up the subset of colors that maximizes the sum of distances of all color pairs in the set.\nTask Input: The input is like the following style.\n\nN M\nL_{0} a_{0} b_{0}\nL_{1} a_{1} b_{1}\n. . . \nL_{N-1} a_{N-1} b_{N-1}\n\nThe first line contains two integers N and M (0 <= M <= N <= 20), where N is the number of colors in the input, and M is the number of friends Taro wants to select the colors for.\nEach of the following N lines contains three decimal integers L(0.0 <= L <= 100.0), a(-134.0 <= a <= 220.0) and b(-140.0 <= b <= 122.0) which represents a single color in Lab color space.\nTask Output: Output the maximal of the total distance.\nThe output should not contain an error greater than 10^{-5}.\nTask Samples: input: 3 2\n0 0 0\n10 10 10\n100 100 100\n output: 30000.00000000000000000000\ninput: 5 3\n12.0 15.0 9.0\n10.0 -3.0 2.2\n3.5 6.8 9.0\n2.1 4.4 5.9\n1.2 4.0 -5.4\n output: 1003.44000000000005456968\ninput: 2 1\n1.0 1.0 1.0\n0.0 0.0 0.0\n output: 0.00000000000000000000\n\n" }, { "title": "Sleeping Time", "content": "Miki is a high school student.\nShe has a part time job, so she cannot take enough sleep on weekdays.\nShe wants to take good sleep on holidays, but she doesn't know the best length of sleeping time for her.\n\nShe is now trying to figure that out with the following algorithm:\n\n Begin with the numbers K, R and L.\n\nShe tries to sleep for H=(R+L)/2 hours.\n\nIf she feels the time is longer than or equal to the optimal length, then update L with H. Otherwise, update R with H.\n\nAfter repeating step 2 and 3 for K nights, she decides her optimal sleeping time to be T' = (R+L)/2.\nIf her feeling is always correct, the steps described above should give her a very accurate optimal sleeping time.\nBut unfortunately, she makes mistake in step 3 with the probability P.\n\n Assume you know the optimal sleeping time T for Miki.\nYou have to calculate the probability PP that the absolute difference of T' and T is smaller or equal to E.\nIt is guaranteed that the answer remains unaffected by the change of E in 10^{-10}.", "constraint": "", "input": "The input follows the format shown below\n\nK R L\nP\nE\nT\nWhere the integers 0 <= K <= 30,0 <= R <= L <= 12 are the parameters for the algorithm described above.\n The decimal numbers on the following three lines of the input gives the parameters for the estimation. You can assume 0 <= P <= 1,0 <= E <= 12,0 <= T <= 12.", "output": "Output PP in one line.\n\nThe output should not contain an error greater than 10^{-5}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 0 2\n0.10000000000\n0.50000000000\n1.00000000000\n output: 0.900000", "input: 3 0 2\n0.10000000000\n0.37499999977\n1.00000000000\n output: 0.810000", "input: 3 0 2\n0.10000000000\n0.00000100000\n0.37500000000\n output: 0.729000", "input: 3 0 2\n0.20000000000\n0.00000100000\n0.37500000000\n output: 0.512000"], "Pid": "p01418", "ProblemText": "Task Description: Miki is a high school student.\nShe has a part time job, so she cannot take enough sleep on weekdays.\nShe wants to take good sleep on holidays, but she doesn't know the best length of sleeping time for her.\n\nShe is now trying to figure that out with the following algorithm:\n\n Begin with the numbers K, R and L.\n\nShe tries to sleep for H=(R+L)/2 hours.\n\nIf she feels the time is longer than or equal to the optimal length, then update L with H. Otherwise, update R with H.\n\nAfter repeating step 2 and 3 for K nights, she decides her optimal sleeping time to be T' = (R+L)/2.\nIf her feeling is always correct, the steps described above should give her a very accurate optimal sleeping time.\nBut unfortunately, she makes mistake in step 3 with the probability P.\n\n Assume you know the optimal sleeping time T for Miki.\nYou have to calculate the probability PP that the absolute difference of T' and T is smaller or equal to E.\nIt is guaranteed that the answer remains unaffected by the change of E in 10^{-10}.\nTask Input: The input follows the format shown below\n\nK R L\nP\nE\nT\nWhere the integers 0 <= K <= 30,0 <= R <= L <= 12 are the parameters for the algorithm described above.\n The decimal numbers on the following three lines of the input gives the parameters for the estimation. You can assume 0 <= P <= 1,0 <= E <= 12,0 <= T <= 12.\nTask Output: Output PP in one line.\n\nThe output should not contain an error greater than 10^{-5}.\nTask Samples: input: 3 0 2\n0.10000000000\n0.50000000000\n1.00000000000\n output: 0.900000\ninput: 3 0 2\n0.10000000000\n0.37499999977\n1.00000000000\n output: 0.810000\ninput: 3 0 2\n0.10000000000\n0.00000100000\n0.37500000000\n output: 0.729000\ninput: 3 0 2\n0.20000000000\n0.00000100000\n0.37500000000\n output: 0.512000\n\n" }, { "title": "On or Off", "content": "Saving electricity is very important!\n\nYou are in the office represented as R * C grid that consists of walls and rooms.\nIt is guaranteed that, for any pair of rooms in the office, there exists exactly one route between the two rooms.\nIt takes 1 unit of time for you to move to the next room (that is, the grid adjacent to the current room).\nRooms are so dark that you need to switch on a light when you enter a room.\nWhen you leave the room, you can either leave the light on, or\nof course you can switch off the light. Each room keeps consuming electric power while the light is on.\n\nToday you have a lot of tasks across the office.\n Tasks are given as a list of coordinates, and they need to be done in the specified order. \nTo save electricity, you want to finish all the tasks with the minimal amount of electric power.\n\nThe problem is not so easy though, because you will consume electricity not only when light is on, but also when you switch on/off the light.\n\nLuckily, you know the cost of power consumption per unit time and also the cost to switch on/off the light for all the rooms in the office.\nBesides, you are so smart that you don't need any time to do the tasks themselves.\nSo please figure out the optimal strategy to minimize the amount of electric power consumed.\n\nAfter you finished all the tasks, please DO NOT leave the light on at any room.\nIt's obviously wasting!", "constraint": "", "input": "The first line of the input contains three positive integers R (0 < R <= 50), C (0 < C <= 50) and M (2 <= M <= 1000).\nThe following R lines, which contain C characters each, describe the layout of the office.\n '. ' describes a room and '#' describes a wall.\nThis is followed by three matrices with R rows, C columns each.\nEvery elements of the matrices are positive integers.\nThe (r, c) element in the first matrix describes the power consumption per unit of time for the room at the coordinate (r, c).\nThe (r, c) element in the second matrix and the third matrix describe the cost to turn on the light and the cost to turn off the light, respectively, in the room at the coordinate (r, c).\n\nEach of the last M lines contains two positive integers, which describe the coodinates of the room for you to do the task.\n\nNote that you cannot do the i-th task if any of the j-th task (0 <= j <= i) is left undone.", "output": "Print one integer that describes the minimal amount of electric power consumed when you finished all the tasks.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 2\n...\n1 1 1\n1 2 1\n1 1 1\n0 0\n0 2\n output: 7", "input: 3 3 5\n...\n.##\n..#\n1 1 1\n1 0 0\n1 1 0\n3 3 3\n3 0 0\n3 3 0\n5 4 5\n4 0 0\n5 4 0\n1 0\n2 1\n0 2\n2 0\n0 0\n output: 77", "input: 5 5 10\n#.###\n#....\n###.#\n..#.#\n#....\n0 12 0 0 0\n0 4 3 2 10\n0 0 0 99 0\n11 13 0 2 0\n0 1 1 2 1\n0 4 0 0 0\n0 13 8 2 4\n0 0 0 16 0\n1 1 0 2 0\n0 2 3 1 99\n0 2 0 0 0\n0 12 2 12 2\n0 0 0 3 0\n4 14 0 16 0\n0 2 14 2 90\n0 1\n3 0\n4 4\n1 4\n1 1\n4 4\n1 1\n4 3\n3 0\n1 4\n output: 777"], "Pid": "p01419", "ProblemText": "Task Description: Saving electricity is very important!\n\nYou are in the office represented as R * C grid that consists of walls and rooms.\nIt is guaranteed that, for any pair of rooms in the office, there exists exactly one route between the two rooms.\nIt takes 1 unit of time for you to move to the next room (that is, the grid adjacent to the current room).\nRooms are so dark that you need to switch on a light when you enter a room.\nWhen you leave the room, you can either leave the light on, or\nof course you can switch off the light. Each room keeps consuming electric power while the light is on.\n\nToday you have a lot of tasks across the office.\n Tasks are given as a list of coordinates, and they need to be done in the specified order. \nTo save electricity, you want to finish all the tasks with the minimal amount of electric power.\n\nThe problem is not so easy though, because you will consume electricity not only when light is on, but also when you switch on/off the light.\n\nLuckily, you know the cost of power consumption per unit time and also the cost to switch on/off the light for all the rooms in the office.\nBesides, you are so smart that you don't need any time to do the tasks themselves.\nSo please figure out the optimal strategy to minimize the amount of electric power consumed.\n\nAfter you finished all the tasks, please DO NOT leave the light on at any room.\nIt's obviously wasting!\nTask Input: The first line of the input contains three positive integers R (0 < R <= 50), C (0 < C <= 50) and M (2 <= M <= 1000).\nThe following R lines, which contain C characters each, describe the layout of the office.\n '. ' describes a room and '#' describes a wall.\nThis is followed by three matrices with R rows, C columns each.\nEvery elements of the matrices are positive integers.\nThe (r, c) element in the first matrix describes the power consumption per unit of time for the room at the coordinate (r, c).\nThe (r, c) element in the second matrix and the third matrix describe the cost to turn on the light and the cost to turn off the light, respectively, in the room at the coordinate (r, c).\n\nEach of the last M lines contains two positive integers, which describe the coodinates of the room for you to do the task.\n\nNote that you cannot do the i-th task if any of the j-th task (0 <= j <= i) is left undone.\nTask Output: Print one integer that describes the minimal amount of electric power consumed when you finished all the tasks.\nTask Samples: input: 1 3 2\n...\n1 1 1\n1 2 1\n1 1 1\n0 0\n0 2\n output: 7\ninput: 3 3 5\n...\n.##\n..#\n1 1 1\n1 0 0\n1 1 0\n3 3 3\n3 0 0\n3 3 0\n5 4 5\n4 0 0\n5 4 0\n1 0\n2 1\n0 2\n2 0\n0 0\n output: 77\ninput: 5 5 10\n#.###\n#....\n###.#\n..#.#\n#....\n0 12 0 0 0\n0 4 3 2 10\n0 0 0 99 0\n11 13 0 2 0\n0 1 1 2 1\n0 4 0 0 0\n0 13 8 2 4\n0 0 0 16 0\n1 1 0 2 0\n0 2 3 1 99\n0 2 0 0 0\n0 12 2 12 2\n0 0 0 3 0\n4 14 0 16 0\n0 2 14 2 90\n0 1\n3 0\n4 4\n1 4\n1 1\n4 4\n1 1\n4 3\n3 0\n1 4\n output: 777\n\n" }, { "title": "Marathon Match", "content": "N people run a marathon.\nThere are M resting places on the way.\nFor each resting place, the i-th runner takes a break with probability P_i percent.\nWhen the i-th runner takes a break, he gets rest for T_i time.\n\nThe i-th runner runs at constant speed V_i, and\nthe distance of the marathon is L.\n\nYou are requested to compute the probability for each runner to win the first place.\nIf a runner arrives at the goal with another person at the same time, they are not considered to win the first place.", "constraint": "", "input": "A dataset is given in the following format:\n\nN M L\nP_1 T_1 V_1\nP_2 T_2 V_2\n. . . \nP_N T_N V_N\n\nThe first line of a dataset contains three integers N (1 <= N <= 100), M (0 <= M <= 50) and L (1 <= L <= 100,000).\nN is the number of runners.\nM is the number of resting places.\nL is the distance of the marathon.\n\nEach of the following N lines contains three integers P_i (0 <= P_i <= 100), T_i (0 <= T_i <= 100) and V_i (0 <= V_i <= 100) describing the i-th runner.\nP_i is the probability to take a break.\nT_i is the time of resting.\nV_i is the speed.", "output": "For each runner, you should answer the probability of winning.\nThe i-th line in the output should be the probability that the i-th runner wins the marathon.\nEach number in the output should not contain an error greater than 10^{-5}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 50\n30 50 1\n30 50 2\n output: 0.28770000\n0.71230000", "input: 2 1 100\n100 100 10\n0 100 1\n output: 0.00000000\n1.00000000", "input: 3 1 100\n50 1 1\n50 1 1\n50 1 1\n output: 0.12500000\n0.12500000\n0.12500000", "input: 2 2 50\n30 0 1\n30 50 2\n output: 0.51000000\n0.49000000"], "Pid": "p01420", "ProblemText": "Task Description: N people run a marathon.\nThere are M resting places on the way.\nFor each resting place, the i-th runner takes a break with probability P_i percent.\nWhen the i-th runner takes a break, he gets rest for T_i time.\n\nThe i-th runner runs at constant speed V_i, and\nthe distance of the marathon is L.\n\nYou are requested to compute the probability for each runner to win the first place.\nIf a runner arrives at the goal with another person at the same time, they are not considered to win the first place.\nTask Input: A dataset is given in the following format:\n\nN M L\nP_1 T_1 V_1\nP_2 T_2 V_2\n. . . \nP_N T_N V_N\n\nThe first line of a dataset contains three integers N (1 <= N <= 100), M (0 <= M <= 50) and L (1 <= L <= 100,000).\nN is the number of runners.\nM is the number of resting places.\nL is the distance of the marathon.\n\nEach of the following N lines contains three integers P_i (0 <= P_i <= 100), T_i (0 <= T_i <= 100) and V_i (0 <= V_i <= 100) describing the i-th runner.\nP_i is the probability to take a break.\nT_i is the time of resting.\nV_i is the speed.\nTask Output: For each runner, you should answer the probability of winning.\nThe i-th line in the output should be the probability that the i-th runner wins the marathon.\nEach number in the output should not contain an error greater than 10^{-5}.\nTask Samples: input: 2 2 50\n30 50 1\n30 50 2\n output: 0.28770000\n0.71230000\ninput: 2 1 100\n100 100 10\n0 100 1\n output: 0.00000000\n1.00000000\ninput: 3 1 100\n50 1 1\n50 1 1\n50 1 1\n output: 0.12500000\n0.12500000\n0.12500000\ninput: 2 2 50\n30 0 1\n30 50 2\n output: 0.51000000\n0.49000000\n\n" }, { "title": "Reverse Roads", "content": "ICP city has an express company whose trucks run from the crossing S to the crossing T.\nThe president of the company is feeling upset because all the roads in the city are one-way, and are severely congested.\nSo, he planned to improve the maximum flow (edge disjoint paths) from the crossing S to the crossing T by reversing the traffic direction on some of the roads.\n\nYour task is writing a program to calculate the maximized flow from S to T by reversing some roads, and the list of the reversed roads.", "constraint": "", "input": "The first line of a data set contains two integers N (2 <= N <= 300) and M (0 <= M <= {\\rm min} (1\\, 000, \\ N(N-1)/2)).\nN is the number of crossings in the city and M is the number of roads.\n\nThe following M lines describe one-way roads in the city.\nThe i-th line (1-based) contains two integers X_i and Y_i (1 <= X_i, Y_i <= N, X_i \\neq Y_i).\nX_i is the ID number (1-based) of the starting point of the i-th road and Y_i is that of the terminal point.\nThe last line contains two integers S and T (1 <= S, T <= N, S \\neq T, 1-based).\n\nThe capacity of each road is 1.\n\nYou can assume that i \\neq j implies either X_i \\neq X_j or Y_i \\neq Y_j,\nand either X_i \\neq Y_j or X_j \\neq Y_i.", "output": "In the first line, print the maximized flow by reversing some roads.\nIn the second line, print the number R of the reversed roads.\nIn each of the following R lines, print the ID number (1-based) of a reversed road.\nYou may not print the same ID number more than once.\n\nIf there are multiple answers which would give us the same flow capacity, you can print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n2 1\n2 1\n output: 1\n0", "input: 2 1\n1 2\n2 1\n output: 1\n1\n1", "input: 3 3\n3 2\n1 2\n3 1\n1 3\n output: 2\n2\n1\n3"], "Pid": "p01421", "ProblemText": "Task Description: ICP city has an express company whose trucks run from the crossing S to the crossing T.\nThe president of the company is feeling upset because all the roads in the city are one-way, and are severely congested.\nSo, he planned to improve the maximum flow (edge disjoint paths) from the crossing S to the crossing T by reversing the traffic direction on some of the roads.\n\nYour task is writing a program to calculate the maximized flow from S to T by reversing some roads, and the list of the reversed roads.\nTask Input: The first line of a data set contains two integers N (2 <= N <= 300) and M (0 <= M <= {\\rm min} (1\\, 000, \\ N(N-1)/2)).\nN is the number of crossings in the city and M is the number of roads.\n\nThe following M lines describe one-way roads in the city.\nThe i-th line (1-based) contains two integers X_i and Y_i (1 <= X_i, Y_i <= N, X_i \\neq Y_i).\nX_i is the ID number (1-based) of the starting point of the i-th road and Y_i is that of the terminal point.\nThe last line contains two integers S and T (1 <= S, T <= N, S \\neq T, 1-based).\n\nThe capacity of each road is 1.\n\nYou can assume that i \\neq j implies either X_i \\neq X_j or Y_i \\neq Y_j,\nand either X_i \\neq Y_j or X_j \\neq Y_i.\nTask Output: In the first line, print the maximized flow by reversing some roads.\nIn the second line, print the number R of the reversed roads.\nIn each of the following R lines, print the ID number (1-based) of a reversed road.\nYou may not print the same ID number more than once.\n\nIf there are multiple answers which would give us the same flow capacity, you can print any of them.\nTask Samples: input: 2 1\n2 1\n2 1\n output: 1\n0\ninput: 2 1\n1 2\n2 1\n output: 1\n1\n1\ninput: 3 3\n3 2\n1 2\n3 1\n1 3\n output: 2\n2\n1\n3\n\n" }, { "title": "Beautiful Currency", "content": "KM country has N kinds of coins and each coin has its value a_i.\n\nThe king of the country, Kita_masa, thought that the current currency system is poor,\nand he decided to make it beautiful by changing the values of some (possibly no) coins.\n\nA currency system is called beautiful\nif each coin has an integer value and the (i+1)-th smallest value is divisible by the i-th smallest value for all i (1 <= i <= N-1).\n\nFor example, the set {1,5,10,50,100,500} is considered as a beautiful system,\nwhile the set {1,5,10,25,50,100} is NOT,\nbecause 25 is not divisible by 10.\n\nSince changing the currency system may confuse citizens,\nthe king, Kita_masa, wants to minimize the maximum value of the confusion ratios.\nHere, the confusion ratio for the change in the i-th coin is defined as |a_i - b_i| / a_i,\nwhere a_i and b_i is the value of i-th coin before and after the structure changes, respectively.\n\nNote that Kita_masa can change the value of each existing coin,\nbut he cannot introduce new coins nor eliminate existing coins.\nAfter the modification, the values of two or more coins may coincide.", "constraint": "", "input": "Each dataset contains two lines.\nThe first line contains a single integer, N,\nand the second line contains N integers, {a_i}.\n\nYou may assume the following constraints:\n\n1 <= N <= 20\n\n1 <= a_1 < a_2 <. . . < a_N < 10^5", "output": "Output one number that represents the minimum of the maximum value of the confusion ratios.\nThe value may be printed with an arbitrary number of decimal digits,\nbut may not contain an absolute error greater than or equal to 10^{-8}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n6 11 12\n output: 0.090909090909", "input: 3\n6 11 24\n output: 0.090909090909", "input: 3\n6 11 30\n output: 0.166666666667"], "Pid": "p01422", "ProblemText": "Task Description: KM country has N kinds of coins and each coin has its value a_i.\n\nThe king of the country, Kita_masa, thought that the current currency system is poor,\nand he decided to make it beautiful by changing the values of some (possibly no) coins.\n\nA currency system is called beautiful\nif each coin has an integer value and the (i+1)-th smallest value is divisible by the i-th smallest value for all i (1 <= i <= N-1).\n\nFor example, the set {1,5,10,50,100,500} is considered as a beautiful system,\nwhile the set {1,5,10,25,50,100} is NOT,\nbecause 25 is not divisible by 10.\n\nSince changing the currency system may confuse citizens,\nthe king, Kita_masa, wants to minimize the maximum value of the confusion ratios.\nHere, the confusion ratio for the change in the i-th coin is defined as |a_i - b_i| / a_i,\nwhere a_i and b_i is the value of i-th coin before and after the structure changes, respectively.\n\nNote that Kita_masa can change the value of each existing coin,\nbut he cannot introduce new coins nor eliminate existing coins.\nAfter the modification, the values of two or more coins may coincide.\nTask Input: Each dataset contains two lines.\nThe first line contains a single integer, N,\nand the second line contains N integers, {a_i}.\n\nYou may assume the following constraints:\n\n1 <= N <= 20\n\n1 <= a_1 < a_2 <. . . < a_N < 10^5\nTask Output: Output one number that represents the minimum of the maximum value of the confusion ratios.\nThe value may be printed with an arbitrary number of decimal digits,\nbut may not contain an absolute error greater than or equal to 10^{-8}.\nTask Samples: input: 3\n6 11 12\n output: 0.090909090909\ninput: 3\n6 11 24\n output: 0.090909090909\ninput: 3\n6 11 30\n output: 0.166666666667\n\n" }, { "title": "Rabbit Party", "content": "A rabbit Taro decided to hold a party and invite some friends as guests.\nHe has n rabbit friends, and m pairs of rabbits are also friends with each other.\n\nFriendliness of each pair is expressed with a positive integer.\nIf two rabbits are not friends, their friendliness is assumed to be 0.\n\nWhen a rabbit is invited to the party, his satisfaction score is defined as the minimal friendliness with any other guests.\n The satisfaction of the party itself is defined as the sum of satisfaction score for all the guests.\n\nTo maximize satisfaction scores for the party, who should Taro invite?\nWrite a program to calculate the maximal possible satisfaction score for the party.", "constraint": "", "input": "The first line of the input contains two integers, n and m (1 <= n <= 100,0 <= m <= 100).\nThe rabbits are numbered from 1 to n.\n\nEach of the following m lines has three integers, u, v and f.\nu and v (1 <= u, v <= n, u \\neq v, 1 <= f <= 1,000,000) stands for the rabbits' number, and f stands for their friendliness.\n\nYou may assume that the friendliness of a pair of rabbits will be given at most once.", "output": "Output the maximal possible satisfaction score of the party in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 3\n2 3 1\n3 1 2\n output: 6", "input: 2 1\n1 2 5\n output: 10", "input: 1 0\n output: 0", "input: 4 5\n1 2 4\n1 3 3\n2 3 7\n2 4 5\n3 4 6\n output: 16"], "Pid": "p01423", "ProblemText": "Task Description: A rabbit Taro decided to hold a party and invite some friends as guests.\nHe has n rabbit friends, and m pairs of rabbits are also friends with each other.\n\nFriendliness of each pair is expressed with a positive integer.\nIf two rabbits are not friends, their friendliness is assumed to be 0.\n\nWhen a rabbit is invited to the party, his satisfaction score is defined as the minimal friendliness with any other guests.\n The satisfaction of the party itself is defined as the sum of satisfaction score for all the guests.\n\nTo maximize satisfaction scores for the party, who should Taro invite?\nWrite a program to calculate the maximal possible satisfaction score for the party.\nTask Input: The first line of the input contains two integers, n and m (1 <= n <= 100,0 <= m <= 100).\nThe rabbits are numbered from 1 to n.\n\nEach of the following m lines has three integers, u, v and f.\nu and v (1 <= u, v <= n, u \\neq v, 1 <= f <= 1,000,000) stands for the rabbits' number, and f stands for their friendliness.\n\nYou may assume that the friendliness of a pair of rabbits will be given at most once.\nTask Output: Output the maximal possible satisfaction score of the party in a line.\nTask Samples: input: 3 3\n1 2 3\n2 3 1\n3 1 2\n output: 6\ninput: 2 1\n1 2 5\n output: 10\ninput: 1 0\n output: 0\ninput: 4 5\n1 2 4\n1 3 3\n2 3 7\n2 4 5\n3 4 6\n output: 16\n\n" }, { "title": "Palindrome Generator", "content": "A palidrome craftsperson starts to work in the early morning, \nwith the clear air allowing him to polish up his palindromes.\n\nOn this morning, he is making his pieces to submit to the International Contest for Palindrome Craftspeople.\n\nBy the way, in order to make palindromes, he uses a special dictionary which contains a set of words and a set of ordered pairs of the words.\nAny words and any ordered pairs of consecutive words in his palindromes must appear in the dictionary.\n\nWe already have his dictionary, so let's estimate how long a palindrome he can make.", "constraint": "", "input": "The first line in the data set consists of two integers N (1 <= N <= 100) and M (0 <= M <= 1\\, 000).\nN describes the number of words in the dictionary and M describes the number of ordered pairs of words.\n\nThe following N lines describe the words he can use.\nThe i-th line (1-based) contains the word i, which consists of only lower-case letters and whose length is between 1 and 10, inclusive.\n\nThe following M lines describe the ordered pairs of consecutive words he can use.\nThe j-th line (1-based) contains two integers X_j and Y_j (1 <= X_j, Y_j <= N).\nX_j describes the (1-based) index of the former word in the palindrome and Y_j describes that of the latter word.", "output": "Print the maximal length of the possible palindrome in a line.\nIf he can make no palidromes, print \"0\".\nIf he can make arbitrary long palindromes, print \"-1\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\nab\nba\n1 1\n1 2\n output: 4", "input: 2 2\nab\nba\n1 1\n2 2\n output: 0", "input: 2 2\nab\na\n1 1\n1 2\n output: -1"], "Pid": "p01424", "ProblemText": "Task Description: A palidrome craftsperson starts to work in the early morning, \nwith the clear air allowing him to polish up his palindromes.\n\nOn this morning, he is making his pieces to submit to the International Contest for Palindrome Craftspeople.\n\nBy the way, in order to make palindromes, he uses a special dictionary which contains a set of words and a set of ordered pairs of the words.\nAny words and any ordered pairs of consecutive words in his palindromes must appear in the dictionary.\n\nWe already have his dictionary, so let's estimate how long a palindrome he can make.\nTask Input: The first line in the data set consists of two integers N (1 <= N <= 100) and M (0 <= M <= 1\\, 000).\nN describes the number of words in the dictionary and M describes the number of ordered pairs of words.\n\nThe following N lines describe the words he can use.\nThe i-th line (1-based) contains the word i, which consists of only lower-case letters and whose length is between 1 and 10, inclusive.\n\nThe following M lines describe the ordered pairs of consecutive words he can use.\nThe j-th line (1-based) contains two integers X_j and Y_j (1 <= X_j, Y_j <= N).\nX_j describes the (1-based) index of the former word in the palindrome and Y_j describes that of the latter word.\nTask Output: Print the maximal length of the possible palindrome in a line.\nIf he can make no palidromes, print \"0\".\nIf he can make arbitrary long palindromes, print \"-1\".\nTask Samples: input: 2 2\nab\nba\n1 1\n1 2\n output: 4\ninput: 2 2\nab\nba\n1 1\n2 2\n output: 0\ninput: 2 2\nab\na\n1 1\n1 2\n output: -1\n\n" }, { "title": "White Bird", "content": "Angry Birds is a mobile game of a big craze all over the world.\nYou were convinced that it was a waste of time to play the game, so you decided to create an automatic solver.\n\nYou are describing a routine that optimizes the white bird's strategy to defeat a pig (enemy) by hitting an egg bomb.\nThe white bird follows a parabolic trajectory from the initial position,\nand it can vertically drop egg bombs on the way.\n\n In order to make it easy to solve, the following conditions hold for the stages.\n\nN obstacles are put on the stage.\n\nEach obstacle is a rectangle whose sides are parallel to the coordinate axes.\n\nThe pig is put on the point (X, Y).\n\nYou can launch the white bird in any direction at an initial velocity V from the origin.\n\nIf the white bird collides with an obstacle, it becomes unable to drop egg bombs.\n\nIf the egg bomb collides with an obstacle, the egg bomb is vanished.\nThe acceleration of gravity is 9.8 {\\rm m/s^2}.\nGravity exerts a force on the objects in the decreasing direction of y-coordinate.", "constraint": "", "input": "A dataset follows the format shown below:\n\nN V X Y\nL_1 B_1 R_1 T_1\n. . . \nL_N B_N R_N T_N\n\nAll inputs are integer.\n\nN: the number of obstacles\n\nV: the initial speed of the white bird\n\nX, Y: the position of the pig\n(0 <= N <= 50,0 <= V <= 50,0 <= X, Y <= 300, X \\neq 0)\n\nfor 1 <= i <= N,\n\nL_i: the x-coordinate of the left side of the i-th obstacle\n\nB_i: the y-coordinate of the bottom side of the i-th obstacle\n\nR_i: the x-coordinate of the right side of the i-th obstacle\n\nT_i: the y-coordinate of the top side of the i-th obstacle\n(0 <= L_i, B_i, R_i, T_i <= 300)\n\nIt is guaranteed that the answer remains unaffected by a change of L_i, B_i, R_i and T_i in 10^{-6}.", "output": "Yes/No\n\nYou should answer whether the white bird can drop an egg bomb toward the pig.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 7 3 1\n output: Yes", "input: 1 7 3 1\n1 1 2 2\n output: No", "input: 1 7 2 2\n0 1 1 2\n output: No"], "Pid": "p01425", "ProblemText": "Task Description: Angry Birds is a mobile game of a big craze all over the world.\nYou were convinced that it was a waste of time to play the game, so you decided to create an automatic solver.\n\nYou are describing a routine that optimizes the white bird's strategy to defeat a pig (enemy) by hitting an egg bomb.\nThe white bird follows a parabolic trajectory from the initial position,\nand it can vertically drop egg bombs on the way.\n\n In order to make it easy to solve, the following conditions hold for the stages.\n\nN obstacles are put on the stage.\n\nEach obstacle is a rectangle whose sides are parallel to the coordinate axes.\n\nThe pig is put on the point (X, Y).\n\nYou can launch the white bird in any direction at an initial velocity V from the origin.\n\nIf the white bird collides with an obstacle, it becomes unable to drop egg bombs.\n\nIf the egg bomb collides with an obstacle, the egg bomb is vanished.\nThe acceleration of gravity is 9.8 {\\rm m/s^2}.\nGravity exerts a force on the objects in the decreasing direction of y-coordinate.\nTask Input: A dataset follows the format shown below:\n\nN V X Y\nL_1 B_1 R_1 T_1\n. . . \nL_N B_N R_N T_N\n\nAll inputs are integer.\n\nN: the number of obstacles\n\nV: the initial speed of the white bird\n\nX, Y: the position of the pig\n(0 <= N <= 50,0 <= V <= 50,0 <= X, Y <= 300, X \\neq 0)\n\nfor 1 <= i <= N,\n\nL_i: the x-coordinate of the left side of the i-th obstacle\n\nB_i: the y-coordinate of the bottom side of the i-th obstacle\n\nR_i: the x-coordinate of the right side of the i-th obstacle\n\nT_i: the y-coordinate of the top side of the i-th obstacle\n(0 <= L_i, B_i, R_i, T_i <= 300)\n\nIt is guaranteed that the answer remains unaffected by a change of L_i, B_i, R_i and T_i in 10^{-6}.\nTask Output: Yes/No\n\nYou should answer whether the white bird can drop an egg bomb toward the pig.\nTask Samples: input: 0 7 3 1\n output: Yes\ninput: 1 7 3 1\n1 1 2 2\n output: No\ninput: 1 7 2 2\n0 1 1 2\n output: No\n\n" }, { "title": "Vector Compression", "content": "You are recording a result of a secret experiment, which consists of a large set of N-dimensional vectors.\nSince the result may become very large, you are thinking of\ncompressing it. Fortunately you already have a good compression method\nfor vectors with small absolute values, all you have to do is to\npreprocess the vectors and make them small.\n\nYou can record the set of vectors in any order you like.\nLet's assume you process them in the order v_1, v_2, . . . , v_M.\nEach vector v_i is recorded either as is, or as a difference vector.\nWhen it is recorded as a difference,\nyou can arbitrarily pick up an already chosen vector v_j (j= 2) is represented as x^\nthe linear term (a_1x) is represented as x;\n the constant (a_0) is represented just by digits;\n these terms are given in the strictly decreasing order of the degrees and connected by a\nplus sign (\"+\");\n just like the standard notations, the is omitted if a_i = 1 for non-constant terms;\n similarly, the entire term is omitted if a_i = 0 for any terms; and\nthe polynomial representations contain no space or characters other than digits, \"x\", \"^\", and \"+\".\n\nFor example, 2x^2 + 3x + 5 is represented as 2x^2+3x+5; 2x^3 + x is represented as 2x^3+x, not 2x^3+0x^2+1x+0 or the like. No polynomial is a constant zero, i. e. the one with all the coefficients being zero.\n\nThe end of input is indicated by a line with two zeros. This line is not part of any dataset.", "output": "For each dataset, print the maximal bandwidth as a polynomial of x. The polynomial should be represented in the same way as the input format except that a constant zero is possible and should be represented by \"0\" (without quotes).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 x+2\n2 3 2x+1\n3 1 x+1\n2 0\n3 2\n1 2 x\n2 3 2\n4 3\n1 2 x^3+2x^2+3x+4\n2 3 x^2+2x+3\n3 4 x+2\n0 0\n output: 2x+3\n0\n2\nx+2"], "Pid": "p01445", "ProblemText": "Task Description: The trafic on the Internet is increasing these days due to smartphones. The wireless carriers\nhave to enhance their network infrastructure.\n\nThe network of a wireless carrier consists of a number of base stations and lines. Each line connects two base stations bi-directionally. The bandwidth of a line increases every year and is given by a polynomial f(x) of the year x.\n\nYour task is, given the network structure, to write a program to calculate the maximal bandwidth between the 1-st and N-th base stations as a polynomial of x.\nTask Input: The input consists of multiple datasets. Each dataset has the following format:\n\nN M\nu_1 v_1 p_1\n. . . \nu_M v_M p_M\n\nThe first line of each dataset contains two integers N (2 <= N <= 50) and M (0 <= M <= 500), which indicates the number of base stations and lines respectively. The following M lines describe the network structure. The i-th of them corresponds to the i-th network line and contains two integers u_i and v_i and a polynomial p_i. u_i and v_i indicate the indices of base stations (1 <= u_i, v_i <= N); p_i indicates the network bandwidth.\n\nEach polynomial has the form of:\n\na_Lx^L + a_L-1x^L-1 + . . . + a_2x^2 + a_1x + a_0\n\nwhere L (0 <= L <= 50) is the degree and a_i's (0 <= i <= L, 0 <= a_i <= 100) are the coefficients. In the input,\n\neach term a_ix^i (for i >= 2) is represented as x^\nthe linear term (a_1x) is represented as x;\n the constant (a_0) is represented just by digits;\n these terms are given in the strictly decreasing order of the degrees and connected by a\nplus sign (\"+\");\n just like the standard notations, the is omitted if a_i = 1 for non-constant terms;\n similarly, the entire term is omitted if a_i = 0 for any terms; and\nthe polynomial representations contain no space or characters other than digits, \"x\", \"^\", and \"+\".\n\nFor example, 2x^2 + 3x + 5 is represented as 2x^2+3x+5; 2x^3 + x is represented as 2x^3+x, not 2x^3+0x^2+1x+0 or the like. No polynomial is a constant zero, i. e. the one with all the coefficients being zero.\n\nThe end of input is indicated by a line with two zeros. This line is not part of any dataset.\nTask Output: For each dataset, print the maximal bandwidth as a polynomial of x. The polynomial should be represented in the same way as the input format except that a constant zero is possible and should be represented by \"0\" (without quotes).\nTask Samples: input: 3 3\n1 2 x+2\n2 3 2x+1\n3 1 x+1\n2 0\n3 2\n1 2 x\n2 3 2\n4 3\n1 2 x^3+2x^2+3x+4\n2 3 x^2+2x+3\n3 4 x+2\n0 0\n output: 2x+3\n0\n2\nx+2\n\n" }, { "title": "Problem J: Blue Forest", "content": "John is playing a famous console game named 'Tales of Algorithmers. ' Now he is facing the last dungeon called 'Blue Forest. ' To find out the fastest path to run through the very complicated dungeon, he tried to draw up the dungeon map.\n\nThe dungeon consists of several floors. Each floor can be described as a connected simple plane graph. Vertices of the graph are identified by X-Y coordinate, and the length of an edge is calculated by Euclidean distance. A vertex may be equipped with a one-way warp gate. If John chooses to use the gate, it brings John to another vertex in a possibly different floor. The distance between a warp gate and its destination is considered as 0.\n\nOne vertex has at most one warp gate, though some vertices might be the destination of multiple warp gates.\n\nHe believed he made one map for each floor, however after drawing maps of all the floors, he\nnoticed that he might have made a few mistakes. He might have drawn the same floor several times, and might have forgotten to mark some warp gates in the maps. However, he was sure he marked all warp gates at least once. So if the maps of same floor are unified to one map, all the warp gates must be described there. Luckily there are no floors which have the same shape\nas the other floors, so if two (or more) maps can be unified, they must be the maps of the same floor. Also, there is no floor which is circular symmetric (e. g. a regular triangle and a square).\n\nMap A and map B can be unified if map B can be transformed to map A using only rotation and parallel translation. Since some of the warp gates on maps might be missing, you should not consider the existence of warp gates when checking unification. If it is possible to unify map A and map B, a vertex on map A and the corresponding vertex on map B are considered as 'identical' vertices. In other words, you should treat warp gates on map B as those on map A where the warp gates are located on the corresponding vertices on map A. Destinations of warp gates should be treated similarly. After that you can forget map B. It is guaranteed that if both map A and map B have warp gates which are on the identical vertices, the destinations of them are also identical.\n\nRemember, your task is to find the shortest path from the entrance to the exit of the dungeon, using the unified maps.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is in the following format.\n\nn\ncomponent_1\ncomponent_2\n. . . \ncomponent_n\nsl sn\ndl dn\n\nn is a positive integer indicating the number of maps. component_i describes the i-th map in the following format.\n\nA\nx_1 y_1\nx_2 y_2\n. . . \nx_A y_A\nB\ns_1 d_1\ns_2 d_2\n. . . \ns_B d_B\nC\nsn_1 dl_1 dn_1\nsn_2 dl_2 dn_2\n. . . \nsn_C dl_C dn_C\n\nA denotes the number of vertices in the map. Each of the following A lines contains two integers\nx_i and y_i representing the coordinates of the i-th vertex in the 2-dimensional plane. B denotes the number of the edges connecting the vertices in the map. Each of the following B lines contains two integers representing the start and the end vertex of each edge. Vertices on the same map are numbered from 1.\n\nC denotes the number of warp gates. Each of the following C lines has three integers describing a warp gate. The first integer is the vertex where the warp gate is located. The second and the third integer are the indices of the map and the vertex representing the destination of the warp gate, respectively. Similarly to vertices, maps are also numbered from 1.\n\nAfter the description of all maps, two lines follow. The \frst line contains two integers sl and dl , meaning that the entrance of the dungeon is located in the sl-th map, at the vertex dl. The last line has two integers sn and dn, similarly describing the location of the exit.\n\nThe values in each dataset satisfy the following conditions:\n\n 1 <= n <= 50,\n\n 3 <= A <= 20,\n\n A - 1 <= B <= A(A - 1)/2,\n\n 0 <= C <= A, and\n\n -10,000 <= x_i, y_i <= 10,000.", "output": "For each dataset, print the distance of the shortest path from the entrance to the exit. The\noutput should not contain an absolute error greater than 10^-1. If there is no route, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n5\n0 0\n10 0\n20 0\n30 0\n30 10\n4\n1 2\n2 3\n3 4\n4 5\n2\n1 2 4\n3 2 2\n5\n-10 0\n0 0\n0 -10\n0 -20\n0 -30\n4\n1 2\n2 3\n3 4\n4 5\n1\n4 1 3\n1 1\n2 1\n4\n3\n4 3\n0 0\n5 0\n2\n1 2\n2 3\n0\n3\n0 0\n3 4\n0 5\n2\n1 2\n1 3\n1\n2 3 4\n4\n0 13\n0 0\n13 0\n13 13\n4\n1 2\n1 4\n2 3\n2 4\n0\n4\n5 12\n0 0\n-7 17\n-12 5\n4\n1 2\n2 3\n2 4\n4 3\n0\n1 1\n4 1\n4\n3\n0 0\n2 0\n0 4\n2\n1 2\n1 3\n0\n3\n0 0\n-2 0\n0 4\n2\n1 2\n1 3\n1\n1 4 1\n3\n0 0\n1 0\n0 2\n2\n1 2\n1 3\n1\n1 4 1\n3\n0 0\n2 0\n0 4\n2\n1 2\n2 3\n0\n1 1\n4 1\n0\n output: 10.0000000000\n41.3847763109\n-1.000000000"], "Pid": "p01446", "ProblemText": "Task Description: John is playing a famous console game named 'Tales of Algorithmers. ' Now he is facing the last dungeon called 'Blue Forest. ' To find out the fastest path to run through the very complicated dungeon, he tried to draw up the dungeon map.\n\nThe dungeon consists of several floors. Each floor can be described as a connected simple plane graph. Vertices of the graph are identified by X-Y coordinate, and the length of an edge is calculated by Euclidean distance. A vertex may be equipped with a one-way warp gate. If John chooses to use the gate, it brings John to another vertex in a possibly different floor. The distance between a warp gate and its destination is considered as 0.\n\nOne vertex has at most one warp gate, though some vertices might be the destination of multiple warp gates.\n\nHe believed he made one map for each floor, however after drawing maps of all the floors, he\nnoticed that he might have made a few mistakes. He might have drawn the same floor several times, and might have forgotten to mark some warp gates in the maps. However, he was sure he marked all warp gates at least once. So if the maps of same floor are unified to one map, all the warp gates must be described there. Luckily there are no floors which have the same shape\nas the other floors, so if two (or more) maps can be unified, they must be the maps of the same floor. Also, there is no floor which is circular symmetric (e. g. a regular triangle and a square).\n\nMap A and map B can be unified if map B can be transformed to map A using only rotation and parallel translation. Since some of the warp gates on maps might be missing, you should not consider the existence of warp gates when checking unification. If it is possible to unify map A and map B, a vertex on map A and the corresponding vertex on map B are considered as 'identical' vertices. In other words, you should treat warp gates on map B as those on map A where the warp gates are located on the corresponding vertices on map A. Destinations of warp gates should be treated similarly. After that you can forget map B. It is guaranteed that if both map A and map B have warp gates which are on the identical vertices, the destinations of them are also identical.\n\nRemember, your task is to find the shortest path from the entrance to the exit of the dungeon, using the unified maps.\nTask Input: The input consists of multiple datasets. Each dataset is in the following format.\n\nn\ncomponent_1\ncomponent_2\n. . . \ncomponent_n\nsl sn\ndl dn\n\nn is a positive integer indicating the number of maps. component_i describes the i-th map in the following format.\n\nA\nx_1 y_1\nx_2 y_2\n. . . \nx_A y_A\nB\ns_1 d_1\ns_2 d_2\n. . . \ns_B d_B\nC\nsn_1 dl_1 dn_1\nsn_2 dl_2 dn_2\n. . . \nsn_C dl_C dn_C\n\nA denotes the number of vertices in the map. Each of the following A lines contains two integers\nx_i and y_i representing the coordinates of the i-th vertex in the 2-dimensional plane. B denotes the number of the edges connecting the vertices in the map. Each of the following B lines contains two integers representing the start and the end vertex of each edge. Vertices on the same map are numbered from 1.\n\nC denotes the number of warp gates. Each of the following C lines has three integers describing a warp gate. The first integer is the vertex where the warp gate is located. The second and the third integer are the indices of the map and the vertex representing the destination of the warp gate, respectively. Similarly to vertices, maps are also numbered from 1.\n\nAfter the description of all maps, two lines follow. The \frst line contains two integers sl and dl , meaning that the entrance of the dungeon is located in the sl-th map, at the vertex dl. The last line has two integers sn and dn, similarly describing the location of the exit.\n\nThe values in each dataset satisfy the following conditions:\n\n 1 <= n <= 50,\n\n 3 <= A <= 20,\n\n A - 1 <= B <= A(A - 1)/2,\n\n 0 <= C <= A, and\n\n -10,000 <= x_i, y_i <= 10,000.\nTask Output: For each dataset, print the distance of the shortest path from the entrance to the exit. The\noutput should not contain an absolute error greater than 10^-1. If there is no route, print -1.\nTask Samples: input: 2\n5\n0 0\n10 0\n20 0\n30 0\n30 10\n4\n1 2\n2 3\n3 4\n4 5\n2\n1 2 4\n3 2 2\n5\n-10 0\n0 0\n0 -10\n0 -20\n0 -30\n4\n1 2\n2 3\n3 4\n4 5\n1\n4 1 3\n1 1\n2 1\n4\n3\n4 3\n0 0\n5 0\n2\n1 2\n2 3\n0\n3\n0 0\n3 4\n0 5\n2\n1 2\n1 3\n1\n2 3 4\n4\n0 13\n0 0\n13 0\n13 13\n4\n1 2\n1 4\n2 3\n2 4\n0\n4\n5 12\n0 0\n-7 17\n-12 5\n4\n1 2\n2 3\n2 4\n4 3\n0\n1 1\n4 1\n4\n3\n0 0\n2 0\n0 4\n2\n1 2\n1 3\n0\n3\n0 0\n-2 0\n0 4\n2\n1 2\n1 3\n1\n1 4 1\n3\n0 0\n1 0\n0 2\n2\n1 2\n1 3\n1\n1 4 1\n3\n0 0\n2 0\n0 4\n2\n1 2\n2 3\n0\n1 1\n4 1\n0\n output: 10.0000000000\n41.3847763109\n-1.000000000\n\n" }, { "title": "Carpenters' Language", "content": "International Carpenters Professionals Company (ICPC) is a top construction company with a lot of expert carpenters.\nWhat makes ICPC a top company is their original language.\n\nThe syntax of the language is simply given in CFG as follows:\n\nS -> SS | (S) | )S( | ε\n\nIn other words, a right parenthesis can be closed by a left parenthesis and a left parenthesis can be closed by a right parenthesis in this language.\n\nAlex, a grad student mastering linguistics, decided to study ICPC's language. \nAs a first step of the study, he needs to judge whether a text is well-formed in the language or not.\nThen, he asked you, a great programmer, to write a program for the judgement.\n\nAlex's request is as follows: You have an empty string S in the beginning, and construct longer string by inserting a sequence of '(' or ')' into the string.\nYou will receive q queries, each of which consists of three elements (p, c, n), where p is \nthe position to insert, n is the number of characters to insert and c is either '(' or ')', the character to insert.\nFor each query, your program should insert c repeated by n times into the p-th position of S from the beginning.\nAlso it should output, after performing each insert operation, \"Yes\" if S is in the language and \"No\" if S is not in the language.\n\nPlease help Alex to support his study, otherwise he will fail to graduate the college.", "constraint": "", "input": "The first line contains one integer q (1 <= q <= 10^5) indicating the number of queries, follows \nq lines of three elements, p_i, c_i, n_i, separated by a single space (1 <= i <= q, c_i = '(' or ')', \n0 <= p_i <= length of S before i-th query, 1 <= n <= 2^{20}).\nIt is guaranteed that all the queries in the input are valid.", "output": "For each query, output \"Yes\" if S is in the language and \"No\" if S is not in the language.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 ( 10\n10 ) 5\n10 ) 5 \n output: No\nNo\nYes", "input: 3\n0 ) 10\n10 ( 5\n10 ( 5\n output: No\nNo\nYes", "input: 3\n0 ( 10\n10 ) 20\n0 ( 10\n output: No\nNo\nYes"], "Pid": "p01457", "ProblemText": "Task Description: International Carpenters Professionals Company (ICPC) is a top construction company with a lot of expert carpenters.\nWhat makes ICPC a top company is their original language.\n\nThe syntax of the language is simply given in CFG as follows:\n\nS -> SS | (S) | )S( | ε\n\nIn other words, a right parenthesis can be closed by a left parenthesis and a left parenthesis can be closed by a right parenthesis in this language.\n\nAlex, a grad student mastering linguistics, decided to study ICPC's language. \nAs a first step of the study, he needs to judge whether a text is well-formed in the language or not.\nThen, he asked you, a great programmer, to write a program for the judgement.\n\nAlex's request is as follows: You have an empty string S in the beginning, and construct longer string by inserting a sequence of '(' or ')' into the string.\nYou will receive q queries, each of which consists of three elements (p, c, n), where p is \nthe position to insert, n is the number of characters to insert and c is either '(' or ')', the character to insert.\nFor each query, your program should insert c repeated by n times into the p-th position of S from the beginning.\nAlso it should output, after performing each insert operation, \"Yes\" if S is in the language and \"No\" if S is not in the language.\n\nPlease help Alex to support his study, otherwise he will fail to graduate the college.\nTask Input: The first line contains one integer q (1 <= q <= 10^5) indicating the number of queries, follows \nq lines of three elements, p_i, c_i, n_i, separated by a single space (1 <= i <= q, c_i = '(' or ')', \n0 <= p_i <= length of S before i-th query, 1 <= n <= 2^{20}).\nIt is guaranteed that all the queries in the input are valid.\nTask Output: For each query, output \"Yes\" if S is in the language and \"No\" if S is not in the language.\nTask Samples: input: 3\n0 ( 10\n10 ) 5\n10 ) 5 \n output: No\nNo\nYes\ninput: 3\n0 ) 10\n10 ( 5\n10 ( 5\n output: No\nNo\nYes\ninput: 3\n0 ( 10\n10 ) 20\n0 ( 10\n output: No\nNo\nYes\n\n" }, { "title": "Kth Sentence", "content": "A student, Kita_masa, is taking an English examination.\nIn this examination, he has to write a sentence of length m.\n\nSince he completely forgot the English grammar, he decided to consider all sentences of length m constructed by concatenating the words he knows and write the K-th sentence among the candidates sorted in lexicographic order.\nHe believes that it must be the correct sentence because K is today's lucky number for him.\n\nEach word may be used multiple times (or it's also fine not to use it at all) and the sentence does not contain any extra character between words.\nTwo sentences are considered different if the order of the words are different even if the concatenation resulted in the same string.", "constraint": "", "input": "The first line contains three integers n (1 <= n <= 100), m (1 <= m <= 2000) and K (1 <= K <= 10^{18}), separated by a single space.\nEach of the following n lines contains a word that Kita_masa knows.\nThe length of each word is between 1 and 200, inclusive, and the words contain only lowercase letters.\nYou may assume all the words given are distinct.", "output": "Print the K-th (1-based) sentence of length m in lexicographic order.\nIf there is no such a sentence, print \"-\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 10 2\nhello\nworld\n output: helloworld", "input: 3 3 6\na\naa\nb\n output: aba", "input: 2 59 1000000000000000000\na\nb\n output: -"], "Pid": "p01458", "ProblemText": "Task Description: A student, Kita_masa, is taking an English examination.\nIn this examination, he has to write a sentence of length m.\n\nSince he completely forgot the English grammar, he decided to consider all sentences of length m constructed by concatenating the words he knows and write the K-th sentence among the candidates sorted in lexicographic order.\nHe believes that it must be the correct sentence because K is today's lucky number for him.\n\nEach word may be used multiple times (or it's also fine not to use it at all) and the sentence does not contain any extra character between words.\nTwo sentences are considered different if the order of the words are different even if the concatenation resulted in the same string.\nTask Input: The first line contains three integers n (1 <= n <= 100), m (1 <= m <= 2000) and K (1 <= K <= 10^{18}), separated by a single space.\nEach of the following n lines contains a word that Kita_masa knows.\nThe length of each word is between 1 and 200, inclusive, and the words contain only lowercase letters.\nYou may assume all the words given are distinct.\nTask Output: Print the K-th (1-based) sentence of length m in lexicographic order.\nIf there is no such a sentence, print \"-\".\nTask Samples: input: 2 10 2\nhello\nworld\n output: helloworld\ninput: 3 3 6\na\naa\nb\n output: aba\ninput: 2 59 1000000000000000000\na\nb\n output: -\n\n" }, { "title": "A Light Road", "content": "There is an evil creature in a square on N-by-M grid (2 <= N, M <= 100),\nand you want to kill it using a laser generator located in a different square.\nSince the location and direction of the laser generator are fixed,\nyou may need to use several mirrors to reflect laser beams.\nThere are some obstacles on the grid and you have a limited number of mirrors.\nPlease find out whether it is possible to kill the creature,\nand if possible, find the minimum number of mirrors.\n\nThere are two types of single-sided mirrors;\ntype P mirrors can be placed at the angle of 45 or 225 degrees from east-west direction,\nand type Q mirrors can be placed with at the angle of 135 or 315 degrees.\nFor example, four mirrors are located properly, laser go through like the following. \n\nNote that mirrors are single-sided,\nand thus back side (the side with cross in the above picture) is not reflective.\nYou have A type P mirrors, and also A type Q mirrors (0 <= A <= 10).\nAlthough you cannot put mirrors onto the squares with the creature or the laser generator,\nlaser beam can pass through the square.\nEvil creature is killed if the laser reaches the square it is in.", "constraint": "", "input": "Each test case consists of several lines.\n\nThe first line contains three integers, N, M, and A.\nEach of the following N lines contains M characters,\nand represents the grid information.\n'#', '. ', 'S', 'G' indicates obstacle, empty square,\nthe location of the laser generator, and the location of the evil creature, respectively.\nThe first line shows the information in northernmost squares\nand the last line shows the information in southernmost squares.\n You can assume that there is exactly one laser generator and exactly one creature,\nand the laser generator emits laser beam always toward the south.", "output": "Output the minimum number of mirrors used if you can kill creature, or -1 otherwise.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3 2\nS#.\n...\n.#G\n output: 2", "input: 3 3 1\nS#.\n...\n.#G\n output: -1", "input: 3 3 1\nS#G\n...\n.#.\n output: 2", "input: 4 3 2\nS..\n...\n..#\n.#G\n output: -1"], "Pid": "p01459", "ProblemText": "Task Description: There is an evil creature in a square on N-by-M grid (2 <= N, M <= 100),\nand you want to kill it using a laser generator located in a different square.\nSince the location and direction of the laser generator are fixed,\nyou may need to use several mirrors to reflect laser beams.\nThere are some obstacles on the grid and you have a limited number of mirrors.\nPlease find out whether it is possible to kill the creature,\nand if possible, find the minimum number of mirrors.\n\nThere are two types of single-sided mirrors;\ntype P mirrors can be placed at the angle of 45 or 225 degrees from east-west direction,\nand type Q mirrors can be placed with at the angle of 135 or 315 degrees.\nFor example, four mirrors are located properly, laser go through like the following. \n\nNote that mirrors are single-sided,\nand thus back side (the side with cross in the above picture) is not reflective.\nYou have A type P mirrors, and also A type Q mirrors (0 <= A <= 10).\nAlthough you cannot put mirrors onto the squares with the creature or the laser generator,\nlaser beam can pass through the square.\nEvil creature is killed if the laser reaches the square it is in.\nTask Input: Each test case consists of several lines.\n\nThe first line contains three integers, N, M, and A.\nEach of the following N lines contains M characters,\nand represents the grid information.\n'#', '. ', 'S', 'G' indicates obstacle, empty square,\nthe location of the laser generator, and the location of the evil creature, respectively.\nThe first line shows the information in northernmost squares\nand the last line shows the information in southernmost squares.\n You can assume that there is exactly one laser generator and exactly one creature,\nand the laser generator emits laser beam always toward the south.\nTask Output: Output the minimum number of mirrors used if you can kill creature, or -1 otherwise.\nTask Samples: input: 3 3 2\nS#.\n...\n.#G\n output: 2\ninput: 3 3 1\nS#.\n...\n.#G\n output: -1\ninput: 3 3 1\nS#G\n...\n.#.\n output: 2\ninput: 4 3 2\nS..\n...\n..#\n.#G\n output: -1\n\n" }, { "title": "Matrix Operation", "content": "You are a student looking for a job.\nToday you had an employment examination for an IT company.\nThey asked you to write an efficient program to perform several operations.\nFirst, they showed you an N * N square matrix and a list of operations.\nAll operations but one modify the matrix, and the last operation outputs the character in a specified cell.\nPlease remember that you need to output the final matrix after you finish all the operations.\n\nFollowings are the detail of the operations:\n
    \n
    WR r c v
    (Write operation) write a integer v into the cell (r, c) (1 <= v <= 1,000,000)
    \n
    CP r1 c1 r2 c2
    (Copy operation) copy a character in the cell (r1, c1) into the cell (r2, c2)
    \n
    SR r1 r2
    (Swap Row operation) swap the r1-th row and r2-th row
    \n
    SC c1 c2
    (Swap Column operation) swap the c1-th column and c2-th column
    \n
    RL
    (Rotate Left operation) rotate the whole matrix in counter-clockwise direction by 90 degrees
    \n
    RR
    (Rotate Right operation) rotate the whole matrix in clockwise direction by 90 degrees
    \n
    RH
    (Reflect Horizontal operation) reverse the order of the rows
    \n
    RV
    (Reflect Vertical operation) reverse the order of the columns
    \n
    ", "constraint": "", "input": "First line of each testcase contains nine integers.\nFirst two integers in the line, N and Q, indicate the size of matrix and the number of queries, respectively (1 <= N, Q <= 40,000).\nNext three integers, A B, and C, are coefficients to calculate values in initial matrix (1 <= A, B, C <= 1,000,000),\nand they are used as follows: A_{r, c} = (r * A + c * B) mod C where r and c are row and column indices, respectively (1<= r, c<= N).\nLast four integers, D, E, F, and G, are coefficients to compute the final hash value mentioned in the next section (1 <= D <= E <= N, 1 <= F <= G <= N, E - D <= 1,000, G - F <= 1,000).\nEach of next Q lines contains one operation in the format as described above.", "output": "Output a hash value h computed from the final matrix B by using following pseudo source code.\n\nh <- 314159265\nfor r = D. . . E\n for c = F. . . G\n h <- (31 * h + B_{r, c}) mod 1,000,000,007\n\nwhere \"<-\" is a destructive assignment operator, \"for i = S. . . T\" indicates a loop for i from S to T (both inclusive), and \"mod\" is a remainder operation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 3 6 12 1 2 1 2\nWR 1 1 1\n output: 676573821", "input: 2 1 3 6 12 1 2 1 2\nRL\n output: 676636559", "input: 2 1 3 6 12 1 2 1 2\nRH\n output: 676547189", "input: 39989 6 999983 999979 999961 1 1000 1 1000\nSR 1 39989\nSC 1 39989\nRL\nRH\nRR\nRV\n output: 458797120"], "Pid": "p01460", "ProblemText": "Task Description: You are a student looking for a job.\nToday you had an employment examination for an IT company.\nThey asked you to write an efficient program to perform several operations.\nFirst, they showed you an N * N square matrix and a list of operations.\nAll operations but one modify the matrix, and the last operation outputs the character in a specified cell.\nPlease remember that you need to output the final matrix after you finish all the operations.\n\nFollowings are the detail of the operations:\n
    \n
    WR r c v
    (Write operation) write a integer v into the cell (r, c) (1 <= v <= 1,000,000)
    \n
    CP r1 c1 r2 c2
    (Copy operation) copy a character in the cell (r1, c1) into the cell (r2, c2)
    \n
    SR r1 r2
    (Swap Row operation) swap the r1-th row and r2-th row
    \n
    SC c1 c2
    (Swap Column operation) swap the c1-th column and c2-th column
    \n
    RL
    (Rotate Left operation) rotate the whole matrix in counter-clockwise direction by 90 degrees
    \n
    RR
    (Rotate Right operation) rotate the whole matrix in clockwise direction by 90 degrees
    \n
    RH
    (Reflect Horizontal operation) reverse the order of the rows
    \n
    RV
    (Reflect Vertical operation) reverse the order of the columns
    \n
    \nTask Input: First line of each testcase contains nine integers.\nFirst two integers in the line, N and Q, indicate the size of matrix and the number of queries, respectively (1 <= N, Q <= 40,000).\nNext three integers, A B, and C, are coefficients to calculate values in initial matrix (1 <= A, B, C <= 1,000,000),\nand they are used as follows: A_{r, c} = (r * A + c * B) mod C where r and c are row and column indices, respectively (1<= r, c<= N).\nLast four integers, D, E, F, and G, are coefficients to compute the final hash value mentioned in the next section (1 <= D <= E <= N, 1 <= F <= G <= N, E - D <= 1,000, G - F <= 1,000).\nEach of next Q lines contains one operation in the format as described above.\nTask Output: Output a hash value h computed from the final matrix B by using following pseudo source code.\n\nh <- 314159265\nfor r = D. . . E\n for c = F. . . G\n h <- (31 * h + B_{r, c}) mod 1,000,000,007\n\nwhere \"<-\" is a destructive assignment operator, \"for i = S. . . T\" indicates a loop for i from S to T (both inclusive), and \"mod\" is a remainder operation.\nTask Samples: input: 2 1 3 6 12 1 2 1 2\nWR 1 1 1\n output: 676573821\ninput: 2 1 3 6 12 1 2 1 2\nRL\n output: 676636559\ninput: 2 1 3 6 12 1 2 1 2\nRH\n output: 676547189\ninput: 39989 6 999983 999979 999961 1 1000 1 1000\nSR 1 39989\nSC 1 39989\nRL\nRH\nRR\nRV\n output: 458797120\n\n" }, { "title": "Multi-ending Story", "content": "You are a programmer who loves bishojo games (a sub-genre of dating simulation games).\nA game, which is titled \"I * C * P * C! \" and was released yesterday, has arrived to you just now.\nThis game has multiple endings. When you complete all of those endings, you can get a special figure of the main heroine, Sakuya.\nSo, you want to hurry and play the game!\nBut, let's calm down a bit and think how to complete all of the endings in the shortest time first.\n\nIn fact, you have a special skill that allows you to know the structure of branching points of games.\nBy using the skill, you have found out that all of the branching points in this game are to select two choices \"Yes\" or \"No\", and once a different choice is taken the branched stories flow to different endings; they won't converge any more, like a binary tree.\nYou also noticed that it takes exactly one minute to proceed the game from a branching point to another branching point or to an ending.\nIn addition, you can assume it only takes negligible time to return to the beginning of the game (``reset'') and to play from the beginning to the first branching point. \n\nThe game has an additional feature called \"Quick Save\", which can significantly reduce the playing time for completion.\nThe feature allows you to record the point where you are currently playing and return there at any time later.\nYou can record any number of times, but you can hold only the last recorded point.\nThat is, when you use Quick Save, you overwrite the previous record. If you want to return to the overwritten point, you must play the game from the beginning once again.\n\nWell, let's estimate how long it will take for completing all of the endings in the shortest time.", "constraint": "", "input": "A data set is given in the following format.\n\nThe first line of the data set contains one integer N (2 <= N <= 500{, }000), which denotes the number of the endings in this game.\nThe following N-1 lines describe the branching points.\nThe i-th line describes the branching point of ID number i and contains two integers Yes_i and No_i (i + 1 <= Yes_i, No_i <= N), which denote the ID numbers of the next branching points when you select Yes or No respectively.\nYes_i = N means that you can reach an ending if you select Yes, and so for No_i = N.\nThe branching point with ID 1 is the first branching point.\nThe branching points with ID between 2 and N-1 (inclusive) appear exactly once in Yes_i's and No_i's.", "output": "Print the shortest time in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 3\n4 4\n4 4\n output: 6", "input: 5\n5 2\n3 5\n5 4\n5 5\n output: 8"], "Pid": "p01461", "ProblemText": "Task Description: You are a programmer who loves bishojo games (a sub-genre of dating simulation games).\nA game, which is titled \"I * C * P * C! \" and was released yesterday, has arrived to you just now.\nThis game has multiple endings. When you complete all of those endings, you can get a special figure of the main heroine, Sakuya.\nSo, you want to hurry and play the game!\nBut, let's calm down a bit and think how to complete all of the endings in the shortest time first.\n\nIn fact, you have a special skill that allows you to know the structure of branching points of games.\nBy using the skill, you have found out that all of the branching points in this game are to select two choices \"Yes\" or \"No\", and once a different choice is taken the branched stories flow to different endings; they won't converge any more, like a binary tree.\nYou also noticed that it takes exactly one minute to proceed the game from a branching point to another branching point or to an ending.\nIn addition, you can assume it only takes negligible time to return to the beginning of the game (``reset'') and to play from the beginning to the first branching point. \n\nThe game has an additional feature called \"Quick Save\", which can significantly reduce the playing time for completion.\nThe feature allows you to record the point where you are currently playing and return there at any time later.\nYou can record any number of times, but you can hold only the last recorded point.\nThat is, when you use Quick Save, you overwrite the previous record. If you want to return to the overwritten point, you must play the game from the beginning once again.\n\nWell, let's estimate how long it will take for completing all of the endings in the shortest time.\nTask Input: A data set is given in the following format.\n\nThe first line of the data set contains one integer N (2 <= N <= 500{, }000), which denotes the number of the endings in this game.\nThe following N-1 lines describe the branching points.\nThe i-th line describes the branching point of ID number i and contains two integers Yes_i and No_i (i + 1 <= Yes_i, No_i <= N), which denote the ID numbers of the next branching points when you select Yes or No respectively.\nYes_i = N means that you can reach an ending if you select Yes, and so for No_i = N.\nThe branching point with ID 1 is the first branching point.\nThe branching points with ID between 2 and N-1 (inclusive) appear exactly once in Yes_i's and No_i's.\nTask Output: Print the shortest time in a line.\nTask Samples: input: 4\n2 3\n4 4\n4 4\n output: 6\ninput: 5\n5 2\n3 5\n5 4\n5 5\n output: 8\n\n" }, { "title": "Network Reliability", "content": "An undirected graph is given.\nEach edge of the graph disappears with a constant probability.\nCalculate the probability with which the remained graph is connected.", "constraint": "", "input": "The first line contains three integers N (1 <= N <= 14), M (0 <= M <= 100) and P (0 <= P <= 100), separated by a single space.\nN is the number of the vertices and M is the number of the edges. P is the probability represented by a percentage.\n\nThe following M lines describe the edges.\nEach line contains two integers v_i and u_i (1 <= u_i, v_i <= N).\n(u_i, v_i) indicates the edge that connects the two vertices u_i and v_i.", "output": "Output a line containing the probability with which the remained graph is connected.\nYour program may output an arbitrary number of digits after the decimal point. However, the absolute error should be 10^{-9} or less.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 50\n1 2\n2 3\n3 1\n output: 0.500000000000", "input: 3 3 10\n1 2\n2 3\n3 1\n output: 0.972000000000", "input: 4 5 50\n1 2\n2 3\n3 4\n4 1\n1 3\n output: 0.437500000000"], "Pid": "p01462", "ProblemText": "Task Description: An undirected graph is given.\nEach edge of the graph disappears with a constant probability.\nCalculate the probability with which the remained graph is connected.\nTask Input: The first line contains three integers N (1 <= N <= 14), M (0 <= M <= 100) and P (0 <= P <= 100), separated by a single space.\nN is the number of the vertices and M is the number of the edges. P is the probability represented by a percentage.\n\nThe following M lines describe the edges.\nEach line contains two integers v_i and u_i (1 <= u_i, v_i <= N).\n(u_i, v_i) indicates the edge that connects the two vertices u_i and v_i.\nTask Output: Output a line containing the probability with which the remained graph is connected.\nYour program may output an arbitrary number of digits after the decimal point. However, the absolute error should be 10^{-9} or less.\nTask Samples: input: 3 3 50\n1 2\n2 3\n3 1\n output: 0.500000000000\ninput: 3 3 10\n1 2\n2 3\n3 1\n output: 0.972000000000\ninput: 4 5 50\n1 2\n2 3\n3 4\n4 1\n1 3\n output: 0.437500000000\n\n" }, { "title": "Runaway Domino", "content": "``Domino effect'' is a famous play using dominoes.\nA player sets up a chain of dominoes stood.\nAfter a chain is formed, the player topples one end of the dominoes.\nThe first domino topples the second domino, the second topples the third and so on.\n\nYou are playing domino effect.\nBefore you finish to set up a chain of domino,\na domino block started to topple, unfortunately.\nYou have to stop the toppling as soon as possible.\n\nThe domino chain forms a polygonal line on a two-dimensional coordinate system without self intersections.\nThe toppling starts from a certain point on the domino chain\nand continues toward the both end of the chain.\nIf the toppling starts on an end of the chain, the toppling continue toward the other end.\nThe toppling of a direction stops when you touch the toppling point or the toppling reaches an end of the domino chain.\n\nYou can assume that:\n\n You are a point without volume on the two-dimensional coordinate system.\n\n The toppling stops soon after touching the toppling point.\n\n You can step over the domino chain without toppling it.\nYou will given the form of the domino chain, the starting point of the toppling,\nyour coordinates when the toppling started, the toppling velocity and the your velocity.\nYou are task is to write a program that calculates your optimal move to stop the toppling at the earliest timing and\ncalculates the minimum time to stop the toppling.", "constraint": "", "input": "The first line contains one integer N,\nwhich denotes the number of vertices in the polygonal line of the domino chain (2 <= N <= 1000).\nThen N lines follow, each consists of two integers x_{i} and y_{i},\nwhich denote the coordinates of the i-th vertex (-10,000 <= x, y <= 10000).\nThe next line consists of three integers x_{t}, y_{t} and v_{t},\nwhich denote the coordinates of the starting point and the velocity of the toppling.\nThe last line consists of three integers x_{p}, y_{p} and v_{p},\nwhich denotes the coordinates of you when the toppling started and the velocity (1 <= v_{t} < v_{p} <= 10).\nYou may assume that the starting point of the toppling lies on the polygonal line.", "output": "Print the minimum time to stop the toppling.\nThe output must have a relative or absolute error less than 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0\n15 0\n5 0 1\n10 10 2\n output: 5.0", "input: 3\n-10 0\n0 0\n0 10\n-1 0 1\n3 0 2\n output: 4.072027", "input: 2\n0 0\n10 0\n5 0 1\n9 0 3 \n output: 2.0"], "Pid": "p01463", "ProblemText": "Task Description: ``Domino effect'' is a famous play using dominoes.\nA player sets up a chain of dominoes stood.\nAfter a chain is formed, the player topples one end of the dominoes.\nThe first domino topples the second domino, the second topples the third and so on.\n\nYou are playing domino effect.\nBefore you finish to set up a chain of domino,\na domino block started to topple, unfortunately.\nYou have to stop the toppling as soon as possible.\n\nThe domino chain forms a polygonal line on a two-dimensional coordinate system without self intersections.\nThe toppling starts from a certain point on the domino chain\nand continues toward the both end of the chain.\nIf the toppling starts on an end of the chain, the toppling continue toward the other end.\nThe toppling of a direction stops when you touch the toppling point or the toppling reaches an end of the domino chain.\n\nYou can assume that:\n\n You are a point without volume on the two-dimensional coordinate system.\n\n The toppling stops soon after touching the toppling point.\n\n You can step over the domino chain without toppling it.\nYou will given the form of the domino chain, the starting point of the toppling,\nyour coordinates when the toppling started, the toppling velocity and the your velocity.\nYou are task is to write a program that calculates your optimal move to stop the toppling at the earliest timing and\ncalculates the minimum time to stop the toppling.\nTask Input: The first line contains one integer N,\nwhich denotes the number of vertices in the polygonal line of the domino chain (2 <= N <= 1000).\nThen N lines follow, each consists of two integers x_{i} and y_{i},\nwhich denote the coordinates of the i-th vertex (-10,000 <= x, y <= 10000).\nThe next line consists of three integers x_{t}, y_{t} and v_{t},\nwhich denote the coordinates of the starting point and the velocity of the toppling.\nThe last line consists of three integers x_{p}, y_{p} and v_{p},\nwhich denotes the coordinates of you when the toppling started and the velocity (1 <= v_{t} < v_{p} <= 10).\nYou may assume that the starting point of the toppling lies on the polygonal line.\nTask Output: Print the minimum time to stop the toppling.\nThe output must have a relative or absolute error less than 10^{-6}.\nTask Samples: input: 2\n0 0\n15 0\n5 0 1\n10 10 2\n output: 5.0\ninput: 3\n-10 0\n0 0\n0 10\n-1 0 1\n3 0 2\n output: 4.072027\ninput: 2\n0 0\n10 0\n5 0 1\n9 0 3 \n output: 2.0\n\n" }, { "title": "Sunny Graph", "content": "The Sun is a great heavenly body.\nThe Sun is worshiped by various religions.\nBob loves the Sun and loves any object that is similar to the Sun.\nHe noticed that he can find the shape of the Sun in certain graphs.\nHe calls such graphs \"Sunny\".\n\nWe define the property \"Sunny\" mathematically.\nA graph G=(V, E) with a vertex v \\in V is called \"Sunny\" when there exists a subgraph G'=(V, E'), E' \\subseteq E that has the following two properties.\n(Be careful, the set of vertices must be the same. )\n\n1. The connected component containing v is a cycle that consists of three or more vertices.\n\n2. Every other component has exactly two vertices.\n\nThe following picture is an example of a subgraph G'=(V, E') that has the above property.\n\nGiven a simple graph (In each edge, two end points are different. Every pair of vertices has one or no edge. ) G=(V, E),\nwrite a program that decides whether the given graph with the vertex 1 is \"Sunny\" or not.", "constraint": "", "input": "The first line contains two integers N (odd, 1 <= N <= 200) and M (0 <= M <= 20,000), separated by a single space.\nN is the number of the vertices and M is the number of the edges.\n\nThe following M lines describe the edges. Each line contains two integers v_i and u_i (1 <= u_i, v_i <= N).\n(u_i, v_i) indicates the edge that connects the two vertices u_i and v_i.\nu_i and v_i are different, and every pair (u_i, v_i) are different.", "output": "Print a line containing \"Yes\" when the graph is \"Sunny\". Otherwise, print \"No\".", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 5\n1 2\n2 3\n3 4\n4 5\n1 3\n output: Yes", "input: 5 5\n1 2\n2 3\n3 4\n4 5\n1 4\n output: No"], "Pid": "p01464", "ProblemText": "Task Description: The Sun is a great heavenly body.\nThe Sun is worshiped by various religions.\nBob loves the Sun and loves any object that is similar to the Sun.\nHe noticed that he can find the shape of the Sun in certain graphs.\nHe calls such graphs \"Sunny\".\n\nWe define the property \"Sunny\" mathematically.\nA graph G=(V, E) with a vertex v \\in V is called \"Sunny\" when there exists a subgraph G'=(V, E'), E' \\subseteq E that has the following two properties.\n(Be careful, the set of vertices must be the same. )\n\n1. The connected component containing v is a cycle that consists of three or more vertices.\n\n2. Every other component has exactly two vertices.\n\nThe following picture is an example of a subgraph G'=(V, E') that has the above property.\n\nGiven a simple graph (In each edge, two end points are different. Every pair of vertices has one or no edge. ) G=(V, E),\nwrite a program that decides whether the given graph with the vertex 1 is \"Sunny\" or not.\nTask Input: The first line contains two integers N (odd, 1 <= N <= 200) and M (0 <= M <= 20,000), separated by a single space.\nN is the number of the vertices and M is the number of the edges.\n\nThe following M lines describe the edges. Each line contains two integers v_i and u_i (1 <= u_i, v_i <= N).\n(u_i, v_i) indicates the edge that connects the two vertices u_i and v_i.\nu_i and v_i are different, and every pair (u_i, v_i) are different.\nTask Output: Print a line containing \"Yes\" when the graph is \"Sunny\". Otherwise, print \"No\".\nTask Samples: input: 5 5\n1 2\n2 3\n3 4\n4 5\n1 3\n output: Yes\ninput: 5 5\n1 2\n2 3\n3 4\n4 5\n1 4\n output: No\n\n" }, { "title": "Testing Circuits", "content": "A Boolean expression is given.\nIn the expression, each variable appears exactly once.\nCalculate the number of variable assignments that make the expression evaluate to true.", "constraint": "", "input": "A data set consists of only one line.\nThe Boolean expression is given by a string which consists of digits, x, (, ), |, &, and ~.\nOther characters such as spaces are not contained.\nThe expression never exceeds 1,000,000 characters.\nThe grammar of the expressions is given by the following BNF.\n\n : : = | \"|\" \n : : = | \"&\" \n : : = | \"~\" | \"(\" \")\"\n : : = \"x\" \n : : = \"1\" | \"2\" |. . . | \"999999\" | \"1000000\"\n\nThe expression obeys this syntax and thus you do not have to care about grammatical errors.\nWhen the expression contains N variables, each variable in {x1, x2, . . . , x N} appears exactly once.", "output": "Output a line containing the number of variable assignments that make the expression evaluate to true in modulo 1,000,000,007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: (x1&x2)\n output: 1", "input: (x1&x2)|(x3&x4)|(~(x5|x6)&(x7&x8))\n output: 121"], "Pid": "p01465", "ProblemText": "Task Description: A Boolean expression is given.\nIn the expression, each variable appears exactly once.\nCalculate the number of variable assignments that make the expression evaluate to true.\nTask Input: A data set consists of only one line.\nThe Boolean expression is given by a string which consists of digits, x, (, ), |, &, and ~.\nOther characters such as spaces are not contained.\nThe expression never exceeds 1,000,000 characters.\nThe grammar of the expressions is given by the following BNF.\n\n : : = | \"|\" \n : : = | \"&\" \n : : = | \"~\" | \"(\" \")\"\n : : = \"x\" \n : : = \"1\" | \"2\" |. . . | \"999999\" | \"1000000\"\n\nThe expression obeys this syntax and thus you do not have to care about grammatical errors.\nWhen the expression contains N variables, each variable in {x1, x2, . . . , x N} appears exactly once.\nTask Output: Output a line containing the number of variable assignments that make the expression evaluate to true in modulo 1,000,000,007.\nTask Samples: input: (x1&x2)\n output: 1\ninput: (x1&x2)|(x3&x4)|(~(x5|x6)&(x7&x8))\n output: 121\n\n" }, { "title": "World Trip", "content": "Kita_masa is planning a trip around the world.\nThis world has N countries and the country i has M_i cities.\nKita_masa wants to visit every city exactly once, and return back to the starting city.\n\nIn this world, people can travel only by airplane.\nThere are two kinds of airlines: domestic and international lines.\nSince international airports require special facilities such as customs and passport control,\nonly a few cities in each country have international airports.\n\nYou are given a list of all flight routes in this world and prices for each route.\nNow it's time to calculate the cheapest route for Kita_masa's world trip!", "constraint": "", "input": "The first line contains two integers N and K, which represent the number of countries and the number of flight routes, respectively.\nThe second line contains N integers, and the i-th integer M_i represents the number of cities in the country i.\nThe third line contains N integers too, and the i-th integer F_i represents the number of international airports in the country i.\nEach of the following K lines contains five integers [Country 1] [City 1] [Country 2] [City 2] [Price].\nThis means that, there is a bi-directional flight route between the [City 1] in [Country 1] and the [City 2] in [Country 2], and its price is [Price].\n\nNote that cities in each country are numbered from 1, and the cities whose city number is smaller or equal to F_i have international airports.\nThat is, if there is a flight route between the city c_1 in the country n_1 and the city c_2 in the country n_2 with n_1 \\neq n_2, it must be c_1 <= F_{n_1} and c_2 <= F_{n_2}.\nYou can assume that there's no flight route which departs from one city and flies back to the same city, and that at most one flight route exists in this world for each pair of cities.\n\nThe following constraints hold for each dataset:\n\n 1 <= N <= 15\n\n 1 <= M_i <= 15\n\n 1 <= F_i <= 4\n\n sum(F_i) <= 15\n\n 1 <= Price <= 10,000", "output": "Print a line that contains a single integer representing the minimum price to make a world trip.\n\nIf such a trip is impossible, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n1 1 1 1\n1 1 1 1\n1 1 2 1 1\n1 1 3 1 2\n1 1 4 1 1\n2 1 3 1 1\n2 1 4 1 2\n3 1 4 1 1\n output: 4", "input: 2 16\n4 4\n2 2\n1 1 1 2 1\n1 1 1 3 2\n1 1 1 4 1\n1 2 1 3 1\n1 2 1 4 2\n1 3 1 4 1\n2 1 2 2 1\n2 1 2 3 2\n2 1 2 4 1\n2 2 2 3 1\n2 2 2 4 2\n2 3 2 4 1\n1 1 2 1 1\n1 1 2 2 2\n1 2 2 1 2\n1 2 2 2 1\n output: 8", "input: 2 2\n2 1\n1 1\n1 1 1 2 1\n1 1 2 1 1\n output: -1"], "Pid": "p01466", "ProblemText": "Task Description: Kita_masa is planning a trip around the world.\nThis world has N countries and the country i has M_i cities.\nKita_masa wants to visit every city exactly once, and return back to the starting city.\n\nIn this world, people can travel only by airplane.\nThere are two kinds of airlines: domestic and international lines.\nSince international airports require special facilities such as customs and passport control,\nonly a few cities in each country have international airports.\n\nYou are given a list of all flight routes in this world and prices for each route.\nNow it's time to calculate the cheapest route for Kita_masa's world trip!\nTask Input: The first line contains two integers N and K, which represent the number of countries and the number of flight routes, respectively.\nThe second line contains N integers, and the i-th integer M_i represents the number of cities in the country i.\nThe third line contains N integers too, and the i-th integer F_i represents the number of international airports in the country i.\nEach of the following K lines contains five integers [Country 1] [City 1] [Country 2] [City 2] [Price].\nThis means that, there is a bi-directional flight route between the [City 1] in [Country 1] and the [City 2] in [Country 2], and its price is [Price].\n\nNote that cities in each country are numbered from 1, and the cities whose city number is smaller or equal to F_i have international airports.\nThat is, if there is a flight route between the city c_1 in the country n_1 and the city c_2 in the country n_2 with n_1 \\neq n_2, it must be c_1 <= F_{n_1} and c_2 <= F_{n_2}.\nYou can assume that there's no flight route which departs from one city and flies back to the same city, and that at most one flight route exists in this world for each pair of cities.\n\nThe following constraints hold for each dataset:\n\n 1 <= N <= 15\n\n 1 <= M_i <= 15\n\n 1 <= F_i <= 4\n\n sum(F_i) <= 15\n\n 1 <= Price <= 10,000\nTask Output: Print a line that contains a single integer representing the minimum price to make a world trip.\n\nIf such a trip is impossible, print -1 instead.\nTask Samples: input: 4 6\n1 1 1 1\n1 1 1 1\n1 1 2 1 1\n1 1 3 1 2\n1 1 4 1 1\n2 1 3 1 1\n2 1 4 1 2\n3 1 4 1 1\n output: 4\ninput: 2 16\n4 4\n2 2\n1 1 1 2 1\n1 1 1 3 2\n1 1 1 4 1\n1 2 1 3 1\n1 2 1 4 2\n1 3 1 4 1\n2 1 2 2 1\n2 1 2 3 2\n2 1 2 4 1\n2 2 2 3 1\n2 2 2 4 2\n2 3 2 4 1\n1 1 2 1 1\n1 1 2 2 2\n1 2 2 1 2\n1 2 2 2 1\n output: 8\ninput: 2 2\n2 1\n1 1\n1 1 1 2 1\n1 1 2 1 1\n output: -1\n\n" }, { "title": "Problem A: Bicube", "content": "Mary Thomas has a number of sheets of squared paper. Some of squares are painted either in black or some colorful color (such as red and blue) on the front side. Cutting off the unpainted part, she will have eight opened-up unit cubes. A unit cube here refers to a cube of which each face consists of one square.\n\nShe is going to build those eight unit cubes with the front side exposed and then a bicube with them. A bicube is a cube of the size 2 * 2 * 2, consisting of eight unit cubes, that satisfies the following conditions:\n\n faces of the unit cubes that comes to the inside of the bicube are all black;\n\n each face of the bicube has a uniform colorful color; and\n\n the faces of the bicube have colors all different.\nYour task is to write a program that reads the specification of a sheet of squared paper and decides whether a\nbicube can be built with the eight unit cubes resulting from it.", "constraint": "", "input": "The input contains the specification of a sheet. The first line contains two integers H and W, which denote the height and width of the sheet (3 <= H, W <= 50). Then H lines follow, each consisting of W characters. These lines show the squares on the front side of the sheet. A character represents the color of a grid: alphabets and digits ('A' to 'Z', 'a' to 'z', '0' to '9') for colorful squares, a hash ('#') for a black square, and a dot ('. ') for an unpainted square. Each alphabet or digit denotes a unique color: squares have the same color if and only if they are represented by the same character.\n\nEach component of connected squares forms one opened-up cube. Squares are regarded as connected when they have a common edge; those just with a common vertex are not.", "output": "Print \"Yes\" if a bicube can be built with the given sheet; \"No\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 40\n.a....a....a....a....f....f....f....f...\n#bc#.#cd#.#de#.#eb#.#cb#.#dc#.#ed#.#be#.\n.#....#....#....#....#....#....#....#...\n output: Yes", "input: 5 35\n.a....a....a....a....f....f....f...\n#bc#.#cd#.#de#.#eb#.#cb#.#dc#.#ed#.\n.#..f.#....#....#....#....#....#...\n..e##..............................\n.b#................................\n output: Yes", "input: 3 40\n.a....a....a....a....f....f....f....f...\n#bc#.#cd#.#de#.#eb#.#cb#.#dc#.#ed#.#eb#.\n.#....#....#....#....#....#....#....#...\n output: No"], "Pid": "p01496", "ProblemText": "Task Description: Mary Thomas has a number of sheets of squared paper. Some of squares are painted either in black or some colorful color (such as red and blue) on the front side. Cutting off the unpainted part, she will have eight opened-up unit cubes. A unit cube here refers to a cube of which each face consists of one square.\n\nShe is going to build those eight unit cubes with the front side exposed and then a bicube with them. A bicube is a cube of the size 2 * 2 * 2, consisting of eight unit cubes, that satisfies the following conditions:\n\n faces of the unit cubes that comes to the inside of the bicube are all black;\n\n each face of the bicube has a uniform colorful color; and\n\n the faces of the bicube have colors all different.\nYour task is to write a program that reads the specification of a sheet of squared paper and decides whether a\nbicube can be built with the eight unit cubes resulting from it.\nTask Input: The input contains the specification of a sheet. The first line contains two integers H and W, which denote the height and width of the sheet (3 <= H, W <= 50). Then H lines follow, each consisting of W characters. These lines show the squares on the front side of the sheet. A character represents the color of a grid: alphabets and digits ('A' to 'Z', 'a' to 'z', '0' to '9') for colorful squares, a hash ('#') for a black square, and a dot ('. ') for an unpainted square. Each alphabet or digit denotes a unique color: squares have the same color if and only if they are represented by the same character.\n\nEach component of connected squares forms one opened-up cube. Squares are regarded as connected when they have a common edge; those just with a common vertex are not.\nTask Output: Print \"Yes\" if a bicube can be built with the given sheet; \"No\" otherwise.\nTask Samples: input: 3 40\n.a....a....a....a....f....f....f....f...\n#bc#.#cd#.#de#.#eb#.#cb#.#dc#.#ed#.#be#.\n.#....#....#....#....#....#....#....#...\n output: Yes\ninput: 5 35\n.a....a....a....a....f....f....f...\n#bc#.#cd#.#de#.#eb#.#cb#.#dc#.#ed#.\n.#..f.#....#....#....#....#....#...\n..e##..............................\n.b#................................\n output: Yes\ninput: 3 40\n.a....a....a....a....f....f....f....f...\n#bc#.#cd#.#de#.#eb#.#cb#.#dc#.#ed#.#eb#.\n.#....#....#....#....#....#....#....#...\n output: No\n\n" }, { "title": "Problem B: Bubble Puzzle", "content": "A browser-based puzzle game called \"Bubble Puzzle\" is now popular on the Internet. \n\nThe puzzle is played on a 4 * 4 grid, and initially there are several bubbles in the grid squares. Each bubble has a state expressed by a positive integer, and the state changes when the bubble gets stimulated. You can stimulate a bubble by clicking on it, and this will increase the bubble's state by 1. You can also click on an empty square. In this case, a bubble with state 1 is newly created in the square.\n\nWhen the state of a bubble becomes 5 or higher, the bubble blows up and disappears, and small waterdrops start flying in four directions (up, down, left and right). These waterdrops move one square per second. At the moment when a bubble blows up, 4 waterdrops are in the square the bubble was in, and one second later they are in the adjacent squares, and so on.\n\nA waterdrop disappears either when it hits a bubble or goes outside the grid. When a waterdrop hits a bubble, the state of the bubble gets increased by 1. Similarly, if a bubble is hit by more than one water drop at the same time, its state is increased by the number of the hitting waterdrops. Please note that waterdrops do not collide with each other.\n\nAs shown in the figure above, waterdrops created by a blow-up may cause other blow-ups. In other words, one blow-up can trigger a chain reaction. You are not allowed to click on any square while waterdrops are flying (i. e. , you have to wait until a chain reaction ends). The goal of this puzzle is to blow up all the bubbles and make all the squares empty as quick as possible.\n\nYour mission is to calculate the minimum number of clicks required to solve the puzzle.", "constraint": "", "input": "The input consists of 4 lines, each contains 4 nonnegative integers smaller than 5. Each integer describes the initial states of bubbles on grid squares. 0 indicates that the corresponding square is empty.", "output": "Output the minimum number of clicks to blow up all the bubbles on the grid in a line. If the answer is bigger than 5, output -1 instead. No extra characters should appear in the output.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 4 4 4\n4 4 4 4\n4 4 4 4\n4 4 4 4\n output: 1", "input: 2 4 4 1\n2 4 4 1\n2 4 4 1\n2 4 4 1\n output: 5", "input: 2 4 3 4\n2 2 4 4\n3 3 2 2\n2 3 3 3\n output: 3"], "Pid": "p01497", "ProblemText": "Task Description: A browser-based puzzle game called \"Bubble Puzzle\" is now popular on the Internet. \n\nThe puzzle is played on a 4 * 4 grid, and initially there are several bubbles in the grid squares. Each bubble has a state expressed by a positive integer, and the state changes when the bubble gets stimulated. You can stimulate a bubble by clicking on it, and this will increase the bubble's state by 1. You can also click on an empty square. In this case, a bubble with state 1 is newly created in the square.\n\nWhen the state of a bubble becomes 5 or higher, the bubble blows up and disappears, and small waterdrops start flying in four directions (up, down, left and right). These waterdrops move one square per second. At the moment when a bubble blows up, 4 waterdrops are in the square the bubble was in, and one second later they are in the adjacent squares, and so on.\n\nA waterdrop disappears either when it hits a bubble or goes outside the grid. When a waterdrop hits a bubble, the state of the bubble gets increased by 1. Similarly, if a bubble is hit by more than one water drop at the same time, its state is increased by the number of the hitting waterdrops. Please note that waterdrops do not collide with each other.\n\nAs shown in the figure above, waterdrops created by a blow-up may cause other blow-ups. In other words, one blow-up can trigger a chain reaction. You are not allowed to click on any square while waterdrops are flying (i. e. , you have to wait until a chain reaction ends). The goal of this puzzle is to blow up all the bubbles and make all the squares empty as quick as possible.\n\nYour mission is to calculate the minimum number of clicks required to solve the puzzle.\nTask Input: The input consists of 4 lines, each contains 4 nonnegative integers smaller than 5. Each integer describes the initial states of bubbles on grid squares. 0 indicates that the corresponding square is empty.\nTask Output: Output the minimum number of clicks to blow up all the bubbles on the grid in a line. If the answer is bigger than 5, output -1 instead. No extra characters should appear in the output.\nTask Samples: input: 4 4 4 4\n4 4 4 4\n4 4 4 4\n4 4 4 4\n output: 1\ninput: 2 4 4 1\n2 4 4 1\n2 4 4 1\n2 4 4 1\n output: 5\ninput: 2 4 3 4\n2 2 4 4\n3 3 2 2\n2 3 3 3\n output: 3\n\n" }, { "title": "Problem D: King Slime", "content": "There is a grid of size W * H surrounded by walls. Some cells in the grid are occupied by slimes. The slimes want to unite with each other and become a \"King Slime\".\n\nIn each move, a slime can move to east, west, south and north direction until it enters a cell occupied by another slime or hit the surrounding wall. If two slimes come together, they unite and become a new slime.\n\nYour task is write a program which calculates the minimum number of moves that all the slimes unite and become a King Slime. Suppose slimes move one by one and they never move simultaneously.", "constraint": "", "input": "The first line contains three integers N (2 <= N <= 40,000), W and H (1 <= W, H <= 100,000), which denote the\nnumber of slimes, the width and the height of the grid respectively.\n\nThe following N lines describe the initial coordinates of the slimes. The i-th line contains two integers x_i (1 <= x_i <= W) and y_i (1 <= y_i <= H), which indicate the coordinates of the i-th slime . All the coordinates are 1-based.\n\nYou may assume that each cell is occupied by at most one slime initially.", "output": "Output the minimum number of moves that all the slimes unite and become a King Slime.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 3\n1 1\n1 3\n3 1\n3 3\n output: 3", "input: 2 3 3\n2 2\n3 3\n output: 2", "input: 2 4 4\n2 2\n3 3\n output: 3", "input: 2 4 4\n2 2\n2 3\n output: 1"], "Pid": "p01498", "ProblemText": "Task Description: There is a grid of size W * H surrounded by walls. Some cells in the grid are occupied by slimes. The slimes want to unite with each other and become a \"King Slime\".\n\nIn each move, a slime can move to east, west, south and north direction until it enters a cell occupied by another slime or hit the surrounding wall. If two slimes come together, they unite and become a new slime.\n\nYour task is write a program which calculates the minimum number of moves that all the slimes unite and become a King Slime. Suppose slimes move one by one and they never move simultaneously.\nTask Input: The first line contains three integers N (2 <= N <= 40,000), W and H (1 <= W, H <= 100,000), which denote the\nnumber of slimes, the width and the height of the grid respectively.\n\nThe following N lines describe the initial coordinates of the slimes. The i-th line contains two integers x_i (1 <= x_i <= W) and y_i (1 <= y_i <= H), which indicate the coordinates of the i-th slime . All the coordinates are 1-based.\n\nYou may assume that each cell is occupied by at most one slime initially.\nTask Output: Output the minimum number of moves that all the slimes unite and become a King Slime.\nTask Samples: input: 4 3 3\n1 1\n1 3\n3 1\n3 3\n output: 3\ninput: 2 3 3\n2 2\n3 3\n output: 2\ninput: 2 4 4\n2 2\n3 3\n output: 3\ninput: 2 4 4\n2 2\n2 3\n output: 1\n\n" }, { "title": "Problem E: Rabbit Game Playing", "content": "Honestly, a rabbit does not matter.\n\nThere is a rabbit playing a stage system action game. In this game, every stage has a difficulty level. The rabbit, which always needs challenges, basically wants to play more difficult stages than he has ever played. However, he sometimes needs rest too. So, to compromise, he admitted to play T or less levels easier stages than the preceding one.\n\nHow many ways are there to play all the stages at once, while honoring the convention above? Maybe the answer will be a large number. So, let me know the answer modulo 1,000,000,007.", "constraint": "", "input": "The first line of input contains two integers N and T (1 <= N <= 100,000,1 <= T <= 10,000). N is the number of stages, and T is the compromise level.\n\nThe following N lines describe the difficulty levels of each stage. The i-th line contains one integer D_i (1 <= D_i <= 100,000), which is the difficulty level of the i-th stage.", "output": "Calculate how many ways to play all the stages at once there are. Print the answer modulo 1,000,000,007 in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1\n2\n3\n output: 4", "input: 5 3\n9\n2\n6\n8\n8\n output: 24", "input: 5 7\n9\n9\n9\n1\n5\n output: 48"], "Pid": "p01499", "ProblemText": "Task Description: Honestly, a rabbit does not matter.\n\nThere is a rabbit playing a stage system action game. In this game, every stage has a difficulty level. The rabbit, which always needs challenges, basically wants to play more difficult stages than he has ever played. However, he sometimes needs rest too. So, to compromise, he admitted to play T or less levels easier stages than the preceding one.\n\nHow many ways are there to play all the stages at once, while honoring the convention above? Maybe the answer will be a large number. So, let me know the answer modulo 1,000,000,007.\nTask Input: The first line of input contains two integers N and T (1 <= N <= 100,000,1 <= T <= 10,000). N is the number of stages, and T is the compromise level.\n\nThe following N lines describe the difficulty levels of each stage. The i-th line contains one integer D_i (1 <= D_i <= 100,000), which is the difficulty level of the i-th stage.\nTask Output: Calculate how many ways to play all the stages at once there are. Print the answer modulo 1,000,000,007 in a line.\nTask Samples: input: 3 1\n1\n2\n3\n output: 4\ninput: 5 3\n9\n2\n6\n8\n8\n output: 24\ninput: 5 7\n9\n9\n9\n1\n5\n output: 48\n\n" }, { "title": "Problem F:\nRabbit Jumping", "content": "There are $K$ rabbits playing on rocks floating in a river. They got tired of playing on the rocks on which they are standing currently, and they decided to move to other rocks. This seemed an easy task initially, but there are so many constraints that they got totally confused.\n\n First of all, by one leap, they can only move to a rock within $R$ meters from the current rock. Also, they can never leap over rocks. That is, when they leap in some direction, they should land on the nearest rock in that direction. Furthermore, since they always want to show off that they are courageous, they will never leap to rocks downriver. Finally, since they never want to admit they have been defeated, they never land on a rock if the rock is already visited by other rabbits.\n\n In this situation, is it possible for them to move to their destination rocks? If possible, please minimize the sum of their moving distance.", "constraint": "", "input": "The first line contains two integers $N$ ($1 <= N <= 100$), $K$ ($1 <= K <= 3$) and a real number $R$ ($0 <= R <= 10^4$), which denote the number of rocks, the number of rabbits, and the maximum distance a rabbit can leap, respectively. The second line contains $K$ numbers $s_1, . . . , s_K$ where $s_i$ denote the rock where the $i$-th rabbit is standing. Similarly, the third line contains $K$ numbers $t_1, . . . , t_K$ where $t_i$ denote the destination rock for the $i$-th rabbit. $s_1, . . . , s_K$ are distinct, and $t_1, . . . , t_K$ are distinct. A destination rock of a rabbit is always different from the rock he/she is standing currently.\n\n Then the following $N$ lines describe the positions of the rocks. The $i$-th line in this block contains two integers $x_i$ and $y_i$ ($0 <= x_i, y_i <= 10,000$), which indicate the coordinates of the $i$-th rock. The river flows along Y-axis, toward the direction where Y-coordinate decreases. No pair of rocks has identical coordinates.\n\nYou may assume that the answer do not change even if you increase $R$ by up to $10^{-5}$.", "output": "If all the rabbits can move to their destination rocks, print the minimum total distance they need to leap. If not, print \"-1\" (without quotes). Your answer may contain at most $10^{-6}$ of absolute error.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3 1.0\n1 2 3\n4 5 6\n0 0\n1 0\n2 0\n0 1\n1 1\n2 1\n output: 3"], "Pid": "p01500", "ProblemText": "Task Description: There are $K$ rabbits playing on rocks floating in a river. They got tired of playing on the rocks on which they are standing currently, and they decided to move to other rocks. This seemed an easy task initially, but there are so many constraints that they got totally confused.\n\n First of all, by one leap, they can only move to a rock within $R$ meters from the current rock. Also, they can never leap over rocks. That is, when they leap in some direction, they should land on the nearest rock in that direction. Furthermore, since they always want to show off that they are courageous, they will never leap to rocks downriver. Finally, since they never want to admit they have been defeated, they never land on a rock if the rock is already visited by other rabbits.\n\n In this situation, is it possible for them to move to their destination rocks? If possible, please minimize the sum of their moving distance.\nTask Input: The first line contains two integers $N$ ($1 <= N <= 100$), $K$ ($1 <= K <= 3$) and a real number $R$ ($0 <= R <= 10^4$), which denote the number of rocks, the number of rabbits, and the maximum distance a rabbit can leap, respectively. The second line contains $K$ numbers $s_1, . . . , s_K$ where $s_i$ denote the rock where the $i$-th rabbit is standing. Similarly, the third line contains $K$ numbers $t_1, . . . , t_K$ where $t_i$ denote the destination rock for the $i$-th rabbit. $s_1, . . . , s_K$ are distinct, and $t_1, . . . , t_K$ are distinct. A destination rock of a rabbit is always different from the rock he/she is standing currently.\n\n Then the following $N$ lines describe the positions of the rocks. The $i$-th line in this block contains two integers $x_i$ and $y_i$ ($0 <= x_i, y_i <= 10,000$), which indicate the coordinates of the $i$-th rock. The river flows along Y-axis, toward the direction where Y-coordinate decreases. No pair of rocks has identical coordinates.\n\nYou may assume that the answer do not change even if you increase $R$ by up to $10^{-5}$.\nTask Output: If all the rabbits can move to their destination rocks, print the minimum total distance they need to leap. If not, print \"-1\" (without quotes). Your answer may contain at most $10^{-6}$ of absolute error.\nTask Samples: input: 6 3 1.0\n1 2 3\n4 5 6\n0 0\n1 0\n2 0\n0 1\n1 1\n2 1\n output: 3\n\n" }, { "title": "Problem G:\nShelter", "content": "Taro lives in a town with N shelters. The shape of the town is a convex polygon.\n\n He'll escape to the nearest shelter in case of emergency. Given the current location, the cost of escape is defined as the square of the distance to the nearest shelter. Because emergency occurs unpredictably, Taro can be at any point inside the town with the same probability. Calculate the expected cost of his escape.", "constraint": "", "input": "The first line contains two integers $M$ and $N$ ($3 <= M <= 100, 1 <= N <= 100$), which denote the number of vertices of the town and the number of shelters respectively.\n\n The following $M$ lines describe the coordinates of the vertices of the town in the conunter-clockwise order. The $i$-th line contains two integers $x_i$ and $y_i$ ($-1000 <= x_i, y_i <= 1000$), which indicate the coordinates of the $i$-th vertex. You may assume the polygon is always simple, that is, the edges do not touch or cross each other except for the end points.\n\n Then the following $N$ lines describe the coordinates of the shelters. The $i$-th line contains two integers $x_i$ and $y_i$, which indicate the coordinates of the $i$-th shelter. You may assume that every shelter is strictly inside the town and any two shelters do not have same coordinates.", "output": "Output the expected cost in a line. The answer with an absolute error of less than or equal to $10^{-4}$ is considered to be correct.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1\n0 0\n3 0\n3 3\n0 3\n1 1\n output: 2.0000000000", "input: 5 2\n2 0\n2 2\n0 2\n-2 0\n0 -2\n0 0\n1 1\n output: 1.0000000000", "input: 4 3\n0 0\n3 0\n3 3\n0 3\n1 1\n1 2\n2 2\n output: 0.7500000000"], "Pid": "p01501", "ProblemText": "Task Description: Taro lives in a town with N shelters. The shape of the town is a convex polygon.\n\n He'll escape to the nearest shelter in case of emergency. Given the current location, the cost of escape is defined as the square of the distance to the nearest shelter. Because emergency occurs unpredictably, Taro can be at any point inside the town with the same probability. Calculate the expected cost of his escape.\nTask Input: The first line contains two integers $M$ and $N$ ($3 <= M <= 100, 1 <= N <= 100$), which denote the number of vertices of the town and the number of shelters respectively.\n\n The following $M$ lines describe the coordinates of the vertices of the town in the conunter-clockwise order. The $i$-th line contains two integers $x_i$ and $y_i$ ($-1000 <= x_i, y_i <= 1000$), which indicate the coordinates of the $i$-th vertex. You may assume the polygon is always simple, that is, the edges do not touch or cross each other except for the end points.\n\n Then the following $N$ lines describe the coordinates of the shelters. The $i$-th line contains two integers $x_i$ and $y_i$, which indicate the coordinates of the $i$-th shelter. You may assume that every shelter is strictly inside the town and any two shelters do not have same coordinates.\nTask Output: Output the expected cost in a line. The answer with an absolute error of less than or equal to $10^{-4}$ is considered to be correct.\nTask Samples: input: 4 1\n0 0\n3 0\n3 3\n0 3\n1 1\n output: 2.0000000000\ninput: 5 2\n2 0\n2 2\n0 2\n-2 0\n0 -2\n0 0\n1 1\n output: 1.0000000000\ninput: 4 3\n0 0\n3 0\n3 3\n0 3\n1 1\n1 2\n2 2\n output: 0.7500000000\n\n" }, { "title": "Problem H:\nSightseeing Tour", "content": "KM city has $N$ sightseeing areas. Currently every pair of area is connected by a bidirectional road.\n\n However for some reason, Mr. KM, the mayor of this city, decided to make all of these roads one-way . It costs $C_{i, j}$ dollars to renovate the road between area $i$ and area $j$ to a one-way road from area $i$ to area $j$. Of course, Mr. KM is economic and wants to minimize the total cost of the renovation.\n\n On the other hand, because tourism is the most important industry for KM city, there must exists a tour that goes through all the sightseeing areas, visiting each area exactly once. The first and last area of the path need not to be the same. Can you calculate the minimum total cost required for the renovation, given this situation?", "constraint": "", "input": "The first line contains the number of sightseeing area $N$ ($1 <= N <= 100$). Next $N$ lines describe the integer matrix $C$, where the $j$-th element of the $i$-th row of the input describes $C_{i, j}$ ($0 <= C_{i, j} <= 1,000,000$). For each $i$, you can assume $C_{i, i}$ is always zero.", "output": "Output the minimum cost in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 2 7\n2 0 4\n5 8 0\n output: 11"], "Pid": "p01502", "ProblemText": "Task Description: KM city has $N$ sightseeing areas. Currently every pair of area is connected by a bidirectional road.\n\n However for some reason, Mr. KM, the mayor of this city, decided to make all of these roads one-way . It costs $C_{i, j}$ dollars to renovate the road between area $i$ and area $j$ to a one-way road from area $i$ to area $j$. Of course, Mr. KM is economic and wants to minimize the total cost of the renovation.\n\n On the other hand, because tourism is the most important industry for KM city, there must exists a tour that goes through all the sightseeing areas, visiting each area exactly once. The first and last area of the path need not to be the same. Can you calculate the minimum total cost required for the renovation, given this situation?\nTask Input: The first line contains the number of sightseeing area $N$ ($1 <= N <= 100$). Next $N$ lines describe the integer matrix $C$, where the $j$-th element of the $i$-th row of the input describes $C_{i, j}$ ($0 <= C_{i, j} <= 1,000,000$). For each $i$, you can assume $C_{i, i}$ is always zero.\nTask Output: Output the minimum cost in a line.\nTask Samples: input: 3\n0 2 7\n2 0 4\n5 8 0\n output: 11\n\n" }, { "title": "Problem I:\nTampopo Machine", "content": "\"Today is another day of endless, tedious work to put a tampopo on sashimi. . . \"\n\n Yaruo works in a sashimi (sliced raw fish) factory. His job is to put tampopos on sashimi packages everyday. Tired of this menial job, he decided to develop a tampopo machine to do the job instead of him.\n\n The tampopo machine has the following properties. Sashimi packages are put on a conveyor belt and move from left to right. The width of a package is $W$ and the interval between two adjacent packages is $D$. The machine has $N$ magic hands placed above the conveyor belt at regular intervals of $M$. These magic hands put tampopos every $T$ seconds.\n\n In initial state, the right end of the first package is under the leftmost magic hand. The magic hands start putting a tampopo as soon as he turns on the power of the machine. The conveyor belt moves one unit length per one second.\n\n Unfortunately, after building the machine, Yaruo noticed that there exist some packages with no tampopos. Calculate the ratio of packages with no tampopos for him.\n\nWhen a magic hand puts a tampopo on the left or right end of a package, you can assume that the tampopo is on the package.", "constraint": "", "input": "The input consists of 5 integers, $W$, $D$, $N$, $M$ and $T$ which are described in the problem statement. \n \n($1 <= W, D, N, M, T <= 1,000,000,000$)", "output": "Output the ratio of packages with no tampopos in a line. The absolute error should be less than or equal to $10^{-9}$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 1 1 1 1\n output: 0.000000000000", "input: 1 2 3 4 5\n output: 0.200000000000", "input: 3 2 2 1 6\n output: 0.166666666667"], "Pid": "p01503", "ProblemText": "Task Description: \"Today is another day of endless, tedious work to put a tampopo on sashimi. . . \"\n\n Yaruo works in a sashimi (sliced raw fish) factory. His job is to put tampopos on sashimi packages everyday. Tired of this menial job, he decided to develop a tampopo machine to do the job instead of him.\n\n The tampopo machine has the following properties. Sashimi packages are put on a conveyor belt and move from left to right. The width of a package is $W$ and the interval between two adjacent packages is $D$. The machine has $N$ magic hands placed above the conveyor belt at regular intervals of $M$. These magic hands put tampopos every $T$ seconds.\n\n In initial state, the right end of the first package is under the leftmost magic hand. The magic hands start putting a tampopo as soon as he turns on the power of the machine. The conveyor belt moves one unit length per one second.\n\n Unfortunately, after building the machine, Yaruo noticed that there exist some packages with no tampopos. Calculate the ratio of packages with no tampopos for him.\n\nWhen a magic hand puts a tampopo on the left or right end of a package, you can assume that the tampopo is on the package.\nTask Input: The input consists of 5 integers, $W$, $D$, $N$, $M$ and $T$ which are described in the problem statement. \n \n($1 <= W, D, N, M, T <= 1,000,000,000$)\nTask Output: Output the ratio of packages with no tampopos in a line. The absolute error should be less than or equal to $10^{-9}$.\nTask Samples: input: 1 1 1 1 1\n output: 0.000000000000\ninput: 1 2 3 4 5\n output: 0.200000000000\ninput: 3 2 2 1 6\n output: 0.166666666667\n\n" }, { "title": "AYBABTU", "content": "There is a tree that has n nodes and n-1 edges.\nThere are military bases on t out of the n nodes.\nWe want to disconnect the bases as much as possible by destroying k edges.\nThe tree will be split into k+1 regions when we destroy k edges.\nGiven the purpose to disconnect the bases, we only consider to split in a way that each of these k+1 regions has at least one base.\nWhen we destroy an edge, we must pay destroying cost.\nFind the minimum destroying cost to split the tree.", "constraint": "", "input": "The input consists of multiple data sets.\nEach data set has the following format.\nThe first line consists of three integers n, t, and k (1 <= n <= 10,000,1 <= t <= n, 0 <= k <= t-1).\nEach of the next n-1 lines consists of three integers representing an edge.\nThe first two integers represent node numbers connected by the edge.\nA node number is a positive integer less than or equal to n.\nThe last one integer represents destroying cost.\nDestroying cost is a non-negative integer less than or equal to 10,000.\nThe next t lines contain a distinct list of integers one in each line, and represent the list of nodes with bases.\nThe input ends with a line containing three zeros, which should not be processed.", "output": "For each test case, print its case number and the minimum destroying cost to split the tree with the case number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 1\n1 2 1\n1\n2\n4 3 2\n1 2 1\n1 3 2\n1 4 3\n2\n3\n4\n0 0 0\n output: Case 1: 1\nCase 2: 3"], "Pid": "p01504", "ProblemText": "Task Description: There is a tree that has n nodes and n-1 edges.\nThere are military bases on t out of the n nodes.\nWe want to disconnect the bases as much as possible by destroying k edges.\nThe tree will be split into k+1 regions when we destroy k edges.\nGiven the purpose to disconnect the bases, we only consider to split in a way that each of these k+1 regions has at least one base.\nWhen we destroy an edge, we must pay destroying cost.\nFind the minimum destroying cost to split the tree.\nTask Input: The input consists of multiple data sets.\nEach data set has the following format.\nThe first line consists of three integers n, t, and k (1 <= n <= 10,000,1 <= t <= n, 0 <= k <= t-1).\nEach of the next n-1 lines consists of three integers representing an edge.\nThe first two integers represent node numbers connected by the edge.\nA node number is a positive integer less than or equal to n.\nThe last one integer represents destroying cost.\nDestroying cost is a non-negative integer less than or equal to 10,000.\nThe next t lines contain a distinct list of integers one in each line, and represent the list of nodes with bases.\nThe input ends with a line containing three zeros, which should not be processed.\nTask Output: For each test case, print its case number and the minimum destroying cost to split the tree with the case number.\nTask Samples: input: 2 2 1\n1 2 1\n1\n2\n4 3 2\n1 2 1\n1 3 2\n1 4 3\n2\n3\n4\n0 0 0\n output: Case 1: 1\nCase 2: 3\n\n" }, { "title": "Billiards Sorting", "content": "Rotation is one of several popular pocket billiards games.\nIt uses 15 balls numbered from 1 to 15, and set them up as illustrated in the following figure at the beginning of a game.\n(Note: the ball order is modified from real-world Rotation rules for simplicity of the problem. )\n\n [ 1]\n [ 2][ 3]\n [ 4][ 5][ 6]\n [ 7][ 8][ 9][10]\n[11][12][13][14][15]\n\nYou are an engineer developing an automatic billiards machine.\nFor the first step you had to build a machine that sets up the initial condition.\nThis project went well, and finally made up a machine that could arrange the balls in the triangular shape.\nHowever, unfortunately, it could not place the balls in the correct order.\n\nSo now you are trying to build another machine that fixes the order of balls by swapping them.\nTo cut off the cost, it is only allowed to swap the ball #1 with its neighboring balls that are not in the same row.\nFor example, in the case below, only the following pairs can be swapped: (1,2), (1,3), (1,8), and (1,9).\n\n [ 5]\n [ 2][ 3]\n [ 4][ 1][ 6]\n [ 7][ 8][ 9][10]\n[11][12][13][14][15]\n\nWrite a program that calculates the minimum number of swaps required.", "constraint": "", "input": "The first line of each test case has an integer N (1 <= N <= 5), which is the number of the rows.\n\nThe following N lines describe how the balls are arranged by the first machine;\nthe i-th of them consists of exactly i integers, which are the ball numbers.\n\nThe input terminates when N = 0. Your program must not output for this case.", "output": "For each test case, print its case number and the minimum number of swaps.\n\nYou can assume that any arrangement can be fixed by not more than 45 swaps.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3\n2 1\n4\n9\n2 4\n8 5 3\n7 1 6 10\n0\n output: Case 1: 1\nCase 2: 13"], "Pid": "p01505", "ProblemText": "Task Description: Rotation is one of several popular pocket billiards games.\nIt uses 15 balls numbered from 1 to 15, and set them up as illustrated in the following figure at the beginning of a game.\n(Note: the ball order is modified from real-world Rotation rules for simplicity of the problem. )\n\n [ 1]\n [ 2][ 3]\n [ 4][ 5][ 6]\n [ 7][ 8][ 9][10]\n[11][12][13][14][15]\n\nYou are an engineer developing an automatic billiards machine.\nFor the first step you had to build a machine that sets up the initial condition.\nThis project went well, and finally made up a machine that could arrange the balls in the triangular shape.\nHowever, unfortunately, it could not place the balls in the correct order.\n\nSo now you are trying to build another machine that fixes the order of balls by swapping them.\nTo cut off the cost, it is only allowed to swap the ball #1 with its neighboring balls that are not in the same row.\nFor example, in the case below, only the following pairs can be swapped: (1,2), (1,3), (1,8), and (1,9).\n\n [ 5]\n [ 2][ 3]\n [ 4][ 1][ 6]\n [ 7][ 8][ 9][10]\n[11][12][13][14][15]\n\nWrite a program that calculates the minimum number of swaps required.\nTask Input: The first line of each test case has an integer N (1 <= N <= 5), which is the number of the rows.\n\nThe following N lines describe how the balls are arranged by the first machine;\nthe i-th of them consists of exactly i integers, which are the ball numbers.\n\nThe input terminates when N = 0. Your program must not output for this case.\nTask Output: For each test case, print its case number and the minimum number of swaps.\n\nYou can assume that any arrangement can be fixed by not more than 45 swaps.\nTask Samples: input: 2\n3\n2 1\n4\n9\n2 4\n8 5 3\n7 1 6 10\n0\n output: Case 1: 1\nCase 2: 13\n\n" }, { "title": "Digit", "content": "For a positive integer a, let S(a) be the sum of the digits in base l.\nAlso let L(a) be the minimum k such that S^k(a) is less than or equal to l-1.\nFind the minimum a such that L(a) = N for a given N, and print a modulo m.", "constraint": "", "input": "The input contains several test cases, followed by a line containing \"0 0 0\".\nEach test case is given by a line with three integers N, m, l (0 <= N <= 10^5,1 <= m <= 10^9,2 <= l <= 10^9).", "output": "For each test case, print its case number and the minimum a modulo m as described above.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 1000 10\n1 1000 10\n0 0 0\n output: Case 1: 1\nCase 2: 10"], "Pid": "p01506", "ProblemText": "Task Description: For a positive integer a, let S(a) be the sum of the digits in base l.\nAlso let L(a) be the minimum k such that S^k(a) is less than or equal to l-1.\nFind the minimum a such that L(a) = N for a given N, and print a modulo m.\nTask Input: The input contains several test cases, followed by a line containing \"0 0 0\".\nEach test case is given by a line with three integers N, m, l (0 <= N <= 10^5,1 <= m <= 10^9,2 <= l <= 10^9).\nTask Output: For each test case, print its case number and the minimum a modulo m as described above.\nTask Samples: input: 0 1000 10\n1 1000 10\n0 0 0\n output: Case 1: 1\nCase 2: 10\n\n" }, { "title": "Dungeon Creation", "content": "The king demon is waiting in his dungeon to defeat a brave man.\nHis dungeon consists of H * W grids.\nEach cell is connected to four (i. e. north, south, east and west) neighboring cells and some cells are occupied by obstacles.\n\nTo attack the brave man, the king demon created and sent a servant that walks around in the dungeon.\nHowever, soon the king demon found that the servant does not work as he wants.\nThe servant is too dumb. If the dungeon had cyclic path, it might keep walking along the cycle forever.\n\nIn order to make sure that the servant eventually find the brave man, the king demon decided to eliminate all cycles by building walls between cells.\nAt the same time, he must be careful so that there is at least one path between any two cells not occupied by obstacles.\n\nYour task is to write a program that computes in how many ways the kind demon can build walls.", "constraint": "", "input": "The first line of each test case has two integers H and W (1 <= H <= 500,1 <= W <= 15), which are the height and the width of the dungeon.\nFollowing H lines consist of exactly W letters each of which is '. ' (there is no obstacle on the cell) or '#' (there is an obstacle).\nYou may assume that there is at least one cell that does not have an obstacle.\n\nThe input terminates when H = 0 and W = 0. Your program must not output for this case.", "output": "For each test case, print its case number and the number of ways that walls can be built in one line. Since the answer can be very big, output in modulo 1,000,000,007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n..\n..\n3 3\n...\n...\n..#\n0 0\n output: Case 1: 4\nCase 2: 56"], "Pid": "p01507", "ProblemText": "Task Description: The king demon is waiting in his dungeon to defeat a brave man.\nHis dungeon consists of H * W grids.\nEach cell is connected to four (i. e. north, south, east and west) neighboring cells and some cells are occupied by obstacles.\n\nTo attack the brave man, the king demon created and sent a servant that walks around in the dungeon.\nHowever, soon the king demon found that the servant does not work as he wants.\nThe servant is too dumb. If the dungeon had cyclic path, it might keep walking along the cycle forever.\n\nIn order to make sure that the servant eventually find the brave man, the king demon decided to eliminate all cycles by building walls between cells.\nAt the same time, he must be careful so that there is at least one path between any two cells not occupied by obstacles.\n\nYour task is to write a program that computes in how many ways the kind demon can build walls.\nTask Input: The first line of each test case has two integers H and W (1 <= H <= 500,1 <= W <= 15), which are the height and the width of the dungeon.\nFollowing H lines consist of exactly W letters each of which is '. ' (there is no obstacle on the cell) or '#' (there is an obstacle).\nYou may assume that there is at least one cell that does not have an obstacle.\n\nThe input terminates when H = 0 and W = 0. Your program must not output for this case.\nTask Output: For each test case, print its case number and the number of ways that walls can be built in one line. Since the answer can be very big, output in modulo 1,000,000,007.\nTask Samples: input: 2 2\n..\n..\n3 3\n...\n...\n..#\n0 0\n output: Case 1: 4\nCase 2: 56\n\n" }, { "title": "Longest Lane", "content": "Mr. KM, the mayor of KM city, decided to build a new elementary school.\nThe site for the school has an awkward polygonal shape, which caused several problems.\nThe most serious problem was that there was not enough space for a short distance racetrack.\nYour task is to help Mr. KM to calculate the maximum possible length for the racetrack\nthat can be built in the site.\nThe track can be considered as a straight line segment whose width can be ignored.\nThe boundary of the site has a simple polygonal shape without self-intersection,\nand the track can touch the boundary.\nNote that the boundary might not be convex.", "constraint": "", "input": "The input consists of multiple test cases, followed by a line containing \"0\".\nEach test case has the following format.\nThe first line contains an integer N (3 <= N <= 100).\nEach of the following N lines contains two integers x_i and y_i (-1,000 <= x_i, y_i <= 1,000),\nwhich describe the coordinates of a vertex of the polygonal border of the site, in counterclockwise order.", "output": "For each test case, print its case number and the maximum possible length of the track in a line.\nThe answer should be given as a floating point number with an absolute error of at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n10 0\n10 10\n0 10\n3\n0 0\n1 0\n0 1\n0\n output: Case 1: 14.142135624\nCase 2: 1.41421356"], "Pid": "p01508", "ProblemText": "Task Description: Mr. KM, the mayor of KM city, decided to build a new elementary school.\nThe site for the school has an awkward polygonal shape, which caused several problems.\nThe most serious problem was that there was not enough space for a short distance racetrack.\nYour task is to help Mr. KM to calculate the maximum possible length for the racetrack\nthat can be built in the site.\nThe track can be considered as a straight line segment whose width can be ignored.\nThe boundary of the site has a simple polygonal shape without self-intersection,\nand the track can touch the boundary.\nNote that the boundary might not be convex.\nTask Input: The input consists of multiple test cases, followed by a line containing \"0\".\nEach test case has the following format.\nThe first line contains an integer N (3 <= N <= 100).\nEach of the following N lines contains two integers x_i and y_i (-1,000 <= x_i, y_i <= 1,000),\nwhich describe the coordinates of a vertex of the polygonal border of the site, in counterclockwise order.\nTask Output: For each test case, print its case number and the maximum possible length of the track in a line.\nThe answer should be given as a floating point number with an absolute error of at most 10^{-6}.\nTask Samples: input: 4\n0 0\n10 0\n10 10\n0 10\n3\n0 0\n1 0\n0 1\n0\n output: Case 1: 14.142135624\nCase 2: 1.41421356\n\n" }, { "title": "PLAY in BASIC", "content": "One sunny day, Dick T. Mustang found an ancient personal computer in the closet.\nHe brought it back to his room and turned it on with a sense of nostalgia, seeing a message coming on the screen:\n\nREADY?\n\nYes. BASIC.\n\nBASIC is a programming language designed for beginners, and was widely used from 1980's to 1990's.\nThere have been quite a few BASIC dialects.\nSome of them provide the PLAY statement, which plays music when called with a string of a musical score written in Music Macro Language (MML).\nDick found this statement is available on his computer and accepts the following commands in MML:\n
    \n
    Notes: Cn, C+n, C-n, Dn, D+n, D-n, En, . . . , . . . (n = 1,2,4,8,16,32,64,128 + dots)
    \nEach note command consists of a musical note followed by a duration specifier.\nEach musical note is one of the seven basic notes: 'C', 'D', 'E', 'F', 'G', 'A', and 'B'. It can be followed by either '+' (indicating a sharp) or '-' (a flat). The notes 'C' through 'B' form an octave as depicted in the figure below. The octave for each command is determined by the current octave, which is set by the octave commands as described later. It is not possible to play the note 'C-' of the lowest octave (1) nor the note 'B+' of the highest octave (8).\nEach duration specifier is basically one of the following numbers: '1', '2', '4', '8', '16', '32', '64', and '128', where '1' denotes a whole note, '2' a half note, '4' a quarter note, '8' an eighth note, and so on. This specifier is optional; when omitted, the duration will be the default one set by the L command (which is described below). In addition, duration specifiers can contain dots next to the numbers. A dot adds the half duration of the basic note. For example, '4. ' denotes the duration of '4' (a quarter) plus '8' (an eighth, i. e. half of a quarter), or as 1.5 times long as '4'. It is possible that a single note has more than one dot, where each extra dot extends the duration by half of the previous one. For example, '4. . ' denotes the duration of '4' plus '8' plus '16', '4. . . ' denotes the duration of '4' plus '8' plus '16' plus '32', and so on. The duration extended by dots cannot be shorter than that of '128' due to limitation of Dick's computer; therefore neither '128. ' nor '32. . . ' will be accepted. The dots specified without the numbers extend the default duration. For example, 'C. ' is equivalent to 'C4. ' when the default duration is '4'. Note that 'C4C8' and 'C4. ' are unequivalent; the former contains two distinct notes, while the latter just one note.
    \n
    Rest: Rn (n = 1,2,4,8,16,32,64,128 + dots)
    \nThe R command rests for the specified duration. The duration should be specified in the same way as the note commands, and it can be omitted, too. Note that 'R4R8' and 'R4. ' are equivalent, unlike 'C4C8' and 'C4. ', since the both rest for the same duration of '4' plus '8'.
    \n
    Octave: On (n = 1-8), <, >
    \nThe O command sets the current octave to the specified number. '>' raises one octave up, and '<' drops one down. It is not allowed to set the octave beyond the range from 1 to 8 by these commands. The octave is initially set to 4.
    \n
    Default duration: Ln (n = 1,2,4,8,16,32,64,128)
    \nThe L command sets the default duration. The duration should be specified in the same way as the note commands, but cannot be omitted nor followed by dots. The default duration is initially set to 4.
    \n
    Volume: Vn (n = 1-255)
    \nThe V command sets the current volume. Larger is louder. The volume is initially set to 100.
    \n
    \nAs an amateur composer, Dick decided to play his pieces of music by the PLAY statement.\nHe managed to write a program with a long MML sequence, and attempted to run the program to play his music -- but unfortunately he encountered an unexpected error: the MML sequence was too long to be handled in his computer's small memory!\n\nSince he didn't want to give up all the efforts he had made to use the PLAY statement, he decided immediately to make the MML sequence shorter so that it fits in the small memory.\nIt was too hard for him, though.\nSo he asked you to write a program that, for each given MML sequence, prints the shortest MML sequence (i. e. MML sequence containing minimum number of characters) that expresses the same music as the given one.\nNote that the final values of octave, volume, and default duration can be differrent from the original MML sequence.", "constraint": "", "input": "The input consists of multiple data sets. Each data set is given by a single line that contains an MML sequence up to 100,000 characters.\nAll sequences only contain the commands described above.\nNote that each sequence contains at least one note, and there is no rest before the first note and after the last note.\n\nThe end of input is indicated by a line that only contains \"*\".\nThis is not part of any data sets and hence should not be processed.", "output": "For each test case, print its case number and the shortest MML sequence on a line.\n\nIf there are multiple solutions, print any of them.", "content_img": true, "lang": "en", "error": false, "samples": ["input: C4C4G4G4A4A4G2F4F4E4E4D4D4C2\nO4C4.C8F4.F8G8F8E8D8C2\nB-8>C8\n
    Notes: Cn, C+n, C-n, Dn, D+n, D-n, En, . . . , . . . (n = 1,2,4,8,16,32,64,128 + dots)
    \nEach note command consists of a musical note followed by a duration specifier.\nEach musical note is one of the seven basic notes: 'C', 'D', 'E', 'F', 'G', 'A', and 'B'. It can be followed by either '+' (indicating a sharp) or '-' (a flat). The notes 'C' through 'B' form an octave as depicted in the figure below. The octave for each command is determined by the current octave, which is set by the octave commands as described later. It is not possible to play the note 'C-' of the lowest octave (1) nor the note 'B+' of the highest octave (8).\nEach duration specifier is basically one of the following numbers: '1', '2', '4', '8', '16', '32', '64', and '128', where '1' denotes a whole note, '2' a half note, '4' a quarter note, '8' an eighth note, and so on. This specifier is optional; when omitted, the duration will be the default one set by the L command (which is described below). In addition, duration specifiers can contain dots next to the numbers. A dot adds the half duration of the basic note. For example, '4. ' denotes the duration of '4' (a quarter) plus '8' (an eighth, i. e. half of a quarter), or as 1.5 times long as '4'. It is possible that a single note has more than one dot, where each extra dot extends the duration by half of the previous one. For example, '4. . ' denotes the duration of '4' plus '8' plus '16', '4. . . ' denotes the duration of '4' plus '8' plus '16' plus '32', and so on. The duration extended by dots cannot be shorter than that of '128' due to limitation of Dick's computer; therefore neither '128. ' nor '32. . . ' will be accepted. The dots specified without the numbers extend the default duration. For example, 'C. ' is equivalent to 'C4. ' when the default duration is '4'. Note that 'C4C8' and 'C4. ' are unequivalent; the former contains two distinct notes, while the latter just one note.
    \n
    Rest: Rn (n = 1,2,4,8,16,32,64,128 + dots)
    \nThe R command rests for the specified duration. The duration should be specified in the same way as the note commands, and it can be omitted, too. Note that 'R4R8' and 'R4. ' are equivalent, unlike 'C4C8' and 'C4. ', since the both rest for the same duration of '4' plus '8'.
    \n
    Octave: On (n = 1-8), <, >
    \nThe O command sets the current octave to the specified number. '>' raises one octave up, and '<' drops one down. It is not allowed to set the octave beyond the range from 1 to 8 by these commands. The octave is initially set to 4.
    \n
    Default duration: Ln (n = 1,2,4,8,16,32,64,128)
    \nThe L command sets the default duration. The duration should be specified in the same way as the note commands, but cannot be omitted nor followed by dots. The default duration is initially set to 4.
    \n
    Volume: Vn (n = 1-255)
    \nThe V command sets the current volume. Larger is louder. The volume is initially set to 100.
    \n\nAs an amateur composer, Dick decided to play his pieces of music by the PLAY statement.\nHe managed to write a program with a long MML sequence, and attempted to run the program to play his music -- but unfortunately he encountered an unexpected error: the MML sequence was too long to be handled in his computer's small memory!\n\nSince he didn't want to give up all the efforts he had made to use the PLAY statement, he decided immediately to make the MML sequence shorter so that it fits in the small memory.\nIt was too hard for him, though.\nSo he asked you to write a program that, for each given MML sequence, prints the shortest MML sequence (i. e. MML sequence containing minimum number of characters) that expresses the same music as the given one.\nNote that the final values of octave, volume, and default duration can be differrent from the original MML sequence.\nTask Input: The input consists of multiple data sets. Each data set is given by a single line that contains an MML sequence up to 100,000 characters.\nAll sequences only contain the commands described above.\nNote that each sequence contains at least one note, and there is no rest before the first note and after the last note.\n\nThe end of input is indicated by a line that only contains \"*\".\nThis is not part of any data sets and hence should not be processed.\nTask Output: For each test case, print its case number and the shortest MML sequence on a line.\n\nIf there are multiple solutions, print any of them.\nTask Samples: input: C4C4G4G4A4A4G2F4F4E4E4D4D4C2\nO4C4.C8F4.F8G8F8E8D8C2\nB-8>C8i| <= C\n, and put the j-th character of the string s_i in the a_j-th column (1 <= j <= |s_i|).\nFor example, when C = 8 and s_i = \"ICPC\", you can put s_i like followings.\nI_C_P_C_\nICPC____\n_IC___PC\n'_' represents an empty cell.\nFor each non-empty cell x, you get a point equal to the number of adjacent cells which have the same character as x.\nTwo cells are adjacent if they share an edge.\nCalculate the maximum total point you can get.", "constraint": "", "input": "The first line contains two integers R and C (1 <= R <= 128,1 <= C <= 16).\n Then R lines follow, each of which contains s_i\n(1 <= |s_i| <= C).\nAll characters of s_i are uppercase letters.", "output": "Output the maximum total point in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 4\nACM\nICPC\n output: 2", "input: 2 9\nPROBLEMF\nCONNECT\n output: 6", "input: 4 16\nINTERNATIONAL\nCOLLEGIATE\nPROGRAMMING\nCONTEST\n output: 18"], "Pid": "p01563", "ProblemText": "Task Description: You are playing a solitaire puzzle called \"Connect\", which uses several letter tiles.\nThere are R * C empty cells.\nFor each i (1 <= i <= R), you must put a string s_i (1 <= |s_i| <= C) in the i-th row of the table, without changing the letter order.\nIn other words, you choose an integer sequence {a_j} such that\n1 <= a_1 < a_2 < . . . < a_|si| <= C\n, and put the j-th character of the string s_i in the a_j-th column (1 <= j <= |s_i|).\nFor example, when C = 8 and s_i = \"ICPC\", you can put s_i like followings.\nI_C_P_C_\nICPC____\n_IC___PC\n'_' represents an empty cell.\nFor each non-empty cell x, you get a point equal to the number of adjacent cells which have the same character as x.\nTwo cells are adjacent if they share an edge.\nCalculate the maximum total point you can get.\nTask Input: The first line contains two integers R and C (1 <= R <= 128,1 <= C <= 16).\n Then R lines follow, each of which contains s_i\n(1 <= |s_i| <= C).\nAll characters of s_i are uppercase letters.\nTask Output: Output the maximum total point in a line.\nTask Samples: input: 2 4\nACM\nICPC\n output: 2\ninput: 2 9\nPROBLEMF\nCONNECT\n output: 6\ninput: 4 16\nINTERNATIONAL\nCOLLEGIATE\nPROGRAMMING\nCONTEST\n output: 18\n\n" }, { "title": "Do use segment tree", "content": "Given a tree with n (1 <= n <= 200,000) nodes and a list of q (1 <= q <= 100,000) queries,\nprocess the queries in order and output a value for each output query.\nThe given tree is connected and each node on the tree has a weight w_i (-10,000 <= w_i <= 10,000).\nEach query consists of a number t_i (t_i = 1,2), which indicates the type of the query , and three numbers a_i, b_i and c_i (1 <= a_i, b_i <= n, -10,000 <= c_i <= 10,000).\nDepending on the query type, process one of the followings:\n (t_i = 1: modification query)\nChange the weights of all nodes on the shortest path between a_i and b_i (both inclusive) to c_i.\n\n (t_i = 2: output query) \nFirst, create a list of weights on the shortest path between a_i and b_i (both inclusive) in order. After that, output the maximum sum of a non-empty continuous subsequence of the weights on the list. c_i is ignored for output queries.", "constraint": "", "input": "The first line contains two integers n and q.\n On the second line, there are n integers which indicate w_1, w_2, . . . , w_n.\nEach of the following n - 1 lines consists of two integers s_i and e_i (1 <= s_i, e_i <= n),\nwhich means that there is an edge between s_i and e_i.\n Finally the following q lines give the list of queries, each of which contains four integers in the format described above.\nQueries must be processed one by one from top to bottom.", "output": "For each output query, output the maximum sum in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n1 2 3\n1 2\n2 3\n2 1 3 0\n1 2 2 -4\n2 1 3 0\n2 2 2 0\n output: 6\n3\n-4", "input: 7 5\n-8 5 5 5 5 5 5\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7\n2 3 7 0\n2 5 2 0\n2 4 3 0\n1 1 1 -1\n2 3 7 0\n output: 12\n10\n10\n19", "input: 21 30\n10 0 -10 -8 5 -5 -4 -3 1 -2 8 -1 -7 2 7 6 -9 -6 3 4 9\n10 3\n3 2\n3 12\n12 4\n4 13\n4 9\n10 21\n21 1\n1 11\n11 14\n1 15\n10 6\n6 17\n6 16\n6 5\n5 18\n5 19\n10 7\n10 8\n8 20\n1 1 21 -10\n1 3 19 10\n2 1 13 0\n1 4 18 8\n1 5 17 -5\n2 16 7 0\n1 6 16 5\n1 7 15 4\n2 4 20 0\n1 8 14 3\n1 9 13 -1\n2 9 18 0\n1 10 12 2\n1 11 11 -8\n2 21 15 0\n1 12 10 1\n1 13 9 7\n2 6 14 0\n1 14 8 -2\n1 15 7 -7\n2 10 2 0\n1 16 6 -6\n1 17 5 9\n2 12 17 0\n1 18 4 6\n1 19 3 -3\n2 11 8 0\n1 20 2 -4\n1 21 1 -9\n2 5 19 0\n output: 20\n9\n29\n27\n10\n12\n1\n18\n-2\n-3"], "Pid": "p01564", "ProblemText": "Task Description: Given a tree with n (1 <= n <= 200,000) nodes and a list of q (1 <= q <= 100,000) queries,\nprocess the queries in order and output a value for each output query.\nThe given tree is connected and each node on the tree has a weight w_i (-10,000 <= w_i <= 10,000).\nEach query consists of a number t_i (t_i = 1,2), which indicates the type of the query , and three numbers a_i, b_i and c_i (1 <= a_i, b_i <= n, -10,000 <= c_i <= 10,000).\nDepending on the query type, process one of the followings:\n (t_i = 1: modification query)\nChange the weights of all nodes on the shortest path between a_i and b_i (both inclusive) to c_i.\n\n (t_i = 2: output query) \nFirst, create a list of weights on the shortest path between a_i and b_i (both inclusive) in order. After that, output the maximum sum of a non-empty continuous subsequence of the weights on the list. c_i is ignored for output queries.\nTask Input: The first line contains two integers n and q.\n On the second line, there are n integers which indicate w_1, w_2, . . . , w_n.\nEach of the following n - 1 lines consists of two integers s_i and e_i (1 <= s_i, e_i <= n),\nwhich means that there is an edge between s_i and e_i.\n Finally the following q lines give the list of queries, each of which contains four integers in the format described above.\nQueries must be processed one by one from top to bottom.\nTask Output: For each output query, output the maximum sum in one line.\nTask Samples: input: 3 4\n1 2 3\n1 2\n2 3\n2 1 3 0\n1 2 2 -4\n2 1 3 0\n2 2 2 0\n output: 6\n3\n-4\ninput: 7 5\n-8 5 5 5 5 5 5\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7\n2 3 7 0\n2 5 2 0\n2 4 3 0\n1 1 1 -1\n2 3 7 0\n output: 12\n10\n10\n19\ninput: 21 30\n10 0 -10 -8 5 -5 -4 -3 1 -2 8 -1 -7 2 7 6 -9 -6 3 4 9\n10 3\n3 2\n3 12\n12 4\n4 13\n4 9\n10 21\n21 1\n1 11\n11 14\n1 15\n10 6\n6 17\n6 16\n6 5\n5 18\n5 19\n10 7\n10 8\n8 20\n1 1 21 -10\n1 3 19 10\n2 1 13 0\n1 4 18 8\n1 5 17 -5\n2 16 7 0\n1 6 16 5\n1 7 15 4\n2 4 20 0\n1 8 14 3\n1 9 13 -1\n2 9 18 0\n1 10 12 2\n1 11 11 -8\n2 21 15 0\n1 12 10 1\n1 13 9 7\n2 6 14 0\n1 14 8 -2\n1 15 7 -7\n2 10 2 0\n1 16 6 -6\n1 17 5 9\n2 12 17 0\n1 18 4 6\n1 19 3 -3\n2 11 8 0\n1 20 2 -4\n1 21 1 -9\n2 5 19 0\n output: 20\n9\n29\n27\n10\n12\n1\n18\n-2\n-3\n\n" }, { "title": "Move On Dice", "content": "There is a cube on a rectangle map with H-rows and W-columns grid.\nTwo special squares a start and a goal are marked on the map.\nInitially, the cube is on the start square. Let's repeat to roll it and take it to the goal square.\nRolling the cube means to select one of four edges which touch the map, and push the cube down without detaching the edge from the map.\nThat is, there are four directions you can move the cube toward.\nDirections where we can roll the cube are limited depending on each square.\nAn instruction is written in each square and represented by a single character as follows:\n
    \n
    '+'
    all
    \n
    '|'
    only vertical
    \n
    '-'
    only horizontal
    \n
    '<'
    only to left
    \n
    '>'
    only to right
    \n
    '^'
    only to up
    \n
    'v'
    only to down
    \n
    '. '
    none
    \n
    Regardless of instructions, it is not allowed to roll the cube to outside of the map.\nOn each face of the cube, a string is written.\nLet's output the string which concatenates strings written on the top face seen during the rollings from the start square to the goal square. \nSince there may be multiple paths that take the cube to the goal square, choose the minimal string in ascending lexicographic order.\nPlease note that there are cases where no path exists from the start to the goal, or the cases you can make the lexicographically minimal string infinitely longer.", "constraint": "", "input": "A data set has following format:\n\nH W\nC_11 . . . C_1W\n . . . \nC_H1 . . . C_HW\nT_1\n . . . \nT_6\nR_S C_S\nR_D C_D\nThe first line of the input contains two integers H (1 <= H <= 12) and W (1 <= W <= 12), which indicate the number of rows and columns of the map respectively.\nThe following W lines describe the map.\nThe j-th character of the i-th line indicates the instruction of the square, which is placed on i-th row (from the top) and j-th column (from the left).\nThen the following 6 lines describe the strings on each face of the cube.\nAll of these strings are not empty and shorter than 12 characters (inclusive).\nIn addition, they only consist of uppercase alphabets or digits.\nThe faces where the strings are written are given as figure 1.\nInitially, the cube is placed on the start square in a direction as the face No. 1 is facing top and the upper direction of face No. 1 faces toward the top row of the map.\n\nFigure 1. a net of a cube\nThe last two lines contain two integers each that indicate the row number and column number of the start square and the goal square in this order.\nYou can assume that the start square and the goal square are always different.", "output": "Print the lexicographically minimal string in a line.\nIf there is no path, print \"no\" in a line.\nIf you can make the lexicographically minimal string infinitely longer, print \"infinite\" in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 3\n+++\n6\n5\n4\n3\n2\n1\n1 3\n1 1\n output: 621", "input: 1 3\n+++\n1\n2\n3\n4\n5\n6\n1 3\n1 1\n output: infinite", "input: 1 3\n...\n1\n2\n3\n4\n5\n6\n1 3\n1 1\n output: no", "input: 3 3\n->|\n..v\n.^<\nJAG\n2012\nSUMMER\nHOGE\nHOGE\nCAMP\n1 1\n2 2\n output: JAGSUMMERCAMP2012JAGSUMMER2012"], "Pid": "p01565", "ProblemText": "Task Description: There is a cube on a rectangle map with H-rows and W-columns grid.\nTwo special squares a start and a goal are marked on the map.\nInitially, the cube is on the start square. Let's repeat to roll it and take it to the goal square.\nRolling the cube means to select one of four edges which touch the map, and push the cube down without detaching the edge from the map.\nThat is, there are four directions you can move the cube toward.\nDirections where we can roll the cube are limited depending on each square.\nAn instruction is written in each square and represented by a single character as follows:\n
    \n
    '+'
    all
    \n
    '|'
    only vertical
    \n
    '-'
    only horizontal
    \n
    '<'
    only to left
    \n
    '>'
    only to right
    \n
    '^'
    only to up
    \n
    'v'
    only to down
    \n
    '. '
    none
    \n
    Regardless of instructions, it is not allowed to roll the cube to outside of the map.\nOn each face of the cube, a string is written.\nLet's output the string which concatenates strings written on the top face seen during the rollings from the start square to the goal square. \nSince there may be multiple paths that take the cube to the goal square, choose the minimal string in ascending lexicographic order.\nPlease note that there are cases where no path exists from the start to the goal, or the cases you can make the lexicographically minimal string infinitely longer.\nTask Input: A data set has following format:\n\nH W\nC_11 . . . C_1W\n . . . \nC_H1 . . . C_HW\nT_1\n . . . \nT_6\nR_S C_S\nR_D C_D\nThe first line of the input contains two integers H (1 <= H <= 12) and W (1 <= W <= 12), which indicate the number of rows and columns of the map respectively.\nThe following W lines describe the map.\nThe j-th character of the i-th line indicates the instruction of the square, which is placed on i-th row (from the top) and j-th column (from the left).\nThen the following 6 lines describe the strings on each face of the cube.\nAll of these strings are not empty and shorter than 12 characters (inclusive).\nIn addition, they only consist of uppercase alphabets or digits.\nThe faces where the strings are written are given as figure 1.\nInitially, the cube is placed on the start square in a direction as the face No. 1 is facing top and the upper direction of face No. 1 faces toward the top row of the map.\n\nFigure 1. a net of a cube\nThe last two lines contain two integers each that indicate the row number and column number of the start square and the goal square in this order.\nYou can assume that the start square and the goal square are always different.\nTask Output: Print the lexicographically minimal string in a line.\nIf there is no path, print \"no\" in a line.\nIf you can make the lexicographically minimal string infinitely longer, print \"infinite\" in a line.\nTask Samples: input: 1 3\n+++\n6\n5\n4\n3\n2\n1\n1 3\n1 1\n output: 621\ninput: 1 3\n+++\n1\n2\n3\n4\n5\n6\n1 3\n1 1\n output: infinite\ninput: 1 3\n...\n1\n2\n3\n4\n5\n6\n1 3\n1 1\n output: no\ninput: 3 3\n->|\n..v\n.^<\nJAG\n2012\nSUMMER\nHOGE\nHOGE\nCAMP\n1 1\n2 2\n output: JAGSUMMERCAMP2012JAGSUMMER2012\n\n" }, { "title": "Pipeline Plans", "content": "There are twelve types of tiles in Fig. 1.\n You were asked to fill a table with R * C cells with these tiles.\nR is the number of rows and C is the number of columns.\nHow many arrangements in the table meet the following constraints?\n Each cell has one tile.\n\n the center of the upper left cell (1,1) and the center of the lower right cell (C, R) are connected by some roads.\n\nFig. 1: the types of tiles", "constraint": "", "input": "The first line contains two integers R and C (2 <= R * C <= 15).\nYou can safely assume at least one of R and C is greater than 1. \nThe second line contains twelve integers, t_1, t_2, . . . , t_12 (0 <= t_1 + . . . . + t_12 <= 15).\nt_i represents the number of the i-th tiles you have.", "output": "Output the number of arrangments in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 3\n4 2 2 0 0 0 0 0 0 0 0 1\n output: 2", "input: 3 3\n0 1 1 0 0 0 0 0 0 0 0 7\n output: 66", "input: 3 3\n0 0 0 0 0 0 0 0 0 0 0 10\n output: 1", "input: 2 4\n0 0 1 1 1 2 0 1 0 0 1 1\n output: 2012", "input: 5 2\n0 1 1 1 0 1 2 1 2 0 0 1\n output: 8512"], "Pid": "p01566", "ProblemText": "Task Description: There are twelve types of tiles in Fig. 1.\n You were asked to fill a table with R * C cells with these tiles.\nR is the number of rows and C is the number of columns.\nHow many arrangements in the table meet the following constraints?\n Each cell has one tile.\n\n the center of the upper left cell (1,1) and the center of the lower right cell (C, R) are connected by some roads.\n\nFig. 1: the types of tiles\nTask Input: The first line contains two integers R and C (2 <= R * C <= 15).\nYou can safely assume at least one of R and C is greater than 1. \nThe second line contains twelve integers, t_1, t_2, . . . , t_12 (0 <= t_1 + . . . . + t_12 <= 15).\nt_i represents the number of the i-th tiles you have.\nTask Output: Output the number of arrangments in a line.\nTask Samples: input: 3 3\n4 2 2 0 0 0 0 0 0 0 0 1\n output: 2\ninput: 3 3\n0 1 1 0 0 0 0 0 0 0 0 7\n output: 66\ninput: 3 3\n0 0 0 0 0 0 0 0 0 0 0 10\n output: 1\ninput: 2 4\n0 0 1 1 1 2 0 1 0 0 1 1\n output: 2012\ninput: 5 2\n0 1 1 1 0 1 2 1 2 0 0 1\n output: 8512\n\n" }, { "title": "Presentation", "content": "You are a researcher investigating algorithms on binary trees.\nBinary tree is a data structure composed of branch nodes and leaf nodes.\nEvery branch nodes have left child and right child, and each child is either a branch node or a leaf node.\nThe root of a binary tree is the branch node which has no parent.\nYou are preparing for your presentation and you have to make a figure of binary trees using a software.\nYou have already made a figure corresponding to a binary tree which is composed of one branch node and two leaf nodes (Figure 1. )\nHowever, suddenly the function of your software to create a figure was broken.\nYou are very upset because in five hours you have to make the presentation in front of large audience.\nYou decided to make the figure of the binary trees using only copy function, shrink function and paste function of the presentation tool.\nThat is, you can do only following two types of operations.\n\n Copy the current figure to the clipboard.\nThe figure copied to the clipboard before is removed.\n\n Paste the copied figure (with shrinking, if needed), putting the root of the pasted figure on a leaf node of the current figure.\n You can paste the copied figure multiple times.\n\nMoreover, you decided to make the figure using the minimum number of paste operations because paste operation is very time cosuming.\nNow, your job is to calculate the minimum possible number of paste operations to produce the target figure.\nFigure 1: initial stateFor example, the answer for the instance of sample 1(Figure 4) is 3, because you can produce the target figure by following operations and this is minimum.\nFigure 2: intermediate 1Figure 3: intermediate 2Figure 4: Goal", "constraint": "", "input": "The input is a line which indicates a binary tree.\nThe grammar of the expression is given by the following BNF.\n\n : : = | \"(\" \")\" : : = \"()\"Every input obeys this syntax.\n\nYou can assume that every tree in the input has at least 1 branch node, and that it has no more than 10^5 branch nodes.", "output": "A line containing the minimum possible number of paste operations to make the given binary tree.", "content_img": true, "lang": "en", "error": false, "samples": ["input: ((()())(((()())(()()))()))\n output: 3", "input: (((()())(()()))(()()))\n output: 4", "input: ((()(()()))((()(()()))()))\n output: 3", "input: (()())\n output: 0"], "Pid": "p01567", "ProblemText": "Task Description: You are a researcher investigating algorithms on binary trees.\nBinary tree is a data structure composed of branch nodes and leaf nodes.\nEvery branch nodes have left child and right child, and each child is either a branch node or a leaf node.\nThe root of a binary tree is the branch node which has no parent.\nYou are preparing for your presentation and you have to make a figure of binary trees using a software.\nYou have already made a figure corresponding to a binary tree which is composed of one branch node and two leaf nodes (Figure 1. )\nHowever, suddenly the function of your software to create a figure was broken.\nYou are very upset because in five hours you have to make the presentation in front of large audience.\nYou decided to make the figure of the binary trees using only copy function, shrink function and paste function of the presentation tool.\nThat is, you can do only following two types of operations.\n\n Copy the current figure to the clipboard.\nThe figure copied to the clipboard before is removed.\n\n Paste the copied figure (with shrinking, if needed), putting the root of the pasted figure on a leaf node of the current figure.\n You can paste the copied figure multiple times.\n\nMoreover, you decided to make the figure using the minimum number of paste operations because paste operation is very time cosuming.\nNow, your job is to calculate the minimum possible number of paste operations to produce the target figure.\nFigure 1: initial stateFor example, the answer for the instance of sample 1(Figure 4) is 3, because you can produce the target figure by following operations and this is minimum.\nFigure 2: intermediate 1Figure 3: intermediate 2Figure 4: Goal\nTask Input: The input is a line which indicates a binary tree.\nThe grammar of the expression is given by the following BNF.\n\n : : = | \"(\" \")\" : : = \"()\"Every input obeys this syntax.\n\nYou can assume that every tree in the input has at least 1 branch node, and that it has no more than 10^5 branch nodes.\nTask Output: A line containing the minimum possible number of paste operations to make the given binary tree.\nTask Samples: input: ((()())(((()())(()()))()))\n output: 3\ninput: (((()())(()()))(()()))\n output: 4\ninput: ((()(()()))((()(()()))()))\n output: 3\ninput: (()())\n output: 0\n\n" }, { "title": "Repairing", "content": "In the International City of Pipe Construction, it is planned to repair the water pipe at a certain point in the water pipe network.\nThe network consists of water pipe segments, stop valves and source point.\nA water pipe is represented by a segment on a 2D-plane and intersected pair of water pipe segments are connected at the intersection point.\nA stop valve, which prevents from water flowing into the repairing point while repairing, is represented by a point on some water pipe segment.\nIn the network, just one source point exists and water is supplied to the network from this point.\nOf course, while repairing, we have to stop water supply in some areas, but,\nin order to reduce the risk of riots, the length of water pipes stopping water supply must be minimized.\nWhat you have to do is to write a program to minimize the length of water pipes needed to stop water supply when the coordinates of end points of water pipe segments, stop valves, source point and repairing point are given.", "constraint": "", "input": "A data set has the following format:\n\nN M\nx_s1 y_s1 x_d1 y_d1\n . . . \nx_s N y_s N x_d N y_d N\nx_v1 y_v1\n . . . \nx_v M y_v M\nx_b y_b\nx_c y_c\nThe first line of the input contains two integers, N (1 <= N <= 300) and M (0 <= M <= 1,000) that indicate the number of water pipe segments and stop valves.\nThe following N lines describe the end points of water pipe segments.\nThe i-th line contains four integers, x_si, y_si, x_di and y_di that indicate the pair of coordinates of end points of i-th water pipe segment.\nThe following M lines describe the points of stop valves.\nThe i-th line contains two integers, x_vi and y_vi that indicate the coordinate of end points of i-th stop valve.\nThe following line contains two integers, x_b and y_b that indicate the coordinate of the source point.\nThe last line contains two integers, x_c and y_c that indicate the coordinate of the repairing point.\nYou may assume that any absolute values of coordinate integers are less than 1,000 (inclusive. ) \nYou may also assume each of the stop valves, the source point and the repairing point is always on one of water pipe segments and that that each pair among the stop valves, the source point and the repairing point are different.\nAnd, there is not more than one intersection between each pair of water pipe segments.\nFinally, the water pipe network is connected, that is, all the water pipes are received water supply initially.", "output": "Print the minimal length of water pipes needed to stop water supply in a line.\nThe absolute or relative error should be less than or 10^-6.\nWhen you cannot stop water supply to the repairing point even though you close all stop valves, print \"-1\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2\n0 0 10 0\n1 0\n9 0\n0 0\n5 0\n output: 9.0", "input: 5 3\n0 4 2 4\n0 2 2 2\n0 0 2 0\n0 0 0 4\n2 0 2 4\n0 2\n1 0\n2 2\n1 4\n2 1\n output: 3.0", "input: 2 1\n0 0 0 4\n0 2 2 2\n1 2\n0 1\n0 3\n output: -1"], "Pid": "p01568", "ProblemText": "Task Description: In the International City of Pipe Construction, it is planned to repair the water pipe at a certain point in the water pipe network.\nThe network consists of water pipe segments, stop valves and source point.\nA water pipe is represented by a segment on a 2D-plane and intersected pair of water pipe segments are connected at the intersection point.\nA stop valve, which prevents from water flowing into the repairing point while repairing, is represented by a point on some water pipe segment.\nIn the network, just one source point exists and water is supplied to the network from this point.\nOf course, while repairing, we have to stop water supply in some areas, but,\nin order to reduce the risk of riots, the length of water pipes stopping water supply must be minimized.\nWhat you have to do is to write a program to minimize the length of water pipes needed to stop water supply when the coordinates of end points of water pipe segments, stop valves, source point and repairing point are given.\nTask Input: A data set has the following format:\n\nN M\nx_s1 y_s1 x_d1 y_d1\n . . . \nx_s N y_s N x_d N y_d N\nx_v1 y_v1\n . . . \nx_v M y_v M\nx_b y_b\nx_c y_c\nThe first line of the input contains two integers, N (1 <= N <= 300) and M (0 <= M <= 1,000) that indicate the number of water pipe segments and stop valves.\nThe following N lines describe the end points of water pipe segments.\nThe i-th line contains four integers, x_si, y_si, x_di and y_di that indicate the pair of coordinates of end points of i-th water pipe segment.\nThe following M lines describe the points of stop valves.\nThe i-th line contains two integers, x_vi and y_vi that indicate the coordinate of end points of i-th stop valve.\nThe following line contains two integers, x_b and y_b that indicate the coordinate of the source point.\nThe last line contains two integers, x_c and y_c that indicate the coordinate of the repairing point.\nYou may assume that any absolute values of coordinate integers are less than 1,000 (inclusive. ) \nYou may also assume each of the stop valves, the source point and the repairing point is always on one of water pipe segments and that that each pair among the stop valves, the source point and the repairing point are different.\nAnd, there is not more than one intersection between each pair of water pipe segments.\nFinally, the water pipe network is connected, that is, all the water pipes are received water supply initially.\nTask Output: Print the minimal length of water pipes needed to stop water supply in a line.\nThe absolute or relative error should be less than or 10^-6.\nWhen you cannot stop water supply to the repairing point even though you close all stop valves, print \"-1\" in a line.\nTask Samples: input: 1 2\n0 0 10 0\n1 0\n9 0\n0 0\n5 0\n output: 9.0\ninput: 5 3\n0 4 2 4\n0 2 2 2\n0 0 2 0\n0 0 0 4\n2 0 2 4\n0 2\n1 0\n2 2\n1 4\n2 1\n output: 3.0\ninput: 2 1\n0 0 0 4\n0 2 2 2\n1 2\n0 1\n0 3\n output: -1\n\n" }, { "title": "Sun and Moon", "content": "In the year 20XX, mankind is hit by an unprecedented crisis.\nThe power balance between the sun and the moon was broken by the total eclipse of the sun, and the end is looming!\nTo save the world, the secret society called \"Sun and Moon\" decided to perform the ritual to balance the power of the sun and the moon called \"Ritual of Sun and Moon\".\nThe ritual consists of \"Ritual of Sun\" and \"Ritual of Moon\". \"Ritual of Moon\" is performed after \"Ritual of Sun\".\nA member of the society is divided into two groups, \"Messengers of Sun\" and \"Messengers of Moon\".\nEach member has some offerings and magic power.\nFirst, the society performs \"Ritual of Sun\".\nIn the ritual, each member sacrifices an offering.\nIf he can not sacrifice an offering here, he will be killed.\nAfter the sacrifice, his magic power is multiplied by the original number of his offerings.\nEach member must perform the sacrifice just once.\nSecond, the society performs \"Ritual of Moon\".\nIn the ritual, each member sacrifices all remaining offerings.\nAfter the sacrifice, his magic power is multiplied by x^p.\nHere x is the number of days from the eclipse (the eclipse is 0th day) and p is the number of his sacrificed offerings.\nEach member must perform the sacrifice just once.\nAfter two rituals, all \"Messengers of Sun\" and \"Messengers of Moon\" give all magic power to the \"magical reactor\".\nIf the total power of \"Messengers of Sun\" and the total power of \"Messengers of Moon\" are equal,\nthe society will succeed in the ritual and save the world.\nIt is very expensive to perform \"Ritual of Sun\".\nIt may not be able to perform \"Ritual of Sun\" because the society is in financial trouble.\nPlease write a program to calculate the minimum number of days from the eclipse in which the society can succeed in \"Ritual of Sun and Moon\" whether \"Ritual of Sun\" can be performed or not.\nThe society cannot perform the ritual on the eclipse day (0-th day).", "constraint": "", "input": "The format of the input is as follows.\n\nNO_1 P_1. . . O_N P_NThe first line contains an integer N that is the number of members of the society (0 <= N <= 1,000).\nEach of the following N lines contains two integers O_i (0 <= O_i <= 1,000,000,000) and P_i (1 <= |P_i| <= 1,000,000,000,000,000).\nO_i is the number of the i-th member's offerings and |P_i| is the strength of his magic power.\nIf P_i is a positive integer, the i-th member belongs to \"Messengers of Sun\", otherwise he belongs to \"Messengers of Moon\".", "output": "If there exists the number of days from the eclipse that satisfies the above condition , print the minimum number of days preceded by \"Yes \".\nOtherwise print \"No\".\nOf course, the answer must be a positive integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\n2 1\n1 -1\n1 -1\n1 -1\n1 -1\n0 1\n0 1\n0 1\n0 1\n output: Yes 2", "input: 2\n1 1\n0 -1\n output: No"], "Pid": "p01569", "ProblemText": "Task Description: In the year 20XX, mankind is hit by an unprecedented crisis.\nThe power balance between the sun and the moon was broken by the total eclipse of the sun, and the end is looming!\nTo save the world, the secret society called \"Sun and Moon\" decided to perform the ritual to balance the power of the sun and the moon called \"Ritual of Sun and Moon\".\nThe ritual consists of \"Ritual of Sun\" and \"Ritual of Moon\". \"Ritual of Moon\" is performed after \"Ritual of Sun\".\nA member of the society is divided into two groups, \"Messengers of Sun\" and \"Messengers of Moon\".\nEach member has some offerings and magic power.\nFirst, the society performs \"Ritual of Sun\".\nIn the ritual, each member sacrifices an offering.\nIf he can not sacrifice an offering here, he will be killed.\nAfter the sacrifice, his magic power is multiplied by the original number of his offerings.\nEach member must perform the sacrifice just once.\nSecond, the society performs \"Ritual of Moon\".\nIn the ritual, each member sacrifices all remaining offerings.\nAfter the sacrifice, his magic power is multiplied by x^p.\nHere x is the number of days from the eclipse (the eclipse is 0th day) and p is the number of his sacrificed offerings.\nEach member must perform the sacrifice just once.\nAfter two rituals, all \"Messengers of Sun\" and \"Messengers of Moon\" give all magic power to the \"magical reactor\".\nIf the total power of \"Messengers of Sun\" and the total power of \"Messengers of Moon\" are equal,\nthe society will succeed in the ritual and save the world.\nIt is very expensive to perform \"Ritual of Sun\".\nIt may not be able to perform \"Ritual of Sun\" because the society is in financial trouble.\nPlease write a program to calculate the minimum number of days from the eclipse in which the society can succeed in \"Ritual of Sun and Moon\" whether \"Ritual of Sun\" can be performed or not.\nThe society cannot perform the ritual on the eclipse day (0-th day).\nTask Input: The format of the input is as follows.\n\nNO_1 P_1. . . O_N P_NThe first line contains an integer N that is the number of members of the society (0 <= N <= 1,000).\nEach of the following N lines contains two integers O_i (0 <= O_i <= 1,000,000,000) and P_i (1 <= |P_i| <= 1,000,000,000,000,000).\nO_i is the number of the i-th member's offerings and |P_i| is the strength of his magic power.\nIf P_i is a positive integer, the i-th member belongs to \"Messengers of Sun\", otherwise he belongs to \"Messengers of Moon\".\nTask Output: If there exists the number of days from the eclipse that satisfies the above condition , print the minimum number of days preceded by \"Yes \".\nOtherwise print \"No\".\nOf course, the answer must be a positive integer.\nTask Samples: input: 9\n2 1\n1 -1\n1 -1\n1 -1\n1 -1\n0 1\n0 1\n0 1\n0 1\n output: Yes 2\ninput: 2\n1 1\n0 -1\n output: No\n\n" }, { "title": "Usoperanto", "content": "Usoperanto is an artificial spoken language designed and regulated by Usoperanto Academy.\nThe academy is now in study to establish Strict Usoperanto, a variation of the language intended for formal documents.\nIn Usoperanto, each word can modify at most one other word, and modifiers are always put before modifiees.\nFor example, with a noun uso (\"truth\") modified by an adjective makka (\"total\"), people say makka uso, not uso makka.\nOn the other hand, there have been no rules about the order among multiple words modifying the same word,\nso in case uso is modified by one more adjective beta (\"obvious\"),\npeople could say both makka beta uso and beta makka uso.\nIn Strict Usoperanto, the word order will be restricted according to modification costs.\nWords in a phrase must be arranged so that the total modification cost is minimized.\nEach pair of a modifier and a modifiee is assigned a cost equal to the number of letters between the two words;\nthe total modification cost is the sum of the costs over all modifier-modifiee pairs in the phrase.\nFor example, the pair of makka and uso in a phrase makka beta uso has the cost of 4 for beta (four letters).\nAs the pair of beta and uso has no words in between and thus the cost of zero, makka beta uso has the total modification cost of 4.\nSimilarly beta makka uso has the total modification cost of 5.\nApplying the \"minimum total modification cost\" rule, makka beta uso is preferred to beta makka uso in Strict Usoperanto.\nYour mission in this problem is to write a program that, given a set of words in a phrase, finds the correct word order in Strict Usoperanto and reports the total modification cost.", "constraint": "", "input": "The format of the input is as follows.\n\nNM_0 L_0. . . M_N-1 L_N-1The first line contains an integer\n\nN (1 <= N <= 10^6).\nN is the number of words in a phrase.\nEach of the following N lines contains two integers\nM_i (1 <= M_i <= 10) and\nL_i (-1 <= L_i <= N - 1, L_i ! = i)\ndescribing the i-th word (0 <= i <= N-1).\nM_i is the number of the letters in the word.\nL_i specifies the modification:\nL_i = -1 indicates it does not modify any word;\notherwise it modifies the L_i-th word.\nNote the first sample input below can be interpreted as the uso-beta-makka case.", "output": "Print the total modification cost.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 -1\n4 0\n5 0\n output: 4", "input: 3\n10 -1\n10 0\n10 1\n output: 0", "input: 4\n1 -1\n1 0\n1 1\n1 0\n output: 1"], "Pid": "p01570", "ProblemText": "Task Description: Usoperanto is an artificial spoken language designed and regulated by Usoperanto Academy.\nThe academy is now in study to establish Strict Usoperanto, a variation of the language intended for formal documents.\nIn Usoperanto, each word can modify at most one other word, and modifiers are always put before modifiees.\nFor example, with a noun uso (\"truth\") modified by an adjective makka (\"total\"), people say makka uso, not uso makka.\nOn the other hand, there have been no rules about the order among multiple words modifying the same word,\nso in case uso is modified by one more adjective beta (\"obvious\"),\npeople could say both makka beta uso and beta makka uso.\nIn Strict Usoperanto, the word order will be restricted according to modification costs.\nWords in a phrase must be arranged so that the total modification cost is minimized.\nEach pair of a modifier and a modifiee is assigned a cost equal to the number of letters between the two words;\nthe total modification cost is the sum of the costs over all modifier-modifiee pairs in the phrase.\nFor example, the pair of makka and uso in a phrase makka beta uso has the cost of 4 for beta (four letters).\nAs the pair of beta and uso has no words in between and thus the cost of zero, makka beta uso has the total modification cost of 4.\nSimilarly beta makka uso has the total modification cost of 5.\nApplying the \"minimum total modification cost\" rule, makka beta uso is preferred to beta makka uso in Strict Usoperanto.\nYour mission in this problem is to write a program that, given a set of words in a phrase, finds the correct word order in Strict Usoperanto and reports the total modification cost.\nTask Input: The format of the input is as follows.\n\nNM_0 L_0. . . M_N-1 L_N-1The first line contains an integer\n\nN (1 <= N <= 10^6).\nN is the number of words in a phrase.\nEach of the following N lines contains two integers\nM_i (1 <= M_i <= 10) and\nL_i (-1 <= L_i <= N - 1, L_i ! = i)\ndescribing the i-th word (0 <= i <= N-1).\nM_i is the number of the letters in the word.\nL_i specifies the modification:\nL_i = -1 indicates it does not modify any word;\notherwise it modifies the L_i-th word.\nNote the first sample input below can be interpreted as the uso-beta-makka case.\nTask Output: Print the total modification cost.\nTask Samples: input: 3\n3 -1\n4 0\n5 0\n output: 4\ninput: 3\n10 -1\n10 0\n10 1\n output: 0\ninput: 4\n1 -1\n1 0\n1 1\n1 0\n output: 1\n\n" }, { "title": "Problem A: Adhoc Translation", "content": "One day, during daily web surfing, you encountered a web page which was written in a language you've never seen. The character set of the language was the same as your native language; moreover, the grammar and words seemed almost the same. Excitedly, you started to \"decipher\" the web page. The first approach you tried was to guess the meaning of each word by selecting a similar word from a dictionary of your native language. The closer two words (although from the different languages) are, the more similar meaning they will have.\n\nYou decided to adopt edit distance for the measurement of similarity between two words. The edit distance between two character sequences is defined as the minimum number of insertions, deletions and substitutions required to morph one sequence into the other. For example, the pair of \"point\" and \"spoon\" has the edit distance of 3: the latter can be obtained from the former by deleting 't', substituting 'i' to 'o', and finally inserting 's' at the beginning.\n\nYou wanted to assign a word in your language to each word in the web text so that the entire assignment has the minimum edit distance. The edit distance of an assignment is calculated as the total sum of edit distances between each word in the text and its counterpart in your language. Words appearing more than once in the text should be counted by the number of appearances.\n\nThe translation must be consistent across the entire text; you may not match different words from your dictionary for different occurrences of any word in the text. Similarly, different words in the text should not have the same meaning in your language.\n\nSuppose the web page says \"qwerty asdf zxcv\" and your dictionary contains the words \"qwert\", \"asf\", \"tyui\", \"zxcvb\" and \"ghjk\". In this case, you can match the words in the page as follows, and the edit distance of this translation is 3: \"qwert\" for \"qwerty\", \"asf\" for \"asdf\" and \"zxcvb\" for \"zxcv\".\n\nWrite a program to calculate the minimum possible edit distance among all translations, for given a web page text and a word set in the dictionary.", "constraint": "", "input": "The first line of the input contains two integers N and M.\n\nThe following N lines represent the text from the web page you've found. This text contains only lowercase alphabets and white spaces. Then M lines, each containing a word, describe the dictionary to use. Every word consists of lowercase alphabets only, and does not contain more than 20 characters.\n\nIt is guaranteed that 1 <= N <= 100 and 1 <= M <= 400. Also it is guaranteed that the dictionary is made up of many enough words, which means the number of words in the dictionary is no less than the kinds of words in the text to translate. The length of each line in the text does not exceed 1000.", "output": "Output the minimum possible edit distance in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 5\nqwerty asdf zxcv\nqwert\nasf\ntyui\nzxcvb\nghjk\n output: 3"], "Pid": "p01571", "ProblemText": "Task Description: One day, during daily web surfing, you encountered a web page which was written in a language you've never seen. The character set of the language was the same as your native language; moreover, the grammar and words seemed almost the same. Excitedly, you started to \"decipher\" the web page. The first approach you tried was to guess the meaning of each word by selecting a similar word from a dictionary of your native language. The closer two words (although from the different languages) are, the more similar meaning they will have.\n\nYou decided to adopt edit distance for the measurement of similarity between two words. The edit distance between two character sequences is defined as the minimum number of insertions, deletions and substitutions required to morph one sequence into the other. For example, the pair of \"point\" and \"spoon\" has the edit distance of 3: the latter can be obtained from the former by deleting 't', substituting 'i' to 'o', and finally inserting 's' at the beginning.\n\nYou wanted to assign a word in your language to each word in the web text so that the entire assignment has the minimum edit distance. The edit distance of an assignment is calculated as the total sum of edit distances between each word in the text and its counterpart in your language. Words appearing more than once in the text should be counted by the number of appearances.\n\nThe translation must be consistent across the entire text; you may not match different words from your dictionary for different occurrences of any word in the text. Similarly, different words in the text should not have the same meaning in your language.\n\nSuppose the web page says \"qwerty asdf zxcv\" and your dictionary contains the words \"qwert\", \"asf\", \"tyui\", \"zxcvb\" and \"ghjk\". In this case, you can match the words in the page as follows, and the edit distance of this translation is 3: \"qwert\" for \"qwerty\", \"asf\" for \"asdf\" and \"zxcvb\" for \"zxcv\".\n\nWrite a program to calculate the minimum possible edit distance among all translations, for given a web page text and a word set in the dictionary.\nTask Input: The first line of the input contains two integers N and M.\n\nThe following N lines represent the text from the web page you've found. This text contains only lowercase alphabets and white spaces. Then M lines, each containing a word, describe the dictionary to use. Every word consists of lowercase alphabets only, and does not contain more than 20 characters.\n\nIt is guaranteed that 1 <= N <= 100 and 1 <= M <= 400. Also it is guaranteed that the dictionary is made up of many enough words, which means the number of words in the dictionary is no less than the kinds of words in the text to translate. The length of each line in the text does not exceed 1000.\nTask Output: Output the minimum possible edit distance in a line.\nTask Samples: input: 1 5\nqwerty asdf zxcv\nqwert\nasf\ntyui\nzxcvb\nghjk\n output: 3\n\n" }, { "title": "Problem B: Artistic Art Museum", "content": "Mr. Knight is a chief architect of the project to build a new art museum. One day, he was struggling to determine the design of the building. He believed that a brilliant art museum must have an artistic building, so he started to search for a good motif of his building. The art museum has one big theme: \"nature and human beings. \" To reflect the theme, he decided to adopt a combination of a cylinder and a prism, which symbolize nature and human beings respectively (between these figures and the theme, there is a profound relationship that only he knows).\n\nShortly after his decision, he remembered that he has to tell an estimate of the cost required to build to the financial manager. He unwillingly calculated it, and he returned home after he finished his report. However, you, an able secretary of Mr. Knight, have found that one field is missing in his report: the length of the fence required to surround the building. Fortunately you are also a good programmer, so you have decided to write a program that calculates the length of the fence.\n\nTo be specific, the form of his building is union of a cylinder and a prism. You may consider the twodimensional projection of the form, i. e. the shape of the building is considered to be union of a circle C and a polygon P. The fence surrounds the outside of the building. The shape of the building may have a hole in it, and the fence is not needed inside the building. An example is shown in the figure below.", "constraint": "", "input": "The input contains one test case.\n\nA test case has the following format:\n\nR\nN x_1 y_1 x_2 y_2 . . . x_n y_n\n\nR is an integer that indicates the radius of C (1 <= R <= 1000), whose center is located at the origin. N is the number of vertices of P, and (x_i, y_i) is the coordinate of the i-th vertex of P. N, x_i and y_i are all integers satisfying the following conditions: 3 <= N <= 100, |x_i| <= 1000 and |y_i| <= 1000.\n\nYou may assume that C and P have one or more intersections.", "output": "Print the length of the fence required to surround the building. The output value should be in a decimal fraction may not contain an absolute error more than 10^-4.\n\nIt is guaranteed that the answer does not change by more than 10^-6 when R is changed by up to 10^-9.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n8 -1 2 1 2 1 -3 2 -3 2 3 -2 3 -2 -3 -1 -3\n output: 22.6303"], "Pid": "p01572", "ProblemText": "Task Description: Mr. Knight is a chief architect of the project to build a new art museum. One day, he was struggling to determine the design of the building. He believed that a brilliant art museum must have an artistic building, so he started to search for a good motif of his building. The art museum has one big theme: \"nature and human beings. \" To reflect the theme, he decided to adopt a combination of a cylinder and a prism, which symbolize nature and human beings respectively (between these figures and the theme, there is a profound relationship that only he knows).\n\nShortly after his decision, he remembered that he has to tell an estimate of the cost required to build to the financial manager. He unwillingly calculated it, and he returned home after he finished his report. However, you, an able secretary of Mr. Knight, have found that one field is missing in his report: the length of the fence required to surround the building. Fortunately you are also a good programmer, so you have decided to write a program that calculates the length of the fence.\n\nTo be specific, the form of his building is union of a cylinder and a prism. You may consider the twodimensional projection of the form, i. e. the shape of the building is considered to be union of a circle C and a polygon P. The fence surrounds the outside of the building. The shape of the building may have a hole in it, and the fence is not needed inside the building. An example is shown in the figure below.\nTask Input: The input contains one test case.\n\nA test case has the following format:\n\nR\nN x_1 y_1 x_2 y_2 . . . x_n y_n\n\nR is an integer that indicates the radius of C (1 <= R <= 1000), whose center is located at the origin. N is the number of vertices of P, and (x_i, y_i) is the coordinate of the i-th vertex of P. N, x_i and y_i are all integers satisfying the following conditions: 3 <= N <= 100, |x_i| <= 1000 and |y_i| <= 1000.\n\nYou may assume that C and P have one or more intersections.\nTask Output: Print the length of the fence required to surround the building. The output value should be in a decimal fraction may not contain an absolute error more than 10^-4.\n\nIt is guaranteed that the answer does not change by more than 10^-6 when R is changed by up to 10^-9.\nTask Samples: input: 2\n8 -1 2 1 2 1 -3 2 -3 2 3 -2 3 -2 -3 -1 -3\n output: 22.6303\n\n" }, { "title": "Problem C: Complex Integer Solutions", "content": "Let f(x) = a_0 + a_1x + a_2x^2 + . . . + a_dx^d be the function where each a_i (0 <= i <= d) is a constant integer (and a_d is non-zero) and x is a variable. Your task is to write a program that finds all complex integer solutions of the equation f(x) = 0 for a given f(x). Here, by complex integers, we mean complex numbers whose\nreal and imaginary parts are both integers.", "constraint": "", "input": "The input consists of two lines. The first line of the input contains d, the degree of f(x). The second line contains (d + 1) integers a_0, . . . , a_d, the coeffcients of the equation. You may assume all the following: 1 <= d <= 10, |a_i| <= 10^6 and a_d ! = 0.", "output": "There should be two lines in the output. In the first line, print the number m of complex integer solutions. In the second line, print m solutions separated by space. Each solution should be counted and printed exactly once even if it is a multiple root. The solutions should be printed in ascending order of their real parts then their imaginary parts, and in the following fashion: 0, -2, i, -3i, 2+i, and 3-4i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n-2 0 0 0 2\n output: 4\n-1 -i i 1", "input: 8\n0 0 25 15 17 -10 1 -1 1\n output: 5\n-1-2i -1+2i 0 2-i 2+i"], "Pid": "p01573", "ProblemText": "Task Description: Let f(x) = a_0 + a_1x + a_2x^2 + . . . + a_dx^d be the function where each a_i (0 <= i <= d) is a constant integer (and a_d is non-zero) and x is a variable. Your task is to write a program that finds all complex integer solutions of the equation f(x) = 0 for a given f(x). Here, by complex integers, we mean complex numbers whose\nreal and imaginary parts are both integers.\nTask Input: The input consists of two lines. The first line of the input contains d, the degree of f(x). The second line contains (d + 1) integers a_0, . . . , a_d, the coeffcients of the equation. You may assume all the following: 1 <= d <= 10, |a_i| <= 10^6 and a_d ! = 0.\nTask Output: There should be two lines in the output. In the first line, print the number m of complex integer solutions. In the second line, print m solutions separated by space. Each solution should be counted and printed exactly once even if it is a multiple root. The solutions should be printed in ascending order of their real parts then their imaginary parts, and in the following fashion: 0, -2, i, -3i, 2+i, and 3-4i.\nTask Samples: input: 4\n-2 0 0 0 2\n output: 4\n-1 -i i 1\ninput: 8\n0 0 25 15 17 -10 1 -1 1\n output: 5\n-1-2i -1+2i 0 2-i 2+i\n\n" }, { "title": "Problem D: Dial Key", "content": "You are a secret agent from the Intelligence Center of Peacemaking Committee. You've just sneaked into a secret laboratory of an evil company, Automated Crime Machines.\n\nYour mission is to get a confidential document kept in the laboratory. To reach the document, you need to unlock the door to the safe where it is kept. You have to unlock the door in a correct way and with a great care; otherwise an alarm would ring and you would be caught by the secret police.\n\nThe lock has a circular dial with N lights around it and a hand pointing to one of them. The lock also has M buttons to control the hand. Each button has a number L_i printed on it.\n\nInitially, all the lights around the dial are turned off. When the i-th button is pressed, the hand revolves clockwise by L_i lights, and the pointed light is turned on. You are allowed to press the buttons exactly N times. The lock opens only when you make all the lights turned on.\n\nFor example, in the case with N = 6, M = 2, L_1 = 2 and L_2 = 5, you can unlock the door by pressing buttons 2,2,2,5,2 and 2 in this order.\n\nThere are a number of doors in the laboratory, and some of them don 't seem to be unlockable. Figure out which lock can be opened, given the values N, M, and L_i's.", "constraint": "", "input": "The input starts with a line containing two integers, which represent N and M respectively. M lines follow, each of which contains an integer representing L_i.\n\nIt is guaranteed that 1 <= N <= 10^9,1 <= M <= 10^5, and 1 <= L_i <= N for each i = 1,2, . . . N.", "output": "Output a line with \"Yes\" (without quotes) if the lock can be opened, and \"No\" otherwise.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 2\n2\n5\n output: Yes", "input: 3 1\n1\n output: Yes", "input: 4 2\n2\n4\n output: No"], "Pid": "p01574", "ProblemText": "Task Description: You are a secret agent from the Intelligence Center of Peacemaking Committee. You've just sneaked into a secret laboratory of an evil company, Automated Crime Machines.\n\nYour mission is to get a confidential document kept in the laboratory. To reach the document, you need to unlock the door to the safe where it is kept. You have to unlock the door in a correct way and with a great care; otherwise an alarm would ring and you would be caught by the secret police.\n\nThe lock has a circular dial with N lights around it and a hand pointing to one of them. The lock also has M buttons to control the hand. Each button has a number L_i printed on it.\n\nInitially, all the lights around the dial are turned off. When the i-th button is pressed, the hand revolves clockwise by L_i lights, and the pointed light is turned on. You are allowed to press the buttons exactly N times. The lock opens only when you make all the lights turned on.\n\nFor example, in the case with N = 6, M = 2, L_1 = 2 and L_2 = 5, you can unlock the door by pressing buttons 2,2,2,5,2 and 2 in this order.\n\nThere are a number of doors in the laboratory, and some of them don 't seem to be unlockable. Figure out which lock can be opened, given the values N, M, and L_i's.\nTask Input: The input starts with a line containing two integers, which represent N and M respectively. M lines follow, each of which contains an integer representing L_i.\n\nIt is guaranteed that 1 <= N <= 10^9,1 <= M <= 10^5, and 1 <= L_i <= N for each i = 1,2, . . . N.\nTask Output: Output a line with \"Yes\" (without quotes) if the lock can be opened, and \"No\" otherwise.\nTask Samples: input: 6 2\n2\n5\n output: Yes\ninput: 3 1\n1\n output: Yes\ninput: 4 2\n2\n4\n output: No\n\n" }, { "title": "Problem E: Dungeon Master", "content": "Once upon a time, in a fantasy world far, far away, monsters dug caves and dungeons for adventurers. They put some obstacles in their caves so it becomes more difficult and more exciting for the adventurers to reach the goal.\n\nOne day, Emils, one of the monsters in the caves, had a question about the caves. How many patterns of a cave can they make, by changing the locations of the obstacles in it?\n\nHere's the detail of the question. A cave consists of W * H squares. Monsters can put obstacles at some of the squares, so that adventurers can't go into them. The total number of obstacles is fixed, and there can't be two or more obstacles in one square. Adventurers enter the cave from the top-left square, and try to reach the bottom-right square. They can move from one square to any of the four adjacent squares, as long as there are no obstacles in the destination square. There must be at least one path between any two squares that don't have obstacles. There must be no obstacles in the top-left square, nor in right-bottom square. The question is, given the width W and height H of the cave, and the number S of obstacles, how many patterns of the caves the monsters can make. As the obstacles have the same look, they should not\nbe distinguished each other.\n\nIt was a very interesting mathematical question. Emils couldn't solve this question by himself, so he told it to his colleagues instead. None of them could answer to it, though. After that, the question soon got popular among the monsters working in the caves, and finally, they became unable to sleep well as they always thought about the question.\n\nYou are requested to write a program that answers to the question.", "constraint": "", "input": "The input has a line, containing three integers W, H, and S, separated by a space. W and H are the horizontal and vertical sizes of the cave, and S is the number of obstacles to put in the cave. It is guaranteed that 2 <= W, H <= 8, and that 0 <= S <= W * H.", "output": "Output the number of patterns of the cave, in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 2\n output: 0", "input: 2 2 1\n output: 2"], "Pid": "p01575", "ProblemText": "Task Description: Once upon a time, in a fantasy world far, far away, monsters dug caves and dungeons for adventurers. They put some obstacles in their caves so it becomes more difficult and more exciting for the adventurers to reach the goal.\n\nOne day, Emils, one of the monsters in the caves, had a question about the caves. How many patterns of a cave can they make, by changing the locations of the obstacles in it?\n\nHere's the detail of the question. A cave consists of W * H squares. Monsters can put obstacles at some of the squares, so that adventurers can't go into them. The total number of obstacles is fixed, and there can't be two or more obstacles in one square. Adventurers enter the cave from the top-left square, and try to reach the bottom-right square. They can move from one square to any of the four adjacent squares, as long as there are no obstacles in the destination square. There must be at least one path between any two squares that don't have obstacles. There must be no obstacles in the top-left square, nor in right-bottom square. The question is, given the width W and height H of the cave, and the number S of obstacles, how many patterns of the caves the monsters can make. As the obstacles have the same look, they should not\nbe distinguished each other.\n\nIt was a very interesting mathematical question. Emils couldn't solve this question by himself, so he told it to his colleagues instead. None of them could answer to it, though. After that, the question soon got popular among the monsters working in the caves, and finally, they became unable to sleep well as they always thought about the question.\n\nYou are requested to write a program that answers to the question.\nTask Input: The input has a line, containing three integers W, H, and S, separated by a space. W and H are the horizontal and vertical sizes of the cave, and S is the number of obstacles to put in the cave. It is guaranteed that 2 <= W, H <= 8, and that 0 <= S <= W * H.\nTask Output: Output the number of patterns of the cave, in a line.\nTask Samples: input: 2 2 2\n output: 0\ninput: 2 2 1\n output: 2\n\n" }, { "title": "Problem F: Exciting Bicycle", "content": "You happened to get a special bicycle. You can run with it incredibly fast because it has a turbo engine. You can't wait to try it off road to enjoy the power.\n\nYou planned to go straight. The ground is very rough with ups and downs, and can be seen as a series of slopes (line segments) when seen from a lateral view. The bicycle runs on the ground at a constant speed of V. Since running very fast, the bicycle jumps off the ground every time it comes to the beginning point of a slope slanting more downward than the previous, as illustrated below. It then goes along a parabola until reaching the ground, affected by the gravity with the acceleration of 9.8m/s^2.\n\nIt is somewhat scary to ride the bicycle without any preparations - you might crash into rocks or fall into pitfalls. So you decided to perform a computer simulation of the ride.\n\nGiven a description of the ground, calculate the trace you will run on the ground by the bicycle. For simplicity, it is sufficient to output its length.", "constraint": "", "input": "The first line of the input has two integers N (2 <= N <= 10000) and V (1 <= V <= 10000), separated by a space. It is followed by N lines. The i-th line has two integers X_i and Y_i (0 <= X_i, Y_i <= 10000). V[m/s] is the ground speed of the bicycle. The (i - 1) line segments (X_i, Y_i)-(X_i+1, Y_i+1) form the slopes on the ground, with the sky in the positive direction of the Y axis. Each coordinate value is measured in meters.\n\nThe start is at (X_1, Y_1), and the goal is at (X_N, Y_N). It is guaranteed that X_i < X_i+1 for 1 <= i <= N - 1.\n\nYou may assume that the distance of x-coordinate between the falling point and any endpoint (except for the jumping point) is not less than 10^-5m.", "output": "Output the length you will run on the ground with the bicycle, in meters. The value may be printed with any number of digits after the decimal point, should have the absolute or relative error not greater than 10^-8.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 10\n0 0\n10 10\n20 0\n30 10\n40 0\n output: 22.22335598", "input: 2 10\n0 0\n10000 0\n output: 10000.00000000", "input: 4 10000\n0 0\n1 1\n9999 0\n10000 10000\n output: 11.21323169", "input: 4 50\n0 10000\n1 10000\n2 0\n10000 0\n output: 7741.23024274"], "Pid": "p01576", "ProblemText": "Task Description: You happened to get a special bicycle. You can run with it incredibly fast because it has a turbo engine. You can't wait to try it off road to enjoy the power.\n\nYou planned to go straight. The ground is very rough with ups and downs, and can be seen as a series of slopes (line segments) when seen from a lateral view. The bicycle runs on the ground at a constant speed of V. Since running very fast, the bicycle jumps off the ground every time it comes to the beginning point of a slope slanting more downward than the previous, as illustrated below. It then goes along a parabola until reaching the ground, affected by the gravity with the acceleration of 9.8m/s^2.\n\nIt is somewhat scary to ride the bicycle without any preparations - you might crash into rocks or fall into pitfalls. So you decided to perform a computer simulation of the ride.\n\nGiven a description of the ground, calculate the trace you will run on the ground by the bicycle. For simplicity, it is sufficient to output its length.\nTask Input: The first line of the input has two integers N (2 <= N <= 10000) and V (1 <= V <= 10000), separated by a space. It is followed by N lines. The i-th line has two integers X_i and Y_i (0 <= X_i, Y_i <= 10000). V[m/s] is the ground speed of the bicycle. The (i - 1) line segments (X_i, Y_i)-(X_i+1, Y_i+1) form the slopes on the ground, with the sky in the positive direction of the Y axis. Each coordinate value is measured in meters.\n\nThe start is at (X_1, Y_1), and the goal is at (X_N, Y_N). It is guaranteed that X_i < X_i+1 for 1 <= i <= N - 1.\n\nYou may assume that the distance of x-coordinate between the falling point and any endpoint (except for the jumping point) is not less than 10^-5m.\nTask Output: Output the length you will run on the ground with the bicycle, in meters. The value may be printed with any number of digits after the decimal point, should have the absolute or relative error not greater than 10^-8.\nTask Samples: input: 5 10\n0 0\n10 10\n20 0\n30 10\n40 0\n output: 22.22335598\ninput: 2 10\n0 0\n10000 0\n output: 10000.00000000\ninput: 4 10000\n0 0\n1 1\n9999 0\n10000 10000\n output: 11.21323169\ninput: 4 50\n0 10000\n1 10000\n2 0\n10000 0\n output: 7741.23024274\n\n" }, { "title": "Problem H: Magic Walls", "content": "You are a magician and have a large farm to grow magical fruits.\n\nOne day, you saw a horde of monsters, approaching your farm. They would ruin your magical farm once they reached your farm. Unfortunately, you are not strong enough to fight against those monsters. To protect your farm against them, you decided to build magic walls around your land.\n\nYou have four magic orbs to build the walls, namely, the orbs of Aquamarine (A), Bloodstone (B), Citrine (C) and Diamond (D). When you place them correctly and then cast a spell, there will be magic walls between the orbs A and B, between B and C, between C and D, and between D and A. The walls are built on the line segments connecting two orbs, and form a quadrangle as a whole. As the monsters cannot cross the magic walls, the inside of the magic walls is protected.\n\nNonetheless, you can protect only a part of your land, since there are a couple of restrictions on building the magic walls. There are N hills in your farm, where the orbs can receive rich power of magic. Each orb should be set on the top of one of the hills. Also, to avoid interference between the orbs, you may not place two or more orbs at the same hill.\n\nNow, you want to maximize the area protected by the magic walls. Please figure it out.", "constraint": "", "input": "The input begins with an integer N (4 <= N <= 1500), the number of the hills. Then N line follow. Each of them has two integers x (0 <= x <= 50000) and y (0 <= y <= 50000), the x- and y-coordinates of the location of a hill.\n\nIt is guaranteed that no two hills have the same location and that no three hills lie on a single line.", "output": "Output the maximum area you can protect. The output value should be printed with one digit after the decimal point, and should be exact.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 0\n0 1\n1 3\n4 2\n3 4\n output: 7.5", "input: 4\n0 0\n0 3\n1 1\n3 0\n output: 3.0"], "Pid": "p01577", "ProblemText": "Task Description: You are a magician and have a large farm to grow magical fruits.\n\nOne day, you saw a horde of monsters, approaching your farm. They would ruin your magical farm once they reached your farm. Unfortunately, you are not strong enough to fight against those monsters. To protect your farm against them, you decided to build magic walls around your land.\n\nYou have four magic orbs to build the walls, namely, the orbs of Aquamarine (A), Bloodstone (B), Citrine (C) and Diamond (D). When you place them correctly and then cast a spell, there will be magic walls between the orbs A and B, between B and C, between C and D, and between D and A. The walls are built on the line segments connecting two orbs, and form a quadrangle as a whole. As the monsters cannot cross the magic walls, the inside of the magic walls is protected.\n\nNonetheless, you can protect only a part of your land, since there are a couple of restrictions on building the magic walls. There are N hills in your farm, where the orbs can receive rich power of magic. Each orb should be set on the top of one of the hills. Also, to avoid interference between the orbs, you may not place two or more orbs at the same hill.\n\nNow, you want to maximize the area protected by the magic walls. Please figure it out.\nTask Input: The input begins with an integer N (4 <= N <= 1500), the number of the hills. Then N line follow. Each of them has two integers x (0 <= x <= 50000) and y (0 <= y <= 50000), the x- and y-coordinates of the location of a hill.\n\nIt is guaranteed that no two hills have the same location and that no three hills lie on a single line.\nTask Output: Output the maximum area you can protect. The output value should be printed with one digit after the decimal point, and should be exact.\nTask Samples: input: 5\n2 0\n0 1\n1 3\n4 2\n3 4\n output: 7.5\ninput: 4\n0 0\n0 3\n1 1\n3 0\n output: 3.0\n\n" }, { "title": "Problem I: Sort by Hand", "content": "It's time to arrange the books on your bookshelf. There are n books in the shelf and each book has a unique number; you want to sort the books according to the numbers. You know that the quick sort and the merge sort are fast sorting methods, but it is too hard for you to simulate them by hand - they are efficient for computers, but not for humans. Thus, you decided to sort the books by inserting the book with the number i into the i-th position. How many insertions are required to complete this task?", "constraint": "", "input": "The first line of the input is n (1 <= n <= 20), which is the number of books. The second line contains n integers v_1, . . . , v_n (1 <= v_i <= n), where v_i indicates the number of the book at the i-th position before the sorting. All v_i's are distinct.", "output": "Print the minimum number of insertions in a line. If it is impossible for him to complete the sort, print \"impossible\" (without quotes).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3\n output: 0", "input: 3\n2 1 3\n output: 1", "input: 3\n3 2 1\n output: 2", "input: 20\n4 14 11 13 17 10 1 12 2 6 16 15 8 7 19 18 3 5 9 20\n output: 14"], "Pid": "p01578", "ProblemText": "Task Description: It's time to arrange the books on your bookshelf. There are n books in the shelf and each book has a unique number; you want to sort the books according to the numbers. You know that the quick sort and the merge sort are fast sorting methods, but it is too hard for you to simulate them by hand - they are efficient for computers, but not for humans. Thus, you decided to sort the books by inserting the book with the number i into the i-th position. How many insertions are required to complete this task?\nTask Input: The first line of the input is n (1 <= n <= 20), which is the number of books. The second line contains n integers v_1, . . . , v_n (1 <= v_i <= n), where v_i indicates the number of the book at the i-th position before the sorting. All v_i's are distinct.\nTask Output: Print the minimum number of insertions in a line. If it is impossible for him to complete the sort, print \"impossible\" (without quotes).\nTask Samples: input: 3\n1 2 3\n output: 0\ninput: 3\n2 1 3\n output: 1\ninput: 3\n3 2 1\n output: 2\ninput: 20\n4 14 11 13 17 10 1 12 2 6 16 15 8 7 19 18 3 5 9 20\n output: 14\n\n" }, { "title": "Problem J: Substring Expression", "content": "Trees are sometimes represented in the form of strings. Here is one of the most popular ways to represent unlabeled trees:\n\n Leaves are represented by \"()\".\n\n Other nodes (i. e. internal nodes) are represented by \"( S_1 S_2 . . . S_n )\", where S_i is the string representing the i-th subnode.\nFor example, the tree depicted in the figure below is represented by a string \"((()())())\".\n\nA strange boy Norward is playing with such strings. He has found that a string sometimes remains valid as the representation of a tree even after one successive portion is removed from it. For example, removing the underlined portion from the string \"((()())())\" results in \"((()))\", which represents the tree depicted below.\n\nHowever, he has no way to know how many ways of such removal there are. Your task is to write a program for it, so that his curiosity is fulfilled.", "constraint": "", "input": "The input contains a string that represents some unlabeled tree. The string consists of up to 100,000 characters.", "output": "Print the number of portions of the given string such that removing them results in strings that represent other valid trees.", "content_img": true, "lang": "en", "error": false, "samples": ["input: ((()())())\n output: 10"], "Pid": "p01579", "ProblemText": "Task Description: Trees are sometimes represented in the form of strings. Here is one of the most popular ways to represent unlabeled trees:\n\n Leaves are represented by \"()\".\n\n Other nodes (i. e. internal nodes) are represented by \"( S_1 S_2 . . . S_n )\", where S_i is the string representing the i-th subnode.\nFor example, the tree depicted in the figure below is represented by a string \"((()())())\".\n\nA strange boy Norward is playing with such strings. He has found that a string sometimes remains valid as the representation of a tree even after one successive portion is removed from it. For example, removing the underlined portion from the string \"((()())())\" results in \"((()))\", which represents the tree depicted below.\n\nHowever, he has no way to know how many ways of such removal there are. Your task is to write a program for it, so that his curiosity is fulfilled.\nTask Input: The input contains a string that represents some unlabeled tree. The string consists of up to 100,000 characters.\nTask Output: Print the number of portions of the given string such that removing them results in strings that represent other valid trees.\nTask Samples: input: ((()())())\n output: 10\n\n" }, { "title": "Problem K: Up Above the World So High", "content": "One of the questions children often ask is \"How many stars are there in the sky? \" Under ideal conditions, even with the naked eye, nearly eight thousands are observable in the northern hemisphere. With a decent telescope, you may find many more, but, as the sight field will be limited, you may find much less at a time.\n\nChildren may ask the same questions to their parents in a spaceship billions of light-years away from the Earth. Their telescopes are similar to ours with circular sight field. It can be rotated freely, that is, the sight vector can take an arbitrary value.\n\nGiven a set of positions of stars and the spec of a telescope, your task is to determine the maximum\nnumber of stars that can be seen through the telescope at a time.\n note:\nThis problem statement is taken from \"How I Wonder What You Are! \" in ACM-ICPC Asia Regional Contest 2006, Yokohoma, with small but substantial changes.", "constraint": "", "input": "The first line of a test case contains a positive integer N not exceeding 100, meaning the number of stars. Each of the N lines following it contains three integers, s_x, s_y and s_z. They give the position (s_x, s_y, s_z) of the star described in Euclidean coordinates. You may assume that -1000 <= s_x <= 1000, -1000 <= s_y <= 1000, -1000 <= s_z <= 1000 and (s_x, s_y, s_z) ! = (0,0,0).\n\nThen comes a line containing a positive integer ψ (0 < ψ < 90), which represents the angular radius, in degrees, of the sight field of the telescope. The telescope is at the origin of the coordinate system (0,0,0).\n\nYou may assume that change of the angular radius ψ by less than 0.01 degrees does not affect the answer, and that ∠POQ is greater than 0.01 degrees for any pair of distinct stars P and Q and the origin O.", "output": "One line containing an integer meaning the maximum number of stars observable through the telescope should be output. No other characters should be contained in the output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 0 0\n0 1 0\n40\n output: 1", "input: 2\n1 0 0\n0 1 0\n50\n output: 2"], "Pid": "p01580", "ProblemText": "Task Description: One of the questions children often ask is \"How many stars are there in the sky? \" Under ideal conditions, even with the naked eye, nearly eight thousands are observable in the northern hemisphere. With a decent telescope, you may find many more, but, as the sight field will be limited, you may find much less at a time.\n\nChildren may ask the same questions to their parents in a spaceship billions of light-years away from the Earth. Their telescopes are similar to ours with circular sight field. It can be rotated freely, that is, the sight vector can take an arbitrary value.\n\nGiven a set of positions of stars and the spec of a telescope, your task is to determine the maximum\nnumber of stars that can be seen through the telescope at a time.\n note:\nThis problem statement is taken from \"How I Wonder What You Are! \" in ACM-ICPC Asia Regional Contest 2006, Yokohoma, with small but substantial changes.\nTask Input: The first line of a test case contains a positive integer N not exceeding 100, meaning the number of stars. Each of the N lines following it contains three integers, s_x, s_y and s_z. They give the position (s_x, s_y, s_z) of the star described in Euclidean coordinates. You may assume that -1000 <= s_x <= 1000, -1000 <= s_y <= 1000, -1000 <= s_z <= 1000 and (s_x, s_y, s_z) ! = (0,0,0).\n\nThen comes a line containing a positive integer ψ (0 < ψ < 90), which represents the angular radius, in degrees, of the sight field of the telescope. The telescope is at the origin of the coordinate system (0,0,0).\n\nYou may assume that change of the angular radius ψ by less than 0.01 degrees does not affect the answer, and that ∠POQ is greater than 0.01 degrees for any pair of distinct stars P and Q and the origin O.\nTask Output: One line containing an integer meaning the maximum number of stars observable through the telescope should be output. No other characters should be contained in the output.\nTask Samples: input: 2\n1 0 0\n0 1 0\n40\n output: 1\ninput: 2\n1 0 0\n0 1 0\n50\n output: 2\n\n" }, { "title": "Problem A: Cache Control", "content": "Mr. Haskins is working on tuning a database system. The database is a simple associative storage that contains key-value pairs. In this database, a key is a distinct identification (ID) number and a value is an object of any type.\n\nIn order to boost the performance, the database system has a cache mechanism. The cache can be accessed much faster than the normal storage, but the number of items it can hold at a time is limited. To implement caching, he selected least recently used (LRU) algorithm: when the cache is full and a new item (not in the cache) is being accessed, the cache discards the least recently accessed entry and adds the new item.\n\nYou are an assistant of Mr. Haskins. He regards you as a trusted programmer, so he gave you a task. He wants you to investigate the cache entries after a specific sequence of accesses.", "constraint": "", "input": "The first line of the input contains two integers N and M. N is the number of accessed IDs, and M is the size of the cache. These values satisfy the following condition: 1 <= N, M <= 100000.\n\nThe following N lines, each containing one ID, represent the sequence of the queries. An ID is a positive integer less than or equal to 10^9.", "output": "Print IDs remaining in the cache after executing all queries. Each line should contain exactly one ID. These IDs should appear in the order of their last access time, from the latest to the earliest.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1\n2\n3\n output: 3\n2", "input: 5 3\n1\n2\n3\n4\n1\n output: 1\n4\n3"], "Pid": "p01581", "ProblemText": "Task Description: Mr. Haskins is working on tuning a database system. The database is a simple associative storage that contains key-value pairs. In this database, a key is a distinct identification (ID) number and a value is an object of any type.\n\nIn order to boost the performance, the database system has a cache mechanism. The cache can be accessed much faster than the normal storage, but the number of items it can hold at a time is limited. To implement caching, he selected least recently used (LRU) algorithm: when the cache is full and a new item (not in the cache) is being accessed, the cache discards the least recently accessed entry and adds the new item.\n\nYou are an assistant of Mr. Haskins. He regards you as a trusted programmer, so he gave you a task. He wants you to investigate the cache entries after a specific sequence of accesses.\nTask Input: The first line of the input contains two integers N and M. N is the number of accessed IDs, and M is the size of the cache. These values satisfy the following condition: 1 <= N, M <= 100000.\n\nThe following N lines, each containing one ID, represent the sequence of the queries. An ID is a positive integer less than or equal to 10^9.\nTask Output: Print IDs remaining in the cache after executing all queries. Each line should contain exactly one ID. These IDs should appear in the order of their last access time, from the latest to the earliest.\nTask Samples: input: 3 2\n1\n2\n3\n output: 3\n2\ninput: 5 3\n1\n2\n3\n4\n1\n output: 1\n4\n3\n\n" }, { "title": "Problem B: Cover Time", "content": "Let G be a connected undirected graph where N vertices of G are labeled by numbers from 1 to N. G is simple, i. e. G has no self loops or parallel edges.\n\nLet P be a particle walking on vertices of G. At the beginning, P is on the vertex 1. In each step, P moves to one of the adjacent vertices. When there are multiple adjacent vertices, each is selected in the same\nprobability.\n\nThe cover time is the expected number of steps necessary for P to visit all the vertices.\n\nYour task is to calculate the cover time for each given graph G.", "constraint": "", "input": "The input has the following format.\n\nN M\na_1 b_1\n. \n. \n. \na_M b_M\n\nN is the number of vertices and M is the number of edges. You can assume that 2 <= N <= 10. a_i and b_i (1 <= i <= M) are positive integers less than or equal to N, which represent the two vertices connected by the i-th edge. You can assume that the input satisfies the constraints written in the problem description, that is, the given graph G is connected and simple.", "output": "There should be one line containing the cover time in the output.\n\nThe answer should be printed with six digits after the decimal point, and should not have an error greater than 10^-6.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n2 3\n output: 4.000000", "input: 4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n output: 5.500000"], "Pid": "p01582", "ProblemText": "Task Description: Let G be a connected undirected graph where N vertices of G are labeled by numbers from 1 to N. G is simple, i. e. G has no self loops or parallel edges.\n\nLet P be a particle walking on vertices of G. At the beginning, P is on the vertex 1. In each step, P moves to one of the adjacent vertices. When there are multiple adjacent vertices, each is selected in the same\nprobability.\n\nThe cover time is the expected number of steps necessary for P to visit all the vertices.\n\nYour task is to calculate the cover time for each given graph G.\nTask Input: The input has the following format.\n\nN M\na_1 b_1\n. \n. \n. \na_M b_M\n\nN is the number of vertices and M is the number of edges. You can assume that 2 <= N <= 10. a_i and b_i (1 <= i <= M) are positive integers less than or equal to N, which represent the two vertices connected by the i-th edge. You can assume that the input satisfies the constraints written in the problem description, that is, the given graph G is connected and simple.\nTask Output: There should be one line containing the cover time in the output.\n\nThe answer should be printed with six digits after the decimal point, and should not have an error greater than 10^-6.\nTask Samples: input: 3 2\n1 2\n2 3\n output: 4.000000\ninput: 4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n output: 5.500000\n\n" }, { "title": "Problem C: Craftsman", "content": "Takeshi, a famous craftsman, accepts many offers from all over Japan. However, the tools which he is using now has become already too old. So he is planning to buy new tools and to replace the old ones before next use of the tools. Some offers may incur him monetary cost, if the offer requires the tools to be replaced. Thus, it is not necessarily best to accept all the orders he has received. Now, you are one of his disciples. Your task is to calculate the set of orders to be accepted, that maximizes his earning for a given list of orders and prices of tools. His earning may shift up and down due to sale income and replacement cost.\n\nHe always purchases tools from his friend's shop. The shop discounts prices for some pairs of items when the pair is purchased at the same time. You have to take the discount into account. The total price to pay may be not equal to the simple sum of individual prices.\n\nYou may assume that all the tools at the shop are tough enough. Takeshi can complete all orders with replaced tools at this time. Thus you have to buy at most one tool for each kind of tool.", "constraint": "", "input": "The input conforms to the following format:\n\nN M P\nX_1 K_1 I_1,1 . . . I_1, K1\n. . . \nX_N K_N I_N, 1 . . . I_N, KN\nY_1\n. . . \nY_M\nJ_1,1 J_1,2 D_1\n. . . \nJ_P, 1 J_P, 2 D_P\n\nwhere N, M, P are the numbers of orders, tools sold in the shop and pairs of discountable items, respectively.\n\nThe following N lines specify the details of orders. X_i is an integer indicating the compensation for the i-th order, and K_i is the number of tools required to complete the order. The remaining part of each line describes the tools required for completing the order. Tools are specified by integers from 1 through M.\n\nThe next M lines are the price list at the shop of Takeshi's friend. An integer Y_i represents the price of the i-th tool.\n\nThe last P lines of each test case represent the pairs of items to be discounted. When Takeshi buys the J_i, 1-th and the J_i, 2-th tool at the same time, he has to pay only D_i yen, instead of the sum of their individual prices. It is guaranteed that no tool appears more than once in the discount list, and that max{Y_i, Y_j} < D_i, j < Y_i + Y_j for every discount prices, where D_i, j is the discount price of i-th and j-th tools bought at the same time.\n\nAlso it is guaranteed that 1 <= N <= 100,2 <= M <= 100,1 <= K_i <= 100,1 <= P <= M/2 and 1 <= X_i, Y_i <= 1000.", "output": "Output the maximum possible earning of Takeshi to the standard output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 2\n100 2 1 2\n100 1 3\n100 1 4\n20\n20\n50\n150\n1 2 30\n3 4 180\n output: 120", "input: 1 2 1\n100 1 2\n20\n40\n1 2 51\n output: 60"], "Pid": "p01583", "ProblemText": "Task Description: Takeshi, a famous craftsman, accepts many offers from all over Japan. However, the tools which he is using now has become already too old. So he is planning to buy new tools and to replace the old ones before next use of the tools. Some offers may incur him monetary cost, if the offer requires the tools to be replaced. Thus, it is not necessarily best to accept all the orders he has received. Now, you are one of his disciples. Your task is to calculate the set of orders to be accepted, that maximizes his earning for a given list of orders and prices of tools. His earning may shift up and down due to sale income and replacement cost.\n\nHe always purchases tools from his friend's shop. The shop discounts prices for some pairs of items when the pair is purchased at the same time. You have to take the discount into account. The total price to pay may be not equal to the simple sum of individual prices.\n\nYou may assume that all the tools at the shop are tough enough. Takeshi can complete all orders with replaced tools at this time. Thus you have to buy at most one tool for each kind of tool.\nTask Input: The input conforms to the following format:\n\nN M P\nX_1 K_1 I_1,1 . . . I_1, K1\n. . . \nX_N K_N I_N, 1 . . . I_N, KN\nY_1\n. . . \nY_M\nJ_1,1 J_1,2 D_1\n. . . \nJ_P, 1 J_P, 2 D_P\n\nwhere N, M, P are the numbers of orders, tools sold in the shop and pairs of discountable items, respectively.\n\nThe following N lines specify the details of orders. X_i is an integer indicating the compensation for the i-th order, and K_i is the number of tools required to complete the order. The remaining part of each line describes the tools required for completing the order. Tools are specified by integers from 1 through M.\n\nThe next M lines are the price list at the shop of Takeshi's friend. An integer Y_i represents the price of the i-th tool.\n\nThe last P lines of each test case represent the pairs of items to be discounted. When Takeshi buys the J_i, 1-th and the J_i, 2-th tool at the same time, he has to pay only D_i yen, instead of the sum of their individual prices. It is guaranteed that no tool appears more than once in the discount list, and that max{Y_i, Y_j} < D_i, j < Y_i + Y_j for every discount prices, where D_i, j is the discount price of i-th and j-th tools bought at the same time.\n\nAlso it is guaranteed that 1 <= N <= 100,2 <= M <= 100,1 <= K_i <= 100,1 <= P <= M/2 and 1 <= X_i, Y_i <= 1000.\nTask Output: Output the maximum possible earning of Takeshi to the standard output.\nTask Samples: input: 3 4 2\n100 2 1 2\n100 1 3\n100 1 4\n20\n20\n50\n150\n1 2 30\n3 4 180\n output: 120\ninput: 1 2 1\n100 1 2\n20\n40\n1 2 51\n output: 60\n\n" }, { "title": "Problem D: Divide the Water", "content": "A scientist Arthur C. Mc Donell is conducting a very complex chemical experiment. This experiment requires a large number of very simple operations to pour water into every column of the vessel at the predetermined ratio. Tired of boring manual work, he was trying to automate the operation.\n\nOne day, he came upon the idea to use three-pronged tubes to divide the water flow. For example, when you want to pour water into two columns at the ratio of 1 : 1, you can use one three-pronged tube to split one source into two.\n\nHe wanted to apply this idea to split water from only one faucet to the experiment vessel at an arbitrary ratio, but it has gradually turned out to be impossible to set the configuration in general, due to the limitations coming from the following conditions:\n\n The vessel he is using has several columns aligned horizontally, and each column has its specific capacity. He cannot rearrange the order of the columns.\n\nThere are enough number of glass tubes, rubber tubes and three-pronged tubes. A three-pronged tube always divides the water flow at the ratio of 1 : 1.\n\n Also there are enough number of fater faucets in his laboratory, but they are in the same height.\n\n A three-pronged tube cannot be used to combine two water flows. Moreover, each flow of water going out of the tubes must be poured into exactly one of the columns; he cannot discard water to the sewage, nor pour water into one column from two or more tubes.\n\nThe water flows only downward. So he cannot place the tubes over the faucets, nor under the exit of another tubes. Moreover, the tubes cannot be crossed.\n\nStill, Arthur did not want to give up. Although one-to-many division at an arbitrary ratio is impossible, he decided to minimize the number of faucets used. He asked you for a help to write a program to calculate the minimum number of faucets required to pour water into the vessel, for the number of columns and the ratio at which each column is going to be filled.", "constraint": "", "input": "The input consists of an integer sequence.\n\nThe first integer indicates N, the number of columns in the vessel. Then the following N integers describe the capacity by which each column should be filled. The i-th integer in this part specifies the ratio at which he is going to pour water into the i-th column.\n\nYou may assume that N <= 100, and for all i, v_i <= 1000000.", "output": "Output the number of the minimum faucet required to complete the operation.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 1 1\n output: 1", "input: 2 3 1\n output: 2", "input: 2 2 1\n output: 2", "input: 4 3 1 1 3\n output: 3", "input: 3 1 2 1\n output: 3", "input: 5 1 2 3 4 5\n output: 5", "input: 7 8 8 1 1 2 4 8\n output: 1"], "Pid": "p01584", "ProblemText": "Task Description: A scientist Arthur C. Mc Donell is conducting a very complex chemical experiment. This experiment requires a large number of very simple operations to pour water into every column of the vessel at the predetermined ratio. Tired of boring manual work, he was trying to automate the operation.\n\nOne day, he came upon the idea to use three-pronged tubes to divide the water flow. For example, when you want to pour water into two columns at the ratio of 1 : 1, you can use one three-pronged tube to split one source into two.\n\nHe wanted to apply this idea to split water from only one faucet to the experiment vessel at an arbitrary ratio, but it has gradually turned out to be impossible to set the configuration in general, due to the limitations coming from the following conditions:\n\n The vessel he is using has several columns aligned horizontally, and each column has its specific capacity. He cannot rearrange the order of the columns.\n\nThere are enough number of glass tubes, rubber tubes and three-pronged tubes. A three-pronged tube always divides the water flow at the ratio of 1 : 1.\n\n Also there are enough number of fater faucets in his laboratory, but they are in the same height.\n\n A three-pronged tube cannot be used to combine two water flows. Moreover, each flow of water going out of the tubes must be poured into exactly one of the columns; he cannot discard water to the sewage, nor pour water into one column from two or more tubes.\n\nThe water flows only downward. So he cannot place the tubes over the faucets, nor under the exit of another tubes. Moreover, the tubes cannot be crossed.\n\nStill, Arthur did not want to give up. Although one-to-many division at an arbitrary ratio is impossible, he decided to minimize the number of faucets used. He asked you for a help to write a program to calculate the minimum number of faucets required to pour water into the vessel, for the number of columns and the ratio at which each column is going to be filled.\nTask Input: The input consists of an integer sequence.\n\nThe first integer indicates N, the number of columns in the vessel. Then the following N integers describe the capacity by which each column should be filled. The i-th integer in this part specifies the ratio at which he is going to pour water into the i-th column.\n\nYou may assume that N <= 100, and for all i, v_i <= 1000000.\nTask Output: Output the number of the minimum faucet required to complete the operation.\nTask Samples: input: 2 1 1\n output: 1\ninput: 2 3 1\n output: 2\ninput: 2 2 1\n output: 2\ninput: 4 3 1 1 3\n output: 3\ninput: 3 1 2 1\n output: 3\ninput: 5 1 2 3 4 5\n output: 5\ninput: 7 8 8 1 1 2 4 8\n output: 1\n\n" }, { "title": "Problem E: Mickle's Beam", "content": "Major Mickle is commanded to protect a secret base which is being attacked by N tanks. Mickle has an ultimate laser rifle called Mickle's beam. Any object shot by this beam will be immediately destroyed, and there is no way for protection. Furthermore, the beam keeps going through even after destroying objects. The beam is such a powerful and horrible weapon, but there is one drawback: the beam consumes a huge amount of energy. For this reason, the number of shots should be always minimized.\n\nYour job is to write a program that calculates the minimum number of shots required to destroy all the enemy tanks.\n\nYou can assume the following:\n\n the base is located on the origin (0,0);\n\n each tank has a rectangular shape with edges parallel to the x- and y-axes;\n\n no tank may touch or include the origin;\n\n no two tanks share the same point;\n\n the width of beam is negligible; and\n\n a beam destroys every tank it touches or crosses.", "constraint": "", "input": "The input consists of an integer sequence.\n\nThe first integer indicates N (N <= 2,000). Each of the following N lines contains four integers which indicates the x- and y-coordinates of the lower-left corner and the upper-right corner of a tank respectively. You can assume that every coordinate may not exceed 10,000 in absolute value.", "output": "Output the minimum number of shots of the beam.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 -1 3 1\n-1 2 1 3\n-3 -1 -2 1\n-1 -3 1 -2\n output: 4", "input: 2\n1 0 2 1\n3 -1 4 0\n output: 1"], "Pid": "p01585", "ProblemText": "Task Description: Major Mickle is commanded to protect a secret base which is being attacked by N tanks. Mickle has an ultimate laser rifle called Mickle's beam. Any object shot by this beam will be immediately destroyed, and there is no way for protection. Furthermore, the beam keeps going through even after destroying objects. The beam is such a powerful and horrible weapon, but there is one drawback: the beam consumes a huge amount of energy. For this reason, the number of shots should be always minimized.\n\nYour job is to write a program that calculates the minimum number of shots required to destroy all the enemy tanks.\n\nYou can assume the following:\n\n the base is located on the origin (0,0);\n\n each tank has a rectangular shape with edges parallel to the x- and y-axes;\n\n no tank may touch or include the origin;\n\n no two tanks share the same point;\n\n the width of beam is negligible; and\n\n a beam destroys every tank it touches or crosses.\nTask Input: The input consists of an integer sequence.\n\nThe first integer indicates N (N <= 2,000). Each of the following N lines contains four integers which indicates the x- and y-coordinates of the lower-left corner and the upper-right corner of a tank respectively. You can assume that every coordinate may not exceed 10,000 in absolute value.\nTask Output: Output the minimum number of shots of the beam.\nTask Samples: input: 4\n2 -1 3 1\n-1 2 1 3\n-3 -1 -2 1\n-1 -3 1 -2\n output: 4\ninput: 2\n1 0 2 1\n3 -1 4 0\n output: 1\n\n" }, { "title": "Problem G: Riffle Swap", "content": "You have a deck of 2^N cards (1 <= N <= 1000000) and want to have them shuffled.\n\nThe most popular shuffling technique is probably the riffle shuffle, in which you split a deck into two halves, place them in your left and right hands, and then interleave the cards alternatively from those hands. The shuffle is called perfect when the deck is divided exactly in half and the cards are interleaved one-by-one from the bottom half. For example, the perfect riffle shuffle of a deck of eight cards <0,1,2,3,4,5,6,7> will result in a deck <0,4,1,5,2,6,3,7>.\n\nSince you are not so good at shuffling that you can perform the perfect riffle shuffle, you have decided to simulate the shuffle by swapping two cards as many times as needed. How many times you will have to perform swapping at least? As the resultant number will obviously become quite huge, your program should report the number modulo M = 1000003.", "constraint": "", "input": "The input just contains a single integer N.", "output": "Print the number of swaps in a line. No extra space or empty line should occur.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n output: 0", "input: 2\n output: 1", "input: 3\n output: 4", "input: 4\n output: 10", "input: 10\n output: 916"], "Pid": "p01587", "ProblemText": "Task Description: You have a deck of 2^N cards (1 <= N <= 1000000) and want to have them shuffled.\n\nThe most popular shuffling technique is probably the riffle shuffle, in which you split a deck into two halves, place them in your left and right hands, and then interleave the cards alternatively from those hands. The shuffle is called perfect when the deck is divided exactly in half and the cards are interleaved one-by-one from the bottom half. For example, the perfect riffle shuffle of a deck of eight cards <0,1,2,3,4,5,6,7> will result in a deck <0,4,1,5,2,6,3,7>.\n\nSince you are not so good at shuffling that you can perform the perfect riffle shuffle, you have decided to simulate the shuffle by swapping two cards as many times as needed. How many times you will have to perform swapping at least? As the resultant number will obviously become quite huge, your program should report the number modulo M = 1000003.\nTask Input: The input just contains a single integer N.\nTask Output: Print the number of swaps in a line. No extra space or empty line should occur.\nTask Samples: input: 1\n output: 0\ninput: 2\n output: 1\ninput: 3\n output: 4\ninput: 4\n output: 10\ninput: 10\n output: 916\n\n" }, { "title": "Problem H: Round Table", "content": "You are the owner of a restaurant, and you are serving for N customers seating in a round table.\n\nYou will distribute M menus to them. Each customer receiving a menu will make the order of plates, and\nthen pass the menu to the customer on the right unless he or she has not make the order. The customer i takes L_i unit time for the ordering.\n\nYour job is to write a program to calculate the minimum time until all customers to call their orders, so you can improve your business performance.", "constraint": "", "input": "The input consists of a sequence of positive integers.\n\nThe first line of the input contains two positive integers N (N <= 50,000) and M (M <= N). The second line contains N positive integers L_1, L_2, . . . , L_N (L_i <= 600).", "output": "Output the minimum possible time required for them to finish ordering.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 5 10\n output: 10", "input: 4 2\n1 2 3 4\n output: 5"], "Pid": "p01588", "ProblemText": "Task Description: You are the owner of a restaurant, and you are serving for N customers seating in a round table.\n\nYou will distribute M menus to them. Each customer receiving a menu will make the order of plates, and\nthen pass the menu to the customer on the right unless he or she has not make the order. The customer i takes L_i unit time for the ordering.\n\nYour job is to write a program to calculate the minimum time until all customers to call their orders, so you can improve your business performance.\nTask Input: The input consists of a sequence of positive integers.\n\nThe first line of the input contains two positive integers N (N <= 50,000) and M (M <= N). The second line contains N positive integers L_1, L_2, . . . , L_N (L_i <= 600).\nTask Output: Output the minimum possible time required for them to finish ordering.\nTask Samples: input: 3 2\n1 5 10\n output: 10\ninput: 4 2\n1 2 3 4\n output: 5\n\n" }, { "title": "Problem I: Strange Currency System", "content": "The currency system in the Kingdom of Yoax-Musty is strange and fairly inefficient. Like other countries, the kingdom has its own currencty unit denoted by K $ (kingdom dollar). However, the Ministry of Finance issues bills for every value between 1 K $ and (2^31 - 1) K $ worth.\n\nOn the other hand, this system often enables people to make many different values just with a small number of bills. For example, if you have four bills of 1 K $, 2 K $, 4 K $, and 8 K $ worth respectively, you can make any values from 1 K #36; to 15 K $.\n\nIn this problem, you are requested to write a program that finds the minimum value that cannot be made with a given set (multiset in a mathematical sense) of bills. For the case with the four bills (1 K $, 2 K $, 4 K $, and 8 K $), since you can make any values up to 15 K $, your program should report 16 K $.", "constraint": "", "input": "The input consists of two lines. The first line contains an integer N (1 <= N <= 10000), the number of bills. The second line contains N integers, each of which represents the value of a bill in K $. There may be multiple bills of the same value.", "output": "Print the minimum value unable to be made on a line. The value should be given in K $ and without any currency sign or name.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 4 8\n output: 16", "input: 5\n1 1 3 11 2\n output: 8"], "Pid": "p01589", "ProblemText": "Task Description: The currency system in the Kingdom of Yoax-Musty is strange and fairly inefficient. Like other countries, the kingdom has its own currencty unit denoted by K $ (kingdom dollar). However, the Ministry of Finance issues bills for every value between 1 K $ and (2^31 - 1) K $ worth.\n\nOn the other hand, this system often enables people to make many different values just with a small number of bills. For example, if you have four bills of 1 K $, 2 K $, 4 K $, and 8 K $ worth respectively, you can make any values from 1 K #36; to 15 K $.\n\nIn this problem, you are requested to write a program that finds the minimum value that cannot be made with a given set (multiset in a mathematical sense) of bills. For the case with the four bills (1 K $, 2 K $, 4 K $, and 8 K $), since you can make any values up to 15 K $, your program should report 16 K $.\nTask Input: The input consists of two lines. The first line contains an integer N (1 <= N <= 10000), the number of bills. The second line contains N integers, each of which represents the value of a bill in K $. There may be multiple bills of the same value.\nTask Output: Print the minimum value unable to be made on a line. The value should be given in K $ and without any currency sign or name.\nTask Samples: input: 4\n1 2 4 8\n output: 16\ninput: 5\n1 1 3 11 2\n output: 8\n\n" }, { "title": "Problem K: Trading Ship", "content": "You are on board a trading ship as a crew.\n\nThe ship is now going to pass through a strait notorious for many pirates often robbing ships. The Maritime Police has attempted to expel those pirates many times, but failed their attempts as the pirates are fairly strong. For this reason, every ship passing through the strait needs to defend themselves from the pirates. \n\nThe navigator has obtained a sea map on which the location of every hideout of pirates is shown. The strait is considered to be a rectangle of W * H on an xy-plane, where the two opposite corners have the coordinates of (0,0) and (W, H). The ship is going to enter and exit the strait at arbitrary points on y = 0 and y = H respectively.\n\nTo minimize the risk of attack, the navigator has decided to take a route as distant from the hideouts as possible. As a talented programmer, you are asked by the navigator to write a program that finds the best route, that is, the route with the maximum possible distance to the closest hideouts. For simplicity, your program just needs to report the distance in this problem.", "constraint": "", "input": "The input begins with a line containing three integers W, H, and N. Here, N indicates the number of hideouts on the strait. Then N lines follow, each of which contains two integers x_i and y_i, which denote the coordinates the i-th hideout is located on.\n\nThe input satisfies the following conditions: 1 <= W, H <= 10^9,1 <= N <= 500,0 <= x_i <= W, 0 <= y_i <= H.", "output": "There should be a line containing the distance from the best route to the closest hideout(s). The distance should be in a decimal fraction and should not contain an absolute error greater than 10^-3.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 10 1\n3 5\n output: 7.000", "input: 10 10 2\n2 2\n8 8\n output: 4.243", "input: 10 10 3\n0 1\n4 4\n8 1\n output: 2.500"], "Pid": "p01590", "ProblemText": "Task Description: You are on board a trading ship as a crew.\n\nThe ship is now going to pass through a strait notorious for many pirates often robbing ships. The Maritime Police has attempted to expel those pirates many times, but failed their attempts as the pirates are fairly strong. For this reason, every ship passing through the strait needs to defend themselves from the pirates. \n\nThe navigator has obtained a sea map on which the location of every hideout of pirates is shown. The strait is considered to be a rectangle of W * H on an xy-plane, where the two opposite corners have the coordinates of (0,0) and (W, H). The ship is going to enter and exit the strait at arbitrary points on y = 0 and y = H respectively.\n\nTo minimize the risk of attack, the navigator has decided to take a route as distant from the hideouts as possible. As a talented programmer, you are asked by the navigator to write a program that finds the best route, that is, the route with the maximum possible distance to the closest hideouts. For simplicity, your program just needs to report the distance in this problem.\nTask Input: The input begins with a line containing three integers W, H, and N. Here, N indicates the number of hideouts on the strait. Then N lines follow, each of which contains two integers x_i and y_i, which denote the coordinates the i-th hideout is located on.\n\nThe input satisfies the following conditions: 1 <= W, H <= 10^9,1 <= N <= 500,0 <= x_i <= W, 0 <= y_i <= H.\nTask Output: There should be a line containing the distance from the best route to the closest hideout(s). The distance should be in a decimal fraction and should not contain an absolute error greater than 10^-3.\nTask Samples: input: 10 10 1\n3 5\n output: 7.000\ninput: 10 10 2\n2 2\n8 8\n output: 4.243\ninput: 10 10 3\n0 1\n4 4\n8 1\n output: 2.500\n\n" }, { "title": "problem a: approximate circle", "content": "Consider a set of n points (x_1, y_1),\n. . . , (x_n, y_n) on a Cartesian space.\nYour task is to write a program for regression to a circle x^2\n+ y^2 + ax + by\n+ c = 0. In other words, your program should find a circle that\nminimizes the error. Here the error is measured by the sum over square distances\nbetween each point and the circle, which is given by:", "constraint": "", "input": "The input begins with a line containing one integer n (3 <= n\n<= 40,000). Then n lines follow. The i-th line contains\ntwo integers x_i and y_i (0 <= x_i,\ny_i <= 1,000), which denote the coordinates of the i-th\npoint. You can assume there are no cases in which all the points lie on a\nstraight line.", "output": "Print three integers a, b and c,\nseparated by space, to show the regressed function. The output values should be\nin a decimal fraction and should not contain an\nerror greater than 0.001.", "content_img": true, "lang": "", "error": false, "samples": ["input: 4\n0 0\n100 0\n100 100\n0 100\n output: -100.000 -100.000 0.000", "input: 3\n0 0\n10 0\n5 100\n output: -10.000 -99.750 0.000"], "Pid": "p01591", "ProblemText": "Task Description: Consider a set of n points (x_1, y_1),\n. . . , (x_n, y_n) on a Cartesian space.\nYour task is to write a program for regression to a circle x^2\n+ y^2 + ax + by\n+ c = 0. In other words, your program should find a circle that\nminimizes the error. Here the error is measured by the sum over square distances\nbetween each point and the circle, which is given by:\nTask Input: The input begins with a line containing one integer n (3 <= n\n<= 40,000). Then n lines follow. The i-th line contains\ntwo integers x_i and y_i (0 <= x_i,\ny_i <= 1,000), which denote the coordinates of the i-th\npoint. You can assume there are no cases in which all the points lie on a\nstraight line.\nTask Output: Print three integers a, b and c,\nseparated by space, to show the regressed function. The output values should be\nin a decimal fraction and should not contain an\nerror greater than 0.001.\nTask Samples: input: 4\n0 0\n100 0\n100 100\n0 100\n output: -100.000 -100.000 0.000\ninput: 3\n0 0\n10 0\n5 100\n output: -10.000 -99.750 0.000\n\n" }, { "title": "problem b: blame game", "content": "Alice and Bob are in a factional dispute. Recently a big serious problem\narised in a project both Alice and Bob had been working for. This problem was\ncaused by lots of faults of Alice's and Bob's sides; those faults are closely\nrelated. Alice and Bob started to blame each other. First, Alice claimed it was\ncaused by Bob's fault. Then Bob insisted his fault was led by Alice's fault.\nSoon after, Alice said that her fault should not have happened without Bob's\nanother fault. So on so forth. It was terrible. It was totally a blame game.\nStill, they had their pride. They would not use the same fault more than once in\ntheir claims. All right, let's see the situation in terms of a game. Alice and Bob have a number of faults. Some pairs of Alice and Bob faults\nhave direct relationship between them. This relationship is bidirectional; if a\nfault X is led by another fault Y, they can say either \"X was due to Y. \" or\n\"even with X, the problem could be avoided without Y. \" Note that not both, since\nthey never pick up the same fault in their claims. Alice and Bob take their turns alternatively. Alice takes the first turn\nby claiming any of Bob's faults. Then Bob makes his claim with Alice's fault\ndirectly related to the claimed fault. Afterward, in each turn, one picks up\nanother's fault directly related to the fault claimed in the previous turn. If\nhe/she has no faults that have not been claimed, then he/she loses this game. By the way, you have been working both under Alice and Bob. You know all\nthe faults and relationships. Your task is to write a program to find out which\nwould win this game, under the assumption that they always take their optimal\nstrategies. If you could choose the winning side, you would not have to take the\nresponsibility for the arisen problem.", "constraint": "", "input": "Each input contains one test case. The first line of the input contains\ntwo integers N and M (0 <= N, M <=\n500), which denote the numbers of Alice's and Bob's faults respectively. Alice's\nfaults are numbered from 1 to N; so are Bob's from 1 to M.\nThen N lines follow to describe the relationships among the faults.\nThe i-th line begins with a non-negative integer K_i\n(0 <= K_i <= M). It is then followed by K_i\npositive integers, where the j-th number b_i, j\n(1 <= b_i, j <= M) indicates there is a direct\nrelationship between the i-th Alice's fault and the b_i, j-th\nBob's fault. It is guaranteed that \nb_i, j ! = b_i, j' \nfor all i, j, j'\nsuch that 1 <= i <= N and 1 <= j < j'\n<= K_i.", "output": "Print either \"Alice\" or \"Bob\" to indicate the winner of the blame game.", "content_img": false, "lang": "", "error": false, "samples": ["input: 1 1\n1 1\n output: Bob", "input: 3 3\n3 1 2 3\n1 3\n1 3\n output: Alice"], "Pid": "p01592", "ProblemText": "Task Description: Alice and Bob are in a factional dispute. Recently a big serious problem\narised in a project both Alice and Bob had been working for. This problem was\ncaused by lots of faults of Alice's and Bob's sides; those faults are closely\nrelated. Alice and Bob started to blame each other. First, Alice claimed it was\ncaused by Bob's fault. Then Bob insisted his fault was led by Alice's fault.\nSoon after, Alice said that her fault should not have happened without Bob's\nanother fault. So on so forth. It was terrible. It was totally a blame game.\nStill, they had their pride. They would not use the same fault more than once in\ntheir claims. All right, let's see the situation in terms of a game. Alice and Bob have a number of faults. Some pairs of Alice and Bob faults\nhave direct relationship between them. This relationship is bidirectional; if a\nfault X is led by another fault Y, they can say either \"X was due to Y. \" or\n\"even with X, the problem could be avoided without Y. \" Note that not both, since\nthey never pick up the same fault in their claims. Alice and Bob take their turns alternatively. Alice takes the first turn\nby claiming any of Bob's faults. Then Bob makes his claim with Alice's fault\ndirectly related to the claimed fault. Afterward, in each turn, one picks up\nanother's fault directly related to the fault claimed in the previous turn. If\nhe/she has no faults that have not been claimed, then he/she loses this game. By the way, you have been working both under Alice and Bob. You know all\nthe faults and relationships. Your task is to write a program to find out which\nwould win this game, under the assumption that they always take their optimal\nstrategies. If you could choose the winning side, you would not have to take the\nresponsibility for the arisen problem.\nTask Input: Each input contains one test case. The first line of the input contains\ntwo integers N and M (0 <= N, M <=\n500), which denote the numbers of Alice's and Bob's faults respectively. Alice's\nfaults are numbered from 1 to N; so are Bob's from 1 to M.\nThen N lines follow to describe the relationships among the faults.\nThe i-th line begins with a non-negative integer K_i\n(0 <= K_i <= M). It is then followed by K_i\npositive integers, where the j-th number b_i, j\n(1 <= b_i, j <= M) indicates there is a direct\nrelationship between the i-th Alice's fault and the b_i, j-th\nBob's fault. It is guaranteed that \nb_i, j ! = b_i, j' \nfor all i, j, j'\nsuch that 1 <= i <= N and 1 <= j < j'\n<= K_i.\nTask Output: Print either \"Alice\" or \"Bob\" to indicate the winner of the blame game.\nTask Samples: input: 1 1\n1 1\n output: Bob\ninput: 3 3\n3 1 2 3\n1 3\n1 3\n output: Alice\n\n" }, { "title": "problem c: earn big", "content": "A group of N people is trying to challenge the following game\nto earn big money. First, N participants are isolated from each other. From this\npoint, they are not allowed to contact each other, or to leave any information\nfor other participants. The game organizer leads each participant, one by one,\nto a room with N boxes. The boxes are all closed at the beginning of\nthe game, and the game organizer closes all the boxes whenever a participant\nenters the room. Each box contains a slip of paper on which a name of a distinct\nparticipant is written. The order of the boxes do not change during the game.\nEach participant is allowed to open up to M boxes. If every\nparticipant is able to open a box that contains a paper of his/her name, then\nthe group wins the game, and everybody in the group earns big money. If anyone\nis failed to open a box that contains a paper of his/her name, then the group\nfails in the game, and nobody in the group gets money. Obviously, if every participant picks up boxes randomly, the winning\nprobability will be (M/N)^N. However, there is a far more\nbetter solution. Before discussing the solution, let us define some concepts. Let P\n= {p_1, p_2, . . . , p_N} be a set of the\nparticipants, and B = {b_1, b_2, . . . , b_N}\nbe a set of the boxes. Let us define f, a mapping from B\nto P, such that f(b) is a participant whose name is\nwritten on a paper in a box b. Here, consider a participant p_i picks up the boxes\nin the following manner:\nLet x : = i.\n\nIf p_i has already opened M boxes,\n\tthen exit as a failure.\n\np_i opens b_x.\n\t\nIf f(b_x) = p_i, then exit as a\n\t\tsuccess.\n\nIf f(b_x) = p_j (i ! = j),\n\t\tthen let x : = j, and go to 2.\nAssuming every participant follows the algorithm above, the result of the\ngame depends only on the initial order of the boxes (i. e. the definition of f).\nLet us define g to be a mapping from P to B,\nsuch that g(p_i) = b_i. The participants win the\ngame if and only if, for every i ∈ {1,2, . . . , N}, there exists\nk(<=M) such that (fg)^k\n(p_i) = p_i. Your task is to write a program that calculates the winning probability\nof this game. You can assume that the boxes are placed randomly.", "constraint": "", "input": "The input consists of one line. It contains two integers N and\nM (1 <= M <= N <= 1,000) in this order,\ndelimited by a space.", "output": "For given N and M, your program should print the\nwinning probability of the game. The output value should be in a decimal fraction and should not contain an error greater than 10^-8.", "content_img": true, "lang": "", "error": false, "samples": ["input: 2 1\n output: 0.50000000", "input: 100 50\n output: 0.31182782"], "Pid": "p01593", "ProblemText": "Task Description: A group of N people is trying to challenge the following game\nto earn big money. First, N participants are isolated from each other. From this\npoint, they are not allowed to contact each other, or to leave any information\nfor other participants. The game organizer leads each participant, one by one,\nto a room with N boxes. The boxes are all closed at the beginning of\nthe game, and the game organizer closes all the boxes whenever a participant\nenters the room. Each box contains a slip of paper on which a name of a distinct\nparticipant is written. The order of the boxes do not change during the game.\nEach participant is allowed to open up to M boxes. If every\nparticipant is able to open a box that contains a paper of his/her name, then\nthe group wins the game, and everybody in the group earns big money. If anyone\nis failed to open a box that contains a paper of his/her name, then the group\nfails in the game, and nobody in the group gets money. Obviously, if every participant picks up boxes randomly, the winning\nprobability will be (M/N)^N. However, there is a far more\nbetter solution. Before discussing the solution, let us define some concepts. Let P\n= {p_1, p_2, . . . , p_N} be a set of the\nparticipants, and B = {b_1, b_2, . . . , b_N}\nbe a set of the boxes. Let us define f, a mapping from B\nto P, such that f(b) is a participant whose name is\nwritten on a paper in a box b. Here, consider a participant p_i picks up the boxes\nin the following manner:\nLet x : = i.\n\nIf p_i has already opened M boxes,\n\tthen exit as a failure.\n\np_i opens b_x.\n\t\nIf f(b_x) = p_i, then exit as a\n\t\tsuccess.\n\nIf f(b_x) = p_j (i ! = j),\n\t\tthen let x : = j, and go to 2.\nAssuming every participant follows the algorithm above, the result of the\ngame depends only on the initial order of the boxes (i. e. the definition of f).\nLet us define g to be a mapping from P to B,\nsuch that g(p_i) = b_i. The participants win the\ngame if and only if, for every i ∈ {1,2, . . . , N}, there exists\nk(<=M) such that (fg)^k\n(p_i) = p_i. Your task is to write a program that calculates the winning probability\nof this game. You can assume that the boxes are placed randomly.\nTask Input: The input consists of one line. It contains two integers N and\nM (1 <= M <= N <= 1,000) in this order,\ndelimited by a space.\nTask Output: For given N and M, your program should print the\nwinning probability of the game. The output value should be in a decimal fraction and should not contain an error greater than 10^-8.\nTask Samples: input: 2 1\n output: 0.50000000\ninput: 100 50\n output: 0.31182782\n\n" }, { "title": "problem d: exportation in space", "content": "In an era of space travelling, Mr. Jonathan A. Goldmine exports a special\nmaterial named \"Interstellar Condensed Powered Copper\". A piece of it consists\nof several spheres floating in the air. There is strange force affecting between\nthe spheres so that their relative positions of them are not changed. If you\nmove one of them, all the others follow it. \nExample of ICPC (left: bare, right: shielded)To transport ICPCs between planets, it needs to be shielded from cosmic\nrays. It will be broken when they hit by strong cosmic rays. Mr. Goldmine needs\nto wrap up each ICPC pieces with anti-cosmic-ray shield, a paper-like material\nwhich cuts all the cosmic rays. To save cost, he wants to know the minimum area\nof the shield he needs to wrap an ICPC piece up. Note that he can't put the shield between the spheres of an ICPC because\nit affects the force between the spheres. So that the only way to shield it is\nto wrap the whole ICPC piece by shield. Mr. Goldmine asked you, an experienced programmer, to calculate the\nminimum area of shield for each material. You can assume that each sphere in an ICPC piece is a point, and you can\nignore the thickness of the shield.", "constraint": "", "input": "Each file consists of one test case, which has the information of one\nICPC piece. A test case starts with a line with an integer N (4 <= N\n<= 50), denoting the number of spheres in the piece of the test case. Then N\nlines follow. The i-th line of them describes the position of the i-th\nsphere. It has 3 integers x_i, y_i and\nz_i (0 <= x, y, z <= 100),\nseparated by a space. They denote the x, y and z\ncoordinates of the i-th sphere, respectively. It is guaranteed that there are no data all of whose spheres are on the\nsame plane, and that no two spheres in a data are on the same coordinate.", "output": "For each input, print the area of the shield Mr. Goldmine needs. The\noutput value should be in a decimal fraction and should not contain an error greater than 0.001.", "content_img": true, "lang": "", "error": false, "samples": ["input: 4\n0 0 0\n0 0 1\n0 1 0\n1 0 0\n output: 2.366", "input: 8\n0 0 0\n0 0 1\n0 1 0\n0 1 1\n1 0 0\n1 0 1\n1 1 0\n1 1 1\n output: 6.000"], "Pid": "p01594", "ProblemText": "Task Description: In an era of space travelling, Mr. Jonathan A. Goldmine exports a special\nmaterial named \"Interstellar Condensed Powered Copper\". A piece of it consists\nof several spheres floating in the air. There is strange force affecting between\nthe spheres so that their relative positions of them are not changed. If you\nmove one of them, all the others follow it. \nExample of ICPC (left: bare, right: shielded)To transport ICPCs between planets, it needs to be shielded from cosmic\nrays. It will be broken when they hit by strong cosmic rays. Mr. Goldmine needs\nto wrap up each ICPC pieces with anti-cosmic-ray shield, a paper-like material\nwhich cuts all the cosmic rays. To save cost, he wants to know the minimum area\nof the shield he needs to wrap an ICPC piece up. Note that he can't put the shield between the spheres of an ICPC because\nit affects the force between the spheres. So that the only way to shield it is\nto wrap the whole ICPC piece by shield. Mr. Goldmine asked you, an experienced programmer, to calculate the\nminimum area of shield for each material. You can assume that each sphere in an ICPC piece is a point, and you can\nignore the thickness of the shield.\nTask Input: Each file consists of one test case, which has the information of one\nICPC piece. A test case starts with a line with an integer N (4 <= N\n<= 50), denoting the number of spheres in the piece of the test case. Then N\nlines follow. The i-th line of them describes the position of the i-th\nsphere. It has 3 integers x_i, y_i and\nz_i (0 <= x, y, z <= 100),\nseparated by a space. They denote the x, y and z\ncoordinates of the i-th sphere, respectively. It is guaranteed that there are no data all of whose spheres are on the\nsame plane, and that no two spheres in a data are on the same coordinate.\nTask Output: For each input, print the area of the shield Mr. Goldmine needs. The\noutput value should be in a decimal fraction and should not contain an error greater than 0.001.\nTask Samples: input: 4\n0 0 0\n0 0 1\n0 1 0\n1 0 0\n output: 2.366\ninput: 8\n0 0 0\n0 0 1\n0 1 0\n0 1 1\n1 0 0\n1 0 1\n1 1 0\n1 1 1\n output: 6.000\n\n" }, { "title": "problem e: laser puzzle", "content": "An explorer John is now at a crisis! He is entrapped in a W\ntimes H rectangular room with a embrasure of laser beam. The\nembrasure is shooting a deadly dangerous laser beam so that he cannot cross or\ntouch the laser beam. On the wall of this room, there are statues and a locked\ndoor. The door lock is opening if the beams are hitting every statue. In this room, there are pillars, mirrors and crystals. A mirror reflects\na laser beam. The angle of a mirror should be vertical, horizontal or diagonal.\nA crystal split a laser beam into two laser beams with θ±(π/4)\nwhere θ is the angle of the incident laser beam. He can push one mirror or\ncrystal at a time. He can push mirrors/crystals multiple times. But he can push\nup to two of mirrors/crystals because the door will be locked forever when he\npushes the third mirrors/crystals. To simplify the situation, the room consists of W times H\nunit square as shown in figure 1. \nFigure 1He can move from a square to the neighboring square vertically or\nhorizontally. Please note that he cannot move diagonal direction. Pillars,\nmirrors and crystals exist on the center of a square. As shown in the figure 2,\nyou can assume that a mirror/crystal moves to the center of the next square at\nthe next moment when he push it. That means, you don't need to consider a state\nabout pushing a mirror/crystal. \nFigure 2You can assume the following conditions:\nthe direction of laser beams are horizontal, vertical or diagonal,\n\nthe embrasure is shooting a laser beam to the center of the\n\tneighboring square,\n\nthe embrasure is on the wall,\n\nhe cannot enter to a square with pillar,\n\na mirror reflects a laser beam at the center of the square,\n\na mirror reflects a laser beam on the both side,\n\na mirror blocks a laser beam if the mirror is parallel to\n\tthe laser beam,\n\na crystal split a laser beam at the center of the square,\n\ndiagonal laser does not hit a statue,\n\nand he cannot leave the room if the door is hit by a vertical, horizontal or\n\tdiagonal laser.\n\nIn order to leave this deadly room, he should push and move mirrors and\ncrystals to the right position and leave the room from the door. Your job is to\nwrite a program to check whether it is possible to leave the room. Figure 3 is an initial situation of the first sample input. \nFigure 3Figure 4 is one of the solution for the first sample input. \nFigure 4", "constraint": "", "input": "The first line of the input contains two positive integers W\nand H (2 < W, H <= 8). The map of the room is\ngiven in the following H lines. The map consists of the following\ncharacters:\n'#': wall of the room,\n\n'*': a pillar,\n\n'S': a statue on the wall,\n\n'/': a diagonal mirror with angle π/4 from the bottom side of the\n\troom,\n\n'\\': a diagonal mirror with angle 3π/4 from the bottom side of the\n\troom,\n\n'-': a horizontal mirror,\n\n'|': a vertical mirror,\n\n'O': a crystal,\n\n'@': the initial position of John,\n\n'. ': an empty floor,\n\n'L': the embrasure,\n\n'D': the door\n\nThe judges also guarantee that this problem can be solved without\nextraordinary optimizations.", "output": "Output \"Yes\" if it is possible for him to leave the room. Otherwise,\noutput \"No\".", "content_img": true, "lang": "", "error": false, "samples": ["input: 7 8\n##S####\n#.....#\nS.O...#\n#.*|..#\nL..*..#\n#.O*..D\n#.@...#\n#######\n output: Yes", "input: 8 3\n###L####\nS.../@.#\n######D#\n output: Yes", "input: 8 3\n##L#####\nS..\\.@.#\n######D#\n output: No"], "Pid": "p01595", "ProblemText": "Task Description: An explorer John is now at a crisis! He is entrapped in a W\ntimes H rectangular room with a embrasure of laser beam. The\nembrasure is shooting a deadly dangerous laser beam so that he cannot cross or\ntouch the laser beam. On the wall of this room, there are statues and a locked\ndoor. The door lock is opening if the beams are hitting every statue. In this room, there are pillars, mirrors and crystals. A mirror reflects\na laser beam. The angle of a mirror should be vertical, horizontal or diagonal.\nA crystal split a laser beam into two laser beams with θ±(π/4)\nwhere θ is the angle of the incident laser beam. He can push one mirror or\ncrystal at a time. He can push mirrors/crystals multiple times. But he can push\nup to two of mirrors/crystals because the door will be locked forever when he\npushes the third mirrors/crystals. To simplify the situation, the room consists of W times H\nunit square as shown in figure 1. \nFigure 1He can move from a square to the neighboring square vertically or\nhorizontally. Please note that he cannot move diagonal direction. Pillars,\nmirrors and crystals exist on the center of a square. As shown in the figure 2,\nyou can assume that a mirror/crystal moves to the center of the next square at\nthe next moment when he push it. That means, you don't need to consider a state\nabout pushing a mirror/crystal. \nFigure 2You can assume the following conditions:\nthe direction of laser beams are horizontal, vertical or diagonal,\n\nthe embrasure is shooting a laser beam to the center of the\n\tneighboring square,\n\nthe embrasure is on the wall,\n\nhe cannot enter to a square with pillar,\n\na mirror reflects a laser beam at the center of the square,\n\na mirror reflects a laser beam on the both side,\n\na mirror blocks a laser beam if the mirror is parallel to\n\tthe laser beam,\n\na crystal split a laser beam at the center of the square,\n\ndiagonal laser does not hit a statue,\n\nand he cannot leave the room if the door is hit by a vertical, horizontal or\n\tdiagonal laser.\n\nIn order to leave this deadly room, he should push and move mirrors and\ncrystals to the right position and leave the room from the door. Your job is to\nwrite a program to check whether it is possible to leave the room. Figure 3 is an initial situation of the first sample input. \nFigure 3Figure 4 is one of the solution for the first sample input. \nFigure 4\nTask Input: The first line of the input contains two positive integers W\nand H (2 < W, H <= 8). The map of the room is\ngiven in the following H lines. The map consists of the following\ncharacters:\n'#': wall of the room,\n\n'*': a pillar,\n\n'S': a statue on the wall,\n\n'/': a diagonal mirror with angle π/4 from the bottom side of the\n\troom,\n\n'\\': a diagonal mirror with angle 3π/4 from the bottom side of the\n\troom,\n\n'-': a horizontal mirror,\n\n'|': a vertical mirror,\n\n'O': a crystal,\n\n'@': the initial position of John,\n\n'. ': an empty floor,\n\n'L': the embrasure,\n\n'D': the door\n\nThe judges also guarantee that this problem can be solved without\nextraordinary optimizations.\nTask Output: Output \"Yes\" if it is possible for him to leave the room. Otherwise,\noutput \"No\".\nTask Samples: input: 7 8\n##S####\n#.....#\nS.O...#\n#.*|..#\nL..*..#\n#.O*..D\n#.@...#\n#######\n output: Yes\ninput: 8 3\n###L####\nS.../@.#\n######D#\n output: Yes\ninput: 8 3\n##L#####\nS..\\.@.#\n######D#\n output: No\n\n" }, { "title": "problem f: magnum tornado", "content": "We have a toy that consists of a small racing circuit and a tiny car. For\nsimplicity you can regard the circuit as a 2-dimensional closed loop, made of\nline segments and circular arcs. The circuit has no branchings. All segments and\narcs are connected smoothly, i. e. there are no sharp corners. The car travels on this circuit with one distinct feature: it is capable\nof jumping, which enables short cuts. It can jump at any time for any distance.\nThe constraints are that 1) the traveling direction will never change during\neach jump, 2) the jumping direction needs to match the traveling direction at\nthe time of take-off, and 3) the car must land on the circuit in parallel to the\ntangent at the landing point. Note that, however, the traveling direction at the\nlanding point may be the opposite of the forward direction (we define forward\ndirection as the direction from the starting point to the ending point of each\nline segment in the circuit. ) That is, the car can traverse part of the circuit\nin the reverse direction. Your job is to write a program which, given the shape of the circuit,\ncalculates the per-lap length of the shortest route. You can ignore the height\nof the jump, i. e. just project the route onto the plane on which the circuit\nresides. The car must start from the starting point of the first line segment,\nheading towards the ending point of that segment, and must come back to the same\nstarting point heading in the same direction. Figure 1 shows the solution for the first sample input. \nFigure 1: The solution for the first sample input", "constraint": "", "input": "The input begins with a line that solely consists of an integer N\n(2 <= N <= 100), the number of line segments in the circuit. This is\nfollowed by N lines, where the i-th line corresponds to\nthe i-th line segment (1 <= i <= N). Each of\nthese N lines contains 4 integers x_0, y_0,\nx_1 and y_1 (-100 <= x_0,\ny_0, x_1, y_1 <=\n100) in this order, separated by a space. Here (x_0, y_0)\nis the starting point and (x_1, y_1)\nis the ending point of the i-th line segment. For each i,\nthe i-th and (i+1)-th line segments are connected smoothly\nby a circular arc, which you may assume exists uniquely (for simplicity, we\nconsider the (N+1)-th line as the 1st line). You may also assume\nthat, while two line segments or circular arcs may cross each other, they will\nnever overlap nor be tangent to each other.", "output": "For each test case, output one line that solely consists of a decimal\nvalue, representing the per-lap length. The output value should be in a decimal fraction and should not contain an error greater\nthan 0.001.", "content_img": true, "lang": "", "error": false, "samples": ["input: 5\n0 1 0 2\n1 3 2 3\n2 2 1 2\n1 1 2 1\n2 0 1 0\n output: 9.712", "input: 12\n4 5 4 6\n3 7 1 7\n0 8 0 10\n1 11 3 11\n4 10 4 9\n5 8 99 8\n100 7 100 4\n99 3 4 3\n3 2 3 1\n2 0 1 0\n0 1 0 3\n1 4 3 4\n output: 27.406"], "Pid": "p01596", "ProblemText": "Task Description: We have a toy that consists of a small racing circuit and a tiny car. For\nsimplicity you can regard the circuit as a 2-dimensional closed loop, made of\nline segments and circular arcs. The circuit has no branchings. All segments and\narcs are connected smoothly, i. e. there are no sharp corners. The car travels on this circuit with one distinct feature: it is capable\nof jumping, which enables short cuts. It can jump at any time for any distance.\nThe constraints are that 1) the traveling direction will never change during\neach jump, 2) the jumping direction needs to match the traveling direction at\nthe time of take-off, and 3) the car must land on the circuit in parallel to the\ntangent at the landing point. Note that, however, the traveling direction at the\nlanding point may be the opposite of the forward direction (we define forward\ndirection as the direction from the starting point to the ending point of each\nline segment in the circuit. ) That is, the car can traverse part of the circuit\nin the reverse direction. Your job is to write a program which, given the shape of the circuit,\ncalculates the per-lap length of the shortest route. You can ignore the height\nof the jump, i. e. just project the route onto the plane on which the circuit\nresides. The car must start from the starting point of the first line segment,\nheading towards the ending point of that segment, and must come back to the same\nstarting point heading in the same direction. Figure 1 shows the solution for the first sample input. \nFigure 1: The solution for the first sample input\nTask Input: The input begins with a line that solely consists of an integer N\n(2 <= N <= 100), the number of line segments in the circuit. This is\nfollowed by N lines, where the i-th line corresponds to\nthe i-th line segment (1 <= i <= N). Each of\nthese N lines contains 4 integers x_0, y_0,\nx_1 and y_1 (-100 <= x_0,\ny_0, x_1, y_1 <=\n100) in this order, separated by a space. Here (x_0, y_0)\nis the starting point and (x_1, y_1)\nis the ending point of the i-th line segment. For each i,\nthe i-th and (i+1)-th line segments are connected smoothly\nby a circular arc, which you may assume exists uniquely (for simplicity, we\nconsider the (N+1)-th line as the 1st line). You may also assume\nthat, while two line segments or circular arcs may cross each other, they will\nnever overlap nor be tangent to each other.\nTask Output: For each test case, output one line that solely consists of a decimal\nvalue, representing the per-lap length. The output value should be in a decimal fraction and should not contain an error greater\nthan 0.001.\nTask Samples: input: 5\n0 1 0 2\n1 3 2 3\n2 2 1 2\n1 1 2 1\n2 0 1 0\n output: 9.712\ninput: 12\n4 5 4 6\n3 7 1 7\n0 8 0 10\n1 11 3 11\n4 10 4 9\n5 8 99 8\n100 7 100 4\n99 3 4 3\n3 2 3 1\n2 0 1 0\n0 1 0 3\n1 4 3 4\n output: 27.406\n\n" }, { "title": "problem g: nezumi's treasure", "content": "There were a mouse and a cat living in a field. The mouse stole a dried\nfish the cat had loved. The theft was found soon later. The mouse started\nrunning as chased by the cat for the dried fish. There were a number of rectangular obstacles in the field. The mouse\nalways went straight ahead as long as possible, but he could not jump over or\npass through these obstacles. When he was blocked by an obstacle, he turned\nleftward to the direction he could go forward, and then he started again to run\nin that way. Note that, at the corner, he might be able to keep going without\nchange of the direction. He found he was going to pass the same point again and again while chased by\nthe cat. He then decided to hide the dried fish at the first point where he\nwas blocked by an obstacle twice from that time.\nIn other words, he decided to hide it at the first turn \nafter he entered into an infinite loop.\nHe thought he could come there again\nafter the chase ended. For example, in the following figure, \nhe first went along the blue line and turned left at point B.\nThen he went along the red lines counter-clockwise,\nand entered into an infinite loop.\nIn this case, he hid dried fish at NOT point B but at point A,\nbecause when he reached point B on line C for the second time,\nhe just passed and didn't turn left. \nExample of dried fish point Finally the cat went away, but he remembered neither where he thought of\nhiding the dried fish nor where he actually hid it. Yes, he was losing his\ndried fish. You are a friend of the mouse and talented programmer. Your task is to\nwrite a program that counts the number of possible points the mouse hid the\ndried fish, where information about the obstacles is given. The mouse should be\nconsidered as a point.", "constraint": "", "input": "The input begins with a line with one integer N (4 <= N\n<= 40,000), which denotes the number of obstacles. Then N lines\nfollow. Each line describes one obstacle with four integers X_i, 1,\nY_i, 1, X_i, 2, and Y_i, 2\n(-100,000,000 <= X_i, 1, Y_i, 1, X_i, 2,\nY_i, 2 <= 100,000,000). (X_i, 1, Y_i, 1)\nand (X_i, 2, Y_i, 2) represent the coordinates of\nthe lower-left and upper-right corners of the obstacle respectively. As usual, X-axis\nand Y-axis go right and upward respectively. No pair of obstacles overlap.", "output": "Print the number of points the mouse could hide the dried fish. You can\nassume this number is positive (i. e. nonzero).", "content_img": true, "lang": "", "error": false, "samples": ["input: 4\n0 0 2 1\n3 0 4 2\n0 2 1 4\n2 3 4 4\n output: 4", "input: 8\n0 0 2 1\n2 2 4 3\n5 3 7 4\n7 5 9 6\n0 2 1 4\n2 4 3 6\n6 0 7 2\n8 2 9 4\n output: 8"], "Pid": "p01597", "ProblemText": "Task Description: There were a mouse and a cat living in a field. The mouse stole a dried\nfish the cat had loved. The theft was found soon later. The mouse started\nrunning as chased by the cat for the dried fish. There were a number of rectangular obstacles in the field. The mouse\nalways went straight ahead as long as possible, but he could not jump over or\npass through these obstacles. When he was blocked by an obstacle, he turned\nleftward to the direction he could go forward, and then he started again to run\nin that way. Note that, at the corner, he might be able to keep going without\nchange of the direction. He found he was going to pass the same point again and again while chased by\nthe cat. He then decided to hide the dried fish at the first point where he\nwas blocked by an obstacle twice from that time.\nIn other words, he decided to hide it at the first turn \nafter he entered into an infinite loop.\nHe thought he could come there again\nafter the chase ended. For example, in the following figure, \nhe first went along the blue line and turned left at point B.\nThen he went along the red lines counter-clockwise,\nand entered into an infinite loop.\nIn this case, he hid dried fish at NOT point B but at point A,\nbecause when he reached point B on line C for the second time,\nhe just passed and didn't turn left. \nExample of dried fish point Finally the cat went away, but he remembered neither where he thought of\nhiding the dried fish nor where he actually hid it. Yes, he was losing his\ndried fish. You are a friend of the mouse and talented programmer. Your task is to\nwrite a program that counts the number of possible points the mouse hid the\ndried fish, where information about the obstacles is given. The mouse should be\nconsidered as a point.\nTask Input: The input begins with a line with one integer N (4 <= N\n<= 40,000), which denotes the number of obstacles. Then N lines\nfollow. Each line describes one obstacle with four integers X_i, 1,\nY_i, 1, X_i, 2, and Y_i, 2\n(-100,000,000 <= X_i, 1, Y_i, 1, X_i, 2,\nY_i, 2 <= 100,000,000). (X_i, 1, Y_i, 1)\nand (X_i, 2, Y_i, 2) represent the coordinates of\nthe lower-left and upper-right corners of the obstacle respectively. As usual, X-axis\nand Y-axis go right and upward respectively. No pair of obstacles overlap.\nTask Output: Print the number of points the mouse could hide the dried fish. You can\nassume this number is positive (i. e. nonzero).\nTask Samples: input: 4\n0 0 2 1\n3 0 4 2\n0 2 1 4\n2 3 4 4\n output: 4\ninput: 8\n0 0 2 1\n2 2 4 3\n5 3 7 4\n7 5 9 6\n0 2 1 4\n2 4 3 6\n6 0 7 2\n8 2 9 4\n output: 8\n\n" }, { "title": "problem h: testing sorting networks", "content": "A N sorting network is a circuit that accepts N\nnumbers as its input, outputs them sorted. Mr. Smith is an engineer of a company\nthat sells various sizes of the circuit. One day, the company got an order of N sorting networks.\nUnfortunately, they didn't have the circuit for N numbers at the\ntime. The clerk once declined the order for being out of stock, but the client\nwas so urgent that he offered much money if he could get the circuit in a week.\nThe deal escalated to a manager, and she asked Mr. Smith for a solution to\nproduce the N sorting networks by the deadline. He came up with an idea to combine several N/2 sorting\nnetworks, because he noticed that they have many stocks of the circuits for N/2\nnumbers. He designed a new circuit using the N/2 sorting networks,\nbut he was not sure if it would really work as an N sorting network.\nSo, he asked a colleague, you, to check if it was actually an N\nsorting network. The circuit he designed consists of multiple stages. Each stage of the\ncircuit consists of two N/2 sorting networks, which makes each stage\naccept a sequence of N numbers as inputs and output a sequence of N\nnumbers. From the 1st to the N/2-th input numbers of a stage goes to\none of those N/2 sorting networks, and from the (N/2+1)-th\nto the N-th input numbers goes to the other. Similarly, the first\nhalf of the output numbers of a stage is the output of the former sorting\nnetwork and the second half is the output of the latter, both of which are\nsorted in ascending order. Each output of a stage is connected to exactly one\ninput of the next stage, and no two inputs are connected to the same output\nline. The input of the last stage is the input of the whole circuit and the\noutput of the first stage is the output of the whole circuit.", "constraint": "", "input": "The input begins with a line containing a positive even integer N\n(4 <= N <= 100) and a positive integer D (1 <= D\n<= 10). N indicates the number of the input and output of the circuit\nand D indicates the number of the stages of the circuit. The i-th\nline of the following D-1 lines contains N integers w_i1,\nw_i2, . . . , w_iN\n(1 <= w_ij <= N ), which describes\nthe wiring between the i-th and (i+1)-th stages. w_ij\nindicates the j-th input of the i-th stage and the w_ij-th\noutput of the (i+1)-th stage are wired. You can assume w_i1,\nw_i2, . . . , w_iN\nare unique for each i.", "output": "Print a line containing \"Yes\" if the circuit works as an N\nsorting network. Print \"No\" otherwise.", "content_img": false, "lang": "", "error": false, "samples": ["input: 4 4\n1 3 4 2 \n1 4 2 3 \n1 3 2 4\n output: Yes", "input: 4 3\n3 1 2 4\n1 3 2 4\n output: No"], "Pid": "p01598", "ProblemText": "Task Description: A N sorting network is a circuit that accepts N\nnumbers as its input, outputs them sorted. Mr. Smith is an engineer of a company\nthat sells various sizes of the circuit. One day, the company got an order of N sorting networks.\nUnfortunately, they didn't have the circuit for N numbers at the\ntime. The clerk once declined the order for being out of stock, but the client\nwas so urgent that he offered much money if he could get the circuit in a week.\nThe deal escalated to a manager, and she asked Mr. Smith for a solution to\nproduce the N sorting networks by the deadline. He came up with an idea to combine several N/2 sorting\nnetworks, because he noticed that they have many stocks of the circuits for N/2\nnumbers. He designed a new circuit using the N/2 sorting networks,\nbut he was not sure if it would really work as an N sorting network.\nSo, he asked a colleague, you, to check if it was actually an N\nsorting network. The circuit he designed consists of multiple stages. Each stage of the\ncircuit consists of two N/2 sorting networks, which makes each stage\naccept a sequence of N numbers as inputs and output a sequence of N\nnumbers. From the 1st to the N/2-th input numbers of a stage goes to\none of those N/2 sorting networks, and from the (N/2+1)-th\nto the N-th input numbers goes to the other. Similarly, the first\nhalf of the output numbers of a stage is the output of the former sorting\nnetwork and the second half is the output of the latter, both of which are\nsorted in ascending order. Each output of a stage is connected to exactly one\ninput of the next stage, and no two inputs are connected to the same output\nline. The input of the last stage is the input of the whole circuit and the\noutput of the first stage is the output of the whole circuit.\nTask Input: The input begins with a line containing a positive even integer N\n(4 <= N <= 100) and a positive integer D (1 <= D\n<= 10). N indicates the number of the input and output of the circuit\nand D indicates the number of the stages of the circuit. The i-th\nline of the following D-1 lines contains N integers w_i1,\nw_i2, . . . , w_iN\n(1 <= w_ij <= N ), which describes\nthe wiring between the i-th and (i+1)-th stages. w_ij\nindicates the j-th input of the i-th stage and the w_ij-th\noutput of the (i+1)-th stage are wired. You can assume w_i1,\nw_i2, . . . , w_iN\nare unique for each i.\nTask Output: Print a line containing \"Yes\" if the circuit works as an N\nsorting network. Print \"No\" otherwise.\nTask Samples: input: 4 4\n1 3 4 2 \n1 4 2 3 \n1 3 2 4\n output: Yes\ninput: 4 3\n3 1 2 4\n1 3 2 4\n output: No\n\n" }, { "title": "problem i: train king", "content": "Roland has been given a mission of dangerous material transfer by Train\nKing. The material is stored in the station A and subject to being transferred\nto the station B. He will bring it by direct trains between A and B, one (or\nzero) unit per ride. Your task is to write a program to find out the most optimal way of his\nbringing. Your program will receive the timetable of trains on the mission day\nand should report how many units of material can be transferred at the end. Be\naware that there can be trains which can go to the past time or the same time\nwhich train leaved the station. Each train consists of one or more cars. Roland is disallowed to ride the\nsame car of the same train multiple times. This restriction avoids time paradox.\nHe is still allowed to get on a different car, though. You can assume he can\nchange trains instantly.", "constraint": "", "input": "The first line contains two integers N_AB and N_BA\n(0 <= N_AB, 0 <= N_BA and N_AB\n+ N_BA <= 50). N_AB denotes the number\nof trains from A to B; N_BA denotes the number from B to A. The next N_AB lines describe the information about\ntrains from A to B. Each line gives the information of one train with three\nintegers C_i, D_i and A_i\n(1 <= C_i <= 10,0 <= D_i, A_i\n< 86400) : the number of cars, the departure time, and the arrival time. The next N_BA lines describe the information about\ntrains from B to A. The information is given in the same format.", "output": "Print the maximum amount, in units, of dangerous material that can be\ntransferred.", "content_img": false, "lang": "", "error": false, "samples": ["input: 1 1\n10 100 0\n10 100 0\n output: 10", "input: 5 5\n10 0 100\n10 200 300\n10 400 500\n10 600 700\n10 800 900\n10 100 200\n10 300 400\n10 500 600\n10 700 800\n10 900 1000\n output: 5"], "Pid": "p01599", "ProblemText": "Task Description: Roland has been given a mission of dangerous material transfer by Train\nKing. The material is stored in the station A and subject to being transferred\nto the station B. He will bring it by direct trains between A and B, one (or\nzero) unit per ride. Your task is to write a program to find out the most optimal way of his\nbringing. Your program will receive the timetable of trains on the mission day\nand should report how many units of material can be transferred at the end. Be\naware that there can be trains which can go to the past time or the same time\nwhich train leaved the station. Each train consists of one or more cars. Roland is disallowed to ride the\nsame car of the same train multiple times. This restriction avoids time paradox.\nHe is still allowed to get on a different car, though. You can assume he can\nchange trains instantly.\nTask Input: The first line contains two integers N_AB and N_BA\n(0 <= N_AB, 0 <= N_BA and N_AB\n+ N_BA <= 50). N_AB denotes the number\nof trains from A to B; N_BA denotes the number from B to A. The next N_AB lines describe the information about\ntrains from A to B. Each line gives the information of one train with three\nintegers C_i, D_i and A_i\n(1 <= C_i <= 10,0 <= D_i, A_i\n< 86400) : the number of cars, the departure time, and the arrival time. The next N_BA lines describe the information about\ntrains from B to A. The information is given in the same format.\nTask Output: Print the maximum amount, in units, of dangerous material that can be\ntransferred.\nTask Samples: input: 1 1\n10 100 0\n10 100 0\n output: 10\ninput: 5 5\n10 0 100\n10 200 300\n10 400 500\n10 600 700\n10 800 900\n10 100 200\n10 300 400\n10 500 600\n10 700 800\n10 900 1000\n output: 5\n\n" }, { "title": "problem j: tree construction", "content": "Consider a two-dimensional space with a set of points (x_i,\ny_i) that satisfy x_i < x_j\nand y_i > y_j for all i < j.\nWe want to have them all connected by a directed tree whose edges go toward\neither right (x positive) or upward (y positive). The\nfigure below shows an example tree. \nFigure 1: An example tree Write a program that finds a tree connecting all given points with the\nshortest total length of edges.", "constraint": "", "input": "The input begins with a line that contains an integer n (1 <=\nn <= 1000), the number of points. Then n lines follow. The\ni-th line contains two integers x_i and y_i\n(0 <= x_i, y_i <= 10000), which give\nthe coordinates of the i-th point.", "output": "Print the total length of edges in a line.", "content_img": true, "lang": "", "error": false, "samples": ["input: 5\n1 5\n2 4\n3 3\n4 2\n5 1\n output: 12", "input: 1\n10000 0\n output: 0"], "Pid": "p01600", "ProblemText": "Task Description: Consider a two-dimensional space with a set of points (x_i,\ny_i) that satisfy x_i < x_j\nand y_i > y_j for all i < j.\nWe want to have them all connected by a directed tree whose edges go toward\neither right (x positive) or upward (y positive). The\nfigure below shows an example tree. \nFigure 1: An example tree Write a program that finds a tree connecting all given points with the\nshortest total length of edges.\nTask Input: The input begins with a line that contains an integer n (1 <=\nn <= 1000), the number of points. Then n lines follow. The\ni-th line contains two integers x_i and y_i\n(0 <= x_i, y_i <= 10000), which give\nthe coordinates of the i-th point.\nTask Output: Print the total length of edges in a line.\nTask Samples: input: 5\n1 5\n2 4\n3 3\n4 2\n5 1\n output: 12\ninput: 1\n10000 0\n output: 0\n\n" }, { "title": "", "content": "We found a dictionary of the Ancient Civilization Mayo (ACM) during excavation of the ruins.\nAfter analysis of the dictionary, we revealed they used a language that had not more than 26 letters.\nSo one of us mapped each letter to a different English alphabet and typed all the words in the dictionary into a computer.\n\nHow the words are ordered in the dictionary, especially whether they are ordered lexicographically, is an interesting topic to many people.\nAs a good programmer, you are requested to write a program to judge whether we can consider the words to be sorted in a lexicographical order.\n\nNote:\nIn a lexicographical order, a word always precedes other words it is a prefix of.\nFor example, ab \nprecedes abc, \nabde, and so on.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is formatted as follows:\n\nn\nstring_1\n. . .\nstring_n\n\nEach dataset consists of n+1 lines.\nThe first line of each dataset contains an integer that indicates n (1 <= n <= 500).\nThe i-th line of the following n lines contains string_i, which consists of up to 10 English lowercase letters.\n\nThe end of the input is 0, and this should not be processed.", "output": "Print either yes or \nno in a line for each dataset, in the order of the input.\nIf all words in the dataset can be considered to be ordered lexicographically, print yes.\nOtherwise, print no.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\ncba\ncab\nb\na\n3\nbca\nab\na\n5\nabc\nacb\nb\nc\nc\n5\nabc\nacb\nc\nb\nb\n0\n output: yes\nno\nyes\nno"], "Pid": "p01646", "ProblemText": "Task Description: We found a dictionary of the Ancient Civilization Mayo (ACM) during excavation of the ruins.\nAfter analysis of the dictionary, we revealed they used a language that had not more than 26 letters.\nSo one of us mapped each letter to a different English alphabet and typed all the words in the dictionary into a computer.\n\nHow the words are ordered in the dictionary, especially whether they are ordered lexicographically, is an interesting topic to many people.\nAs a good programmer, you are requested to write a program to judge whether we can consider the words to be sorted in a lexicographical order.\n\nNote:\nIn a lexicographical order, a word always precedes other words it is a prefix of.\nFor example, ab \nprecedes abc, \nabde, and so on.\nTask Input: The input consists of multiple datasets. Each dataset is formatted as follows:\n\nn\nstring_1\n. . .\nstring_n\n\nEach dataset consists of n+1 lines.\nThe first line of each dataset contains an integer that indicates n (1 <= n <= 500).\nThe i-th line of the following n lines contains string_i, which consists of up to 10 English lowercase letters.\n\nThe end of the input is 0, and this should not be processed.\nTask Output: Print either yes or \nno in a line for each dataset, in the order of the input.\nIf all words in the dataset can be considered to be ordered lexicographically, print yes.\nOtherwise, print no.\nTask Samples: input: 4\ncba\ncab\nb\na\n3\nbca\nab\na\n5\nabc\nacb\nb\nc\nc\n5\nabc\nacb\nc\nb\nb\n0\n output: yes\nno\nyes\nno\n\n" }, { "title": "", "content": "Texas hold 'em is one of the standard poker games, originated in Texas, United States.\nIt is played with a standard deck of 52 cards, which has 4 suits (spades, hearts, diamonds and clubs) and 13 ranks (A, K, Q, J and 10-2), without jokers.\n\nWith betting aside, a game goes as described below.\n\nAt the beginning each player is dealt with two cards face down.\nThese cards are called hole cards or pocket cards, and do not have to be revealed until the showdown.\nThen the dealer deals three cards face up as community cards, i. e. cards shared by all players.\nThese three cards are called the flop.\nThe flop is followed by another community card called the turn then one more community card called the river.\n\nAfter the river, the game goes on to the showdown.\nAll players reveal their hole cards at this point.\nThen each player chooses five out of the seven cards, i. e. their two hole cards and the five community cards, to form a hand.\nThe player forming the strongest hand wins the game.\nThere are ten possible kinds of hands, listed from the strongest to the weakest:\n\n Royal straight flush: A, K, Q, J and 10 of the same suit. This is a special case of straight flush.\n\n Straight flush: Five cards in sequence (e. g. 7,6,5,4 and 3) and of the same suit.\n\n Four of a kind: Four cards of the same rank.\n\n Full house: Three cards of the same rank, plus a pair of another rank.\n\n Flush: Five cards of the same suit, but not in sequence.\n\n Straight: Five cards in sequence, but not of the same suit.\n\n Three of a kind: Just three cards of the same rank.\n\n Two pairs: Two cards of the same rank, and two other cards of another same rank.\n\n One pair: Just a pair of cards (two cards) of the same rank.\n\n High card: Any other hand.\nFor the purpose of a sequence, J, Q and K are treated as 11,12 and 13 respectively.\nA can be seen as a rank either next above K or next below 2, thus both A-K-Q-J-10 and 5-4-3-2-A are possible (but not 3-2-A-K-Q or the likes).\n\nIf more than one player has the same kind of hand, ties are broken by comparing the ranks of the cards.\nThe basic idea is to compare first those forming sets (pairs, triples or quads) then the rest cards one by one from the highest-ranked to the lowest-ranked, until ties are broken.\nMore specifically:\n\n Royal straight flush: (ties are not broken)\n\n Straight flush: Compare the highest-ranked card.\n\n Four of a kind: Compare the four cards, then the remaining one.\n\n Full house: Compare the three cards, then the pair.\n\n Flush: Compare all cards one by one.\n\n Straight: Compare the highest-ranked card.\n\n Three of a kind: Compare the three cards, then the remaining two.\n\n Two pairs: Compare the higher-ranked pair, then the lower-ranked, then the last one.\n\n One pair: Compare the pair, then the remaining three.\n\n High card: Compare all cards one by one.\nThe order of the ranks is A, K, Q, J, 10,9, . . . , 2, from the highest to the lowest,\nexcept for A next to 2 in a straight regarded as lower than 2.\nNote that there are exceptional cases where ties remain.\nAlso note that the suits are not considered at all in tie-breaking.\n\nHere are a few examples of comparison (note these are only intended for explanatory purpose; some combinations cannot happen in Texas Hold 'em):\n\nJ-J-J-6-3 and K-K-Q-Q-8.\nThe former beats the latter since three of a kind is stronger than two pairs.\n\nJ-J-J-6-3 and K-Q-8-8-8.\nSince both are three of a kind, the triples are considered first, J and 8 in this case.\nJ is higher, hence the former is a stronger hand.\nThe remaining cards, 6-3 and K-Q, are not considered as the tie is already broken.\n\nQ-J-8-6-3 and Q-J-8-5-3.\nBoth are high cards, assuming hands not of a single suit (i. e. flush).\nThe three highest-ranked cards Q-J-8 are the same, so the fourth highest are compared.\nThe former is stronger since 6 is higher than 5.\n\n9-9-Q-7-2 and 9-9-J-8-5.\nBoth are one pair, with the pair of the same rank (9). \nSo the remaining cards, Q-7-2 and J-8-5, are compared from the highest to the lowest,\nand the former wins as Q is higher than J.\n\nNow suppose you are playing a game of Texas Hold 'em with one opponent, and the hole cards and the flop have already been dealt.\nYou are surprisingly telepathic and able to know the cards the opponent has.\nYour ability is not, however, as strong as you can predict which the turn and the river will be.\n\nYour task is to write a program that calculates the probability of your winning the game,\nassuming the turn and the river are chosen uniformly randomly from the remaining cards.\nYou and the opponent always have to choose the hand strongest possible.\nTies should be included in the calculation, i. e. should be counted as losses.", "constraint": "", "input": "The input consists of multiple datasets, each of which has the following format:\n\nYour Card_1 Your Card_2\nOpponent Card_1 Opponent Card_2\nCommunity Card_1 Community Card_2 Community Card_3\n\nEach dataset consists of three lines.\nThe first and second lines contain the hole cards of yours and the opponent's respectively.\nThe third line contains the flop, i. e. the first three community cards.\nThese cards are separated by spaces.\n\nEach card is represented by two characters.\nThe first one indicates the suit: S (spades), H (hearts), D (diamonds) or C (clubs).\nThe second one indicates the rank: A, K, Q, J, T (10) or 9-2.\n\nThe end of the input is indicated by a line with #.\nThis should not be processed.", "output": "Print the probability in a line.\nThe number may contain an arbitrary number of digits after the decimal point,\nbut should not contain an absolute error greater than 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: SA SK\nDA CA\nSQ SJ ST\nSA HA\nD2 C3\nH4 S5 DA\nHA D9\nH6 C9\nH3 H4 H5\n#\n output: 1.00000000000000000000\n0.34444444444444444198\n0.63030303030303025391"], "Pid": "p01647", "ProblemText": "Task Description: Texas hold 'em is one of the standard poker games, originated in Texas, United States.\nIt is played with a standard deck of 52 cards, which has 4 suits (spades, hearts, diamonds and clubs) and 13 ranks (A, K, Q, J and 10-2), without jokers.\n\nWith betting aside, a game goes as described below.\n\nAt the beginning each player is dealt with two cards face down.\nThese cards are called hole cards or pocket cards, and do not have to be revealed until the showdown.\nThen the dealer deals three cards face up as community cards, i. e. cards shared by all players.\nThese three cards are called the flop.\nThe flop is followed by another community card called the turn then one more community card called the river.\n\nAfter the river, the game goes on to the showdown.\nAll players reveal their hole cards at this point.\nThen each player chooses five out of the seven cards, i. e. their two hole cards and the five community cards, to form a hand.\nThe player forming the strongest hand wins the game.\nThere are ten possible kinds of hands, listed from the strongest to the weakest:\n\n Royal straight flush: A, K, Q, J and 10 of the same suit. This is a special case of straight flush.\n\n Straight flush: Five cards in sequence (e. g. 7,6,5,4 and 3) and of the same suit.\n\n Four of a kind: Four cards of the same rank.\n\n Full house: Three cards of the same rank, plus a pair of another rank.\n\n Flush: Five cards of the same suit, but not in sequence.\n\n Straight: Five cards in sequence, but not of the same suit.\n\n Three of a kind: Just three cards of the same rank.\n\n Two pairs: Two cards of the same rank, and two other cards of another same rank.\n\n One pair: Just a pair of cards (two cards) of the same rank.\n\n High card: Any other hand.\nFor the purpose of a sequence, J, Q and K are treated as 11,12 and 13 respectively.\nA can be seen as a rank either next above K or next below 2, thus both A-K-Q-J-10 and 5-4-3-2-A are possible (but not 3-2-A-K-Q or the likes).\n\nIf more than one player has the same kind of hand, ties are broken by comparing the ranks of the cards.\nThe basic idea is to compare first those forming sets (pairs, triples or quads) then the rest cards one by one from the highest-ranked to the lowest-ranked, until ties are broken.\nMore specifically:\n\n Royal straight flush: (ties are not broken)\n\n Straight flush: Compare the highest-ranked card.\n\n Four of a kind: Compare the four cards, then the remaining one.\n\n Full house: Compare the three cards, then the pair.\n\n Flush: Compare all cards one by one.\n\n Straight: Compare the highest-ranked card.\n\n Three of a kind: Compare the three cards, then the remaining two.\n\n Two pairs: Compare the higher-ranked pair, then the lower-ranked, then the last one.\n\n One pair: Compare the pair, then the remaining three.\n\n High card: Compare all cards one by one.\nThe order of the ranks is A, K, Q, J, 10,9, . . . , 2, from the highest to the lowest,\nexcept for A next to 2 in a straight regarded as lower than 2.\nNote that there are exceptional cases where ties remain.\nAlso note that the suits are not considered at all in tie-breaking.\n\nHere are a few examples of comparison (note these are only intended for explanatory purpose; some combinations cannot happen in Texas Hold 'em):\n\nJ-J-J-6-3 and K-K-Q-Q-8.\nThe former beats the latter since three of a kind is stronger than two pairs.\n\nJ-J-J-6-3 and K-Q-8-8-8.\nSince both are three of a kind, the triples are considered first, J and 8 in this case.\nJ is higher, hence the former is a stronger hand.\nThe remaining cards, 6-3 and K-Q, are not considered as the tie is already broken.\n\nQ-J-8-6-3 and Q-J-8-5-3.\nBoth are high cards, assuming hands not of a single suit (i. e. flush).\nThe three highest-ranked cards Q-J-8 are the same, so the fourth highest are compared.\nThe former is stronger since 6 is higher than 5.\n\n9-9-Q-7-2 and 9-9-J-8-5.\nBoth are one pair, with the pair of the same rank (9). \nSo the remaining cards, Q-7-2 and J-8-5, are compared from the highest to the lowest,\nand the former wins as Q is higher than J.\n\nNow suppose you are playing a game of Texas Hold 'em with one opponent, and the hole cards and the flop have already been dealt.\nYou are surprisingly telepathic and able to know the cards the opponent has.\nYour ability is not, however, as strong as you can predict which the turn and the river will be.\n\nYour task is to write a program that calculates the probability of your winning the game,\nassuming the turn and the river are chosen uniformly randomly from the remaining cards.\nYou and the opponent always have to choose the hand strongest possible.\nTies should be included in the calculation, i. e. should be counted as losses.\nTask Input: The input consists of multiple datasets, each of which has the following format:\n\nYour Card_1 Your Card_2\nOpponent Card_1 Opponent Card_2\nCommunity Card_1 Community Card_2 Community Card_3\n\nEach dataset consists of three lines.\nThe first and second lines contain the hole cards of yours and the opponent's respectively.\nThe third line contains the flop, i. e. the first three community cards.\nThese cards are separated by spaces.\n\nEach card is represented by two characters.\nThe first one indicates the suit: S (spades), H (hearts), D (diamonds) or C (clubs).\nThe second one indicates the rank: A, K, Q, J, T (10) or 9-2.\n\nThe end of the input is indicated by a line with #.\nThis should not be processed.\nTask Output: Print the probability in a line.\nThe number may contain an arbitrary number of digits after the decimal point,\nbut should not contain an absolute error greater than 10^{-6}.\nTask Samples: input: SA SK\nDA CA\nSQ SJ ST\nSA HA\nD2 C3\nH4 S5 DA\nHA D9\nH6 C9\nH3 H4 H5\n#\n output: 1.00000000000000000000\n0.34444444444444444198\n0.63030303030303025391\n\n" }, { "title": "", "content": "You are given a connected undirected graph which has even numbers of nodes.\nA connected graph is a graph in which all nodes are connected directly or indirectly by edges.\n\nYour task is to find a spanning tree whose median value of edges' costs is minimum.\nA spanning tree of a graph means that a tree which contains all nodes of the graph.", "constraint": "", "input": "The input consists of multiple datasets.\n\nThe format of each dataset is as follows.\n\nn m\ns_1 t_1 c_1\n. . .\ns_m t_m c_m\n\nThe first line contains an even number n (2 <= n <= 1,000) and an integer m (n-1 <= m <= 10,000).\nn is the nubmer of nodes and m is the number of edges in the graph.\n\nThen m lines follow, each of which contains s_i (1 <= s_i <= n), t_i (1 <= s_i <= n, t_i \\neq s_i) and c_i (1 <= c_i <= 1,000).\nThis means there is an edge between the nodes s_i and t_i and its cost is c_i.\nThere is no more than one edge which connects s_i and t_i.\n\nThe input terminates when n=0 and m=0.\nYour program must not output anything for this case.", "output": "Print the median value in a line for each dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n1 2 5\n4 6\n1 2 1\n1 3 2\n1 4 3\n2 3 4\n2 4 5\n3 4 6\n8 17\n1 4 767\n3 1 609\n8 3 426\n6 5 972\n8 1 607\n6 4 51\n5 1 683\n3 6 451\n3 4 630\n8 7 912\n3 7 43\n4 7 421\n3 5 582\n8 4 538\n5 7 832\n1 6 345\n8 2 608\n0 0\n output: 5\n2\n421"], "Pid": "p01648", "ProblemText": "Task Description: You are given a connected undirected graph which has even numbers of nodes.\nA connected graph is a graph in which all nodes are connected directly or indirectly by edges.\n\nYour task is to find a spanning tree whose median value of edges' costs is minimum.\nA spanning tree of a graph means that a tree which contains all nodes of the graph.\nTask Input: The input consists of multiple datasets.\n\nThe format of each dataset is as follows.\n\nn m\ns_1 t_1 c_1\n. . .\ns_m t_m c_m\n\nThe first line contains an even number n (2 <= n <= 1,000) and an integer m (n-1 <= m <= 10,000).\nn is the nubmer of nodes and m is the number of edges in the graph.\n\nThen m lines follow, each of which contains s_i (1 <= s_i <= n), t_i (1 <= s_i <= n, t_i \\neq s_i) and c_i (1 <= c_i <= 1,000).\nThis means there is an edge between the nodes s_i and t_i and its cost is c_i.\nThere is no more than one edge which connects s_i and t_i.\n\nThe input terminates when n=0 and m=0.\nYour program must not output anything for this case.\nTask Output: Print the median value in a line for each dataset.\nTask Samples: input: 2 1\n1 2 5\n4 6\n1 2 1\n1 3 2\n1 4 3\n2 3 4\n2 4 5\n3 4 6\n8 17\n1 4 767\n3 1 609\n8 3 426\n6 5 972\n8 1 607\n6 4 51\n5 1 683\n3 6 451\n3 4 630\n8 7 912\n3 7 43\n4 7 421\n3 5 582\n8 4 538\n5 7 832\n1 6 345\n8 2 608\n0 0\n output: 5\n2\n421\n\n" }, { "title": "", "content": "You have a billiard table.\nThe playing area of the table is rectangular.\nThis billiard table is special as it has no pockets, and the playing area is completely surrounded with a cushion.\n\nYou succeeded in producing a ultra-precision billiards playing robot.\nWhen you put some balls on the table, the machine hits one of those balls.\nThe hit ball stops after 10,000 unit distance in total moved.\n\nWhen a ball collided with the cushion of the table, the ball takes the orbit like mirror reflection.\nWhen a ball collided with the corner, the ball bounces back on the course that came.\n\nYour mission is to predict which ball collides first with the ball which the robot hits .", "constraint": "", "input": "The input is a sequence of datasets.\nThe number of datasets is less than 100.\nEach dataset is formatted as follows.\n\nn\nw h r v_x v_y\nx_1 y_1\n. . .\nx_n y_n\n\nFirst line of a dataset contains an positive integer n, which represents the number of balls on the table (2 <= n <= 11).\nThe next line contains five integers (w, h, r, v_x, v_y) separated by a single space,\nwhere w and h are the width and the length of the playing area of the table respectively (4 <= w, h <= 1,000),\nr is the radius of the balls (1 <= r <= 100).\nThe robot hits the ball in the vector (v_x, v_y) direction (-10,000 <= v_x, v_y <= 10,000 and (v_x, v_y) \\neq (0,0) ).\n\nThe following n lines give position of balls.\nEach line consists two integers separated by a single space,\n(x_i, y_i) means the center position of the i-th ball on the table in the initial state (r < x_i < w - r, r < y_i < h - r).\n(0,0) indicates the position of the north-west corner of the playing area,\nand (w, h) indicates the position of the south-east corner of the playing area.\nYou can assume that, in the initial state, the balls do not touch each other nor the cushion.\n\nThe robot always hits the first ball in the list.\nYou can assume that the given values do not have errors.\n\nThe end of the input is indicated by a line containing a single zero.", "output": "For each dataset, print the index of the ball which first collides with the ball the robot hits.\nWhen the hit ball collides with no ball until it stops moving, print -1.\n\nYou can assume that no more than one ball collides with the hit ball first, at the same time.\n\nIt is also guaranteed that, when r changes by eps (eps < 10^{-9}), \nthe ball which collides first and the way of the collision do not change.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n26 16 1 8 4\n10 6\n9 2\n9 10\n3\n71 363 4 8 0\n52 238\n25 33\n59 288\n0\n output: 3\n-1"], "Pid": "p01649", "ProblemText": "Task Description: You have a billiard table.\nThe playing area of the table is rectangular.\nThis billiard table is special as it has no pockets, and the playing area is completely surrounded with a cushion.\n\nYou succeeded in producing a ultra-precision billiards playing robot.\nWhen you put some balls on the table, the machine hits one of those balls.\nThe hit ball stops after 10,000 unit distance in total moved.\n\nWhen a ball collided with the cushion of the table, the ball takes the orbit like mirror reflection.\nWhen a ball collided with the corner, the ball bounces back on the course that came.\n\nYour mission is to predict which ball collides first with the ball which the robot hits .\nTask Input: The input is a sequence of datasets.\nThe number of datasets is less than 100.\nEach dataset is formatted as follows.\n\nn\nw h r v_x v_y\nx_1 y_1\n. . .\nx_n y_n\n\nFirst line of a dataset contains an positive integer n, which represents the number of balls on the table (2 <= n <= 11).\nThe next line contains five integers (w, h, r, v_x, v_y) separated by a single space,\nwhere w and h are the width and the length of the playing area of the table respectively (4 <= w, h <= 1,000),\nr is the radius of the balls (1 <= r <= 100).\nThe robot hits the ball in the vector (v_x, v_y) direction (-10,000 <= v_x, v_y <= 10,000 and (v_x, v_y) \\neq (0,0) ).\n\nThe following n lines give position of balls.\nEach line consists two integers separated by a single space,\n(x_i, y_i) means the center position of the i-th ball on the table in the initial state (r < x_i < w - r, r < y_i < h - r).\n(0,0) indicates the position of the north-west corner of the playing area,\nand (w, h) indicates the position of the south-east corner of the playing area.\nYou can assume that, in the initial state, the balls do not touch each other nor the cushion.\n\nThe robot always hits the first ball in the list.\nYou can assume that the given values do not have errors.\n\nThe end of the input is indicated by a line containing a single zero.\nTask Output: For each dataset, print the index of the ball which first collides with the ball the robot hits.\nWhen the hit ball collides with no ball until it stops moving, print -1.\n\nYou can assume that no more than one ball collides with the hit ball first, at the same time.\n\nIt is also guaranteed that, when r changes by eps (eps < 10^{-9}), \nthe ball which collides first and the way of the collision do not change.\nTask Samples: input: 3\n26 16 1 8 4\n10 6\n9 2\n9 10\n3\n71 363 4 8 0\n52 238\n25 33\n59 288\n0\n output: 3\n-1\n\n" }, { "title": "", "content": "There is a maze which can be described as a W * H grid.\nThe upper-left cell is denoted as (1,1), and the lower-right cell is (W, H).\nYou are now at the cell (1,1) and have to go to the cell (W, H).\nHowever, you can only move to the right adjacent cell or to the lower adjacent cell.\nThe following figure is an example of a maze.\n\n. . . #. . . . . .\na###. #####\n. bc. . . A. . .\n##. #C#d#. #\n. #B#. #. ###\n. #. . . #e. D.\n. #A. . ###. #\n. . e. c#. . E.\n####d###. #\n#. . . . #. #. #\n##E. . . d. C.\n\nIn the maze, some cells are free (denoted by . ) and some cells are occupied by rocks (denoted by #), where you cannot enter.\nAlso there are jewels (denoted by lowercase alphabets) in some of the free cells and holes to place jewels (denoted by uppercase alphabets).\nDifferent alphabets correspond to different types of jewels, i. e. a cell denoted by a contains a jewel of type A, and a cell denoted by A contains a hole to place a jewel of type A.\nIt is said that, when we place a jewel to a corresponding hole, something happy will happen.\n\nAt the cells with jewels, you can choose whether you pick a jewel or not.\nSimilarly, at the cells with holes, you can choose whether you place a jewel you have or not.\nInitially you do not have any jewels.\nYou have a very big bag, so you can bring arbitrarily many jewels.\nHowever, your bag is a stack, that is, you can only place the jewel that you picked up last.\n\nOn the way from cell (1,1) to cell (W, H), how many jewels can you place to correct holes?", "constraint": "", "input": "The input contains a sequence of datasets.\nThe end of the input is indicated by a line containing two zeroes.\nEach dataset is formatted as follows.\n\nH W\nC_{11} C_{12} . . . C_{1W}\nC_{21} C_{22} . . . C_{2W}\n. . .\nC_{H1} C_{H2} . . . C_{HW}\n\nHere, H and W are the height and width of the grid.\nYou may assume 1 <= W, H <= 50.\nThe rest of the datasets consists of H lines, each of which is composed of W letters.\nEach letter C_{ij} specifies the type of the cell (i, j) as described before.\nIt is guaranteed that C_{11} and C_{WH} are never #.\n\nYou may also assume that each lowercase or uppercase alphabet appear at most 10 times in each dataset.", "output": "For each dataset, output the maximum number of jewels that you can place to corresponding holes.\nIf you cannot reach the cell (W, H), output -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\nac#\nb#C\n.BA\n3 3\naaZ\na#Z\naZZ\n3 3\n..#\n.#.\n#..\n1 50\nabcdefghijklmnopqrstuvwxyYXWVUTSRQPONMLKJIHGFEDCBA\n1 50\naAbBcCdDeEfFgGhHiIjJkKlLmMnNoOpPqQrRsStTuUvVwWxXyY\n1 50\nabcdefghijklmnopqrstuvwxyABCDEFGHIJKLMNOPQRSTUVWXY\n1 50\naaaaaaaaaabbbbbbbbbbcccccCCCCCBBBBBBBBBBAAAAAAAAAA\n10 10\n...#......\na###.#####\n.bc...A...\n##.#C#d#.#\n.#B#.#.###\n.#...#e.D.\n.#A..###.#\n..e.c#..E.\n####d###.#\n##E...D.C.\n0 0\n output: 2\n0\n-1\n25\n25\n1\n25\n4"], "Pid": "p01650", "ProblemText": "Task Description: There is a maze which can be described as a W * H grid.\nThe upper-left cell is denoted as (1,1), and the lower-right cell is (W, H).\nYou are now at the cell (1,1) and have to go to the cell (W, H).\nHowever, you can only move to the right adjacent cell or to the lower adjacent cell.\nThe following figure is an example of a maze.\n\n. . . #. . . . . .\na###. #####\n. bc. . . A. . .\n##. #C#d#. #\n. #B#. #. ###\n. #. . . #e. D.\n. #A. . ###. #\n. . e. c#. . E.\n####d###. #\n#. . . . #. #. #\n##E. . . d. C.\n\nIn the maze, some cells are free (denoted by . ) and some cells are occupied by rocks (denoted by #), where you cannot enter.\nAlso there are jewels (denoted by lowercase alphabets) in some of the free cells and holes to place jewels (denoted by uppercase alphabets).\nDifferent alphabets correspond to different types of jewels, i. e. a cell denoted by a contains a jewel of type A, and a cell denoted by A contains a hole to place a jewel of type A.\nIt is said that, when we place a jewel to a corresponding hole, something happy will happen.\n\nAt the cells with jewels, you can choose whether you pick a jewel or not.\nSimilarly, at the cells with holes, you can choose whether you place a jewel you have or not.\nInitially you do not have any jewels.\nYou have a very big bag, so you can bring arbitrarily many jewels.\nHowever, your bag is a stack, that is, you can only place the jewel that you picked up last.\n\nOn the way from cell (1,1) to cell (W, H), how many jewels can you place to correct holes?\nTask Input: The input contains a sequence of datasets.\nThe end of the input is indicated by a line containing two zeroes.\nEach dataset is formatted as follows.\n\nH W\nC_{11} C_{12} . . . C_{1W}\nC_{21} C_{22} . . . C_{2W}\n. . .\nC_{H1} C_{H2} . . . C_{HW}\n\nHere, H and W are the height and width of the grid.\nYou may assume 1 <= W, H <= 50.\nThe rest of the datasets consists of H lines, each of which is composed of W letters.\nEach letter C_{ij} specifies the type of the cell (i, j) as described before.\nIt is guaranteed that C_{11} and C_{WH} are never #.\n\nYou may also assume that each lowercase or uppercase alphabet appear at most 10 times in each dataset.\nTask Output: For each dataset, output the maximum number of jewels that you can place to corresponding holes.\nIf you cannot reach the cell (W, H), output -1.\nTask Samples: input: 3 3\nac#\nb#C\n.BA\n3 3\naaZ\na#Z\naZZ\n3 3\n..#\n.#.\n#..\n1 50\nabcdefghijklmnopqrstuvwxyYXWVUTSRQPONMLKJIHGFEDCBA\n1 50\naAbBcCdDeEfFgGhHiIjJkKlLmMnNoOpPqQrRsStTuUvVwWxXyY\n1 50\nabcdefghijklmnopqrstuvwxyABCDEFGHIJKLMNOPQRSTUVWXY\n1 50\naaaaaaaaaabbbbbbbbbbcccccCCCCCBBBBBBBBBBAAAAAAAAAA\n10 10\n...#......\na###.#####\n.bc...A...\n##.#C#d#.#\n.#B#.#.###\n.#...#e.D.\n.#A..###.#\n..e.c#..E.\n####d###.#\n##E...D.C.\n0 0\n output: 2\n0\n-1\n25\n25\n1\n25\n4\n\n" }, { "title": "", "content": "Let b_i(x) be the i-th least significant bit of x, i. e. the i-th least significant digit of x in base 2 (i >= 1).\nFor example, since 6 = (110)_2, b_1(6) = 0, b_2(6) = 1, b_3(6) = 1, b_4(6) = 0, b_5(6) = 0, and so on.\n\nLet A and B be integers that satisfy 1 <= A <= B <= 10^{18},\nand k_i be the number of integers x such that A <= x <= B and b_i(x) = 1.\n\nYour task is to write a program that determines A and B for a given \\{k_i\\}.", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of datasets is no more than 100,000.\nEach dataset has the following format:\n\nn\nk_1\nk_2\n. . .\nk_n\n\nThe first line of each dataset contains an integer n (1 <= n <= 64).\nThen n lines follow, each of which contains k_i (0 <= k_i <= 2^{63} - 1).\nFor all i > n, k_i = 0.\n\nThe input is terminated by n = 0.\nYour program must not produce output for it.", "output": "For each dataset, print one line.\n\n If A and B can be uniquely determined, output A and B. Separate the numbers by a single space.\n\n If there exists more than one possible pair of A and B, output Many (without quotes).\n\n Otherwise, i. e. if there exists no possible pair, output None (without quotes).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2\n2\n1\n49\n95351238128934\n95351238128934\n95351238128932\n95351238128936\n95351238128936\n95351238128936\n95351238128960\n95351238128900\n95351238128896\n95351238129096\n95351238128772\n95351238129096\n95351238129096\n95351238126156\n95351238131712\n95351238131712\n95351238149576\n95351238093388\n95351238084040\n95351237962316\n95351238295552\n95351237911684\n95351237911684\n95351235149824\n95351233717380\n95351249496652\n95351249496652\n95351226761216\n95351226761216\n95351082722436\n95351082722436\n95352054803020\n95352156464260\n95348273971200\n95348273971200\n95354202286668\n95356451431556\n95356451431556\n95346024826312\n95356451431556\n95356451431556\n94557999988736\n94256939803780\n94256939803780\n102741546035788\n87649443431880\n87649443431880\n140737488355328\n32684288648324\n64\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n19\n20\n21\n22\n23\n24\n25\n26\n27\n28\n29\n30\n31\n32\n33\n34\n35\n36\n37\n38\n39\n40\n41\n42\n43\n44\n45\n46\n47\n48\n49\n50\n51\n52\n53\n54\n55\n56\n57\n58\n59\n60\n61\n62\n63\n11\n0\n0\n1\n1\n1\n0\n1\n1\n1\n1\n1\n63\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n1\n4\n1\n1\n1\n1\n0\n output: 1 4\n123456789101112 314159265358979\nNone\n2012 2012\nNone\nMany"], "Pid": "p01651", "ProblemText": "Task Description: Let b_i(x) be the i-th least significant bit of x, i. e. the i-th least significant digit of x in base 2 (i >= 1).\nFor example, since 6 = (110)_2, b_1(6) = 0, b_2(6) = 1, b_3(6) = 1, b_4(6) = 0, b_5(6) = 0, and so on.\n\nLet A and B be integers that satisfy 1 <= A <= B <= 10^{18},\nand k_i be the number of integers x such that A <= x <= B and b_i(x) = 1.\n\nYour task is to write a program that determines A and B for a given \\{k_i\\}.\nTask Input: The input consists of multiple datasets.\nThe number of datasets is no more than 100,000.\nEach dataset has the following format:\n\nn\nk_1\nk_2\n. . .\nk_n\n\nThe first line of each dataset contains an integer n (1 <= n <= 64).\nThen n lines follow, each of which contains k_i (0 <= k_i <= 2^{63} - 1).\nFor all i > n, k_i = 0.\n\nThe input is terminated by n = 0.\nYour program must not produce output for it.\nTask Output: For each dataset, print one line.\n\n If A and B can be uniquely determined, output A and B. Separate the numbers by a single space.\n\n If there exists more than one possible pair of A and B, output Many (without quotes).\n\n Otherwise, i. e. if there exists no possible pair, output None (without quotes).\nTask Samples: input: 3\n2\n2\n1\n49\n95351238128934\n95351238128934\n95351238128932\n95351238128936\n95351238128936\n95351238128936\n95351238128960\n95351238128900\n95351238128896\n95351238129096\n95351238128772\n95351238129096\n95351238129096\n95351238126156\n95351238131712\n95351238131712\n95351238149576\n95351238093388\n95351238084040\n95351237962316\n95351238295552\n95351237911684\n95351237911684\n95351235149824\n95351233717380\n95351249496652\n95351249496652\n95351226761216\n95351226761216\n95351082722436\n95351082722436\n95352054803020\n95352156464260\n95348273971200\n95348273971200\n95354202286668\n95356451431556\n95356451431556\n95346024826312\n95356451431556\n95356451431556\n94557999988736\n94256939803780\n94256939803780\n102741546035788\n87649443431880\n87649443431880\n140737488355328\n32684288648324\n64\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n19\n20\n21\n22\n23\n24\n25\n26\n27\n28\n29\n30\n31\n32\n33\n34\n35\n36\n37\n38\n39\n40\n41\n42\n43\n44\n45\n46\n47\n48\n49\n50\n51\n52\n53\n54\n55\n56\n57\n58\n59\n60\n61\n62\n63\n11\n0\n0\n1\n1\n1\n0\n1\n1\n1\n1\n1\n63\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n1\n4\n1\n1\n1\n1\n0\n output: 1 4\n123456789101112 314159265358979\nNone\n2012 2012\nNone\nMany\n\n" }, { "title": "", "content": "One day in a forest, Alice found an old monolith.\nShe investigated the monolith, and found this was a sentence written in an old language.\nA sentence consists of glyphs and rectangles which surrounds them.\nFor the above example, there are following glyphs.\nNotice that some glyphs are flipped horizontally in a sentence.\n\nShe decided to transliterate it using ASCII letters assigning an alphabet to each glyph, and [ and ] to rectangles.\nIf a sentence contains a flipped glyph, she transliterates it from right to left.\nFor example, she could assign a and b to the above glyphs respectively.\nThen the above sentence would be transliterated into [[ab][ab]a].\n\nAfter examining the sentence, Alice figured out that the sentence was organized by the following structure:\n\n A sentence is a sequence consists of zero or more s. \n\n A term is either a glyph or a . A glyph may be flipped.\n\n is a rectangle surrounding a . The height of a box is larger than any glyphs inside.\nNow, the sentence written on the monolith is a nonempty .\nEach term in the sequence fits in a rectangular bounding box, although the boxes are not explicitly indicated for glyphs. Those bounding boxes for adjacent terms have no overlap to each other.\nAlice formalized the transliteration rules as follows.\n\nLet f be the transliterate function.\n\nEach sequence s = t_1 t_2 . . . t_m is written either from left to right, or from right to left.\nHowever, please note here t_1 corresponds to the leftmost term in the sentence, t_2 to the 2nd term from the left, and so on.\n\nLet's define ḡ to be the flipped glyph g.\nA sequence must have been written from right to left, when a sequence contains one or more single-glyph term which is unreadable without flipping, i. e. there exists an integer i where t_i is a single glyph g, and g is not in the glyph dictionary given separately whereas ḡ is.\nIn such cases f(s) is defined to be f(t_m) f(t_{m-1}) . . . f(t_1), otherwise f(s) = f(t_1) f(t_2) . . . f(t_m).\nIt is guaranteed that all the glyphs in the sequence are flipped if there is one or more glyph which is unreadable without flipping.\n\nIf the term t_i is a box enclosing a sequence s', f(t_i) = [ f(s') ].\nIf the term t_i is a glyph g, f(t_i) is mapped to an alphabet letter corresponding to the glyph g, or ḡ if the sequence containing g is written from right to left.\n\nPlease make a program to transliterate the sentences on the monoliths to help Alice.", "constraint": "", "input": "The input consists of several datasets.\nThe end of the input is denoted by two zeros separated by a single-space.\n\nEach dataset has the following format.\n\nn m\nglyph_1\n. . .\nglyph_n\nstring_1\n. . .\nstring_m\n\nn (1<= n<= 26) is the number of glyphs and m (1<= m<= 10) is the number of monoliths.\nglyph_i is given by the following format.\n\nc h w\nb_{11}. . . b_{1w}\n. . .\nb_{h1}. . . b_{hw}\n\nc is a lower-case alphabet that Alice assigned to the glyph.\nh and w (1 <= h <= 15,1 <= w <= 15) specify the height and width of the bitmap of the glyph, respectively.\nThe matrix b indicates the bitmap.\nA white cell is represented by . and a black cell is represented by *.\n\nYou can assume that all the glyphs are assigned distinct characters.\nYou can assume that every column of the bitmap contains at least one black cell, and the first and last row of the bitmap contains at least one black cell.\nEvery bitmap is different to each other, but it is possible that a flipped bitmap is same to another bitmap.\nMoreover there may be symmetric bitmaps.\n\nstring_i is given by the following format.\n\nh w\nb_{11}. . . b_{1w}\n. . .\nb_{h1}. . . b_{hw}\n\nh and w (1 <= h <= 100,1 <= w <= 1000) is the height and width of the bitmap of the sequence.\nSimilarly to the glyph dictionary, b indicates the bitmap where A white cell is represented by . and a black cell by *.\n\nThere is no noise: every black cell in the bitmap belongs to either one glyph or one rectangle box.\nThe height of a rectangle is at least 3 and more than the maximum height of the tallest glyph.\nThe width of a rectangle is at least 3.\n\nA box must have a margin of 1 pixel around the edge of it.\n\nYou can assume the glyphs are never arranged vertically.\nMoreover, you can assume that if two rectangles, or a rectangle and a glyph, are in the same column, then one of them contains the other.\nFor all bounding boxes of glyphs and black cells of rectangles, there is at least one white cell between every two of them.\nYou can assume at least one cell in the bitmap is black.", "output": "For each monolith, output the transliterated sentence in one line.\nAfter the output for one dataset, output # in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 1\na 11 9\n****.....\n.*.*.....\n.*.*.....\n.*..*....\n.**..*...\n..**..*..\n..*.*....\n..**.*.*.\n..*..*.*.\n..*****.*\n******.**\nb 10 6\n....*.\n....*.\n....*.\n....*.\n....*.\n....*.\n....*.\n....*.\n.**..*\n*****.\n19 55\n*******************************************************\n*.....................................................*\n*.********************.********************...........*\n*.*..................*.*..................*...........*\n*.*.****.............*.*.............****.*.****......*\n*.*..*.*..........*..*.*..*..........*.*..*..*.*......*\n*.*..*.*..........*..*.*..*..........*.*..*..*.*......*\n*.*..*..*.........*..*.*..*.........*..*..*..*..*.....*\n*.*..**..*........*..*.*..*........*..**..*..**..*....*\n*.*...**..*.......*..*.*..*.......*..**...*...**..*...*\n*.*...*.*.........*..*.*..*.........*.*...*...*.*.....*\n*.*...**.*.*......*..*.*..*......*.*.**...*...**.*.*..*\n*.*...*..*.*......*..*.*..*......*.*..*...*...*..*.*..*\n*.*...*****.*..**..*.*.*.*..**..*.*****...*...*****.*.*\n*.*.******.**.*****..*.*..*****.**.******.*.******.**.*\n*.*..................*.*..................*...........*\n*.********************.********************...........*\n*.....................................................*\n*******************************************************\n2 3\na 2 3\n.*.\n***\nb 3 3\n.*.\n***\n.*.\n2 3\n.*.\n***\n4 3\n***\n*.*\n*.*\n***\n9 13\n************.\n*..........*.\n*.......*..*.\n*...*..***.*.\n*..***.....*.\n*...*......*.\n*..........*.\n************.\n.............\n3 1\na 2 2\n.*\n**\nb 2 1\n*\n*\nc 3 3\n***\n*.*\n***\n11 16\n****************\n*..............*\n*....*********.*\n*....*.......*.*\n*.*..*.***...*.*\n*.**.*.*.*.*.*.*\n*....*.***.*.*.*\n*....*.......*.*\n*....*********.*\n*..............*\n****************\n0 0\n output: [[ab][ab]a]\n#\na\n[]\n[ba]\n#\n[[cb]a]\n#"], "Pid": "p01652", "ProblemText": "Task Description: One day in a forest, Alice found an old monolith.\nShe investigated the monolith, and found this was a sentence written in an old language.\nA sentence consists of glyphs and rectangles which surrounds them.\nFor the above example, there are following glyphs.\nNotice that some glyphs are flipped horizontally in a sentence.\n\nShe decided to transliterate it using ASCII letters assigning an alphabet to each glyph, and [ and ] to rectangles.\nIf a sentence contains a flipped glyph, she transliterates it from right to left.\nFor example, she could assign a and b to the above glyphs respectively.\nThen the above sentence would be transliterated into [[ab][ab]a].\n\nAfter examining the sentence, Alice figured out that the sentence was organized by the following structure:\n\n A sentence is a sequence consists of zero or more s. \n\n A term is either a glyph or a . A glyph may be flipped.\n\n is a rectangle surrounding a . The height of a box is larger than any glyphs inside.\nNow, the sentence written on the monolith is a nonempty .\nEach term in the sequence fits in a rectangular bounding box, although the boxes are not explicitly indicated for glyphs. Those bounding boxes for adjacent terms have no overlap to each other.\nAlice formalized the transliteration rules as follows.\n\nLet f be the transliterate function.\n\nEach sequence s = t_1 t_2 . . . t_m is written either from left to right, or from right to left.\nHowever, please note here t_1 corresponds to the leftmost term in the sentence, t_2 to the 2nd term from the left, and so on.\n\nLet's define ḡ to be the flipped glyph g.\nA sequence must have been written from right to left, when a sequence contains one or more single-glyph term which is unreadable without flipping, i. e. there exists an integer i where t_i is a single glyph g, and g is not in the glyph dictionary given separately whereas ḡ is.\nIn such cases f(s) is defined to be f(t_m) f(t_{m-1}) . . . f(t_1), otherwise f(s) = f(t_1) f(t_2) . . . f(t_m).\nIt is guaranteed that all the glyphs in the sequence are flipped if there is one or more glyph which is unreadable without flipping.\n\nIf the term t_i is a box enclosing a sequence s', f(t_i) = [ f(s') ].\nIf the term t_i is a glyph g, f(t_i) is mapped to an alphabet letter corresponding to the glyph g, or ḡ if the sequence containing g is written from right to left.\n\nPlease make a program to transliterate the sentences on the monoliths to help Alice.\nTask Input: The input consists of several datasets.\nThe end of the input is denoted by two zeros separated by a single-space.\n\nEach dataset has the following format.\n\nn m\nglyph_1\n. . .\nglyph_n\nstring_1\n. . .\nstring_m\n\nn (1<= n<= 26) is the number of glyphs and m (1<= m<= 10) is the number of monoliths.\nglyph_i is given by the following format.\n\nc h w\nb_{11}. . . b_{1w}\n. . .\nb_{h1}. . . b_{hw}\n\nc is a lower-case alphabet that Alice assigned to the glyph.\nh and w (1 <= h <= 15,1 <= w <= 15) specify the height and width of the bitmap of the glyph, respectively.\nThe matrix b indicates the bitmap.\nA white cell is represented by . and a black cell is represented by *.\n\nYou can assume that all the glyphs are assigned distinct characters.\nYou can assume that every column of the bitmap contains at least one black cell, and the first and last row of the bitmap contains at least one black cell.\nEvery bitmap is different to each other, but it is possible that a flipped bitmap is same to another bitmap.\nMoreover there may be symmetric bitmaps.\n\nstring_i is given by the following format.\n\nh w\nb_{11}. . . b_{1w}\n. . .\nb_{h1}. . . b_{hw}\n\nh and w (1 <= h <= 100,1 <= w <= 1000) is the height and width of the bitmap of the sequence.\nSimilarly to the glyph dictionary, b indicates the bitmap where A white cell is represented by . and a black cell by *.\n\nThere is no noise: every black cell in the bitmap belongs to either one glyph or one rectangle box.\nThe height of a rectangle is at least 3 and more than the maximum height of the tallest glyph.\nThe width of a rectangle is at least 3.\n\nA box must have a margin of 1 pixel around the edge of it.\n\nYou can assume the glyphs are never arranged vertically.\nMoreover, you can assume that if two rectangles, or a rectangle and a glyph, are in the same column, then one of them contains the other.\nFor all bounding boxes of glyphs and black cells of rectangles, there is at least one white cell between every two of them.\nYou can assume at least one cell in the bitmap is black.\nTask Output: For each monolith, output the transliterated sentence in one line.\nAfter the output for one dataset, output # in one line.\nTask Samples: input: 2 1\na 11 9\n****.....\n.*.*.....\n.*.*.....\n.*..*....\n.**..*...\n..**..*..\n..*.*....\n..**.*.*.\n..*..*.*.\n..*****.*\n******.**\nb 10 6\n....*.\n....*.\n....*.\n....*.\n....*.\n....*.\n....*.\n....*.\n.**..*\n*****.\n19 55\n*******************************************************\n*.....................................................*\n*.********************.********************...........*\n*.*..................*.*..................*...........*\n*.*.****.............*.*.............****.*.****......*\n*.*..*.*..........*..*.*..*..........*.*..*..*.*......*\n*.*..*.*..........*..*.*..*..........*.*..*..*.*......*\n*.*..*..*.........*..*.*..*.........*..*..*..*..*.....*\n*.*..**..*........*..*.*..*........*..**..*..**..*....*\n*.*...**..*.......*..*.*..*.......*..**...*...**..*...*\n*.*...*.*.........*..*.*..*.........*.*...*...*.*.....*\n*.*...**.*.*......*..*.*..*......*.*.**...*...**.*.*..*\n*.*...*..*.*......*..*.*..*......*.*..*...*...*..*.*..*\n*.*...*****.*..**..*.*.*.*..**..*.*****...*...*****.*.*\n*.*.******.**.*****..*.*..*****.**.******.*.******.**.*\n*.*..................*.*..................*...........*\n*.********************.********************...........*\n*.....................................................*\n*******************************************************\n2 3\na 2 3\n.*.\n***\nb 3 3\n.*.\n***\n.*.\n2 3\n.*.\n***\n4 3\n***\n*.*\n*.*\n***\n9 13\n************.\n*..........*.\n*.......*..*.\n*...*..***.*.\n*..***.....*.\n*...*......*.\n*..........*.\n************.\n.............\n3 1\na 2 2\n.*\n**\nb 2 1\n*\n*\nc 3 3\n***\n*.*\n***\n11 16\n****************\n*..............*\n*....*********.*\n*....*.......*.*\n*.*..*.***...*.*\n*.**.*.*.*.*.*.*\n*....*.***.*.*.*\n*....*.......*.*\n*....*********.*\n*..............*\n****************\n0 0\n output: [[ab][ab]a]\n#\na\n[]\n[ba]\n#\n[[cb]a]\n#\n\n" }, { "title": "", "content": "A magician lives in a country which consists of N islands and M bridges. \nSome of the bridges are magical bridges, which are created by the magician.\nHer magic can change all the lengths of the magical bridges to the same non-negative integer simultaneously.\n\nThis country has a famous 2-player race game.\nPlayer 1 starts from island S_1 and Player 2 starts from island S_2. \nA player who reached the island T first is a winner.\n\nSince the magician loves to watch this game, she decided to make the game most exiting by changing the length of the magical bridges\nso that the difference between the shortest-path distance from S_1 to T and the shortest-path distance from S_2 to T is as small as possible. We ignore the movement inside the islands.\n\nYour job is to calculate how small the gap can be.\n\nNote that she assigns a length of the magical bridges before the race starts once, \nand does not change the length during the race.", "constraint": "", "input": "The input consists of several datasets. The end of the input is denoted by five zeros separated by a single-space. Each dataset obeys the following format. Every number in the inputs is integer. \n\nN M S_1 S_2 T\na_1 b_1 w_1\na_2 b_2 w_2\n. . .\na_M b_M w_M\n\n(a_i, b_i) indicates the bridge i connects the two islands a_i and b_i.\n\nw_i is either a non-negative integer or a letter x (quotes for clarity). If w_i is an integer, it indicates the bridge i is normal and its length is w_i. Otherwise, it indicates the bridge i is magical.\n\nYou can assume the following:\n\n 1<= N <= 1,000\n\n 1<= M <= 2,000\n\n 1<= S_1, S_2, T <= N\n\n S_1, S_2, T are all different.\n\n 1<= a_i, b_i <= N\n\n a_i \\neq b_i\n\n For all normal bridge i, 0 <= w_i <= 1,000,000,000\n\n The number of magical bridges <= 100", "output": "For each dataset, print the answer in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 2 3 1\n1 2 1\n1 3 2\n4 3 1 4 2\n2 1 3\n2 3 x\n4 3 x\n0 0 0 0 0\n output: 1\n1"], "Pid": "p01653", "ProblemText": "Task Description: A magician lives in a country which consists of N islands and M bridges. \nSome of the bridges are magical bridges, which are created by the magician.\nHer magic can change all the lengths of the magical bridges to the same non-negative integer simultaneously.\n\nThis country has a famous 2-player race game.\nPlayer 1 starts from island S_1 and Player 2 starts from island S_2. \nA player who reached the island T first is a winner.\n\nSince the magician loves to watch this game, she decided to make the game most exiting by changing the length of the magical bridges\nso that the difference between the shortest-path distance from S_1 to T and the shortest-path distance from S_2 to T is as small as possible. We ignore the movement inside the islands.\n\nYour job is to calculate how small the gap can be.\n\nNote that she assigns a length of the magical bridges before the race starts once, \nand does not change the length during the race.\nTask Input: The input consists of several datasets. The end of the input is denoted by five zeros separated by a single-space. Each dataset obeys the following format. Every number in the inputs is integer. \n\nN M S_1 S_2 T\na_1 b_1 w_1\na_2 b_2 w_2\n. . .\na_M b_M w_M\n\n(a_i, b_i) indicates the bridge i connects the two islands a_i and b_i.\n\nw_i is either a non-negative integer or a letter x (quotes for clarity). If w_i is an integer, it indicates the bridge i is normal and its length is w_i. Otherwise, it indicates the bridge i is magical.\n\nYou can assume the following:\n\n 1<= N <= 1,000\n\n 1<= M <= 2,000\n\n 1<= S_1, S_2, T <= N\n\n S_1, S_2, T are all different.\n\n 1<= a_i, b_i <= N\n\n a_i \\neq b_i\n\n For all normal bridge i, 0 <= w_i <= 1,000,000,000\n\n The number of magical bridges <= 100\nTask Output: For each dataset, print the answer in a line.\nTask Samples: input: 3 2 2 3 1\n1 2 1\n1 3 2\n4 3 1 4 2\n2 1 3\n2 3 x\n4 3 x\n0 0 0 0 0\n output: 1\n1\n\n" }, { "title": "", "content": "Chelsea is a modern artist. She decided to make her next work with ladders. She wants to combine some ladders and paint some beautiful pattern. \n\nA ladder can be considered as a graph called hashigo. There are n hashigos numbered from 0 to n-1. \nHashigo i of length l_i has 2 l_{i} + 6 vertices v_{i, 0}, v_{i, 1}, . . . , v_{i, 2 l_{i} + 5}\nand has edges between the pair of vertices (v_{i, j}, v_{i, j+2}) (0 <= j <= 2 l_i +3) and (v_{i, 2j}, v_{i, 2j+1}) (1 <= j <= l_i+1).\nThe figure below is example of a hashigo of length 2. This corresponds to the graph given in the first dataset in the sample input.\nTwo hashigos i and j are combined at position p (0 <= p <= l_{i}-1) and q (0 <= q <= l_{j}-1) by marged each pair of vertices (v_{i, 2p+2}, v_{j, 2q+2}), (v_{i, 2p+3}, v_{j, 2q+4}), (v_{i, 2p+4}, v_{j, 2q+3}) and (v_{i, 2p+5}, v_{j, 2q+5}). \n\nChelsea performs this operation n-1 times to combine the n hashigos.\nAfter this operation, the graph should be connected and the maximum degree of the graph should not exceed 4.\nThe figure below is a example of the graph obtained by combining three hashigos. This corresponds to the graph given in the second dataset in the sample input.\nNow she decided to paint each vertex by black or white with satisfying the following condition:\n\n The maximum components formed by the connected vertices painted by the same color is less than or equals to k. \nShe would like to try all the patterns and choose the best. However, the number of painting way can be very huge.\nSince she is not good at math nor computing, she cannot calculate the number. So please help her with your superb programming skill!", "constraint": "", "input": "The input contains several datasets, and each dataset is in the following format.\n\nn k\nl_0 l_1 . . . l_{n-1}\nf_0 p_0 t_0 q_0\n. . .\nf_{n-2} p_{n-2} t_{n-2} q_{n-2}\n\nThe first line contains two integers n (1 <= n <= 30) and k (1 <= k <= 8).\n\nThe next line contains n integers l_i (1 <= l_i <= 30), each denotes the length of hashigo i.\n\nThe following n-1 lines each contains four integers f_i (0 <= f_i <= n-1), p_i (0 <= p_i <= l_{f_i}-1), t_i (0 <= t_i <= n-1), q_i (0 <= q_i <= l_{t_i}-1). It represents the hashigo f_i and the hashigo t_i are combined at the position p_i and the position q_i. You may assume that the graph obtained by combining n hashigos is connected and the degree of each vertex of the graph does not exceed 4.\n\nThe last dataset is followed by a line containing two zeros.", "output": "For each dataset, print the number of different colorings modulo 1,000,000,007 in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 5\n2\n3 7\n2 3 1\n0 1 1 0\n1 2 2 0\n2 8\n5 6\n0 2 1 2\n2 8\n1 1\n0 0 1 0\n2 2\n2 2\n0 1 1 0\n2 3\n3 3\n0 2 1 1\n2 4\n3 1\n1 0 0 1\n0 0\n output: 708\n1900484\n438404500\n3878\n496\n14246\n9768"], "Pid": "p01654", "ProblemText": "Task Description: Chelsea is a modern artist. She decided to make her next work with ladders. She wants to combine some ladders and paint some beautiful pattern. \n\nA ladder can be considered as a graph called hashigo. There are n hashigos numbered from 0 to n-1. \nHashigo i of length l_i has 2 l_{i} + 6 vertices v_{i, 0}, v_{i, 1}, . . . , v_{i, 2 l_{i} + 5}\nand has edges between the pair of vertices (v_{i, j}, v_{i, j+2}) (0 <= j <= 2 l_i +3) and (v_{i, 2j}, v_{i, 2j+1}) (1 <= j <= l_i+1).\nThe figure below is example of a hashigo of length 2. This corresponds to the graph given in the first dataset in the sample input.\nTwo hashigos i and j are combined at position p (0 <= p <= l_{i}-1) and q (0 <= q <= l_{j}-1) by marged each pair of vertices (v_{i, 2p+2}, v_{j, 2q+2}), (v_{i, 2p+3}, v_{j, 2q+4}), (v_{i, 2p+4}, v_{j, 2q+3}) and (v_{i, 2p+5}, v_{j, 2q+5}). \n\nChelsea performs this operation n-1 times to combine the n hashigos.\nAfter this operation, the graph should be connected and the maximum degree of the graph should not exceed 4.\nThe figure below is a example of the graph obtained by combining three hashigos. This corresponds to the graph given in the second dataset in the sample input.\nNow she decided to paint each vertex by black or white with satisfying the following condition:\n\n The maximum components formed by the connected vertices painted by the same color is less than or equals to k. \nShe would like to try all the patterns and choose the best. However, the number of painting way can be very huge.\nSince she is not good at math nor computing, she cannot calculate the number. So please help her with your superb programming skill!\nTask Input: The input contains several datasets, and each dataset is in the following format.\n\nn k\nl_0 l_1 . . . l_{n-1}\nf_0 p_0 t_0 q_0\n. . .\nf_{n-2} p_{n-2} t_{n-2} q_{n-2}\n\nThe first line contains two integers n (1 <= n <= 30) and k (1 <= k <= 8).\n\nThe next line contains n integers l_i (1 <= l_i <= 30), each denotes the length of hashigo i.\n\nThe following n-1 lines each contains four integers f_i (0 <= f_i <= n-1), p_i (0 <= p_i <= l_{f_i}-1), t_i (0 <= t_i <= n-1), q_i (0 <= q_i <= l_{t_i}-1). It represents the hashigo f_i and the hashigo t_i are combined at the position p_i and the position q_i. You may assume that the graph obtained by combining n hashigos is connected and the degree of each vertex of the graph does not exceed 4.\n\nThe last dataset is followed by a line containing two zeros.\nTask Output: For each dataset, print the number of different colorings modulo 1,000,000,007 in a line.\nTask Samples: input: 1 5\n2\n3 7\n2 3 1\n0 1 1 0\n1 2 2 0\n2 8\n5 6\n0 2 1 2\n2 8\n1 1\n0 0 1 0\n2 2\n2 2\n0 1 1 0\n2 3\n3 3\n0 2 1 1\n2 4\n3 1\n1 0 0 1\n0 0\n output: 708\n1900484\n438404500\n3878\n496\n14246\n9768\n\n" }, { "title": "", "content": "You bought 3 ancient scrolls from a magician. These scrolls have a long string, and the lengths of the strings are the same. He said that these scrolls are copies of the key string to enter a dungeon with a secret treasure.\nHowever, he also said, they were copied so many times by hand, so the string will contain some errors, though the length seems correct. \n\nYour job is to recover the original string from these strings. When finding the original string, you decided to use the following assumption. \n\n The copied string will contain at most d errors. In other words, the Hamming distance of the original string and the copied string is at most d. \n\n If there exist many candidates, the lexicographically minimum string is the original string.\nCan you find the orignal string?", "constraint": "", "input": "The input contains a series of datasets.\n\nEach dataset has the following format:\n\nl d\nstr_1\nstr_2\nstr_3\n\nThe first line contains two integers l (1 <= l <= 100,000) and d (0 <= d <= 5,000. )\nl describes the length of 3 given strings and d describes acceptable maximal Hamming distance.\nThe following 3 lines have given strings, whose lengths are l.\nThese 3 strings consist of only lower and upper case alphabets.\n\nThe input ends with a line containing two zeros, which should not be processed.", "output": "Print the lexicographically minimum satisfying the condition in a line.\nIf there do not exist such strings, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\nACM\nIBM\nICM\n5 2\niwzwz\niziwi\nzwizi\n1 0\nA\nB\nC\n10 5\njLRNlNyGWx\nyyLnlyyGDA\nyLRnvyyGDA\n0 0\n output: ICM\niwiwi\n-1\nAARAlNyGDA"], "Pid": "p01655", "ProblemText": "Task Description: You bought 3 ancient scrolls from a magician. These scrolls have a long string, and the lengths of the strings are the same. He said that these scrolls are copies of the key string to enter a dungeon with a secret treasure.\nHowever, he also said, they were copied so many times by hand, so the string will contain some errors, though the length seems correct. \n\nYour job is to recover the original string from these strings. When finding the original string, you decided to use the following assumption. \n\n The copied string will contain at most d errors. In other words, the Hamming distance of the original string and the copied string is at most d. \n\n If there exist many candidates, the lexicographically minimum string is the original string.\nCan you find the orignal string?\nTask Input: The input contains a series of datasets.\n\nEach dataset has the following format:\n\nl d\nstr_1\nstr_2\nstr_3\n\nThe first line contains two integers l (1 <= l <= 100,000) and d (0 <= d <= 5,000. )\nl describes the length of 3 given strings and d describes acceptable maximal Hamming distance.\nThe following 3 lines have given strings, whose lengths are l.\nThese 3 strings consist of only lower and upper case alphabets.\n\nThe input ends with a line containing two zeros, which should not be processed.\nTask Output: Print the lexicographically minimum satisfying the condition in a line.\nIf there do not exist such strings, print -1.\nTask Samples: input: 3 1\nACM\nIBM\nICM\n5 2\niwzwz\niziwi\nzwizi\n1 0\nA\nB\nC\n10 5\njLRNlNyGWx\nyyLnlyyGDA\nyLRnvyyGDA\n0 0\n output: ICM\niwiwi\n-1\nAARAlNyGDA\n\n" }, { "title": "A - Everlasting Zero", "content": "You are very absorbed in a famous role-playing game (RPG), \"Everlasting -Zero-\". An RPG is a game in which players assume the roles of characters in a fictional setting. While you play the game, you can forget your \"real life\" and become a different person.\n\nTo play the game more effectively, you have to understand two notions, a skill point and a special command. A character can boost up by accumulating his experience points. When a character boosts up, he can gain skill points.\n\nYou can arbitrarily allocate the skill points to the character's skills to enhance the character's abilities. If skill points of each skill meets some conditions simultaneously (e. g. , the skill points of some skills are are greater than or equal to the threshold values and those of others are less than or equal to the values) , the character learns a special command. One important thing is that once a character learned the command, he will never forget it. And once skill points are allocated to the character, you cannot revoke the allocation. In addition, the initial values of each skill is 0.\n\nThe system is so complicated that it is difficult for ordinary players to know whether a character can learn all the special commands or not. Luckily, in the \"real\" world, you are a great programmer, so you decided to write a program to tell whether a character can learn all the special commnads or not. If it turns out to be feasible, you will be more absorbed in the game and become happy.", "constraint": "", "input": "The input is formatted as follows.\n\nM N\nK_1\ns_{1,1} cond_{1,1} t_{1,1}\ns_{1,2} cond_{1,2} t_{1,2}\n. . .\ns_{1, K_1} cond_{1, K_1} t_{1, K_1}\nK_2\n. . .\nK_M\ns_{M, 1} cond_{M, 1} t_{M, 1}\ns_{M, 2} cond_{M, 2} t_{M, 2}\n. . .\ns_{M, K_M} cond_{M, K_M} t_{M, K_M}\n\nThe first line of the input contains two integers (M, N), where M is the number of special commands (1 <= M <= 100), N is the number of skills (1 <= N <= 100).\nAll special commands and skills are numbered from 1.\n\nThen M set of conditions follows.\nThe first line of a condition set contains a single integer K_i (0 <= K_i <= 100), where K_i is the number of conditions to learn the i-th command.\nThe following K_i lines describe the conditions on the skill values.\ns_{i, j} is an integer to identify the skill required to learn the command.\ncond_{i, j} is given by string \"<=\" or \">=\".\nIf cond_{i, j} is \"<=\", the skill point of s_{i, j}-th skill must be less than or equal to the threshold value t_{i, j} (0 <= t_{i, j} <= 100).\nOtherwise, i. e. if cond_{i, j}\nis \">=\", the skill point of s_{i, j} must be greater than or equal to t_{i, j}.", "output": "Output \"Yes\" (without quotes) if a character can learn all the special commands in given conditions, otherwise \"No\" (without quotes).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n2\n1 >= 3\n2 <= 5\n2\n1 >= 4\n2 >= 3\n output: Yes", "input: 2 2\n2\n1 >= 5\n2 >= 5\n2\n1 <= 4\n2 <= 3\n output: Yes", "input: 2 2\n2\n1 >= 3\n2 <= 3\n2\n1 <= 2\n2 >= 5\n output: No", "input: 1 2\n2\n1 <= 10\n1 >= 15\n output: No", "input: 5 5\n3\n2 <= 1\n3 <= 1\n4 <= 1\n4\n2 >= 2\n3 <= 1\n4 <= 1\n5 <= 1\n3\n3 >= 2\n4 <= 1\n5 <= 1\n2\n4 >= 2\n5 <= 1\n1\n5 >= 2\n output: Yes"], "Pid": "p01667", "ProblemText": "Task Description: You are very absorbed in a famous role-playing game (RPG), \"Everlasting -Zero-\". An RPG is a game in which players assume the roles of characters in a fictional setting. While you play the game, you can forget your \"real life\" and become a different person.\n\nTo play the game more effectively, you have to understand two notions, a skill point and a special command. A character can boost up by accumulating his experience points. When a character boosts up, he can gain skill points.\n\nYou can arbitrarily allocate the skill points to the character's skills to enhance the character's abilities. If skill points of each skill meets some conditions simultaneously (e. g. , the skill points of some skills are are greater than or equal to the threshold values and those of others are less than or equal to the values) , the character learns a special command. One important thing is that once a character learned the command, he will never forget it. And once skill points are allocated to the character, you cannot revoke the allocation. In addition, the initial values of each skill is 0.\n\nThe system is so complicated that it is difficult for ordinary players to know whether a character can learn all the special commands or not. Luckily, in the \"real\" world, you are a great programmer, so you decided to write a program to tell whether a character can learn all the special commnads or not. If it turns out to be feasible, you will be more absorbed in the game and become happy.\nTask Input: The input is formatted as follows.\n\nM N\nK_1\ns_{1,1} cond_{1,1} t_{1,1}\ns_{1,2} cond_{1,2} t_{1,2}\n. . .\ns_{1, K_1} cond_{1, K_1} t_{1, K_1}\nK_2\n. . .\nK_M\ns_{M, 1} cond_{M, 1} t_{M, 1}\ns_{M, 2} cond_{M, 2} t_{M, 2}\n. . .\ns_{M, K_M} cond_{M, K_M} t_{M, K_M}\n\nThe first line of the input contains two integers (M, N), where M is the number of special commands (1 <= M <= 100), N is the number of skills (1 <= N <= 100).\nAll special commands and skills are numbered from 1.\n\nThen M set of conditions follows.\nThe first line of a condition set contains a single integer K_i (0 <= K_i <= 100), where K_i is the number of conditions to learn the i-th command.\nThe following K_i lines describe the conditions on the skill values.\ns_{i, j} is an integer to identify the skill required to learn the command.\ncond_{i, j} is given by string \"<=\" or \">=\".\nIf cond_{i, j} is \"<=\", the skill point of s_{i, j}-th skill must be less than or equal to the threshold value t_{i, j} (0 <= t_{i, j} <= 100).\nOtherwise, i. e. if cond_{i, j}\nis \">=\", the skill point of s_{i, j} must be greater than or equal to t_{i, j}.\nTask Output: Output \"Yes\" (without quotes) if a character can learn all the special commands in given conditions, otherwise \"No\" (without quotes).\nTask Samples: input: 2 2\n2\n1 >= 3\n2 <= 5\n2\n1 >= 4\n2 >= 3\n output: Yes\ninput: 2 2\n2\n1 >= 5\n2 >= 5\n2\n1 <= 4\n2 <= 3\n output: Yes\ninput: 2 2\n2\n1 >= 3\n2 <= 3\n2\n1 <= 2\n2 >= 5\n output: No\ninput: 1 2\n2\n1 <= 10\n1 >= 15\n output: No\ninput: 5 5\n3\n2 <= 1\n3 <= 1\n4 <= 1\n4\n2 >= 2\n3 <= 1\n4 <= 1\n5 <= 1\n3\n3 >= 2\n4 <= 1\n5 <= 1\n2\n4 >= 2\n5 <= 1\n1\n5 >= 2\n output: Yes\n\n" }, { "title": "B - Integer in Integer", "content": "Given an integer interval \\[A, B\\] and an integer C, your job is to calculate the number of occurrences of C as string in the interval.\n\nFor example, 33 appears in 333 twice, and appears in 334 once. Thus the number of occurrences of 33 in \\[333,334\\] is 3.", "constraint": "", "input": "The test case is given by a line with the three integers, A, B, C (0 <= A <= B <= 10^{10000}, 0 <= C <= 10^{500}).", "output": "Print the number of occurrences of C mod 1000000007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 2\n output: 1", "input: 333 334 33\n output: 3", "input: 0 10 0\n output: 2"], "Pid": "p01668", "ProblemText": "Task Description: Given an integer interval \\[A, B\\] and an integer C, your job is to calculate the number of occurrences of C as string in the interval.\n\nFor example, 33 appears in 333 twice, and appears in 334 once. Thus the number of occurrences of 33 in \\[333,334\\] is 3.\nTask Input: The test case is given by a line with the three integers, A, B, C (0 <= A <= B <= 10^{10000}, 0 <= C <= 10^{500}).\nTask Output: Print the number of occurrences of C mod 1000000007.\nTask Samples: input: 1 3 2\n output: 1\ninput: 333 334 33\n output: 3\ninput: 0 10 0\n output: 2\n\n" }, { "title": "C - Iyasugigappa", "content": "Three animals Frog, Kappa (Water Imp) and Weasel are playing a card game.\n\nIn this game, players make use of three kinds of items: a guillotine, twelve noble cards and six action cards. Some integer value is written on the face of each noble card and each action card. Before stating the game, players put twelve noble cards in a line on the table and put the guillotine on the right of the noble cards. And then each player are dealt two action cards. Here, all the noble cards and action cards are opened, so the players share all the information in this game.\n\nNext, the game begins. Each player takes turns in turn. Frog takes the first turn, Kappa takes the second turn, Weasel takes the third turn, and Frog takes the fourth turn, etc. Each turn consists of two phases: action phase and execution phase in this order.\n\nIn action phase, if a player has action cards, he may use one of them. When he uses an action card with value on the face y, y-th (1-based) noble card from the front of the guillotine on the table is moved to in front of the guillotine, if there are at least y noble cards on the table. If there are less than y cards, nothing happens. After the player uses the action card, he must discard it from his hand.\n\nIn execution phase, a player just remove a noble card in front of the guillotine. And then the player scores x points, where x is the value of the removed noble card.\n\nThe game ends when all the noble cards are removed.\n\nEach player follows the following strategy:\nEach player assume that other players would follow a strategy such that their final score is maximized.\n\nActually, Frog and Weasel follows such strategy.\n\nHowever, Kappa does not. Kappa plays so that Frog's final score is minimized.\n\nKappa knows that Frog and Weasel would play under ``wrong'' assumption: They think that Kappa would maximize his score.\n\nAs a tie-breaker of multiple optimum choises for each strategy, assume that players prefer to keep as many action cards as possible at the end of the turn.\n\nIf there are still multiple optimum choises, players prefer to maximuze the total value of remaining action cards.\n\nYour task in this problem is to calculate the final score of each player.", "constraint": "", "input": "The input is formatted as follows.\n\nx_{12} x_{11} x_{10} x_9 x_8 x_7 x_6 x_5 x_4 x_3 x_2 x_1\ny_1 y_2\ny_3 y_4\ny_5 y_6\n\nThe first line of the input contains twelve integers x_{12}, x_{11}, …, x_{1} (-2 <= x_i <= 5).\nx_i is integer written on i-th noble card from the guillotine.\nFollowing three lines contains six integers y_1, …, y_6 (1 <= y_j <= 4).\ny_1, y_2 are values on Frog's action cards, y_3, y_4 are those on Kappa's action cards, and y_5, y_6 are those on Weasel's action cards.", "output": "Print three space-separated integers: the final scores of Frog, Kappa and Weasel.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 1 3 2 1 3 2 1 3 2 1\n1 1\n1 1\n1 1\n output: 4 8 12", "input: 4 4 4 3 3 3 2 2 2 1 1 1\n1 2\n2 3\n3 4\n output: 8 10 12", "input: 0 0 0 0 0 0 0 -2 0 -2 5 0\n1 1\n4 1\n1 1\n output: -2 -2 5"], "Pid": "p01669", "ProblemText": "Task Description: Three animals Frog, Kappa (Water Imp) and Weasel are playing a card game.\n\nIn this game, players make use of three kinds of items: a guillotine, twelve noble cards and six action cards. Some integer value is written on the face of each noble card and each action card. Before stating the game, players put twelve noble cards in a line on the table and put the guillotine on the right of the noble cards. And then each player are dealt two action cards. Here, all the noble cards and action cards are opened, so the players share all the information in this game.\n\nNext, the game begins. Each player takes turns in turn. Frog takes the first turn, Kappa takes the second turn, Weasel takes the third turn, and Frog takes the fourth turn, etc. Each turn consists of two phases: action phase and execution phase in this order.\n\nIn action phase, if a player has action cards, he may use one of them. When he uses an action card with value on the face y, y-th (1-based) noble card from the front of the guillotine on the table is moved to in front of the guillotine, if there are at least y noble cards on the table. If there are less than y cards, nothing happens. After the player uses the action card, he must discard it from his hand.\n\nIn execution phase, a player just remove a noble card in front of the guillotine. And then the player scores x points, where x is the value of the removed noble card.\n\nThe game ends when all the noble cards are removed.\n\nEach player follows the following strategy:\nEach player assume that other players would follow a strategy such that their final score is maximized.\n\nActually, Frog and Weasel follows such strategy.\n\nHowever, Kappa does not. Kappa plays so that Frog's final score is minimized.\n\nKappa knows that Frog and Weasel would play under ``wrong'' assumption: They think that Kappa would maximize his score.\n\nAs a tie-breaker of multiple optimum choises for each strategy, assume that players prefer to keep as many action cards as possible at the end of the turn.\n\nIf there are still multiple optimum choises, players prefer to maximuze the total value of remaining action cards.\n\nYour task in this problem is to calculate the final score of each player.\nTask Input: The input is formatted as follows.\n\nx_{12} x_{11} x_{10} x_9 x_8 x_7 x_6 x_5 x_4 x_3 x_2 x_1\ny_1 y_2\ny_3 y_4\ny_5 y_6\n\nThe first line of the input contains twelve integers x_{12}, x_{11}, …, x_{1} (-2 <= x_i <= 5).\nx_i is integer written on i-th noble card from the guillotine.\nFollowing three lines contains six integers y_1, …, y_6 (1 <= y_j <= 4).\ny_1, y_2 are values on Frog's action cards, y_3, y_4 are those on Kappa's action cards, and y_5, y_6 are those on Weasel's action cards.\nTask Output: Print three space-separated integers: the final scores of Frog, Kappa and Weasel.\nTask Samples: input: 3 2 1 3 2 1 3 2 1 3 2 1\n1 1\n1 1\n1 1\n output: 4 8 12\ninput: 4 4 4 3 3 3 2 2 2 1 1 1\n1 2\n2 3\n3 4\n output: 8 10 12\ninput: 0 0 0 0 0 0 0 -2 0 -2 5 0\n1 1\n4 1\n1 1\n output: -2 -2 5\n\n" }, { "title": "D - Medical Inspection", "content": "The government has declared a state of emergency due to the MOFU syndrome epidemic in your country. Persons in the country suffer from MOFU syndrome and cannot get out of bed in the morning. You are a programmer working for the Department of Health. You have to take prompt measures.\n\nThe country consists of n islands numbered from 1 to n and there are ocean liners between some pair of islands.\nThe Department of Health decided to establish the quarantine stations in some islands and restrict an infected person's moves to prevent the expansion of the epidemic.\nTo carry out this plan, there must not be any liner such that there is no quarantine station in both the source and the destination of the liner.\nThe problem is the department can build at most K quarantine stations due to the lack of budget.\n\nYour task is to calculate whether this objective is possible or not.\nAnd if it is possible, you must calculate the minimum required number of quarantine stations.", "constraint": "", "input": "The test case starts with a line containing three integers N (2 <= N <= 3{, }000), M (1 <= M <= 30{, }000) and K (1 <= K <= 32).\nEach line in the next M lines contains two integers a_i (1 <= a_i <= N) and b_i (1 <= b_i <= N). This represents i-th ocean liner connects island a_i and b_i.\nYou may assume a_i \\neq b_i for all i, and there are at most one ocean liner between all the pairs of islands.", "output": "If there is no way to build quarantine stations that satisfies the objective, print \"Impossible\" (without quotes). Otherwise, print the minimum required number of quarantine stations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 2\n1 2\n2 3\n3 1\n output: 2", "input: 3 3 1\n1 2\n2 3\n3 1\n output: Impossible", "input: 7 6 5\n1 3\n2 4\n3 5\n4 6\n5 7\n6 2\n output: 4", "input: 10 10 10\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5\n output: 4"], "Pid": "p01670", "ProblemText": "Task Description: The government has declared a state of emergency due to the MOFU syndrome epidemic in your country. Persons in the country suffer from MOFU syndrome and cannot get out of bed in the morning. You are a programmer working for the Department of Health. You have to take prompt measures.\n\nThe country consists of n islands numbered from 1 to n and there are ocean liners between some pair of islands.\nThe Department of Health decided to establish the quarantine stations in some islands and restrict an infected person's moves to prevent the expansion of the epidemic.\nTo carry out this plan, there must not be any liner such that there is no quarantine station in both the source and the destination of the liner.\nThe problem is the department can build at most K quarantine stations due to the lack of budget.\n\nYour task is to calculate whether this objective is possible or not.\nAnd if it is possible, you must calculate the minimum required number of quarantine stations.\nTask Input: The test case starts with a line containing three integers N (2 <= N <= 3{, }000), M (1 <= M <= 30{, }000) and K (1 <= K <= 32).\nEach line in the next M lines contains two integers a_i (1 <= a_i <= N) and b_i (1 <= b_i <= N). This represents i-th ocean liner connects island a_i and b_i.\nYou may assume a_i \\neq b_i for all i, and there are at most one ocean liner between all the pairs of islands.\nTask Output: If there is no way to build quarantine stations that satisfies the objective, print \"Impossible\" (without quotes). Otherwise, print the minimum required number of quarantine stations.\nTask Samples: input: 3 3 2\n1 2\n2 3\n3 1\n output: 2\ninput: 3 3 1\n1 2\n2 3\n3 1\n output: Impossible\ninput: 7 6 5\n1 3\n2 4\n3 5\n4 6\n5 7\n6 2\n output: 4\ninput: 10 10 10\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5\n output: 4\n\n" }, { "title": "E - Minimum Spanning Tree", "content": "You are given an undirected weighted graph G with n nodes and m edges.\nEach edge is numbered from 1 to m.\n\nLet G_i be an graph that is made by erasing i-th edge from G. Your task is to compute the cost of minimum spanning tree in G_i for each i.", "constraint": "", "input": "The dataset is formatted as follows.\n\nn m\na_1 b_1 w_1\n. . .\na_m b_m w_m\n\nThe first line of the input contains two integers n (2 <= n <= 100{, }000) and m (1 <= m <= 200{, }000).\nn is the number of nodes and m is the number of edges in the graph.\nThen m lines follow, each of which contains a_i (1 <= a_i <= n), b_i (1 <= b_i <= n) and w_i (0 <= w_i <= 1{, }000{, }000).\nThis means that there is an edge between node a_i and node b_i and its cost is w_i.\nIt is guaranteed that the given graph is simple: That is, for any pair of nodes, there is at most one edge that connects them, and a_i \\neq b_i for all i.", "output": "Print the cost of minimum spanning tree in G_i for each i, in m line. If there is no spanning trees in G_i, print \"-1\" (quotes for clarity) instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n1 2 2\n1 3 6\n1 4 3\n2 3 1\n2 4 4\n3 4 5\n output: 8\n6\n7\n10\n6\n6", "input: 4 4\n1 2 1\n1 3 10\n2 3 100\n3 4 1000\n output: 1110\n1101\n1011\n-1", "input: 7 10\n1 2 1\n1 3 2\n2 3 3\n2 4 4\n2 5 5\n3 6 6\n3 7 7\n4 5 8\n5 6 9\n6 7 10\n output: 27\n26\n25\n29\n28\n28\n28\n25\n25\n25", "input: 3 1\n1 3 999\n output: -1"], "Pid": "p01671", "ProblemText": "Task Description: You are given an undirected weighted graph G with n nodes and m edges.\nEach edge is numbered from 1 to m.\n\nLet G_i be an graph that is made by erasing i-th edge from G. Your task is to compute the cost of minimum spanning tree in G_i for each i.\nTask Input: The dataset is formatted as follows.\n\nn m\na_1 b_1 w_1\n. . .\na_m b_m w_m\n\nThe first line of the input contains two integers n (2 <= n <= 100{, }000) and m (1 <= m <= 200{, }000).\nn is the number of nodes and m is the number of edges in the graph.\nThen m lines follow, each of which contains a_i (1 <= a_i <= n), b_i (1 <= b_i <= n) and w_i (0 <= w_i <= 1{, }000{, }000).\nThis means that there is an edge between node a_i and node b_i and its cost is w_i.\nIt is guaranteed that the given graph is simple: That is, for any pair of nodes, there is at most one edge that connects them, and a_i \\neq b_i for all i.\nTask Output: Print the cost of minimum spanning tree in G_i for each i, in m line. If there is no spanning trees in G_i, print \"-1\" (quotes for clarity) instead.\nTask Samples: input: 4 6\n1 2 2\n1 3 6\n1 4 3\n2 3 1\n2 4 4\n3 4 5\n output: 8\n6\n7\n10\n6\n6\ninput: 4 4\n1 2 1\n1 3 10\n2 3 100\n3 4 1000\n output: 1110\n1101\n1011\n-1\ninput: 7 10\n1 2 1\n1 3 2\n2 3 3\n2 4 4\n2 5 5\n3 6 6\n3 7 7\n4 5 8\n5 6 9\n6 7 10\n output: 27\n26\n25\n29\n28\n28\n28\n25\n25\n25\ninput: 3 1\n1 3 999\n output: -1\n\n" }, { "title": "F - Point Distance", "content": "You work for invention center as a part time programmer. This center researches movement of protein molecules. It needs how molecules make clusters, so it will calculate distance of all pair molecules and will make a histogram.\nMolecules ' positions are given by a N x N grid map.\nValue C_{xy} of cell (x, y) in a grid map means that C_{xy} molecules are in the position (x, y).\n\nYou are given a grid map, please calculate histogram of all pair molecules.", "constraint": "", "input": "Input is formatted as follows.\n\nN\nC_{11} C_{12} . . . C_{1N}\nC_{21} C_{22} . . . C_{2N}\n. . .\nC_{N1} C_{N2} . . . C_{NN}\n\nFirst line contains the grid map size N (1 <= N <= 1024).\nEach next N line contains N numbers.\nEach numbers C_{xy} (0 <= C_{xy} <= 9) means the number of molecule in position (x, y).\nThere are at least 2 molecules.", "output": "Output is formatted as follows.\n\nD_{ave}\nd_{1} c_{1}\nd_{2} c_{2}\n. . .\nd_{m} c_{m}\n\nPrint D_{ave} which an average distance of all pair molecules on first line.\nNext, print histogram of all pair distance.\nEach line contains a distance d_i and the number of pair molecules c_i(0 < c_i).\nThe distance d_i should be calculated by squared Euclidean distance and sorted as increasing order.\nIf the number of different distance is more than 10,000, please show the first 10,000 lines.\nThe answer may be printed with an arbitrary number of decimal digits, but may not contain an absolute or relative error greater than or equal to 10^{-8}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 0\n0 1\n output: 1.4142135624\n2 1", "input: 3\n1 1 1\n1 1 1\n1 1 1\n output: 1.6349751825\n1 12\n2 8\n4 6\n5 8\n8 2", "input: 5\n0 1 2 3 4\n5 6 7 8 9\n1 2 3 2 1\n0 0 0 0 0\n0 0 0 0 1\n output: 1.8589994382\n0 125\n1 379\n2 232\n4 186\n5 200\n8 27\n9 111\n10 98\n13 21\n16 50\n17 37\n18 6\n20 7\n25 6"], "Pid": "p01672", "ProblemText": "Task Description: You work for invention center as a part time programmer. This center researches movement of protein molecules. It needs how molecules make clusters, so it will calculate distance of all pair molecules and will make a histogram.\nMolecules ' positions are given by a N x N grid map.\nValue C_{xy} of cell (x, y) in a grid map means that C_{xy} molecules are in the position (x, y).\n\nYou are given a grid map, please calculate histogram of all pair molecules.\nTask Input: Input is formatted as follows.\n\nN\nC_{11} C_{12} . . . C_{1N}\nC_{21} C_{22} . . . C_{2N}\n. . .\nC_{N1} C_{N2} . . . C_{NN}\n\nFirst line contains the grid map size N (1 <= N <= 1024).\nEach next N line contains N numbers.\nEach numbers C_{xy} (0 <= C_{xy} <= 9) means the number of molecule in position (x, y).\nThere are at least 2 molecules.\nTask Output: Output is formatted as follows.\n\nD_{ave}\nd_{1} c_{1}\nd_{2} c_{2}\n. . .\nd_{m} c_{m}\n\nPrint D_{ave} which an average distance of all pair molecules on first line.\nNext, print histogram of all pair distance.\nEach line contains a distance d_i and the number of pair molecules c_i(0 < c_i).\nThe distance d_i should be calculated by squared Euclidean distance and sorted as increasing order.\nIf the number of different distance is more than 10,000, please show the first 10,000 lines.\nThe answer may be printed with an arbitrary number of decimal digits, but may not contain an absolute or relative error greater than or equal to 10^{-8}.\nTask Samples: input: 2\n1 0\n0 1\n output: 1.4142135624\n2 1\ninput: 3\n1 1 1\n1 1 1\n1 1 1\n output: 1.6349751825\n1 12\n2 8\n4 6\n5 8\n8 2\ninput: 5\n0 1 2 3 4\n5 6 7 8 9\n1 2 3 2 1\n0 0 0 0 0\n0 0 0 0 1\n output: 1.8589994382\n0 125\n1 379\n2 232\n4 186\n5 200\n8 27\n9 111\n10 98\n13 21\n16 50\n17 37\n18 6\n20 7\n25 6\n\n" }, { "title": "G - Revenge of Minimum Cost Flow", "content": "Flora is a freelance carrier pigeon.\nSince she is an excellent pigeon, there are too much task requests to her.\nIt is impossible to do all tasks, so she decided to outsource some tasks to Industrial Carrier Pigeon Company.\n\nThere are N cities numbered from 0 to N-1.\nThe task she wants to outsource is carrying f freight units from city s to city t.\nThere are M pigeons in the company.\nThe i-th pigeon carries freight from city s_i to t_i, and carrying cost of u units is u a_i if u is smaller than or equals to d_i, otherwise d_i a_i + (u-d_i)b_i.\nNote that i-th pigeon cannot carry from city t_i to s_i.\nEach pigeon can carry any amount of freights.\nIf the pigeon carried freight multiple times, the cost is calculated from total amount of freight units he/she carried.\n\nFlora wants to minimize the total costs.\nPlease calculate minimum cost for her.", "constraint": "", "input": "The test case starts with a line containing five integers N (2 <= N <= 100), M (1 <= M <= 1{, }000), s (0 <= s <= N-1), t (0 <= t <= N-1) and f (1 <= f <= 200).\nYou may assume s \\neq t.\nEach of the next M lines contains five integers s_i (0 <= s_i <= N-1), t_i (0 <= t_i <= N-1), a_i (0 <= a_i <= 1{, }000), b_i (0 <= b_i <= 1{, }000) and d_i (1 <= d_i <= 200).\nEach denotes i-th pigeon's information.\nYou may assume at most one pair of a_i and b_i satisfies a_i < b_i, all others satisfies a_i > b_i.", "output": "Print the minimum cost to carry f freight units from city s to city t in a line.\nIf it is impossible to carry, print \"Impossible\" (quotes for clarity).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 0 1 5\n0 1 3 0 3\n0 1 2 1 6\n output: 9", "input: 4 4 0 3 5\n0 1 3 0 3\n1 3 3 0 3\n0 2 2 1 6\n2 3 2 1 6\n output: 18", "input: 2 1 0 1 1\n1 0 1 0 1\n output: Impossible", "input: 2 2 0 1 2\n0 1 5 1 2\n0 1 6 3 1\n output: 9", "input: 3 3 0 2 4\n0 2 3 4 2\n0 1 4 1 3\n1 2 3 1 1\n output: 14"], "Pid": "p01673", "ProblemText": "Task Description: Flora is a freelance carrier pigeon.\nSince she is an excellent pigeon, there are too much task requests to her.\nIt is impossible to do all tasks, so she decided to outsource some tasks to Industrial Carrier Pigeon Company.\n\nThere are N cities numbered from 0 to N-1.\nThe task she wants to outsource is carrying f freight units from city s to city t.\nThere are M pigeons in the company.\nThe i-th pigeon carries freight from city s_i to t_i, and carrying cost of u units is u a_i if u is smaller than or equals to d_i, otherwise d_i a_i + (u-d_i)b_i.\nNote that i-th pigeon cannot carry from city t_i to s_i.\nEach pigeon can carry any amount of freights.\nIf the pigeon carried freight multiple times, the cost is calculated from total amount of freight units he/she carried.\n\nFlora wants to minimize the total costs.\nPlease calculate minimum cost for her.\nTask Input: The test case starts with a line containing five integers N (2 <= N <= 100), M (1 <= M <= 1{, }000), s (0 <= s <= N-1), t (0 <= t <= N-1) and f (1 <= f <= 200).\nYou may assume s \\neq t.\nEach of the next M lines contains five integers s_i (0 <= s_i <= N-1), t_i (0 <= t_i <= N-1), a_i (0 <= a_i <= 1{, }000), b_i (0 <= b_i <= 1{, }000) and d_i (1 <= d_i <= 200).\nEach denotes i-th pigeon's information.\nYou may assume at most one pair of a_i and b_i satisfies a_i < b_i, all others satisfies a_i > b_i.\nTask Output: Print the minimum cost to carry f freight units from city s to city t in a line.\nIf it is impossible to carry, print \"Impossible\" (quotes for clarity).\nTask Samples: input: 2 2 0 1 5\n0 1 3 0 3\n0 1 2 1 6\n output: 9\ninput: 4 4 0 3 5\n0 1 3 0 3\n1 3 3 0 3\n0 2 2 1 6\n2 3 2 1 6\n output: 18\ninput: 2 1 0 1 1\n1 0 1 0 1\n output: Impossible\ninput: 2 2 0 1 2\n0 1 5 1 2\n0 1 6 3 1\n output: 9\ninput: 3 3 0 2 4\n0 2 3 4 2\n0 1 4 1 3\n1 2 3 1 1\n output: 14\n\n" }, { "title": "H - Rings", "content": "There are two circles with radius 1 in 3D space. Please check two circles are connected as chained rings.", "constraint": "", "input": "The input is formatted as follows.\n\n{c_x}_1 {c_y}_1 {c_z}_1\n{v_x}_{1,1} {v_y}_{1,1} {v_z}_{1,1} {v_x}_{1,2} {v_y}_{1,2} {v_z}_{1,2}\n{c_x}_2 {c_y}_2 {c_z}_2\n{v_x}_{2,1} {v_y}_{2,1} {v_z}_{2,1} {v_x}_{2,2} {v_y}_{2,2} {v_z}_{2,2}\n\nFirst line contains three real numbers(-3 <= {c_x}_i, {c_y}_i, {c_z}_i <= 3).\nIt shows a circle's center position.\nSecond line contains six real numbers(-1 <= {v_x}_{i, j}, {v_y}_{i, j}, {v_z}_{i, j} <= 1).\nA unit vector ({v_x}_{1,1}, {v_y}_{1,1}, {v_z}_{1,1}) is directed to the circumference of the circle from center of the circle.\nThe other unit vector ({v_x}_{1,2}, {v_y}_{1,2}, {v_z}_{1,2}) is also directed to the circumference of the circle from center of the circle.\nThese two vectors are orthogonalized.\nThird and fourth lines show the other circle information in the same way of first and second lines.\nThere are no cases that two circles touch.", "output": "If two circles are connected as chained rings, you should print \"YES\". The other case, you should print \"NO\". (quotes for clarity)", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0.0 0.0 0.0\n1.0 0.0 0.0 0.0 1.0 0.0\n1.0 0.0 0.5\n1.0 0.0 0.0 0.0 0.0 1.0\n output: YES", "input: 0.0 0.0 0.0\n1.0 0.0 0.0 0.0 1.0 0.0\n0.0 3.0 0.0\n0.0 1.0 0.0 -1.0 0.0 0.0\n output: NO", "input: 1.2 2.3 -0.5\n1.0 0.0 0.0 0.0 1.0 0.0\n1.1 2.3 -0.4\n1.0 0.0 0.0 0.0 0.70710678 0.70710678\n output: YES", "input: 1.2 2.3 -0.5\n1.0 0.0 0.0 0.0 1.0 0.0\n1.1 2.7 -0.1\n1.0 0.0 0.0 0.0 0.70710678 0.70710678\n output: NO"], "Pid": "p01674", "ProblemText": "Task Description: There are two circles with radius 1 in 3D space. Please check two circles are connected as chained rings.\nTask Input: The input is formatted as follows.\n\n{c_x}_1 {c_y}_1 {c_z}_1\n{v_x}_{1,1} {v_y}_{1,1} {v_z}_{1,1} {v_x}_{1,2} {v_y}_{1,2} {v_z}_{1,2}\n{c_x}_2 {c_y}_2 {c_z}_2\n{v_x}_{2,1} {v_y}_{2,1} {v_z}_{2,1} {v_x}_{2,2} {v_y}_{2,2} {v_z}_{2,2}\n\nFirst line contains three real numbers(-3 <= {c_x}_i, {c_y}_i, {c_z}_i <= 3).\nIt shows a circle's center position.\nSecond line contains six real numbers(-1 <= {v_x}_{i, j}, {v_y}_{i, j}, {v_z}_{i, j} <= 1).\nA unit vector ({v_x}_{1,1}, {v_y}_{1,1}, {v_z}_{1,1}) is directed to the circumference of the circle from center of the circle.\nThe other unit vector ({v_x}_{1,2}, {v_y}_{1,2}, {v_z}_{1,2}) is also directed to the circumference of the circle from center of the circle.\nThese two vectors are orthogonalized.\nThird and fourth lines show the other circle information in the same way of first and second lines.\nThere are no cases that two circles touch.\nTask Output: If two circles are connected as chained rings, you should print \"YES\". The other case, you should print \"NO\". (quotes for clarity)\nTask Samples: input: 0.0 0.0 0.0\n1.0 0.0 0.0 0.0 1.0 0.0\n1.0 0.0 0.5\n1.0 0.0 0.0 0.0 0.0 1.0\n output: YES\ninput: 0.0 0.0 0.0\n1.0 0.0 0.0 0.0 1.0 0.0\n0.0 3.0 0.0\n0.0 1.0 0.0 -1.0 0.0 0.0\n output: NO\ninput: 1.2 2.3 -0.5\n1.0 0.0 0.0 0.0 1.0 0.0\n1.1 2.3 -0.4\n1.0 0.0 0.0 0.0 0.70710678 0.70710678\n output: YES\ninput: 1.2 2.3 -0.5\n1.0 0.0 0.0 0.0 1.0 0.0\n1.1 2.7 -0.1\n1.0 0.0 0.0 0.0 0.70710678 0.70710678\n output: NO\n\n" }, { "title": "I - The J-th Number", "content": "You are given N empty arrays, t_1, . . . , t_n. At first, you execute M queries as follows.\n\nadd a value v to array t_i (a <= i <= b)\nNext, you process Q following output queries.\n\noutput the j-th number of the sequence sorted all values in t_i (x <= i <= y)", "constraint": "", "input": "The dataset is formatted as follows.\n\nN M Q\na_1 b_1 v_1\n. . .\na_M b_M v_M\nx_1 y_1 j_1\n. . .\nx_Q y_Q j_Q\n\nThe first line contains three integers N (1 <= N <= 10^9), M (1 <= M <= 10^5) and Q (1 <= Q <= 10^5). Each of the following M lines consists of three integers a_i, b_i and v_i (1 <= a_i <= b_i <= N, 1 <= v_i <= 10^9). Finally the following Q lines give the list of output queries, each of these lines consists of three integers x_i, y_i and j_i (1 <= x_i <= y_i <= N, 1 <= j_i <= Σ_{x_i <= k <= y_i} |t_k|).", "output": "For each output query, print in a line the j-th number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 1\n1 5 1\n1 1 3\n4 5 1\n3 4 2\n1 3 4\n output: 2\nAfter the M\n-th query is executed, each t_i\n is as follows:\n[1,3], [1], [1,2], [1,1,2], [1,1]\nThe sequence sorted values in t_1\n, t_2\n and t_3\n is [1,1,1,2,3]. In the sequence, the 4-th number is 2.", "input: 10 4 4\n1 4 11\n2 3 22\n6 9 33\n8 9 44\n1 1 1\n4 5 1\n4 6 2\n1 10 12\n output: 11\n11\n33\n44"], "Pid": "p01675", "ProblemText": "Task Description: You are given N empty arrays, t_1, . . . , t_n. At first, you execute M queries as follows.\n\nadd a value v to array t_i (a <= i <= b)\nNext, you process Q following output queries.\n\noutput the j-th number of the sequence sorted all values in t_i (x <= i <= y)\nTask Input: The dataset is formatted as follows.\n\nN M Q\na_1 b_1 v_1\n. . .\na_M b_M v_M\nx_1 y_1 j_1\n. . .\nx_Q y_Q j_Q\n\nThe first line contains three integers N (1 <= N <= 10^9), M (1 <= M <= 10^5) and Q (1 <= Q <= 10^5). Each of the following M lines consists of three integers a_i, b_i and v_i (1 <= a_i <= b_i <= N, 1 <= v_i <= 10^9). Finally the following Q lines give the list of output queries, each of these lines consists of three integers x_i, y_i and j_i (1 <= x_i <= y_i <= N, 1 <= j_i <= Σ_{x_i <= k <= y_i} |t_k|).\nTask Output: For each output query, print in a line the j-th number.\nTask Samples: input: 5 4 1\n1 5 1\n1 1 3\n4 5 1\n3 4 2\n1 3 4\n output: 2\nAfter the M\n-th query is executed, each t_i\n is as follows:\n[1,3], [1], [1,2], [1,1,2], [1,1]\nThe sequence sorted values in t_1\n, t_2\n and t_3\n is [1,1,1,2,3]. In the sequence, the 4-th number is 2.\ninput: 10 4 4\n1 4 11\n2 3 22\n6 9 33\n8 9 44\n1 1 1\n4 5 1\n4 6 2\n1 10 12\n output: 11\n11\n33\n44\n\n" }, { "title": "J - Tree Reconstruction", "content": "You have a directed graph.\nSome non-negative value is assigned on each edge of the graph.\nYou know that the value of the graph satisfies the flow conservation law\nThat is, for every node v, the sum of values on edges incoming to v equals to\nthe sum of values of edges outgoing from v.\nFor example, the following directed graph satisfies the flow conservation law.\n\nSuppose that you choose a subset of edges in the graph, denoted by E',\nand then you erase all the values on edges other than E'.\nNow you want to recover the erased values by seeing only remaining information.\nDue to the flow conservation law, it may be possible to recover all the erased values.\nYour task is to calculate the smallest possible size for such E'.\n\nFor example, the smallest subset E' for the above graph will be green edges in the following figure.\nBy the flow conservation law, we can recover values on gray edges.", "constraint": "", "input": "The input consists of multiple test cases.\nThe format of each test case is as follows.\n\nN M\ns_1 t_1\n. . .\ns_M t_M\n\nThe first line contains two integers N (1 <= N <= 500) and M (0 <= M <= 3,000) that indicate the number of nodes and edges, respectively.\nEach of the following M lines consists of two integers s_i and t_i (1 <= s_i, t_i <= N). This means that there is an edge from s_i to t_i in the graph.\n\nYou may assume that the given graph is simple:\n\nThere are no self-loops: s_i \\neq t_i.\n\nThere are no multi-edges: for all i < j, \\{s_i, t_i\\} \\neq \\{s_j, t_j\\}.\nAlso, it is guaranteed that each component of the given graph is strongly connected.\nThat is, for every pair of nodes v and u, if there exist a path from v to u, then there exists a path from u to v.\n\nNote that you are NOT given information of values on edges because it does not effect the answer.", "output": "For each test case, print an answer in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 9 13\n1 2\n1 3\n2 9\n3 4\n3 5\n3 6\n4 9\n5 7\n6 7\n6 8\n7 9\n8 9\n9 1\n output: 5", "input: 7 9\n1 2\n1 3\n2 4\n3 4\n4 5\n4 6\n5 7\n6 7\n7 1\n output: 3", "input: 4 4\n1 2\n2 1\n3 4\n4 3\n output: 2"], "Pid": "p01676", "ProblemText": "Task Description: You have a directed graph.\nSome non-negative value is assigned on each edge of the graph.\nYou know that the value of the graph satisfies the flow conservation law\nThat is, for every node v, the sum of values on edges incoming to v equals to\nthe sum of values of edges outgoing from v.\nFor example, the following directed graph satisfies the flow conservation law.\n\nSuppose that you choose a subset of edges in the graph, denoted by E',\nand then you erase all the values on edges other than E'.\nNow you want to recover the erased values by seeing only remaining information.\nDue to the flow conservation law, it may be possible to recover all the erased values.\nYour task is to calculate the smallest possible size for such E'.\n\nFor example, the smallest subset E' for the above graph will be green edges in the following figure.\nBy the flow conservation law, we can recover values on gray edges.\nTask Input: The input consists of multiple test cases.\nThe format of each test case is as follows.\n\nN M\ns_1 t_1\n. . .\ns_M t_M\n\nThe first line contains two integers N (1 <= N <= 500) and M (0 <= M <= 3,000) that indicate the number of nodes and edges, respectively.\nEach of the following M lines consists of two integers s_i and t_i (1 <= s_i, t_i <= N). This means that there is an edge from s_i to t_i in the graph.\n\nYou may assume that the given graph is simple:\n\nThere are no self-loops: s_i \\neq t_i.\n\nThere are no multi-edges: for all i < j, \\{s_i, t_i\\} \\neq \\{s_j, t_j\\}.\nAlso, it is guaranteed that each component of the given graph is strongly connected.\nThat is, for every pair of nodes v and u, if there exist a path from v to u, then there exists a path from u to v.\n\nNote that you are NOT given information of values on edges because it does not effect the answer.\nTask Output: For each test case, print an answer in one line.\nTask Samples: input: 9 13\n1 2\n1 3\n2 9\n3 4\n3 5\n3 6\n4 9\n5 7\n6 7\n6 8\n7 9\n8 9\n9 1\n output: 5\ninput: 7 9\n1 2\n1 3\n2 4\n3 4\n4 5\n4 6\n5 7\n6 7\n7 1\n output: 3\ninput: 4 4\n1 2\n2 1\n3 4\n4 3\n output: 2\n\n" }, { "title": "Problem Statement", "content": "Nathan O. Davis is a student at the department of integrated systems.\nToday's agenda in the class is audio signal processing.\nNathan was given a lot of homework out.\nOne of the homework was to write a program to process an audio signal.\nHe copied the given audio signal to his USB memory and brought it back to his home.\nWhen he started his homework, he unfortunately dropped the USB memory to the floor.\nHe checked the contents of the USB memory and found that the audio signal data got broken.\nThere are several characteristics in the audio signal that he copied.\n The audio signal is a sequence of $N$ samples.\n\n Each sample in the audio signal is numbered from $1$ to $N$ and represented as an integer value.\n\n Each value of the odd-numbered sample(s) is strictly smaller than the value(s) of its neighboring sample(s).\n\n Each value of the even-numbered sample(s) is strictly larger than the value(s) of its neighboring sample(s).\n\nHe got into a panic and asked you for a help.\nYou tried to recover the audio signal from his USB memory but some samples of the audio signal are broken and could not be recovered.\nFortunately, you found from the metadata that all the broken samples have the same integer value.\nYour task is to write a program,\nwhich takes the broken audio signal extracted from his USB memory as its input, \nto detect whether the audio signal can be recovered uniquely.", "constraint": "", "input": "The input consists of multiple datasets.\nThe form of each dataset is described below.\n$N$$a_{1}$ $a_{2}$ . . . $a_{N}$The first line of each dataset consists of an integer, $N (2 <= N <= 1{, }000)$.\n$N$ denotes the number of samples in the given audio signal.\nThe second line of each dataset consists of $N$ values separated by spaces.\nThe $i$-th value, $a_{i}$, is either a character x or an integer between $-10^9$ and $10^9$, inclusive.\nIt represents the $i$-th sample of the broken audio signal.\nIf $a_{i}$ is a character x , it denotes that $i$-th sample in the audio signal is broken.\nOtherwise it denotes the value of the $i$-th sample.\nThe end of input is indicated by a single $0$.\nThis is not included in the datasets.\nYou may assume that the number of the datasets does not exceed $100$.", "output": "For each dataset, output the value of the broken samples in one line if the original audio signal can be recovered uniquely.\nIf there are multiple possible values, output ambiguous.\nIf there are no possible values, output none.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 x 2 4 x\n2\nx x\n2\n1 2\n2\n2 1\n2\n1000000000 x\n4\nx 2 1 x\n0\n output: 3\nnone\nambiguous\nnone\nambiguous\nnone"], "Pid": "p01677", "ProblemText": "Task Description: Nathan O. Davis is a student at the department of integrated systems.\nToday's agenda in the class is audio signal processing.\nNathan was given a lot of homework out.\nOne of the homework was to write a program to process an audio signal.\nHe copied the given audio signal to his USB memory and brought it back to his home.\nWhen he started his homework, he unfortunately dropped the USB memory to the floor.\nHe checked the contents of the USB memory and found that the audio signal data got broken.\nThere are several characteristics in the audio signal that he copied.\n The audio signal is a sequence of $N$ samples.\n\n Each sample in the audio signal is numbered from $1$ to $N$ and represented as an integer value.\n\n Each value of the odd-numbered sample(s) is strictly smaller than the value(s) of its neighboring sample(s).\n\n Each value of the even-numbered sample(s) is strictly larger than the value(s) of its neighboring sample(s).\n\nHe got into a panic and asked you for a help.\nYou tried to recover the audio signal from his USB memory but some samples of the audio signal are broken and could not be recovered.\nFortunately, you found from the metadata that all the broken samples have the same integer value.\nYour task is to write a program,\nwhich takes the broken audio signal extracted from his USB memory as its input, \nto detect whether the audio signal can be recovered uniquely.\nTask Input: The input consists of multiple datasets.\nThe form of each dataset is described below.\n$N$$a_{1}$ $a_{2}$ . . . $a_{N}$The first line of each dataset consists of an integer, $N (2 <= N <= 1{, }000)$.\n$N$ denotes the number of samples in the given audio signal.\nThe second line of each dataset consists of $N$ values separated by spaces.\nThe $i$-th value, $a_{i}$, is either a character x or an integer between $-10^9$ and $10^9$, inclusive.\nIt represents the $i$-th sample of the broken audio signal.\nIf $a_{i}$ is a character x , it denotes that $i$-th sample in the audio signal is broken.\nOtherwise it denotes the value of the $i$-th sample.\nThe end of input is indicated by a single $0$.\nThis is not included in the datasets.\nYou may assume that the number of the datasets does not exceed $100$.\nTask Output: For each dataset, output the value of the broken samples in one line if the original audio signal can be recovered uniquely.\nIf there are multiple possible values, output ambiguous.\nIf there are no possible values, output none.\nTask Samples: input: 5\n1 x 2 4 x\n2\nx x\n2\n1 2\n2\n2 1\n2\n1000000000 x\n4\nx 2 1 x\n0\n output: 3\nnone\nambiguous\nnone\nambiguous\nnone\n\n" }, { "title": "Problem Statement", "content": "The Animal School is a primary school for animal children.\nYou are a fox attending this school.\nOne day, you are given a problem called \"Arithmetical Restorations\" from the rabbit teacher, Hanako.\nArithmetical Restorations are the problems like the following:\n You are given three positive integers, $A$, $B$ and $C$.\n\n Several digits in these numbers have been erased.\n\n You should assign a digit in each blank position so that the numbers satisfy the formula $A+B=C$.\n\n The first digit of each number must not be zero. It is also the same for single-digit numbers.\n\nYou are clever in mathematics, so you immediately solved this problem.\nFurthermore, you decided to think of a more difficult problem, to calculate the number of possible assignments to the given Arithmetical Restorations problem.\nIf you can solve this difficult problem, you will get a good grade.\nShortly after beginning the new task, you noticed that there may be too many possible assignments to enumerate by hand. So, being the best programmer in the school as well, you are now trying to write a program to count the number of possible assignments to Arithmetical Restoration problems.\n note: The answer of the first dataset is 2. They are shown below.\n 384 + 122 = 506\n\n 394 + 122 = 516", "constraint": "", "input": "The input is a sequence of datasets.\nThe number of datasets is less than 100.\nEach dataset is formatted as follows.\n\n$A$$B$$C$Each dataset consists of three strings, $A$, $B$ and $C$.\nThey indicate that the sum of $A$ and $B$ should be $C$.\nEach string consists of digits (0-9) and/or question mark (? ).\nA question mark (? ) indicates an erased digit.\nYou may assume that the first character of each string is not 0 and each dataset has at least one ? .\nIt is guaranteed that each string contains between 1 and 50 characters, inclusive.\nYou can also assume that the lengths of three strings are equal.\nThe end of input is indicated by a line with a single zero.", "output": "For each dataset, output the number of possible assignments to the given problem modulo 1,000,000,007.\nNote that there may be no way to solve the given problems because Ms. Hanako is a careless rabbit.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3?4\n12?\n5?6\n?2?4\n5?7?\n?9?2\n?????\n?????\n?????\n0\n output: 2\n40\n200039979"], "Pid": "p01678", "ProblemText": "Task Description: The Animal School is a primary school for animal children.\nYou are a fox attending this school.\nOne day, you are given a problem called \"Arithmetical Restorations\" from the rabbit teacher, Hanako.\nArithmetical Restorations are the problems like the following:\n You are given three positive integers, $A$, $B$ and $C$.\n\n Several digits in these numbers have been erased.\n\n You should assign a digit in each blank position so that the numbers satisfy the formula $A+B=C$.\n\n The first digit of each number must not be zero. It is also the same for single-digit numbers.\n\nYou are clever in mathematics, so you immediately solved this problem.\nFurthermore, you decided to think of a more difficult problem, to calculate the number of possible assignments to the given Arithmetical Restorations problem.\nIf you can solve this difficult problem, you will get a good grade.\nShortly after beginning the new task, you noticed that there may be too many possible assignments to enumerate by hand. So, being the best programmer in the school as well, you are now trying to write a program to count the number of possible assignments to Arithmetical Restoration problems.\n note: The answer of the first dataset is 2. They are shown below.\n 384 + 122 = 506\n\n 394 + 122 = 516\nTask Input: The input is a sequence of datasets.\nThe number of datasets is less than 100.\nEach dataset is formatted as follows.\n\n$A$$B$$C$Each dataset consists of three strings, $A$, $B$ and $C$.\nThey indicate that the sum of $A$ and $B$ should be $C$.\nEach string consists of digits (0-9) and/or question mark (? ).\nA question mark (? ) indicates an erased digit.\nYou may assume that the first character of each string is not 0 and each dataset has at least one ? .\nIt is guaranteed that each string contains between 1 and 50 characters, inclusive.\nYou can also assume that the lengths of three strings are equal.\nThe end of input is indicated by a line with a single zero.\nTask Output: For each dataset, output the number of possible assignments to the given problem modulo 1,000,000,007.\nNote that there may be no way to solve the given problems because Ms. Hanako is a careless rabbit.\nTask Samples: input: 3?4\n12?\n5?6\n?2?4\n5?7?\n?9?2\n?????\n?????\n?????\n0\n output: 2\n40\n200039979\n\n" }, { "title": "Problem Statement", "content": "You are now participating in the Summer Training Camp for Programming Contests with your friend Jiro, who is an enthusiast of the ramen chain SIRO.\nSince every SIRO restaurant has its own tasteful ramen, he wants to try them at as many different restaurants as possible in the night.\nHe doesn't have plenty of time tonight, however, because he has to get up early in the morning tomorrow to join a training session.\nSo he asked you to find the maximum number of different restaurants to which he would be able to go to eat ramen in the limited time.\nThere are $n$ railway stations in the city, which are numbered $1$ through $n$. The station $s$ is the nearest to the camp venue.\n$m$ pairs of stations are directly connected by the railway: you can move between the stations $a_i$ and $b_i$ in $c_i$ minutes in the both directions.\nAmong the stations, there are $l$ stations where a SIRO restaurant is located nearby. There is at most one SIRO restaurant around each of the stations, and there are no restaurants near the station $s$.\nIt takes $e_i$ minutes for Jiro to eat ramen at the restaurant near the station $j_i$.\nIt takes only a negligibly short time to go back and forth between a station and its nearby SIRO restaurant.\nYou can also assume that Jiro doesn't have to wait for the ramen to be served in the restaurants.\nJiro is now at the station $s$ and have to come back to the station in $t$ minutes. How many different SIRO's can he taste?", "constraint": "", "input": "The input is a sequence of datasets. The number of the datasets does not exceed $100$. Each dataset is formatted as follows:\n$n$ $m$ $l$ $s$ $t$$a_1$ $b_1$ $c_1$: : $a_m$ $b_m$ $c_m$$j_1$ $e_1$: : $j_l$ $e_l$The first line of each dataset contains five integers:\n $n$ for the number of stations,\n\n $m$ for the number of directly connected pairs of stations,\n\n $l$ for the number of SIRO restaurants,\n\n $s$ for the starting-point station, and\n\n $t$ for the time limit for Jiro.\n\nEach of the following $m$ lines contains three integers:\n $a_i$ and $b_i$ for the connected stations, and\n\n $c_i$ for the time it takes to move between the two stations.\n\nEach of the following $l$ lines contains two integers:\n $j_i$ for the station where a SIRO restaurant is located, and\n\n $e_i$ for the time it takes for Jiro to eat at the restaurant.\n\nThe end of the input is indicated by a line with five zeros, which is not included in the datasets.\nThe datasets satisfy the following constraints:\n $2 <= n <= 300$\n\n $1 <= m <= 5{, }000$\n\n $1 <= l <= 16$\n\n $1 <= s <= n$\n\n $1 <= t <= 100{, }000$\n\n $1 <= a_i, b_i <= n$\n\n $1 <= c_i <= 1{, }000$\n\n $1 <= j_i <= n$\n\n $1 <= e_i <= 15$\n\n $s \\ne j_i$\n\n $j_i$'s are distinct.\n\n $a_i \\ne b_i$\n\n $(a_i, b_i) \\ne (a_j, b_j)$ and $(a_i, b_i) \\ne (b_j, a_j)$ for any $i \\ne j$\n\nNote that there may be some stations not reachable from the starting point $s$.", "output": "For each data set, output the maximum number of different restaurants where Jiro can go within the time limit.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 1 1 10\n1 2 3\n2 4\n2 1 1 1 9\n1 2 3\n2 4\n4 2 2 4 50\n1 2 5\n3 4 5\n2 15\n3 15\n4 6 3 1 29\n1 2 20\n3 2 10\n4 1 5\n3 1 5\n2 4 3\n3 4 4\n2 1\n4 5\n3 3\n0 0 0 0 0\n output: 1\n0\n1\n3"], "Pid": "p01679", "ProblemText": "Task Description: You are now participating in the Summer Training Camp for Programming Contests with your friend Jiro, who is an enthusiast of the ramen chain SIRO.\nSince every SIRO restaurant has its own tasteful ramen, he wants to try them at as many different restaurants as possible in the night.\nHe doesn't have plenty of time tonight, however, because he has to get up early in the morning tomorrow to join a training session.\nSo he asked you to find the maximum number of different restaurants to which he would be able to go to eat ramen in the limited time.\nThere are $n$ railway stations in the city, which are numbered $1$ through $n$. The station $s$ is the nearest to the camp venue.\n$m$ pairs of stations are directly connected by the railway: you can move between the stations $a_i$ and $b_i$ in $c_i$ minutes in the both directions.\nAmong the stations, there are $l$ stations where a SIRO restaurant is located nearby. There is at most one SIRO restaurant around each of the stations, and there are no restaurants near the station $s$.\nIt takes $e_i$ minutes for Jiro to eat ramen at the restaurant near the station $j_i$.\nIt takes only a negligibly short time to go back and forth between a station and its nearby SIRO restaurant.\nYou can also assume that Jiro doesn't have to wait for the ramen to be served in the restaurants.\nJiro is now at the station $s$ and have to come back to the station in $t$ minutes. How many different SIRO's can he taste?\nTask Input: The input is a sequence of datasets. The number of the datasets does not exceed $100$. Each dataset is formatted as follows:\n$n$ $m$ $l$ $s$ $t$$a_1$ $b_1$ $c_1$: : $a_m$ $b_m$ $c_m$$j_1$ $e_1$: : $j_l$ $e_l$The first line of each dataset contains five integers:\n $n$ for the number of stations,\n\n $m$ for the number of directly connected pairs of stations,\n\n $l$ for the number of SIRO restaurants,\n\n $s$ for the starting-point station, and\n\n $t$ for the time limit for Jiro.\n\nEach of the following $m$ lines contains three integers:\n $a_i$ and $b_i$ for the connected stations, and\n\n $c_i$ for the time it takes to move between the two stations.\n\nEach of the following $l$ lines contains two integers:\n $j_i$ for the station where a SIRO restaurant is located, and\n\n $e_i$ for the time it takes for Jiro to eat at the restaurant.\n\nThe end of the input is indicated by a line with five zeros, which is not included in the datasets.\nThe datasets satisfy the following constraints:\n $2 <= n <= 300$\n\n $1 <= m <= 5{, }000$\n\n $1 <= l <= 16$\n\n $1 <= s <= n$\n\n $1 <= t <= 100{, }000$\n\n $1 <= a_i, b_i <= n$\n\n $1 <= c_i <= 1{, }000$\n\n $1 <= j_i <= n$\n\n $1 <= e_i <= 15$\n\n $s \\ne j_i$\n\n $j_i$'s are distinct.\n\n $a_i \\ne b_i$\n\n $(a_i, b_i) \\ne (a_j, b_j)$ and $(a_i, b_i) \\ne (b_j, a_j)$ for any $i \\ne j$\n\nNote that there may be some stations not reachable from the starting point $s$.\nTask Output: For each data set, output the maximum number of different restaurants where Jiro can go within the time limit.\nTask Samples: input: 2 1 1 1 10\n1 2 3\n2 4\n2 1 1 1 9\n1 2 3\n2 4\n4 2 2 4 50\n1 2 5\n3 4 5\n2 15\n3 15\n4 6 3 1 29\n1 2 20\n3 2 10\n4 1 5\n3 1 5\n2 4 3\n3 4 4\n2 1\n4 5\n3 3\n0 0 0 0 0\n output: 1\n0\n1\n3\n\n" }, { "title": "Problem Statement", "content": "\"Everlasting -One-\" is an award-winning online game launched this year. This game has rapidly become famous for its large number of characters you can play.\nIn this game, a character is characterized by attributes. There are $N$ attributes in this game, numbered $1$ through $N$. Each attribute takes one of the two states, light or darkness. It means there are $2^N$ kinds of characters in this game.\nYou can change your character by job change. Although this is the only way to change your character's attributes, it is allowed to change jobs as many times as you want.\nThe rule of job change is a bit complex. It is possible to change a character from $A$ to $B$ if and only if there exist two attributes $a$ and $b$ such that they satisfy the following four conditions:\n The state of attribute $a$ of character $A$ is light.\n\n The state of attribute $b$ of character $B$ is light.\n\n There exists no attribute $c$ such that both characters $A$ and $B$ have the light state of attribute $c$.\n\n A pair of attribute $(a, b)$ is compatible.\n\nHere, we say a pair of attribute $(a, b)$ is compatible if there exists a sequence of attributes $c_1, c_2, \\ldots, c_n$ satisfying the following three conditions:\n $c_1 = a$.\n\n $c_n = b$.\n\n Either $(c_i, c_{i+1})$ or $(c_{i+1}, c_i)$ is a special pair for all $i = 1,2, \\ldots, n-1$. You will be given the list of special pairs.\n\nSince you love this game with enthusiasm, you are trying to play the game with all characters (it's really crazy). However, you have immediately noticed that one character can be changed to a limited set of characters with this game's job change rule. We say character $A$ and $B$ are essentially different if you cannot change character $A$ into character $B$ by repeating job changes.\nThen, the following natural question arises; how many essentially different characters are there?\nSince the output may be very large, you should calculate the answer modulo $1{, }000{, }000{, }007$.", "constraint": "", "input": "The input is a sequence of datasets.\nThe number of datasets is not more than $50$ and the total size of input is less than $5$ MB. \nEach dataset is formatted as follows.\n$N$ $M$$a_1$ $b_1$: : $a_M$ $b_M$The first line of each dataset contains two integers $N$ and $M$ ($1 <= N <= 10^5$ and $0 <= M <= 10^5$).\nThen $M$ lines follow.\nThe $i$-th line contains two integers $a_i$ and $b_i$ ($1 <= a_i < b_i <= N$) which denote the $i$-th special pair.\nThe input is terminated by two zeroes.\nIt is guaranteed that $(a_i, b_i) \\ne (a_j, b_j)$ if $i \\ne j$.", "output": "For each dataset, output the number of essentially different characters modulo $1{, }000{, }000{, }007$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n2 3\n5 0\n100000 0\n0 0\n output: 3\n32\n607723520"], "Pid": "p01680", "ProblemText": "Task Description: \"Everlasting -One-\" is an award-winning online game launched this year. This game has rapidly become famous for its large number of characters you can play.\nIn this game, a character is characterized by attributes. There are $N$ attributes in this game, numbered $1$ through $N$. Each attribute takes one of the two states, light or darkness. It means there are $2^N$ kinds of characters in this game.\nYou can change your character by job change. Although this is the only way to change your character's attributes, it is allowed to change jobs as many times as you want.\nThe rule of job change is a bit complex. It is possible to change a character from $A$ to $B$ if and only if there exist two attributes $a$ and $b$ such that they satisfy the following four conditions:\n The state of attribute $a$ of character $A$ is light.\n\n The state of attribute $b$ of character $B$ is light.\n\n There exists no attribute $c$ such that both characters $A$ and $B$ have the light state of attribute $c$.\n\n A pair of attribute $(a, b)$ is compatible.\n\nHere, we say a pair of attribute $(a, b)$ is compatible if there exists a sequence of attributes $c_1, c_2, \\ldots, c_n$ satisfying the following three conditions:\n $c_1 = a$.\n\n $c_n = b$.\n\n Either $(c_i, c_{i+1})$ or $(c_{i+1}, c_i)$ is a special pair for all $i = 1,2, \\ldots, n-1$. You will be given the list of special pairs.\n\nSince you love this game with enthusiasm, you are trying to play the game with all characters (it's really crazy). However, you have immediately noticed that one character can be changed to a limited set of characters with this game's job change rule. We say character $A$ and $B$ are essentially different if you cannot change character $A$ into character $B$ by repeating job changes.\nThen, the following natural question arises; how many essentially different characters are there?\nSince the output may be very large, you should calculate the answer modulo $1{, }000{, }000{, }007$.\nTask Input: The input is a sequence of datasets.\nThe number of datasets is not more than $50$ and the total size of input is less than $5$ MB. \nEach dataset is formatted as follows.\n$N$ $M$$a_1$ $b_1$: : $a_M$ $b_M$The first line of each dataset contains two integers $N$ and $M$ ($1 <= N <= 10^5$ and $0 <= M <= 10^5$).\nThen $M$ lines follow.\nThe $i$-th line contains two integers $a_i$ and $b_i$ ($1 <= a_i < b_i <= N$) which denote the $i$-th special pair.\nThe input is terminated by two zeroes.\nIt is guaranteed that $(a_i, b_i) \\ne (a_j, b_j)$ if $i \\ne j$.\nTask Output: For each dataset, output the number of essentially different characters modulo $1{, }000{, }000{, }007$.\nTask Samples: input: 3 2\n1 2\n2 3\n5 0\n100000 0\n0 0\n output: 3\n32\n607723520\n\n" }, { "title": "Problem Statement", "content": "Fox Ciel is practicing miniature golf, a golf game played with a putter club only. For improving golf skills, she believes it is important how well she bounces the ball against walls.\nThe field of miniature golf is in a two-dimensional plane and surrounded by $N$ walls forming a convex polygon. At first, the ball is placed at $(s_x, s_y)$ inside the field. The ball is small enough to be regarded as a point.\nCiel can shoot the ball to any direction and stop the ball whenever she wants. The ball will move in a straight line. When the ball hits the wall, it rebounds like mirror reflection (i. e. incidence angle equals reflection angle).\nFor practice, Ciel decided to make a single shot under the following conditions:\n The ball hits each wall of the field exactly once.\n\n The ball does NOT hit the corner of the field.\n\nCount the number of possible orders in which the ball hits the walls.", "constraint": "", "input": "The input contains several datasets. The number of datasets does not exceed $100$. Each dataset is in the following format.\n$N$$s_x$ $s_y$$x_1$ $y_1$: : $x_N$ $y_N$The first line contains an integer $N$ ($3 <= N <= 8$). The next line contains two integers $s_x$ and $s_y$ ($-50 <= s_x, s_y <= 50$), which describe the coordinates of the initial position of the ball. Each of the following $N$ lines contains two integers $x_i$ and $y_i$ ($-50 <= x_i, y_i <= 50$), which describe the coordinates of each corner of the field. The corners are given in counterclockwise order. You may assume given initial position $(s_x, s_y)$ is inside the field and the field is convex.\nIt is guaranteed that there exists a shoot direction for each valid order of the walls that satisfies the following condition: distance between the ball and the corners of the field $(x_i, y_i)$ is always greater than $10^{-6}$ until the ball hits the last wall.\nThe last dataset is followed by a line containing a single zero.", "output": "For each dataset in the input, print the number of valid orders of the walls in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n-10 -10\n10 -10\n10 10\n-10 10\n0\n output: 8"], "Pid": "p01681", "ProblemText": "Task Description: Fox Ciel is practicing miniature golf, a golf game played with a putter club only. For improving golf skills, she believes it is important how well she bounces the ball against walls.\nThe field of miniature golf is in a two-dimensional plane and surrounded by $N$ walls forming a convex polygon. At first, the ball is placed at $(s_x, s_y)$ inside the field. The ball is small enough to be regarded as a point.\nCiel can shoot the ball to any direction and stop the ball whenever she wants. The ball will move in a straight line. When the ball hits the wall, it rebounds like mirror reflection (i. e. incidence angle equals reflection angle).\nFor practice, Ciel decided to make a single shot under the following conditions:\n The ball hits each wall of the field exactly once.\n\n The ball does NOT hit the corner of the field.\n\nCount the number of possible orders in which the ball hits the walls.\nTask Input: The input contains several datasets. The number of datasets does not exceed $100$. Each dataset is in the following format.\n$N$$s_x$ $s_y$$x_1$ $y_1$: : $x_N$ $y_N$The first line contains an integer $N$ ($3 <= N <= 8$). The next line contains two integers $s_x$ and $s_y$ ($-50 <= s_x, s_y <= 50$), which describe the coordinates of the initial position of the ball. Each of the following $N$ lines contains two integers $x_i$ and $y_i$ ($-50 <= x_i, y_i <= 50$), which describe the coordinates of each corner of the field. The corners are given in counterclockwise order. You may assume given initial position $(s_x, s_y)$ is inside the field and the field is convex.\nIt is guaranteed that there exists a shoot direction for each valid order of the walls that satisfies the following condition: distance between the ball and the corners of the field $(x_i, y_i)$ is always greater than $10^{-6}$ until the ball hits the last wall.\nThe last dataset is followed by a line containing a single zero.\nTask Output: For each dataset in the input, print the number of valid orders of the walls in a line.\nTask Samples: input: 4\n0 0\n-10 -10\n10 -10\n10 10\n-10 10\n0\n output: 8\n\n" }, { "title": "Problem Statement", "content": "Dr. Suposupo developed a programming language called Shipura. Shipura supports only one binary operator ${\\tt >>}$ and only one unary function ${\\tt S<\\ >}$.\n$x {\\tt >>} y$ is evaluated to $\\lfloor x / 2^y \\rfloor$ (that is, the greatest integer not exceeding $x / 2^y$), and ${\\tt S<} x {\\tt >}$ is evaluated to $x^2 \\bmod 1{, }000{, }000{, }007$ (that is, the remainder when $x^2$ is divided by $1{, }000{, }000{, }007$). \nThe operator ${\\tt >>}$ is left-associative. For example, the expression $x {\\tt >>} y {\\tt >>} z$ is interpreted as $(x {\\tt >>} y) {\\tt >>} z$, not as $x {\\tt >>} (y {\\tt >>} z)$. Note that these parentheses do not appear in actual Shipura expressions. \nThe syntax of Shipura is given (in BNF; Backus-Naur Form) as follows:\nexpr : : = term | expr sp \">>\" sp term\nterm : : = number | \"S\" sp \"<\" sp expr sp \">\"\nsp : : = \"\" | sp \" \"\nnumber : : = digit | number digit\ndigit : : = \"0\" | \"1\" | \"2\" | \"3\" | \"4\" | \"5\" | \"6\" | \"7\" | \"8\" | \"9\"The start symbol of this syntax is $\\tt expr$ that represents an expression in Shipura. In addition, $\\tt number$ is an integer between $0$ and $1{, }000{, }000{, }000$ inclusive, written without extra leading zeros.\nWrite a program to evaluate Shipura expressions.", "constraint": "", "input": "The input is a sequence of datasets. Each dataset is represented by a line which contains a valid expression in Shipura.\nA line containing a single ${\\tt \\#}$ indicates the end of the input. You can assume the number of datasets is at most $100$ and the total size of the input file does not exceed $2{, }000{, }000$ bytes.", "output": "For each dataset, output a line containing the evaluated value of the expression.", "content_img": false, "lang": "en", "error": false, "samples": ["input: S< S< 12 >> 2 > >\n123 >> 1 >> 1\n1000000000 >>129\nS>>>>\nS >> 11 >>> 10 >\n#\n output: 81\n30\n0\n294967268\n14592400"], "Pid": "p01682", "ProblemText": "Task Description: Dr. Suposupo developed a programming language called Shipura. Shipura supports only one binary operator ${\\tt >>}$ and only one unary function ${\\tt S<\\ >}$.\n$x {\\tt >>} y$ is evaluated to $\\lfloor x / 2^y \\rfloor$ (that is, the greatest integer not exceeding $x / 2^y$), and ${\\tt S<} x {\\tt >}$ is evaluated to $x^2 \\bmod 1{, }000{, }000{, }007$ (that is, the remainder when $x^2$ is divided by $1{, }000{, }000{, }007$). \nThe operator ${\\tt >>}$ is left-associative. For example, the expression $x {\\tt >>} y {\\tt >>} z$ is interpreted as $(x {\\tt >>} y) {\\tt >>} z$, not as $x {\\tt >>} (y {\\tt >>} z)$. Note that these parentheses do not appear in actual Shipura expressions. \nThe syntax of Shipura is given (in BNF; Backus-Naur Form) as follows:\nexpr : : = term | expr sp \">>\" sp term\nterm : : = number | \"S\" sp \"<\" sp expr sp \">\"\nsp : : = \"\" | sp \" \"\nnumber : : = digit | number digit\ndigit : : = \"0\" | \"1\" | \"2\" | \"3\" | \"4\" | \"5\" | \"6\" | \"7\" | \"8\" | \"9\"The start symbol of this syntax is $\\tt expr$ that represents an expression in Shipura. In addition, $\\tt number$ is an integer between $0$ and $1{, }000{, }000{, }000$ inclusive, written without extra leading zeros.\nWrite a program to evaluate Shipura expressions.\nTask Input: The input is a sequence of datasets. Each dataset is represented by a line which contains a valid expression in Shipura.\nA line containing a single ${\\tt \\#}$ indicates the end of the input. You can assume the number of datasets is at most $100$ and the total size of the input file does not exceed $2{, }000{, }000$ bytes.\nTask Output: For each dataset, output a line containing the evaluated value of the expression.\nTask Samples: input: S< S< 12 >> 2 > >\n123 >> 1 >> 1\n1000000000 >>129\nS>>>>\nS >> 11 >>> 10 >\n#\n output: 81\n30\n0\n294967268\n14592400\n\n" }, { "title": "Problem Statement", "content": "You have just arrived in a small country. Unfortunately a huge hurricane swept across the country a few days ago.\nThe country is made up of $n$ islands, numbered $1$ through $n$. Many bridges connected the islands, but all the bridges were washed away by a flood. People in the islands need new bridges to travel among the islands again.\nThe problem is cost. The country is not very wealthy. The government has to keep spending down. They asked you, a great programmer, to calculate the minimum cost to rebuild bridges. Write a program to calculate it!\nEach bridge connects two islands bidirectionally. Each island $i$ has two parameters $d_i$ and $p_i$. An island $i$ can have at most $d_i$ bridges connected. The cost to build a bridge between an island $i$ and another island $j$ is calculated by $|p_i - p_j|$. Note that it may be impossible to rebuild new bridges within given limitations although people need to travel between any pair of islands over (a sequence of) bridges.", "constraint": "", "input": "The input is a sequence of datasets.\nThe number of datasets is less than or equal to $60$.\nEach dataset is formatted as follows.\n$n$$p_1$ $d_1$$p_2$ $d_2$: : $p_n$ $d_n$Everything in the input is an integer.\n$n$ ($2 <= n <= 4{, }000$) on the first line indicates the number of islands.\nThen $n$ lines follow, which contain the parameters of the islands.\n$p_i$ ($1 <= p_i <= 10^9$) and $d_i$ ($1 <= d_i <= n$) denote the parameters of the island $i$.\nThe end of the input is indicated by a line with a single zero.", "output": "For each dataset, output the minimum cost in a line if it is possible to rebuild bridges within given limitations in the dataset. Otherwise, output $-1$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 1\n8 2\n9 1\n14 2\n4\n181 4\n815 4\n634 4\n370 4\n4\n52 1\n40 1\n81 2\n73 1\n10\n330 1\n665 3\n260 1\n287 2\n196 3\n243 1\n815 1\n287 3\n330 1\n473 4\n0\n output: 18\n634\n-1\n916"], "Pid": "p01683", "ProblemText": "Task Description: You have just arrived in a small country. Unfortunately a huge hurricane swept across the country a few days ago.\nThe country is made up of $n$ islands, numbered $1$ through $n$. Many bridges connected the islands, but all the bridges were washed away by a flood. People in the islands need new bridges to travel among the islands again.\nThe problem is cost. The country is not very wealthy. The government has to keep spending down. They asked you, a great programmer, to calculate the minimum cost to rebuild bridges. Write a program to calculate it!\nEach bridge connects two islands bidirectionally. Each island $i$ has two parameters $d_i$ and $p_i$. An island $i$ can have at most $d_i$ bridges connected. The cost to build a bridge between an island $i$ and another island $j$ is calculated by $|p_i - p_j|$. Note that it may be impossible to rebuild new bridges within given limitations although people need to travel between any pair of islands over (a sequence of) bridges.\nTask Input: The input is a sequence of datasets.\nThe number of datasets is less than or equal to $60$.\nEach dataset is formatted as follows.\n$n$$p_1$ $d_1$$p_2$ $d_2$: : $p_n$ $d_n$Everything in the input is an integer.\n$n$ ($2 <= n <= 4{, }000$) on the first line indicates the number of islands.\nThen $n$ lines follow, which contain the parameters of the islands.\n$p_i$ ($1 <= p_i <= 10^9$) and $d_i$ ($1 <= d_i <= n$) denote the parameters of the island $i$.\nThe end of the input is indicated by a line with a single zero.\nTask Output: For each dataset, output the minimum cost in a line if it is possible to rebuild bridges within given limitations in the dataset. Otherwise, output $-1$ in a line.\nTask Samples: input: 4\n1 1\n8 2\n9 1\n14 2\n4\n181 4\n815 4\n634 4\n370 4\n4\n52 1\n40 1\n81 2\n73 1\n10\n330 1\n665 3\n260 1\n287 2\n196 3\n243 1\n815 1\n287 3\n330 1\n473 4\n0\n output: 18\n634\n-1\n916\n\n" }, { "title": "Problem Statement", "content": "Alice is a private teacher.\nOne of her job is to prepare the learning materials for her student.\nNow, as part of the materials, she is drawing a Venn diagram between two sets $A$ and $B$.\nVenn diagram is a diagram which illustrates the relationships among one or more sets.\nFor example, a Venn diagram between two sets $A$ and $B$ is drawn as illustrated below.\nThe rectangle corresponds to the universal set $U$.\nThe two circles in the rectangle correspond to two sets $A$ and $B$, respectively.\nThe intersection of the two circles corresponds to the intersection of the two sets, i. e. $A \\cap B$.\nFig: Venn diagram between two sets\nAlice, the mathematics personified, came up with a special condition to make her Venn diagram more beautiful.\nHer condition is that the area of each part of her Venn diagram is equal to the number of elements in its corresponding set.\nIn other words, one circle must have the area equal to $|A|$, the other circle must have the area equal to $|B|$, and their intersection must have the area equal to $|A \\cap B|$. Here, $|X|$ denotes the number of elements in a set $X$.\nAlice already drew a rectangle, but has been having a trouble figuring out where to draw the rest, two circles, because she cannot even stand with a small error human would make.\nAs an old friend of Alice's, your task is to help her by writing a program to determine the centers and radii of two circles so that they satisfy the above condition.", "constraint": "", "input": "The input is a sequence of datasets.\nThe number of datasets is not more than $300$.\nEach dataset is formatted as follows.\n$U_W$ $U_H$ $|A|$ $|B|$ $|A \\cap B|$The first two integers $U_W$ and $U_H$ ($1 <= U_W, U_H <= 100$) denote the width and height of the rectangle which corresponds to the universal set $U$, respectively.\nThe next three integers $|A|$, $|B|$ and $|A \\cap B|$ ($1 <= |A|, |B| <= 10{, }000$ and $0 <= |A \\cap B| <= \\min\\{|A|, |B|\\}$) denote the numbers of elements of the set $A$, $B$ and $A \\cap B$, respectively.\nThe input is terminated by five zeroes.\nYou may assume that, even if $U_W$ and $U_H$ would vary within $\\pm 0.01$, it would not change whether you can draw two circles under the Alice's condition.", "output": "For each dataset, output the centers and radii of the two circles that satisfy the Alice's condition as follows:\n$X_A$ $Y_A$ $R_A$ $X_B$ $Y_B$ $R_B$$X_A$ and $Y_A$ are the coordinates of the center of the circle which corresponds to the set $A$.\n$R_A$ is the radius of the circle which corresponds to the set $A$.\n$X_B$, $Y_B$ and $R_B$ are the values for the set B.\nThese values must be separated by a space.\nIf it is impossible to satisfy the condition, output:\nimpossibleThe area of each part must not have an absolute error greater than $0.0001$.\nAlso, the two circles must stay inside the rectangle with a margin of $0.0001$ for error, or more precisely, all of the following four conditions must be satisfied:\n $X_A - R_A >= -0.0001$\n\n $X_A + R_A <= U_W + 0.0001$\n\n $Y_A - R_A >= -0.0001$\n\n $Y_A + R_A <= U_H + 0.0001$\n\nThe same conditions must hold for $X_B$, $Y_B$ and $R_B$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10 5 1 1 0\n10 5 2 2 1\n10 10 70 70 20\n0 0 0 0 0\n output: 1 1 0.564189584 3 1 0.564189584\n1 1 0.797884561 1.644647246 1 0.797884561\nimpossible"], "Pid": "p01684", "ProblemText": "Task Description: Alice is a private teacher.\nOne of her job is to prepare the learning materials for her student.\nNow, as part of the materials, she is drawing a Venn diagram between two sets $A$ and $B$.\nVenn diagram is a diagram which illustrates the relationships among one or more sets.\nFor example, a Venn diagram between two sets $A$ and $B$ is drawn as illustrated below.\nThe rectangle corresponds to the universal set $U$.\nThe two circles in the rectangle correspond to two sets $A$ and $B$, respectively.\nThe intersection of the two circles corresponds to the intersection of the two sets, i. e. $A \\cap B$.\nFig: Venn diagram between two sets\nAlice, the mathematics personified, came up with a special condition to make her Venn diagram more beautiful.\nHer condition is that the area of each part of her Venn diagram is equal to the number of elements in its corresponding set.\nIn other words, one circle must have the area equal to $|A|$, the other circle must have the area equal to $|B|$, and their intersection must have the area equal to $|A \\cap B|$. Here, $|X|$ denotes the number of elements in a set $X$.\nAlice already drew a rectangle, but has been having a trouble figuring out where to draw the rest, two circles, because she cannot even stand with a small error human would make.\nAs an old friend of Alice's, your task is to help her by writing a program to determine the centers and radii of two circles so that they satisfy the above condition.\nTask Input: The input is a sequence of datasets.\nThe number of datasets is not more than $300$.\nEach dataset is formatted as follows.\n$U_W$ $U_H$ $|A|$ $|B|$ $|A \\cap B|$The first two integers $U_W$ and $U_H$ ($1 <= U_W, U_H <= 100$) denote the width and height of the rectangle which corresponds to the universal set $U$, respectively.\nThe next three integers $|A|$, $|B|$ and $|A \\cap B|$ ($1 <= |A|, |B| <= 10{, }000$ and $0 <= |A \\cap B| <= \\min\\{|A|, |B|\\}$) denote the numbers of elements of the set $A$, $B$ and $A \\cap B$, respectively.\nThe input is terminated by five zeroes.\nYou may assume that, even if $U_W$ and $U_H$ would vary within $\\pm 0.01$, it would not change whether you can draw two circles under the Alice's condition.\nTask Output: For each dataset, output the centers and radii of the two circles that satisfy the Alice's condition as follows:\n$X_A$ $Y_A$ $R_A$ $X_B$ $Y_B$ $R_B$$X_A$ and $Y_A$ are the coordinates of the center of the circle which corresponds to the set $A$.\n$R_A$ is the radius of the circle which corresponds to the set $A$.\n$X_B$, $Y_B$ and $R_B$ are the values for the set B.\nThese values must be separated by a space.\nIf it is impossible to satisfy the condition, output:\nimpossibleThe area of each part must not have an absolute error greater than $0.0001$.\nAlso, the two circles must stay inside the rectangle with a margin of $0.0001$ for error, or more precisely, all of the following four conditions must be satisfied:\n $X_A - R_A >= -0.0001$\n\n $X_A + R_A <= U_W + 0.0001$\n\n $Y_A - R_A >= -0.0001$\n\n $Y_A + R_A <= U_H + 0.0001$\n\nThe same conditions must hold for $X_B$, $Y_B$ and $R_B$.\nTask Samples: input: 10 5 1 1 0\n10 5 2 2 1\n10 10 70 70 20\n0 0 0 0 0\n output: 1 1 0.564189584 3 1 0.564189584\n1 1 0.797884561 1.644647246 1 0.797884561\nimpossible\n\n" }, { "title": "Problem Statement", "content": "You have a rectangular board with square cells arranged in $H$ rows and $W$ columns.\nThe rows are numbered $1$ through $H$ from top to bottom, and the columns are numbered $1$ through $W$ from left to right. \nThe cell at the row $i$ and the column $j$ is denoted by $(i, j)$. \nEach cell on the board is colored in either Black or White.\nYou will paint the board as follows:\n Choose a cell $(i, j)$ and a color $c$, each uniformly at random, where $1 <= i <= H$, $1 <= j <= W$, and $c \\in \\{{\\rm Black}, {\\rm White}\\}$.\n\n Paint the cells $(i', j')$ with the color $c$ for any $1 <= i' <= i$ and $1 <= j' <= j$.\n\nHere's an example of the painting operation.\nYou have a $3 * 4$ board with the coloring depicted in the left side of the figure below.\nIf your random choice is the cell $(2,3)$ and the color Black, the board will become as shown in the right side of the figure.\n$6$ cells will be painted with Black as the result of this operation.\nNote that we count the cells \"painted\" even if the color is not actually changed by the operation, like the cell $(1,2)$ in this example.\nFig: An example of the painting operation\nGiven the initial coloring of the board and the desired coloring, you are supposed to perform the painting operations repeatedly until the board turns into the desired coloring.\nWrite a program to calculate the expected total number of painted cells in the sequence of operations.", "constraint": "", "input": "The input consists of several datasets. The number of datasets is at most $100$.\nThe first line of each dataset contains two integers $H$ and $W$ ($1 <= H, W <= 5$), the numbers of rows and columns of the board respectively.\nThen given are two coloring configurations of the board, where the former is the initial coloring and the latter is the desired coloring.\nA coloring configuration is described in $H$ lines, each of which consists of $W$ characters. Each character is either B or W, denoting a Black cell or a White cell, respectively.\nThere is one blank line between two configurations, and also after each dataset.\nYou can assume that the resulting expected value for each dataset will not exceed $10^9$.\nThe input is terminated by a line with two zeros, and your program should not process this as a dataset.", "output": "For each dataset, your program should output the expected value in a line. The absolute error or the relative error in your answer must be less than $10^{-6}$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 2\nBB\n\nWW\n\n2 1\nB\nW\n\nB\nW\n\n2 2\nBW\nBW\n\nWW\nWW\n\n3 4\nBBBB\nBBBB\nBBBB\n\nWWWW\nWWWW\nWWWW\n\n5 5\nBBBBB\nBBBBB\nBBBBB\nBBBBB\nBBBBB\n\nBBBBB\nBBBWB\nBBBBB\nBWBBB\nBBBBB\n\n0 0\n output: 6.0000000000\n0.0000000000\n12.8571428571\n120.0000000000\n23795493.8449918639"], "Pid": "p01685", "ProblemText": "Task Description: You have a rectangular board with square cells arranged in $H$ rows and $W$ columns.\nThe rows are numbered $1$ through $H$ from top to bottom, and the columns are numbered $1$ through $W$ from left to right. \nThe cell at the row $i$ and the column $j$ is denoted by $(i, j)$. \nEach cell on the board is colored in either Black or White.\nYou will paint the board as follows:\n Choose a cell $(i, j)$ and a color $c$, each uniformly at random, where $1 <= i <= H$, $1 <= j <= W$, and $c \\in \\{{\\rm Black}, {\\rm White}\\}$.\n\n Paint the cells $(i', j')$ with the color $c$ for any $1 <= i' <= i$ and $1 <= j' <= j$.\n\nHere's an example of the painting operation.\nYou have a $3 * 4$ board with the coloring depicted in the left side of the figure below.\nIf your random choice is the cell $(2,3)$ and the color Black, the board will become as shown in the right side of the figure.\n$6$ cells will be painted with Black as the result of this operation.\nNote that we count the cells \"painted\" even if the color is not actually changed by the operation, like the cell $(1,2)$ in this example.\nFig: An example of the painting operation\nGiven the initial coloring of the board and the desired coloring, you are supposed to perform the painting operations repeatedly until the board turns into the desired coloring.\nWrite a program to calculate the expected total number of painted cells in the sequence of operations.\nTask Input: The input consists of several datasets. The number of datasets is at most $100$.\nThe first line of each dataset contains two integers $H$ and $W$ ($1 <= H, W <= 5$), the numbers of rows and columns of the board respectively.\nThen given are two coloring configurations of the board, where the former is the initial coloring and the latter is the desired coloring.\nA coloring configuration is described in $H$ lines, each of which consists of $W$ characters. Each character is either B or W, denoting a Black cell or a White cell, respectively.\nThere is one blank line between two configurations, and also after each dataset.\nYou can assume that the resulting expected value for each dataset will not exceed $10^9$.\nThe input is terminated by a line with two zeros, and your program should not process this as a dataset.\nTask Output: For each dataset, your program should output the expected value in a line. The absolute error or the relative error in your answer must be less than $10^{-6}$.\nTask Samples: input: 1 2\nBB\n\nWW\n\n2 1\nB\nW\n\nB\nW\n\n2 2\nBW\nBW\n\nWW\nWW\n\n3 4\nBBBB\nBBBB\nBBBB\n\nWWWW\nWWWW\nWWWW\n\n5 5\nBBBBB\nBBBBB\nBBBBB\nBBBBB\nBBBBB\n\nBBBBB\nBBBWB\nBBBBB\nBWBBB\nBBBBB\n\n0 0\n output: 6.0000000000\n0.0000000000\n12.8571428571\n120.0000000000\n23795493.8449918639\n\n" }, { "title": "Problem Statement", "content": "You are given a rectangular board divided into square cells. The number of rows and columns in this board are $3$ and $3 M + 1$, respectively, where $M$ is a positive integer. The rows are numbered $1$ through $3$ from top to bottom, and the columns are numbered $1$ through $3 M + 1$ from left to right. The cell at the $i$-th row and the $j$-th column is denoted by $(i, j)$. \nEach cell is either a floor cell or a wall cell. In addition, cells in columns $2,3,5,6, \\ldots, 3 M - 1,3 M$ (numbers of form $3 k - 1$ or $3 k$, for $k = 1,2, \\ldots, M$) are painted in some color. There are $26$ colors which can be used for painting, and they are numbered $1$ through $26$. The other cells (in columns $1,4,7, \\ldots, 3 M + 1$) are not painted and each of them is a floor cell. \nYou are going to play the following game. First, you put a token at cell $(2,1)$. Then, you repeatedly move it to an adjacent floor cell. Two cells are considered adjacent if they share an edge. It is forbidden to move the token to a wall cell or out of the board. The objective of this game is to move the token to cell $(2,3 M + 1)$. \nFor this game, $26$ magical switches are available for you! Switches are numbered $1$ through $26$ and each switch corresponds to the color with the same number. When you push switch $x$, each floor cell painted in color $x$ becomes a wall cell and each wall cell painted in color $x$ becomes a floor cell, simultaneously. \nYou are allowed to push some of the magical switches ONLY BEFORE you start moving the token. Determine whether there exists a set of switches to push such that you can achieve the objective of the game, and if there does, find such a set.", "constraint": "", "input": "The input is a sequence of at most $130$ datasets. Each dataset begins with a line containing an integer $M$ ($1 <= M <= 1{, }000$). The following three lines, each containing $3 M + 1$ characters, represent the board. The $j$-th character in the $i$-th of those lines describes the information of cell $(i, j)$, as follows: \n The $x$-th uppercase letter indicates that cell $(i, j)$ is painted in color $x$ and it is initially a floor cell. \n\n The $x$-th lowercase letter indicates that cell $(i, j)$ is painted in color $x$ and it is initially a wall cell. \n\n A period (. ) indicates that cell $(i, j)$ is not painted and so it is a floor cell. \n\nHere you can assume that $j$ will be one of $1,4,7, \\ldots, 3 M + 1$ if and only if that character is a period. \nThe end of the input is indicated by a line with a single zero.", "output": "For each dataset, output $-1$ if you cannot achieve the objective. Otherwise, output the set of switches you push in order to achieve the objective, in the following format: \n$n$ $s_1$ $s_2$ . . . $s_n$Here, $n$ is the number of switches you push and $s_1, s_2, \\ldots, s_n$ are uppercase letters corresponding to switches you push, where the $x$-th uppercase letter denotes switch $x$. These uppercase letters $s_1, s_2, \\ldots, s_n$ must be distinct, while the order of them does not matter. Note that it is allowed to output $n = 0$ (with no following uppercase letters) if you do not have to push any switches. See the sample output for clarification. \nIf there are multiple solutions, output any one of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n.aa.cA.Cc.\n.bb.Bb.AC.\n.cc.ac.Ab.\n1\n.Xx.\n.Yy.\n.Zz.\n6\n.Aj.fA.aW.zA.Jf.Gz.\n.gW.GW.Fw.ZJ.AG.JW.\n.bZ.jZ.Ga.Fj.gF.Za.\n9\n.ab.gh.mn.st.yz.EF.KL.QR.WA.\n.cd.ij.op.uv.AB.GH.MN.ST.XB.\n.ef.kl.qr.wx.CD.IJ.OP.UV.yz.\n2\n.AC.Mo.\n.IC.PC.\n.oA.CM.\n20\n.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.qb.\n.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.\n.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.qb.\n0\n output: 3 B C E\n-1\n3 J A G\n10 A B G H M N S T Y Z\n0\n2 Q B"], "Pid": "p01686", "ProblemText": "Task Description: You are given a rectangular board divided into square cells. The number of rows and columns in this board are $3$ and $3 M + 1$, respectively, where $M$ is a positive integer. The rows are numbered $1$ through $3$ from top to bottom, and the columns are numbered $1$ through $3 M + 1$ from left to right. The cell at the $i$-th row and the $j$-th column is denoted by $(i, j)$. \nEach cell is either a floor cell or a wall cell. In addition, cells in columns $2,3,5,6, \\ldots, 3 M - 1,3 M$ (numbers of form $3 k - 1$ or $3 k$, for $k = 1,2, \\ldots, M$) are painted in some color. There are $26$ colors which can be used for painting, and they are numbered $1$ through $26$. The other cells (in columns $1,4,7, \\ldots, 3 M + 1$) are not painted and each of them is a floor cell. \nYou are going to play the following game. First, you put a token at cell $(2,1)$. Then, you repeatedly move it to an adjacent floor cell. Two cells are considered adjacent if they share an edge. It is forbidden to move the token to a wall cell or out of the board. The objective of this game is to move the token to cell $(2,3 M + 1)$. \nFor this game, $26$ magical switches are available for you! Switches are numbered $1$ through $26$ and each switch corresponds to the color with the same number. When you push switch $x$, each floor cell painted in color $x$ becomes a wall cell and each wall cell painted in color $x$ becomes a floor cell, simultaneously. \nYou are allowed to push some of the magical switches ONLY BEFORE you start moving the token. Determine whether there exists a set of switches to push such that you can achieve the objective of the game, and if there does, find such a set.\nTask Input: The input is a sequence of at most $130$ datasets. Each dataset begins with a line containing an integer $M$ ($1 <= M <= 1{, }000$). The following three lines, each containing $3 M + 1$ characters, represent the board. The $j$-th character in the $i$-th of those lines describes the information of cell $(i, j)$, as follows: \n The $x$-th uppercase letter indicates that cell $(i, j)$ is painted in color $x$ and it is initially a floor cell. \n\n The $x$-th lowercase letter indicates that cell $(i, j)$ is painted in color $x$ and it is initially a wall cell. \n\n A period (. ) indicates that cell $(i, j)$ is not painted and so it is a floor cell. \n\nHere you can assume that $j$ will be one of $1,4,7, \\ldots, 3 M + 1$ if and only if that character is a period. \nThe end of the input is indicated by a line with a single zero.\nTask Output: For each dataset, output $-1$ if you cannot achieve the objective. Otherwise, output the set of switches you push in order to achieve the objective, in the following format: \n$n$ $s_1$ $s_2$ . . . $s_n$Here, $n$ is the number of switches you push and $s_1, s_2, \\ldots, s_n$ are uppercase letters corresponding to switches you push, where the $x$-th uppercase letter denotes switch $x$. These uppercase letters $s_1, s_2, \\ldots, s_n$ must be distinct, while the order of them does not matter. Note that it is allowed to output $n = 0$ (with no following uppercase letters) if you do not have to push any switches. See the sample output for clarification. \nIf there are multiple solutions, output any one of them.\nTask Samples: input: 3\n.aa.cA.Cc.\n.bb.Bb.AC.\n.cc.ac.Ab.\n1\n.Xx.\n.Yy.\n.Zz.\n6\n.Aj.fA.aW.zA.Jf.Gz.\n.gW.GW.Fw.ZJ.AG.JW.\n.bZ.jZ.Ga.Fj.gF.Za.\n9\n.ab.gh.mn.st.yz.EF.KL.QR.WA.\n.cd.ij.op.uv.AB.GH.MN.ST.XB.\n.ef.kl.qr.wx.CD.IJ.OP.UV.yz.\n2\n.AC.Mo.\n.IC.PC.\n.oA.CM.\n20\n.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.qb.\n.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.\n.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.qb.\n0\n output: 3 B C E\n-1\n3 J A G\n10 A B G H M N S T Y Z\n0\n2 Q B\n\n" }, { "title": "", "content": "We can describe detailed direction by repeating the directional names: north, south, east and west. For example, northwest is the direction halfway between north and west, and northnorthwest is between north and northwest. \nIn this problem, we describe more detailed direction between north and west as follows.\n\"north\" means $0$ degrees.\n\n\"west\" means $90$ degrees.\n\nIf the direction $dir$ means $a$ degrees and the sum of the occurrences of \"north\" and \"west\" in $dir$ is $n$ ($>=$ 1),\n\"north\"$dir$ (the concatenation of \"north\" and $dir$) means $a - \\frac{90}{2^n}$ degrees and \"west\"$dir$ means $a + \\frac{90}{2^n}$ degrees.\n\nYour task is to calculate the angle in degrees described by the given direction.", "constraint": "", "input": "The input contains several datasets. The number of datasets does not exceed $100$. \nEach dataset is described by a single line that contains a string denoting a direction.\nYou may assume the given string can be obtained by concatenating some \"north\" and \"west\",\nthe sum of the occurrences of \"north\" and \"west\" in the given string is between $1$ and $20$, inclusive,\nand the angle denoted by the given direction is between $0$ and $90$, inclusive.\nThe final dataset is followed by a single line containing only a single \"#\".", "output": "For each dataset, print an integer if the angle described by the given direction can be represented as an integer, otherwise print it as an irreducible fraction. Follow the format of the sample output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: north\nwest\nnorthwest\nnorthnorthwest\nwestwestwestnorth\n#\n output: 0\n90\n45\n45/2\n315/4"], "Pid": "p01701", "ProblemText": "Task Description: We can describe detailed direction by repeating the directional names: north, south, east and west. For example, northwest is the direction halfway between north and west, and northnorthwest is between north and northwest. \nIn this problem, we describe more detailed direction between north and west as follows.\n\"north\" means $0$ degrees.\n\n\"west\" means $90$ degrees.\n\nIf the direction $dir$ means $a$ degrees and the sum of the occurrences of \"north\" and \"west\" in $dir$ is $n$ ($>=$ 1),\n\"north\"$dir$ (the concatenation of \"north\" and $dir$) means $a - \\frac{90}{2^n}$ degrees and \"west\"$dir$ means $a + \\frac{90}{2^n}$ degrees.\n\nYour task is to calculate the angle in degrees described by the given direction.\nTask Input: The input contains several datasets. The number of datasets does not exceed $100$. \nEach dataset is described by a single line that contains a string denoting a direction.\nYou may assume the given string can be obtained by concatenating some \"north\" and \"west\",\nthe sum of the occurrences of \"north\" and \"west\" in the given string is between $1$ and $20$, inclusive,\nand the angle denoted by the given direction is between $0$ and $90$, inclusive.\nThe final dataset is followed by a single line containing only a single \"#\".\nTask Output: For each dataset, print an integer if the angle described by the given direction can be represented as an integer, otherwise print it as an irreducible fraction. Follow the format of the sample output.\nTask Samples: input: north\nwest\nnorthwest\nnorthnorthwest\nwestwestwestnorth\n#\n output: 0\n90\n45\n45/2\n315/4\n\n" }, { "title": "", "content": "In the headquarter building of ICPC (International Company of Plugs & Connectors), there are $M$ light bulbs and they are controlled by $N$ switches.\nEach light bulb can be turned on or off by exactly one switch.\nEach switch may control multiple light bulbs.\nWhen you operate a switch, all the light bulbs controlled by the switch change their states.\nYou lost the table that recorded the correspondence between the switches and the light bulbs, and want to restore it.\nYou decided to restore the correspondence by the following procedure.\nAt first, every switch is off and every light bulb is off.\n\nYou operate some switches represented by $S_1$.\n\nYou check the states of the light bulbs represented by $B_1$.\n\nYou operate some switches represented by $S_2$.\n\nYou check the states of the light bulbs represented by $B_2$.\n\n. . .\n\nYou operate some switches represented by $S_Q$.\n\nYou check the states of the light bulbs represented by $B_Q$.\n\nAfter you operate some switches and check the states of the light bulbs, the states of the switches and the light bulbs are kept for next operations.\nCan you restore the correspondence between the switches and the light bulbs using the information about the switches you have operated and the states of the light bulbs you have checked?", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of dataset is no more than $50$ and the file size is no more than $10\\mathrm{MB}$.\nEach dataset is formatted as follows.\n
    $N$ $M$ $Q$$S_1$ $B_1$: : $S_Q$ $B_Q$The first line of each dataset contains three integers $N$ ($1 <= N <= 36$), $M$ ($1 <= M <= 1{, }000$), $Q$ ($0 <= Q <= 1{, }000$), which denote the number of switches, the number of light bulbs and the number of operations respectively.\nThe following $Q$ lines describe the information about the switches you have operated and the states of the light bulbs you have checked.\nThe $i$-th of them contains two strings $S_i$ and $B_i$ of lengths $N$ and $M$ respectively.\nEach $S_i$ denotes the set of the switches you have operated: $S_{ij}$ is either $0$ or $1$, which denotes the $j$-th switch is not operated or operated respectively.\nEach $B_i$ denotes the states of the light bulbs: $B_{ij}$ is either $0$ or $1$, which denotes the $j$-th light bulb is off or on respectively.\nYou can assume that there exists a correspondence between the switches and the light bulbs which is consistent with the given information.\nThe end of input is indicated by a line containing three zeros.", "output": "For each dataset, output the correspondence between the switches and the light bulbs consisting of $M$ numbers written in base-$36$.\nIn the base-$36$ system for this problem, the values $0$-$9$ and $10$-$35$ are represented by the characters '0'-'9' and 'A'-'Z' respectively.\nThe $i$-th character of the correspondence means the number of the switch controlling the $i$-th light bulb.\nIf you cannot determine which switch controls the $i$-th light bulb, output '? ' as the $i$-th character instead of the number of a switch.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 10 3\n000 0000000000\n110 0000001111\n101 1111111100\n2 2 0\n1 1 0\n2 1 1\n01 1\n11 11 10\n10000000000 10000000000\n11000000000 01000000000\n01100000000 00100000000\n00110000000 00010000000\n00011000000 00001000000\n00001100000 00000100000\n00000110000 00000010000\n00000011000 00000001000\n00000001100 00000000100\n00000000110 00000000010\n0 0 0\n output: 2222221100\n??\n0\n1\n0123456789A"], "Pid": "p01702", "ProblemText": "Task Description: In the headquarter building of ICPC (International Company of Plugs & Connectors), there are $M$ light bulbs and they are controlled by $N$ switches.\nEach light bulb can be turned on or off by exactly one switch.\nEach switch may control multiple light bulbs.\nWhen you operate a switch, all the light bulbs controlled by the switch change their states.\nYou lost the table that recorded the correspondence between the switches and the light bulbs, and want to restore it.\nYou decided to restore the correspondence by the following procedure.\nAt first, every switch is off and every light bulb is off.\n\nYou operate some switches represented by $S_1$.\n\nYou check the states of the light bulbs represented by $B_1$.\n\nYou operate some switches represented by $S_2$.\n\nYou check the states of the light bulbs represented by $B_2$.\n\n. . .\n\nYou operate some switches represented by $S_Q$.\n\nYou check the states of the light bulbs represented by $B_Q$.\n\nAfter you operate some switches and check the states of the light bulbs, the states of the switches and the light bulbs are kept for next operations.\nCan you restore the correspondence between the switches and the light bulbs using the information about the switches you have operated and the states of the light bulbs you have checked?\nTask Input: The input consists of multiple datasets.\nThe number of dataset is no more than $50$ and the file size is no more than $10\\mathrm{MB}$.\nEach dataset is formatted as follows.\n
    $N$ $M$ $Q$$S_1$ $B_1$: : $S_Q$ $B_Q$The first line of each dataset contains three integers $N$ ($1 <= N <= 36$), $M$ ($1 <= M <= 1{, }000$), $Q$ ($0 <= Q <= 1{, }000$), which denote the number of switches, the number of light bulbs and the number of operations respectively.\nThe following $Q$ lines describe the information about the switches you have operated and the states of the light bulbs you have checked.\nThe $i$-th of them contains two strings $S_i$ and $B_i$ of lengths $N$ and $M$ respectively.\nEach $S_i$ denotes the set of the switches you have operated: $S_{ij}$ is either $0$ or $1$, which denotes the $j$-th switch is not operated or operated respectively.\nEach $B_i$ denotes the states of the light bulbs: $B_{ij}$ is either $0$ or $1$, which denotes the $j$-th light bulb is off or on respectively.\nYou can assume that there exists a correspondence between the switches and the light bulbs which is consistent with the given information.\nThe end of input is indicated by a line containing three zeros.\nTask Output: For each dataset, output the correspondence between the switches and the light bulbs consisting of $M$ numbers written in base-$36$.\nIn the base-$36$ system for this problem, the values $0$-$9$ and $10$-$35$ are represented by the characters '0'-'9' and 'A'-'Z' respectively.\nThe $i$-th character of the correspondence means the number of the switch controlling the $i$-th light bulb.\nIf you cannot determine which switch controls the $i$-th light bulb, output '? ' as the $i$-th character instead of the number of a switch.\nTask Samples: input: 3 10 3\n000 0000000000\n110 0000001111\n101 1111111100\n2 2 0\n1 1 0\n2 1 1\n01 1\n11 11 10\n10000000000 10000000000\n11000000000 01000000000\n01100000000 00100000000\n00110000000 00010000000\n00011000000 00001000000\n00001100000 00000100000\n00000110000 00000010000\n00000011000 00000001000\n00000001100 00000000100\n00000000110 00000000010\n0 0 0\n output: 2222221100\n??\n0\n1\n0123456789A\n\n" }, { "title": "", "content": "Infinite Chronicle -Princess Castle- is a simple role-playing game. \nThere are $n + 1$ checkpoints, numbered $0$ through $n$, \nand for each $i = 1,2, \\ldots, n$, there is a unique one-way road running from checkpoint $i - 1$ to $i$. \nThe game starts at checkpoint $0$ and ends at checkpoint $n$. \nEvil monsters will appear on the roads and the hero will have battles against them. \nYou can save your game progress at any checkpoint; if you lose a battle, you can restart the game from the checkpoint where you have saved for the last time. \nAt the beginning of the game, the progress is automatically saved at checkpoint $0$ with no time. \nRabbit Hanako is fond of this game and now interested in speedrunning. \nAlthough Hanako is an expert of the game, she cannot always win the battles because of random factors. \nFor each $i$, she estimated the probability $p_i$ to win all the battles along the road from checkpoint $i - 1$ to $i$. \nEverytime she starts at checkpoint $i - 1$, after exactly one miniutes, \nshe will be at checkpoint $i$ with probability $p_i$ and where she saved for the last time with probability $1 - p_i$. \nWhat puzzles Hanako is that it also takes one minute (! ) to save your progress at a checkpoint, \nso it might be a good idea to pass some checkpoints without saving in order to proceed quickly. \nThe task is to compute the minimum possible expected time needed to complete the game.", "constraint": "", "input": "The input consists of multiple datasets. The number of datasets is no more than $50$. \nEach dataset has two lines: the first line contains an integer $n$ ($1 <= n <= 10^5$), representing the number of roads, \nand the second line contains $n$ numbers $p_1, p_2, \\ldots, p_n$ ($0 < p_i <= 1$), representing the winning probabilities.\nEach $p_i$ has exactly two digits after the decimal point.\nThe end of input is denoted as a line containing only a single zero.", "output": "For each dataset, display the minimum expected time in minutes with a relative error of at most $10^{-8}$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0.50 0.40\n2\n0.70 0.60\n4\n0.99 1.00 1.00 0.01\n0\n output: 5.5000000000\n4.0476190476\n104.0101010101"], "Pid": "p01703", "ProblemText": "Task Description: Infinite Chronicle -Princess Castle- is a simple role-playing game. \nThere are $n + 1$ checkpoints, numbered $0$ through $n$, \nand for each $i = 1,2, \\ldots, n$, there is a unique one-way road running from checkpoint $i - 1$ to $i$. \nThe game starts at checkpoint $0$ and ends at checkpoint $n$. \nEvil monsters will appear on the roads and the hero will have battles against them. \nYou can save your game progress at any checkpoint; if you lose a battle, you can restart the game from the checkpoint where you have saved for the last time. \nAt the beginning of the game, the progress is automatically saved at checkpoint $0$ with no time. \nRabbit Hanako is fond of this game and now interested in speedrunning. \nAlthough Hanako is an expert of the game, she cannot always win the battles because of random factors. \nFor each $i$, she estimated the probability $p_i$ to win all the battles along the road from checkpoint $i - 1$ to $i$. \nEverytime she starts at checkpoint $i - 1$, after exactly one miniutes, \nshe will be at checkpoint $i$ with probability $p_i$ and where she saved for the last time with probability $1 - p_i$. \nWhat puzzles Hanako is that it also takes one minute (! ) to save your progress at a checkpoint, \nso it might be a good idea to pass some checkpoints without saving in order to proceed quickly. \nThe task is to compute the minimum possible expected time needed to complete the game.\nTask Input: The input consists of multiple datasets. The number of datasets is no more than $50$. \nEach dataset has two lines: the first line contains an integer $n$ ($1 <= n <= 10^5$), representing the number of roads, \nand the second line contains $n$ numbers $p_1, p_2, \\ldots, p_n$ ($0 < p_i <= 1$), representing the winning probabilities.\nEach $p_i$ has exactly two digits after the decimal point.\nThe end of input is denoted as a line containing only a single zero.\nTask Output: For each dataset, display the minimum expected time in minutes with a relative error of at most $10^{-8}$ in a line.\nTask Samples: input: 2\n0.50 0.40\n2\n0.70 0.60\n4\n0.99 1.00 1.00 0.01\n0\n output: 5.5000000000\n4.0476190476\n104.0101010101\n\n" }, { "title": "", "content": "We have planted $N$ flower seeds, all of which come into different flowers.\nWe want to make all the flowers come out together.\nEach plant has a value called vitality, which is initially zero.\nWatering and spreading fertilizers cause changes on it, and the $i$-th plant will come into flower if its vitality is equal to or greater than $\\mathit{th}_i$.\nNote that $\\mathit{th}_i$ may be negative because some flowers require no additional nutrition.\nWatering effects on all the plants.\nWatering the plants with $W$ liters of water changes the vitality of the $i$-th plant by $W * \\mathit{vw}_i$ for all $i$ ($1 <= i <= n$), and costs $W * \\mathit{pw}$ yen, where $W$ need not be an integer.\n$\\mathit{vw}_i$ may be negative because some flowers hate water.\nWe have $N$ kinds of fertilizers, and the $i$-th fertilizer effects only on the $i$-th plant.\nSpreading $F_i$ kilograms of the $i$-th fertilizer changes the vitality of the $i$-th plant by $F_i * \\mathit{vf}_i$, and costs $F_i * \\mathit{pf}_i$ yen, where $F_i$ need not be an integer as well.\nEach fertilizer is specially made for the corresponding plant, therefore $\\mathit{vf}_i$ is guaranteed to be positive.\nOf course, we also want to minimize the cost.\nFormally, our purpose is described as \"to minimize $W * \\mathit{pw} + \\sum_{i=1}^{N}(F_i * \\mathit{pf}_i)$ under $W * \\mathit{vw}_i + F_i * \\mathit{vf}_i >= \\mathit{th}_i$, $W >= 0$, and $F_i >= 0$ for all $i$ ($1 <= i <= N$)\".\nYour task is to calculate the minimum cost.", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of datasets does not exceed $100$, and the data size of the input does not exceed $20\\mathrm{MB}$.\nEach dataset is formatted as follows.\n
    $N$$\\mathit{pw}$$\\mathit{vw}_1$ $\\mathit{pf}_1$ $\\mathit{vf}_1$ $\\mathit{th}_1$: : $\\mathit{vw}_N$ $\\mathit{pf}_N$ $\\mathit{vf}_N$ $\\mathit{th}_N$The first line of a dataset contains a single integer $N$, number of flower seeds.\nThe second line of a dataset contains a single integer $\\mathit{pw}$, cost of watering one liter.\nEach of the following $N$ lines describes a flower. The $i$-th line contains four integers, $\\mathit{vw}_i$, $\\mathit{pf}_i$, $\\mathit{vf}_i$, and $\\mathit{th}_i$, separated by a space.\nYou can assume that $1 <= N <= 10^5$, $1 <= \\mathit{pw} <= 100$, $-100 <= \\mathit{vw}_i <= 100$, $1 <= \\mathit{pf}_i <= 100$, $1 <= \\mathit{vf}_i <= 100$, and $-100 <= \\mathit{th}_i <= 100$.\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output a line containing the minimum cost to make all the flowers come out.\nThe output must have an absolute or relative error at most $10^{-4}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10\n4 3 4 10\n5 4 5 20\n6 5 6 30\n3\n7\n-4 3 4 -10\n5 4 5 20\n6 5 6 30\n3\n1\n-4 3 4 -10\n-5 4 5 -20\n6 5 6 30\n3\n10\n-4 3 4 -10\n-5 4 5 -20\n-6 5 6 -30\n0\n output: 43.5\n36\n13.5\n0"], "Pid": "p01704", "ProblemText": "Task Description: We have planted $N$ flower seeds, all of which come into different flowers.\nWe want to make all the flowers come out together.\nEach plant has a value called vitality, which is initially zero.\nWatering and spreading fertilizers cause changes on it, and the $i$-th plant will come into flower if its vitality is equal to or greater than $\\mathit{th}_i$.\nNote that $\\mathit{th}_i$ may be negative because some flowers require no additional nutrition.\nWatering effects on all the plants.\nWatering the plants with $W$ liters of water changes the vitality of the $i$-th plant by $W * \\mathit{vw}_i$ for all $i$ ($1 <= i <= n$), and costs $W * \\mathit{pw}$ yen, where $W$ need not be an integer.\n$\\mathit{vw}_i$ may be negative because some flowers hate water.\nWe have $N$ kinds of fertilizers, and the $i$-th fertilizer effects only on the $i$-th plant.\nSpreading $F_i$ kilograms of the $i$-th fertilizer changes the vitality of the $i$-th plant by $F_i * \\mathit{vf}_i$, and costs $F_i * \\mathit{pf}_i$ yen, where $F_i$ need not be an integer as well.\nEach fertilizer is specially made for the corresponding plant, therefore $\\mathit{vf}_i$ is guaranteed to be positive.\nOf course, we also want to minimize the cost.\nFormally, our purpose is described as \"to minimize $W * \\mathit{pw} + \\sum_{i=1}^{N}(F_i * \\mathit{pf}_i)$ under $W * \\mathit{vw}_i + F_i * \\mathit{vf}_i >= \\mathit{th}_i$, $W >= 0$, and $F_i >= 0$ for all $i$ ($1 <= i <= N$)\".\nYour task is to calculate the minimum cost.\nTask Input: The input consists of multiple datasets.\nThe number of datasets does not exceed $100$, and the data size of the input does not exceed $20\\mathrm{MB}$.\nEach dataset is formatted as follows.\n
    $N$$\\mathit{pw}$$\\mathit{vw}_1$ $\\mathit{pf}_1$ $\\mathit{vf}_1$ $\\mathit{th}_1$: : $\\mathit{vw}_N$ $\\mathit{pf}_N$ $\\mathit{vf}_N$ $\\mathit{th}_N$The first line of a dataset contains a single integer $N$, number of flower seeds.\nThe second line of a dataset contains a single integer $\\mathit{pw}$, cost of watering one liter.\nEach of the following $N$ lines describes a flower. The $i$-th line contains four integers, $\\mathit{vw}_i$, $\\mathit{pf}_i$, $\\mathit{vf}_i$, and $\\mathit{th}_i$, separated by a space.\nYou can assume that $1 <= N <= 10^5$, $1 <= \\mathit{pw} <= 100$, $-100 <= \\mathit{vw}_i <= 100$, $1 <= \\mathit{pf}_i <= 100$, $1 <= \\mathit{vf}_i <= 100$, and $-100 <= \\mathit{th}_i <= 100$.\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output a line containing the minimum cost to make all the flowers come out.\nThe output must have an absolute or relative error at most $10^{-4}$.\nTask Samples: input: 3\n10\n4 3 4 10\n5 4 5 20\n6 5 6 30\n3\n7\n-4 3 4 -10\n5 4 5 20\n6 5 6 30\n3\n1\n-4 3 4 -10\n-5 4 5 -20\n6 5 6 30\n3\n10\n-4 3 4 -10\n-5 4 5 -20\n-6 5 6 -30\n0\n output: 43.5\n36\n13.5\n0\n\n" }, { "title": "", "content": "Circles Island is known for its mysterious shape:\nit is a completely flat island with its shape being a union of circles whose centers are on the $x$-axis and their inside regions.\nThe King of Circles Island plans to build a large square on Circles Island in order to celebrate the fiftieth anniversary of his accession.\nThe King wants to make the square as large as possible.\nThe whole area of the square must be on the surface of Circles Island, but any area of Circles Island can be used for the square.\nHe also requires that the shape of the square is square (of course! ) and at least one side of the square is parallel to the $x$-axis.\nYou, a minister of Circles Island, are now ordered to build the square.\nFirst, the King wants to know how large the square can be.\nYou are given the positions and radii of the circles that constitute Circles Island.\nAnswer the side length of the largest possible square.\n$N$ circles are given in an ascending order of their centers' $x$-coordinates.\nYou can assume that for all $i$ ($1 <= i <= N-1$), the $i$-th and $(i+1)$-st circles overlap each other.\nYou can also assume that no circles are completely overlapped by other circles.\n\n[fig. 1 : Shape of Circles Island and one of the largest possible squares for test case #1 of sample input]", "constraint": "", "input": "The input consists of multiple datasets. The number of datasets does not exceed $30$.\nEach dataset is formatted as follows.\n
    $N$$X_1$ $R_1$: : $X_N$ $R_N$The first line of a dataset contains a single integer $N$ ($1 <= N <= 50{, }000$), the number of circles that constitute Circles Island.\nEach of the following $N$ lines describes a circle.\nThe $(i+1)$-st line contains two integers $X_i$ ($-100{, }000 <= X_i <= 100{, }000$) and $R_i$ ($1 <= R_i <= 100{, }000$).\n$X_i$ denotes the $x$-coordinate of the center of the $i$-th circle and $R_i$ denotes the radius of the $i$-th circle.\nThe $y$-coordinate of every circle is $0$, that is, the center of the $i$-th circle is at ($X_i$, $0$).\nYou can assume the followings.\n For all $i$ ($1 <= i <= N-1$), $X_i$ is strictly less than $X_{i+1}$.\n\n For all $i$ ($1 <= i <= N-1$), the $i$-th circle and the $(i+1)$-st circle have at least one common point ($X_{i+1} - X_i <= R_i + R_{i+1}$).\n\n Every circle has at least one point that is not inside or on the boundary of any other circles.\n\nThe end of the input is indicated by a line containing a zero.", "output": "For each dataset, output a line containing the side length of the square with the largest area.\nThe output must have an absolute or relative error at most $10^{-4}$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n0 8\n10 8\n2\n0 7\n10 7\n0\n output: 12.489995996796796\n9.899494936611665"], "Pid": "p01705", "ProblemText": "Task Description: Circles Island is known for its mysterious shape:\nit is a completely flat island with its shape being a union of circles whose centers are on the $x$-axis and their inside regions.\nThe King of Circles Island plans to build a large square on Circles Island in order to celebrate the fiftieth anniversary of his accession.\nThe King wants to make the square as large as possible.\nThe whole area of the square must be on the surface of Circles Island, but any area of Circles Island can be used for the square.\nHe also requires that the shape of the square is square (of course! ) and at least one side of the square is parallel to the $x$-axis.\nYou, a minister of Circles Island, are now ordered to build the square.\nFirst, the King wants to know how large the square can be.\nYou are given the positions and radii of the circles that constitute Circles Island.\nAnswer the side length of the largest possible square.\n$N$ circles are given in an ascending order of their centers' $x$-coordinates.\nYou can assume that for all $i$ ($1 <= i <= N-1$), the $i$-th and $(i+1)$-st circles overlap each other.\nYou can also assume that no circles are completely overlapped by other circles.\n\n[fig. 1 : Shape of Circles Island and one of the largest possible squares for test case #1 of sample input]\nTask Input: The input consists of multiple datasets. The number of datasets does not exceed $30$.\nEach dataset is formatted as follows.\n
    $N$$X_1$ $R_1$: : $X_N$ $R_N$The first line of a dataset contains a single integer $N$ ($1 <= N <= 50{, }000$), the number of circles that constitute Circles Island.\nEach of the following $N$ lines describes a circle.\nThe $(i+1)$-st line contains two integers $X_i$ ($-100{, }000 <= X_i <= 100{, }000$) and $R_i$ ($1 <= R_i <= 100{, }000$).\n$X_i$ denotes the $x$-coordinate of the center of the $i$-th circle and $R_i$ denotes the radius of the $i$-th circle.\nThe $y$-coordinate of every circle is $0$, that is, the center of the $i$-th circle is at ($X_i$, $0$).\nYou can assume the followings.\n For all $i$ ($1 <= i <= N-1$), $X_i$ is strictly less than $X_{i+1}$.\n\n For all $i$ ($1 <= i <= N-1$), the $i$-th circle and the $(i+1)$-st circle have at least one common point ($X_{i+1} - X_i <= R_i + R_{i+1}$).\n\n Every circle has at least one point that is not inside or on the boundary of any other circles.\n\nThe end of the input is indicated by a line containing a zero.\nTask Output: For each dataset, output a line containing the side length of the square with the largest area.\nThe output must have an absolute or relative error at most $10^{-4}$.\nTask Samples: input: 2\n0 8\n10 8\n2\n0 7\n10 7\n0\n output: 12.489995996796796\n9.899494936611665\n\n" }, { "title": "", "content": "JAG Kingdom is a strange kingdom such that its $N$ cities are connected only by one-way roads.\nThe $N$ cities are numbered $1$ through $N$.\nICPC (International Characteristic Product Corporation) transports its products from the factory at the city $S$ to the storehouse at the city $T$ in JAG Kingdom every day.\nFor efficiency, ICPC uses multiple trucks at once.\nEach truck starts from $S$ and reaches $T$ on the one-way road network, passing through some cities (or directly).\nIn order to reduce risks of traffic jams and accidents, no pair of trucks takes the same road.\nNow, ICPC wants to improve the efficiency of daily transports, while ICPC operates daily transports by as many trucks as possible under the above constraint.\nJAG Kingdom, whose finances are massively affected by ICPC, considers to change the direction of one-way roads in order to increase the number of trucks for daily transports of ICPC.\nBecause reversal of many roads causes confusion, JAG Kingdom decides to reverse at most a single road.\nIf there is no road such that reversal of the road can improve the transport efficiency, JAG Kingdom need not reverse any roads.\nCheck whether reversal of a single road can improve the current maximum number of trucks for daily transports.\nAnd if so, calculate the maximum number of trucks which take disjoint sets of roads when a one-way road can be reversed, and the number of roads which can be chosen as the road to be reversed to realize the maximum.", "constraint": "", "input": "The input consists of multiple datasets. The number of dataset is no more than $100$.\nEach dataset is formatted as follows.\n
    $N$ $M$ $S$ $T$$a_1$ $b_1$$a_2$ $b_2$: : $a_M$ $b_M$The first line of each dataset contains four integers:\nthe number of cities $N$ ($2 <= N <= 1{, }000$), the number of roads $M$ ($1 <= M <= 10{, }000$), the city with the factory $S$ and the city with the storehouse $T$ ($1 <= S, T <= N$, $S \\neq T$).\nThe following $M$ lines describe the information of the roads.\nThe $i$-th line of them contains two integers $a_i$ and $b_i$ ($1 <= a_i, b_i <= N$, $a_i \\neq b_i$), meaning that the $i$-th road is directed from $a_i$ to $b_i$.\nThe end of input is indicated by a line containing four zeros.", "output": "For each dataset, output two integers separated by a single space in a line as follows:\nIf reversal of a single road improves the current maximum number of trucks for daily transports, the first output integer is the new maximum after reversal of a road, and the second output integer is the number of roads which can be chosen as the road to be reversed to realize the new maximum.\nOtherwise, i. e. if the current maximum cannot be increased by any reversal of a road, the first output integer is the current maximum and the second output integer is $0$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4 1 4\n1 2\n3 1\n4 2\n3 4\n7 8 1 7\n1 2\n1 3\n2 4\n3 4\n4 5\n4 6\n5 7\n7 6\n6 4 5 2\n1 2\n1 3\n4 5\n5 6\n10 21 9 10\n9 1\n9 2\n9 3\n9 4\n10 1\n10 2\n10 3\n10 4\n1 5\n2 5\n2 6\n3 6\n3 7\n4 7\n4 8\n1 8\n5 10\n6 10\n7 10\n10 8\n10 9\n2 15 1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n0 0 0 0\n output: 1 2\n2 1\n0 0\n4 6\n15 0"], "Pid": "p01706", "ProblemText": "Task Description: JAG Kingdom is a strange kingdom such that its $N$ cities are connected only by one-way roads.\nThe $N$ cities are numbered $1$ through $N$.\nICPC (International Characteristic Product Corporation) transports its products from the factory at the city $S$ to the storehouse at the city $T$ in JAG Kingdom every day.\nFor efficiency, ICPC uses multiple trucks at once.\nEach truck starts from $S$ and reaches $T$ on the one-way road network, passing through some cities (or directly).\nIn order to reduce risks of traffic jams and accidents, no pair of trucks takes the same road.\nNow, ICPC wants to improve the efficiency of daily transports, while ICPC operates daily transports by as many trucks as possible under the above constraint.\nJAG Kingdom, whose finances are massively affected by ICPC, considers to change the direction of one-way roads in order to increase the number of trucks for daily transports of ICPC.\nBecause reversal of many roads causes confusion, JAG Kingdom decides to reverse at most a single road.\nIf there is no road such that reversal of the road can improve the transport efficiency, JAG Kingdom need not reverse any roads.\nCheck whether reversal of a single road can improve the current maximum number of trucks for daily transports.\nAnd if so, calculate the maximum number of trucks which take disjoint sets of roads when a one-way road can be reversed, and the number of roads which can be chosen as the road to be reversed to realize the maximum.\nTask Input: The input consists of multiple datasets. The number of dataset is no more than $100$.\nEach dataset is formatted as follows.\n
    $N$ $M$ $S$ $T$$a_1$ $b_1$$a_2$ $b_2$: : $a_M$ $b_M$The first line of each dataset contains four integers:\nthe number of cities $N$ ($2 <= N <= 1{, }000$), the number of roads $M$ ($1 <= M <= 10{, }000$), the city with the factory $S$ and the city with the storehouse $T$ ($1 <= S, T <= N$, $S \\neq T$).\nThe following $M$ lines describe the information of the roads.\nThe $i$-th line of them contains two integers $a_i$ and $b_i$ ($1 <= a_i, b_i <= N$, $a_i \\neq b_i$), meaning that the $i$-th road is directed from $a_i$ to $b_i$.\nThe end of input is indicated by a line containing four zeros.\nTask Output: For each dataset, output two integers separated by a single space in a line as follows:\nIf reversal of a single road improves the current maximum number of trucks for daily transports, the first output integer is the new maximum after reversal of a road, and the second output integer is the number of roads which can be chosen as the road to be reversed to realize the new maximum.\nOtherwise, i. e. if the current maximum cannot be increased by any reversal of a road, the first output integer is the current maximum and the second output integer is $0$.\nTask Samples: input: 4 4 1 4\n1 2\n3 1\n4 2\n3 4\n7 8 1 7\n1 2\n1 3\n2 4\n3 4\n4 5\n4 6\n5 7\n7 6\n6 4 5 2\n1 2\n1 3\n4 5\n5 6\n10 21 9 10\n9 1\n9 2\n9 3\n9 4\n10 1\n10 2\n10 3\n10 4\n1 5\n2 5\n2 6\n3 6\n3 7\n4 7\n4 8\n1 8\n5 10\n6 10\n7 10\n10 8\n10 9\n2 15 1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n0 0 0 0\n output: 1 2\n2 1\n0 0\n4 6\n15 0\n\n" }, { "title": "", "content": "One day, my grandmas left $N$ cookies.\nMy elder sister and I were going to eat them immediately, but there was the instruction.\nIt said\n Cookies will go bad; you should eat all of them within $D$ days.\n\n Be careful about overeating; you should eat strictly less than $X$ cookies in a day.\n\nMy sister said \"How many ways are there to eat all of the cookies? Let's try counting! \"\nTwo ways are considered different if there exists a day such that the numbers of the cookies eaten on that day are different in the two ways.\nFor example, if $N$, $D$ and $X$ are $5$, $2$ and $5$ respectively, the number of the ways is $4$:\n Eating $1$ cookie on the first day and $4$ cookies on the second day.\n\n Eating $2$ cookies on the first day and $3$ cookies on the second day.\n\n Eating $3$ cookies on the first day and $2$ cookies on the second day.\n\n Eating $4$ cookies on the first day and $1$ cookie on the second day.\n\nI noticed the number of the ways would be very huge and my sister would die before counting it.\nTherefore, I tried to count it by a computer program to save the life of my sister.", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of datasets is no more than $100$.\nFor each dataset, three numbers $N$ ($1 <= N <= 2{, }000$), $D$ ($1 <= D <= 10^{12}$) and $X$ ($1 <= X <= 2{, }000$) are written in a line and separated by a space.\nThe end of input is denoted by a line that contains three zeros.", "output": "Print the number of the ways modulo $1{, }000{, }000{, }007$ in a line for each dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 5\n3 3 3\n5 4 5\n4 1 2\n1 5 1\n1250 50 50\n0 0 0\n output: 4\n7\n52\n0\n0\n563144298"], "Pid": "p01707", "ProblemText": "Task Description: One day, my grandmas left $N$ cookies.\nMy elder sister and I were going to eat them immediately, but there was the instruction.\nIt said\n Cookies will go bad; you should eat all of them within $D$ days.\n\n Be careful about overeating; you should eat strictly less than $X$ cookies in a day.\n\nMy sister said \"How many ways are there to eat all of the cookies? Let's try counting! \"\nTwo ways are considered different if there exists a day such that the numbers of the cookies eaten on that day are different in the two ways.\nFor example, if $N$, $D$ and $X$ are $5$, $2$ and $5$ respectively, the number of the ways is $4$:\n Eating $1$ cookie on the first day and $4$ cookies on the second day.\n\n Eating $2$ cookies on the first day and $3$ cookies on the second day.\n\n Eating $3$ cookies on the first day and $2$ cookies on the second day.\n\n Eating $4$ cookies on the first day and $1$ cookie on the second day.\n\nI noticed the number of the ways would be very huge and my sister would die before counting it.\nTherefore, I tried to count it by a computer program to save the life of my sister.\nTask Input: The input consists of multiple datasets.\nThe number of datasets is no more than $100$.\nFor each dataset, three numbers $N$ ($1 <= N <= 2{, }000$), $D$ ($1 <= D <= 10^{12}$) and $X$ ($1 <= X <= 2{, }000$) are written in a line and separated by a space.\nThe end of input is denoted by a line that contains three zeros.\nTask Output: Print the number of the ways modulo $1{, }000{, }000{, }007$ in a line for each dataset.\nTask Samples: input: 5 2 5\n3 3 3\n5 4 5\n4 1 2\n1 5 1\n1250 50 50\n0 0 0\n output: 4\n7\n52\n0\n0\n563144298\n\n" }, { "title": "", "content": "One day, you found an old scroll with strange texts on it.\nYou revealed that the text was actually an expression denoting the position of\ntreasure. The expression consists of following three operations:\n From two points, yield a line on which the points lie.\n\n From a point and a line, yield a point that is symmetric to the given point with respect to the line.\n\n From two lines, yield a point that is the intersection of the lines.\n\nThe syntax of the expression is denoted by following BNF:\n\n : : = \n \t : : = | \"@\" | \"@\" | \"@\" \n : : = \"(\" \", \" \")\" | \"(\" \")\"\n : : = | \"@\" \n : : = \"(\" \")\"\n : : = | | \n : : = | \n : : = \"-\" \n : : = | \n : : = \"0\"\n : : = \"1\" | \"2\" | \"3\" | \"4\" | \"5\" | \"6\" | \"7\" | \"8\" | \"9\"

    Each or denotes a point, whereas each or denotes a line. The former notion of $(X, Y)$ represents a point which has $X$ for $x$-coordinate and $Y$ for $y$-coordinate on the $2$-dimensional plane.\n\"@\" indicates the operations on two operands. Since each operation is distinguishable from others by its operands' types (i. e. a point or a line),\nall of these operations are denoted by the same character \"@\". \nNote that \"@\" is left-associative, as can be seen from the BNF.\nYour task is to determine where the treasure is placed.", "constraint": "", "input": "The input consists of multiple datasets. Each dataset is a single line which\ncontains an expression denoting the position of treasure.\nIt is guaranteed that each dataset satisfies the following conditions:\n The length of the string never exceeds $10^2$.\n\n If both operands of \"@\" are points, their distance is greater than $1$.\n\n If both operands of \"@\" are lines, they are never parallel.\n\n The absolute values of points' coordinates never exceed $10^2$ at any point of evaluation.\n\nYou can also assume that there are at most $100$ datasets.\nThe input ends with a line that contains only a single \"#\".", "output": "For each dataset, print the $X$ and $Y$ coordinates of the point, denoted by\nthe expression, in this order.\nThe output will be considered correct if its absolute or relative error is at most $10^{-2}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ((0,0)@(1,1))@((4,1)@(2,5))\n((0,0)@(3,1))@((1,-3)@(2,-1))\n(0,0)@(1,1)@(4,1)\n(0,0)@((1,1)@(4,1))\n(((0,0)@((10,20)@(((30,40))))))\n((0,0)@(3,1))@((1,-3)@(2,-1))@(100,-100)@(100,100)\n#\n output: 3.00000000 3.00000000\n3.00000000 1.00000000\n1.00000000 4.00000000\n0.00000000 2.00000000\n-10.00000000 10.00000000\n-99.83681795 -91.92248853"], "Pid": "p01708", "ProblemText": "Task Description: One day, you found an old scroll with strange texts on it.\nYou revealed that the text was actually an expression denoting the position of\ntreasure. The expression consists of following three operations:\n From two points, yield a line on which the points lie.\n\n From a point and a line, yield a point that is symmetric to the given point with respect to the line.\n\n From two lines, yield a point that is the intersection of the lines.\n\nThe syntax of the expression is denoted by following BNF:\n\n : : = \n \t : : = | \"@\" | \"@\" | \"@\" \n : : = \"(\" \", \" \")\" | \"(\" \")\"\n : : = | \"@\" \n : : = \"(\" \")\"\n : : = | | \n : : = | \n : : = \"-\" \n : : = | \n : : = \"0\"\n : : = \"1\" | \"2\" | \"3\" | \"4\" | \"5\" | \"6\" | \"7\" | \"8\" | \"9\"

    Each or denotes a point, whereas each or denotes a line. The former notion of $(X, Y)$ represents a point which has $X$ for $x$-coordinate and $Y$ for $y$-coordinate on the $2$-dimensional plane.\n\"@\" indicates the operations on two operands. Since each operation is distinguishable from others by its operands' types (i. e. a point or a line),\nall of these operations are denoted by the same character \"@\". \nNote that \"@\" is left-associative, as can be seen from the BNF.\nYour task is to determine where the treasure is placed.\nTask Input: The input consists of multiple datasets. Each dataset is a single line which\ncontains an expression denoting the position of treasure.\nIt is guaranteed that each dataset satisfies the following conditions:\n The length of the string never exceeds $10^2$.\n\n If both operands of \"@\" are points, their distance is greater than $1$.\n\n If both operands of \"@\" are lines, they are never parallel.\n\n The absolute values of points' coordinates never exceed $10^2$ at any point of evaluation.\n\nYou can also assume that there are at most $100$ datasets.\nThe input ends with a line that contains only a single \"#\".\nTask Output: For each dataset, print the $X$ and $Y$ coordinates of the point, denoted by\nthe expression, in this order.\nThe output will be considered correct if its absolute or relative error is at most $10^{-2}$.\nTask Samples: input: ((0,0)@(1,1))@((4,1)@(2,5))\n((0,0)@(3,1))@((1,-3)@(2,-1))\n(0,0)@(1,1)@(4,1)\n(0,0)@((1,1)@(4,1))\n(((0,0)@((10,20)@(((30,40))))))\n((0,0)@(3,1))@((1,-3)@(2,-1))@(100,-100)@(100,100)\n#\n output: 3.00000000 3.00000000\n3.00000000 1.00000000\n1.00000000 4.00000000\n0.00000000 2.00000000\n-10.00000000 10.00000000\n-99.83681795 -91.92248853\n\n" }, { "title": "", "content": "You have just transferred to another world, and got a map of this world.\nThere are several countries in this world.\nEach country has a connected territory,\nwhich is drawn on the map as a simple polygon consisting of its border segments in the $2$-dimensional plane.\nYou are strange to this world, so you would like to paint countries on the map to distinguish them.\nIf you paint adjacent countries with same color, it would be rather difficult to distinguish the countries.\nTherefore, you want to paint adjacent countries with different colors.\nHere, we define two countries are adjacent if their borders have at least one common segment whose length is strictly greater than $0$.\nNote that two countries are NOT considered adjacent if the borders only touch at points.\nBecause you don't have the currency of this world, it is hard for you to prepare many colors.\nWhat is the minimum number of colors to paint the map such that adjacent countries can be painted with different colors?", "constraint": "", "input": "The input consists of multiple datasets. The number of dataset is no more than $35$.\nEach dataset is formatted as follows.\n

    $n$$m_1$$x_{1,1}$ $y_{1,1}$ : : $x_{1, m_1}$ $y_{1, m_1}$: : $m_n$$x_{n, 1}$ $y_{n, 1}$: : $x_{n, m_n}$ $y_{n, m_n}$The first line of each dataset contains an integer $n$ ($1 <= n <= 35$),\nwhich denotes the number of countries in this world.\nThe rest of each dataset describes the information of $n$ polygons representing the countries.\nThe first line of the information of the $i$-th polygon contains an integer $m_i$ ($3 <= m_i <= 50$), which denotes the number of vertices.\nThe following $m_i$ lines describe the coordinates of the vertices in the counter-clockwise order.\nThe $j$-th line of them contains two integers $x_{i, j}$ and $y_{i, j}$ ($|x_{i, j}|, |y_{i, j}| <= 10^3$),\nwhich denote the coordinates of the $j$-th vertex of the $i$-th polygon.\nYou can assume the followings.\n Each polygon has an area greater than $0$.\n\n Two vertices of the same polygon have distinct coordinates.\n\n Two segments of the same polygon do not have any common points except that exactly two segments meet at each vertex.\n\n Two polygons have no common area.\n\nThe end of input is indicated by a line containing a single zero.", "output": "For each dataset, output the minimum number of colors to paint the map such that adjacent countries are painted with different colors in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n3\n0 0\n1 0\n0 1\n4\n4\n0 0\n10 0\n10 10\n0 10\n4\n10 0\n20 0\n20 10\n10 10\n4\n0 10\n10 10\n10 20\n0 20\n4\n10 10\n20 10\n20 20\n10 20\n3\n4\n-10 -10\n2 2\n10 10\n-11 7\n3\n-1 -1\n1 -1\n0 0\n3\n0 0\n3 -3\n20 20\n7\n4\n46 12\n52 12\n53 15\n45 15\n32\n67 1\n70 0\n73 1\n77 3\n79 5\n80 8\n77 8\n76 5\n74 4\n71 3\n70 3\n67 4\n65 6\n63 8\n62 14\n64 19\n66 21\n70 22\n75 21\n78 16\n80 16\n80 17\n79 20\n78 22\n74 24\n67 24\n63 22\n61 19\n60 15\n60 10\n62 5\n64 3\n5\n74 14\n80 14\n80 16\n78 16\n74 16\n19\n34 0\n37 0\n37 19\n36 22\n35 23\n32 24\n30 24\n27 24\n25 23\n23 20\n23 18\n23 15\n26 15\n26 18\n27 20\n29 21\n32 21\n34 20\n34 18\n4\n47 0\n50 0\n42 24\n39 24\n4\n79 20\n80 17\n80 22\n78 22\n4\n50 0\n58 24\n56 24\n49 3\n4\n10\n34 21\n34 14\n35 14\n35 19\n40 19\n40 20\n35 20\n35 22\n30 22\n30 21\n16\n20 24\n21 24\n21 33\n42 33\n42 20\n40 20\n40 19\n45 19\n45 5\n40 5\n40 4\n46 4\n46 20\n43 20\n43 34\n20 34\n10\n26 21\n26 14\n27 14\n27 21\n30 21\n30 22\n21 22\n21 24\n20 24\n20 21\n12\n34 8\n34 4\n40 4\n40 5\n35 5\n35 14\n34 14\n34 9\n27 9\n27 14\n26 14\n26 8\n0\n output: 1\n2\n3\n3\n4"], "Pid": "p01709", "ProblemText": "Task Description: You have just transferred to another world, and got a map of this world.\nThere are several countries in this world.\nEach country has a connected territory,\nwhich is drawn on the map as a simple polygon consisting of its border segments in the $2$-dimensional plane.\nYou are strange to this world, so you would like to paint countries on the map to distinguish them.\nIf you paint adjacent countries with same color, it would be rather difficult to distinguish the countries.\nTherefore, you want to paint adjacent countries with different colors.\nHere, we define two countries are adjacent if their borders have at least one common segment whose length is strictly greater than $0$.\nNote that two countries are NOT considered adjacent if the borders only touch at points.\nBecause you don't have the currency of this world, it is hard for you to prepare many colors.\nWhat is the minimum number of colors to paint the map such that adjacent countries can be painted with different colors?\nTask Input: The input consists of multiple datasets. The number of dataset is no more than $35$.\nEach dataset is formatted as follows.\n
    $n$$m_1$$x_{1,1}$ $y_{1,1}$ : : $x_{1, m_1}$ $y_{1, m_1}$: : $m_n$$x_{n, 1}$ $y_{n, 1}$: : $x_{n, m_n}$ $y_{n, m_n}$The first line of each dataset contains an integer $n$ ($1 <= n <= 35$),\nwhich denotes the number of countries in this world.\nThe rest of each dataset describes the information of $n$ polygons representing the countries.\nThe first line of the information of the $i$-th polygon contains an integer $m_i$ ($3 <= m_i <= 50$), which denotes the number of vertices.\nThe following $m_i$ lines describe the coordinates of the vertices in the counter-clockwise order.\nThe $j$-th line of them contains two integers $x_{i, j}$ and $y_{i, j}$ ($|x_{i, j}|, |y_{i, j}| <= 10^3$),\nwhich denote the coordinates of the $j$-th vertex of the $i$-th polygon.\nYou can assume the followings.\n Each polygon has an area greater than $0$.\n\n Two vertices of the same polygon have distinct coordinates.\n\n Two segments of the same polygon do not have any common points except that exactly two segments meet at each vertex.\n\n Two polygons have no common area.\n\nThe end of input is indicated by a line containing a single zero.\nTask Output: For each dataset, output the minimum number of colors to paint the map such that adjacent countries are painted with different colors in a line.\nTask Samples: input: 1\n3\n0 0\n1 0\n0 1\n4\n4\n0 0\n10 0\n10 10\n0 10\n4\n10 0\n20 0\n20 10\n10 10\n4\n0 10\n10 10\n10 20\n0 20\n4\n10 10\n20 10\n20 20\n10 20\n3\n4\n-10 -10\n2 2\n10 10\n-11 7\n3\n-1 -1\n1 -1\n0 0\n3\n0 0\n3 -3\n20 20\n7\n4\n46 12\n52 12\n53 15\n45 15\n32\n67 1\n70 0\n73 1\n77 3\n79 5\n80 8\n77 8\n76 5\n74 4\n71 3\n70 3\n67 4\n65 6\n63 8\n62 14\n64 19\n66 21\n70 22\n75 21\n78 16\n80 16\n80 17\n79 20\n78 22\n74 24\n67 24\n63 22\n61 19\n60 15\n60 10\n62 5\n64 3\n5\n74 14\n80 14\n80 16\n78 16\n74 16\n19\n34 0\n37 0\n37 19\n36 22\n35 23\n32 24\n30 24\n27 24\n25 23\n23 20\n23 18\n23 15\n26 15\n26 18\n27 20\n29 21\n32 21\n34 20\n34 18\n4\n47 0\n50 0\n42 24\n39 24\n4\n79 20\n80 17\n80 22\n78 22\n4\n50 0\n58 24\n56 24\n49 3\n4\n10\n34 21\n34 14\n35 14\n35 19\n40 19\n40 20\n35 20\n35 22\n30 22\n30 21\n16\n20 24\n21 24\n21 33\n42 33\n42 20\n40 20\n40 19\n45 19\n45 5\n40 5\n40 4\n46 4\n46 20\n43 20\n43 34\n20 34\n10\n26 21\n26 14\n27 14\n27 21\n30 21\n30 22\n21 22\n21 24\n20 24\n20 21\n12\n34 8\n34 4\n40 4\n40 5\n35 5\n35 14\n34 14\n34 9\n27 9\n27 14\n26 14\n26 8\n0\n output: 1\n2\n3\n3\n4\n\n" }, { "title": "", "content": "You want to compete in ICPC (Internet Contest of Point Collection).\nIn this contest, we move around in $N$ websites, numbered $1$ through $N$, within a time limit and collect points as many as possible.\nWe can start and end on any website.\nThere are $M$ links between the websites, and we can move between websites using these links.\nYou can assume that it doesn't take time to move between websites.\nThese links are directed and websites may have links to themselves.\nIn each website $i$, there is an advertisement and we can get $p_i$ point(s) by watching this advertisement in $t_i$ seconds.\nWhen we start on or move into a website, we can decide whether to watch the advertisement or not.\nBut we cannot watch the same advertisement more than once before using any link in the website, while we can watch it again if we have moved among websites and returned to the website using one or more links, including ones connecting a website to itself.\nAlso we cannot watch the advertisement in website $i$ more than $k_i$ times.\nYou want to win this contest by collecting as many points as you can.\nSo you decided to compute the maximum points that you can collect within $T$ seconds.", "constraint": "", "input": "The input consists of multiple datasets.\nThe number of dataset is no more than $60$.\nEach dataset is formatted as follows.\n
    $N$ $M$ $T$$p_1$ $t_1$ $k_1$: : $p_N$ $t_N$ $k_N$$a_1$ $b_1$: : $a_M$ $b_M$The first line of each dataset contains three integers $N$ ($1 <= N <= 100$), $M$ ($0 <= M <= 1{, }000$) and $T$ ($1 <= T <= 10{, }000$), which denote the number of websites, the number of links, and the time limit, respectively.\nAll the time given in the input is expressed in seconds.\nThe following $N$ lines describe the information of advertisements.\nThe $i$-th of them contains three integers $p_i$ ($1 <= p_i <= 10{, }000$), $t_i$ ($1 <= t_i <= 10{, }000$) and $k_i$ ($1 <= k_i <= 10{, }000$), which denote the points of the advertisement, the time required to watch the advertisement, and the maximum number of times you can watch the advertisement in website $i$, respectively.\nThe following $M$ lines describe the information of links.\nEach line contains two integers $a_i$ and $b_i$ ($1 <= a_i, b_i <= N$), which mean that we can move from website $a_i$ to website $b_i$ using a link.\nThe end of input is indicated by a line containing three zeros.", "output": "For each dataset, output the maximum points that you can collect within $T$ seconds.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 10\n4 3 1\n6 4 3\n3 2 4\n2 2 1\n8 5 3\n1 2\n2 3\n3 4\n4 5\n3 3 1000\n1000 1 100\n1 7 100\n10 9 100\n1 2\n2 3\n3 2\n1 0 5\n25 25 2\n1 0 25\n25 25 2\n5 5 100\n1 1 20\n1 1 20\n10 1 1\n10 1 1\n10 1 1\n1 2\n2 1\n3 4\n4 5\n5 3\n3 3 100\n70 20 10\n50 15 20\n90 10 10\n1 2\n2 2\n2 3\n0 0 0\n output: 15\n2014\n0\n25\n40\n390"], "Pid": "p01710", "ProblemText": "Task Description: You want to compete in ICPC (Internet Contest of Point Collection).\nIn this contest, we move around in $N$ websites, numbered $1$ through $N$, within a time limit and collect points as many as possible.\nWe can start and end on any website.\nThere are $M$ links between the websites, and we can move between websites using these links.\nYou can assume that it doesn't take time to move between websites.\nThese links are directed and websites may have links to themselves.\nIn each website $i$, there is an advertisement and we can get $p_i$ point(s) by watching this advertisement in $t_i$ seconds.\nWhen we start on or move into a website, we can decide whether to watch the advertisement or not.\nBut we cannot watch the same advertisement more than once before using any link in the website, while we can watch it again if we have moved among websites and returned to the website using one or more links, including ones connecting a website to itself.\nAlso we cannot watch the advertisement in website $i$ more than $k_i$ times.\nYou want to win this contest by collecting as many points as you can.\nSo you decided to compute the maximum points that you can collect within $T$ seconds.\nTask Input: The input consists of multiple datasets.\nThe number of dataset is no more than $60$.\nEach dataset is formatted as follows.\n
    $N$ $M$ $T$$p_1$ $t_1$ $k_1$: : $p_N$ $t_N$ $k_N$$a_1$ $b_1$: : $a_M$ $b_M$The first line of each dataset contains three integers $N$ ($1 <= N <= 100$), $M$ ($0 <= M <= 1{, }000$) and $T$ ($1 <= T <= 10{, }000$), which denote the number of websites, the number of links, and the time limit, respectively.\nAll the time given in the input is expressed in seconds.\nThe following $N$ lines describe the information of advertisements.\nThe $i$-th of them contains three integers $p_i$ ($1 <= p_i <= 10{, }000$), $t_i$ ($1 <= t_i <= 10{, }000$) and $k_i$ ($1 <= k_i <= 10{, }000$), which denote the points of the advertisement, the time required to watch the advertisement, and the maximum number of times you can watch the advertisement in website $i$, respectively.\nThe following $M$ lines describe the information of links.\nEach line contains two integers $a_i$ and $b_i$ ($1 <= a_i, b_i <= N$), which mean that we can move from website $a_i$ to website $b_i$ using a link.\nThe end of input is indicated by a line containing three zeros.\nTask Output: For each dataset, output the maximum points that you can collect within $T$ seconds.\nTask Samples: input: 5 4 10\n4 3 1\n6 4 3\n3 2 4\n2 2 1\n8 5 3\n1 2\n2 3\n3 4\n4 5\n3 3 1000\n1000 1 100\n1 7 100\n10 9 100\n1 2\n2 3\n3 2\n1 0 5\n25 25 2\n1 0 25\n25 25 2\n5 5 100\n1 1 20\n1 1 20\n10 1 1\n10 1 1\n10 1 1\n1 2\n2 1\n3 4\n4 5\n5 3\n3 3 100\n70 20 10\n50 15 20\n90 10 10\n1 2\n2 2\n2 3\n0 0 0\n output: 15\n2014\n0\n25\n40\n390\n\n" }, { "title": "", "content": "Let's consider operations on monochrome images that consist of hexagonal pixels, each of which is colored in either black or white. Because of the shape of pixels, each of them has exactly six neighbors (e. g. pixels that share an edge with it. )\n\"Filtering\" is an operation to determine the color of a pixel from the colors of itself and its six neighbors. Examples of filterings are shown below.\nExample 1: Color a pixel in white when all of its neighboring pixels are white. Otherwise the color will not change.\n\nPerforming this operation on all the pixels simultaneously results in \"noise canceling, \" which removes isolated black pixels.\nExample 2: Color a pixel in white when its all neighboring pixels are black. Otherwise the color will not change.\n\nPerforming this operation on all the pixels simultaneously results in \"edge detection, \" which leaves only the edges of filled areas.\nExample 3: Color a pixel with the color of the pixel just below it, ignoring any other neighbors.\n\nPerforming this operation on all the pixels simultaneously results in \"shifting up\" the whole image by one pixel.\nApplying some filter, such as \"noise canceling\" and \"edge detection, \" twice to any image yields the exactly same result as if they were applied only once.\nWe call such filters idempotent. The \"shifting up\" filter is not idempotent since every repeated application shifts the image up by one pixel.\nYour task is to determine whether the given filter is idempotent or not.", "constraint": "", "input": "The input consists of multiple datasets. The number of dataset is less than $100$.\nEach dataset is a string representing a filter and has the following format (without spaces between digits).\n
    $c_0c_1\\cdots{}c_{127}$$c_i$ is either '0' (represents black) or '1' (represents white), which indicates the output of the filter for a pixel when the binary representation of the pixel and its neighboring six pixels is $i$. \nThe mapping from the pixels to the bits is as following:\n\nand the binary representation $i$ is defined as $i = \\sum_{j=0}^6{\\mathit{bit}_j * 2^j}$,\nwhere $\\mathit{bit}_j$ is $0$ or $1$ if the corresponding pixel is in black or white, respectively.\nNote that the filter is applied on the center pixel, denoted as bit 3.\nThe input ends with a line that contains only a single \"#\".", "output": "For each dataset, print \"yes\" in a line if the given filter is idempotent, or \"no\" otherwise (quotes are for clarity).", "content_img": true, "lang": "en", "error": false, "samples": ["input: 00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111\n10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111\n01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101\n#\n output: yes\nyes\nno"], "Pid": "p01711", "ProblemText": "Task Description: Let's consider operations on monochrome images that consist of hexagonal pixels, each of which is colored in either black or white. Because of the shape of pixels, each of them has exactly six neighbors (e. g. pixels that share an edge with it. )\n\"Filtering\" is an operation to determine the color of a pixel from the colors of itself and its six neighbors. Examples of filterings are shown below.\nExample 1: Color a pixel in white when all of its neighboring pixels are white. Otherwise the color will not change.\n\nPerforming this operation on all the pixels simultaneously results in \"noise canceling, \" which removes isolated black pixels.\nExample 2: Color a pixel in white when its all neighboring pixels are black. Otherwise the color will not change.\n\nPerforming this operation on all the pixels simultaneously results in \"edge detection, \" which leaves only the edges of filled areas.\nExample 3: Color a pixel with the color of the pixel just below it, ignoring any other neighbors.\n\nPerforming this operation on all the pixels simultaneously results in \"shifting up\" the whole image by one pixel.\nApplying some filter, such as \"noise canceling\" and \"edge detection, \" twice to any image yields the exactly same result as if they were applied only once.\nWe call such filters idempotent. The \"shifting up\" filter is not idempotent since every repeated application shifts the image up by one pixel.\nYour task is to determine whether the given filter is idempotent or not.\nTask Input: The input consists of multiple datasets. The number of dataset is less than $100$.\nEach dataset is a string representing a filter and has the following format (without spaces between digits).\n
    $c_0c_1\\cdots{}c_{127}$$c_i$ is either '0' (represents black) or '1' (represents white), which indicates the output of the filter for a pixel when the binary representation of the pixel and its neighboring six pixels is $i$. \nThe mapping from the pixels to the bits is as following:\n\nand the binary representation $i$ is defined as $i = \\sum_{j=0}^6{\\mathit{bit}_j * 2^j}$,\nwhere $\\mathit{bit}_j$ is $0$ or $1$ if the corresponding pixel is in black or white, respectively.\nNote that the filter is applied on the center pixel, denoted as bit 3.\nThe input ends with a line that contains only a single \"#\".\nTask Output: For each dataset, print \"yes\" in a line if the given filter is idempotent, or \"no\" otherwise (quotes are for clarity).\nTask Samples: input: 00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111\n10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111\n01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101\n#\n output: yes\nyes\nno\n\n" }, { "title": "Input", "content": "Nathan O. Davis has been running an electronic bulletin board system named JAG-channel. He is now having hard time to add a new feature there --- threaded view.\nLike many other bulletin board systems, JAG-channel is thread-based. Here a thread (also called a topic) refers to a single conversation with a collection of posts. Each post can be an opening post, which initiates a new thread, or a reply to a previous post in an existing thread.\nThreaded view is a tree-like view that reflects the logical reply structure among the posts: each post forms a node of the tree and contains its replies as its subnodes in the chronological order (i. e. older replies precede newer ones). Note that a post along with its direct and indirect replies forms a subtree as a whole.\nLet us take an example. Suppose: a user made an opening post with a message hoge; another user replied to it with fuga; yet another user also replied to the opening post with piyo; someone else replied to the second post (i. e. fuga”) with foobar; and the fifth user replied to the same post with jagjag.\nThe tree of this thread would look like:\nhoge\n├─fuga\n│　├─foobar\n│　└─jagjag\n└─piyo\nFor easier implementation, Nathan is thinking of a simpler format: the depth of each post from the opening post is represented by dots. Each reply gets one more dot than its parent post. The tree of the above thread would then look like:\nhoge\n. fuga\n. . foobar\n. . jagjag\n. piyo\nYour task in this problem is to help Nathan by writing a program that prints a tree in the Nathan's format for the given posts in a single thread.", "constraint": "", "input": "Input contains a single dataset in the following format:\nn\nk_1\nM_1\nk_2\nM_2\n:\n:\nk_n\nM_n\nThe first line contains an integer n (1 <= n <= 1,000), which is the number of posts in the thread.\nThen 2n lines follow.\nEach post is represented by two lines:\nthe first line contains an integer k_i (k_1 = 0,1 <= k_i < i for 2 <= i <= n) and indicates the i-th post is a reply to the k_i-th post;\nthe second line contains a string M_i and represents the message of the i-th post.\nk_1 is always 0, which means the first post is not replying to any other post, i. e. it is an opening post.\nEach message contains 1 to 50 characters, consisting of uppercase, lowercase, and numeric letters.", "output": "Print the given n messages as specified in the problem statement.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n0\nicpc\n output: icpc", "input: 5\n0\nhoge\n1\nfuga\n1\npiyo\n2\nfoobar\n2\njagjag\n output: hoge\n.fuga\n..foobar\n..jagjag\n.piyo", "input: 8\n0\njagjag\n1\nhogehoge\n1\nbuhihi\n2\nfugafuga\n4\nponyoponyo\n5\nevaeva\n4\nnowawa\n5\npokemon\n output: jagjag\n.hogehoge\n..fugafuga\n...ponyoponyo\n....evaeva\n....pokemon\n...nowawa\n.buhihi", "input: 6\n0\nnakachan\n1\nfan\n2\nyamemasu\n3\nnennryou2\n4\ndannyaku4\n5\nkouzai11\n output: nakachan\n.fan\n..yamemasu\n...nennryou2\n....dannyaku4\n.....kouzai11", "input: 34\n0\nLoveLive\n1\nhonoka\n2\nborarara\n2\nsunohare\n2\nmogyu\n1\neri\n6\nkasikoi\n7\nkawaii\n8\neriichika\n1\nkotori\n10\nWR\n10\nhaetekurukotori\n10\nichigo\n1\numi\n14\nlove\n15\narrow\n16\nshoot\n1\nrin\n18\nnyanyanya\n1\nmaki\n20\n6th\n20\nstar\n22\nnishikino\n1\nnozomi\n24\nspiritual\n25\npower\n1\nhanayo\n27\ndarekatasukete\n28\nchottomattete\n1\nniko\n30\nnatsuiro\n30\nnikkonikkoni\n30\nsekaino\n33\nYAZAWA\n output: LoveLive\n.honoka\n..borarara\n..sunohare\n..mogyu\n.eri\n..kasikoi\n...kawaii\n....eriichika\n.kotori\n..WR\n..haetekurukotori\n..ichigo\n.umi\n..love\n...arrow\n....shoot\n.rin\n..nyanyanya\n.maki\n..6th\n..star\n...nishikino\n.nozomi\n..spiritual\n...power\n.hanayo\n..darekatasukete\n...chottomattete\n.niko\n..natsuiro\n..nikkonikkoni\n..sekaino\n...YAZAWA", "input: 6\n0\n2ch\n1\n1ostu\n1\n2get\n1\n1otsu\n1\n1ostu\n3\npgr\n output: 2ch\n.1ostu\n.2get\n..pgr\n.1otsu\n.1ostu"], "Pid": "p01731", "ProblemText": "Task Description: Nathan O. Davis has been running an electronic bulletin board system named JAG-channel. He is now having hard time to add a new feature there --- threaded view.\nLike many other bulletin board systems, JAG-channel is thread-based. Here a thread (also called a topic) refers to a single conversation with a collection of posts. Each post can be an opening post, which initiates a new thread, or a reply to a previous post in an existing thread.\nThreaded view is a tree-like view that reflects the logical reply structure among the posts: each post forms a node of the tree and contains its replies as its subnodes in the chronological order (i. e. older replies precede newer ones). Note that a post along with its direct and indirect replies forms a subtree as a whole.\nLet us take an example. Suppose: a user made an opening post with a message hoge; another user replied to it with fuga; yet another user also replied to the opening post with piyo; someone else replied to the second post (i. e. fuga”) with foobar; and the fifth user replied to the same post with jagjag.\nThe tree of this thread would look like:\nhoge\n├─fuga\n│　├─foobar\n│　└─jagjag\n└─piyo\nFor easier implementation, Nathan is thinking of a simpler format: the depth of each post from the opening post is represented by dots. Each reply gets one more dot than its parent post. The tree of the above thread would then look like:\nhoge\n. fuga\n. . foobar\n. . jagjag\n. piyo\nYour task in this problem is to help Nathan by writing a program that prints a tree in the Nathan's format for the given posts in a single thread.\nTask Input: Input contains a single dataset in the following format:\nn\nk_1\nM_1\nk_2\nM_2\n:\n:\nk_n\nM_n\nThe first line contains an integer n (1 <= n <= 1,000), which is the number of posts in the thread.\nThen 2n lines follow.\nEach post is represented by two lines:\nthe first line contains an integer k_i (k_1 = 0,1 <= k_i < i for 2 <= i <= n) and indicates the i-th post is a reply to the k_i-th post;\nthe second line contains a string M_i and represents the message of the i-th post.\nk_1 is always 0, which means the first post is not replying to any other post, i. e. it is an opening post.\nEach message contains 1 to 50 characters, consisting of uppercase, lowercase, and numeric letters.\nTask Output: Print the given n messages as specified in the problem statement.\nTask Samples: input: 1\n0\nicpc\n output: icpc\ninput: 5\n0\nhoge\n1\nfuga\n1\npiyo\n2\nfoobar\n2\njagjag\n output: hoge\n.fuga\n..foobar\n..jagjag\n.piyo\ninput: 8\n0\njagjag\n1\nhogehoge\n1\nbuhihi\n2\nfugafuga\n4\nponyoponyo\n5\nevaeva\n4\nnowawa\n5\npokemon\n output: jagjag\n.hogehoge\n..fugafuga\n...ponyoponyo\n....evaeva\n....pokemon\n...nowawa\n.buhihi\ninput: 6\n0\nnakachan\n1\nfan\n2\nyamemasu\n3\nnennryou2\n4\ndannyaku4\n5\nkouzai11\n output: nakachan\n.fan\n..yamemasu\n...nennryou2\n....dannyaku4\n.....kouzai11\ninput: 34\n0\nLoveLive\n1\nhonoka\n2\nborarara\n2\nsunohare\n2\nmogyu\n1\neri\n6\nkasikoi\n7\nkawaii\n8\neriichika\n1\nkotori\n10\nWR\n10\nhaetekurukotori\n10\nichigo\n1\numi\n14\nlove\n15\narrow\n16\nshoot\n1\nrin\n18\nnyanyanya\n1\nmaki\n20\n6th\n20\nstar\n22\nnishikino\n1\nnozomi\n24\nspiritual\n25\npower\n1\nhanayo\n27\ndarekatasukete\n28\nchottomattete\n1\nniko\n30\nnatsuiro\n30\nnikkonikkoni\n30\nsekaino\n33\nYAZAWA\n output: LoveLive\n.honoka\n..borarara\n..sunohare\n..mogyu\n.eri\n..kasikoi\n...kawaii\n....eriichika\n.kotori\n..WR\n..haetekurukotori\n..ichigo\n.umi\n..love\n...arrow\n....shoot\n.rin\n..nyanyanya\n.maki\n..6th\n..star\n...nishikino\n.nozomi\n..spiritual\n...power\n.hanayo\n..darekatasukete\n...chottomattete\n.niko\n..natsuiro\n..nikkonikkoni\n..sekaino\n...YAZAWA\ninput: 6\n0\n2ch\n1\n1ostu\n1\n2get\n1\n1otsu\n1\n1ostu\n3\npgr\n output: 2ch\n.1ostu\n.2get\n..pgr\n.1otsu\n.1ostu\n\n" }, { "title": "Input", "content": "Nathan O. Davis is running a company. His company owns a web service which has a lot of users. So his office is full of servers, routers and messy LAN cables.\nHe is now very puzzling over the messy cables, because they are causing many kinds of problems. For example, staff working at the company often trip over a cable. No damage if the cable is disconnected. It's just lucky. Computers may fall down and get broken if the cable is connected. He is about to introduce a new computer and a new cable. He wants to minimize staff's steps over the new cable.\nHis office is laid-out in a two-dimensional grid with H \times W cells. The new cable should weave along edges of the cells. Each end of the cable is at a corner of a cell. The grid is expressed in zero-origin coordinates, where the upper left corner is (0,0).\nEach staff starts his/her work from inside a certain cell and walks in the office along the grid in a fixed repeated pattern every day. A walking pattern is described by a string of four characters U, D, L and R. U means moving up, D means moving down, R means moving to the right, and L means moving to the left. For example, UULLDDRR means moving up, up, left, left, down, down, right and right in order. The staff repeats the pattern fixed T times. Note that the staff stays in the cell if the staff is going out of the grid through the wall.\nYou have the moving patterns of all staff and the positions of both ends of the new cable. Your job is to find an optimal placement of the new cable, which minimizes the total number his staff would step over the cable.", "constraint": "", "input": "The first line of the input contains three integers which represent the dimension of the office W, H (1 <= W, H <= 500), and the number of staff N (1 <= N <= 1000), respectively.\nThe next line contains two x-y pairs (0 <= x <= W, 0 <= y <= H), which mean the position of two endpoints of a LAN cable to be connected.\nThese values represents the coordinates of the cells to which the cable is plugged in its top-left corner.\nExceptionally, x = W means the right edge of the rightmost cell, and y = H means the bottom edge of the bottommost cell.\nFollowing lines describe staff's initial positions and their moving patterns.\nThe first line includes an x-y pair (0 <= x < W, 0 <= y < H), which represents the coordinate of a staff's initial cell.\nThe next line has an integer T (1 <= T <= 100) and a string which consists of U, D, L and R, whose meaning is described as above.\nThe length of a pattern string is greater than or equal to 1, and no more than 1,000.\nThese two lines are repeated N times.", "output": "Output the minimum number of times his staff step over the cable in a single line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 1\n1 1 3 3\n0 0\n1 RRDDLLUU\n output: 1", "input: 3 3 1\n0 0 3 3\n0 0\n1 RRDDLLUU\n output: 0", "input: 3 3 1\n1 1 3 3\n0 0\n10 RRDDLLUU\n output: 10", "input: 3 3 4\n1 1 3 3\n0 0\n10 R\n2 0\n10 D\n2 2\n10 L\n0 2\n10 U\n output: 1"], "Pid": "p01732", "ProblemText": "Task Description: Nathan O. Davis is running a company. His company owns a web service which has a lot of users. So his office is full of servers, routers and messy LAN cables.\nHe is now very puzzling over the messy cables, because they are causing many kinds of problems. For example, staff working at the company often trip over a cable. No damage if the cable is disconnected. It's just lucky. Computers may fall down and get broken if the cable is connected. He is about to introduce a new computer and a new cable. He wants to minimize staff's steps over the new cable.\nHis office is laid-out in a two-dimensional grid with H \times W cells. The new cable should weave along edges of the cells. Each end of the cable is at a corner of a cell. The grid is expressed in zero-origin coordinates, where the upper left corner is (0,0).\nEach staff starts his/her work from inside a certain cell and walks in the office along the grid in a fixed repeated pattern every day. A walking pattern is described by a string of four characters U, D, L and R. U means moving up, D means moving down, R means moving to the right, and L means moving to the left. For example, UULLDDRR means moving up, up, left, left, down, down, right and right in order. The staff repeats the pattern fixed T times. Note that the staff stays in the cell if the staff is going out of the grid through the wall.\nYou have the moving patterns of all staff and the positions of both ends of the new cable. Your job is to find an optimal placement of the new cable, which minimizes the total number his staff would step over the cable.\nTask Input: The first line of the input contains three integers which represent the dimension of the office W, H (1 <= W, H <= 500), and the number of staff N (1 <= N <= 1000), respectively.\nThe next line contains two x-y pairs (0 <= x <= W, 0 <= y <= H), which mean the position of two endpoints of a LAN cable to be connected.\nThese values represents the coordinates of the cells to which the cable is plugged in its top-left corner.\nExceptionally, x = W means the right edge of the rightmost cell, and y = H means the bottom edge of the bottommost cell.\nFollowing lines describe staff's initial positions and their moving patterns.\nThe first line includes an x-y pair (0 <= x < W, 0 <= y < H), which represents the coordinate of a staff's initial cell.\nThe next line has an integer T (1 <= T <= 100) and a string which consists of U, D, L and R, whose meaning is described as above.\nThe length of a pattern string is greater than or equal to 1, and no more than 1,000.\nThese two lines are repeated N times.\nTask Output: Output the minimum number of times his staff step over the cable in a single line.\nTask Samples: input: 3 3 1\n1 1 3 3\n0 0\n1 RRDDLLUU\n output: 1\ninput: 3 3 1\n0 0 3 3\n0 0\n1 RRDDLLUU\n output: 0\ninput: 3 3 1\n1 1 3 3\n0 0\n10 RRDDLLUU\n output: 10\ninput: 3 3 4\n1 1 3 3\n0 0\n10 R\n2 0\n10 D\n2 2\n10 L\n0 2\n10 U\n output: 1\n\n" }, { "title": "Input", "content": "Ievan Ritola is a researcher of behavioral ecology. Her group visited a forest to analyze an ecological system of some kinds of foxes.\nThe forest can be expressed as a two-dimensional plane. With her previous research, foxes in the forest are known to live at lattice points. Here, lattice points are the points whose x and y coordinates are both integers. Two or more foxes might live at the same point.\nTo observe the biology of these foxes, they decided to put a pair of sensors in the forest. The sensors can be put at lattice points. Then, they will be able to observe all foxes inside the bounding rectangle (including the boundary) where the sensors are catty-corner to each other. The sensors cannot be placed at the points that have the same x or y coordinate; in other words the rectangle must have non-zero area.\nThe more foxes can be observed, the more data can be collected; on the other hand, monitoring a large area consumes a large amount of energy. So they want to maximize the value given by N' / (|x_1 − x_2| × |y_1 − y_2|), where N' is the number of foxes observed and (x_1, y_1) and (x_2, y_2) are the positions of the two sensors.\nLet's help her observe cute foxes!", "constraint": "", "input": "Output the maximized value as a fraction:\na / b\nwhere a and b are integers representing the numerator and the denominato respectively.\n There should be exactly one space before and after the slash.\nThe fraction should be written in the simplest form, that is, a and b must not have a common integer divisor greater than one.\nIf the value becomes an integer, print a fraction with the denominator of one (e. g. 5 / 1 to represent 5).\nThis implies zero should be printed as 0 / 1 (without quotes).", "output": "5 / 10 / 1", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 1 2\n2 2 3\n output: 5 / 1"], "Pid": "p01733", "ProblemText": "Task Description: Ievan Ritola is a researcher of behavioral ecology. Her group visited a forest to analyze an ecological system of some kinds of foxes.\nThe forest can be expressed as a two-dimensional plane. With her previous research, foxes in the forest are known to live at lattice points. Here, lattice points are the points whose x and y coordinates are both integers. Two or more foxes might live at the same point.\nTo observe the biology of these foxes, they decided to put a pair of sensors in the forest. The sensors can be put at lattice points. Then, they will be able to observe all foxes inside the bounding rectangle (including the boundary) where the sensors are catty-corner to each other. The sensors cannot be placed at the points that have the same x or y coordinate; in other words the rectangle must have non-zero area.\nThe more foxes can be observed, the more data can be collected; on the other hand, monitoring a large area consumes a large amount of energy. So they want to maximize the value given by N' / (|x_1 − x_2| × |y_1 − y_2|), where N' is the number of foxes observed and (x_1, y_1) and (x_2, y_2) are the positions of the two sensors.\nLet's help her observe cute foxes!\nTask Input: Output the maximized value as a fraction:\na / b\nwhere a and b are integers representing the numerator and the denominato respectively.\n There should be exactly one space before and after the slash.\nThe fraction should be written in the simplest form, that is, a and b must not have a common integer divisor greater than one.\nIf the value becomes an integer, print a fraction with the denominator of one (e. g. 5 / 1 to represent 5).\nThis implies zero should be printed as 0 / 1 (without quotes).\nTask Output: 5 / 10 / 1\nTask Samples: input: 2\n1 1 2\n2 2 3\n output: 5 / 1\n\n" }, { "title": "Input", "content": "Ayimok is a wizard.\nHis daily task is to arrange magical tiles in a line, and then cast a magic spell.\nMagical tiles and their arrangement follow the rules below:\n Each magical tile has the shape of a trapezoid with a height of 1.\n Some magical tiles may overlap with other magical tiles.\n Magical tiles are arranged on the 2D coordinate system.\n Magical tiles' upper edge lay on a horizontal line, where its y coordinate is 1.\n Magical tiles' lower edge lay on a horizontal line, where its y coordinate is 0.\nHe has to remove these magical tiles away after he finishes casting a magic spell.\nOne day, he found that removing a number of magical tiles is so tiresome, so he decided to simplify its process.\nNow, he has learned \"Magnetization Spell\" to remove magical tiles efficiently. The spell removes a set of magical tiles at once. Any pair of two magical tiles in the set must overlap with each other.\nFor example, in Fig. 1, he can cast Magnetization Spell on all of three magical tiles to remove them away at once, since they all overlap with each other. (Note that the heights of magical tiles are intentionally changed for easier understandings. )\nHowever, in Fig. 2, he can not cast Magnetization Spell on all of three magical tiles at once, since tile 1 and tile 3 are not overlapped.\nHe wants to remove all the magical tiles with the minimum number of Magnetization Spells, because casting the spell requires magic power exhaustively.\nLet's consider Fig. 3 case. He can remove all of magical tiles by casting Magnetization Spell three times; first spell for tile 1 and 2, second spell for tile 3 and 4, and third spell for tile 5 and 6.\nActually, he can remove all of the magical tiles with casting Magnetization Spell just twice; first spell for tile 1,2 and 3, second spell for tile 4,5 and 6.\nAnd it is the minimum number of required spells for removing all magical tiles.\nGiven a set of magical tiles, your task is to create a program which outputs the minimum number of casting Magnetization Spell to remove all of these magical tiles away.\nThere might be a magical tile which does not overlap with other tiles, however, he still needs to cast Magnetization Spell to remove it.", "constraint": "", "input": "Input follows the following format:\nN\nx Lower_{11} x Lower_{12} x Upper_{11} x Upper_{12}\nx Lower_{21} x Lower_{22} x Upper_{21} x Upper_{22}\nx Lower_{31} x Lower_{32} x Upper_{31} x Upper_{32}\n:\n:\nx Lower_{N1} x Lower_{N2} x Upper_{N1} x Upper_{N2}\nThe first line contains an integer N, which means the number of magical tiles.\nThen, N lines which contain the information of magical tiles follow.\nThe (i+1)-th line includes four integers x Lower_{i1}, x Lower_{i2}, x Upper_{i1}, and x Upper_{i2}, which means i-th magical tile's corner points are located at (x Lower_{i1}, 0), (x Lower_{i2}, 0), (x Upper_{i1}, 1), (x Upper_{i2}, 1).\nYou can assume that no two magical tiles will share their corner points.\nThat is, all x Lower_{ij} are distinct, and all x Upper_{ij} are also distinct.\nThe input follows the following constraints:\n1 <= N <= 10^5\n1 <= x Lower_{i1} < x Lower_{i2} <= 10^9\n1 <= x Upper_{i1} < x Upper_{i2} <= 10^9\nAll x Lower_{ij} are distinct.\nAll x Upper_{ij} are distinct.", "output": "Your program must output the required minimum number of casting Magnetization Spell to remove all the magical tiles.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n26 29 9 12\n6 10 15 16\n8 17 18 19\n output: 1", "input: 3\n2 10 1 11\n5 18 9 16\n12 19 15 20\n output: 2", "input: 6\n2 8 1 14\n6 16 3 10\n3 20 11 13\n17 28 18 21\n22 29 25 31\n23 24 33 34\n output: 2"], "Pid": "p01734", "ProblemText": "Task Description: Ayimok is a wizard.\nHis daily task is to arrange magical tiles in a line, and then cast a magic spell.\nMagical tiles and their arrangement follow the rules below:\n Each magical tile has the shape of a trapezoid with a height of 1.\n Some magical tiles may overlap with other magical tiles.\n Magical tiles are arranged on the 2D coordinate system.\n Magical tiles' upper edge lay on a horizontal line, where its y coordinate is 1.\n Magical tiles' lower edge lay on a horizontal line, where its y coordinate is 0.\nHe has to remove these magical tiles away after he finishes casting a magic spell.\nOne day, he found that removing a number of magical tiles is so tiresome, so he decided to simplify its process.\nNow, he has learned \"Magnetization Spell\" to remove magical tiles efficiently. The spell removes a set of magical tiles at once. Any pair of two magical tiles in the set must overlap with each other.\nFor example, in Fig. 1, he can cast Magnetization Spell on all of three magical tiles to remove them away at once, since they all overlap with each other. (Note that the heights of magical tiles are intentionally changed for easier understandings. )\nHowever, in Fig. 2, he can not cast Magnetization Spell on all of three magical tiles at once, since tile 1 and tile 3 are not overlapped.\nHe wants to remove all the magical tiles with the minimum number of Magnetization Spells, because casting the spell requires magic power exhaustively.\nLet's consider Fig. 3 case. He can remove all of magical tiles by casting Magnetization Spell three times; first spell for tile 1 and 2, second spell for tile 3 and 4, and third spell for tile 5 and 6.\nActually, he can remove all of the magical tiles with casting Magnetization Spell just twice; first spell for tile 1,2 and 3, second spell for tile 4,5 and 6.\nAnd it is the minimum number of required spells for removing all magical tiles.\nGiven a set of magical tiles, your task is to create a program which outputs the minimum number of casting Magnetization Spell to remove all of these magical tiles away.\nThere might be a magical tile which does not overlap with other tiles, however, he still needs to cast Magnetization Spell to remove it.\nTask Input: Input follows the following format:\nN\nx Lower_{11} x Lower_{12} x Upper_{11} x Upper_{12}\nx Lower_{21} x Lower_{22} x Upper_{21} x Upper_{22}\nx Lower_{31} x Lower_{32} x Upper_{31} x Upper_{32}\n:\n:\nx Lower_{N1} x Lower_{N2} x Upper_{N1} x Upper_{N2}\nThe first line contains an integer N, which means the number of magical tiles.\nThen, N lines which contain the information of magical tiles follow.\nThe (i+1)-th line includes four integers x Lower_{i1}, x Lower_{i2}, x Upper_{i1}, and x Upper_{i2}, which means i-th magical tile's corner points are located at (x Lower_{i1}, 0), (x Lower_{i2}, 0), (x Upper_{i1}, 1), (x Upper_{i2}, 1).\nYou can assume that no two magical tiles will share their corner points.\nThat is, all x Lower_{ij} are distinct, and all x Upper_{ij} are also distinct.\nThe input follows the following constraints:\n1 <= N <= 10^5\n1 <= x Lower_{i1} < x Lower_{i2} <= 10^9\n1 <= x Upper_{i1} < x Upper_{i2} <= 10^9\nAll x Lower_{ij} are distinct.\nAll x Upper_{ij} are distinct.\nTask Output: Your program must output the required minimum number of casting Magnetization Spell to remove all the magical tiles.\nTask Samples: input: 3\n26 29 9 12\n6 10 15 16\n8 17 18 19\n output: 1\ninput: 3\n2 10 1 11\n5 18 9 16\n12 19 15 20\n output: 2\ninput: 6\n2 8 1 14\n6 16 3 10\n3 20 11 13\n17 28 18 21\n22 29 25 31\n23 24 33 34\n output: 2\n\n" }, { "title": "Input", "content": "Fox Ciel is developing an artificial intelligence (AI) for a game. This game is described as a game tree T with n vertices.\nEach node in the game has an evaluation value which shows how good a situation is.\nThis value is the same as maximum value of child nodes' values multiplied by -1. Values on leaf nodes are evaluated with Ciel's special function -- which is a bit heavy.\nSo, she will use alpha-beta pruning for getting root node's evaluation value to decrease the number of leaf nodes to be calculated.\nBy the way, changing evaluation order of child nodes affects the number of calculation on the leaf nodes.\nTherefore, Ciel wants to know the minimum and maximum number of times to calculate in leaf nodes when she could evaluate child node in arbitrary order.\nShe asked you to calculate minimum evaluation number of times and maximum evaluation number of times in leaf nodes.\nCiel uses following algotithm:\nfunction negamax(node, α , β )\n if node is a terminal node\n return value of leaf node\n else\n foreach child of node\n val : = -negamax(child, -β , -α )\n if val >= β\n return val\n if val > α\n α : = val\n return α", "constraint": "", "input": "Input follows following format:\nn\np_1 p_2 . . . p_n\nk_1 t_{11} t_{12} . . . t_{1k}\n:\n:\nk_n t_{n1} t_{n2} . . . t_{nk}\nThe first line contains an integer n, which means the number of vertices in game tree T.\nThe second line contains n integers p_i, which means the evaluation value of vertex i.\nThen, next n lines which contain the information of game tree T.\nk_i is the number of child nodes of vertex i, and t_{ij} is the indices of the child node of vertex i.\nInput follows following constraints:\n 2 <= n <= 100\n -10,000 <= p_i <= 10,000\n 0 <= k_i <= 5\n 2 <= t_{ij} <= n\n Index of root node is 1.\n Evaluation value except leaf node is always 0. This does not mean the evaluation values of non-leaf nodes are 0. You have to calculate them if necessary.\n Leaf node sometimes have evaluation value of 0.\n Game tree T is tree structure.", "output": "Print the minimum evaluation number of times and the maximum evaluation number of times in leaf node.\nPlease separated by whitespace between minimum and maximum.\nminimum maximum", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 1 1\n2 2 3\n0\n0\n output: 2 2", "input: 8\n0 0 100 100 0 -100 -100 -100\n2 2 5\n2 3 4\n0\n0\n3 6 7 8\n0\n0\n0\n output: 3 5", "input: 8\n0 0 100 100 0 100 100 100\n2 2 5\n2 3 4\n0\n0\n3 6 7 8\n0\n0\n0\n output: 3 4", "input: 19\n0 100 0 100 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10\n2 2 3\n0\n2 4 5\n0\n3 6 7 8\n3 9 10 11\n3 12 13 14\n3 15 16 17\n2 18 19\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n output: 7 12"], "Pid": "p01735", "ProblemText": "Task Description: Fox Ciel is developing an artificial intelligence (AI) for a game. This game is described as a game tree T with n vertices.\nEach node in the game has an evaluation value which shows how good a situation is.\nThis value is the same as maximum value of child nodes' values multiplied by -1. Values on leaf nodes are evaluated with Ciel's special function -- which is a bit heavy.\nSo, she will use alpha-beta pruning for getting root node's evaluation value to decrease the number of leaf nodes to be calculated.\nBy the way, changing evaluation order of child nodes affects the number of calculation on the leaf nodes.\nTherefore, Ciel wants to know the minimum and maximum number of times to calculate in leaf nodes when she could evaluate child node in arbitrary order.\nShe asked you to calculate minimum evaluation number of times and maximum evaluation number of times in leaf nodes.\nCiel uses following algotithm:\nfunction negamax(node, α , β )\n if node is a terminal node\n return value of leaf node\n else\n foreach child of node\n val : = -negamax(child, -β , -α )\n if val >= β\n return val\n if val > α\n α : = val\n return α\nTask Input: Input follows following format:\nn\np_1 p_2 . . . p_n\nk_1 t_{11} t_{12} . . . t_{1k}\n:\n:\nk_n t_{n1} t_{n2} . . . t_{nk}\nThe first line contains an integer n, which means the number of vertices in game tree T.\nThe second line contains n integers p_i, which means the evaluation value of vertex i.\nThen, next n lines which contain the information of game tree T.\nk_i is the number of child nodes of vertex i, and t_{ij} is the indices of the child node of vertex i.\nInput follows following constraints:\n 2 <= n <= 100\n -10,000 <= p_i <= 10,000\n 0 <= k_i <= 5\n 2 <= t_{ij} <= n\n Index of root node is 1.\n Evaluation value except leaf node is always 0. This does not mean the evaluation values of non-leaf nodes are 0. You have to calculate them if necessary.\n Leaf node sometimes have evaluation value of 0.\n Game tree T is tree structure.\nTask Output: Print the minimum evaluation number of times and the maximum evaluation number of times in leaf node.\nPlease separated by whitespace between minimum and maximum.\nminimum maximum\nTask Samples: input: 3\n0 1 1\n2 2 3\n0\n0\n output: 2 2\ninput: 8\n0 0 100 100 0 -100 -100 -100\n2 2 5\n2 3 4\n0\n0\n3 6 7 8\n0\n0\n0\n output: 3 5\ninput: 8\n0 0 100 100 0 100 100 100\n2 2 5\n2 3 4\n0\n0\n3 6 7 8\n0\n0\n0\n output: 3 4\ninput: 19\n0 100 0 100 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10\n2 2 3\n0\n2 4 5\n0\n3 6 7 8\n3 9 10 11\n3 12 13 14\n3 15 16 17\n2 18 19\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n output: 7 12\n\n" }, { "title": "Input", "content": "You and your grandma are playing with graph automata, which is generalization of cell automata.\nA graph automaton is expressed by a graph. The vertices of the graph have a time-dependent value, which can be either 0 or 1.\nThere is no more than one edge between any of two vertices, but self-loops might exist.\nThe values of vertices change regularly according to the following rule:\nAt time t+1, the value of vertex i will be 1 if and only if there are an odd number of edges from the vertex i to a vertex which has the value 1 at time t; otherwise 0.\nNow, your forgetful grandma forgot the past states of the automaton. Your task is to write a program which recovers the past states from the current time and states --- time machines are way too expensive.\nThere may be multiple candidates or no consistent states.\nFor such cases, you must print an appropriate error message.", "constraint": "", "input": "The input is formatted as follows: N\na_{11} . . . a_{1N}\n:\n:\na_{N1} . . . a_{NN}\nv_1\n:\n:\nv_N\nT\n The first line contains one integer N (2 <= N <= 300).\nN indicates the number of vertices.\nThe following N lines indicate the adjacent matrix of the graph.\nWhen (i, j)-element is 1, there is an edge from vertex i to vertex j.\nOtherwise, there is no edge.\nThe following N lines indicate the value vector of the vertices.\nThe i-th element indicates the value of vertex i at time 0.\nEach element of the matrix and the vector can be 0 or 1.\nThe last line contains one integer T (1 <= T <= 100,000,000).\n-T is the time your grandma wants to know the status at.", "output": "Print the value vector at time -T separated one white space in one line as follows:\nv_1 . . . v_N\nEach value must be separated with one white space.\nIf there is no consistent value vectors, you should print none in one line.\nOr if there are multiple candidates and the solution is not unique (i. e. the solution is not unique), you should print ambiguous in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 1\n0 1\n1\n1\n1\n output: 0 1", "input: 2\n0 1\n0 0\n1\n0\n1\n output: ambiguous", "input: 2\n0 1\n0 0\n1\n0\n2\n output: none"], "Pid": "p01736", "ProblemText": "Task Description: You and your grandma are playing with graph automata, which is generalization of cell automata.\nA graph automaton is expressed by a graph. The vertices of the graph have a time-dependent value, which can be either 0 or 1.\nThere is no more than one edge between any of two vertices, but self-loops might exist.\nThe values of vertices change regularly according to the following rule:\nAt time t+1, the value of vertex i will be 1 if and only if there are an odd number of edges from the vertex i to a vertex which has the value 1 at time t; otherwise 0.\nNow, your forgetful grandma forgot the past states of the automaton. Your task is to write a program which recovers the past states from the current time and states --- time machines are way too expensive.\nThere may be multiple candidates or no consistent states.\nFor such cases, you must print an appropriate error message.\nTask Input: The input is formatted as follows: N\na_{11} . . . a_{1N}\n:\n:\na_{N1} . . . a_{NN}\nv_1\n:\n:\nv_N\nT\n The first line contains one integer N (2 <= N <= 300).\nN indicates the number of vertices.\nThe following N lines indicate the adjacent matrix of the graph.\nWhen (i, j)-element is 1, there is an edge from vertex i to vertex j.\nOtherwise, there is no edge.\nThe following N lines indicate the value vector of the vertices.\nThe i-th element indicates the value of vertex i at time 0.\nEach element of the matrix and the vector can be 0 or 1.\nThe last line contains one integer T (1 <= T <= 100,000,000).\n-T is the time your grandma wants to know the status at.\nTask Output: Print the value vector at time -T separated one white space in one line as follows:\nv_1 . . . v_N\nEach value must be separated with one white space.\nIf there is no consistent value vectors, you should print none in one line.\nOr if there are multiple candidates and the solution is not unique (i. e. the solution is not unique), you should print ambiguous in one line.\nTask Samples: input: 2\n1 1\n0 1\n1\n1\n1\n output: 0 1\ninput: 2\n0 1\n0 0\n1\n0\n1\n output: ambiguous\ninput: 2\n0 1\n0 0\n1\n0\n2\n output: none\n\n" }, { "title": "Input", "content": "Ciel, an idol whose appearance and behavior are similar to a fox, is participating in a rehearsal for the live concert which takes place in a few days.\nTo become a top idol, a large amount of effort is required!\nThe live stage can be expressed as a two-dimensional surface.\nThe live stage has N spotlights to illuminate the stage.\nThe i-th spotlight casts a light in the range of a circle with radius r_{i}.\nThe center of the light cast by the i-th spotlight moves along an orbital path R_{i}.\nR_{i} is described as a closed polygon, though R_{i} might contain self-intersections.\nThe spotlight begins to move from the first vertex of R_{i}.\nAll of the orbital period of each spotlight are the same.\nEach spotlight moves at a constant speed, and all of them return to the starting point at the same time.\nIn the rehearsal, Ciel has to move from the starting point to the ending point indicated on the live stage.\nTo achieve her goal, it is not allowed to fall out from the area illuminated with the spotlight.\nBut, she doesn't have to be illuminated with the spotlight as long as she is standing on the starting point.\nYou may assume that she can move fast enough.\nAnswer if it is possible for her to move to the ending point.", "constraint": "", "input": "Each input dataset is given in the following format:\nN sx sy ex ey\nr_{1} K_{1} x_{11} y_{11} x_{12} y_{12} . . . x_{1K_{1}} y_{1K_{1}}\nr_{2} K_{2} x_{21} y_{21} x_{22} y_{22} . . . x_{2K_{2}} y_{2K_{2}}\n:\n:\nr_{N} K_{N} x_{N1} y_{N1} x_{N2} y_{N2} . . . x_{NK_{N}} y_{NK_{N}}\nAll inputs are integer. All coordinate information satisfies -10,000 <= x, y <= 10,000.\nN (1 <= N <= 100) indicates the number of spotlights. (sx, sy) and (ex, ey) indicate the starting point and the ending point of Ciel's path, respectively.\nThe following N lines denote the information of each spotlight.\nr_{i} (1 <= r_{i} <= 100) indicates the radius of the spotlight.\nK_{i} (2 <= K_{i} <= 10) indicates the number of vertices in the orbital path.\nThen, K_{i} vertices are given. Two consecutive vertices on the same orbital path are located at different places.\nThe spotlight moves from the first point (x_{i1}, y_{i1}) to the second point (x_{i2}, y_{i2}), then moves to the third point (x_{i3}, y_{i3}), and so on.\nAfter moving to the K_{i}-th point (x_{i K_{i}}, y_{i K_{i}}), the spotlight returns to the first point (x_{i1}, y_{i1}) and repeats again its movement.\nLet d_{ij} be the closest distance between two central points of spotlight i and spotlight j. d_{ij} satisfies either of the following:\n d_{ij} > r_{i} + r_{j} + 0.000001\n d_{ij} < r_{i} + r_{j} - 0.000001\nFurthermore, let d_{i} be the closest distance between a central point of spotlight i and either the starting point or the ending point. d_{i} satisfies either of the following:\n d_{i} > r_{i} + 0.000001\n d_{i} < r_{i} - 0.000001", "output": "If it is possible for Ciel to move the ending point without falling out from the illuminated area,\noutput Yes in one line.\nOtherwise, output No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 1 9 -1\n2 2 1 1 -9 1\n1 2 -1 -1 9 -1\n output: Yes", "input: 2 1 1 9 -1\n2 2 1 1 -9 1\n1 2 9 -1 -1 -1\n output: No", "input: 2 11 6 -9 1\n6 4 10 5 10 0 5 0 5 5\n5 4 -10 0 -10 5 -5 5 -5 0\n output: Yes", "input: 1 1 9999 -1 0\n100 2 0 0 0 10000\n output: Yes"], "Pid": "p01737", "ProblemText": "Task Description: Ciel, an idol whose appearance and behavior are similar to a fox, is participating in a rehearsal for the live concert which takes place in a few days.\nTo become a top idol, a large amount of effort is required!\nThe live stage can be expressed as a two-dimensional surface.\nThe live stage has N spotlights to illuminate the stage.\nThe i-th spotlight casts a light in the range of a circle with radius r_{i}.\nThe center of the light cast by the i-th spotlight moves along an orbital path R_{i}.\nR_{i} is described as a closed polygon, though R_{i} might contain self-intersections.\nThe spotlight begins to move from the first vertex of R_{i}.\nAll of the orbital period of each spotlight are the same.\nEach spotlight moves at a constant speed, and all of them return to the starting point at the same time.\nIn the rehearsal, Ciel has to move from the starting point to the ending point indicated on the live stage.\nTo achieve her goal, it is not allowed to fall out from the area illuminated with the spotlight.\nBut, she doesn't have to be illuminated with the spotlight as long as she is standing on the starting point.\nYou may assume that she can move fast enough.\nAnswer if it is possible for her to move to the ending point.\nTask Input: Each input dataset is given in the following format:\nN sx sy ex ey\nr_{1} K_{1} x_{11} y_{11} x_{12} y_{12} . . . x_{1K_{1}} y_{1K_{1}}\nr_{2} K_{2} x_{21} y_{21} x_{22} y_{22} . . . x_{2K_{2}} y_{2K_{2}}\n:\n:\nr_{N} K_{N} x_{N1} y_{N1} x_{N2} y_{N2} . . . x_{NK_{N}} y_{NK_{N}}\nAll inputs are integer. All coordinate information satisfies -10,000 <= x, y <= 10,000.\nN (1 <= N <= 100) indicates the number of spotlights. (sx, sy) and (ex, ey) indicate the starting point and the ending point of Ciel's path, respectively.\nThe following N lines denote the information of each spotlight.\nr_{i} (1 <= r_{i} <= 100) indicates the radius of the spotlight.\nK_{i} (2 <= K_{i} <= 10) indicates the number of vertices in the orbital path.\nThen, K_{i} vertices are given. Two consecutive vertices on the same orbital path are located at different places.\nThe spotlight moves from the first point (x_{i1}, y_{i1}) to the second point (x_{i2}, y_{i2}), then moves to the third point (x_{i3}, y_{i3}), and so on.\nAfter moving to the K_{i}-th point (x_{i K_{i}}, y_{i K_{i}}), the spotlight returns to the first point (x_{i1}, y_{i1}) and repeats again its movement.\nLet d_{ij} be the closest distance between two central points of spotlight i and spotlight j. d_{ij} satisfies either of the following:\n d_{ij} > r_{i} + r_{j} + 0.000001\n d_{ij} < r_{i} + r_{j} - 0.000001\nFurthermore, let d_{i} be the closest distance between a central point of spotlight i and either the starting point or the ending point. d_{i} satisfies either of the following:\n d_{i} > r_{i} + 0.000001\n d_{i} < r_{i} - 0.000001\nTask Output: If it is possible for Ciel to move the ending point without falling out from the illuminated area,\noutput Yes in one line.\nOtherwise, output No.\nTask Samples: input: 2 1 1 9 -1\n2 2 1 1 -9 1\n1 2 -1 -1 9 -1\n output: Yes\ninput: 2 1 1 9 -1\n2 2 1 1 -9 1\n1 2 9 -1 -1 -1\n output: No\ninput: 2 11 6 -9 1\n6 4 10 5 10 0 5 0 5 5\n5 4 -10 0 -10 5 -5 5 -5 0\n output: Yes\ninput: 1 1 9999 -1 0\n100 2 0 0 0 10000\n output: Yes\n\n" }, { "title": "", "content": "H W\nm A1 m A2 m B1 m B2 m X\nM_{1,1}M_{1,2}. . . M_{1, W}\nM_{2,1}M_{2,2}. . . M_{2, W}\n:\n:\nM_{H, 1}M_{H, 2}. . . M_{H, W}ABX. ABX", "constraint": "", "input": "The input is formatted as follows.\n \nH W\nm A1 m A2 m B1 m B2 m X\nM_{1,1}M_{1,2}. . . M_{1, W}\nM_{2,1}M_{2,2}. . . M_{2, W}\n:\n:\nM_{H, 1}M_{H, 2}. . . M_{H, W} The first line of the input contains two integers H and W (1 <= H, W <= 50) separated by a space, where H and W are the numbers of rows and columns of given matrix.\n The second line of the input contains five integers m A1, m A2, m B1, m B2 and m X (1 <= m A1 < m A2 <= 100,1 <= m B1 < m B2 <= 100 and 1 <= m X <= 100) separated by a space.\n The following H lines, each consisting of W characters, denote given matrix.\nIn those H lines, A, B and X denote a piece of type A, type B and type X respectively, and . denotes empty cell to place no piece.\nThere are no other characters in those H lines.\n Of the cell at i-th row in j-th column, the coordinate of the left top corner is (i, j), and the coordinate of the right bottom corner is (i+1, j+1).\n You may assume that given matrix has at least one A, B and X each and all pieces are connected on at least one edge.\nAlso, you may assume that the probability that the x-coordinate of the center of gravity of the object is an integer is equal to zero and the probability that the y-coordinate of the center of gravity of the object is an integer is equal to zero.", "output": "Print the probability that the center of gravity of the object is on the object.\nThe output should not contain an error greater than 10^{-8}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n2 4 1 2 1\nXAX\nB.B\nXAX\n output: 0.0000000000000", "input: 4 2\n1 100 1 100 50\nAX\nXB\nBA\nXB\n output: 1.0", "input: 2 3\n1 2 3 4 2\nX.B\nAXX\n output: 0.500", "input: 10 10\n1 100 1 100 1\nAXXXXXXXXX\nX........X\nX........X\nX..XXXXXXX\nX........X\nXXXXXX...X\nX........X\nX......X.X\nX......X.X\nXXXXXXXXXB\n output: 0.4930639462354", "input: 25 38\n42 99 40 89 3\n...........X...............X..........\n...........XXX..........XXXX..........\n...........XXXXX.......XXXX...........\n............XXXXXXXXXXXXXXX...........\n............XXXXXXXXXXXXXXX...........\n............XXXXXXXXXXXXXX............\n.............XXXXXXXXXXXXX............\n............XXXXXXXXXXXXXXX...........\n...........XXXXXXXXXXXXXXXXX..........\n.......X...XXXXXXXXXXXXXXXXX...X......\n.......XX.XXXXXXXXXXXXXXXXXX..XX......\n........XXXXXXXXXXXXXXXXXXXX.XX.......\n..........XXXXXXXXXXXXXXXXXXXX........\n.........XXXXX..XXXXXXXX..XXXXX.......\n.......XXXXXX....XXXXX....XXXXXX......\n......XXXXXXXX...XXXXX..XXXXXXXX.X....\n....XXXXXXX..X...XXXXX..X..XXXXXXXX...\n..BBBXXXXXX.....XXXXXXX......XXXAAAA..\n...BBBXXXX......XXXXXXX........AAA....\n..BBBB.........XXXXXXXXX........AAA...\n...............XXXXXXXXX..............\n..............XXXXXXXXXX..............\n..............XXXXXXXXXX..............\n...............XXXXXXXX...............\n...............XXXXXXXX...............\n output: 0.9418222212582"], "Pid": "p01738", "ProblemText": "Task Description: H W\nm A1 m A2 m B1 m B2 m X\nM_{1,1}M_{1,2}. . . M_{1, W}\nM_{2,1}M_{2,2}. . . M_{2, W}\n:\n:\nM_{H, 1}M_{H, 2}. . . M_{H, W}ABX. ABX\nTask Input: The input is formatted as follows.\n \nH W\nm A1 m A2 m B1 m B2 m X\nM_{1,1}M_{1,2}. . . M_{1, W}\nM_{2,1}M_{2,2}. . . M_{2, W}\n:\n:\nM_{H, 1}M_{H, 2}. . . M_{H, W} The first line of the input contains two integers H and W (1 <= H, W <= 50) separated by a space, where H and W are the numbers of rows and columns of given matrix.\n The second line of the input contains five integers m A1, m A2, m B1, m B2 and m X (1 <= m A1 < m A2 <= 100,1 <= m B1 < m B2 <= 100 and 1 <= m X <= 100) separated by a space.\n The following H lines, each consisting of W characters, denote given matrix.\nIn those H lines, A, B and X denote a piece of type A, type B and type X respectively, and . denotes empty cell to place no piece.\nThere are no other characters in those H lines.\n Of the cell at i-th row in j-th column, the coordinate of the left top corner is (i, j), and the coordinate of the right bottom corner is (i+1, j+1).\n You may assume that given matrix has at least one A, B and X each and all pieces are connected on at least one edge.\nAlso, you may assume that the probability that the x-coordinate of the center of gravity of the object is an integer is equal to zero and the probability that the y-coordinate of the center of gravity of the object is an integer is equal to zero.\nTask Output: Print the probability that the center of gravity of the object is on the object.\nThe output should not contain an error greater than 10^{-8}.\nTask Samples: input: 3 3\n2 4 1 2 1\nXAX\nB.B\nXAX\n output: 0.0000000000000\ninput: 4 2\n1 100 1 100 50\nAX\nXB\nBA\nXB\n output: 1.0\ninput: 2 3\n1 2 3 4 2\nX.B\nAXX\n output: 0.500\ninput: 10 10\n1 100 1 100 1\nAXXXXXXXXX\nX........X\nX........X\nX..XXXXXXX\nX........X\nXXXXXX...X\nX........X\nX......X.X\nX......X.X\nXXXXXXXXXB\n output: 0.4930639462354\ninput: 25 38\n42 99 40 89 3\n...........X...............X..........\n...........XXX..........XXXX..........\n...........XXXXX.......XXXX...........\n............XXXXXXXXXXXXXXX...........\n............XXXXXXXXXXXXXXX...........\n............XXXXXXXXXXXXXX............\n.............XXXXXXXXXXXXX............\n............XXXXXXXXXXXXXXX...........\n...........XXXXXXXXXXXXXXXXX..........\n.......X...XXXXXXXXXXXXXXXXX...X......\n.......XX.XXXXXXXXXXXXXXXXXX..XX......\n........XXXXXXXXXXXXXXXXXXXX.XX.......\n..........XXXXXXXXXXXXXXXXXXXX........\n.........XXXXX..XXXXXXXX..XXXXX.......\n.......XXXXXX....XXXXX....XXXXXX......\n......XXXXXXXX...XXXXX..XXXXXXXX.X....\n....XXXXXXX..X...XXXXX..X..XXXXXXXX...\n..BBBXXXXXX.....XXXXXXX......XXXAAAA..\n...BBBXXXX......XXXXXXX........AAA....\n..BBBB.........XXXXXXXXX........AAA...\n...............XXXXXXXXX..............\n..............XXXXXXXXXX..............\n..............XXXXXXXXXX..............\n...............XXXXXXXX...............\n...............XXXXXXXX...............\n output: 0.9418222212582\n\n" }, { "title": "Input", "content": "A data set is given in the following format.\n\nn\nk_{1} t_{11} c_{12} . . . t_{1k_{1}} c_{1k_{1}}\n:\n:\nk_{n} t_{n1} c_{n2} . . . t_{nk_{n}} c_{nk_{n}}\nThe first line of the data set contains one integer n (2 <= n <= 1{, }000), which denotes the number of the branching points in this game. The following n lines describe the branching points. The i-th line describes the branching point of ID number i. The first integer k_{i} (0 <= k_{i} <= 50) is the number of choices at the i-th branching point. k_{i} >= 0 means that the i-th branching point is an ending. Next 2k_{i} integers t_{ij} (1 <= t_{ij} <= n) and c_{ij} (0 <= c_{ij} <= 300) are the information of choices. t_{ij} denotes the ID numbers of the next branching points when you select the j-th choice. c_{ij} denotes the time to read the story between the i-th branching point and the t_{ij}-th branching point. The branching point with ID 1 is the first branching point. You may assume all the branching point and endings are reachable from the first branching point. You may also assume that there is no loop in the game, that is, no branching point can be reached more than once without a reset.", "constraint": "", "input": "en", "output": "Print the shortest time in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2 2\n0\n output: 2", "input: 6\n2 2 1 3 2\n2 4 3 5 4\n2 5 5 6 6\n0\n0\n0\n output: 24", "input: 6\n3 2 100 3 10 3 10\n1 4 100\n1 4 10\n3 5 1 5 1 6 1\n0\n0\n output: 243"], "Pid": "p01739", "ProblemText": "Task Description: A data set is given in the following format.\n\nn\nk_{1} t_{11} c_{12} . . . t_{1k_{1}} c_{1k_{1}}\n:\n:\nk_{n} t_{n1} c_{n2} . . . t_{nk_{n}} c_{nk_{n}}\nThe first line of the data set contains one integer n (2 <= n <= 1{, }000), which denotes the number of the branching points in this game. The following n lines describe the branching points. The i-th line describes the branching point of ID number i. The first integer k_{i} (0 <= k_{i} <= 50) is the number of choices at the i-th branching point. k_{i} >= 0 means that the i-th branching point is an ending. Next 2k_{i} integers t_{ij} (1 <= t_{ij} <= n) and c_{ij} (0 <= c_{ij} <= 300) are the information of choices. t_{ij} denotes the ID numbers of the next branching points when you select the j-th choice. c_{ij} denotes the time to read the story between the i-th branching point and the t_{ij}-th branching point. The branching point with ID 1 is the first branching point. You may assume all the branching point and endings are reachable from the first branching point. You may also assume that there is no loop in the game, that is, no branching point can be reached more than once without a reset.\nTask Input: en\nTask Output: Print the shortest time in a line.\nTask Samples: input: 2\n1 2 2\n0\n output: 2\ninput: 6\n2 2 1 3 2\n2 4 3 5 4\n2 5 5 6 6\n0\n0\n0\n output: 24\ninput: 6\n3 2 100 3 10 3 10\n1 4 100\n1 4 10\n3 5 1 5 1 6 1\n0\n0\n output: 243\n\n" }, { "title": "", "content": "W\ns_{11}s_{11}. . . s_{1W}\ns_{21}s_{21}. . . s_{2W}\n\nt_{11}t_{11}. . . t_{1W}\nt_{21}t_{21}. . . t_{2W}\no. o. *", "constraint": "", "input": "The input is formatted as follows.\n \nW\ns_{11}s_{11}. . . s_{1W}\ns_{21}s_{21}. . . s_{2W}\nt_{11}t_{11}. . . t_{1W}\nt_{21}t_{21}. . . t_{2W}\n The first line of the input contains an integer W (2 <= W <= 2,000), the width of the board. The following two lines contain the information of the initial arrangement. If a cell (i, j) contains a checker in the initial arrangement, s_{ij} is o. Otherwise, s_{ij} is . . Then an empty line follows. The following two lines contain the information of the desired arrangement. Similarly, if a cell (i, j) must contain a checker at last, t_{ij} is o. If a cell (i, j) must not contain a checker at last, t_{ij} is . . If there is no condition for a cell (i, j), t_{ij} is *.\nYou may assume that a solution always exists.", "output": "Output the minimum required number of operations in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n.oo\no..\n\no.o\no..\n output: 1", "input: 5\n.o.o.\no.o.o\n\no.o.o\n.o.o.\n output: 3", "input: 4\no.o.\no.o.\n\n.*.o\n.o.*\n output: 4", "input: 20\noooo.....ooo......oo\n.o..o....o..oooo...o\n\n...o*.o.oo..*o*.*o..\n.*.o.o.*o*o*..*.o...\n output: 25", "input: 30\n...o...oo.o..o...o.o........o.\n.o.oo..o.oo...o.....o........o\n\n**o.*....*...*.**...**....o...\n**..o...*...**..o..o.*........\n output: 32"], "Pid": "p01740", "ProblemText": "Task Description: W\ns_{11}s_{11}. . . s_{1W}\ns_{21}s_{21}. . . s_{2W}\n\nt_{11}t_{11}. . . t_{1W}\nt_{21}t_{21}. . . t_{2W}\no. o. *\nTask Input: The input is formatted as follows.\n \nW\ns_{11}s_{11}. . . s_{1W}\ns_{21}s_{21}. . . s_{2W}\nt_{11}t_{11}. . . t_{1W}\nt_{21}t_{21}. . . t_{2W}\n The first line of the input contains an integer W (2 <= W <= 2,000), the width of the board. The following two lines contain the information of the initial arrangement. If a cell (i, j) contains a checker in the initial arrangement, s_{ij} is o. Otherwise, s_{ij} is . . Then an empty line follows. The following two lines contain the information of the desired arrangement. Similarly, if a cell (i, j) must contain a checker at last, t_{ij} is o. If a cell (i, j) must not contain a checker at last, t_{ij} is . . If there is no condition for a cell (i, j), t_{ij} is *.\nYou may assume that a solution always exists.\nTask Output: Output the minimum required number of operations in one line.\nTask Samples: input: 3\n.oo\no..\n\no.o\no..\n output: 1\ninput: 5\n.o.o.\no.o.o\n\no.o.o\n.o.o.\n output: 3\ninput: 4\no.o.\no.o.\n\n.*.o\n.o.*\n output: 4\ninput: 20\noooo.....ooo......oo\n.o..o....o..oooo...o\n\n...o*.o.oo..*o*.*o..\n.*.o.o.*o*o*..*.o...\n output: 25\ninput: 30\n...o...oo.o..o...o.o........o.\n.o.oo..o.oo...o.....o........o\n\n**o.*....*...*.**...**....o...\n**..o...*...**..o..o.*........\n output: 32\n\n" }, { "title": "A - Breadth-First Search by Foxpower", "content": "Fox Ciel went to JAG Kingdom by bicycle, but she forgot a place where she parked her bicycle. So she needs to search it from a bicycle-parking area before returning home.\n\nThe parking area is formed as a unweighted rooted tree $T$ with $n$ vertices, numbered $1$ through $n$. Each vertex has a space for parking one or more bicycles. Ciel thought that she parked her bicycle near the vertex $1$, so she decided to search it from there by the breadth-first search. That is, she searches it at the vertices in the increasing order of their distances from the vertex $1$. If multiple vertices have the same distance, she gives priority to the vertices in the order of searching at their parents. If multiple vertices have the same parent, she searches at the vertex with minimum number at first.\n\nUnlike a computer, she can't go to a next vertex by random access. Thus, if she goes to the vertex $j$ after the vertex $i$, she needs to walk the distance between the vertices $i$ and $j$. BFS by fox power perhaps takes a long time, so she asks you to calculate the total moving distance in the worst case starting from the vertex $1$.", "constraint": "", "input": "The input is formatted as follows.\n$n$$p_2$ $p_3$ $p_4$ $\\cdots$ $p_n$\nThe first line contains an integer $n$ ($1 <= n <= 10^5$), which is the number of vertices on the unweighted rooted tree $T$.\nThe second line contains $n-1$ integers $p_i$ ($1 <= p_i < i$), which are the parent of the vertex $i$.\nThe vertex $1$ is a root node, so $p_1$ does not exist.", "output": "Print the total moving distance in the worst case in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 1 2\n output: 6", "input: 4\n1 1 3\n output: 4", "input: 11\n1 1 3 3 2 4 1 3 2 9\n output: 25"], "Pid": "p01780", "ProblemText": "Task Description: Fox Ciel went to JAG Kingdom by bicycle, but she forgot a place where she parked her bicycle. So she needs to search it from a bicycle-parking area before returning home.\n\nThe parking area is formed as a unweighted rooted tree $T$ with $n$ vertices, numbered $1$ through $n$. Each vertex has a space for parking one or more bicycles. Ciel thought that she parked her bicycle near the vertex $1$, so she decided to search it from there by the breadth-first search. That is, she searches it at the vertices in the increasing order of their distances from the vertex $1$. If multiple vertices have the same distance, she gives priority to the vertices in the order of searching at their parents. If multiple vertices have the same parent, she searches at the vertex with minimum number at first.\n\nUnlike a computer, she can't go to a next vertex by random access. Thus, if she goes to the vertex $j$ after the vertex $i$, she needs to walk the distance between the vertices $i$ and $j$. BFS by fox power perhaps takes a long time, so she asks you to calculate the total moving distance in the worst case starting from the vertex $1$.\nTask Input: The input is formatted as follows.\n$n$$p_2$ $p_3$ $p_4$ $\\cdots$ $p_n$\nThe first line contains an integer $n$ ($1 <= n <= 10^5$), which is the number of vertices on the unweighted rooted tree $T$.\nThe second line contains $n-1$ integers $p_i$ ($1 <= p_i < i$), which are the parent of the vertex $i$.\nThe vertex $1$ is a root node, so $p_1$ does not exist.\nTask Output: Print the total moving distance in the worst case in one line.\nTask Samples: input: 4\n1 1 2\n output: 6\ninput: 4\n1 1 3\n output: 4\ninput: 11\n1 1 3 3 2 4 1 3 2 9\n output: 25\n\n" }, { "title": "B - Cube Coloring", "content": "Great painter Cubic is famous for using cubes for his art. Now, he is engaged in a new work of art. He tries to form an $X * Y * Z$ rectangular parallelepiped by arranging and piling up many $1 * 1 * 1$ cubes such that the adjacent surfaces of cubes are fully shared.\n\nOf course, he won't finish his work only arranging and piling up cubes. The position of each cube is denoted by $(0,0,0)$ through $(X-1, Y-1, Z-1)$ as by the ordinary coordinate system, and Cubic calls the cube $(A, B, C)$ the origin cube. Then, he paints a pattern on the rectangular parallelepiped with different colors according to the distance between each cube and the origin cube. He paints all cubes regardless of whether or not a cube is visible externally. This is his artistic policy. He uses Manhattan distance as the distance between cubes. The Manhattan distance between two cubes $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is defined as $|x_1-x_2| + |y_1-y_2| + |z_1-z_2|$.\n\nOn the current work, Cubic decides to use $N$ colors, which are numbered from $1$ to $N$. He paints a cube with the $(i+1)$-th color if the distance $D$ between the cube and the origin cube satisfies $D \\equiv i \\pmod{N}$. \n\nCubic wants to estimate the consumption of each color in order to prepare for the current work. He asks a great programmer, you, to write a program calculating the number of cubes that will be painted by each color.", "constraint": "", "input": "The input contains seven integers $X$, $Y$, $Z$, $A$, $B$, $C$, and $N$. All integers are in one line and separated by a single space. Three integers $X$, $Y$, and $Z$ ($1 <= X, Y, Z <= 10^6$) represent the length of each side of the rectangular parallelepiped that Cubic tries to form. Three integers $A$, $B$, and $C$ ($0 <= A < X$, $0 <= B < Y$, $0 <= C < Z$) represent the position of the origin cube. The number of kinds of colors is denoted by $N$ ($1 <= N <= 1{, }000$).", "output": "The output contains $N$ integers in one line. The $i$-th integer ($1 <= i <= N$) represents the number of the cubes that will be painted by the $i$-th color. All integers must be separated by a single space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 2 0 0 0 5\n output: 1 3 3 1 0", "input: 4 3 3 1 1 1 3\n output: 13 10 13", "input: 2000 2000 2000 1000 1000 1000 1\n output: 8000000000"], "Pid": "p01781", "ProblemText": "Task Description: Great painter Cubic is famous for using cubes for his art. Now, he is engaged in a new work of art. He tries to form an $X * Y * Z$ rectangular parallelepiped by arranging and piling up many $1 * 1 * 1$ cubes such that the adjacent surfaces of cubes are fully shared.\n\nOf course, he won't finish his work only arranging and piling up cubes. The position of each cube is denoted by $(0,0,0)$ through $(X-1, Y-1, Z-1)$ as by the ordinary coordinate system, and Cubic calls the cube $(A, B, C)$ the origin cube. Then, he paints a pattern on the rectangular parallelepiped with different colors according to the distance between each cube and the origin cube. He paints all cubes regardless of whether or not a cube is visible externally. This is his artistic policy. He uses Manhattan distance as the distance between cubes. The Manhattan distance between two cubes $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is defined as $|x_1-x_2| + |y_1-y_2| + |z_1-z_2|$.\n\nOn the current work, Cubic decides to use $N$ colors, which are numbered from $1$ to $N$. He paints a cube with the $(i+1)$-th color if the distance $D$ between the cube and the origin cube satisfies $D \\equiv i \\pmod{N}$. \n\nCubic wants to estimate the consumption of each color in order to prepare for the current work. He asks a great programmer, you, to write a program calculating the number of cubes that will be painted by each color.\nTask Input: The input contains seven integers $X$, $Y$, $Z$, $A$, $B$, $C$, and $N$. All integers are in one line and separated by a single space. Three integers $X$, $Y$, and $Z$ ($1 <= X, Y, Z <= 10^6$) represent the length of each side of the rectangular parallelepiped that Cubic tries to form. Three integers $A$, $B$, and $C$ ($0 <= A < X$, $0 <= B < Y$, $0 <= C < Z$) represent the position of the origin cube. The number of kinds of colors is denoted by $N$ ($1 <= N <= 1{, }000$).\nTask Output: The output contains $N$ integers in one line. The $i$-th integer ($1 <= i <= N$) represents the number of the cubes that will be painted by the $i$-th color. All integers must be separated by a single space.\nTask Samples: input: 2 2 2 0 0 0 5\n output: 1 3 3 1 0\ninput: 4 3 3 1 1 1 3\n output: 13 10 13\ninput: 2000 2000 2000 1000 1000 1000 1\n output: 8000000000\n\n" }, { "title": "C - Decoding Ancient Messages", "content": "Professor Y's work is to dig up ancient artifacts. Recently, he found a lot of strange stone plates, each of which has $N^2$ characters arranged in an $N * N$ matrix. Further research revealed that each plate represents a message of length $N$. Also, the procedure to decode the message from a plate was turned out to be the following:\n\nSelect $N$ characters from the plate one by one so that any two characters are neither in the same row nor in the same column.\n\nCreate a string by concatenating the selected characters.\n\nAmong all possible strings obtained by the above steps, find the lexicographically smallest one. It is the message represented by this plate.\nNOTE: The order of the characters is defined as the same as the order of their ASCII values (that is, $\\mathtt{A} < \\mathtt{B} < \\cdots < \\mathtt{Z} < \\mathtt{a} < \\mathtt{b} < \\cdots < \\mathtt{z}$).\n\nAfter struggling with the plates, Professor Y gave up decoding messages by hand. You, a great programmer and Y's old friend, was asked for a help. Your task is to write a program to decode the messages hidden in the plates.", "constraint": "", "input": "The input is formated as follows:\n$N$$c_{11} c_{12} \\cdots c_{1N}$$c_{21} c_{22} \\cdots c_{2N}$: : $c_{N1} c_{N2} \\cdots c_{NN}$\nThe first line contains an integer $N$ ($1 <= N <= 50$). Each of the subsequent $N$ lines contains a string of $N$ characters. Each character in the string is an uppercase or lowercase English letter (A-Z, a-z).", "output": "Print the message represented by the plate in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\naab\nczc\nbaa\n output: aac", "input: 36\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiQiiiiiiiiiiiiiiiQiiiiiiiii\niiiiiiiiiiQQQiiiiiiiiiiQQQQiiiiiiiii\niiiiiiiiiiQQQQQiiiiiiiQQQQiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQQiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQQiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQiiiiiiiiiii\niiiiiiiiiiiiQQQQQQQQQQQQQiiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQQiiiiiiiiii\niiiiiiiiiiQQQQQQQQQQQQQQQQQiiiiiiiii\niiiiiiQiiiQQQQQQQQQQQQQQQQQiiiQiiiii\niiiiiiQQiQQQQQQQQQQQQQQQQQQiiQQiiiii\niiiiiiiQQQQQQQQQQQQQQQQQQQQiQQiiiiii\niiiiiiiiiQQQQQQQQQQQQQQQQQQQQiiiiiii\niiiiiiiiQQQQQiiQQQQQQQQiiQQQQQiiiiii\niiiiiiQQQQQQiiiiQQQQQiiiiQQQQQQiiiii\niiiiiQQQQQQQQiiiQQQQQiiQQQQQQQQiQiii\niiiQQQQQQQiiQiiiQQQQQiiQiiQQQQQQQQii\niQQQQQQQQQiiiiiQQQQQQQiiiiiiQQQQQQQi\niiQQQQQQQiiiiiiQQQQQQQiiiiiiiiQQQiii\niQQQQiiiiiiiiiQQQQQQQQQiiiiiiiiQQQii\niiiiiiiiiiiiiiQQQQQQQQQiiiiiiiiiiiii\niiiiiiiiiiiiiQQQQQQQQQQiiiiiiiiiiiii\niiiiiiiiiiiiiQQQQQQQQQQiiiiiiiiiiiii\niiiiiiiiiiiiiiQQQQQQQQiiiiiiiiiiiiii\niiiiiiiiiiiiiiQQQQQQQQiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n output: QQQQQQQQQQQQQQQQQQQQQQQQQiiiiiiiiiii", "input: 3\nAcm\naCm\nacM\n output: ACM"], "Pid": "p01782", "ProblemText": "Task Description: Professor Y's work is to dig up ancient artifacts. Recently, he found a lot of strange stone plates, each of which has $N^2$ characters arranged in an $N * N$ matrix. Further research revealed that each plate represents a message of length $N$. Also, the procedure to decode the message from a plate was turned out to be the following:\n\nSelect $N$ characters from the plate one by one so that any two characters are neither in the same row nor in the same column.\n\nCreate a string by concatenating the selected characters.\n\nAmong all possible strings obtained by the above steps, find the lexicographically smallest one. It is the message represented by this plate.\nNOTE: The order of the characters is defined as the same as the order of their ASCII values (that is, $\\mathtt{A} < \\mathtt{B} < \\cdots < \\mathtt{Z} < \\mathtt{a} < \\mathtt{b} < \\cdots < \\mathtt{z}$).\n\nAfter struggling with the plates, Professor Y gave up decoding messages by hand. You, a great programmer and Y's old friend, was asked for a help. Your task is to write a program to decode the messages hidden in the plates.\nTask Input: The input is formated as follows:\n$N$$c_{11} c_{12} \\cdots c_{1N}$$c_{21} c_{22} \\cdots c_{2N}$: : $c_{N1} c_{N2} \\cdots c_{NN}$\nThe first line contains an integer $N$ ($1 <= N <= 50$). Each of the subsequent $N$ lines contains a string of $N$ characters. Each character in the string is an uppercase or lowercase English letter (A-Z, a-z).\nTask Output: Print the message represented by the plate in a line.\nTask Samples: input: 3\naab\nczc\nbaa\n output: aac\ninput: 36\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiQiiiiiiiiiiiiiiiQiiiiiiiii\niiiiiiiiiiQQQiiiiiiiiiiQQQQiiiiiiiii\niiiiiiiiiiQQQQQiiiiiiiQQQQiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQQiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQQiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQiiiiiiiiiii\niiiiiiiiiiiiQQQQQQQQQQQQQiiiiiiiiiii\niiiiiiiiiiiQQQQQQQQQQQQQQQiiiiiiiiii\niiiiiiiiiiQQQQQQQQQQQQQQQQQiiiiiiiii\niiiiiiQiiiQQQQQQQQQQQQQQQQQiiiQiiiii\niiiiiiQQiQQQQQQQQQQQQQQQQQQiiQQiiiii\niiiiiiiQQQQQQQQQQQQQQQQQQQQiQQiiiiii\niiiiiiiiiQQQQQQQQQQQQQQQQQQQQiiiiiii\niiiiiiiiQQQQQiiQQQQQQQQiiQQQQQiiiiii\niiiiiiQQQQQQiiiiQQQQQiiiiQQQQQQiiiii\niiiiiQQQQQQQQiiiQQQQQiiQQQQQQQQiQiii\niiiQQQQQQQiiQiiiQQQQQiiQiiQQQQQQQQii\niQQQQQQQQQiiiiiQQQQQQQiiiiiiQQQQQQQi\niiQQQQQQQiiiiiiQQQQQQQiiiiiiiiQQQiii\niQQQQiiiiiiiiiQQQQQQQQQiiiiiiiiQQQii\niiiiiiiiiiiiiiQQQQQQQQQiiiiiiiiiiiii\niiiiiiiiiiiiiQQQQQQQQQQiiiiiiiiiiiii\niiiiiiiiiiiiiQQQQQQQQQQiiiiiiiiiiiii\niiiiiiiiiiiiiiQQQQQQQQiiiiiiiiiiiiii\niiiiiiiiiiiiiiQQQQQQQQiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n output: QQQQQQQQQQQQQQQQQQQQQQQQQiiiiiiiiiii\ninput: 3\nAcm\naCm\nacM\n output: ACM\n\n" }, { "title": "D - LR", "content": "JAG Kingdom will hold a contest called ICPC (Interesting Contest for Producing Calculation). \n\nAt the contest, you are given a string composed of ? s and usable characters. You should replace all ? s in the string with the usable characters to make the string valid mathematical expression, before submitting it. The usable characters are L, R, (, ), , , 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. \n\nFor example, suppose that you are given the string \"R(? ? 3, ? ? 1? 78? ? 1? )? \", then you can submit \"R(123, L(1678,213))\" as an example. \n\nThe submitted string will be scored as follows.\n\nLet $L$ and $R$ be functions defined by $L(x, y)=x$, $R(x, y)=y$, where $x$ and $y$ are non-negative integers.\nThe submitted string will be regarded as a mathematical expression, whose value will be the score. For example, the score of the string \"R(123, L(1678,213))\" is $R(123, L(1678,213)) = R(123,1678) = 1678$.\nIf the string cannot be evaluated as a mathematical expression about the functions $L$ and $R$, the string will be rejected. For example, \"R\", \"R(3)\", \"R(3,2\", \"R(3,2,4)\" and \"LR(3,2)\" are all invalid. \n\nAnd strings that contain numbers with extra leading zeros, will be rejected. For example, \"R(04,18)\" is invalid, while \"R(0,18)\" is valid.\nThe winner of the contest will be the person getting the highest score. Your friend Jagger, who is going to join the contest, wants to be the winner. You are asked by Jagger to make the program finding the possible highest score for the input string.", "constraint": "", "input": "The input contains one string in a line, whose length $N$ is between $1$ and $50$, inclusive. \n\nYou can assume that each element in the string is one of L, R, (, ), , , 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or ? .", "output": "Display the possible highest score in a line for the given string. \n\nIf it's impossible to get valid strings for the input string, print \"invalid\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: R?????,2?)\n output: 29", "input: ???3??\n output: 999399", "input: ????,??,???\n output: invalid", "input: ?????,??,???\n output: 99", "input: L(1111111111111111111111111111111111111111111,2)\n output: 1111111111111111111111111111111111111111111", "input: L?1???????????????????????????????????????????????\n output: 199999999999999999999999999999999999999999999", "input: L?0???????????????????????????????????????????????\n output: 0"], "Pid": "p01783", "ProblemText": "Task Description: JAG Kingdom will hold a contest called ICPC (Interesting Contest for Producing Calculation). \n\nAt the contest, you are given a string composed of ? s and usable characters. You should replace all ? s in the string with the usable characters to make the string valid mathematical expression, before submitting it. The usable characters are L, R, (, ), , , 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. \n\nFor example, suppose that you are given the string \"R(? ? 3, ? ? 1? 78? ? 1? )? \", then you can submit \"R(123, L(1678,213))\" as an example. \n\nThe submitted string will be scored as follows.\n\nLet $L$ and $R$ be functions defined by $L(x, y)=x$, $R(x, y)=y$, where $x$ and $y$ are non-negative integers.\nThe submitted string will be regarded as a mathematical expression, whose value will be the score. For example, the score of the string \"R(123, L(1678,213))\" is $R(123, L(1678,213)) = R(123,1678) = 1678$.\nIf the string cannot be evaluated as a mathematical expression about the functions $L$ and $R$, the string will be rejected. For example, \"R\", \"R(3)\", \"R(3,2\", \"R(3,2,4)\" and \"LR(3,2)\" are all invalid. \n\nAnd strings that contain numbers with extra leading zeros, will be rejected. For example, \"R(04,18)\" is invalid, while \"R(0,18)\" is valid.\nThe winner of the contest will be the person getting the highest score. Your friend Jagger, who is going to join the contest, wants to be the winner. You are asked by Jagger to make the program finding the possible highest score for the input string.\nTask Input: The input contains one string in a line, whose length $N$ is between $1$ and $50$, inclusive. \n\nYou can assume that each element in the string is one of L, R, (, ), , , 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or ? .\nTask Output: Display the possible highest score in a line for the given string. \n\nIf it's impossible to get valid strings for the input string, print \"invalid\" in a line.\nTask Samples: input: R?????,2?)\n output: 29\ninput: ???3??\n output: 999399\ninput: ????,??,???\n output: invalid\ninput: ?????,??,???\n output: 99\ninput: L(1111111111111111111111111111111111111111111,2)\n output: 1111111111111111111111111111111111111111111\ninput: L?1???????????????????????????????????????????????\n output: 199999999999999999999999999999999999999999999\ninput: L?0???????????????????????????????????????????????\n output: 0\n\n" }, { "title": "E - Parentheses", "content": "You are given $n$ strings $\\mathit{str}_1, \\mathit{str}_2, \\ldots, \\mathit{str}_n$, each consisting of ( and ). The objective is to determine whether it is possible to permute the $n$ strings so that the concatenation of the strings represents a valid string.\n\nValidity of strings are defined as follows:\n\n The empty string is valid. \n\n If $A$ and $B$ are valid, then the concatenation of $A$ and $B$ is valid. \n\n If $A$ is valid, then the string obtained by putting $A$ in a pair of matching parentheses is valid. \n\n Any other string is not valid. \nFor example, \"()()\" and \"(())\" are valid, while \"())\" and \"((()\" are not valid.", "constraint": "", "input": "The first line of the input contains an integer $n$ ($1 <= n <= 100$), representing the number of strings. Then $n$ lines follow, each of which contains $\\mathit{str}_i$ ($1 <= \\lvert \\mathit{str}_i \\rvert <= 100$). All characters in $\\mathit{str}_i$ are ( or ).", "output": "Output a line with \"Yes\" (without quotes) if you can make a valid string, or \"No\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n()(()((\n))()()(()\n)())(())\n output: Yes", "input: 2\n))()((\n))((())(\n output: No"], "Pid": "p01784", "ProblemText": "Task Description: You are given $n$ strings $\\mathit{str}_1, \\mathit{str}_2, \\ldots, \\mathit{str}_n$, each consisting of ( and ). The objective is to determine whether it is possible to permute the $n$ strings so that the concatenation of the strings represents a valid string.\n\nValidity of strings are defined as follows:\n\n The empty string is valid. \n\n If $A$ and $B$ are valid, then the concatenation of $A$ and $B$ is valid. \n\n If $A$ is valid, then the string obtained by putting $A$ in a pair of matching parentheses is valid. \n\n Any other string is not valid. \nFor example, \"()()\" and \"(())\" are valid, while \"())\" and \"((()\" are not valid.\nTask Input: The first line of the input contains an integer $n$ ($1 <= n <= 100$), representing the number of strings. Then $n$ lines follow, each of which contains $\\mathit{str}_i$ ($1 <= \\lvert \\mathit{str}_i \\rvert <= 100$). All characters in $\\mathit{str}_i$ are ( or ).\nTask Output: Output a line with \"Yes\" (without quotes) if you can make a valid string, or \"No\" otherwise.\nTask Samples: input: 3\n()(()((\n))()()(()\n)())(())\n output: Yes\ninput: 2\n))()((\n))((())(\n output: No\n\n" }, { "title": "F - Polygon Guards", "content": "You are an IT system administrator in the Ministry of Defense of Polygon Country. \n\nPolygon Country's border forms the polygon with $N$ vertices. Drawn on the 2D-plane, all of its vertices are at the lattice points and all of its edges are parallel with either the $x$-axis or the $y$-axis. \n\nIn order to prevent enemies from invading the country, it is surrounded by very strong defense walls along its border. However, on the vertices, the junctions of walls have unavoidable structural weaknesses. Therefore, enemies might attack and invade from the vertices. \n\nTo observe the vertices and find an invasion by enemies as soon as possible, the ministry decided to hire some guards. The ministry plans to locate them on some vertices such that all the vertices are observed by at least one guard. A guard at the vertex $A$ can observe a vertex $B$ if the entire segment connecting $A$ and $B$ is inside or on the edge of Polygon Country. Of course, guards can observe the vertices they are located on. And a guard can observe simultaneously all the vertices he or she can observe.\n\nTo reduce the defense expense, the ministry wants to minimize the number of guards. Your task is to calculate the minimum number of guards required to observe all the vertices of Polygon Country.", "constraint": "", "input": "The input is formatted as follows.\n$N$$X_1$ $Y_1$: : $X_N$ $Y_N$\nThe first line contains an even integer $N$ ($4 <= N < 40$). The following $N$ lines describe the vertices of Polygon Country. Each of the lines contains two integers, $X_i$ and $Y_i$ ($1 <= i <= N$, $\\lvert X_i \\rvert <= 1{, }000$, $\\lvert Y_i \\rvert <= 1{, }000$), separated by one space. The position of the $i$-th vertex is $(X_i, Y_i)$.\n\nIf $i$ is odd, $X_i = X_{i+1}$, $Y_i \\ne Y_{i+1}$. Otherwise, $X_i \\ne X_{i+1}$, $Y_i = Y_{i+1}$. Here, we regard that $X_{N+1} = X_1$, and $Y_{N+1} = Y_1$. The vertices are given in counterclockwise order under the coordinate system that the $x$-axis goes right, and the $y$-axis goes up. The shape of Polygon Country is simple. That is, each edge doesn 't share any points with other edges except that its both end points are shared with its neighbor edges.", "output": "Print the minimum number of guards in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n0 2\n0 0\n2 0\n2 1\n3 1\n3 3\n1 3\n1 2\n output: 1", "input: 12\n0 0\n0 -13\n3 -13\n3 -10\n10 -10\n10 10\n-1 10\n-1 13\n-4 13\n-4 10\n-10 10\n-10 0\n output: 2"], "Pid": "p01785", "ProblemText": "Task Description: You are an IT system administrator in the Ministry of Defense of Polygon Country. \n\nPolygon Country's border forms the polygon with $N$ vertices. Drawn on the 2D-plane, all of its vertices are at the lattice points and all of its edges are parallel with either the $x$-axis or the $y$-axis. \n\nIn order to prevent enemies from invading the country, it is surrounded by very strong defense walls along its border. However, on the vertices, the junctions of walls have unavoidable structural weaknesses. Therefore, enemies might attack and invade from the vertices. \n\nTo observe the vertices and find an invasion by enemies as soon as possible, the ministry decided to hire some guards. The ministry plans to locate them on some vertices such that all the vertices are observed by at least one guard. A guard at the vertex $A$ can observe a vertex $B$ if the entire segment connecting $A$ and $B$ is inside or on the edge of Polygon Country. Of course, guards can observe the vertices they are located on. And a guard can observe simultaneously all the vertices he or she can observe.\n\nTo reduce the defense expense, the ministry wants to minimize the number of guards. Your task is to calculate the minimum number of guards required to observe all the vertices of Polygon Country.\nTask Input: The input is formatted as follows.\n$N$$X_1$ $Y_1$: : $X_N$ $Y_N$\nThe first line contains an even integer $N$ ($4 <= N < 40$). The following $N$ lines describe the vertices of Polygon Country. Each of the lines contains two integers, $X_i$ and $Y_i$ ($1 <= i <= N$, $\\lvert X_i \\rvert <= 1{, }000$, $\\lvert Y_i \\rvert <= 1{, }000$), separated by one space. The position of the $i$-th vertex is $(X_i, Y_i)$.\n\nIf $i$ is odd, $X_i = X_{i+1}$, $Y_i \\ne Y_{i+1}$. Otherwise, $X_i \\ne X_{i+1}$, $Y_i = Y_{i+1}$. Here, we regard that $X_{N+1} = X_1$, and $Y_{N+1} = Y_1$. The vertices are given in counterclockwise order under the coordinate system that the $x$-axis goes right, and the $y$-axis goes up. The shape of Polygon Country is simple. That is, each edge doesn 't share any points with other edges except that its both end points are shared with its neighbor edges.\nTask Output: Print the minimum number of guards in one line.\nTask Samples: input: 8\n0 2\n0 0\n2 0\n2 1\n3 1\n3 3\n1 3\n1 2\n output: 1\ninput: 12\n0 0\n0 -13\n3 -13\n3 -10\n10 -10\n10 10\n-1 10\n-1 13\n-4 13\n-4 10\n-10 10\n-10 0\n output: 2\n\n" }, { "title": "G - Proportional Representation", "content": "An election selecting the members of the parliament in JAG Kingdom was held. The only system adopted in this country is the party-list proportional representation. In this system, each citizen votes for a political party, and the number of seats a party wins will be proportional to the number of votes it receives. Since the total number of seats in the parliament is an integer, of course, it is often impossible to allocate seats exactly proportionaly. In JAG Kingdom, the following method, known as the D'Hondt method, is used to determine the number of seats for each party. \n\nAssume that every party has an unlimited supply of candidates and the candidates of each party are ordered in some way. To the $y$-th candidate of a party which received $x$ votes, assign the value $\\dfrac{x}{y}$. Then all the candidates are sorted in the decreasing order of their assigned values. The first $T$ candidates are considered to win, where $T$ is the total number of seats, and the number of seats a party win is the number of its winning candidates. \n\nThe table below shows an example with three parties. The first party received $40$ votes, the second $60$ votes, and the third $30$ votes. If the total number of seats is $T = 9$, the first party will win $3$ seats, the second $4$ seats, and the third $2$ seats. \n\nWhen selecting winning candidates, ties are broken by lottery; any tied candidates will have a chance to win. For instance, in the example above, if $T = 5$ then two candidates tie for the value $20$ and there are two possible outcomes: \n\n The first party wins $2$ seats, the second $2$ seats, and the third $1$ seat. \n\n The first party wins $1$ seat, the second $3$ seats, and the third $1$ seat. \n\nYou have just heard the results of the election on TV. Knowing the total number of valid votes and the number of seats each party won, you wonder how many votes each party received. \n\nGiven $N$, $M$, and $S_i$ ($1 <= i <= M$), denoting the total number of valid votes, the number of parties, and the number of seats the $i$-th party won, respectively, your task is to determine for each party the minimum and the maximum possible number of votes it received. Note that for some cases there might be no such situation with the given $N$, $M$, and $S_i$.", "constraint": "", "input": "The first line of the input contains two integers $N$ ($1 <= N <= 10^9$) and $M$ ($1 <= M <= 30{, }000$), where $N$ is the total number of valid votes and $M$ is the number of parties. $M$ lines follow, the $i$-th of which contains a single integer $S_i$ ($0 <= S_i <= 30{, }000$), representing the number of seats the $i$-th party won. You can assume that there exists $i$ with $S_i \\ne 0$.", "output": "If there is no situation with the given $N$, $M$, and $S_i$, display the word \"impossible\". Otherwise, output $M$ lines, each containing two integers. The first integer and the second integer in the $i$-th line should be the minimum and the maximum possible number of votes the $i$-th party received, respectively.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10 2\n2\n1\n output: 5 7\n3 5", "input: 5 6\n0\n2\n0\n2\n6\n0\n output: 0 0\n1 1\n0 0\n1 1\n3 3\n0 0", "input: 2000 5\n200\n201\n202\n203\n204\n output: 396 397\n397 399\n399 401\n401 403\n403 404", "input: 15 10\n1\n1\n1\n1\n1\n1\n1\n1\n1\n13\n output: impossible", "input: 1000000000 9\n12507\n16653\n26746\n21516\n29090\n10215\n28375\n21379\n18494\n output: 67611619 67619582\n90024490 90033301\n144586260 144597136\n116313392 116323198\n157257695 157269050\n55221291 55228786\n153392475 153403684\n115572783 115582561\n99976756 99985943"], "Pid": "p01786", "ProblemText": "Task Description: An election selecting the members of the parliament in JAG Kingdom was held. The only system adopted in this country is the party-list proportional representation. In this system, each citizen votes for a political party, and the number of seats a party wins will be proportional to the number of votes it receives. Since the total number of seats in the parliament is an integer, of course, it is often impossible to allocate seats exactly proportionaly. In JAG Kingdom, the following method, known as the D'Hondt method, is used to determine the number of seats for each party. \n\nAssume that every party has an unlimited supply of candidates and the candidates of each party are ordered in some way. To the $y$-th candidate of a party which received $x$ votes, assign the value $\\dfrac{x}{y}$. Then all the candidates are sorted in the decreasing order of their assigned values. The first $T$ candidates are considered to win, where $T$ is the total number of seats, and the number of seats a party win is the number of its winning candidates. \n\nThe table below shows an example with three parties. The first party received $40$ votes, the second $60$ votes, and the third $30$ votes. If the total number of seats is $T = 9$, the first party will win $3$ seats, the second $4$ seats, and the third $2$ seats. \n\nWhen selecting winning candidates, ties are broken by lottery; any tied candidates will have a chance to win. For instance, in the example above, if $T = 5$ then two candidates tie for the value $20$ and there are two possible outcomes: \n\n The first party wins $2$ seats, the second $2$ seats, and the third $1$ seat. \n\n The first party wins $1$ seat, the second $3$ seats, and the third $1$ seat. \n\nYou have just heard the results of the election on TV. Knowing the total number of valid votes and the number of seats each party won, you wonder how many votes each party received. \n\nGiven $N$, $M$, and $S_i$ ($1 <= i <= M$), denoting the total number of valid votes, the number of parties, and the number of seats the $i$-th party won, respectively, your task is to determine for each party the minimum and the maximum possible number of votes it received. Note that for some cases there might be no such situation with the given $N$, $M$, and $S_i$.\nTask Input: The first line of the input contains two integers $N$ ($1 <= N <= 10^9$) and $M$ ($1 <= M <= 30{, }000$), where $N$ is the total number of valid votes and $M$ is the number of parties. $M$ lines follow, the $i$-th of which contains a single integer $S_i$ ($0 <= S_i <= 30{, }000$), representing the number of seats the $i$-th party won. You can assume that there exists $i$ with $S_i \\ne 0$.\nTask Output: If there is no situation with the given $N$, $M$, and $S_i$, display the word \"impossible\". Otherwise, output $M$ lines, each containing two integers. The first integer and the second integer in the $i$-th line should be the minimum and the maximum possible number of votes the $i$-th party received, respectively.\nTask Samples: input: 10 2\n2\n1\n output: 5 7\n3 5\ninput: 5 6\n0\n2\n0\n2\n6\n0\n output: 0 0\n1 1\n0 0\n1 1\n3 3\n0 0\ninput: 2000 5\n200\n201\n202\n203\n204\n output: 396 397\n397 399\n399 401\n401 403\n403 404\ninput: 15 10\n1\n1\n1\n1\n1\n1\n1\n1\n1\n13\n output: impossible\ninput: 1000000000 9\n12507\n16653\n26746\n21516\n29090\n10215\n28375\n21379\n18494\n output: 67611619 67619582\n90024490 90033301\n144586260 144597136\n116313392 116323198\n157257695 157269050\n55221291 55228786\n153392475 153403684\n115572783 115582561\n99976756 99985943\n\n" }, { "title": "H - RLE Replacement", "content": "In JAG Kingdom, ICPC (Intentionally Compressible Programming Code) is one of the common programming languages. Programs in this language only contain uppercase English letters and the same letters often appear repeatedly in ICPC programs. Thus, programmers in JAG Kingdom prefer to compress ICPC programs by Run Length Encoding in order to manage very large-scale ICPC programs.\n\nRun Length Encoding (RLE) is a string compression method such that each maximal sequence of the same letters is encoded by a pair of the letter and the length. For example, the string \"RRRRLEEE\" is represented as \"R4L1E3\" in RLE.\n\nNow, you manage many ICPC programs encoded by RLE. You are developing an editor for ICPC programs encoded by RLE, and now you would like to implement a replacement function. Given three strings $A$, $B$, and $C$ that are encoded by RLE, your task is to implement a function replacing the first occurrence of the substring $B$ in $A$ with $C$, and outputting the edited string encoded by RLE. If $B$ does not occur in $A$, you must output $A$ encoded by RLE without changes.", "constraint": "", "input": "The input consists of three lines.\n $A$ $B$ $C$\nThe lines represent strings $A$, $B$, and $C$ that are encoded by RLE, respectively. Each of the lines has the following format:\n $c_1$ $l_1$ $c_2$ $l_2$ $\\ldots$ $c_n$ $l_n$ \\$\nEach $c_i$ ($1 <= i <= n$) is an uppercase English letter (A-Z) and $l_i$ ($1 <= i <= n$, $1 <= l_i <= 10^8$) is an integer which represents the length of the repetition of $c_i$. The number $n$ of the pairs of a letter and an integer satisfies $1 <= n <= 10^3$. A terminal symbol $ indicates the end of a string encoded by RLE. The letters and the integers are separated by a single space. It is guaranteed that $c_i \\neq c_{i+1}$ holds for any $1 <= i <= n-1$.", "output": "Replace the first occurrence of the substring $B$ in $A$ with $C$ if $B$ occurs in $A$, and output the string encoded by RLE. The output must have the following format:\n $c_1$ $l_1$ $c_2$ $l_2$ $\\ldots$ $c_m$ $l_m$ \\$\nHere, $c_i \\neq c_{i+1}$ for $1 <= i <= m-1$ and $l_i > 0$ for $1 <= i <= m$ must hold.", "content_img": false, "lang": "en", "error": false, "samples": ["input: R 100 L 20 E 10 \\$\nR 5 L 10 \\$\nX 20 \\$\n output: R 95 X 20 L 10 E 10 \\$", "input: A 3 B 3 A 3 \\$\nA 1 B 3 A 1 \\$\nA 2 \\$\n output: A 6 \\$"], "Pid": "p01787", "ProblemText": "Task Description: In JAG Kingdom, ICPC (Intentionally Compressible Programming Code) is one of the common programming languages. Programs in this language only contain uppercase English letters and the same letters often appear repeatedly in ICPC programs. Thus, programmers in JAG Kingdom prefer to compress ICPC programs by Run Length Encoding in order to manage very large-scale ICPC programs.\n\nRun Length Encoding (RLE) is a string compression method such that each maximal sequence of the same letters is encoded by a pair of the letter and the length. For example, the string \"RRRRLEEE\" is represented as \"R4L1E3\" in RLE.\n\nNow, you manage many ICPC programs encoded by RLE. You are developing an editor for ICPC programs encoded by RLE, and now you would like to implement a replacement function. Given three strings $A$, $B$, and $C$ that are encoded by RLE, your task is to implement a function replacing the first occurrence of the substring $B$ in $A$ with $C$, and outputting the edited string encoded by RLE. If $B$ does not occur in $A$, you must output $A$ encoded by RLE without changes.\nTask Input: The input consists of three lines.\n $A$ $B$ $C$\nThe lines represent strings $A$, $B$, and $C$ that are encoded by RLE, respectively. Each of the lines has the following format:\n $c_1$ $l_1$ $c_2$ $l_2$ $\\ldots$ $c_n$ $l_n$ \\$\nEach $c_i$ ($1 <= i <= n$) is an uppercase English letter (A-Z) and $l_i$ ($1 <= i <= n$, $1 <= l_i <= 10^8$) is an integer which represents the length of the repetition of $c_i$. The number $n$ of the pairs of a letter and an integer satisfies $1 <= n <= 10^3$. A terminal symbol $ indicates the end of a string encoded by RLE. The letters and the integers are separated by a single space. It is guaranteed that $c_i \\neq c_{i+1}$ holds for any $1 <= i <= n-1$.\nTask Output: Replace the first occurrence of the substring $B$ in $A$ with $C$ if $B$ occurs in $A$, and output the string encoded by RLE. The output must have the following format:\n $c_1$ $l_1$ $c_2$ $l_2$ $\\ldots$ $c_m$ $l_m$ \\$\nHere, $c_i \\neq c_{i+1}$ for $1 <= i <= m-1$ and $l_i > 0$ for $1 <= i <= m$ must hold.\nTask Samples: input: R 100 L 20 E 10 \\$\nR 5 L 10 \\$\nX 20 \\$\n output: R 95 X 20 L 10 E 10 \\$\ninput: A 3 B 3 A 3 \\$\nA 1 B 3 A 1 \\$\nA 2 \\$\n output: A 6 \\$\n\n" }, { "title": "I - Tokyo Olympics Center", "content": "You are participating in the Summer Training Camp for Programming Cotests. The camp is held in an accommodation facility called Tokyo Olympics Center. Today is the last day of the camp. Unfortunately, you are ordered to check if all the participants have properly cleaned their rooms.\n\nThe accommodation facility is a rectangular field whose height is $H$ and width is $W$. The field is divided into square cells. The rows are numbered $1$ through $H$ from top to bottom and the columns are numbered $1$ through $W$ from left to right. The cell in row $i$, column $j$ is denoted by $(i, j)$. Two cells are adjacent if they share an edge.\n\nEach cell is called either a wall cell or a floor cell. A wall cell represents a wall which no one can enter. \nA floor cell is a part of the inside of the accommodation facility. Everybody can move between two adjacent floor cells. The floor cells are divided into several units. Each unit is assigned an uppercase English letter (A, B, C, . . . ). A floor cell adjacent to exactly one floor cell is called a room. Otherwise the floor cell is called an aisle. For example, the accommodation facility can be shown as the following figure. We denote a wall cell by . (single period).\n. . . . . . . . . . . . . . . . . . .\n. . . . . AAABBBBBBB. . . .\n. . . A. AA. A. . . B. B. . B.\n. . AAAAAAAABBBBBBBB.\n. . . A. . A. A. . . . . B. . . .\n. . . . . . A. . . . . . . BBBB.\n. . . . A. AA. . C. C. . . B. .\n. . . AAAAACCCCCCBBBB.\n. . . A. . A. . . C. C. . . B. .\n. . . . . . . . . . . . . . . . . . .\nIn the above figure, there are $7$ rooms in unit A, $4$ rooms in unit B, and $4$ rooms in unit C.\n\nBecause the accommodation facility is too large to explore alone, you asked the other participants of the camp to check the rooms. For simplicity's sake, we call them staffs. Now, there are $K$ staffs at the cell $(s, t)$. You decided to check the rooms according to the following procedure.\n\n First, you assign each staff to some of units. Every unit must be assigned to exactly one staff. Note that it is allowed to assign all the units to one staff or to assign no units to some staffs.\n\n Then, each staff starts to check the rooms in the assigned units at the same time. The staffs can move between two adjacent floor cells in $T_{\\mathit{move}}$ time. To check the room at $(i, j)$, the staffs must move to the cell $(i, j)$ and spend $T_{\\mathit{check}}$ time there. Each staff first determines the order of the units to check and he or she must check the rooms according to the order. For example, suppose that there is a staff who is assigned units A, C, and E. He may decide that the order is E->A->C. After that, he must check all the rooms in unit E at first. Then, he must check all the rooms in unit A, and so on. The staffs can pass any floor cells. However, the staffs cannot check rooms that are not assigned to them. Further, the staffs cannot check rooms against the order of units that they have decided. \n\n After checking all the assigned rooms, the staffs must return to the cell $(s, t)$. \n\n When every staff returns to the cell $(s, t)$, the task is done. \nBecause you do not have enough time before the next contest, you want to minimize the total time to check all the rooms.", "constraint": "", "input": "The first line of the input contains three integers $H$, $W$, and $K$ ($1 <= H <= 50$, $1 <= W <= 50$, $1 <= K <= 12$). The second line contains four integers $s$, $t$, $T_{\\mathit{move}}$, and $T_{\\mathit{check}}$ ($1 <= s <= H$, $1 <= t <= W$, $1 <= T_{\\mathit{move}}, T_{\\mathit{check}} <= 10{, }000$). Each of the following $H$ lines contains exactly $W$ characters. Each character represents a cell in the accommodation facility. The $j$-th character in the $i$-th line of these lines is . if the cell $(i, j)$ is a wall cell. Otherwise, the character is an uppercase English letter (A-L) representing the unit to which the cell $(i, j)$ belongs.\n\nYou can assume that the following conditions are satisfied.\n\n The number of rooms in each unit is between $1$ and $12$, inclusive. \n\n The cell $(s, t)$ is guaranteed to be an aisle.\n\n Floor cells in each unit are connected.\n\n Floor cells in the field are connected.\n\n Every unit contains at least two cells.", "output": "Output the minimum required time to check all the rooms in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 1\n1 1 10 10\nAAA\nA..\nA..\n output: 100", "input: 3 3 2\n1 1 10 10\nABB\nA..\nA..\n output: 50", "input: 5 10 3\n3 6 1 100\n...G.H.A..\n.AAGAHAABB\nFFAAAAAAA.\n.EEAAADACC\n..E...D...\n output: 316", "input: 10 19 2\n6 15 3 10\n...................\n.....AAABBBBBBB....\n...A.AA.A...B.B..B.\n..AAAAAAAABBBBBBBB.\n...A..A.A.....B....\n......A.......BBBB.\n....A.AA..C.C...B..\n...AAAAACCCCCCBBBB.\n...A..A...C.C...B..\n...................\n output: 232", "input: 27 36 6\n24 19 616 1933\n....................................\n..........B...............B.........\n..........BBB..........BBBB.........\n..........BBBBB.......BBBB..........\n...........BBBBBBBBBBBBBBB..........\n...........BBBBBBBBBBBBBBB..........\n...........BBBBBBBBBBBBBB...........\n............BBBBBBBBBBBBB...........\n...........BBBBBBBBBBBBBBB..........\n..........BBBBBBBBBBBBBBBBB.........\n......B...BBBBBBBBBBBBBBBBB...B.....\n......BB.BBBBBBBBBBBBBBBBBB..BB.....\n.......BBBBBBBBBBBBBBBBBBBB.BB......\n.........BBBBBBBBBBBBBBBBBBBB.......\n........BBBBB..BBBBBBBB..BBBBB......\n......BBBBBB....BBBBB....BBBBBB.....\n.....BBBBBBBB...BBBBB..BBBBBBBB.B...\n...BBBBBBB..B...BBBBB..B..BBBBBBBB..\n.BBBBBBBBB.....BBBBBBB......BBBBBBB.\n..BBBBBBB......BBBBBBB........BBB...\n.BBBB.........BBBBBBBBB........BBB..\n..............BBBBBBBBB.............\n.............BBBBBBBBBB.............\n.............BBBBBBBBBB.............\n..............BBBBBBBB..............\n..............BBBBBBBB..............\n....................................\n output: 137071"], "Pid": "p01788", "ProblemText": "Task Description: You are participating in the Summer Training Camp for Programming Cotests. The camp is held in an accommodation facility called Tokyo Olympics Center. Today is the last day of the camp. Unfortunately, you are ordered to check if all the participants have properly cleaned their rooms.\n\nThe accommodation facility is a rectangular field whose height is $H$ and width is $W$. The field is divided into square cells. The rows are numbered $1$ through $H$ from top to bottom and the columns are numbered $1$ through $W$ from left to right. The cell in row $i$, column $j$ is denoted by $(i, j)$. Two cells are adjacent if they share an edge.\n\nEach cell is called either a wall cell or a floor cell. A wall cell represents a wall which no one can enter. \nA floor cell is a part of the inside of the accommodation facility. Everybody can move between two adjacent floor cells. The floor cells are divided into several units. Each unit is assigned an uppercase English letter (A, B, C, . . . ). A floor cell adjacent to exactly one floor cell is called a room. Otherwise the floor cell is called an aisle. For example, the accommodation facility can be shown as the following figure. We denote a wall cell by . (single period).\n. . . . . . . . . . . . . . . . . . .\n. . . . . AAABBBBBBB. . . .\n. . . A. AA. A. . . B. B. . B.\n. . AAAAAAAABBBBBBBB.\n. . . A. . A. A. . . . . B. . . .\n. . . . . . A. . . . . . . BBBB.\n. . . . A. AA. . C. C. . . B. .\n. . . AAAAACCCCCCBBBB.\n. . . A. . A. . . C. C. . . B. .\n. . . . . . . . . . . . . . . . . . .\nIn the above figure, there are $7$ rooms in unit A, $4$ rooms in unit B, and $4$ rooms in unit C.\n\nBecause the accommodation facility is too large to explore alone, you asked the other participants of the camp to check the rooms. For simplicity's sake, we call them staffs. Now, there are $K$ staffs at the cell $(s, t)$. You decided to check the rooms according to the following procedure.\n\n First, you assign each staff to some of units. Every unit must be assigned to exactly one staff. Note that it is allowed to assign all the units to one staff or to assign no units to some staffs.\n\n Then, each staff starts to check the rooms in the assigned units at the same time. The staffs can move between two adjacent floor cells in $T_{\\mathit{move}}$ time. To check the room at $(i, j)$, the staffs must move to the cell $(i, j)$ and spend $T_{\\mathit{check}}$ time there. Each staff first determines the order of the units to check and he or she must check the rooms according to the order. For example, suppose that there is a staff who is assigned units A, C, and E. He may decide that the order is E->A->C. After that, he must check all the rooms in unit E at first. Then, he must check all the rooms in unit A, and so on. The staffs can pass any floor cells. However, the staffs cannot check rooms that are not assigned to them. Further, the staffs cannot check rooms against the order of units that they have decided. \n\n After checking all the assigned rooms, the staffs must return to the cell $(s, t)$. \n\n When every staff returns to the cell $(s, t)$, the task is done. \nBecause you do not have enough time before the next contest, you want to minimize the total time to check all the rooms.\nTask Input: The first line of the input contains three integers $H$, $W$, and $K$ ($1 <= H <= 50$, $1 <= W <= 50$, $1 <= K <= 12$). The second line contains four integers $s$, $t$, $T_{\\mathit{move}}$, and $T_{\\mathit{check}}$ ($1 <= s <= H$, $1 <= t <= W$, $1 <= T_{\\mathit{move}}, T_{\\mathit{check}} <= 10{, }000$). Each of the following $H$ lines contains exactly $W$ characters. Each character represents a cell in the accommodation facility. The $j$-th character in the $i$-th line of these lines is . if the cell $(i, j)$ is a wall cell. Otherwise, the character is an uppercase English letter (A-L) representing the unit to which the cell $(i, j)$ belongs.\n\nYou can assume that the following conditions are satisfied.\n\n The number of rooms in each unit is between $1$ and $12$, inclusive. \n\n The cell $(s, t)$ is guaranteed to be an aisle.\n\n Floor cells in each unit are connected.\n\n Floor cells in the field are connected.\n\n Every unit contains at least two cells.\nTask Output: Output the minimum required time to check all the rooms in one line.\nTask Samples: input: 3 3 1\n1 1 10 10\nAAA\nA..\nA..\n output: 100\ninput: 3 3 2\n1 1 10 10\nABB\nA..\nA..\n output: 50\ninput: 5 10 3\n3 6 1 100\n...G.H.A..\n.AAGAHAABB\nFFAAAAAAA.\n.EEAAADACC\n..E...D...\n output: 316\ninput: 10 19 2\n6 15 3 10\n...................\n.....AAABBBBBBB....\n...A.AA.A...B.B..B.\n..AAAAAAAABBBBBBBB.\n...A..A.A.....B....\n......A.......BBBB.\n....A.AA..C.C...B..\n...AAAAACCCCCCBBBB.\n...A..A...C.C...B..\n...................\n output: 232\ninput: 27 36 6\n24 19 616 1933\n....................................\n..........B...............B.........\n..........BBB..........BBBB.........\n..........BBBBB.......BBBB..........\n...........BBBBBBBBBBBBBBB..........\n...........BBBBBBBBBBBBBBB..........\n...........BBBBBBBBBBBBBB...........\n............BBBBBBBBBBBBB...........\n...........BBBBBBBBBBBBBBB..........\n..........BBBBBBBBBBBBBBBBB.........\n......B...BBBBBBBBBBBBBBBBB...B.....\n......BB.BBBBBBBBBBBBBBBBBB..BB.....\n.......BBBBBBBBBBBBBBBBBBBB.BB......\n.........BBBBBBBBBBBBBBBBBBBB.......\n........BBBBB..BBBBBBBB..BBBBB......\n......BBBBBB....BBBBB....BBBBBB.....\n.....BBBBBBBB...BBBBB..BBBBBBBB.B...\n...BBBBBBB..B...BBBBB..B..BBBBBBBB..\n.BBBBBBBBB.....BBBBBBB......BBBBBBB.\n..BBBBBBB......BBBBBBB........BBB...\n.BBBB.........BBBBBBBBB........BBB..\n..............BBBBBBBBB.............\n.............BBBBBBBBBB.............\n.............BBBBBBBBBB.............\n..............BBBBBBBB..............\n..............BBBBBBBB..............\n....................................\n output: 137071\n\n" }, { "title": "J - Unfair Game", "content": "Rabbit Hanako and Fox Jiro are great friends going to JAG primary school. Today they decided to play the following game during the lunch break. \n\nThis game is played by two players with $N$ heaps of some number of stones. The players alternatively take their turn to play the game. Jiro is a kind gentleman, so he yielded the first turn to Hanako. In each turn, the player must take some stones, satisfying the following conditions:\n\nIf the player is Hanako, she must take between $1$ to $A$ stones, inclusive, from a heap.\n\nIf the player is Jiro, he must take between $1$ to $B$ stones, inclusive, from a heap.\nThe winner is the player who takes the last stone. Jiro thinks it is rude to go easy on her because he is a perfect gentleman. Therefore, he does him best. Of course, Hanako also does so.\n\nJiro is worried that he may lose the game. Being a cadet teacher working at JAG primary school as well as a professional competitive programmer, you should help him by programming. Your task is to write a program calculating the winner, assuming that they both play optimally.", "constraint": "", "input": "The first line contains three integers $N$, $A$, and $B$. $N$ ($1 <= N <= 10^5$) is the number of heaps. $A$ and $B$ ($1 <= A, B <= 10^9$) are the maximum numbers of stones that Hanako and Jiro can take in a turn, respectively. Then $N$ lines follow, each of which contains a single integer $S_i$ ($1 <= S_i <= 10^9$), representing the number of stones in the $i$-th heap at the beginning of the game.", "output": "Output a line with \"Hanako\" if Hanako wins the game or \"Jiro\" in the other case.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 4\n3\n6\n12\n output: Hanako", "input: 4 7 8\n8\n3\n14\n5\n output: Jiro"], "Pid": "p01789", "ProblemText": "Task Description: Rabbit Hanako and Fox Jiro are great friends going to JAG primary school. Today they decided to play the following game during the lunch break. \n\nThis game is played by two players with $N$ heaps of some number of stones. The players alternatively take their turn to play the game. Jiro is a kind gentleman, so he yielded the first turn to Hanako. In each turn, the player must take some stones, satisfying the following conditions:\n\nIf the player is Hanako, she must take between $1$ to $A$ stones, inclusive, from a heap.\n\nIf the player is Jiro, he must take between $1$ to $B$ stones, inclusive, from a heap.\nThe winner is the player who takes the last stone. Jiro thinks it is rude to go easy on her because he is a perfect gentleman. Therefore, he does him best. Of course, Hanako also does so.\n\nJiro is worried that he may lose the game. Being a cadet teacher working at JAG primary school as well as a professional competitive programmer, you should help him by programming. Your task is to write a program calculating the winner, assuming that they both play optimally.\nTask Input: The first line contains three integers $N$, $A$, and $B$. $N$ ($1 <= N <= 10^5$) is the number of heaps. $A$ and $B$ ($1 <= A, B <= 10^9$) are the maximum numbers of stones that Hanako and Jiro can take in a turn, respectively. Then $N$ lines follow, each of which contains a single integer $S_i$ ($1 <= S_i <= 10^9$), representing the number of stones in the $i$-th heap at the beginning of the game.\nTask Output: Output a line with \"Hanako\" if Hanako wins the game or \"Jiro\" in the other case.\nTask Samples: input: 3 5 4\n3\n6\n12\n output: Hanako\ninput: 4 7 8\n8\n3\n14\n5\n output: Jiro\n\n" }, { "title": "Problem A\nBalanced Paths", "content": "You are given an undirected tree with $n$ nodes. The nodes are numbered 1 through $n$. Each node is labeled with either '(' or ')'. Let $l[u \\rightarrow v]$ denote the string obtained by concatenating the labels of the nodes on the simple path from $u$ to $v$. (Note that the simple path between two nodes is uniquely determined on a tree. ) A balanced string is defined as follows:\n\n The empty string is balanced.\n\n For any balanced string $s$, the string \"(\" $s$ \")\" is balanced.\n\n For any balanced strings $s$ and $t$, the string $st$ (the concatenation of $s$ and $t$) is balanced.\n\n Any other string is NOT balanced.\nCalculate the number of the ordered pairs of the nodes ($u$, $v$) such that $l[u \\rightarrow v]$ is balanced.", "constraint": "", "input": "The input consists of a single test case. The input starts with an integer $n (2 <= n <= 10^5)$, which is the number of nodes of the tree. The next line contains a string of length $n$, each character of which is either '(' or ')'. The $x$-th character of the string represents the label of the node $x$ of the tree. Each of the following $n - 1$ lines contains two integers $a_i$ and $b_i$ $(1 <= a_i, b_i <= n)$, which represents that the node $a_i$ and the node $b_i$ are connected by an edge. The given graph is guaranteed to be a tree.", "output": "Display a line containing the number of the ordered pairs ($u$, $v$) such that $l[u \\rightarrow v]$ is balanced.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n()\n1 2\n output: 1", "input: 4\n(())\n1 2\n2 3\n3 4\n output: 2", "input: 5\n()())\n1 2\n2 3\n2 4\n1 5\n output: 4"], "Pid": "p01790", "ProblemText": "Task Description: You are given an undirected tree with $n$ nodes. The nodes are numbered 1 through $n$. Each node is labeled with either '(' or ')'. Let $l[u \\rightarrow v]$ denote the string obtained by concatenating the labels of the nodes on the simple path from $u$ to $v$. (Note that the simple path between two nodes is uniquely determined on a tree. ) A balanced string is defined as follows:\n\n The empty string is balanced.\n\n For any balanced string $s$, the string \"(\" $s$ \")\" is balanced.\n\n For any balanced strings $s$ and $t$, the string $st$ (the concatenation of $s$ and $t$) is balanced.\n\n Any other string is NOT balanced.\nCalculate the number of the ordered pairs of the nodes ($u$, $v$) such that $l[u \\rightarrow v]$ is balanced.\nTask Input: The input consists of a single test case. The input starts with an integer $n (2 <= n <= 10^5)$, which is the number of nodes of the tree. The next line contains a string of length $n$, each character of which is either '(' or ')'. The $x$-th character of the string represents the label of the node $x$ of the tree. Each of the following $n - 1$ lines contains two integers $a_i$ and $b_i$ $(1 <= a_i, b_i <= n)$, which represents that the node $a_i$ and the node $b_i$ are connected by an edge. The given graph is guaranteed to be a tree.\nTask Output: Display a line containing the number of the ordered pairs ($u$, $v$) such that $l[u \\rightarrow v]$ is balanced.\nTask Samples: input: 2\n()\n1 2\n output: 1\ninput: 4\n(())\n1 2\n2 3\n3 4\n output: 2\ninput: 5\n()())\n1 2\n2 3\n2 4\n1 5\n output: 4\n\n" }, { "title": "Problem B\nCard Game Strategy", "content": "Alice and Bob are going to play a card game. There are $n$ cards, each having an integer written on it. The game proceeds as follows:\n\n Alice chooses an integer between $a$ and $b$, inclusive. Call this integer $t$. Alice then tells Bob the value of $t$.\n\n Bob chooses $k$ out of the $n$ cards. Compute the sum of the integers written on the $k$ cards Bob chooses. Call this sum $u$.\n\nAlice's objective is to make $|t - u|$ as large as possible and Bob's is to make $|t - u|$ as small as possible.\n\nPrior to the game, both Alice and Bob know the values of $n$, $k$, $a$, and $b$, and also the integers on the cards. Both Alice and Bob will play optimally. In particular, Alice will make a choice, knowing that Bob will surely minimize $|t - u|$ for told $t$. Additionally, assume that Alice prefers to choose smaller $t$ if she has multiple equally good choices.\n\nYour task is to determine the outcome of the game: the value of $t$ Alice will choose and the $k$ cards Bob will choose for that $t$.", "constraint": "", "input": "The input consists of two lines representing a single test case. The first line contains four integers $n$, $k$, $a$, and $b$ $(1 <= k <= n <= 600,0 <= a <= b <= 180,000)$. The second line contains $n$ integers $x_1, . . . , x_n$ $(0 <= x_i <= 300)$, denoting that $x_i$ is written on the $i$-th card.", "output": "Display two lines: The first line should contain an integer representing the value of $t$ Alice will choose. The second line should contain k distinct integers between 1 and $n$, inclusive, representing the indices of the cards Bob will choose. If Bob has multiple equally good choices, display any one of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 58 100\n10 10 50 80\n output: 75\n2 3", "input: 8 3 1300 1800\n2 0 1 5 0 4 1 9\n output: 1800\n4 6 8"], "Pid": "p01791", "ProblemText": "Task Description: Alice and Bob are going to play a card game. There are $n$ cards, each having an integer written on it. The game proceeds as follows:\n\n Alice chooses an integer between $a$ and $b$, inclusive. Call this integer $t$. Alice then tells Bob the value of $t$.\n\n Bob chooses $k$ out of the $n$ cards. Compute the sum of the integers written on the $k$ cards Bob chooses. Call this sum $u$.\n\nAlice's objective is to make $|t - u|$ as large as possible and Bob's is to make $|t - u|$ as small as possible.\n\nPrior to the game, both Alice and Bob know the values of $n$, $k$, $a$, and $b$, and also the integers on the cards. Both Alice and Bob will play optimally. In particular, Alice will make a choice, knowing that Bob will surely minimize $|t - u|$ for told $t$. Additionally, assume that Alice prefers to choose smaller $t$ if she has multiple equally good choices.\n\nYour task is to determine the outcome of the game: the value of $t$ Alice will choose and the $k$ cards Bob will choose for that $t$.\nTask Input: The input consists of two lines representing a single test case. The first line contains four integers $n$, $k$, $a$, and $b$ $(1 <= k <= n <= 600,0 <= a <= b <= 180,000)$. The second line contains $n$ integers $x_1, . . . , x_n$ $(0 <= x_i <= 300)$, denoting that $x_i$ is written on the $i$-th card.\nTask Output: Display two lines: The first line should contain an integer representing the value of $t$ Alice will choose. The second line should contain k distinct integers between 1 and $n$, inclusive, representing the indices of the cards Bob will choose. If Bob has multiple equally good choices, display any one of them.\nTask Samples: input: 4 2 58 100\n10 10 50 80\n output: 75\n2 3\ninput: 8 3 1300 1800\n2 0 1 5 0 4 1 9\n output: 1800\n4 6 8\n\n" }, { "title": "Problem C\nCasino", "content": "Taro, who owes a debt of $n$ dollars, decides to make money in a casino, where he can double his wager with probability $p$ percent in a single play of a game. Taro is going to play the game repetitively. He can choose the amount of the bet in each play, as long as it is a positive integer in dollars and at most the money in his hand.\n\nTaro possesses $m$ dollars now. Find out the maximum probability and the optimum first bet that he can repay all his debt, that is, to make his possession greater than or equal to his debt.", "constraint": "", "input": "The input consists of a single test case, which consists of three integers $p$, $m$, and $n$ separated by single\nspaces $(0 <= p <= 100,0 < m < n <= 10^9)$.", "output": "Display three lines: The first line should contain the maximum probability that Taro can repay all his debt. This value must have an absolute error at most $10^{-6}$. The second line should contain an integer representing how many optimum first bets are there. Here, a first bet is optimum if the bet is necessary to achieve the maximum probability. If the number of the optimum first bets does not exceed 200, the third line should contain all of them in ascending order and separated by single spaces. Otherwise the third line should contain the 100 smallest bets and the 100 largest bets in ascending order and separated by single spaces.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 60 2 3\n output: 0.789473\n1\n1", "input: 25 3 8\n output: 0.109375\n2\n1 3"], "Pid": "p01792", "ProblemText": "Task Description: Taro, who owes a debt of $n$ dollars, decides to make money in a casino, where he can double his wager with probability $p$ percent in a single play of a game. Taro is going to play the game repetitively. He can choose the amount of the bet in each play, as long as it is a positive integer in dollars and at most the money in his hand.\n\nTaro possesses $m$ dollars now. Find out the maximum probability and the optimum first bet that he can repay all his debt, that is, to make his possession greater than or equal to his debt.\nTask Input: The input consists of a single test case, which consists of three integers $p$, $m$, and $n$ separated by single\nspaces $(0 <= p <= 100,0 < m < n <= 10^9)$.\nTask Output: Display three lines: The first line should contain the maximum probability that Taro can repay all his debt. This value must have an absolute error at most $10^{-6}$. The second line should contain an integer representing how many optimum first bets are there. Here, a first bet is optimum if the bet is necessary to achieve the maximum probability. If the number of the optimum first bets does not exceed 200, the third line should contain all of them in ascending order and separated by single spaces. Otherwise the third line should contain the 100 smallest bets and the 100 largest bets in ascending order and separated by single spaces.\nTask Samples: input: 60 2 3\n output: 0.789473\n1\n1\ninput: 25 3 8\n output: 0.109375\n2\n1 3\n\n" }, { "title": "Problem D\nContent Delivery", "content": "You are given a computer network with n nodes. This network forms an undirected tree graph. The $i$-th edge connects the $a_i$-th node with the $b_i$-th node and its distance is $c_i$. Every node has different data and the size of the data on the $i$-th node is $s_i$. The network users can deliver any data from any node to any node. Delivery cost is defined as the product of the data size the user deliver and the distance from the source to the destination. Data goes through the shortest path in the delivery. Every node makes cache to reduce the load of this network. In every delivery, delivered data is cached to all nodes which relay the data including the destination node. From the next time of delivery, the data can be delivered from any node with a cache of the data. Thus, delivery cost reduces to the product of the original data size and the distance between the nearest node with a cache and the destination.\n\nCalculate the maximum cost of the $m$ subsequent deliveries on the given network. All the nodes have no cached data at the beginning. Users can choose the source and destination of each delivery arbitrarily.", "constraint": "", "input": "The input consists of a single test case. The first line contains two integers $n$ $(2 <= n <= 2,000)$ and $m$ $(1 <= m <= 10^9)$. $n$ and $m$ denote the number of the nodes in the network and the number of the deliveries, respectively. The following $n - 1$ lines describe the network structure. The $i$-th line of them contains three integers $a_i$, $b_i$ $(1 <= a_i, b_i <= n)$ and $c_i$ $(1 <= c_i <= 10,000)$ in this order, which means the $a_i$-th node and the $b_i$-th node are connected by an edge with the distance $c_i$. The next line contains $n$ integers. The $j$-th integer denotes $s_j$ $(1 <= s_j <= 10,000)$, which means the data size of the $j$-th node. The given network is guaranteed to be a tree graph.", "output": "Display a line containing the maximum cost of the $m$ subsequent deliveries in the given network.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2 1\n2 3 2\n1 10 100\n output: 320", "input: 2 100\n1 2 1\n1 1\n output: 2"], "Pid": "p01793", "ProblemText": "Task Description: You are given a computer network with n nodes. This network forms an undirected tree graph. The $i$-th edge connects the $a_i$-th node with the $b_i$-th node and its distance is $c_i$. Every node has different data and the size of the data on the $i$-th node is $s_i$. The network users can deliver any data from any node to any node. Delivery cost is defined as the product of the data size the user deliver and the distance from the source to the destination. Data goes through the shortest path in the delivery. Every node makes cache to reduce the load of this network. In every delivery, delivered data is cached to all nodes which relay the data including the destination node. From the next time of delivery, the data can be delivered from any node with a cache of the data. Thus, delivery cost reduces to the product of the original data size and the distance between the nearest node with a cache and the destination.\n\nCalculate the maximum cost of the $m$ subsequent deliveries on the given network. All the nodes have no cached data at the beginning. Users can choose the source and destination of each delivery arbitrarily.\nTask Input: The input consists of a single test case. The first line contains two integers $n$ $(2 <= n <= 2,000)$ and $m$ $(1 <= m <= 10^9)$. $n$ and $m$ denote the number of the nodes in the network and the number of the deliveries, respectively. The following $n - 1$ lines describe the network structure. The $i$-th line of them contains three integers $a_i$, $b_i$ $(1 <= a_i, b_i <= n)$ and $c_i$ $(1 <= c_i <= 10,000)$ in this order, which means the $a_i$-th node and the $b_i$-th node are connected by an edge with the distance $c_i$. The next line contains $n$ integers. The $j$-th integer denotes $s_j$ $(1 <= s_j <= 10,000)$, which means the data size of the $j$-th node. The given network is guaranteed to be a tree graph.\nTask Output: Display a line containing the maximum cost of the $m$ subsequent deliveries in the given network.\nTask Samples: input: 3 2\n1 2 1\n2 3 2\n1 10 100\n output: 320\ninput: 2 100\n1 2 1\n1 1\n output: 2\n\n" }, { "title": "Problem E\nCost Performance Flow", "content": "Yayoi is a professional of money saving. Yayoi does not select items just because they are cheap; her motto is \"cost performance\". This is one of the reasons why she is good at cooking with bean sprouts. Due to her saving skill, Yayoi often receives requests to save various costs. This time, her task is optimization of \"network flow\".\n\nNetwork flow is a problem on graph theory. Now, we consider a directed graph $G = (V, E)$, where $V = \\{1,2, . . . , |V|\\}$ is a vertex set and $E \\subset V * V$ is an edge set. Each edge $e$ in $E$ has a capacity $u(e)$ and a cost $c(e)$. For two vertices $s$ and $t$, a function $f_{s, t} : E \\rightarrow R$, where $R$ is the set of real numbers, is called an $s$-$t$ flow if the following conditions hold:\n\n For all $e$ in $E$, $f_{s, t}$ is non-negative and no more than $u(e)$. Namely, $0 <= f_{s, t}(e) <= u(e)$ holds.\n\n For all $v$ in $V \\setminus \\{s, t\\}$, the sum of $f_{s, t}$ of out-edges from $v$ equals the sum of $f_{s, t}$ of in-edges to $v$. Namely, $\\sum_{e=(u, v) \\in E} f_{s, t}(e) = \\sum_{e=(v, w) \\in E} f_{s, t}(e)$ holds.\n\nHere, we define flow $F( f_{s, t})$ and cost $C( f_{s, t})$ of $f_{s, t}$ as $F( f_{s, t}) = \\sum_{e=(s, v)\\in E} f_{s, t}(e) - \\sum_{e=(u, s)\\in E} f_{s, t}(e)$ and $C( f_{s, t}) = \\sum_{e\\in E} f_{s, t}(e)c(e)$, respectively.\n\nUsually, optimization of network flow is defined as cost minimization under the maximum flow. However, Yayoi's motto is \"cost performance\". She defines a balanced function $B( f_{s, t})$ for $s$-$t$ flow as the sum of the square of the cost $C( f_{s, t})$ and the difference between the maximum flow $M = max_{f : s-t flow} F( f )$ and the flow $F( f_{s, t})$, i. e. $B( f_{s, t}) = C( f_{s, t})^2 + (M - F( f_{s, t}))^2$. Then, Yayoi considers that the best cost performance flow yields the minimum of $B( f_{s, t})$.\n\nYour task is to write a program for Yayoi calculating $B( f_{s, t}^*)$ for the best cost performance flow $f_{s, t}^*$.", "constraint": "", "input": "The input consists of a single test case. The first line gives two integers separated by a single space: the number of vertices $N$ $(2 <= N <= 100)$ and the number of edges $M$ $(1 <= M <= 1,000)$. The second line gives two integers separated by a single space: two vertices $s$ and $t$ $(1 <= s, t <= N, s \\ne t)$. The $i$-th line of the following $M$ lines describes the $i$-th edges as four integers $a_i$, $b_i$, $u_i$, and $c_i$: the $i$-th edge from $a_i$ $(1 <= a_i <= N)$ to $b_i$ $(1 <= b_i <= N)$ has the capacity $u_i$ $(1 <= u_i <= 100)$ and the cost $c_i$ $(1 <= c_i <= 100)$ . You can assume that $a_i \\ne b_i$ for all $1 <= i <= M$, and $a_i \\ne a_j$ or $b_i \\ne b_j$ if $i \\ne j$ for all $1 <= i, j <= M$.", "output": "Display $B( f_{s, t}^*)$, the minimum of balanced function under $s$-$t$ flow, as a fraction in a line. More precisely, output \"$u/d$\", where $u$ is the numerator and $d$ is the denominator of $B( f_{s, t}^*)$, respectively. Note that $u$ and\n$d$ must be non-negative integers and relatively prime, i. e. the greatest common divisor of $u$ and $d$ is 1. You can assume that the answers for all the test cases are rational numbers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n1 2\n1 2 1 1\n output: 1/2", "input: 3 3\n1 2\n1 2 1 1\n1 3 3 1\n3 2 3 2\n output: 10/1", "input: 3 3\n1 2\n1 2 1 1\n1 3 7 1\n3 2 7 1\n output: 45/1"], "Pid": "p01794", "ProblemText": "Task Description: Yayoi is a professional of money saving. Yayoi does not select items just because they are cheap; her motto is \"cost performance\". This is one of the reasons why she is good at cooking with bean sprouts. Due to her saving skill, Yayoi often receives requests to save various costs. This time, her task is optimization of \"network flow\".\n\nNetwork flow is a problem on graph theory. Now, we consider a directed graph $G = (V, E)$, where $V = \\{1,2, . . . , |V|\\}$ is a vertex set and $E \\subset V * V$ is an edge set. Each edge $e$ in $E$ has a capacity $u(e)$ and a cost $c(e)$. For two vertices $s$ and $t$, a function $f_{s, t} : E \\rightarrow R$, where $R$ is the set of real numbers, is called an $s$-$t$ flow if the following conditions hold:\n\n For all $e$ in $E$, $f_{s, t}$ is non-negative and no more than $u(e)$. Namely, $0 <= f_{s, t}(e) <= u(e)$ holds.\n\n For all $v$ in $V \\setminus \\{s, t\\}$, the sum of $f_{s, t}$ of out-edges from $v$ equals the sum of $f_{s, t}$ of in-edges to $v$. Namely, $\\sum_{e=(u, v) \\in E} f_{s, t}(e) = \\sum_{e=(v, w) \\in E} f_{s, t}(e)$ holds.\n\nHere, we define flow $F( f_{s, t})$ and cost $C( f_{s, t})$ of $f_{s, t}$ as $F( f_{s, t}) = \\sum_{e=(s, v)\\in E} f_{s, t}(e) - \\sum_{e=(u, s)\\in E} f_{s, t}(e)$ and $C( f_{s, t}) = \\sum_{e\\in E} f_{s, t}(e)c(e)$, respectively.\n\nUsually, optimization of network flow is defined as cost minimization under the maximum flow. However, Yayoi's motto is \"cost performance\". She defines a balanced function $B( f_{s, t})$ for $s$-$t$ flow as the sum of the square of the cost $C( f_{s, t})$ and the difference between the maximum flow $M = max_{f : s-t flow} F( f )$ and the flow $F( f_{s, t})$, i. e. $B( f_{s, t}) = C( f_{s, t})^2 + (M - F( f_{s, t}))^2$. Then, Yayoi considers that the best cost performance flow yields the minimum of $B( f_{s, t})$.\n\nYour task is to write a program for Yayoi calculating $B( f_{s, t}^*)$ for the best cost performance flow $f_{s, t}^*$.\nTask Input: The input consists of a single test case. The first line gives two integers separated by a single space: the number of vertices $N$ $(2 <= N <= 100)$ and the number of edges $M$ $(1 <= M <= 1,000)$. The second line gives two integers separated by a single space: two vertices $s$ and $t$ $(1 <= s, t <= N, s \\ne t)$. The $i$-th line of the following $M$ lines describes the $i$-th edges as four integers $a_i$, $b_i$, $u_i$, and $c_i$: the $i$-th edge from $a_i$ $(1 <= a_i <= N)$ to $b_i$ $(1 <= b_i <= N)$ has the capacity $u_i$ $(1 <= u_i <= 100)$ and the cost $c_i$ $(1 <= c_i <= 100)$ . You can assume that $a_i \\ne b_i$ for all $1 <= i <= M$, and $a_i \\ne a_j$ or $b_i \\ne b_j$ if $i \\ne j$ for all $1 <= i, j <= M$.\nTask Output: Display $B( f_{s, t}^*)$, the minimum of balanced function under $s$-$t$ flow, as a fraction in a line. More precisely, output \"$u/d$\", where $u$ is the numerator and $d$ is the denominator of $B( f_{s, t}^*)$, respectively. Note that $u$ and\n$d$ must be non-negative integers and relatively prime, i. e. the greatest common divisor of $u$ and $d$ is 1. You can assume that the answers for all the test cases are rational numbers.\nTask Samples: input: 2 1\n1 2\n1 2 1 1\n output: 1/2\ninput: 3 3\n1 2\n1 2 1 1\n1 3 3 1\n3 2 3 2\n output: 10/1\ninput: 3 3\n1 2\n1 2 1 1\n1 3 7 1\n3 2 7 1\n output: 45/1\n\n" }, { "title": "Problem F\nICPC Teams", "content": "You are a coach of the International Collegiate Programming Contest (ICPC) club in your university. There are 3N students in the ICPC club and you want to make $N$ teams for the next ICPC. All teams in ICPC consist of 3 members. Every student belongs to exactly one team.\n\nWhen you form the teams, you should consider several relationships among the students. Some student has an extremely good relationship with other students. If they belong to a same team, their performance will improve surprisingly. The contrary situation also occurs for a student pair with a bad relationship. In short, students with a good relationship must be in the same team, and students with a bad relationship must be in different teams. Since you are a competent coach, you know all $M$ relationships among the students.\n\nYour task is to write a program that calculates the number of possible team assignments. Two assignments are considered different if and only if there exists a pair of students such that in one assignment they are in the same team and in the other they are not.", "constraint": "", "input": "The input consists of a single test case. The first line contains two integers $N$ $(1 <= N <= 10^6)$ and $M$ $(1 <= M <= 18)$. The $i$-th line of the following $M$ lines contains three integers $A_i$, $B_i$ $(1 <= A_i, B_i <= 3N, A_i \\ne B_i)$, and $C_i$ $(C_i \\in \\{0,1\\})$. $A_i$ and $B_i$ denote indices of the students and $C_i$ denotes the relation type. If $C_i$ is 0, the $A_i$-th student and the $B_i$-th student have a good relation. If $C_i$ is 1, they have a bad relation. You can assume that $\\{A_i, B_i\\} \\ne \\{A_j, B_j\\}$ if $i \\ne j$ for all $1 <= i, j <= M$.", "output": "Display a line containing the number of the possible team assignments modulo $10^9 + 9$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n1 2 0\n3 4 1\n output: 2"], "Pid": "p01795", "ProblemText": "Task Description: You are a coach of the International Collegiate Programming Contest (ICPC) club in your university. There are 3N students in the ICPC club and you want to make $N$ teams for the next ICPC. All teams in ICPC consist of 3 members. Every student belongs to exactly one team.\n\nWhen you form the teams, you should consider several relationships among the students. Some student has an extremely good relationship with other students. If they belong to a same team, their performance will improve surprisingly. The contrary situation also occurs for a student pair with a bad relationship. In short, students with a good relationship must be in the same team, and students with a bad relationship must be in different teams. Since you are a competent coach, you know all $M$ relationships among the students.\n\nYour task is to write a program that calculates the number of possible team assignments. Two assignments are considered different if and only if there exists a pair of students such that in one assignment they are in the same team and in the other they are not.\nTask Input: The input consists of a single test case. The first line contains two integers $N$ $(1 <= N <= 10^6)$ and $M$ $(1 <= M <= 18)$. The $i$-th line of the following $M$ lines contains three integers $A_i$, $B_i$ $(1 <= A_i, B_i <= 3N, A_i \\ne B_i)$, and $C_i$ $(C_i \\in \\{0,1\\})$. $A_i$ and $B_i$ denote indices of the students and $C_i$ denotes the relation type. If $C_i$ is 0, the $A_i$-th student and the $B_i$-th student have a good relation. If $C_i$ is 1, they have a bad relation. You can assume that $\\{A_i, B_i\\} \\ne \\{A_j, B_j\\}$ if $i \\ne j$ for all $1 <= i, j <= M$.\nTask Output: Display a line containing the number of the possible team assignments modulo $10^9 + 9$.\nTask Samples: input: 2 2\n1 2 0\n3 4 1\n output: 2\n\n" }, { "title": "Problem G\nJAG-channel II", "content": "JAG (Japan Alumni Group) is a group of $N$ members that devotes themselves to activation of the competitive programming world. The JAG staff members talk every day on the BBS called JAG-channel. There are several threads in JAG-channel and these are kept sorted by the time of their latest posts in descending order.\n\nOne night, each of the $N$ members, identified by the first $N$ uppercase letters respectively, created a thread in JAG-channel. The next morning, each of the $N$ members posted in exactly $K$ different threads which had been created last night. Since they think speed is important, they viewed the threads from top to bottom and posted in the thread immediately whenever they came across an interesting thread. Each member viewed the threads in a different period of time, that is, there was no post of other members while he/she was submitting his/her $K$ posts.\n\nYour task is to estimate the order of the members with respect to the periods of time when members posted in the threads. Though you do not know the order of the threads created, you know the order of the posts of each member. Since the threads are always kept sorted, there may be invalid orders of the members such that some members cannot post in the top-to-bottom order of the threads due to the previous posts of other members. Find out the lexicographically smallest valid order of the members.", "constraint": "", "input": "The input consists of a single test case. The first line contains two integers separated by a space: $N$ $(4 <= N <= 16)$ and $K$ $(N - 3 <= K <= N - 1)$. Then $N$ lines of strings follow. Each of the $N$ lines consists of exactly $K$ distinct characters. The $j$-th character of the $i$-th line denotes the $j$-th thread in which the\nmember denoted by the $i$-th uppercase letter posted. Each thread is represented by its creator (e. g. 'B' represents the thread created by member B, the second member).\n\nIt is guaranteed that at least one valid order exists.", "output": "Display a string that consists of exactly $N$ characters in a line, which denotes the valid order in which the members posted in the threads. The $i$-th character of the output should represent the member who posted in the $i$-th period. In case there are multiple valid orders, output the lexicographically smallest one.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 4\nDEFG\nFEDA\nEFGB\nBGEA\nAGFD\nDABC\nCADE\n output: ABCDEFG", "input: 4 3\nCDB\nDAC\nBAD\nABC\n output: DCBA", "input: 16 13\nNDHPFJIBLMCGK\nCMDJKPOLGIHNE\nMOLBIEJFPHADN\nKPNAOHBLMCGEI\nFCMLBHDOANJPK\nNHIGLOAPKJDMC\nKMLBIPHDEOANJ\nIEGCMLBOAPKJD\nJNAOEDHBLMCGF\nOEDHPFIBLMGKC\nGMLBIFPHDNAEO\nENHGOPKJDMCAF\nJKPAOBLGEIHNF\nHPKFGJEIBLCOM\nLBINEJDAGFKPH\nFGMOCADJENIBL\n output: PONCAKJGIEDHMFBL"], "Pid": "p01796", "ProblemText": "Task Description: JAG (Japan Alumni Group) is a group of $N$ members that devotes themselves to activation of the competitive programming world. The JAG staff members talk every day on the BBS called JAG-channel. There are several threads in JAG-channel and these are kept sorted by the time of their latest posts in descending order.\n\nOne night, each of the $N$ members, identified by the first $N$ uppercase letters respectively, created a thread in JAG-channel. The next morning, each of the $N$ members posted in exactly $K$ different threads which had been created last night. Since they think speed is important, they viewed the threads from top to bottom and posted in the thread immediately whenever they came across an interesting thread. Each member viewed the threads in a different period of time, that is, there was no post of other members while he/she was submitting his/her $K$ posts.\n\nYour task is to estimate the order of the members with respect to the periods of time when members posted in the threads. Though you do not know the order of the threads created, you know the order of the posts of each member. Since the threads are always kept sorted, there may be invalid orders of the members such that some members cannot post in the top-to-bottom order of the threads due to the previous posts of other members. Find out the lexicographically smallest valid order of the members.\nTask Input: The input consists of a single test case. The first line contains two integers separated by a space: $N$ $(4 <= N <= 16)$ and $K$ $(N - 3 <= K <= N - 1)$. Then $N$ lines of strings follow. Each of the $N$ lines consists of exactly $K$ distinct characters. The $j$-th character of the $i$-th line denotes the $j$-th thread in which the\nmember denoted by the $i$-th uppercase letter posted. Each thread is represented by its creator (e. g. 'B' represents the thread created by member B, the second member).\n\nIt is guaranteed that at least one valid order exists.\nTask Output: Display a string that consists of exactly $N$ characters in a line, which denotes the valid order in which the members posted in the threads. The $i$-th character of the output should represent the member who posted in the $i$-th period. In case there are multiple valid orders, output the lexicographically smallest one.\nTask Samples: input: 7 4\nDEFG\nFEDA\nEFGB\nBGEA\nAGFD\nDABC\nCADE\n output: ABCDEFG\ninput: 4 3\nCDB\nDAC\nBAD\nABC\n output: DCBA\ninput: 16 13\nNDHPFJIBLMCGK\nCMDJKPOLGIHNE\nMOLBIEJFPHADN\nKPNAOHBLMCGEI\nFCMLBHDOANJPK\nNHIGLOAPKJDMC\nKMLBIPHDEOANJ\nIEGCMLBOAPKJD\nJNAOEDHBLMCGF\nOEDHPFIBLMGKC\nGMLBIFPHDNAEO\nENHGOPKJDMCAF\nJKPAOBLGEIHNF\nHPKFGJEIBLCOM\nLBINEJDAGFKPH\nFGMOCADJENIBL\n output: PONCAKJGIEDHMFBL\n\n" }, { "title": "Problem H\nKimagure Cleaner", "content": "Ichiro won the newest model cleaner as a prize of a programming contest. This cleaner automatically moves around in a house for cleaning. Because Ichiro's house is very large, it can be modeled as an infinite two-dimensional Cartesian plane, whose axes are called $X$ and $Y$. The positive direction of the $Y$-axis is to the left if you face the positive direction of the $X$-axis.\n\nThe cleaner performs a sequence of actions for cleaning. Each action consists of a turn and a run. In an action, first the cleaner turns right or left by 90 degrees, and then runs straight by an integer length to the direction that the cleaner faces. At the end of a day, the cleaner reports the log of its actions in the day to Ichiro, in order to inform him where it has cleaned and where it hasn't.\n\nUnlike common cleaners, this cleaner has human-like artificial intelligence. Therefore, the cleaner is very forgetful (like humans) and it is possible that the cleaner forgets the direction of a turn, or the cleaner only remembers the length of a run as a very rough range. However, in order to pretend to be operating correctly, the cleaner has to recover the complete log of actions after finishing the cleaning.\n\nThe cleaner was initially at the point $(0,0)$, facing the positive direction of $X$-axis. You are given the cleaner's location after cleaning, $(X, Y)$, and an incomplete log of the cleaner's actions that the cleaner remembered. Please recover a complete log from the given incomplete log. The actions in the recovered log must satisfy the following constraints:\n\n The number of actions must be the same as that in the incomplete log.\n\n The direction of the $i$-th turn must be the same as that in the incomplete log if it is recorded in the incomplete log.\n\n The length of the $i$-th run must be within the range of the length specified in the incomplete log.\n\n The cleaner must be at $(X, Y)$ after finishing all actions. The direction of the cleaner after cleaning is not important and you do not have to care about it, because the cleaner can turn freely after cleaning, though it cannot run after cleaning. You are not required to recover the actual path, because Ichiro only checks the format of the log and the location of the cleaner after cleaning.", "constraint": "", "input": "The input consists of a single test case. The first line contains three integers $N$ $(1 <= N <= 50)$, $X$, and $Y$ $(-10^9 <= X, Y <= 10^9)$. $N$ represents the number of actions in the incomplete log. $X$ and $Y$ represent the cleaner's location $(X, Y)$ after cleaning. The $i$-th line of the following $N$ lines contains a character $D_i$ and two integers $LL_i$ and $LU_i$. $D_i$ represents the direction of the $i$-th turn: 'L', 'R', and '? ' represents left, right, and not recorded respectively. $LL_i$ and $LU_i$ represent a lower and upper bound of the length of the $i$-th run, respectively. You can assume $1 <= LL_i <= LU_i <= 55,555,555$.", "output": "Display the recovered log. In the first line, display N, the number of actions in the log. In the $i$-th line of the following $N$ lines, display the direction of the $i$-th turn in a character and the length of the $i$-th run separated by a single space. Represent a right turn by a single character 'R', and a left turn by a single character 'L'. The recovered log must satisfy the constraints in the problem. If there are multiple\nlogs that satisfy the constraints, you can display any of them. Display $-1$ in a line if there is no log that satisfies the constraints.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 -3 4\nL 2 5\n? 3 5\n output: 2\nL 4\nL 3", "input: 5 3 -4\n? 1 5\n? 1 5\n? 1 5\n? 1 5\n? 1 5\n output: 5\nL 1\nR 2\nR 4\nL 1\nR 1"], "Pid": "p01797", "ProblemText": "Task Description: Ichiro won the newest model cleaner as a prize of a programming contest. This cleaner automatically moves around in a house for cleaning. Because Ichiro's house is very large, it can be modeled as an infinite two-dimensional Cartesian plane, whose axes are called $X$ and $Y$. The positive direction of the $Y$-axis is to the left if you face the positive direction of the $X$-axis.\n\nThe cleaner performs a sequence of actions for cleaning. Each action consists of a turn and a run. In an action, first the cleaner turns right or left by 90 degrees, and then runs straight by an integer length to the direction that the cleaner faces. At the end of a day, the cleaner reports the log of its actions in the day to Ichiro, in order to inform him where it has cleaned and where it hasn't.\n\nUnlike common cleaners, this cleaner has human-like artificial intelligence. Therefore, the cleaner is very forgetful (like humans) and it is possible that the cleaner forgets the direction of a turn, or the cleaner only remembers the length of a run as a very rough range. However, in order to pretend to be operating correctly, the cleaner has to recover the complete log of actions after finishing the cleaning.\n\nThe cleaner was initially at the point $(0,0)$, facing the positive direction of $X$-axis. You are given the cleaner's location after cleaning, $(X, Y)$, and an incomplete log of the cleaner's actions that the cleaner remembered. Please recover a complete log from the given incomplete log. The actions in the recovered log must satisfy the following constraints:\n\n The number of actions must be the same as that in the incomplete log.\n\n The direction of the $i$-th turn must be the same as that in the incomplete log if it is recorded in the incomplete log.\n\n The length of the $i$-th run must be within the range of the length specified in the incomplete log.\n\n The cleaner must be at $(X, Y)$ after finishing all actions. The direction of the cleaner after cleaning is not important and you do not have to care about it, because the cleaner can turn freely after cleaning, though it cannot run after cleaning. You are not required to recover the actual path, because Ichiro only checks the format of the log and the location of the cleaner after cleaning.\nTask Input: The input consists of a single test case. The first line contains three integers $N$ $(1 <= N <= 50)$, $X$, and $Y$ $(-10^9 <= X, Y <= 10^9)$. $N$ represents the number of actions in the incomplete log. $X$ and $Y$ represent the cleaner's location $(X, Y)$ after cleaning. The $i$-th line of the following $N$ lines contains a character $D_i$ and two integers $LL_i$ and $LU_i$. $D_i$ represents the direction of the $i$-th turn: 'L', 'R', and '? ' represents left, right, and not recorded respectively. $LL_i$ and $LU_i$ represent a lower and upper bound of the length of the $i$-th run, respectively. You can assume $1 <= LL_i <= LU_i <= 55,555,555$.\nTask Output: Display the recovered log. In the first line, display N, the number of actions in the log. In the $i$-th line of the following $N$ lines, display the direction of the $i$-th turn in a character and the length of the $i$-th run separated by a single space. Represent a right turn by a single character 'R', and a left turn by a single character 'L'. The recovered log must satisfy the constraints in the problem. If there are multiple\nlogs that satisfy the constraints, you can display any of them. Display $-1$ in a line if there is no log that satisfies the constraints.\nTask Samples: input: 2 -3 4\nL 2 5\n? 3 5\n output: 2\nL 4\nL 3\ninput: 5 3 -4\n? 1 5\n? 1 5\n? 1 5\n? 1 5\n? 1 5\n output: 5\nL 1\nR 2\nR 4\nL 1\nR 1\n\n" }, { "title": "Problem I\nMidpoint", "content": "One day, you found $L + M + N$ points on a 2D plane, which you named $A_1, . . . , A_L, B_1, . . . , B_M, C_1, . . . , C_N$. Note that two or more points of them can be at the same coordinate. These were named after the following properties:\n\n the points $A_1, . . . , A_L$ were located on a single straight line,\n\n the points $B_1, . . . , B_M$ were located on a single straight line, and\n\n the points $C_1, . . . , C_N$ were located on a single straight line.\nNow, you are interested in a triplet $(i, j, k)$ such that $C_k$ is the midpoint between $A_i$ and $B_j$. Your task is counting such triplets.", "constraint": "", "input": "The first line contains three space-separated positive integers $L$, $M$, and $N$ $(1 <= L, M, N <= 10^5)$. The next $L$ lines describe $A$. The $i$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $A_i$. The next $M$ lines describe $B$. The $j$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $B_j$. The next $N$ lines describe $C$. The $k$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $C_k$. It is guaranteed that the absolute values of all the coordinates do not exceed $10^5$.", "output": "Print the number of the triplets which fulfill the constraint.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 3\n0 0\n2 0\n0 0\n0 2\n0 0\n1 1\n1 1\n output: 3", "input: 4 4 4\n3 5\n0 4\n6 6\n9 7\n8 2\n11 3\n2 0\n5 1\n4 3\n7 4\n10 5\n1 2\n output: 8", "input: 4 4 4\n0 0\n3 2\n6 4\n9 6\n7 14\n9 10\n10 8\n13 2\n4 2\n5 4\n6 6\n8 10\n output: 3"], "Pid": "p01798", "ProblemText": "Task Description: One day, you found $L + M + N$ points on a 2D plane, which you named $A_1, . . . , A_L, B_1, . . . , B_M, C_1, . . . , C_N$. Note that two or more points of them can be at the same coordinate. These were named after the following properties:\n\n the points $A_1, . . . , A_L$ were located on a single straight line,\n\n the points $B_1, . . . , B_M$ were located on a single straight line, and\n\n the points $C_1, . . . , C_N$ were located on a single straight line.\nNow, you are interested in a triplet $(i, j, k)$ such that $C_k$ is the midpoint between $A_i$ and $B_j$. Your task is counting such triplets.\nTask Input: The first line contains three space-separated positive integers $L$, $M$, and $N$ $(1 <= L, M, N <= 10^5)$. The next $L$ lines describe $A$. The $i$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $A_i$. The next $M$ lines describe $B$. The $j$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $B_j$. The next $N$ lines describe $C$. The $k$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $C_k$. It is guaranteed that the absolute values of all the coordinates do not exceed $10^5$.\nTask Output: Print the number of the triplets which fulfill the constraint.\nTask Samples: input: 2 2 3\n0 0\n2 0\n0 0\n0 2\n0 0\n1 1\n1 1\n output: 3\ninput: 4 4 4\n3 5\n0 4\n6 6\n9 7\n8 2\n11 3\n2 0\n5 1\n4 3\n7 4\n10 5\n1 2\n output: 8\ninput: 4 4 4\n0 0\n3 2\n6 4\n9 6\n7 14\n9 10\n10 8\n13 2\n4 2\n5 4\n6 6\n8 10\n output: 3\n\n" }, { "title": "Problem J\nNew Game AI", "content": "Aoba is a beginner programmer who works for a game company. She was appointed to develop a battle strategy for the enemy AI (Artificial Intelligence) in a new game. In this game, each character has two parameters, hit point ($hp$) and defence point ($dp$). No two characters have the same $hp$ and $dp$ at the same time. The player forms a party by selecting one or more characters to battle with the enemy. Aoba decided to develop a strategy in which the AI attacks the weakest character in the party: that is, the AI attacks the character with the minimum hit point in the party (or, if there are several such characters, the character with the minimum defense point among them). She wrote a function select Target($v$) that takes an array of characters representing a party and returns a character that her AI will attack.\n\nHowever, the project manager Ms. Yagami was not satisfied with the behavior of her AI. Ms. Yagami said this AI was not interesting.\n\nAoba struggled a lot, and eventually she found that it is interesting if she substitutes one of the constant zeros in her program with a constant $C$. The rewritten program is as follows. Note that Character is a type representing a character and has fields $hp$ and $dp$ which represent the hit point and the defense point of the character respectively.\n\nint C = ;\n\nCharacter select Target(Character v[]) {\n int n = length(v);\n int r = 0;\n for (int i = 1; i < n; i++) {\n if (abs(v[r]. hp - v[i]. hp) > C) {\n if (v[r]. hp > v[i]. hp) r = i;\n } else {\n if (v[r]. dp > v[i]. dp) r = i;\n }\n }\n return v[r];\n}\n\nBy the way, this function may return different characters according to the order of the characters in $v$, even if $v$ contains the same set of characters. Ms. Yagami wants to know how many characters in a party may become the target of the new AI. Aoba's next task is to write a program that takes a given party $v$ and a constant $C$, and then counts the number of characters that may become the return value of select Target($v$) if $v$ is re-ordered.", "constraint": "", "input": "The input consists of a single test case. The first line contains two integers $N$ $(1 <= N <= 50,000)$ and $C$ $(0 <= C <= 10^9)$. The first integer $N$ represents the size of $v$. The second integer $C$ represents the constant $C$ in Aoba's program. The i-th line of the following $N$ lines contains two integers $hp_i$ and $dp_i$ $(0 <= hp_i, dp_i <= 10^9)$. $hp_i$ represents the hit point of the $i$-th character in $v$, and $dp_i$ represents the defense point of the $i$-th character in $v$. You can assume that $hp_i \\ne hp_j$ or $dpi \\ne dp_j$ if $i \\ne j$ for any $1 <= i, j <= N$.", "output": "Display the number of characters that may become the return value of select Target($v$), if $v$ is shuffled in an arbitrary order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 5\n3 4\n5 3\n7 2\n9 1\n output: 5", "input: 3 2\n1 2\n3 1\n5 1\n output: 2", "input: 4 1\n2 0\n0 4\n1 1\n5 9\n output: 3", "input: 5 9\n4 10\n12 4\n2 14\n9 19\n7 15\n output: 3"], "Pid": "p01799", "ProblemText": "Task Description: Aoba is a beginner programmer who works for a game company. She was appointed to develop a battle strategy for the enemy AI (Artificial Intelligence) in a new game. In this game, each character has two parameters, hit point ($hp$) and defence point ($dp$). No two characters have the same $hp$ and $dp$ at the same time. The player forms a party by selecting one or more characters to battle with the enemy. Aoba decided to develop a strategy in which the AI attacks the weakest character in the party: that is, the AI attacks the character with the minimum hit point in the party (or, if there are several such characters, the character with the minimum defense point among them). She wrote a function select Target($v$) that takes an array of characters representing a party and returns a character that her AI will attack.\n\nHowever, the project manager Ms. Yagami was not satisfied with the behavior of her AI. Ms. Yagami said this AI was not interesting.\n\nAoba struggled a lot, and eventually she found that it is interesting if she substitutes one of the constant zeros in her program with a constant $C$. The rewritten program is as follows. Note that Character is a type representing a character and has fields $hp$ and $dp$ which represent the hit point and the defense point of the character respectively.\n\nint C = ;\n\nCharacter select Target(Character v[]) {\n int n = length(v);\n int r = 0;\n for (int i = 1; i < n; i++) {\n if (abs(v[r]. hp - v[i]. hp) > C) {\n if (v[r]. hp > v[i]. hp) r = i;\n } else {\n if (v[r]. dp > v[i]. dp) r = i;\n }\n }\n return v[r];\n}\n\nBy the way, this function may return different characters according to the order of the characters in $v$, even if $v$ contains the same set of characters. Ms. Yagami wants to know how many characters in a party may become the target of the new AI. Aoba's next task is to write a program that takes a given party $v$ and a constant $C$, and then counts the number of characters that may become the return value of select Target($v$) if $v$ is re-ordered.\nTask Input: The input consists of a single test case. The first line contains two integers $N$ $(1 <= N <= 50,000)$ and $C$ $(0 <= C <= 10^9)$. The first integer $N$ represents the size of $v$. The second integer $C$ represents the constant $C$ in Aoba's program. The i-th line of the following $N$ lines contains two integers $hp_i$ and $dp_i$ $(0 <= hp_i, dp_i <= 10^9)$. $hp_i$ represents the hit point of the $i$-th character in $v$, and $dp_i$ represents the defense point of the $i$-th character in $v$. You can assume that $hp_i \\ne hp_j$ or $dpi \\ne dp_j$ if $i \\ne j$ for any $1 <= i, j <= N$.\nTask Output: Display the number of characters that may become the return value of select Target($v$), if $v$ is shuffled in an arbitrary order.\nTask Samples: input: 5 3\n1 5\n3 4\n5 3\n7 2\n9 1\n output: 5\ninput: 3 2\n1 2\n3 1\n5 1\n output: 2\ninput: 4 1\n2 0\n0 4\n1 1\n5 9\n output: 3\ninput: 5 9\n4 10\n12 4\n2 14\n9 19\n7 15\n output: 3\n\n" }, { "title": "Problem K\nRunner and Sniper", "content": "You are escaping from an enemy for some reason. The enemy is a sniper equipped with a high-tech laser gun, and you will be immediately defeated if you get shot. You are a very good runner, but just wondering how fast you have to run in order not to be shot by the sniper. The situation is as follows:\n\nYou and the sniper are on the $xy$-plane whose $x$-axis and $y$-axis are directed to the right and the top, respectively. You can assume that the plane is infinitely large, and that there is no obstacle that blocks the laser or your movement.\n\nThe sniper and the laser gun are at $(0,0)$ and cannot move from the initial location. The sniper can continuously rotate the laser gun by at most $\\omega$ degrees per unit time, either clockwise or counterclockwise, and can change the direction of rotation at any time. The laser gun is initially directed $\\theta$ degrees counterclockwise from the positive direction of the $x$-axis.\n\nYou are initially at ($x$, $y$) on the plane and can move in any direction at speed not more than $v$ (you can arbitrarily determine the value of $v$ since you are a very good runner). You will be shot by the sniper exactly when the laser gun is directed toward your position, that is, you can ignore the time that the laser reaches you from the laser gun. Assume that your body is a point and the laser is a half-line whose end point is (0,0).\n\nFind the maximum speed $v$ at which you are shot by the sniper in finite time when you and the sniper behave optimally.", "constraint": "", "input": "The input consists of a single test case. The input contains four integers in a line, $x$, $y$, $\\theta$ and $\\omega$. The two integers $x$ and $y$ $(0 <= |x|, |y| <= 1,000$, ($x$, $y$) $\\ne$ (0,0)) represent your initial position on the $xy$-plane. The integer $\\theta$ $(0 <= \\theta < 360)$ represents the initial direction of the laser gun: it is the counterclockwise angle in degrees from the positive direction of the $x$-axis. The integer $\\omega$ $(1 <= \\omega <= 100)$ is the angle which the laser gun can rotate in unit time. You can assume that you are not shot by the sniper at the initial position.", "output": "Display a line containing the maximum speed $v$ at which you are shot by the sniper in finite time. The\nabsolute error or the relative error should be less than $10^{-6}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100 100 0 1\n output: 1.16699564"], "Pid": "p01800", "ProblemText": "Task Description: You are escaping from an enemy for some reason. The enemy is a sniper equipped with a high-tech laser gun, and you will be immediately defeated if you get shot. You are a very good runner, but just wondering how fast you have to run in order not to be shot by the sniper. The situation is as follows:\n\nYou and the sniper are on the $xy$-plane whose $x$-axis and $y$-axis are directed to the right and the top, respectively. You can assume that the plane is infinitely large, and that there is no obstacle that blocks the laser or your movement.\n\nThe sniper and the laser gun are at $(0,0)$ and cannot move from the initial location. The sniper can continuously rotate the laser gun by at most $\\omega$ degrees per unit time, either clockwise or counterclockwise, and can change the direction of rotation at any time. The laser gun is initially directed $\\theta$ degrees counterclockwise from the positive direction of the $x$-axis.\n\nYou are initially at ($x$, $y$) on the plane and can move in any direction at speed not more than $v$ (you can arbitrarily determine the value of $v$ since you are a very good runner). You will be shot by the sniper exactly when the laser gun is directed toward your position, that is, you can ignore the time that the laser reaches you from the laser gun. Assume that your body is a point and the laser is a half-line whose end point is (0,0).\n\nFind the maximum speed $v$ at which you are shot by the sniper in finite time when you and the sniper behave optimally.\nTask Input: The input consists of a single test case. The input contains four integers in a line, $x$, $y$, $\\theta$ and $\\omega$. The two integers $x$ and $y$ $(0 <= |x|, |y| <= 1,000$, ($x$, $y$) $\\ne$ (0,0)) represent your initial position on the $xy$-plane. The integer $\\theta$ $(0 <= \\theta < 360)$ represents the initial direction of the laser gun: it is the counterclockwise angle in degrees from the positive direction of the $x$-axis. The integer $\\omega$ $(1 <= \\omega <= 100)$ is the angle which the laser gun can rotate in unit time. You can assume that you are not shot by the sniper at the initial position.\nTask Output: Display a line containing the maximum speed $v$ at which you are shot by the sniper in finite time. The\nabsolute error or the relative error should be less than $10^{-6}$.\nTask Samples: input: 100 100 0 1\n output: 1.16699564\n\n" }, { "title": "Problem L\nWall Making Game", "content": "The game Wall Making Game, a two-player board game, is all the rage.\n\nThis game is played on an $H * W$ board. Each cell of the board is one of empty, marked, or wall. At the beginning of the game, there is no wall on the board.\n\nIn this game, two players alternately move as follows:\n\n A player chooses one of the empty cells (not marked and not wall). If the player can't choose a cell, he loses.\n\n Towards each of the four directions (upper, lower, left, and right) from the chosen cell, the player changes cells (including the chosen cell) to walls until the player first reaches a wall or the outside of the board.\n\nNote that marked cells cannot be chosen in step 1, but they can be changed to walls in step 2.\n\nFig. 1 shows an example of a move in which a player chooses the cell at the third row and the fourth\ncolumn.\nFig. 1: An example of a move in Wall Making Game.\n\nYour task is to write a program that determines which player wins the game if the two players play optimally from a given initial board.", "constraint": "", "input": "The first line of the input consists of two integers $H$ and $W$ $(1 <= H, W <= 20)$, where $H$ and $W$ are the height and the width of the board respectively. The following $H$ lines represent the initial board. Each of the $H$ lines consists of $W$ characters.\n\nThe $j$-th character of the $i$-th line is '. ' if the cell at the $j$-th column of the $i$-th row is empty, or 'X' if the cell is marked.", "output": "Print \"First\" (without the quotes) in a line if the first player wins the given game. Otherwise, print \"Second\" (also without the quotes) in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2 2\n..\n..\n output: Second", "input: 2 2\nX.\n..\n output: First", "input: 4 5\nX....\n...X.\n.....\n.....\n output: First"], "Pid": "p01801", "ProblemText": "Task Description: The game Wall Making Game, a two-player board game, is all the rage.\n\nThis game is played on an $H * W$ board. Each cell of the board is one of empty, marked, or wall. At the beginning of the game, there is no wall on the board.\n\nIn this game, two players alternately move as follows:\n\n A player chooses one of the empty cells (not marked and not wall). If the player can't choose a cell, he loses.\n\n Towards each of the four directions (upper, lower, left, and right) from the chosen cell, the player changes cells (including the chosen cell) to walls until the player first reaches a wall or the outside of the board.\n\nNote that marked cells cannot be chosen in step 1, but they can be changed to walls in step 2.\n\nFig. 1 shows an example of a move in which a player chooses the cell at the third row and the fourth\ncolumn.\nFig. 1: An example of a move in Wall Making Game.\n\nYour task is to write a program that determines which player wins the game if the two players play optimally from a given initial board.\nTask Input: The first line of the input consists of two integers $H$ and $W$ $(1 <= H, W <= 20)$, where $H$ and $W$ are the height and the width of the board respectively. The following $H$ lines represent the initial board. Each of the $H$ lines consists of $W$ characters.\n\nThe $j$-th character of the $i$-th line is '. ' if the cell at the $j$-th column of the $i$-th row is empty, or 'X' if the cell is marked.\nTask Output: Print \"First\" (without the quotes) in a line if the first player wins the given game. Otherwise, print \"Second\" (also without the quotes) in a line.\nTask Samples: input: 2 2\n..\n..\n output: Second\ninput: 2 2\nX.\n..\n output: First\ninput: 4 5\nX....\n...X.\n.....\n.....\n output: First\n\n" }, { "title": "Problem A:\nWhere is the Boundary", "content": "An island country JAGAN in a certain planet is very long and narrow, and extends east and\nwest. This long country is said to consist of two major cultural areas | the eastern and the\nwestern. Regions in the east tend to have the eastern cultural features and regions in the west\ntend to have the western cultural features, but, of course, the boundary between the two cultural\nareas is not clear, which has been an issue.\n\nYou are given an assignment estimating the boundary using a given data set.\n\nMore precise specification of the assignment is as follows:\n\n JAGAN is divided into $n$ prefectures forming a line in the east-west direction. Each\nprefecture is numbered 1,2, . . . , $n$ from WEST to EAST.\n\n Each data set consists of $m$ features, which has 'E' (east) or 'W' (west) for each prefecture.\nThese data indicate that each prefecture has eastern or western features from $m$ different\npoint of views, for example, food, clothing, and so on.\n\n In the estimation, you have to choose a cultural boundary achieving the minimal errors.\nThat is, you have to minimize the sum of 'W's in the eastern side and 'E's in the western\nside.\n\n In the estimation, you can choose a cultural boundary only from the boundaries between\ntwo prefectures.\nSometimes all prefectures may be estimated to be the eastern or the western cultural area.\nIn these cases, to simplify, you must virtually consider that the boundary is placed between\nprefecture No. 0 and No. 1 or between prefecture No. $n$ and No. $n+1$. When you get multiple\nminimums, you must output the most western (least-numbered) result.\n\nWrite a program to solve the assignment.", "constraint": "", "input": "Each input is formatted as follows: \n\n$n$ $m$\n$d_{11} . . . d_{1n}$\n: \n: \n$d_{m1} . . . d_{mn}$\nThe first line consists of two integers $n$ ($1 <= n <= 10,000$), $m$ ($1 <= m <= 100$), which indicate\nthe number of prefectures and the number of features in the assignment. The following m lines\nare the given data set in the assignment. Each line contains exactly $n$ characters. The $j$-th\ncharacter in the $i$-th line $d_{ij}$ is 'E' (east) or 'W' (west), which indicates $j$-th prefecture has the\neastern or the western feature from the $i$-th point of view.", "output": "Print the estimated result in a line. The output consists of two integers sorted in the ascending\norder which indicate two prefectures touching the boundary.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\nWEW\n output: 1 2\nYou cannot assume that 'E's and 'W's are separated."], "Pid": "p01819", "ProblemText": "Task Description: An island country JAGAN in a certain planet is very long and narrow, and extends east and\nwest. This long country is said to consist of two major cultural areas | the eastern and the\nwestern. Regions in the east tend to have the eastern cultural features and regions in the west\ntend to have the western cultural features, but, of course, the boundary between the two cultural\nareas is not clear, which has been an issue.\n\nYou are given an assignment estimating the boundary using a given data set.\n\nMore precise specification of the assignment is as follows:\n\n JAGAN is divided into $n$ prefectures forming a line in the east-west direction. Each\nprefecture is numbered 1,2, . . . , $n$ from WEST to EAST.\n\n Each data set consists of $m$ features, which has 'E' (east) or 'W' (west) for each prefecture.\nThese data indicate that each prefecture has eastern or western features from $m$ different\npoint of views, for example, food, clothing, and so on.\n\n In the estimation, you have to choose a cultural boundary achieving the minimal errors.\nThat is, you have to minimize the sum of 'W's in the eastern side and 'E's in the western\nside.\n\n In the estimation, you can choose a cultural boundary only from the boundaries between\ntwo prefectures.\nSometimes all prefectures may be estimated to be the eastern or the western cultural area.\nIn these cases, to simplify, you must virtually consider that the boundary is placed between\nprefecture No. 0 and No. 1 or between prefecture No. $n$ and No. $n+1$. When you get multiple\nminimums, you must output the most western (least-numbered) result.\n\nWrite a program to solve the assignment.\nTask Input: Each input is formatted as follows: \n\n$n$ $m$\n$d_{11} . . . d_{1n}$\n: \n: \n$d_{m1} . . . d_{mn}$\nThe first line consists of two integers $n$ ($1 <= n <= 10,000$), $m$ ($1 <= m <= 100$), which indicate\nthe number of prefectures and the number of features in the assignment. The following m lines\nare the given data set in the assignment. Each line contains exactly $n$ characters. The $j$-th\ncharacter in the $i$-th line $d_{ij}$ is 'E' (east) or 'W' (west), which indicates $j$-th prefecture has the\neastern or the western feature from the $i$-th point of view.\nTask Output: Print the estimated result in a line. The output consists of two integers sorted in the ascending\norder which indicate two prefectures touching the boundary.\nTask Samples: input: 3 1\nWEW\n output: 1 2\nYou cannot assume that 'E's and 'W's are separated.\n\n" }, { "title": "Problem B:\nVector Field", "content": "In 20015, JAG (Jagan Acceleration Group) has succeeded in inventing a new accelerator named\nForce Point for an experiment of proton collision on the two-dimensional $xy$-plane. If a proton\ntouches a Force Point, it is accelerated to twice its speed and its movement direction is veered. A\nproton may be veered by a Force Field in four ways: the positive or negative directions parallel\nto the $x$- or the $y$-axis. The direction in which a proton veers is determined by the type of the\nForce Point. A Force Point can accelerate a proton only once because the Force Point disappears\nimmediately after the acceleration. Generating many Force Points on the two-dimensional plane,\nwhich is called a 2D Force Point Field, allows us to accelerate a proton up to a target speed by\nsequentially accelerating the proton with the Force Points in the 2D Force Point Filed.\n\nThe Force Point generation method is still under experiment and JAG has the following technical\nlimitations:\n\n JAG cannot generate a Force Point with a specified position and a type.\n\n JAG cannot generate a Force Point after putting a proton into a 2D Force Point Field.\n\n JAG cannot move Force Points.\n\n JAG cannot change a protons direction except by the effect of Force Points.\n\n JAG can use only one proton for a 2D Force Point Field.\n\n JAG can put a proton moving in any direction with its speed 1 at any position in a 2D\nForce Point Field.\nIn order to achieve the maximum speed of a proton, the engineers at JAG have to choose the\noptimal initial position and the optimal initial direction of the proton so that the proton is\naccelerated by as many Force Points as possible, after carefully observing the generated 2D\nForce Point Field.\n\nBy observing a generated 2D Force Point Field, the number of the generated Force Points is\nknown to be $n$. The position ($x_i$, $y_i$) and the direction veering type $d_i$ of the $i$-th point are\nalso known. Your task is to write a program to calculate the maximum speed of a proton by\nacceleration on a given 2D Force Point Field when JAG puts a proton optimally.", "constraint": "", "input": "The input consists of a single test case which describes a 2D Force Point Field in the following\nformat. \n\n$n$\n$x_1$ $y_1$ $d_1$\n. . . \n$x_n$ $y_n$ $d_n$\n\n

    \nThe first line contains one integer $n$ ($1 <= n <= 3,000$) which is the number of the Force Points on\nthe 2D Force Point Field. Each of the next $n$ lines contains two integers $x_i$ and $y_i$ ($|x_i|$, $|y_i| <= 10^9$)\nand one character $d_i$ ($d_i$ is one of '>', 'v', '<' or '^'). $x_i$ and $y_i$ represent a coordinate of the $i$-th\nForce Point, and $d_i$ is the direction veering type of the $i$-th force point. A force point with a type\n'>' changes protons direction to the positive direction of the $x$-axis, 'v' represents the positive\ndirection of the $y$-axis, '<' represents the negative direction of the $x$-axis, and '^' represents the\nnegative direction of the $y$-axis. You can assume that any two Force Points are not generated\non the same coordinates.", "output": "Display a line containing the integer $log_2 v_{max}$, where $v_{max}$ is the protons possible fastest speed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\n0 0 ^\n1 0 ^\n2 0 ^\n0 1 <\n1 1 ^\n2 1 >\n0 2 v\n1 2 v\n2 2 v\n output: 2"], "Pid": "p01820", "ProblemText": "Task Description: In 20015, JAG (Jagan Acceleration Group) has succeeded in inventing a new accelerator named\nForce Point for an experiment of proton collision on the two-dimensional $xy$-plane. If a proton\ntouches a Force Point, it is accelerated to twice its speed and its movement direction is veered. A\nproton may be veered by a Force Field in four ways: the positive or negative directions parallel\nto the $x$- or the $y$-axis. The direction in which a proton veers is determined by the type of the\nForce Point. A Force Point can accelerate a proton only once because the Force Point disappears\nimmediately after the acceleration. Generating many Force Points on the two-dimensional plane,\nwhich is called a 2D Force Point Field, allows us to accelerate a proton up to a target speed by\nsequentially accelerating the proton with the Force Points in the 2D Force Point Filed.\n\nThe Force Point generation method is still under experiment and JAG has the following technical\nlimitations:\n\n JAG cannot generate a Force Point with a specified position and a type.\n\n JAG cannot generate a Force Point after putting a proton into a 2D Force Point Field.\n\n JAG cannot move Force Points.\n\n JAG cannot change a protons direction except by the effect of Force Points.\n\n JAG can use only one proton for a 2D Force Point Field.\n\n JAG can put a proton moving in any direction with its speed 1 at any position in a 2D\nForce Point Field.\nIn order to achieve the maximum speed of a proton, the engineers at JAG have to choose the\noptimal initial position and the optimal initial direction of the proton so that the proton is\naccelerated by as many Force Points as possible, after carefully observing the generated 2D\nForce Point Field.\n\nBy observing a generated 2D Force Point Field, the number of the generated Force Points is\nknown to be $n$. The position ($x_i$, $y_i$) and the direction veering type $d_i$ of the $i$-th point are\nalso known. Your task is to write a program to calculate the maximum speed of a proton by\nacceleration on a given 2D Force Point Field when JAG puts a proton optimally.\nTask Input: The input consists of a single test case which describes a 2D Force Point Field in the following\nformat. \n\n$n$\n$x_1$ $y_1$ $d_1$\n. . . \n$x_n$ $y_n$ $d_n$\n\n

    \nThe first line contains one integer $n$ ($1 <= n <= 3,000$) which is the number of the Force Points on\nthe 2D Force Point Field. Each of the next $n$ lines contains two integers $x_i$ and $y_i$ ($|x_i|$, $|y_i| <= 10^9$)\nand one character $d_i$ ($d_i$ is one of '>', 'v', '<' or '^'). $x_i$ and $y_i$ represent a coordinate of the $i$-th\nForce Point, and $d_i$ is the direction veering type of the $i$-th force point. A force point with a type\n'>' changes protons direction to the positive direction of the $x$-axis, 'v' represents the positive\ndirection of the $y$-axis, '<' represents the negative direction of the $x$-axis, and '^' represents the\nnegative direction of the $y$-axis. You can assume that any two Force Points are not generated\non the same coordinates.\nTask Output: Display a line containing the integer $log_2 v_{max}$, where $v_{max}$ is the protons possible fastest speed.\nTask Samples: input: 9\n0 0 ^\n1 0 ^\n2 0 ^\n0 1 <\n1 1 ^\n2 1 >\n0 2 v\n1 2 v\n2 2 v\n output: 2\n\n" }, { "title": "Problem D:\nIdentity Function", "content": "You are given an integer $N$, which is greater than 1. \nConsider the following functions:\n\n $f(a) = a^N$ mod $N$ \n\n $F_1(a) = f(a)$\n\n $F_{k+1}(a) = F_k(f(a))$ $(k = 1,2,3, . . . )$\nNote that we use mod to represent the integer modulo operation. For a non-negative integer $x$\nand a positive integer $y$, $x$ mod $y$ is the remainder of $x$ divided by $y$.\n\nOutput the minimum positive integer $k$ such that $F_k(a) = a$ for all positive integers $a$ less than\n$N$. If no such $k$ exists, output -1.", "constraint": "", "input": "The input consists of a single line that contains an integer $N$ ($2 <= N <= 10^9$), whose meaning is\ndescribed in the problem statement.", "output": "Output the minimum positive integer $k$ such that $F_k(a) = a$ for all positive integers $a$ less than\n$N$, or -1 if no such $k$ exists.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15\n output: 2"], "Pid": "p01821", "ProblemText": "Task Description: You are given an integer $N$, which is greater than 1. \nConsider the following functions:\n\n $f(a) = a^N$ mod $N$ \n\n $F_1(a) = f(a)$\n\n $F_{k+1}(a) = F_k(f(a))$ $(k = 1,2,3, . . . )$\nNote that we use mod to represent the integer modulo operation. For a non-negative integer $x$\nand a positive integer $y$, $x$ mod $y$ is the remainder of $x$ divided by $y$.\n\nOutput the minimum positive integer $k$ such that $F_k(a) = a$ for all positive integers $a$ less than\n$N$. If no such $k$ exists, output -1.\nTask Input: The input consists of a single line that contains an integer $N$ ($2 <= N <= 10^9$), whose meaning is\ndescribed in the problem statement.\nTask Output: Output the minimum positive integer $k$ such that $F_k(a) = a$ for all positive integers $a$ less than\n$N$, or -1 if no such $k$ exists.\nTask Samples: input: 15\n output: 2\n\n" }, { "title": "Problem E:\nEnclose Points", "content": "There are $N$ points and $M$ segments on the $xy$-plane. Each segment connects two of these\npoints and they don't intersect each other except at the endpoints. You are also given $Q$ points\nas queries. Your task is to determine for each query point whether you can make a polygon that\nencloses the query point using some of the given segments. Note that the polygon should not\nnecessarily be convex.", "constraint": "", "input": "Each input is formatted as follows. \n\n$N$ $M$ $Q$\n$x_1$ $y_1$\n. . . \n$x_N$ $y_N$\n$a_1$ $b_1$\n. . . \n$a_M$ $b_M$\n$qx_1$ $qy_1$\n. . . \n$qx_Q$ $qy_Q$\nThe first line contains three integers $N$ ($2 <= N <= 100,000$), $M$ ($1 <= M <= 100,000$), and $Q$\n($1 <= Q <= 100,000$), which represent the number of points, the number of segments, and the\nnumber of queries, respectively. Each of the following $N$ lines contains two integers $x_i$ and $y_i$\n($-100,000 <= x_i, y_i <= 100,000$), the coordinates of the $i$-th point. The points are guaranteed to be\ndistinct, that is, $(x_i, y_i) \\ne (x_j, y_j)$ when $i \\ne j$. Each of the following $M$ lines contains two integers\n$a_i$ and $b_i$ ($1 <= a_i < b_i <= N$), which indicate that the $i$-th segment connects the $a_i$-th point and\nthe $b_i$-th point. Assume that those segments do not intersect each other except at the endpoints.\nEach of the following $Q$ lines contains two integers $qx_i$ and $qy_i$ ($-100,000 <= qx_i, qy_i <= 100,000$),\nthe coordinates of the $i$-th query point.\n\nYou can assume that, for any pair of query point and segment, the distance between them is at\nleast $10^{-4}$.", "output": "The output should contain $Q$ lines. Print \"Yes\" on the $i$-th line if there is a polygon that\ncontains the $i$-th query point. Otherwise print \"No\" on the $i$-th line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 8 5\n-20 -10\n-10 -10\n-10 10\n-20 10\n10 -10\n20 -10\n20 10\n10 10\n1 2\n2 3\n3 4\n1 4\n5 6\n6 7\n7 8\n5 8\n-30 0\n-15 0\n0 0\n15 0\n30 0\n output: No\nYes\nNo\nYes\nNo"], "Pid": "p01822", "ProblemText": "Task Description: There are $N$ points and $M$ segments on the $xy$-plane. Each segment connects two of these\npoints and they don't intersect each other except at the endpoints. You are also given $Q$ points\nas queries. Your task is to determine for each query point whether you can make a polygon that\nencloses the query point using some of the given segments. Note that the polygon should not\nnecessarily be convex.\nTask Input: Each input is formatted as follows. \n\n$N$ $M$ $Q$\n$x_1$ $y_1$\n. . . \n$x_N$ $y_N$\n$a_1$ $b_1$\n. . . \n$a_M$ $b_M$\n$qx_1$ $qy_1$\n. . . \n$qx_Q$ $qy_Q$\nThe first line contains three integers $N$ ($2 <= N <= 100,000$), $M$ ($1 <= M <= 100,000$), and $Q$\n($1 <= Q <= 100,000$), which represent the number of points, the number of segments, and the\nnumber of queries, respectively. Each of the following $N$ lines contains two integers $x_i$ and $y_i$\n($-100,000 <= x_i, y_i <= 100,000$), the coordinates of the $i$-th point. The points are guaranteed to be\ndistinct, that is, $(x_i, y_i) \\ne (x_j, y_j)$ when $i \\ne j$. Each of the following $M$ lines contains two integers\n$a_i$ and $b_i$ ($1 <= a_i < b_i <= N$), which indicate that the $i$-th segment connects the $a_i$-th point and\nthe $b_i$-th point. Assume that those segments do not intersect each other except at the endpoints.\nEach of the following $Q$ lines contains two integers $qx_i$ and $qy_i$ ($-100,000 <= qx_i, qy_i <= 100,000$),\nthe coordinates of the $i$-th query point.\n\nYou can assume that, for any pair of query point and segment, the distance between them is at\nleast $10^{-4}$.\nTask Output: The output should contain $Q$ lines. Print \"Yes\" on the $i$-th line if there is a polygon that\ncontains the $i$-th query point. Otherwise print \"No\" on the $i$-th line.\nTask Samples: input: 8 8 5\n-20 -10\n-10 -10\n-10 10\n-20 10\n10 -10\n20 -10\n20 10\n10 10\n1 2\n2 3\n3 4\n1 4\n5 6\n6 7\n7 8\n5 8\n-30 0\n-15 0\n0 0\n15 0\n30 0\n output: No\nYes\nNo\nYes\nNo\n\n" }, { "title": "Problem F:\nMarching Course", "content": "Since members of Kitafuji High School Brass Band Club succeeded in convincing their stern\ncoach of their playing skills, they will be able to participate in Moon Light Festival as a marching\nband. This festival is a prelude in terms of appealing their presence for the coming domestic\ncontest. Hence, they want to attract a festival audience by their performance.\n\nAlthough this festival restricts performance time up to $P$ minutes, each team can freely determine\ntheir performance course from a provided area. The provided area consists of $N$ checkpoints,\nnumbered 1 through $N$, and $M$ bidirectional roads connecting two checkpoints. Kitafuji Brass\nBand already has the information about each road: its length and the expected number of people\non its roadside. Each team must start at the checkpoint 1, and return back to the checkpoint\n1 in $P$ minutes. In order to show the performance ability of Kitafuji Brass Band to a festival\naudience, their stern coach would like to determine their performance course so that many people\nlisten their march as long as possible.\n\nThe coach uses \"impression degree\" to determine their best course. If they play $m$ minutes on\nthe road with length $d$ and the expected number $v$ of people, then the impression degree will be\n$m * v/d$. The impression degree of a course is the sum of impression degree of their performance\non the course. Marching bands must move at a constant speed during marching: 1 unit length\nper 1 minute. On the other hand, they can turn in the opposite direction at any time, any place\nincluding a point on a road. The impression degree is accumulated even if they pass the same\ninterval two or more times.\n\nYour task is to write a program to determine a course with the maximum impression degree in\norder to show the performance ability of Kitafuji Brass Band to an audience as much as possible.", "constraint": "", "input": "The input is formatted as follows. \n\n$N$ $M$ $P$\n$s_1$ $t_1$ $d_1$ $v_1$\n: : : \n$s_M$ $t_M$ $d_M$ $v_M$\nThe first line contains three integers $N$, $M$, and $P$: the number of checkpoints $N$ ($2 <= N <=\n200$), the number of roads $M$ ($N - 1 <= M <= N(N - 1)/2$), and the performance time $P$\n($1 <= P <= 1,000$). The following $M$ lines represent the information about roads. The $i$-th line\nof them contains four integers $s_i$, $t_i$, $d_i$, and $v_i$: the $i$-th road bidirectionally connects between\ncheckpoints $s_i$ and $t_i$ ($1 <= s_i, t_i <= N, s_i \\ne t_i$) with length $d_i$ ($1 <= d_i <= 1,000$) and the expected\nnumber $v_i$ ($1 <= v_i <= 1,000$) of people.\n\nYou can assume that any two checkpoints are directly or indirectly connected with one or more\nroads. You can also assume that there are no pair of roads having the same pair of endpoints.", "output": "Output the maximum impression degree of a course for a $P$-minute performance. The absolute\nerror should be less than $10^{-4}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 10\n1 2 3 1\n1 3 4 5\n2 3 2 10\n output: 22"], "Pid": "p01823", "ProblemText": "Task Description: Since members of Kitafuji High School Brass Band Club succeeded in convincing their stern\ncoach of their playing skills, they will be able to participate in Moon Light Festival as a marching\nband. This festival is a prelude in terms of appealing their presence for the coming domestic\ncontest. Hence, they want to attract a festival audience by their performance.\n\nAlthough this festival restricts performance time up to $P$ minutes, each team can freely determine\ntheir performance course from a provided area. The provided area consists of $N$ checkpoints,\nnumbered 1 through $N$, and $M$ bidirectional roads connecting two checkpoints. Kitafuji Brass\nBand already has the information about each road: its length and the expected number of people\non its roadside. Each team must start at the checkpoint 1, and return back to the checkpoint\n1 in $P$ minutes. In order to show the performance ability of Kitafuji Brass Band to a festival\naudience, their stern coach would like to determine their performance course so that many people\nlisten their march as long as possible.\n\nThe coach uses \"impression degree\" to determine their best course. If they play $m$ minutes on\nthe road with length $d$ and the expected number $v$ of people, then the impression degree will be\n$m * v/d$. The impression degree of a course is the sum of impression degree of their performance\non the course. Marching bands must move at a constant speed during marching: 1 unit length\nper 1 minute. On the other hand, they can turn in the opposite direction at any time, any place\nincluding a point on a road. The impression degree is accumulated even if they pass the same\ninterval two or more times.\n\nYour task is to write a program to determine a course with the maximum impression degree in\norder to show the performance ability of Kitafuji Brass Band to an audience as much as possible.\nTask Input: The input is formatted as follows. \n\n$N$ $M$ $P$\n$s_1$ $t_1$ $d_1$ $v_1$\n: : : \n$s_M$ $t_M$ $d_M$ $v_M$\nThe first line contains three integers $N$, $M$, and $P$: the number of checkpoints $N$ ($2 <= N <=\n200$), the number of roads $M$ ($N - 1 <= M <= N(N - 1)/2$), and the performance time $P$\n($1 <= P <= 1,000$). The following $M$ lines represent the information about roads. The $i$-th line\nof them contains four integers $s_i$, $t_i$, $d_i$, and $v_i$: the $i$-th road bidirectionally connects between\ncheckpoints $s_i$ and $t_i$ ($1 <= s_i, t_i <= N, s_i \\ne t_i$) with length $d_i$ ($1 <= d_i <= 1,000$) and the expected\nnumber $v_i$ ($1 <= v_i <= 1,000$) of people.\n\nYou can assume that any two checkpoints are directly or indirectly connected with one or more\nroads. You can also assume that there are no pair of roads having the same pair of endpoints.\nTask Output: Output the maximum impression degree of a course for a $P$-minute performance. The absolute\nerror should be less than $10^{-4}$.\nTask Samples: input: 3 3 10\n1 2 3 1\n1 3 4 5\n2 3 2 10\n output: 22\n\n" }, { "title": "Problem G:\nSurface Area of Cubes", "content": "Taro likes a single player game \"Surface Area of Cubes\".\n\nIn this game, he initially has an $A * B * C$ rectangular solid formed by $A * B * C$ unit cubes\n(which are all 1 by 1 by 1 cubes). The center of each unit cube is placed at 3-dimentional\ncoordinates $(x, y, z)$ where $x$, $y$, $z$ are all integers ($0 <= x <= A-1,0 <= y <= B -1,0 <= z <= C - 1$).\nThen, $N$ distinct unit cubes are removed from the rectangular solid by the game master. After\nthe $N$ cubes are removed, he must precisely tell the total surface area of this object in order to\nwin the game.\n\nNote that the removing operation does not change the positions of the cubes which are not\nremoved. Also, not only the cubes on the surface of the rectangular solid but also the cubes\nat the inside can be removed. Moreover, the object can be divided into multiple parts by the\nremoval of the cubes. Notice that a player of this game also has to count up the surface areas\nwhich are not accessible from the outside.\n\nTaro knows how many and which cubes were removed but this game is very difficult for him,\nso he wants to win this game by cheating! You are Taro's friend, and your job is to make a\nprogram to calculate the total surface area of the object on behalf of Taro when you are given\nthe size of the rectangular solid and the coordinates of the removed cubes.", "constraint": "", "input": "The input is formatted as follows.\n\nThe first line of a test case contains four integers $A$, $B$, $C$, and $N$ ($1 <= A, B, C <= 10^8,0 <= N <=\n$ min{$1,000, A * B * C - 1$}).\n\nEach of the next $N$ lines contains non-negative integers $x$, $y$, and $z$ which represent the coordinate\nof a removed cube. You may assume that these coordinates are distinct.", "output": "Output the total surface area of the object from which the $N$ cubes were removed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 3 1\n1 1 1\n output: 60"], "Pid": "p01824", "ProblemText": "Task Description: Taro likes a single player game \"Surface Area of Cubes\".\n\nIn this game, he initially has an $A * B * C$ rectangular solid formed by $A * B * C$ unit cubes\n(which are all 1 by 1 by 1 cubes). The center of each unit cube is placed at 3-dimentional\ncoordinates $(x, y, z)$ where $x$, $y$, $z$ are all integers ($0 <= x <= A-1,0 <= y <= B -1,0 <= z <= C - 1$).\nThen, $N$ distinct unit cubes are removed from the rectangular solid by the game master. After\nthe $N$ cubes are removed, he must precisely tell the total surface area of this object in order to\nwin the game.\n\nNote that the removing operation does not change the positions of the cubes which are not\nremoved. Also, not only the cubes on the surface of the rectangular solid but also the cubes\nat the inside can be removed. Moreover, the object can be divided into multiple parts by the\nremoval of the cubes. Notice that a player of this game also has to count up the surface areas\nwhich are not accessible from the outside.\n\nTaro knows how many and which cubes were removed but this game is very difficult for him,\nso he wants to win this game by cheating! You are Taro's friend, and your job is to make a\nprogram to calculate the total surface area of the object on behalf of Taro when you are given\nthe size of the rectangular solid and the coordinates of the removed cubes.\nTask Input: The input is formatted as follows.\n\nThe first line of a test case contains four integers $A$, $B$, $C$, and $N$ ($1 <= A, B, C <= 10^8,0 <= N <=\n$ min{$1,000, A * B * C - 1$}).\n\nEach of the next $N$ lines contains non-negative integers $x$, $y$, and $z$ which represent the coordinate\nof a removed cube. You may assume that these coordinates are distinct.\nTask Output: Output the total surface area of the object from which the $N$ cubes were removed.\nTask Samples: input: 3 3 3 1\n1 1 1\n output: 60\n\n" }, { "title": "Problem H:\nLaser Cutter", "content": "Ciel is going to do woodworking. Ciel wants to make a cut in a wooden board using a laser\ncutter.\n\nTo make it simple, we assume that the board is a two-dimensional plane. There are several\nsegments on the board along which Ciel wants to cut the board. Each segment has a direction\nand Ciel must cut those segments along their directions. Those segments are connected when\nyou ignore the directions, that is, any two points on the segments are directly or indirectly\nconnected by the segments.\n\nWhile the laser cutter is powered on, it emits a laser which hits the board at a point and cuts\nthe board along its trace. The laser initially points to $(x, y)$. Ciel can conduct the following two\noperations:\n\n Move the laser cutter with its power on and cut (a part of) a segment along its direction,\nor\n\n Move the laser cutter to any position with its power off. Ciel should not necessarily cut\nthe whole segment at a time; she can start or stop cutting a segment at any point on the\nsegments.\nCiel likes to be efficient, so she wants to know the shortest route such that the laser cutter cuts\nthe whole parts of all the segments and then move back to the initial point. Your task is to\nwrite a program that calculates the minimum total moving distance of the laser cutter.", "constraint": "", "input": "The first line of the input contains an integer $n$ ($1 <= n <= 300$), the number of segments. The\nnext line contains two integers $x$ and $y$ ($-1,000 <= x, y <= 1,000$), which is the initial position\n$(x, y)$ of the laser. The $i$-th of the following $n$ lines contains four integers $sx_i$, $sy_i$, $tx_i$ and $ty_i$ ($-1,000 <= sx_i, sy_i, tx_i, ty_i <= 1,000$), which indicate that they are the end points of the $i$-th\nsegment, and that the laser cutter can cut the board in the direction from $(sx_i, sy_i)$ to $(tx_i, ty_i)$.\nThe input satisfies the following conditions: For all $i$ ($1 <= i <= n$), $(sx_i, sy_i) \\ne (tx_i, ty_i)$. The\ninitial point $(x, y)$ lies on at least one of the given segments. For all distinct $i, j$ ($1 <= i, j <= n$),\nthe $i$-th segment and the $j$-th segment share at most one point.", "output": "Output a line containing the minimum total moving distance the laser cutter needs to travel to\ncut all the segments and move back to the initial point. The absolute error or the relative error\nshould be less than $10^{-6}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 0\n0 0 1 0\n1 1 -1 1\n-1 1 -1 -1\n-1 -1 1 -1\n1 -1 1 1\n output: 10.0000000000000000"], "Pid": "p01825", "ProblemText": "Task Description: Ciel is going to do woodworking. Ciel wants to make a cut in a wooden board using a laser\ncutter.\n\nTo make it simple, we assume that the board is a two-dimensional plane. There are several\nsegments on the board along which Ciel wants to cut the board. Each segment has a direction\nand Ciel must cut those segments along their directions. Those segments are connected when\nyou ignore the directions, that is, any two points on the segments are directly or indirectly\nconnected by the segments.\n\nWhile the laser cutter is powered on, it emits a laser which hits the board at a point and cuts\nthe board along its trace. The laser initially points to $(x, y)$. Ciel can conduct the following two\noperations:\n\n Move the laser cutter with its power on and cut (a part of) a segment along its direction,\nor\n\n Move the laser cutter to any position with its power off. Ciel should not necessarily cut\nthe whole segment at a time; she can start or stop cutting a segment at any point on the\nsegments.\nCiel likes to be efficient, so she wants to know the shortest route such that the laser cutter cuts\nthe whole parts of all the segments and then move back to the initial point. Your task is to\nwrite a program that calculates the minimum total moving distance of the laser cutter.\nTask Input: The first line of the input contains an integer $n$ ($1 <= n <= 300$), the number of segments. The\nnext line contains two integers $x$ and $y$ ($-1,000 <= x, y <= 1,000$), which is the initial position\n$(x, y)$ of the laser. The $i$-th of the following $n$ lines contains four integers $sx_i$, $sy_i$, $tx_i$ and $ty_i$ ($-1,000 <= sx_i, sy_i, tx_i, ty_i <= 1,000$), which indicate that they are the end points of the $i$-th\nsegment, and that the laser cutter can cut the board in the direction from $(sx_i, sy_i)$ to $(tx_i, ty_i)$.\nThe input satisfies the following conditions: For all $i$ ($1 <= i <= n$), $(sx_i, sy_i) \\ne (tx_i, ty_i)$. The\ninitial point $(x, y)$ lies on at least one of the given segments. For all distinct $i, j$ ($1 <= i, j <= n$),\nthe $i$-th segment and the $j$-th segment share at most one point.\nTask Output: Output a line containing the minimum total moving distance the laser cutter needs to travel to\ncut all the segments and move back to the initial point. The absolute error or the relative error\nshould be less than $10^{-6}$.\nTask Samples: input: 5\n0 0\n0 0 1 0\n1 1 -1 1\n-1 1 -1 -1\n-1 -1 1 -1\n1 -1 1 1\n output: 10.0000000000000000\n\n" }, { "title": "Problem I:\nLive Programming", "content": "A famous Japanese idol group, JAG48, is planning the program for its next live performance.\nThey have $N$ different songs, $song_1$, $song_2$, . . . , and $song_N$. Each song has three integer param-\neters, $t_i$, $p_i$, and $f_i$: $t_i$ denotes the length of $song_i$, $p_i$ denotes the basic satisfaction points the\naudience will get when $song_i$ is performed, and $f_i$ denotes the feature value of songi that affects\nthe audience's satisfaction. During the live performance, JAG48 can perform any number (but\nat least one) of the $N$ songs, unless the total length of the chosen songs exceeds the length of\nthe live performance $T$. They can decide the order of the songs to perform, but they cannot\nperform the same song twice or more.\n\nThe goal of this live performance is to maximize the total satisfaction points that the audience\nwill get. In addition to the basic satisfaction points of each song, the difference between the\nfeature values of the two songs that are performed consecutively affects the total satisfaction\npoints. If there is no difference, the audience will feel comfortable. However, the larger the\ndifference will be, the more frustrated the audience will be.\n\nThus, the total satisfaction points will be calculated as follows:\n\n If $song_x$ is the first song of the live performance, the total satisfaction points just after\n$song_x$ is equal to $p_x$.\n\n If $song_x$ is the second or subsequent song of the live performance and is performed just\nafter $song_y$, $p_x -(f_x -f_y)^2$ is added to the total satisfaction points, because the audience\nwill get frustrated if $f_x$ and $f_y$ are different.\nHelp JAG48 find a program with the maximum total satisfaction points.", "constraint": "", "input": "The input is formatted as follows. \n\n$N$ $T$\n$t_1$ $p_1$ $f_1$\n: : : \n$t_N$ $p_N$ $f_N$\nThe first line contains two integers $N$ and $T$: the number of the available $song_s$ $N$ ($1 <= N <=\n4,000$), and the length of the live performance $T$ ($1 <= T <= 4,000$).\n\nThe following $N$ lines represent the parameters of the songs. The $i$-th line of them contains three\nintegers, which are the parameters of $song_i$: the length $t_i$ ($1 <= t_i <= 4,000$), the basic satisfaction\npoints $p_i$ ($1 <= p_i <= 10^8$), and the feature value $f_i$ ($1 <= f_i <= 10^4$).\n\nYou can assume that there is at least one song whose length is less than or equal to $T$.", "output": "Output the maximum total satisfaction points that the audience can get during the live performance.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 61\n14 49 7\n31 46 4\n30 55 5\n52 99 1\n34 70 3\n output: 103"], "Pid": "p01826", "ProblemText": "Task Description: A famous Japanese idol group, JAG48, is planning the program for its next live performance.\nThey have $N$ different songs, $song_1$, $song_2$, . . . , and $song_N$. Each song has three integer param-\neters, $t_i$, $p_i$, and $f_i$: $t_i$ denotes the length of $song_i$, $p_i$ denotes the basic satisfaction points the\naudience will get when $song_i$ is performed, and $f_i$ denotes the feature value of songi that affects\nthe audience's satisfaction. During the live performance, JAG48 can perform any number (but\nat least one) of the $N$ songs, unless the total length of the chosen songs exceeds the length of\nthe live performance $T$. They can decide the order of the songs to perform, but they cannot\nperform the same song twice or more.\n\nThe goal of this live performance is to maximize the total satisfaction points that the audience\nwill get. In addition to the basic satisfaction points of each song, the difference between the\nfeature values of the two songs that are performed consecutively affects the total satisfaction\npoints. If there is no difference, the audience will feel comfortable. However, the larger the\ndifference will be, the more frustrated the audience will be.\n\nThus, the total satisfaction points will be calculated as follows:\n\n If $song_x$ is the first song of the live performance, the total satisfaction points just after\n$song_x$ is equal to $p_x$.\n\n If $song_x$ is the second or subsequent song of the live performance and is performed just\nafter $song_y$, $p_x -(f_x -f_y)^2$ is added to the total satisfaction points, because the audience\nwill get frustrated if $f_x$ and $f_y$ are different.\nHelp JAG48 find a program with the maximum total satisfaction points.\nTask Input: The input is formatted as follows. \n\n$N$ $T$\n$t_1$ $p_1$ $f_1$\n: : : \n$t_N$ $p_N$ $f_N$\nThe first line contains two integers $N$ and $T$: the number of the available $song_s$ $N$ ($1 <= N <=\n4,000$), and the length of the live performance $T$ ($1 <= T <= 4,000$).\n\nThe following $N$ lines represent the parameters of the songs. The $i$-th line of them contains three\nintegers, which are the parameters of $song_i$: the length $t_i$ ($1 <= t_i <= 4,000$), the basic satisfaction\npoints $p_i$ ($1 <= p_i <= 10^8$), and the feature value $f_i$ ($1 <= f_i <= 10^4$).\n\nYou can assume that there is at least one song whose length is less than or equal to $T$.\nTask Output: Output the maximum total satisfaction points that the audience can get during the live performance.\nTask Samples: input: 5 61\n14 49 7\n31 46 4\n30 55 5\n52 99 1\n34 70 3\n output: 103\n\n" }, { "title": "Problem J:\nBlack Company", "content": "JAG Company is a sweatshop (sweatshop is called \"burakku kigyo\" in Japanese), and you are\nthe CEO for the company.\n\nYou are planning to determine $N$ employees' salary as low as possible (employees are numbered\nfrom 1 to $N$). Each employee's salary amount must be a positive integer greater than zero. At\nthat time, you should pay attention to the employees' contribution degree. If the employee $i$'s\ncontribution degree $c_i$ is greater than the employee $j$'s contribution degree $c_j$ , the employee i\nmust get higher salary than the employee $j$'s salary. If the condition is not satisfied, employees\nmay complain about their salary amount.\n\nHowever, it is not necessarily satisfied in all pairs of the employees, because each employee can\nonly know his/her close employees' contribution degree and salary amount. Therefore, as long as\nthe following two conditions are satisfied, employees do not complain to you about their salary\namount.\n\n If the employees $i$ and $j$ are close to each other, $c_i < c_j \\Leftrightarrow p_i < p_j$ must be satisfied, where\n$p_i$ is the employee $i$'s salary amount.\n\n If the employee $i$ is close to the employees $j$ and $k$, $c_j < c_k \\Leftrightarrow p_j < p_k$ must be satisfied.\nWrite a program that computes the minimum sum of all employees' salary amount such that no\nemployee complains about their salary.", "constraint": "", "input": "Each input is formatted as follows: \n\n$N$\n$c_1$ . . . $c_N$\n$M$\n$a_1$ $b_1$\n. . . \n$a_M$ $b_M$\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which indicates the number of employees.\nThe second line contains $N$ integers $c_i$ ($1 <= c_i <= 100,000$) representing the contribution degree\nof employee $i$.\n\nThe third line contains an integer $M$ ($0 <= M <= 200,000$), which specifies the number of relationships. Each of the following $M$ lines contains two integers $a_i$ and $b_i$ ($a_i \\ne b_i, 1 <= a_i, b_i <= N$).\nIt represents that the employees $a_i$ and $b_i$ are close to each other. There is no more than one\nrelationship between each pair of the employees.", "output": "Print the minimum sum of all employees' salary amounts in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n4 3 2 1 5 3\n7\n4 2\n1 5\n2 6\n6 5\n4 1\n1 6\n6 3\n output: 13"], "Pid": "p01827", "ProblemText": "Task Description: JAG Company is a sweatshop (sweatshop is called \"burakku kigyo\" in Japanese), and you are\nthe CEO for the company.\n\nYou are planning to determine $N$ employees' salary as low as possible (employees are numbered\nfrom 1 to $N$). Each employee's salary amount must be a positive integer greater than zero. At\nthat time, you should pay attention to the employees' contribution degree. If the employee $i$'s\ncontribution degree $c_i$ is greater than the employee $j$'s contribution degree $c_j$ , the employee i\nmust get higher salary than the employee $j$'s salary. If the condition is not satisfied, employees\nmay complain about their salary amount.\n\nHowever, it is not necessarily satisfied in all pairs of the employees, because each employee can\nonly know his/her close employees' contribution degree and salary amount. Therefore, as long as\nthe following two conditions are satisfied, employees do not complain to you about their salary\namount.\n\n If the employees $i$ and $j$ are close to each other, $c_i < c_j \\Leftrightarrow p_i < p_j$ must be satisfied, where\n$p_i$ is the employee $i$'s salary amount.\n\n If the employee $i$ is close to the employees $j$ and $k$, $c_j < c_k \\Leftrightarrow p_j < p_k$ must be satisfied.\nWrite a program that computes the minimum sum of all employees' salary amount such that no\nemployee complains about their salary.\nTask Input: Each input is formatted as follows: \n\n$N$\n$c_1$ . . . $c_N$\n$M$\n$a_1$ $b_1$\n. . . \n$a_M$ $b_M$\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which indicates the number of employees.\nThe second line contains $N$ integers $c_i$ ($1 <= c_i <= 100,000$) representing the contribution degree\nof employee $i$.\n\nThe third line contains an integer $M$ ($0 <= M <= 200,000$), which specifies the number of relationships. Each of the following $M$ lines contains two integers $a_i$ and $b_i$ ($a_i \\ne b_i, 1 <= a_i, b_i <= N$).\nIt represents that the employees $a_i$ and $b_i$ are close to each other. There is no more than one\nrelationship between each pair of the employees.\nTask Output: Print the minimum sum of all employees' salary amounts in a line.\nTask Samples: input: 6\n4 3 2 1 5 3\n7\n4 2\n1 5\n2 6\n6 5\n4 1\n1 6\n6 3\n output: 13\n\n" }, { "title": "M and A", "content": "The CEO of the company named $S$ is planning M&A with another company named $T$. M&A is an abbreviation for \"Mergers and Acquisitions\". The CEO wants to keep the original company name $S$ through the M&A on the plea that both company names are mixed into a new one.\n\nThe CEO insists that the mixed company name after the M&A is produced as follows.\n\nLet $s$ be an arbitrary subsequence of $S$, and $t$ be an arbitrary subsequence of $T$. The new company name must be a string of the same length to $S$ obtained by alternatively lining up the characters in $s$ and $t$. More formally, $s_0 + t_0 + s_1 + t_1 + . . . $ or $t_0 + s_0 + t_1 + s_1 + . . . $ can be used as the company name after M&A. Here, $s_k$ denotes the $k$-th (0-based) character of string $s$. Please note that the lengths of $s$ and $t$ will be different if the length of $S$ is odd. In this case, the company name after M&A is obtained by $s_0 + t_0 + . . . + t_{|S|/2} + s_{|S|/2+1}$ or $t_0 + s_0 + . . . + s_{|S|/2} + t_{|S|/2+1}$ ($|S|$ denotes the length of $S$ and \"/\" denotes integer division).\n\nA subsequence of a string is a string which is obtained by erasing zero or more characters from the original string. For example, the strings \"abe\", \"abcde\" and \"\" (the empty string) are all subsequences of the string \"abcde\".\n\nYou are a programmer employed by the acquiring company. You are assigned a task to write a program that determines whether it is possible to make $S$, which is the original company name, by mixing the two company names.", "constraint": "", "input": "The input consists of a single test case. The test case consists of two lines.\n\nThe first line contains a string $S$ which denotes the name of the company that you belong to. The second line contains a string $T$ which denotes the name of the target company of the planned M&A. The two names $S$ and $T$ are non-empty and of the same length no longer than 1,000 characters, and all the characters used in the names are lowercase English letters.", "output": "Print \"Yes\" in a line if it is possible to make original company name by combining $S$ and $T$. Otherwise, print \"No\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: acmicpc\ntsukuba\n output: No", "input: hoge\nmoen\n output: Yes", "input: abcdefg\nxacxegx\n output: Yes"], "Pid": "p01828", "ProblemText": "Task Description: The CEO of the company named $S$ is planning M&A with another company named $T$. M&A is an abbreviation for \"Mergers and Acquisitions\". The CEO wants to keep the original company name $S$ through the M&A on the plea that both company names are mixed into a new one.\n\nThe CEO insists that the mixed company name after the M&A is produced as follows.\n\nLet $s$ be an arbitrary subsequence of $S$, and $t$ be an arbitrary subsequence of $T$. The new company name must be a string of the same length to $S$ obtained by alternatively lining up the characters in $s$ and $t$. More formally, $s_0 + t_0 + s_1 + t_1 + . . . $ or $t_0 + s_0 + t_1 + s_1 + . . . $ can be used as the company name after M&A. Here, $s_k$ denotes the $k$-th (0-based) character of string $s$. Please note that the lengths of $s$ and $t$ will be different if the length of $S$ is odd. In this case, the company name after M&A is obtained by $s_0 + t_0 + . . . + t_{|S|/2} + s_{|S|/2+1}$ or $t_0 + s_0 + . . . + s_{|S|/2} + t_{|S|/2+1}$ ($|S|$ denotes the length of $S$ and \"/\" denotes integer division).\n\nA subsequence of a string is a string which is obtained by erasing zero or more characters from the original string. For example, the strings \"abe\", \"abcde\" and \"\" (the empty string) are all subsequences of the string \"abcde\".\n\nYou are a programmer employed by the acquiring company. You are assigned a task to write a program that determines whether it is possible to make $S$, which is the original company name, by mixing the two company names.\nTask Input: The input consists of a single test case. The test case consists of two lines.\n\nThe first line contains a string $S$ which denotes the name of the company that you belong to. The second line contains a string $T$ which denotes the name of the target company of the planned M&A. The two names $S$ and $T$ are non-empty and of the same length no longer than 1,000 characters, and all the characters used in the names are lowercase English letters.\nTask Output: Print \"Yes\" in a line if it is possible to make original company name by combining $S$ and $T$. Otherwise, print \"No\" in a line.\nTask Samples: input: acmicpc\ntsukuba\n output: No\ninput: hoge\nmoen\n output: Yes\ninput: abcdefg\nxacxegx\n output: Yes\n\n" }, { "title": "Change a Password", "content": "Password authentication is used in a lot of facilities. The office of JAG also uses password authentication. A password is required to enter their office. A password is a string of $N$ digits '0'-'9'. This password is changed on a regular basis. Taro, a staff of the security division of JAG, decided to use the following rules to generate a new password from an old one.\n\n The new password consists of the same number $N$ of digits to the original one and each digit appears at most once in the new password. It can have a leading zero. (Note that an old password may contain same digits twice or more. )\n\n The new password maximizes the difference from the old password within constraints described above. (Definition of the difference between two passwords is described below. )\n\n If there are two or more candidates, the one which has the minimum value when it is read as an integer will be selected.\nThe difference between two passwords is defined by min($|a - b|, 10^N - |a - b|$), where $a$ and $b$ are the integers represented by the two passwords. For example, the difference between \"11\" and \"42\" is 31, and the difference between \"987\" and \"012\" is 25.\n\nTaro would like to use a computer to calculate a new password correctly, but he is not good at programming. Therefore, he asked you to write a program. Your task is to write a program that generates a new password from an old password.", "constraint": "", "input": "The input consists of a single test case. The first line of the input contains a string $S$ which denotes the old password. You can assume that the length of $S$ is no less than 1 and no greater than 10. Note that old password $S$ may contain same digits twice or more, and may have leading zeros.", "output": "Print the new password in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 201\n output: 701", "input: 512\n output: 012", "input: 99999\n output: 49876", "input: 765876346\n output: 265874931"], "Pid": "p01829", "ProblemText": "Task Description: Password authentication is used in a lot of facilities. The office of JAG also uses password authentication. A password is required to enter their office. A password is a string of $N$ digits '0'-'9'. This password is changed on a regular basis. Taro, a staff of the security division of JAG, decided to use the following rules to generate a new password from an old one.\n\n The new password consists of the same number $N$ of digits to the original one and each digit appears at most once in the new password. It can have a leading zero. (Note that an old password may contain same digits twice or more. )\n\n The new password maximizes the difference from the old password within constraints described above. (Definition of the difference between two passwords is described below. )\n\n If there are two or more candidates, the one which has the minimum value when it is read as an integer will be selected.\nThe difference between two passwords is defined by min($|a - b|, 10^N - |a - b|$), where $a$ and $b$ are the integers represented by the two passwords. For example, the difference between \"11\" and \"42\" is 31, and the difference between \"987\" and \"012\" is 25.\n\nTaro would like to use a computer to calculate a new password correctly, but he is not good at programming. Therefore, he asked you to write a program. Your task is to write a program that generates a new password from an old password.\nTask Input: The input consists of a single test case. The first line of the input contains a string $S$ which denotes the old password. You can assume that the length of $S$ is no less than 1 and no greater than 10. Note that old password $S$ may contain same digits twice or more, and may have leading zeros.\nTask Output: Print the new password in a line.\nTask Samples: input: 201\n output: 701\ninput: 512\n output: 012\ninput: 99999\n output: 49876\ninput: 765876346\n output: 265874931\n\n" }, { "title": "Delete Files", "content": "You are using an operating system named \"Jaguntu\". Jaguntu provides \"Filer\", a file manager with a graphical user interface.\n\nWhen you open a folder with Filer, the name list of files in the folder is displayed on a Filer window. Each filename is displayed within a rectangular region, and this region is called a filename region. Each filename region is aligned to the left side of the Filer window. The height of each filename region is 1, and the width of each filename region is the filename length. For example, when three files \"acm. in1\", \"acm. c~\", and \"acm. c\" are stored in this order in a folder, it looks like Fig. C-1 on the Filer window.\n\nYou can delete files by taking the following steps. First, you select a rectangular region with dragging a mouse. This region is called selection region. Next, you press the delete key on your keyboard. A file is deleted if and only if its filename region intersects with the selection region. After the deletion, Filer shifts each filename region to the upside on the Filer window not to leave any top margin on any remaining filename region. For example, if you select a region like Fig. C-2, then the two files \"acm. in1\" and \"acm. c~\" are deleted, and the remaining file \"acm. c\" is displayed on the top of the Filer window as Fig. C-3.\n\nYou are opening a folder storing $N$ files with Filer. Since you have almost run out of disk space, you want to delete unnecessary files in the folder. Your task is to write a program that calculates the minimum number of times to perform deletion operation described above.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows. \n$N$\n$D_1$ $L_1$\n$D_2$ $L_2$\n. . . \n$D_N$ $L_N$\n\nThe first line contains one integer $N$ ($1 <= N <= 1,000$), which is the number of files in a folder. Each of the next $N$ lines contains a character $D_i$ and an integer $L_i$: $D_i$ indicates whether the $i$-th file should be deleted or not, and $L_i$ ($1 <= L_i <= 1,000$) is the filename length of the $i$-th file. If $D_i$ is 'y', the $i$-th file should be deleted. Otherwise, $D_i$ is always 'n', and you should not delete the $i$-th file.", "output": "Output the minimum number of deletion operations to delete only all the unnecessary files.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\ny 7\ny 6\nn 5\n output: 1", "input: 3\ny 7\nn 6\ny 5\n output: 2", "input: 6\ny 4\nn 5\ny 4\ny 6\nn 3\ny 6\n output: 2"], "Pid": "p01830", "ProblemText": "Task Description: You are using an operating system named \"Jaguntu\". Jaguntu provides \"Filer\", a file manager with a graphical user interface.\n\nWhen you open a folder with Filer, the name list of files in the folder is displayed on a Filer window. Each filename is displayed within a rectangular region, and this region is called a filename region. Each filename region is aligned to the left side of the Filer window. The height of each filename region is 1, and the width of each filename region is the filename length. For example, when three files \"acm. in1\", \"acm. c~\", and \"acm. c\" are stored in this order in a folder, it looks like Fig. C-1 on the Filer window.\n\nYou can delete files by taking the following steps. First, you select a rectangular region with dragging a mouse. This region is called selection region. Next, you press the delete key on your keyboard. A file is deleted if and only if its filename region intersects with the selection region. After the deletion, Filer shifts each filename region to the upside on the Filer window not to leave any top margin on any remaining filename region. For example, if you select a region like Fig. C-2, then the two files \"acm. in1\" and \"acm. c~\" are deleted, and the remaining file \"acm. c\" is displayed on the top of the Filer window as Fig. C-3.\n\nYou are opening a folder storing $N$ files with Filer. Since you have almost run out of disk space, you want to delete unnecessary files in the folder. Your task is to write a program that calculates the minimum number of times to perform deletion operation described above.\nTask Input: The input consists of a single test case. The test case is formatted as follows. \n$N$\n$D_1$ $L_1$\n$D_2$ $L_2$\n. . . \n$D_N$ $L_N$\n\nThe first line contains one integer $N$ ($1 <= N <= 1,000$), which is the number of files in a folder. Each of the next $N$ lines contains a character $D_i$ and an integer $L_i$: $D_i$ indicates whether the $i$-th file should be deleted or not, and $L_i$ ($1 <= L_i <= 1,000$) is the filename length of the $i$-th file. If $D_i$ is 'y', the $i$-th file should be deleted. Otherwise, $D_i$ is always 'n', and you should not delete the $i$-th file.\nTask Output: Output the minimum number of deletion operations to delete only all the unnecessary files.\nTask Samples: input: 3\ny 7\ny 6\nn 5\n output: 1\ninput: 3\ny 7\nn 6\ny 5\n output: 2\ninput: 6\ny 4\nn 5\ny 4\ny 6\nn 3\ny 6\n output: 2\n\n" }, { "title": "Line Gimmick", "content": "You are in front of a linear gimmick of a game. It consists of $N$ panels in a row, and each of them displays a right or a left arrow.\n\nYou can step in this gimmick from any panel. Once you get on a panel, you are forced to move following the direction of the arrow shown on the panel and the panel will be removed immediately. You keep moving in the same direction until you get on another panel, and if you reach a panel, you turn in (or keep) the direction of the arrow on the panel. The panels you passed are also removed. You repeat this procedure, and when there is no panel in your current direction, you get out of the gimmick.\n\nFor example, when the gimmick is the following image and you first get on the 2nd panel from the left, your moves are as follows.\n\n Move right and remove the 2nd panel.\n\n Move left and remove the 3rd panel.\n\n Move right and remove the 1st panel.\n\n Move right and remove the 4th panel.\n\n Move left and remove the 5th panel.\n\n Get out of the gimmick.\nYou are given a gimmick with $N$ panels. Compute the maximum number of removed panels after you get out of the gimmick.", "constraint": "", "input": "The input consists of two lines. The first line contains an integer $N$ ($1 <= N <= 100,000$) which represents the number of the panels in the gimmick. The second line contains a character string $S$ of length $N$, which consists of '>' or '<'. The $i$-th character of $S$ corresponds to the direction of the arrow on the $i$-th panel from the left. '<' and '>' denote left and right directions respectively.", "output": "Output the maximum number of removed panels after you get out of the gimmick.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 7\n>><><<<\n output: 7", "input: 5\n>><<<\n output: 5", "input: 6\n><<><<\n output: 6", "input: 7\n<<><<>>\n output: 5"], "Pid": "p01831", "ProblemText": "Task Description: You are in front of a linear gimmick of a game. It consists of $N$ panels in a row, and each of them displays a right or a left arrow.\n\nYou can step in this gimmick from any panel. Once you get on a panel, you are forced to move following the direction of the arrow shown on the panel and the panel will be removed immediately. You keep moving in the same direction until you get on another panel, and if you reach a panel, you turn in (or keep) the direction of the arrow on the panel. The panels you passed are also removed. You repeat this procedure, and when there is no panel in your current direction, you get out of the gimmick.\n\nFor example, when the gimmick is the following image and you first get on the 2nd panel from the left, your moves are as follows.\n\n Move right and remove the 2nd panel.\n\n Move left and remove the 3rd panel.\n\n Move right and remove the 1st panel.\n\n Move right and remove the 4th panel.\n\n Move left and remove the 5th panel.\n\n Get out of the gimmick.\nYou are given a gimmick with $N$ panels. Compute the maximum number of removed panels after you get out of the gimmick.\nTask Input: The input consists of two lines. The first line contains an integer $N$ ($1 <= N <= 100,000$) which represents the number of the panels in the gimmick. The second line contains a character string $S$ of length $N$, which consists of '>' or '<'. The $i$-th character of $S$ corresponds to the direction of the arrow on the $i$-th panel from the left. '<' and '>' denote left and right directions respectively.\nTask Output: Output the maximum number of removed panels after you get out of the gimmick.\nTask Samples: input: 7\n>><><<<\n output: 7\ninput: 5\n>><<<\n output: 5\ninput: 6\n><<><<\n output: 6\ninput: 7\n<<><<>>\n output: 5\n\n" }, { "title": "Shifting a Matrix", "content": "You are given $N * N$ matrix $A$ initialized with $A_{i, j} = (i - 1)N + j$, where $A_{i, j}$ is the entry of the $i$-th row and the $j$-th column of $A$. Note that $i$ and $j$ are 1-based.\n\nYou are also given an operation sequence which consists of the four types of shift operations: left, right, up, and down shifts. More precisely, these operations are defined as follows:\n\n Left shift with $i$: circular shift of the $i$-th row to the left, i. e. , setting previous $A_{i, k}$ to new $A_{i, k-1}$ for $2 <= k <= N$, and previous $A_{i, 1}$ to new $A_{i, N}$.\n\n Right shift with $i$: circular shift of the $i$-th row to the right, i. e. , setting previous $A_{i, k}$ to new $A_{i, k+1}$ for $1 <= k <= N - 1$, and previous $A_{i, N}$ to new $A_{i, 1}$.\n\n Up shift with $j$: circular shift of the $j$-th column to the above, i. e. , setting previous $A_{k, j}$ to new $A_{k-1, j}$ for $2 <= k <= N$, and previous $A_{1, j}$ to new $A_{N, j}$.\n\n Down shift with $j$: circular shift of the $j$-th column to the below, i. e. , setting previous $A_{k, j}$ to new $A_{k+1, j}$ for $1 <= k <= N - 1$, and previous $A_{N, j}$ to new $A_{1, j}$.\nAn operation sequence is given as a string. You have to apply operations to a given matrix from left to right in a given string. Left, right, up, and down shifts are referred as 'L', 'R', 'U', and 'D' respectively in a string, and the following number indicates the row/column to be shifted. For example, \"R25\" means we should perform right shift with 25. In addition, the notion supports repetition of operation sequences. An operation sequence surrounded by a pair of parentheses must be repeated exactly $m$ times, where $m$ is the number following the close parenthesis. For example, \"(L1R2)10\" means we should repeat exactly 10 times the set of the two operations:\nleft shift with 1 and right shift with 2 in this order.\n\nGiven operation sequences are guaranteed to follow the following BNF:\n\n : = | | | \n : = '('')'\n : = \n : = 'L' | 'R' | 'U' | 'D'\n : = |\n : = '0' | \n : = '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'\n\nGiven $N$ and an operation sequence as a string, make a program to compute the $N * N$ matrix after operations indicated by the operation sequence.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows. \n\n$N$ $L$\n$S$\n\nThe first line contains two integers $N$ and $L$, where $N$ ($1 <= N <= 100$) is the size of the given matrix and $L$ ($2 <= L <= 1,000$) is the length of the following string. The second line contains a string $S$ representing the given operation sequence. You can assume that $S$ follows the above BNF. You can also assume numbers representing rows and columns are no less than 1 and no more than $N$, and the number of each repetition is no less than 1 and no more than $10^9$ in the given string.", "output": "Output the matrix after the operations in $N$ lines, where the $i$-th line contains single-space separated $N$ integers representing the $i$-th row of $A$ after the operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\nR1\n output: 3 1 2\n4 5 6\n7 8 9", "input: 3 7\n(U2)300\n output: 1 2 3\n4 5 6\n7 8 9", "input: 3 7\n(R1D1)3\n output: 3 4 7\n1 5 6\n2 8 9"], "Pid": "p01832", "ProblemText": "Task Description: You are given $N * N$ matrix $A$ initialized with $A_{i, j} = (i - 1)N + j$, where $A_{i, j}$ is the entry of the $i$-th row and the $j$-th column of $A$. Note that $i$ and $j$ are 1-based.\n\nYou are also given an operation sequence which consists of the four types of shift operations: left, right, up, and down shifts. More precisely, these operations are defined as follows:\n\n Left shift with $i$: circular shift of the $i$-th row to the left, i. e. , setting previous $A_{i, k}$ to new $A_{i, k-1}$ for $2 <= k <= N$, and previous $A_{i, 1}$ to new $A_{i, N}$.\n\n Right shift with $i$: circular shift of the $i$-th row to the right, i. e. , setting previous $A_{i, k}$ to new $A_{i, k+1}$ for $1 <= k <= N - 1$, and previous $A_{i, N}$ to new $A_{i, 1}$.\n\n Up shift with $j$: circular shift of the $j$-th column to the above, i. e. , setting previous $A_{k, j}$ to new $A_{k-1, j}$ for $2 <= k <= N$, and previous $A_{1, j}$ to new $A_{N, j}$.\n\n Down shift with $j$: circular shift of the $j$-th column to the below, i. e. , setting previous $A_{k, j}$ to new $A_{k+1, j}$ for $1 <= k <= N - 1$, and previous $A_{N, j}$ to new $A_{1, j}$.\nAn operation sequence is given as a string. You have to apply operations to a given matrix from left to right in a given string. Left, right, up, and down shifts are referred as 'L', 'R', 'U', and 'D' respectively in a string, and the following number indicates the row/column to be shifted. For example, \"R25\" means we should perform right shift with 25. In addition, the notion supports repetition of operation sequences. An operation sequence surrounded by a pair of parentheses must be repeated exactly $m$ times, where $m$ is the number following the close parenthesis. For example, \"(L1R2)10\" means we should repeat exactly 10 times the set of the two operations:\nleft shift with 1 and right shift with 2 in this order.\n\nGiven operation sequences are guaranteed to follow the following BNF:\n\n : = | | | \n : = '('')'\n : = \n : = 'L' | 'R' | 'U' | 'D'\n : = |\n : = '0' | \n : = '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'\n\nGiven $N$ and an operation sequence as a string, make a program to compute the $N * N$ matrix after operations indicated by the operation sequence.\nTask Input: The input consists of a single test case. The test case is formatted as follows. \n\n$N$ $L$\n$S$\n\nThe first line contains two integers $N$ and $L$, where $N$ ($1 <= N <= 100$) is the size of the given matrix and $L$ ($2 <= L <= 1,000$) is the length of the following string. The second line contains a string $S$ representing the given operation sequence. You can assume that $S$ follows the above BNF. You can also assume numbers representing rows and columns are no less than 1 and no more than $N$, and the number of each repetition is no less than 1 and no more than $10^9$ in the given string.\nTask Output: Output the matrix after the operations in $N$ lines, where the $i$-th line contains single-space separated $N$ integers representing the $i$-th row of $A$ after the operations.\nTask Samples: input: 3 2\nR1\n output: 3 1 2\n4 5 6\n7 8 9\ninput: 3 7\n(U2)300\n output: 1 2 3\n4 5 6\n7 8 9\ninput: 3 7\n(R1D1)3\n output: 3 4 7\n1 5 6\n2 8 9\n\n" }, { "title": "Modern Announce Network", "content": "Today, modern teenagers use SNS to communicate with each other.\n\nIn a high school, $N$ students are using an SNS called ICPC (International Community for Programming Contest). Some pairs of these $N$ students are 'friends' on this SNS, and can send messages to each other. Among these $N$ students, $A$ first grade students, $B$ second grade students, and $C$ third grade students are members of the Programming Society. Note that there may be some students who are not the members of the Programming Society, so $A+B +C$ can be less than $N$.\n\nThere are good relationships between members of the same grade in the Society. Thus, there is a chat group in the SNS for each grade, and the Society members of the same grade can communicate with each other instantly via their group chat. On the other hand, the relationships between any different grades are not so good, and there are no chat group for the entire Society and the entire high school.\n\nIn order to broadcast a message to all the Society members on the SNS, the administrator of the Society came up with a method: the administrator tells the message to one of the $N$ students and have them spread the message on the SNS via the chat groups and their friends. (The administrator itself does not have an account for the SNS. ) As the members of the same grade can broadcast the message by the chat group for the grade, we can assume that if one of a grade gets the message, all other members of that grade also get the message instantly. Therefore, if the message is told to at least one member of each grade, we can assume that the message is broadcasted to the all members of the Society on the SNS.\n\nBecause it is bothering to communicate between friends, we want to minimize the number of communications between friends. What is the minimum number of communications between friends to broadcast a message to all the Society members? Who is the first person to whom the administrator should tell the message to achieve the minimum communications?", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows: \n\n$N$ $A$ $B$ $C$\n$a_1$ . . . $a_A$\n$b_1$ . . . $b_B$\n$c_1$ . . . $c_C$\n$M$\n$x_1$ $y_1$\n. . . \n$x_M$ $y_M$\n\nThe first line contains four integers $N$, $A$, $B$, and $C$. $N$ ($3 <= N <= 10,000$) denotes the number of students in the SNS, and $A$, $B$ and $C$ ($1 <= A, B, C <= N$ and $A + B + C <= N$) denote the number of members of the first, second, and third grade respectively. Each student on the SNS is represented by a unique numeric ID between 1 and $N$. The second line contains $A$ integers $a_1, . . . , a_A$ ($1 <= a_1, . . . , a_A <= N$), which are the IDs of members of the first grade. The third line contains $B$ integers $b_1, . . . , b_B$ ($1 <= b_1, . . . , b_B <= N$), which are the IDs of members of the second grade. The fourth line contains $C$ integers $c_1, . . . , c_C$ ($1 <= c_1, . . . , c_C <= N$), which are the IDs of members of the third grade. You can assume that $a_1, . . . , a_A, b_1, . . . , b_B, c_1, . . . , c_C$ are distinct. The fifth line contains an integer $M$ ($2 <= M <= 500,000$). $M$ denotes the number of pairs of students who are friends in the SNS. The $i$-th line of the following $M$ lines contains two integers $x_i$ and $y_i$ ($1 <= x_i, y_i <= N$), which means the student with ID $x_i$ and the student with ID $y_i$ are friends in the SNS. You can assume that $x_i \\ne y_i$ ($1 <= i <= M$), and ($x_i \\ne x_j$ or $y_i \\ne y_j$) and ($x_i \\ne y_j$ or $y_i \\ne x_j$) if $i \\ne j$ ($1 <= i, j <= M$). You can also assume that a message can be delivered from any student to any student in the SNS via the friends and group chat.", "output": "Output the minimum number of communications between friends (not including group chat) to broadcast a message among all the Society members, and the ID of the student to whom the administrator should tell the message in order to achieve the minimum number of communications, separated by a single space. If there are multiple students that satisfy the above constraints, output the minimum ID of such students.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 1 1\n1 2\n3\n4\n3\n1 2\n2 4\n3 4\n output: 2 1", "input: 4 1 1 1\n2\n3\n4\n4\n1 2\n1 3\n1 4\n2 4\n output: 3 1", "input: 8 1 2 2\n5\n4 6\n3 8\n7\n1 2\n2 3\n3 4\n5 6\n6 7\n7 8\n2 6\n output: 2 3"], "Pid": "p01833", "ProblemText": "Task Description: Today, modern teenagers use SNS to communicate with each other.\n\nIn a high school, $N$ students are using an SNS called ICPC (International Community for Programming Contest). Some pairs of these $N$ students are 'friends' on this SNS, and can send messages to each other. Among these $N$ students, $A$ first grade students, $B$ second grade students, and $C$ third grade students are members of the Programming Society. Note that there may be some students who are not the members of the Programming Society, so $A+B +C$ can be less than $N$.\n\nThere are good relationships between members of the same grade in the Society. Thus, there is a chat group in the SNS for each grade, and the Society members of the same grade can communicate with each other instantly via their group chat. On the other hand, the relationships between any different grades are not so good, and there are no chat group for the entire Society and the entire high school.\n\nIn order to broadcast a message to all the Society members on the SNS, the administrator of the Society came up with a method: the administrator tells the message to one of the $N$ students and have them spread the message on the SNS via the chat groups and their friends. (The administrator itself does not have an account for the SNS. ) As the members of the same grade can broadcast the message by the chat group for the grade, we can assume that if one of a grade gets the message, all other members of that grade also get the message instantly. Therefore, if the message is told to at least one member of each grade, we can assume that the message is broadcasted to the all members of the Society on the SNS.\n\nBecause it is bothering to communicate between friends, we want to minimize the number of communications between friends. What is the minimum number of communications between friends to broadcast a message to all the Society members? Who is the first person to whom the administrator should tell the message to achieve the minimum communications?\nTask Input: The input consists of a single test case. The test case is formatted as follows: \n\n$N$ $A$ $B$ $C$\n$a_1$ . . . $a_A$\n$b_1$ . . . $b_B$\n$c_1$ . . . $c_C$\n$M$\n$x_1$ $y_1$\n. . . \n$x_M$ $y_M$\n\nThe first line contains four integers $N$, $A$, $B$, and $C$. $N$ ($3 <= N <= 10,000$) denotes the number of students in the SNS, and $A$, $B$ and $C$ ($1 <= A, B, C <= N$ and $A + B + C <= N$) denote the number of members of the first, second, and third grade respectively. Each student on the SNS is represented by a unique numeric ID between 1 and $N$. The second line contains $A$ integers $a_1, . . . , a_A$ ($1 <= a_1, . . . , a_A <= N$), which are the IDs of members of the first grade. The third line contains $B$ integers $b_1, . . . , b_B$ ($1 <= b_1, . . . , b_B <= N$), which are the IDs of members of the second grade. The fourth line contains $C$ integers $c_1, . . . , c_C$ ($1 <= c_1, . . . , c_C <= N$), which are the IDs of members of the third grade. You can assume that $a_1, . . . , a_A, b_1, . . . , b_B, c_1, . . . , c_C$ are distinct. The fifth line contains an integer $M$ ($2 <= M <= 500,000$). $M$ denotes the number of pairs of students who are friends in the SNS. The $i$-th line of the following $M$ lines contains two integers $x_i$ and $y_i$ ($1 <= x_i, y_i <= N$), which means the student with ID $x_i$ and the student with ID $y_i$ are friends in the SNS. You can assume that $x_i \\ne y_i$ ($1 <= i <= M$), and ($x_i \\ne x_j$ or $y_i \\ne y_j$) and ($x_i \\ne y_j$ or $y_i \\ne x_j$) if $i \\ne j$ ($1 <= i, j <= M$). You can also assume that a message can be delivered from any student to any student in the SNS via the friends and group chat.\nTask Output: Output the minimum number of communications between friends (not including group chat) to broadcast a message among all the Society members, and the ID of the student to whom the administrator should tell the message in order to achieve the minimum number of communications, separated by a single space. If there are multiple students that satisfy the above constraints, output the minimum ID of such students.\nTask Samples: input: 4 2 1 1\n1 2\n3\n4\n3\n1 2\n2 4\n3 4\n output: 2 1\ninput: 4 1 1 1\n2\n3\n4\n4\n1 2\n1 3\n1 4\n2 4\n output: 3 1\ninput: 8 1 2 2\n5\n4 6\n3 8\n7\n1 2\n2 3\n3 4\n5 6\n6 7\n7 8\n2 6\n output: 2 3\n\n" }, { "title": "Cube Dividing", "content": "Pablo Cubarson is a well-known cubism artist. He is producing a new piece of work using a cuboid which consists of $A * B * C$ unit cubes. He plans to make a beautiful shape by removing $N$ units cubes from the cuboid. When he is about to begin the work, he has noticed that by the removal the cuboid may be divided into several parts disconnected to each other. It is against his aesthetics to divide a cuboid. So he wants to know how many parts are created in his plan.\n\nYour task is to calculate the number of connected components in the cuboid after removing the $N$ cubes. Two cubes are connected if they share one face.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows: \n\n$A$ $B$ $C$ $N$\n$X_1$ $Y_1$ $Z_1$\n. . . \n$X_N$ $Y_N$ $Z_N$\n\nThe first line contains four integers $A$, $B$, $C$ and $N$. $A$, $B$ and $C$ ($1 <= A, B, C <= 10^6$) denote the size of the cuboid $-$ the cuboid has an $A$ unit width from left to right and a $B$ unit height from bottom to top, and a $C$ unit depth from front to back. $N$ ($0 <= N <= 20,000, N <= A * B * C - 1$) denotes the number of the cubes removed in the Cubarson's plan. Each of the following $N$ lines contains three integers $X_i$ ($0 <= X_i <= A-1$), $Y_i$ ($0 <= Y_i <= B-1$) and $Z_i$ ($0 <= Z_i <= C - 1$). They denote that the cube located at the $X_i$-th position from the left, the $Y_i$-th from the bottom and the $Z_i$-th from the front will be removed in the plan. You may assume the given positions are distinct.", "output": "Print the number of the connected components in the cuboid after removing the specified cubes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 2 4\n0 0 0\n1 1 0\n1 0 1\n0 1 1\n output: 4", "input: 3 3 3 1\n1 1 1\n output: 1", "input: 1 1 3 2\n0 0 0\n0 0 2\n output: 1"], "Pid": "p01834", "ProblemText": "Task Description: Pablo Cubarson is a well-known cubism artist. He is producing a new piece of work using a cuboid which consists of $A * B * C$ unit cubes. He plans to make a beautiful shape by removing $N$ units cubes from the cuboid. When he is about to begin the work, he has noticed that by the removal the cuboid may be divided into several parts disconnected to each other. It is against his aesthetics to divide a cuboid. So he wants to know how many parts are created in his plan.\n\nYour task is to calculate the number of connected components in the cuboid after removing the $N$ cubes. Two cubes are connected if they share one face.\nTask Input: The input consists of a single test case. The test case is formatted as follows: \n\n$A$ $B$ $C$ $N$\n$X_1$ $Y_1$ $Z_1$\n. . . \n$X_N$ $Y_N$ $Z_N$\n\nThe first line contains four integers $A$, $B$, $C$ and $N$. $A$, $B$ and $C$ ($1 <= A, B, C <= 10^6$) denote the size of the cuboid $-$ the cuboid has an $A$ unit width from left to right and a $B$ unit height from bottom to top, and a $C$ unit depth from front to back. $N$ ($0 <= N <= 20,000, N <= A * B * C - 1$) denotes the number of the cubes removed in the Cubarson's plan. Each of the following $N$ lines contains three integers $X_i$ ($0 <= X_i <= A-1$), $Y_i$ ($0 <= Y_i <= B-1$) and $Z_i$ ($0 <= Z_i <= C - 1$). They denote that the cube located at the $X_i$-th position from the left, the $Y_i$-th from the bottom and the $Z_i$-th from the front will be removed in the plan. You may assume the given positions are distinct.\nTask Output: Print the number of the connected components in the cuboid after removing the specified cubes.\nTask Samples: input: 2 2 2 4\n0 0 0\n1 1 0\n1 0 1\n0 1 1\n output: 4\ninput: 3 3 3 1\n1 1 1\n output: 1\ninput: 1 1 3 2\n0 0 0\n0 0 2\n output: 1\n\n" }, { "title": "Donut Decoration", "content": "Donut maker's morning is early. Mr. D, who is also called Mr. Donuts, is an awesome donut maker. Also today, he goes to his kitchen and prepares to make donuts before sunrise.\n\nIn a twinkling, Mr. D finishes frying $N$ donuts with a practiced hand. But these donuts as they are must not be displayed in a showcase. Filling cream, dipping in chocolate, topping somehow cute, colorful things, etc. , several decoration tasks are needed. There are $K$ tasks numbered 1 through $K$, and each of them must be done exactly once in the order $1,2, . . . , K$ to finish the donuts as items on sale.\n\nInstantly, Mr. D arranges the $N$ donuts in a row. He seems to intend to accomplish each decoration tasks sequentially at once. However, what in the world is he doing? Mr. D, who stayed up late at yesterday night, decorates only a part of the donuts in a consecutive interval for each task. It's clearly a mistake! Not only that, he does some tasks zero or several times, and the order of tasks is also disordered. The donuts which are not decorated by correct process cannot be provided as items on sale, so he should trash them.\n\nFortunately, there are data recording a sequence of tasks he did. The data contain the following information: for each task, the consecutive interval $[l, r]$ of the decorated donuts and the ID $x$ of the task. Please write a program enumerating the number of the donuts which can be displayed in a showcase as items on sale for given recorded data.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows. \n\n$N$ $K$\n$T$\n$l_1$ $r_1$ $x_1$\n. . . \n$l_T$ $r_T$ $x_T$\n\nThe first line contains two integers $N$ and $K$, where $N$ ($1 <= N <= 200,000$) is the number of the donuts fried by Mr. D, and $K$ ($1 <= K <= 200,000$) is the number of decoration tasks should be applied to the donuts. The second line contains a single integer $T$ ($1 <= T <= 200,000$), which means the number of information about tasks Mr. D did. Each of next $T$ lines contains three\nintegers $l_i$, $r_i$, and $x_i$ representing the $i$-th task Mr. D did: the $i$-th task was applied to the interval $[l_i, r_i]$ ($1 <= l_i <= r_i <= N$) of the donuts inclusive, and has ID $x_i$ ($1 <= x_i <= K$).", "output": "Output the number of the donuts that can be provided as items on sale.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n3\n1 2 1\n2 3 2\n3 3 1\n output: 1", "input: 5 3\n6\n2 3 1\n1 3 2\n4 5 1\n2 4 3\n3 5 2\n5 5 3\n output: 2", "input: 10 1\n2\n2 9 1\n5 7 1\n output: 5"], "Pid": "p01835", "ProblemText": "Task Description: Donut maker's morning is early. Mr. D, who is also called Mr. Donuts, is an awesome donut maker. Also today, he goes to his kitchen and prepares to make donuts before sunrise.\n\nIn a twinkling, Mr. D finishes frying $N$ donuts with a practiced hand. But these donuts as they are must not be displayed in a showcase. Filling cream, dipping in chocolate, topping somehow cute, colorful things, etc. , several decoration tasks are needed. There are $K$ tasks numbered 1 through $K$, and each of them must be done exactly once in the order $1,2, . . . , K$ to finish the donuts as items on sale.\n\nInstantly, Mr. D arranges the $N$ donuts in a row. He seems to intend to accomplish each decoration tasks sequentially at once. However, what in the world is he doing? Mr. D, who stayed up late at yesterday night, decorates only a part of the donuts in a consecutive interval for each task. It's clearly a mistake! Not only that, he does some tasks zero or several times, and the order of tasks is also disordered. The donuts which are not decorated by correct process cannot be provided as items on sale, so he should trash them.\n\nFortunately, there are data recording a sequence of tasks he did. The data contain the following information: for each task, the consecutive interval $[l, r]$ of the decorated donuts and the ID $x$ of the task. Please write a program enumerating the number of the donuts which can be displayed in a showcase as items on sale for given recorded data.\nTask Input: The input consists of a single test case. The test case is formatted as follows. \n\n$N$ $K$\n$T$\n$l_1$ $r_1$ $x_1$\n. . . \n$l_T$ $r_T$ $x_T$\n\nThe first line contains two integers $N$ and $K$, where $N$ ($1 <= N <= 200,000$) is the number of the donuts fried by Mr. D, and $K$ ($1 <= K <= 200,000$) is the number of decoration tasks should be applied to the donuts. The second line contains a single integer $T$ ($1 <= T <= 200,000$), which means the number of information about tasks Mr. D did. Each of next $T$ lines contains three\nintegers $l_i$, $r_i$, and $x_i$ representing the $i$-th task Mr. D did: the $i$-th task was applied to the interval $[l_i, r_i]$ ($1 <= l_i <= r_i <= N$) of the donuts inclusive, and has ID $x_i$ ($1 <= x_i <= K$).\nTask Output: Output the number of the donuts that can be provided as items on sale.\nTask Samples: input: 3 2\n3\n1 2 1\n2 3 2\n3 3 1\n output: 1\ninput: 5 3\n6\n2 3 1\n1 3 2\n4 5 1\n2 4 3\n3 5 2\n5 5 3\n output: 2\ninput: 10 1\n2\n2 9 1\n5 7 1\n output: 5\n\n" }, { "title": "Shortest Bridge", "content": "There is a city whose shape is a 1,000 $*$ 1,000 square. The city has a big river, which flows from the north to the south and separates the city into just two parts: the west and the east.\n\nRecently, the city mayor has decided to build a highway from a point $s$ on the west part to a point $t$ on the east part. A highway consists of a bridge on the river, and two roads: one of the roads connects $s$ and the west end of the bridge, and the other one connects $t$ and the east end of the bridge. Note that each road doesn't have to be a straight line, but the intersection length with the river must be zero.\n\nIn order to cut building costs, the mayor intends to build a highway satisfying the following conditions:\n\n Since bridge will cost more than roads, at first the length of a bridge connecting the east part and the west part must be as short as possible.\n\n Under the above condition, the sum of the length of two roads is minimum.\nYour task is to write a program computing the total length of a highway satisfying the above conditions.", "constraint": "", "input": "The input consists of a single test case. The test case is formatted as follows. \n\n$sx$ $sy$ $tx$ $ty$\n$N$\n$wx_1$ $wy_1$\n. . . \n$wx_N$ $wy_N$\n$M$\n$ex_1$ $ey_1$\n. . . \n$ex_M$ $ey_M$\n\nAt first, we refer to a point on the city by a coordinate ($x, y$): the distance from the west side is $x$ and the distance from the north side is $y$.\n\nThe first line contains four integers $sx$, $sy$, $tx$, and $ty$ ($0 <= sx, sy, tx, ty <= 1,000$): points $s$ and $t$ are located at ($sx, sy$) and ($tx, ty$) respectively. The next line contains an integer $N$ ($2 <= N <= 20$), where $N$ is the number of points composing the west riverside. Each of the following $N$ lines contains two integers $wx_i$ and $wy_i$ ($0 <= wx_i, wy_i <= 1,000$): the coordinate of the $i$-th point of the west riverside is ($wx_i, wy_i$). The west riverside is a polygonal line obtained by connecting the segments between ($wx_i, wy_i$) and ($wx_{i+1}, wy_{i+1}$) for all $1 <= i <= N -1$. The next line contains an integer $M$ ($2 <= M <= 20$), where $M$ is the number of points composing the east riverside. Each of the following $M$ lines contains two integers $ex_i$ and $ey_i$ ($0 <= ex_i, ey_i <= 1,000$): the coordinate of the $i$-th point of the east riverside is ($ex_i, ey_i$). The east riverside is a polygonal line obtained by connecting the segments between ($ex_i, ey_i$) and ($ex_{i+1}, ey_{i+1}$) for all $1 <= i <= M - 1$.\n\nYou can assume that test cases are under the following conditions.\n\n $wy_1$ and $ey_1$ must be 0, and $wy_N$ and $ey_M$ must be 1,000.\n\n Each polygonal line has no self-intersection.\n\n Two polygonal lines representing the west and the east riverside have no cross point.\n\n A point $s$ must be on the west part of the city. More precisely, $s$ must be on the region surrounded by the square side of the city and the polygonal line of the west riverside and not containing the east riverside points.\n\n A point $t$ must be on the east part of the city. More precisely, $t$ must be on the region surrounded by the square side of the city and the polygonal line of the east riverside and not containing the west riverside points.\n\n Each polygonal line intersects with the square only at the two end points. In other words, $0 < wx_i, wy_i < 1,000$ holds for $2 <= i <= N - 1$ and $0 < ex_i, ey_i < 1,000$ holds for $2 <= i <= M - 1$.", "output": "Output single-space separated two numbers in a line: the length of a bridge and the total length of a highway (i. e. a bridge and two roads) satisfying the above mayor's demand. The output can contain an absolute or a relative error no more than $10^{-8}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 200 500 800 500\n3\n400 0\n450 500\n400 1000\n3\n600 0\n550 500\n600 1000\n output: 100 600", "input: 300 300 700 100\n5\n300 0\n400 100\n300 200\n400 300\n400 1000\n4\n700 0\n600 100\n700 200\n700 1000\n output: 200 541.421356237", "input: 300 400 700 600\n2\n400 0\n400 1000\n2\n600 0\n600 1000\n output: 200 482.842712475", "input: 200 500 800 500\n3\n400 0\n450 500\n400 1000\n5\n600 0\n550 500\n600 100\n650 500\n600 1000\n output: 100 1200.326482915"], "Pid": "p01836", "ProblemText": "Task Description: There is a city whose shape is a 1,000 $*$ 1,000 square. The city has a big river, which flows from the north to the south and separates the city into just two parts: the west and the east.\n\nRecently, the city mayor has decided to build a highway from a point $s$ on the west part to a point $t$ on the east part. A highway consists of a bridge on the river, and two roads: one of the roads connects $s$ and the west end of the bridge, and the other one connects $t$ and the east end of the bridge. Note that each road doesn't have to be a straight line, but the intersection length with the river must be zero.\n\nIn order to cut building costs, the mayor intends to build a highway satisfying the following conditions:\n\n Since bridge will cost more than roads, at first the length of a bridge connecting the east part and the west part must be as short as possible.\n\n Under the above condition, the sum of the length of two roads is minimum.\nYour task is to write a program computing the total length of a highway satisfying the above conditions.\nTask Input: The input consists of a single test case. The test case is formatted as follows. \n\n$sx$ $sy$ $tx$ $ty$\n$N$\n$wx_1$ $wy_1$\n. . . \n$wx_N$ $wy_N$\n$M$\n$ex_1$ $ey_1$\n. . . \n$ex_M$ $ey_M$\n\nAt first, we refer to a point on the city by a coordinate ($x, y$): the distance from the west side is $x$ and the distance from the north side is $y$.\n\nThe first line contains four integers $sx$, $sy$, $tx$, and $ty$ ($0 <= sx, sy, tx, ty <= 1,000$): points $s$ and $t$ are located at ($sx, sy$) and ($tx, ty$) respectively. The next line contains an integer $N$ ($2 <= N <= 20$), where $N$ is the number of points composing the west riverside. Each of the following $N$ lines contains two integers $wx_i$ and $wy_i$ ($0 <= wx_i, wy_i <= 1,000$): the coordinate of the $i$-th point of the west riverside is ($wx_i, wy_i$). The west riverside is a polygonal line obtained by connecting the segments between ($wx_i, wy_i$) and ($wx_{i+1}, wy_{i+1}$) for all $1 <= i <= N -1$. The next line contains an integer $M$ ($2 <= M <= 20$), where $M$ is the number of points composing the east riverside. Each of the following $M$ lines contains two integers $ex_i$ and $ey_i$ ($0 <= ex_i, ey_i <= 1,000$): the coordinate of the $i$-th point of the east riverside is ($ex_i, ey_i$). The east riverside is a polygonal line obtained by connecting the segments between ($ex_i, ey_i$) and ($ex_{i+1}, ey_{i+1}$) for all $1 <= i <= M - 1$.\n\nYou can assume that test cases are under the following conditions.\n\n $wy_1$ and $ey_1$ must be 0, and $wy_N$ and $ey_M$ must be 1,000.\n\n Each polygonal line has no self-intersection.\n\n Two polygonal lines representing the west and the east riverside have no cross point.\n\n A point $s$ must be on the west part of the city. More precisely, $s$ must be on the region surrounded by the square side of the city and the polygonal line of the west riverside and not containing the east riverside points.\n\n A point $t$ must be on the east part of the city. More precisely, $t$ must be on the region surrounded by the square side of the city and the polygonal line of the east riverside and not containing the west riverside points.\n\n Each polygonal line intersects with the square only at the two end points. In other words, $0 < wx_i, wy_i < 1,000$ holds for $2 <= i <= N - 1$ and $0 < ex_i, ey_i < 1,000$ holds for $2 <= i <= M - 1$.\nTask Output: Output single-space separated two numbers in a line: the length of a bridge and the total length of a highway (i. e. a bridge and two roads) satisfying the above mayor's demand. The output can contain an absolute or a relative error no more than $10^{-8}$.\nTask Samples: input: 200 500 800 500\n3\n400 0\n450 500\n400 1000\n3\n600 0\n550 500\n600 1000\n output: 100 600\ninput: 300 300 700 100\n5\n300 0\n400 100\n300 200\n400 300\n400 1000\n4\n700 0\n600 100\n700 200\n700 1000\n output: 200 541.421356237\ninput: 300 400 700 600\n2\n400 0\n400 1000\n2\n600 0\n600 1000\n output: 200 482.842712475\ninput: 200 500 800 500\n3\n400 0\n450 500\n400 1000\n5\n600 0\n550 500\n600 100\n650 500\n600 1000\n output: 100 1200.326482915\n\n" }, { "title": "Longest Shortest Path", "content": "You are given a directed graph and two nodes $s$ and $t$. The given graph may contain multiple edges between the same node pair but not self loops. Each edge $e$ has its initial length $d_e$ and the cost $c_e$. You can extend an edge by paying a cost. Formally, it costs $x \\cdot c_e$ to change the length of an edge $e$ from $d_e$ to $d_e + x$. (Note that $x$ can be a non-integer. ) Edges cannot be shortened.\n\nYour task is to maximize the length of the shortest path from node $s$ to node $t$ by lengthening some edges within cost $P$. You can assume that there is at least one path from $s$ to $t$.", "constraint": "", "input": "The input consists of a single test case formatted as follows. \n\n$N$ $M$ $P$ $s$ $t$\n$v_1$ $u_1$ $d_1$ $c_1$\n. . . \n$v_M$ $u_M$ $d_M$ $c_M$\n\nThe first line contains five integers $N$, $M$, $P$, $s$, and $t$: $N$ ($2 <= N <= 200$) and $M$ ($1 <= M <= 2,000$) are the number of the nodes and the edges of the given graph respectively, $P$ ($0 <= P <= 10^6$) is the cost limit that you can pay, and $s$ and $t$ ($1 <= s, t <= N, s \\ne t$) are the start and the end node of objective path respectively. Each of the following $M$ lines contains four integers $v_i$, $u_i$, $d_i$, and $c_i$, which mean there is an edge from $v_i$ to $u_i$ ($1 <= v_i, u_i <= N, v_i \\ne u_i$) with the initial length $d_i$ ($1 <= d_i <= 10$) and the cost $c_i$ ($1 <= c_i <= 10$).", "output": "", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 3 1 3\n1 2 2 1\n2 3 1 2\n output: 6.0000000", "input: 3 3 2 1 3\n1 2 1 1\n2 3 1 1\n1 3 1 1\n output: 2.5000000", "input: 3 4 5 1 3\n1 2 1 2\n2 3 1 1\n1 3 3 2\n1 3 4 1\n output: 4.2500000"], "Pid": "p01837", "ProblemText": "Task Description: You are given a directed graph and two nodes $s$ and $t$. The given graph may contain multiple edges between the same node pair but not self loops. Each edge $e$ has its initial length $d_e$ and the cost $c_e$. You can extend an edge by paying a cost. Formally, it costs $x \\cdot c_e$ to change the length of an edge $e$ from $d_e$ to $d_e + x$. (Note that $x$ can be a non-integer. ) Edges cannot be shortened.\n\nYour task is to maximize the length of the shortest path from node $s$ to node $t$ by lengthening some edges within cost $P$. You can assume that there is at least one path from $s$ to $t$.\nTask Input: The input consists of a single test case formatted as follows. \n\n$N$ $M$ $P$ $s$ $t$\n$v_1$ $u_1$ $d_1$ $c_1$\n. . . \n$v_M$ $u_M$ $d_M$ $c_M$\n\nThe first line contains five integers $N$, $M$, $P$, $s$, and $t$: $N$ ($2 <= N <= 200$) and $M$ ($1 <= M <= 2,000$) are the number of the nodes and the edges of the given graph respectively, $P$ ($0 <= P <= 10^6$) is the cost limit that you can pay, and $s$ and $t$ ($1 <= s, t <= N, s \\ne t$) are the start and the end node of objective path respectively. Each of the following $M$ lines contains four integers $v_i$, $u_i$, $d_i$, and $c_i$, which mean there is an edge from $v_i$ to $u_i$ ($1 <= v_i, u_i <= N, v_i \\ne u_i$) with the initial length $d_i$ ($1 <= d_i <= 10$) and the cost $c_i$ ($1 <= c_i <= 10$).\nTask Output: \nTask Samples: input: 3 2 3 1 3\n1 2 2 1\n2 3 1 2\n output: 6.0000000\ninput: 3 3 2 1 3\n1 2 1 1\n2 3 1 1\n1 3 1 1\n output: 2.5000000\ninput: 3 4 5 1 3\n1 2 1 2\n2 3 1 1\n1 3 3 2\n1 3 4 1\n output: 4.2500000\n\n" }, { "title": "Optimal Tournament", "content": "In 21XX, an annual programming contest \"Japan Algorithmist Grand Prix (JAG)\" has been one of the most popular mind sport events. You, the chairperson of JAG, are preparing this year's JAG competition.\n\nJAG is conducted as a knockout tournament. This year, $N$ contestants will compete in JAG. A tournament is represented as a binary tree having $N$ leaf nodes, to which the contestants are allocated one-to-one. In each match, two contestants compete. The winner proceeds to the next round, and the loser is eliminated from the tournament. The only contestant surviving over the other contestants is the champion. The final match corresponds to the root node of the binary tree.\n\nYou know the strength of each contestant, $A_1, A_2, . . . , A_N$, which is represented as an integer. When two contestants compete, the one having greater strength always wins. If their strengths are the same, the winner is determined randomly. \n\nIn the past JAG, some audience complained that there were too many boring one-sided games. To make JAG more attractive, you want to find a good tournament configuration.\n\nLet's define the boringness of a match and a tournament. For a match in which the $i$-th contestant and the $j$-th contestant compete, we define the boringness of the match as the difference of the strength of the two contestants, $|A_i - A_j|$. And the boringness of a tournament is defined as the sum of the boringness of all matches in the tournament.\n\nYour purpose is to minimize the boringness of the tournament.\n\nYou may consider any shape of the tournament, including unbalanced ones, under the constraint that the height of the tournament must be less than or equal to $K$. The height of the tournament is defined as the maximum number of the matches on the simple path from the root node to any of the leaf nodes of the binary tree.\n\nFigure K-1 shows two possible tournaments for Sample Input 1. The height of the left one is 2, and the height of the right one is 3.\n\nWrite a program that calculates the minimum boringness of the tournament.", "constraint": "", "input": "The input consists of a single test case with the following format. \n\n$N$ $K$\n$A_1$ $A_2$ . . . $A_N$\n\nThe first line of the input contains two integers $N$ ($2 <= N <= 1,000$) and $K$ ($1 <= K <= 50$). You can assume that $N <= 2^K$. The second line contains $N$ integers $A_1, A_2, . . . , A_N$. $A_i$ ($1 <= A_i <= 100,000$) represents the strength of the $i$-th contestant.", "output": "Output the minimum boringness value achieved by the optimal tournament configuration.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 3\n1 3 4 7\n output: 6", "input: 5 3\n1 3 4 7 9\n output: 10", "input: 18 7\n67 64 52 18 39 92 84 66 19 64 1 66 35 34 45 2 79 34\n output: 114"], "Pid": "p01838", "ProblemText": "Task Description: In 21XX, an annual programming contest \"Japan Algorithmist Grand Prix (JAG)\" has been one of the most popular mind sport events. You, the chairperson of JAG, are preparing this year's JAG competition.\n\nJAG is conducted as a knockout tournament. This year, $N$ contestants will compete in JAG. A tournament is represented as a binary tree having $N$ leaf nodes, to which the contestants are allocated one-to-one. In each match, two contestants compete. The winner proceeds to the next round, and the loser is eliminated from the tournament. The only contestant surviving over the other contestants is the champion. The final match corresponds to the root node of the binary tree.\n\nYou know the strength of each contestant, $A_1, A_2, . . . , A_N$, which is represented as an integer. When two contestants compete, the one having greater strength always wins. If their strengths are the same, the winner is determined randomly. \n\nIn the past JAG, some audience complained that there were too many boring one-sided games. To make JAG more attractive, you want to find a good tournament configuration.\n\nLet's define the boringness of a match and a tournament. For a match in which the $i$-th contestant and the $j$-th contestant compete, we define the boringness of the match as the difference of the strength of the two contestants, $|A_i - A_j|$. And the boringness of a tournament is defined as the sum of the boringness of all matches in the tournament.\n\nYour purpose is to minimize the boringness of the tournament.\n\nYou may consider any shape of the tournament, including unbalanced ones, under the constraint that the height of the tournament must be less than or equal to $K$. The height of the tournament is defined as the maximum number of the matches on the simple path from the root node to any of the leaf nodes of the binary tree.\n\nFigure K-1 shows two possible tournaments for Sample Input 1. The height of the left one is 2, and the height of the right one is 3.\n\nWrite a program that calculates the minimum boringness of the tournament.\nTask Input: The input consists of a single test case with the following format. \n\n$N$ $K$\n$A_1$ $A_2$ . . . $A_N$\n\nThe first line of the input contains two integers $N$ ($2 <= N <= 1,000$) and $K$ ($1 <= K <= 50$). You can assume that $N <= 2^K$. The second line contains $N$ integers $A_1, A_2, . . . , A_N$. $A_i$ ($1 <= A_i <= 100,000$) represents the strength of the $i$-th contestant.\nTask Output: Output the minimum boringness value achieved by the optimal tournament configuration.\nTask Samples: input: 4 3\n1 3 4 7\n output: 6\ninput: 5 3\n1 3 4 7 9\n output: 10\ninput: 18 7\n67 64 52 18 39 92 84 66 19 64 1 66 35 34 45 2 79 34\n output: 114\n\n" }, { "title": "Best Matched Pair", "content": "You are working for a worldwide game company as an engineer in Tokyo. This company holds an annual event for all the staff members of the company every summer. This year's event will take place in Tokyo. You will participate in the event on the side of the organizing staff. And you have been assigned to plan a recreation game which all the participants will play at the same time.\n\nAfter you had thought out various ideas, you designed the rules of the game as below.\n\n Each player is given a positive integer before the start of the game.\n\n Each player attempts to make a pair with another player in this game, and formed pairs compete with each other by comparing the products of two integers.\n\n Each player can change the partner any number of times before the end of the game, but cannot have two or more partners at the same time.\n\n At the end of the game, the pair with the largest product wins the game.\nIn addition, regarding the given integers, the next condition must be satisfied for making a pair.\n\n The sequence of digits obtained by considering the product of the two integers of a pair as a string must be increasing and consecutive from left to right. For example, 2,23, and 56789 meet this condition, but 21,334,135 or 89012 do not.\nSetting the rules as above, you noticed that multiple pairs may be the winners who have the same product depending on the situation. However, you can find out what is the largest product of two integers when a set of integers is given.\n\nYour task is, given a set of distinct integers which will be assigned to the players, to compute the largest possible product of two integers, satisfying the rules of the game mentioned above.", "constraint": "", "input": "The input consists of a single test case formatted as follows. \n\n$N$\n$a_1$ $a_2$ . . . $a_N$\n\nThe first line contains a positive integer $N$ which indicates the number of the players of the game. $N$ is an integer between 1 and 1,000. The second line has $N$ positive integers that indicate the numbers given to the players. For $i = 1,2, . . . , N - 1$, there is a space between $a_i$ and $a_{i+1}$. $a_i$ is between 1 and 10,000 for $i = 1,2, . . . , N$, and if $i \\ne j$, then $a_i \\ne a_j$.", "output": "Print the largest possible product of the two integers satisfying the conditions for making a pair. If any two players cannot make a pair, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2\n output: 2", "input: 3\n3 22 115\n output: 345", "input: 2\n1 11\n output: -1", "input: 2\n5 27\n output: -1", "input: 2\n17 53\n output: -1", "input: 10\n53 43 36 96 99 2 27 86 93 23\n output: 3456"], "Pid": "p01880", "ProblemText": "Task Description: You are working for a worldwide game company as an engineer in Tokyo. This company holds an annual event for all the staff members of the company every summer. This year's event will take place in Tokyo. You will participate in the event on the side of the organizing staff. And you have been assigned to plan a recreation game which all the participants will play at the same time.\n\nAfter you had thought out various ideas, you designed the rules of the game as below.\n\n Each player is given a positive integer before the start of the game.\n\n Each player attempts to make a pair with another player in this game, and formed pairs compete with each other by comparing the products of two integers.\n\n Each player can change the partner any number of times before the end of the game, but cannot have two or more partners at the same time.\n\n At the end of the game, the pair with the largest product wins the game.\nIn addition, regarding the given integers, the next condition must be satisfied for making a pair.\n\n The sequence of digits obtained by considering the product of the two integers of a pair as a string must be increasing and consecutive from left to right. For example, 2,23, and 56789 meet this condition, but 21,334,135 or 89012 do not.\nSetting the rules as above, you noticed that multiple pairs may be the winners who have the same product depending on the situation. However, you can find out what is the largest product of two integers when a set of integers is given.\n\nYour task is, given a set of distinct integers which will be assigned to the players, to compute the largest possible product of two integers, satisfying the rules of the game mentioned above.\nTask Input: The input consists of a single test case formatted as follows. \n\n$N$\n$a_1$ $a_2$ . . . $a_N$\n\nThe first line contains a positive integer $N$ which indicates the number of the players of the game. $N$ is an integer between 1 and 1,000. The second line has $N$ positive integers that indicate the numbers given to the players. For $i = 1,2, . . . , N - 1$, there is a space between $a_i$ and $a_{i+1}$. $a_i$ is between 1 and 10,000 for $i = 1,2, . . . , N$, and if $i \\ne j$, then $a_i \\ne a_j$.\nTask Output: Print the largest possible product of the two integers satisfying the conditions for making a pair. If any two players cannot make a pair, print -1.\nTask Samples: input: 2\n1 2\n output: 2\ninput: 3\n3 22 115\n output: 345\ninput: 2\n1 11\n output: -1\ninput: 2\n5 27\n output: -1\ninput: 2\n17 53\n output: -1\ninput: 10\n53 43 36 96 99 2 27 86 93 23\n output: 3456\n\n" }, { "title": "Help the Princess!", "content": "The people of a certain kingdom make a revolution against the bad government of the princess. The revolutionary army invaded the royal palace in which the princess lives. The soldiers of the army are exploring the palace to catch the princess. Your job is writing a program to decide that the princess can escape from the royal palace or not.\n\n For simplicity, the ground of the palace is a rectangle divided into a grid. There are two kinds of cells in the grid: one is a cell that soldiers and the princess can enter, the other is a cell that soldiers or the princess cannot enter. We call the former an empty cell, the latter a wall. The princess and soldiers are in different empty cells at the beginning. There is only one escape hatch in the grid. If the princess arrives the hatch, then the princess can escape from the palace. There are more than or equal to zero soldiers in the palace.\n\nThe princess and all soldiers take an action at the same time in each unit time. In other words, the princess and soldiers must decide their action without knowing a next action of the other people. In each unit time, the princess and soldiers can move to a horizontally or vertically adjacent cell, or stay at the current cell. Furthermore the princess and soldiers cannot move out of the ground of the palace. If the princess and one or more soldiers exist in the same cell after their move, then the princess will be caught. It is guaranteed that the princess can reach the escape hatch via only empty cells if all soldiers are removed from the palace.\n\nIf there is a route for the princess such that soldiers cannot catch the princess even if soldiers make any moves, then the princess can escape the soldiers. Note that if the princess and a soldier arrive the escape hatch at the same time, the princess will be caught. Can the princess escape from the palace?", "constraint": "", "input": "Each dataset is formatted as follows. \n\n$H$ $W$\n$map_1$\n$map_2$\n. . . \n$map_H$\n\nThe first line of a dataset contains two positive integers $H$ and $W$ delimited by a space, where $H$ is the height of the grid and $W$ is the width of the grid ($2 <= H, W <= 200$).\n\nThe $i$-th line of the subsequent $H$ lines gives a string $map_i$, which represents situation in the ground of palace.\n\n$map_i$ is a string of length $W$, and the $j$-th character of $map_i$ represents the state of the cell of the $i$-th row and the $j$-th column.\n\n'@', '\\$', '%', '. ', and '#' represent the princess, a soldier, the escape hatch, an empty cell, and a wall, respectively. It is guaranteed that there exists only one '@', only one '%', and more than or equal to zero '\\$' in the grid.", "output": "Output a line containing a word \"Yes\", if the princess can escape from the palace. Otherwise, output \"No\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 4\n%.@\\$\n..\\$\\$\n output: Yes", "input: 3 4\n.%..\n.##.\n.@\\$.\n output: Yes", "input: 2 3\n%\\$@\n###\n output: No", "input: 2 3\n@#\\$\n.%.\n output: No", "input: 2 2\n@%\n..\n output: Yes"], "Pid": "p01881", "ProblemText": "Task Description: The people of a certain kingdom make a revolution against the bad government of the princess. The revolutionary army invaded the royal palace in which the princess lives. The soldiers of the army are exploring the palace to catch the princess. Your job is writing a program to decide that the princess can escape from the royal palace or not.\n\n For simplicity, the ground of the palace is a rectangle divided into a grid. There are two kinds of cells in the grid: one is a cell that soldiers and the princess can enter, the other is a cell that soldiers or the princess cannot enter. We call the former an empty cell, the latter a wall. The princess and soldiers are in different empty cells at the beginning. There is only one escape hatch in the grid. If the princess arrives the hatch, then the princess can escape from the palace. There are more than or equal to zero soldiers in the palace.\n\nThe princess and all soldiers take an action at the same time in each unit time. In other words, the princess and soldiers must decide their action without knowing a next action of the other people. In each unit time, the princess and soldiers can move to a horizontally or vertically adjacent cell, or stay at the current cell. Furthermore the princess and soldiers cannot move out of the ground of the palace. If the princess and one or more soldiers exist in the same cell after their move, then the princess will be caught. It is guaranteed that the princess can reach the escape hatch via only empty cells if all soldiers are removed from the palace.\n\nIf there is a route for the princess such that soldiers cannot catch the princess even if soldiers make any moves, then the princess can escape the soldiers. Note that if the princess and a soldier arrive the escape hatch at the same time, the princess will be caught. Can the princess escape from the palace?\nTask Input: Each dataset is formatted as follows. \n\n$H$ $W$\n$map_1$\n$map_2$\n. . . \n$map_H$\n\nThe first line of a dataset contains two positive integers $H$ and $W$ delimited by a space, where $H$ is the height of the grid and $W$ is the width of the grid ($2 <= H, W <= 200$).\n\nThe $i$-th line of the subsequent $H$ lines gives a string $map_i$, which represents situation in the ground of palace.\n\n$map_i$ is a string of length $W$, and the $j$-th character of $map_i$ represents the state of the cell of the $i$-th row and the $j$-th column.\n\n'@', '\\$', '%', '. ', and '#' represent the princess, a soldier, the escape hatch, an empty cell, and a wall, respectively. It is guaranteed that there exists only one '@', only one '%', and more than or equal to zero '\\$' in the grid.\nTask Output: Output a line containing a word \"Yes\", if the princess can escape from the palace. Otherwise, output \"No\".\nTask Samples: input: 2 4\n%.@\\$\n..\\$\\$\n output: Yes\ninput: 3 4\n.%..\n.##.\n.@\\$.\n output: Yes\ninput: 2 3\n%\\$@\n###\n output: No\ninput: 2 3\n@#\\$\n.%.\n output: No\ninput: 2 2\n@%\n..\n output: Yes\n\n" }, { "title": "We don't wanna work!", "content": "ACM is an organization of programming contests. The purpose of ACM does not matter to you. The only important thing is that workstyles of ACM members are polarized: each member is either a workhorse or an idle fellow.\n\nEach member of ACM has a motivation level. The members are ranked by their motivation levels: a member who has a higher motivation level is ranked higher. When several members have the same value of motivation levels, the member who joined ACM later have a higher rank. The top 20% highest ranked members work hard, and the other (80%) members never (! ) work. Note that if 20% of the number of ACM members is not an integer, its fraction part is rounded down.\n\nYou, a manager of ACM, tried to know whether each member is a workhorse or an idle fellow to manage ACM. Finally, you completed to evaluate motivation levels of all the current members. However, your task is not accomplished yet because the members of ACM are dynamically changed from day to day due to incoming and outgoing of members. So, you want to record transitions of members from workhorses to idle fellows, and vice versa.\n\nYou are given a list of the current members of ACM and their motivation levels in chronological order of their incoming date to ACM. You are also given a list of incoming/outgoing of members in chronological order.\n\nYour task is to write a program that computes changes of workstyles of ACM members.", "constraint": "", "input": "The first line of the input contains a single integer $N$ ($1 <= N <= 50,000$) that means the number of initial members of ACM. The ($i$ + 1)-th line of the input contains a string $s_i$ and an integer $a_i$ ($0 <= a_i <= 10^5$), separated by a single space. $s_i$ means the name of the $i$-th initial member and $a_i$ means the motivation level of the $i$-th initial member. Each character of $s_i$ is an English letter, and $1 <= |s_i| <= 20$. Note that those $N$ lines are ordered in chronological order of incoming dates to ACM of each member.\n\nThe ($N$ + 2)-th line of the input contains a single integer $M$ ($1 <= M <= 20,000$) that means the number of changes of ACM members. The ($N$ + 2 + $j$)-th line of the input contains information of the $j$-th incoming/outgoing member. When the $j$-th information represents an incoming of a member, the information is formatted as \"$+ t_j b_j$\", where $t_j$ is the name of the incoming member and $b_j$ ($0 <= b_j <= 10^5$) is his motivation level. On the other hand, when the $j$-th information represents an outgoing of a member, the information is formatted as \"$- t_j$\", where $t_j$ means the name of the outgoing member. Each character of $t_j$ is an English letter, and $1 <= |t_j| <= 20$. Note that uppercase letters and lowercase letters are distinguished. Note that those $M$ lines are ordered in chronological order of dates when each event happens.\n\nNo two incoming/outgoing events never happen at the same time. No two members have the same name, but members who left ACM once may join ACM again.", "output": "Print the log, a sequence of changes in chronological order. When each of the following four changes happens, you should print a message corresponding to the type of the change as follows:\n\n Member $name$ begins to work hard : \"$name$ is working hard now. \"\n\n Member $name$ begins to not work : \"$name$ is not working now. \"\nFor each incoming/outgoing, changes happen in the following order:\n\n Some member joins/leaves.\n\n When a member joins, the member is added to either workhorses or idle fellows.\n\n Some member may change from a workhorse to an idle fellow and vice versa. Note that there are no cases such that two or more members change their workstyles at the same time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nDurett 7\nGayles 3\nFacenda 6\nDaughtery 0\n1\n+ Mccourtney 2\n output: Mccourtney is not working now.\nDurett is working hard now.\nInitially, no member works because $4 * 20$% $< 1$. When one member joins ACM, Durrett begins to work hard.", "input: 3\nBurdon 2\nOrlin 8\nTrumper 5\n1\n+ Lukaszewicz 7\n output: Lukaszewicz is not working now.\n\nNo member works.", "input: 5\nAndy 3\nBob 4\nCindy 10\nDavid 1\nEmile 1\n3\n+ Fred 10\n- David\n+ Gustav 3\n output: Fred is working hard now.\nCindy is not working now.\nGustav is not working now.", "input: 7\nLaplant 5\nVarnes 2\nWarchal 7\nDegregorio 3\nChalender 9\nRascon 5\nBurdon 0\n7\n+ Mccarroll 1\n- Chalender\n+ Orlin 2\n+ Chalender 1\n+ Marnett 10\n- Chalender\n+ Chalender 0\n output: Mccarroll is not working now.\nWarchal is working hard now.\nOrlin is not working now.\nChalender is not working now.\nMarnett is working hard now.\nWarchal is not working now.\nChalender is not working now.\nWarchal is working hard now.\nSome member may repeat incoming and outgoing.", "input: 4\nAoba 100\nYun 70\nHifumi 120\nHajime 50\n2\n- Yun\n- Aoba\n output: (blank)"], "Pid": "p01882", "ProblemText": "Task Description: ACM is an organization of programming contests. The purpose of ACM does not matter to you. The only important thing is that workstyles of ACM members are polarized: each member is either a workhorse or an idle fellow.\n\nEach member of ACM has a motivation level. The members are ranked by their motivation levels: a member who has a higher motivation level is ranked higher. When several members have the same value of motivation levels, the member who joined ACM later have a higher rank. The top 20% highest ranked members work hard, and the other (80%) members never (! ) work. Note that if 20% of the number of ACM members is not an integer, its fraction part is rounded down.\n\nYou, a manager of ACM, tried to know whether each member is a workhorse or an idle fellow to manage ACM. Finally, you completed to evaluate motivation levels of all the current members. However, your task is not accomplished yet because the members of ACM are dynamically changed from day to day due to incoming and outgoing of members. So, you want to record transitions of members from workhorses to idle fellows, and vice versa.\n\nYou are given a list of the current members of ACM and their motivation levels in chronological order of their incoming date to ACM. You are also given a list of incoming/outgoing of members in chronological order.\n\nYour task is to write a program that computes changes of workstyles of ACM members.\nTask Input: The first line of the input contains a single integer $N$ ($1 <= N <= 50,000$) that means the number of initial members of ACM. The ($i$ + 1)-th line of the input contains a string $s_i$ and an integer $a_i$ ($0 <= a_i <= 10^5$), separated by a single space. $s_i$ means the name of the $i$-th initial member and $a_i$ means the motivation level of the $i$-th initial member. Each character of $s_i$ is an English letter, and $1 <= |s_i| <= 20$. Note that those $N$ lines are ordered in chronological order of incoming dates to ACM of each member.\n\nThe ($N$ + 2)-th line of the input contains a single integer $M$ ($1 <= M <= 20,000$) that means the number of changes of ACM members. The ($N$ + 2 + $j$)-th line of the input contains information of the $j$-th incoming/outgoing member. When the $j$-th information represents an incoming of a member, the information is formatted as \"$+ t_j b_j$\", where $t_j$ is the name of the incoming member and $b_j$ ($0 <= b_j <= 10^5$) is his motivation level. On the other hand, when the $j$-th information represents an outgoing of a member, the information is formatted as \"$- t_j$\", where $t_j$ means the name of the outgoing member. Each character of $t_j$ is an English letter, and $1 <= |t_j| <= 20$. Note that uppercase letters and lowercase letters are distinguished. Note that those $M$ lines are ordered in chronological order of dates when each event happens.\n\nNo two incoming/outgoing events never happen at the same time. No two members have the same name, but members who left ACM once may join ACM again.\nTask Output: Print the log, a sequence of changes in chronological order. When each of the following four changes happens, you should print a message corresponding to the type of the change as follows:\n\n Member $name$ begins to work hard : \"$name$ is working hard now. \"\n\n Member $name$ begins to not work : \"$name$ is not working now. \"\nFor each incoming/outgoing, changes happen in the following order:\n\n Some member joins/leaves.\n\n When a member joins, the member is added to either workhorses or idle fellows.\n\n Some member may change from a workhorse to an idle fellow and vice versa. Note that there are no cases such that two or more members change their workstyles at the same time.\nTask Samples: input: 4\nDurett 7\nGayles 3\nFacenda 6\nDaughtery 0\n1\n+ Mccourtney 2\n output: Mccourtney is not working now.\nDurett is working hard now.\nInitially, no member works because $4 * 20$% $< 1$. When one member joins ACM, Durrett begins to work hard.\ninput: 3\nBurdon 2\nOrlin 8\nTrumper 5\n1\n+ Lukaszewicz 7\n output: Lukaszewicz is not working now.\n\nNo member works.\ninput: 5\nAndy 3\nBob 4\nCindy 10\nDavid 1\nEmile 1\n3\n+ Fred 10\n- David\n+ Gustav 3\n output: Fred is working hard now.\nCindy is not working now.\nGustav is not working now.\ninput: 7\nLaplant 5\nVarnes 2\nWarchal 7\nDegregorio 3\nChalender 9\nRascon 5\nBurdon 0\n7\n+ Mccarroll 1\n- Chalender\n+ Orlin 2\n+ Chalender 1\n+ Marnett 10\n- Chalender\n+ Chalender 0\n output: Mccarroll is not working now.\nWarchal is working hard now.\nOrlin is not working now.\nChalender is not working now.\nMarnett is working hard now.\nWarchal is not working now.\nChalender is not working now.\nWarchal is working hard now.\nSome member may repeat incoming and outgoing.\ninput: 4\nAoba 100\nYun 70\nHifumi 120\nHajime 50\n2\n- Yun\n- Aoba\n output: (blank)\n\n" }, { "title": "Parentheses", "content": "Dave loves strings consisting only of '(' and ')'. Especially, he is interested in balanced strings. Any balanced strings can be constructed using the following rules:\n\n A string \"()\" is balanced.\n\n Concatenation of two balanced strings are balanced.\n\n If $T$ is a balanced string, concatenation of '(', $T$, and ')' in this order is balanced. For example, \"()()\" and \"(()())\" are balanced strings. \")(\" and \")()(()\" are not balanced strings.\nDave has a string consisting only of '(' and ')'. It satis\fes the followings:\n\n You can make it balanced by swapping adjacent characters exactly $A$ times. \n\n For any non-negative integer $B$ ($B < A$), you cannot make it balanced by $B$ swaps of adjacent characters.\n\n It is the shortest of all strings satisfying the above conditions.\nYour task is to compute Dave's string. If there are multiple candidates, output the minimum in lexicographic order. As is the case with ASCII, '(' is less than ')'.", "constraint": "", "input": "The input consists of a single test case, which contains an integer $A$ ($1 <= A <= 10^9$).", "output": "Output Dave's string in one line. If there are multiple candidates, output the minimum in lexicographic order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n output: )(\nThere are infinitely many strings which can be balanced by only one swap. Dave's string is the shortest of them.", "input: 4\n output: )())((\nString \"))(()(\" can be balanced by 4 swaps, but the output should be \")())((\" because it is the minimum in lexicographic order."], "Pid": "p01883", "ProblemText": "Task Description: Dave loves strings consisting only of '(' and ')'. Especially, he is interested in balanced strings. Any balanced strings can be constructed using the following rules:\n\n A string \"()\" is balanced.\n\n Concatenation of two balanced strings are balanced.\n\n If $T$ is a balanced string, concatenation of '(', $T$, and ')' in this order is balanced. For example, \"()()\" and \"(()())\" are balanced strings. \")(\" and \")()(()\" are not balanced strings.\nDave has a string consisting only of '(' and ')'. It satis\fes the followings:\n\n You can make it balanced by swapping adjacent characters exactly $A$ times. \n\n For any non-negative integer $B$ ($B < A$), you cannot make it balanced by $B$ swaps of adjacent characters.\n\n It is the shortest of all strings satisfying the above conditions.\nYour task is to compute Dave's string. If there are multiple candidates, output the minimum in lexicographic order. As is the case with ASCII, '(' is less than ')'.\nTask Input: The input consists of a single test case, which contains an integer $A$ ($1 <= A <= 10^9$).\nTask Output: Output Dave's string in one line. If there are multiple candidates, output the minimum in lexicographic order.\nTask Samples: input: 1\n output: )(\nThere are infinitely many strings which can be balanced by only one swap. Dave's string is the shortest of them.\ninput: 4\n output: )())((\nString \"))(()(\" can be balanced by 4 swaps, but the output should be \")())((\" because it is the minimum in lexicographic order.\n\n" }, { "title": "Similarity of Subtrees", "content": "Define the depth of a node in a rooted tree by applying the following rules recursively:\n\n The depth of a root node is 0.\n\n The depths of child nodes whose parents are with depth $d$ are $d + 1$.\nLet $S(T, d)$ be the number of nodes of $T$ with depth $d$. Two rooted trees $T$ and $T'$ are similar if and only if $S(T, d)$ equals $S(T', d)$ for all non-negative integer $d$.\n\nYou are given a rooted tree $T$ with $N$ nodes. The nodes of $T$ are numbered from 1 to $N$. Node 1 is the root node of $T$. Let $T_i$ be the rooted subtree of $T$ whose root is node $i$. Your task is to write a program which calculates the number of pairs $(i, j)$ such that $T_i$ and $T_j$ are similar and $i < j$.", "constraint": "", "input": "The input consists of a single test case. \n\n$N$\n$a_1$ $b_1$\n$a_2$ $b_2$\n. . . \n$a_{N-1}$ $b_{N-1}$\n\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which is the number of nodes in a tree. The following $N -1$ lines give information of branches: the $i$-th line of them contains $a_i$ and $b_i$, which indicates that a node $a_i$ is a parent of a node $b_i$. ($1 <= a_i, b_i <= N, a_i \\ne b_i$) The root node is numbered by 1. It is guaranteed that a given graph is a rooted tree, i. e. there is exactly one parent for each node except the node 1, and the graph is connected.", "output": "Print the number of the pairs $(x, y)$ of the nodes such that the subtree with the root $x$ and the subtree with the root $y$ are similar and $x < y$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n1 3\n1 4\n1 5\n output: 6", "input: 6\n1 2\n2 3\n3 4\n1 5\n5 6\n output: 2", "input: 13\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7\n4 8\n4 9\n6 10\n7 11\n8 12\n11 13\n output: 14"], "Pid": "p01884", "ProblemText": "Task Description: Define the depth of a node in a rooted tree by applying the following rules recursively:\n\n The depth of a root node is 0.\n\n The depths of child nodes whose parents are with depth $d$ are $d + 1$.\nLet $S(T, d)$ be the number of nodes of $T$ with depth $d$. Two rooted trees $T$ and $T'$ are similar if and only if $S(T, d)$ equals $S(T', d)$ for all non-negative integer $d$.\n\nYou are given a rooted tree $T$ with $N$ nodes. The nodes of $T$ are numbered from 1 to $N$. Node 1 is the root node of $T$. Let $T_i$ be the rooted subtree of $T$ whose root is node $i$. Your task is to write a program which calculates the number of pairs $(i, j)$ such that $T_i$ and $T_j$ are similar and $i < j$.\nTask Input: The input consists of a single test case. \n\n$N$\n$a_1$ $b_1$\n$a_2$ $b_2$\n. . . \n$a_{N-1}$ $b_{N-1}$\n\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which is the number of nodes in a tree. The following $N -1$ lines give information of branches: the $i$-th line of them contains $a_i$ and $b_i$, which indicates that a node $a_i$ is a parent of a node $b_i$. ($1 <= a_i, b_i <= N, a_i \\ne b_i$) The root node is numbered by 1. It is guaranteed that a given graph is a rooted tree, i. e. there is exactly one parent for each node except the node 1, and the graph is connected.\nTask Output: Print the number of the pairs $(x, y)$ of the nodes such that the subtree with the root $x$ and the subtree with the root $y$ are similar and $x < y$.\nTask Samples: input: 5\n1 2\n1 3\n1 4\n1 5\n output: 6\ninput: 6\n1 2\n2 3\n3 4\n1 5\n5 6\n output: 2\ninput: 13\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7\n4 8\n4 9\n6 10\n7 11\n8 12\n11 13\n output: 14\n\n" }, { "title": "Escape from the Hell", "content": "One day, Buddha looked into the hell and found an office worker. He did evil, such as enforcing hard work on his subordinates. However, he made only one good in his life. He refused an unreasonable request from his customer to save the lives of his subordinates. Buddha thought that, as the reward of the good, the office worker should have had a chance to escape from the hell. Buddha took a spider silk and put down to the hell.\n\nThe office worker climbed up with the spider silk, however the length of the way $L$ meters was too long to escape one day. He had $N$ energy drinks and drunk one of them each day. The day he drunk the i-th energy drink he could climb $A_i$ meters in the daytime and after that slided down $B_i$ meters in the night. If he could reach at the height greater than or equal to the $L$ meters in the daytime, he could escape without sliding down. After the $N$ days the silk would be cut.\n\nHe realized that other sinners climbed the silk in the night. They climbed $C_i$ meters in the $i$-th night without sliding down in the daytime. If they catched up with the office worker, they should have conflicted and the silk would be cut. Therefore he needed to escape before other sinners catched him. Your task is to write a program computing the best order of energy drink and output the earliest day which he could escape. If he could not escape, your program should output -1.", "constraint": "", "input": "The input consists of a single test case. \n\n$N$ $L$\n$A_1$ $B_1$\n$A_2$ $B_2$\n. . . \n$A_N$ $B_N$\n$C_1$\n$C_2$\n. . . \n$C_N$\n\nThe first line contains two integers $N$ ($1 <= N <= 10^5$) and $L$ ($1 <= L <= 10^9$), which mean the number of energy drinks and the length of the spider silk respectively. The following $N$ lines show the information of the drinks: the $i$-th of them indicates the $i$-th energy drink, he climbed up $A_i$ ($1 <= A_i <= 10^9$) meters and slided down $B_i$ ($1 <= B_i <= 10^9$) meters. Next $N$ lines show how far other sinners climbed: the $i$-th of them contains an integer $C_i$ ($1 <= C_i <= 10^9$), which means they climbed up $C_i$ meters in the $i$-th day.", "output": "Print the earliest day which he could escape. If he could not escape, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 9\n6 3\n5 2\n3 1\n2\n2\n2\n output: 2", "input: 5 20\n3 2\n4 2\n6 3\n8 4\n10 5\n4\n2\n3\n4\n5\n output: -1", "input: 5 20\n6 5\n7 3\n10 3\n10 14\n4 7\n2\n5\n3\n9\n2\n output: 3", "input: 4 12\n8 4\n6 4\n2 1\n2 1\n1\n1\n4\n4\n output: -1"], "Pid": "p01885", "ProblemText": "Task Description: One day, Buddha looked into the hell and found an office worker. He did evil, such as enforcing hard work on his subordinates. However, he made only one good in his life. He refused an unreasonable request from his customer to save the lives of his subordinates. Buddha thought that, as the reward of the good, the office worker should have had a chance to escape from the hell. Buddha took a spider silk and put down to the hell.\n\nThe office worker climbed up with the spider silk, however the length of the way $L$ meters was too long to escape one day. He had $N$ energy drinks and drunk one of them each day. The day he drunk the i-th energy drink he could climb $A_i$ meters in the daytime and after that slided down $B_i$ meters in the night. If he could reach at the height greater than or equal to the $L$ meters in the daytime, he could escape without sliding down. After the $N$ days the silk would be cut.\n\nHe realized that other sinners climbed the silk in the night. They climbed $C_i$ meters in the $i$-th night without sliding down in the daytime. If they catched up with the office worker, they should have conflicted and the silk would be cut. Therefore he needed to escape before other sinners catched him. Your task is to write a program computing the best order of energy drink and output the earliest day which he could escape. If he could not escape, your program should output -1.\nTask Input: The input consists of a single test case. \n\n$N$ $L$\n$A_1$ $B_1$\n$A_2$ $B_2$\n. . . \n$A_N$ $B_N$\n$C_1$\n$C_2$\n. . . \n$C_N$\n\nThe first line contains two integers $N$ ($1 <= N <= 10^5$) and $L$ ($1 <= L <= 10^9$), which mean the number of energy drinks and the length of the spider silk respectively. The following $N$ lines show the information of the drinks: the $i$-th of them indicates the $i$-th energy drink, he climbed up $A_i$ ($1 <= A_i <= 10^9$) meters and slided down $B_i$ ($1 <= B_i <= 10^9$) meters. Next $N$ lines show how far other sinners climbed: the $i$-th of them contains an integer $C_i$ ($1 <= C_i <= 10^9$), which means they climbed up $C_i$ meters in the $i$-th day.\nTask Output: Print the earliest day which he could escape. If he could not escape, print -1 instead.\nTask Samples: input: 3 9\n6 3\n5 2\n3 1\n2\n2\n2\n output: 2\ninput: 5 20\n3 2\n4 2\n6 3\n8 4\n10 5\n4\n2\n3\n4\n5\n output: -1\ninput: 5 20\n6 5\n7 3\n10 3\n10 14\n4 7\n2\n5\n3\n9\n2\n output: 3\ninput: 4 12\n8 4\n6 4\n2 1\n2 1\n1\n1\n4\n4\n output: -1\n\n" }, { "title": "Share the Ruins Preservation", "content": "Two organizations International Community for Preservation of Constructions (ICPC) and Japanese Archaeologist Group (JAG) engage in ruins preservation. Recently, many ruins were found in a certain zone. The two organizations decided to share the preservation of the ruins by assigning some of the ruins to ICPC and the other ruins to JAG.\n\nNow, ICPC and JAG make a rule for assignment as follows:\n\n Draw a vertical straight line from the north to the south, avoiding to intersect ruins.\n\n Ruins located to the west of the line are preserved by ICPC. On the other hand, ruins located to the east of the line are preserved by JAG. (It is possible that no ruins are located to the east/west of the line; in this case, ICPC/JAG will preserve no ruins. )\nA problem is where to draw a straight line. For each organization, the way to preserve its assigned ruins is to make exactly one fence such that all the assigned ruins are in the region surrounded by the fence. Furthermore, they should minimize the length of such a fence for their budget. If the surrounded areas are vast, expensive costs will be needed to maintain the inside of areas. Therefore, they want to minimize the total preservation cost, i. e. the sum of the areas surrounded by two fences. Your task is to write a program computing the minimum sum of the areas surrounded by two fences, yielded by drawing an appropriate straight line.", "constraint": "", "input": "The input consists of a single test case. \n\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . . \n$x_N$ $y_N$\n\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which is the number of founded ruins. The following $N$ lines represent the location of the ruins. The $i$-th line of them consists of two integers $x_i$ and $y_i$, which indicate the location of the $i$-th ruin is $x_i$ east and $y_i$ north from a certain location in the zone. You can assume the following things for the ruins:\n\n$-10^9 <= x_i, y_i <= 10^9$\n\nYou can ignore the sizes of ruins. That is, you can assume ruins are points.\n\nNo pair of ruins has the same location.", "output": "Print the minimum total preservation cost yielded by drawing an appropriate straight line. You should round off the cost to the nearest integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n-10 0\n-10 5\n-5 5\n-5 0\n10 0\n10 -5\n5 -5\n5 0\n output: 50", "input: 5\n0 0\n0 1\n0 2\n1 0\n1 1\n output: 0", "input: 6\n1 5\n1 6\n0 5\n0 -5\n-1 -5\n-1 -6\n output: 6", "input: 10\n2 5\n4 6\n9 5\n8 8\n1 3\n6 4\n5 9\n7 3\n7 7\n3 9\n output: 17"], "Pid": "p01886", "ProblemText": "Task Description: Two organizations International Community for Preservation of Constructions (ICPC) and Japanese Archaeologist Group (JAG) engage in ruins preservation. Recently, many ruins were found in a certain zone. The two organizations decided to share the preservation of the ruins by assigning some of the ruins to ICPC and the other ruins to JAG.\n\nNow, ICPC and JAG make a rule for assignment as follows:\n\n Draw a vertical straight line from the north to the south, avoiding to intersect ruins.\n\n Ruins located to the west of the line are preserved by ICPC. On the other hand, ruins located to the east of the line are preserved by JAG. (It is possible that no ruins are located to the east/west of the line; in this case, ICPC/JAG will preserve no ruins. )\nA problem is where to draw a straight line. For each organization, the way to preserve its assigned ruins is to make exactly one fence such that all the assigned ruins are in the region surrounded by the fence. Furthermore, they should minimize the length of such a fence for their budget. If the surrounded areas are vast, expensive costs will be needed to maintain the inside of areas. Therefore, they want to minimize the total preservation cost, i. e. the sum of the areas surrounded by two fences. Your task is to write a program computing the minimum sum of the areas surrounded by two fences, yielded by drawing an appropriate straight line.\nTask Input: The input consists of a single test case. \n\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . . \n$x_N$ $y_N$\n\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which is the number of founded ruins. The following $N$ lines represent the location of the ruins. The $i$-th line of them consists of two integers $x_i$ and $y_i$, which indicate the location of the $i$-th ruin is $x_i$ east and $y_i$ north from a certain location in the zone. You can assume the following things for the ruins:\n\n$-10^9 <= x_i, y_i <= 10^9$\n\nYou can ignore the sizes of ruins. That is, you can assume ruins are points.\n\nNo pair of ruins has the same location.\nTask Output: Print the minimum total preservation cost yielded by drawing an appropriate straight line. You should round off the cost to the nearest integer.\nTask Samples: input: 8\n-10 0\n-10 5\n-5 5\n-5 0\n10 0\n10 -5\n5 -5\n5 0\n output: 50\ninput: 5\n0 0\n0 1\n0 2\n1 0\n1 1\n output: 0\ninput: 6\n1 5\n1 6\n0 5\n0 -5\n-1 -5\n-1 -6\n output: 6\ninput: 10\n2 5\n4 6\n9 5\n8 8\n1 3\n6 4\n5 9\n7 3\n7 7\n3 9\n output: 17\n\n" }, { "title": "Pipe Fitter and the Fierce Dogs", "content": "You, a proud pipe fitter of ICPC (International Community for Pipe Connection), undertake a new task. The area in which you will take charge of piping work is a rectangular shape with $W$ blocks from west to east and $H$ blocks from north to south. We refer to the block at the $i$-th from west and the $j$-th from north as $(i, j)$. The westernmost and northernmost block is $(1,1)$, and the easternmost and southernmost block is $(W, H)$. To make the area good scenery, the block $(i, j)$ has exactly one house if and only if both of $i$ and $j$ are odd numbers.\nYour task is to construct a water pipe network in the area such that every house in the area is supplied water through the network. A water pipe network consists of pipelines. A pipeline is made by connecting one or more pipes, and a pipeline with l pipes is constructed as follows:\n choose a first house, and connect the house to an underground water source with a special pipe.\n choose an $i$-th house ($2 <=i <=l$), and connect the $i$-th house to the ($i - 1$)-th house with a common pipe. In this case, there is a condition to choose a next $i$-th house because the area is slope land. Let $(x, y)$ be the block of the ($i - 1$)-th house. An $i$-th house must be located at either $(x - 2, y + 2)$, $(x, y + 2)$, or $(x + 2, y + 2)$. A common pipe connecting two houses must be located at $(x - 1, y + 1)$, $(x, y + 1)$, or $(x + 1, y + 1)$, respectively.\nIn addition, you should notice the followings when you construct several pipelines:\n For each house, exactly one pipeline is through the house.\n Multiple pipes can be located at one block.\nIn your task, common pipes are common, so you can use any number of common pipes. On the other hand, special pipes are special, so the number of available special pipes in this task is restricted under ICPC regulation.\nBesides the restriction of available special pipes, there is another factor obstructing your pipe work: fierce dogs. Some of the blocks which do not contain a house seem to be home of fierce dogs. Each dog always stays at his/her home block. Since several dogs must not live at the same block as their home, you can assume each block is home of only one dog, or not home of any dogs.\nThe figure below is an example of a water pipe network in a 5 $\times$ 5 area with 4 special pipes. This corresponds to the first sample.\nLocating a common pipe at a no-dog block costs 1 unit time, but locating a common pipe at a dog-living block costs 2 unit time because you have to fight against the fierce dog. Note that when you locate multiple pipes at the same block, each pipe-locating costs 1 unit time for no-dog blocks and 2 for dog-living blocks, respectively. By the way, special pipes are very special, so locating a special pipe costs 0 unit time.\nYou, a proud pipe fitter, want to accomplish this task as soon as possible. Fortunately, you get a list of blocks which are home of dogs. You have frequently participated in programming contests before being a pipe fitter. Hence, you decide to make a program determining whether or not you can construct a water pipe network such that every house is supplied water through the network with a restricted number of special pipes, and if so, computing the minimum total time cost to construct it.", "constraint": "", "input": "The input consists of a single test case. \n\n$W$ $H$ $K$\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . . \n$x_N$ $y_N$\n\nAll numbers in a test case are integers. The first line contains three integers $W$, $H$, and $K$. $W$ and $H$ represent the size of the rectangle area. $W$ is the number of blocks from west to east ($1 <= W < 10,000$), and $H$ is the number of blocks from north to south ($1 <= H < 10,000$). $W$ and $H$ must be odd numbers. $K$ is the number of special pipes that you can use in this task ($1 <= K <= 100,000,000$). The second line has an integer $N$ ($0 <= N <= 100,000$), which is the number of dogs in the area. Each of the following $N$ lines contains two integers $x_i$ and $y_i$, which indicates home of the $i$-th fierce dog is the block $(x_i, y_i)$. These numbers satisfy the following conditions:\n\n $1 <= x_i <= W, 1 <= y_i <= H$.\n At least one of $x_i$ and $y_i$ is even number.\n $i \\ne j$ implies $(x_i, y_i) \\ne (x_j, y_j)$. That is, two or more dogs are not in the same block.", "output": "If we can construct a water pipe network such that every house is supplied water through the network with a restricted number of special pipes, print the minimum total time cost to construct it. If not, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5 4\n6\n3 2\n4 2\n5 2\n1 4\n3 4\n5 4\n output: 6", "input: 5 3 1\n0\n output: -1", "input: 9 5 100\n5\n2 1\n1 2\n3 4\n4 3\n2 2\n output: 0", "input: 5 5 3\n4\n1 2\n5 2\n1 4\n5 4\n output: 8", "input: 9 5 5\n10\n2 1\n2 2\n3 2\n5 2\n8 2\n4 3\n2 4\n3 4\n5 4\n8 4\n output: 10"], "Pid": "p01887", "ProblemText": "Task Description: You, a proud pipe fitter of ICPC (International Community for Pipe Connection), undertake a new task. The area in which you will take charge of piping work is a rectangular shape with $W$ blocks from west to east and $H$ blocks from north to south. We refer to the block at the $i$-th from west and the $j$-th from north as $(i, j)$. The westernmost and northernmost block is $(1,1)$, and the easternmost and southernmost block is $(W, H)$. To make the area good scenery, the block $(i, j)$ has exactly one house if and only if both of $i$ and $j$ are odd numbers.\nYour task is to construct a water pipe network in the area such that every house in the area is supplied water through the network. A water pipe network consists of pipelines. A pipeline is made by connecting one or more pipes, and a pipeline with l pipes is constructed as follows:\n choose a first house, and connect the house to an underground water source with a special pipe.\n choose an $i$-th house ($2 <=i <=l$), and connect the $i$-th house to the ($i - 1$)-th house with a common pipe. In this case, there is a condition to choose a next $i$-th house because the area is slope land. Let $(x, y)$ be the block of the ($i - 1$)-th house. An $i$-th house must be located at either $(x - 2, y + 2)$, $(x, y + 2)$, or $(x + 2, y + 2)$. A common pipe connecting two houses must be located at $(x - 1, y + 1)$, $(x, y + 1)$, or $(x + 1, y + 1)$, respectively.\nIn addition, you should notice the followings when you construct several pipelines:\n For each house, exactly one pipeline is through the house.\n Multiple pipes can be located at one block.\nIn your task, common pipes are common, so you can use any number of common pipes. On the other hand, special pipes are special, so the number of available special pipes in this task is restricted under ICPC regulation.\nBesides the restriction of available special pipes, there is another factor obstructing your pipe work: fierce dogs. Some of the blocks which do not contain a house seem to be home of fierce dogs. Each dog always stays at his/her home block. Since several dogs must not live at the same block as their home, you can assume each block is home of only one dog, or not home of any dogs.\nThe figure below is an example of a water pipe network in a 5 $\times$ 5 area with 4 special pipes. This corresponds to the first sample.\nLocating a common pipe at a no-dog block costs 1 unit time, but locating a common pipe at a dog-living block costs 2 unit time because you have to fight against the fierce dog. Note that when you locate multiple pipes at the same block, each pipe-locating costs 1 unit time for no-dog blocks and 2 for dog-living blocks, respectively. By the way, special pipes are very special, so locating a special pipe costs 0 unit time.\nYou, a proud pipe fitter, want to accomplish this task as soon as possible. Fortunately, you get a list of blocks which are home of dogs. You have frequently participated in programming contests before being a pipe fitter. Hence, you decide to make a program determining whether or not you can construct a water pipe network such that every house is supplied water through the network with a restricted number of special pipes, and if so, computing the minimum total time cost to construct it.\nTask Input: The input consists of a single test case. \n\n$W$ $H$ $K$\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . . \n$x_N$ $y_N$\n\nAll numbers in a test case are integers. The first line contains three integers $W$, $H$, and $K$. $W$ and $H$ represent the size of the rectangle area. $W$ is the number of blocks from west to east ($1 <= W < 10,000$), and $H$ is the number of blocks from north to south ($1 <= H < 10,000$). $W$ and $H$ must be odd numbers. $K$ is the number of special pipes that you can use in this task ($1 <= K <= 100,000,000$). The second line has an integer $N$ ($0 <= N <= 100,000$), which is the number of dogs in the area. Each of the following $N$ lines contains two integers $x_i$ and $y_i$, which indicates home of the $i$-th fierce dog is the block $(x_i, y_i)$. These numbers satisfy the following conditions:\n\n $1 <= x_i <= W, 1 <= y_i <= H$.\n At least one of $x_i$ and $y_i$ is even number.\n $i \\ne j$ implies $(x_i, y_i) \\ne (x_j, y_j)$. That is, two or more dogs are not in the same block.\nTask Output: If we can construct a water pipe network such that every house is supplied water through the network with a restricted number of special pipes, print the minimum total time cost to construct it. If not, print -1.\nTask Samples: input: 5 5 4\n6\n3 2\n4 2\n5 2\n1 4\n3 4\n5 4\n output: 6\ninput: 5 3 1\n0\n output: -1\ninput: 9 5 100\n5\n2 1\n1 2\n3 4\n4 3\n2 2\n output: 0\ninput: 5 5 3\n4\n1 2\n5 2\n1 4\n5 4\n output: 8\ninput: 9 5 5\n10\n2 1\n2 2\n3 2\n5 2\n8 2\n4 3\n2 4\n3 4\n5 4\n8 4\n output: 10\n\n" }, { "title": "Multisect", "content": "We are developing the world's coolest AI robot product. After the long struggle, we finally managed to send our product at revision $R_{RC}$ to QA team as a release candidate. However, they reported that some tests failed! Because we were too lazy to set up a continuous integration system, we have no idea when our software corrupted. We only know that the software passed all the test at the past revision $R_{PASS}$. To determine the revision $R_{ENBUG}$ ($R_{PASS} < R_{ENBUG} <= R_{RC}$) in which our software started to fail, we must test our product revision-by-revision.\n\nHere, we can assume the following conditions:\n\n When we test at the revision $R$, the test passes if $R < R_{ENBUG}$, or fails otherwise.\n\n It is equally possible, which revision between $R_{PASS} + 1$ and $R_{RC}$ is $R_{ENBUG}$.\nFrom the first assumption, we don't need to test all the revisions. All we have to do is to find the revision $R$ such that the test at $R - 1$ passes and the test at $R$ fails. We have $K$ testing devices. Using them, we can test at most $K$ different revisions simultaneously. We call this \"parallel testing\". By the restriction of the testing environment, we cannot start new tests until a current parallel testing finishes, even if we don't use all the $K$ devices.\n\nParallel testings take some cost. The more tests fail, the more costly the parallel testing becomes. If $i$ tests fail in a parallel testing, its cost is $T_i$ ($0 <= i <= K$). And if we run parallel testings multiple times, the total cost is the sum of their costs.\n\nOf course we want to minimize the total cost to determine $R_{ENBUG}$, by choosing carefully how many and which revisions to test on each parallel testing. What is the minimum expected value of the total cost if we take an optimal strategy?", "constraint": "", "input": "The input consists of a single test case with the following format. \n\n$R_{PASS}$ $R_{RC}$ $K$\n$T_0$ $T_1$ . . . $T_K$\n\n$R_{PASS}$ and $R_{RC}$ are integers that represent the revision numbers of our software at which the test passed and failed, respectively. $1 <= R_{PASS} < R_{RC} <= 1,000$ holds. $K$ ($1 <= K <= 30$) is the maximum number of revisions we can test in a single parallel testing. $T_i$ is an integer that represents the cost of a parallel testing in which $i$ tests fail ($0 <= i <= K$). You can assume $1 <= T_0 <= T_1 <= . . . <= T_K <= 100,000$.", "output": "Output the minimum expected value of the total cost. The output should not contain an error greater than 0.0001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 10 2\n1 1 1\n output: 2.0", "input: 1 100 1\n100 100\n output: 670.7070707", "input: 100 200 4\n1 1 2 2 3\n output: 4.6400000", "input: 2 3 4\n1 2 3 4 5\n output: 0.0", "input: 998 1000 4\n10 100 1000 10000 100000\n output: 55.0"], "Pid": "p01888", "ProblemText": "Task Description: We are developing the world's coolest AI robot product. After the long struggle, we finally managed to send our product at revision $R_{RC}$ to QA team as a release candidate. However, they reported that some tests failed! Because we were too lazy to set up a continuous integration system, we have no idea when our software corrupted. We only know that the software passed all the test at the past revision $R_{PASS}$. To determine the revision $R_{ENBUG}$ ($R_{PASS} < R_{ENBUG} <= R_{RC}$) in which our software started to fail, we must test our product revision-by-revision.\n\nHere, we can assume the following conditions:\n\n When we test at the revision $R$, the test passes if $R < R_{ENBUG}$, or fails otherwise.\n\n It is equally possible, which revision between $R_{PASS} + 1$ and $R_{RC}$ is $R_{ENBUG}$.\nFrom the first assumption, we don't need to test all the revisions. All we have to do is to find the revision $R$ such that the test at $R - 1$ passes and the test at $R$ fails. We have $K$ testing devices. Using them, we can test at most $K$ different revisions simultaneously. We call this \"parallel testing\". By the restriction of the testing environment, we cannot start new tests until a current parallel testing finishes, even if we don't use all the $K$ devices.\n\nParallel testings take some cost. The more tests fail, the more costly the parallel testing becomes. If $i$ tests fail in a parallel testing, its cost is $T_i$ ($0 <= i <= K$). And if we run parallel testings multiple times, the total cost is the sum of their costs.\n\nOf course we want to minimize the total cost to determine $R_{ENBUG}$, by choosing carefully how many and which revisions to test on each parallel testing. What is the minimum expected value of the total cost if we take an optimal strategy?\nTask Input: The input consists of a single test case with the following format. \n\n$R_{PASS}$ $R_{RC}$ $K$\n$T_0$ $T_1$ . . . $T_K$\n\n$R_{PASS}$ and $R_{RC}$ are integers that represent the revision numbers of our software at which the test passed and failed, respectively. $1 <= R_{PASS} < R_{RC} <= 1,000$ holds. $K$ ($1 <= K <= 30$) is the maximum number of revisions we can test in a single parallel testing. $T_i$ is an integer that represents the cost of a parallel testing in which $i$ tests fail ($0 <= i <= K$). You can assume $1 <= T_0 <= T_1 <= . . . <= T_K <= 100,000$.\nTask Output: Output the minimum expected value of the total cost. The output should not contain an error greater than 0.0001.\nTask Samples: input: 1 10 2\n1 1 1\n output: 2.0\ninput: 1 100 1\n100 100\n output: 670.7070707\ninput: 100 200 4\n1 1 2 2 3\n output: 4.6400000\ninput: 2 3 4\n1 2 3 4 5\n output: 0.0\ninput: 998 1000 4\n10 100 1000 10000 100000\n output: 55.0\n\n" }, { "title": "Compressed Formula", "content": "You are given a simple, but long formula in a compressed format. A compressed formula is a sequence of $N$ pairs of an integer $r_i$ and a string $s_i$, which consists only of digits ('0'-'9'), '+', '-', and '*'. To restore the original formula from a compressed formula, first we generate strings obtained by repeating $s_i$ $r_i$ times for all $i$, then we concatenate them in order of the sequence.\n\nYou can assume that a restored original formula is well-formed. More precisely, a restored formula satisfies the following BNF:\n\n : = | '+' | '-' \n : = | * \n : = | \n : = '0' | \n : = '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'\n\nHere, '+' means addition, '-' means subtraction, and '*' means multiplication of integers.\n\nYour task is to write a program computing the answer of a given formula modulo 1,000,000,007, where $x$ modulo $m$ is a non-negative integer $r$ such that there exists an integer $k$ satisfying $x = km + r$ and $0 <= r < m$; it is guaranteed that such $r$ is uniquely determined for integers $x$ and $m$.", "constraint": "", "input": "The input consists of a single test case. \n\n$N$\n$r_1$ $s_1$\n$r_2$ $s_2$\n. . . \n$r_N$ $s_N$\n\nThe first line contains a single integer $N$ ($1 <= N <= 10^4$), which is the length of a sequence of a compressed formula. The following $N$ lines represents pieces of a compressed formula. The $i$-th line consists of an integer $r_i$ ($1 <= r_i <= 10^9$) and a string $s_i$ ($1 <= |s_i| <= 10$), where $t_i$ is the number of repetition of $s_i$, and $s_i$ is a piece of an original formula. You can assume that an original formula, restored from a given compressed formula by concatenation of repetition of pieces, satisfies the BNF in the problem statement.", "output": "Print the answer of a given compressed formula modulo 1,000,000,007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n5 1\n output: 11111", "input: 2\n19 2*\n1 2\n output: 1048576", "input: 2\n1 1-10\n10 01*2+1\n output: 999999825", "input: 4\n3 12+45-12\n4 12-3*2*1\n5 12345678\n3 11*23*45\n output: 20008570"], "Pid": "p01889", "ProblemText": "Task Description: You are given a simple, but long formula in a compressed format. A compressed formula is a sequence of $N$ pairs of an integer $r_i$ and a string $s_i$, which consists only of digits ('0'-'9'), '+', '-', and '*'. To restore the original formula from a compressed formula, first we generate strings obtained by repeating $s_i$ $r_i$ times for all $i$, then we concatenate them in order of the sequence.\n\nYou can assume that a restored original formula is well-formed. More precisely, a restored formula satisfies the following BNF:\n\n : = | '+' | '-' \n : = | * \n : = | \n : = '0' | \n : = '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'\n\nHere, '+' means addition, '-' means subtraction, and '*' means multiplication of integers.\n\nYour task is to write a program computing the answer of a given formula modulo 1,000,000,007, where $x$ modulo $m$ is a non-negative integer $r$ such that there exists an integer $k$ satisfying $x = km + r$ and $0 <= r < m$; it is guaranteed that such $r$ is uniquely determined for integers $x$ and $m$.\nTask Input: The input consists of a single test case. \n\n$N$\n$r_1$ $s_1$\n$r_2$ $s_2$\n. . . \n$r_N$ $s_N$\n\nThe first line contains a single integer $N$ ($1 <= N <= 10^4$), which is the length of a sequence of a compressed formula. The following $N$ lines represents pieces of a compressed formula. The $i$-th line consists of an integer $r_i$ ($1 <= r_i <= 10^9$) and a string $s_i$ ($1 <= |s_i| <= 10$), where $t_i$ is the number of repetition of $s_i$, and $s_i$ is a piece of an original formula. You can assume that an original formula, restored from a given compressed formula by concatenation of repetition of pieces, satisfies the BNF in the problem statement.\nTask Output: Print the answer of a given compressed formula modulo 1,000,000,007.\nTask Samples: input: 1\n5 1\n output: 11111\ninput: 2\n19 2*\n1 2\n output: 1048576\ninput: 2\n1 1-10\n10 01*2+1\n output: 999999825\ninput: 4\n3 12+45-12\n4 12-3*2*1\n5 12345678\n3 11*23*45\n output: 20008570\n\n" }, { "title": "Non-redundant Drive", "content": "The people of JAG kingdom hate redundancy. For example, the N cities in JAG kingdom are connected with just $N - 1$ bidirectional roads such that any city is reachable from any city through some roads. Under the condition, the number of paths from a city to another city is exactly one for all pairs of the cities. This is a non-redundant road network : )\n\nOne day, you, a citizen of JAG kingdom, decided to travel as many cities in the kingdom as possible with a car. The car that you will use has an infinitely large tank, but initially the tank is empty. The fuel consumption of your car is 1 liter per 1 km, i. e. it consumes 1 liter of gasoline to move 1 km.\n\nEach city has exactly one gas station, and you can supply $g_x$ liters of gasoline to your car at the gas station of the city $x$. Of course, you have a choice not to visit some of the gas stations in your travel. But you will not supply gasoline twice or more at the same gas station, because it is redundant. Each road in the kingdom has a distance between two cities: the distance of $i$-th road is $d_i$ km. You will not pass the same city or the same road twice or more, of course, because it is redundant.\n\nIf a quantity of stored gasoline becomes zero, the car cannot move, and hence your travel will end there. But then, you may concern about an initially empty tank. Don't worry. You can start at any gas station of the cities in the kingdom. Furthermore, each road directly connects the gas stations of the its two ends (because the spirit of non-redundancy avoids redundant moves in a city), you therefore can supply gasoline to your car even if your car tank becomes empty just when you arrive the city. \n\nYour task is to write a program computing the maximum number of cities so that you can travel under your non-redundancy policy.", "constraint": "", "input": "The input consists of a single test case. \n\n$N$\n$g_1$ $g_2$ . . . $g_N$\n$a_1$ $b_1$ $d_1$\n$a_2$ $b_2$ $d_2$\n. . . \n$a_{N-1}$ $b_{N-1}$ $d_{N-1}$\n\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which is the number of cities in JAG kingdom. The second line contains $N$ integers: the $i$-th of them is $g_i$ ($1 <= g_i <= 10,000$), the amount of gasoline can be supplied at the gas station of the city $i$. The following $N - 1$ lines give information of roads: the $j$-th line of them contains $a_j$ and $b_j$ , which indicates that the $j$-th road bidirectionally connects the cities $a_j$ and $b_j$ ($1 <= a_j, b_j <= N, a_j \\ne b_j$) with distance $d_j$ ($1 <= d_j <= 10,000$). You can assume that all cities in the kingdom are connected by the roads.", "output": "Print the maximum number of cities you can travel from any city under the constraint such that you can supply gasoline at most once per a gas station.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n5 8 1 3 5\n1 2 4\n2 3 3\n2 4 3\n1 5 7\n output: 4", "input: 2\n10 1\n1 2 10\n output: 2", "input: 5\n1 3 5 1 1\n1 2 5\n2 3 3\n2 4 3\n1 5 5\n output: 3"], "Pid": "p01890", "ProblemText": "Task Description: The people of JAG kingdom hate redundancy. For example, the N cities in JAG kingdom are connected with just $N - 1$ bidirectional roads such that any city is reachable from any city through some roads. Under the condition, the number of paths from a city to another city is exactly one for all pairs of the cities. This is a non-redundant road network : )\n\nOne day, you, a citizen of JAG kingdom, decided to travel as many cities in the kingdom as possible with a car. The car that you will use has an infinitely large tank, but initially the tank is empty. The fuel consumption of your car is 1 liter per 1 km, i. e. it consumes 1 liter of gasoline to move 1 km.\n\nEach city has exactly one gas station, and you can supply $g_x$ liters of gasoline to your car at the gas station of the city $x$. Of course, you have a choice not to visit some of the gas stations in your travel. But you will not supply gasoline twice or more at the same gas station, because it is redundant. Each road in the kingdom has a distance between two cities: the distance of $i$-th road is $d_i$ km. You will not pass the same city or the same road twice or more, of course, because it is redundant.\n\nIf a quantity of stored gasoline becomes zero, the car cannot move, and hence your travel will end there. But then, you may concern about an initially empty tank. Don't worry. You can start at any gas station of the cities in the kingdom. Furthermore, each road directly connects the gas stations of the its two ends (because the spirit of non-redundancy avoids redundant moves in a city), you therefore can supply gasoline to your car even if your car tank becomes empty just when you arrive the city. \n\nYour task is to write a program computing the maximum number of cities so that you can travel under your non-redundancy policy.\nTask Input: The input consists of a single test case. \n\n$N$\n$g_1$ $g_2$ . . . $g_N$\n$a_1$ $b_1$ $d_1$\n$a_2$ $b_2$ $d_2$\n. . . \n$a_{N-1}$ $b_{N-1}$ $d_{N-1}$\n\nThe first line contains an integer $N$ ($1 <= N <= 100,000$), which is the number of cities in JAG kingdom. The second line contains $N$ integers: the $i$-th of them is $g_i$ ($1 <= g_i <= 10,000$), the amount of gasoline can be supplied at the gas station of the city $i$. The following $N - 1$ lines give information of roads: the $j$-th line of them contains $a_j$ and $b_j$ , which indicates that the $j$-th road bidirectionally connects the cities $a_j$ and $b_j$ ($1 <= a_j, b_j <= N, a_j \\ne b_j$) with distance $d_j$ ($1 <= d_j <= 10,000$). You can assume that all cities in the kingdom are connected by the roads.\nTask Output: Print the maximum number of cities you can travel from any city under the constraint such that you can supply gasoline at most once per a gas station.\nTask Samples: input: 5\n5 8 1 3 5\n1 2 4\n2 3 3\n2 4 3\n1 5 7\n output: 4\ninput: 2\n10 1\n1 2 10\n output: 2\ninput: 5\n1 3 5 1 1\n1 2 5\n2 3 3\n2 4 3\n1 5 5\n output: 3\n\n" }, { "title": "Star in Parentheses", "content": "You are given a string $S$, which is balanced parentheses with a star symbol '*' inserted.\n\n Any balanced parentheses can be constructed using the following rules:\n\nAn empty string is balanced.\n\nConcatenation of two balanced parentheses is balanced.\n\nIf $T$ is balanced parentheses, concatenation of '(', $T$, and ')' in this order is balanced.\n For example, '()()' and '(()())' are balanced parentheses. ')(' and ')()(()' are not balanced parentheses.\n\n Your task is to count how many matching pairs of parentheses surround the star.\n\nLet $S_i$be the $i$-th character of a string $S$. The pair of $S_l$ and $S_r$ ($l < r$) is called a matching pair of parentheses if $S_l$ is '(', $S_r$ is ')' and the surrounded string by them is balanced when ignoring a star symbol.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$S$\n\n$S$ is balanced parentheses with exactly one '*' inserted somewhere. The length of $S$ is between 1 and 100, inclusive.", "output": "Print the answer in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ((*)())\n output: 2", "input: (*)\n output: 1", "input: (()())*\n output: 0", "input: ()*()\n output: 0", "input: ((((((((((*))))))))))\n output: 10", "input: *\n output: 0"], "Pid": "p01945", "ProblemText": "Task Description: You are given a string $S$, which is balanced parentheses with a star symbol '*' inserted.\n\n Any balanced parentheses can be constructed using the following rules:\n\nAn empty string is balanced.\n\nConcatenation of two balanced parentheses is balanced.\n\nIf $T$ is balanced parentheses, concatenation of '(', $T$, and ')' in this order is balanced.\n For example, '()()' and '(()())' are balanced parentheses. ')(' and ')()(()' are not balanced parentheses.\n\n Your task is to count how many matching pairs of parentheses surround the star.\n\nLet $S_i$be the $i$-th character of a string $S$. The pair of $S_l$ and $S_r$ ($l < r$) is called a matching pair of parentheses if $S_l$ is '(', $S_r$ is ')' and the surrounded string by them is balanced when ignoring a star symbol.\nTask Input: The input consists of a single test case formatted as follows.\n\n$S$\n\n$S$ is balanced parentheses with exactly one '*' inserted somewhere. The length of $S$ is between 1 and 100, inclusive.\nTask Output: Print the answer in one line.\nTask Samples: input: ((*)())\n output: 2\ninput: (*)\n output: 1\ninput: (()())*\n output: 0\ninput: ()*()\n output: 0\ninput: ((((((((((*))))))))))\n output: 10\ninput: *\n output: 0\n\n" }, { "title": "Slimming Plan", "content": "Chokudai loves eating so much. However, his doctor Akensho told him that he was overweight, so he finally decided to lose his weight.\n\n Chokudai made a slimming plan of a $D$-day cycle. It is represented by $D$ integers $w_0, . . . , w_{D-1}$. His weight is $S$ on the 0-th day of the plan and he aims to reduce it to $T$ ($S > T$). If his weight on the $i$-th day of the plan is $x$, it will be $x + w_{i\\%D}$ on the $(i+1)$-th day. Note that $i\\%D$ is the remainder obtained by dividing $i$ by $D$. If his weight successfully gets less than or equal to $T$, he will stop slimming immediately.\n\n If his slimming plan takes too many days or even does not end forever, he should reconsider it.\n\n Determine whether it ends or not, and report how many days it takes if it ends.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$S$ $T$ $D$\n$w_0 . . . w_{D-1}$\n\n The first line consists of three integers $S$, $T$, $D$ ($1 <= S, T, D <= 100,000, S > T$). The second line consists of $D$ integers $w_0, . . . , w_{D-1}$ ($-100,000 <= w_i <= 100,000$ for each $i$).", "output": "If Chokudai's slimming plan ends on the $d$-th day, print $d$ in one line. If it never ends, print $-1$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 65 60 3\n-2 3 -4\n output: 4\n Chokudai's weight will change as follows: $65 \\rightarrow 63 \\rightarrow 66 \\rightarrow 62 \\rightarrow 60$.", "input: 65 60 3\n-2 10 -3\n output: -1\n Chokudai's weight will change as follows: $65 \\rightarrow 63 \\rightarrow 73 \\rightarrow 70 \\rightarrow 68 \\rightarrow 78 \\rightarrow 75 \\rightarrow ...$.", "input: 100000 1 1\n-1\n output: 99999", "input: 60 59 1\n-123\n output: 1"], "Pid": "p01946", "ProblemText": "Task Description: Chokudai loves eating so much. However, his doctor Akensho told him that he was overweight, so he finally decided to lose his weight.\n\n Chokudai made a slimming plan of a $D$-day cycle. It is represented by $D$ integers $w_0, . . . , w_{D-1}$. His weight is $S$ on the 0-th day of the plan and he aims to reduce it to $T$ ($S > T$). If his weight on the $i$-th day of the plan is $x$, it will be $x + w_{i\\%D}$ on the $(i+1)$-th day. Note that $i\\%D$ is the remainder obtained by dividing $i$ by $D$. If his weight successfully gets less than or equal to $T$, he will stop slimming immediately.\n\n If his slimming plan takes too many days or even does not end forever, he should reconsider it.\n\n Determine whether it ends or not, and report how many days it takes if it ends.\nTask Input: The input consists of a single test case formatted as follows.\n\n$S$ $T$ $D$\n$w_0 . . . w_{D-1}$\n\n The first line consists of three integers $S$, $T$, $D$ ($1 <= S, T, D <= 100,000, S > T$). The second line consists of $D$ integers $w_0, . . . , w_{D-1}$ ($-100,000 <= w_i <= 100,000$ for each $i$).\nTask Output: If Chokudai's slimming plan ends on the $d$-th day, print $d$ in one line. If it never ends, print $-1$.\nTask Samples: input: 65 60 3\n-2 3 -4\n output: 4\n Chokudai's weight will change as follows: $65 \\rightarrow 63 \\rightarrow 66 \\rightarrow 62 \\rightarrow 60$.\ninput: 65 60 3\n-2 10 -3\n output: -1\n Chokudai's weight will change as follows: $65 \\rightarrow 63 \\rightarrow 73 \\rightarrow 70 \\rightarrow 68 \\rightarrow 78 \\rightarrow 75 \\rightarrow ...$.\ninput: 100000 1 1\n-1\n output: 99999\ninput: 60 59 1\n-123\n output: 1\n\n" }, { "title": "Ninja Map", "content": "Intersections of Crossing Path City are aligned to a grid. There are $N$ east-west streets which are numbered from 1 to $N$, from north to south. There are also $N$ north-south streets which are numbered from 1 to $N$, from west to east. Every pair of east-west and north-south streets has an intersection; therefore there are $N^2$ intersections which are numbered from 1 to $N^2$.\n\n Surprisingly, all of the residents in the city are Ninja. To prevent outsiders from knowing their locations, the numbering of intersections is shuffled.\n\nYou know the connections between the intersections and try to deduce their positions from the information. If there are more than one possible set of positions, you can output any of them.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$\n$a_1$ $b_1$\n. . .\n$a_{2N^2-2N}$ $\\; $ $b_{2N^2-2N}$\n\n The first line consists of an integer $N$ ($2 <= N <= 100$). The following $2N^2 - 2N$ lines represent connections between intersections. The ($i+1$)-th line consists of two integers $a_i$ and $b_i$ ($1 <= a_i, b_i <= N^2, a_i \\ne b_i$), which represent that the $a_i$-th and $b_i$-th intersections are adjacent. More precisely, let's denote by ($r, c$) the intersection of the $r$-th east-west street and the $c$-th north-south street. If the intersection number of ($r, c$) is $a_i$ for some $r$ and $c$, then the intersection\n number of either ($r-1, c$), ($r+1, c$), ($r, c-1$) or ($r, c+1$) must be $b_i$. All inputs of adjacencies are different, i. e. , ($a_i, b_i$) $\\ne$ ($a_j, b_j$) and ($a_i, b_i$) $\\ne$ ($b_j, a_j$) for all $1 <= i < j <= 2N^2-2N$. This means that you are given information of all adjacencies on the grid.\n\nThe input is guaranteed to describe a valid map.", "output": "Print a possible set of positions of the intersections. More precisely, the output consists of $N$ lines each of which has space-separated $N$ integers. The $c$-th integer of the $r$-th line should be the intersection number of ($r, c$).\n\nIf there are more than one possible set of positions, you can output any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n4 7\n8 6\n2 3\n8 9\n5 3\n4 6\n5 6\n7 8\n1 4\n2 6\n5 9\n output: 7 4 1\n8 6 2\n9 5 3\n The following output will also be accepted.\n1 2 3\n4 6 5\n7 8 9", "input: 4\n12 1\n3 8\n10 7\n13 14\n8 2\n9 12\n6 14\n11 3\n3 13\n1 10\n11 15\n4 15\n4 9\n14 10\n5 7\n2 5\n6 1\n14 5\n16 11\n15 6\n15 13\n9 6\n16 4\n13 2\n output: 8 2 5 7\n3 13 14 10\n11 15 6 1\n16 4 9 12"], "Pid": "p01947", "ProblemText": "Task Description: Intersections of Crossing Path City are aligned to a grid. There are $N$ east-west streets which are numbered from 1 to $N$, from north to south. There are also $N$ north-south streets which are numbered from 1 to $N$, from west to east. Every pair of east-west and north-south streets has an intersection; therefore there are $N^2$ intersections which are numbered from 1 to $N^2$.\n\n Surprisingly, all of the residents in the city are Ninja. To prevent outsiders from knowing their locations, the numbering of intersections is shuffled.\n\nYou know the connections between the intersections and try to deduce their positions from the information. If there are more than one possible set of positions, you can output any of them.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$\n$a_1$ $b_1$\n. . .\n$a_{2N^2-2N}$ $\\; $ $b_{2N^2-2N}$\n\n The first line consists of an integer $N$ ($2 <= N <= 100$). The following $2N^2 - 2N$ lines represent connections between intersections. The ($i+1$)-th line consists of two integers $a_i$ and $b_i$ ($1 <= a_i, b_i <= N^2, a_i \\ne b_i$), which represent that the $a_i$-th and $b_i$-th intersections are adjacent. More precisely, let's denote by ($r, c$) the intersection of the $r$-th east-west street and the $c$-th north-south street. If the intersection number of ($r, c$) is $a_i$ for some $r$ and $c$, then the intersection\n number of either ($r-1, c$), ($r+1, c$), ($r, c-1$) or ($r, c+1$) must be $b_i$. All inputs of adjacencies are different, i. e. , ($a_i, b_i$) $\\ne$ ($a_j, b_j$) and ($a_i, b_i$) $\\ne$ ($b_j, a_j$) for all $1 <= i < j <= 2N^2-2N$. This means that you are given information of all adjacencies on the grid.\n\nThe input is guaranteed to describe a valid map.\nTask Output: Print a possible set of positions of the intersections. More precisely, the output consists of $N$ lines each of which has space-separated $N$ integers. The $c$-th integer of the $r$-th line should be the intersection number of ($r, c$).\n\nIf there are more than one possible set of positions, you can output any of them.\nTask Samples: input: 3\n1 2\n4 7\n8 6\n2 3\n8 9\n5 3\n4 6\n5 6\n7 8\n1 4\n2 6\n5 9\n output: 7 4 1\n8 6 2\n9 5 3\n The following output will also be accepted.\n1 2 3\n4 6 5\n7 8 9\ninput: 4\n12 1\n3 8\n10 7\n13 14\n8 2\n9 12\n6 14\n11 3\n3 13\n1 10\n11 15\n4 15\n4 9\n14 10\n5 7\n2 5\n6 1\n14 5\n16 11\n15 6\n15 13\n9 6\n16 4\n13 2\n output: 8 2 5 7\n3 13 14 10\n11 15 6 1\n16 4 9 12\n\n" }, { "title": "Janken Master", "content": "You are supposed to play the rock-paper-scissors game. There are $N$ players including you.\n\n This game consists of multiple rounds. While the rounds go, the number of remaining players decreases. In each round, each remaining player will select an arbitrary shape independently. People who show rocks win if all of the other people show scissors. In this same manner, papers win rocks, scissors win papers. There is no draw situation due to the special rule of this game: if a round is tied based on the normal rock-paper-scissors game rule, the player who has the highest programming contest rating (this is nothing to do with the round! ) will be the only winner of the round. Thus, some players win and the other players lose on each round. The losers drop out of the game and the winners proceed to a new round. They repeat it until only one player becomes the winner.\n\nEach player is numbered from $1$ to $N$. Your number is $1$. You know which shape the other $N-1$ players tend to\nshow, that is to say, you know the probabilities each player shows rock, paper and scissors. The $i$-th player shows rock with $r_i\\%$ probability, paper with $p_i\\%$ probability, and scissors with $s_i\\%$ probability. The rating of programming contest of the player numbered $i$ is $a_i$. There are no two players whose ratings are the same. Your task is to calculate your probability to win the game when you take an optimal strategy based on each player's tendency and rating.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$\n$a_1$\n$a_2$ $r_2$ $p_2$ $s_2$\n. . .\n$a_N$ $r_N$ $p_N$ $s_N$\n\nThe first line consists of a single integer $N$ ($2 <= N <= 14$). The second line consists of a single integer\n$a_i$ ($1 <= a_i <= N$). The ($i+1$)-th line consists of four integers $a_i, r_i, p_i$ and $s_i$ ($1 <= a_i <= N, 0 <= r_i, p_i, s_i <= 100, $ $r_i + p_i + s_i = 100$) for $i=2, . . . , N$. It is guaranteed that $a_1, . . . , a_N$ are pairwise distinct.", "output": "Print the probability to win the game in one line. Your answer will be accepted if its absolute or relative error does not exceed $10^{-6}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n2\n1 40 40 20\n output: 0.8\nSince you have the higher rating than the other player, you will win the game if you win or draw in the first round.", "input: 2\n1\n2 50 50 0\n output: 0.5\nYou must win in the first round.", "input: 3\n2\n1 50 0 50\n3 0 0 100\n output: 1\nIn the first round, your best strategy is to show a rock. You will win the game with $50\\%$ in this round. With the other $50\\%$, you and the second player proceed to the second round and you must show a rock to win the game.", "input: 3\n2\n3 40 40 20\n1 30 10 60\n output: 0.27", "input: 4\n4\n1 34 33 33\n2 33 34 33\n3 33 33 34\n output: 0.6591870816"], "Pid": "p01948", "ProblemText": "Task Description: You are supposed to play the rock-paper-scissors game. There are $N$ players including you.\n\n This game consists of multiple rounds. While the rounds go, the number of remaining players decreases. In each round, each remaining player will select an arbitrary shape independently. People who show rocks win if all of the other people show scissors. In this same manner, papers win rocks, scissors win papers. There is no draw situation due to the special rule of this game: if a round is tied based on the normal rock-paper-scissors game rule, the player who has the highest programming contest rating (this is nothing to do with the round! ) will be the only winner of the round. Thus, some players win and the other players lose on each round. The losers drop out of the game and the winners proceed to a new round. They repeat it until only one player becomes the winner.\n\nEach player is numbered from $1$ to $N$. Your number is $1$. You know which shape the other $N-1$ players tend to\nshow, that is to say, you know the probabilities each player shows rock, paper and scissors. The $i$-th player shows rock with $r_i\\%$ probability, paper with $p_i\\%$ probability, and scissors with $s_i\\%$ probability. The rating of programming contest of the player numbered $i$ is $a_i$. There are no two players whose ratings are the same. Your task is to calculate your probability to win the game when you take an optimal strategy based on each player's tendency and rating.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$\n$a_1$\n$a_2$ $r_2$ $p_2$ $s_2$\n. . .\n$a_N$ $r_N$ $p_N$ $s_N$\n\nThe first line consists of a single integer $N$ ($2 <= N <= 14$). The second line consists of a single integer\n$a_i$ ($1 <= a_i <= N$). The ($i+1$)-th line consists of four integers $a_i, r_i, p_i$ and $s_i$ ($1 <= a_i <= N, 0 <= r_i, p_i, s_i <= 100, $ $r_i + p_i + s_i = 100$) for $i=2, . . . , N$. It is guaranteed that $a_1, . . . , a_N$ are pairwise distinct.\nTask Output: Print the probability to win the game in one line. Your answer will be accepted if its absolute or relative error does not exceed $10^{-6}$.\nTask Samples: input: 2\n2\n1 40 40 20\n output: 0.8\nSince you have the higher rating than the other player, you will win the game if you win or draw in the first round.\ninput: 2\n1\n2 50 50 0\n output: 0.5\nYou must win in the first round.\ninput: 3\n2\n1 50 0 50\n3 0 0 100\n output: 1\nIn the first round, your best strategy is to show a rock. You will win the game with $50\\%$ in this round. With the other $50\\%$, you and the second player proceed to the second round and you must show a rock to win the game.\ninput: 3\n2\n3 40 40 20\n1 30 10 60\n output: 0.27\ninput: 4\n4\n1 34 33 33\n2 33 34 33\n3 33 33 34\n output: 0.6591870816\n\n" }, { "title": "Route Calculator", "content": "You have a grid with $H$ rows and $W$ columns. $H + W$ is even. We denote the cell at the $i$-th row from the top and the $j$-th column from the left by ($i, j$). In any cell ($i, j$), an integer between $1$ and $9$ is written if $i+j$ is even, and either '+' or '*' is written if $i+j$ is odd.\n\nYou can get a mathematical expression by moving right or down $H + W - 2$ times from ($1,1$) to ($H, W$) and concatenating all the characters written in the cells you passed in order. Your task is to maximize the calculated value of the resulting mathematical expression by choosing an arbitrary path from ($1,1$) to ($H, W$). If the maximum value is $10^{15}$ or less, print the value. Otherwise, print $-1$.", "constraint": "", "input": "The input consists of a single test case in the format below.\n\n$H$ $W$\n$a_{1,1}$ . . . $a_{1, W}$\n. . .\n$a_{H, 1}$ . . . $a_{H, W}$\n\nThe first line consists of two $H$ integers and $W$ ($1 <= H, W <= 50$). It is guaranteed that $H + W$ is even. The following $H$ lines represent the characters on the grid. $a_{i, j}$ represents the character written in the cell ($i, j$). In any cell ($i, j$), an integer between $1$ and $9$ is written if $i+j$ is even, and either '+' or '*' is written if $i+1$ is odd.", "output": "Print the answer in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1+2\n+9*\n1*5\n output: 46\nThe maximum value is obtained by passing through the following cells: $(1,1), (2,1), (2,2), (2,3), (3,3)$.", "input: 1 31\n9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9\n output: -1\nYou can obtain $9^{16}$, but it's too large.", "input: 5 5\n2+2+1\n+1+1+\n1+2+2\n+1+1+\n1+1+2\n output: 10", "input: 9 7\n8+9*4*8\n*5*2+3+\n1*3*2*2\n*5*1+9+\n1+2*2*2\n*3*6*2*\n7*7+6*5\n*5+7*2+\n3+3*6+8\n output: 86408"], "Pid": "p01949", "ProblemText": "Task Description: You have a grid with $H$ rows and $W$ columns. $H + W$ is even. We denote the cell at the $i$-th row from the top and the $j$-th column from the left by ($i, j$). In any cell ($i, j$), an integer between $1$ and $9$ is written if $i+j$ is even, and either '+' or '*' is written if $i+j$ is odd.\n\nYou can get a mathematical expression by moving right or down $H + W - 2$ times from ($1,1$) to ($H, W$) and concatenating all the characters written in the cells you passed in order. Your task is to maximize the calculated value of the resulting mathematical expression by choosing an arbitrary path from ($1,1$) to ($H, W$). If the maximum value is $10^{15}$ or less, print the value. Otherwise, print $-1$.\nTask Input: The input consists of a single test case in the format below.\n\n$H$ $W$\n$a_{1,1}$ . . . $a_{1, W}$\n. . .\n$a_{H, 1}$ . . . $a_{H, W}$\n\nThe first line consists of two $H$ integers and $W$ ($1 <= H, W <= 50$). It is guaranteed that $H + W$ is even. The following $H$ lines represent the characters on the grid. $a_{i, j}$ represents the character written in the cell ($i, j$). In any cell ($i, j$), an integer between $1$ and $9$ is written if $i+j$ is even, and either '+' or '*' is written if $i+1$ is odd.\nTask Output: Print the answer in one line.\nTask Samples: input: 3 3\n1+2\n+9*\n1*5\n output: 46\nThe maximum value is obtained by passing through the following cells: $(1,1), (2,1), (2,2), (2,3), (3,3)$.\ninput: 1 31\n9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9\n output: -1\nYou can obtain $9^{16}$, but it's too large.\ninput: 5 5\n2+2+1\n+1+1+\n1+2+2\n+1+1+\n1+1+2\n output: 10\ninput: 9 7\n8+9*4*8\n*5*2+3+\n1*3*2*2\n*5*1+9+\n1+2*2*2\n*3*6*2*\n7*7+6*5\n*5+7*2+\n3+3*6+8\n output: 86408\n\n" }, { "title": "Endless BFS", "content": "Mr. Endo wanted to write the code that performs breadth-first search (BFS), which is a search algorithm to explore all vertices on an undirected graph. An example of pseudo code of BFS is as follows:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: $visited <=ftarrow current$\n3: while $visited \\ne $ the set of all the vertices\n4: $found <=ftarrow \\{\\}$\n5: for $v$ in $current$\n6: for each $u$ adjacent to $v$\n7: $found <=ftarrow found \\cup\\{u\\}$\n8: $current <=ftarrow found \\setminus visited$\n9: $visited <=ftarrow visited \\cup found$\n\nHowever, Mr. Endo apparently forgot to manage visited vertices in his code. More precisely, he wrote the following\ncode:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: while $current \\ne $ the set of all the vertices\n3: $found <=ftarrow \\{\\}$\n4: for $v$ in $current$\n5: for each $u$ adjacent to $v$\n6: $found <=ftarrow found \\cup \\{u\\}$\n7: $current <=ftarrow found$\n\nYou may notice that for some graphs, Mr. Endo's program will not stop because it keeps running infinitely. Notice that it does not necessarily mean the program cannot explore all the vertices within finite steps. See example 2 below for more details. Your task here is to make a program that determines whether Mr. Endo's program will stop within finite steps for a given graph in order to point out the bug to him. Also, calculate the minimum number of loop iterations required for the program to stop if it is finite.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$ $M$\n$U_1$ $V_1$\n. . .\n$U_M$ $V_M$\n\n The first line consists of two integers $N$ ($2 <= N <= 100,000$) and $M$ ($1 <= M <= 100,000$), where $N$ is the number of vertices and $M$ is the number of edges in a given undirected graph, respectively. The $i$-th line of the following $M$ lines consists of two integers $U_i$ and $V_i$ ($1 <= U_i, V_i <= N$), which means the vertices $U_i$ and $V_i$ are adjacent in the given graph. The vertex 1 is the start vertex, i. e. $start\\_vertex$ in the pseudo codes. You can assume that the given graph also meets the following conditions.\n\nThe graph has no self-loop, i. e. , $U_i \\ne V_i$ for all $1 <= i <= M$.\n\nThe graph has no multi-edge, i. e. , $\\{Ui, Vi\\} \\ne \\{U_j, V_j\\}$ for all $1 <= i < j <= M$.\n\nThe graph is connected, i. e. , there is at least one path from $U$ to $V$ (and vice versa) for all vertices $1 <= U, V <= N$", "output": "If Mr. Endo's wrong BFS code cannot stop within finite steps for the given input graph, print -1 in a line. Otherwise, print the minimum number of loop iterations required to stop.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2\n1 3\n2 3\n output: 2", "input: 4 3\n1 2\n2 3\n3 4\n output: -1\nTransition of $current$ is $\\{1\\} \\rightarrow \\{2\\} \\rightarrow \\{1,3\\} \\rightarrow \\{2,4\\} \\rightarrow \\{1,3\\} \\rightarrow \\{2,4\\} \\rightarrow ... $. Although Mr. Endo's program will achieve to visit all the vertices (in 3 steps), will never become the same set as all the vertices.", "input: 4 4\n1 2\n2 3\n3 4\n4 1\n output: -1", "input: 8 9\n2 1\n3 5\n1 6\n2 5\n3 1\n8 4\n2 7\n7 1\n7 4\n output: 3"], "Pid": "p01950", "ProblemText": "Task Description: Mr. Endo wanted to write the code that performs breadth-first search (BFS), which is a search algorithm to explore all vertices on an undirected graph. An example of pseudo code of BFS is as follows:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: $visited <=ftarrow current$\n3: while $visited \\ne $ the set of all the vertices\n4: $found <=ftarrow \\{\\}$\n5: for $v$ in $current$\n6: for each $u$ adjacent to $v$\n7: $found <=ftarrow found \\cup\\{u\\}$\n8: $current <=ftarrow found \\setminus visited$\n9: $visited <=ftarrow visited \\cup found$\n\nHowever, Mr. Endo apparently forgot to manage visited vertices in his code. More precisely, he wrote the following\ncode:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: while $current \\ne $ the set of all the vertices\n3: $found <=ftarrow \\{\\}$\n4: for $v$ in $current$\n5: for each $u$ adjacent to $v$\n6: $found <=ftarrow found \\cup \\{u\\}$\n7: $current <=ftarrow found$\n\nYou may notice that for some graphs, Mr. Endo's program will not stop because it keeps running infinitely. Notice that it does not necessarily mean the program cannot explore all the vertices within finite steps. See example 2 below for more details. Your task here is to make a program that determines whether Mr. Endo's program will stop within finite steps for a given graph in order to point out the bug to him. Also, calculate the minimum number of loop iterations required for the program to stop if it is finite.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$ $M$\n$U_1$ $V_1$\n. . .\n$U_M$ $V_M$\n\n The first line consists of two integers $N$ ($2 <= N <= 100,000$) and $M$ ($1 <= M <= 100,000$), where $N$ is the number of vertices and $M$ is the number of edges in a given undirected graph, respectively. The $i$-th line of the following $M$ lines consists of two integers $U_i$ and $V_i$ ($1 <= U_i, V_i <= N$), which means the vertices $U_i$ and $V_i$ are adjacent in the given graph. The vertex 1 is the start vertex, i. e. $start\\_vertex$ in the pseudo codes. You can assume that the given graph also meets the following conditions.\n\nThe graph has no self-loop, i. e. , $U_i \\ne V_i$ for all $1 <= i <= M$.\n\nThe graph has no multi-edge, i. e. , $\\{Ui, Vi\\} \\ne \\{U_j, V_j\\}$ for all $1 <= i < j <= M$.\n\nThe graph is connected, i. e. , there is at least one path from $U$ to $V$ (and vice versa) for all vertices $1 <= U, V <= N$\nTask Output: If Mr. Endo's wrong BFS code cannot stop within finite steps for the given input graph, print -1 in a line. Otherwise, print the minimum number of loop iterations required to stop.\nTask Samples: input: 3 3\n1 2\n1 3\n2 3\n output: 2\ninput: 4 3\n1 2\n2 3\n3 4\n output: -1\nTransition of $current$ is $\\{1\\} \\rightarrow \\{2\\} \\rightarrow \\{1,3\\} \\rightarrow \\{2,4\\} \\rightarrow \\{1,3\\} \\rightarrow \\{2,4\\} \\rightarrow ... $. Although Mr. Endo's program will achieve to visit all the vertices (in 3 steps), will never become the same set as all the vertices.\ninput: 4 4\n1 2\n2 3\n3 4\n4 1\n output: -1\ninput: 8 9\n2 1\n3 5\n1 6\n2 5\n3 1\n8 4\n2 7\n7 1\n7 4\n output: 3\n\n" }, { "title": "Low Range-Sum Matrix", "content": "You received a card at a banquet. On the card, a matrix of $N$ rows and $M$ columns and two integers $K$ and $S$ are written. All the elements in the matrix are integers, and an integer at the $i$-th row from the top and the $j$-th column from the left is denoted by $A_{i, j}$.\n\n You can select up to $K$ elements from the matrix and invert the sign of the elements. If you can make a matrix such that there is no vertical or horizontal contiguous subsequence whose sum is greater than $S$, you can exchange your card for a prize.\n\nYour task is to determine if you can exchange a given card for a prize.", "constraint": "", "input": "The input consists of a single test case of the following form.\n\n$N$ $M$ $K$ $S$\n$A_{1,1}$ $A_{1,2}$ . . . $A_{1, M}$\n:\n$A_{N, 1}$ $A_{N, 2}$ . . . $A_{N, M}$\n\nThe first line consists of four integers $N, M, K$ and $S$ ($1 <= N, M <= 10,1 <= K <= 5,1 <= S <= 10^6$). The following $N$ lines represent the matrix in your card. The ($i+1$)-th line consists of $M$ integers $A_{i, 1}, A_{i, 2}, . . . , A_{i, M}$ ($-10^5 <= A_{i, j} <= 10^5$).", "output": "If you can exchange your card for a prize, print 'Yes'. Otherwise, print 'No'.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 2 10\n5 3 7\n2 6 1\n3 4 1\n output: Yes\nThe sum of a horizontal contiguous subsequence from $A_{1,1}$ to $A_{1,3}$ is $15$. The sum of a vertical contiguous subsequence from $A_{1,2}$ to $A_{3,2}$ is $13$. If you flip the sign of $A_{1,2}$, there is no vertical or horizontal contiguous subsequence whose sum is greater than $S$.", "input: 2 3 1 5\n4 8 -2\n-2 -5 -3\n output: Yes", "input: 2 3 1 5\n9 8 -2\n-2 -5 -3\n output: No", "input: 2 2 3 100\n0 0\n0 0\n output: Yes"], "Pid": "p01951", "ProblemText": "Task Description: You received a card at a banquet. On the card, a matrix of $N$ rows and $M$ columns and two integers $K$ and $S$ are written. All the elements in the matrix are integers, and an integer at the $i$-th row from the top and the $j$-th column from the left is denoted by $A_{i, j}$.\n\n You can select up to $K$ elements from the matrix and invert the sign of the elements. If you can make a matrix such that there is no vertical or horizontal contiguous subsequence whose sum is greater than $S$, you can exchange your card for a prize.\n\nYour task is to determine if you can exchange a given card for a prize.\nTask Input: The input consists of a single test case of the following form.\n\n$N$ $M$ $K$ $S$\n$A_{1,1}$ $A_{1,2}$ . . . $A_{1, M}$\n:\n$A_{N, 1}$ $A_{N, 2}$ . . . $A_{N, M}$\n\nThe first line consists of four integers $N, M, K$ and $S$ ($1 <= N, M <= 10,1 <= K <= 5,1 <= S <= 10^6$). The following $N$ lines represent the matrix in your card. The ($i+1$)-th line consists of $M$ integers $A_{i, 1}, A_{i, 2}, . . . , A_{i, M}$ ($-10^5 <= A_{i, j} <= 10^5$).\nTask Output: If you can exchange your card for a prize, print 'Yes'. Otherwise, print 'No'.\nTask Samples: input: 3 3 2 10\n5 3 7\n2 6 1\n3 4 1\n output: Yes\nThe sum of a horizontal contiguous subsequence from $A_{1,1}$ to $A_{1,3}$ is $15$. The sum of a vertical contiguous subsequence from $A_{1,2}$ to $A_{3,2}$ is $13$. If you flip the sign of $A_{1,2}$, there is no vertical or horizontal contiguous subsequence whose sum is greater than $S$.\ninput: 2 3 1 5\n4 8 -2\n-2 -5 -3\n output: Yes\ninput: 2 3 1 5\n9 8 -2\n-2 -5 -3\n output: No\ninput: 2 2 3 100\n0 0\n0 0\n output: Yes\n\n" }, { "title": "Tiny Room", "content": "You are an employee of Automatic Cleaning Machine (ACM) and a member of the development team of Intelligent Circular Perfect Cleaner (ICPC). ICPC is a robot that cleans up the dust of the place which it passed through.\n\n Your task is an inspection of ICPC. This inspection is performed by checking whether the center of ICPC reaches all the $N$ given points.\n\nHowever, since the laboratory is small, it may be impossible to place all the points in the laboratory so that the entire body of ICPC is contained in the laboratory during the inspection. The laboratory is a rectangle of $H * W$ and ICPC is a circle of radius $R$. You decided to write a program to check whether you can place all the points in the laboratory by rotating and/or translating them while maintaining the distance between arbitrary two points.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$N$ $H$ $W$ $R$\n$x_1$ $y_1$\n:\n$x_N$ $y_N$\n\nThe first line consists of four integers $N, H, W$ and $R$ ($1 <= N <= 100$, $1 <= H, W <= 10^9$, $1 <= R <= 10^6$). The following $N$ lines represent the coordinates of the points which the center of ICPC must reach. The ($i+1$)-th line consists of two integers $x_i$ and $y_i$ ($0 <= x_i, y_i <= 10^9$). $x_i$ and $y_i$ represent the $x$ and $y$ coordinates of the $i$-th point, respectively. It is guaranteed that the answer will not change even if $R$ changes by $1$.", "output": "If all the points can be placed in the laboratory, print 'Yes'. Otherwise, print 'No'.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 20 20 1\n10 0\n20 10\n10 20\n0 10\n output: Yes\n All the points can be placed in the laboratory by rotating them through $45$ degrees.", "input: 2 5 55 1\n0 0\n30 40\n output: Yes", "input: 2 5 49 1\n0 0\n30 40\n output: No", "input: 1 3 3 1\n114 514\n output: Yes"], "Pid": "p01952", "ProblemText": "Task Description: You are an employee of Automatic Cleaning Machine (ACM) and a member of the development team of Intelligent Circular Perfect Cleaner (ICPC). ICPC is a robot that cleans up the dust of the place which it passed through.\n\n Your task is an inspection of ICPC. This inspection is performed by checking whether the center of ICPC reaches all the $N$ given points.\n\nHowever, since the laboratory is small, it may be impossible to place all the points in the laboratory so that the entire body of ICPC is contained in the laboratory during the inspection. The laboratory is a rectangle of $H * W$ and ICPC is a circle of radius $R$. You decided to write a program to check whether you can place all the points in the laboratory by rotating and/or translating them while maintaining the distance between arbitrary two points.\nTask Input: The input consists of a single test case of the following format.\n\n$N$ $H$ $W$ $R$\n$x_1$ $y_1$\n:\n$x_N$ $y_N$\n\nThe first line consists of four integers $N, H, W$ and $R$ ($1 <= N <= 100$, $1 <= H, W <= 10^9$, $1 <= R <= 10^6$). The following $N$ lines represent the coordinates of the points which the center of ICPC must reach. The ($i+1$)-th line consists of two integers $x_i$ and $y_i$ ($0 <= x_i, y_i <= 10^9$). $x_i$ and $y_i$ represent the $x$ and $y$ coordinates of the $i$-th point, respectively. It is guaranteed that the answer will not change even if $R$ changes by $1$.\nTask Output: If all the points can be placed in the laboratory, print 'Yes'. Otherwise, print 'No'.\nTask Samples: input: 4 20 20 1\n10 0\n20 10\n10 20\n0 10\n output: Yes\n All the points can be placed in the laboratory by rotating them through $45$ degrees.\ninput: 2 5 55 1\n0 0\n30 40\n output: Yes\ninput: 2 5 49 1\n0 0\n30 40\n output: No\ninput: 1 3 3 1\n114 514\n output: Yes\n\n" }, { "title": "Librarian's Work", "content": "Japanese Animal Girl Library (JAG Library) is famous for a long bookshelf. It contains $N$ books numbered from $1$ to $N$ from left to right. The weight of the $i$-th book is $w_i$.\n\nOne day, naughty Fox Jiro shuffled the order of the books on the shelf! The order has become a permutation $b_1, . . . , b_N$ from left to right. Fox Hanako, a librarian of JAG Library, must restore the original order. She can rearrange a permutation of books $p_1, . . . , p_N$ by performing either operation A or operation B described below, with\narbitrary two integers $l$ and $r$ such that $1 <= l < r <= N$ holds.\n\t\t \n Operation A:\n\nA-1. Remove $p_l$ from the shelf.\n\nA-2. Shift books between $p_{l+1}$ and $p_r$ to $left$.\n\nA-3. Insert $p_l$ into the $right$ of $p_r$.\n Operation B:\n\nB-1. Remove $p_r$ from the shelf.\n\nB-2. Shift books between $p_l$ and $p_{r-1}$ to $right$.\n\nB-3. Insert $p_r$ into the $left$ of $p_l$.\nThis picture illustrates the orders of the books before and after applying operation A and B for $p = (3,1,4,5,2,6), l = 2, r = 5$.\n\nSince the books are heavy, operation A needs $\\sum_{i=l+1}^r w_{p_i} + C * (r-l) * w_{p_l}$ units of labor and operation B needs $\\sum_{i=l}^{r-1} w_{p_i} + C * (r-l) * w_{p_r}$ units of labor, where $C$ is a given constant positive integer.\n\nHanako must restore the initial order from $b_i, . . . , b_N$ by performing these operations repeatedly. Find the minimum sum of labor to achieve it.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$ $C$\n$b_1$ $w_{b_1}$\n:\n$b_N$ $w_{b_N}$\n\nThe first line conists of two integers $N$ and $C$ ($1 <= N <= 10^5,1 <= C <= 100$). The ($i+1$)-th line consists of two integers $b_i$ and $w_{b_i}$ ($1 <= b_i <= N, 1 <= w_{b_i} <= 10^5$). The sequence ($b_1, . . . , b_N$) is a permutation of ($1, . . . , N$).", "output": "Print the minimum sum of labor in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3 2\n2 3\n3 4\n1 2\n output: 15\nPerforming operation B with $l = 1, r = 3$, i.e. removing book 1 then inserting it into the left of book 2 is an optimal solution. It costs $(3+4)+2*2*2=15$ units of labor.", "input: 3 2\n1 2\n2 3\n3 3\n output: 0", "input: 10 5\n8 3\n10 6\n5 8\n2 7\n7 6\n1 9\n9 3\n6 2\n4 5\n3 5\n output: 824"], "Pid": "p01953", "ProblemText": "Task Description: Japanese Animal Girl Library (JAG Library) is famous for a long bookshelf. It contains $N$ books numbered from $1$ to $N$ from left to right. The weight of the $i$-th book is $w_i$.\n\nOne day, naughty Fox Jiro shuffled the order of the books on the shelf! The order has become a permutation $b_1, . . . , b_N$ from left to right. Fox Hanako, a librarian of JAG Library, must restore the original order. She can rearrange a permutation of books $p_1, . . . , p_N$ by performing either operation A or operation B described below, with\narbitrary two integers $l$ and $r$ such that $1 <= l < r <= N$ holds.\n\t\t \n Operation A:\n\nA-1. Remove $p_l$ from the shelf.\n\nA-2. Shift books between $p_{l+1}$ and $p_r$ to $left$.\n\nA-3. Insert $p_l$ into the $right$ of $p_r$.\n Operation B:\n\nB-1. Remove $p_r$ from the shelf.\n\nB-2. Shift books between $p_l$ and $p_{r-1}$ to $right$.\n\nB-3. Insert $p_r$ into the $left$ of $p_l$.\nThis picture illustrates the orders of the books before and after applying operation A and B for $p = (3,1,4,5,2,6), l = 2, r = 5$.\n\nSince the books are heavy, operation A needs $\\sum_{i=l+1}^r w_{p_i} + C * (r-l) * w_{p_l}$ units of labor and operation B needs $\\sum_{i=l}^{r-1} w_{p_i} + C * (r-l) * w_{p_r}$ units of labor, where $C$ is a given constant positive integer.\n\nHanako must restore the initial order from $b_i, . . . , b_N$ by performing these operations repeatedly. Find the minimum sum of labor to achieve it.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$ $C$\n$b_1$ $w_{b_1}$\n:\n$b_N$ $w_{b_N}$\n\nThe first line conists of two integers $N$ and $C$ ($1 <= N <= 10^5,1 <= C <= 100$). The ($i+1$)-th line consists of two integers $b_i$ and $w_{b_i}$ ($1 <= b_i <= N, 1 <= w_{b_i} <= 10^5$). The sequence ($b_1, . . . , b_N$) is a permutation of ($1, . . . , N$).\nTask Output: Print the minimum sum of labor in one line.\nTask Samples: input: 3 2\n2 3\n3 4\n1 2\n output: 15\nPerforming operation B with $l = 1, r = 3$, i.e. removing book 1 then inserting it into the left of book 2 is an optimal solution. It costs $(3+4)+2*2*2=15$ units of labor.\ninput: 3 2\n1 2\n2 3\n3 3\n output: 0\ninput: 10 5\n8 3\n10 6\n5 8\n2 7\n7 6\n1 9\n9 3\n6 2\n4 5\n3 5\n output: 824\n\n" }, { "title": "Sum Source Detection", "content": "JAG members began a game with integers. The game consists of $N + M + 1$ players: $N$ open number holders, $M$ secret number holders, and one answerer, you.\n\n In the preparation, an integer $K$ is told to all $N + M + 1$ players. $N + M$ number holders choose their own integers per person under the following restrictions:\n\nEach holder owns a positive integer.\n\nThe sum of all the integers equals $K$.\n\nEvery integer owned by secret number holders is strictly less than any integers owned by open number holders.\n After the choices, $N$ open number holders show their integers $O_1, . . . , O_N$ to the answerer while secret number holders do not.\n\nThe game has $Q$ rounds. At the beginning of each round, $M$ secret number holders can change their numbers under\nthe above restrictions, while open number holders cannot. Then $N + M$ number holders select part of members among\nthem arbitrary, calculate the sum $X$ of the integers owned by the selected members, and tell $X$ to the answerer. For\neach round, the answerer tries to identify the definitely selected open number holders from the information $K$, $X$, and $O_1, . . . , O_N$: The answerer will get points per actually selected open number holder in the answer. On the other hand, if the answer contains at least one non-selected member, you lose your points got in the round. Thus, the answerer, you, must answer only the open number holders such that the holders are definitely selected.\n\nYour task in this problem is to write a program to determine all the open number holders whose integers are necessary to the sum for each round in order to maximize your points.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$ $M$ $K$ $Q$\n$O_1$ . . . $O_N$\n$X_1$ . . . $X_Q$\n\n The first line consists of four integers $N, M, K, $ and $Q$. $N$ and $M$ are the numbers of open number holders and secret number holders respectively ($1 <= N, 0 <= M, N + M <= 40$). $K$ is an integer ($1 <= K <= 200,000$). $Q$ is the number of rounds of the game ($1 <= Q <= 10,000$).\n\n The second line contains $N$ integers $O_1, . . . , O_N$, as the $i$-th open number holder owns $O_i$ ($1 <= O_1 <= . . . <= O_N <= K$).\n\n The third line indicates $Q$ integers $X_1, . . . , X_Q$ ($0 <= X_i <= K$). $X_i$ is the sum of the integers owned by the selected members in the $i$-th round.\n\n It is guaranteed that there is at least one way to compose $X_i$. In other words, you can assume that there is at least one integer sequence $S_1, . . . , S_M$, which represents integers owned by secret number holders, satisfying the followings:\n\n$0 < S_j < O_1$ for $1 <= j <= M$. Note that $O_1 = min_{1<= k <= N}O_k$ holds.\n\n$\\sum_{j=1}^N O_j + \\sum_{k=1}^M S_k = K$.\n\nThere is at least one pair of subsets $U \\subseteq \\{1, . . . , N\\}$ and $V \\subseteq \\{1, . . . , M\\}$ such that $\\sum_{j\\in U} O_j + \\sum_{k\\in V}S_k = X_i$ holds.", "output": "On each sum $X_i$, print the indices of the open number holders whose integers are required to make up $X_i$. The output for each sum has to be printed in one line, in ascending order, and separated by a single space. If there is no open number holder whose integer is certainly used for $X_i$, print $-1$ in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 23 2\n7 10\n9 10\n output: 1\n-1\nThe first sum 9 can be achieved only by the first open number holder's 7 plus 2 of a secret number holder. In this case, secret number holders have 2 and 4. The second open number holder's 10 is a candidate for the second sum 10. The first open holder's 7 plus 3 is also possible one, as secret number holders have two 3s.", "input: 1 1 100 3\n51\n49 51 100\n output: -1\n1\n1\nThe only secret number holder owns 49. The output for the first sum is $-1$ because the open number holder's 51 is not selected.", "input: 2 1 58152 4\n575 57500\n575 57577 77 0\n output: 1\n2\n-1\n-1\nIn this case, the only secret number holder definitely has 77. The output for the last sum 0 is -1 because no integer of open number holders is needed to form 0.", "input: 3 2 1500 1\n99 300 1000\n99\n output: 1\nThe only way to compose 99 is to select the first open number holder only; secret number holders have two integers\nbetween 1 and 98, while the sum of them must be 101.", "input: 3 2 20 19\n3 3 11\n1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20\n output: -1\n-1\n-1\n-1\n-1\n-1\n1 2\n1 2\n1 2\n3\n3\n3\n3\n3\n3\n3\n1 2 3\n1 2 3\n1 2 3\nThe numbers owned by the two secret number holders are 1 and 2. At least one open number holder's 3 is required to\ncompose 5 and 6 respectively, but it is impossible to determine the definitely selected open number holder(s). On the other hand, 7 needs the two open number holders who both own 3."], "Pid": "p01954", "ProblemText": "Task Description: JAG members began a game with integers. The game consists of $N + M + 1$ players: $N$ open number holders, $M$ secret number holders, and one answerer, you.\n\n In the preparation, an integer $K$ is told to all $N + M + 1$ players. $N + M$ number holders choose their own integers per person under the following restrictions:\n\nEach holder owns a positive integer.\n\nThe sum of all the integers equals $K$.\n\nEvery integer owned by secret number holders is strictly less than any integers owned by open number holders.\n After the choices, $N$ open number holders show their integers $O_1, . . . , O_N$ to the answerer while secret number holders do not.\n\nThe game has $Q$ rounds. At the beginning of each round, $M$ secret number holders can change their numbers under\nthe above restrictions, while open number holders cannot. Then $N + M$ number holders select part of members among\nthem arbitrary, calculate the sum $X$ of the integers owned by the selected members, and tell $X$ to the answerer. For\neach round, the answerer tries to identify the definitely selected open number holders from the information $K$, $X$, and $O_1, . . . , O_N$: The answerer will get points per actually selected open number holder in the answer. On the other hand, if the answer contains at least one non-selected member, you lose your points got in the round. Thus, the answerer, you, must answer only the open number holders such that the holders are definitely selected.\n\nYour task in this problem is to write a program to determine all the open number holders whose integers are necessary to the sum for each round in order to maximize your points.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$ $M$ $K$ $Q$\n$O_1$ . . . $O_N$\n$X_1$ . . . $X_Q$\n\n The first line consists of four integers $N, M, K, $ and $Q$. $N$ and $M$ are the numbers of open number holders and secret number holders respectively ($1 <= N, 0 <= M, N + M <= 40$). $K$ is an integer ($1 <= K <= 200,000$). $Q$ is the number of rounds of the game ($1 <= Q <= 10,000$).\n\n The second line contains $N$ integers $O_1, . . . , O_N$, as the $i$-th open number holder owns $O_i$ ($1 <= O_1 <= . . . <= O_N <= K$).\n\n The third line indicates $Q$ integers $X_1, . . . , X_Q$ ($0 <= X_i <= K$). $X_i$ is the sum of the integers owned by the selected members in the $i$-th round.\n\n It is guaranteed that there is at least one way to compose $X_i$. In other words, you can assume that there is at least one integer sequence $S_1, . . . , S_M$, which represents integers owned by secret number holders, satisfying the followings:\n\n$0 < S_j < O_1$ for $1 <= j <= M$. Note that $O_1 = min_{1<= k <= N}O_k$ holds.\n\n$\\sum_{j=1}^N O_j + \\sum_{k=1}^M S_k = K$.\n\nThere is at least one pair of subsets $U \\subseteq \\{1, . . . , N\\}$ and $V \\subseteq \\{1, . . . , M\\}$ such that $\\sum_{j\\in U} O_j + \\sum_{k\\in V}S_k = X_i$ holds.\nTask Output: On each sum $X_i$, print the indices of the open number holders whose integers are required to make up $X_i$. The output for each sum has to be printed in one line, in ascending order, and separated by a single space. If there is no open number holder whose integer is certainly used for $X_i$, print $-1$ in one line.\nTask Samples: input: 2 2 23 2\n7 10\n9 10\n output: 1\n-1\nThe first sum 9 can be achieved only by the first open number holder's 7 plus 2 of a secret number holder. In this case, secret number holders have 2 and 4. The second open number holder's 10 is a candidate for the second sum 10. The first open holder's 7 plus 3 is also possible one, as secret number holders have two 3s.\ninput: 1 1 100 3\n51\n49 51 100\n output: -1\n1\n1\nThe only secret number holder owns 49. The output for the first sum is $-1$ because the open number holder's 51 is not selected.\ninput: 2 1 58152 4\n575 57500\n575 57577 77 0\n output: 1\n2\n-1\n-1\nIn this case, the only secret number holder definitely has 77. The output for the last sum 0 is -1 because no integer of open number holders is needed to form 0.\ninput: 3 2 1500 1\n99 300 1000\n99\n output: 1\nThe only way to compose 99 is to select the first open number holder only; secret number holders have two integers\nbetween 1 and 98, while the sum of them must be 101.\ninput: 3 2 20 19\n3 3 11\n1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20\n output: -1\n-1\n-1\n-1\n-1\n-1\n1 2\n1 2\n1 2\n3\n3\n3\n3\n3\n3\n3\n1 2 3\n1 2 3\n1 2 3\nThe numbers owned by the two secret number holders are 1 and 2. At least one open number holder's 3 is required to\ncompose 5 and 6 respectively, but it is impossible to determine the definitely selected open number holder(s). On the other hand, 7 needs the two open number holders who both own 3.\n\n" }, { "title": "Permutation Period", "content": "You have a permutation $p$ of $N$ integers. Initially $p_i = i$ holds for $1 <= i <= N$. For each $j$ ($1 <= j <= N$), let's denote $p_{j}^0 = j$ and $p_{j}^k = p_{p_j}^{k-1}$ for any $k>= 1$. The period of $p$ is defined as the minimum positive integer $k$ which satisfies $p_{j}^k = j$ for every $j$ ($1 <= j <= N$).\n\n You are given $Q$ queries. The $i$-th query is characterized by two distinct indices $x_i$ and $y_i$. For each query, swap $p_{x_i}$ and $p_{y_i}$ and then calculate the period of updated $p$ modulo $10^9 + 7$ in the given order.\n\nIt can be proved that the period of $p$ always exists.", "constraint": "", "input": "The input consists of a single test case of the following format.\n\n$N$ $Q$\n$x_1$ $y_1$\n. . .\n$x_Q$ $y_Q$\n\nThe first line consists of two integers $N$ and $Q$ ($2 <= N <= 10^5,1 <= Q <= 10^5$). The ($i+1$)-th line consists of two integers $x_i$ and $y_i$ ($1 <= x_i, y_i <= N, x_i \\ne y_i$).", "output": "Print the answer in one line for each query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n2 5\n2 4\n1 3\n1 2\n output: 2\n3\n6\n5\n$p$ changes as follows: $[1,2,3,4,5] \\rightarrow [1,5,3,4,2] \\rightarrow [1,4,3,5,2] \\rightarrow [3,4,1,5,2] \\rightarrow [4,3,1,5,2]$.", "input: 2 2\n1 2\n1 2\n output: 2\n1\n$p$ changes as follows: $[1,2] \\rightarrow [2,1] \\rightarrow [1,2]$.", "input: 10 10\n5 6\n5 9\n8 2\n1 6\n8 1\n7 1\n2 6\n8 1\n7 4\n8 10\n output: 2\n3\n6\n4\n6\n7\n12\n7\n8\n9"], "Pid": "p01955", "ProblemText": "Task Description: You have a permutation $p$ of $N$ integers. Initially $p_i = i$ holds for $1 <= i <= N$. For each $j$ ($1 <= j <= N$), let's denote $p_{j}^0 = j$ and $p_{j}^k = p_{p_j}^{k-1}$ for any $k>= 1$. The period of $p$ is defined as the minimum positive integer $k$ which satisfies $p_{j}^k = j$ for every $j$ ($1 <= j <= N$).\n\n You are given $Q$ queries. The $i$-th query is characterized by two distinct indices $x_i$ and $y_i$. For each query, swap $p_{x_i}$ and $p_{y_i}$ and then calculate the period of updated $p$ modulo $10^9 + 7$ in the given order.\n\nIt can be proved that the period of $p$ always exists.\nTask Input: The input consists of a single test case of the following format.\n\n$N$ $Q$\n$x_1$ $y_1$\n. . .\n$x_Q$ $y_Q$\n\nThe first line consists of two integers $N$ and $Q$ ($2 <= N <= 10^5,1 <= Q <= 10^5$). The ($i+1$)-th line consists of two integers $x_i$ and $y_i$ ($1 <= x_i, y_i <= N, x_i \\ne y_i$).\nTask Output: Print the answer in one line for each query.\nTask Samples: input: 5 4\n2 5\n2 4\n1 3\n1 2\n output: 2\n3\n6\n5\n$p$ changes as follows: $[1,2,3,4,5] \\rightarrow [1,5,3,4,2] \\rightarrow [1,4,3,5,2] \\rightarrow [3,4,1,5,2] \\rightarrow [4,3,1,5,2]$.\ninput: 2 2\n1 2\n1 2\n output: 2\n1\n$p$ changes as follows: $[1,2] \\rightarrow [2,1] \\rightarrow [1,2]$.\ninput: 10 10\n5 6\n5 9\n8 2\n1 6\n8 1\n7 1\n2 6\n8 1\n7 4\n8 10\n output: 2\n3\n6\n4\n6\n7\n12\n7\n8\n9\n\n" }, { "title": "Window", "content": "In the building of Jewelry Art Gallery (JAG), there is a long corridor in the east-west direction. There is a window on the north side of the corridor, and $N$ windowpanes are attached to this window. The width of each windowpane is $W$, and the height is $H$. The $i$-th windowpane from the west covers the horizontal range between $W*(i-1)$ and $W* i$ from the west edge of the window.\n You received instructions from the manager of JAG about how to slide the windowpanes. These instructions consist of $N$ integers $x_1, x_2, . . . , x_N$, and $x_i <=W$ is satisfied for all $i$. For the $i$-th windowpane, if $i$ is odd, you have to slide $i$-th windowpane to the east by $x_i$, otherwise, you have to slide $i$-th windowpane to the west by $x_i$.\n You can assume that the windowpanes will not collide each other even if you slide windowpanes according to the instructions. In more detail, $N$ windowpanes are alternately mounted on two rails. That is, the $i$-th windowpane is attached to the inner rail of the building if $i$ is odd, otherwise, it is attached to the outer rail of the building.\nBefore you execute the instructions, you decide to obtain the area where the window is open after the instructions.", "constraint": "", "input": "The input consists of a single test case in the format below.\n\n$N$ $H$ $W$\n$x_1$ . . . $x_N$\n\nThe first line consists of three integers $N, H, $ and $W$ ($1 <= N <= 100,1 <= H, W <= 100$). It is guaranteed that $N$ is even. The following line consists of $N$ integers $x_1, . . . , x_N$ while represent the instructions from the manager of JAG. $x_i$ represents the distance to slide the $i$-th windowpane ($0 <= x_i <= W$).", "output": "Print the area where the window is open after the instructions in one line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4 3 3\n1 1 2 3\n output: 9", "input: 8 10 18\n2 12 16 14 18 4 17 16\n output: 370", "input: 6 2 2\n0 2 2 2 2 0\n output: 8", "input: 4 1 4\n3 3 2 2\n output: 6", "input: 8 7 15\n5 0 9 14 0 4 4 15\n output: 189\nFigure A2. Illustration of Sample Input 1"], "Pid": "p01956", "ProblemText": "Task Description: In the building of Jewelry Art Gallery (JAG), there is a long corridor in the east-west direction. There is a window on the north side of the corridor, and $N$ windowpanes are attached to this window. The width of each windowpane is $W$, and the height is $H$. The $i$-th windowpane from the west covers the horizontal range between $W*(i-1)$ and $W* i$ from the west edge of the window.\n You received instructions from the manager of JAG about how to slide the windowpanes. These instructions consist of $N$ integers $x_1, x_2, . . . , x_N$, and $x_i <=W$ is satisfied for all $i$. For the $i$-th windowpane, if $i$ is odd, you have to slide $i$-th windowpane to the east by $x_i$, otherwise, you have to slide $i$-th windowpane to the west by $x_i$.\n You can assume that the windowpanes will not collide each other even if you slide windowpanes according to the instructions. In more detail, $N$ windowpanes are alternately mounted on two rails. That is, the $i$-th windowpane is attached to the inner rail of the building if $i$ is odd, otherwise, it is attached to the outer rail of the building.\nBefore you execute the instructions, you decide to obtain the area where the window is open after the instructions.\nTask Input: The input consists of a single test case in the format below.\n\n$N$ $H$ $W$\n$x_1$ . . . $x_N$\n\nThe first line consists of three integers $N, H, $ and $W$ ($1 <= N <= 100,1 <= H, W <= 100$). It is guaranteed that $N$ is even. The following line consists of $N$ integers $x_1, . . . , x_N$ while represent the instructions from the manager of JAG. $x_i$ represents the distance to slide the $i$-th windowpane ($0 <= x_i <= W$).\nTask Output: Print the area where the window is open after the instructions in one line.\nTask Samples: input: 4 3 3\n1 1 2 3\n output: 9\ninput: 8 10 18\n2 12 16 14 18 4 17 16\n output: 370\ninput: 6 2 2\n0 2 2 2 2 0\n output: 8\ninput: 4 1 4\n3 3 2 2\n output: 6\ninput: 8 7 15\n5 0 9 14 0 4 4 15\n output: 189\nFigure A2. Illustration of Sample Input 1\n\n" }, { "title": "Tournament Chart", "content": "In 21XX, an annual programming contest, Japan Algorithmist Grand Prix (JAG) has become one of the most popular mind sports events.\n\n JAG is conducted as a knockout tournament. This year, $N$ contestants will compete in JAG. A tournament chart is represented as a string. '[[a-b]-[c-d]]' is an easy example. In this case, there are 4 contestants named a, b, c, and d, and all matches are described as follows:\n\nMatch 1 is the match between a and b.\n\nMatch 2 is the match between c and d.\n\nMatch 3 is the match between [the winner of match 1] and [the winner of match 2].\n More precisely, the tournament chart satisfies the following BNF:\n\n : : = | \"[\" \"-\" \"]\"\n\n : : = \"a\" | \"b\" | \"c\" | . . . | \"z\"\n\n

    \n You, the chairperson of JAG, are planning to announce the results of this year's JAG competition. However, you made a mistake and lost the results of all the matches. Fortunately, you found the tournament chart that was printed before all of the matches of the tournament. Of course, it does not contains results at all. Therefore, you asked every contestant for the number of wins in the tournament, and got $N$ pieces of information in the form of \"The contestant $a_i$ won $v_i$ times\".\n\nNow, your job is to determine whether all of these replies can be true.", "constraint": "", "input": "The input consists of a single test case in the format below.\n\n$S$\n$a_1$ $v_1$\n:\n$a_N$ $v_N$\n\n$S$ represents the tournament chart. $S$ satisfies the above BNF. The following $N$ lines represent the information of the number of wins. The ($i+1$)-th line consists of a lowercase letter $a_i$ and a non-negative integer $v_i$ ($v_i <= 26$) separated by a space, and this means that the contestant $a_i$ won $v_i$ times. Note that $N$ ($2 <= N <= 26$) means that the number of contestants and it can be identified by string $S$. You can assume that each letter $a_i$ is distinct. It is guaranteed that $S$ contains each $a_i$ exactly once and doesn't contain any other lowercase letters.", "output": "Print 'Yes' in one line if replies are all valid for the tournament chart. Otherwise, print 'No' in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: [[m-y]-[a-o]]\no 0\na 1\ny 2\nm 0\n output: Yes", "input: [[r-i]-[m-e]]\ne 0\nr 1\ni 1\nm 2\n output: No"], "Pid": "p01957", "ProblemText": "Task Description: In 21XX, an annual programming contest, Japan Algorithmist Grand Prix (JAG) has become one of the most popular mind sports events.\n\n JAG is conducted as a knockout tournament. This year, $N$ contestants will compete in JAG. A tournament chart is represented as a string. '[[a-b]-[c-d]]' is an easy example. In this case, there are 4 contestants named a, b, c, and d, and all matches are described as follows:\n\nMatch 1 is the match between a and b.\n\nMatch 2 is the match between c and d.\n\nMatch 3 is the match between [the winner of match 1] and [the winner of match 2].\n More precisely, the tournament chart satisfies the following BNF:\n\n : : = | \"[\" \"-\" \"]\"\n\n : : = \"a\" | \"b\" | \"c\" | . . . | \"z\"\n\n

    \n You, the chairperson of JAG, are planning to announce the results of this year's JAG competition. However, you made a mistake and lost the results of all the matches. Fortunately, you found the tournament chart that was printed before all of the matches of the tournament. Of course, it does not contains results at all. Therefore, you asked every contestant for the number of wins in the tournament, and got $N$ pieces of information in the form of \"The contestant $a_i$ won $v_i$ times\".\n\nNow, your job is to determine whether all of these replies can be true.\nTask Input: The input consists of a single test case in the format below.\n\n$S$\n$a_1$ $v_1$\n:\n$a_N$ $v_N$\n\n$S$ represents the tournament chart. $S$ satisfies the above BNF. The following $N$ lines represent the information of the number of wins. The ($i+1$)-th line consists of a lowercase letter $a_i$ and a non-negative integer $v_i$ ($v_i <= 26$) separated by a space, and this means that the contestant $a_i$ won $v_i$ times. Note that $N$ ($2 <= N <= 26$) means that the number of contestants and it can be identified by string $S$. You can assume that each letter $a_i$ is distinct. It is guaranteed that $S$ contains each $a_i$ exactly once and doesn't contain any other lowercase letters.\nTask Output: Print 'Yes' in one line if replies are all valid for the tournament chart. Otherwise, print 'No' in one line.\nTask Samples: input: [[m-y]-[a-o]]\no 0\na 1\ny 2\nm 0\n output: Yes\ninput: [[r-i]-[m-e]]\ne 0\nr 1\ni 1\nm 2\n output: No\n\n" }, { "title": "Prime-Factor Prime", "content": "A positive integer is called a \"prime-factor prime\" when the number of its prime factors is prime. For example, $12$ is a prime-factor prime because the number of prime factors of $12 = 2 * 2 * 3$ is $3$, which is prime. On the other hand, $210$ is not a prime-factor prime because the number of prime factors of $210 = 2 * 3 * 5 * 7$ is $4$, which is a composite number.\n\nIn this problem, you are given an integer interval $[l, r]$. Your task is to write a program which counts the number of prime-factor prime numbers in the interval, i. e. the number of prime-factor prime numbers between $l$ and $r$, inclusive.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$l$ $r$\n\nA line contains two integers $l$ and $r$ ($1 <= l <= r <= 10^9$), which presents an integer interval $[l, r]$. You can assume that $0 <= r-l < 1,000,000$.", "output": "Print the number of prime-factor prime numbers in $[l, r]$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 9\n output: 4", "input: 10 20\n output: 6", "input: 575 57577\n output: 36172", "input: 180 180\n output: 1", "input: 9900001 10000000\n output: 60997", "input: 999000001 1000000000\n output: 592955\nIn the first example, there are 4 prime-factor primes in $[l,r]$: $4,6,8,$ and $9$."], "Pid": "p01958", "ProblemText": "Task Description: A positive integer is called a \"prime-factor prime\" when the number of its prime factors is prime. For example, $12$ is a prime-factor prime because the number of prime factors of $12 = 2 * 2 * 3$ is $3$, which is prime. On the other hand, $210$ is not a prime-factor prime because the number of prime factors of $210 = 2 * 3 * 5 * 7$ is $4$, which is a composite number.\n\nIn this problem, you are given an integer interval $[l, r]$. Your task is to write a program which counts the number of prime-factor prime numbers in the interval, i. e. the number of prime-factor prime numbers between $l$ and $r$, inclusive.\nTask Input: The input consists of a single test case formatted as follows.\n\n$l$ $r$\n\nA line contains two integers $l$ and $r$ ($1 <= l <= r <= 10^9$), which presents an integer interval $[l, r]$. You can assume that $0 <= r-l < 1,000,000$.\nTask Output: Print the number of prime-factor prime numbers in $[l, r]$.\nTask Samples: input: 1 9\n output: 4\ninput: 10 20\n output: 6\ninput: 575 57577\n output: 36172\ninput: 180 180\n output: 1\ninput: 9900001 10000000\n output: 60997\ninput: 999000001 1000000000\n output: 592955\nIn the first example, there are 4 prime-factor primes in $[l,r]$: $4,6,8,$ and $9$.\n\n" }, { "title": "Revenge of the Broken Door", "content": "The JAG Kingdom consists of $N$ cities and $M$ bidirectional roads. The $i$-th road ($u_i, v_i, c_i$) connects the city $u_i$ and the city $v_i$ with the length $c_i$. One day, you, a citizen of the JAG Kingdom, decided to go to the city $T$ from the city $S$. However, you know that one of the roads in the JAG Kingdom is currently under construction and you cannot pass the road. You don't know which road it is. You can know whether a road is under construction only when you are in either city connected by the road.\n\nYour task is to minimize the total length of the route in the worst case. You don't need to decide a route in advance of departure and you can choose where to go next at any time. If you cannot reach the city $T$ in the worst case, output '-1'.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$ $M$ $S$ $T$\n$u_1$ $v_1$ $c_1$\n:\n$u_M$ $v_M$ $c_M$\n\nThe first line contains four integers $N, M, S, $ and $T$, where $N$ is the number of the cities ($2 <= N <= 100,000$), $M$ is the number of the bidirectional roads ($1 <= M <= 200,000$), $S$ is the city you start from ($1 <= S <= N$), and $T$ is the city you want to reach to ($1 <= T <= N, S \\ne T$). The following $M$ lines represent road information: the $i$-th line of the $M$ lines consists of three integers $u_i, v_i, c_i, $ which means the $i$-th road connects the cities $u_i$ and $v_i$ ($1 <= u_i, v_i <= N, u_i \\ne v_i$) with the length $c_i$ ($1 <= c_i <= 10^9$). You can assume that all the pairs of the cities are connected if no road is under construction. That is, there is at least one route from city $x$ to city $y$ with given roads, for all cities $x$ and $y$. It is also guaranteed that there are no multiple-edges, i. e. , $\\{u_i, v_i\\} \\ne \\{u_j, v_j\\}$ for all $1 <= i < j <= M$.", "output": "Output the minimum total length of the route in the worst case. If you cannot reach the city $T$ in the worst case, output '-1'.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 1 3\n1 2 1\n2 3 5\n1 3 3\n output: 6", "input: 4 4 1 4\n1 2 1\n2 4 1\n1 3 1\n3 4 1\n output: 4", "input: 5 4 4 1\n1 2 3\n2 3 4\n3 4 5\n4 5 6\n output: -1"], "Pid": "p01959", "ProblemText": "Task Description: The JAG Kingdom consists of $N$ cities and $M$ bidirectional roads. The $i$-th road ($u_i, v_i, c_i$) connects the city $u_i$ and the city $v_i$ with the length $c_i$. One day, you, a citizen of the JAG Kingdom, decided to go to the city $T$ from the city $S$. However, you know that one of the roads in the JAG Kingdom is currently under construction and you cannot pass the road. You don't know which road it is. You can know whether a road is under construction only when you are in either city connected by the road.\n\nYour task is to minimize the total length of the route in the worst case. You don't need to decide a route in advance of departure and you can choose where to go next at any time. If you cannot reach the city $T$ in the worst case, output '-1'.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$ $M$ $S$ $T$\n$u_1$ $v_1$ $c_1$\n:\n$u_M$ $v_M$ $c_M$\n\nThe first line contains four integers $N, M, S, $ and $T$, where $N$ is the number of the cities ($2 <= N <= 100,000$), $M$ is the number of the bidirectional roads ($1 <= M <= 200,000$), $S$ is the city you start from ($1 <= S <= N$), and $T$ is the city you want to reach to ($1 <= T <= N, S \\ne T$). The following $M$ lines represent road information: the $i$-th line of the $M$ lines consists of three integers $u_i, v_i, c_i, $ which means the $i$-th road connects the cities $u_i$ and $v_i$ ($1 <= u_i, v_i <= N, u_i \\ne v_i$) with the length $c_i$ ($1 <= c_i <= 10^9$). You can assume that all the pairs of the cities are connected if no road is under construction. That is, there is at least one route from city $x$ to city $y$ with given roads, for all cities $x$ and $y$. It is also guaranteed that there are no multiple-edges, i. e. , $\\{u_i, v_i\\} \\ne \\{u_j, v_j\\}$ for all $1 <= i < j <= M$.\nTask Output: Output the minimum total length of the route in the worst case. If you cannot reach the city $T$ in the worst case, output '-1'.\nTask Samples: input: 3 3 1 3\n1 2 1\n2 3 5\n1 3 3\n output: 6\ninput: 4 4 1 4\n1 2 1\n2 4 1\n1 3 1\n3 4 1\n output: 4\ninput: 5 4 4 1\n1 2 3\n2 3 4\n3 4 5\n4 5 6\n output: -1\n\n" }, { "title": "Tree Separator", "content": "You are given a tree $T$ and an integer $K$. You can choose arbitrary distinct two vertices $u$ and $v$ on $T$. Let $P$ be the simple path between $u$ and $v$. Then, remove vertices in $P$, and edges such that one or both of its end vertices is in $P$ from $T$. Your task is to choose $u$ and $v$ to maximize the number of connected components with $K$ or more vertices of $T$ after that operation.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$ $K$\n$u_1$ $v_1$\n:\n$u_{N-1}$ $v_{N-1}$\n\nThe first line consists of two integers $N, K$ ($2 <= N <= 100,000,1 <= K <= N$). The following $N-1$ lines represent the information of edges. The ($i+1$)-th line consists of two integers $u_i, v_i$ ($1 <= u_i, v_i <= N$ and $u_i \\ne v_i $ for each $i$). Each $\\{u_i, v_i\\}$ is an edge of $T$. It's guaranteed that these edges form a tree.", "output": "Print the maximum number of connected components with $K$ or more vertices in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n1 2\n output: 0", "input: 7 3\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n output: 1", "input: 12 2\n1 2\n2 3\n3 4\n4 5\n3 6\n6 7\n7 8\n8 9\n6 10\n10 11\n11 12\n output: 4", "input: 3 1\n1 2\n2 3\n output: 1", "input: 3 2\n1 2\n2 3\n output: 0", "input: 9 3\n1 2\n1 3\n1 4\n4 5\n4 6\n4 7\n7 8\n7 9\n output: 2"], "Pid": "p01960", "ProblemText": "Task Description: You are given a tree $T$ and an integer $K$. You can choose arbitrary distinct two vertices $u$ and $v$ on $T$. Let $P$ be the simple path between $u$ and $v$. Then, remove vertices in $P$, and edges such that one or both of its end vertices is in $P$ from $T$. Your task is to choose $u$ and $v$ to maximize the number of connected components with $K$ or more vertices of $T$ after that operation.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$ $K$\n$u_1$ $v_1$\n:\n$u_{N-1}$ $v_{N-1}$\n\nThe first line consists of two integers $N, K$ ($2 <= N <= 100,000,1 <= K <= N$). The following $N-1$ lines represent the information of edges. The ($i+1$)-th line consists of two integers $u_i, v_i$ ($1 <= u_i, v_i <= N$ and $u_i \\ne v_i $ for each $i$). Each $\\{u_i, v_i\\}$ is an edge of $T$. It's guaranteed that these edges form a tree.\nTask Output: Print the maximum number of connected components with $K$ or more vertices in one line.\nTask Samples: input: 2 1\n1 2\n output: 0\ninput: 7 3\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n output: 1\ninput: 12 2\n1 2\n2 3\n3 4\n4 5\n3 6\n6 7\n7 8\n8 9\n6 10\n10 11\n11 12\n output: 4\ninput: 3 1\n1 2\n2 3\n output: 1\ninput: 3 2\n1 2\n2 3\n output: 0\ninput: 9 3\n1 2\n1 3\n1 4\n4 5\n4 6\n4 7\n7 8\n7 9\n output: 2\n\n" }, { "title": "RPG Maker", "content": "You are planning to create a map of an RPG. This map is represented by a grid whose size is $H * W$. Each cell in this grid is either '@', '*', '#', or '. '. The meanings of the symbols are as follows.\n\n'@': The start cell. The story should start from this cell.\n\n'*': A city cell. The story goes through or ends with this cell.\n\n'#': A road cell.\n\n'. ': An empty cell.\n You have already located the start cell and all city cells under some constraints described in the input section, but no road cells have been located yet. Then, you should decide which cells to set as road cells.\n\n Here, you want a \"journey\" exists on this map. Because you want to remove the branch of the story, the journey has to be unforked. More formally, the journey is a sequence of cells and must satisfy the following conditions:\n\n The journey must contain as many city cells as possible. \n\n The journey must consist of distinct non-empty cells in this map.\n\n The journey must begin with the start cell.\n\n The journey must end with one of the city cells.\n\n The journey must contain all road cells. That is, road cells not included in the journey must not exist.\n\n The journey must be unforked. In more detail, all road cells and city cells except for a cell at the end of the journey must share edges with the other two cells both of which are also contained in the journey. Then, each of the start cell and a cell at the end of the journey must share an edge with another cell contained in the journey.\n\n You do not have to consider the order of the cities to visit during the journey.\nInitially, the map contains no road cells. You can change any empty cells to road cells to make a journey satisfying the conditions above. Your task is to print a map which maximizes the number of cities in the journey.", "constraint": "", "input": "The input consists of a single test case of the following form.\n\n$H$ $W$\n$S_1$\n$S_2$\n:\n$S_H$\n\nThe first line consists of two integers $N$ and $W$. $H$ and $W$ are guaranteed to satisfy $H = 4n - 1$ and $W = 4m -1$ for some positive integers $n$ and $m$ ($1 <= n, m <= 10$). The following $H$ lines represent a map without road cells. The ($i+1$)-th line consists of a string $S_i$ of length $W$. The $j$-th character of $S_i$ is either '*', '@' or '. ' if both $i$ and $j$ are odd, otherwise '. '. The number of occurrences of '@' in the grid is exactly one. It is guaranteed that there are one or more city cells on the grid.", "output": "Print a map indicating a journey. If several maps satisfy the condition, you can print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11 7\n.......\n.......\n*.....*\n.......\n..@....\n.......\n*......\n.......\n....*..\n.......\n.......\n output: .......\n.......\n*#####*\n......#\n..@...#\n..#.###\n*##.#..\n#...#..\n####*..\n.......\n.......", "input: 7 11\n........*..\n...........\n...........\n...........\n....*...*..\n...........\n..*.@...*..\n output: ........*..\n........#..\n........#..\n........#..\n..##*##.*..\n..#...#.#..\n..*#@.##*.."], "Pid": "p01961", "ProblemText": "Task Description: You are planning to create a map of an RPG. This map is represented by a grid whose size is $H * W$. Each cell in this grid is either '@', '*', '#', or '. '. The meanings of the symbols are as follows.\n\n'@': The start cell. The story should start from this cell.\n\n'*': A city cell. The story goes through or ends with this cell.\n\n'#': A road cell.\n\n'. ': An empty cell.\n You have already located the start cell and all city cells under some constraints described in the input section, but no road cells have been located yet. Then, you should decide which cells to set as road cells.\n\n Here, you want a \"journey\" exists on this map. Because you want to remove the branch of the story, the journey has to be unforked. More formally, the journey is a sequence of cells and must satisfy the following conditions:\n\n The journey must contain as many city cells as possible. \n\n The journey must consist of distinct non-empty cells in this map.\n\n The journey must begin with the start cell.\n\n The journey must end with one of the city cells.\n\n The journey must contain all road cells. That is, road cells not included in the journey must not exist.\n\n The journey must be unforked. In more detail, all road cells and city cells except for a cell at the end of the journey must share edges with the other two cells both of which are also contained in the journey. Then, each of the start cell and a cell at the end of the journey must share an edge with another cell contained in the journey.\n\n You do not have to consider the order of the cities to visit during the journey.\nInitially, the map contains no road cells. You can change any empty cells to road cells to make a journey satisfying the conditions above. Your task is to print a map which maximizes the number of cities in the journey.\nTask Input: The input consists of a single test case of the following form.\n\n$H$ $W$\n$S_1$\n$S_2$\n:\n$S_H$\n\nThe first line consists of two integers $N$ and $W$. $H$ and $W$ are guaranteed to satisfy $H = 4n - 1$ and $W = 4m -1$ for some positive integers $n$ and $m$ ($1 <= n, m <= 10$). The following $H$ lines represent a map without road cells. The ($i+1$)-th line consists of a string $S_i$ of length $W$. The $j$-th character of $S_i$ is either '*', '@' or '. ' if both $i$ and $j$ are odd, otherwise '. '. The number of occurrences of '@' in the grid is exactly one. It is guaranteed that there are one or more city cells on the grid.\nTask Output: Print a map indicating a journey. If several maps satisfy the condition, you can print any of them.\nTask Samples: input: 11 7\n.......\n.......\n*.....*\n.......\n..@....\n.......\n*......\n.......\n....*..\n.......\n.......\n output: .......\n.......\n*#####*\n......#\n..@...#\n..#.###\n*##.#..\n#...#..\n####*..\n.......\n.......\ninput: 7 11\n........*..\n...........\n...........\n...........\n....*...*..\n...........\n..*.@...*..\n output: ........*..\n........#..\n........#..\n........#..\n..##*##.*..\n..#...#.#..\n..*#@.##*..\n\n" }, { "title": "Coin Slider", "content": "You are playing a coin puzzle. The rule of this puzzle is as follows:\n\n There are $N$ coins on a table. The $i$-th coin is a circle with $r_i$ radius, and its center is initially placed at ($sx_i, sy_i$). Each coin also has a target position: you should move the $i$-th coin so that its center is at ($tx_i, ty_i$). You can move coins one by one and can move each coin at most once. When you move a coin, it must move from its initial position to its target position along the straight line. In addition, coins cannot collide with each other, including in the middle of moves.\n\nThe score of the puzzle is the number of the coins you move from their initial position to their target position. Your task is to write a program that determines the maximum score for a given puzzle instance.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$\n$r_1$ $sx_1$ $sy_1$ $tx_1$ $ty_1$\n:\n$r_N$ $sx_N$ $sy_N$ $tx_1$ $ty_N$\n\nThe first line contains an integer $N$ ($1 <= N <= 16$), which is the number of coins used in the puzzle. The $i$-th line of the following $N$ lines consists of five integers: $r_i, sx_i, sy_i, tx_i, $ and $ty_i$ ($1 <= r_i <= 1,000, -1,000 <= sx_i, sy_i, tx_i, ty_i <= 1,000, (sx_i, sy_i) \\ne (tx_i, ty_i)$). They describe the information of the $i$-th coin: $r_i$\nis the radius of the $i$-th coin, $(sx_i, sy_i)$ is the initial position of the $i$-th coin, and $(tx_i, ty_i)$ is the target position of the $i$-th coin.\n\nYou can assume that the coins do not contact or are not overlapped with each other at the initial positions. You can also assume that the maximum score does not change even if the radius of each coin changes by $10^{-5}$.", "output": "Print the maximum score of the given puzzle instance in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n2 0 0 1 0\n2 0 5 1 5\n4 1 -10 -5 10\n output: 2", "input: 3\n1 0 0 5 0\n1 0 5 0 0\n1 5 5 0 5\n output: 3", "input: 4\n1 0 0 5 0\n1 0 5 0 0\n1 5 5 0 5\n1 5 0 0 0\n output: 0\nIn the first example, the third coin cannot move because it is disturbed by the other two coins."], "Pid": "p01962", "ProblemText": "Task Description: You are playing a coin puzzle. The rule of this puzzle is as follows:\n\n There are $N$ coins on a table. The $i$-th coin is a circle with $r_i$ radius, and its center is initially placed at ($sx_i, sy_i$). Each coin also has a target position: you should move the $i$-th coin so that its center is at ($tx_i, ty_i$). You can move coins one by one and can move each coin at most once. When you move a coin, it must move from its initial position to its target position along the straight line. In addition, coins cannot collide with each other, including in the middle of moves.\n\nThe score of the puzzle is the number of the coins you move from their initial position to their target position. Your task is to write a program that determines the maximum score for a given puzzle instance.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$\n$r_1$ $sx_1$ $sy_1$ $tx_1$ $ty_1$\n:\n$r_N$ $sx_N$ $sy_N$ $tx_1$ $ty_N$\n\nThe first line contains an integer $N$ ($1 <= N <= 16$), which is the number of coins used in the puzzle. The $i$-th line of the following $N$ lines consists of five integers: $r_i, sx_i, sy_i, tx_i, $ and $ty_i$ ($1 <= r_i <= 1,000, -1,000 <= sx_i, sy_i, tx_i, ty_i <= 1,000, (sx_i, sy_i) \\ne (tx_i, ty_i)$). They describe the information of the $i$-th coin: $r_i$\nis the radius of the $i$-th coin, $(sx_i, sy_i)$ is the initial position of the $i$-th coin, and $(tx_i, ty_i)$ is the target position of the $i$-th coin.\n\nYou can assume that the coins do not contact or are not overlapped with each other at the initial positions. You can also assume that the maximum score does not change even if the radius of each coin changes by $10^{-5}$.\nTask Output: Print the maximum score of the given puzzle instance in a line.\nTask Samples: input: 3\n2 0 0 1 0\n2 0 5 1 5\n4 1 -10 -5 10\n output: 2\ninput: 3\n1 0 0 5 0\n1 0 5 0 0\n1 5 5 0 5\n output: 3\ninput: 4\n1 0 0 5 0\n1 0 5 0 0\n1 5 5 0 5\n1 5 0 0 0\n output: 0\nIn the first example, the third coin cannot move because it is disturbed by the other two coins.\n\n" }, { "title": "Separate String", "content": "You are given a string $t$ and a set $S$ of $N$ different strings. You need to separate $t$ such that each part is included in $S$.\n\n For example, the following 4 separation methods satisfy the condition when $t = abab$ and $S = \\{a, ab, b\\}$.\n\n$a, b, a, b$\n\n$a, b, ab$\n\n$ab, a, b$\n\n$ab, ab$\nYour task is to count the number of ways to separate $t$. Because the result can be large, you should output the remainder divided by $1,000,000,007$.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$\n$s_1$\n:\n$s_N$\n$t$\n\nThe first line consists of an integer $N$ ($1 <= N <= 100,000$) which is the number of the elements of $S$. The following $N$ lines consist of $N$ distinct strings separated by line breaks. The $i$-th string $s_i$ represents the $i$-th element of $S$. $s_i$ consists of lowercase letters and the length is between $1$ and $100,000$, inclusive. The summation of length of $s_i$ ($1 <= i <= N$) is at most $200,000$. The next line consists of a string $t$ which consists of lowercase letters and represents the string to be separated and the length is between $1$ and $100,000$, inclusive.", "output": "Calculate the number of ways to separate $t$ and print the remainder divided by $1,000,000,007$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\na\nb\nab\nabab\n output: 4", "input: 3\na\nb\nc\nxyz\n output: 0", "input: 7\nabc\nab\nbc\na\nb\nc\naa\naaabcbccababbc\n output: 160", "input: 10\na\naa\naaa\naaaa\naaaaa\naaaaaa\naaaaaaa\naaaaaaaa\naaaaaaaaa\naaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n output: 461695029"], "Pid": "p01963", "ProblemText": "Task Description: You are given a string $t$ and a set $S$ of $N$ different strings. You need to separate $t$ such that each part is included in $S$.\n\n For example, the following 4 separation methods satisfy the condition when $t = abab$ and $S = \\{a, ab, b\\}$.\n\n$a, b, a, b$\n\n$a, b, ab$\n\n$ab, a, b$\n\n$ab, ab$\nYour task is to count the number of ways to separate $t$. Because the result can be large, you should output the remainder divided by $1,000,000,007$.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$\n$s_1$\n:\n$s_N$\n$t$\n\nThe first line consists of an integer $N$ ($1 <= N <= 100,000$) which is the number of the elements of $S$. The following $N$ lines consist of $N$ distinct strings separated by line breaks. The $i$-th string $s_i$ represents the $i$-th element of $S$. $s_i$ consists of lowercase letters and the length is between $1$ and $100,000$, inclusive. The summation of length of $s_i$ ($1 <= i <= N$) is at most $200,000$. The next line consists of a string $t$ which consists of lowercase letters and represents the string to be separated and the length is between $1$ and $100,000$, inclusive.\nTask Output: Calculate the number of ways to separate $t$ and print the remainder divided by $1,000,000,007$.\nTask Samples: input: 3\na\nb\nab\nabab\n output: 4\ninput: 3\na\nb\nc\nxyz\n output: 0\ninput: 7\nabc\nab\nbc\na\nb\nc\naa\naaabcbccababbc\n output: 160\ninput: 10\na\naa\naaa\naaaa\naaaaa\naaaaaa\naaaaaaa\naaaaaaaa\naaaaaaaaa\naaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n output: 461695029\n\n" }, { "title": "Revenge of the Endless BFS", "content": "Mr. Endo wanted to write the code that performs breadth-first search (BFS), which is a search algorithm to explore all vertices on a directed graph. An example of pseudo code of BFS is as follows:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: $visited <=ftarrow current$\n3: while $visited \\ne$ the set of all the vertices\n4: $found <=ftarrow \\{\\}$\n5: for $u$ in $current$\n6: for each $v$ such that there is an edge from $u$ to $v$\n7: $found <=ftarrow found \\cup \\{v\\}$\n8: $current <=ftarrow found \\setminus visited$\n9: $visited <=ftarrow visited \\cup found$\n\n However, Mr. Endo apparently forgot to manage visited vertices in his code. More precisely, he wrote the following code:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: while $current \\ne$ the set of all the vertices\n3: $found <=ftarrow \\{\\}$\n4: for $u$ in $current$\n5: for each $v$ such that there is an edge from $u$ to $v$\n6: $found <=ftarrow found \\cup \\{v\\}$\n7: $current <=ftarrow found$\n\n You may notice that for some graphs, Mr. Endo's program will not stop because it keeps running infinitely. Notice that it does not necessarily mean the program cannot explore all the vertices within finite steps. Your task here is to make a program that determines whether Mr. Endo's program will stop within finite steps for a given directed graph in order to point out the bug to him. Also, calculate the minimum number of loop iterations required for the program to stop if it is finite. Since the answer might be huge, thus print the answer modulo $10^9 +7$, which is a prime number.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$ $M$\n$u_1$ $v_1$\n:\n$u_M$ $v_M$\n\n The first line consists of two integers $N$ ($2 <= N <= 500$) and $M$ ($1 <= M <= 200,000$), where $N$ is the number of vertices and $M$ is the number of edges in a given directed graph, respectively. The $i$-th line of the following $M$ lines consists of two integers $u_i$ and $v_i$ ($1 <= u_i, v_i <= N$), which means there is an edge from $u_i$ to $v_i$ in the given graph. The vertex $1$ is the start vertex, i. e. $start\\_vertex$ in the pseudo codes. You can assume that the given graph also meets the following conditions.\n\nThe graph has no self-loop, i. e. , $u_i \\ne v_i$ for all $1 <= i <= M$.\n\nThe graph has no multi-edge, i. e. , $(u_i, v_i) <= (u_j, v_j)$ for all $1 <= i < j <= M$.\n\nFor each vertex $v$, there is at least one path from the start vertex $1$ to $v$.", "output": "If Mr. Endo's wrong BFS code cannot stop within finite steps for the given input directed graph, print '-1' in a line. Otherwise, print the minimum number of loop iterations required to stop modulo $10^9+7$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n1 2\n2 3\n3 4\n4 1\n output: -1", "input: 4 5\n1 2\n2 3\n3 4\n4 1\n1 3\n output: 7", "input: 5 13\n4 2\n2 4\n1 2\n5 4\n5 1\n2 1\n5 3\n4 3\n1 5\n4 5\n2 3\n5 2\n1 3\n output: 3"], "Pid": "p01964", "ProblemText": "Task Description: Mr. Endo wanted to write the code that performs breadth-first search (BFS), which is a search algorithm to explore all vertices on a directed graph. An example of pseudo code of BFS is as follows:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: $visited <=ftarrow current$\n3: while $visited \\ne$ the set of all the vertices\n4: $found <=ftarrow \\{\\}$\n5: for $u$ in $current$\n6: for each $v$ such that there is an edge from $u$ to $v$\n7: $found <=ftarrow found \\cup \\{v\\}$\n8: $current <=ftarrow found \\setminus visited$\n9: $visited <=ftarrow visited \\cup found$\n\n However, Mr. Endo apparently forgot to manage visited vertices in his code. More precisely, he wrote the following code:\n\n1: $current <=ftarrow \\{start\\_vertex\\}$\n2: while $current \\ne$ the set of all the vertices\n3: $found <=ftarrow \\{\\}$\n4: for $u$ in $current$\n5: for each $v$ such that there is an edge from $u$ to $v$\n6: $found <=ftarrow found \\cup \\{v\\}$\n7: $current <=ftarrow found$\n\n You may notice that for some graphs, Mr. Endo's program will not stop because it keeps running infinitely. Notice that it does not necessarily mean the program cannot explore all the vertices within finite steps. Your task here is to make a program that determines whether Mr. Endo's program will stop within finite steps for a given directed graph in order to point out the bug to him. Also, calculate the minimum number of loop iterations required for the program to stop if it is finite. Since the answer might be huge, thus print the answer modulo $10^9 +7$, which is a prime number.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$ $M$\n$u_1$ $v_1$\n:\n$u_M$ $v_M$\n\n The first line consists of two integers $N$ ($2 <= N <= 500$) and $M$ ($1 <= M <= 200,000$), where $N$ is the number of vertices and $M$ is the number of edges in a given directed graph, respectively. The $i$-th line of the following $M$ lines consists of two integers $u_i$ and $v_i$ ($1 <= u_i, v_i <= N$), which means there is an edge from $u_i$ to $v_i$ in the given graph. The vertex $1$ is the start vertex, i. e. $start\\_vertex$ in the pseudo codes. You can assume that the given graph also meets the following conditions.\n\nThe graph has no self-loop, i. e. , $u_i \\ne v_i$ for all $1 <= i <= M$.\n\nThe graph has no multi-edge, i. e. , $(u_i, v_i) <= (u_j, v_j)$ for all $1 <= i < j <= M$.\n\nFor each vertex $v$, there is at least one path from the start vertex $1$ to $v$.\nTask Output: If Mr. Endo's wrong BFS code cannot stop within finite steps for the given input directed graph, print '-1' in a line. Otherwise, print the minimum number of loop iterations required to stop modulo $10^9+7$.\nTask Samples: input: 4 4\n1 2\n2 3\n3 4\n4 1\n output: -1\ninput: 4 5\n1 2\n2 3\n3 4\n4 1\n1 3\n output: 7\ninput: 5 13\n4 2\n2 4\n1 2\n5 4\n5 1\n2 1\n5 3\n4 3\n1 5\n4 5\n2 3\n5 2\n1 3\n output: 3\n\n" }, { "title": "Farm Village", "content": "There is a village along a road. This village has $N$ houses numbered $1$ to $N$ in order along the road. Each house has a field that can make up to two units of the crop and needs just one unit of the crop. The total cost to distribute one unit of the crop to each house is the summation of carrying costs and growing costs.\n\nThe carrying cost: The cost to carry one unit of the crop between the $i$-th house and the ($i+1$)-th house is $d_i$. It takes the same cost in either direction to carry.\n\nThe growing cost: The cost to grow one unit of the crop in the $i$-th house's field is $g_i$.\n Your task is to calculate the minimum total cost to supply one unit of the crop to each house.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$\n$d_1$ . . . $d_{N-1}$\n$g_1$ . . . $g_{N}$\n\n The first line consists of an integer $N$ ($2 <= 200,000$), which is the number of the houses. The second line consists of $N-1$ integers separated by spaces. The $i$-th integer $d_i$ ($1 <= d_i <= 10^9$, $1 <= i <= N-1$)represents the carrying cost between the $i$-th and the ($i+1$)-th houses. The third line consists of $N$ integers separated by spaces. The $i$-th integer $g_i$ ($1 <= g_i <= 10^9$, $1 <= i <= N$) represents the growing cost of the $i$-th house's field.", "output": "Print the minimum cost to supply one unit of the crop to each house.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3\n1 5\n output: 5", "input: 3\n100 100\n1 2 3\n output: 6", "input: 4\n1 2 3\n1 1 100 100\n output: 12"], "Pid": "p01965", "ProblemText": "Task Description: There is a village along a road. This village has $N$ houses numbered $1$ to $N$ in order along the road. Each house has a field that can make up to two units of the crop and needs just one unit of the crop. The total cost to distribute one unit of the crop to each house is the summation of carrying costs and growing costs.\n\nThe carrying cost: The cost to carry one unit of the crop between the $i$-th house and the ($i+1$)-th house is $d_i$. It takes the same cost in either direction to carry.\n\nThe growing cost: The cost to grow one unit of the crop in the $i$-th house's field is $g_i$.\n Your task is to calculate the minimum total cost to supply one unit of the crop to each house.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$\n$d_1$ . . . $d_{N-1}$\n$g_1$ . . . $g_{N}$\n\n The first line consists of an integer $N$ ($2 <= 200,000$), which is the number of the houses. The second line consists of $N-1$ integers separated by spaces. The $i$-th integer $d_i$ ($1 <= d_i <= 10^9$, $1 <= i <= N-1$)represents the carrying cost between the $i$-th and the ($i+1$)-th houses. The third line consists of $N$ integers separated by spaces. The $i$-th integer $g_i$ ($1 <= g_i <= 10^9$, $1 <= i <= N$) represents the growing cost of the $i$-th house's field.\nTask Output: Print the minimum cost to supply one unit of the crop to each house.\nTask Samples: input: 2\n3\n1 5\n output: 5\ninput: 3\n100 100\n1 2 3\n output: 6\ninput: 4\n1 2 3\n1 1 100 100\n output: 12\n\n" }, { "title": "Conveyor Belt", "content": "Awesome Conveyor Machine (ACM) is the most important equipment of a factory of Industrial Conveyor Product Corporation (ICPC). ACM has a long conveyor belt to deliver their products from some points to other points. You are a programmer hired to make efficient schedule plan for product delivery.\n\n ACM's conveyor belt goes through $N$ points at equal intervals. The conveyor has plates on each of which at most one product can be put. Initially, there are no plates at any points. The conveyor belt moves by exactly one plate length per unit time; after one second, a plate is at position 1 while there are no plates at the other positions. After further 1 seconds, the plate at position 1 is moved to position 2 and a new plate comes at position 1, and so on. Note that the conveyor has the unlimited number of plates: after $N$ seconds or later, each of the $N$ positions has exactly one plate.\n\n A delivery task is represented by positions $a$ and $b$; delivery is accomplished by putting a product on a plate on the belt at $a$, and retrieving it at $b$ after $b - a$ seconds ($a < b$). (Of course, it is necessary that an empty plate exists at the position at the putting time. ) In addition, putting and retrieving products must bedone in the following manner:\n \nWhen putting and retrieving a product, a plate must be located just at the position. That is, products must be put and retrieved at integer seconds.\n\nPutting and retrieving at the same position cannot be done at the same time. On the other hand, putting and retrieving at the different positions can be done at the same time.\n If there are several tasks, the time to finish all the tasks may be reduced by changing schedule when each product is put on the belt. Your job is to write a program minimizing the time to complete all the tasks. . . wait, wait. When have you started misunderstanding that you can know all the tasks initially? New delivery requests are coming moment by moment, like plates on the conveyor! So you should update your optimal schedule per every new request.\n \nA request consists of a start point $a$, a goal point $b$, and the number $p$ of products to deliver from $a$ to $b$. Delivery requests will be added $Q$ times. Your (true) job is to write a program such that for each $1 <= i <= Q$, minimizing the entire time to complete delivery tasks in requests 1 to $i$.", "constraint": "", "input": "The input consists of a single test case formatted as follows.\n\n$N$ $Q$\n$a_1$ $b_1$ $p_1$\n:\n$a_Q$ $b_Q$ $p_Q$\n\nA first line includes two integers $N$ and $Q$ ($2 <= N <= 10^5,1 <= Q <= 10^5$): $N$ is the number of positions the conveyor belt goes through and $Q$ is the number of requests will come. The $i$-th line of the following $Q$ lines consists of three integers $a_i, b_i, $ and $p_i$ ($1 <= a_i < b_i <= N, 1 <= p_i <= 10^9$), which mean that the $i$-th request requires $p_i$ products to be delivered from position $a_i$ to position $b_i$.", "output": "In the $i$-th line, print the minimum time to complete all the tasks required by requests $1$ to $i$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 2\n1 4 1\n2 3 1\n output: 4\n4", "input: 5 2\n1 4 1\n2 3 5\n output: 4\n8", "input: 5 2\n1 3 3\n3 5 1\n output: 5\n6", "input: 10 4\n3 5 2\n5 7 5\n8 9 2\n1 7 5\n output: 6\n11\n11\n16\nRegarding the first example, the minimum time to complete only the first request is 4 seconds. All the two requests can be completed within 4 seconds too. See the below figure."], "Pid": "p01966", "ProblemText": "Task Description: Awesome Conveyor Machine (ACM) is the most important equipment of a factory of Industrial Conveyor Product Corporation (ICPC). ACM has a long conveyor belt to deliver their products from some points to other points. You are a programmer hired to make efficient schedule plan for product delivery.\n\n ACM's conveyor belt goes through $N$ points at equal intervals. The conveyor has plates on each of which at most one product can be put. Initially, there are no plates at any points. The conveyor belt moves by exactly one plate length per unit time; after one second, a plate is at position 1 while there are no plates at the other positions. After further 1 seconds, the plate at position 1 is moved to position 2 and a new plate comes at position 1, and so on. Note that the conveyor has the unlimited number of plates: after $N$ seconds or later, each of the $N$ positions has exactly one plate.\n\n A delivery task is represented by positions $a$ and $b$; delivery is accomplished by putting a product on a plate on the belt at $a$, and retrieving it at $b$ after $b - a$ seconds ($a < b$). (Of course, it is necessary that an empty plate exists at the position at the putting time. ) In addition, putting and retrieving products must bedone in the following manner:\n \nWhen putting and retrieving a product, a plate must be located just at the position. That is, products must be put and retrieved at integer seconds.\n\nPutting and retrieving at the same position cannot be done at the same time. On the other hand, putting and retrieving at the different positions can be done at the same time.\n If there are several tasks, the time to finish all the tasks may be reduced by changing schedule when each product is put on the belt. Your job is to write a program minimizing the time to complete all the tasks. . . wait, wait. When have you started misunderstanding that you can know all the tasks initially? New delivery requests are coming moment by moment, like plates on the conveyor! So you should update your optimal schedule per every new request.\n \nA request consists of a start point $a$, a goal point $b$, and the number $p$ of products to deliver from $a$ to $b$. Delivery requests will be added $Q$ times. Your (true) job is to write a program such that for each $1 <= i <= Q$, minimizing the entire time to complete delivery tasks in requests 1 to $i$.\nTask Input: The input consists of a single test case formatted as follows.\n\n$N$ $Q$\n$a_1$ $b_1$ $p_1$\n:\n$a_Q$ $b_Q$ $p_Q$\n\nA first line includes two integers $N$ and $Q$ ($2 <= N <= 10^5,1 <= Q <= 10^5$): $N$ is the number of positions the conveyor belt goes through and $Q$ is the number of requests will come. The $i$-th line of the following $Q$ lines consists of three integers $a_i, b_i, $ and $p_i$ ($1 <= a_i < b_i <= N, 1 <= p_i <= 10^9$), which mean that the $i$-th request requires $p_i$ products to be delivered from position $a_i$ to position $b_i$.\nTask Output: In the $i$-th line, print the minimum time to complete all the tasks required by requests $1$ to $i$.\nTask Samples: input: 5 2\n1 4 1\n2 3 1\n output: 4\n4\ninput: 5 2\n1 4 1\n2 3 5\n output: 4\n8\ninput: 5 2\n1 3 3\n3 5 1\n output: 5\n6\ninput: 10 4\n3 5 2\n5 7 5\n8 9 2\n1 7 5\n output: 6\n11\n11\n16\nRegarding the first example, the minimum time to complete only the first request is 4 seconds. All the two requests can be completed within 4 seconds too. See the below figure.\n\n" }, { "title": "a: many kinds of apples", "content": "Apple Farmer Mon has two kinds of tasks: \"harvest apples\" and \"ship apples\". There are N different species of apples, and N distinguishable boxes. Apples are labeled by the species, and boxes are also labeled, from 1 to N. The i-th species of apples are stored in the i-th box. For each i, the i-th box can store at most c_i apples, and it is initially empty (no apple exists). Mon receives Q instructions from his boss Kukui, and Mon completely follows in order. Each instruction is either of two types below.\n \"harvest apples\": put d x-th apples into the x-th box.\n\n \"ship apples\": take d x-th apples out from the x-th box.\n\nHowever, not all instructions are possible to carry out. Now we call an instruction which meets either of following conditions \"impossible instruction\":\n When Mon harvest apples, the amount of apples exceeds the capacity of that box.\n\n When Mon tries to ship apples, there are not enough apples to ship.\n\nYour task is to detect the instruction which is impossible to carry out.", "constraint": "All input values are integers, and satisfy following constraints.\n 1 <= N <= 1,000\n\n 1 <= c_i <= 100,000 (1 <= i <= N)\n\n 1 <= Q <= 100,000\n\n t_i \\in \\{1,2\\} (1 <= i <= Q)\n\n 1 <= x_i <= N (1 <= i <= Q)\n\n 1 <= d_i <= 100,000 (1 <= i <= Q)", "input": "Input is given in the following format.\nN\nc_1 c_2 $\\cdots$ c_N\nQ\nt_1 x_1 d_1\nt_2 x_2 d_2\n$\\vdots$\nt_Q x_Q d_Q\nIn line 1, you are given the integer N, which indicates the number of species of apples. In line 2, given c_i (1 <= i <= N) separated by whitespaces. c_i indicates the capacity of the i-th box. In line 3, given Q, which indicates the number of instructions. Instructions are given successive Q lines. t_i x_i d_i means what kind of instruction, which apple Mon handles in this instruction, how many apples Mon handles, respectively. If t_i is equal to 1, it means Mon does the task of \"harvest apples\", else if t_i is equal to 2, it means Mon does the task of \"ship apples\".", "output": "If there is \"impossible instruction\", output the index of the apples which have something to do with the first \"impossible instruction\". Otherwise, output 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 3\n4\n1 1 2\n1 2 3\n2 1 3\n2 2 3\n output: 1\nIn this case, there are not enough apples to ship in the first box.", "input: 2\n3 3\n4\n1 1 3\n2 1 2\n1 2 3\n1 1 3\n output: 1\nIn this case, the amount of apples exceeds the capacity of the first box.", "input: 3\n3 4 5\n4\n1 1 3\n1 2 3\n1 3 5\n2 2 2\n output: 0", "input: 6\n28 56 99 3 125 37\n10\n1 1 10\n1 1 14\n1 3 90\n1 5 10\n2 3 38\n2 1 5\n1 3 92\n1 6 18\n2 5 9\n2 1 4\n output: 3"], "Pid": "p01967", "ProblemText": "Task Description: Apple Farmer Mon has two kinds of tasks: \"harvest apples\" and \"ship apples\". There are N different species of apples, and N distinguishable boxes. Apples are labeled by the species, and boxes are also labeled, from 1 to N. The i-th species of apples are stored in the i-th box. For each i, the i-th box can store at most c_i apples, and it is initially empty (no apple exists). Mon receives Q instructions from his boss Kukui, and Mon completely follows in order. Each instruction is either of two types below.\n \"harvest apples\": put d x-th apples into the x-th box.\n\n \"ship apples\": take d x-th apples out from the x-th box.\n\nHowever, not all instructions are possible to carry out. Now we call an instruction which meets either of following conditions \"impossible instruction\":\n When Mon harvest apples, the amount of apples exceeds the capacity of that box.\n\n When Mon tries to ship apples, there are not enough apples to ship.\n\nYour task is to detect the instruction which is impossible to carry out.\nTask Constraint: All input values are integers, and satisfy following constraints.\n 1 <= N <= 1,000\n\n 1 <= c_i <= 100,000 (1 <= i <= N)\n\n 1 <= Q <= 100,000\n\n t_i \\in \\{1,2\\} (1 <= i <= Q)\n\n 1 <= x_i <= N (1 <= i <= Q)\n\n 1 <= d_i <= 100,000 (1 <= i <= Q)\nTask Input: Input is given in the following format.\nN\nc_1 c_2 $\\cdots$ c_N\nQ\nt_1 x_1 d_1\nt_2 x_2 d_2\n$\\vdots$\nt_Q x_Q d_Q\nIn line 1, you are given the integer N, which indicates the number of species of apples. In line 2, given c_i (1 <= i <= N) separated by whitespaces. c_i indicates the capacity of the i-th box. In line 3, given Q, which indicates the number of instructions. Instructions are given successive Q lines. t_i x_i d_i means what kind of instruction, which apple Mon handles in this instruction, how many apples Mon handles, respectively. If t_i is equal to 1, it means Mon does the task of \"harvest apples\", else if t_i is equal to 2, it means Mon does the task of \"ship apples\".\nTask Output: If there is \"impossible instruction\", output the index of the apples which have something to do with the first \"impossible instruction\". Otherwise, output 0.\nTask Samples: input: 2\n3 3\n4\n1 1 2\n1 2 3\n2 1 3\n2 2 3\n output: 1\nIn this case, there are not enough apples to ship in the first box.\ninput: 2\n3 3\n4\n1 1 3\n2 1 2\n1 2 3\n1 1 3\n output: 1\nIn this case, the amount of apples exceeds the capacity of the first box.\ninput: 3\n3 4 5\n4\n1 1 3\n1 2 3\n1 3 5\n2 2 2\n output: 0\ninput: 6\n28 56 99 3 125 37\n10\n1 1 10\n1 1 14\n1 3 90\n1 5 10\n2 3 38\n2 1 5\n1 3 92\n1 6 18\n2 5 9\n2 1 4\n output: 3\n\n" }, { "title": "b: hierarchical calculator", "content": "problem: Ebi-chan has N formulae: y = a_i x for i =1, . . . , N (inclusive). Now she considers a subsequence of indices with length k: s_1, s_2, . . . , s_k. At first, let x_0 be 1 and evaluate s_1-th formulae with x = x_0. Next, let x_1 be the output of s_1 and evaluate s_2-th formulae with x = x_1, and so on. She wants to maximize the final output of the procedure, x_{s_k}. If there are many candidates, she wants the \"\"\"shortest one\"\"\". If there are still many candidates, she wants the \"\"\"lexicographically smallest one\"\"\". Sequence s is lexicographically smaller than sequence t, if and only if either of the following conditions hold:\n there exists m < |s| such that s_i = t_i for i in 1 to m (inclusive) and s_{m+1} < t_{m+1}, or\n\n s_i = t_i for i in 1 to |s| (inclusive) and |s| < |t|,\n\nwhere |s| is the length of the s.", "constraint": "1 <= N <= 60\n\n -2 <= a_i <= 2 for i=1, ...,N (inclusive)\n\n Every input is given as the integer.", "input": "N\na_1 a_2 $\\cdots$ a_N", "output": "Output k+1 lines. First line, the length of the sequence, k. Following k lines, the index of the i-th element of the subsequence, s_i (one element per line).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 0 -2 1\n output: 1\n1\n\nShe evaluates the first one and gets the maximum value 2\n.", "input: 3\n2 -2 -2\n output: 3\n1\n2\n3\n\nShe evaluates all of them and gets the maximum value 8\n.", "input: 2\n-1 0\n output: 0\nShe evaluates none of them and gets the maximum value 0\n. Empty sequence is the shorter and lexicographically smaller than any other sequences.", "input: 5\n-1 2 1 -2 -1\n output: 3\n1\n2\n4\n\nShe evaluates $\\langle$ 1,2,4 \n$\\rangle$ ones and gets the maximum value 4\n. Note that $\\langle$ 2,4,5 \n$\\rangle$ is not lexicographically smallest one."], "Pid": "p01968", "ProblemText": "Task Description: problem: Ebi-chan has N formulae: y = a_i x for i =1, . . . , N (inclusive). Now she considers a subsequence of indices with length k: s_1, s_2, . . . , s_k. At first, let x_0 be 1 and evaluate s_1-th formulae with x = x_0. Next, let x_1 be the output of s_1 and evaluate s_2-th formulae with x = x_1, and so on. She wants to maximize the final output of the procedure, x_{s_k}. If there are many candidates, she wants the \"\"\"shortest one\"\"\". If there are still many candidates, she wants the \"\"\"lexicographically smallest one\"\"\". Sequence s is lexicographically smaller than sequence t, if and only if either of the following conditions hold:\n there exists m < |s| such that s_i = t_i for i in 1 to m (inclusive) and s_{m+1} < t_{m+1}, or\n\n s_i = t_i for i in 1 to |s| (inclusive) and |s| < |t|,\n\nwhere |s| is the length of the s.\nTask Constraint: 1 <= N <= 60\n\n -2 <= a_i <= 2 for i=1, ...,N (inclusive)\n\n Every input is given as the integer.\nTask Input: N\na_1 a_2 $\\cdots$ a_N\nTask Output: Output k+1 lines. First line, the length of the sequence, k. Following k lines, the index of the i-th element of the subsequence, s_i (one element per line).\nTask Samples: input: 4\n2 0 -2 1\n output: 1\n1\n\nShe evaluates the first one and gets the maximum value 2\n.\ninput: 3\n2 -2 -2\n output: 3\n1\n2\n3\n\nShe evaluates all of them and gets the maximum value 8\n.\ninput: 2\n-1 0\n output: 0\nShe evaluates none of them and gets the maximum value 0\n. Empty sequence is the shorter and lexicographically smaller than any other sequences.\ninput: 5\n-1 2 1 -2 -1\n output: 3\n1\n2\n4\n\nShe evaluates $\\langle$ 1,2,4 \n$\\rangle$ ones and gets the maximum value 4\n. Note that $\\langle$ 2,4,5 \n$\\rangle$ is not lexicographically smallest one.\n\n" }, { "title": "c: aa graph", "content": "problem: Given a graph as an ASCII Art (AA), please print the length of shortest paths from the vertex s to the vertex t. The AA of the graph satisfies the following constraints. A vertex is represented by an uppercase alphabet and symbols \\no\\n in 8 neighbors as follows.\nHorizontal edges and vertical edges are represented by symbols \\n-\\n and \\n|\\n, respectively.\nLengths of all edges are 1, that is, it do not depends on the number of continuous symbols \\n-\\n or \\n|\\n.\nAll edges do not cross each other, and all vertices do not overlap and touch each other.\n\nFor each vertex, outgoing edges are at most 1 for each directions top, bottom, left, and right.\nEach edge is connected to a symbol \\no\\n that is adjacent to an uppercase alphabet in 4 neighbors as follows.\nTherefore, for example, following inputs are not given. (Edges do not satisfies the constraint about their position. )(Two vertices are adjacent each other. )", "constraint": "3 <= h, w <= 50\n s and t are selected by uppercase alphabets from a to z, and s <> t.\n a_i (1 <= i <= h) consists of uppercase alphabets and symbols o, -, |, and . .\n each uppercase alphabet occurs at most once in the aa.\n it is guaranteed that there are two vertices representing s and t.\n the aa represents a connected graph.", "input": "H W s t\na_1\n$\\vdots$\na_H\n In line 1, two integers H and W, and two characters s and t are given. H and W is the width and height of the AA, respectively. s and t is the start and end vertices, respectively. They are given in separating by en spaces.\n In line 1 + i where 1 <= i <= H, the string representing line i of the AA is given.", "output": "Print the length of the shortest paths from s to t in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 14 16 a l \nooo.....ooo.....\noao-----oho.....\nooo.....ooo..ooo\n.|.......|...olo\nooo..ooo.|...ooo\noko--oyo.|....|.\nooo..ooo.|....|.\n.|....|.ooo...|.\n.|....|.ogo...|.\n.|....|.ooo...|.\n.|....|.......|.\nooo..ooo.....ooo\nofo--oxo-----oeo\nooo..ooo.....ooo\n output: 5", "input: 21 17 f l\n.................\n.....ooo.....ooo.\n.....oao-----obo.\n.....ooo.....ooo.\n......|.......|..\n.ooo..|..ooo..|..\n.oco..|..odo.ooo.\n.ooo.ooo.ooo.oeo.\n..|..ofo..|..ooo.\n..|..ooo..|...|..\n..|...|...|...|..\n..|...|...|...|..\n..|...|...|...|..\n.ooo.ooo.ooo..|..\n.ogo-oho-oio..|..\n.ooo.ooo.ooo..|..\n..|...........|..\n.ooo...ooo...ooo.\n.ojo---oko---olo.\n.ooo...ooo...ooo.\n.................\n output: 4"], "Pid": "p01969", "ProblemText": "Task Description: problem: Given a graph as an ASCII Art (AA), please print the length of shortest paths from the vertex s to the vertex t. The AA of the graph satisfies the following constraints. A vertex is represented by an uppercase alphabet and symbols \\no\\n in 8 neighbors as follows.\nHorizontal edges and vertical edges are represented by symbols \\n-\\n and \\n|\\n, respectively.\nLengths of all edges are 1, that is, it do not depends on the number of continuous symbols \\n-\\n or \\n|\\n.\nAll edges do not cross each other, and all vertices do not overlap and touch each other.\n\nFor each vertex, outgoing edges are at most 1 for each directions top, bottom, left, and right.\nEach edge is connected to a symbol \\no\\n that is adjacent to an uppercase alphabet in 4 neighbors as follows.\nTherefore, for example, following inputs are not given. (Edges do not satisfies the constraint about their position. )(Two vertices are adjacent each other. )\nTask Constraint: 3 <= h, w <= 50\n s and t are selected by uppercase alphabets from a to z, and s <> t.\n a_i (1 <= i <= h) consists of uppercase alphabets and symbols o, -, |, and . .\n each uppercase alphabet occurs at most once in the aa.\n it is guaranteed that there are two vertices representing s and t.\n the aa represents a connected graph.\nTask Input: H W s t\na_1\n$\\vdots$\na_H\n In line 1, two integers H and W, and two characters s and t are given. H and W is the width and height of the AA, respectively. s and t is the start and end vertices, respectively. They are given in separating by en spaces.\n In line 1 + i where 1 <= i <= H, the string representing line i of the AA is given.\nTask Output: Print the length of the shortest paths from s to t in one line.\nTask Samples: input: 14 16 a l \nooo.....ooo.....\noao-----oho.....\nooo.....ooo..ooo\n.|.......|...olo\nooo..ooo.|...ooo\noko--oyo.|....|.\nooo..ooo.|....|.\n.|....|.ooo...|.\n.|....|.ogo...|.\n.|....|.ooo...|.\n.|....|.......|.\nooo..ooo.....ooo\nofo--oxo-----oeo\nooo..ooo.....ooo\n output: 5\ninput: 21 17 f l\n.................\n.....ooo.....ooo.\n.....oao-----obo.\n.....ooo.....ooo.\n......|.......|..\n.ooo..|..ooo..|..\n.oco..|..odo.ooo.\n.ooo.ooo.ooo.oeo.\n..|..ofo..|..ooo.\n..|..ooo..|...|..\n..|...|...|...|..\n..|...|...|...|..\n..|...|...|...|..\n.ooo.ooo.ooo..|..\n.ogo-oho-oio..|..\n.ooo.ooo.ooo..|..\n..|...........|..\n.ooo...ooo...ooo.\n.ojo---oko---olo.\n.ooo...ooo...ooo.\n.................\n output: 4\n\n" }, { "title": "d: the diversity of prime factorization", "content": "problem: Ebi-chan has the FACTORIZATION MACHINE, which can factorize natural numbers M (greater than 1) in O($\\log$ M) time! But unfortunately, the machine could display only digits and whitespaces. In general, we consider the factorization of M as p_1^{e_1} * p_2^{e_2} * . . . * p_K^{e_K} where (1) i < j implies p_i < p_j and (2) p_i is prime. Now, she gives M to the machine, and the machine displays according to the following rules in ascending order with respect to i:\n If e_i = 1, then displays p_i,\n\n otherwise, displays p_i e_i.\n\nFor example, if she gives either 22 or 2048, then 2 11 is displayed. If either 24 or 54, then 2 3 3. Okay, Ebi-chan has written down the output of the machine, but she notices that she has forgotten to write down the input! Now, your task is to count how many natural numbers result in a noted output. Note that Ebi-chan has mistaken writing and no input could result in the output. The answer could be too large, so, you must output it modulo 10^9+7 (prime number).", "constraint": "1 <= N <= 10^5\n\n 2 <= q_i <= 10^6 (1 <= i <= N)", "input": "N\nq_1 q_2 $\\cdots$ q_N\nIn the first line, the number of the output of the machine is given. In the second line, the output of the machine is given.", "output": "Print the number of the natural numbers that result in the given output of the machine.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3 3\n output: 2\n24 = 2^3 * 3\n and 54 = 2 * 3^3\n satisfy the condition.", "input: 3\n2 3 4\n output: 1\nOnly 162 = 2 * 3^4\n satisfies the condition. Note that 4\n is not prime.", "input: 3\n3 5 2\n output: 1\nSince 2 < 3 < 5\n, only 75 = 3 * 5^2\n satisfies the condition.", "input: 1\n4\n output: 0\nEbi-chan should have written down it more carefully."], "Pid": "p01970", "ProblemText": "Task Description: problem: Ebi-chan has the FACTORIZATION MACHINE, which can factorize natural numbers M (greater than 1) in O($\\log$ M) time! But unfortunately, the machine could display only digits and whitespaces. In general, we consider the factorization of M as p_1^{e_1} * p_2^{e_2} * . . . * p_K^{e_K} where (1) i < j implies p_i < p_j and (2) p_i is prime. Now, she gives M to the machine, and the machine displays according to the following rules in ascending order with respect to i:\n If e_i = 1, then displays p_i,\n\n otherwise, displays p_i e_i.\n\nFor example, if she gives either 22 or 2048, then 2 11 is displayed. If either 24 or 54, then 2 3 3. Okay, Ebi-chan has written down the output of the machine, but she notices that she has forgotten to write down the input! Now, your task is to count how many natural numbers result in a noted output. Note that Ebi-chan has mistaken writing and no input could result in the output. The answer could be too large, so, you must output it modulo 10^9+7 (prime number).\nTask Constraint: 1 <= N <= 10^5\n\n 2 <= q_i <= 10^6 (1 <= i <= N)\nTask Input: N\nq_1 q_2 $\\cdots$ q_N\nIn the first line, the number of the output of the machine is given. In the second line, the output of the machine is given.\nTask Output: Print the number of the natural numbers that result in the given output of the machine.\nTask Samples: input: 3\n2 3 3\n output: 2\n24 = 2^3 * 3\n and 54 = 2 * 3^3\n satisfy the condition.\ninput: 3\n2 3 4\n output: 1\nOnly 162 = 2 * 3^4\n satisfies the condition. Note that 4\n is not prime.\ninput: 3\n3 5 2\n output: 1\nSince 2 < 3 < 5\n, only 75 = 3 * 5^2\n satisfies the condition.\ninput: 1\n4\n output: 0\nEbi-chan should have written down it more carefully.\n\n" }, { "title": "E: Broccoli or Cauliflower", "content": "problem:\n U = $\\{$ u \\in V \\ \\ | \\ \\ u $\\text{ is the descendant of }$ v $\\}$\n Let v be a vertex. If a vertex u \\in U has the label G, then we change the label of u G to W. Otherwise, we change the label of u W to G.", "constraint": "1 <= n <= 100,000 ( n is odd. )\n\n 1 <= q <= 100,000\n\n 1 <= p_i < i（2 <= i <= n）\n\n c_j is G or W. (1 <= j <= n)\n\n 1 <= v_i <= n（1 <= i <= q）", "input": "An input is the following format.\nn q\np_2 . . . p_n\nc_1 . . . c_n\nv_1\n$\\vdots$\nv_q\nIn line 1, there are two integers n and q, where n is the number of vertices in T and q is the number of queries. Note that n is odd.\nIn line 2, there are n - 1 integers p_2 to p_n. p_i represents the parent of a vertex v_i.\nIn line 3, there are n characters c_1 to c_n. c_i represents the label of v_i. \nFinally, in line j + 3, there is an integer v_j. We perform the operation for T_{v_j}.", "output": "An output consists q lines and output \"broccoli\" or \"cauliflower\" in each line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 4\n1 1 2 2 3 3\ng g w w w g g \n2\n1\n3\n4\n output: broccoli\ncauliflower\ncauliflower\nbroccoli", "input: 17 18\n1 1 1 3 1 4 2 4 3 6 10 9 3 4 5 15\nw w w w w w w w g w g g w g w w w\n6\n7\n1\n9\n14\n6\n4\n5\n3\n7\n8\n13\n9\n6\n14\n12\n9\n13\n output: cauliflower\ncauliflower\nbroccoli\nbroccoli\nbroccoli\nbroccoli\nbroccoli\nbroccoli\nbroccoli\ncauliflower\ncauliflower\ncauliflower\ncauliflower\ncauliflower\nbroccoli\ncauliflower\ncauliflower\ncauliflower"], "Pid": "p01971", "ProblemText": "Task Description: problem:\n U = $\\{$ u \\in V \\ \\ | \\ \\ u $\\text{ is the descendant of }$ v $\\}$\n Let v be a vertex. If a vertex u \\in U has the label G, then we change the label of u G to W. Otherwise, we change the label of u W to G.\nTask Constraint: 1 <= n <= 100,000 ( n is odd. )\n\n 1 <= q <= 100,000\n\n 1 <= p_i < i（2 <= i <= n）\n\n c_j is G or W. (1 <= j <= n)\n\n 1 <= v_i <= n（1 <= i <= q）\nTask Input: An input is the following format.\nn q\np_2 . . . p_n\nc_1 . . . c_n\nv_1\n$\\vdots$\nv_q\nIn line 1, there are two integers n and q, where n is the number of vertices in T and q is the number of queries. Note that n is odd.\nIn line 2, there are n - 1 integers p_2 to p_n. p_i represents the parent of a vertex v_i.\nIn line 3, there are n characters c_1 to c_n. c_i represents the label of v_i. \nFinally, in line j + 3, there is an integer v_j. We perform the operation for T_{v_j}.\nTask Output: An output consists q lines and output \"broccoli\" or \"cauliflower\" in each line.\nTask Samples: input: 7 4\n1 1 2 2 3 3\ng g w w w g g \n2\n1\n3\n4\n output: broccoli\ncauliflower\ncauliflower\nbroccoli\ninput: 17 18\n1 1 1 3 1 4 2 4 3 6 10 9 3 4 5 15\nw w w w w w w w g w g g w g w w w\n6\n7\n1\n9\n14\n6\n4\n5\n3\n7\n8\n13\n9\n6\n14\n12\n9\n13\n output: cauliflower\ncauliflower\nbroccoli\nbroccoli\nbroccoli\nbroccoli\nbroccoli\nbroccoli\nbroccoli\ncauliflower\ncauliflower\ncauliflower\ncauliflower\ncauliflower\nbroccoli\ncauliflower\ncauliflower\ncauliflower\n\n" }, { "title": "f: ebi-chan lengthens shortest paths", "content": "problem:\n She can lengthen each edges independently.\n\n When she lengthens an edge, she must select the additional distance from positive integers.\n\n The ith edge takes a cost c_i per additional distance 1.", "constraint": "2 <= N <= 200\n\n 1 <= M <= 2,000\n\n 1 <= s, t <= N, s \\neq t\n\n 1 <= u_i, v_i <= N, u_i \\neq v_i (1 <= i <= M) \n\n For each i, j (1 <= i < j <= M), u_i \\neq u_j or v_i \\neq v_j are satisfied.\n\n 1 <= d_i <= 10 (1 <= i <= M)\n\n 1 <= c_i <= 10 (1 <= i <= M)\n\n It is guaranteed that there is at least one path from s to t.", "input": "An input is given in the following format.\nN M s t\nu_1 v_1 d_1 c_1\n$\\vdots$\nu_M v_M d_M c_M\nIn line 1, four integers N, M, s, and t are given in separating by en spaces. N and M is the number of vertices and edges, respectively. Ebi-chan tries to lengthen shortest paths from the vertex s to the vertex t.\nLine 1 + i, where 1 <= i <= M, has the information of the ith edge. u_i and v_i are the start and end vertices of the edge, respectively. d_i and c_i represents the original distance and cost of the edge, respectively. These integers are given in separating by en spaces.", "output": "Print the minimum cost, that is to lengthen the distance of shortest paths from s to t at least 1, in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 1 3\n1 2 1 1\n2 3 1 1\n1 3 1 1\n output: 1 ebi-chan should lengthen 3rd edge with additional distance 1.", "input: 8 15 5 7\n1 5 2 3\n3 8 3 6\n8 7 1 3\n2 7 6 4\n3 7 5 5\n8 3 1 3\n5 6 3 5\n1 7 3 2\n4 3 2 4\n5 4 4 3\n2 3 2 2\n2 8 6 5\n6 2 1 3\n4 2 1 6\n6 1 4 2\n output: 8"], "Pid": "p01972", "ProblemText": "Task Description: problem:\n She can lengthen each edges independently.\n\n When she lengthens an edge, she must select the additional distance from positive integers.\n\n The ith edge takes a cost c_i per additional distance 1.\nTask Constraint: 2 <= N <= 200\n\n 1 <= M <= 2,000\n\n 1 <= s, t <= N, s \\neq t\n\n 1 <= u_i, v_i <= N, u_i \\neq v_i (1 <= i <= M) \n\n For each i, j (1 <= i < j <= M), u_i \\neq u_j or v_i \\neq v_j are satisfied.\n\n 1 <= d_i <= 10 (1 <= i <= M)\n\n 1 <= c_i <= 10 (1 <= i <= M)\n\n It is guaranteed that there is at least one path from s to t.\nTask Input: An input is given in the following format.\nN M s t\nu_1 v_1 d_1 c_1\n$\\vdots$\nu_M v_M d_M c_M\nIn line 1, four integers N, M, s, and t are given in separating by en spaces. N and M is the number of vertices and edges, respectively. Ebi-chan tries to lengthen shortest paths from the vertex s to the vertex t.\nLine 1 + i, where 1 <= i <= M, has the information of the ith edge. u_i and v_i are the start and end vertices of the edge, respectively. d_i and c_i represents the original distance and cost of the edge, respectively. These integers are given in separating by en spaces.\nTask Output: Print the minimum cost, that is to lengthen the distance of shortest paths from s to t at least 1, in one line.\nTask Samples: input: 3 3 1 3\n1 2 1 1\n2 3 1 1\n1 3 1 1\n output: 1 ebi-chan should lengthen 3rd edge with additional distance 1.\ninput: 8 15 5 7\n1 5 2 3\n3 8 3 6\n8 7 1 3\n2 7 6 4\n3 7 5 5\n8 3 1 3\n5 6 3 5\n1 7 3 2\n4 3 2 4\n5 4 4 3\n2 3 2 2\n2 8 6 5\n6 2 1 3\n4 2 1 6\n6 1 4 2\n output: 8\n\n" }, { "title": "g: censored string", "content": "You are given the string S, and the set of strings \\mathcal P whose size is N. Now we consider applying the following operation to S:\n Choose exactly one character in S, and replace it with '*'.\n\nLet s_i be a i-th character of S, S_{ij} be a consecutive substring in S such that S = s_i s_{i+1} $\\cdots$ s_j, and p_k as the k-th string of P. Your task is to calculate the minimum number of operations for satisfying the following condition.\n For all pairs (S_{ij}, p_k), it is satisfied that S_{ij} \\neq p_k.", "constraint": "1 <= |S| <= 10^5\n\n 1 <= N <= 10^5\n\n 1 <= |p_1| + |p_2| + $\\cdots$ + |p_N| <= 10^5\n\n If i \\neq j, it is guaranteed that p_i \\neq p_j\n\n S, and p_i include lowercase letters only", "input": "An input is given in the following format.\nS\nN\np_1\np_2\n$\\vdots$\np_N\n\n In line 1, you are given the string S.\n\n In line 2, given an integer N. N means the size of P. \n\n From line 3 to the end, given p_i, the i-th string of P.", "output": "Print the minimum number of operations in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: brainfuck\n1\nfuck\n output: 1\nFor example, if you change \"brainfuck\" into \"brainf*ck\", you can satisfy the condition. You have to perform operation at least once, and it is the minimum value.", "input: aaa\n1\na\n output: 3\nYou have to operate for all characters.", "input: hellshakeyano\n3\nhell\nshake\nkey\n output: 2\nIn this case, for example, if you change \"hellshakeyano\" into \"h*llsha*eyano\", you can satisfy the condition. Notice if you replace one character, it might happen that several strings in the set P\n, which appear as the consecutive substring of S\n, simultaneously disappear."], "Pid": "p01973", "ProblemText": "Task Description: You are given the string S, and the set of strings \\mathcal P whose size is N. Now we consider applying the following operation to S:\n Choose exactly one character in S, and replace it with '*'.\n\nLet s_i be a i-th character of S, S_{ij} be a consecutive substring in S such that S = s_i s_{i+1} $\\cdots$ s_j, and p_k as the k-th string of P. Your task is to calculate the minimum number of operations for satisfying the following condition.\n For all pairs (S_{ij}, p_k), it is satisfied that S_{ij} \\neq p_k.\nTask Constraint: 1 <= |S| <= 10^5\n\n 1 <= N <= 10^5\n\n 1 <= |p_1| + |p_2| + $\\cdots$ + |p_N| <= 10^5\n\n If i \\neq j, it is guaranteed that p_i \\neq p_j\n\n S, and p_i include lowercase letters only\nTask Input: An input is given in the following format.\nS\nN\np_1\np_2\n$\\vdots$\np_N\n\n In line 1, you are given the string S.\n\n In line 2, given an integer N. N means the size of P. \n\n From line 3 to the end, given p_i, the i-th string of P.\nTask Output: Print the minimum number of operations in one line.\nTask Samples: input: brainfuck\n1\nfuck\n output: 1\nFor example, if you change \"brainfuck\" into \"brainf*ck\", you can satisfy the condition. You have to perform operation at least once, and it is the minimum value.\ninput: aaa\n1\na\n output: 3\nYou have to operate for all characters.\ninput: hellshakeyano\n3\nhell\nshake\nkey\n output: 2\nIn this case, for example, if you change \"hellshakeyano\" into \"h*llsha*eyano\", you can satisfy the condition. Notice if you replace one character, it might happen that several strings in the set P\n, which appear as the consecutive substring of S\n, simultaneously disappear.\n\n" }, { "title": "Problem A. Guru Guru", "content": "You are playing a game called Guru Guru Gururin. In this game, you can move with the vehicle called Gururin. There are two commands you can give to Gururin: 'R' and 'L'. When 'R' is sent, Gururin rotates clockwise by 90 degrees. Otherwise, when 'L' is sent, Gururin rotates counterclockwise by 90 degrees.\n\n During the game, you noticed that Gururin obtains magical power by performing special commands. In short, Gururin obtains magical power every time when it performs one round in the clockwise direction from north to north. In more detail, the conditions under which magical power can be obtained is as follows.\n\nAt the beginning of the special commands, Gururin faces north.\n\nAt the end of special commands, Gururin faces north.\n\nExcept for the beginning and the end of special commands, Gururin does not face north.\n\nDuring the special commands, Gururin faces north, east, south, and west one or more times, respectively, after the command of 'R'.\n At the beginning of the game, Gururin faces north. For example, if the sequence of commands Gururin received in order is 'RRRR' or 'RRLRRLRR', Gururin can obtain magical power. Otherwise, if the sequence of commands is 'LLLL' or 'RLLR', Gururin cannot obtain magical power.\n\n Your task is to calculate how many times Gururin obtained magical power throughout the game. In other words, given the sequence of the commands Gururin received, calculate how many special commands exists in it.", "constraint": "", "input": "The input consists of a single test case in the format below.\n\n$S$\n\n The first line consists of a string $S$, which represents the sequence of commands Gururin received. $S$ consists of 'L' and 'R'. The length of $S$ is between $1$ and $10^3$ inclusive.", "output": "Print the number of times Gururin obtained magical power throughout the game in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: RRRRLLLLRRRR\n output: 2", "input: RLLRLLLLRRRLLLRRR\n output: 0", "input: LR\n output: 0", "input: RRLRRLRRRRLRRLRRRRLRRLRRRRLRRLRR\n output: 4"], "Pid": "p02004", "ProblemText": "Task Description: You are playing a game called Guru Guru Gururin. In this game, you can move with the vehicle called Gururin. There are two commands you can give to Gururin: 'R' and 'L'. When 'R' is sent, Gururin rotates clockwise by 90 degrees. Otherwise, when 'L' is sent, Gururin rotates counterclockwise by 90 degrees.\n\n During the game, you noticed that Gururin obtains magical power by performing special commands. In short, Gururin obtains magical power every time when it performs one round in the clockwise direction from north to north. In more detail, the conditions under which magical power can be obtained is as follows.\n\nAt the beginning of the special commands, Gururin faces north.\n\nAt the end of special commands, Gururin faces north.\n\nExcept for the beginning and the end of special commands, Gururin does not face north.\n\nDuring the special commands, Gururin faces north, east, south, and west one or more times, respectively, after the command of 'R'.\n At the beginning of the game, Gururin faces north. For example, if the sequence of commands Gururin received in order is 'RRRR' or 'RRLRRLRR', Gururin can obtain magical power. Otherwise, if the sequence of commands is 'LLLL' or 'RLLR', Gururin cannot obtain magical power.\n\n Your task is to calculate how many times Gururin obtained magical power throughout the game. In other words, given the sequence of the commands Gururin received, calculate how many special commands exists in it.\nTask Input: The input consists of a single test case in the format below.\n\n$S$\n\n The first line consists of a string $S$, which represents the sequence of commands Gururin received. $S$ consists of 'L' and 'R'. The length of $S$ is between $1$ and $10^3$ inclusive.\nTask Output: Print the number of times Gururin obtained magical power throughout the game in one line.\nTask Samples: input: RRRRLLLLRRRR\n output: 2\ninput: RLLRLLLLRRRLLLRRR\n output: 0\ninput: LR\n output: 0\ninput: RRLRRLRRRRLRRLRRRRLRRLRRRRLRRLRR\n output: 4\n\n" }, { "title": "Problem B. Colorful Drink", "content": "You cannot use a mixed colored liquid as a layer. Thus, for instance, you cannot create a new liquid with a new color by mixing two or more different colored liquids, nor create a liquid with a density between two or more liquids with the same color by mixing them.\n\nOnly a colored liquid with strictly less density can be an upper layer of a denser colored liquid in a drink. That is, you can put a layer of a colored liquid with density $x$ directly above the layer of a colored liquid with density $y$ if $x < y$ holds.", "constraint": "", "input": "The input consists of a single test case in the format below.\n$N$\n$C_1$ $D_1$\n$\\vdots$\n$C_N$ $D_N$\n$M$\n$O_1$\n$\\vdots$\n$O_M$\n The first line consists of an integer $N$ ($1 <= N <= 10^5$), which represents the number of the prepared colored liquids. The following $N$ lines consists of $C_i$ and $D_i$ ($1 <= i <= N$). $C_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th prepared colored liquid. The length of $C_i$ is between $1$ and $20$ inclusive. $D_i$ is an integer and represents the density of the $i$-th prepared colored liquid. The value of $D_i$ is between $1$ and $10^5$ inclusive. The ($N+2$)-nd line consists of an integer $M$ ($1 <= M <= 10^5$), which represents the number of color layers of a drink request. The following $M$ lines consists of $O_i$ ($1 <= i <= M$). $O_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th layer from the top of the drink request. The length of $O_i$ is between $1$ and $20$ inclusive.", "output": "Yes No", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\nwhite 20\nblack 10\n2\nblack\nwhite\n output: yes", "input: 2\nwhite 10\nblack 10\n2\nblack\nwhite\n output: no", "input: 2\nwhite 20\nblack 10\n2\nblack\norange\n output: no", "input: 3\nwhite 10\nred 20\nwhite 30\n3\nwhite\nred\nwhite\n output: yes", "input: 4\nred 3444\nred 3018\nred 3098\nred 3319\n4\nred\nred\nred\nred\n output: yes"], "Pid": "p02005", "ProblemText": "Task Description: You cannot use a mixed colored liquid as a layer. Thus, for instance, you cannot create a new liquid with a new color by mixing two or more different colored liquids, nor create a liquid with a density between two or more liquids with the same color by mixing them.\n\nOnly a colored liquid with strictly less density can be an upper layer of a denser colored liquid in a drink. That is, you can put a layer of a colored liquid with density $x$ directly above the layer of a colored liquid with density $y$ if $x < y$ holds.\nTask Input: The input consists of a single test case in the format below.\n$N$\n$C_1$ $D_1$\n$\\vdots$\n$C_N$ $D_N$\n$M$\n$O_1$\n$\\vdots$\n$O_M$\n The first line consists of an integer $N$ ($1 <= N <= 10^5$), which represents the number of the prepared colored liquids. The following $N$ lines consists of $C_i$ and $D_i$ ($1 <= i <= N$). $C_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th prepared colored liquid. The length of $C_i$ is between $1$ and $20$ inclusive. $D_i$ is an integer and represents the density of the $i$-th prepared colored liquid. The value of $D_i$ is between $1$ and $10^5$ inclusive. The ($N+2$)-nd line consists of an integer $M$ ($1 <= M <= 10^5$), which represents the number of color layers of a drink request. The following $M$ lines consists of $O_i$ ($1 <= i <= M$). $O_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th layer from the top of the drink request. The length of $O_i$ is between $1$ and $20$ inclusive.\nTask Output: Yes No\nTask Samples: input: 2\nwhite 20\nblack 10\n2\nblack\nwhite\n output: yes\ninput: 2\nwhite 10\nblack 10\n2\nblack\nwhite\n output: no\ninput: 2\nwhite 20\nblack 10\n2\nblack\norange\n output: no\ninput: 3\nwhite 10\nred 20\nwhite 30\n3\nwhite\nred\nwhite\n output: yes\ninput: 4\nred 3444\nred 3018\nred 3098\nred 3319\n4\nred\nred\nred\nred\n output: yes\n\n" }, { "title": "Problem C. Santa's Gift", "content": "Santa is going to pack gifts into a bag for a family. There are $N$ kinds of gifts. The size and the price of the $i$-th gift ($1 <= i <= N$) are $s_i$ and $p_i$, respectively. The size of the bag is $C$, thus Santa can pack gifts so that the total size of the gifts does not exceed $C$. Children are unhappy if they are given multiple items of the same kind gift, so Santa has to choose at most one gift of the same kind per child.\n\n In addition, if a child did not receive a gift that the other children in the same family receive, he/she will complain about that. Hence Santa must distribute gifts fairly to all the children of a family, by giving the same set of gifts to each child. In other words, for a family with $k$ children, Santa must pack zero or $k$ items for each kind of gifts. Santa gives one bag to one family, therefore, the total size of the gifts for each family does not exceed $C$.\n\n Santa wants to maximize the total price of packed items for a family but does not know the number of children in the family he is going to visit yet. The number seems at most $M$. To prepare all the possible cases, calculate the maximum total price of items for a family with $k$ children for each $1 <= k <= M$.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$C$ $N$ $M$\n$s_1$ $p_1$\n$. . . $\n$s_N$ $p_N$\n\n The first line contains three integers $C$, $N$ and $M$, where $C$ ($1 <= C <= 10^4$) is the size of the bag, $N$ ($1 <= N <= 10^4$) is the number of kinds of the gifts, and $M$ ($1 <= M <= 10^4$) is the maximum number of children in the family. The $i$-th line of the following $N$ lines contains two integers $s_i$ and $p_i$ ($1 <= s_i, p_i <= 10^4$), where $s_i$ and $p_i$ are the size and the price of the $i$-th gift, respectively.", "output": "The output should consist of $M$ lines. In the $k$-th line, print the maximum total price of gifts for a family with $k$ children.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3 2\n1 2\n2 10\n3 5\n output: 17\n24", "input: 200 5 5\n31 41\n59 26\n53 58\n97 93\n23 84\n output: 235\n284\n375\n336\n420", "input: 1 1 2\n1 1\n output: 1\n0", "input: 2 2 2\n1 1\n2 100\n output: 100\n2"], "Pid": "p02006", "ProblemText": "Task Description: Santa is going to pack gifts into a bag for a family. There are $N$ kinds of gifts. The size and the price of the $i$-th gift ($1 <= i <= N$) are $s_i$ and $p_i$, respectively. The size of the bag is $C$, thus Santa can pack gifts so that the total size of the gifts does not exceed $C$. Children are unhappy if they are given multiple items of the same kind gift, so Santa has to choose at most one gift of the same kind per child.\n\n In addition, if a child did not receive a gift that the other children in the same family receive, he/she will complain about that. Hence Santa must distribute gifts fairly to all the children of a family, by giving the same set of gifts to each child. In other words, for a family with $k$ children, Santa must pack zero or $k$ items for each kind of gifts. Santa gives one bag to one family, therefore, the total size of the gifts for each family does not exceed $C$.\n\n Santa wants to maximize the total price of packed items for a family but does not know the number of children in the family he is going to visit yet. The number seems at most $M$. To prepare all the possible cases, calculate the maximum total price of items for a family with $k$ children for each $1 <= k <= M$.\nTask Input: The input consists of a single test case in the following format.\n\n$C$ $N$ $M$\n$s_1$ $p_1$\n$. . . $\n$s_N$ $p_N$\n\n The first line contains three integers $C$, $N$ and $M$, where $C$ ($1 <= C <= 10^4$) is the size of the bag, $N$ ($1 <= N <= 10^4$) is the number of kinds of the gifts, and $M$ ($1 <= M <= 10^4$) is the maximum number of children in the family. The $i$-th line of the following $N$ lines contains two integers $s_i$ and $p_i$ ($1 <= s_i, p_i <= 10^4$), where $s_i$ and $p_i$ are the size and the price of the $i$-th gift, respectively.\nTask Output: The output should consist of $M$ lines. In the $k$-th line, print the maximum total price of gifts for a family with $k$ children.\nTask Samples: input: 6 3 2\n1 2\n2 10\n3 5\n output: 17\n24\ninput: 200 5 5\n31 41\n59 26\n53 58\n97 93\n23 84\n output: 235\n284\n375\n336\n420\ninput: 1 1 2\n1 1\n output: 1\n0\ninput: 2 2 2\n1 1\n2 100\n output: 100\n2\n\n" }, { "title": "Problem D. Prefix Suffix Search", "content": "As an English learner, sometimes you cannot remember the entire spelling of English words perfectly, but you can only remember their prefixes and suffixes. For example, you may want to use a word which begins with 'appr' and ends with 'iate', but forget the middle part of the word. It may be 'appreciate', 'appropriate', or something like them.\n\n By using an ordinary dictionary, you can look up words beginning with a certain prefix, but it is inconvenient for further filtering words ending with a certain suffix. Thus it is helpful to achieve dictionary functionality which can be used for finding words with a given prefix and suffix. In the beginning, let's count the number of such words instead of explicitly listing them.\n\n More formally, you are given a list of $N$ words. Next, you are given $Q$ queries consisting of two strings. Your task is to write a program which outputs the number of words with the prefix and suffix for each query in the given list.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$N$ $Q$\n$w_1$\n$. . . $\n$w_N$\n$p_1$ $s_1$\n$. . . $\n$p_Q$ $s_Q$\n\n The first line contains two integers $N$ and $Q$, where $N$ ($1 <= N <= 10^5$) is the number of words in the list, and $Q$ ($1 <= Q <= 10^5$) is the number of queries. The $i$-th line of the following $N$ lines contains a string $w_i$. The $i$-th of the following $Q$ lines contains two strings $p_i$ and $s_i$, which are a prefix and suffix of words to be searched, respectively.\n\n You can assume the followings:\n\nAll the strings in an input are non-empty and consist only of lowercase English letters.\n\nThe total length of input strings does not exceed $2,500,000$.\n\nWords in the given list are unique: $w_i \\ne w_j$ if $i \\ne j$.\n\nPairs of a prefix and suffix are unique: $(p_i, s_i) \\ne (p_j, s_j)$ if $i \\ne j$.", "output": "For each query, output the number of words with a given prefix and suffix in the given list per a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 7\nappreciate\nappropriate\nacceptance\nace\nacm\nacetylene\nappr iate\na e\na a\nac ce\nace e\nacceptance acceptance\nno match\n output: 2\n5\n0\n2\n2\n1\n0", "input: 5 5\nd\ndd\nddd\ndddd\nddddd\nd d\ndd dd\nddd ddd\nd dddd\nddddd dd\n output: 5\n4\n3\n2\n1", "input: 7 4\nconnected\ndisconnected\ngraph\ndirected\ndiameter\ndistance\nminor\nc ed\ndi ed\ndis ed\ndis e\n output: 1\n2\n1\n1"], "Pid": "p02007", "ProblemText": "Task Description: As an English learner, sometimes you cannot remember the entire spelling of English words perfectly, but you can only remember their prefixes and suffixes. For example, you may want to use a word which begins with 'appr' and ends with 'iate', but forget the middle part of the word. It may be 'appreciate', 'appropriate', or something like them.\n\n By using an ordinary dictionary, you can look up words beginning with a certain prefix, but it is inconvenient for further filtering words ending with a certain suffix. Thus it is helpful to achieve dictionary functionality which can be used for finding words with a given prefix and suffix. In the beginning, let's count the number of such words instead of explicitly listing them.\n\n More formally, you are given a list of $N$ words. Next, you are given $Q$ queries consisting of two strings. Your task is to write a program which outputs the number of words with the prefix and suffix for each query in the given list.\nTask Input: The input consists of a single test case in the following format.\n\n$N$ $Q$\n$w_1$\n$. . . $\n$w_N$\n$p_1$ $s_1$\n$. . . $\n$p_Q$ $s_Q$\n\n The first line contains two integers $N$ and $Q$, where $N$ ($1 <= N <= 10^5$) is the number of words in the list, and $Q$ ($1 <= Q <= 10^5$) is the number of queries. The $i$-th line of the following $N$ lines contains a string $w_i$. The $i$-th of the following $Q$ lines contains two strings $p_i$ and $s_i$, which are a prefix and suffix of words to be searched, respectively.\n\n You can assume the followings:\n\nAll the strings in an input are non-empty and consist only of lowercase English letters.\n\nThe total length of input strings does not exceed $2,500,000$.\n\nWords in the given list are unique: $w_i \\ne w_j$ if $i \\ne j$.\n\nPairs of a prefix and suffix are unique: $(p_i, s_i) \\ne (p_j, s_j)$ if $i \\ne j$.\nTask Output: For each query, output the number of words with a given prefix and suffix in the given list per a line.\nTask Samples: input: 6 7\nappreciate\nappropriate\nacceptance\nace\nacm\nacetylene\nappr iate\na e\na a\nac ce\nace e\nacceptance acceptance\nno match\n output: 2\n5\n0\n2\n2\n1\n0\ninput: 5 5\nd\ndd\nddd\ndddd\nddddd\nd d\ndd dd\nddd ddd\nd dddd\nddddd dd\n output: 5\n4\n3\n2\n1\ninput: 7 4\nconnected\ndisconnected\ngraph\ndirected\ndiameter\ndistance\nminor\nc ed\ndi ed\ndis ed\ndis e\n output: 1\n2\n1\n1\n\n" }, { "title": "Problem E. Magic Triangles", "content": "Fallen angel Yohane plans to draw a magic symbol composed of triangles on the earth. By casting some magic spell on the symbol, she will obtain magic power; this is the purpose for which she will draw a magic symbol. The magic power yielded from the magic symbol is determined only by the common area of all the triangles. Suppose the earth is a two-dimensional plane and the vertices of the triangles are points on the plane. Yohane has already had a design of the magic symbol, i. e. the positions, sizes, shapes of the triangles. However, she does not know how much magic power will be obtained from the symbol. Your task as a familiar of the fallen angel is to write a program calculating the common area of given triangles on a two-dimensional plane.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$N$\n$x_{1,1}$ $y_{1,1}$ $x_{1,2}$ $y_{1,2}$ $x_{1,3}$ $y_{1,3}$\n$. . . $\n$x_{N, 1}$ $y_{N, 1}$ $x_{N, 2}$ $y_{N, 2}$ $x_{N, 3}$ $y_{N, 3}$\n\n The first line contains an integer $N$, which is the number of triangles ($1 <= N <= 10^5$). The $i$-th line of the following $N$ lines contains six integers $x_{i, 1}$, $y_{i, 1}$, $x_{i, 2}$, $y_{i, 2}$, $x_{i, 3}$, and $y_{i, 3}$, where ($x_{i, j}, y_{i, j}$)is the coordinate of the $j$-th vertex of the $i$-th triangle ($-1,000 <= x_{i, j}, y_{i, j} <= 1,000$).\n\n You can assume the followings:\n\nEvery triangle has a positive area.\n\nThe vertices of every triangle are in the counter-clockwise order.", "output": "Output the common area of given triangles in a line. The output can contain an absolute or relative error no more than $10^{-6}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0 2 0 0 2\n0 1 2 1 0 3\n output: 0.5", "input: 2\n0 0 100 0 50 100\n50 -50 100 50 0 50\n output: 3125", "input: 5\n0 0 1 0 0 1\n0 0 2 0 0 2\n0 0 3 0 0 3\n0 0 4 0 0 4\n0 0 5 0 0 5\n output: 0.5"], "Pid": "p02008", "ProblemText": "Task Description: Fallen angel Yohane plans to draw a magic symbol composed of triangles on the earth. By casting some magic spell on the symbol, she will obtain magic power; this is the purpose for which she will draw a magic symbol. The magic power yielded from the magic symbol is determined only by the common area of all the triangles. Suppose the earth is a two-dimensional plane and the vertices of the triangles are points on the plane. Yohane has already had a design of the magic symbol, i. e. the positions, sizes, shapes of the triangles. However, she does not know how much magic power will be obtained from the symbol. Your task as a familiar of the fallen angel is to write a program calculating the common area of given triangles on a two-dimensional plane.\nTask Input: The input consists of a single test case in the following format.\n\n$N$\n$x_{1,1}$ $y_{1,1}$ $x_{1,2}$ $y_{1,2}$ $x_{1,3}$ $y_{1,3}$\n$. . . $\n$x_{N, 1}$ $y_{N, 1}$ $x_{N, 2}$ $y_{N, 2}$ $x_{N, 3}$ $y_{N, 3}$\n\n The first line contains an integer $N$, which is the number of triangles ($1 <= N <= 10^5$). The $i$-th line of the following $N$ lines contains six integers $x_{i, 1}$, $y_{i, 1}$, $x_{i, 2}$, $y_{i, 2}$, $x_{i, 3}$, and $y_{i, 3}$, where ($x_{i, j}, y_{i, j}$)is the coordinate of the $j$-th vertex of the $i$-th triangle ($-1,000 <= x_{i, j}, y_{i, j} <= 1,000$).\n\n You can assume the followings:\n\nEvery triangle has a positive area.\n\nThe vertices of every triangle are in the counter-clockwise order.\nTask Output: Output the common area of given triangles in a line. The output can contain an absolute or relative error no more than $10^{-6}$.\nTask Samples: input: 2\n0 0 2 0 0 2\n0 1 2 1 0 3\n output: 0.5\ninput: 2\n0 0 100 0 50 100\n50 -50 100 50 0 50\n output: 3125\ninput: 5\n0 0 1 0 0 1\n0 0 2 0 0 2\n0 0 3 0 0 3\n0 0 4 0 0 4\n0 0 5 0 0 5\n output: 0.5\n\n" }, { "title": "Problem F. Nim without Zero", "content": "Alice: \"Hi, Bob! Let's play Nim! \"\nBob: \"Are you serious? I don't want to play it. I know how to win the game. \"\nAlice: \"Right, there is an algorithm to calculate the optimal move using XOR. How about changing the rule so that a player loses a game if he or she makes the XOR to $0$? \"\nBob: \"It sounds much better now, but I suspect you know the surefire way to win. \"\nAlice: \"Do you wanna test me? \"\nThis game is defined as follows. \n\n The game starts with $N$ heaps where the $i$-th of them consists of $a_i$ stones.\n\n A player takes any positive number of stones from any single one of the heaps in one move.\n\n Alice moves first. The two players alternately move.\n\n If the XOR sum, $a_1$ XOR $a_2$ XOR $. . . $ XOR $a_N$, of the numbers of remaining stones of these heaps becomes $0$ as a result of a player's move, the player loses.\n Your task is to find which player will win if they do the best move.", "constraint": "", "input": "The input consists of a single test case in the format below.\n\n$N$\n$a_1$\n$\\vdots$\n$a_N$\n\n The first line contains an integer $N$ which is the number of the heaps ($1 <= N <= 10^5$). Each of the following $N$ lines gives the number of stones in each heap ($1 <= a_i <= 10^9$).", "output": "Output the winner, Alice or Bob, when they do the best move.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1\n1\n output: Alice", "input: 5\n1\n2\n3\n4\n5\n output: Bob", "input: 10\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n output: Alice\n In the first example, the XOR sum is 0 in the initial state, but the game is going because nobody moves yet. First Alice takes a stone and the XOR sum becomes 1, then Bob takes the last stone and the XOR sum becomes 0. Therefore, Alice will win, and Bob will lose."], "Pid": "p02009", "ProblemText": "Task Description: Alice: \"Hi, Bob! Let's play Nim! \"\nBob: \"Are you serious? I don't want to play it. I know how to win the game. \"\nAlice: \"Right, there is an algorithm to calculate the optimal move using XOR. How about changing the rule so that a player loses a game if he or she makes the XOR to $0$? \"\nBob: \"It sounds much better now, but I suspect you know the surefire way to win. \"\nAlice: \"Do you wanna test me? \"\nThis game is defined as follows. \n\n The game starts with $N$ heaps where the $i$-th of them consists of $a_i$ stones.\n\n A player takes any positive number of stones from any single one of the heaps in one move.\n\n Alice moves first. The two players alternately move.\n\n If the XOR sum, $a_1$ XOR $a_2$ XOR $. . . $ XOR $a_N$, of the numbers of remaining stones of these heaps becomes $0$ as a result of a player's move, the player loses.\n Your task is to find which player will win if they do the best move.\nTask Input: The input consists of a single test case in the format below.\n\n$N$\n$a_1$\n$\\vdots$\n$a_N$\n\n The first line contains an integer $N$ which is the number of the heaps ($1 <= N <= 10^5$). Each of the following $N$ lines gives the number of stones in each heap ($1 <= a_i <= 10^9$).\nTask Output: Output the winner, Alice or Bob, when they do the best move.\nTask Samples: input: 2\n1\n1\n output: Alice\ninput: 5\n1\n2\n3\n4\n5\n output: Bob\ninput: 10\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n output: Alice\n In the first example, the XOR sum is 0 in the initial state, but the game is going because nobody moves yet. First Alice takes a stone and the XOR sum becomes 1, then Bob takes the last stone and the XOR sum becomes 0. Therefore, Alice will win, and Bob will lose.\n\n" }, { "title": "Problem G. Additions", "content": "You are given an integer $N$ and a string consisting of '+' and digits. You are asked to transform the string into a valid formula whose calculation result is smaller than or equal to $N$ by modifying some characters. Here, you replace one character with another character any number of times, and the converted string should still consist of '+' and digits. Note that leading zeros and unary positive are prohibited.\n\n For instance, '0123+456' is assumed as invalid because leading zero is prohibited. Similarly, '+1+2' and '2++3' are also invalid as they each contain a unary expression. On the other hand, '12345', '0+1+2' and '1234+0+0' are all valid.\n\n Your task is to find the minimum number of the replaced characters. If there is no way to make a valid formula smaller than or equal to $N$, output $-1$ instead of the number of the replaced characters.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$N$\n$S$\n\n The first line contains an integer $N$, which is the upper limit of the formula ($1 <= N <= 10^9$). The second line contains a string $S$, which consists of '+' and digits and whose length is between $1$ and $1,000$, inclusive. Note that it is not guaranteed that initially $S$ is a valid formula.", "output": "Output the minimized number of the replaced characters. If there is no way to replace, output $-1$ instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100\n+123\n output: 2", "input: 10\n+123\n output: 4", "input: 1\n+123\n output: -1", "input: 10\n++1+\n output: 2", "input: 2000\n1234++7890\n output: 2\n In the first example, you can modify the first two characters and make a formula '1+23\n', for instance. In the second example, you should make '0+10\n' or '10+0\n' by replacing all the characters. In the third example, you cannot make any valid formula less than or equal to $1$."], "Pid": "p02010", "ProblemText": "Task Description: You are given an integer $N$ and a string consisting of '+' and digits. You are asked to transform the string into a valid formula whose calculation result is smaller than or equal to $N$ by modifying some characters. Here, you replace one character with another character any number of times, and the converted string should still consist of '+' and digits. Note that leading zeros and unary positive are prohibited.\n\n For instance, '0123+456' is assumed as invalid because leading zero is prohibited. Similarly, '+1+2' and '2++3' are also invalid as they each contain a unary expression. On the other hand, '12345', '0+1+2' and '1234+0+0' are all valid.\n\n Your task is to find the minimum number of the replaced characters. If there is no way to make a valid formula smaller than or equal to $N$, output $-1$ instead of the number of the replaced characters.\nTask Input: The input consists of a single test case in the following format.\n\n$N$\n$S$\n\n The first line contains an integer $N$, which is the upper limit of the formula ($1 <= N <= 10^9$). The second line contains a string $S$, which consists of '+' and digits and whose length is between $1$ and $1,000$, inclusive. Note that it is not guaranteed that initially $S$ is a valid formula.\nTask Output: Output the minimized number of the replaced characters. If there is no way to replace, output $-1$ instead.\nTask Samples: input: 100\n+123\n output: 2\ninput: 10\n+123\n output: 4\ninput: 1\n+123\n output: -1\ninput: 10\n++1+\n output: 2\ninput: 2000\n1234++7890\n output: 2\n In the first example, you can modify the first two characters and make a formula '1+23\n', for instance. In the second example, you should make '0+10\n' or '10+0\n' by replacing all the characters. In the third example, you cannot make any valid formula less than or equal to $1$.\n\n" }, { "title": "Problem H. Enlarge Circles", "content": "You are given $N$ distinct points on the 2-D plane. For each point, you are going to make a single circle whose center is located at the point. Your task is to maximize the sum of perimeters of these $N$ circles so that circles do not overlap each other. Here, \"overlap\" means that two circles have a common point which is not on the circumference of at least either of them. Therefore, the circumferences can be touched. Note that you are allowed to make a circle with radius $0$.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$N$\n$x_1$ $y_1$\n$\\vdots$\n$x_N$ $y_N$\n\n The first line contains an integer $N$, which is the number of points ($2 <= N <= 200$). Each of the following $N$ lines gives the coordinates of a point. Integers $x_i$ and $y_i$ ($-100 <= x_i, y_i <= 100$) in the $i$-th line of them give the $x$- and $y$-coordinates, respectively, of the $i$-th point. These points are distinct, in other words, $(x_i, y_i) \\ne (x_j, y_j)$ is satisfied if $i$ and $j$ are different.", "output": "Output the maximized sum of perimeters. The output can contain an absolute or a relative error no more than $10^{-6}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0\n3 0\n5 0\n output: 31.415926535", "input: 3\n0 0\n5 0\n0 5\n output: 53.630341225", "input: 9\n91 -18\n13 93\n73 -34\n15 2\n-46 0\n69 -42\n-23 -13\n-87 41\n38 68\n output: 1049.191683488"], "Pid": "p02011", "ProblemText": "Task Description: You are given $N$ distinct points on the 2-D plane. For each point, you are going to make a single circle whose center is located at the point. Your task is to maximize the sum of perimeters of these $N$ circles so that circles do not overlap each other. Here, \"overlap\" means that two circles have a common point which is not on the circumference of at least either of them. Therefore, the circumferences can be touched. Note that you are allowed to make a circle with radius $0$.\nTask Input: The input consists of a single test case in the following format.\n\n$N$\n$x_1$ $y_1$\n$\\vdots$\n$x_N$ $y_N$\n\n The first line contains an integer $N$, which is the number of points ($2 <= N <= 200$). Each of the following $N$ lines gives the coordinates of a point. Integers $x_i$ and $y_i$ ($-100 <= x_i, y_i <= 100$) in the $i$-th line of them give the $x$- and $y$-coordinates, respectively, of the $i$-th point. These points are distinct, in other words, $(x_i, y_i) \\ne (x_j, y_j)$ is satisfied if $i$ and $j$ are different.\nTask Output: Output the maximized sum of perimeters. The output can contain an absolute or a relative error no more than $10^{-6}$.\nTask Samples: input: 3\n0 0\n3 0\n5 0\n output: 31.415926535\ninput: 3\n0 0\n5 0\n0 5\n output: 53.630341225\ninput: 9\n91 -18\n13 93\n73 -34\n15 2\n-46 0\n69 -42\n-23 -13\n-87 41\n38 68\n output: 1049.191683488\n\n" }, { "title": "Problem I. Sum of QQ", "content": "You received a card with an integer $S$ and a multiplication table of infinite size. All the elements in the table are integers, and an integer at the $i$-th row from the top and the $j$-th column from the left is $A_{i, j} = i * j$ ($i, j >= 1$). The table has infinite size, i. e. , the number of the rows and the number of the columns are infinite.\n\n You love rectangular regions of the table in which the sum of numbers is $S$. Your task is to count the number of integer tuples $(a, b, c, d)$ that satisfies $1 <= a <= b, 1 <= c <= d$ and $\\sum_{i=a}^b \\sum_{j=c}^d A_{i, j} = S$.", "constraint": "", "input": "The input consists of a single test case of the following form.\n\n$S$ \n\n The first line consists of one integer $S$ ($1 <= S <= 10^5$), representing the summation of rectangular regions you have to find.", "output": "Print the number of rectangular regions whose summation is $S$ in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 25\n output: 10", "input: 1\n output: 1", "input: 5\n output: 4", "input: 83160\n output: 5120"], "Pid": "p02012", "ProblemText": "Task Description: You received a card with an integer $S$ and a multiplication table of infinite size. All the elements in the table are integers, and an integer at the $i$-th row from the top and the $j$-th column from the left is $A_{i, j} = i * j$ ($i, j >= 1$). The table has infinite size, i. e. , the number of the rows and the number of the columns are infinite.\n\n You love rectangular regions of the table in which the sum of numbers is $S$. Your task is to count the number of integer tuples $(a, b, c, d)$ that satisfies $1 <= a <= b, 1 <= c <= d$ and $\\sum_{i=a}^b \\sum_{j=c}^d A_{i, j} = S$.\nTask Input: The input consists of a single test case of the following form.\n\n$S$ \n\n The first line consists of one integer $S$ ($1 <= S <= 10^5$), representing the summation of rectangular regions you have to find.\nTask Output: Print the number of rectangular regions whose summation is $S$ in one line.\nTask Samples: input: 25\n output: 10\ninput: 1\n output: 1\ninput: 5\n output: 4\ninput: 83160\n output: 5120\n\n" }, { "title": "Problem J. Prime Routing", "content": "Fox Jiro is one of the staffs of the ACM-ICPC 2018 Asia Yokohama Regional Contest and is responsible for designing the network for the venue of the contest. His network consists of $N$ computers, which are connected by $M$ cables. The $i$-th cable connects the $a_i$-th computer and the $b_i$-th computer, and it carries data in both directions. Your team will use the $S$-th computer in the contest, and a judge server is the $T$-th computer.\n\n He decided to adjust the routing algorithm of the network to maximize the performance of the contestants through the magical power of prime numbers. In this algorithm, a packet (a unit of data carried by the network) is sent from your computer to the judge server passing through the cables a prime number of times if possible. If it is impossible, the contestants cannot benefit by the magical power of prime numbers. To accomplish this target, a packet is allowed to pass through the same cable multiple times.\n\n You decided to write a program to calculate the minimum number of times a packet from $S$ to $T$ needed to pass through the cables. If the number of times a packet passes through the cables cannot be a prime number, print $-1$.", "constraint": "", "input": "The input consists of a single test case, formatted as follows.\n\n$N$ $M$ $S$ $T$\n$a_1$ $b_1$\n$\\vdots$\n$a_M$ $b_M$\n\n The first line consists of four integers $N, M, S, $ and $T$ ($2 <= N <= 10^5,1 <= M <= 10^5,1 <= S, T <= N, S \\ne T$). The $i$-th line of the following $M$ lines consists of two integers $a_i$ and $b_i$ ($1 <= a_i < b_i <= N$), which means the $i$-th cables connects the $a_i$-th computer and the $b_i$-th computer in the network. You can assume that the network satisfies the following conditions.\n\t \nThe network has no multi-edge, i. e. , $(a_i, b_i) \\ne (a_j, b_j)$ for all $i, j$ ($1 <= i < j <= M$).\n\nThe packets from $N$ computers are reachable to $T$ by passing through some number of cables. The number is not necessarily a prime.", "output": "If there are ways such that the number of times a packet sent from $S$ to $T$ passes through the cables is a prime number, print the minimum prime number of times in one line. Otherwise, print $-1$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5 1 5\n1 2\n1 4\n2 3\n3 4\n3 5\n output: 3", "input: 5 4 1 5\n1 2\n2 3\n3 4\n4 5\n output: -1", "input: 2 1 1 2\n1 2\n output: 3", "input: 3 3 1 2\n1 2\n1 3\n2 3\n output: 2"], "Pid": "p02013", "ProblemText": "Task Description: Fox Jiro is one of the staffs of the ACM-ICPC 2018 Asia Yokohama Regional Contest and is responsible for designing the network for the venue of the contest. His network consists of $N$ computers, which are connected by $M$ cables. The $i$-th cable connects the $a_i$-th computer and the $b_i$-th computer, and it carries data in both directions. Your team will use the $S$-th computer in the contest, and a judge server is the $T$-th computer.\n\n He decided to adjust the routing algorithm of the network to maximize the performance of the contestants through the magical power of prime numbers. In this algorithm, a packet (a unit of data carried by the network) is sent from your computer to the judge server passing through the cables a prime number of times if possible. If it is impossible, the contestants cannot benefit by the magical power of prime numbers. To accomplish this target, a packet is allowed to pass through the same cable multiple times.\n\n You decided to write a program to calculate the minimum number of times a packet from $S$ to $T$ needed to pass through the cables. If the number of times a packet passes through the cables cannot be a prime number, print $-1$.\nTask Input: The input consists of a single test case, formatted as follows.\n\n$N$ $M$ $S$ $T$\n$a_1$ $b_1$\n$\\vdots$\n$a_M$ $b_M$\n\n The first line consists of four integers $N, M, S, $ and $T$ ($2 <= N <= 10^5,1 <= M <= 10^5,1 <= S, T <= N, S \\ne T$). The $i$-th line of the following $M$ lines consists of two integers $a_i$ and $b_i$ ($1 <= a_i < b_i <= N$), which means the $i$-th cables connects the $a_i$-th computer and the $b_i$-th computer in the network. You can assume that the network satisfies the following conditions.\n\t \nThe network has no multi-edge, i. e. , $(a_i, b_i) \\ne (a_j, b_j)$ for all $i, j$ ($1 <= i < j <= M$).\n\nThe packets from $N$ computers are reachable to $T$ by passing through some number of cables. The number is not necessarily a prime.\nTask Output: If there are ways such that the number of times a packet sent from $S$ to $T$ passes through the cables is a prime number, print the minimum prime number of times in one line. Otherwise, print $-1$.\nTask Samples: input: 5 5 1 5\n1 2\n1 4\n2 3\n3 4\n3 5\n output: 3\ninput: 5 4 1 5\n1 2\n2 3\n3 4\n4 5\n output: -1\ninput: 2 1 1 2\n1 2\n output: 3\ninput: 3 3 1 2\n1 2\n1 3\n2 3\n output: 2\n\n" }, { "title": "Problem K. Rough Sorting", "content": "For skilled programmers, it is very easy to implement a sorting function. Moreover, they often avoid full sorting to reduce computation time if it is not necessary. Here, we consider \"rough sorting\" which sorts an array except for some pairs of elements. More formally, we define an array is \"$K$-roughly sorted\" if an array is sorted except that at most $K$ pairs are in reversed order. For example, '1 3 2 4' is 1-roughly sorted because (3,2) is only the reversed pair. In the same way, '1 4 2 3' is 2-roughly sorted because (4,2) and (4,3) are reversed.\n\n Considering rough sorting by exchanging adjacent elements repeatedly, you need less number of swaps than full sorting. For example, '4 1 2 3' needs three exchanges for full sorting, but you only need to exchange once for 2-rough sorting.\n\n Given an array and an integer $K$, your task is to find the result of the $K$-rough sorting with a minimum number of exchanges. If there are several possible results, you should output the lexicographically minimum result. Here, the lexicographical order is defined by the order of the first different elements.", "constraint": "", "input": "The input consists of a single test case in the following format.\n\n$N$ $K$\n$x_1$\n$\\vdots$\n$x_N$\n \n The first line contains two integers $N$ and $K$. The integer $N$ is the number of the elements of the array ($1 <= N <= 10^5$). The integer $K$ gives how many reversed pairs are allowed ($1 <= K <= 10^9$). Each of the following $N$ lines gives the element of the array. The array consists of the permutation of $1$ to $N$, therefore $1 <= x_i <= N$ and $x_i \\ne x_j$ ($i \\ne j$) are satisfied.", "output": "The output should contain $N$ lines. The $i$-th line should be the $i$-th element of the result of the $K$-rough sorting. If there are several possible results, you should output the minimum result with the lexicographical order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n3\n2\n1\n output: 1\n3\n2", "input: 3 100\n3\n2\n1\n output: 3\n2\n1", "input: 5 3\n5\n3\n2\n1\n4\n output: 1\n3\n5\n2\n4", "input: 5 3\n1\n2\n3\n4\n5\n output: 1\n2\n3\n4\n5\nIn the last example, the input array is already sorted, which means the input is already a 3-roughly sorted array and no swapping is needed."], "Pid": "p02014", "ProblemText": "Task Description: For skilled programmers, it is very easy to implement a sorting function. Moreover, they often avoid full sorting to reduce computation time if it is not necessary. Here, we consider \"rough sorting\" which sorts an array except for some pairs of elements. More formally, we define an array is \"$K$-roughly sorted\" if an array is sorted except that at most $K$ pairs are in reversed order. For example, '1 3 2 4' is 1-roughly sorted because (3,2) is only the reversed pair. In the same way, '1 4 2 3' is 2-roughly sorted because (4,2) and (4,3) are reversed.\n\n Considering rough sorting by exchanging adjacent elements repeatedly, you need less number of swaps than full sorting. For example, '4 1 2 3' needs three exchanges for full sorting, but you only need to exchange once for 2-rough sorting.\n\n Given an array and an integer $K$, your task is to find the result of the $K$-rough sorting with a minimum number of exchanges. If there are several possible results, you should output the lexicographically minimum result. Here, the lexicographical order is defined by the order of the first different elements.\nTask Input: The input consists of a single test case in the following format.\n\n$N$ $K$\n$x_1$\n$\\vdots$\n$x_N$\n \n The first line contains two integers $N$ and $K$. The integer $N$ is the number of the elements of the array ($1 <= N <= 10^5$). The integer $K$ gives how many reversed pairs are allowed ($1 <= K <= 10^9$). Each of the following $N$ lines gives the element of the array. The array consists of the permutation of $1$ to $N$, therefore $1 <= x_i <= N$ and $x_i \\ne x_j$ ($i \\ne j$) are satisfied.\nTask Output: The output should contain $N$ lines. The $i$-th line should be the $i$-th element of the result of the $K$-rough sorting. If there are several possible results, you should output the minimum result with the lexicographical order.\nTask Samples: input: 3 1\n3\n2\n1\n output: 1\n3\n2\ninput: 3 100\n3\n2\n1\n output: 3\n2\n1\ninput: 5 3\n5\n3\n2\n1\n4\n output: 1\n3\n5\n2\n4\ninput: 5 3\n1\n2\n3\n4\n5\n output: 1\n2\n3\n4\n5\nIn the last example, the input array is already sorted, which means the input is already a 3-roughly sorted array and no swapping is needed.\n\n" }, { "title": "Problem Statement", "content": "Recently, AIs which play Go (a traditional board game) are well investigated.\nYour friend Hikaru is planning to develop a new awesome Go AI named Sai and promote it to company F or company G in the future.\nAs a first step, Hikaru has decided to develop an AI for 1D-Go, a restricted version of the original Go. In both of the original Go and 1D-Go, capturing stones is an important strategy.\nHikaru asked you to implement one of the functions of capturing. In 1D-Go, the game board consists of $L$ grids lie in a row.\nA state of 1D-go is described by a string $S$ of length $L$.\nThe $i$-th character of $S$ describes the $i$-th grid as the following:\nWhen the $i$-th character of $S$ is B, the $i$-th grid contains a stone which is colored black.\n\nWhen the $i$-th character of $S$ is W, the $i$-th grid contains a stone which is colored white.\n\nWhen the $i$-th character of $S$ is . , the $i$-th grid is empty.\n\nMaximal continuous stones of the same color are called a chain.\nWhen a chain is surrounded by stones with opponent's color, the chain will be captured. More precisely, if $i$-th grid and $j$-th grids ($1 < i + 1 < j <= L$) contain white stones and every grid of index $k$ ($i < k < j$) contains a black stone, these black stones will be captured, and vice versa about color. Please note that some of the rules of 1D-Go are quite different from the original Go.\nSome of the intuition obtained from the original Go may curse cause some mistakes. You are given a state of 1D-Go that next move will be played by the player with white stones.\nThe player can put a white stone into one of the empty cells.\nHowever, the player can not make a chain of white stones which is surrounded by black stones even if it simultaneously makes some chains of black stones be surrounded.\nIt is guaranteed that the given state has at least one grid where the player can put a white stone and there are no chains which are already surrounded. Write a program that computes the maximum number of black stones which can be captured by the next move of the white stones player.

    ", "constraint": "", "input": "The input consists of one line and has the following format: $L$ $S$$L$ ($1 <= L <= 100$) means the length of the game board and $S$ ($|S| = L$) is a string which describes the state of 1D-Go. The given state has at least one grid where the player can put a white stone and there are no chains which are already surrounded.", "output": "Output the maximum number of stones which can be captured by the next move in a line.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02067", "ProblemText": "Task Description: Recently, AIs which play Go (a traditional board game) are well investigated.\nYour friend Hikaru is planning to develop a new awesome Go AI named Sai and promote it to company F or company G in the future.\nAs a first step, Hikaru has decided to develop an AI for 1D-Go, a restricted version of the original Go. In both of the original Go and 1D-Go, capturing stones is an important strategy.\nHikaru asked you to implement one of the functions of capturing. In 1D-Go, the game board consists of $L$ grids lie in a row.\nA state of 1D-go is described by a string $S$ of length $L$.\nThe $i$-th character of $S$ describes the $i$-th grid as the following:\nWhen the $i$-th character of $S$ is B, the $i$-th grid contains a stone which is colored black.\n\nWhen the $i$-th character of $S$ is W, the $i$-th grid contains a stone which is colored white.\n\nWhen the $i$-th character of $S$ is . , the $i$-th grid is empty.\n\nMaximal continuous stones of the same color are called a chain.\nWhen a chain is surrounded by stones with opponent's color, the chain will be captured. More precisely, if $i$-th grid and $j$-th grids ($1 < i + 1 < j <= L$) contain white stones and every grid of index $k$ ($i < k < j$) contains a black stone, these black stones will be captured, and vice versa about color. Please note that some of the rules of 1D-Go are quite different from the original Go.\nSome of the intuition obtained from the original Go may curse cause some mistakes. You are given a state of 1D-Go that next move will be played by the player with white stones.\nThe player can put a white stone into one of the empty cells.\nHowever, the player can not make a chain of white stones which is surrounded by black stones even if it simultaneously makes some chains of black stones be surrounded.\nIt is guaranteed that the given state has at least one grid where the player can put a white stone and there are no chains which are already surrounded. Write a program that computes the maximum number of black stones which can be captured by the next move of the white stones player.
    \nTask Input: The input consists of one line and has the following format: $L$ $S$$L$ ($1 <= L <= 100$) means the length of the game board and $S$ ($|S| = L$) is a string which describes the state of 1D-Go. The given state has at least one grid where the player can put a white stone and there are no chains which are already surrounded.\nTask Output: Output the maximum number of stones which can be captured by the next move in a line.\n\n" }, { "title": "Problem Statement", "content": "You are given a positive integer sequence $A$ of length $N$. You can remove any numbers from the sequence to make the sequence “friendly\". \nA sequence is called friendly if there exists an integer $k$ (>1) such that every number in the sequence is a multiple of $k$.\nSince the empty sequence is friendly, it is guaranteed that you can make the initial sequence friendly. You noticed that there may be multiple ways to make the sequence friendly. So you decide to maximize the sum of all the numbers in the friendly sequence. Please calculate the maximum sum of the all numbers in the friendly sequence which can be obtained from the initial sequence.
    ", "constraint": "", "input": "The input consists of a single test case formatted as follows. $N$\n$A_1$\n$\\vdots$\n$A_N$The first line consists of a single integer $N$ ($1 <= N <= 1000$). The $i+1$-st line consists of an integer $A_i$ ($1 <= A_i <= 10^9$ for $1 <= i <= N$).", "output": "Print the maximum sum of all the numbers in the friendly sequence which can be obtained from the initial sequence.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02068", "ProblemText": "Task Description: You are given a positive integer sequence $A$ of length $N$. You can remove any numbers from the sequence to make the sequence “friendly\". \nA sequence is called friendly if there exists an integer $k$ (>1) such that every number in the sequence is a multiple of $k$.\nSince the empty sequence is friendly, it is guaranteed that you can make the initial sequence friendly. You noticed that there may be multiple ways to make the sequence friendly. So you decide to maximize the sum of all the numbers in the friendly sequence. Please calculate the maximum sum of the all numbers in the friendly sequence which can be obtained from the initial sequence.
    \nTask Input: The input consists of a single test case formatted as follows. $N$\n$A_1$\n$\\vdots$\n$A_N$The first line consists of a single integer $N$ ($1 <= N <= 1000$). The $i+1$-st line consists of an integer $A_i$ ($1 <= A_i <= 10^9$ for $1 <= i <= N$).\nTask Output: Print the maximum sum of all the numbers in the friendly sequence which can be obtained from the initial sequence.\n\n" }, { "title": "Problem Statement", "content": "You are given a list of $N$ intervals. The $i$-th interval is $[l_i, r_i)$, which denotes a range of numbers greater than or equal to $l_i$ and strictly less than $r_i$. In this task, you consider the following two numbers:\nThe minimum integer $x$ such that you can select $x$ intervals from the given $N$ intervals so that the union of the selected intervals is $[0, L)$.\n\nThe minimum integer $y$ such that for all possible combinations of $y$ intervals from the given $N$ interval, it does cover $[0, L)$.\n\nWe ask you to write a program to compute these two numbers.
    ", "constraint": "", "input": "The input consists of a single test case formatted as follows. $N$ $L$\n$l_1$ $r_1$\n$l_2$ $r_2$\n$\\vdots$\n$l_N$ $r_N$The first line contains two integers $N$ ($1 <= N <= 2 * 10^5$) and $L$ ($1 <= L <= 10^{12}$), where $N$ is the number of intervals and $L$ is the length of range to be covered, respectively. The $i$-th of the following $N$ lines contains two integers $l_i$ and $r_i$ ($0 <= l_i < r_i <= L$), representing the range of the $i$-th interval $[l_i, r_i)$. You can assume that the union of all the $N$ intervals is $[0, L)$", "output": "Output two integers $x$ and $y$ mentioned in the problem statement, separated by a single space, in a line.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02069", "ProblemText": "Task Description: You are given a list of $N$ intervals. The $i$-th interval is $[l_i, r_i)$, which denotes a range of numbers greater than or equal to $l_i$ and strictly less than $r_i$. In this task, you consider the following two numbers:\nThe minimum integer $x$ such that you can select $x$ intervals from the given $N$ intervals so that the union of the selected intervals is $[0, L)$.\n\nThe minimum integer $y$ such that for all possible combinations of $y$ intervals from the given $N$ interval, it does cover $[0, L)$.\n\nWe ask you to write a program to compute these two numbers.
    \nTask Input: The input consists of a single test case formatted as follows. $N$ $L$\n$l_1$ $r_1$\n$l_2$ $r_2$\n$\\vdots$\n$l_N$ $r_N$The first line contains two integers $N$ ($1 <= N <= 2 * 10^5$) and $L$ ($1 <= L <= 10^{12}$), where $N$ is the number of intervals and $L$ is the length of range to be covered, respectively. The $i$-th of the following $N$ lines contains two integers $l_i$ and $r_i$ ($0 <= l_i < r_i <= L$), representing the range of the $i$-th interval $[l_i, r_i)$. You can assume that the union of all the $N$ intervals is $[0, L)$\nTask Output: Output two integers $x$ and $y$ mentioned in the problem statement, separated by a single space, in a line.\n\n" }, { "title": "Problem Statement", "content": "One day (call it day 0), you find a permutation $P$ of $N$ integers written on the blackboard in a single row. \nFortunately you have another permutation $Q$ of $N$ integers, so you decide to play with these permutations. Every morning of the day 1,2,3, . . . , you rewrite every number on the blackboard in such a way that erases the number $x$ and write the number $Q_x$ at the same position. Please find the minimum non-negative integer $d$ such that in the evening of the day $d$ the sequence on the blackboard is sorted in increasing order.
    ", "constraint": "", "input": "The input consists of a single test case in the format below. $N$\n$P_1$ $\\ldots$ $P_N$\n$Q_1$ $\\ldots$ $Q_N$The first line contains an integer $N$ ($1 <= N <= 200$). The second line contains $N$ integers $P_1, \\ldots, P_N$ ($1 <= P_i <= N$) which represent the permutation $P$. The third line contains $N$ integers $Q_1, \\ldots, Q_N$ ($1 <= Q_i <= N$) which represent the permutation $Q$.", "output": "Print the minimum non-negative integer $d$ such that in the evening of the day $d$ the sequence on the blackboard is sorted in increasing order. If such $d$ does not exist, print -1 instead. It is guaranteed that the answer does not exceed $10^{18}$.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02070", "ProblemText": "Task Description: One day (call it day 0), you find a permutation $P$ of $N$ integers written on the blackboard in a single row. \nFortunately you have another permutation $Q$ of $N$ integers, so you decide to play with these permutations. Every morning of the day 1,2,3, . . . , you rewrite every number on the blackboard in such a way that erases the number $x$ and write the number $Q_x$ at the same position. Please find the minimum non-negative integer $d$ such that in the evening of the day $d$ the sequence on the blackboard is sorted in increasing order.
    \nTask Input: The input consists of a single test case in the format below. $N$\n$P_1$ $\\ldots$ $P_N$\n$Q_1$ $\\ldots$ $Q_N$The first line contains an integer $N$ ($1 <= N <= 200$). The second line contains $N$ integers $P_1, \\ldots, P_N$ ($1 <= P_i <= N$) which represent the permutation $P$. The third line contains $N$ integers $Q_1, \\ldots, Q_N$ ($1 <= Q_i <= N$) which represent the permutation $Q$.\nTask Output: Print the minimum non-negative integer $d$ such that in the evening of the day $d$ the sequence on the blackboard is sorted in increasing order. If such $d$ does not exist, print -1 instead. It is guaranteed that the answer does not exceed $10^{18}$.\n\n" }, { "title": "Problem Statement", "content": "Your company is developing a video game. In this game, players can exchange items. This trading follows the rule set by the developers. The rule is defined as the following format: \"Players can exchange one item $A_i$ and $x_i$ item $B_i$\". Note that the trading can be done in both directions. Items are exchanged between players and the game system. Therefore players can exchange items any number of times. Sometimes, testers find bugs that a repetition of a specific sequence of tradings causes the unlimited increment of items. For example, the following rule set can cause this bug.\nPlayers can exchange one item 1 and two item 2.\n\nPlayers can exchange one item 2 and two item 3.\n\nPlayers can exchange one item 1 and three item 3.\n\nIn this rule set, players can increase items unlimitedly. For example, players start tradings with one item 1. Using rules 1 and 2, they can exchange it for four item 3. And, using rule 3, they can get one item 1 and one item 3. By repeating this sequence, the amount of item 3 increases unlimitedly. These bugs can spoil the game, therefore the developers decided to introduce the system which prevents the inconsistent trading. Your task is to write a program which detects whether the rule set contains the bug or not.
    ", "constraint": "", "input": "The input consists of a single test case in the format below. $N$ $M$\n$A_{1}$ $B_{1}$ $x_{1}$\n$\\vdots$\n$A_{M}$ $B_{M}$ $x_{M}$The first line contains two integers $N$ and $M$ which are the number of types of items and the number of rules, respectively ($1 <= N <= 100 000$, $1 <= M <= 100 000$). Each of the following $M$ lines gives the trading rule that one item $A_{i}$ and $x_{i}$ item $B_{i}$ ($1 <= A_{i}, B_{i} <= N$, $1 <= x_{i} <= 1 000 000 000$) can be exchanged in both directions. There are no exchange between same items, i. e. , $A_{i} \\ne B_{i}$.", "output": "If there are no bugs, i. e. , repetition of any sequence of tradings does not cause an unlimited increment of items, output \"Yes\". If not, output \"No\".", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02071", "ProblemText": "Task Description: Your company is developing a video game. In this game, players can exchange items. This trading follows the rule set by the developers. The rule is defined as the following format: \"Players can exchange one item $A_i$ and $x_i$ item $B_i$\". Note that the trading can be done in both directions. Items are exchanged between players and the game system. Therefore players can exchange items any number of times. Sometimes, testers find bugs that a repetition of a specific sequence of tradings causes the unlimited increment of items. For example, the following rule set can cause this bug.\nPlayers can exchange one item 1 and two item 2.\n\nPlayers can exchange one item 2 and two item 3.\n\nPlayers can exchange one item 1 and three item 3.\n\nIn this rule set, players can increase items unlimitedly. For example, players start tradings with one item 1. Using rules 1 and 2, they can exchange it for four item 3. And, using rule 3, they can get one item 1 and one item 3. By repeating this sequence, the amount of item 3 increases unlimitedly. These bugs can spoil the game, therefore the developers decided to introduce the system which prevents the inconsistent trading. Your task is to write a program which detects whether the rule set contains the bug or not.
    \nTask Input: The input consists of a single test case in the format below. $N$ $M$\n$A_{1}$ $B_{1}$ $x_{1}$\n$\\vdots$\n$A_{M}$ $B_{M}$ $x_{M}$The first line contains two integers $N$ and $M$ which are the number of types of items and the number of rules, respectively ($1 <= N <= 100 000$, $1 <= M <= 100 000$). Each of the following $M$ lines gives the trading rule that one item $A_{i}$ and $x_{i}$ item $B_{i}$ ($1 <= A_{i}, B_{i} <= N$, $1 <= x_{i} <= 1 000 000 000$) can be exchanged in both directions. There are no exchange between same items, i. e. , $A_{i} \\ne B_{i}$.\nTask Output: If there are no bugs, i. e. , repetition of any sequence of tradings does not cause an unlimited increment of items, output \"Yes\". If not, output \"No\".\n\n" }, { "title": "Problem Statement", "content": "In A. D. 2101, war was beginning. The enemy has taken over all of our bases. To recapture the bases, we decided to set up a headquarters. We need to define the location of the headquarters so that all bases are not so far away from the headquarters. Therefore, we decided to choose the location to minimize the sum of the distances from the headquarters to the furthest $K$ bases. The bases are on the 2-D plane, and we can set up the headquarters in any place on this plane even if it is not on a grid point. Your task is to determine the optimal headquarters location from the given base positions.
    ", "constraint": "", "input": "The input consists of a single test case in the format below. $N$ $K$\n$x_{1}$ $y_{1}$\n$\\vdots$\n$x_{N}$ $y_{N}$The first line contains two integers $N$ and $K$. The integer $N$ is the number of the bases ($1 <= N <= 200$). The integer $K$ gives how many bases are considered for calculation ($1 <= K <= N$). Each of the following $N$ lines gives the x and y coordinates of each base. All of the absolute values of given coordinates are less than or equal to $1000$, i. e. , $-1000 <= x_{i}, y_{i} <= 1000$ is satisfied.", "output": "Output the minimum sum of the distances from the headquarters to the furthest $K$ bases. The output can contain an absolute or a relative error no more than $10^{-3}$.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02072", "ProblemText": "Task Description: In A. D. 2101, war was beginning. The enemy has taken over all of our bases. To recapture the bases, we decided to set up a headquarters. We need to define the location of the headquarters so that all bases are not so far away from the headquarters. Therefore, we decided to choose the location to minimize the sum of the distances from the headquarters to the furthest $K$ bases. The bases are on the 2-D plane, and we can set up the headquarters in any place on this plane even if it is not on a grid point. Your task is to determine the optimal headquarters location from the given base positions.
    \nTask Input: The input consists of a single test case in the format below. $N$ $K$\n$x_{1}$ $y_{1}$\n$\\vdots$\n$x_{N}$ $y_{N}$The first line contains two integers $N$ and $K$. The integer $N$ is the number of the bases ($1 <= N <= 200$). The integer $K$ gives how many bases are considered for calculation ($1 <= K <= N$). Each of the following $N$ lines gives the x and y coordinates of each base. All of the absolute values of given coordinates are less than or equal to $1000$, i. e. , $-1000 <= x_{i}, y_{i} <= 1000$ is satisfied.\nTask Output: Output the minimum sum of the distances from the headquarters to the furthest $K$ bases. The output can contain an absolute or a relative error no more than $10^{-3}$.\n\n" }, { "title": "Problem Statement", "content": "You have a grid with $H$ rows and $W$ columns. Each cell contains one of the following 11 characters: an addition operator +, a multiplication operator *, or a digit between $1$ and $9$. There are paths from the top-left cell to the bottom-right cell by moving right or down $H+W-2$ times. Let us define the value of a path by the evaluation result of the mathematical expression you can obtain by concatenating all the characters contained in the cells on the path in order.\nYour task is to compute the sum of values of any possible paths. Since the sum can be large, find it modulo $M$. It is guaranteed the top-left cell and the bottom-right cell contain digits. Moreover, if two cells share an edge, at least one of them contains a digit. In other words, each expression you can obtain from a path is mathematically valid.
    ", "constraint": "", "input": "The input consists of a single test case in the format below. $H$ $W$ $M$\n$a_{1,1}$ $\\cdots$ $a_{1, W}$\n$\\ldots$\n$a_{H, 1}$ $\\cdots$ $a_{H, W}$The first line consists of three integers $H$, $W$ and $M$ ($1 <= H, W <= 2 000$, $2 <= M <= 10^{9}$). The following $H$ lines represent the characters on the grid. $a_{i, j}$ represents the character contained in the cell at the $i$-th row and $j$-th column. Each $a_{i, j}$ is either +, *, or a digit between $1$ and $9$. $a_{1,1}$ and $a_{H, W}$ are both digits. If two cells share an edge, at least one of them contain a digit.", "output": "Print the sum of values of all possible paths modulo $M$.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02073", "ProblemText": "Task Description: You have a grid with $H$ rows and $W$ columns. Each cell contains one of the following 11 characters: an addition operator +, a multiplication operator *, or a digit between $1$ and $9$. There are paths from the top-left cell to the bottom-right cell by moving right or down $H+W-2$ times. Let us define the value of a path by the evaluation result of the mathematical expression you can obtain by concatenating all the characters contained in the cells on the path in order.\nYour task is to compute the sum of values of any possible paths. Since the sum can be large, find it modulo $M$. It is guaranteed the top-left cell and the bottom-right cell contain digits. Moreover, if two cells share an edge, at least one of them contains a digit. In other words, each expression you can obtain from a path is mathematically valid.
    \nTask Input: The input consists of a single test case in the format below. $H$ $W$ $M$\n$a_{1,1}$ $\\cdots$ $a_{1, W}$\n$\\ldots$\n$a_{H, 1}$ $\\cdots$ $a_{H, W}$The first line consists of three integers $H$, $W$ and $M$ ($1 <= H, W <= 2 000$, $2 <= M <= 10^{9}$). The following $H$ lines represent the characters on the grid. $a_{i, j}$ represents the character contained in the cell at the $i$-th row and $j$-th column. Each $a_{i, j}$ is either +, *, or a digit between $1$ and $9$. $a_{1,1}$ and $a_{H, W}$ are both digits. If two cells share an edge, at least one of them contain a digit.\nTask Output: Print the sum of values of all possible paths modulo $M$.\n\n" }, { "title": "Problem Statement", "content": "Have you experienced $10$-by-$10$ grid calculation? It's a mathematical exercise common in Japan. In this problem, we consider the generalization of the exercise, $N$-by-$M$ grid calculation. In this exercise, you are given an $N$-by-$M$ grid (i. e. a grid with $N$ rows and $M$ columns) with an additional column and row at the top and the left of the grid, respectively. Each cell of the additional column and row has a positive integer. Let's denote the sequence of integers on the column and row by $a$ and $b$, and the $i$-th integer from the top in the column is $a_i$ and the $j$-th integer from the left in the row is $b_j$, respectively. Initially, each cell in the grid (other than the additional column and row) is blank. Let $(i, j)$ be the cell at the $i$-th from the top and the $j$-th from the left. The exercise expects you to fill all the cells so that the cell $(i, j)$ has $a_i * b_j$. You have to start at the top-left cell. You repeat to calculate the multiplication $a_i * b_j$ for a current cell $(i, j)$, and then move from left to right until you reach the rightmost cell, then move to the leftmost cell of the next row below. At the end of the exercise, you will write a lot, really a lot of digits on the cells. Your teacher, who gave this exercise to you, looks like bothering to check entire cells on the grid to confirm that you have done this exercise. So the teacher thinks it is OK if you can answer the $d$-th digit (not integer, see an example below), you have written for randomly chosen $x$. Let's see an example. For this example, you calculate values on cells, which are $8$, $56$, $24$, $1$, $7$, $3$ in order. Thus, you would write digits 8,5,6,2,4,1,7,3. So the answer to a question $4$ is $2$. You noticed that you can answer such questions even if you haven't completed the given exercise. Given a column $a$, a row $b$, and $Q$ integers $d_1, d_2, \\dots, d_Q$, your task is to answer the $d_k$-th digit you would write if you had completed this exercise on the given grid for each $k$. Note that your teacher is not so kind (unfortunately), so may ask you numbers greater than you would write. For such questions, you should answer 'x' instead of a digit.
    ", "constraint": "", "input": "The input consists of a single test case formatted as follows. $N$ $M$\n$a_1$ $\\ldots$ $a_N$\n$b_1$ $\\ldots$ $b_M$\n$Q$\n$d_1$ $\\ldots$ $d_Q$The first line contains two integers $N$ ($1 <= N <= 10^5$) and $M$ ($1 <= M <= 10^5$), which are the number of rows and columns of the grid, respectively. The second line represents a sequence $a$ of $N$ integers, the $i$-th of which is the integer at the $i$-th from the top of the additional column on the left. It holds $1 <= a_i <= 10^9$ for $1 <= i <= N$. The third line represents a sequence $b$ of $M$ integers, the $j$-th of which is the integer at the $j$-th from the left of the additional row on the top. It holds $1 <= b_j <= 10^9$ for $1 <= j <= M$. The fourth line contains an integer $Q$ ($1 <= Q <= 3* 10^5$), which is the number of questions your teacher would ask. The fifth line contains a sequence $d$ of $Q$ integers, the $k$-th of which is the $k$-th question from the teacher, and it means you should answer the $d_k$-th digit you would write in this exercise. It holds $1 <= d_k <= 10^{15}$ for $1 <= k <= Q$.", "output": "Output a string with $Q$ characters, the $k$-th of which is the answer to the $k$-th question in one line, where the answer to $k$-th question is the $d_k$-th digit you would write if $d_k$ is no more than the number of digits you would write, otherwise 'x'.", "content_img": true, "lang": "en", "error": false, "samples": [], "Pid": "p02074", "ProblemText": "Task Description: Have you experienced $10$-by-$10$ grid calculation? It's a mathematical exercise common in Japan. In this problem, we consider the generalization of the exercise, $N$-by-$M$ grid calculation. In this exercise, you are given an $N$-by-$M$ grid (i. e. a grid with $N$ rows and $M$ columns) with an additional column and row at the top and the left of the grid, respectively. Each cell of the additional column and row has a positive integer. Let's denote the sequence of integers on the column and row by $a$ and $b$, and the $i$-th integer from the top in the column is $a_i$ and the $j$-th integer from the left in the row is $b_j$, respectively. Initially, each cell in the grid (other than the additional column and row) is blank. Let $(i, j)$ be the cell at the $i$-th from the top and the $j$-th from the left. The exercise expects you to fill all the cells so that the cell $(i, j)$ has $a_i * b_j$. You have to start at the top-left cell. You repeat to calculate the multiplication $a_i * b_j$ for a current cell $(i, j)$, and then move from left to right until you reach the rightmost cell, then move to the leftmost cell of the next row below. At the end of the exercise, you will write a lot, really a lot of digits on the cells. Your teacher, who gave this exercise to you, looks like bothering to check entire cells on the grid to confirm that you have done this exercise. So the teacher thinks it is OK if you can answer the $d$-th digit (not integer, see an example below), you have written for randomly chosen $x$. Let's see an example. For this example, you calculate values on cells, which are $8$, $56$, $24$, $1$, $7$, $3$ in order. Thus, you would write digits 8,5,6,2,4,1,7,3. So the answer to a question $4$ is $2$. You noticed that you can answer such questions even if you haven't completed the given exercise. Given a column $a$, a row $b$, and $Q$ integers $d_1, d_2, \\dots, d_Q$, your task is to answer the $d_k$-th digit you would write if you had completed this exercise on the given grid for each $k$. Note that your teacher is not so kind (unfortunately), so may ask you numbers greater than you would write. For such questions, you should answer 'x' instead of a digit.
    \nTask Input: The input consists of a single test case formatted as follows. $N$ $M$\n$a_1$ $\\ldots$ $a_N$\n$b_1$ $\\ldots$ $b_M$\n$Q$\n$d_1$ $\\ldots$ $d_Q$The first line contains two integers $N$ ($1 <= N <= 10^5$) and $M$ ($1 <= M <= 10^5$), which are the number of rows and columns of the grid, respectively. The second line represents a sequence $a$ of $N$ integers, the $i$-th of which is the integer at the $i$-th from the top of the additional column on the left. It holds $1 <= a_i <= 10^9$ for $1 <= i <= N$. The third line represents a sequence $b$ of $M$ integers, the $j$-th of which is the integer at the $j$-th from the left of the additional row on the top. It holds $1 <= b_j <= 10^9$ for $1 <= j <= M$. The fourth line contains an integer $Q$ ($1 <= Q <= 3* 10^5$), which is the number of questions your teacher would ask. The fifth line contains a sequence $d$ of $Q$ integers, the $k$-th of which is the $k$-th question from the teacher, and it means you should answer the $d_k$-th digit you would write in this exercise. It holds $1 <= d_k <= 10^{15}$ for $1 <= k <= Q$.\nTask Output: Output a string with $Q$ characters, the $k$-th of which is the answer to the $k$-th question in one line, where the answer to $k$-th question is the $d_k$-th digit you would write if $d_k$ is no more than the number of digits you would write, otherwise 'x'.\n\n" }, { "title": "Problem Statement", "content": "Your friend, Tatsumi, is a producer of Immortal Culture Production in Chiba (ICPC). His company is planning to form a zombie rock band named Gray Faces and cheer Chiba Prefecture up. But, unfortunately, there is only one zombie in ICPC. So, Tatsumi decided to release the zombie on a platform of Soga station to produce a sufficient number of zombies. As you may know, a zombie changes a human into a new zombie by passing by the human. In other words, a human becomes a zombie when the human and a zombie are at the same point. Note that a zombie who used to be a human changes a human into a zombie too. The platform of Soga station is represented by an infinitely long line, and Tatsumi will release a zombie at a point with coordinate $x_Z$. After the release, the zombie will start walking in the positive direction at $v_Z$ per second. If $v_Z$ is negative, the zombie will walk in the negative direction at $|v_Z|$ per second. There are $N$ humans on the platform. When Tatsumi releases the zombie, the $i$-th human will be at a point with coordinate $x_i$ and will start walking in the positive direction at $v_i$ per second. If $v_i$ is negative, the human will walk in the negative direction at $|v_i|$ per second as well as the zombie. For each human on the platform, Tatsumi wants to know when the human becomes a zombie. Please help him by writing a program that calculates a time when each human on the platform becomes a zombie.
    ", "constraint": "", "input": "The input consists of a single test case in the following format. $N$\n$x_Z$ $v_Z$\n$x_1$ $v_1$\n$\\vdots$\n$x_N$ $v_N$The first line consists of an integer $N \\, (1 <= N <= 2 * 10^5)$ which is the number of humans on a platform of Soga station. The second line consists of two integers $x_Z \\, (-10^9 <= x_Z <= 10^9)$ and $v_Z \\, (-10^9 <= v_Z <= 10^9)$ separated by a space, where $x_Z$ is an initial position of a zombie Tatsumi will release and $v_Z$ is the velocity of the zombie. The $i$-th line in the following $N$ lines contains two integers $x_i \\, (-10^9 <= x_i <= 10^9)$ and $v_i \\, (-10^9 <= v_i <= 10^9)$ separated by a space, where the $x_i$ is an initial position of the $i$-th human and $v_i$ is the velocity of the human. There is no human that shares their initial position with the zombie. In addition, initial positions of the humans are different from each other.", "output": "The output consists of $N$ lines. In the $i$-th line, print how many seconds it will take for the $i$-th human to become a zombie. If the $i$-th human will never become a zombie, print $-1$ instead. The answer will be considered as correct if the values output have an absolute or relative error less than $10^{-9}$.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02075", "ProblemText": "Task Description: Your friend, Tatsumi, is a producer of Immortal Culture Production in Chiba (ICPC). His company is planning to form a zombie rock band named Gray Faces and cheer Chiba Prefecture up. But, unfortunately, there is only one zombie in ICPC. So, Tatsumi decided to release the zombie on a platform of Soga station to produce a sufficient number of zombies. As you may know, a zombie changes a human into a new zombie by passing by the human. In other words, a human becomes a zombie when the human and a zombie are at the same point. Note that a zombie who used to be a human changes a human into a zombie too. The platform of Soga station is represented by an infinitely long line, and Tatsumi will release a zombie at a point with coordinate $x_Z$. After the release, the zombie will start walking in the positive direction at $v_Z$ per second. If $v_Z$ is negative, the zombie will walk in the negative direction at $|v_Z|$ per second. There are $N$ humans on the platform. When Tatsumi releases the zombie, the $i$-th human will be at a point with coordinate $x_i$ and will start walking in the positive direction at $v_i$ per second. If $v_i$ is negative, the human will walk in the negative direction at $|v_i|$ per second as well as the zombie. For each human on the platform, Tatsumi wants to know when the human becomes a zombie. Please help him by writing a program that calculates a time when each human on the platform becomes a zombie.
    \nTask Input: The input consists of a single test case in the following format. $N$\n$x_Z$ $v_Z$\n$x_1$ $v_1$\n$\\vdots$\n$x_N$ $v_N$The first line consists of an integer $N \\, (1 <= N <= 2 * 10^5)$ which is the number of humans on a platform of Soga station. The second line consists of two integers $x_Z \\, (-10^9 <= x_Z <= 10^9)$ and $v_Z \\, (-10^9 <= v_Z <= 10^9)$ separated by a space, where $x_Z$ is an initial position of a zombie Tatsumi will release and $v_Z$ is the velocity of the zombie. The $i$-th line in the following $N$ lines contains two integers $x_i \\, (-10^9 <= x_i <= 10^9)$ and $v_i \\, (-10^9 <= v_i <= 10^9)$ separated by a space, where the $x_i$ is an initial position of the $i$-th human and $v_i$ is the velocity of the human. There is no human that shares their initial position with the zombie. In addition, initial positions of the humans are different from each other.\nTask Output: The output consists of $N$ lines. In the $i$-th line, print how many seconds it will take for the $i$-th human to become a zombie. If the $i$-th human will never become a zombie, print $-1$ instead. The answer will be considered as correct if the values output have an absolute or relative error less than $10^{-9}$.\n\n" }, { "title": "Problem Statement", "content": "\"Rooks Game\" is a single-player game and uses a chessboard which has $N * N$ grid and $M$ rook pieces. A rook moves through any number of unoccupied squares horizontally or vertically. When a rook can attack another rook, it can capture the rook and move to the square which was occupied. Note that, in Rooks Game, we don't distinguish between white and black, in other words, every rook can capture any of other rooks. Initially, there are $M$ rooks on the board. In each move, a rook captures another rook. The player repeats captures until any rook cannot be captured. There are two types of goal of this game. One is to minimize the number of captured rooks, and the other is to maximize it. In this problem, you are requested to calculate the minimum and maximum values of the number of captured rooks.
    ", "constraint": "", "input": "The input consists of a single test case in the format below. $N$ $M$\n$x_{1}$ $y_{1}$\n$\\vdots$\n$x_{M}$ $y_{M}$The first line contains two integers $N$ and $M$ which are the size of the chessboard and the number of rooks, respectively ($1 <= N, M <= 1000$). Each of the following $M$ lines gives the position of each rook. The $i$-th line with $x_{i}$ and $y_{i}$ means that the $i$-th rook is in the $x_{i}$-th column and $y_{i}$-th row ($1 <= x_{i}, y_{i} <= N$). You can assume any two rooks are not in the same place.", "output": "Output the minimum and maximum values of the number of captured rooks separated by a single space.", "content_img": true, "lang": "en", "error": false, "samples": [], "Pid": "p02076", "ProblemText": "Task Description: \"Rooks Game\" is a single-player game and uses a chessboard which has $N * N$ grid and $M$ rook pieces. A rook moves through any number of unoccupied squares horizontally or vertically. When a rook can attack another rook, it can capture the rook and move to the square which was occupied. Note that, in Rooks Game, we don't distinguish between white and black, in other words, every rook can capture any of other rooks. Initially, there are $M$ rooks on the board. In each move, a rook captures another rook. The player repeats captures until any rook cannot be captured. There are two types of goal of this game. One is to minimize the number of captured rooks, and the other is to maximize it. In this problem, you are requested to calculate the minimum and maximum values of the number of captured rooks.
    \nTask Input: The input consists of a single test case in the format below. $N$ $M$\n$x_{1}$ $y_{1}$\n$\\vdots$\n$x_{M}$ $y_{M}$The first line contains two integers $N$ and $M$ which are the size of the chessboard and the number of rooks, respectively ($1 <= N, M <= 1000$). Each of the following $M$ lines gives the position of each rook. The $i$-th line with $x_{i}$ and $y_{i}$ means that the $i$-th rook is in the $x_{i}$-th column and $y_{i}$-th row ($1 <= x_{i}, y_{i} <= N$). You can assume any two rooks are not in the same place.\nTask Output: Output the minimum and maximum values of the number of captured rooks separated by a single space.\n\n" }, { "title": "Problem Statement", "content": "JAG land is a country, which is represented as an $M * M$ grid. Its top-left cell is $(1,1)$ and its bottom-right cell is $(M, M)$. Suddenly, a bomber invaded JAG land and dropped bombs to the country. Its bombing pattern is always fixed and represented by an $N * N$ grid. Each symbol in the bombing pattern is either X or . . The meaning of each symbol is as follows.\nX: Bomb \n\n. : Empty\n\nHere, suppose that a bomber is in $(br, bc)$ in the land and drops a bomb. The cell $(br + i - 1, bc + j - 1)$ will be damaged if the symbol in the $i$-th row and the $j$-th column of the bombing pattern is X ($1 <= i, j <= N$). Initially, the bomber reached $(1,1)$ in JAG land. The bomber repeated to move to either of $4$-directions and then dropped a bomb just $L$ times. During this attack, the values of the coordinates of the bomber were between $1$ and $M - N + 1$, inclusive, while it dropped bombs. Finally, the bomber left the country. The moving pattern of the bomber is described as $L$ characters. The $i$-th character corresponds to the $i$-th move and the meaning of each character is as follows.\nU: Up\n\nD: Down\n\nL: Left\n\nR: Right\n\nYour task is to write a program to analyze the damage situation in JAG land. To investigate damage overview in the land, calculate the number of cells which were damaged by the bomber at least $K$ times.
    ", "constraint": "", "input": "The input consists of a single test case in the format below. $N$ $M$ $K$ $L$\n$B_{1}$\n$\\vdots$\n$B_{N}$\n$S$The first line contains four integers $N$, $M$, $K$ and $L$($1 <= N < M <= 500$, $1 <= K <= L <= 2 * 10^{5}$).\nThe following $N$ lines represent the bombing pattern.\n$B_i$ is a string of length $N$. Each character of $B_i$ is either X or . . The last line denotes the moving pattern. \n$S$ is a string of length $L$, which consists of either U, D, L or R. \nIt's guaranteed that the values of the coordinates of the bomber are between $1$ and $M - N + 1$, inclusive, while it drops bombs in the country.", "output": "Print the number of cells which were damaged by the bomber at least $K$ times.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p02077", "ProblemText": "Task Description: JAG land is a country, which is represented as an $M * M$ grid. Its top-left cell is $(1,1)$ and its bottom-right cell is $(M, M)$. Suddenly, a bomber invaded JAG land and dropped bombs to the country. Its bombing pattern is always fixed and represented by an $N * N$ grid. Each symbol in the bombing pattern is either X or . . The meaning of each symbol is as follows.\nX: Bomb \n\n. : Empty\n\nHere, suppose that a bomber is in $(br, bc)$ in the land and drops a bomb. The cell $(br + i - 1, bc + j - 1)$ will be damaged if the symbol in the $i$-th row and the $j$-th column of the bombing pattern is X ($1 <= i, j <= N$). Initially, the bomber reached $(1,1)$ in JAG land. The bomber repeated to move to either of $4$-directions and then dropped a bomb just $L$ times. During this attack, the values of the coordinates of the bomber were between $1$ and $M - N + 1$, inclusive, while it dropped bombs. Finally, the bomber left the country. The moving pattern of the bomber is described as $L$ characters. The $i$-th character corresponds to the $i$-th move and the meaning of each character is as follows.\nU: Up\n\nD: Down\n\nL: Left\n\nR: Right\n\nYour task is to write a program to analyze the damage situation in JAG land. To investigate damage overview in the land, calculate the number of cells which were damaged by the bomber at least $K$ times.
    \nTask Input: The input consists of a single test case in the format below. $N$ $M$ $K$ $L$\n$B_{1}$\n$\\vdots$\n$B_{N}$\n$S$The first line contains four integers $N$, $M$, $K$ and $L$($1 <= N < M <= 500$, $1 <= K <= L <= 2 * 10^{5}$).\nThe following $N$ lines represent the bombing pattern.\n$B_i$ is a string of length $N$. Each character of $B_i$ is either X or . . The last line denotes the moving pattern. \n$S$ is a string of length $L$, which consists of either U, D, L or R. \nIt's guaranteed that the values of the coordinates of the bomber are between $1$ and $M - N + 1$, inclusive, while it drops bombs in the country.\nTask Output: Print the number of cells which were damaged by the bomber at least $K$ times.\n\n" }, { "title": "A: Union Ball", "content": "There are N balls in a box. The i-th ball is labeled with a positive integer A_i. You can interact with balls in the box by taking actions under the following rules:\n If integers on balls in the box are all odd or all even, you cannot take actions anymore.\n\n Otherwise, you select arbitrary two balls in the box and remove them from the box. Then, you generate a new ball labeled with the sum of the integers on the two balls and put it into the box.\n\nFor given balls, what is the maximum number of actions you can take under the above rules?", "constraint": "1 <= N <= 2 * 10^5\n\n 1 <= A_i <= 10^9\n\n Inputs consist only of integers.", "input": "N\nA_1 A_2 . . . A_N\n\n The first line gives an integer N representing the initial number of balls in a box.\n\n The second line contains N integers, the i-th of which is the integer on the i-th ball.", "output": "Output the maximum number of actions you can take in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n4 5 6\n output: 2\n\nFirst, you select and remove balls labeled with 4\n and 5\n, respectively, and add a ball labeled with 9\n.\nNext, you select and remove balls labeled with 6\n and 9\n, respectively, and add a ball labeled with 15\n.\nNow, the balls in the box only have odd numbers. So you cannot take any actions anymore. The number of actions you took is two, and there is no way to achieve three actions or more. Thus the maximum is two and the series of the above actions is one of the optimal ways.", "input: 4\n4 2 4 2\n output: 0\nYou cannot take any actions in this case."], "Pid": "p02088", "ProblemText": "Task Description: There are N balls in a box. The i-th ball is labeled with a positive integer A_i. You can interact with balls in the box by taking actions under the following rules:\n If integers on balls in the box are all odd or all even, you cannot take actions anymore.\n\n Otherwise, you select arbitrary two balls in the box and remove them from the box. Then, you generate a new ball labeled with the sum of the integers on the two balls and put it into the box.\n\nFor given balls, what is the maximum number of actions you can take under the above rules?\nTask Constraint: 1 <= N <= 2 * 10^5\n\n 1 <= A_i <= 10^9\n\n Inputs consist only of integers.\nTask Input: N\nA_1 A_2 . . . A_N\n\n The first line gives an integer N representing the initial number of balls in a box.\n\n The second line contains N integers, the i-th of which is the integer on the i-th ball.\nTask Output: Output the maximum number of actions you can take in one line.\nTask Samples: input: 3\n4 5 6\n output: 2\n\nFirst, you select and remove balls labeled with 4\n and 5\n, respectively, and add a ball labeled with 9\n.\nNext, you select and remove balls labeled with 6\n and 9\n, respectively, and add a ball labeled with 15\n.\nNow, the balls in the box only have odd numbers. So you cannot take any actions anymore. The number of actions you took is two, and there is no way to achieve three actions or more. Thus the maximum is two and the series of the above actions is one of the optimal ways.\ninput: 4\n4 2 4 2\n output: 0\nYou cannot take any actions in this case.\n\n" }, { "title": "B: Add Mul Sub Div", "content": "You have an array A of N integers. A_i denotes the i-th element of A. You have to process one of the following queries Q times:\n Query 1: The query consists of non-negative integer x, and two positive integers s, t. For all the elements greater than or equal to x in A, you have to add s to the elements, and then multiply them by t. That is, an element with v (v >= x) becomes t(v + s) after this query.\n Query 2: The query consists of non-negative integer x, and two positive integers s, t. For all the elements less than or equal to x in A, you have to subtract s from the elements, and then divide them by t. If the result is not an integer, you truncate it towards zero. That is, an element with v (v <= x) becomes $\\mathrm{trunc}$ ( \\frac{v - s}{t} ) after this query, where $\\mathrm{trunc}$ ( y ) is the integer obtained by truncating y towards zero. \n\n \"Truncating towards zero\" means converting a decimal number to an integer so that if x = 0.0 then 0 , otherwise an integer whose absolute value is the maximum integer no more than |x| and whose sign is same as x. For example, truncating 3.5 towards zero is 3, and truncating -2.8 towards zero is -2.\nAfter applying Q queries one by one, how many elements in A are no less than L and no more than R?", "constraint": "1 <= N <= 2 * 10^5\n\n 1 <= Q <= 2 * 10^5\n\n -2^{63} < L <= R < 2^{63}\n\n 0 <= |A_i| <= 10^9\n\n q_j \\in \\{ 1,2 \\}\n\n 0 <= x_j < 2^{63}\n\n 1 <= s_j, t_j <= 10^9\n\n Inputs consist only of integers.\n\n The absolute value of any element in the array dosen't exceed 2^{63} at any point during query processing.", "input": "N Q L R\nA_1 A_2 . . . A_N\nq_1 x_1 s_1 t_1\n:\nq_Q x_Q s_Q t_Q\n\n The first line contains four integers N, Q, L, and R. N is the number of elements in an integer array A, Q is the number of queries, and L and R specify the range of integers you want to count within after the queries.\n\n The second line consists of N integers, the i-th of which is the i-th element of A.\n\n The following Q lines represent information of queries. The j-th line of them corresponds to the j-th query and consists of four integers q_j, x_j, s_j, and t_j. Here, q_j = 1 stands for the j-th query is Query 1, and q_j = 2 stands for the j-th query is Query 2. x_j, s_j, and t_j are parameters used for the j-th query.", "output": "Output the number of elements in A that are no less than L and no more than R after processing all given queries in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 3 10\n1 -2 3\n1 2 2 3\n2 20 1 3\n2 1 20 5\n output: 1"], "Pid": "p02089", "ProblemText": "Task Description: You have an array A of N integers. A_i denotes the i-th element of A. You have to process one of the following queries Q times:\n Query 1: The query consists of non-negative integer x, and two positive integers s, t. For all the elements greater than or equal to x in A, you have to add s to the elements, and then multiply them by t. That is, an element with v (v >= x) becomes t(v + s) after this query.\n Query 2: The query consists of non-negative integer x, and two positive integers s, t. For all the elements less than or equal to x in A, you have to subtract s from the elements, and then divide them by t. If the result is not an integer, you truncate it towards zero. That is, an element with v (v <= x) becomes $\\mathrm{trunc}$ ( \\frac{v - s}{t} ) after this query, where $\\mathrm{trunc}$ ( y ) is the integer obtained by truncating y towards zero. \n\n \"Truncating towards zero\" means converting a decimal number to an integer so that if x = 0.0 then 0 , otherwise an integer whose absolute value is the maximum integer no more than |x| and whose sign is same as x. For example, truncating 3.5 towards zero is 3, and truncating -2.8 towards zero is -2.\nAfter applying Q queries one by one, how many elements in A are no less than L and no more than R?\nTask Constraint: 1 <= N <= 2 * 10^5\n\n 1 <= Q <= 2 * 10^5\n\n -2^{63} < L <= R < 2^{63}\n\n 0 <= |A_i| <= 10^9\n\n q_j \\in \\{ 1,2 \\}\n\n 0 <= x_j < 2^{63}\n\n 1 <= s_j, t_j <= 10^9\n\n Inputs consist only of integers.\n\n The absolute value of any element in the array dosen't exceed 2^{63} at any point during query processing.\nTask Input: N Q L R\nA_1 A_2 . . . A_N\nq_1 x_1 s_1 t_1\n:\nq_Q x_Q s_Q t_Q\n\n The first line contains four integers N, Q, L, and R. N is the number of elements in an integer array A, Q is the number of queries, and L and R specify the range of integers you want to count within after the queries.\n\n The second line consists of N integers, the i-th of which is the i-th element of A.\n\n The following Q lines represent information of queries. The j-th line of them corresponds to the j-th query and consists of four integers q_j, x_j, s_j, and t_j. Here, q_j = 1 stands for the j-th query is Query 1, and q_j = 2 stands for the j-th query is Query 2. x_j, s_j, and t_j are parameters used for the j-th query.\nTask Output: Output the number of elements in A that are no less than L and no more than R after processing all given queries in one line.\nTask Samples: input: 3 3 3 10\n1 -2 3\n1 2 2 3\n2 20 1 3\n2 1 20 5\n output: 1\n\n" }, { "title": "C: Shuttle Run", "content": "At the beginning of a shuttle run, Homura-chan is at 0 in a positive direction on a number line. During the shuttle run, Homura-chan repeats the following moves:\n Move in a positive direction until reaching M.\n\n When reaching M, change the direction to negative.\n\n Move in a negative direction until reaching 0 .\n\n When reaching 0 , change the direction to positive.\n\nDuring the moves, Homura-chan also eats yokans on the number line. There are N yokans on the number line. Initially, the i-th yokan, whose length is R_i - L_i, is at an interval [L_i, R_i] on the number line. When Homura-chan reaches L_i in a positive direction (or R_i in a negative direction), she can start eating the i-th yokan from L_i to R_i (or from R_i to L_i), and then the i-th yokan disappears. Unfortunately, Homura-chan has only one mouth. So she cannot eat two yokans at the same moment, including even when she starts eating and finishes eating (See the example below). Also, note that she cannot stop eating in the middle of yokan and has to continue eating until she reaches the other end of the yokan she starts eating; it's her belief. Calculate the minimum distance Homura-chan runs to finish eating all the yokans. The shuttle run never ends until Homura-chan eats all the yokans. story:\nUniversity H has a unique physical fitness test program, aiming to grow the mindset of students.\nAmong the items in the program, shuttle run is well-known as especially eccentric one. Surprisingly, there are yokans (sweet beans jellies) on a route of the shuttle run. Greedy Homura-chan would like to challenge to eat all the yokans. And lazy Homura-chan wants to make the distance she would run as short as possible. For her, you decided to write a program to compute the minimum distance she would run required to eat all the yokans.", "constraint": "1 <= N <= 2 * 10^5\n\n3 <= M <= 10^9\n\n0 < L_i < R_i < M\n\n Inputs consist only of integers.", "input": "N M\nL_1 R_1\n:\nL_N R_N\nThe first line contains two integers N and M. The following N lines represent the information of yokan, where the i-th of them contains two integers L_i and R_i corresponding to the interval [L_i, R_i] the i-th yokan is.", "output": "Output the minimum distance Homura-chan runs to eat all the given yokan in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3\n1 2\n output: 2", "input: 2 5\n1 2\n2 4\n output: 8\nNote that when Homura-chan is at the coordinate 2\n, she cannot eat the first and second yokan at the same time.\n"], "Pid": "p02090", "ProblemText": "Task Description: At the beginning of a shuttle run, Homura-chan is at 0 in a positive direction on a number line. During the shuttle run, Homura-chan repeats the following moves:\n Move in a positive direction until reaching M.\n\n When reaching M, change the direction to negative.\n\n Move in a negative direction until reaching 0 .\n\n When reaching 0 , change the direction to positive.\n\nDuring the moves, Homura-chan also eats yokans on the number line. There are N yokans on the number line. Initially, the i-th yokan, whose length is R_i - L_i, is at an interval [L_i, R_i] on the number line. When Homura-chan reaches L_i in a positive direction (or R_i in a negative direction), she can start eating the i-th yokan from L_i to R_i (or from R_i to L_i), and then the i-th yokan disappears. Unfortunately, Homura-chan has only one mouth. So she cannot eat two yokans at the same moment, including even when she starts eating and finishes eating (See the example below). Also, note that she cannot stop eating in the middle of yokan and has to continue eating until she reaches the other end of the yokan she starts eating; it's her belief. Calculate the minimum distance Homura-chan runs to finish eating all the yokans. The shuttle run never ends until Homura-chan eats all the yokans. story:\nUniversity H has a unique physical fitness test program, aiming to grow the mindset of students.\nAmong the items in the program, shuttle run is well-known as especially eccentric one. Surprisingly, there are yokans (sweet beans jellies) on a route of the shuttle run. Greedy Homura-chan would like to challenge to eat all the yokans. And lazy Homura-chan wants to make the distance she would run as short as possible. For her, you decided to write a program to compute the minimum distance she would run required to eat all the yokans.\nTask Constraint: 1 <= N <= 2 * 10^5\n\n3 <= M <= 10^9\n\n0 < L_i < R_i < M\n\n Inputs consist only of integers.\nTask Input: N M\nL_1 R_1\n:\nL_N R_N\nThe first line contains two integers N and M. The following N lines represent the information of yokan, where the i-th of them contains two integers L_i and R_i corresponding to the interval [L_i, R_i] the i-th yokan is.\nTask Output: Output the minimum distance Homura-chan runs to eat all the given yokan in a line.\nTask Samples: input: 1 3\n1 2\n output: 2\ninput: 2 5\n1 2\n2 4\n output: 8\nNote that when Homura-chan is at the coordinate 2\n, she cannot eat the first and second yokan at the same time.\n\n\n" }, { "title": "D: XORANDORBAN", "content": "You are given a positive integer N. Your task is to determine a set S of 2^N integers satisfying the following conditions:\n All the integers in S are at least 0 and less than 2^{N+1}.\n\n All the integers in S are distinct.\n\n You are also given three integers X, A, and O, where 0 <= X, A, O < 2^{N+1}. Then, any two integers (a, b) in S must satisfy a {\\it xor} b \\neq X, a {\\it and} b \\neq A, a {\\it or} b \\neq O, where {\\it xor}, {\\it and}, {\\it or} are bitwise xor, bitwise and, bitwise or, respectively. Note that a and b are not necessarily different.", "constraint": "1 <= N <= 13\n\n 0 <= X, A, O < 2^{N+1}\n\n Inputs consist only of integers.", "input": "N X A O", "output": "If there is no set satisfying the conditions mentioned in the problem statement, output No in a line. Otherwise, output Yes in the first line, and then output 2^N integers in such a set in the second line. If there are multiple sets satisfying the conditions, you can output any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 6 1 5\n output: Yes\n0 3 4 7", "input: 3 0 5 1\n output: No", "input: 3 4 2 5\n output: Yes\n1 0 6 15 8 9 14 7"], "Pid": "p02091", "ProblemText": "Task Description: You are given a positive integer N. Your task is to determine a set S of 2^N integers satisfying the following conditions:\n All the integers in S are at least 0 and less than 2^{N+1}.\n\n All the integers in S are distinct.\n\n You are also given three integers X, A, and O, where 0 <= X, A, O < 2^{N+1}. Then, any two integers (a, b) in S must satisfy a {\\it xor} b \\neq X, a {\\it and} b \\neq A, a {\\it or} b \\neq O, where {\\it xor}, {\\it and}, {\\it or} are bitwise xor, bitwise and, bitwise or, respectively. Note that a and b are not necessarily different.\nTask Constraint: 1 <= N <= 13\n\n 0 <= X, A, O < 2^{N+1}\n\n Inputs consist only of integers.\nTask Input: N X A O\nTask Output: If there is no set satisfying the conditions mentioned in the problem statement, output No in a line. Otherwise, output Yes in the first line, and then output 2^N integers in such a set in the second line. If there are multiple sets satisfying the conditions, you can output any of them.\nTask Samples: input: 2 6 1 5\n output: Yes\n0 3 4 7\ninput: 3 0 5 1\n output: No\ninput: 3 4 2 5\n output: Yes\n1 0 6 15 8 9 14 7\n\n" }, { "title": "E: Red Black Balloons", "content": "ICPC Asia regional contest in Sapporo plans to provide N problems to contestants. Homura-chan is a professional of contest preparation, so she already knows how many contestants would get acceptance for each problem (! ! ), a_i contestants for the i-th problem. You can assume the prediction is perfectly accurate. Ideally, Homura-chan would assign a distinct color of a balloon to each problem respectively. But you know, she has only two colors red and black now. Thus, Homura-chan comes up with the idea to differentiate the size of balloons in K levels, that is, each problem has a balloon with a distinct pair of (color, size). Homura-chan now has r_i red balloons with size i (1 <= i <= K) and b_j black balloons with size j (1 <= j <= K). Suppose we assign a pair (c_i, s_i) of a color c_i (red or black) and a size s_i to the i-th problem, for each i. As noted, we have to assign distinct pairs to each problem, more precisely, (c_i, s_i) \\neq (c_j, s_j) holds for i \\neq j. Moreover, the number of balloons with (c_i, s_i) must be no less than a_i. In the case that there are no such assignments, Homura-chan can change the size of balloons by her magic power. Note that Homura-chan doesn't know magic to change the color of balloons, so it's impossible. Your task is to write a program computing the minimum number of balloons whose size is changed by Homura-chan's magic to realize an assignment satisfying the above-mentioned conditions. If there is no way to achieve such an assignment even if Homura-chan changes the size of balloons infinitely, output -1 instead. story: Homura-chan's dream comes true. It means ICPC Asia regional contest 20xx will be held in Sapporo! Homura-chan has been working hard for the preparation. And finally, it's the previous day of the contest. Homura-chan started to stock balloons to be delivered to contestants who get accepted. However, she noticed that there were only two colors of balloons: red and black.", "constraint": "1 <= N,K <= 60\n\n N <= 2K\n\n 1 <= a_i <= 50 (1 <= i <= N) \n\n 1 <= r_j,b_j <= 50 (1 <= j <= K) \n\n Inputs consist only of integers.", "input": "N K\na_1 . . . a_N\nr_1 . . . r_K\nb_1 . . . b_K", "output": "Output the minimum number of balloons whose size is changed to achieve an assignment in a line. If there are no ways to achieve assignments, output -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n6 5 4\n8 1\n7 1\n output: 3\nHomura-chan changes the size of three red balloons from 1 to 2. Then she can assign (black,1) to the problem 1, (red,1) to the problem 2, and (red,2) to the problem 3.", "input: 2 1\n50 50\n2\n3\n output: -1", "input: 4 3\n3 10 28 43\n40 18 2\n26 7 11\n output: 5"], "Pid": "p02092", "ProblemText": "Task Description: ICPC Asia regional contest in Sapporo plans to provide N problems to contestants. Homura-chan is a professional of contest preparation, so she already knows how many contestants would get acceptance for each problem (! ! ), a_i contestants for the i-th problem. You can assume the prediction is perfectly accurate. Ideally, Homura-chan would assign a distinct color of a balloon to each problem respectively. But you know, she has only two colors red and black now. Thus, Homura-chan comes up with the idea to differentiate the size of balloons in K levels, that is, each problem has a balloon with a distinct pair of (color, size). Homura-chan now has r_i red balloons with size i (1 <= i <= K) and b_j black balloons with size j (1 <= j <= K). Suppose we assign a pair (c_i, s_i) of a color c_i (red or black) and a size s_i to the i-th problem, for each i. As noted, we have to assign distinct pairs to each problem, more precisely, (c_i, s_i) \\neq (c_j, s_j) holds for i \\neq j. Moreover, the number of balloons with (c_i, s_i) must be no less than a_i. In the case that there are no such assignments, Homura-chan can change the size of balloons by her magic power. Note that Homura-chan doesn't know magic to change the color of balloons, so it's impossible. Your task is to write a program computing the minimum number of balloons whose size is changed by Homura-chan's magic to realize an assignment satisfying the above-mentioned conditions. If there is no way to achieve such an assignment even if Homura-chan changes the size of balloons infinitely, output -1 instead. story: Homura-chan's dream comes true. It means ICPC Asia regional contest 20xx will be held in Sapporo! Homura-chan has been working hard for the preparation. And finally, it's the previous day of the contest. Homura-chan started to stock balloons to be delivered to contestants who get accepted. However, she noticed that there were only two colors of balloons: red and black.\nTask Constraint: 1 <= N,K <= 60\n\n N <= 2K\n\n 1 <= a_i <= 50 (1 <= i <= N) \n\n 1 <= r_j,b_j <= 50 (1 <= j <= K) \n\n Inputs consist only of integers.\nTask Input: N K\na_1 . . . a_N\nr_1 . . . r_K\nb_1 . . . b_K\nTask Output: Output the minimum number of balloons whose size is changed to achieve an assignment in a line. If there are no ways to achieve assignments, output -1 instead.\nTask Samples: input: 3 2\n6 5 4\n8 1\n7 1\n output: 3\nHomura-chan changes the size of three red balloons from 1 to 2. Then she can assign (black,1) to the problem 1, (red,1) to the problem 2, and (red,2) to the problem 3.\ninput: 2 1\n50 50\n2\n3\n output: -1\ninput: 4 3\n3 10 28 43\n40 18 2\n26 7 11\n output: 5\n\n" }, { "title": "F: Invariant Tree", "content": "You have a permutation p_1, p_2, . . . , p_N of integers from 1 to N. You also have vertices numbered 1 through N. Find the number of trees while satisfying the following condition. Here, two trees T and T' are different if and only if there is a pair of vertices where T has an edge between them but T ' does not have an edge between them.\n For all integer pairs i, j (1<= i < j <= N), if there is an edge between vertices i and j, there is an edge between vertices p_i and p_j as well.\n\nSince this number can be extremely large, output the number modulo 998244353.", "constraint": "1<= N <= 3 * 10^5\n\n p_1, p_2, ... , p_N is a permutation of integers 1 through N.", "input": "N\np_1 p_2 . . . p_N", "output": "Output the number in a single line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 1 4 3\n output: 4\nLet (u, v)\n denote that there is an edge between u\n and v\n. The following 4\n ways can make a tree satisfying the condition.\n (1,2\n), (1,3\n), (2,4\n)\n (1,2\n), (1,4\n), (2,3\n)\n (1,3\n), (2,4\n), (3,4\n)\n (1,4\n), (2,3\n), (3,4\n)", "input: 3\n1 2 3\n output: 3", "input: 3\n2 3 1\n output: 0", "input: 20\n9 2 15 16 5 13 11 18 1 10 7 3 6 14 12 4 20 19 8 17\n output: 98344960"], "Pid": "p02093", "ProblemText": "Task Description: You have a permutation p_1, p_2, . . . , p_N of integers from 1 to N. You also have vertices numbered 1 through N. Find the number of trees while satisfying the following condition. Here, two trees T and T' are different if and only if there is a pair of vertices where T has an edge between them but T ' does not have an edge between them.\n For all integer pairs i, j (1<= i < j <= N), if there is an edge between vertices i and j, there is an edge between vertices p_i and p_j as well.\n\nSince this number can be extremely large, output the number modulo 998244353.\nTask Constraint: 1<= N <= 3 * 10^5\n\n p_1, p_2, ... , p_N is a permutation of integers 1 through N.\nTask Input: N\np_1 p_2 . . . p_N\nTask Output: Output the number in a single line.\nTask Samples: input: 4\n2 1 4 3\n output: 4\nLet (u, v)\n denote that there is an edge between u\n and v\n. The following 4\n ways can make a tree satisfying the condition.\n (1,2\n), (1,3\n), (2,4\n)\n (1,2\n), (1,4\n), (2,3\n)\n (1,3\n), (2,4\n), (3,4\n)\n (1,4\n), (2,3\n), (3,4\n)\ninput: 3\n1 2 3\n output: 3\ninput: 3\n2 3 1\n output: 0\ninput: 20\n9 2 15 16 5 13 11 18 1 10 7 3 6 14 12 4 20 19 8 17\n output: 98344960\n\n" }, { "title": "G: Toss Cut Tree", "content": "You are given two trees T, U. Each tree has N vertices that are numbered 1 through N. The i-th edge (1 <= i <= N-1) of tree T connects vertices a_i and b_i. The i-th edge (1 <= i <= N-1) of tree U connects vertices c_i and d_i. The operation described below will be performed N times.\n On the i-th operation, flip a fair coin.\n\n If it lands heads up, remove vertex i and all edges directly connecting to it from tree T.\n\n If it lands tails up, remove vertex i and all edges directly connecting to it from tree U. \n\nAfter N operations, each tree will be divided into several connected components. Let X and Y be the number of connected components originated from tree T and U, respectively.\nYour task is to compute the expected value of X * Y. More specifically, your program must output an integer R described below.\nFirst, you can prove X * Y is a rational number. Let P and Q be coprime integers that satisfies \\frac{P}{Q} = X * Y. R is the only integer that satisfies R * Q $\\equiv$ P $ \\bmod \\; $ 998244353,0 <= R < 998244353.", "constraint": "1 <= N <= 2 * 10^5\n\n 1 <= a_i, b_i, c_i, d_i <= N\n\n The given two graphs are trees.\n\n All values in the input are integers.", "input": "N\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 d_1\n:\nc_{N-1} d_{N-1}", "output": "Print R described above in a single line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3\n1 2\n3 1\n output: 1\nA coin is flipped 3\n times. Therefore, there are 2^3 = 8\n outcomes in total.\nSuppose that the outcome was (tail, head, tail) in this order. Vertex 2\n of tree T\n and vertex 1\n, 3\n of tree U\n are removed along with all edges connecting to them. T\n, U\n are decomposed to 2\n, 1\n connected components, respectively. Thus, the value of XY\n is 2 * 1 = 2\n in this case.\nIt is possible to calculate XY\n for the other cases in the same way and the expected value of XY\n is 1\n.", "input: 4\n1 2\n1 4\n2 3\n1 4\n4 2\n2 3\n output: 374341634\nThe expected number of XY\n is \\frac{13}{8}\n."], "Pid": "p02094", "ProblemText": "Task Description: You are given two trees T, U. Each tree has N vertices that are numbered 1 through N. The i-th edge (1 <= i <= N-1) of tree T connects vertices a_i and b_i. The i-th edge (1 <= i <= N-1) of tree U connects vertices c_i and d_i. The operation described below will be performed N times.\n On the i-th operation, flip a fair coin.\n\n If it lands heads up, remove vertex i and all edges directly connecting to it from tree T.\n\n If it lands tails up, remove vertex i and all edges directly connecting to it from tree U. \n\nAfter N operations, each tree will be divided into several connected components. Let X and Y be the number of connected components originated from tree T and U, respectively.\nYour task is to compute the expected value of X * Y. More specifically, your program must output an integer R described below.\nFirst, you can prove X * Y is a rational number. Let P and Q be coprime integers that satisfies \\frac{P}{Q} = X * Y. R is the only integer that satisfies R * Q $\\equiv$ P $ \\bmod \\; $ 998244353,0 <= R < 998244353.\nTask Constraint: 1 <= N <= 2 * 10^5\n\n 1 <= a_i, b_i, c_i, d_i <= N\n\n The given two graphs are trees.\n\n All values in the input are integers.\nTask Input: N\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 d_1\n:\nc_{N-1} d_{N-1}\nTask Output: Print R described above in a single line.\nTask Samples: input: 3\n1 2\n2 3\n1 2\n3 1\n output: 1\nA coin is flipped 3\n times. Therefore, there are 2^3 = 8\n outcomes in total.\nSuppose that the outcome was (tail, head, tail) in this order. Vertex 2\n of tree T\n and vertex 1\n, 3\n of tree U\n are removed along with all edges connecting to them. T\n, U\n are decomposed to 2\n, 1\n connected components, respectively. Thus, the value of XY\n is 2 * 1 = 2\n in this case.\nIt is possible to calculate XY\n for the other cases in the same way and the expected value of XY\n is 1\n.\ninput: 4\n1 2\n1 4\n2 3\n1 4\n4 2\n2 3\n output: 374341634\nThe expected number of XY\n is \\frac{13}{8}\n.\n\n" }, { "title": "H: Colorful Tree", "content": "You are given a rooted tree G with N vertices indexed with 1 through N. The root is vertex 1. There are K kinds of colors indexed with 1 through K. You can paint vertex i with either color c_i or d_i. Note that c_i = d_i may hold, and if so you have to paint vertex i with c_i (=d_i). Let the colorfulness of tree T be the number of different colors in T. Your task is to write a program that calculates maximum colorfulness for all rooted subtrees. Note that coloring for each rooted subtree is done independently, so previous coloring does not affect to other coloring. story:\nYamiuchi (assassination) is a traditional event that is held annually in JAG summer camp. Every team displays a decorated tree in the dark and all teams' trees are compared from the point of view of their colorfulness. In this competition, it is allowed to cut the other teams ' tree to reduce its colorfulness. Despite a team would get a penalty if it were discovered that the team cuts the tree of another team, many teams do this obstruction.\nYou decided to compete in Yamiuchi and write a program that maximizes the colorfulness of your team 's tree. The program has to calculate maximum scores for all subtrees in case the other teams cut your tree.", "constraint": "1 <= N <= 10^5\n\n1 <= K <= 2* 10^5\n\n1 <= u_i , v_i <= N\n\n1 <= c_i , d_i <= K\n\nThe input graph is a tree.\n\n All inputs are integers.", "input": "N K\nu_1 v_1\n:\nu_{N-1} v_{N-1}\nc_1 d_1\n:\nc_N d_N\nThe first line contains two integers N and K in this order. The following N-1 lines provide information about the edges of G. The i-th line of them contains two integers u_i and v_i, meaning these two vertices are connected with an edge. The following N lines provide information about color constraints. The i-th line of them contains two integers c_i and d_i explained above.", "output": "Output N lines. The i-th line of them contains the maximum colorfulness of the rooted subtree of G whose root is i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 10\n1 2\n1 9\n8 7\n output: 2\n1", "input: 3 2\n1 2\n1 3\n1 2\n1 1\n1 2\n output: 2\n1\n1\n\nNote that two color options of a vertex can be the same.", "input: 5 100000\n4 3\n3 5\n1 3\n2 1\n3 2\n1 3\n2 1\n4 2\n1 4\n output: 4\n1\n3\n1\n1"], "Pid": "p02095", "ProblemText": "Task Description: You are given a rooted tree G with N vertices indexed with 1 through N. The root is vertex 1. There are K kinds of colors indexed with 1 through K. You can paint vertex i with either color c_i or d_i. Note that c_i = d_i may hold, and if so you have to paint vertex i with c_i (=d_i). Let the colorfulness of tree T be the number of different colors in T. Your task is to write a program that calculates maximum colorfulness for all rooted subtrees. Note that coloring for each rooted subtree is done independently, so previous coloring does not affect to other coloring. story:\nYamiuchi (assassination) is a traditional event that is held annually in JAG summer camp. Every team displays a decorated tree in the dark and all teams' trees are compared from the point of view of their colorfulness. In this competition, it is allowed to cut the other teams ' tree to reduce its colorfulness. Despite a team would get a penalty if it were discovered that the team cuts the tree of another team, many teams do this obstruction.\nYou decided to compete in Yamiuchi and write a program that maximizes the colorfulness of your team 's tree. The program has to calculate maximum scores for all subtrees in case the other teams cut your tree.\nTask Constraint: 1 <= N <= 10^5\n\n1 <= K <= 2* 10^5\n\n1 <= u_i , v_i <= N\n\n1 <= c_i , d_i <= K\n\nThe input graph is a tree.\n\n All inputs are integers.\nTask Input: N K\nu_1 v_1\n:\nu_{N-1} v_{N-1}\nc_1 d_1\n:\nc_N d_N\nThe first line contains two integers N and K in this order. The following N-1 lines provide information about the edges of G. The i-th line of them contains two integers u_i and v_i, meaning these two vertices are connected with an edge. The following N lines provide information about color constraints. The i-th line of them contains two integers c_i and d_i explained above.\nTask Output: Output N lines. The i-th line of them contains the maximum colorfulness of the rooted subtree of G whose root is i.\nTask Samples: input: 2 10\n1 2\n1 9\n8 7\n output: 2\n1\ninput: 3 2\n1 2\n1 3\n1 2\n1 1\n1 2\n output: 2\n1\n1\n\nNote that two color options of a vertex can be the same.\ninput: 5 100000\n4 3\n3 5\n1 3\n2 1\n3 2\n1 3\n2 1\n4 2\n1 4\n output: 4\n1\n3\n1\n1\n\n" }, { "title": "I: Add", "content": "Mr. T has had an integer sequence of N elements a_1, a_2, . . . , a_N and an integer K. Mr. T has created N integer sequences B_1, B_2, . . . , B_N such that B_i has i elements.\n B_{N, j} = a_j (1 <= j <= N) \n\n B_{i, j} = K * B_{i+1, j} + B_{i+1, j+1} (1<= i <= N-1,1 <= j <= i)\n\nMr. T was so careless that he lost almost all elements of these sequences a and B_i. Fortunately, B_{1,1}, B_{2,1}, . . . , B_{N, 1} and K are not lost. Your task is to write a program that restores the elements of the initial sequence a for him. Output the modulo 65537 of each element instead because the absolute value of these elements can be extremely large. More specifically, for all integers i (1 <= i <= N), output r_i that satisfies r_i $\\equiv$ a_i $ \\bmod \\; $ 65537,0 <= r_i < 65537. Here, we can prove that the original sequence Mr. T had can be uniquely determined under the given constraints.", "constraint": "1 <= T <= 10\n\n 1 <= N <= 50000\n\n |K| <= 10^9\n\n |B_{i,1}| <= 10^9 \n\n All input values are integers.", "input": "T\nN_1 K_1\nC_{1,1} C_{1,2} . . . C_{1, N}\nN_2 K_2\nC_{2,1} C_{2,2} . . . C_{2, N}\n:\nN_T K_T\nC_{T, 1} C_{T, 2} . . . C_{T, N}\nThe first line contains a single integer T that denotes the number of test cases. Each test case consists of 2 lines. The first line of the i-th test case contains two integers N_i and K_i. The second line of the i-th test case contains N_i integers C_{i, j} (1 <= j <= N_i). These values denote that N = N_i , K = K_i , B_{j, 1} = C_{i, j} (1 <= j <= N_i) in the i-th test case.", "output": "Output T lines. For the i-th line, output the answer for the i-th test case a_1, a_2, . . . , a_N in this order. Each number must be separated by a single space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 0\n1 2 3\n3 1\n1 2 3\n output: 3 2 1\n3 65536 0"], "Pid": "p02096", "ProblemText": "Task Description: Mr. T has had an integer sequence of N elements a_1, a_2, . . . , a_N and an integer K. Mr. T has created N integer sequences B_1, B_2, . . . , B_N such that B_i has i elements.\n B_{N, j} = a_j (1 <= j <= N) \n\n B_{i, j} = K * B_{i+1, j} + B_{i+1, j+1} (1<= i <= N-1,1 <= j <= i)\n\nMr. T was so careless that he lost almost all elements of these sequences a and B_i. Fortunately, B_{1,1}, B_{2,1}, . . . , B_{N, 1} and K are not lost. Your task is to write a program that restores the elements of the initial sequence a for him. Output the modulo 65537 of each element instead because the absolute value of these elements can be extremely large. More specifically, for all integers i (1 <= i <= N), output r_i that satisfies r_i $\\equiv$ a_i $ \\bmod \\; $ 65537,0 <= r_i < 65537. Here, we can prove that the original sequence Mr. T had can be uniquely determined under the given constraints.\nTask Constraint: 1 <= T <= 10\n\n 1 <= N <= 50000\n\n |K| <= 10^9\n\n |B_{i,1}| <= 10^9 \n\n All input values are integers.\nTask Input: T\nN_1 K_1\nC_{1,1} C_{1,2} . . . C_{1, N}\nN_2 K_2\nC_{2,1} C_{2,2} . . . C_{2, N}\n:\nN_T K_T\nC_{T, 1} C_{T, 2} . . . C_{T, N}\nThe first line contains a single integer T that denotes the number of test cases. Each test case consists of 2 lines. The first line of the i-th test case contains two integers N_i and K_i. The second line of the i-th test case contains N_i integers C_{i, j} (1 <= j <= N_i). These values denote that N = N_i , K = K_i , B_{j, 1} = C_{i, j} (1 <= j <= N_i) in the i-th test case.\nTask Output: Output T lines. For the i-th line, output the answer for the i-th test case a_1, a_2, . . . , a_N in this order. Each number must be separated by a single space.\nTask Samples: input: 2\n3 0\n1 2 3\n3 1\n1 2 3\n output: 3 2 1\n3 65536 0\n\n" }, { "title": "J: Horizontal-Vertical Permutation", "content": "You are given a positive integer N. Your task is to determine if there exists a square matrix A whose dimension is N that satisfies the following conditions and provide an example of such matrices if it exists. A_{i, j} denotes the element of matrix A at the i-th row and j-th column.\n For all i, j (1 <= i, j <= N), A_{i, j} is an integer that satisfies 1 <= A_{i, j} <= 2N - 1.\n\n For all k = 1,2, . . . , N, a set consists of 2N - 1 elements from the k-th row or k-th column is \\{1,2, . . . , 2N - 1\\}.\n\nIf there are more than one possible matrices, output any of them.", "constraint": "N is an integer that satisfies 1 <= N <= 500.", "input": "NInput consists of one line, which contains the integer N that is the size of a square matrix to construct.", "output": "Output No in a single line if such a square matrix does not exist. If such a square matrix A exists, output Yes on the first line and A after that. More specifically, follow the following format.\nYes\nA_{1,1} A_{1,2} . . . A_{1, N}\nA_{2,1} A_{2,2} . . . A_{2, N}\n:\nA_{N, 1} A_{N, 2} . . . A_{N, N}", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n output: Yes\n2 6 3 7\n4 5 2 1\n1 7 5 6\n5 3 4 2", "input: 3\n output: No"], "Pid": "p02097", "ProblemText": "Task Description: You are given a positive integer N. Your task is to determine if there exists a square matrix A whose dimension is N that satisfies the following conditions and provide an example of such matrices if it exists. A_{i, j} denotes the element of matrix A at the i-th row and j-th column.\n For all i, j (1 <= i, j <= N), A_{i, j} is an integer that satisfies 1 <= A_{i, j} <= 2N - 1.\n\n For all k = 1,2, . . . , N, a set consists of 2N - 1 elements from the k-th row or k-th column is \\{1,2, . . . , 2N - 1\\}.\n\nIf there are more than one possible matrices, output any of them.\nTask Constraint: N is an integer that satisfies 1 <= N <= 500.\nTask Input: NInput consists of one line, which contains the integer N that is the size of a square matrix to construct.\nTask Output: Output No in a single line if such a square matrix does not exist. If such a square matrix A exists, output Yes on the first line and A after that. More specifically, follow the following format.\nYes\nA_{1,1} A_{1,2} . . . A_{1, N}\nA_{2,1} A_{2,2} . . . A_{2, N}\n:\nA_{N, 1} A_{N, 2} . . . A_{N, N}\nTask Samples: input: 4\n output: Yes\n2 6 3 7\n4 5 2 1\n1 7 5 6\n5 3 4 2\ninput: 3\n output: No\n\n" }, { "title": "Fibonacci Number", "content": "Write a program which prints $n$-th fibonacci number for a given integer $n$. The $n$-th fibonacci number is defined by the following recursive formula:", "constraint": "$0 <= n <= 44$", "input": "An integer $n$ is given.", "output": "Print the $n$-th fibonacci number in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n output: 3"], "Pid": "p02233", "ProblemText": "Task Description: Write a program which prints $n$-th fibonacci number for a given integer $n$. The $n$-th fibonacci number is defined by the following recursive formula:\nTask Constraint: $0 <= n <= 44$\nTask Input: An integer $n$ is given.\nTask Output: Print the $n$-th fibonacci number in a line.\nTask Samples: input: 3\n output: 3\n\n" }, { "title": "Matrix-chain Multiplication", "content": "The goal of the matrix-chain multiplication problem is to find the most efficient way to multiply given $n$ matrices $M_1, M_2, M_3, . . . , M_n$.\n\n Write a program which reads dimensions of $M_i$, and finds the minimum number of scalar multiplications to compute the maxrix-chain multiplication $M_1M_2. . . M_n$.", "constraint": "$1 <= n <= 100$\n\n$1 <= r, c <= 100$", "input": "In the first line, an integer $n$ is given. In the following $n$ lines, the dimension of matrix $M_i$ ($i = 1. . . n$) is given by two integers $r$ and $c$ which respectively represents the number of rows and columns of $M_i$.", "output": "Print the minimum number of scalar multiplication in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n30 35\n35 15\n15 5\n5 10\n10 20\n20 25\n output: 15125"], "Pid": "p02234", "ProblemText": "Task Description: The goal of the matrix-chain multiplication problem is to find the most efficient way to multiply given $n$ matrices $M_1, M_2, M_3, . . . , M_n$.\n\n Write a program which reads dimensions of $M_i$, and finds the minimum number of scalar multiplications to compute the maxrix-chain multiplication $M_1M_2. . . M_n$.\nTask Constraint: $1 <= n <= 100$\n\n$1 <= r, c <= 100$\nTask Input: In the first line, an integer $n$ is given. In the following $n$ lines, the dimension of matrix $M_i$ ($i = 1. . . n$) is given by two integers $r$ and $c$ which respectively represents the number of rows and columns of $M_i$.\nTask Output: Print the minimum number of scalar multiplication in a line.\nTask Samples: input: 6\n30 35\n35 15\n15 5\n5 10\n10 20\n20 25\n output: 15125\n\n" }, { "title": "Longest Common Subsequence", "content": "For given two sequences $X$ and $Y$, a sequence $Z$ is a common subsequence of $X$ and $Y$ if $Z$ is a subsequence of both $X$ and $Y$. For example, if $X = \\{a, b, c, b, d, a, b\\}$ and $Y = \\{b, d, c, a, b, a\\}$, the sequence $\\{b, c, a\\}$ is a common subsequence of both $X$ and $Y$. On the other hand, the sequence $\\{b, c, a\\}$ is not a longest common subsequence (LCS) of $X$ and $Y$, since it has length 3 and the sequence $\\{b, c, b, a\\}$, which is also common to both $X$ and $Y$, has length 4. The sequence $\\{b, c, b, a\\}$ is an LCS of $X$ and $Y$, since there is no common subsequence of length 5 or greater.\n\n Write a program which finds the length of LCS of given two sequences $X$ and $Y$. The sequence consists of alphabetical characters.", "constraint": "$1 <= q <= 150$\n\n$1 <=$ length of $X$ and $Y$ $<= 1,000$\n\n$q <= 20$ if the dataset includes a sequence whose length is more than 100", "input": "The input consists of multiple datasets. In the first line, an integer $q$ which is the number of datasets is given. In the following $2 * q$ lines, each dataset which consists of the two sequences $X$ and $Y$ are given.", "output": "For each dataset, print the length of LCS of $X$ and $Y$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nabcbdab\nbdcaba\nabc\nabc\nabc\nbc\n output: 4\n3\n2"], "Pid": "p02235", "ProblemText": "Task Description: For given two sequences $X$ and $Y$, a sequence $Z$ is a common subsequence of $X$ and $Y$ if $Z$ is a subsequence of both $X$ and $Y$. For example, if $X = \\{a, b, c, b, d, a, b\\}$ and $Y = \\{b, d, c, a, b, a\\}$, the sequence $\\{b, c, a\\}$ is a common subsequence of both $X$ and $Y$. On the other hand, the sequence $\\{b, c, a\\}$ is not a longest common subsequence (LCS) of $X$ and $Y$, since it has length 3 and the sequence $\\{b, c, b, a\\}$, which is also common to both $X$ and $Y$, has length 4. The sequence $\\{b, c, b, a\\}$ is an LCS of $X$ and $Y$, since there is no common subsequence of length 5 or greater.\n\n Write a program which finds the length of LCS of given two sequences $X$ and $Y$. The sequence consists of alphabetical characters.\nTask Constraint: $1 <= q <= 150$\n\n$1 <=$ length of $X$ and $Y$ $<= 1,000$\n\n$q <= 20$ if the dataset includes a sequence whose length is more than 100\nTask Input: The input consists of multiple datasets. In the first line, an integer $q$ which is the number of datasets is given. In the following $2 * q$ lines, each dataset which consists of the two sequences $X$ and $Y$ are given.\nTask Output: For each dataset, print the length of LCS of $X$ and $Y$ in a line.\nTask Samples: input: 3\nabcbdab\nbdcaba\nabc\nabc\nabc\nbc\n output: 4\n3\n2\n\n" }, { "title": "Optimal Binary Search Tree", "content": "Optimal Binary Search Tree is a binary search tree constructed from $n$ keys and $n+1$ dummy keys so as to minimize the expected value of cost for a search operation.\n\n We are given a sequence $K = {k_1, k_2, . . . , k_n}$ of $n$ distinct keys in sorted order $(k_1 < k_2 < . . . < k_n)$, and we wish to construct a binary search tree. For each key $k_i$, we have a probability $p_i$ that a search will be for $k_i$. Some searches may be for values not in $K$, and so we also have $n+1$ dummy keys $d_0, d_1, d_2, . . . , d_n$ representing values not in $K$. The dummy keys $d_i (0 <= i <= n)$ are defined as follows:\n\t \nif $i=0$, then $d_i$ represents all values less than $k_1$\n\nif $i=n$, then $d_i$ represents all values greater than $k_n$\n\nif $1 <= i <= n-1$, then $d_i$ represents all values between $k_i$ and $k_{i+1}$\n For each dummy key $d_i$, we have a probability $q_i$ that a search will correspond to $d_i$.\nFor $p_i (1 <= i <= n)$ and $q_i (0 <= i <= n)$, we have \n\n \\[\n \\sum_{i=1}^n p_i + \\sum_{i=0}^n q_i = 1\n \\]\n\n Then the expected cost of a search in a binary search tree $T$ is\n\n \\[\n E_T = \\sum_{i=1}^n (depth_T(k_i) + 1) \\cdot p_i + \\sum_{i=0}^n (depth_T(d_i) + 1) \\cdot q_i\n \\]\n\n where $depth_T(v)$ is the depth of node $v$ in $T$.\n\n For a given set of probabilities, our goal is to construct a binary search tree whose expected search cost is smallest. We call such a tree an optimal binary search tree.\nEach key $k_i$ is an internal node and each dummy key $d_i$ is a leaf. For example, the following figure shows the optimal binary search tree obtained from Sample Input 1.\n task:\nWrite a program which calculates the expected value of a search operation on the optimal binary search tree obtained by given $p_i$ that a search will be for $k_i$ and $q_i$ that a search will correspond to $d_i$.", "constraint": "$1 <= n <= 500$\n\n$0 < p_i, q_i < 1$\n\n$\\displaystyle \\sum_{i=1}^n p_i + \\sum_{i=0}^n q_i = 1$", "input": "$n$\n$p_1$ $p_2$ . . . $p_n$\n$q_0$ $q_1$ $q_2$ . . . $q_n$\n\n In the first line, an integer $n$ which represents the number of keys is given. \nIn the second line, $p_i (1 <= i <= n)$ are given in real numbers with four decimal places. \nIn the third line, $q_i (0 <= i <= n)$ are given in real numbers with four decimal places.", "output": "Print the expected value for a search operation on the optimal binary search tree in a line.\nThe output must not contain an error greater than $10^{-4}$.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n0.1500 0.1000 0.0500 0.1000 0.2000\n0.0500 0.1000 0.0500 0.0500 0.0500 0.1000\n output: 2.75000000", "input: 7\n0.0400 0.0600 0.0800 0.0200 0.1000 0.1200 0.1400\n0.0600 0.0600 0.0600 0.0600 0.0500 0.0500 0.0500 0.0500\n output: 3.12000000"], "Pid": "p02236", "ProblemText": "Task Description: Optimal Binary Search Tree is a binary search tree constructed from $n$ keys and $n+1$ dummy keys so as to minimize the expected value of cost for a search operation.\n\n We are given a sequence $K = {k_1, k_2, . . . , k_n}$ of $n$ distinct keys in sorted order $(k_1 < k_2 < . . . < k_n)$, and we wish to construct a binary search tree. For each key $k_i$, we have a probability $p_i$ that a search will be for $k_i$. Some searches may be for values not in $K$, and so we also have $n+1$ dummy keys $d_0, d_1, d_2, . . . , d_n$ representing values not in $K$. The dummy keys $d_i (0 <= i <= n)$ are defined as follows:\n\t \nif $i=0$, then $d_i$ represents all values less than $k_1$\n\nif $i=n$, then $d_i$ represents all values greater than $k_n$\n\nif $1 <= i <= n-1$, then $d_i$ represents all values between $k_i$ and $k_{i+1}$\n For each dummy key $d_i$, we have a probability $q_i$ that a search will correspond to $d_i$.\nFor $p_i (1 <= i <= n)$ and $q_i (0 <= i <= n)$, we have \n\n \\[\n \\sum_{i=1}^n p_i + \\sum_{i=0}^n q_i = 1\n \\]\n\n Then the expected cost of a search in a binary search tree $T$ is\n\n \\[\n E_T = \\sum_{i=1}^n (depth_T(k_i) + 1) \\cdot p_i + \\sum_{i=0}^n (depth_T(d_i) + 1) \\cdot q_i\n \\]\n\n where $depth_T(v)$ is the depth of node $v$ in $T$.\n\n For a given set of probabilities, our goal is to construct a binary search tree whose expected search cost is smallest. We call such a tree an optimal binary search tree.\nEach key $k_i$ is an internal node and each dummy key $d_i$ is a leaf. For example, the following figure shows the optimal binary search tree obtained from Sample Input 1.\n task:\nWrite a program which calculates the expected value of a search operation on the optimal binary search tree obtained by given $p_i$ that a search will be for $k_i$ and $q_i$ that a search will correspond to $d_i$.\nTask Constraint: $1 <= n <= 500$\n\n$0 < p_i, q_i < 1$\n\n$\\displaystyle \\sum_{i=1}^n p_i + \\sum_{i=0}^n q_i = 1$\nTask Input: $n$\n$p_1$ $p_2$ . . . $p_n$\n$q_0$ $q_1$ $q_2$ . . . $q_n$\n\n In the first line, an integer $n$ which represents the number of keys is given. \nIn the second line, $p_i (1 <= i <= n)$ are given in real numbers with four decimal places. \nIn the third line, $q_i (0 <= i <= n)$ are given in real numbers with four decimal places.\nTask Output: Print the expected value for a search operation on the optimal binary search tree in a line.\nThe output must not contain an error greater than $10^{-4}$.\nTask Samples: input: 5\n0.1500 0.1000 0.0500 0.1000 0.2000\n0.0500 0.1000 0.0500 0.0500 0.0500 0.1000\n output: 2.75000000\ninput: 7\n0.0400 0.0600 0.0800 0.0200 0.1000 0.1200 0.1400\n0.0600 0.0600 0.0600 0.0600 0.0500 0.0500 0.0500 0.0500\n output: 3.12000000\n\n" }, { "title": "Graph", "content": "There are two standard ways to represent a graph $G = (V, E)$, where $V$ is a set of vertices and $E$ is a set of edges; Adjacency list representation and Adjacency matrix representation.\n\n An adjacency-list representation consists of an array $Adj[|V|]$ of $|V|$ lists, one for each vertex in $V$. For each $u \\in V$, the adjacency list $Adj[u]$ contains all vertices $v$ such that there is an edge $(u, v) \\in E$. That is, $Adj[u]$ consists of all vertices adjacent to $u$ in $G$.\n\n An adjacency-matrix representation consists of $|V| * |V|$ matrix $A = a_{ij}$ such that $a_{ij} = 1$ if $(i, j) \\in E$, $a_{ij} = 0$ otherwise.\n\n Write a program which reads a directed graph $G$ represented by the adjacency list, and prints its adjacency-matrix representation. $G$ consists of $n\\; (=|V|)$ vertices identified by their IDs $1,2, . . , n$ respectively.", "constraint": "$1 <= n <= 100$", "input": "In the first line, an integer $n$ is given. In the next $n$ lines, an adjacency list $Adj[u]$ for vertex $u$ are given in the following format:\n\n$u$ $k$ $v_1$ $v_2$ . . . $v_k$\n\n $u$ is vertex ID and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.", "output": "As shown in the following sample output, print the adjacent-matrix representation of $G$. Put a single space character between $a_{ij}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 2 4\n2 1 4\n3 0\n4 1 3\n output: 0 1 0 1\n0 0 0 1\n0 0 0 0\n0 0 1 0"], "Pid": "p02237", "ProblemText": "Task Description: There are two standard ways to represent a graph $G = (V, E)$, where $V$ is a set of vertices and $E$ is a set of edges; Adjacency list representation and Adjacency matrix representation.\n\n An adjacency-list representation consists of an array $Adj[|V|]$ of $|V|$ lists, one for each vertex in $V$. For each $u \\in V$, the adjacency list $Adj[u]$ contains all vertices $v$ such that there is an edge $(u, v) \\in E$. That is, $Adj[u]$ consists of all vertices adjacent to $u$ in $G$.\n\n An adjacency-matrix representation consists of $|V| * |V|$ matrix $A = a_{ij}$ such that $a_{ij} = 1$ if $(i, j) \\in E$, $a_{ij} = 0$ otherwise.\n\n Write a program which reads a directed graph $G$ represented by the adjacency list, and prints its adjacency-matrix representation. $G$ consists of $n\\; (=|V|)$ vertices identified by their IDs $1,2, . . , n$ respectively.\nTask Constraint: $1 <= n <= 100$\nTask Input: In the first line, an integer $n$ is given. In the next $n$ lines, an adjacency list $Adj[u]$ for vertex $u$ are given in the following format:\n\n$u$ $k$ $v_1$ $v_2$ . . . $v_k$\n\n $u$ is vertex ID and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.\nTask Output: As shown in the following sample output, print the adjacent-matrix representation of $G$. Put a single space character between $a_{ij}$.\nTask Samples: input: 4\n1 2 2 4\n2 1 4\n3 0\n4 1 3\n output: 0 1 0 1\n0 0 0 1\n0 0 0 0\n0 0 1 0\n\n" }, { "title": "Depth First Search", "content": "Depth-first search (DFS) follows the strategy to search ”deeper” in the graph whenever possible. In DFS, edges are recursively explored out of the most recently discovered vertex $v$ that still has unexplored edges leaving it. When all of $v$'s edges have been explored, the search ”backtracks” to explore edges leaving the vertex from which $v$ was discovered.\n\n This process continues until all the vertices that are reachable from the original source vertex have been discovered. If any undiscovered vertices remain, then one of them is selected as a new source and the search is repeated from that source.\n\n DFS timestamps each vertex as follows:\n\n$d[v]$ records when $v$ is first discovered.\n\n$f[v]$ records when the search finishes examining $v$ 's adjacency list.\n Write a program which reads a directed graph $G = (V, E)$ and demonstrates DFS on the graph based on the following rules:\n\n$G$ is given in an adjacency-list. Vertices are identified by IDs $1,2, . . . n$ respectively.\n\nIDs in the adjacency list are arranged in ascending order.\n\nThe program should report the discover time and the finish time for each vertex.\n\nWhen there are several candidates to visit during DFS, the algorithm should select the vertex with the smallest ID.\n\nThe timestamp starts with 1.", "constraint": "$1 <= n <= 100$", "input": "In the first line, an integer $n$ denoting the number of vertices of $G$ is given. In the next $n$ lines, adjacency lists of $u$ are given in the following format:\n\n$u$ $k$ $v_1$ $v_2$ . . . $v_k$\n\n$u$ is ID of the vertex and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.", "output": "For each vertex, print $id$, $d$ and $f$ separated by a space character in a line. $id$ is ID of the vertex, $d$ and $f$ is the discover time and the finish time respectively. Print in order of vertex IDs.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1 1 2\n2 1 4\n3 0\n4 1 3\n output: 1 1 8\n2 2 7\n3 4 5\n4 3 6", "input: 6\n1 2 2 3\n2 2 3 4\n3 1 5\n4 1 6\n5 1 6\n6 0\n output: 1 1 12\n2 2 11\n3 3 8\n4 9 10\n5 4 7\n6 5 6\n This is example for Sample Input 2 (discover/finish)"], "Pid": "p02238", "ProblemText": "Task Description: Depth-first search (DFS) follows the strategy to search ”deeper” in the graph whenever possible. In DFS, edges are recursively explored out of the most recently discovered vertex $v$ that still has unexplored edges leaving it. When all of $v$'s edges have been explored, the search ”backtracks” to explore edges leaving the vertex from which $v$ was discovered.\n\n This process continues until all the vertices that are reachable from the original source vertex have been discovered. If any undiscovered vertices remain, then one of them is selected as a new source and the search is repeated from that source.\n\n DFS timestamps each vertex as follows:\n\n$d[v]$ records when $v$ is first discovered.\n\n$f[v]$ records when the search finishes examining $v$ 's adjacency list.\n Write a program which reads a directed graph $G = (V, E)$ and demonstrates DFS on the graph based on the following rules:\n\n$G$ is given in an adjacency-list. Vertices are identified by IDs $1,2, . . . n$ respectively.\n\nIDs in the adjacency list are arranged in ascending order.\n\nThe program should report the discover time and the finish time for each vertex.\n\nWhen there are several candidates to visit during DFS, the algorithm should select the vertex with the smallest ID.\n\nThe timestamp starts with 1.\nTask Constraint: $1 <= n <= 100$\nTask Input: In the first line, an integer $n$ denoting the number of vertices of $G$ is given. In the next $n$ lines, adjacency lists of $u$ are given in the following format:\n\n$u$ $k$ $v_1$ $v_2$ . . . $v_k$\n\n$u$ is ID of the vertex and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.\nTask Output: For each vertex, print $id$, $d$ and $f$ separated by a space character in a line. $id$ is ID of the vertex, $d$ and $f$ is the discover time and the finish time respectively. Print in order of vertex IDs.\nTask Samples: input: 4\n1 1 2\n2 1 4\n3 0\n4 1 3\n output: 1 1 8\n2 2 7\n3 4 5\n4 3 6\ninput: 6\n1 2 2 3\n2 2 3 4\n3 1 5\n4 1 6\n5 1 6\n6 0\n output: 1 1 12\n2 2 11\n3 3 8\n4 9 10\n5 4 7\n6 5 6\n This is example for Sample Input 2 (discover/finish)\n\n" }, { "title": "Breadth First Search", "content": "Write a program which reads an directed graph $G = (V, E)$, and finds the shortest distance from vertex $1$ to each vertex (the number of edges in the shortest path). Vertices are identified by IDs $1,2, . . . n$.", "constraint": "$1 <= n <= 100$", "input": "In the first line, an integer $n$ denoting the number of vertices, is given. In the next $n$ lines, adjacent lists of vertex $u$ are given in the following format:\n\n$u$ $k$ $v_1$ $v_2$ . . . $v_k$\n\n$u$ is ID of the vertex and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.", "output": "For each vertex $u$, print $id$ and $d$ in a line. $id$ is ID of vertex $u$ and $d$ is the distance from vertex $1$ to vertex $u$. If there are no path from vertex $1$ to vertex $u$, print -1 as the shortest distance. Print in order of IDs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 2 4\n2 1 4\n3 0\n4 1 3\n output: 1 0\n2 1\n3 2\n4 1"], "Pid": "p02239", "ProblemText": "Task Description: Write a program which reads an directed graph $G = (V, E)$, and finds the shortest distance from vertex $1$ to each vertex (the number of edges in the shortest path). Vertices are identified by IDs $1,2, . . . n$.\nTask Constraint: $1 <= n <= 100$\nTask Input: In the first line, an integer $n$ denoting the number of vertices, is given. In the next $n$ lines, adjacent lists of vertex $u$ are given in the following format:\n\n$u$ $k$ $v_1$ $v_2$ . . . $v_k$\n\n$u$ is ID of the vertex and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.\nTask Output: For each vertex $u$, print $id$ and $d$ in a line. $id$ is ID of vertex $u$ and $d$ is the distance from vertex $1$ to vertex $u$. If there are no path from vertex $1$ to vertex $u$, print -1 as the shortest distance. Print in order of IDs.\nTask Samples: input: 4\n1 2 2 4\n2 1 4\n3 0\n4 1 3\n output: 1 0\n2 1\n3 2\n4 1\n\n" }, { "title": "Connected Components", "content": "Write a program which reads relations in a SNS (Social Network Service), and judges that given pairs of users are reachable each other through the network.", "constraint": "$2 <= n <= 100,000$\n\n$0 <= m <= 100,000$\n\n$1 <= q <= 10,000$", "input": "In the first line, two integer $n$ and $m$ are given. $n$ is the number of users in the SNS and $m$ is the number of relations in the SNS. The users in the SNS are identified by IDs $0,1, . . . , n-1$.\n\n In the following $m$ lines, the relations are given. Each relation is given by two integers $s$ and $t$ that represents $s$ and $t$ are friends (and reachable each other).\n\n In the next line, the number of queries $q$ is given. In the following $q$ lines, $q$ queries are given respectively. Each query consists of two integers $s$ and $t$ separated by a space character.", "output": "For each query, print \"yes\" if $t$ is reachable from $s$ through the social network, \"no\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 9\n0 1\n0 2\n3 4\n5 7\n5 6\n6 7\n6 8\n7 8\n8 9\n3\n0 1\n5 9\n1 3\n output: yes\nyes\nno"], "Pid": "p02240", "ProblemText": "Task Description: Write a program which reads relations in a SNS (Social Network Service), and judges that given pairs of users are reachable each other through the network.\nTask Constraint: $2 <= n <= 100,000$\n\n$0 <= m <= 100,000$\n\n$1 <= q <= 10,000$\nTask Input: In the first line, two integer $n$ and $m$ are given. $n$ is the number of users in the SNS and $m$ is the number of relations in the SNS. The users in the SNS are identified by IDs $0,1, . . . , n-1$.\n\n In the following $m$ lines, the relations are given. Each relation is given by two integers $s$ and $t$ that represents $s$ and $t$ are friends (and reachable each other).\n\n In the next line, the number of queries $q$ is given. In the following $q$ lines, $q$ queries are given respectively. Each query consists of two integers $s$ and $t$ separated by a space character.\nTask Output: For each query, print \"yes\" if $t$ is reachable from $s$ through the social network, \"no\" otherwise.\nTask Samples: input: 10 9\n0 1\n0 2\n3 4\n5 7\n5 6\n6 7\n6 8\n7 8\n8 9\n3\n0 1\n5 9\n1 3\n output: yes\nyes\nno\n\n" }, { "title": "Minimum Spanning Tree", "content": "For a given weighted graph $G = (V, E)$, find the minimum spanning tree (MST) of $G$ and print total weight of edges belong to the MST.", "constraint": "$1 <= n <= 100$\n\n$0 <= a_{ij} <= 2,000$ (if $a_{ij} \\neq -1$)\n\n$a_{ij} = a_{ji}$\n\n$G$ is a connected graph", "input": "In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, a $n * n$ adjacency matrix $A$ which represents $G$ is given.\n$a_{ij}$ denotes the weight of edge connecting vertex $i$ and vertex $j$. If there is no edge between $i$ and $j$, $a_{ij}$ is given by -1.", "output": "Print the total weight of the minimum spanning tree of $G$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n -1 2 3 1 -1\n 2 -1 -1 4 -1\n 3 -1 -1 1 1\n 1 4 1 -1 3\n -1 -1 1 3 -1\n output: 5"], "Pid": "p02241", "ProblemText": "Task Description: For a given weighted graph $G = (V, E)$, find the minimum spanning tree (MST) of $G$ and print total weight of edges belong to the MST.\nTask Constraint: $1 <= n <= 100$\n\n$0 <= a_{ij} <= 2,000$ (if $a_{ij} \\neq -1$)\n\n$a_{ij} = a_{ji}$\n\n$G$ is a connected graph\nTask Input: In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, a $n * n$ adjacency matrix $A$ which represents $G$ is given.\n$a_{ij}$ denotes the weight of edge connecting vertex $i$ and vertex $j$. If there is no edge between $i$ and $j$, $a_{ij}$ is given by -1.\nTask Output: Print the total weight of the minimum spanning tree of $G$.\nTask Samples: input: 5\n -1 2 3 1 -1\n 2 -1 -1 4 -1\n 3 -1 -1 1 1\n 1 4 1 -1 3\n -1 -1 1 3 -1\n output: 5\n\n" }, { "title": "Single Source Shortest Path", "content": "For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.", "constraint": "$1 <= n <= 100$\n\n$0 <= c_i <= 100,000$\n\n$|E| <= 10,000$\n\nAll vertices are reachable from vertex $0$", "input": "In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:\n\n$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ . . . $v_k$ $c_k$\n\n Vertices in $G$ are named with IDs $0,1, . . . , n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1,2, . . . k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).", "output": "For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 3 2 3 3 1 1 2\n1 2 0 2 3 4\n2 3 0 3 3 1 4 1\n3 4 2 1 0 1 1 4 4 3\n4 2 2 1 3 3\n output: 0 0\n1 2\n2 2\n3 1\n4 3"], "Pid": "p02242", "ProblemText": "Task Description: For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.\nTask Constraint: $1 <= n <= 100$\n\n$0 <= c_i <= 100,000$\n\n$|E| <= 10,000$\n\nAll vertices are reachable from vertex $0$\nTask Input: In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:\n\n$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ . . . $v_k$ $c_k$\n\n Vertices in $G$ are named with IDs $0,1, . . . , n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1,2, . . . k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).\nTask Output: For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.\nTask Samples: input: 5\n0 3 2 3 3 1 1 2\n1 2 0 2 3 4\n2 3 0 3 3 1 4 1\n3 4 2 1 0 1 1 4 4 3\n4 2 2 1 3 3\n output: 0 0\n1 2\n2 2\n3 1\n4 3\n\n" }, { "title": "Single Source Shortest Path II", "content": "For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.", "constraint": "$1 <= n <= 10,000$\n\n$0 <= c_i <= 100,000$\n\n$|E| < 500,000$\n\nAll vertices are reachable from vertex $0$", "input": "In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:\n\n$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ . . . $v_k$ $c_k$\n\n Vertices in $G$ are named with IDs $0,1, . . . , n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1,2, . . . k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).", "output": "For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 3 2 3 3 1 1 2\n1 2 0 2 3 4\n2 3 0 3 3 1 4 1\n3 4 2 1 0 1 1 4 4 3\n4 2 2 1 3 3\n output: 0 0\n1 2\n2 2\n3 1\n4 3"], "Pid": "p02243", "ProblemText": "Task Description: For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.\nTask Constraint: $1 <= n <= 10,000$\n\n$0 <= c_i <= 100,000$\n\n$|E| < 500,000$\n\nAll vertices are reachable from vertex $0$\nTask Input: In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:\n\n$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ . . . $v_k$ $c_k$\n\n Vertices in $G$ are named with IDs $0,1, . . . , n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1,2, . . . k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).\nTask Output: For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.\nTask Samples: input: 5\n0 3 2 3 3 1 1 2\n1 2 0 2 3 4\n2 3 0 3 3 1 4 1\n3 4 2 1 0 1 1 4 4 3\n4 2 2 1 3 3\n output: 0 0\n1 2\n2 2\n3 1\n4 3\n\n" }, { "title": "8 Queens Problem", "content": "The goal of 8 Queens Problem is to put eight queens on a chess-board such that none of them threatens any of others. A queen threatens the squares in the same row, in the same column, or on the same diagonals as shown in the following figure.\n\n For a given chess board where $k$ queens are already placed, find the solution of the 8 queens problem.", "constraint": "There is exactly one solution", "input": "In the first line, an integer $k$ is given. In the following $k$ lines, each square where a queen is already placed is given by two integers $r$ and $c$. $r$ and $c$ respectively denotes the row number and the column number. The row/column numbers start with 0.", "output": "Print a $8 * 8$ chess board by strings where a square with a queen is represented by 'Q' and an empty square is represented by '. '.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 2\n2 2\n5 3\n output: ......Q.\nQ.......\n..Q.....\n.......Q\n.....Q..\n...Q....\n.Q......\n....Q..."], "Pid": "p02244", "ProblemText": "Task Description: The goal of 8 Queens Problem is to put eight queens on a chess-board such that none of them threatens any of others. A queen threatens the squares in the same row, in the same column, or on the same diagonals as shown in the following figure.\n\n For a given chess board where $k$ queens are already placed, find the solution of the 8 queens problem.\nTask Constraint: There is exactly one solution\nTask Input: In the first line, an integer $k$ is given. In the following $k$ lines, each square where a queen is already placed is given by two integers $r$ and $c$. $r$ and $c$ respectively denotes the row number and the column number. The row/column numbers start with 0.\nTask Output: Print a $8 * 8$ chess board by strings where a square with a queen is represented by 'Q' and an empty square is represented by '. '.\nTask Samples: input: 2\n2 2\n5 3\n output: ......Q.\nQ.......\n..Q.....\n.......Q\n.....Q..\n...Q....\n.Q......\n....Q...\n\n" }, { "title": "8 Puzzle", "content": "The goal of the 8 puzzle problem is to complete pieces on $3 * 3$ cells where one of the cells is empty space. \n\n In this problem, the space is represented by 0 and pieces are represented by integers from 1 to 8 as shown below.\n\n1 3 0\n4 2 5\n7 8 6\n\n You can move a piece toward the empty space at one step. Your goal is to make the pieces the following configuration in the shortest move (fewest steps).\n\n1 2 3\n4 5 6\n7 8 0\n\n Write a program which reads an initial state of the puzzle and prints the fewest steps to solve the puzzle.", "constraint": "There is a solution.", "input": "The $3 * 3$ integers denoting the pieces or space are given.", "output": "Print the fewest steps in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 0\n4 2 5\n7 8 6\n output: 4"], "Pid": "p02245", "ProblemText": "Task Description: The goal of the 8 puzzle problem is to complete pieces on $3 * 3$ cells where one of the cells is empty space. \n\n In this problem, the space is represented by 0 and pieces are represented by integers from 1 to 8 as shown below.\n\n1 3 0\n4 2 5\n7 8 6\n\n You can move a piece toward the empty space at one step. Your goal is to make the pieces the following configuration in the shortest move (fewest steps).\n\n1 2 3\n4 5 6\n7 8 0\n\n Write a program which reads an initial state of the puzzle and prints the fewest steps to solve the puzzle.\nTask Constraint: There is a solution.\nTask Input: The $3 * 3$ integers denoting the pieces or space are given.\nTask Output: Print the fewest steps in a line.\nTask Samples: input: 1 3 0\n4 2 5\n7 8 6\n output: 4\n\n" }, { "title": "15 Puzzle", "content": "The goal of the 15 puzzle problem is to complete pieces on $4 * 4$ cells where one of the cells is empty space.\n\n In this problem, the space is represented by 0 and pieces are represented by integers from 1 to 15 as shown below.\n\n1 2 3 4\n6 7 8 0\n5 10 11 12\n9 13 14 15\n\n You can move a piece toward the empty space at one step. Your goal is to make the pieces the following configuration in the shortest move (fewest steps).\n\n1 2 3 4\n5 6 7 8\n9 10 11 12\n13 14 15 0\n\n Write a program which reads an initial state of the puzzle and prints the fewest steps to solve the puzzle.", "constraint": "The given puzzle is solvable in at most 45 steps.", "input": "The $4 * 4$ integers denoting the pieces or space are given.", "output": "Print the fewest steps in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 3 4\n6 7 8 0\n5 10 11 12\n9 13 14 15\n output: 8"], "Pid": "p02246", "ProblemText": "Task Description: The goal of the 15 puzzle problem is to complete pieces on $4 * 4$ cells where one of the cells is empty space.\n\n In this problem, the space is represented by 0 and pieces are represented by integers from 1 to 15 as shown below.\n\n1 2 3 4\n6 7 8 0\n5 10 11 12\n9 13 14 15\n\n You can move a piece toward the empty space at one step. Your goal is to make the pieces the following configuration in the shortest move (fewest steps).\n\n1 2 3 4\n5 6 7 8\n9 10 11 12\n13 14 15 0\n\n Write a program which reads an initial state of the puzzle and prints the fewest steps to solve the puzzle.\nTask Constraint: The given puzzle is solvable in at most 45 steps.\nTask Input: The $4 * 4$ integers denoting the pieces or space are given.\nTask Output: Print the fewest steps in a line.\nTask Samples: input: 1 2 3 4\n6 7 8 0\n5 10 11 12\n9 13 14 15\n output: 8\n\n" }, { "title": "Naive String Search", "content": "Find places where a string P is found within a text T.\n \n Print all indices of T where P found. The indices of T start with 0.", "constraint": "1 <= length of T <= 1000 \n\n 1 <= length of P <= 1000 \n\nThe input consists of alphabetical characters and digits", "input": "In the first line, a text T is given. In the second line, a string P is given.", "output": "Print an index of T where P found in a line. Print the indices in ascending order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aabaaa\naa\n output: 0\n3\n4", "input: xyzz\nyz\n output: 1", "input: abc\nxyz\n output: \n\nThe ouput should be empty."], "Pid": "p02247", "ProblemText": "Task Description: Find places where a string P is found within a text T.\n \n Print all indices of T where P found. The indices of T start with 0.\nTask Constraint: 1 <= length of T <= 1000 \n\n 1 <= length of P <= 1000 \n\nThe input consists of alphabetical characters and digits\nTask Input: In the first line, a text T is given. In the second line, a string P is given.\nTask Output: Print an index of T where P found in a line. Print the indices in ascending order.\nTask Samples: input: aabaaa\naa\n output: 0\n3\n4\ninput: xyzz\nyz\n output: 1\ninput: abc\nxyz\n output: \n\nThe ouput should be empty.\n\n" }, { "title": "String Search", "content": "Find places where a string P is found within a text T.\n Print all indices of T where P found. The indices of T start with 0.", "constraint": "1 <= length of T <= 1000000 \n\n 1 <= length of P <= 10000 \n\nThe input consists of alphabetical characters and digits", "input": "In the first line, a text T is given. In the second line, a string P is given.", "output": "Print an index of T where P found in a line. Print the indices in ascending order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aabaaa\naa\n output: 0\n3\n4", "input: xyzz\nyz\n output: 1", "input: abc\nxyz\n output: \n\nThe output should be empty."], "Pid": "p02248", "ProblemText": "Task Description: Find places where a string P is found within a text T.\n Print all indices of T where P found. The indices of T start with 0.\nTask Constraint: 1 <= length of T <= 1000000 \n\n 1 <= length of P <= 10000 \n\nThe input consists of alphabetical characters and digits\nTask Input: In the first line, a text T is given. In the second line, a string P is given.\nTask Output: Print an index of T where P found in a line. Print the indices in ascending order.\nTask Samples: input: aabaaa\naa\n output: 0\n3\n4\ninput: xyzz\nyz\n output: 1\ninput: abc\nxyz\n output: \n\nThe output should be empty.\n\n" }, { "title": "Pattern Search", "content": "Find places where a R * C pattern is found within a H * W region. Print top-left coordinates (i, j) of sub-regions where the pattern found. The top-left and bottom-right coordinates of the region is (0,0) and (H-1, W-1) respectively.", "constraint": "1 <= H, W <= 1000 \n\n 1 <= R, C <= 1000 \n\nThe input consists of alphabetical characters and digits", "input": "In the first line, two integers H and W are given. In the following H lines, i-th lines of the region are given.\n\n In the next line, two integers R and C are given. In the following R lines, i-th lines of the pattern are given.", "output": "For each sub-region found, print a coordinate i and j separated by a space character in a line. Print the coordinates in ascending order of the row numbers (i), or the column numbers (j) in case of a tie.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n00010\n00101\n00010\n00100\n3 2\n10\n01\n10\n output: 0 3\n1 2"], "Pid": "p02249", "ProblemText": "Task Description: Find places where a R * C pattern is found within a H * W region. Print top-left coordinates (i, j) of sub-regions where the pattern found. The top-left and bottom-right coordinates of the region is (0,0) and (H-1, W-1) respectively.\nTask Constraint: 1 <= H, W <= 1000 \n\n 1 <= R, C <= 1000 \n\nThe input consists of alphabetical characters and digits\nTask Input: In the first line, two integers H and W are given. In the following H lines, i-th lines of the region are given.\n\n In the next line, two integers R and C are given. In the following R lines, i-th lines of the pattern are given.\nTask Output: For each sub-region found, print a coordinate i and j separated by a space character in a line. Print the coordinates in ascending order of the row numbers (i), or the column numbers (j) in case of a tie.\nTask Samples: input: 4 5\n00010\n00101\n00010\n00100\n3 2\n10\n01\n10\n output: 0 3\n1 2\n\n" }, { "title": "String Search", "content": "Determine whether a text T includes a pattern P. Your program should answer for given queries consisting of P_i.", "constraint": "1 <= length of T <= 1000000 \n\n 1 <= length of P_i <= 1000 \n\n 1 <= Q <= 10000 \n\nThe input consists of alphabetical characters and digits", "input": "In the first line, a text T is given. In the second line, an integer Q denoting the number of queries is given. In the following Q lines, the patterns P_i are given respectively.", "output": "For each question, print 1 if the text includes P_i, or print 0 otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aabaaa\n4\naa\nba\nbb\nxyz\n output: 1\n1\n0\n0"], "Pid": "p02250", "ProblemText": "Task Description: Determine whether a text T includes a pattern P. Your program should answer for given queries consisting of P_i.\nTask Constraint: 1 <= length of T <= 1000000 \n\n 1 <= length of P_i <= 1000 \n\n 1 <= Q <= 10000 \n\nThe input consists of alphabetical characters and digits\nTask Input: In the first line, a text T is given. In the second line, an integer Q denoting the number of queries is given. In the following Q lines, the patterns P_i are given respectively.\nTask Output: For each question, print 1 if the text includes P_i, or print 0 otherwise.\nTask Samples: input: aabaaa\n4\naa\nba\nbb\nxyz\n output: 1\n1\n0\n0\n\n" }, { "title": "Change-Making Problem", "content": "You want to make change for $n$ cents. Assuming that you have infinite supply of coins of 1,5,10 and/or 25 cents coins respectively, find the minimum number of coins you need.", "constraint": "$1 <= n <= 10^9$", "input": "$n$\nThe integer $n$ is given in a line.", "output": "Print the minimum number of coins you need in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100\n output: 4", "input: 54321\n output: 2175"], "Pid": "p02251", "ProblemText": "Task Description: You want to make change for $n$ cents. Assuming that you have infinite supply of coins of 1,5,10 and/or 25 cents coins respectively, find the minimum number of coins you need.\nTask Constraint: $1 <= n <= 10^9$\nTask Input: $n$\nThe integer $n$ is given in a line.\nTask Output: Print the minimum number of coins you need in a line.\nTask Samples: input: 100\n output: 4\ninput: 54321\n output: 2175\n\n" }, { "title": "Fractional Knapsack Problem", "content": "You have $N$ items that you want to put them into a knapsack of capacity $W$. Item $i$ ($1 <= i <= N$) has weight $w_i$ and value $v_i$ for the weight. When you put some items into the knapsack, the following conditions must be satisfied:\nThe total value of the items is as large as possible.\n\nThe total weight of the selected items is at most $W$.\n\nYou can break some items if you want. If you put $w'$($0 <= w' <= w_i$) of item $i$, its value becomes $\\displaystyle v_i * \\frac{w'}{w_i}. $\n\nFind the maximum total value of items in the knapsack.", "constraint": "$1 <= N <= 10^5$\n\n$1 <= W <= 10^9$\n\n$1 <= v_i <= 10^9 (1 <= i <= N)$\n\n$1 <= w_i <= 10^9 (1 <= i <= N)$", "input": "$N$ $W$\n$v_1$ $w_1$\n$v_2$ $w_2$\n:\n$v_N$ $w_N$\nThe first line consists of the integers $N$ and $W$. In the following $N$ lines, the value and weight of the $i$-th item are given.", "output": "Print the maximum total value of the items in a line. The output must not contain an error greater than $10^{-6}$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 50\n60 10\n100 20\n120 30\n output: 240\n\nWhen you put 10 of item $1$, 20 of item $2$ and 20 of item $3$, the total value is maximized.", "input: 3 50\n60 13\n100 23\n120 33\n output: 210.90909091\n\nWhen you put 13 of item $1$, 23 of item $2$ and 14 of item $3$, the total value is maximized. Note some outputs can be a real number.", "input: 1 100\n100000 100000\n output: 100"], "Pid": "p02252", "ProblemText": "Task Description: You have $N$ items that you want to put them into a knapsack of capacity $W$. Item $i$ ($1 <= i <= N$) has weight $w_i$ and value $v_i$ for the weight. When you put some items into the knapsack, the following conditions must be satisfied:\nThe total value of the items is as large as possible.\n\nThe total weight of the selected items is at most $W$.\n\nYou can break some items if you want. If you put $w'$($0 <= w' <= w_i$) of item $i$, its value becomes $\\displaystyle v_i * \\frac{w'}{w_i}. $\n\nFind the maximum total value of items in the knapsack.\nTask Constraint: $1 <= N <= 10^5$\n\n$1 <= W <= 10^9$\n\n$1 <= v_i <= 10^9 (1 <= i <= N)$\n\n$1 <= w_i <= 10^9 (1 <= i <= N)$\nTask Input: $N$ $W$\n$v_1$ $w_1$\n$v_2$ $w_2$\n:\n$v_N$ $w_N$\nThe first line consists of the integers $N$ and $W$. In the following $N$ lines, the value and weight of the $i$-th item are given.\nTask Output: Print the maximum total value of the items in a line. The output must not contain an error greater than $10^{-6}$.\nTask Samples: input: 3 50\n60 10\n100 20\n120 30\n output: 240\n\nWhen you put 10 of item $1$, 20 of item $2$ and 20 of item $3$, the total value is maximized.\ninput: 3 50\n60 13\n100 23\n120 33\n output: 210.90909091\n\nWhen you put 13 of item $1$, 23 of item $2$ and 14 of item $3$, the total value is maximized. Note some outputs can be a real number.\ninput: 1 100\n100000 100000\n output: 100\n\n" }, { "title": "Activity Selection Problem", "content": "There are $n$ acitivities with start times $\\{s_i\\}$ and finish times $\\{t_i\\}$. Assuming that a person can only work on a single activity at a time, find the maximum number of activities that can be performed by a single person.", "constraint": "$1 <= n <= 10^5$\n\n$1 <= s_i < t_i <= 10^9 (1 <= i <= n)$", "input": "$n$\n$s_1$ $t_1$\n$s_2$ $t_2$\n:\n$s_n$ $t_n$\nThe first line consists of the integer $n$. In the following $n$ lines, the start time $s_i$ and the finish time $t_i$ of the activity $i$ are given.", "output": "Print the maximum number of activities in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n3 9\n3 5\n5 9\n6 8\n output: 3", "input: 3\n1 5\n3 4\n2 5\n output: 1", "input: 3\n1 2\n2 3\n3 4\n output: 2"], "Pid": "p02253", "ProblemText": "Task Description: There are $n$ acitivities with start times $\\{s_i\\}$ and finish times $\\{t_i\\}$. Assuming that a person can only work on a single activity at a time, find the maximum number of activities that can be performed by a single person.\nTask Constraint: $1 <= n <= 10^5$\n\n$1 <= s_i < t_i <= 10^9 (1 <= i <= n)$\nTask Input: $n$\n$s_1$ $t_1$\n$s_2$ $t_2$\n:\n$s_n$ $t_n$\nThe first line consists of the integer $n$. In the following $n$ lines, the start time $s_i$ and the finish time $t_i$ of the activity $i$ are given.\nTask Output: Print the maximum number of activities in a line.\nTask Samples: input: 5\n1 2\n3 9\n3 5\n5 9\n6 8\n output: 3\ninput: 3\n1 5\n3 4\n2 5\n output: 1\ninput: 3\n1 2\n2 3\n3 4\n output: 2\n\n" }, { "title": "Huffman Coding", "content": "We want to encode a given string $S$ to a binary string. Each alphabet character in $S$ should be mapped to a different variable-length code and the code must not be a prefix of others. Huffman coding is known as one of ways to obtain a code table for such encoding. For example, we consider that appearance frequencycies of each alphabet character in $S$ are as follows:
    \n a b c d e f \n\n freq. 45 13 12 16 9 5 \n\n code 0 101 100 111 1101 1100 \n\n We can obtain \"Huffman codes\" (the third row of the table) using Huffman's algorithm. The algorithm finds a full binary tree called \"Huffman tree\" as shown in the following figure.\n\nTo obtain a Huffman tree, for each alphabet character, we first prepare a node which has no parents and a frequency (weight) of the alphabet character. Then, we repeat the following steps:\nChoose two nodes, $x$ and $y$, which has no parents and the smallest weights.\n\nCreate a new node $z$ whose weight is the sum of $x$'s and $y$'s.\n\nAdd edge linking $z$ to $x$ with label $0$ and to $y$ with label $1$. Then $z$ become their parent.\n\nIf there is only one node without a parent, which is the root, finish the algorithm. Otherwise, go to step 1.\n\nFinally, we can find a \"Huffman code\" in a path from the root to leaves. Task Given a string $S$, output the length of a binary string obtained by using Huffman coding for $S$.", "constraint": "$1 <= |S| <= 10^5$\n\n$S$ consists of lowercase English letters.", "input": "$S$\nA string $S$ is given in a line.", "output": "Print the length of a binary string in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: abca\n output: 6", "input: aaabbcccdeeeffg\n output: 41", "input: z\n output: 1"], "Pid": "p02254", "ProblemText": "Task Description: We want to encode a given string $S$ to a binary string. Each alphabet character in $S$ should be mapped to a different variable-length code and the code must not be a prefix of others. Huffman coding is known as one of ways to obtain a code table for such encoding. For example, we consider that appearance frequencycies of each alphabet character in $S$ are as follows:
    \n a b c d e f \n\n freq. 45 13 12 16 9 5 \n\n code 0 101 100 111 1101 1100 \n\n We can obtain \"Huffman codes\" (the third row of the table) using Huffman's algorithm. The algorithm finds a full binary tree called \"Huffman tree\" as shown in the following figure.\n\nTo obtain a Huffman tree, for each alphabet character, we first prepare a node which has no parents and a frequency (weight) of the alphabet character. Then, we repeat the following steps:\nChoose two nodes, $x$ and $y$, which has no parents and the smallest weights.\n\nCreate a new node $z$ whose weight is the sum of $x$'s and $y$'s.\n\nAdd edge linking $z$ to $x$ with label $0$ and to $y$ with label $1$. Then $z$ become their parent.\n\nIf there is only one node without a parent, which is the root, finish the algorithm. Otherwise, go to step 1.\n\nFinally, we can find a \"Huffman code\" in a path from the root to leaves. Task Given a string $S$, output the length of a binary string obtained by using Huffman coding for $S$.\nTask Constraint: $1 <= |S| <= 10^5$\n\n$S$ consists of lowercase English letters.\nTask Input: $S$\nA string $S$ is given in a line.\nTask Output: Print the length of a binary string in a line.\nTask Samples: input: abca\n output: 6\ninput: aaabbcccdeeeffg\n output: 41\ninput: z\n output: 1\n\n" }, { "title": "Insertion Sort", "content": "Write a program of the Insertion Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:\n\nfor i = 1 to A. length-1\n key = A[i]\n /* insert A[i] into the sorted sequence A[0, . . . , j-1] */\n j = i - 1\n while j >= 0 and A[j] > key\n A[j+1] = A[j]\n j--\n A[j+1] = key\n\nNote that, indices for array elements are based on 0-origin.\n\nTo illustrate the algorithms, your program should trace intermediate result for each step.", "constraint": "1 <= N <= 100", "input": "The first line of the input includes an integer N, the number of elements in the sequence.\n\nIn the second line, N elements of the sequence are given separated by a single space.", "output": "The output consists of N lines. Please output the intermediate sequence in a line for each step. Elements of the sequence should be separated by single space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n5 2 4 6 1 3\n output: 5 2 4 6 1 3\n2 5 4 6 1 3\n2 4 5 6 1 3\n2 4 5 6 1 3\n1 2 4 5 6 3\n1 2 3 4 5 6", "input: 3\n1 2 3\n output: 1 2 3\n1 2 3\n1 2 3"], "Pid": "p02255", "ProblemText": "Task Description: Write a program of the Insertion Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:\n\nfor i = 1 to A. length-1\n key = A[i]\n /* insert A[i] into the sorted sequence A[0, . . . , j-1] */\n j = i - 1\n while j >= 0 and A[j] > key\n A[j+1] = A[j]\n j--\n A[j+1] = key\n\nNote that, indices for array elements are based on 0-origin.\n\nTo illustrate the algorithms, your program should trace intermediate result for each step.\nTask Constraint: 1 <= N <= 100\nTask Input: The first line of the input includes an integer N, the number of elements in the sequence.\n\nIn the second line, N elements of the sequence are given separated by a single space.\nTask Output: The output consists of N lines. Please output the intermediate sequence in a line for each step. Elements of the sequence should be separated by single space.\nTask Samples: input: 6\n5 2 4 6 1 3\n output: 5 2 4 6 1 3\n2 5 4 6 1 3\n2 4 5 6 1 3\n2 4 5 6 1 3\n1 2 4 5 6 3\n1 2 3 4 5 6\ninput: 3\n1 2 3\n output: 1 2 3\n1 2 3\n1 2 3\n\n" }, { "title": "Greatest Common Divisor", "content": "Write a program which finds the greatest common divisor of two natural numbers a and b\n hint:\nYou can use the following observation:\n\nFor integers x and y, if x >= y, then gcd(x, y) = gcd(y, x%y)", "constraint": "1 <= a, b <= 10^9", "input": "a and b are given in a line sparated by a single space.", "output": "Output the greatest common divisor of a and b.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 54 20\n output: 2", "input: 147 105\n output: 21"], "Pid": "p02256", "ProblemText": "Task Description: Write a program which finds the greatest common divisor of two natural numbers a and b\n hint:\nYou can use the following observation:\n\nFor integers x and y, if x >= y, then gcd(x, y) = gcd(y, x%y)\nTask Constraint: 1 <= a, b <= 10^9\nTask Input: a and b are given in a line sparated by a single space.\nTask Output: Output the greatest common divisor of a and b.\nTask Samples: input: 54 20\n output: 2\ninput: 147 105\n output: 21\n\n" }, { "title": "Prime Numbers", "content": "A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2,3,5 and 7.\n\nWrite a program which reads a list of N integers and prints the number of prime numbers in the list.", "constraint": "1 <= N <= 10000\n\n2 <= an element of the list <= 10^8", "input": "The first line contains an integer N, the number of elements in the list.\n\nN numbers are given in the following lines.", "output": "Print the number of prime numbers in the given list.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2\n3\n4\n5\n6\n output: 3", "input: 11\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n output: 4"], "Pid": "p02257", "ProblemText": "Task Description: A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2,3,5 and 7.\n\nWrite a program which reads a list of N integers and prints the number of prime numbers in the list.\nTask Constraint: 1 <= N <= 10000\n\n2 <= an element of the list <= 10^8\nTask Input: The first line contains an integer N, the number of elements in the list.\n\nN numbers are given in the following lines.\nTask Output: Print the number of prime numbers in the given list.\nTask Samples: input: 5\n2\n3\n4\n5\n6\n output: 3\ninput: 11\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n output: 4\n\n" }, { "title": "Maximum Profit", "content": "You can obtain profits from foreign exchange margin transactions. For example, if you buy 1000 dollar at a rate of 100 yen per dollar, and sell them at a rate of 108 yen per dollar, you can obtain (108 - 100) * 1000 = 8000 yen.\n\n Write a program which reads values of a currency $R_t$ at a certain time $t$ ($t = 0,1,2, . . . n-1$), and reports the maximum value of $R_j - R_i$ where $j > i$ .", "constraint": "$2 <= n <= 200,000$\n\n$1 <= R_t <= 10^9$", "input": "The first line contains an integer $n$. In the following $n$ lines, $R_t$ ($t = 0,1,2, . . . n-1$) are given in order.", "output": "Print the maximum value in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n5\n3\n1\n3\n4\n3\n output: 3", "input: 3\n4\n3\n2\n output: -1"], "Pid": "p02258", "ProblemText": "Task Description: You can obtain profits from foreign exchange margin transactions. For example, if you buy 1000 dollar at a rate of 100 yen per dollar, and sell them at a rate of 108 yen per dollar, you can obtain (108 - 100) * 1000 = 8000 yen.\n\n Write a program which reads values of a currency $R_t$ at a certain time $t$ ($t = 0,1,2, . . . n-1$), and reports the maximum value of $R_j - R_i$ where $j > i$ .\nTask Constraint: $2 <= n <= 200,000$\n\n$1 <= R_t <= 10^9$\nTask Input: The first line contains an integer $n$. In the following $n$ lines, $R_t$ ($t = 0,1,2, . . . n-1$) are given in order.\nTask Output: Print the maximum value in a line.\nTask Samples: input: 6\n5\n3\n1\n3\n4\n3\n output: 3\ninput: 3\n4\n3\n2\n output: -1\n\n" }, { "title": "Bubble Sort", "content": "Write a program of the Bubble Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:\n\nBubble Sort(A)\n1 for i = 0 to A. length-1\n2 for j = A. length-1 downto i+1\n3 if A[j] < A[j-1]\n4 swap A[j] and A[j-1]\n\nNote that, indices for array elements are based on 0-origin.\n\nYour program should also print the number of swap operations defined in line 4 of the pseudocode.", "constraint": "1 <= N <= 100", "input": "The first line of the input includes an integer N, the number of elements in the sequence.\n\nIn the second line, N elements of the sequence are given separated by spaces characters.", "output": "The output consists of 2 lines. \n\nIn the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.\n\nIn the second line, please print the number of swap operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n5 3 2 4 1\n output: 1 2 3 4 5\n8", "input: 6\n5 2 4 6 1 3\n output: 1 2 3 4 5 6\n9"], "Pid": "p02259", "ProblemText": "Task Description: Write a program of the Bubble Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:\n\nBubble Sort(A)\n1 for i = 0 to A. length-1\n2 for j = A. length-1 downto i+1\n3 if A[j] < A[j-1]\n4 swap A[j] and A[j-1]\n\nNote that, indices for array elements are based on 0-origin.\n\nYour program should also print the number of swap operations defined in line 4 of the pseudocode.\nTask Constraint: 1 <= N <= 100\nTask Input: The first line of the input includes an integer N, the number of elements in the sequence.\n\nIn the second line, N elements of the sequence are given separated by spaces characters.\nTask Output: The output consists of 2 lines. \n\nIn the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.\n\nIn the second line, please print the number of swap operations.\nTask Samples: input: 5\n5 3 2 4 1\n output: 1 2 3 4 5\n8\ninput: 6\n5 2 4 6 1 3\n output: 1 2 3 4 5 6\n9\n\n" }, { "title": "Selection Sort", "content": "Write a program of the Selection Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:\n\nSelection Sort(A)\n1 for i = 0 to A. length-1\n2 mini = i\n3 for j = i to A. length-1\n4 if A[j] < A[mini]\n5 mini = j\n6 swap A[i] and A[mini]\n\nNote that, indices for array elements are based on 0-origin.\n\nYour program should also print the number of swap operations defined in line 6 of the pseudocode in the case where i ! = mini.", "constraint": "1 <= N <= 100", "input": "The first line of the input includes an integer N, the number of elements in the sequence.\n\nIn the second line, N elements of the sequence are given separated by space characters.", "output": "The output consists of 2 lines. \n\nIn the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.\n\nIn the second line, please print the number of swap operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n5 6 4 2 1 3\n output: 1 2 3 4 5 6\n4", "input: 6\n5 2 4 6 1 3\n output: 1 2 3 4 5 6\n3"], "Pid": "p02260", "ProblemText": "Task Description: Write a program of the Selection Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:\n\nSelection Sort(A)\n1 for i = 0 to A. length-1\n2 mini = i\n3 for j = i to A. length-1\n4 if A[j] < A[mini]\n5 mini = j\n6 swap A[i] and A[mini]\n\nNote that, indices for array elements are based on 0-origin.\n\nYour program should also print the number of swap operations defined in line 6 of the pseudocode in the case where i ! = mini.\nTask Constraint: 1 <= N <= 100\nTask Input: The first line of the input includes an integer N, the number of elements in the sequence.\n\nIn the second line, N elements of the sequence are given separated by space characters.\nTask Output: The output consists of 2 lines. \n\nIn the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.\n\nIn the second line, please print the number of swap operations.\nTask Samples: input: 6\n5 6 4 2 1 3\n output: 1 2 3 4 5 6\n4\ninput: 6\n5 2 4 6 1 3\n output: 1 2 3 4 5 6\n3\n\n" }, { "title": "Stable Sort", "content": "Let's arrange a deck of cards. There are totally 36 cards of 4 suits(S, H, C, D) and 9 values (1,2, . . . 9). For example, 'eight of heart' is represented by H8 and 'one of diamonds' is represented by D1.\n\nYour task is to write a program which sorts a given set of cards in ascending order by their values using the Bubble Sort algorithms and the Selection Sort algorithm respectively. These algorithms should be based on the following pseudocode:\n\nBubble Sort(C)\n1 for i = 0 to C. length-1\n2 for j = C. length-1 downto i+1\n3 if C[j]. value < C[j-1]. value\n4 swap C[j] and C[j-1]\n\nSelection Sort(C)\n1 for i = 0 to C. length-1\n2 mini = i\n3 for j = i to C. length-1\n4 if C[j]. value < C[mini]. value\n5 mini = j\n6 swap C[i] and C[mini]\n\nNote that, indices for array elements are based on 0-origin.", "constraint": "1 <= N <= 36", "input": "The first line contains an integer N, the number of cards.\n\nN cards are given in the following line. Each card is represented by two characters. Two consecutive cards are separated by a space character.", "output": "In the first line, print the arranged cards provided by the Bubble Sort algorithm. Two consecutive cards should be separated by a space character.\n\nIn the second line, print the stability (\"Stable\" or \"Not stable\") of this output.\n\nIn the third line, print the arranged cards provided by the Selection Sort algorithm. Two consecutive cards should be separated by a space character.\n\nIn the fourth line, print the stability (\"Stable\" or \"Not stable\") of this output.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nH4 C9 S4 D2 C3\n output: D2 C3 H4 S4 C9\nStable\nD2 C3 S4 H4 C9\nNot stable", "input: 2\nS1 H1\n output: S1 H1\nStable\nS1 H1\nStable"], "Pid": "p02261", "ProblemText": "Task Description: Let's arrange a deck of cards. There are totally 36 cards of 4 suits(S, H, C, D) and 9 values (1,2, . . . 9). For example, 'eight of heart' is represented by H8 and 'one of diamonds' is represented by D1.\n\nYour task is to write a program which sorts a given set of cards in ascending order by their values using the Bubble Sort algorithms and the Selection Sort algorithm respectively. These algorithms should be based on the following pseudocode:\n\nBubble Sort(C)\n1 for i = 0 to C. length-1\n2 for j = C. length-1 downto i+1\n3 if C[j]. value < C[j-1]. value\n4 swap C[j] and C[j-1]\n\nSelection Sort(C)\n1 for i = 0 to C. length-1\n2 mini = i\n3 for j = i to C. length-1\n4 if C[j]. value < C[mini]. value\n5 mini = j\n6 swap C[i] and C[mini]\n\nNote that, indices for array elements are based on 0-origin.\nTask Constraint: 1 <= N <= 36\nTask Input: The first line contains an integer N, the number of cards.\n\nN cards are given in the following line. Each card is represented by two characters. Two consecutive cards are separated by a space character.\nTask Output: In the first line, print the arranged cards provided by the Bubble Sort algorithm. Two consecutive cards should be separated by a space character.\n\nIn the second line, print the stability (\"Stable\" or \"Not stable\") of this output.\n\nIn the third line, print the arranged cards provided by the Selection Sort algorithm. Two consecutive cards should be separated by a space character.\n\nIn the fourth line, print the stability (\"Stable\" or \"Not stable\") of this output.\nTask Samples: input: 5\nH4 C9 S4 D2 C3\n output: D2 C3 H4 S4 C9\nStable\nD2 C3 S4 H4 C9\nNot stable\ninput: 2\nS1 H1\n output: S1 H1\nStable\nS1 H1\nStable\n\n" }, { "title": "shell sort", "content": "Shell Sort is a generalization of Insertion Sort to arrange a list of $n$ elements $A$.\n\n1 insertion Sort(A, n, g)\n2 for i = g to n-1\n3 v = A[i]\n4 j = i - g\n5 while j >= 0 && A[j] > v\n6 A[j+g] = A[j]\n7 j = j - g\n8 cnt++\n9 A[j+g] = v\n10\n11 shell Sort(A, n)\n12 cnt = 0\n13 m = ?\n14 G[] = {? , ? , . . . , ? }\n15 for i = 0 to m-1\n16 insertion Sort(A, n, G[i])\n\n A function shell Sort(A, n) performs a function insertion Sort(A, n, g), which considers every $g$-th elements. Beginning with large values of $g$, it repeats the insertion sort with smaller $g$. \n\nYour task is to complete the above program by filling ? . Write a program which reads an integer $n$ and a sequence $A$, and prints $m$, $G_i (i = 0,1, . . . , m - 1)$ in the pseudo code and the sequence $A$ in ascending order. The output of your program must meet the following requirements:\n\n$1 <= m <= 100$\n\n$0 <= G_i <= n$\n\ncnt does not exceed $\\lceil n^{1.5}\\rceil$", "constraint": "$1 <= n <= 1,000,000$\n\n$0 <= A_i <= 10^9$", "input": "In the first line, an integer $n$ is given. In the following $n$ lines, $A_i (i=0,1, . . . , n-1)$ are given for each line.", "output": "In the first line, print an integer $m$. In the second line, print $m$ integers $G_i (i=0,1, . . . , m-1)$ separated by single space character in a line. \n\n In the third line, print cnt in a line. In the following $n$ lines, print $A_i (i=0,1, . . . , n-1)$ respectively.\n\n This problem has multiple solutions and the judge will be performed by a special validator.", "content_img": false, "lang": "", "error": false, "samples": ["input: 5\n5\n1\n4\n3\n2\n output: 2\n4 1\n3\n1\n2\n3\n4\n5", "input: 3\n3\n2\n1\n output: 1\n1\n3\n1\n2\n3"], "Pid": "p02262", "ProblemText": "Task Description: Shell Sort is a generalization of Insertion Sort to arrange a list of $n$ elements $A$.\n\n1 insertion Sort(A, n, g)\n2 for i = g to n-1\n3 v = A[i]\n4 j = i - g\n5 while j >= 0 && A[j] > v\n6 A[j+g] = A[j]\n7 j = j - g\n8 cnt++\n9 A[j+g] = v\n10\n11 shell Sort(A, n)\n12 cnt = 0\n13 m = ?\n14 G[] = {? , ? , . . . , ? }\n15 for i = 0 to m-1\n16 insertion Sort(A, n, G[i])\n\n A function shell Sort(A, n) performs a function insertion Sort(A, n, g), which considers every $g$-th elements. Beginning with large values of $g$, it repeats the insertion sort with smaller $g$. \n\nYour task is to complete the above program by filling ? . Write a program which reads an integer $n$ and a sequence $A$, and prints $m$, $G_i (i = 0,1, . . . , m - 1)$ in the pseudo code and the sequence $A$ in ascending order. The output of your program must meet the following requirements:\n\n$1 <= m <= 100$\n\n$0 <= G_i <= n$\n\ncnt does not exceed $\\lceil n^{1.5}\\rceil$\nTask Constraint: $1 <= n <= 1,000,000$\n\n$0 <= A_i <= 10^9$\nTask Input: In the first line, an integer $n$ is given. In the following $n$ lines, $A_i (i=0,1, . . . , n-1)$ are given for each line.\nTask Output: In the first line, print an integer $m$. In the second line, print $m$ integers $G_i (i=0,1, . . . , m-1)$ separated by single space character in a line. \n\n In the third line, print cnt in a line. In the following $n$ lines, print $A_i (i=0,1, . . . , n-1)$ respectively.\n\n This problem has multiple solutions and the judge will be performed by a special validator.\nTask Samples: input: 5\n5\n1\n4\n3\n2\n output: 2\n4 1\n3\n1\n2\n3\n4\n5\ninput: 3\n3\n2\n1\n output: 1\n1\n3\n1\n2\n3\n\n" }, { "title": "", "content": "", "constraint": "2 <= the number of operands in the expression <= 100
    \n1 <= the number of operators in the expression <= 99
    \n-1 * 10^9 <= values in the stack <= 10^9
    ", "input": "An expression is given in a line. Two consequtive symbols (operand or operator) are separated by a space character.\n\nYou can assume that +, - and * are given as the operator and an operand is a positive integer less than 10^6", "output": "Print the computational result in a line.", "content_img": false, "lang": "en", "error": true, "samples": ["input: 1 2 +\n output: 3", "input: 1 2 + 3 4 - *\n output: -3"], "Pid": "p02263", "ProblemText": "Task Description: \nTask Constraint: 2 <= the number of operands in the expression <= 100
    \n1 <= the number of operators in the expression <= 99
    \n-1 * 10^9 <= values in the stack <= 10^9
    \nTask Input: An expression is given in a line. Two consequtive symbols (operand or operator) are separated by a space character.\n\nYou can assume that +, - and * are given as the operator and an operand is a positive integer less than 10^6\nTask Output: Print the computational result in a line.\nTask Samples: input: 1 2 +\n output: 3\ninput: 1 2 + 3 4 - *\n output: -3\n\n" }, { "title": "", "content": "", "constraint": "1 <= n <= 100000\n\n1 <= q <= 1000\n\n1 <= time_i <= 50000\n\n1 <= length of name_i <= 10\n\n1 <= Sum of time_i <= 1000000", "input": "n q\nname_1 time_1\nname_2 time_2\n. . . \nname_n time_n\n\nIn the first line the number of processes n and the quantum q are given separated by a single space.\n\nIn the following n lines, names and times for the n processes are given. name_i and time_i are separated by a single space.", "output": "For each process, prints its name and the time the process finished in order.", "content_img": false, "lang": "en", "error": true, "samples": ["input: 5 100\np1 150\np2 80\np3 200\np4 350\np5 20\n output: p2 180\np5 400\np1 450\np3 550\np4 800"], "Pid": "p02264", "ProblemText": "Task Description: \nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 1000\n\n1 <= time_i <= 50000\n\n1 <= length of name_i <= 10\n\n1 <= Sum of time_i <= 1000000\nTask Input: n q\nname_1 time_1\nname_2 time_2\n. . . \nname_n time_n\n\nIn the first line the number of processes n and the quantum q are given separated by a single space.\n\nIn the following n lines, names and times for the n processes are given. name_i and time_i are separated by a single space.\nTask Output: For each process, prints its name and the time the process finished in order.\nTask Samples: input: 5 100\np1 150\np2 80\np3 200\np4 350\np5 20\n output: p2 180\np5 400\np1 450\np3 550\np4 800\n\n" }, { "title": "Doubly Linked List", "content": "Your task is to implement a double linked list.\n\nWrite a program which performs the following operations:\n\ninsert x: insert an element with key x into the front of the list.\n\ndelete x: delete the first element which has the key of x from the list. If there is not such element, you need not do anything.\n\ndelete First: delete the first element from the list. \n\ndelete Last: delete the last element from the list.", "constraint": "The number of operations <= 2,000,000\n\nThe number of delete operations <= 20\n\n0 <= value of a key <= 10^9\n\nThe number of elements in the list does not exceed 10^6\n\nFor a delete, deleteFirst or deleteLast operation, there is at least one element in the list.", "input": "The input is given in the following format:\n\nn\ncommand_1 \ncommand_2 \n. . . \ncommand_n \n\nIn the first line, the number of operations n is given. In the following n lines, the above mentioned operations are given in the following format:\n\ninsert x\n\ndelete x\n\ndelete First \n\ndelete Last", "output": "Print all the element (key) in the list after the given operations. Two consequtive keys should be separated by a single space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\ninsert 5\ninsert 2\ninsert 3\ninsert 1\ndelete 3\ninsert 6\ndelete 5\n output: 6 1 2", "input: 9\ninsert 5\ninsert 2\ninsert 3\ninsert 1\ndelete 3\ninsert 6\ndelete 5\ndeleteFirst\ndeleteLast\n output: 1"], "Pid": "p02265", "ProblemText": "Task Description: Your task is to implement a double linked list.\n\nWrite a program which performs the following operations:\n\ninsert x: insert an element with key x into the front of the list.\n\ndelete x: delete the first element which has the key of x from the list. If there is not such element, you need not do anything.\n\ndelete First: delete the first element from the list. \n\ndelete Last: delete the last element from the list.\nTask Constraint: The number of operations <= 2,000,000\n\nThe number of delete operations <= 20\n\n0 <= value of a key <= 10^9\n\nThe number of elements in the list does not exceed 10^6\n\nFor a delete, deleteFirst or deleteLast operation, there is at least one element in the list.\nTask Input: The input is given in the following format:\n\nn\ncommand_1 \ncommand_2 \n. . . \ncommand_n \n\nIn the first line, the number of operations n is given. In the following n lines, the above mentioned operations are given in the following format:\n\ninsert x\n\ndelete x\n\ndelete First \n\ndelete Last\nTask Output: Print all the element (key) in the list after the given operations. Two consequtive keys should be separated by a single space.\nTask Samples: input: 7\ninsert 5\ninsert 2\ninsert 3\ninsert 1\ndelete 3\ninsert 6\ndelete 5\n output: 6 1 2\ninput: 9\ninsert 5\ninsert 2\ninsert 3\ninsert 1\ndelete 3\ninsert 6\ndelete 5\ndeleteFirst\ndeleteLast\n output: 1\n\n" }, { "title": "areas on the cross-section diagram", "content": "Your task is to simulate a flood damage.\n\n For a given cross-section diagram, reports areas of flooded sections.\n
    \n\n Assume that rain is falling endlessly in the region and the water overflowing from the region is falling in the sea at the both sides.\nFor example, for the above cross-section diagram, the rain will create floods which have areas of 4,2,1,19 and 9 respectively.", "constraint": "$1 <=$ length of the string $<= 20,000$", "input": "A string, which represents slopes and flatlands by '/', '\\' and '_' respectively, is given in a line. For example, the region of the above example is given by a string \"\\\\///\\_/\\/\\\\\\\\/_/\\\\///__\\\\\\_\\\\/_\\/_/\\\".", "output": "Report the areas of floods in the following format:\n\n$A$\n$k$ $L_1$ $L_2$ . . . $L_k$\n\n In the first line, print the total area $A$ of created floods.\n\n In the second line, print the number of floods $k$ and areas $L_i (i = 1,2, . . . , k)$ for each flood from the left side of the cross-section diagram. Print a space character before $L_i$.", "content_img": true, "lang": "", "error": false, "samples": ["input: \\\\//\n output: 4\n1 4", "input: \\\\///\\_/\\/\\\\\\\\/_/\\\\///__\\\\\\_\\\\/_\\/_/\\\n output: 35\n5 4 2 1 19 9"], "Pid": "p02266", "ProblemText": "Task Description: Your task is to simulate a flood damage.\n\n For a given cross-section diagram, reports areas of flooded sections.\n
    \n\n Assume that rain is falling endlessly in the region and the water overflowing from the region is falling in the sea at the both sides.\nFor example, for the above cross-section diagram, the rain will create floods which have areas of 4,2,1,19 and 9 respectively.\nTask Constraint: $1 <=$ length of the string $<= 20,000$\nTask Input: A string, which represents slopes and flatlands by '/', '\\' and '_' respectively, is given in a line. For example, the region of the above example is given by a string \"\\\\///\\_/\\/\\\\\\\\/_/\\\\///__\\\\\\_\\\\/_\\/_/\\\".\nTask Output: Report the areas of floods in the following format:\n\n$A$\n$k$ $L_1$ $L_2$ . . . $L_k$\n\n In the first line, print the total area $A$ of created floods.\n\n In the second line, print the number of floods $k$ and areas $L_i (i = 1,2, . . . , k)$ for each flood from the left side of the cross-section diagram. Print a space character before $L_i$.\nTask Samples: input: \\\\//\n output: 4\n1 4\ninput: \\\\///\\_/\\/\\\\\\\\/_/\\\\///__\\\\\\_\\\\/_\\/_/\\\n output: 35\n5 4 2 1 19 9\n\n" }, { "title": "Search I", "content": "You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.\n note:", "constraint": "n <= 10000\n\n q <= 500 \n\n0 <= an element in S <= 10^9\n\n0 <= an element in T <= 10^9", "input": "In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.", "output": "Print C in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 4 5\n3\n3 4 1\n output: 3", "input: 3\n3 1 2\n1\n5\n output: 0", "input: 5\n1 1 2 2 3\n2\n1 2\n output: 2"], "Pid": "p02267", "ProblemText": "Task Description: You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.\n note:\nTask Constraint: n <= 10000\n\n q <= 500 \n\n0 <= an element in S <= 10^9\n\n0 <= an element in T <= 10^9\nTask Input: In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.\nTask Output: Print C in a line.\nTask Samples: input: 5\n1 2 3 4 5\n3\n3 4 1\n output: 3\ninput: 3\n3 1 2\n1\n5\n output: 0\ninput: 5\n1 1 2 2 3\n2\n1 2\n output: 2\n\n" }, { "title": "Search II", "content": "You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.\n note:", "constraint": "Elements in S is sorted in ascending order\n\nn <= 100000\n\n q <= 50000 \n\n0 <= an element in S <= 10^9\n\n0 <= an element in T <= 10^9", "input": "In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.", "output": "Print C in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 4 5\n3\n3 4 1\n output: 3", "input: 3\n1 2 3\n1\n5\n output: 0", "input: 5\n1 1 2 2 3\n2\n1 2\n output: 2"], "Pid": "p02268", "ProblemText": "Task Description: You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.\n note:\nTask Constraint: Elements in S is sorted in ascending order\n\nn <= 100000\n\n q <= 50000 \n\n0 <= an element in S <= 10^9\n\n0 <= an element in T <= 10^9\nTask Input: In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.\nTask Output: Print C in a line.\nTask Samples: input: 5\n1 2 3 4 5\n3\n3 4 1\n output: 3\ninput: 3\n1 2 3\n1\n5\n output: 0\ninput: 5\n1 1 2 2 3\n2\n1 2\n output: 2\n\n" }, { "title": "Search III", "content": "Your task is to write a program of a simple dictionary which implements the following instructions:\n\ninsert str: insert a string str in to the dictionary\n\nfind str: if the distionary contains str, then print 'yes', otherwise print 'no'", "constraint": "A string consists of 'A', 'C', 'G', or 'T'\n\n1 <= length of a string <= 12\n\n n <= 1000000", "input": "In the first line n, the number of instructions is given. In the following n lines, n instructions are given in the above mentioned format.", "output": "Print yes or no for each find instruction in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\ninsert A\ninsert T\ninsert C\nfind G\nfind A\n output: no\nyes", "input: 13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T\n output: yes\nno\nno\nyes\nyes\nyes"], "Pid": "p02269", "ProblemText": "Task Description: Your task is to write a program of a simple dictionary which implements the following instructions:\n\ninsert str: insert a string str in to the dictionary\n\nfind str: if the distionary contains str, then print 'yes', otherwise print 'no'\nTask Constraint: A string consists of 'A', 'C', 'G', or 'T'\n\n1 <= length of a string <= 12\n\n n <= 1000000\nTask Input: In the first line n, the number of instructions is given. In the following n lines, n instructions are given in the above mentioned format.\nTask Output: Print yes or no for each find instruction in a line.\nTask Samples: input: 5\ninsert A\ninsert T\ninsert C\nfind G\nfind A\n output: no\nyes\ninput: 13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T\n output: yes\nno\nno\nyes\nyes\nyes\n\n" }, { "title": "", "content": "You are given $n$ packages of $w_i$ kg from a belt conveyor in order ($i = 0,1, . . . n-1$). You should load all packages onto $k$ trucks which have the common maximum load $P$. Each truck can load consecutive packages (more than or equals to zero) from the belt conveyor unless the total weights of the packages in the sequence does not exceed the maximum load $P$. Write a program which reads $n$, $k$ and $w_i$, and reports the minimum value of the maximum load $P$ to load all packages from the belt conveyor.", "constraint": "$1 <= n <= 100,000$\n\n $1 <= k <= 100,000$\n\n $1 <= w_i <= 10,000$", "input": "In the first line, two integers $n$ and $k$ are given separated by a space character. In the following $n$ lines, $w_i$ are given respectively.", "output": "Print the minimum value of $P$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n8\n1\n7\n3\n9\n output: 10\n If the first truck loads two packages of $\\{8,1\\}$, the second truck loads two packages of $\\{7,3\\}$ and the third truck loads a package of $\\{9\\}$, then the minimum value of the maximum load $P$ shall be 10.", "input: 4 2\n1\n2\n2\n6\n output: 6\n If the first truck loads three packages of $\\{1,2,2\\}$ and the second truck loads a package of $\\{6\\}$, then the minimum value of the maximum load $P$ shall be 6."], "Pid": "p02270", "ProblemText": "Task Description: You are given $n$ packages of $w_i$ kg from a belt conveyor in order ($i = 0,1, . . . n-1$). You should load all packages onto $k$ trucks which have the common maximum load $P$. Each truck can load consecutive packages (more than or equals to zero) from the belt conveyor unless the total weights of the packages in the sequence does not exceed the maximum load $P$. Write a program which reads $n$, $k$ and $w_i$, and reports the minimum value of the maximum load $P$ to load all packages from the belt conveyor.\nTask Constraint: $1 <= n <= 100,000$\n\n $1 <= k <= 100,000$\n\n $1 <= w_i <= 10,000$\nTask Input: In the first line, two integers $n$ and $k$ are given separated by a space character. In the following $n$ lines, $w_i$ are given respectively.\nTask Output: Print the minimum value of $P$ in a line.\nTask Samples: input: 5 3\n8\n1\n7\n3\n9\n output: 10\n If the first truck loads two packages of $\\{8,1\\}$, the second truck loads two packages of $\\{7,3\\}$ and the third truck loads a package of $\\{9\\}$, then the minimum value of the maximum load $P$ shall be 10.\ninput: 4 2\n1\n2\n2\n6\n output: 6\n If the first truck loads three packages of $\\{1,2,2\\}$ and the second truck loads a package of $\\{6\\}$, then the minimum value of the maximum load $P$ shall be 6.\n\n" }, { "title": "Exhaustive Search", "content": "Write a program which reads a sequence A of n elements and an integer M, and outputs \"yes\" if you can make M by adding elements in A, otherwise \"no\". You can use an element only once.\n\nYou are given the sequence A and q questions where each question contains M_i.\n note:\nYou can solve this problem by a Burte Force approach. Suppose solve(p, t) is a function which checkes whether you can make t by selecting elements after p-th element (inclusive). Then you can recursively call the following functions:\n\nsolve(0, M) \nsolve(1, M-{sum created from elements before 1st element}) \nsolve(2, M-{sum created from elements before 2nd element}) \n. . .\n\nThe recursive function has two choices: you selected p-th element and not. So, you can check solve(p+1, t-A[p]) and solve(p+1, t) in solve(p, t) to check the all combinations.\n\nFor example, the following figure shows that 8 can be made by A[0] + A[2].", "constraint": "n <= 20\n\n q <= 200 \n\n1 <= elements in A <= 2000\n\n1 <= M_i <= 2000", "input": "In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers (M_i) are given.", "output": "For each question M_i, print yes or no.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n1 5 7 10 21\n8\n2 4 17 8 22 21 100 35\n output: no\nno\nyes\nyes\nyes\nyes\nno\nno"], "Pid": "p02271", "ProblemText": "Task Description: Write a program which reads a sequence A of n elements and an integer M, and outputs \"yes\" if you can make M by adding elements in A, otherwise \"no\". You can use an element only once.\n\nYou are given the sequence A and q questions where each question contains M_i.\n note:\nYou can solve this problem by a Burte Force approach. Suppose solve(p, t) is a function which checkes whether you can make t by selecting elements after p-th element (inclusive). Then you can recursively call the following functions:\n\nsolve(0, M) \nsolve(1, M-{sum created from elements before 1st element}) \nsolve(2, M-{sum created from elements before 2nd element}) \n. . .\n\nThe recursive function has two choices: you selected p-th element and not. So, you can check solve(p+1, t-A[p]) and solve(p+1, t) in solve(p, t) to check the all combinations.\n\nFor example, the following figure shows that 8 can be made by A[0] + A[2].\nTask Constraint: n <= 20\n\n q <= 200 \n\n1 <= elements in A <= 2000\n\n1 <= M_i <= 2000\nTask Input: In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers (M_i) are given.\nTask Output: For each question M_i, print yes or no.\nTask Samples: input: 5\n1 5 7 10 21\n8\n2 4 17 8 22 21 100 35\n output: no\nno\nyes\nyes\nyes\nyes\nno\nno\n\n" }, { "title": "Merge Sort", "content": "Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.\n\nMerge(A, left, mid, right)\n n1 = mid - left;\n n2 = right - mid;\n create array L[0. . . n1], R[0. . . n2]\n for i = 0 to n1-1\n do L[i] = A[left + i]\n for i = 0 to n2-1\n do R[i] = A[mid + i]\n L[n1] = SENTINEL\n R[n2] = SENTINEL\n i = 0;\n j = 0;\n for k = left to right-1\n if L[i] <= R[j]\n then A[k] = L[i]\n i = i + 1\n else A[k] = R[j]\n j = j + 1\n\nMerge-Sort(A, left, right){\n if left+1 < right\n then mid = (left + right)/2;\n call Merge-Sort(A, left, mid)\n call Merge-Sort(A, mid, right)\n call Merge(A, left, mid, right)\n note:", "constraint": "n <= 500000\n\n0 <= an element in S <= 10^9", "input": "In the first line n is given. In the second line, n integers are given.", "output": "In the first line, print the sequence S. Two consequtive elements should be separated by a space character.\n\nIn the second line, print the number of comparisons.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\n8 5 9 2 6 3 7 1 10 4\n output: 1 2 3 4 5 6 7 8 9 10\n34"], "Pid": "p02272", "ProblemText": "Task Description: Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.\n\nMerge(A, left, mid, right)\n n1 = mid - left;\n n2 = right - mid;\n create array L[0. . . n1], R[0. . . n2]\n for i = 0 to n1-1\n do L[i] = A[left + i]\n for i = 0 to n2-1\n do R[i] = A[mid + i]\n L[n1] = SENTINEL\n R[n2] = SENTINEL\n i = 0;\n j = 0;\n for k = left to right-1\n if L[i] <= R[j]\n then A[k] = L[i]\n i = i + 1\n else A[k] = R[j]\n j = j + 1\n\nMerge-Sort(A, left, right){\n if left+1 < right\n then mid = (left + right)/2;\n call Merge-Sort(A, left, mid)\n call Merge-Sort(A, mid, right)\n call Merge(A, left, mid, right)\n note:\nTask Constraint: n <= 500000\n\n0 <= an element in S <= 10^9\nTask Input: In the first line n is given. In the second line, n integers are given.\nTask Output: In the first line, print the sequence S. Two consequtive elements should be separated by a space character.\n\nIn the second line, print the number of comparisons.\nTask Samples: input: 10\n8 5 9 2 6 3 7 1 10 4\n output: 1 2 3 4 5 6 7 8 9 10\n34\n\n" }, { "title": "Koch Curve", "content": "Write a program which reads an integer n and draws a Koch curve based on recursive calles of depth n.\n\nThe Koch curve is well known as a kind of fractals.\n\nYou can draw a Koch curve in the following algorithm:\n\nDivide a given segment (p1, p2) into three equal segments.\n\nReplace the middle segment by the two sides of an equilateral triangle (s, u, t) of the same length as the segment.\n\nRepeat this procedure recursively for new segments (p1, s), (s, u), (u, t), (t, p2).\nYou should start (0,0), (100,0) as the first segment.\n note:", "constraint": "0 <= n <= 6", "input": "An integer n is given.", "output": "Print each point (x, y) of the Koch curve. Print a point in a line. You should start the point(0,0), which is the endpoint of the first segment and end with the point (100,0), the other endpoint so that you can draw the Koch curve as an unbroken line. Each solution should be given as a decimal with an arbitrary number of fractional digits, and with an absolute error of at most 10-4.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1\n output: 0.00000000 0.00000000\n33.33333333 0.00000000\n50.00000000 28.86751346\n66.66666667 0.00000000\n100.00000000 0.00000000", "input: 2\n output: 0.00000000 0.00000000\n11.11111111 0.00000000\n16.66666667 9.62250449\n22.22222222 0.00000000\n33.33333333 0.00000000\n38.88888889 9.62250449\n33.33333333 19.24500897\n44.44444444 19.24500897\n50.00000000 28.86751346\n55.55555556 19.24500897\n66.66666667 19.24500897\n61.11111111 9.62250449\n66.66666667 0.00000000\n77.77777778 0.00000000\n83.33333333 9.62250449\n88.88888889 0.00000000\n100.00000000 0.00000000"], "Pid": "p02273", "ProblemText": "Task Description: Write a program which reads an integer n and draws a Koch curve based on recursive calles of depth n.\n\nThe Koch curve is well known as a kind of fractals.\n\nYou can draw a Koch curve in the following algorithm:\n\nDivide a given segment (p1, p2) into three equal segments.\n\nReplace the middle segment by the two sides of an equilateral triangle (s, u, t) of the same length as the segment.\n\nRepeat this procedure recursively for new segments (p1, s), (s, u), (u, t), (t, p2).\nYou should start (0,0), (100,0) as the first segment.\n note:\nTask Constraint: 0 <= n <= 6\nTask Input: An integer n is given.\nTask Output: Print each point (x, y) of the Koch curve. Print a point in a line. You should start the point(0,0), which is the endpoint of the first segment and end with the point (100,0), the other endpoint so that you can draw the Koch curve as an unbroken line. Each solution should be given as a decimal with an arbitrary number of fractional digits, and with an absolute error of at most 10-4.\nTask Samples: input: 1\n output: 0.00000000 0.00000000\n33.33333333 0.00000000\n50.00000000 28.86751346\n66.66666667 0.00000000\n100.00000000 0.00000000\ninput: 2\n output: 0.00000000 0.00000000\n11.11111111 0.00000000\n16.66666667 9.62250449\n22.22222222 0.00000000\n33.33333333 0.00000000\n38.88888889 9.62250449\n33.33333333 19.24500897\n44.44444444 19.24500897\n50.00000000 28.86751346\n55.55555556 19.24500897\n66.66666667 19.24500897\n61.11111111 9.62250449\n66.66666667 0.00000000\n77.77777778 0.00000000\n83.33333333 9.62250449\n88.88888889 0.00000000\n100.00000000 0.00000000\n\n" }, { "title": "The Number of Inversions", "content": "For a given sequence $A = \\{a_0, a_1, . . . a_{n-1}\\}$, the number of pairs $(i, j)$ where $a_i > a_j$ and $i < j$, is called the number of inversions. The number of inversions is equal to the number of swaps of Bubble Sort defined in the following program:\n\nbubble Sort(A)\n cnt = 0 // the number of inversions\n for i = 0 to A. length-1\n for j = A. length-1 downto i+1\n if A[j] < A[j-1]\n\tswap(A[j], A[j-1])\n\tcnt++\n\n return cnt\n\n For the given sequence $A$, print the number of inversions of $A$. Note that you should not use the above program, which brings Time Limit Exceeded.", "constraint": "$ 1 <= n <= 200,000$\n\n$ 0 <= a_i <= 10^9$\n\n$a_i$ are all different", "input": "In the first line, an integer $n$, the number of elements in $A$, is given. In the second line, the elements $a_i$ ($i = 0,1, . . n-1$) are given separated by space characters.", "output": "Print the number of inversions in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3 5 2 1 4\n output: 6", "input: 3\n3 1 2\n output: 2"], "Pid": "p02274", "ProblemText": "Task Description: For a given sequence $A = \\{a_0, a_1, . . . a_{n-1}\\}$, the number of pairs $(i, j)$ where $a_i > a_j$ and $i < j$, is called the number of inversions. The number of inversions is equal to the number of swaps of Bubble Sort defined in the following program:\n\nbubble Sort(A)\n cnt = 0 // the number of inversions\n for i = 0 to A. length-1\n for j = A. length-1 downto i+1\n if A[j] < A[j-1]\n\tswap(A[j], A[j-1])\n\tcnt++\n\n return cnt\n\n For the given sequence $A$, print the number of inversions of $A$. Note that you should not use the above program, which brings Time Limit Exceeded.\nTask Constraint: $ 1 <= n <= 200,000$\n\n$ 0 <= a_i <= 10^9$\n\n$a_i$ are all different\nTask Input: In the first line, an integer $n$, the number of elements in $A$, is given. In the second line, the elements $a_i$ ($i = 0,1, . . n-1$) are given separated by space characters.\nTask Output: Print the number of inversions in a line.\nTask Samples: input: 5\n3 5 2 1 4\n output: 6\ninput: 3\n3 1 2\n output: 2\n\n" }, { "title": "Counting Sort", "content": "Counting sort can be used for sorting elements in an array which each of the n input elements is an integer in the range 0 to k. The idea of counting sort is to determine, for each input element x, the number of elements less than x as C[x]. This information can be used to place element x directly into its position in the output array B. This scheme must be modified to handle the situation in which several elements have the same value. Please see the following pseudocode for the detail:\n\nCounting-Sort(A, B, k)\n1 for i = 0 to k\n2 do C[i] = 0\n3 for j = 1 to length[A]\n4 do C[A[j]] = C[A[j]]+1\n5 /* C[i] now contains the number of elements equal to i */\n6 for i = 1 to k\n7 do C[i] = C[i] + C[i-1]\n8 /* C[i] now contains the number of elements less than or equal to i */\n9 for j = length[A] downto 1\n10 do B[C[A[j]]] = A[j]\n11 C[A[j]] = C[A[j]]-1\n\nWrite a program which sorts elements of given array ascending order based on the counting sort.", "constraint": "1 <= n <= 2,000,000\n\n0 <= A[i] <= 10,000", "input": "The first line of the input includes an integer n, the number of elements in the sequence.\n\nIn the second line, n elements of the sequence are given separated by spaces characters.", "output": "Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n2 5 1 3 2 3 0\n output: 0 1 2 2 3 3 5"], "Pid": "p02275", "ProblemText": "Task Description: Counting sort can be used for sorting elements in an array which each of the n input elements is an integer in the range 0 to k. The idea of counting sort is to determine, for each input element x, the number of elements less than x as C[x]. This information can be used to place element x directly into its position in the output array B. This scheme must be modified to handle the situation in which several elements have the same value. Please see the following pseudocode for the detail:\n\nCounting-Sort(A, B, k)\n1 for i = 0 to k\n2 do C[i] = 0\n3 for j = 1 to length[A]\n4 do C[A[j]] = C[A[j]]+1\n5 /* C[i] now contains the number of elements equal to i */\n6 for i = 1 to k\n7 do C[i] = C[i] + C[i-1]\n8 /* C[i] now contains the number of elements less than or equal to i */\n9 for j = length[A] downto 1\n10 do B[C[A[j]]] = A[j]\n11 C[A[j]] = C[A[j]]-1\n\nWrite a program which sorts elements of given array ascending order based on the counting sort.\nTask Constraint: 1 <= n <= 2,000,000\n\n0 <= A[i] <= 10,000\nTask Input: The first line of the input includes an integer n, the number of elements in the sequence.\n\nIn the second line, n elements of the sequence are given separated by spaces characters.\nTask Output: Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.\nTask Samples: input: 7\n2 5 1 3 2 3 0\n output: 0 1 2 2 3 3 5\n\n" }, { "title": "Partition", "content": "Quick sort is based on the Divide-and-conquer approach. In Quick Sort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p. . r] into two subarrays A[p. . q-1] and A[q+1. . r] such that each element of A[p. . q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1. . r]. It also computes the index q.\n\nIn the conquer processes, the two subarrays A[p. . q-1] and A[q+1. . r] are sorted by recursive calls of Quick Sort(A, p, q-1) and Quick Sort(A, q+1, r).\n\nYour task is to read a sequence A and perform the Partition based on the following pseudocode:\n\nPartition(A, p, r)\n1 x = A[r]\n2 i = p-1\n3 for j = p to r-1\n4 do if A[j] <= x\n5 then i = i+1\n6 exchange A[i] and A[j] \n7 exchange A[i+1] and A[r]\n8 return i+1", "constraint": "1 <= n <= 100,000\n\n0 <= A_i <= 100,000", "input": "The first line of the input includes an integer n, the number of elements in the sequence A.\n\nIn the second line, A_i (i = 1,2, . . . , n), elements of the sequence are given separated by space characters.", "output": "Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [  ].", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12\n13 19 9 5 12 8 7 4 21 2 6 11\n output: 9 5 8 7 4 2 6 [11] 21 13 19 12"], "Pid": "p02276", "ProblemText": "Task Description: Quick sort is based on the Divide-and-conquer approach. In Quick Sort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p. . r] into two subarrays A[p. . q-1] and A[q+1. . r] such that each element of A[p. . q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1. . r]. It also computes the index q.\n\nIn the conquer processes, the two subarrays A[p. . q-1] and A[q+1. . r] are sorted by recursive calls of Quick Sort(A, p, q-1) and Quick Sort(A, q+1, r).\n\nYour task is to read a sequence A and perform the Partition based on the following pseudocode:\n\nPartition(A, p, r)\n1 x = A[r]\n2 i = p-1\n3 for j = p to r-1\n4 do if A[j] <= x\n5 then i = i+1\n6 exchange A[i] and A[j] \n7 exchange A[i+1] and A[r]\n8 return i+1\nTask Constraint: 1 <= n <= 100,000\n\n0 <= A_i <= 100,000\nTask Input: The first line of the input includes an integer n, the number of elements in the sequence A.\n\nIn the second line, A_i (i = 1,2, . . . , n), elements of the sequence are given separated by space characters.\nTask Output: Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [  ].\nTask Samples: input: 12\n13 19 9 5 12 8 7 4 21 2 6 11\n output: 9 5 8 7 4 2 6 [11] 21 13 19 12\n\n" }, { "title": "Quick Sort", "content": "Let's arrange a deck of cards. Your task is to sort totally n cards. A card consists of a part of a suit (S, H, C or D) and an number. Write a program which sorts such cards based on the following pseudocode:\n\nPartition(A, p, r)\n1 x = A[r]\n2 i = p-1\n3 for j = p to r-1\n4 do if A[j] <= x\n5 then i = i+1\n6 exchange A[i] and A[j] \n7 exchange A[i+1] and A[r]\n8 return i+1\nQuicksort(A, p, r)\n1 if p < r\n2 then q = Partition(A, p, r)\n3 run Quicksort(A, p, q-1)\n4 run Quicksort(A, q+1, r)\n\nHere, A is an array which represents a deck of cards and comparison operations are performed based on the numbers.\n\nYour program should also report the stability of the output for the given input (instance). Here, 'stability of the output' means that: cards with the same value appear in the output in the same order as they do in the input (instance).", "constraint": "1 <= n <= 100,000\n\n1 <= the number of a card <= 10^9\n\nThere are no identical card in the input", "input": "The first line contains an integer n, the number of cards.\n\nn cards are given in the following lines. Each card is given in a line and represented by a pair of a character and an integer separated by a single space.", "output": "In the first line, print the stability (\"Stable\" or \"Not stable\") of this output.\n\nIn the following lines, print the arranged cards in the same manner of that of the input.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\nD 3\nH 2\nD 1\nS 3\nD 2\nC 1\n output: Not stable\nD 1\nC 1\nD 2\nH 2\nD 3\nS 3", "input: 2\nS 1\nH 1\n output: Stable\nS 1\nH 1"], "Pid": "p02277", "ProblemText": "Task Description: Let's arrange a deck of cards. Your task is to sort totally n cards. A card consists of a part of a suit (S, H, C or D) and an number. Write a program which sorts such cards based on the following pseudocode:\n\nPartition(A, p, r)\n1 x = A[r]\n2 i = p-1\n3 for j = p to r-1\n4 do if A[j] <= x\n5 then i = i+1\n6 exchange A[i] and A[j] \n7 exchange A[i+1] and A[r]\n8 return i+1\nQuicksort(A, p, r)\n1 if p < r\n2 then q = Partition(A, p, r)\n3 run Quicksort(A, p, q-1)\n4 run Quicksort(A, q+1, r)\n\nHere, A is an array which represents a deck of cards and comparison operations are performed based on the numbers.\n\nYour program should also report the stability of the output for the given input (instance). Here, 'stability of the output' means that: cards with the same value appear in the output in the same order as they do in the input (instance).\nTask Constraint: 1 <= n <= 100,000\n\n1 <= the number of a card <= 10^9\n\nThere are no identical card in the input\nTask Input: The first line contains an integer n, the number of cards.\n\nn cards are given in the following lines. Each card is given in a line and represented by a pair of a character and an integer separated by a single space.\nTask Output: In the first line, print the stability (\"Stable\" or \"Not stable\") of this output.\n\nIn the following lines, print the arranged cards in the same manner of that of the input.\nTask Samples: input: 6\nD 3\nH 2\nD 1\nS 3\nD 2\nC 1\n output: Not stable\nD 1\nC 1\nD 2\nH 2\nD 3\nS 3\ninput: 2\nS 1\nH 1\n output: Stable\nS 1\nH 1\n\n" }, { "title": "Minimum Cost Sort", "content": "You are given $n$ integers $w_i (i = 0,1, . . . , n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.\n\n Write a program which reports the minimal total cost to sort the given integers.", "constraint": "$1 <= n <= 1,000$\n\n$0 <= w_i<= 10^4$\n\n$w_i$ are all different", "input": "In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0,1,2, . . . n-1)$ separated by space characters are given.", "output": "Print the minimal cost in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 5 3 4 2\n output: 7", "input: 4\n4 3 2 1\n output: 10"], "Pid": "p02278", "ProblemText": "Task Description: You are given $n$ integers $w_i (i = 0,1, . . . , n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.\n\n Write a program which reports the minimal total cost to sort the given integers.\nTask Constraint: $1 <= n <= 1,000$\n\n$0 <= w_i<= 10^4$\n\n$w_i$ are all different\nTask Input: In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0,1,2, . . . n-1)$ separated by space characters are given.\nTask Output: Print the minimal cost in a line.\nTask Samples: input: 5\n1 5 3 4 2\n output: 7\ninput: 4\n4 3 2 1\n output: 10\n\n" }, { "title": "Rooted Trees", "content": "A graph G = (V, E) is a data structure where V is a finite set of vertices and E is a binary relation on V represented by a set of edges. Fig. 1 illustrates an example of a graph (or graphs).\nFig. 1\n\nA free tree is a connnected, acyclic, undirected graph. A rooted tree is a free tree in which one of the vertices is distinguished from the others. A vertex of a rooted tree is called \"node. \"\n\nYour task is to write a program which reports the following information for each node u of a given rooted tree T:\n\nnode ID of u\n\nparent of u\n\ndepth of u\n\nnode type (root, internal node or leaf)\n\na list of chidlren of u\nIf the last edge on the path from the root r of a tree T to a node x is (p, x), then p is the parent of x, and x is a child of p. The root is the only node in T with no parent.\n\nA node with no children is an external node or leaf. A nonleaf node is an internal node\n\nThe number of children of a node x in a rooted tree T is called the degree of x.\n\nThe length of the path from the root r to a node x is the depth of x in T.\n\nHere, the given tree consists of n nodes and evey node has a unique ID from 0 to n-1.\n\nFig. 2 shows an example of rooted trees where ID of each node is indicated by a number in a circle (node). The example corresponds to the first sample input.\nFig. 2\n note:\nYou can use a left-child, right-sibling representation to implement a tree which has the following data:\n\nthe parent of u\n\nthe leftmost child of u\n\nthe immediate right sibling of u", "constraint": "1 <= n <= 100000", "input": "The first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n lines, the information of each node u is given in the following format:\n\nid k c_1 c_2 . . . c_k\n\nwhere id is the node ID of u, k is the degree of u, c_1 . . . c_k are node IDs of 1st, . . . kth child of u. If the node does not have a child, the k is 0.", "output": "Print the information of each node in the following format ordered by IDs:\n\nnode id: parent = p, depth = d, type, [c_1. . . c_k]\n\np is ID of its parent. If the node does not have a parent, print -1.\n\nd is depth of the node.\n\ntype is a type of nodes represented by a string (root, internal node or leaf). If the root can be considered as a leaf or an internal node, print root.\n\nc_1. . . c_k is the list of children as a ordered tree.\n\nPlease follow the format presented in a sample output below.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 13\n0 3 1 4 10\n1 2 2 3\n2 0\n3 0\n4 3 5 6 7\n5 0\n6 0\n7 2 8 9\n8 0\n9 0\n10 2 11 12\n11 0\n12 0\n output: node 0: parent = -1, depth = 0, root, [1,4,10]\nnode 1: parent = 0, depth = 1, internal node, [2,3]\nnode 2: parent = 1, depth = 2, leaf, []\nnode 3: parent = 1, depth = 2, leaf, []\nnode 4: parent = 0, depth = 1, internal node, [5,6,7]\nnode 5: parent = 4, depth = 2, leaf, []\nnode 6: parent = 4, depth = 2, leaf, []\nnode 7: parent = 4, depth = 2, internal node, [8,9]\nnode 8: parent = 7, depth = 3, leaf, []\nnode 9: parent = 7, depth = 3, leaf, []\nnode 10: parent = 0, depth = 1, internal node, [11,12]\nnode 11: parent = 10, depth = 2, leaf, []\nnode 12: parent = 10, depth = 2, leaf, []", "input: 4\n1 3 3 2 0\n0 0\n3 0\n2 0\n output: node 0: parent = 1, depth = 1, leaf, []\nnode 1: parent = -1, depth = 0, root, [3,2,0]\nnode 2: parent = 1, depth = 1, leaf, []\nnode 3: parent = 1, depth = 1, leaf, []"], "Pid": "p02279", "ProblemText": "Task Description: A graph G = (V, E) is a data structure where V is a finite set of vertices and E is a binary relation on V represented by a set of edges. Fig. 1 illustrates an example of a graph (or graphs).\nFig. 1\n\nA free tree is a connnected, acyclic, undirected graph. A rooted tree is a free tree in which one of the vertices is distinguished from the others. A vertex of a rooted tree is called \"node. \"\n\nYour task is to write a program which reports the following information for each node u of a given rooted tree T:\n\nnode ID of u\n\nparent of u\n\ndepth of u\n\nnode type (root, internal node or leaf)\n\na list of chidlren of u\nIf the last edge on the path from the root r of a tree T to a node x is (p, x), then p is the parent of x, and x is a child of p. The root is the only node in T with no parent.\n\nA node with no children is an external node or leaf. A nonleaf node is an internal node\n\nThe number of children of a node x in a rooted tree T is called the degree of x.\n\nThe length of the path from the root r to a node x is the depth of x in T.\n\nHere, the given tree consists of n nodes and evey node has a unique ID from 0 to n-1.\n\nFig. 2 shows an example of rooted trees where ID of each node is indicated by a number in a circle (node). The example corresponds to the first sample input.\nFig. 2\n note:\nYou can use a left-child, right-sibling representation to implement a tree which has the following data:\n\nthe parent of u\n\nthe leftmost child of u\n\nthe immediate right sibling of u\nTask Constraint: 1 <= n <= 100000\nTask Input: The first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n lines, the information of each node u is given in the following format:\n\nid k c_1 c_2 . . . c_k\n\nwhere id is the node ID of u, k is the degree of u, c_1 . . . c_k are node IDs of 1st, . . . kth child of u. If the node does not have a child, the k is 0.\nTask Output: Print the information of each node in the following format ordered by IDs:\n\nnode id: parent = p, depth = d, type, [c_1. . . c_k]\n\np is ID of its parent. If the node does not have a parent, print -1.\n\nd is depth of the node.\n\ntype is a type of nodes represented by a string (root, internal node or leaf). If the root can be considered as a leaf or an internal node, print root.\n\nc_1. . . c_k is the list of children as a ordered tree.\n\nPlease follow the format presented in a sample output below.\nTask Samples: input: 13\n0 3 1 4 10\n1 2 2 3\n2 0\n3 0\n4 3 5 6 7\n5 0\n6 0\n7 2 8 9\n8 0\n9 0\n10 2 11 12\n11 0\n12 0\n output: node 0: parent = -1, depth = 0, root, [1,4,10]\nnode 1: parent = 0, depth = 1, internal node, [2,3]\nnode 2: parent = 1, depth = 2, leaf, []\nnode 3: parent = 1, depth = 2, leaf, []\nnode 4: parent = 0, depth = 1, internal node, [5,6,7]\nnode 5: parent = 4, depth = 2, leaf, []\nnode 6: parent = 4, depth = 2, leaf, []\nnode 7: parent = 4, depth = 2, internal node, [8,9]\nnode 8: parent = 7, depth = 3, leaf, []\nnode 9: parent = 7, depth = 3, leaf, []\nnode 10: parent = 0, depth = 1, internal node, [11,12]\nnode 11: parent = 10, depth = 2, leaf, []\nnode 12: parent = 10, depth = 2, leaf, []\ninput: 4\n1 3 3 2 0\n0 0\n3 0\n2 0\n output: node 0: parent = 1, depth = 1, leaf, []\nnode 1: parent = -1, depth = 0, root, [3,2,0]\nnode 2: parent = 1, depth = 1, leaf, []\nnode 3: parent = 1, depth = 1, leaf, []\n\n" }, { "title": "Binary Tree", "content": "A rooted binary tree is a tree with a root node in which every node has at most two children.\n\nYour task is to write a program which reads a rooted binary tree T and prints the following information for each node u of T:\n\nnode ID of u\n\nparent of u\n\nsibling of u\n\nthe number of children of u\n\ndepth of u\n\nheight of u\n\nnode type (root, internal node or leaf)\nIf two nodes have the same parent, they are siblings. Here, if u and v have the same parent, we say u is a sibling of v (vice versa).\n\nThe height of a node in a tree is the number of edges on the longest simple downward path from the node to a leaf.\n\nHere, the given binary tree consists of n nodes and evey node has a unique ID from 0 to n-1.", "constraint": "1 <= n <= 25", "input": "The first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n lines, the information of each node is given in the following format:\n\nid left right\n\nid is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1.", "output": "Print the information of each node in the following format:\n\nnode id: parent = p, sibling = s, degree = deg, depth = dep, height = h, type\n\np is ID of its parent. If the node does not have a parent, print -1.\n\ns is ID of its sibling. If the node does not have a sibling, print -1.\n\ndeg, dep and h are the number of children, depth and height of the node respectively.\n\ntype is a type of nodes represented by a string (root, internal node or leaf. If the root can be considered as a leaf or an internal node, print root.\n\nPlease follow the format presented in a sample output below.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 9\n0 1 4\n1 2 3\n2 -1 -1\n3 -1 -1\n4 5 8\n5 6 7\n6 -1 -1\n7 -1 -1\n8 -1 -1\n output: node 0: parent = -1, sibling = -1, degree = 2, depth = 0, height = 3, root\nnode 1: parent = 0, sibling = 4, degree = 2, depth = 1, height = 1, internal node\nnode 2: parent = 1, sibling = 3, degree = 0, depth = 2, height = 0, leaf\nnode 3: parent = 1, sibling = 2, degree = 0, depth = 2, height = 0, leaf\nnode 4: parent = 0, sibling = 1, degree = 2, depth = 1, height = 2, internal node\nnode 5: parent = 4, sibling = 8, degree = 2, depth = 2, height = 1, internal node\nnode 6: parent = 5, sibling = 7, degree = 0, depth = 3, height = 0, leaf\nnode 7: parent = 5, sibling = 6, degree = 0, depth = 3, height = 0, leaf\nnode 8: parent = 4, sibling = 5, degree = 0, depth = 2, height = 0, leaf"], "Pid": "p02280", "ProblemText": "Task Description: A rooted binary tree is a tree with a root node in which every node has at most two children.\n\nYour task is to write a program which reads a rooted binary tree T and prints the following information for each node u of T:\n\nnode ID of u\n\nparent of u\n\nsibling of u\n\nthe number of children of u\n\ndepth of u\n\nheight of u\n\nnode type (root, internal node or leaf)\nIf two nodes have the same parent, they are siblings. Here, if u and v have the same parent, we say u is a sibling of v (vice versa).\n\nThe height of a node in a tree is the number of edges on the longest simple downward path from the node to a leaf.\n\nHere, the given binary tree consists of n nodes and evey node has a unique ID from 0 to n-1.\nTask Constraint: 1 <= n <= 25\nTask Input: The first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n lines, the information of each node is given in the following format:\n\nid left right\n\nid is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1.\nTask Output: Print the information of each node in the following format:\n\nnode id: parent = p, sibling = s, degree = deg, depth = dep, height = h, type\n\np is ID of its parent. If the node does not have a parent, print -1.\n\ns is ID of its sibling. If the node does not have a sibling, print -1.\n\ndeg, dep and h are the number of children, depth and height of the node respectively.\n\ntype is a type of nodes represented by a string (root, internal node or leaf. If the root can be considered as a leaf or an internal node, print root.\n\nPlease follow the format presented in a sample output below.\nTask Samples: input: 9\n0 1 4\n1 2 3\n2 -1 -1\n3 -1 -1\n4 5 8\n5 6 7\n6 -1 -1\n7 -1 -1\n8 -1 -1\n output: node 0: parent = -1, sibling = -1, degree = 2, depth = 0, height = 3, root\nnode 1: parent = 0, sibling = 4, degree = 2, depth = 1, height = 1, internal node\nnode 2: parent = 1, sibling = 3, degree = 0, depth = 2, height = 0, leaf\nnode 3: parent = 1, sibling = 2, degree = 0, depth = 2, height = 0, leaf\nnode 4: parent = 0, sibling = 1, degree = 2, depth = 1, height = 2, internal node\nnode 5: parent = 4, sibling = 8, degree = 2, depth = 2, height = 1, internal node\nnode 6: parent = 5, sibling = 7, degree = 0, depth = 3, height = 0, leaf\nnode 7: parent = 5, sibling = 6, degree = 0, depth = 3, height = 0, leaf\nnode 8: parent = 4, sibling = 5, degree = 0, depth = 2, height = 0, leaf\n\n" }, { "title": "Tree Walk", "content": "Binary trees are defined recursively. A binary tree T is a structure defined on a finite set of nodes that either\n\ncontains no nodes, or\n\nis composed of three disjoint sets of nodes: \n\n- a root node. \n- a binary tree called its left subtree. \n- a binary tree called its right subtree. \n\nYour task is to write a program which perform tree walks (systematically traverse all nodes in a tree) based on the following algorithms:\n\nPrint the root, the left subtree and right subtree (preorder).\n\nPrint the left subtree, the root and right subtree (inorder).\n\nPrint the left subtree, right subtree and the root (postorder).\nHere, the given binary tree consists of n nodes and evey node has a unique ID from 0 to n-1.", "constraint": "1 <= n <= 25", "input": "The first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n linen, the information of each node is given in the following format:\n\nid left right\n\nid is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1", "output": "In the 1st line, print \"Preorder\", and in the 2nd line print a list of node IDs obtained by the preorder tree walk.\n\nIn the 3rd line, print \"Inorder\", and in the 4th line print a list of node IDs obtained by the inorder tree walk.\n\nIn the 5th line, print \"Postorder\", and in the 6th line print a list of node IDs obtained by the postorder tree walk.\n\nPrint a space character before each node ID.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 9\n0 1 4\n1 2 3\n2 -1 -1\n3 -1 -1\n4 5 8\n5 6 7\n6 -1 -1\n7 -1 -1\n8 -1 -1\n output: Preorder\n 0 1 2 3 4 5 6 7 8\nInorder\n 2 1 3 0 6 5 7 4 8\nPostorder\n 2 3 1 6 7 5 8 4 0"], "Pid": "p02281", "ProblemText": "Task Description: Binary trees are defined recursively. A binary tree T is a structure defined on a finite set of nodes that either\n\ncontains no nodes, or\n\nis composed of three disjoint sets of nodes: \n\n- a root node. \n- a binary tree called its left subtree. \n- a binary tree called its right subtree. \n\nYour task is to write a program which perform tree walks (systematically traverse all nodes in a tree) based on the following algorithms:\n\nPrint the root, the left subtree and right subtree (preorder).\n\nPrint the left subtree, the root and right subtree (inorder).\n\nPrint the left subtree, right subtree and the root (postorder).\nHere, the given binary tree consists of n nodes and evey node has a unique ID from 0 to n-1.\nTask Constraint: 1 <= n <= 25\nTask Input: The first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n linen, the information of each node is given in the following format:\n\nid left right\n\nid is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1\nTask Output: In the 1st line, print \"Preorder\", and in the 2nd line print a list of node IDs obtained by the preorder tree walk.\n\nIn the 3rd line, print \"Inorder\", and in the 4th line print a list of node IDs obtained by the inorder tree walk.\n\nIn the 5th line, print \"Postorder\", and in the 6th line print a list of node IDs obtained by the postorder tree walk.\n\nPrint a space character before each node ID.\nTask Samples: input: 9\n0 1 4\n1 2 3\n2 -1 -1\n3 -1 -1\n4 5 8\n5 6 7\n6 -1 -1\n7 -1 -1\n8 -1 -1\n output: Preorder\n 0 1 2 3 4 5 6 7 8\nInorder\n 2 1 3 0 6 5 7 4 8\nPostorder\n 2 3 1 6 7 5 8 4 0\n\n" }, { "title": "Reconstruction of a Tree", "content": "Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.", "constraint": "$1 <= n <= 40$", "input": "In the first line, an integer $n$, which is the number of nodes in the binary tree, is given. \n In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters. \n In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.\n\n Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.", "output": "Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 4 5\n3 2 4 1 5\n output: 3 4 2 5 1", "input: 4\n1 2 3 4\n1 2 3 4\n output: 4 3 2 1"], "Pid": "p02282", "ProblemText": "Task Description: Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.\nTask Constraint: $1 <= n <= 40$\nTask Input: In the first line, an integer $n$, which is the number of nodes in the binary tree, is given. \n In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters. \n In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.\n\n Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.\nTask Output: Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.\nTask Samples: input: 5\n1 2 3 4 5\n3 2 4 1 5\n output: 3 4 2 5 1\ninput: 4\n1 2 3 4\n1 2 3 4\n output: 4 3 2 1\n\n" }, { "title": "Binary Search Tree I", "content": "Search trees are data structures that support dynamic set operations including insert, search, delete and so on. Thus a search tree can be used both as a dictionary and as a priority queue. \n\n Binary search tree is one of fundamental search trees. The keys in a binary search tree are always stored in such a way as to satisfy the following binary search tree property:\n\n Let $x$ be a node in a binary search tree. If $y$ is a node in the left subtree of $x$, then $y. key <= x. key$. If $y$ is a node in the right subtree of $x$, then $x. key <= y. key$.\n\n The following figure shows an example of the binary search tree.\n\n For example, keys of nodes which belong to the left sub-tree of the node containing 80 are less than or equal to 80, and keys of nodes which belong to the right sub-tree are more than or equal to 80. The binary search tree property allows us to print out all the keys in the tree in sorted order by an inorder tree walk.\n\n A binary search tree should be implemented in such a way that the binary search tree property continues to hold after modifications by insertions and deletions. A binary search tree can be represented by a linked data structure in which each node is an object. In addition to a key field and satellite data, each node contains fields left, right, and p that point to the nodes corresponding to its left child, its right child, and its parent, respectively.\n\n To insert a new value $v$ into a binary search tree $T$, we can use the procedure insert as shown in the following pseudo code. The insert procedure is passed a node $z$ for which $z. key = v$, $z. left = NIL$, and $z. right = NIL$. The procedure modifies $T$ and some of the fields of $z$ in such a way that $z$ is inserted into an appropriate position in the tree.\n\n1 insert(T, z)\n2 y = NIL // parent of x\n3 x = 'the root of T'\n4 while x ! = NIL\n5 y = x // set the parent\n6 if z. key < x. key\n7 x = x. left // move to the left child\n8 else \n9 x = x. right // move to the right child\n10 z. p = y\n11\n12 if y == NIL // T is empty\n13 'the root of T' = z\n14 else if z. key < y. key\n15 y. left = z // z is the left child of y\n16 else \n17 y. right = z // z is the right child of y\n\n Write a program which performs the following operations to a binary search tree $T$.\n\ninsert $k$: Insert a node containing $k$ as key into $T$.\n\nprint: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.\n You should use the above pseudo code to implement the insert operation. $T$ is empty at the initial state.", "constraint": "The number of operations $<= 500,000$\n\nThe number of print operations $<= 10$.\n\n$-2,000,000,000 <= key <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 100 if you employ the above pseudo code.\n\nThe keys in the binary search tree are all different.", "input": "In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$ or print are given.", "output": "For each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8\ninsert 30\ninsert 88\ninsert 12\ninsert 1\ninsert 20\ninsert 17\ninsert 25\nprint\n output: 1 12 17 20 25 30 88\n 30 12 1 20 17 25 88"], "Pid": "p02283", "ProblemText": "Task Description: Search trees are data structures that support dynamic set operations including insert, search, delete and so on. Thus a search tree can be used both as a dictionary and as a priority queue. \n\n Binary search tree is one of fundamental search trees. The keys in a binary search tree are always stored in such a way as to satisfy the following binary search tree property:\n\n Let $x$ be a node in a binary search tree. If $y$ is a node in the left subtree of $x$, then $y. key <= x. key$. If $y$ is a node in the right subtree of $x$, then $x. key <= y. key$.\n\n The following figure shows an example of the binary search tree.\n\n For example, keys of nodes which belong to the left sub-tree of the node containing 80 are less than or equal to 80, and keys of nodes which belong to the right sub-tree are more than or equal to 80. The binary search tree property allows us to print out all the keys in the tree in sorted order by an inorder tree walk.\n\n A binary search tree should be implemented in such a way that the binary search tree property continues to hold after modifications by insertions and deletions. A binary search tree can be represented by a linked data structure in which each node is an object. In addition to a key field and satellite data, each node contains fields left, right, and p that point to the nodes corresponding to its left child, its right child, and its parent, respectively.\n\n To insert a new value $v$ into a binary search tree $T$, we can use the procedure insert as shown in the following pseudo code. The insert procedure is passed a node $z$ for which $z. key = v$, $z. left = NIL$, and $z. right = NIL$. The procedure modifies $T$ and some of the fields of $z$ in such a way that $z$ is inserted into an appropriate position in the tree.\n\n1 insert(T, z)\n2 y = NIL // parent of x\n3 x = 'the root of T'\n4 while x ! = NIL\n5 y = x // set the parent\n6 if z. key < x. key\n7 x = x. left // move to the left child\n8 else \n9 x = x. right // move to the right child\n10 z. p = y\n11\n12 if y == NIL // T is empty\n13 'the root of T' = z\n14 else if z. key < y. key\n15 y. left = z // z is the left child of y\n16 else \n17 y. right = z // z is the right child of y\n\n Write a program which performs the following operations to a binary search tree $T$.\n\ninsert $k$: Insert a node containing $k$ as key into $T$.\n\nprint: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.\n You should use the above pseudo code to implement the insert operation. $T$ is empty at the initial state.\nTask Constraint: The number of operations $<= 500,000$\n\nThe number of print operations $<= 10$.\n\n$-2,000,000,000 <= key <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 100 if you employ the above pseudo code.\n\nThe keys in the binary search tree are all different.\nTask Input: In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$ or print are given.\nTask Output: For each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.\nTask Samples: input: 8\ninsert 30\ninsert 88\ninsert 12\ninsert 1\ninsert 20\ninsert 17\ninsert 25\nprint\n output: 1 12 17 20 25 30 88\n 30 12 1 20 17 25 88\n\n" }, { "title": "Binary Search Tree II", "content": "Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.\n\ninsert $k$: Insert a node containing $k$ as key into $T$.\n\nfind $k$: Report whether $T$ has a node containing $k$. \n\nprint: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.", "constraint": "The number of operations $<= 500,000$\n\nThe number of print operations $<= 10$.\n\n$-2,000,000,000 <= key <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 100 if you employ the above pseudo code.\n\nThe keys in the binary search tree are all different.", "input": "In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ or print are given.", "output": "For each find $k$ operation, print \"yes\" if $T$ has a node containing $k$, \"no\" if not.\n\n In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\ninsert 30\ninsert 88\ninsert 12\ninsert 1\ninsert 20\nfind 12\ninsert 17\ninsert 25\nfind 16\nprint\n output: yes\nno\n 1 12 17 20 25 30 88\n 30 12 1 20 17 25 88"], "Pid": "p02284", "ProblemText": "Task Description: Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.\n\ninsert $k$: Insert a node containing $k$ as key into $T$.\n\nfind $k$: Report whether $T$ has a node containing $k$. \n\nprint: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.\nTask Constraint: The number of operations $<= 500,000$\n\nThe number of print operations $<= 10$.\n\n$-2,000,000,000 <= key <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 100 if you employ the above pseudo code.\n\nThe keys in the binary search tree are all different.\nTask Input: In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ or print are given.\nTask Output: For each find $k$ operation, print \"yes\" if $T$ has a node containing $k$, \"no\" if not.\n\n In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.\nTask Samples: input: 10\ninsert 30\ninsert 88\ninsert 12\ninsert 1\ninsert 20\nfind 12\ninsert 17\ninsert 25\nfind 16\nprint\n output: yes\nno\n 1 12 17 20 25 30 88\n 30 12 1 20 17 25 88\n\n" }, { "title": "Binary Search Tree III", "content": "Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.\n\ninsert $k$: Insert a node containing $k$ as key into $T$.\n\nfind $k$: Report whether $T$ has a node containing $k$. \n\ndelete $k$: Delete a node containing $k$.\n\nprint: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.\nThe operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:\n\n If $z$ has no children, we modify its parent $z. p$ to replace $z$ with NIL as its child (delete $z$).\n\n If $z$ has only a single child, we \"splice out\" $z$ by making a new link between its child and its parent.\n\n If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.", "constraint": "The number of operations $<= 500,000$\n\nThe number of print operations $<= 10$.\n\n$-2,000,000,000 <= key <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 100 if you employ the above pseudo code.\n\nThe keys in the binary search tree are all different.", "input": "In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ or print are given.", "output": "For each find $k$ operation, print \"yes\" if $T$ has a node containing $k$, \"no\" if not.\n\n In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key", "content_img": false, "lang": "en", "error": false, "samples": ["input: 18\ninsert 8\ninsert 2\ninsert 3\ninsert 7\ninsert 22\ninsert 1\nfind 1\nfind 2\nfind 3\nfind 4\nfind 5\nfind 6\nfind 7\nfind 8\nprint\ndelete 3\ndelete 7\nprint\n output: yes\nyes\nyes\nno\nno\nno\nyes\nyes\n 1 2 3 7 8 22\n 8 2 1 3 7 22\n 1 2 8 22\n 8 2 1 22"], "Pid": "p02285", "ProblemText": "Task Description: Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.\n\ninsert $k$: Insert a node containing $k$ as key into $T$.\n\nfind $k$: Report whether $T$ has a node containing $k$. \n\ndelete $k$: Delete a node containing $k$.\n\nprint: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.\nThe operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:\n\n If $z$ has no children, we modify its parent $z. p$ to replace $z$ with NIL as its child (delete $z$).\n\n If $z$ has only a single child, we \"splice out\" $z$ by making a new link between its child and its parent.\n\n If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.\nTask Constraint: The number of operations $<= 500,000$\n\nThe number of print operations $<= 10$.\n\n$-2,000,000,000 <= key <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 100 if you employ the above pseudo code.\n\nThe keys in the binary search tree are all different.\nTask Input: In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ or print are given.\nTask Output: For each find $k$ operation, print \"yes\" if $T$ has a node containing $k$, \"no\" if not.\n\n In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key\nTask Samples: input: 18\ninsert 8\ninsert 2\ninsert 3\ninsert 7\ninsert 22\ninsert 1\nfind 1\nfind 2\nfind 3\nfind 4\nfind 5\nfind 6\nfind 7\nfind 8\nprint\ndelete 3\ndelete 7\nprint\n output: yes\nyes\nyes\nno\nno\nno\nyes\nyes\n 1 2 3 7 8 22\n 8 2 1 3 7 22\n 1 2 8 22\n 8 2 1 22\n\n" }, { "title": "Treap", "content": "A binary search tree can be unbalanced depending on features of data. For example, if we insert $n$ elements into a binary search tree in ascending order, the tree become a list, leading to long search times. One of strategies is to randomly shuffle the elements to be inserted. However, we should consider to maintain the balanced binary tree where different operations can be performed one by one depending on requirement.\n\n We can maintain the balanced binary search tree by assigning a priority randomly selected to each node and by ordering nodes based on the following properties. Here, we assume that all priorities are distinct and also that all keys are distinct.\n\nbinary-search-tree property. If $v$ is a left child of $u$, then $v. key < u. key$ and if $v$ is a right child of $u$, then $u. key < v. key$\n\nheap property. If $v$ is a child of $u$, then $v. priority < u. priority$\n This combination of properties is why the tree is called Treap (tree + heap).\n\n An example of Treap is shown in the following figure.\n\nInsert\n To insert a new element into a Treap, first of all, insert a node which a randomly selected priority value is assigned in the same way for ordinal binary search tree. For example, the following figure shows the Treap after a node with key = 6 and priority = 90 is inserted.\n\nIt is clear that this Treap violates the heap property, so we need to modify the structure of the tree by rotate operations. The rotate operation is to change parent-child relation while maintaing the binary-search-tree property.\n\n The rotate operations can be implemented as follows.\n \n \n
    \n\nright Rotate(Node t)\n Node s = t. left\n t. left = s. right\n s. right = t\n return s // the new root of subtree\n\n \n\n\nleft Rotate(Node t)\n Node s = t. right\n t. right = s. left\n s. left = t\n return s // the new root of subtree\n\n \n \n The following figure shows processes of the rotate operations after the insert operation to maintain the properties.\n\n The insert operation with rotate operations can be implemented as follows.\n\ninsert(Node t, int key, int priority) // search the corresponding place recursively\n if t == NIL\n return Node(key, priority) // create a new node when you reach a leaf\n if key == t. key\n return t // ignore duplicated keys\n\n if key < t. key // move to the left child\n t. left = insert(t. left, key, priority) // update the pointer to the left child\n if t. priority < t. left. priority // rotate right if the left child has higher priority\n t = right Rotate(t)\n else // move to the right child\n t. right = insert(t. right, key, priority) // update the pointer to the right child\n if t. priority < t. right. priority // rotate left if the right child has higher priority\n t = left Rotate(t)\n\n return t\n\nDelete\n To delete a node from the Treap, first of all, the target node should be moved until it becomes a leaf by rotate operations. Then, you can remove the node (the leaf). These processes can be implemented as follows.\n\ndelete(Node t, int key) // seach the target recursively\n if t == NIL\n return NIL\n if key < t. key // search the target recursively\n t. left = delete(t. left, key)\n else if key > t. key\n t. right = delete(t. right, key)\n else\n return _delete(t, key)\n return t\n\n_delete(Node t, int key) // if t is the target node\n if t. left == NIL && t. right == NIL // if t is a leaf\n return NIL\n else if t. left == NIL // if t has only the right child, then perform left rotate\n t = left Rotate(t)\n else if t. right == NIL // if t has only the left child, then perform right rotate\n t = right Rotate(t)\n else // if t has both the left and right child\n if t. left. priority > t. right. priority // pull up the child with higher priority\n t = right Rotate(t)\n else\n t = left Rotate(t)\n return delete(t, key)\n\n Write a program which performs the following operations to a Treap $T$ based on the above described algorithm.\n\ninsert ($k$, $p$): Insert a node containing $k$ as key and $p$ as priority to $T$.\n\nfind ($k$): Report whether $T$ has a node containing $k$.\n\ndelete ($k$): Delete a node containing $k$.\n\nprint(): Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.", "constraint": "The number of operations $ <= 200,000$\n\n$0 <= k, p <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 50 if you employ the above algorithm\n\nThe keys in the binary search tree are all different.\n\nThe priorities in the binary search tree are all different.\n\nThe size of output $<= 10$ MB", "input": "In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k \\; p$, find $k$, delete $k$ or print are given.", "output": "For each find($k$) operation, print \"yes\" if $T$ has a node containing $k$, \"no\" if not.\n\n In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 16\ninsert 35 99\ninsert 3 80\ninsert 1 53\ninsert 14 25\ninsert 80 76\ninsert 42 3\ninsert 86 47\ninsert 21 12\ninsert 7 10\ninsert 6 90\nprint\nfind 21\nfind 22\ndelete 35\ndelete 99\nprint\n output: 1 3 6 7 14 21 35 42 80 86\n 35 6 3 1 14 7 21 80 42 86\nyes\nno\n 1 3 6 7 14 21 42 80 86\n 6 3 1 80 14 7 21 42 86"], "Pid": "p02286", "ProblemText": "Task Description: A binary search tree can be unbalanced depending on features of data. For example, if we insert $n$ elements into a binary search tree in ascending order, the tree become a list, leading to long search times. One of strategies is to randomly shuffle the elements to be inserted. However, we should consider to maintain the balanced binary tree where different operations can be performed one by one depending on requirement.\n\n We can maintain the balanced binary search tree by assigning a priority randomly selected to each node and by ordering nodes based on the following properties. Here, we assume that all priorities are distinct and also that all keys are distinct.\n\nbinary-search-tree property. If $v$ is a left child of $u$, then $v. key < u. key$ and if $v$ is a right child of $u$, then $u. key < v. key$\n\nheap property. If $v$ is a child of $u$, then $v. priority < u. priority$\n This combination of properties is why the tree is called Treap (tree + heap).\n\n An example of Treap is shown in the following figure.\n\nInsert\n To insert a new element into a Treap, first of all, insert a node which a randomly selected priority value is assigned in the same way for ordinal binary search tree. For example, the following figure shows the Treap after a node with key = 6 and priority = 90 is inserted.\n\nIt is clear that this Treap violates the heap property, so we need to modify the structure of the tree by rotate operations. The rotate operation is to change parent-child relation while maintaing the binary-search-tree property.\n\n The rotate operations can be implemented as follows.\n \n \n\n\nright Rotate(Node t)\n Node s = t. left\n t. left = s. right\n s. right = t\n return s // the new root of subtree\n\n \n\n\nleft Rotate(Node t)\n Node s = t. right\n t. right = s. left\n s. left = t\n return s // the new root of subtree\n\n \n \n The following figure shows processes of the rotate operations after the insert operation to maintain the properties.\n\n The insert operation with rotate operations can be implemented as follows.\n\ninsert(Node t, int key, int priority) // search the corresponding place recursively\n if t == NIL\n return Node(key, priority) // create a new node when you reach a leaf\n if key == t. key\n return t // ignore duplicated keys\n\n if key < t. key // move to the left child\n t. left = insert(t. left, key, priority) // update the pointer to the left child\n if t. priority < t. left. priority // rotate right if the left child has higher priority\n t = right Rotate(t)\n else // move to the right child\n t. right = insert(t. right, key, priority) // update the pointer to the right child\n if t. priority < t. right. priority // rotate left if the right child has higher priority\n t = left Rotate(t)\n\n return t\n\nDelete\n To delete a node from the Treap, first of all, the target node should be moved until it becomes a leaf by rotate operations. Then, you can remove the node (the leaf). These processes can be implemented as follows.\n\ndelete(Node t, int key) // seach the target recursively\n if t == NIL\n return NIL\n if key < t. key // search the target recursively\n t. left = delete(t. left, key)\n else if key > t. key\n t. right = delete(t. right, key)\n else\n return _delete(t, key)\n return t\n\n_delete(Node t, int key) // if t is the target node\n if t. left == NIL && t. right == NIL // if t is a leaf\n return NIL\n else if t. left == NIL // if t has only the right child, then perform left rotate\n t = left Rotate(t)\n else if t. right == NIL // if t has only the left child, then perform right rotate\n t = right Rotate(t)\n else // if t has both the left and right child\n if t. left. priority > t. right. priority // pull up the child with higher priority\n t = right Rotate(t)\n else\n t = left Rotate(t)\n return delete(t, key)\n\n Write a program which performs the following operations to a Treap $T$ based on the above described algorithm.\n\ninsert ($k$, $p$): Insert a node containing $k$ as key and $p$ as priority to $T$.\n\nfind ($k$): Report whether $T$ has a node containing $k$.\n\ndelete ($k$): Delete a node containing $k$.\n\nprint(): Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.\nTask Constraint: The number of operations $ <= 200,000$\n\n$0 <= k, p <= 2,000,000,000$\n\nThe height of the binary tree does not exceed 50 if you employ the above algorithm\n\nThe keys in the binary search tree are all different.\n\nThe priorities in the binary search tree are all different.\n\nThe size of output $<= 10$ MB\nTask Input: In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k \\; p$, find $k$, delete $k$ or print are given.\nTask Output: For each find($k$) operation, print \"yes\" if $T$ has a node containing $k$, \"no\" if not.\n\n In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.\nTask Samples: input: 16\ninsert 35 99\ninsert 3 80\ninsert 1 53\ninsert 14 25\ninsert 80 76\ninsert 42 3\ninsert 86 47\ninsert 21 12\ninsert 7 10\ninsert 6 90\nprint\nfind 21\nfind 22\ndelete 35\ndelete 99\nprint\n output: 1 3 6 7 14 21 35 42 80 86\n 35 6 3 1 14 7 21 80 42 86\nyes\nno\n 1 3 6 7 14 21 42 80 86\n 6 3 1 80 14 7 21 42 86\n\n" }, { "title": "Complete Binary Tree", "content": "A complete binary tree is a binary tree in which every internal node has two children and all leaves have the same depth. A binary tree in which if last level is not completely filled but all nodes (leaves) are pushed across to the left, is also (nearly) a complete binary tree.\n\n A binary heap data structure is an array that can be viewed as a nearly complete binary tree as shown in the following figure.\n\n Each node of a nearly complete binary tree corresponds to an element of the array that stores the value in the node. An array $A$ that represents a binary heap has the heap size $H$, the number of elements in the heap, and each element of the binary heap is stored into $A[1. . . H]$ respectively. The root of the tree is $A[1]$, and given the index $i$ of a node, the indices of its parent $parent(i)$, left child $left(i)$, right child $right(i)$ can be computed simply by $\\lfloor i / 2 \\rfloor$, $2 * i$ and $2 * i + 1$ respectively.\n\n Write a program which reads a binary heap represented by a nearly complete binary tree, and prints properties of nodes of the binary heap in the following format:\n\nnode $id$: key = $k$, parent key = $pk$, left key = $lk$, right key = $rk$, \n\n $id$, $k$, $pk$, $lk$ and $rk$ represent id (index) of the node, value of the node, value of its parent, value of its left child and value of its right child respectively. Print these properties in this order. If there are no appropriate nodes, print nothing.", "constraint": "$H <= 250$\n\n$-2,000,000,000 <=$ value of a node $<= 2,000,000,000$", "input": "In the first line, an integer $H$, the size of the binary heap, is given. In the second line, $H$ integers which correspond to values assigned to nodes of the binary heap are given in order of node id (from $1$ to $H$).", "output": "Print the properties of the binary heap in the above format from node $1$ to $H$ in order. Note that, the last character of each line is a single space character.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5\n7 8 1 2 3\n output: node 1: key = 7, left key = 8, right key = 1, \nnode 2: key = 8, parent key = 7, left key = 2, right key = 3, \nnode 3: key = 1, parent key = 7, \nnode 4: key = 2, parent key = 8, \nnode 5: key = 3, parent key = 8,"], "Pid": "p02287", "ProblemText": "Task Description: A complete binary tree is a binary tree in which every internal node has two children and all leaves have the same depth. A binary tree in which if last level is not completely filled but all nodes (leaves) are pushed across to the left, is also (nearly) a complete binary tree.\n\n A binary heap data structure is an array that can be viewed as a nearly complete binary tree as shown in the following figure.\n\n Each node of a nearly complete binary tree corresponds to an element of the array that stores the value in the node. An array $A$ that represents a binary heap has the heap size $H$, the number of elements in the heap, and each element of the binary heap is stored into $A[1. . . H]$ respectively. The root of the tree is $A[1]$, and given the index $i$ of a node, the indices of its parent $parent(i)$, left child $left(i)$, right child $right(i)$ can be computed simply by $\\lfloor i / 2 \\rfloor$, $2 * i$ and $2 * i + 1$ respectively.\n\n Write a program which reads a binary heap represented by a nearly complete binary tree, and prints properties of nodes of the binary heap in the following format:\n\nnode $id$: key = $k$, parent key = $pk$, left key = $lk$, right key = $rk$, \n\n $id$, $k$, $pk$, $lk$ and $rk$ represent id (index) of the node, value of the node, value of its parent, value of its left child and value of its right child respectively. Print these properties in this order. If there are no appropriate nodes, print nothing.\nTask Constraint: $H <= 250$\n\n$-2,000,000,000 <=$ value of a node $<= 2,000,000,000$\nTask Input: In the first line, an integer $H$, the size of the binary heap, is given. In the second line, $H$ integers which correspond to values assigned to nodes of the binary heap are given in order of node id (from $1$ to $H$).\nTask Output: Print the properties of the binary heap in the above format from node $1$ to $H$ in order. Note that, the last character of each line is a single space character.\nTask Samples: input: 5\n7 8 1 2 3\n output: node 1: key = 7, left key = 8, right key = 1, \nnode 2: key = 8, parent key = 7, left key = 2, right key = 3, \nnode 3: key = 1, parent key = 7, \nnode 4: key = 2, parent key = 8, \nnode 5: key = 3, parent key = 8,\n\n" }, { "title": "Maximum Heap", "content": "A binary heap which satisfies max-heap property is called max-heap. In a max-heap, for every node $i$ other than the root, $A[i] <= A[parent(i)]$, that is, the value of a node is at most the value of its parent. The largest element in a max-heap is stored at the root, and the subtree rooted at a node contains values no larger than that contained at the node itself.\n\n Here is an example of a max-heap.\n\n Write a program which reads an array and constructs a max-heap from the array based on the following pseudo code.\n\n $max Heapify(A, i)$ move the value of $A[i]$ down to leaves to make a sub-tree of node $i$ a max-heap. Here, $H$ is the size of the heap.\n\n1 max Heapify(A, i)\n2 l = left(i)\n3 r = right(i)\n4 // select the node which has the maximum value\n5 if l <= H and A[l] > A[i]\n6 largest = l\n7 else \n8 largest = i\n9 if r <= H and A[r] > A[largest]\n10 largest = r\n11\n12 if largest ! = i　// value of children is larger than that of i\n13 swap A[i] and A[largest]\n14 max Heapify(A, largest) // call recursively\n\n The following procedure build Max Heap(A) makes $A$ a max-heap by performing max Heapify in a bottom-up manner.\n\n1 build Max Heap(A)\n2 for i = H/2 downto 1\n3 max Heapify(A, i)", "constraint": "$1 <= H <= 500,000$\n\n$-2,000,000,000 <=$ value of a node $<= 2,000,000,000$", "input": "In the first line, an integer $H$ is given. In the second line, $H$ integers which represent elements in the binary heap are given in order of node id (from $1$ to $H$).", "output": "Print values of nodes in the max-heap in order of their id (from $1$ to $H$). Print a single space character before each value.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 10\n4 1 3 2 16 9 10 14 8 7\n output: 16 14 10 8 7 9 3 2 4 1"], "Pid": "p02288", "ProblemText": "Task Description: A binary heap which satisfies max-heap property is called max-heap. In a max-heap, for every node $i$ other than the root, $A[i] <= A[parent(i)]$, that is, the value of a node is at most the value of its parent. The largest element in a max-heap is stored at the root, and the subtree rooted at a node contains values no larger than that contained at the node itself.\n\n Here is an example of a max-heap.\n\n Write a program which reads an array and constructs a max-heap from the array based on the following pseudo code.\n\n $max Heapify(A, i)$ move the value of $A[i]$ down to leaves to make a sub-tree of node $i$ a max-heap. Here, $H$ is the size of the heap.\n\n1 max Heapify(A, i)\n2 l = left(i)\n3 r = right(i)\n4 // select the node which has the maximum value\n5 if l <= H and A[l] > A[i]\n6 largest = l\n7 else \n8 largest = i\n9 if r <= H and A[r] > A[largest]\n10 largest = r\n11\n12 if largest ! = i　// value of children is larger than that of i\n13 swap A[i] and A[largest]\n14 max Heapify(A, largest) // call recursively\n\n The following procedure build Max Heap(A) makes $A$ a max-heap by performing max Heapify in a bottom-up manner.\n\n1 build Max Heap(A)\n2 for i = H/2 downto 1\n3 max Heapify(A, i)\nTask Constraint: $1 <= H <= 500,000$\n\n$-2,000,000,000 <=$ value of a node $<= 2,000,000,000$\nTask Input: In the first line, an integer $H$ is given. In the second line, $H$ integers which represent elements in the binary heap are given in order of node id (from $1$ to $H$).\nTask Output: Print values of nodes in the max-heap in order of their id (from $1$ to $H$). Print a single space character before each value.\nTask Samples: input: 10\n4 1 3 2 16 9 10 14 8 7\n output: 16 14 10 8 7 9 3 2 4 1\n\n" }, { "title": "Priority Queue", "content": "A priority queue is a data structure which maintains a set $S$ of elements, each of with an associated value (key), and supports the following operations:\n\n$insert(S, k)$: insert an element $k$ into the set $S$\n\n$extract Max(S)$: remove and return the element of $S$ with the largest key\n Write a program which performs the $insert(S, k)$ and $extract Max(S)$ operations to a priority queue $S$.\n The priority queue manages a set of integers, which are also keys for the priority.", "constraint": "The number of operations $<= 2,000,000$\n\n$0 <= k <= 2,000,000,000$", "input": "Multiple operations to the priority queue $S$ are given. Each operation is given by \"insert $k$\", \"extract\" or \"end\" in a line. Here, $k$ represents an integer element to be inserted to the priority queue.\n\nThe input ends with \"end\" operation.", "output": "For each \"extract\" operation, print the element extracted from the priority queue $S$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: insert 8\ninsert 2\nextract\ninsert 10\nextract\ninsert 11\nextract\nextract\nend\n output: 8\n10\n11\n2"], "Pid": "p02289", "ProblemText": "Task Description: A priority queue is a data structure which maintains a set $S$ of elements, each of with an associated value (key), and supports the following operations:\n\n$insert(S, k)$: insert an element $k$ into the set $S$\n\n$extract Max(S)$: remove and return the element of $S$ with the largest key\n Write a program which performs the $insert(S, k)$ and $extract Max(S)$ operations to a priority queue $S$.\n The priority queue manages a set of integers, which are also keys for the priority.\nTask Constraint: The number of operations $<= 2,000,000$\n\n$0 <= k <= 2,000,000,000$\nTask Input: Multiple operations to the priority queue $S$ are given. Each operation is given by \"insert $k$\", \"extract\" or \"end\" in a line. Here, $k$ represents an integer element to be inserted to the priority queue.\n\nThe input ends with \"end\" operation.\nTask Output: For each \"extract\" operation, print the element extracted from the priority queue $S$ in a line.\nTask Samples: input: insert 8\ninsert 2\nextract\ninsert 10\nextract\ninsert 11\nextract\nextract\nend\n output: 8\n10\n11\n2\n\n" }, { "title": "Projection", "content": "For given three points p1, p2, p, find the projection point x of p onto p1p2.", "constraint": "1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\np1 and p2 are not identical.", "input": "x_p1 y_p1 x_p2 y_p2\nq\nx_p0 y_p0\nx_p1 y_p1\n. . .\nx_pq-1 y_pq-1\n\nIn the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.", "output": "For each query, print the coordinate of the projection point x. The output values should be in a decimal fraction with an error less than 0.00000001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 0 2 0\n3\n-1 1\n0 1\n1 1\n output: -1.0000000000 0.0000000000\n0.0000000000 0.0000000000\n1.0000000000 0.0000000000", "input: 0 0 3 4\n1\n2 5\n output: 3.1200000000 4.1600000000"], "Pid": "p02290", "ProblemText": "Task Description: For given three points p1, p2, p, find the projection point x of p onto p1p2.\nTask Constraint: 1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\np1 and p2 are not identical.\nTask Input: x_p1 y_p1 x_p2 y_p2\nq\nx_p0 y_p0\nx_p1 y_p1\n. . .\nx_pq-1 y_pq-1\n\nIn the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.\nTask Output: For each query, print the coordinate of the projection point x. The output values should be in a decimal fraction with an error less than 0.00000001.\nTask Samples: input: 0 0 2 0\n3\n-1 1\n0 1\n1 1\n output: -1.0000000000 0.0000000000\n0.0000000000 0.0000000000\n1.0000000000 0.0000000000\ninput: 0 0 3 4\n1\n2 5\n output: 3.1200000000 4.1600000000\n\n" }, { "title": "Reflection", "content": "For given three points p1, p2, p, find the reflection point x of p onto p1p2.", "constraint": "1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\np1 and p2 are not identical.", "input": "x_p1 y_p1 x_p2 y_p2\nq\nx_p0 y_p0\nx_p1 y_p1\n. . .\nx_pq-1 y_pq-1\n\nIn the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.", "output": "For each query, print the coordinate of the reflection point x. The output values should be in a decimal fraction with an error less than 0.00000001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 0 2 0\n3\n-1 1\n0 1\n1 1\n output: -1.0000000000 -1.0000000000\n0.0000000000 -1.0000000000\n1.0000000000 -1.0000000000", "input: 0 0 3 4\n3\n2 5\n1 4\n0 3\n output: 4.2400000000 3.3200000000\n3.5600000000 2.0800000000\n2.8800000000 0.8400000000"], "Pid": "p02291", "ProblemText": "Task Description: For given three points p1, p2, p, find the reflection point x of p onto p1p2.\nTask Constraint: 1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\np1 and p2 are not identical.\nTask Input: x_p1 y_p1 x_p2 y_p2\nq\nx_p0 y_p0\nx_p1 y_p1\n. . .\nx_pq-1 y_pq-1\n\nIn the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.\nTask Output: For each query, print the coordinate of the reflection point x. The output values should be in a decimal fraction with an error less than 0.00000001.\nTask Samples: input: 0 0 2 0\n3\n-1 1\n0 1\n1 1\n output: -1.0000000000 -1.0000000000\n0.0000000000 -1.0000000000\n1.0000000000 -1.0000000000\ninput: 0 0 3 4\n3\n2 5\n1 4\n0 3\n output: 4.2400000000 3.3200000000\n3.5600000000 2.0800000000\n2.8800000000 0.8400000000\n\n" }, { "title": "Counter-Clockwise", "content": "For given three points p0, p1, p2, print\n\nCOUNTER_CLOCKWISE\n\nif p0, p1, p2 make a counterclockwise turn (1),\n\nCLOCKWISE\n\nif p0, p1, p2 make a clockwise turn (2),\n\nONLINE_BACK\n\nif p2 is on a line p2, p0, p1 in this order (3),\n\nONLINE_FRONT\n\nif p2 is on a line p0, p1, p2 in this order (4),\n\nON_SEGMENT\n\nif p2 is on a segment p0p1 (5).", "constraint": "1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\np0 and p1 are not identical.", "input": "x_p0 y_p0 x_p1 y_p1\nq\nx_p20 y_p20\nx_p21 y_p21\n. . .\nx_p2q-1 y_p2q-1\n\nIn the first line, integer coordinates of p0 and p1 are given. Then, q queries are given for integer coordinates of p2.", "output": "For each query, print the above mentioned status.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 0 0 2 0\n2\n-1 1\n-1 -1\n output: COUNTER_CLOCKWISE\nCLOCKWISE", "input: 0 0 2 0\n3\n-1 0\n0 0\n3 0\n output: ONLINE_BACK\nON_SEGMENT\nONLINE_FRONT"], "Pid": "p02292", "ProblemText": "Task Description: For given three points p0, p1, p2, print\n\nCOUNTER_CLOCKWISE\n\nif p0, p1, p2 make a counterclockwise turn (1),\n\nCLOCKWISE\n\nif p0, p1, p2 make a clockwise turn (2),\n\nONLINE_BACK\n\nif p2 is on a line p2, p0, p1 in this order (3),\n\nONLINE_FRONT\n\nif p2 is on a line p0, p1, p2 in this order (4),\n\nON_SEGMENT\n\nif p2 is on a segment p0p1 (5).\nTask Constraint: 1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\np0 and p1 are not identical.\nTask Input: x_p0 y_p0 x_p1 y_p1\nq\nx_p20 y_p20\nx_p21 y_p21\n. . .\nx_p2q-1 y_p2q-1\n\nIn the first line, integer coordinates of p0 and p1 are given. Then, q queries are given for integer coordinates of p2.\nTask Output: For each query, print the above mentioned status.\nTask Samples: input: 0 0 2 0\n2\n-1 1\n-1 -1\n output: COUNTER_CLOCKWISE\nCLOCKWISE\ninput: 0 0 2 0\n3\n-1 0\n0 0\n3 0\n output: ONLINE_BACK\nON_SEGMENT\nONLINE_FRONT\n\n" }, { "title": "Parallel/Orthogonal", "content": "For given two lines s1 and s2, print \"2\" if they are parallel, \"1\" if they are orthogonal, or \"0\" otherwise.\n\ns1 crosses points p0 and p1, and\ns2 crosses points p2 and p3.", "constraint": "1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.", "input": "The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of the points p0, p1, p2, p3 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3", "output": "For each query, print \"2\", \"1\" or \"0\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 3 0 0 2 3 2\n0 0 3 0 1 1 1 4\n0 0 3 0 1 1 2 2\n output: 2\n1\n0"], "Pid": "p02293", "ProblemText": "Task Description: For given two lines s1 and s2, print \"2\" if they are parallel, \"1\" if they are orthogonal, or \"0\" otherwise.\n\ns1 crosses points p0 and p1, and\ns2 crosses points p2 and p3.\nTask Constraint: 1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.\nTask Input: The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of the points p0, p1, p2, p3 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3\nTask Output: For each query, print \"2\", \"1\" or \"0\".\nTask Samples: input: 3\n0 0 3 0 0 2 3 2\n0 0 3 0 1 1 1 4\n0 0 3 0 1 1 2 2\n output: 2\n1\n0\n\n" }, { "title": "Intersection", "content": "For given two segments s1 and s2, print \"1\" if they are intersect, \"0\" otherwise.\n\ns1 is formed by end points p0 and p1, and\ns2 is formed by end points p2 and p3.", "constraint": "1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.", "input": "The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of end points of s1 and s2 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3", "output": "For each query, print \"1\" or \"0\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 3 0 1 1 2 -1\n0 0 3 0 3 1 3 -1\n0 0 3 0 3 -2 5 0\n output: 1\n1\n0"], "Pid": "p02294", "ProblemText": "Task Description: For given two segments s1 and s2, print \"1\" if they are intersect, \"0\" otherwise.\n\ns1 is formed by end points p0 and p1, and\ns2 is formed by end points p2 and p3.\nTask Constraint: 1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.\nTask Input: The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of end points of s1 and s2 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3\nTask Output: For each query, print \"1\" or \"0\".\nTask Samples: input: 3\n0 0 3 0 1 1 2 -1\n0 0 3 0 3 1 3 -1\n0 0 3 0 3 -2 5 0\n output: 1\n1\n0\n\n" }, { "title": "Cross Point", "content": "For given two segments s1 and s2, print the coordinate of the cross point of them.\n\ns1 is formed by end points p0 and p1, and\ns2 is formed by end points p2 and p3.", "constraint": "1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.\n\nThe given segments have a cross point and are not in parallel.", "input": "The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of end points of s1 and s2 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3", "output": "For each query, print the coordinate of the cross point. The output values should be in a decimal fraction with an error less than 0.00000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 2 0 1 1 1 -1\n0 0 1 1 0 1 1 0\n0 0 1 1 1 0 0 1\n output: 1.0000000000 0.0000000000\n0.5000000000 0.5000000000\n0.5000000000 0.5000000000"], "Pid": "p02295", "ProblemText": "Task Description: For given two segments s1 and s2, print the coordinate of the cross point of them.\n\ns1 is formed by end points p0 and p1, and\ns2 is formed by end points p2 and p3.\nTask Constraint: 1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.\n\nThe given segments have a cross point and are not in parallel.\nTask Input: The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of end points of s1 and s2 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3\nTask Output: For each query, print the coordinate of the cross point. The output values should be in a decimal fraction with an error less than 0.00000001.\nTask Samples: input: 3\n0 0 2 0 1 1 1 -1\n0 0 1 1 0 1 1 0\n0 0 1 1 1 0 0 1\n output: 1.0000000000 0.0000000000\n0.5000000000 0.5000000000\n0.5000000000 0.5000000000\n\n" }, { "title": "Distance", "content": "For given two segments s1 and s2, print the distance between them.\n\ns1 is formed by end points p0 and p1, and\ns2 is formed by end points p2 and p3.", "constraint": "1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.", "input": "The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of end points of s1 and s2 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3", "output": "For each query, print the distance. The output values should be in a decimal fraction with an error less than 0.00000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 1 0 0 1 1 1\n0 0 1 0 2 1 1 2\n-1 0 1 0 0 1 0 -1\n output: 1.0000000000\n1.4142135624\n0.0000000000"], "Pid": "p02296", "ProblemText": "Task Description: For given two segments s1 and s2, print the distance between them.\n\ns1 is formed by end points p0 and p1, and\ns2 is formed by end points p2 and p3.\nTask Constraint: 1 <= q <= 1000\n\n-10000 <= x_pi, y_pi <= 10000\n\np0 != p1 and\np2 != p3.\nTask Input: The entire input looks like:\n\nq (the number of queries)\n1st query\n2nd query\n. . .\nqth query\n\nEach query consists of integer coordinates of end points of s1 and s2 in the following format:\n\nx_p0 y_p0 x_p1 y_p1 x_p2 y_p2 x_p3 y_p3\nTask Output: For each query, print the distance. The output values should be in a decimal fraction with an error less than 0.00000001.\nTask Samples: input: 3\n0 0 1 0 0 1 1 1\n0 0 1 0 2 1 1 2\n-1 0 1 0 0 1 0 -1\n output: 1.0000000000\n1.4142135624\n0.0000000000\n\n" }, { "title": "Area", "content": "For a given polygon g, computes the area of the polygon.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of g. The line segment connecting p_n and p_1 is also a side of the polygon.\n\nNote that the polygon is not necessarily convex.", "constraint": "3 <= n <= 100\n\n-10000 <= x_i, y_i <= 10000\n\nNo point will occur more than once.\n\nTwo sides can intersect only at a common endpoint.", "input": "The input consists of coordinates of the points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of a point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them.", "output": "Print the area of the polygon in a line. The area should be printed with one digit to the right of the decimal point.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0\n2 2\n-1 1\n output: 2.0", "input: 4\n0 0\n1 1\n1 2\n0 2\n output: 1.5"], "Pid": "p02297", "ProblemText": "Task Description: For a given polygon g, computes the area of the polygon.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of g. The line segment connecting p_n and p_1 is also a side of the polygon.\n\nNote that the polygon is not necessarily convex.\nTask Constraint: 3 <= n <= 100\n\n-10000 <= x_i, y_i <= 10000\n\nNo point will occur more than once.\n\nTwo sides can intersect only at a common endpoint.\nTask Input: The input consists of coordinates of the points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of a point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them.\nTask Output: Print the area of the polygon in a line. The area should be printed with one digit to the right of the decimal point.\nTask Samples: input: 3\n0 0\n2 2\n-1 1\n output: 2.0\ninput: 4\n0 0\n1 1\n1 2\n0 2\n output: 1.5\n\n" }, { "title": "Is-Convex", "content": "For a given polygon g, print \"1\" if g is a convex polygon, \"0\" otherwise. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of the polygon. The line segment connecting p_n and p_1 is also a side of the polygon.", "constraint": "3 <= n <= 100\n\n-10000 <= x_i, y_i <= 10000\n\nNo point of the polygon will occur more than once.\n\nTwo sides of the polygon can intersect only at a common endpoint.", "input": "g is given by coordinates of the points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of a point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them.", "output": "Print \"1\" or \"0\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n3 1\n2 3\n0 3\n output: 1", "input: 5\n0 0\n2 0 \n1 1\n2 2\n0 2\n output: 0"], "Pid": "p02298", "ProblemText": "Task Description: For a given polygon g, print \"1\" if g is a convex polygon, \"0\" otherwise. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of the polygon. The line segment connecting p_n and p_1 is also a side of the polygon.\nTask Constraint: 3 <= n <= 100\n\n-10000 <= x_i, y_i <= 10000\n\nNo point of the polygon will occur more than once.\n\nTwo sides of the polygon can intersect only at a common endpoint.\nTask Input: g is given by coordinates of the points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of a point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them.\nTask Output: Print \"1\" or \"0\" in a line.\nTask Samples: input: 4\n0 0\n3 1\n2 3\n0 3\n output: 1\ninput: 5\n0 0\n2 0 \n1 1\n2 2\n0 2\n output: 0\n\n" }, { "title": "Polygon-Point-Containment", "content": "For a given polygon g and target points t, print \"2\" if g contains t, \"1\" if t is on a segment of g, \"0\" otherwise.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of the polygon. The line segment connecting p_n and p_1 is also a side of the polygon.\n\nNote that the polygon is not necessarily convex.", "constraint": "3 <= n <= 100\n\n1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\nNo point of the polygon will occur more than once.\n\nTwo sides of the polygon can intersect only at a common endpoint.", "input": "The entire input looks like:\n\ng (the sequence of the points of the polygon)\nq (the number of queris = the number of target points)\n1st query\n2nd query\n:\nqth query\n\ng is given by coordinates of the points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of a point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them.\n\nEach query consists of the coordinate of a target point t. The coordinate is given by two intgers x and y.", "output": "For each query, print \"2\", \"1\" or \"0\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n3 1\n2 3\n0 3\n3\n2 1\n0 2\n3 2\n output: 2\n1\n0"], "Pid": "p02299", "ProblemText": "Task Description: For a given polygon g and target points t, print \"2\" if g contains t, \"1\" if t is on a segment of g, \"0\" otherwise.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of the polygon. The line segment connecting p_n and p_1 is also a side of the polygon.\n\nNote that the polygon is not necessarily convex.\nTask Constraint: 3 <= n <= 100\n\n1 <= q <= 1000\n\n-10000 <= x_i, y_i <= 10000\n\nNo point of the polygon will occur more than once.\n\nTwo sides of the polygon can intersect only at a common endpoint.\nTask Input: The entire input looks like:\n\ng (the sequence of the points of the polygon)\nq (the number of queris = the number of target points)\n1st query\n2nd query\n:\nqth query\n\ng is given by coordinates of the points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of a point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them.\n\nEach query consists of the coordinate of a target point t. The coordinate is given by two intgers x and y.\nTask Output: For each query, print \"2\", \"1\" or \"0\".\nTask Samples: input: 4\n0 0\n3 1\n2 3\n0 3\n3\n2 1\n0 2\n3 2\n output: 2\n1\n0\n\n" }, { "title": "Convex Hull", "content": "Find the convex hull of a given set of points P. In other words, find the smallest convex polygon containing all the points of P. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.\n\nPlease note that you should find all the points of P on both corner and boundary of the convex polygon.", "constraint": "3 <= n <= 100000\n\n-10000 <= x_i, y_i <= 10000\n\nNo point in the P will occur more than once.", "input": "n\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points in P. The coordinate of the i-th point p_i is given by two integers x_i and y_i.", "output": "In the first line, print the number of points on the corner/boundary of the convex polygon. In the following lines, print x y coordinates of the set of points.\nThe coordinates should be given in the order of counter-clockwise visit of them starting from the point in P with the minimum y-coordinate, or the leftmost such point in case of a tie.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n2 1\n0 0\n1 2\n2 2\n4 2\n1 3\n3 3\n output: 5\n0 0\n2 1\n4 2\n3 3\n1 3", "input: 4\n0 0\n2 2\n0 2\n0 1\n output: 4\n0 0\n2 2\n0 2\n0 1"], "Pid": "p02300", "ProblemText": "Task Description: Find the convex hull of a given set of points P. In other words, find the smallest convex polygon containing all the points of P. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.\n\nPlease note that you should find all the points of P on both corner and boundary of the convex polygon.\nTask Constraint: 3 <= n <= 100000\n\n-10000 <= x_i, y_i <= 10000\n\nNo point in the P will occur more than once.\nTask Input: n\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points in P. The coordinate of the i-th point p_i is given by two integers x_i and y_i.\nTask Output: In the first line, print the number of points on the corner/boundary of the convex polygon. In the following lines, print x y coordinates of the set of points.\nThe coordinates should be given in the order of counter-clockwise visit of them starting from the point in P with the minimum y-coordinate, or the leftmost such point in case of a tie.\nTask Samples: input: 7\n2 1\n0 0\n1 2\n2 2\n4 2\n1 3\n3 3\n output: 5\n0 0\n2 1\n4 2\n3 3\n1 3\ninput: 4\n0 0\n2 2\n0 2\n0 1\n output: 4\n0 0\n2 2\n0 2\n0 1\n\n" }, { "title": "Diameter of a Convex Polygon", "content": "Find the diameter of a convex polygon g. In other words, find a pair of points that have maximum distance between them.", "constraint": "3 <= n <= 80000\n\n-100 <= x_i, y_i <= 100\n\nNo point in the g will occur more than once.", "input": "n\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points in g. \n\nIn the following lines, the coordinate of the i-th point p_i is given by two real numbers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them. Each value is a real number with at most 6 digits after the decimal point.", "output": "Print the diameter of g in a line. The output values should be in a decimal fraction with an error less than 0.000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0.0 0.0\n4.0 0.0\n2.0 2.0\n output: 4.00", "input: 4\n0.0 0.0\n1.0 0.0\n1.0 1.0\n0.0 1.0\n output: 1.414213562373"], "Pid": "p02301", "ProblemText": "Task Description: Find the diameter of a convex polygon g. In other words, find a pair of points that have maximum distance between them.\nTask Constraint: 3 <= n <= 80000\n\n-100 <= x_i, y_i <= 100\n\nNo point in the g will occur more than once.\nTask Input: n\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points in g. \n\nIn the following lines, the coordinate of the i-th point p_i is given by two real numbers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them. Each value is a real number with at most 6 digits after the decimal point.\nTask Output: Print the diameter of g in a line. The output values should be in a decimal fraction with an error less than 0.000001.\nTask Samples: input: 3\n0.0 0.0\n4.0 0.0\n2.0 2.0\n output: 4.00\ninput: 4\n0.0 0.0\n1.0 0.0\n1.0 1.0\n0.0 1.0\n output: 1.414213562373\n\n" }, { "title": "Convex Cut", "content": "As shown in the figure above, cut a convex polygon g by a line p1p2 and print the area of the cut polygon which is on the left-hand side of the line.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of the convex polygon. The line segment connecting p_n and p_1 is also a side of the polygon.", "constraint": "3 <= n <= 100\n\n1 <= q <= 100\n\n-10000 <= x_i, y_i <= 10000\n\n-10000 <= p1x,p1y,p2x,p2y <= 10000\n\nNo point in g will occur more than once.\n\np1 != p2", "input": "The input is given in the following format:\n\ng (the sequence of the points of the polygon)\nq (the number of queries = the number of target lines)\n1st query\n2nd query\n:\nqth query\n\ng is given as a sequence of points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of the i-th point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them. Note that all interior angles of given convex polygons are less than or equal to 180.\n\n For each query, a line represented by two points p1 and p2 is given. The coordinates of the points are given by four integers p1x, p1y, p2x and p2y.", "output": "For each query, print the area of the cut polygon. The output values should be in a decimal fraction with an error less than 0.00001.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 4\n1 1\n4 1\n4 3\n1 3\n2\n2 0 2 4\n2 4 2 0\n output: 2.00000000\n4.00000000"], "Pid": "p02302", "ProblemText": "Task Description: As shown in the figure above, cut a convex polygon g by a line p1p2 and print the area of the cut polygon which is on the left-hand side of the line.\n\ng is represented by a sequence of points p_1, p_2, . . . , p_n where line segments connecting p_i and p_i+1 (1 <= i <= n-1) are sides of the convex polygon. The line segment connecting p_n and p_1 is also a side of the polygon.\nTask Constraint: 3 <= n <= 100\n\n1 <= q <= 100\n\n-10000 <= x_i, y_i <= 10000\n\n-10000 <= p1x,p1y,p2x,p2y <= 10000\n\nNo point in g will occur more than once.\n\np1 != p2\nTask Input: The input is given in the following format:\n\ng (the sequence of the points of the polygon)\nq (the number of queries = the number of target lines)\n1st query\n2nd query\n:\nqth query\n\ng is given as a sequence of points p_1, . . . , p_n in the following format:\n\nn\nx_1 y_1 \nx_2 y_2\n:\nx_n y_n\n\nThe first integer n is the number of points. The coordinate of the i-th point p_i is given by two integers x_i and y_i. The coordinates of points are given in the order of counter-clockwise visit of them. Note that all interior angles of given convex polygons are less than or equal to 180.\n\n For each query, a line represented by two points p1 and p2 is given. The coordinates of the points are given by four integers p1x, p1y, p2x and p2y.\nTask Output: For each query, print the area of the cut polygon. The output values should be in a decimal fraction with an error less than 0.00001.\nTask Samples: input: 4\n1 1\n4 1\n4 3\n1 3\n2\n2 0 2 4\n2 4 2 0\n output: 2.00000000\n4.00000000\n\n" }, { "title": "Closest Pair", "content": "For given n points in metric space, find the distance of the closest points.", "constraint": "2 <= n <= 100,000\n\n-100 <= x, y <= 100", "input": "n\nx_0 y_0\nx_1 y_1\n:\nx_n-1 y_n-1\n\nThe first integer n is the number of points.\n\nIn the following n lines, the coordinate of the i-th point is given by two real numbers x_i and y_i. Each value is a real number with at most 6 digits after the decimal point.", "output": "Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0.0 0.0\n1.0 0.0\n output: 1.000000", "input: 3\n0.0 0.0\n2.0 0.0\n1.0 1.0\n output: 1.41421356237"], "Pid": "p02303", "ProblemText": "Task Description: For given n points in metric space, find the distance of the closest points.\nTask Constraint: 2 <= n <= 100,000\n\n-100 <= x, y <= 100\nTask Input: n\nx_0 y_0\nx_1 y_1\n:\nx_n-1 y_n-1\n\nThe first integer n is the number of points.\n\nIn the following n lines, the coordinate of the i-th point is given by two real numbers x_i and y_i. Each value is a real number with at most 6 digits after the decimal point.\nTask Output: Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.\nTask Samples: input: 2\n0.0 0.0\n1.0 0.0\n output: 1.000000\ninput: 3\n0.0 0.0\n2.0 0.0\n1.0 1.0\n output: 1.41421356237\n\n" }, { "title": "Segment Intersections: Manhattan Geometry", "content": "For given $n$ segments which are parallel to X-axis or Y-axis, find the number of intersections of them.", "constraint": "$1 <= n <= 100,000$\n\n$ -1,000,000,000 <= x_1, y_1, x_2, y_2 <= 1,000,000,000$\n\nTwo parallel segments never overlap or touch.\nThe number of intersections $<= 1,000,000$", "input": "In the first line, the number of segments $n$ is given. In the following $n$ lines, the $i$-th segment is given by coordinates of its end points in the following format:\n\n$x_1 \\; y_1 \\; x_2 \\; y_2$\n\nThe coordinates are given in integers.", "output": "Print the number of intersections in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n2 2 2 5\n1 3 5 3\n4 1 4 4\n5 2 7 2\n6 1 6 3\n6 5 6 7\n output: 3"], "Pid": "p02304", "ProblemText": "Task Description: For given $n$ segments which are parallel to X-axis or Y-axis, find the number of intersections of them.\nTask Constraint: $1 <= n <= 100,000$\n\n$ -1,000,000,000 <= x_1, y_1, x_2, y_2 <= 1,000,000,000$\n\nTwo parallel segments never overlap or touch.\nThe number of intersections $<= 1,000,000$\nTask Input: In the first line, the number of segments $n$ is given. In the following $n$ lines, the $i$-th segment is given by coordinates of its end points in the following format:\n\n$x_1 \\; y_1 \\; x_2 \\; y_2$\n\nThe coordinates are given in integers.\nTask Output: Print the number of intersections in a line.\nTask Samples: input: 6\n2 2 2 5\n1 3 5 3\n4 1 4 4\n5 2 7 2\n6 1 6 3\n6 5 6 7\n output: 3\n\n" }, { "title": "Intersection of Circles", "content": "For given two circles $c1$ and $c2$, print\n\n4\n\nif they do not cross (there are 4 common tangent lines),\n\n3\n\nif they are circumscribed (there are 3 common tangent lines),\n\n2\n\nif they intersect (there are 2 common tangent lines),\n\n1\n\nif a circle is inscribed in another (there are 1 common tangent line),\n\n0\n\nif a circle includes another (there is no common tangent line).", "constraint": "$-1,000 <= c1x, c1y, c2x, c2y <= 1,000$\n\n$1 <= c1r, c2r <= 1,000$\n\n$c1$ and $c2$ are different", "input": "Coordinates and radii of $c1$ and $c2$ are given in the following format.\n\n$c1x \\; c1y \\; c1r$ \n$c2x \\; c2y \\; c2r$\n\n $c1x$, $c1y$ and $c1r$ represent the center coordinate and radius of the first circle.\n $c2x$, $c2y$ and $c2r$ represent the center coordinate and radius of the second circle.\n All input values are given in integers.", "output": "Print \"4\", \"3\", \"2\", \"1\" or \"0\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 1\n6 2 2\n output: 4", "input: 1 2 1\n4 2 2\n output: 3", "input: 1 2 1\n3 2 2\n output: 2", "input: 0 0 1\n1 0 2\n output: 1", "input: 0 0 1\n0 0 2\n output: 0"], "Pid": "p02305", "ProblemText": "Task Description: For given two circles $c1$ and $c2$, print\n\n4\n\nif they do not cross (there are 4 common tangent lines),\n\n3\n\nif they are circumscribed (there are 3 common tangent lines),\n\n2\n\nif they intersect (there are 2 common tangent lines),\n\n1\n\nif a circle is inscribed in another (there are 1 common tangent line),\n\n0\n\nif a circle includes another (there is no common tangent line).\nTask Constraint: $-1,000 <= c1x, c1y, c2x, c2y <= 1,000$\n\n$1 <= c1r, c2r <= 1,000$\n\n$c1$ and $c2$ are different\nTask Input: Coordinates and radii of $c1$ and $c2$ are given in the following format.\n\n$c1x \\; c1y \\; c1r$ \n$c2x \\; c2y \\; c2r$\n\n $c1x$, $c1y$ and $c1r$ represent the center coordinate and radius of the first circle.\n $c2x$, $c2y$ and $c2r$ represent the center coordinate and radius of the second circle.\n All input values are given in integers.\nTask Output: Print \"4\", \"3\", \"2\", \"1\" or \"0\" in a line.\nTask Samples: input: 1 1 1\n6 2 2\n output: 4\ninput: 1 2 1\n4 2 2\n output: 3\ninput: 1 2 1\n3 2 2\n output: 2\ninput: 0 0 1\n1 0 2\n output: 1\ninput: 0 0 1\n0 0 2\n output: 0\n\n" }, { "title": "Incircle of a Triangle", "content": "Write a program which prints the central coordinate ($cx$, $cy$) and the radius $r$ of a incircle of a triangle which is constructed by three points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) on the plane surface.", "constraint": "$-10000 <= x_i, y_i <= 10000$\n\nThe three points are not on the same straight line", "input": "The input is given in the following format\n$x_1$ $y_1$\n$x_2$ $y_2$\n$x_3$ $y_3$\n\nAll the input are integers.", "output": "Print $cx$, $cy$ and $r$ separated by a single space in a line. The output values should be in a decimal fraction with an error less than 0.000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 -2\n3 2\n-2 0\n output: 0.53907943898209422325 -0.26437392711448356856 1.18845545916395465278", "input: 0 3\n4 0\n0 0\n output: 1.00000000000000000000 1.00000000000000000000 1.00000000000000000000"], "Pid": "p02306", "ProblemText": "Task Description: Write a program which prints the central coordinate ($cx$, $cy$) and the radius $r$ of a incircle of a triangle which is constructed by three points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) on the plane surface.\nTask Constraint: $-10000 <= x_i, y_i <= 10000$\n\nThe three points are not on the same straight line\nTask Input: The input is given in the following format\n$x_1$ $y_1$\n$x_2$ $y_2$\n$x_3$ $y_3$\n\nAll the input are integers.\nTask Output: Print $cx$, $cy$ and $r$ separated by a single space in a line. The output values should be in a decimal fraction with an error less than 0.000001.\nTask Samples: input: 1 -2\n3 2\n-2 0\n output: 0.53907943898209422325 -0.26437392711448356856 1.18845545916395465278\ninput: 0 3\n4 0\n0 0\n output: 1.00000000000000000000 1.00000000000000000000 1.00000000000000000000\n\n" }, { "title": "Circumscribed Circle of a Triangle", "content": "Write a program which prints the central coordinate ($cx$, $cy$) and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) on the plane surface.", "constraint": "$-10000 <= x_i, y_i <= 10000$\n\nThe three points are not on the same straight line", "input": "The input is given in the following format\n$x_1$ $y_1$\n$x_2$ $y_2$\n$x_3$ $y_3$\n\nAll the input are integers.", "output": "Print $cx$, $cy$ and $r$ separated by a single space in a line. The output val ues should be in a decimal fraction with an error less than 0.000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 -2\n3 2\n-2 0\n output: 0.62500000000000000000 0.68750000000000000000 2.71353666826155124291", "input: 0 3\n4 0\n0 0\n output: 2.00000000000000000000 1.50000000000000000000 2.50000000000000000000"], "Pid": "p02307", "ProblemText": "Task Description: Write a program which prints the central coordinate ($cx$, $cy$) and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) on the plane surface.\nTask Constraint: $-10000 <= x_i, y_i <= 10000$\n\nThe three points are not on the same straight line\nTask Input: The input is given in the following format\n$x_1$ $y_1$\n$x_2$ $y_2$\n$x_3$ $y_3$\n\nAll the input are integers.\nTask Output: Print $cx$, $cy$ and $r$ separated by a single space in a line. The output val ues should be in a decimal fraction with an error less than 0.000001.\nTask Samples: input: 1 -2\n3 2\n-2 0\n output: 0.62500000000000000000 0.68750000000000000000 2.71353666826155124291\ninput: 0 3\n4 0\n0 0\n output: 2.00000000000000000000 1.50000000000000000000 2.50000000000000000000\n\n" }, { "title": "Cross Points of a Circe and a Line", "content": "For given a circle $c$ and a line $l$, print the coordinates of the cross points of them.", "constraint": "$p1$ and $p2$ are different\n\nThe circle and line have at least one cross point\n\n$1 <= q <= 1,000$\n\n$-10,000 <= cx, cy, x1, y1, x2, y2 <= 10,000$\n\n$1 <= r <= 10,000$", "input": "The input is given in the following format.\n\n$cx\\; cy\\; r$\n$q$\n$Line_1$\n$Line_2$\n: \n$Line_q$\n\n In the first line, the center coordinate of the circle and its radius are given by $cx$, $cy$ and $r$. In the second line, the number of queries $q$ is given.\n\n In the following $q$ lines, as queries, $Line_i$ are given ($1 <= i <= q$) in the following format.\n\n$x_1\\; y_1\\; x_2\\; y_2$\n\n Each line is represented by two points $p1$ and $p2$ which the line crosses. The coordinate of $p1$ and $p2$ are given by ($x1$, $y1$) and ($x2$, $y2$) respectively. All input values are given in integers.", "output": "For each query, print the coordinates of the cross points in the following rules.\n\nIf there is one cross point, print two coordinates with the same values.\n\nPrint the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n The output values should be in a decimal fraction with an error less than 0.000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 1\n2\n0 1 4 1\n3 0 3 3\n output: 1.00000000 1.00000000 3.00000000 1.00000000\n3.00000000 1.00000000 3.00000000 1.00000000"], "Pid": "p02308", "ProblemText": "Task Description: For given a circle $c$ and a line $l$, print the coordinates of the cross points of them.\nTask Constraint: $p1$ and $p2$ are different\n\nThe circle and line have at least one cross point\n\n$1 <= q <= 1,000$\n\n$-10,000 <= cx, cy, x1, y1, x2, y2 <= 10,000$\n\n$1 <= r <= 10,000$\nTask Input: The input is given in the following format.\n\n$cx\\; cy\\; r$\n$q$\n$Line_1$\n$Line_2$\n: \n$Line_q$\n\n In the first line, the center coordinate of the circle and its radius are given by $cx$, $cy$ and $r$. In the second line, the number of queries $q$ is given.\n\n In the following $q$ lines, as queries, $Line_i$ are given ($1 <= i <= q$) in the following format.\n\n$x_1\\; y_1\\; x_2\\; y_2$\n\n Each line is represented by two points $p1$ and $p2$ which the line crosses. The coordinate of $p1$ and $p2$ are given by ($x1$, $y1$) and ($x2$, $y2$) respectively. All input values are given in integers.\nTask Output: For each query, print the coordinates of the cross points in the following rules.\n\nIf there is one cross point, print two coordinates with the same values.\n\nPrint the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n The output values should be in a decimal fraction with an error less than 0.000001.\nTask Samples: input: 2 1 1\n2\n0 1 4 1\n3 0 3 3\n output: 1.00000000 1.00000000 3.00000000 1.00000000\n3.00000000 1.00000000 3.00000000 1.00000000\n\n" }, { "title": "Cross Points of Circles", "content": "For given two circles $c1$ and $c2$, print the coordinates of the cross points of them.", "constraint": "The given circle have at least one cross point and have different center coordinates.\n\n$-10,000 <= c1x, c1y, c2x, c2y <= 10,000$\n\n$1 <= c1r, c2r <= 10,000$", "input": "The input is given in the following format.\n\n$c1x\\; c1y\\; c1r$ \n$c2x\\; c2y\\; c2r$ \n\n $c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle.\n $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle.\n All input values are given in integers.", "output": "Print the coordinates ($x1$, $y1$) and ($x2$, $y2$) of the cross points $p1$ and $p2$ respectively in the following rules.\n\nIf there is one cross point, print two coordinates with the same values.\n\nPrint the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n The output values should be in a decimal fraction with an error less than 0.000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0 2\n2 0 2\n output: 1.00000000 -1.73205080 1.00000000 1.73205080", "input: 0 0 2\n0 3 1\n output: 0.00000000 2.00000000 0.00000000 2.00000000"], "Pid": "p02309", "ProblemText": "Task Description: For given two circles $c1$ and $c2$, print the coordinates of the cross points of them.\nTask Constraint: The given circle have at least one cross point and have different center coordinates.\n\n$-10,000 <= c1x, c1y, c2x, c2y <= 10,000$\n\n$1 <= c1r, c2r <= 10,000$\nTask Input: The input is given in the following format.\n\n$c1x\\; c1y\\; c1r$ \n$c2x\\; c2y\\; c2r$ \n\n $c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle.\n $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle.\n All input values are given in integers.\nTask Output: Print the coordinates ($x1$, $y1$) and ($x2$, $y2$) of the cross points $p1$ and $p2$ respectively in the following rules.\n\nIf there is one cross point, print two coordinates with the same values.\n\nPrint the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n The output values should be in a decimal fraction with an error less than 0.000001.\nTask Samples: input: 0 0 2\n2 0 2\n output: 1.00000000 -1.73205080 1.00000000 1.73205080\ninput: 0 0 2\n0 3 1\n output: 0.00000000 2.00000000 0.00000000 2.00000000\n\n" }, { "title": "Tangent to a Circle", "content": "Find the tangent lines between a point $p$ and a circle $c$.", "constraint": "$-1,000 <= px, py, cx, cy <= 1,000$\n\n$1 <= r <= 1,000$\n\nDistance between $p$ and the center of $c$ is greater than the radius of $c$.", "input": "The input is given in the following format.\n\n$px \\; py$ \n$cx \\; cy \\; r$\n\n$px$ and $py$ represents the coordinate of the point $p$. $cx$, $cy$ and $r$ represents the center coordinate and radius of the circle $c$ respectively. All input values are given in integers.", "output": "Print coordinates of the tangent points on the circle $c$ based on the following rules.\n\n Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n The output values should be in a decimal fraction with an error less than 0.00001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0\n2 2 2\n output: 0.0000000000 2.0000000000\n2.0000000000 0.0000000000", "input: -3 0\n2 2 2\n output: 0.6206896552 3.4482758621\n2.0000000000 0.0000000000"], "Pid": "p02310", "ProblemText": "Task Description: Find the tangent lines between a point $p$ and a circle $c$.\nTask Constraint: $-1,000 <= px, py, cx, cy <= 1,000$\n\n$1 <= r <= 1,000$\n\nDistance between $p$ and the center of $c$ is greater than the radius of $c$.\nTask Input: The input is given in the following format.\n\n$px \\; py$ \n$cx \\; cy \\; r$\n\n$px$ and $py$ represents the coordinate of the point $p$. $cx$, $cy$ and $r$ represents the center coordinate and radius of the circle $c$ respectively. All input values are given in integers.\nTask Output: Print coordinates of the tangent points on the circle $c$ based on the following rules.\n\n Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n The output values should be in a decimal fraction with an error less than 0.00001.\nTask Samples: input: 0 0\n2 2 2\n output: 0.0000000000 2.0000000000\n2.0000000000 0.0000000000\ninput: -3 0\n2 2 2\n output: 0.6206896552 3.4482758621\n2.0000000000 0.0000000000\n\n" }, { "title": "Common Tangent", "content": "Find common tangent lines of two circles $c1$ and $c2$.", "constraint": "$-1,000 <= c1x, c1y, c2x, c2y <= 1,000$\n\n$1 <= c1r, c2r <= 1,000$\n\n$c1$ and $c2$ are different", "input": "Center coordinates ($cix$, $ciy$) and radii $cir$ of two circles $c1$ are $c2$ are given in the following format.\n\n$c1x \\; c1y \\; c1r$ \n$c2x \\; c2y \\; c2r$\n\nAll input values are given in integers.", "output": "Print coordinates of the tangent points on circle $c1$ based on the following rules.\n\nPrint the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n \n The output values should be in a decimal fraction with an error less than 0.00001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 1\n6 2 2\n output: 0.6153846154 1.9230769231\n1.0000000000 0.0000000000\n1.4183420913 1.9082895434\n1.7355040625 0.3224796874", "input: 1 2 1\n4 2 2\n output: 0.6666666667 1.0571909584\n0.6666666667 2.9428090416\n2.0000000000 2.0000000000", "input: 1 2 1\n3 2 2\n output: 0.5000000000 1.1339745962\n0.5000000000 2.8660254038", "input: 0 0 1\n1 0 2\n output: -1.0000000000 0.0000000000", "input: 0 0 1\n0 0 2\n output: \n\nNo output."], "Pid": "p02311", "ProblemText": "Task Description: Find common tangent lines of two circles $c1$ and $c2$.\nTask Constraint: $-1,000 <= c1x, c1y, c2x, c2y <= 1,000$\n\n$1 <= c1r, c2r <= 1,000$\n\n$c1$ and $c2$ are different\nTask Input: Center coordinates ($cix$, $ciy$) and radii $cir$ of two circles $c1$ are $c2$ are given in the following format.\n\n$c1x \\; c1y \\; c1r$ \n$c2x \\; c2y \\; c2r$\n\nAll input values are given in integers.\nTask Output: Print coordinates of the tangent points on circle $c1$ based on the following rules.\n\nPrint the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.\n \n The output values should be in a decimal fraction with an error less than 0.00001.\nTask Samples: input: 1 1 1\n6 2 2\n output: 0.6153846154 1.9230769231\n1.0000000000 0.0000000000\n1.4183420913 1.9082895434\n1.7355040625 0.3224796874\ninput: 1 2 1\n4 2 2\n output: 0.6666666667 1.0571909584\n0.6666666667 2.9428090416\n2.0000000000 2.0000000000\ninput: 1 2 1\n3 2 2\n output: 0.5000000000 1.1339745962\n0.5000000000 2.8660254038\ninput: 0 0 1\n1 0 2\n output: -1.0000000000 0.0000000000\ninput: 0 0 1\n0 0 2\n output: \n\nNo output.\n\n" }, { "title": "Intersection of a Circle and a Polygon", "content": "Find the area of intersection between a circle $c$ and a polygon $g$. The center coordinate of the circle is ($0,0$).\n\n The polygon $g$ is represented by a sequence of points $p_1$, $p_2$, . . . , $p_n$ where line segments connecting $p_i$ and $p_{i+1}$ ($1 <= i <= n-1$) are sides of the polygon. The line segment connecting $p_n$ and $p_1$ is also a side of the polygon.\n \nNote that the polygon is not necessarily convex.", "constraint": "$3 <= n <= 100$\n\n$1 <= r <= 100$\n\n$-100 <= x_i, y_i <= 100$", "input": "The input is given in the following format. \n\n$n$ $r$\n$x_1$ $y_1$\n$x_2$ $y_2$\n : \n$x_n$ $y_n$\n\n In the first line, an integer n representing the number of points in the polygon is given. The coordinate of a point $p_i$ is given by two integers $x_i$ and $y_i$. The coordinates of the points are given in the order of counter-clockwise visit of them. All input values are given in integers.", "output": "Print the area of intersection in a line.\n The output values should be in a decimal fraction with an error less than 0.00001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n1 1\n4 1\n5 5\n output: 4.639858417607", "input: 4 5\n0 0\n-3 -6\n1 -3\n5 -4\n output: 11.787686807576"], "Pid": "p02312", "ProblemText": "Task Description: Find the area of intersection between a circle $c$ and a polygon $g$. The center coordinate of the circle is ($0,0$).\n\n The polygon $g$ is represented by a sequence of points $p_1$, $p_2$, . . . , $p_n$ where line segments connecting $p_i$ and $p_{i+1}$ ($1 <= i <= n-1$) are sides of the polygon. The line segment connecting $p_n$ and $p_1$ is also a side of the polygon.\n \nNote that the polygon is not necessarily convex.\nTask Constraint: $3 <= n <= 100$\n\n$1 <= r <= 100$\n\n$-100 <= x_i, y_i <= 100$\nTask Input: The input is given in the following format. \n\n$n$ $r$\n$x_1$ $y_1$\n$x_2$ $y_2$\n : \n$x_n$ $y_n$\n\n In the first line, an integer n representing the number of points in the polygon is given. The coordinate of a point $p_i$ is given by two integers $x_i$ and $y_i$. The coordinates of the points are given in the order of counter-clockwise visit of them. All input values are given in integers.\nTask Output: Print the area of intersection in a line.\n The output values should be in a decimal fraction with an error less than 0.00001.\nTask Samples: input: 3 5\n1 1\n4 1\n5 5\n output: 4.639858417607\ninput: 4 5\n0 0\n-3 -6\n1 -3\n5 -4\n output: 11.787686807576\n\n" }, { "title": "Area of Intersection between Two Circles", "content": "Write a program which prints the area of intersection between given circles $c1$ and $c2$.", "constraint": "$-10,000 <= c1x, c1y, c2x, c2y <= 10,000$\n\n$1 <= c1r, c2r <= 10,000$", "input": "The input is given in the following format.\n\n$c1x\\; c1y\\; c1r$ \n$c2x\\; c2y\\; c2r$ \n\n$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle. $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle. All input values are given in integers.", "output": "Output the area in a line.\n The output values should be in a decimal fraction with an error less than 0.000001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0 1\n2 0 2\n output: 1.40306643968573875104", "input: 1 0 1\n0 0 3\n output: 3.14159265358979311600"], "Pid": "p02313", "ProblemText": "Task Description: Write a program which prints the area of intersection between given circles $c1$ and $c2$.\nTask Constraint: $-10,000 <= c1x, c1y, c2x, c2y <= 10,000$\n\n$1 <= c1r, c2r <= 10,000$\nTask Input: The input is given in the following format.\n\n$c1x\\; c1y\\; c1r$ \n$c2x\\; c2y\\; c2r$ \n\n$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle. $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle. All input values are given in integers.\nTask Output: Output the area in a line.\n The output values should be in a decimal fraction with an error less than 0.000001.\nTask Samples: input: 0 0 1\n2 0 2\n output: 1.40306643968573875104\ninput: 1 0 1\n0 0 3\n output: 3.14159265358979311600\n\n" }, { "title": "Coin Changing Problem", "content": "Find the minimum number of coins to make change for n cents using coins of denominations d_1, d_2, . . , d_m. The coins can be used any number of times.", "constraint": "1 <= n <= 50000\n\n1 <= m <= 20\n\n1 <= denomination <= 10000\n\nThe denominations are all different and contain 1.", "input": "n m\nd_1 d_2 . . . d_m\n\nTwo integers n and m are given in the first line. The available denominations are given in the second line.", "output": "Print the minimum number of coins in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 55 4\n1 5 10 50\n output: 2", "input: 15 6\n1 2 7 8 12 50\n output: 2", "input: 65 6\n1 2 7 8 12 50\n output: 3"], "Pid": "p02314", "ProblemText": "Task Description: Find the minimum number of coins to make change for n cents using coins of denominations d_1, d_2, . . , d_m. The coins can be used any number of times.\nTask Constraint: 1 <= n <= 50000\n\n1 <= m <= 20\n\n1 <= denomination <= 10000\n\nThe denominations are all different and contain 1.\nTask Input: n m\nd_1 d_2 . . . d_m\n\nTwo integers n and m are given in the first line. The available denominations are given in the second line.\nTask Output: Print the minimum number of coins in a line.\nTask Samples: input: 55 4\n1 5 10 50\n output: 2\ninput: 15 6\n1 2 7 8 12 50\n output: 2\ninput: 65 6\n1 2 7 8 12 50\n output: 3\n\n" }, { "title": "0-1 Knapsack Problem", "content": "You have N items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\nFind the maximum total value of items in the knapsack.", "constraint": "1 <= N <= 100\n\n 1 <= v_i <= 1000\n\n 1 <= w_i <= 1000\n\n 1 <= W <= 10000", "input": "N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.", "output": "Print the maximum total values of the items in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n4 2\n5 2\n2 1\n8 3\n output: 13", "input: 2 20\n5 9\n4 10\n output: 9"], "Pid": "p02315", "ProblemText": "Task Description: You have N items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\nFind the maximum total value of items in the knapsack.\nTask Constraint: 1 <= N <= 100\n\n 1 <= v_i <= 1000\n\n 1 <= w_i <= 1000\n\n 1 <= W <= 10000\nTask Input: N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.\nTask Output: Print the maximum total values of the items in a line.\nTask Samples: input: 4 5\n4 2\n5 2\n2 1\n8 3\n output: 13\ninput: 2 20\n5 9\n4 10\n output: 9\n\n" }, { "title": "Knapsack Problem", "content": "You have N kinds of items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\n\nYou can select as many items as possible into a knapsack for each kind.\nFind the maximum total value of items in the knapsack.", "constraint": "1 <= N <= 100\n\n 1 <= v_i <= 1000\n\n 1 <= w_i <= 1000\n\n 1 <= W <= 10000", "input": "N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.", "output": "Print the maximum total values of the items in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 8\n4 2\n5 2\n2 1\n8 3\n output: 21", "input: 2 20\n5 9\n4 10\n output: 10", "input: 3 9\n2 1\n3 1\n5 2\n output: 27"], "Pid": "p02316", "ProblemText": "Task Description: You have N kinds of items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\n\nYou can select as many items as possible into a knapsack for each kind.\nFind the maximum total value of items in the knapsack.\nTask Constraint: 1 <= N <= 100\n\n 1 <= v_i <= 1000\n\n 1 <= w_i <= 1000\n\n 1 <= W <= 10000\nTask Input: N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.\nTask Output: Print the maximum total values of the items in a line.\nTask Samples: input: 4 8\n4 2\n5 2\n2 1\n8 3\n output: 21\ninput: 2 20\n5 9\n4 10\n output: 10\ninput: 3 9\n2 1\n3 1\n5 2\n output: 27\n\n" }, { "title": "Longest Increasing Subsequence", "content": "For a given sequence A = {a_0, a_1, . . . , a_n-1}, find the length of the longest increasing subsequnece (LIS) in A.\n\nAn increasing subsequence of A is defined by a subsequence {a_i0, a_i1, . . . , a_ik} where 0 <= i_0 < i_1 < . . . < i_k < n and a_i0 < a_i1 < . . . < a_ik.", "constraint": "1 <= n <= 100000\n\n0 <= a_i <= 10^9", "input": "n\na_0\na_1\n:\na_n-1\nIn the first line, an integer n is given. In the next n lines, elements of A are given.", "output": "The length of the longest increasing subsequence of A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n5\n1\n3\n2\n4\n output: 3", "input: 3\n1\n1\n1\n output: 1"], "Pid": "p02317", "ProblemText": "Task Description: For a given sequence A = {a_0, a_1, . . . , a_n-1}, find the length of the longest increasing subsequnece (LIS) in A.\n\nAn increasing subsequence of A is defined by a subsequence {a_i0, a_i1, . . . , a_ik} where 0 <= i_0 < i_1 < . . . < i_k < n and a_i0 < a_i1 < . . . < a_ik.\nTask Constraint: 1 <= n <= 100000\n\n0 <= a_i <= 10^9\nTask Input: n\na_0\na_1\n:\na_n-1\nIn the first line, an integer n is given. In the next n lines, elements of A are given.\nTask Output: The length of the longest increasing subsequence of A.\nTask Samples: input: 5\n5\n1\n3\n2\n4\n output: 3\ninput: 3\n1\n1\n1\n output: 1\n\n" }, { "title": "Edit Distance (Levenshtein Distance)", "content": "Find the edit distance between given two words s1 and s2.\n\nThe disntace is the minimum number of single-character edits required to change one word into the other. The edits including the following operations:\n\ninsertion: Insert a character at a particular position.\n\ndeletion: Delete a character at a particular position. \n\nsubstitution: Change the character at a particular position to a different character", "constraint": "1 <= length of s1 <= 1000\n\n1 <= length of s2 <= 1000", "input": "s1\ns2\n\nTwo words s1 and s2 are given in the first line and the second line respectively. The words will consist of lower case characters.", "output": "Print the edit distance in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: acac\nacm\n output: 2", "input: icpc\nicpc\n output: 0"], "Pid": "p02318", "ProblemText": "Task Description: Find the edit distance between given two words s1 and s2.\n\nThe disntace is the minimum number of single-character edits required to change one word into the other. The edits including the following operations:\n\ninsertion: Insert a character at a particular position.\n\ndeletion: Delete a character at a particular position. \n\nsubstitution: Change the character at a particular position to a different character\nTask Constraint: 1 <= length of s1 <= 1000\n\n1 <= length of s2 <= 1000\nTask Input: s1\ns2\n\nTwo words s1 and s2 are given in the first line and the second line respectively. The words will consist of lower case characters.\nTask Output: Print the edit distance in a line.\nTask Samples: input: acac\nacm\n output: 2\ninput: icpc\nicpc\n output: 0\n\n" }, { "title": "0-1 Knapsack Problem II", "content": "You have N items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\nFind the maximum total value of items in the knapsack.", "constraint": "1 <= N <= 100\n\n 1 <= v_i <= 100\n\n 1 <= w_i <= 10,000,000\n\n 1 <= W <= 1,000,000,000", "input": "N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.", "output": "Print the maximum total values of the items in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n4 2\n5 2\n2 1\n8 3\n output: 13", "input: 2 20\n5 9\n4 10\n output: 9"], "Pid": "p02319", "ProblemText": "Task Description: You have N items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\nFind the maximum total value of items in the knapsack.\nTask Constraint: 1 <= N <= 100\n\n 1 <= v_i <= 100\n\n 1 <= w_i <= 10,000,000\n\n 1 <= W <= 1,000,000,000\nTask Input: N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.\nTask Output: Print the maximum total values of the items in a line.\nTask Samples: input: 4 5\n4 2\n5 2\n2 1\n8 3\n output: 13\ninput: 2 20\n5 9\n4 10\n output: 9\n\n" }, { "title": "Knapsack Problem with Limitations", "content": "You have N items that you want to put them into a knapsack. Item i has value v_i, weight w_i and limitation m_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\n\nYou can select at most m_i items for ith item.\nFind the maximum total value of items in the knapsack.", "constraint": "1 <= N <= 100\n\n 1 <= v_i <= 1,000\n\n 1 <= w_i <= 1,000\n\n 1 <= m_i <= 10,000\n\n 1 <= W <= 10,000", "input": "N W\nv_1 w_1 m_1\nv_2 w_2 m_2\n:\nv_N w_N m_N\n\nThe first line consists of the integers N and W. In the following N lines, the value, weight and limitation of the i-th item are given.", "output": "Print the maximum total values of the items in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 8\n4 3 2\n2 1 1\n1 2 4\n3 2 2\n output: 12", "input: 2 100\n1 1 100\n2 1 50\n output: 150"], "Pid": "p02320", "ProblemText": "Task Description: You have N items that you want to put them into a knapsack. Item i has value v_i, weight w_i and limitation m_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\n\nYou can select at most m_i items for ith item.\nFind the maximum total value of items in the knapsack.\nTask Constraint: 1 <= N <= 100\n\n 1 <= v_i <= 1,000\n\n 1 <= w_i <= 1,000\n\n 1 <= m_i <= 10,000\n\n 1 <= W <= 10,000\nTask Input: N W\nv_1 w_1 m_1\nv_2 w_2 m_2\n:\nv_N w_N m_N\n\nThe first line consists of the integers N and W. In the following N lines, the value, weight and limitation of the i-th item are given.\nTask Output: Print the maximum total values of the items in a line.\nTask Samples: input: 4 8\n4 3 2\n2 1 1\n1 2 4\n3 2 2\n output: 12\ninput: 2 100\n1 1 100\n2 1 50\n output: 150\n\n" }, { "title": "Huge Knapsack Problem", "content": "You have N items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\nFind the maximum total value of items in the knapsack.", "constraint": "1 <= N <= 40\n\n 1 <= v_i <= 10^15\n\n 1 <= w_i <= 10^15\n\n 1 <= W <= 10^15", "input": "N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.", "output": "Print the maximum total values of the items in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n4 2\n5 2\n2 1\n8 3\n output: 13", "input: 2 20\n5 9\n4 10\n output: 9"], "Pid": "p02321", "ProblemText": "Task Description: You have N items that you want to put them into a knapsack. Item i has value v_i and weight w_i.\n\nYou want to find a subset of items to put such that:\n\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most W, that is capacity of the knapsack.\nFind the maximum total value of items in the knapsack.\nTask Constraint: 1 <= N <= 40\n\n 1 <= v_i <= 10^15\n\n 1 <= w_i <= 10^15\n\n 1 <= W <= 10^15\nTask Input: N W\nv_1 w_1\nv_2 w_2\n:\nv_N w_N\n\nThe first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.\nTask Output: Print the maximum total values of the items in a line.\nTask Samples: input: 4 5\n4 2\n5 2\n2 1\n8 3\n output: 13\ninput: 2 20\n5 9\n4 10\n output: 9\n\n" }, { "title": "Knapsack Problem with Limitations II", "content": "You have $N$ items that you want to put them into a knapsack. Item $i$ has value $v_i$, weight $w_i$ and limitation $m_i$. You want to find a subset of items to put such that:\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most $W$, that is capacity of the knapsack.\n\nYou can select at most $m_i$ items for $i$-th item.\n\nFind the maximum total value of items in the knapsack.", "constraint": "$1 <= N <= 50$\n\n$1 <= v_i <= 50$\n\n$1 <= w_i <= 10^9$\n\n$1 <= m_i <= 10^9$\n\n$1 <= W <= 10^9$", "input": "$N$ $W$\n$v_1$ $w_1$ $m_1$\n$v_2$ $w_2$ $m_2$\n:\n$v_N$ $w_N$ $m_N$\nThe first line consists of the integers $N$ and $W$. In the following $N$ lines, the value, weight and limitation of the $i$-th item are given.", "output": "Print the maximum total values of the items in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 8\n4 3 2\n2 1 1\n1 2 4\n3 2 2\n output: 12", "input: 2 100\n1 1 100\n2 1 50\n output: 150", "input: 5 1000000000\n3 5 1000000000\n7 6 1000000000\n4 4 1000000000\n6 8 1000000000\n2 5 1000000000\n output: 1166666666"], "Pid": "p02322", "ProblemText": "Task Description: You have $N$ items that you want to put them into a knapsack. Item $i$ has value $v_i$, weight $w_i$ and limitation $m_i$. You want to find a subset of items to put such that:\nThe total value of the items is as large as possible.\n\nThe items have combined weight at most $W$, that is capacity of the knapsack.\n\nYou can select at most $m_i$ items for $i$-th item.\n\nFind the maximum total value of items in the knapsack.\nTask Constraint: $1 <= N <= 50$\n\n$1 <= v_i <= 50$\n\n$1 <= w_i <= 10^9$\n\n$1 <= m_i <= 10^9$\n\n$1 <= W <= 10^9$\nTask Input: $N$ $W$\n$v_1$ $w_1$ $m_1$\n$v_2$ $w_2$ $m_2$\n:\n$v_N$ $w_N$ $m_N$\nThe first line consists of the integers $N$ and $W$. In the following $N$ lines, the value, weight and limitation of the $i$-th item are given.\nTask Output: Print the maximum total values of the items in a line.\nTask Samples: input: 4 8\n4 3 2\n2 1 1\n1 2 4\n3 2 2\n output: 12\ninput: 2 100\n1 1 100\n2 1 50\n output: 150\ninput: 5 1000000000\n3 5 1000000000\n7 6 1000000000\n4 4 1000000000\n6 8 1000000000\n2 5 1000000000\n output: 1166666666\n\n" }, { "title": "Traveling Salesman Problem", "content": "For a given weighted directed graph G(V, E), find the distance of the shortest route that meets the following criteria:\n\nIt is a closed cycle where it ends at the same point it starts.\n\nIt visits each vertex exactly once.", "constraint": "2 <= |V| <= 15\n\n 0 <= d_i <= 1,000\n\n There are no multiedge", "input": "|V| |E|\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n|V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the distance between s_i and t_i (the i-th edge).", "output": "Print the shortest distance in a line. If there is no solution, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n0 1 2\n1 2 3\n1 3 9\n2 0 1\n2 3 6\n3 2 4\n output: 16", "input: 3 3\n0 1 1\n1 2 1\n0 2 1\n output: -1"], "Pid": "p02323", "ProblemText": "Task Description: For a given weighted directed graph G(V, E), find the distance of the shortest route that meets the following criteria:\n\nIt is a closed cycle where it ends at the same point it starts.\n\nIt visits each vertex exactly once.\nTask Constraint: 2 <= |V| <= 15\n\n 0 <= d_i <= 1,000\n\n There are no multiedge\nTask Input: |V| |E|\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n|V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the distance between s_i and t_i (the i-th edge).\nTask Output: Print the shortest distance in a line. If there is no solution, print -1.\nTask Samples: input: 4 6\n0 1 2\n1 2 3\n1 3 9\n2 0 1\n2 3 6\n3 2 4\n output: 16\ninput: 3 3\n0 1 1\n1 2 1\n0 2 1\n output: -1\n\n" }, { "title": "Chinese Postman Problem", "content": "For a given weighted undirected graph G(V, E), find the distance of the shortest route that meets the following criteria:\n\nIt is a closed cycle where it ends at the same point it starts.\n\nThe route must go through every edge at least once.", "constraint": "2 <= |V| <= 15\n\n0 <= |E| <= 1,000\n\n0 <= d_i <= 1,000\n\n s_i != t_i\n\nThe graph is connected", "input": "|V| |E|\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target verticess of i-th edge (undirected) and d_i represents the distance between s_i and t_i (the i-th edge).\n\nNote that there can be multiple edges between a pair of vertices.", "output": "Print the shortest distance in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n0 1 1\n0 2 2\n1 3 3\n2 3 4\n output: 10", "input: 4 5\n0 1 1\n0 2 2\n1 3 3\n2 3 4\n1 2 5\n output: 18", "input: 2 3\n0 1 1\n0 1 2\n0 1 3\n output: 7"], "Pid": "p02324", "ProblemText": "Task Description: For a given weighted undirected graph G(V, E), find the distance of the shortest route that meets the following criteria:\n\nIt is a closed cycle where it ends at the same point it starts.\n\nThe route must go through every edge at least once.\nTask Constraint: 2 <= |V| <= 15\n\n0 <= |E| <= 1,000\n\n0 <= d_i <= 1,000\n\n s_i != t_i\n\nThe graph is connected\nTask Input: |V| |E|\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target verticess of i-th edge (undirected) and d_i represents the distance between s_i and t_i (the i-th edge).\n\nNote that there can be multiple edges between a pair of vertices.\nTask Output: Print the shortest distance in a line.\nTask Samples: input: 4 4\n0 1 1\n0 2 2\n1 3 3\n2 3 4\n output: 10\ninput: 4 5\n0 1 1\n0 2 2\n1 3 3\n2 3 4\n1 2 5\n output: 18\ninput: 2 3\n0 1 1\n0 1 2\n0 1 3\n output: 7\n\n" }, { "title": "Bitonic Traveling Salesman Problem (Bitonic TSP)", "content": "For given $N$ points in the 2D Euclidean plane, find the distance of the shortest tour that meets the following criteria:\n\nVisit the points according to the following steps:\n \nIt starts from the leftmost point (starting point), goes strictly from left to right, and then visits the rightmost point (turn-around point). \n\nThen it starts from the turn-around point, goes strictly from right to left, and then back to the starting point.\nThrough the processes 1.2. , the tour must visit each point at least once.", "constraint": "$2 <= N <= 1000$ \n\n $-1000 <= x_i, y_i <= 1000$\n\n $x_i$ differ from each other\n\n The given points are already sorted by x-coordinates", "input": "The input data is given in the following format:\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . . \n$x_N$ $y_N$", "output": "Print the distance of the shortest tour in a line. The output should not have an error greater than 0.0001.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0\n1 1\n2 0\n output: 4.82842712", "input: 4\n0 1\n1 2\n2 0\n3 1\n output: 7.30056308", "input: 5\n0 0\n1 2\n2 1\n3 2\n4 0\n output: 10.94427191"], "Pid": "p02325", "ProblemText": "Task Description: For given $N$ points in the 2D Euclidean plane, find the distance of the shortest tour that meets the following criteria:\n\nVisit the points according to the following steps:\n \nIt starts from the leftmost point (starting point), goes strictly from left to right, and then visits the rightmost point (turn-around point). \n\nThen it starts from the turn-around point, goes strictly from right to left, and then back to the starting point.\nThrough the processes 1.2. , the tour must visit each point at least once.\nTask Constraint: $2 <= N <= 1000$ \n\n $-1000 <= x_i, y_i <= 1000$\n\n $x_i$ differ from each other\n\n The given points are already sorted by x-coordinates\nTask Input: The input data is given in the following format:\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n. . . \n$x_N$ $y_N$\nTask Output: Print the distance of the shortest tour in a line. The output should not have an error greater than 0.0001.\nTask Samples: input: 3\n0 0\n1 1\n2 0\n output: 4.82842712\ninput: 4\n0 1\n1 2\n2 0\n3 1\n output: 7.30056308\ninput: 5\n0 0\n1 2\n2 1\n3 2\n4 0\n output: 10.94427191\n\n" }, { "title": "Largest Square", "content": "Given a matrix (H * W) which contains only 1 and 0, find the area of the largest square matrix which only contains 0s.", "constraint": "1 <= H, W <= 1,400", "input": "H W\nc_1,1 c_1,2 . . . c_1, W\nc_2,1 c_2,2 . . . c_2, W\n:\nc_H, 1 c_H, 2 . . . c_H, W\n\n In the first line, two integers H and W separated by a space character are given. In the following H lines, c_i, j, elements of the H * W matrix, are given.", "output": "Print the area (the number of 0s) of the largest square.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n0 0 1 0 0\n1 0 0 0 0\n0 0 0 1 0\n0 0 0 1 0\n output: 4"], "Pid": "p02326", "ProblemText": "Task Description: Given a matrix (H * W) which contains only 1 and 0, find the area of the largest square matrix which only contains 0s.\nTask Constraint: 1 <= H, W <= 1,400\nTask Input: H W\nc_1,1 c_1,2 . . . c_1, W\nc_2,1 c_2,2 . . . c_2, W\n:\nc_H, 1 c_H, 2 . . . c_H, W\n\n In the first line, two integers H and W separated by a space character are given. In the following H lines, c_i, j, elements of the H * W matrix, are given.\nTask Output: Print the area (the number of 0s) of the largest square.\nTask Samples: input: 4 5\n0 0 1 0 0\n1 0 0 0 0\n0 0 0 1 0\n0 0 0 1 0\n output: 4\n\n" }, { "title": "Largest Rectangle", "content": "Given a matrix (H * W) which contains only 1 and 0, find the area of the largest rectangle which only contains 0s.", "constraint": "1 <= H, W <= 1,400", "input": "H W\nc_1,1 c_1,2 . . . c_1, W\nc_2,1 c_2,2 . . . c_2, W\n:\nc_H, 1 c_H, 2 . . . c_H, W\n\n In the first line, two integers H and W separated by a space character are given. In the following H lines, c_i, j, elements of the H * W matrix, are given.", "output": "Print the area (the number of 0s) of the largest rectangle.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n0 0 1 0 0\n1 0 0 0 0\n0 0 0 1 0\n0 0 0 1 0\n output: 6"], "Pid": "p02327", "ProblemText": "Task Description: Given a matrix (H * W) which contains only 1 and 0, find the area of the largest rectangle which only contains 0s.\nTask Constraint: 1 <= H, W <= 1,400\nTask Input: H W\nc_1,1 c_1,2 . . . c_1, W\nc_2,1 c_2,2 . . . c_2, W\n:\nc_H, 1 c_H, 2 . . . c_H, W\n\n In the first line, two integers H and W separated by a space character are given. In the following H lines, c_i, j, elements of the H * W matrix, are given.\nTask Output: Print the area (the number of 0s) of the largest rectangle.\nTask Samples: input: 4 5\n0 0 1 0 0\n1 0 0 0 0\n0 0 0 1 0\n0 0 0 1 0\n output: 6\n\n" }, { "title": "Largest Rectangle in a Histogram", "content": "A histogram is made of a number of contiguous bars, which have same width.\n\n For a given histogram with $N$ bars which have a width of 1 and a height of $h_i$ = $h_1, h_2, . . . , h_N$ respectively, find the area of the largest rectangular area.", "constraint": "$1 <= N <= 10^5$ \n\n $0 <= h_i <= 10^9$", "input": "The input is given in the following format.\n$N$\n$h_1$ $h_2$ . . . $h_N$", "output": "Print the area of the largest rectangle.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 8\n2 1 3 5 3 4 2 1\n output: 12", "input: 3\n2 0 1\n output: 2"], "Pid": "p02328", "ProblemText": "Task Description: A histogram is made of a number of contiguous bars, which have same width.\n\n For a given histogram with $N$ bars which have a width of 1 and a height of $h_i$ = $h_1, h_2, . . . , h_N$ respectively, find the area of the largest rectangular area.\nTask Constraint: $1 <= N <= 10^5$ \n\n $0 <= h_i <= 10^9$\nTask Input: The input is given in the following format.\n$N$\n$h_1$ $h_2$ . . . $h_N$\nTask Output: Print the area of the largest rectangle.\nTask Samples: input: 8\n2 1 3 5 3 4 2 1\n output: 12\ninput: 3\n2 0 1\n output: 2\n\n" }, { "title": "Coin Combination Problem", "content": "You have 4 bags A, B, C and D each of which includes N coins (there are totally 4N coins). Values of the coins in each bag are a_i, b_i, c_i and d_i respectively.\n\n Find the number of combinations that result when you choose one coin from each bag (totally 4 coins) in such a way that the total value of the coins is V. You should distinguish the coins in a bag.", "constraint": "1 <= N <= 1000 \n\n 1 <= a_i, b_i, c_i, d_i <= 10^16\n\n 1 <= V <= 10^16\n\n All input values are given in integers", "input": "The input is given in the following format.\n\nN V\na_1 a_2 . . . a_N\nb_1 b_2 . . . b_N\nc_1 c_2 . . . c_N\nd_1 d_2 . . . d_N", "output": "Print the number of combinations in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 14\n3 1 2\n4 8 2\n1 2 3\n7 3 2\n output: 9", "input: 5 4\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n output: 625"], "Pid": "p02329", "ProblemText": "Task Description: You have 4 bags A, B, C and D each of which includes N coins (there are totally 4N coins). Values of the coins in each bag are a_i, b_i, c_i and d_i respectively.\n\n Find the number of combinations that result when you choose one coin from each bag (totally 4 coins) in such a way that the total value of the coins is V. You should distinguish the coins in a bag.\nTask Constraint: 1 <= N <= 1000 \n\n 1 <= a_i, b_i, c_i, d_i <= 10^16\n\n 1 <= V <= 10^16\n\n All input values are given in integers\nTask Input: The input is given in the following format.\n\nN V\na_1 a_2 . . . a_N\nb_1 b_2 . . . b_N\nc_1 c_2 . . . c_N\nd_1 d_2 . . . d_N\nTask Output: Print the number of combinations in a line.\nTask Samples: input: 3 14\n3 1 2\n4 8 2\n1 2 3\n7 3 2\n output: 9\ninput: 5 4\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n output: 625\n\n" }, { "title": "Coin Combination Problem II", "content": "You have N coins each of which has a value a_i.\nFind the number of combinations that result when you choose K different coins in such a way that the total value of the coins is greater than or equal to L and less than or equal to R.", "constraint": "1 <= K <= N <= 40 \n\n 1 <= a_i <= 10^16\n\n 1 <= L <= R <= 10^16\n\n All input values are given in integers", "input": "The input is given in the following format.\n\nN K L R\na_1 a_2 . . . a_N", "output": "Print the number of combinations in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 1 9\n5 1\n output: 1", "input: 5 2 7 19\n3 5 4 2 2\n output: 5"], "Pid": "p02330", "ProblemText": "Task Description: You have N coins each of which has a value a_i.\nFind the number of combinations that result when you choose K different coins in such a way that the total value of the coins is greater than or equal to L and less than or equal to R.\nTask Constraint: 1 <= K <= N <= 40 \n\n 1 <= a_i <= 10^16\n\n 1 <= L <= R <= 10^16\n\n All input values are given in integers\nTask Input: The input is given in the following format.\n\nN K L R\na_1 a_2 . . . a_N\nTask Output: Print the number of combinations in a line.\nTask Samples: input: 2 2 1 9\n5 1\n output: 1\ninput: 5 2 7 19\n3 5 4 2 2\n output: 5\n\n" }, { "title": "Balls and Boxes 1", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable
    1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n output: 9", "input: 10 5\n output: 9765625", "input: 100 100\n output: 424090053"], "Pid": "p02331", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable
    1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 2 3\n output: 9\ninput: 10 5\n output: 9765625\ninput: 100 100\n output: 424090053\n\n" }, { "title": "Balls and Boxes 2", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1
    2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n output: 6", "input: 3 2\n output: 0", "input: 100 100\n output: 437918130"], "Pid": "p02332", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1
    2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 2 3\n output: 6\ninput: 3 2\n output: 0\ninput: 100 100\n output: 437918130\n\n" }, { "title": "Balls and Boxes 3", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2
    3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n output: 36", "input: 10 3\n output: 55980", "input: 100 100\n output: 437918130"], "Pid": "p02333", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2
    3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 4 3\n output: 36\ninput: 10 3\n output: 55980\ninput: 100 100\n output: 437918130\n\n" }, { "title": "Balls and Boxes 4", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable
    4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n output: 21", "input: 10 5\n output: 1001", "input: 100 100\n output: 703668401"], "Pid": "p02334", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable
    4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 5 3\n output: 21\ninput: 10 5\n output: 1001\ninput: 100 100\n output: 703668401\n\n" }, { "title": "Balls and Boxes 5", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4
    5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n output: 10", "input: 5 10\n output: 252", "input: 100 200\n output: 407336795"], "Pid": "p02335", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4
    5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 3 5\n output: 10\ninput: 5 10\n output: 252\ninput: 100 200\n output: 407336795\n\n" }, { "title": "Balls and Boxes 6", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5
    6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n output: 6", "input: 10 5\n output: 126", "input: 100 30\n output: 253579538"], "Pid": "p02336", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5
    6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 5 3\n output: 6\ninput: 10 5\n output: 126\ninput: 100 30\n output: 253579538\n\n" }, { "title": "Balls and Boxes 7", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable
    7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n output: 5", "input: 5 3\n output: 41", "input: 100 100\n output: 193120002"], "Pid": "p02337", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable
    7 8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 3 5\n output: 5\ninput: 5 3\n output: 41\ninput: 100 100\n output: 193120002\n\n" }, { "title": "Balls and Boxes 8", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7
    8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 10\n output: 1", "input: 200 100\n output: 0"], "Pid": "p02338", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7
    8 9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 5 10\n output: 1\ninput: 200 100\n output: 0\n\n" }, { "title": "Balls and Boxes 9", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8
    9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n output: 6", "input: 10 5\n output: 42525", "input: 100 30\n output: 203169470"], "Pid": "p02339", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8
    9 \n\n Indistinguishable Indistinguishable 10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 4 3\n output: 6\ninput: 10 5\n output: 42525\ninput: 100 30\n output: 203169470\n\n" }, { "title": "Balls and Boxes 10", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable
    10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n output: 5", "input: 10 5\n output: 30", "input: 100 100\n output: 190569292"], "Pid": "p02340", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable
    10 11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain an arbitrary number of balls (including zero).\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 5 3\n output: 5\ninput: 10 5\n output: 30\ninput: 100 100\n output: 190569292\n\n" }, { "title": "Balls and Boxes 11", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10
    11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 10\n output: 1", "input: 200 100\n output: 0"], "Pid": "p02341", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10
    11 12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box can contain at most one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 5 10\n output: 1\ninput: 200 100\n output: 0\n\n" }, { "title": "Balls and Boxes 12", "content": "\n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11
    12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.", "constraint": "$1 <= n <= 1000$\n\n$1 <= k <= 1000$", "input": "$n$ $k$\nThe first line will contain two integers $n$ and $k$.", "output": "Print the number of ways modulo $10^9+7$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 5\n output: 7", "input: 30 15\n output: 176", "input: 100 30\n output: 3910071"], "Pid": "p02342", "ProblemText": "Task Description: \n Balls Boxes Any way At most one ball At least one ball \n\n Distinguishable Distinguishable 1 2 3 \n\n Indistinguishable Distinguishable 4 5 6 \n\n Distinguishable Indistinguishable 7 8 9 \n\n Indistinguishable Indistinguishable 10 11
    12 \n\n problem: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions:\nEach ball is not distinguished from the other.\n\nEach box is not distinguished from the other.\n\nEach ball can go into only one box and no one remains outside of the boxes.\n\nEach box must contain at least one ball.\n\nNote that you must print this count modulo $10^9+7$.\nTask Constraint: $1 <= n <= 1000$\n\n$1 <= k <= 1000$\nTask Input: $n$ $k$\nThe first line will contain two integers $n$ and $k$.\nTask Output: Print the number of ways modulo $10^9+7$ in a line.\nTask Samples: input: 10 5\n output: 7\ninput: 30 15\n output: 176\ninput: 100 30\n output: 3910071\n\n" }, { "title": "Disjoint Set", "content": "Write a program which manipulates a disjoint set S = {S_1, S_2, . . . , S_k}.\n\nFirst of all, the program should read an integer n, then make a disjoint set where each element consists of 0,1, . . . n-1 respectively.\n\nNext, the program should read an integer q and manipulate the set for q queries. There are two kinds of queries for different operations:\n\nunite(x, y): unites sets that contain x and y, say S_x and S_y, into a new set.\nsame(x, y): determine whether x and y are in the same set.", "constraint": "1 <= n <= 10000\n\n1 <= q <= 100000\n\nx != y", "input": "n q\ncom_1 x_1 y_1\ncom_2 x_2 y_2\n. . .\ncom_q x_q y_q\n\nIn the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.", "output": "For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 12\n0 1 4\n0 2 3\n1 1 2\n1 3 4\n1 1 4\n1 3 2\n0 1 3\n1 2 4\n1 3 0\n0 0 4\n1 0 2\n1 3 0\n output: 0\n0\n1\n1\n1\n0\n1\n1"], "Pid": "p02343", "ProblemText": "Task Description: Write a program which manipulates a disjoint set S = {S_1, S_2, . . . , S_k}.\n\nFirst of all, the program should read an integer n, then make a disjoint set where each element consists of 0,1, . . . n-1 respectively.\n\nNext, the program should read an integer q and manipulate the set for q queries. There are two kinds of queries for different operations:\n\nunite(x, y): unites sets that contain x and y, say S_x and S_y, into a new set.\nsame(x, y): determine whether x and y are in the same set.\nTask Constraint: 1 <= n <= 10000\n\n1 <= q <= 100000\n\nx != y\nTask Input: n q\ncom_1 x_1 y_1\ncom_2 x_2 y_2\n. . .\ncom_q x_q y_q\n\nIn the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.\nTask Output: For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.\nTask Samples: input: 5 12\n0 1 4\n0 2 3\n1 1 2\n1 3 4\n1 1 4\n1 3 2\n0 1 3\n1 2 4\n1 3 0\n0 0 4\n1 0 2\n1 3 0\n output: 0\n0\n1\n1\n1\n0\n1\n1\n\n" }, { "title": "Weighted Union Find Trees", "content": "There is a sequence $A = a_0, a_1, . . . , a_{n-1}$. You are given the following information and questions.\n\nrelate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$\n\ndiff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$", "constraint": "$2 <= n <= 100,000$\n\n $1 <= q <= 200,000$\n\n $0 <= x, y < n$\n\n $x \\ne y$\n\n $0 <= z <= 10000$\n\nThere are no inconsistency in the given information", "input": "$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.\n\n0 $x \\; y\\; z$\n\n or\n\n1 $x \\; y$\n\nwhere '0' of the first digit denotes the relate information and '1' denotes the diff question.", "output": "For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 6\n0 0 2 5\n0 1 2 3\n1 0 1\n1 1 3\n0 1 4 8\n1 0 4\n output: 2\n?\n10"], "Pid": "p02344", "ProblemText": "Task Description: There is a sequence $A = a_0, a_1, . . . , a_{n-1}$. You are given the following information and questions.\n\nrelate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$\n\ndiff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$\nTask Constraint: $2 <= n <= 100,000$\n\n $1 <= q <= 200,000$\n\n $0 <= x, y < n$\n\n $x \\ne y$\n\n $0 <= z <= 10000$\n\nThere are no inconsistency in the given information\nTask Input: $n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.\n\n0 $x \\; y\\; z$\n\n or\n\n1 $x \\; y$\n\nwhere '0' of the first digit denotes the relate information and '1' denotes the diff question.\nTask Output: For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.\nTask Samples: input: 5 6\n0 0 2 5\n0 1 2 3\n1 0 1\n1 1 3\n0 1 4 8\n1 0 4\n output: 2\n?\n10\n\n" }, { "title": "Range Minimum Query (RMQ)", "content": "Write a program which manipulates a sequence A = {a_0, a_1, . . . , a_n-1} with the following operations:\n\nfind(s, t): report the minimum element in a_s, a_s+1, . . . , a_t.\n\nupdate(i, x): change a_i to x.\nNote that the initial values of a_i (i = 0,1, . . . , n-1) are 2^31-1.", "constraint": "1 <= n <= 100000\n\n1 <= q <= 100000\n\nIf com_i is 0, then 0 <= x_i < n, 0 <= y_i < 2^31-1.\n\nIf com_i is 1, then 0 <= x_i < n, 0 <= y_i < n.", "input": "n q\ncom_0 x_0 y_0\ncom_1 x_1 y_1\n. . .\ncom_q-1 x_q-1 y_q-1\n\nIn the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes update(x_i, y_i) and '1' denotes find(x_i, y_i).", "output": "For each find operation, print the minimum element.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n0 0 1\n0 1 2\n0 2 3\n1 0 2\n1 1 2\n output: 1\n2", "input: 1 3\n1 0 0\n0 0 5\n1 0 0\n output: 2147483647\n5"], "Pid": "p02345", "ProblemText": "Task Description: Write a program which manipulates a sequence A = {a_0, a_1, . . . , a_n-1} with the following operations:\n\nfind(s, t): report the minimum element in a_s, a_s+1, . . . , a_t.\n\nupdate(i, x): change a_i to x.\nNote that the initial values of a_i (i = 0,1, . . . , n-1) are 2^31-1.\nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 100000\n\nIf com_i is 0, then 0 <= x_i < n, 0 <= y_i < 2^31-1.\n\nIf com_i is 1, then 0 <= x_i < n, 0 <= y_i < n.\nTask Input: n q\ncom_0 x_0 y_0\ncom_1 x_1 y_1\n. . .\ncom_q-1 x_q-1 y_q-1\n\nIn the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes update(x_i, y_i) and '1' denotes find(x_i, y_i).\nTask Output: For each find operation, print the minimum element.\nTask Samples: input: 3 5\n0 0 1\n0 1 2\n0 2 3\n1 0 2\n1 1 2\n output: 1\n2\ninput: 1 3\n1 0 0\n0 0 5\n1 0 0\n output: 2147483647\n5\n\n" }, { "title": "Range Sum Query", "content": "Write a program which manipulates a sequence A = {a_1, a_2, . . . , a_n} with the following operations:\n\nadd(i, x): add x to a_i.\n\nget Sum(s, t): print the sum of a_s, a_s+1, . . . , a_t.\nNote that the initial values of a_i (i = 1,2, . . . , n) are 0.", "constraint": "1 <= n <= 100000\n\n1 <= q <= 100000\n\nIf com_i is 0, then 1 <= x_i <= n, 0 <= y_i <= 1000.\n\nIf com_i is 1, then 1 <= x_i <= n, 1 <= y_i <= n.", "input": "n q\ncom_1 x_1 y_1\ncom_2 x_2 y_2\n. . .\ncom_q x_q y_q\n\nIn the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes add(x_i, y_i) and '1' denotes get Sum(x_i, y_i).", "output": "For each get Sum operation, print the sum in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n0 1 1\n0 2 2\n0 3 3\n1 1 2\n1 2 2\n output: 3\n2"], "Pid": "p02346", "ProblemText": "Task Description: Write a program which manipulates a sequence A = {a_1, a_2, . . . , a_n} with the following operations:\n\nadd(i, x): add x to a_i.\n\nget Sum(s, t): print the sum of a_s, a_s+1, . . . , a_t.\nNote that the initial values of a_i (i = 1,2, . . . , n) are 0.\nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 100000\n\nIf com_i is 0, then 1 <= x_i <= n, 0 <= y_i <= 1000.\n\nIf com_i is 1, then 1 <= x_i <= n, 1 <= y_i <= n.\nTask Input: n q\ncom_1 x_1 y_1\ncom_2 x_2 y_2\n. . .\ncom_q x_q y_q\n\nIn the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes add(x_i, y_i) and '1' denotes get Sum(x_i, y_i).\nTask Output: For each get Sum operation, print the sum in a line.\nTask Samples: input: 3 5\n0 1 1\n0 2 2\n0 3 3\n1 1 2\n1 2 2\n output: 3\n2\n\n" }, { "title": "Range Search (k D Tree)", "content": "The range search problem consists of a set of attributed records S to determine which records from S intersect with a given range.\n\nFor n points on a plane, report a set of points which are within in a given range. Note that you do not need to consider insert and delete operations for the set.", "constraint": "0 <= n <= 500,000\n\n0 <= q <= 20,000\n\n-1,000,000,000 <= x, y, sx, tx, sy, ty <= 1,000,000,000\n\nsx <= tx\n\nsy <= ty\n\nFor each query, the number of points which are within the range is less than or equal to 100.", "input": "n\nx_0 y_0\nx_1 y_1\n:\nx_n-1 y_n-1\nq\nsx_0 tx_0 sy_0 ty_0\nsx_1 tx_1 sy_1 ty_1\n:\nsx_q-1 tx_q-1 sy_q-1 ty_q-1\n\nThe first integer n is the number of points. In the following n lines, the coordinate of the i-th point is given by two integers x_i and y_i. \n\nThe next integer q is the number of queries. In the following q lines, each query is given by four integers, \nsx_i, \ntx_i, \nsy_i, \nty_i.", "output": "For each query, report IDs of points such that \nsx_i <= x <= tx_i and\nsy_i <= y <= ty_i.\nThe IDs should be reported in ascending order. Print an ID in a line, and print a blank line at the end of output for the each query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n2 1\n2 2\n4 2\n6 2\n3 3\n5 4\n2\n2 4 0 4\n4 10 2 5\n output: 0\n1\n2\n4\n\n2\n3\n5"], "Pid": "p02347", "ProblemText": "Task Description: The range search problem consists of a set of attributed records S to determine which records from S intersect with a given range.\n\nFor n points on a plane, report a set of points which are within in a given range. Note that you do not need to consider insert and delete operations for the set.\nTask Constraint: 0 <= n <= 500,000\n\n0 <= q <= 20,000\n\n-1,000,000,000 <= x, y, sx, tx, sy, ty <= 1,000,000,000\n\nsx <= tx\n\nsy <= ty\n\nFor each query, the number of points which are within the range is less than or equal to 100.\nTask Input: n\nx_0 y_0\nx_1 y_1\n:\nx_n-1 y_n-1\nq\nsx_0 tx_0 sy_0 ty_0\nsx_1 tx_1 sy_1 ty_1\n:\nsx_q-1 tx_q-1 sy_q-1 ty_q-1\n\nThe first integer n is the number of points. In the following n lines, the coordinate of the i-th point is given by two integers x_i and y_i. \n\nThe next integer q is the number of queries. In the following q lines, each query is given by four integers, \nsx_i, \ntx_i, \nsy_i, \nty_i.\nTask Output: For each query, report IDs of points such that \nsx_i <= x <= tx_i and\nsy_i <= y <= ty_i.\nThe IDs should be reported in ascending order. Print an ID in a line, and print a blank line at the end of output for the each query.\nTask Samples: input: 6\n2 1\n2 2\n4 2\n6 2\n3 3\n5 4\n2\n2 4 0 4\n4 10 2 5\n output: 0\n1\n2\n4\n\n2\n3\n5\n\n" }, { "title": "Range Update Query (RUQ)", "content": "Write a program which manipulates a sequence A = {a_0, a_1, . . . , a_n-1} with the following operations:\n\nupdate(s, t, x): change a_s, a_s+1, . . . , a_t to x.\n\nfind(i): output the value of a_i.\nNote that the initial values of a_i (i = 0,1, . . . , n-1) are 2^31-1.", "constraint": "1 <= n <= 100000\n\n1 <= q <= 100000\n\n0 <= s <= t < n\n\n0 <= i < n\n\n0 <= x < 2^31-1", "input": "n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 i\n\n The first digit represents the type of the query. '0' denotes update(s, t, x) and '1' denotes find(i).", "output": "For each find operation, print the value.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n0 0 1 1\n0 1 2 3\n0 2 2 2\n1 0\n1 1\n output: 1\n3", "input: 1 3\n1 0\n0 0 0 5\n1 0\n output: 2147483647\n5"], "Pid": "p02348", "ProblemText": "Task Description: Write a program which manipulates a sequence A = {a_0, a_1, . . . , a_n-1} with the following operations:\n\nupdate(s, t, x): change a_s, a_s+1, . . . , a_t to x.\n\nfind(i): output the value of a_i.\nNote that the initial values of a_i (i = 0,1, . . . , n-1) are 2^31-1.\nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 100000\n\n0 <= s <= t < n\n\n0 <= i < n\n\n0 <= x < 2^31-1\nTask Input: n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 i\n\n The first digit represents the type of the query. '0' denotes update(s, t, x) and '1' denotes find(i).\nTask Output: For each find operation, print the value.\nTask Samples: input: 3 5\n0 0 1 1\n0 1 2 3\n0 2 2 2\n1 0\n1 1\n output: 1\n3\ninput: 1 3\n1 0\n0 0 0 5\n1 0\n output: 2147483647\n5\n\n" }, { "title": "Range Add Query (RAQ)", "content": "Write a program which manipulates a sequence A = {a_1, a_2, . . . , a_n} with the following operations:\n\nadd(s, t, x): add x to a_s, a_s+1, . . . , a_t.\n\nget(i): output the value of a_i.\nNote that the initial values of a_i (i = 1,2, . . . , n) are 0.", "constraint": "1 <= n <= 100000\n\n1 <= q <= 100000\n\n1 <= s <= t <= n\n\n1 <= i <= n\n\n0 <= x <= 1000", "input": "n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 t\n\n The first digit represents the type of the query. '0' denotes add(s, t, x) and '1' denotes get(i).", "output": "For each get operation, print the value.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n0 1 2 1\n0 2 3 2\n0 3 3 3\n1 2\n1 3\n output: 3\n5", "input: 4 3\n1 2\n0 1 4 1\n1 2\n output: 0\n1"], "Pid": "p02349", "ProblemText": "Task Description: Write a program which manipulates a sequence A = {a_1, a_2, . . . , a_n} with the following operations:\n\nadd(s, t, x): add x to a_s, a_s+1, . . . , a_t.\n\nget(i): output the value of a_i.\nNote that the initial values of a_i (i = 1,2, . . . , n) are 0.\nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 100000\n\n1 <= s <= t <= n\n\n1 <= i <= n\n\n0 <= x <= 1000\nTask Input: n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 t\n\n The first digit represents the type of the query. '0' denotes add(s, t, x) and '1' denotes get(i).\nTask Output: For each get operation, print the value.\nTask Samples: input: 3 5\n0 1 2 1\n0 2 3 2\n0 3 3 3\n1 2\n1 3\n output: 3\n5\ninput: 4 3\n1 2\n0 1 4 1\n1 2\n output: 0\n1\n\n" }, { "title": "RMQ and RUQ", "content": "Write a program which manipulates a sequence A = {a_0, a_1, . . . , a_n-1} with the following operations:\n\nupdate(s, t, x): change a_s, a_s+1, . . . , a_t to x.\n\nfind(s, t): report the minimum element in a_s, a_s+1, . . . , a_t.\nNote that the initial values of a_i (i = 0,1, . . . , n-1) are 2^31-1.", "constraint": "1 <= n <= 100000\n\n1 <= q <= 100000\n\n0 <= s <= t < n\n\n0 <= x < 2^31-1", "input": "n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 s t\n\n The first digit represents the type of the query. '0' denotes update(s, t, x) and '1' denotes find(s, t).", "output": "For each find operation, print the minimum value.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n0 0 1 1\n0 1 2 3\n0 2 2 2\n1 0 2\n1 1 2\n output: 1\n2", "input: 1 3\n1 0 0\n0 0 0 5\n1 0 0\n output: 2147483647\n5"], "Pid": "p02350", "ProblemText": "Task Description: Write a program which manipulates a sequence A = {a_0, a_1, . . . , a_n-1} with the following operations:\n\nupdate(s, t, x): change a_s, a_s+1, . . . , a_t to x.\n\nfind(s, t): report the minimum element in a_s, a_s+1, . . . , a_t.\nNote that the initial values of a_i (i = 0,1, . . . , n-1) are 2^31-1.\nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 100000\n\n0 <= s <= t < n\n\n0 <= x < 2^31-1\nTask Input: n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 s t\n\n The first digit represents the type of the query. '0' denotes update(s, t, x) and '1' denotes find(s, t).\nTask Output: For each find operation, print the minimum value.\nTask Samples: input: 3 5\n0 0 1 1\n0 1 2 3\n0 2 2 2\n1 0 2\n1 1 2\n output: 1\n2\ninput: 1 3\n1 0 0\n0 0 0 5\n1 0 0\n output: 2147483647\n5\n\n" }, { "title": "RSQ and RAQ", "content": "Write a program which manipulates a sequence A = {a_1, a_2, . . . , a_n} with the following operations:\n\nadd(s, t, x): add x to a_s, a_s+1, . . . , a_t.\n\nget Sum(s, t): report the sum of a_s, a_s+1, . . . , a_t.\nNote that the initial values of a_i (i = 1,2, . . . , n) are 0.", "constraint": "1 <= n <= 100000\n\n1 <= q <= 100000\n\n1 <= s <= t <= n\n\n0 <= x < 1000", "input": "n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 s t\n\n The first digit represents the type of the query. '0' denotes add(s, t, x) and '1' denotes get Sum(s, t).", "output": "For each get Sum operation, print the sum;", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n0 1 2 1\n0 2 3 2\n0 3 3 3\n1 1 2\n1 2 3\n output: 4\n8", "input: 4 3\n1 1 4\n0 1 4 1\n1 1 4\n output: 0\n4"], "Pid": "p02351", "ProblemText": "Task Description: Write a program which manipulates a sequence A = {a_1, a_2, . . . , a_n} with the following operations:\n\nadd(s, t, x): add x to a_s, a_s+1, . . . , a_t.\n\nget Sum(s, t): report the sum of a_s, a_s+1, . . . , a_t.\nNote that the initial values of a_i (i = 1,2, . . . , n) are 0.\nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 100000\n\n1 <= s <= t <= n\n\n0 <= x < 1000\nTask Input: n q\nquery_1\nquery_2\n:\nquery_q\n\n In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query query_i is given in the following format:\n\n0 s t x \n\n or\n\n1 s t\n\n The first digit represents the type of the query. '0' denotes add(s, t, x) and '1' denotes get Sum(s, t).\nTask Output: For each get Sum operation, print the sum;\nTask Samples: input: 3 5\n0 1 2 1\n0 2 3 2\n0 3 3 3\n1 1 2\n1 2 3\n output: 4\n8\ninput: 4 3\n1 1 4\n0 1 4 1\n1 1 4\n output: 0\n4\n\n" }, { "title": "RMQ and RAQ", "content": "Write a program which manipulates a sequence $A$ = {$a_0, a_1, . . . , a_{n-1}$} with the following operations:\n\n $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, . . . , a_t$.\n\n $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, . . . , a_t$.\n Note that the initial values of $a_i ( i = 0,1, . . . , n-1 )$ are 0.", "constraint": "$1 <= n <= 100000$\n\n$1 <= q <= 100000$\n\n$0 <= s <= t < n$\n\n$-1000 <= x <= 1000$", "input": "$n$ $q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format:\n\n0 $s$ $t$ $x$\nor\n1 $s$ $t$\n\n The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$.", "output": "For each $find$ query, print the minimum value.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 7\n0 1 3 1\n0 2 4 -2\n1 0 5\n1 0 1\n0 3 5 3\n1 3 4\n1 0 5\n output: -2\n0\n1\n-1"], "Pid": "p02352", "ProblemText": "Task Description: Write a program which manipulates a sequence $A$ = {$a_0, a_1, . . . , a_{n-1}$} with the following operations:\n\n $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, . . . , a_t$.\n\n $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, . . . , a_t$.\n Note that the initial values of $a_i ( i = 0,1, . . . , n-1 )$ are 0.\nTask Constraint: $1 <= n <= 100000$\n\n$1 <= q <= 100000$\n\n$0 <= s <= t < n$\n\n$-1000 <= x <= 1000$\nTask Input: $n$ $q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format:\n\n0 $s$ $t$ $x$\nor\n1 $s$ $t$\n\n The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$.\nTask Output: For each $find$ query, print the minimum value.\nTask Samples: input: 6 7\n0 1 3 1\n0 2 4 -2\n1 0 5\n1 0 1\n0 3 5 3\n1 3 4\n1 0 5\n output: -2\n0\n1\n-1\n\n" }, { "title": "RSQ and RUQ", "content": "Write a program which manipulates a sequence $A$ = {$a_0, a_1, . . . , a_{n-1}$} with the following operations:\n $update(s, t, x)$: change $a_s, a_{s+1}, . . . , a_t$ to $x$.\n\n $get Sum(s, t)$: print the sum of $a_s, a_{s+1}, . . . , a_t$.\n\n Note that the initial values of $a_i ( i = 0,1, . . . , n-1 )$ are 0.", "constraint": "$1 <= n <= 100000$\n\n$1 <= q <= 100000$\n\n$0 <= s <= t < n$\n\n$-1000 <= x <= 1000$", "input": "$n$ $q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nIn the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$-th query $query_i$ is given in the following format:\n\n0 $s$ $t$ $x$\nor\n1 $s$ $t$\n\n The first digit represents the type of the query. '0' denotes $update(s, t, x)$\n and '1' denotes $find(s, t)$.", "output": "For each $get Sum$ query, print the sum in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 7\n0 1 3 1\n0 2 4 -2\n1 0 5\n1 0 1\n0 3 5 3\n1 3 4\n1 0 5\n output: -5\n1\n6\n8"], "Pid": "p02353", "ProblemText": "Task Description: Write a program which manipulates a sequence $A$ = {$a_0, a_1, . . . , a_{n-1}$} with the following operations:\n $update(s, t, x)$: change $a_s, a_{s+1}, . . . , a_t$ to $x$.\n\n $get Sum(s, t)$: print the sum of $a_s, a_{s+1}, . . . , a_t$.\n\n Note that the initial values of $a_i ( i = 0,1, . . . , n-1 )$ are 0.\nTask Constraint: $1 <= n <= 100000$\n\n$1 <= q <= 100000$\n\n$0 <= s <= t < n$\n\n$-1000 <= x <= 1000$\nTask Input: $n$ $q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nIn the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$-th query $query_i$ is given in the following format:\n\n0 $s$ $t$ $x$\nor\n1 $s$ $t$\n\n The first digit represents the type of the query. '0' denotes $update(s, t, x)$\n and '1' denotes $find(s, t)$.\nTask Output: For each $get Sum$ query, print the sum in a line.\nTask Samples: input: 6 7\n0 1 3 1\n0 2 4 -2\n1 0 5\n1 0 1\n0 3 5 3\n1 3 4\n1 0 5\n output: -5\n1\n6\n8\n\n" }, { "title": "The Smallest Window I", "content": "For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and an integer $S$, find the smallest sub-array size (smallest window length) where the sum of the sub-array is greater than or equal to $S$. If there is not such sub-array, report 0.", "constraint": "$1 <= N <= 10^5$ \n\n $1 <= S <= 10^9$\n\n $1 <= a_i <= 10^4$", "input": "The input is given in the following format.\n$N$ $S$\n$a_1$ $a_2$ . . . $a_N$", "output": "Print the smallest sub-array size in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 4\n1 2 1 2 3 2\n output: 2", "input: 6 6\n1 2 1 2 3 2\n output: 3", "input: 3 7\n1 2 3\n output: 0"], "Pid": "p02354", "ProblemText": "Task Description: For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and an integer $S$, find the smallest sub-array size (smallest window length) where the sum of the sub-array is greater than or equal to $S$. If there is not such sub-array, report 0.\nTask Constraint: $1 <= N <= 10^5$ \n\n $1 <= S <= 10^9$\n\n $1 <= a_i <= 10^4$\nTask Input: The input is given in the following format.\n$N$ $S$\n$a_1$ $a_2$ . . . $a_N$\nTask Output: Print the smallest sub-array size in a line.\nTask Samples: input: 6 4\n1 2 1 2 3 2\n output: 2\ninput: 6 6\n1 2 1 2 3 2\n output: 3\ninput: 3 7\n1 2 3\n output: 0\n\n" }, { "title": "The Smallest Window II", "content": "For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and an integer $K$, find the smallest sub-array size (smallest window length) where the elements in the sub-array contains all integers in range [$1,2, . . . , K$]. If there is no such sub-array, report 0.", "constraint": "$1 <= N <= 10^5$ \n\n $1 <= K <= 10^5$\n\n $1 <= a_i <= 10^5$", "input": "The input is given in the following format.\n$N$ $K$\n$a_1$ $a_2$ . . . $a_N$", "output": "Print the smallest sub-array size in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 2\n4 1 2 1 3 5\n output: 2", "input: 6 3\n4 1 2 1 3 5\n output: 3", "input: 3 4\n1 2 3\n output: 0"], "Pid": "p02355", "ProblemText": "Task Description: For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and an integer $K$, find the smallest sub-array size (smallest window length) where the elements in the sub-array contains all integers in range [$1,2, . . . , K$]. If there is no such sub-array, report 0.\nTask Constraint: $1 <= N <= 10^5$ \n\n $1 <= K <= 10^5$\n\n $1 <= a_i <= 10^5$\nTask Input: The input is given in the following format.\n$N$ $K$\n$a_1$ $a_2$ . . . $a_N$\nTask Output: Print the smallest sub-array size in a line.\nTask Samples: input: 6 2\n4 1 2 1 3 5\n output: 2\ninput: 6 3\n4 1 2 1 3 5\n output: 3\ninput: 3 4\n1 2 3\n output: 0\n\n" }, { "title": "The Number of Windows", "content": "For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and $Q$ integers $x_i$ as queries, for each query, print the number of combinations of two integers $(l, r)$ which satisfies the condition: $1 <= l <= r <= N$ and $a_l + a_{l+1} + . . . + a_{r-1} + a_r <= x_i$.", "constraint": "$1 <= N <= 10^5$ \n\n $1 <= Q <= 500$\n\n $1 <= a_i <= 10^9$\n\n $1 <= x_i <= 10^{14}$", "input": "The input is given in the following format.\n$N$ $Q$\n$a_1$ $a_2$ . . . $a_N$\n$x_1$ $x_2$ . . . $x_Q$", "output": "For each query, print the number of combinations in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 5\n1 2 3 4 5 6\n6 9 12 21 15\n output: 9\n12\n15\n21\n18"], "Pid": "p02356", "ProblemText": "Task Description: For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and $Q$ integers $x_i$ as queries, for each query, print the number of combinations of two integers $(l, r)$ which satisfies the condition: $1 <= l <= r <= N$ and $a_l + a_{l+1} + . . . + a_{r-1} + a_r <= x_i$.\nTask Constraint: $1 <= N <= 10^5$ \n\n $1 <= Q <= 500$\n\n $1 <= a_i <= 10^9$\n\n $1 <= x_i <= 10^{14}$\nTask Input: The input is given in the following format.\n$N$ $Q$\n$a_1$ $a_2$ . . . $a_N$\n$x_1$ $x_2$ . . . $x_Q$\nTask Output: For each query, print the number of combinations in a line.\nTask Samples: input: 6 5\n1 2 3 4 5 6\n6 9 12 21 15\n output: 9\n12\n15\n21\n18\n\n" }, { "title": "Sliding Minimum Element", "content": "For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1,7,7,4,8,1,6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1,7,7\\}$, $\\{7,7,4\\}$, $\\{7,4,8\\}$, $\\{4,8,1\\}$, $\\{8,1,6\\}$ and the minimum of each sub-array is 1,4,4,1,1 respectively.", "constraint": "$1 <= N <= 10^6$ \n\n $1 <= L <= 10^6$\n\n $1 <= a_i <= 10^9$\n\n $L <= N$", "input": "The input is given in the following format.\n$N$ $L$\n$a_1$ $a_2$ . . . $a_N$", "output": "Print a sequence of the minimum in a line. Print a space character between adjacent elements.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 3\n1 7 7 4 8 1 6\n output: 1 4 4 1 1"], "Pid": "p02357", "ProblemText": "Task Description: For a given array $a_1, a_2, a_3, . . . , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1,7,7,4,8,1,6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1,7,7\\}$, $\\{7,7,4\\}$, $\\{7,4,8\\}$, $\\{4,8,1\\}$, $\\{8,1,6\\}$ and the minimum of each sub-array is 1,4,4,1,1 respectively.\nTask Constraint: $1 <= N <= 10^6$ \n\n $1 <= L <= 10^6$\n\n $1 <= a_i <= 10^9$\n\n $L <= N$\nTask Input: The input is given in the following format.\n$N$ $L$\n$a_1$ $a_2$ . . . $a_N$\nTask Output: Print a sequence of the minimum in a line. Print a space character between adjacent elements.\nTask Samples: input: 7 3\n1 7 7 4 8 1 6\n output: 1 4 4 1 1\n\n" }, { "title": "Union of Rectangles", "content": "Given a set of $N$ axis-aligned rectangles in the plane, find the area of regions which are covered by at least one rectangle.", "constraint": "$ 1 <= N <= 2000 $\n\n$ -10^9 <= x1_i < x2_i<= 10^9 $\n\n$ -10^9 <= y1_i < y2_i<= 10^9 $", "input": "The input is given in the following format.\n\n$N$\n$x1_1$ $y1_1$ $x2_1$ $y2_1$\n$x1_2$ $y1_2$ $x2_2$ $y2_2$\n: \n$x1_N$ $y1_N$ $x2_N$ $y2_N$\n\n($x1_i, y1_i$) and ($x2_i, y2_i$) are the coordinates of the top-left corner and the bottom-right corner of the $i$-th rectangle respectively.", "output": "Print the area of the regions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0 3 4\n1 2 4 3\n output: 13", "input: 3\n1 1 2 5\n2 1 5 2\n1 2 2 5\n output: 7", "input: 4\n0 0 3 1\n0 0 1 3\n0 2 3 3\n2 0 3 3\n output: 8"], "Pid": "p02358", "ProblemText": "Task Description: Given a set of $N$ axis-aligned rectangles in the plane, find the area of regions which are covered by at least one rectangle.\nTask Constraint: $ 1 <= N <= 2000 $\n\n$ -10^9 <= x1_i < x2_i<= 10^9 $\n\n$ -10^9 <= y1_i < y2_i<= 10^9 $\nTask Input: The input is given in the following format.\n\n$N$\n$x1_1$ $y1_1$ $x2_1$ $y2_1$\n$x1_2$ $y1_2$ $x2_2$ $y2_2$\n: \n$x1_N$ $y1_N$ $x2_N$ $y2_N$\n\n($x1_i, y1_i$) and ($x2_i, y2_i$) are the coordinates of the top-left corner and the bottom-right corner of the $i$-th rectangle respectively.\nTask Output: Print the area of the regions.\nTask Samples: input: 2\n0 0 3 4\n1 2 4 3\n output: 13\ninput: 3\n1 1 2 5\n2 1 5 2\n1 2 2 5\n output: 7\ninput: 4\n0 0 3 1\n0 0 1 3\n0 2 3 3\n2 0 3 3\n output: 8\n\n" }, { "title": "The Maximum Number of Customers", "content": "$N$ persons visited a restaurant. The restaurant is open from 0 to $T$. The $i$-th person entered the restaurant at $l_i$ and left at $r_i$. Find the maximum number of persons during the business hours.", "constraint": "$ 1 <= N <= 10^5 $\n\n$ 1 <= T <= 10^5 $\n\n$ 0 <= l_i < r_i <= T $", "input": "The input is given in the following format.\n\n$N$ $T$\n$l_1$ $r_1$\n$l_2$ $r_2$\n: \n$l_N$ $r_N$", "output": "Print the maximum number of persons in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 10\n0 2\n1 3\n2 6\n3 8\n4 10\n5 10\n output: 4", "input: 2 2\n0 1\n1 2\n output: 1"], "Pid": "p02359", "ProblemText": "Task Description: $N$ persons visited a restaurant. The restaurant is open from 0 to $T$. The $i$-th person entered the restaurant at $l_i$ and left at $r_i$. Find the maximum number of persons during the business hours.\nTask Constraint: $ 1 <= N <= 10^5 $\n\n$ 1 <= T <= 10^5 $\n\n$ 0 <= l_i < r_i <= T $\nTask Input: The input is given in the following format.\n\n$N$ $T$\n$l_1$ $r_1$\n$l_2$ $r_2$\n: \n$l_N$ $r_N$\nTask Output: Print the maximum number of persons in a line.\nTask Samples: input: 6 10\n0 2\n1 3\n2 6\n3 8\n4 10\n5 10\n output: 4\ninput: 2 2\n0 1\n1 2\n output: 1\n\n" }, { "title": "The Maximum Number of Overlaps", "content": "Given a set of $N$ axis-aligned rectangular seals, find the number of overlapped seals on the region which has the maximum number of overlapped seals.", "constraint": "$ 1 <= N <= 100000 $\n\n$ 0 <= x1_i < x2_i <= 1000 $\n\n$ 0 <= y1_i < y2_i <= 1000 $\n\n$ x1_i, y1_i, x2_i, y2_i$ are given in integers", "input": "The input is given in the following format.\n\n$N$\n$x1_1$ $y1_1$ $x2_1$ $y2_1$\n$x1_2$ $y1_2$ $x2_2$ $y2_2$\n: \n$x1_N$ $y1_N$ $x2_N$ $y2_N$\n\n($x1_i, y1_i$) and ($x2_i, y2_i$) are the coordinates of the top-left and the bottom-right corner of the $i$-th seal respectively.", "output": "Print the maximum number of overlapped seals in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0 3 2\n2 1 4 3\n output: 2", "input: 2\n0 0 2 2\n2 0 4 2\n output: 1", "input: 3\n0 0 2 2\n0 0 2 2\n0 0 2 2\n output: 3"], "Pid": "p02360", "ProblemText": "Task Description: Given a set of $N$ axis-aligned rectangular seals, find the number of overlapped seals on the region which has the maximum number of overlapped seals.\nTask Constraint: $ 1 <= N <= 100000 $\n\n$ 0 <= x1_i < x2_i <= 1000 $\n\n$ 0 <= y1_i < y2_i <= 1000 $\n\n$ x1_i, y1_i, x2_i, y2_i$ are given in integers\nTask Input: The input is given in the following format.\n\n$N$\n$x1_1$ $y1_1$ $x2_1$ $y2_1$\n$x1_2$ $y1_2$ $x2_2$ $y2_2$\n: \n$x1_N$ $y1_N$ $x2_N$ $y2_N$\n\n($x1_i, y1_i$) and ($x2_i, y2_i$) are the coordinates of the top-left and the bottom-right corner of the $i$-th seal respectively.\nTask Output: Print the maximum number of overlapped seals in a line.\nTask Samples: input: 2\n0 0 3 2\n2 1 4 3\n output: 2\ninput: 2\n0 0 2 2\n2 0 4 2\n output: 1\ninput: 3\n0 0 2 2\n0 0 2 2\n0 0 2 2\n output: 3\n\n" }, { "title": "Single Source Shortest Path", "content": "For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).", "constraint": "1 <= |V| <= 100000\n\n0 <= d_i <= 10000\n\n 0 <= |E| <= 500000\n\n There are no parallel edges\n\n There are no self-loops", "input": "An edge-weighted graph G (V, E) and the source r.\n\n|V| |E| r\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively. r is the source of the graph.\n\ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the cost of the i-th edge.", "output": "Print the costs of SSSP in the following format.\n\nc_0\nc_1\n:\nc_|V|-1\n\nThe output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0,1, . . . |V|-1 in order. If there is no path from the source to a vertex, print INF.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 0\n0 1 1\n0 2 4\n1 2 2\n2 3 1\n1 3 5\n output: 0\n1\n3\n4", "input: 4 6 1\n0 1 1\n0 2 4\n2 0 1\n1 2 2\n3 1 1\n3 2 5\n output: 3\n0\n2\nINF"], "Pid": "p02361", "ProblemText": "Task Description: For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).\nTask Constraint: 1 <= |V| <= 100000\n\n0 <= d_i <= 10000\n\n 0 <= |E| <= 500000\n\n There are no parallel edges\n\n There are no self-loops\nTask Input: An edge-weighted graph G (V, E) and the source r.\n\n|V| |E| r\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively. r is the source of the graph.\n\ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the cost of the i-th edge.\nTask Output: Print the costs of SSSP in the following format.\n\nc_0\nc_1\n:\nc_|V|-1\n\nThe output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0,1, . . . |V|-1 in order. If there is no path from the source to a vertex, print INF.\nTask Samples: input: 4 5 0\n0 1 1\n0 2 4\n1 2 2\n2 3 1\n1 3 5\n output: 0\n1\n3\n4\ninput: 4 6 1\n0 1 1\n0 2 4\n2 0 1\n1 2 2\n3 1 1\n3 2 5\n output: 3\n0\n2\nINF\n\n" }, { "title": "Single Source Shortest Path (Negative Edges)", "content": "", "constraint": "1 <= |V| <= 1000\n\n 0 <= |E| <= 2000\n\n -10000 <= d_i <= 10000\n\n There are no parallel edges\n\n There are no self-loops", "input": "an edge-weighted graph g (v, e) and the source r.\n \n|v| |e| r\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|e|-1 t_|e|-1 d_|e|-1\n \n|v| is the number of vertices and |e| is the number of edges in g. the graph vertices are named with the numbers 0,1, . . . , |v|-1 respectively. r is the source of the graph.\n \ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the cost of the i-th edge.", "output": "INF", "content_img": false, "lang": "en", "error": true, "samples": ["input: 4 5 0\n0 1 2\n0 2 3\n1 2 -5\n1 3 1\n2 3 2\n output: 0\n2\n-3\n-1", "input: 4 6 0\n0 1 2\n0 2 3\n1 2 -5\n1 3 1\n2 3 2\n3 1 0\n output: negative cycle", "input: 4 5 1\n0 1 2\n0 2 3\n1 2 -5\n1 3 1\n2 3 2\n output: inf\n0\n-5\n-3"], "Pid": "p02362", "ProblemText": "Task Description: \nTask Constraint: 1 <= |V| <= 1000\n\n 0 <= |E| <= 2000\n\n -10000 <= d_i <= 10000\n\n There are no parallel edges\n\n There are no self-loops\nTask Input: an edge-weighted graph g (v, e) and the source r.\n \n|v| |e| r\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|e|-1 t_|e|-1 d_|e|-1\n \n|v| is the number of vertices and |e| is the number of edges in g. the graph vertices are named with the numbers 0,1, . . . , |v|-1 respectively. r is the source of the graph.\n \ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the cost of the i-th edge.\nTask Output: INF\nTask Samples: input: 4 5 0\n0 1 2\n0 2 3\n1 2 -5\n1 3 1\n2 3 2\n output: 0\n2\n-3\n-1\ninput: 4 6 0\n0 1 2\n0 2 3\n1 2 -5\n1 3 1\n2 3 2\n3 1 0\n output: negative cycle\ninput: 4 5 1\n0 1 2\n0 2 3\n1 2 -5\n1 3 1\n2 3 2\n output: inf\n0\n-5\n-3\n\n" }, { "title": "All Pairs Shortest Path", "content": "", "constraint": "1 <= |V| <= 100\n\n 0 <= |E| <= 9900\n\n -2 * 10^7 <= d_i <= 2 * 10^7\n\n There are no parallel edges\n\n There are no self-loops", "input": "An edge-weighted graph G (V, E).\n\n|V| |E|\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the cost of the i-th edge.", "output": "If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value), print \nNEGATIVE CYCLE\n\n

    \nin a line.\nOtherwise, print\nD_0,0 D_0,1 . . . D_0, |V|-1\nD_1,0 D_1,1 . . . D_1, |V|-1\n:\nD_|V|-1,0 D_1,1 . . . D_|V|-1, |V|-1\nThe output consists of |V| lines. For each ith line, print the cost of the shortest path from vertex i to each vertex j (j = 0,1, . . . |V|-1) respectively. If there is no path from vertex i to vertex j, print \"INF\". Print a space between the costs.", "content_img": false, "lang": "en", "error": true, "samples": ["input: 4 6\n0 1 1\n0 2 5\n1 2 2\n1 3 4\n2 3 1\n3 2 7\n output: 0 1 3 4\nINF 0 2 3\nINF INF 0 1\nINF INF 7 0", "input: 4 6\n0 1 1\n0 2 -5\n1 2 2\n1 3 4\n2 3 1\n3 2 7\n output: 0 1 -5 -4\nINF 0 2 3\nINF INF 0 1\nINF INF 7 0", "input: 4 6\n0 1 1\n0 2 5\n1 2 2\n1 3 4\n2 3 1\n3 2 -7\n output: NEGATIVE CYCLE"], "Pid": "p02363", "ProblemText": "Task Description: \nTask Constraint: 1 <= |V| <= 100\n\n 0 <= |E| <= 9900\n\n -2 * 10^7 <= d_i <= 2 * 10^7\n\n There are no parallel edges\n\n There are no self-loops\nTask Input: An edge-weighted graph G (V, E).\n\n|V| |E|\ns_0 t_0 d_0\ns_1 t_1 d_1\n:\ns_|E|-1 t_|E|-1 d_|E|-1\n\n|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target vertices of i-th edge (directed) and d_i represents the cost of the i-th edge.\nTask Output: If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value), print \nNEGATIVE CYCLE\n\n

    \nin a line.\nOtherwise, print\nD_0,0 D_0,1 . . . D_0, |V|-1\nD_1,0 D_1,1 . . . D_1, |V|-1\n:\nD_|V|-1,0 D_1,1 . . . D_|V|-1, |V|-1\nThe output consists of |V| lines. For each ith line, print the cost of the shortest path from vertex i to each vertex j (j = 0,1, . . . |V|-1) respectively. If there is no path from vertex i to vertex j, print \"INF\". Print a space between the costs.\nTask Samples: input: 4 6\n0 1 1\n0 2 5\n1 2 2\n1 3 4\n2 3 1\n3 2 7\n output: 0 1 3 4\nINF 0 2 3\nINF INF 0 1\nINF INF 7 0\ninput: 4 6\n0 1 1\n0 2 -5\n1 2 2\n1 3 4\n2 3 1\n3 2 7\n output: 0 1 -5 -4\nINF 0 2 3\nINF INF 0 1\nINF INF 7 0\ninput: 4 6\n0 1 1\n0 2 5\n1 2 2\n1 3 4\n2 3 1\n3 2 -7\n output: NEGATIVE CYCLE\n\n" }, { "title": "Minimum Spanning Tree", "content": "Find the sum of weights of edges of the Minimum Spanning Tree for a given weighted undirected graph G = (V, E).", "constraint": "1 <= |V| <= 10,000\n\n0 <= |E| <= 100,000\n\n0 <= w_i <= 10,000\n\nThe graph is connected\n\nThere are no parallel edges\n\nThere are no self-loops", "input": "|V| |E|\ns_0 t_0 w_0\ns_1 t_1 w_1\n:\ns_|E|-1 t_|E|-1 w_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target verticess of i-th edge (undirected) and w_i represents the weight of the i-th edge.", "output": "Print the sum of the weights of the Minimum Spanning Tree.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n0 1 2\n1 2 1\n2 3 1\n3 0 1\n0 2 3\n1 3 5\n output: 3", "input: 6 9\n0 1 1\n0 2 3\n1 2 1\n1 3 7\n2 4 1\n1 4 3\n3 4 1\n3 5 1\n4 5 6\n output: 5"], "Pid": "p02364", "ProblemText": "Task Description: Find the sum of weights of edges of the Minimum Spanning Tree for a given weighted undirected graph G = (V, E).\nTask Constraint: 1 <= |V| <= 10,000\n\n0 <= |E| <= 100,000\n\n0 <= w_i <= 10,000\n\nThe graph is connected\n\nThere are no parallel edges\n\nThere are no self-loops\nTask Input: |V| |E|\ns_0 t_0 w_0\ns_1 t_1 w_1\n:\ns_|E|-1 t_|E|-1 w_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target verticess of i-th edge (undirected) and w_i represents the weight of the i-th edge.\nTask Output: Print the sum of the weights of the Minimum Spanning Tree.\nTask Samples: input: 4 6\n0 1 2\n1 2 1\n2 3 1\n3 0 1\n0 2 3\n1 3 5\n output: 3\ninput: 6 9\n0 1 1\n0 2 3\n1 2 1\n1 3 7\n2 4 1\n1 4 3\n3 4 1\n3 5 1\n4 5 6\n output: 5\n\n" }, { "title": "Minimum-Cost Arborescence", "content": "Find the sum of the weights of edges of the Minimum-Cost Arborescence with the root r for a given weighted directed graph G = (V, E).", "constraint": "1 <= |V| <= 100\n\n0 <= |E| <= 1,000\n\n0 <= w_i <= 10,000\n\nG has arborescence(s) with the root r", "input": "|V| |E| r\ns_0 t_0 w_0\ns_1 t_1 w_1\n:\ns_|E|-1 t_|E|-1 w_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively. r is the root of the Minimum-Cost Arborescence.\n\ns_i and t_i represent source and target verticess of i-th directed edge. w_i represents the weight of the i-th directed edge.", "output": "Print the sum of the weights the Minimum-Cost Arborescence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6 0\n0 1 3\n0 2 2\n2 0 1\n2 3 1\n3 0 1\n3 1 5\n output: 6", "input: 6 10 0\n0 2 7\n0 1 1\n0 3 5\n1 4 9\n2 1 6\n1 3 2\n3 4 3\n4 2 2\n2 5 8\n3 5 3\n output: 11"], "Pid": "p02365", "ProblemText": "Task Description: Find the sum of the weights of edges of the Minimum-Cost Arborescence with the root r for a given weighted directed graph G = (V, E).\nTask Constraint: 1 <= |V| <= 100\n\n0 <= |E| <= 1,000\n\n0 <= w_i <= 10,000\n\nG has arborescence(s) with the root r\nTask Input: |V| |E| r\ns_0 t_0 w_0\ns_1 t_1 w_1\n:\ns_|E|-1 t_|E|-1 w_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively. r is the root of the Minimum-Cost Arborescence.\n\ns_i and t_i represent source and target verticess of i-th directed edge. w_i represents the weight of the i-th directed edge.\nTask Output: Print the sum of the weights the Minimum-Cost Arborescence.\nTask Samples: input: 4 6 0\n0 1 3\n0 2 2\n2 0 1\n2 3 1\n3 0 1\n3 1 5\n output: 6\ninput: 6 10 0\n0 2 7\n0 1 1\n0 3 5\n1 4 9\n2 1 6\n1 3 2\n3 4 3\n4 2 2\n2 5 8\n3 5 3\n output: 11\n\n" }, { "title": "Articulation Points", "content": "Find articulation points of a given undirected graph G(V, E).\n\nA vertex in an undirected graph is an articulation point (or cut vertex) iff removing it disconnects the graph.", "constraint": "1 <= |V| <= 100,000\n\n0 <= |E| <= 100,000\n\nThe graph is connected\n\nThere are no parallel edges\n\nThere are no self-loops", "input": "|V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target verticess of i-th edge (undirected).", "output": "A list of articulation points of the graph G ordered by name.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n0 1\n0 2\n1 2\n2 3\n output: 2", "input: 5 4\n0 1\n1 2\n2 3\n3 4\n output: 1\n2\n3"], "Pid": "p02366", "ProblemText": "Task Description: Find articulation points of a given undirected graph G(V, E).\n\nA vertex in an undirected graph is an articulation point (or cut vertex) iff removing it disconnects the graph.\nTask Constraint: 1 <= |V| <= 100,000\n\n0 <= |E| <= 100,000\n\nThe graph is connected\n\nThere are no parallel edges\n\nThere are no self-loops\nTask Input: |V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\n\n, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target verticess of i-th edge (undirected).\nTask Output: A list of articulation points of the graph G ordered by name.\nTask Samples: input: 4 4\n0 1\n0 2\n1 2\n2 3\n output: 2\ninput: 5 4\n0 1\n1 2\n2 3\n3 4\n output: 1\n2\n3\n\n" }, { "title": "Bridges", "content": "Find bridges of an undirected graph G(V, E).\n\nA bridge (also known as a cut-edge) is an edge whose deletion increase the number of connected components.", "constraint": "1 <= |V| <= 100,000\n\n0 <= |E| <= 100,000\n\nThe graph is connected\n\nThere are no parallel edges\n\nThere are no self-loops", "input": "|V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\n\n, where |V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target nodes of i-th edge (undirected).", "output": "A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n0 1\n0 2\n1 2\n2 3\n output: 2 3", "input: 5 4\n0 1\n1 2\n2 3\n3 4\n output: 0 1\n1 2\n2 3\n3 4"], "Pid": "p02367", "ProblemText": "Task Description: Find bridges of an undirected graph G(V, E).\n\nA bridge (also known as a cut-edge) is an edge whose deletion increase the number of connected components.\nTask Constraint: 1 <= |V| <= 100,000\n\n0 <= |E| <= 100,000\n\nThe graph is connected\n\nThere are no parallel edges\n\nThere are no self-loops\nTask Input: |V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\n\n, where |V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target nodes of i-th edge (undirected).\nTask Output: A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.\nTask Samples: input: 4 4\n0 1\n0 2\n1 2\n2 3\n output: 2 3\ninput: 5 4\n0 1\n1 2\n2 3\n3 4\n output: 0 1\n1 2\n2 3\n3 4\n\n" }, { "title": "Strongly Connected Components", "content": "A direced graph is strongly connected if every two nodes are reachable from each other. In a strongly connected component of a directed graph, every two nodes of the component are mutually reachable.", "constraint": "1 <= |V| <= 10,000\n\n0 <= |E| <= 30,000\n\n1 <= Q <= 100,000", "input": "A directed graph G(V, E) and a sequence of queries where each query contains a pair of nodes u and v.\n\n|V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\nQ\nu_0 v_0\nu_1 v_1\n:\nu_Q-1 v_Q-1\n\n|V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target nodes of i-th edge (directed).\n\nu_i and v_i represent a pair of nodes given as the i-th query.", "output": "For each query, pinrt \"1\" if the given nodes belong to the same strongly connected component, \"0\" otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 6\n0 1\n1 0\n1 2\n2 4\n4 3\n3 2\n4\n0 1\n0 3\n2 3\n3 4\n output: 1\n0\n1\n1"], "Pid": "p02368", "ProblemText": "Task Description: A direced graph is strongly connected if every two nodes are reachable from each other. In a strongly connected component of a directed graph, every two nodes of the component are mutually reachable.\nTask Constraint: 1 <= |V| <= 10,000\n\n0 <= |E| <= 30,000\n\n1 <= Q <= 100,000\nTask Input: A directed graph G(V, E) and a sequence of queries where each query contains a pair of nodes u and v.\n\n|V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\nQ\nu_0 v_0\nu_1 v_1\n:\nu_Q-1 v_Q-1\n\n|V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target nodes of i-th edge (directed).\n\nu_i and v_i represent a pair of nodes given as the i-th query.\nTask Output: For each query, pinrt \"1\" if the given nodes belong to the same strongly connected component, \"0\" otherwise.\nTask Samples: input: 5 6\n0 1\n1 0\n1 2\n2 4\n4 3\n3 2\n4\n0 1\n0 3\n2 3\n3 4\n output: 1\n0\n1\n1\n\n" }, { "title": "Cycle Detection for a Directed Graph", "content": "Find a cycle in a directed graph G(V, E).", "constraint": "1 <= |V| <= 100\n\n 0 <= |E| <= 1,000\n\n s_i != t_i", "input": "A directed graph G is given in the following format:\n\n|V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\n\n|V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target nodes of i-th edge (directed).", "output": "Print 1 if G has cycle(s), 0 otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n0 1\n0 2\n1 2\n output: 0", "input: 3 3\n0 1\n1 2\n2 0\n output: 1"], "Pid": "p02369", "ProblemText": "Task Description: Find a cycle in a directed graph G(V, E).\nTask Constraint: 1 <= |V| <= 100\n\n 0 <= |E| <= 1,000\n\n s_i != t_i\nTask Input: A directed graph G is given in the following format:\n\n|V| |E|\ns_0 t_0\ns_1 t_1\n:\ns_|E|-1 t_|E|-1\n\n|V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0,1, . . . , |V|-1 respectively.\n\ns_i and t_i represent source and target nodes of i-th edge (directed).\nTask Output: Print 1 if G has cycle(s), 0 otherwise.\nTask Samples: input: 3 3\n0 1\n0 2\n1 2\n output: 0\ninput: 3 3\n0 1\n1 2\n2 0\n output: 1\n\n" }, { "title": "Topological Sort", "content": "A directed acyclic graph (DAG) can be used to represent the ordering of tasks. Tasks are represented by vertices and constraints where one task can begin before another, are represented by edges. For example, in the above example, you can undertake task B after both task A and task B are finished. You can obtain the proper sequence of all the tasks by a topological sort.\n\nGiven a DAG $G$, print the order of vertices after the topological sort.", "constraint": "$1 <= |V| <= 10,000$\n\n $0 <= |E| <= 100,000$\n\n There are no parallel edges in $G$\n\n There are no self loops in $G$", "input": "A directed graph $G$ is given in the following format:\n$|V|\\; |E|$\n$s_0 \\; t_0$\n$s_1 \\; t_1$\n: \n$s_{|E|-1} \\; t_{|E|-1}$\n$|V|$ is the number of vertices and $|E|$ is the number of edges in the graph. The graph vertices are named with the numbers $0,1, . . . , |V|-1$ respectively.\n\n$s_i$ and $t_i$ represent source and target nodes of $i$-th edge (directed).", "output": "Print the vertices numbers in order. Print a number in a line.\n\nIf there are multiple possible solutions, print any one of them (the solution is judged by a special validator).", "content_img": true, "lang": "en", "error": false, "samples": ["input: 6 6\n0 1\n1 2\n3 1\n3 4\n4 5\n5 2\n output: 0\n3\n1\n4\n5\n2"], "Pid": "p02370", "ProblemText": "Task Description: A directed acyclic graph (DAG) can be used to represent the ordering of tasks. Tasks are represented by vertices and constraints where one task can begin before another, are represented by edges. For example, in the above example, you can undertake task B after both task A and task B are finished. You can obtain the proper sequence of all the tasks by a topological sort.\n\nGiven a DAG $G$, print the order of vertices after the topological sort.\nTask Constraint: $1 <= |V| <= 10,000$\n\n $0 <= |E| <= 100,000$\n\n There are no parallel edges in $G$\n\n There are no self loops in $G$\nTask Input: A directed graph $G$ is given in the following format:\n$|V|\\; |E|$\n$s_0 \\; t_0$\n$s_1 \\; t_1$\n: \n$s_{|E|-1} \\; t_{|E|-1}$\n$|V|$ is the number of vertices and $|E|$ is the number of edges in the graph. The graph vertices are named with the numbers $0,1, . . . , |V|-1$ respectively.\n\n$s_i$ and $t_i$ represent source and target nodes of $i$-th edge (directed).\nTask Output: Print the vertices numbers in order. Print a number in a line.\n\nIf there are multiple possible solutions, print any one of them (the solution is judged by a special validator).\nTask Samples: input: 6 6\n0 1\n1 2\n3 1\n3 4\n4 5\n5 2\n output: 0\n3\n1\n4\n5\n2\n\n" }, { "title": "", "content": "Given a tree T with non-negative weight, find the diameter of the tree. The diameter of a tree is the maximum distance between two nodes in a tree.", "constraint": "1 <= n <= 100,000\n\n 0 <= w_i <= 1,000", "input": "n\ns_1 t_1 w_1\ns_2 t_2 w_2\n:\ns_n-1 t_n-1 w_n-1\n\nThe first line consists of an integer n which represents the number of nodes in the tree. Every node has a unique ID from 0 to n-1 respectively.\n\nIn the following n-1 lines, edges of the tree are given.\n\ns_i and t_i represent end-points of the i-th edge (undirected) and w_i represents the weight (distance) of the i-th edge.", "output": "Print the diameter of the tree in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 1 2\n1 2 1\n1 3 3\n output: 5", "input: 4\n0 1 1\n1 2 2\n2 3 4\n output: 7"], "Pid": "p02371", "ProblemText": "Task Description: Given a tree T with non-negative weight, find the diameter of the tree. The diameter of a tree is the maximum distance between two nodes in a tree.\nTask Constraint: 1 <= n <= 100,000\n\n 0 <= w_i <= 1,000\nTask Input: n\ns_1 t_1 w_1\ns_2 t_2 w_2\n:\ns_n-1 t_n-1 w_n-1\n\nThe first line consists of an integer n which represents the number of nodes in the tree. Every node has a unique ID from 0 to n-1 respectively.\n\nIn the following n-1 lines, edges of the tree are given.\n\ns_i and t_i represent end-points of the i-th edge (undirected) and w_i represents the weight (distance) of the i-th edge.\nTask Output: Print the diameter of the tree in a line.\nTask Samples: input: 4\n0 1 2\n1 2 1\n1 3 3\n output: 5\ninput: 4\n0 1 1\n1 2 2\n2 3 4\n output: 7\n\n" }, { "title": "Height of a Tree", "content": "Given a tree T with non-negative weight, find the height of each node of the tree. For each node, the height is the distance to the most distant leaf from the node.", "constraint": "1 <= n <= 10,000\n\n 0 <= w_i <= 1,000", "input": "n\ns_1 t_1 w_1\ns_2 t_2 w_2\n:\ns_n-1 t_n-1 w_n-1\n\nThe first line consists of an integer n which represents the number of nodes in the tree. Every node has a unique ID from 0 to n-1 respectively.\n\nIn the following n-1 lines, edges of the tree are given.\n\ns_i and t_i represent end-points of the i-th edge (undirected) and w_i represents the weight (distance) of the i-th edge.", "output": "The output consists of n lines. Print the height of each node 0,1,2, . . . , n-1 in order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 1 2\n1 2 1\n1 3 3\n output: 5\n3\n4\n5"], "Pid": "p02372", "ProblemText": "Task Description: Given a tree T with non-negative weight, find the height of each node of the tree. For each node, the height is the distance to the most distant leaf from the node.\nTask Constraint: 1 <= n <= 10,000\n\n 0 <= w_i <= 1,000\nTask Input: n\ns_1 t_1 w_1\ns_2 t_2 w_2\n:\ns_n-1 t_n-1 w_n-1\n\nThe first line consists of an integer n which represents the number of nodes in the tree. Every node has a unique ID from 0 to n-1 respectively.\n\nIn the following n-1 lines, edges of the tree are given.\n\ns_i and t_i represent end-points of the i-th edge (undirected) and w_i represents the weight (distance) of the i-th edge.\nTask Output: The output consists of n lines. Print the height of each node 0,1,2, . . . , n-1 in order.\nTask Samples: input: 4\n0 1 2\n1 2 1\n1 3 3\n output: 5\n3\n4\n5\n\n" }, { "title": "LCA: Lowest Common Ancestor", "content": "For a rooted tree, find the lowest common ancestor of two nodes u and v.\n\nThe given tree consists of n nodes and every node has a unique ID from 0 to n-1 where 0 is the root.", "constraint": "1 <= n <= 100000\n\n1 <= q <= 100000", "input": "n\nk_0 c_1 c_2 . . . c_k0\nk_1 c_1 c_2 . . . c_k1\n:\nk_n-1 c_1 c_2 . . . c_kn-1\nq\nu_1 v_1\nu_2 v_2\n:\nu_q v_q\n\nThe first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n lines, the information of node i is given. k_i is the number of children of node i, and c_1, . . . c_ki are node IDs of 1st, . . . kth child of node i. \n\nIn the next line, the number of queryies q is given. In the next q lines, pairs of u and v are given as the queries.", "output": "For each query, print the LCA of u and v in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n3 1 2 3\n2 4 5\n0\n0\n0\n2 6 7\n0\n0\n4\n4 6\n4 7\n4 3\n5 2\n output: 1\n1\n0\n0"], "Pid": "p02373", "ProblemText": "Task Description: For a rooted tree, find the lowest common ancestor of two nodes u and v.\n\nThe given tree consists of n nodes and every node has a unique ID from 0 to n-1 where 0 is the root.\nTask Constraint: 1 <= n <= 100000\n\n1 <= q <= 100000\nTask Input: n\nk_0 c_1 c_2 . . . c_k0\nk_1 c_1 c_2 . . . c_k1\n:\nk_n-1 c_1 c_2 . . . c_kn-1\nq\nu_1 v_1\nu_2 v_2\n:\nu_q v_q\n\nThe first line of the input includes an integer n, the number of nodes of the tree.\n\nIn the next n lines, the information of node i is given. k_i is the number of children of node i, and c_1, . . . c_ki are node IDs of 1st, . . . kth child of node i. \n\nIn the next line, the number of queryies q is given. In the next q lines, pairs of u and v are given as the queries.\nTask Output: For each query, print the LCA of u and v in a line.\nTask Samples: input: 8\n3 1 2 3\n2 4 5\n0\n0\n0\n2 6 7\n0\n0\n4\n4 6\n4 7\n4 3\n5 2\n output: 1\n1\n0\n0\n\n" }, { "title": "Range Query on a Tree", "content": "Write a program which manipulates a weighted rooted tree $T$ with the following operations:\n\n$add(v, w)$: add $w$ to the edge which connects node $v$ and its parent\n$get Sum(u)$: report the sum of weights of all edges from the root to node $u$\n The given tree $T$ consists of $n$ nodes and every node has a unique ID from $0$ to $n-1$ respectively where ID of the root is $0$.\n Note that all weights are initialized to zero.", "constraint": "All the inputs are given in integers\n\n$ 2 <= n <= 100000 $\n\n$ c_j < c_{j+1} $   $( 1 <= j <= k-1 )$\n\n$ 2 <= q <= 200000 $\n\n$ 1 <= u,v <= n-1 $\n\n$ 1 <= w <= 10000 $", "input": "The input is given in the following format.\n\n$n$\n$node_0$\n$node_1$\n$node_2$\n$: $\n$node_{n-1}$\n$q$\n$query_1$\n$query_2$\n$: $\n$query_{q}$\n\n The first line of the input includes an integer $n$, the number of nodes in the tree.\n\n In the next $n$ lines, the information of node $i$ is given in the following format:\n\nk_i c_1 c_2 . . . c_k\n\n $k_i$ is the number of children of node $i$, and $c_1$ $c_2$ . . . $c_{k_i}$ are node IDs of 1st, . . . $k$th child of node $i$.\n\n In the next line, the number of queries $q$ is given. In the next $q$ lines, $i$th query is given in the following format:\n\n0 v w\n\nor\n\n1 u\n\n The first integer represents the type of queries. '0' denotes $add(v, w)$ and '1' denotes $get Sum(u)$.", "output": "For each $get Sum$ query, print the sum in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n2 1 2\n2 3 5\n0\n0\n0\n1 4\n7\n1 1\n0 3 10\n1 2\n0 4 20\n1 3\n0 5 40\n1 4\n output: 0\n0\n10\n60", "input: 4\n1 1\n1 2\n1 3\n0\n6\n0 3 1000\n0 2 1000\n0 1 1000\n1 1\n1 2\n1 3\n output: 1000\n2000\n3000", "input: 2\n1 1\n0\n4\n0 1 1\n1 1\n0 1 1\n1 1\n output: 1\n2"], "Pid": "p02374", "ProblemText": "Task Description: Write a program which manipulates a weighted rooted tree $T$ with the following operations:\n\n$add(v, w)$: add $w$ to the edge which connects node $v$ and its parent\n$get Sum(u)$: report the sum of weights of all edges from the root to node $u$\n The given tree $T$ consists of $n$ nodes and every node has a unique ID from $0$ to $n-1$ respectively where ID of the root is $0$.\n Note that all weights are initialized to zero.\nTask Constraint: All the inputs are given in integers\n\n$ 2 <= n <= 100000 $\n\n$ c_j < c_{j+1} $   $( 1 <= j <= k-1 )$\n\n$ 2 <= q <= 200000 $\n\n$ 1 <= u,v <= n-1 $\n\n$ 1 <= w <= 10000 $\nTask Input: The input is given in the following format.\n\n$n$\n$node_0$\n$node_1$\n$node_2$\n$: $\n$node_{n-1}$\n$q$\n$query_1$\n$query_2$\n$: $\n$query_{q}$\n\n The first line of the input includes an integer $n$, the number of nodes in the tree.\n\n In the next $n$ lines, the information of node $i$ is given in the following format:\n\nk_i c_1 c_2 . . . c_k\n\n $k_i$ is the number of children of node $i$, and $c_1$ $c_2$ . . . $c_{k_i}$ are node IDs of 1st, . . . $k$th child of node $i$.\n\n In the next line, the number of queries $q$ is given. In the next $q$ lines, $i$th query is given in the following format:\n\n0 v w\n\nor\n\n1 u\n\n The first integer represents the type of queries. '0' denotes $add(v, w)$ and '1' denotes $get Sum(u)$.\nTask Output: For each $get Sum$ query, print the sum in a line.\nTask Samples: input: 6\n2 1 2\n2 3 5\n0\n0\n0\n1 4\n7\n1 1\n0 3 10\n1 2\n0 4 20\n1 3\n0 5 40\n1 4\n output: 0\n0\n10\n60\ninput: 4\n1 1\n1 2\n1 3\n0\n6\n0 3 1000\n0 2 1000\n0 1 1000\n1 1\n1 2\n1 3\n output: 1000\n2000\n3000\ninput: 2\n1 1\n0\n4\n0 1 1\n1 1\n0 1 1\n1 1\n output: 1\n2\n\n" }, { "title": "Range Query on a Tree II", "content": "Write a program which manipulates a weighted rooted tree $T$ with the following operations:\n\n$add(v, w)$: add $w$ to all edges from the root to node $u$\n$get Sum(u)$: report the sum of weights of all edges from the root to node $u$\n The given tree $T$ consists of $n$ nodes and every node has a unique ID from $0$ to $n-1$ respectively where ID of the root is $0$.\n Note that all weights are initialized to zero.", "constraint": "All the inputs are given in integers\n\n$ 2 <= n <= 100000 $\n\n$ c_j < c_{j+1} $   $( 1 <= j <= k-1 )$\n\n$ 2 <= q <= 200000 $\n\n$ 1 <= u,v <= n-1 $\n\n$ 1 <= w <= 10000 $", "input": "The input is given in the following format.\n\n$n$\n$node_0$\n$node_1$\n$node_2$\n$: $\n$node_{n-1}$\n$q$\n$query_1$\n$query_2$\n$: $\n$query_{q}$\n\n The first line of the input includes an integer $n$, the number of nodes in the tree.\n\n In the next $n$ lines, the information of node $i$ is given in the following format:\n\nk_i c_1 c_2 . . . c_k\n\n $k_i$ is the number of children of node $i$, and $c_1$ $c_2$ . . . $c_{k_i}$ are node IDs of 1st, . . . $k$th child of node $i$.\n\n In the next line, the number of queries $q$ is given. In the next $q$ lines, $i$th query is given in the following format:\n\n0 v w\n\nor\n\n1 u\n\n The first integer represents the type of queries. '0' denotes $add(v, w)$ and '1' denotes $get Sum(u)$.", "output": "For each $get Sum$ query, print the sum in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n2 1 2\n2 3 5\n0\n0\n0\n1 4\n7\n1 1\n0 3 10\n1 2\n0 4 20\n1 3\n0 5 40\n1 4\n output: 0\n0\n40\n150", "input: 4\n1 1\n1 2\n1 3\n0\n6\n0 3 1000\n0 2 1000\n0 1 1000\n1 1\n1 2\n1 3\n output: 3000\n5000\n6000"], "Pid": "p02375", "ProblemText": "Task Description: Write a program which manipulates a weighted rooted tree $T$ with the following operations:\n\n$add(v, w)$: add $w$ to all edges from the root to node $u$\n$get Sum(u)$: report the sum of weights of all edges from the root to node $u$\n The given tree $T$ consists of $n$ nodes and every node has a unique ID from $0$ to $n-1$ respectively where ID of the root is $0$.\n Note that all weights are initialized to zero.\nTask Constraint: All the inputs are given in integers\n\n$ 2 <= n <= 100000 $\n\n$ c_j < c_{j+1} $   $( 1 <= j <= k-1 )$\n\n$ 2 <= q <= 200000 $\n\n$ 1 <= u,v <= n-1 $\n\n$ 1 <= w <= 10000 $\nTask Input: The input is given in the following format.\n\n$n$\n$node_0$\n$node_1$\n$node_2$\n$: $\n$node_{n-1}$\n$q$\n$query_1$\n$query_2$\n$: $\n$query_{q}$\n\n The first line of the input includes an integer $n$, the number of nodes in the tree.\n\n In the next $n$ lines, the information of node $i$ is given in the following format:\n\nk_i c_1 c_2 . . . c_k\n\n $k_i$ is the number of children of node $i$, and $c_1$ $c_2$ . . . $c_{k_i}$ are node IDs of 1st, . . . $k$th child of node $i$.\n\n In the next line, the number of queries $q$ is given. In the next $q$ lines, $i$th query is given in the following format:\n\n0 v w\n\nor\n\n1 u\n\n The first integer represents the type of queries. '0' denotes $add(v, w)$ and '1' denotes $get Sum(u)$.\nTask Output: For each $get Sum$ query, print the sum in a line.\nTask Samples: input: 6\n2 1 2\n2 3 5\n0\n0\n0\n1 4\n7\n1 1\n0 3 10\n1 2\n0 4 20\n1 3\n0 5 40\n1 4\n output: 0\n0\n40\n150\ninput: 4\n1 1\n1 2\n1 3\n0\n6\n0 3 1000\n0 2 1000\n0 1 1000\n1 1\n1 2\n1 3\n output: 3000\n5000\n6000\n\n" }, { "title": "Maximum Flow", "content": "A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.", "constraint": "$2 <= |V| <= 100$\n\n $1 <= |E| <= 1000$\n\n $0 <= c_i <= 10000$", "input": "A flow network is given in the following format.\n\n$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0,1, . . . , $|V|-1$. The source is 0 and the sink is $|V|-1$.\n\n$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network.\nA pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.", "output": "Print the maximum flow.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n0 1 2\n0 2 1\n1 2 1\n1 3 1\n2 3 2\n output: 3"], "Pid": "p02376", "ProblemText": "Task Description: A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.\nTask Constraint: $2 <= |V| <= 100$\n\n $1 <= |E| <= 1000$\n\n $0 <= c_i <= 10000$\nTask Input: A flow network is given in the following format.\n\n$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0,1, . . . , $|V|-1$. The source is 0 and the sink is $|V|-1$.\n\n$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network.\nA pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.\nTask Output: Print the maximum flow.\nTask Samples: input: 4 5\n0 1 2\n0 2 1\n1 2 1\n1 3 1\n2 3 2\n output: 3\n\n" }, { "title": "Minimum Cost Flow", "content": "Find the minimum cost to send a certain amount of flow through a flow network.\n\n The flow network is a directed graph where each edge $e$ has capacity $c(e)$ and cost $d(e)$. Each edge $e$ can send an amount of flow $f(e)$ where $f(e) <= c(e)$. Find the minimum value of $\\sum_{e} (f(e) * d(e))$ to send an amount of flow $F$ from source $s$ to sink $t$.", "constraint": "2 <= $|V|$ <= 100\n\n 1 <= $|E|$ <= 1000\n\n 0 <= $F$ <= 1000\n\n 0 <= $c_i$, $d_i$ <= 1000\n\n $u_i$ $\\ne$ $v_i$\n\n If there is an edge from vertex $x$ to vertex $y$, there is no edge from vertex $y$ to vertex $x$.", "input": "A flow network $G(V, E)$ is given in the following format.\n\n$|V|\\; |E|\\; F$\n$u_0\\; v_0\\; c_0\\; d_0$\n$u_1\\; v_1\\; c_1\\; d_1$\n: \n$u_{|E|1}\\; v_{|E|-1}\\; c_{|E|-1}\\; d_{|E|-1}$\n\n $|V|$, $|E|$, $F$ are the number of vertices, the number of edges, and the amount of flow of the flow network respectively. The vertices in $G$ are named with the numbers $0,1, . . . , |V|-1$. The source is $0$ and the sink is $|V|-1$.\n\n$u_i$, $v_i$, $c_i$, $d_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$, and $c_i$ and $d_i$ are the capacity and the cost of $i$-th edge respectively.", "output": "Print the minimum value in a line. If it is impossible to send the flow from the source $s$ to the sink $t$, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1\n output: 6"], "Pid": "p02377", "ProblemText": "Task Description: Find the minimum cost to send a certain amount of flow through a flow network.\n\n The flow network is a directed graph where each edge $e$ has capacity $c(e)$ and cost $d(e)$. Each edge $e$ can send an amount of flow $f(e)$ where $f(e) <= c(e)$. Find the minimum value of $\\sum_{e} (f(e) * d(e))$ to send an amount of flow $F$ from source $s$ to sink $t$.\nTask Constraint: 2 <= $|V|$ <= 100\n\n 1 <= $|E|$ <= 1000\n\n 0 <= $F$ <= 1000\n\n 0 <= $c_i$, $d_i$ <= 1000\n\n $u_i$ $\\ne$ $v_i$\n\n If there is an edge from vertex $x$ to vertex $y$, there is no edge from vertex $y$ to vertex $x$.\nTask Input: A flow network $G(V, E)$ is given in the following format.\n\n$|V|\\; |E|\\; F$\n$u_0\\; v_0\\; c_0\\; d_0$\n$u_1\\; v_1\\; c_1\\; d_1$\n: \n$u_{|E|1}\\; v_{|E|-1}\\; c_{|E|-1}\\; d_{|E|-1}$\n\n $|V|$, $|E|$, $F$ are the number of vertices, the number of edges, and the amount of flow of the flow network respectively. The vertices in $G$ are named with the numbers $0,1, . . . , |V|-1$. The source is $0$ and the sink is $|V|-1$.\n\n$u_i$, $v_i$, $c_i$, $d_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$, and $c_i$ and $d_i$ are the capacity and the cost of $i$-th edge respectively.\nTask Output: Print the minimum value in a line. If it is impossible to send the flow from the source $s$ to the sink $t$, print -1.\nTask Samples: input: 4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1\n output: 6\n\n" }, { "title": "Bipartite Matching", "content": "A bipartite graph G = (V, E) is a graph in which the vertex set V can be divided into two disjoint subsets X and Y such that every edge e ∈ E has one end point in X and the other end point in Y.\n\nA matching M is a subset of edges such that each node in V appears in at most one edge in M.\n\nGiven a bipartite graph, find the size of the matching which has the largest size.", "constraint": "1 <= |X|, |Y| <= 100\n\n0 <= |E| <= 10,000", "input": "|X| |Y| |E|\nx_0 y_0\nx_1 y_1\n:\nx_|E|-1 y_|E|-1\n\n|X| and |Y| are the number of vertices in X and Y respectively, and |E| is the number of edges in the graph G. The vertices in X are named with the numbers 0,1, . . . , |X|-1, and vertices in Y are named with the numbers 0,1, . . . , |Y|-1, respectively.\n\nx_i and y_i are the node numbers from X and Y respectevely which represent the end-points of the i-th edge.", "output": "Print the largest size of the matching.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 6\n0 0\n0 2\n0 3\n1 1\n2 1\n2 3\n output: 3"], "Pid": "p02378", "ProblemText": "Task Description: A bipartite graph G = (V, E) is a graph in which the vertex set V can be divided into two disjoint subsets X and Y such that every edge e ∈ E has one end point in X and the other end point in Y.\n\nA matching M is a subset of edges such that each node in V appears in at most one edge in M.\n\nGiven a bipartite graph, find the size of the matching which has the largest size.\nTask Constraint: 1 <= |X|, |Y| <= 100\n\n0 <= |E| <= 10,000\nTask Input: |X| |Y| |E|\nx_0 y_0\nx_1 y_1\n:\nx_|E|-1 y_|E|-1\n\n|X| and |Y| are the number of vertices in X and Y respectively, and |E| is the number of edges in the graph G. The vertices in X are named with the numbers 0,1, . . . , |X|-1, and vertices in Y are named with the numbers 0,1, . . . , |Y|-1, respectively.\n\nx_i and y_i are the node numbers from X and Y respectevely which represent the end-points of the i-th edge.\nTask Output: Print the largest size of the matching.\nTask Samples: input: 3 4 6\n0 0\n0 2\n0 3\n1 1\n2 1\n2 3\n output: 3\n\n" }, { "title": "Distance", "content": "Write a program which calculates the distance between two points P1(x1, y1) and P2(x2, y2).", "constraint": "", "input": "Four real numbers x1, y1, x2 and y2 are given in a line.", "output": "Print the distance in real number. The output should not contain an absolute error greater than 10^-4.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0 1 1\n output: 1.41421356"], "Pid": "p02379", "ProblemText": "Task Description: Write a program which calculates the distance between two points P1(x1, y1) and P2(x2, y2).\nTask Input: Four real numbers x1, y1, x2 and y2 are given in a line.\nTask Output: Print the distance in real number. The output should not contain an absolute error greater than 10^-4.\nTask Samples: input: 0 0 1 1\n output: 1.41421356\n\n" }, { "title": "Triangle", "content": "For given two sides of a triangle a and b and the angle C between them, calculate the following properties:\n\nS: Area of the triangle\n\nL: The length of the circumference of the triangle\n\nh: The height of the triangle with side a as a bottom edge", "constraint": "", "input": "The length of a, the length of b and the angle C are given in integers.", "output": "Print S, L and h in a line respectively. The output should not contain an absolute error greater than 10^-4.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 90\n output: 6.00000000\n12.00000000\n3.00000000"], "Pid": "p02380", "ProblemText": "Task Description: For given two sides of a triangle a and b and the angle C between them, calculate the following properties:\n\nS: Area of the triangle\n\nL: The length of the circumference of the triangle\n\nh: The height of the triangle with side a as a bottom edge\nTask Input: The length of a, the length of b and the angle C are given in integers.\nTask Output: Print S, L and h in a line respectively. The output should not contain an absolute error greater than 10^-4.\nTask Samples: input: 4 3 90\n output: 6.00000000\n12.00000000\n3.00000000\n\n" }, { "title": "Standard Deviation", "content": "You have final scores of an examination for n students. Calculate standard deviation of the scores s_1, s_2 . . . s_n.\n\nThe variance α^2 is defined by \n\nα^2 = (∑^n_i=1(s_i - m)^2)/n\n\n where m is an average of s_i.\n\n The standard deviation of the scores is the square root of their variance.", "constraint": "n <= 1000\n\n0 <= s_i <= 100", "input": "The input consists of multiple datasets. Each dataset is given in the following format:\n\nn\ns_1 s_2 . . . s_n\n\n The input ends with single zero for n.", "output": "For each dataset, print the standard deviation in a line. The output should not contain an absolute error greater than 10^-4.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n70 80 100 90 20\n3\n80 80 80\n0\n output: 27.85677655\n0.00000000"], "Pid": "p02381", "ProblemText": "Task Description: You have final scores of an examination for n students. Calculate standard deviation of the scores s_1, s_2 . . . s_n.\n\nThe variance α^2 is defined by \n\nα^2 = (∑^n_i=1(s_i - m)^2)/n\n\n where m is an average of s_i.\n\n The standard deviation of the scores is the square root of their variance.\nTask Constraint: n <= 1000\n\n0 <= s_i <= 100\nTask Input: The input consists of multiple datasets. Each dataset is given in the following format:\n\nn\ns_1 s_2 . . . s_n\n\n The input ends with single zero for n.\nTask Output: For each dataset, print the standard deviation in a line. The output should not contain an absolute error greater than 10^-4.\nTask Samples: input: 5\n70 80 100 90 20\n3\n80 80 80\n0\n output: 27.85677655\n0.00000000\n\n" }, { "title": "Distance II", "content": "Your task is to calculate the distance between two $n$ dimensional vectors $x = \\{x_1, x_2, . . . , x_n\\}$ and $y = \\{y_1, y_2, . . . , y_n\\}$.\n\n The Minkowski's distance defined below is a metric which is a generalization of both the Manhattan distance and the Euclidean distance.\n\n\\[\nD_{xy} = (\\sum_{i=1}^n |x_i - y_i|^p)^{\\frac{1}{p}}\n\\]\nIt can be the Manhattan distance \n\\[\nD_{xy} = |x_1 - y_1| + |x_2 - y_2| + . . . + |x_n - y_n|\n\\]\nwhere $p = 1 $.\n\nIt can be the Euclidean distance\n\n\\[\nD_{xy} = \\sqrt{(|x_1 - y_1|)^{2} + (|x_2 - y_2|)^{2} + . . . + (|x_n - y_n|)^{2}}\n\\]\n\nwhere $p = 2 $.\n\nAlso, it can be the Chebyshev distance\n\\[\nD_{xy} = max_{i=1}^n (|x_i - y_i|)\n\\]\nwhere $p = \\infty$\n\nWrite a program which reads two $n$ dimensional vectors $x$ and $y$, and calculates Minkowski's distance where $p = 1,2,3, \\infty$ respectively.", "constraint": "$1 <= n <= 100$\n\n$0 <= x_i, y_i <= 1000$", "input": "In the first line, an integer $n$ is given. In the second and third line, $x = \\{x_1, x_2, . . . x_n\\}$ and $y = \\{y_1, y_2, . . . y_n\\}$ are given respectively. The elements in $x$ and $y$ are given in integers.", "output": "Print the distance where $p = 1,2,3$ and $\\infty$ in a line respectively.\nThe output should not contain an absolute error greater than 10^-5.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3\n2 0 4\n output: 4.000000\n2.449490\n2.154435\n2.000000"], "Pid": "p02382", "ProblemText": "Task Description: Your task is to calculate the distance between two $n$ dimensional vectors $x = \\{x_1, x_2, . . . , x_n\\}$ and $y = \\{y_1, y_2, . . . , y_n\\}$.\n\n The Minkowski's distance defined below is a metric which is a generalization of both the Manhattan distance and the Euclidean distance.\n\n\\[\nD_{xy} = (\\sum_{i=1}^n |x_i - y_i|^p)^{\\frac{1}{p}}\n\\]\nIt can be the Manhattan distance \n\\[\nD_{xy} = |x_1 - y_1| + |x_2 - y_2| + . . . + |x_n - y_n|\n\\]\nwhere $p = 1 $.\n\nIt can be the Euclidean distance\n\n\\[\nD_{xy} = \\sqrt{(|x_1 - y_1|)^{2} + (|x_2 - y_2|)^{2} + . . . + (|x_n - y_n|)^{2}}\n\\]\n\nwhere $p = 2 $.\n\nAlso, it can be the Chebyshev distance\n\\[\nD_{xy} = max_{i=1}^n (|x_i - y_i|)\n\\]\nwhere $p = \\infty$\n\nWrite a program which reads two $n$ dimensional vectors $x$ and $y$, and calculates Minkowski's distance where $p = 1,2,3, \\infty$ respectively.\nTask Constraint: $1 <= n <= 100$\n\n$0 <= x_i, y_i <= 1000$\nTask Input: In the first line, an integer $n$ is given. In the second and third line, $x = \\{x_1, x_2, . . . x_n\\}$ and $y = \\{y_1, y_2, . . . y_n\\}$ are given respectively. The elements in $x$ and $y$ are given in integers.\nTask Output: Print the distance where $p = 1,2,3$ and $\\infty$ in a line respectively.\nThe output should not contain an absolute error greater than 10^-5.\nTask Samples: input: 3\n1 2 3\n2 0 4\n output: 4.000000\n2.449490\n2.154435\n2.000000\n\n" }, { "title": "Dice I", "content": "Write a program to simulate rolling a dice, which can be constructed by the following net.\n As shown in the figures, each face is identified by a different label from 1 to 6.\n\n Write a program which reads integers assigned to each face identified by the label and a sequence of commands to roll the dice, and prints the integer on the top face. At the initial state, the dice is located as shown in the above figures.", "constraint": "$0 <= $ the integer assigned to a face $ <= 100$\n\n$0 <= $ the length of the command $<= 100$", "input": "In the first line, six integers assigned to faces are given in ascending order of their corresponding labels.\n\n In the second line, a string which represents a sequence of commands, is given. The command is one of 'E', 'N', 'S' and 'W' representing four directions shown in the above figures.", "output": "Print the integer which appears on the top face after the simulation.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 2 4 8 16 32\nSE\n output: 8\nYou are given a dice where 1,2,4,8,16 are 32 are assigned to a face labeled by 1,2, ..., 6 respectively. After you roll the dice to the direction S\n and then to the direction E\n, you can see 8 on the top face.", "input: 1 2 4 8 16 32\nEESWN\n output: 32"], "Pid": "p02383", "ProblemText": "Task Description: Write a program to simulate rolling a dice, which can be constructed by the following net.\n As shown in the figures, each face is identified by a different label from 1 to 6.\n\n Write a program which reads integers assigned to each face identified by the label and a sequence of commands to roll the dice, and prints the integer on the top face. At the initial state, the dice is located as shown in the above figures.\nTask Constraint: $0 <= $ the integer assigned to a face $ <= 100$\n\n$0 <= $ the length of the command $<= 100$\nTask Input: In the first line, six integers assigned to faces are given in ascending order of their corresponding labels.\n\n In the second line, a string which represents a sequence of commands, is given. The command is one of 'E', 'N', 'S' and 'W' representing four directions shown in the above figures.\nTask Output: Print the integer which appears on the top face after the simulation.\nTask Samples: input: 1 2 4 8 16 32\nSE\n output: 8\nYou are given a dice where 1,2,4,8,16 are 32 are assigned to a face labeled by 1,2, ..., 6 respectively. After you roll the dice to the direction S\n and then to the direction E\n, you can see 8 on the top face.\ninput: 1 2 4 8 16 32\nEESWN\n output: 32\n\n" }, { "title": "Dice II", "content": "Construct a dice from a given sequence of integers in the same way as Dice I.\n\n You are given integers on the top face and the front face after the dice was rolled in the same way as Dice I. Write a program to print an integer on the right side face.", "constraint": "$0 <= $ the integer assigned to a face $ <= 100$\n\nThe integers are all different\n\n$1 <= q <= 24$", "input": "In the first line, six integers assigned to faces are given in ascending order of their corresponding labels.\nIn the second line, the number of questions $q$ is given.\n\n In the following $q$ lines, $q$ questions are given. Each question consists of two integers on the top face and the front face respectively.", "output": "For each question, print the integer on the right side face.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 2 3 4 5 6\n3\n6 5\n1 3\n3 2\n output: 3\n5\n6"], "Pid": "p02384", "ProblemText": "Task Description: Construct a dice from a given sequence of integers in the same way as Dice I.\n\n You are given integers on the top face and the front face after the dice was rolled in the same way as Dice I. Write a program to print an integer on the right side face.\nTask Constraint: $0 <= $ the integer assigned to a face $ <= 100$\n\nThe integers are all different\n\n$1 <= q <= 24$\nTask Input: In the first line, six integers assigned to faces are given in ascending order of their corresponding labels.\nIn the second line, the number of questions $q$ is given.\n\n In the following $q$ lines, $q$ questions are given. Each question consists of two integers on the top face and the front face respectively.\nTask Output: For each question, print the integer on the right side face.\nTask Samples: input: 1 2 3 4 5 6\n3\n6 5\n1 3\n3 2\n output: 3\n5\n6\n\n" }, { "title": "Dice III", "content": "Write a program which reads the two dices constructed in the same way as Dice I, and determines whether these two dices are identical. You can roll a dice in the same way as Dice I, and if all integers observed from the six directions are the same as that of another dice, these dices can be considered as identical.", "constraint": "$0 <= $ the integer assigned to a face $ <= 100$", "input": "In the first line, six integers assigned to faces of a dice are given in ascending order of their corresponding labels. \n In the second line, six integers assigned to faces of another dice are given in ascending order of their corresponding labels.", "output": "Print \"Yes\" if two dices are identical, otherwise \"No\" in a line.\n", "content_img": true, "lang": "en", "error": false, "samples": ["input: 1 2 3 4 5 6\n6 2 4 3 5 1\n output: Yes", "input: 1 2 3 4 5 6\n6 5 4 3 2 1\n output: No"], "Pid": "p02385", "ProblemText": "Task Description: Write a program which reads the two dices constructed in the same way as Dice I, and determines whether these two dices are identical. You can roll a dice in the same way as Dice I, and if all integers observed from the six directions are the same as that of another dice, these dices can be considered as identical.\nTask Constraint: $0 <= $ the integer assigned to a face $ <= 100$\nTask Input: In the first line, six integers assigned to faces of a dice are given in ascending order of their corresponding labels. \n In the second line, six integers assigned to faces of another dice are given in ascending order of their corresponding labels.\nTask Output: Print \"Yes\" if two dices are identical, otherwise \"No\" in a line.\n\nTask Samples: input: 1 2 3 4 5 6\n6 2 4 3 5 1\n output: Yes\ninput: 1 2 3 4 5 6\n6 5 4 3 2 1\n output: No\n\n" }, { "title": "Dice IV", "content": "Write a program which reads $n$ dices constructed in the same way as Dice I, and determines whether they are all different. For the determination, use the same way as Dice III.", "constraint": "$2 <= n <= 100$\n\n$0 <= $ the integer assigned to a face $ <= 100$", "input": "In the first line, the number of dices $n$ is given. In the following $n$ lines, six integers assigned to the dice faces are given respectively in the same way as Dice III.", "output": "Print \"Yes\" if given dices are all different, otherwise \"No\" in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 4 5 6\n6 2 4 3 5 1\n6 5 4 3 2 1\n output: No", "input: 3\n1 2 3 4 5 6\n6 5 4 3 2 1\n5 4 3 2 1 6\n output: Yes"], "Pid": "p02386", "ProblemText": "Task Description: Write a program which reads $n$ dices constructed in the same way as Dice I, and determines whether they are all different. For the determination, use the same way as Dice III.\nTask Constraint: $2 <= n <= 100$\n\n$0 <= $ the integer assigned to a face $ <= 100$\nTask Input: In the first line, the number of dices $n$ is given. In the following $n$ lines, six integers assigned to the dice faces are given respectively in the same way as Dice III.\nTask Output: Print \"Yes\" if given dices are all different, otherwise \"No\" in a line.\nTask Samples: input: 3\n1 2 3 4 5 6\n6 2 4 3 5 1\n6 5 4 3 2 1\n output: No\ninput: 3\n1 2 3 4 5 6\n6 5 4 3 2 1\n5 4 3 2 1 6\n output: Yes\n\n" }, { "title": "Hello World", "content": "Welcome to Online Judge!\n\nWrite a program which prints \"Hello World\" to standard output.", "constraint": "", "input": "There is no input for this problem.", "output": "Print \"Hello World\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: No input\n output: Hello World"], "Pid": "p02387", "ProblemText": "Task Description: Welcome to Online Judge!\n\nWrite a program which prints \"Hello World\" to standard output.\nTask Input: There is no input for this problem.\nTask Output: Print \"Hello World\" in a line.\nTask Samples: input: No input\n output: Hello World\n\n" }, { "title": "X Cubic", "content": "Write a program which calculates the cube of a given integer x.", "constraint": "1 <= x <= 100", "input": "An integer x is given in a line.", "output": "Print the cube of x in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n output: 8", "input: 3\n output: 27"], "Pid": "p02388", "ProblemText": "Task Description: Write a program which calculates the cube of a given integer x.\nTask Constraint: 1 <= x <= 100\nTask Input: An integer x is given in a line.\nTask Output: Print the cube of x in a line.\nTask Samples: input: 2\n output: 8\ninput: 3\n output: 27\n\n" }, { "title": "Rectangle", "content": "Write a program which calculates the area and perimeter of a given rectangle.", "constraint": "1 <= a, b <= 100", "input": "The length a and breadth b of the rectangle are given in a line separated by a single space.", "output": "Print the area and perimeter of the rectangle in a line. The two integers should be separated by a single space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n output: 15 16"], "Pid": "p02389", "ProblemText": "Task Description: Write a program which calculates the area and perimeter of a given rectangle.\nTask Constraint: 1 <= a, b <= 100\nTask Input: The length a and breadth b of the rectangle are given in a line separated by a single space.\nTask Output: Print the area and perimeter of the rectangle in a line. The two integers should be separated by a single space.\nTask Samples: input: 3 5\n output: 15 16\n\n" }, { "title": "Watch", "content": "Write a program which reads an integer $S$ [second] and converts it to $h: m: s$ where $h$, $m$, $s$ denote hours, minutes (less than 60) and seconds (less than 60) respectively.", "constraint": "$0 <= S <= 86400$", "input": "An integer $S$ is given in a line.", "output": "Print $h$, $m$ and $s$ separated by ': '. You do not need to put '0' for a value, which consists of a digit.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 46979\n output: 13:2:59"], "Pid": "p02390", "ProblemText": "Task Description: Write a program which reads an integer $S$ [second] and converts it to $h: m: s$ where $h$, $m$, $s$ denote hours, minutes (less than 60) and seconds (less than 60) respectively.\nTask Constraint: $0 <= S <= 86400$\nTask Input: An integer $S$ is given in a line.\nTask Output: Print $h$, $m$ and $s$ separated by ': '. You do not need to put '0' for a value, which consists of a digit.\nTask Samples: input: 46979\n output: 13:2:59\n\n" }, { "title": "Small, Large, or Equal", "content": "Write a program which prints small/large/equal relation of given two integers a and b.", "constraint": "-1000 <= a, b <= 1000", "input": "Two integers a and b separated by a single space are given in a line.", "output": "For given two integers a and b, print\n\na < b\n\n if a is less than b,\n\na > b\n\n if a is greater than b, and\n\na == b\n\n if a equals to b.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2\n output: a < b", "input: 4 3\n output: a > b", "input: 5 5\n output: a == b"], "Pid": "p02391", "ProblemText": "Task Description: Write a program which prints small/large/equal relation of given two integers a and b.\nTask Constraint: -1000 <= a, b <= 1000\nTask Input: Two integers a and b separated by a single space are given in a line.\nTask Output: For given two integers a and b, print\n\na < b\n\n if a is less than b,\n\na > b\n\n if a is greater than b, and\n\na == b\n\n if a equals to b.\nTask Samples: input: 1 2\n output: a < b\ninput: 4 3\n output: a > b\ninput: 5 5\n output: a == b\n\n" }, { "title": "Range", "content": "Write a program which reads three integers a, b and c, and prints \"Yes\" if a < b < c, otherwise \"No\".", "constraint": "0 <= a, b, c <= 100", "input": "Three integers a, b and c separated by a single space are given in a line.", "output": "Print \"Yes\" or \"No\" in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 8\n output: Yes", "input: 3 8 1\n output: No"], "Pid": "p02392", "ProblemText": "Task Description: Write a program which reads three integers a, b and c, and prints \"Yes\" if a < b < c, otherwise \"No\".\nTask Constraint: 0 <= a, b, c <= 100\nTask Input: Three integers a, b and c separated by a single space are given in a line.\nTask Output: Print \"Yes\" or \"No\" in a line.\nTask Samples: input: 1 3 8\n output: Yes\ninput: 3 8 1\n output: No\n\n" }, { "title": "Sorting Three Numbers", "content": "Write a program which reads three integers, and prints them in ascending order.", "constraint": "1 <= the three integers <= 10000", "input": "Three integers separated by a single space are given in a line.", "output": "Print the given integers in ascending order in a line. Put a single space between two integers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 8 1\n output: 1 3 8"], "Pid": "p02393", "ProblemText": "Task Description: Write a program which reads three integers, and prints them in ascending order.\nTask Constraint: 1 <= the three integers <= 10000\nTask Input: Three integers separated by a single space are given in a line.\nTask Output: Print the given integers in ascending order in a line. Put a single space between two integers.\nTask Samples: input: 3 8 1\n output: 1 3 8\n\n" }, { "title": "Circle in a Rectangle", "content": "Write a program which reads a rectangle and a circle, and determines whether the circle is arranged inside the rectangle. As shown in the following figures, the upper right coordinate $(W, H)$ of the rectangle and the central coordinate $(x, y)$ and radius $r$ of the circle are given.", "constraint": "$ -100 <= x, y <= 100$\n\n$ 0 < W, H, r <= 100$", "input": "Five integers $W$, $H$, $x$, $y$ and $r$ separated by a single space are given in a line.", "output": "Print \"Yes\" if the circle is placed inside the rectangle, otherwise \"No\" in a line.", "content_img": true, "lang": "en", "error": false, "samples": ["input: 5 4 2 2 1\n output: Yes", "input: 5 4 2 4 1\n output: No"], "Pid": "p02394", "ProblemText": "Task Description: Write a program which reads a rectangle and a circle, and determines whether the circle is arranged inside the rectangle. As shown in the following figures, the upper right coordinate $(W, H)$ of the rectangle and the central coordinate $(x, y)$ and radius $r$ of the circle are given.\nTask Constraint: $ -100 <= x, y <= 100$\n\n$ 0 < W, H, r <= 100$\nTask Input: Five integers $W$, $H$, $x$, $y$ and $r$ separated by a single space are given in a line.\nTask Output: Print \"Yes\" if the circle is placed inside the rectangle, otherwise \"No\" in a line.\nTask Samples: input: 5 4 2 2 1\n output: Yes\ninput: 5 4 2 4 1\n output: No\n\n" }, { "title": "Print Many Hello World", "content": "Write a program which prints 1000 \"Hello World\".", "constraint": "", "input": "There is no input for this problem.", "output": "The output consists of 1000 lines. Print \"Hello World\" in each line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: No input\n output: Hello World\nHello World\nHello World\nHello World\nHello World\nHello World\nHello World\n.\n.\n.\n.\n.\n.\nHello World"], "Pid": "p02395", "ProblemText": "Task Description: Write a program which prints 1000 \"Hello World\".\nTask Input: There is no input for this problem.\nTask Output: The output consists of 1000 lines. Print \"Hello World\" in each line.\nTask Samples: input: No input\n output: Hello World\nHello World\nHello World\nHello World\nHello World\nHello World\nHello World\n.\n.\n.\n.\n.\n.\nHello World\n\n" }, { "title": "Print Test Cases", "content": "In the online judge system, a judge file may include multiple datasets to check whether the submitted program outputs a correct answer for each test case. This task is to practice solving a problem with multiple datasets.\n\nWrite a program which reads an integer x and print it as is. Note that multiple datasets are given for this problem.", "constraint": "1 <= x <= 10000\n\nThe number of datasets <= 10000", "input": "The input consists of multiple datasets. Each dataset consists of an integer x in a line.\n\nThe input ends with an integer 0. You program should not process (print) for this terminal symbol.", "output": "For each dataset, print x in the following format:\n\nCase i: x\n\nwhere i is the case number which starts with 1. Put a single space between \"Case\" and i. Also, put a single space between ': ' and x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n5\n11\n7\n8\n19\n0\n output: Case 1: 3\nCase 2: 5\nCase 3: 11\nCase 4: 7\nCase 5: 8\nCase 6: 19"], "Pid": "p02396", "ProblemText": "Task Description: In the online judge system, a judge file may include multiple datasets to check whether the submitted program outputs a correct answer for each test case. This task is to practice solving a problem with multiple datasets.\n\nWrite a program which reads an integer x and print it as is. Note that multiple datasets are given for this problem.\nTask Constraint: 1 <= x <= 10000\n\nThe number of datasets <= 10000\nTask Input: The input consists of multiple datasets. Each dataset consists of an integer x in a line.\n\nThe input ends with an integer 0. You program should not process (print) for this terminal symbol.\nTask Output: For each dataset, print x in the following format:\n\nCase i: x\n\nwhere i is the case number which starts with 1. Put a single space between \"Case\" and i. Also, put a single space between ': ' and x.\nTask Samples: input: 3\n5\n11\n7\n8\n19\n0\n output: Case 1: 3\nCase 2: 5\nCase 3: 11\nCase 4: 7\nCase 5: 8\nCase 6: 19\n\n" }, { "title": "Swapping Two Numbers", "content": "Write a program which reads two integers x and y, and prints them in ascending order.", "constraint": "0 <= x, y <= 10000\n\n the number of datasets <= 3000", "input": "The input consists of multiple datasets. Each dataset consists of two integers x and y separated by a single space.\n\nThe input ends with two 0 (when both x and y are zero). Your program should not process for these terminal symbols.", "output": "For each dataset, print x and y in ascending order in a line. Put a single space between x and y.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n2 2\n5 3\n0 0\n output: 2 3\n2 2\n3 5"], "Pid": "p02397", "ProblemText": "Task Description: Write a program which reads two integers x and y, and prints them in ascending order.\nTask Constraint: 0 <= x, y <= 10000\n\n the number of datasets <= 3000\nTask Input: The input consists of multiple datasets. Each dataset consists of two integers x and y separated by a single space.\n\nThe input ends with two 0 (when both x and y are zero). Your program should not process for these terminal symbols.\nTask Output: For each dataset, print x and y in ascending order in a line. Put a single space between x and y.\nTask Samples: input: 3 2\n2 2\n5 3\n0 0\n output: 2 3\n2 2\n3 5\n\n" }, { "title": "", "content": "Write a program which reads three integers a, b and c, and prints the number of divisors of c between a and b.", "constraint": "1 <= a, b, c <= 10000\n\n a <= b", "input": "Three integers a, b and c are given in a line separated by a single space.", "output": "Print the number of divisors in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 14 80\n output: 3"], "Pid": "p02398", "ProblemText": "Task Description: Write a program which reads three integers a, b and c, and prints the number of divisors of c between a and b.\nTask Constraint: 1 <= a, b, c <= 10000\n\n a <= b\nTask Input: Three integers a, b and c are given in a line separated by a single space.\nTask Output: Print the number of divisors in a line.\nTask Samples: input: 5 14 80\n output: 3\n\n" }, { "title": "A/B Problem", "content": "Write a program which reads two integers a and b, and calculates the following values:\n\na ÷ b: d (in integer)\n\nremainder of a ÷ b: r (in integer)\n\na ÷ b: f (in real number)", "constraint": "1 <= a, b <= 10^9", "input": "Two integers a and b are given in a line.", "output": "Print d, r and f separated by a space in a line. For f, the output should not contain an absolute error greater than 10^-5.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n output: 1 1 1.50000"], "Pid": "p02399", "ProblemText": "Task Description: Write a program which reads two integers a and b, and calculates the following values:\n\na ÷ b: d (in integer)\n\nremainder of a ÷ b: r (in integer)\n\na ÷ b: f (in real number)\nTask Constraint: 1 <= a, b <= 10^9\nTask Input: Two integers a and b are given in a line.\nTask Output: Print d, r and f separated by a space in a line. For f, the output should not contain an absolute error greater than 10^-5.\nTask Samples: input: 3 2\n output: 1 1 1.50000\n\n" }, { "title": "Circle", "content": "Write a program which calculates the area and circumference of a circle for given radius r.", "constraint": "0 < r < 10000", "input": "A real number r is given.", "output": "Print the area and circumference of the circle in a line. Put a single space between them. The output should not contain an absolute error greater than 10^-5.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n output: 12.566371 12.566371", "input: 3\n output: 28.274334 18.849556"], "Pid": "p02400", "ProblemText": "Task Description: Write a program which calculates the area and circumference of a circle for given radius r.\nTask Constraint: 0 < r < 10000\nTask Input: A real number r is given.\nTask Output: Print the area and circumference of the circle in a line. Put a single space between them. The output should not contain an absolute error greater than 10^-5.\nTask Samples: input: 2\n output: 12.566371 12.566371\ninput: 3\n output: 28.274334 18.849556\n\n" }, { "title": "Simple Calculator", "content": "Write a program which reads two integers a, b and an operator op, and then prints the value of a op b.\n\nThe operator op is '+', '-', '*' or '/' (sum, difference, product or quotient). The division should truncate any fractional part.", "constraint": "0 <= a, b <= 20000\n\nNo divisions by zero are given.", "input": "The input consists of multiple datasets. Each dataset is given in the following format.\n\na op b\n\nThe input ends with a dataset where op = '? '. Your program should not process for this dataset.", "output": "For each dataset, print the value in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 + 2\n56 - 18\n13 * 2\n100 / 10\n27 + 81\n0 ? 0\n output: 3\n38\n26\n10\n108"], "Pid": "p02401", "ProblemText": "Task Description: Write a program which reads two integers a, b and an operator op, and then prints the value of a op b.\n\nThe operator op is '+', '-', '*' or '/' (sum, difference, product or quotient). The division should truncate any fractional part.\nTask Constraint: 0 <= a, b <= 20000\n\nNo divisions by zero are given.\nTask Input: The input consists of multiple datasets. Each dataset is given in the following format.\n\na op b\n\nThe input ends with a dataset where op = '? '. Your program should not process for this dataset.\nTask Output: For each dataset, print the value in a line.\nTask Samples: input: 1 + 2\n56 - 18\n13 * 2\n100 / 10\n27 + 81\n0 ? 0\n output: 3\n38\n26\n10\n108\n\n" }, { "title": "Min, Max and Sum", "content": "Write a program which reads a sequence of $n$ integers $a_i (i = 1,2, . . . n)$, and prints the minimum value, maximum value and sum of the sequence.", "constraint": "$0 < n <= 10000$\n\n$-1000000 <= a_i <= 1000000$", "input": "In the first line, an integer $n$ is given. In the next line, $n$ integers $a_i$ are given in a line.", "output": "Print the minimum value, maximum value and sum in a line. Put a single space between the values.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n10 1 5 4 17\n output: 1 17 37"], "Pid": "p02402", "ProblemText": "Task Description: Write a program which reads a sequence of $n$ integers $a_i (i = 1,2, . . . n)$, and prints the minimum value, maximum value and sum of the sequence.\nTask Constraint: $0 < n <= 10000$\n\n$-1000000 <= a_i <= 1000000$\nTask Input: In the first line, an integer $n$ is given. In the next line, $n$ integers $a_i$ are given in a line.\nTask Output: Print the minimum value, maximum value and sum in a line. Put a single space between the values.\nTask Samples: input: 5\n10 1 5 4 17\n output: 1 17 37\n\n" }, { "title": "Print a Rectangle", "content": "Draw a rectangle which has a height of H cm and a width of W cm. Draw a 1-cm square by single '#'.", "constraint": "1 <= H <= 300\n\n1 <= W <= 300", "input": "The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.\n\n The input ends with two 0 (when both H and W are zero).", "output": "For each dataset, print the rectangle made of H * W '#'.\n\n Print a blank line after each dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n5 6\n2 2\n0 0\n output: ####\n####\n####\n\n######\n######\n######\n######\n######\n\n##\n##"], "Pid": "p02403", "ProblemText": "Task Description: Draw a rectangle which has a height of H cm and a width of W cm. Draw a 1-cm square by single '#'.\nTask Constraint: 1 <= H <= 300\n\n1 <= W <= 300\nTask Input: The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.\n\n The input ends with two 0 (when both H and W are zero).\nTask Output: For each dataset, print the rectangle made of H * W '#'.\n\n Print a blank line after each dataset.\nTask Samples: input: 3 4\n5 6\n2 2\n0 0\n output: ####\n####\n####\n\n######\n######\n######\n######\n######\n\n##\n##\n\n" }, { "title": "Print a Frame", "content": "Draw a frame which has a height of H cm and a width of W cm. For example, the following figure shows a frame which has a height of 6 cm and a width of 10 cm.\n\n##########\n#. . . . . . . . #\n#. . . . . . . . #\n#. . . . . . . . #\n#. . . . . . . . #\n##########", "constraint": "3 <= H <= 300\n\n3 <= W <= 300", "input": "The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.\n\n The input ends with two 0 (when both H and W are zero).", "output": "For each dataset, print the frame made of '#' and '. '.\n\n Print a blank line after each dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n5 6\n3 3\n0 0\n output: ####\n#..#\n####\n\n######\n#....#\n#....#\n#....#\n######\n\n###\n#.#\n###"], "Pid": "p02404", "ProblemText": "Task Description: Draw a frame which has a height of H cm and a width of W cm. For example, the following figure shows a frame which has a height of 6 cm and a width of 10 cm.\n\n##########\n#. . . . . . . . #\n#. . . . . . . . #\n#. . . . . . . . #\n#. . . . . . . . #\n##########\nTask Constraint: 3 <= H <= 300\n\n3 <= W <= 300\nTask Input: The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.\n\n The input ends with two 0 (when both H and W are zero).\nTask Output: For each dataset, print the frame made of '#' and '. '.\n\n Print a blank line after each dataset.\nTask Samples: input: 3 4\n5 6\n3 3\n0 0\n output: ####\n#..#\n####\n\n######\n#....#\n#....#\n#....#\n######\n\n###\n#.#\n###\n\n" }, { "title": "Print a Chessboard", "content": "Draw a chessboard which has a height of H cm and a width of W cm. For example, the following figure shows a chessboard which has a height of 6 cm and a width of 10 cm.\n\n#. #. #. #. #.\n. #. #. #. #. #\n#. #. #. #. #.\n. #. #. #. #. #\n#. #. #. #. #.\n. #. #. #. #. #\n\nNote that the top left corner should be drawn by '#'.", "constraint": "1 <= H <= 300\n\n1 <= W <= 300", "input": "The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.\n\n The input ends with two 0 (when both H and W are zero).", "output": "For each dataset, print the chessboard made of '#' and '. '.\n\n Print a blank line after each dataset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n5 6\n3 3\n2 2\n1 1\n0 0\n output: #.#.\n.#.#\n#.#.\n\n#.#.#.\n.#.#.#\n#.#.#.\n.#.#.#\n#.#.#.\n\n#.#\n.#.\n#.#\n\n#.\n.#\n\n#"], "Pid": "p02405", "ProblemText": "Task Description: Draw a chessboard which has a height of H cm and a width of W cm. For example, the following figure shows a chessboard which has a height of 6 cm and a width of 10 cm.\n\n#. #. #. #. #.\n. #. #. #. #. #\n#. #. #. #. #.\n. #. #. #. #. #\n#. #. #. #. #.\n. #. #. #. #. #\n\nNote that the top left corner should be drawn by '#'.\nTask Constraint: 1 <= H <= 300\n\n1 <= W <= 300\nTask Input: The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.\n\n The input ends with two 0 (when both H and W are zero).\nTask Output: For each dataset, print the chessboard made of '#' and '. '.\n\n Print a blank line after each dataset.\nTask Samples: input: 3 4\n5 6\n3 3\n2 2\n1 1\n0 0\n output: #.#.\n.#.#\n#.#.\n\n#.#.#.\n.#.#.#\n#.#.#.\n.#.#.#\n#.#.#.\n\n#.#\n.#.\n#.#\n\n#.\n.#\n\n#\n\n" }, { "title": "Structured Programming", "content": "In programming languages like C/C++, a goto statement provides an unconditional jump from the \"goto\" to a labeled statement. For example, a statement \"goto CHECK_NUM; \" is executed, control of the program jumps to CHECK_NUM. Using these constructs, you can implement, for example, loops.\n\nNote that use of goto statement is highly discouraged, because it is difficult to trace the control flow of a program which includes goto.\n\nWrite a program which does precisely the same thing as the following program (this example is wrtten in C++). Let's try to write the program without goto statements.\n\nvoid call(int n){\n int i = 1;\n CHECK_NUM:\n int x = i;\n if ( x % 3 == 0 ){\n cout << \" \" << i;\n goto END_CHECK_NUM;\n }\n INCLUDE3:\n if ( x % 10 == 3 ){\n cout << \" \" << i;\n goto END_CHECK_NUM;\n }\n x /= 10;\n if ( x ) goto INCLUDE3;\n END_CHECK_NUM:\n if ( ++i <= n ) goto CHECK_NUM;\n\n cout << endl;\n}", "constraint": "3 <= n <= 10000", "input": "An integer n is given in a line.", "output": "Print the output result of the above program for given integer n.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 30\n output: 3 6 9 12 13 15 18 21 23 24 27 30\n Put a single space character before each element."], "Pid": "p02406", "ProblemText": "Task Description: In programming languages like C/C++, a goto statement provides an unconditional jump from the \"goto\" to a labeled statement. For example, a statement \"goto CHECK_NUM; \" is executed, control of the program jumps to CHECK_NUM. Using these constructs, you can implement, for example, loops.\n\nNote that use of goto statement is highly discouraged, because it is difficult to trace the control flow of a program which includes goto.\n\nWrite a program which does precisely the same thing as the following program (this example is wrtten in C++). Let's try to write the program without goto statements.\n\nvoid call(int n){\n int i = 1;\n CHECK_NUM:\n int x = i;\n if ( x % 3 == 0 ){\n cout << \" \" << i;\n goto END_CHECK_NUM;\n }\n INCLUDE3:\n if ( x % 10 == 3 ){\n cout << \" \" << i;\n goto END_CHECK_NUM;\n }\n x /= 10;\n if ( x ) goto INCLUDE3;\n END_CHECK_NUM:\n if ( ++i <= n ) goto CHECK_NUM;\n\n cout << endl;\n}\nTask Constraint: 3 <= n <= 10000\nTask Input: An integer n is given in a line.\nTask Output: Print the output result of the above program for given integer n.\nTask Samples: input: 30\n output: 3 6 9 12 13 15 18 21 23 24 27 30\n Put a single space character before each element.\n\n" }, { "title": "Reversing Numbers", "content": "Write a program which reads a sequence and prints it in the reverse order.", "constraint": "n <= 100\n\n0 <= a_i < 1000", "input": "The input is given in the following format:\n\nn\na_1 a_2 . . . a_n\n\nn is the size of the sequence and a_i is the ith element of the sequence.", "output": "Print the reversed sequence in a line. Print a single space character between adjacent elements (Note that your program should not put a space character after the last element).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 4 5\n output: 5 4 3 2 1", "input: 8\n3 3 4 4 5 8 7 9\n output: 9 7 8 5 4 4 3 3"], "Pid": "p02407", "ProblemText": "Task Description: Write a program which reads a sequence and prints it in the reverse order.\nTask Constraint: n <= 100\n\n0 <= a_i < 1000\nTask Input: The input is given in the following format:\n\nn\na_1 a_2 . . . a_n\n\nn is the size of the sequence and a_i is the ith element of the sequence.\nTask Output: Print the reversed sequence in a line. Print a single space character between adjacent elements (Note that your program should not put a space character after the last element).\nTask Samples: input: 5\n1 2 3 4 5\n output: 5 4 3 2 1\ninput: 8\n3 3 4 4 5 8 7 9\n output: 9 7 8 5 4 4 3 3\n\n" }, { "title": "Finding Missing Cards", "content": "Taro is going to play a card game. However, now he has only n cards, even though there should be 52 cards (he has no Jokers).\n\nThe 52 cards include 13 ranks of each of the four suits: spade, heart, club and diamond.", "constraint": "", "input": "In the first line, the number of cards n (n <= 52) is given.\n\n In the following n lines, data of the n cards are given. Each card is given by a pair of a character and an integer which represent its suit and rank respectively. A suit is represented by 'S', 'H', 'C' and 'D' for spades, hearts, clubs and diamonds respectively. A rank is represented by an integer from 1 to 13.", "output": "Print the missing cards. The same as the input format, each card should be printed with a character and an integer separated by a space character in a line.\n Arrange the missing cards in the following priorities:\n\nPrint cards of spades, hearts, clubs and diamonds in this order.\n\nIf the suits are equal, print cards with lower ranks first.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 47\nS 10\nS 11\nS 12\nS 13\nH 1\nH 2\nS 6\nS 7\nS 8\nS 9\nH 6\nH 8\nH 9\nH 10\nH 11\nH 4\nH 5\nS 2\nS 3\nS 4\nS 5\nH 12\nH 13\nC 1\nC 2\nD 1\nD 2\nD 3\nD 4\nD 5\nD 6\nD 7\nC 3\nC 4\nC 5\nC 6\nC 7\nC 8\nC 9\nC 10\nC 11\nC 13\nD 9\nD 10\nD 11\nD 12\nD 13\n output: S 1\nH 3\nH 7\nC 12\nD 8"], "Pid": "p02408", "ProblemText": "Task Description: Taro is going to play a card game. However, now he has only n cards, even though there should be 52 cards (he has no Jokers).\n\nThe 52 cards include 13 ranks of each of the four suits: spade, heart, club and diamond.\nTask Input: In the first line, the number of cards n (n <= 52) is given.\n\n In the following n lines, data of the n cards are given. Each card is given by a pair of a character and an integer which represent its suit and rank respectively. A suit is represented by 'S', 'H', 'C' and 'D' for spades, hearts, clubs and diamonds respectively. A rank is represented by an integer from 1 to 13.\nTask Output: Print the missing cards. The same as the input format, each card should be printed with a character and an integer separated by a space character in a line.\n Arrange the missing cards in the following priorities:\n\nPrint cards of spades, hearts, clubs and diamonds in this order.\n\nIf the suits are equal, print cards with lower ranks first.\nTask Samples: input: 47\nS 10\nS 11\nS 12\nS 13\nH 1\nH 2\nS 6\nS 7\nS 8\nS 9\nH 6\nH 8\nH 9\nH 10\nH 11\nH 4\nH 5\nS 2\nS 3\nS 4\nS 5\nH 12\nH 13\nC 1\nC 2\nD 1\nD 2\nD 3\nD 4\nD 5\nD 6\nD 7\nC 3\nC 4\nC 5\nC 6\nC 7\nC 8\nC 9\nC 10\nC 11\nC 13\nD 9\nD 10\nD 11\nD 12\nD 13\n output: S 1\nH 3\nH 7\nC 12\nD 8\n\n" }, { "title": "Official House", "content": "You manage 4 buildings, each of which has 3 floors, each of which consists of 10 rooms. Write a program which reads a sequence of tenant/leaver notices, and reports the number of tenants for each room.\n\n For each notice, you are given four integers b, f, r and v which represent that v persons entered to room r of fth floor at building b. If v is negative, it means that -v persons left.\n\nAssume that initially no person lives in the building.", "constraint": "No incorrect building, floor and room numbers are given.\n\n0 <= the number of tenants during the management <= 9", "input": "In the first line, the number of notices n is given. In the following n lines, a set of four integers b, f, r and v which represents ith notice is given in a line.", "output": "For each building, print the information of 1st, 2nd and 3rd floor in this order. For each floor information, print the number of tenants of 1st, 2nd, . . and 10th room in this order. Print a single space character before the number of tenants. Print \"####################\" (20 '#') between buildings.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1 3 8\n3 2 2 7\n4 3 8 1\n output: 0 0 8 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n####################\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n####################\n 0 0 0 0 0 0 0 0 0 0\n 0 7 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n####################\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 1 0 0"], "Pid": "p02409", "ProblemText": "Task Description: You manage 4 buildings, each of which has 3 floors, each of which consists of 10 rooms. Write a program which reads a sequence of tenant/leaver notices, and reports the number of tenants for each room.\n\n For each notice, you are given four integers b, f, r and v which represent that v persons entered to room r of fth floor at building b. If v is negative, it means that -v persons left.\n\nAssume that initially no person lives in the building.\nTask Constraint: No incorrect building, floor and room numbers are given.\n\n0 <= the number of tenants during the management <= 9\nTask Input: In the first line, the number of notices n is given. In the following n lines, a set of four integers b, f, r and v which represents ith notice is given in a line.\nTask Output: For each building, print the information of 1st, 2nd and 3rd floor in this order. For each floor information, print the number of tenants of 1st, 2nd, . . and 10th room in this order. Print a single space character before the number of tenants. Print \"####################\" (20 '#') between buildings.\nTask Samples: input: 3\n1 1 3 8\n3 2 2 7\n4 3 8 1\n output: 0 0 8 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n####################\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n####################\n 0 0 0 0 0 0 0 0 0 0\n 0 7 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n####################\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 1 0 0\n\n" }, { "title": "Matrix Vector Multiplication", "content": "Write a program which reads a $ n * m$ matrix $A$ and a $m * 1$ vector $b$, and prints their product $Ab$.\n\n A column vector with m elements is represented by the following equation.\n\n A $n * m$ matrix with $m$ column vectors, each of which consists of $n$ elements, is represented by the following equation.\n\n $i$-th element of a $m * 1$ column vector $b$ is represented by $b_i$ ($i = 1,2, . . . , m$), and the element in $i$-th row and $j$-th column of a matrix $A$ is represented by $a_{ij}$ ($i = 1,2, . . . , n, $ $j = 1,2, . . . , m$).\n\nThe product of a $n * m$ matrix $A$ and a $m * 1$ column vector $b$ is a $n * 1$ column vector $c$, and $c_i$ is obtained by the following formula:", "constraint": "$1 <= n, m <= 100$\n\n$0 <= b_i, a_{ij} <= 1000$", "input": "In the first line, two integers $n$ and $m$ are given. In the following $n$ lines, $a_{ij}$ are given separated by a single space character. In the next $m$ lines, $b_i$ is given in a line.", "output": "The output consists of $n$ lines. Print $c_i$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n1 2 0 1\n0 3 0 1\n4 1 1 0\n1\n2\n3\n0\n output: 5\n6\n9"], "Pid": "p02410", "ProblemText": "Task Description: Write a program which reads a $ n * m$ matrix $A$ and a $m * 1$ vector $b$, and prints their product $Ab$.\n\n A column vector with m elements is represented by the following equation.\n\n A $n * m$ matrix with $m$ column vectors, each of which consists of $n$ elements, is represented by the following equation.\n\n $i$-th element of a $m * 1$ column vector $b$ is represented by $b_i$ ($i = 1,2, . . . , m$), and the element in $i$-th row and $j$-th column of a matrix $A$ is represented by $a_{ij}$ ($i = 1,2, . . . , n, $ $j = 1,2, . . . , m$).\n\nThe product of a $n * m$ matrix $A$ and a $m * 1$ column vector $b$ is a $n * 1$ column vector $c$, and $c_i$ is obtained by the following formula:\nTask Constraint: $1 <= n, m <= 100$\n\n$0 <= b_i, a_{ij} <= 1000$\nTask Input: In the first line, two integers $n$ and $m$ are given. In the following $n$ lines, $a_{ij}$ are given separated by a single space character. In the next $m$ lines, $b_i$ is given in a line.\nTask Output: The output consists of $n$ lines. Print $c_i$ in a line.\nTask Samples: input: 3 4\n1 2 0 1\n0 3 0 1\n4 1 1 0\n1\n2\n3\n0\n output: 5\n6\n9\n\n" }, { "title": "Grading", "content": "Write a program which reads a list of student test scores and evaluates the performance for each student.\n\n The test scores for a student include scores of the midterm examination m (out of 50), the final examination f (out of 50) and the makeup examination r (out of 100). If the student does not take the examination, the score is indicated by -1.\n\n The final performance of a student is evaluated by the following procedure:\n\nIf the student does not take the midterm or final examination, the student's grade shall be F.\n\nIf the total score of the midterm and final examination is greater than or equal to 80, the student's grade shall be A.\n\nIf the total score of the midterm and final examination is greater than or equal to 65 and less than 80, the student's grade shall be B.\n\nIf the total score of the midterm and final examination is greater than or equal to 50 and less than 65, the student's grade shall be C.\n\nIf the total score of the midterm and final examination is greater than or equal to 30 and less than 50, the student's grade shall be D. However, if the score of the makeup examination is greater than or equal to 50, the grade shall be C.\n\nIf the total score of the midterm and final examination is less than 30, the student's grade shall be F.", "constraint": "", "input": "The input consists of multiple datasets. For each dataset, three integers m, f and r are given in a line.\n\n The input ends with three -1 for m, f and r respectively. Your program should not process for the terminal symbols.\n\nThe number of datasets (the number of students) does not exceed 50.", "output": "For each dataset, print the grade (A, B, C, D or F) in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 40 42 -1\n20 30 -1\n0 2 -1\n-1 -1 -1\n output: A\nC\nF"], "Pid": "p02411", "ProblemText": "Task Description: Write a program which reads a list of student test scores and evaluates the performance for each student.\n\n The test scores for a student include scores of the midterm examination m (out of 50), the final examination f (out of 50) and the makeup examination r (out of 100). If the student does not take the examination, the score is indicated by -1.\n\n The final performance of a student is evaluated by the following procedure:\n\nIf the student does not take the midterm or final examination, the student's grade shall be F.\n\nIf the total score of the midterm and final examination is greater than or equal to 80, the student's grade shall be A.\n\nIf the total score of the midterm and final examination is greater than or equal to 65 and less than 80, the student's grade shall be B.\n\nIf the total score of the midterm and final examination is greater than or equal to 50 and less than 65, the student's grade shall be C.\n\nIf the total score of the midterm and final examination is greater than or equal to 30 and less than 50, the student's grade shall be D. However, if the score of the makeup examination is greater than or equal to 50, the grade shall be C.\n\nIf the total score of the midterm and final examination is less than 30, the student's grade shall be F.\nTask Input: The input consists of multiple datasets. For each dataset, three integers m, f and r are given in a line.\n\n The input ends with three -1 for m, f and r respectively. Your program should not process for the terminal symbols.\n\nThe number of datasets (the number of students) does not exceed 50.\nTask Output: For each dataset, print the grade (A, B, C, D or F) in a line.\nTask Samples: input: 40 42 -1\n20 30 -1\n0 2 -1\n-1 -1 -1\n output: A\nC\nF\n\n" }, { "title": "How many ways?", "content": "Write a program which identifies the number of combinations of three integers which satisfy the following conditions:\n\nYou should select three distinct integers from 1 to n.\n\nA total sum of the three integers is x.\n For example, there are two combinations for n = 5 and x = 9.\n\n1 + 3 + 5 = 9\n\n2 + 3 + 4 = 9", "constraint": "3 <= n <= 100\n\n0 <= x <= 300", "input": "The input consists of multiple datasets. For each dataset, two integers n and x are given in a line.\n\n The input ends with two zeros for n and x respectively. Your program should not process for these terminal symbols.", "output": "For each dataset, print the number of combinations in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 9\n0 0\n output: 2"], "Pid": "p02412", "ProblemText": "Task Description: Write a program which identifies the number of combinations of three integers which satisfy the following conditions:\n\nYou should select three distinct integers from 1 to n.\n\nA total sum of the three integers is x.\n For example, there are two combinations for n = 5 and x = 9.\n\n1 + 3 + 5 = 9\n\n2 + 3 + 4 = 9\nTask Constraint: 3 <= n <= 100\n\n0 <= x <= 300\nTask Input: The input consists of multiple datasets. For each dataset, two integers n and x are given in a line.\n\n The input ends with two zeros for n and x respectively. Your program should not process for these terminal symbols.\nTask Output: For each dataset, print the number of combinations in a line.\nTask Samples: input: 5 9\n0 0\n output: 2\n\n" }, { "title": "Spreadsheet", "content": "Your task is to perform a simple table calculation.\n\n Write a program which reads the number of rows r, columns c and a table of r * c elements, and prints a new table, which includes the total sum for each row and column.", "constraint": "1 <= r, c <= 100\n\n 0 <= an element of the table <= 100", "input": "In the first line, two integers r and c are given. Next, the table is given by r lines, each of which consists of c integers separated by space characters.", "output": "Print the new table of (r+1) * (c+1) elements. Put a single space character between adjacent elements. For each row, print the sum of it's elements in the last column. For each column, print the sum of it's elements in the last row. Print the total sum of the elements at the bottom right corner of the table.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n1 1 3 4 5\n2 2 2 4 5\n3 3 0 1 1\n2 3 4 4 6\n output: 1 1 3 4 5 14\n2 2 2 4 5 15\n3 3 0 1 1 8\n2 3 4 4 6 19\n8 9 9 13 17 56"], "Pid": "p02413", "ProblemText": "Task Description: Your task is to perform a simple table calculation.\n\n Write a program which reads the number of rows r, columns c and a table of r * c elements, and prints a new table, which includes the total sum for each row and column.\nTask Constraint: 1 <= r, c <= 100\n\n 0 <= an element of the table <= 100\nTask Input: In the first line, two integers r and c are given. Next, the table is given by r lines, each of which consists of c integers separated by space characters.\nTask Output: Print the new table of (r+1) * (c+1) elements. Put a single space character between adjacent elements. For each row, print the sum of it's elements in the last column. For each column, print the sum of it's elements in the last row. Print the total sum of the elements at the bottom right corner of the table.\nTask Samples: input: 4 5\n1 1 3 4 5\n2 2 2 4 5\n3 3 0 1 1\n2 3 4 4 6\n output: 1 1 3 4 5 14\n2 2 2 4 5 15\n3 3 0 1 1 8\n2 3 4 4 6 19\n8 9 9 13 17 56\n\n" }, { "title": "Matrix Multiplication", "content": "Write a program which reads a $n * m$ matrix $A$ and a $m * l$ matrix $B$, and prints their product, a $n * l$ matrix $C$. An element of matrix $C$ is obtained by the following formula:\n\n where $a_{ij}$, $b_{ij}$ and $c_{ij}$ are elements of $A$, $B$ and $C$ respectively.", "constraint": "$1 <= n, m, l <= 100$\n\n$0 <= a_{ij}, b_{ij} <= 10000$", "input": "In the first line, three integers $n$, $m$ and $l$ are given separated by space characters\n\n In the following lines, the $n * m$ matrix $A$ and the $m * l$ matrix $B$ are given.", "output": "Print elements of the $n * l$ matrix $C$ ($c_{ij}$). Print a single space character between adjacent elements.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 3\n1 2\n0 3\n4 5\n1 2 1\n0 3 2\n output: 1 8 5\n0 9 6\n4 23 14"], "Pid": "p02414", "ProblemText": "Task Description: Write a program which reads a $n * m$ matrix $A$ and a $m * l$ matrix $B$, and prints their product, a $n * l$ matrix $C$. An element of matrix $C$ is obtained by the following formula:\n\n where $a_{ij}$, $b_{ij}$ and $c_{ij}$ are elements of $A$, $B$ and $C$ respectively.\nTask Constraint: $1 <= n, m, l <= 100$\n\n$0 <= a_{ij}, b_{ij} <= 10000$\nTask Input: In the first line, three integers $n$, $m$ and $l$ are given separated by space characters\n\n In the following lines, the $n * m$ matrix $A$ and the $m * l$ matrix $B$ are given.\nTask Output: Print elements of the $n * l$ matrix $C$ ($c_{ij}$). Print a single space character between adjacent elements.\nTask Samples: input: 3 2 3\n1 2\n0 3\n4 5\n1 2 1\n0 3 2\n output: 1 8 5\n0 9 6\n4 23 14\n\n" }, { "title": "Toggling Cases", "content": "Write a program which converts uppercase/lowercase letters to lowercase/uppercase for a given string.", "constraint": "The length of the input string < 1200", "input": "A string is given in a line.", "output": "Print the converted string in a line. Note that you do not need to convert any characters other than alphabetical letters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: fAIR, LATER, OCCASIONALLY CLOUDY.\n output: Fair, later, occasionally cloudy."], "Pid": "p02415", "ProblemText": "Task Description: Write a program which converts uppercase/lowercase letters to lowercase/uppercase for a given string.\nTask Constraint: The length of the input string < 1200\nTask Input: A string is given in a line.\nTask Output: Print the converted string in a line. Note that you do not need to convert any characters other than alphabetical letters.\nTask Samples: input: fAIR, LATER, OCCASIONALLY CLOUDY.\n output: Fair, later, occasionally cloudy.\n\n" }, { "title": "Sum of Numbers", "content": "Write a program which reads an integer and prints sum of its digits.", "constraint": "", "input": "The input consists of multiple datasets. For each dataset, an integer x is given in a line. The number of digits in x does not exceed 1000.\n\nThe input ends with a line including single zero. Your program should not process for this terminal symbol.", "output": "For each dataset, print the sum of digits in x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 123\n55\n1000\n0\n output: 6\n10\n1"], "Pid": "p02416", "ProblemText": "Task Description: Write a program which reads an integer and prints sum of its digits.\nTask Input: The input consists of multiple datasets. For each dataset, an integer x is given in a line. The number of digits in x does not exceed 1000.\n\nThe input ends with a line including single zero. Your program should not process for this terminal symbol.\nTask Output: For each dataset, print the sum of digits in x.\nTask Samples: input: 123\n55\n1000\n0\n output: 6\n10\n1\n\n" }, { "title": "Counting Characters", "content": "Write a program which counts and reports the number of each alphabetical letter. Ignore the case of characters.", "constraint": "The number of characters in the sentence < 1200", "input": "A sentence in English is given in several lines.", "output": "Prints the number of alphabetical letters in the following format:\n\na : The number of 'a'\nb : The number of 'b'\nc : The number of 'c'\n .\n .\nz : The number of 'z'", "content_img": false, "lang": "en", "error": false, "samples": ["input: This is a pen.\n output: a : 1\nb : 0\nc : 0\nd : 0\ne : 1\nf : 0\ng : 0\nh : 1\ni : 2\nj : 0\nk : 0\nl : 0\nm : 0\nn : 1\no : 0\np : 1\nq : 0\nr : 0\ns : 2\nt : 1\nu : 0\nv : 0\nw : 0\nx : 0\ny : 0\nz : 0"], "Pid": "p02417", "ProblemText": "Task Description: Write a program which counts and reports the number of each alphabetical letter. Ignore the case of characters.\nTask Constraint: The number of characters in the sentence < 1200\nTask Input: A sentence in English is given in several lines.\nTask Output: Prints the number of alphabetical letters in the following format:\n\na : The number of 'a'\nb : The number of 'b'\nc : The number of 'c'\n .\n .\nz : The number of 'z'\nTask Samples: input: This is a pen.\n output: a : 1\nb : 0\nc : 0\nd : 0\ne : 1\nf : 0\ng : 0\nh : 1\ni : 2\nj : 0\nk : 0\nl : 0\nm : 0\nn : 1\no : 0\np : 1\nq : 0\nr : 0\ns : 2\nt : 1\nu : 0\nv : 0\nw : 0\nx : 0\ny : 0\nz : 0\n\n" }, { "title": "Ring", "content": "Write a program which finds a pattern $p$ in a ring shaped text $s$.", "constraint": "$1 <= $ length of $p <= $ length of $s <= 100$\n\n$s$ and $p$ consists of lower-case letters", "input": "In the first line, the text $s$ is given. \n In the second line, the pattern $p$ is given.", "output": "If $p$ is in $s$, print Yes in a line, otherwise No.", "content_img": true, "lang": "en", "error": false, "samples": ["input: vanceknowledgetoad\nadvance\n output: Yes", "input: vanceknowledgetoad\nadvanced\n output: No"], "Pid": "p02418", "ProblemText": "Task Description: Write a program which finds a pattern $p$ in a ring shaped text $s$.\nTask Constraint: $1 <= $ length of $p <= $ length of $s <= 100$\n\n$s$ and $p$ consists of lower-case letters\nTask Input: In the first line, the text $s$ is given. \n In the second line, the pattern $p$ is given.\nTask Output: If $p$ is in $s$, print Yes in a line, otherwise No.\nTask Samples: input: vanceknowledgetoad\nadvance\n output: Yes\ninput: vanceknowledgetoad\nadvanced\n output: No\n\n" }, { "title": "Finding a Word", "content": "Write a program which reads a word W and a text T, and prints the number of word W which appears in text T\n\nT consists of string T_i separated by space characters and newlines. Count the number of T_i which equals to W. The word and text are case insensitive.", "constraint": "The length of W <= 10\n\nW consists of lower case letters\n\nThe length of T in a line <= 1000", "input": "In the first line, the word W is given. In the following lines, the text T is given separated by space characters and newlines.\n\n\"END_OF_TEXT\" indicates the end of the text.", "output": "Print the number of W in the text.", "content_img": false, "lang": "en", "error": false, "samples": ["input: computer\nNurtures computer scientists and highly-skilled computer engineers\nwho will create and exploit \"knowledge\" for the new era.\nProvides an outstanding computer environment.\nEND_OF_TEXT\n output: 3"], "Pid": "p02419", "ProblemText": "Task Description: Write a program which reads a word W and a text T, and prints the number of word W which appears in text T\n\nT consists of string T_i separated by space characters and newlines. Count the number of T_i which equals to W. The word and text are case insensitive.\nTask Constraint: The length of W <= 10\n\nW consists of lower case letters\n\nThe length of T in a line <= 1000\nTask Input: In the first line, the word W is given. In the following lines, the text T is given separated by space characters and newlines.\n\n\"END_OF_TEXT\" indicates the end of the text.\nTask Output: Print the number of W in the text.\nTask Samples: input: computer\nNurtures computer scientists and highly-skilled computer engineers\nwho will create and exploit \"knowledge\" for the new era.\nProvides an outstanding computer environment.\nEND_OF_TEXT\n output: 3\n\n" }, { "title": "Shuffle", "content": "Your task is to shuffle a deck of n cards, each of which is marked by a alphabetical letter.\n\n A single shuffle action takes out h cards from the bottom of the deck and moves them to the top of the deck.\n\n The deck of cards is represented by a string as follows.\n\nabcdeefab\n\n The first character and the last character correspond to the card located at the bottom of the deck and the card on the top of the deck respectively.\n\n For example, a shuffle with h = 4 to the above deck, moves the first 4 characters \"abcd\" to the end of the remaining characters \"eefab\", and generates the following deck:\n\neefababcd\n\n You can repeat such shuffle operations.\n\n Write a program which reads a deck (a string) and a sequence of h, and prints the final state (a string).", "constraint": "The length of the string <= 200\n\n1 <= m <= 100\n\n1 <= h_i < The length of the string\n\n The number of datasets <= 10", "input": "The input consists of multiple datasets. Each dataset is given in the following format:\n\nA string which represents a deck\nThe number of shuffle m\nh_1\nh_2\n .\n .\nh_m\n\n The input ends with a single character '-' for the string.", "output": "For each dataset, print a string which represents the final state in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aabc\n3\n1\n2\n1\nvwxyz\n2\n3\n4\n-\n output: aabc\nxyzvw"], "Pid": "p02420", "ProblemText": "Task Description: Your task is to shuffle a deck of n cards, each of which is marked by a alphabetical letter.\n\n A single shuffle action takes out h cards from the bottom of the deck and moves them to the top of the deck.\n\n The deck of cards is represented by a string as follows.\n\nabcdeefab\n\n The first character and the last character correspond to the card located at the bottom of the deck and the card on the top of the deck respectively.\n\n For example, a shuffle with h = 4 to the above deck, moves the first 4 characters \"abcd\" to the end of the remaining characters \"eefab\", and generates the following deck:\n\neefababcd\n\n You can repeat such shuffle operations.\n\n Write a program which reads a deck (a string) and a sequence of h, and prints the final state (a string).\nTask Constraint: The length of the string <= 200\n\n1 <= m <= 100\n\n1 <= h_i < The length of the string\n\n The number of datasets <= 10\nTask Input: The input consists of multiple datasets. Each dataset is given in the following format:\n\nA string which represents a deck\nThe number of shuffle m\nh_1\nh_2\n .\n .\nh_m\n\n The input ends with a single character '-' for the string.\nTask Output: For each dataset, print a string which represents the final state in a line.\nTask Samples: input: aabc\n3\n1\n2\n1\nvwxyz\n2\n3\n4\n-\n output: aabc\nxyzvw\n\n" }, { "title": "Card Game", "content": "Taro and Hanako are playing card games. They have n cards each, and they compete n turns. At each turn Taro and Hanako respectively puts out a card.\n The name of the animal consisting of alphabetical letters is written on each card, and the bigger one in lexicographical order becomes the winner of that turn. The winner obtains 3 points. In the case of a draw, they obtain 1 point each.\n\n Write a program which reads a sequence of cards Taro and Hanako have and reports the final scores of the game.", "constraint": "n <= 1000\n\nThe length of the string <= 100", "input": "In the first line, the number of cards n is given. In the following n lines, the cards for n turns are given respectively. For each line, the first string represents the Taro's card and the second one represents Hanako's card.", "output": "Print the final scores of Taro and Hanako respectively. Put a single space character between them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\ncat dog\nfish fish\nlion tiger\n output: 1 7"], "Pid": "p02421", "ProblemText": "Task Description: Taro and Hanako are playing card games. They have n cards each, and they compete n turns. At each turn Taro and Hanako respectively puts out a card.\n The name of the animal consisting of alphabetical letters is written on each card, and the bigger one in lexicographical order becomes the winner of that turn. The winner obtains 3 points. In the case of a draw, they obtain 1 point each.\n\n Write a program which reads a sequence of cards Taro and Hanako have and reports the final scores of the game.\nTask Constraint: n <= 1000\n\nThe length of the string <= 100\nTask Input: In the first line, the number of cards n is given. In the following n lines, the cards for n turns are given respectively. For each line, the first string represents the Taro's card and the second one represents Hanako's card.\nTask Output: Print the final scores of Taro and Hanako respectively. Put a single space character between them.\nTask Samples: input: 3\ncat dog\nfish fish\nlion tiger\n output: 1 7\n\n" }, { "title": "transformation", "content": "Write a program which performs a sequence of commands to a given string $str$. The command is one of:\n\nprint a b: print from the a-th character to the b-th character of $str$\n\nreverse a b: reverse from the a-th character to the b-th character of $str$\n\nreplace a b p: replace from the a-th character to the b-th character of $str$ with p\n Note that the indices of $str$ start with 0.", "constraint": "$1 <= $ length of $str <= 1000$\n\n$1 <= q <= 100$\n\n$0 <= a <= b < $ length of $str$\n\nfor replace command, $b - a + 1 = $ length of $p$", "input": "In the first line, a string $str$ is given. $str$ consists of lowercase letters. In the second line, the number of commands q is given. In the next q lines, each command is given in the above mentioned format.", "output": "For each print command, print a string in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abcde\n3\nreplace 1 3 xyz\nreverse 0 2\nprint 1 4\n output: xaze", "input: xyz\n3\nprint 0 2\nreplace 0 2 abc\nprint 0 2\n output: xyz\nabc"], "Pid": "p02422", "ProblemText": "Task Description: Write a program which performs a sequence of commands to a given string $str$. The command is one of:\n\nprint a b: print from the a-th character to the b-th character of $str$\n\nreverse a b: reverse from the a-th character to the b-th character of $str$\n\nreplace a b p: replace from the a-th character to the b-th character of $str$ with p\n Note that the indices of $str$ start with 0.\nTask Constraint: $1 <= $ length of $str <= 1000$\n\n$1 <= q <= 100$\n\n$0 <= a <= b < $ length of $str$\n\nfor replace command, $b - a + 1 = $ length of $p$\nTask Input: In the first line, a string $str$ is given. $str$ consists of lowercase letters. In the second line, the number of commands q is given. In the next q lines, each command is given in the above mentioned format.\nTask Output: For each print command, print a string in a line.\nTask Samples: input: abcde\n3\nreplace 1 3 xyz\nreverse 0 2\nprint 1 4\n output: xaze\ninput: xyz\n3\nprint 0 2\nreplace 0 2 abc\nprint 0 2\n output: xyz\nabc\n\n" }, { "title": "Bit Operation I", "content": "Given a non-negative decimal integer $x$, convert it to binary representation $b$ of 32 bits. Then, print the result of the following operations to $b$ respecitvely.\n\nInversion: change the state of each bit to the opposite state\n\nLogical left shift: shift left by 1\n\nLogical right shift: shift right by 1", "constraint": "$0 <= x <= 2^{32} - 1$", "input": "The input is given in the following format.\n\n$x$", "output": "Print the given bits, results of inversion, left shift and right shift in a line respectively.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n output: 00000000000000000000000000001000\n11111111111111111111111111110111\n00000000000000000000000000010000\n00000000000000000000000000000100", "input: 13\n output: 00000000000000000000000000001101\n11111111111111111111111111110010\n00000000000000000000000000011010\n00000000000000000000000000000110"], "Pid": "p02423", "ProblemText": "Task Description: Given a non-negative decimal integer $x$, convert it to binary representation $b$ of 32 bits. Then, print the result of the following operations to $b$ respecitvely.\n\nInversion: change the state of each bit to the opposite state\n\nLogical left shift: shift left by 1\n\nLogical right shift: shift right by 1\nTask Constraint: $0 <= x <= 2^{32} - 1$\nTask Input: The input is given in the following format.\n\n$x$\nTask Output: Print the given bits, results of inversion, left shift and right shift in a line respectively.\nTask Samples: input: 8\n output: 00000000000000000000000000001000\n11111111111111111111111111110111\n00000000000000000000000000010000\n00000000000000000000000000000100\ninput: 13\n output: 00000000000000000000000000001101\n11111111111111111111111111110010\n00000000000000000000000000011010\n00000000000000000000000000000110\n\n" }, { "title": "Bit Operation II", "content": "Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.", "constraint": "$0 <= a, b <= 2^{32} - 1$", "input": "The input is given in the following format.\n\n$a \\; b$", "output": "Print results of AND, OR and XOR in a line respectively.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 10\n output: 00000000000000000000000000001000\n00000000000000000000000000001010\n00000000000000000000000000000010"], "Pid": "p02424", "ProblemText": "Task Description: Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.\nTask Constraint: $0 <= a, b <= 2^{32} - 1$\nTask Input: The input is given in the following format.\n\n$a \\; b$\nTask Output: Print results of AND, OR and XOR in a line respectively.\nTask Samples: input: 8 10\n output: 00000000000000000000000000001000\n00000000000000000000000000001010\n00000000000000000000000000000010\n\n" }, { "title": "Bit Flag", "content": "A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0,1, . . . , n-1$ -th flag corresponds to 1 (ON) or 0 (OFF).\n The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary representation where each bit is 0 or 1.\n\n Given a sequence of bits with 64 flags which represent a state, perform the following operations. Note that each flag of the bits is initialized by OFF.\n\ntest(i): \t\tPrint 1 if $i$-th flag is ON, otherwise 0\n\nset(i): \t\tSet $i$-th flag to ON\n\nclear(i):\t\tSet $i$-th flag to OFF\n\nflip(i): \t\tInverse $i$-th flag\n\nall:\t\tPrint 1 if all flags are ON, otherwise 0\n\nany:\t\tPrint 1 if at least one flag is ON, otherwise 0\n\nnone:\t\tPrint 1 if all flags are OFF, otherwise 0\n\ncount:\t\tPrint the number of ON flags\n\nval:\t\tPrint the decimal value of the state", "constraint": "$1 <= q <= 200,000$\n\n$0 <= i < 64$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given in the following format:\n\n0 $i$\nor\n1 $i$\nor\n2 $i$\nor\n3 $i$\nor\n4\nor\n5\nor\n6\nor\n7\nor\n8\n\n The first digit 0,1, . . . , 8 represents the operation test(i), set(i), clear(i), flip(i), all, any, none, count or val respectively.", "output": "Print the result in a line for each test, all, any, none, count and val operation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 14\n1 0\n1 1\n1 2\n2 1\n0 0\n0 1\n0 2\n0 3\n3 3\n4\n5\n6\n7\n8\n output: 1\n0\n1\n0\n0\n1\n0\n3\n13"], "Pid": "p02425", "ProblemText": "Task Description: A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0,1, . . . , n-1$ -th flag corresponds to 1 (ON) or 0 (OFF).\n The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary representation where each bit is 0 or 1.\n\n Given a sequence of bits with 64 flags which represent a state, perform the following operations. Note that each flag of the bits is initialized by OFF.\n\ntest(i): \t\tPrint 1 if $i$-th flag is ON, otherwise 0\n\nset(i): \t\tSet $i$-th flag to ON\n\nclear(i):\t\tSet $i$-th flag to OFF\n\nflip(i): \t\tInverse $i$-th flag\n\nall:\t\tPrint 1 if all flags are ON, otherwise 0\n\nany:\t\tPrint 1 if at least one flag is ON, otherwise 0\n\nnone:\t\tPrint 1 if all flags are OFF, otherwise 0\n\ncount:\t\tPrint the number of ON flags\n\nval:\t\tPrint the decimal value of the state\nTask Constraint: $1 <= q <= 200,000$\n\n$0 <= i < 64$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given in the following format:\n\n0 $i$\nor\n1 $i$\nor\n2 $i$\nor\n3 $i$\nor\n4\nor\n5\nor\n6\nor\n7\nor\n8\n\n The first digit 0,1, . . . , 8 represents the operation test(i), set(i), clear(i), flip(i), all, any, none, count or val respectively.\nTask Output: Print the result in a line for each test, all, any, none, count and val operation.\nTask Samples: input: 14\n1 0\n1 1\n1 2\n2 1\n0 0\n0 1\n0 2\n0 3\n3 3\n4\n5\n6\n7\n8\n output: 1\n0\n1\n0\n0\n1\n0\n3\n13\n\n" }, { "title": "Bit Mask", "content": "A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0,1, . . . , n-1$ th flag corresponds to 1 (ON) or 0 (OFF).\n The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary representation where each bit is 0 or 1.\n\n On the other hand, a mask is a special bit sequence which can be used to set specified bits of a given bit sequence to ON/OFF. It can also be used to extract/exclude a bit sequence based on a specified pattern.\n\n Given a sequence of bits with 64 flags which represent a state, perform the following operations using a set of pre-defined masks. Note that each flag of the bits is initialized by OFF.\n\ntest(i): \tPrint 1 if $i$-th flag is ON, otherwise 0\n\nset(m): \tSet flags specified by mask $m$ to ON\n\nclear(m):\tSet flags specified by mask $m$ to OFF\n\nflip(m):\tInverse flags specified by mask $m$\n\nall(m):\tPrint 1 if all flags specified by mask $m$ are ON, otherwise 0\n\nany(m):\tPrint 1 if at least one flag specified by mask $m$ is ON, otherwise 0\n\nnone(m):\tPrint 1 if all flags specified by mask $m$ are OFF, otherwise 0\n\ncount(m):\tPrint the number of flags specifed by mask $m$ with ON\n\nval(m):\tPrint the decimal value of the state specified by mask $m$", "constraint": "$1 <= n <= 10$\n\n$1 <= k <= 64$\n\n$1 <= q <= 200,000$\n\n$0 <= i < 64$\n\n$0 <= m < n$", "input": "The input is given in the following format.\n\n$n$\n$mask_0$\n$mask_1$\n:\n$mask_{n-1}$\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n $n$ represents the number of masks. $mask_i$ represents state of $i$-th mask and is given in the following format:\n\n$k$ $b_0$ $b_1$ . . . $b_k$\n\n$k$ is the number of ON in the bits. The following $k$ integers $b_j$ show that $b_j$-th bit is ON.\n\n$query_i$ represents $i$-th query and is given in the following format:\n\n0 $i$\nor\n1 $m$\nor\n2 $m$\nor\n3 $m$\nor\n4 $m$\nor\n5 $m$\nor\n6 $m$\nor\n7 $m$\nor\n8 $m$\n\nThe first digit 0,1, . . . , 8 represents the operation test(i), set(m), clear(m), flip(m), all(m), any(m), none(m), count(m) or val(m) respectively.", "output": "Print the result in a line for each test, all, any, none, count and val operation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 0 1 3\n1 3\n3 0 1 2\n8\n1 0\n2 1\n3 1\n4 2\n5 2\n6 2\n7 2\n8 2\n output: 0\n1\n0\n2\n3"], "Pid": "p02426", "ProblemText": "Task Description: A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0,1, . . . , n-1$ th flag corresponds to 1 (ON) or 0 (OFF).\n The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary representation where each bit is 0 or 1.\n\n On the other hand, a mask is a special bit sequence which can be used to set specified bits of a given bit sequence to ON/OFF. It can also be used to extract/exclude a bit sequence based on a specified pattern.\n\n Given a sequence of bits with 64 flags which represent a state, perform the following operations using a set of pre-defined masks. Note that each flag of the bits is initialized by OFF.\n\ntest(i): \tPrint 1 if $i$-th flag is ON, otherwise 0\n\nset(m): \tSet flags specified by mask $m$ to ON\n\nclear(m):\tSet flags specified by mask $m$ to OFF\n\nflip(m):\tInverse flags specified by mask $m$\n\nall(m):\tPrint 1 if all flags specified by mask $m$ are ON, otherwise 0\n\nany(m):\tPrint 1 if at least one flag specified by mask $m$ is ON, otherwise 0\n\nnone(m):\tPrint 1 if all flags specified by mask $m$ are OFF, otherwise 0\n\ncount(m):\tPrint the number of flags specifed by mask $m$ with ON\n\nval(m):\tPrint the decimal value of the state specified by mask $m$\nTask Constraint: $1 <= n <= 10$\n\n$1 <= k <= 64$\n\n$1 <= q <= 200,000$\n\n$0 <= i < 64$\n\n$0 <= m < n$\nTask Input: The input is given in the following format.\n\n$n$\n$mask_0$\n$mask_1$\n:\n$mask_{n-1}$\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n $n$ represents the number of masks. $mask_i$ represents state of $i$-th mask and is given in the following format:\n\n$k$ $b_0$ $b_1$ . . . $b_k$\n\n$k$ is the number of ON in the bits. The following $k$ integers $b_j$ show that $b_j$-th bit is ON.\n\n$query_i$ represents $i$-th query and is given in the following format:\n\n0 $i$\nor\n1 $m$\nor\n2 $m$\nor\n3 $m$\nor\n4 $m$\nor\n5 $m$\nor\n6 $m$\nor\n7 $m$\nor\n8 $m$\n\nThe first digit 0,1, . . . , 8 represents the operation test(i), set(m), clear(m), flip(m), all(m), any(m), none(m), count(m) or val(m) respectively.\nTask Output: Print the result in a line for each test, all, any, none, count and val operation.\nTask Samples: input: 3\n3 0 1 3\n1 3\n3 0 1 2\n8\n1 0\n2 1\n3 1\n4 2\n5 2\n6 2\n7 2\n8 2\n output: 0\n1\n0\n2\n3\n\n" }, { "title": "Enumeration of Subsets I", "content": "Print all subsets of a set $S$, which contains $0,1, . . . n-1$ as elements. Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.", "constraint": "$1 <= n <= 18$", "input": "The input is given in the following format.\n\n$n$", "output": "Print subsets ordered by their decimal integers. Print a subset in a line in the following format.\n\n$d$: $e_0$ $e_1$ . . . \n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Seprate two adjacency elements by a space character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n output: 0:\n1: 0\n2: 1\n3: 0 1\n4: 2\n5: 0 2\n6: 1 2\n7: 0 1 2\n8: 3\n9: 0 3\n10: 1 3\n11: 0 1 3\n12: 2 3\n13: 0 2 3\n14: 1 2 3\n15: 0 1 2 3\n Note that if the subset is empty, your program should not output a space character after ':\n'."], "Pid": "p02427", "ProblemText": "Task Description: Print all subsets of a set $S$, which contains $0,1, . . . n-1$ as elements. Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.\nTask Constraint: $1 <= n <= 18$\nTask Input: The input is given in the following format.\n\n$n$\nTask Output: Print subsets ordered by their decimal integers. Print a subset in a line in the following format.\n\n$d$: $e_0$ $e_1$ . . . \n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Seprate two adjacency elements by a space character.\nTask Samples: input: 4\n output: 0:\n1: 0\n2: 1\n3: 0 1\n4: 2\n5: 0 2\n6: 1 2\n7: 0 1 2\n8: 3\n9: 0 3\n10: 1 3\n11: 0 1 3\n12: 2 3\n13: 0 2 3\n14: 1 2 3\n15: 0 1 2 3\n Note that if the subset is empty, your program should not output a space character after ':\n'.\n\n" }, { "title": "Enumeration of Subsets II", "content": "You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0,1, . . . n-1$.\n\n Print all sets, each of which is a subset of $U$ and includes $T$ as a subset.\n\n Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.", "constraint": "$1 <= n <= 18$\n\n$0 <= k <= n$\n\n$0 <= b_i < n$", "input": "The input is given in the following format.\n\n$n$\n$k \\; b_0 \\; b_1 \\; . . . \\; b_{k-1}$\n\n$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.", "output": "Print the subsets ordered by their decimal integers. Print a subset in the following format.\n\n$d$: $e_0$ $e_1$ . . .\n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 0 2\n output: 5: 0 2\n7: 0 1 2\n13: 0 2 3\n15: 0 1 2 3"], "Pid": "p02428", "ProblemText": "Task Description: You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0,1, . . . n-1$.\n\n Print all sets, each of which is a subset of $U$ and includes $T$ as a subset.\n\n Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.\nTask Constraint: $1 <= n <= 18$\n\n$0 <= k <= n$\n\n$0 <= b_i < n$\nTask Input: The input is given in the following format.\n\n$n$\n$k \\; b_0 \\; b_1 \\; . . . \\; b_{k-1}$\n\n$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.\nTask Output: Print the subsets ordered by their decimal integers. Print a subset in the following format.\n\n$d$: $e_0$ $e_1$ . . .\n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.\nTask Samples: input: 4\n2 0 2\n output: 5: 0 2\n7: 0 1 2\n13: 0 2 3\n15: 0 1 2 3\n\n" }, { "title": "Enumeration of Subsets III", "content": "You are given a set $T$, which is a subset of $S$. The set $S$ consists of $0,1, . . . n-1$.\n\n Print all subsets of $T$.\n\n Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.", "constraint": "$1 <= n <= 28$\n\n$0 <= k <= 18$\n\n$k <= n$\n\n$0 <= b_i < n$", "input": "The input is given in the following format.\n\n$n$\n$k \\; b_0 \\; b_1 \\; . . . \\; b_{k-1}$\n\n$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.", "output": "Print the subsets ordered by their decimal integers. Print a subset in the following format.\n\n$d$: $e_0$ $e_1$ . . .\n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 0 2\n output: 0:\n1: 0\n4: 2\n5: 0 2"], "Pid": "p02429", "ProblemText": "Task Description: You are given a set $T$, which is a subset of $S$. The set $S$ consists of $0,1, . . . n-1$.\n\n Print all subsets of $T$.\n\n Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.\nTask Constraint: $1 <= n <= 28$\n\n$0 <= k <= 18$\n\n$k <= n$\n\n$0 <= b_i < n$\nTask Input: The input is given in the following format.\n\n$n$\n$k \\; b_0 \\; b_1 \\; . . . \\; b_{k-1}$\n\n$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.\nTask Output: Print the subsets ordered by their decimal integers. Print a subset in the following format.\n\n$d$: $e_0$ $e_1$ . . .\n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.\nTask Samples: input: 4\n2 0 2\n output: 0:\n1: 0\n4: 2\n5: 0 2\n\n" }, { "title": "Enumeration of Combinations", "content": "Print all combinations which can be made by $k$ different elements from $0,1, . . . , n-1$.\n\n Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a combination is calculated by bitwise OR of the selected elements.", "constraint": "$1 <= n <= 18$\n\n$k <= n$", "input": "The input is given in the following format.\n\n$n \\; k$", "output": "Print the combinations ordered by their decimal integers. Print a combination in the following format.\n\n$d$: $e_0$ $e_1$ . . .\n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the combination in ascending order. Separate two adjacency elements by a space character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n output: 7: 0 1 2\n11: 0 1 3\n13: 0 2 3\n14: 1 2 3\n19: 0 1 4\n21: 0 2 4\n22: 1 2 4\n25: 0 3 4\n26: 1 3 4\n28: 2 3 4"], "Pid": "p02430", "ProblemText": "Task Description: Print all combinations which can be made by $k$ different elements from $0,1, . . . , n-1$.\n\n Note that we represent $0,1, . . . n-1$ as 00. . . 0001,00. . . 0010,00. . . 0100, . . . , 10. . . 0000 in binary respectively and the integer representation of a combination is calculated by bitwise OR of the selected elements.\nTask Constraint: $1 <= n <= 18$\n\n$k <= n$\nTask Input: The input is given in the following format.\n\n$n \\; k$\nTask Output: Print the combinations ordered by their decimal integers. Print a combination in the following format.\n\n$d$: $e_0$ $e_1$ . . .\n\n Print ': ' after the integer value $d$, then print elements $e_i$ in the combination in ascending order. Separate two adjacency elements by a space character.\nTask Samples: input: 5 3\n output: 7: 0 1 2\n11: 0 1 3\n13: 0 2 3\n14: 1 2 3\n19: 0 1 4\n21: 0 2 4\n22: 1 2 4\n25: 0 3 4\n26: 1 3 4\n28: 2 3 4\n\n" }, { "title": "Vector", "content": "For a dynamic array $A = \\{a_0, a_1, . . . \\}$ of integers, perform a sequence of the following operations:\n\npush Back($x$): add element $x$ at the end of $A$\n\nrandom Access($p$): print element $a_p$\n\npop Back(): delete the last element of $A$\n \n$A$ is a 0-origin array and it is empty in the initial state.", "constraint": "$1 <= q <= 200,000$\n\n$0 <= p < $ the size of $A$\n\n$-1,000,000,000 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n Each query $query_i$ is given by\n\n0 $x$\nor\n1 $p$\nor\n2\n\n where the first digits 0,1 and 2 represent push Back, random Access and pop Back operations respectively.\n\n random Access and pop Back operations will not be given for an empty array.", "output": "For each random Access, print $a_p$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n0 1\n0 2\n0 3\n2\n0 4\n1 0\n1 1\n1 2\n output: 1\n2\n4"], "Pid": "p02431", "ProblemText": "Task Description: For a dynamic array $A = \\{a_0, a_1, . . . \\}$ of integers, perform a sequence of the following operations:\n\npush Back($x$): add element $x$ at the end of $A$\n\nrandom Access($p$): print element $a_p$\n\npop Back(): delete the last element of $A$\n \n$A$ is a 0-origin array and it is empty in the initial state.\nTask Constraint: $1 <= q <= 200,000$\n\n$0 <= p < $ the size of $A$\n\n$-1,000,000,000 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\n Each query $query_i$ is given by\n\n0 $x$\nor\n1 $p$\nor\n2\n\n where the first digits 0,1 and 2 represent push Back, random Access and pop Back operations respectively.\n\n random Access and pop Back operations will not be given for an empty array.\nTask Output: For each random Access, print $a_p$ in a line.\nTask Samples: input: 8\n0 1\n0 2\n0 3\n2\n0 4\n1 0\n1 1\n1 2\n output: 1\n2\n4\n\n" }, { "title": "Deque", "content": "For a dynamic array $A = \\{a_0, a_1, . . . \\}$ of integers, perform a sequence of the following operations:\n\npush($d$, $x$): Add element $x$ at the begining of $A$, if $d = 0$. Add element $x$ at the end of $A$, if $d = 1$.\n\nrandom Access($p$): Print element $a_p$.\n\npop($d$): Delete the first element of $A$, if $d = 0$. Delete the last element of $A$, if $d = 1$.\n $A$ is a 0-origin array and it is empty in the initial state.", "constraint": "$1 <= q <= 400,000$\n\n$0 <= p < $ the size of $A$\n\n$-1,000,000,000 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $d$ $x$\nor\n1 $p$\nor\n2 $d$\n\n where the first digits 0,1 and 2 represent push, random Access and pop operations respectively.\n\n random Access and pop operations will not be given for an empty array.", "output": "For each random Access, print $a_p$ in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11\n0 0 1\n0 0 2\n0 1 3\n1 0\n1 1\n1 2\n2 0\n2 1\n0 0 4\n1 0\n1 1\n output: 2\n1\n3\n4\n1"], "Pid": "p02432", "ProblemText": "Task Description: For a dynamic array $A = \\{a_0, a_1, . . . \\}$ of integers, perform a sequence of the following operations:\n\npush($d$, $x$): Add element $x$ at the begining of $A$, if $d = 0$. Add element $x$ at the end of $A$, if $d = 1$.\n\nrandom Access($p$): Print element $a_p$.\n\npop($d$): Delete the first element of $A$, if $d = 0$. Delete the last element of $A$, if $d = 1$.\n $A$ is a 0-origin array and it is empty in the initial state.\nTask Constraint: $1 <= q <= 400,000$\n\n$0 <= p < $ the size of $A$\n\n$-1,000,000,000 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $d$ $x$\nor\n1 $p$\nor\n2 $d$\n\n where the first digits 0,1 and 2 represent push, random Access and pop operations respectively.\n\n random Access and pop operations will not be given for an empty array.\nTask Output: For each random Access, print $a_p$ in a line.\nTask Samples: input: 11\n0 0 1\n0 0 2\n0 1 3\n1 0\n1 1\n1 2\n2 0\n2 1\n0 0 4\n1 0\n1 1\n output: 2\n1\n3\n4\n1\n\n" }, { "title": "List", "content": "For a dynamic list $L$ of integers, perform a sequence of the following operations. $L$ has a special element called END at the end of the list and an element of $L$ is indicated by a cursor.\n\ninsert($x$): Insert $x$ before the element indicated by the cursor. After this operation, the cursor points the inserted element.\n\nmove($d$): Move the cursor to the end by $d$, if $d$ is positive. Move the cursor to the front by $d$, if $d$ is negative.\n\nerase(): Delete the element indicated by the cursor. After this operation, the cursor points the element next to the deleted element. In case there is no such element, the cursor should point END.\n \n In the initial state, $L$ is empty and the cursor points END.", "constraint": "$1 <= q <= 500,000$\n\nThe cursor indicates an element of $L$ or END during the operations\n\nErase operation will not given when the cursor points END\n\n$-1,000,000,000 <= x <= 1,000,000,000$\n\nMoving distance of the cursor ($\\sum{|d|}$) does not exceed 1,000,000\n\n$L$ is not empty after performing all operations", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $d$\nor\n2\n\n where the first digits 0,1 and 2 represent insert, move and erase operations respectively.", "output": "Print all elements of the list in order after performing given operations. Print an element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 1\n0 2\n0 3\n1 1\n2\n output: 3\n1"], "Pid": "p02433", "ProblemText": "Task Description: For a dynamic list $L$ of integers, perform a sequence of the following operations. $L$ has a special element called END at the end of the list and an element of $L$ is indicated by a cursor.\n\ninsert($x$): Insert $x$ before the element indicated by the cursor. After this operation, the cursor points the inserted element.\n\nmove($d$): Move the cursor to the end by $d$, if $d$ is positive. Move the cursor to the front by $d$, if $d$ is negative.\n\nerase(): Delete the element indicated by the cursor. After this operation, the cursor points the element next to the deleted element. In case there is no such element, the cursor should point END.\n \n In the initial state, $L$ is empty and the cursor points END.\nTask Constraint: $1 <= q <= 500,000$\n\nThe cursor indicates an element of $L$ or END during the operations\n\nErase operation will not given when the cursor points END\n\n$-1,000,000,000 <= x <= 1,000,000,000$\n\nMoving distance of the cursor ($\\sum{|d|}$) does not exceed 1,000,000\n\n$L$ is not empty after performing all operations\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $d$\nor\n2\n\n where the first digits 0,1 and 2 represent insert, move and erase operations respectively.\nTask Output: Print all elements of the list in order after performing given operations. Print an element in a line.\nTask Samples: input: 5\n0 1\n0 2\n0 3\n1 1\n2\n output: 3\n1\n\n" }, { "title": "Vector II", "content": "For $n$ dynamic arrays $A_i$ ($i = 0,1, . . . , n-1$), perform a sequence of the following operations:\n\npush Back($t$, $x$): Add element $x$ at the end of $A_t$.\n\ndump($t$): Print all elements in $A_t$.\n\nclear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.\n $A_i$ is a 0-origin array and it is empty in the initial state.", "constraint": "$1 <= n <= 1,000$\n\n$1 <= q <= 500,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$\n\nThe total number of elements printed by dump operations do not exceed 500,000", "input": "The input is given in the following format.\n\n$n$ $q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\nwhere the first digits 0,1 and 2 represent push Back, dump and clear operations respectively.", "output": "For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 13\n0 0 1\n0 0 2\n0 0 3\n0 1 -1\n0 2 4\n0 2 5\n1 0\n1 1\n1 2\n2 1\n1 0\n1 1\n1 2\n output: 1 2 3\n-1\n4 5\n1 2 3\n\n4 5"], "Pid": "p02434", "ProblemText": "Task Description: For $n$ dynamic arrays $A_i$ ($i = 0,1, . . . , n-1$), perform a sequence of the following operations:\n\npush Back($t$, $x$): Add element $x$ at the end of $A_t$.\n\ndump($t$): Print all elements in $A_t$.\n\nclear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.\n $A_i$ is a 0-origin array and it is empty in the initial state.\nTask Constraint: $1 <= n <= 1,000$\n\n$1 <= q <= 500,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$\n\nThe total number of elements printed by dump operations do not exceed 500,000\nTask Input: The input is given in the following format.\n\n$n$ $q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\nwhere the first digits 0,1 and 2 represent push Back, dump and clear operations respectively.\nTask Output: For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.\nTask Samples: input: 3 13\n0 0 1\n0 0 2\n0 0 3\n0 1 -1\n0 2 4\n0 2 5\n1 0\n1 1\n1 2\n2 1\n1 0\n1 1\n1 2\n output: 1 2 3\n-1\n4 5\n1 2 3\n\n4 5\n\n" }, { "title": "Stack", "content": "Stack is a container of elements that are inserted and deleted according to LIFO (Last In First Out).\n\n For $n$ stack $S_i$ ($i = 0,1, . . . , n-1$), perform a sequence of the following operations.\n\npush($t$, $x$): Insert an integer $x$ to $S_t$.\n\ntop($t$): Report the value which should be deleted next from $S_t$. If $S_t$ is empty, do nothing.\n\npop($t$): Delete an element from $S_t$. If $S_t$ is empty, do nothing.\nIn the initial state, all stacks are empty.", "constraint": "$1 <= n <= 1,000$\n\n$1 <= q <= 200,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\n where the first digits 0,1 and 2 represent push, top and pop operations respectively.", "output": "For each top operation, print an integer in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 9\n0 0 1\n0 0 2\n0 0 3\n0 2 4\n0 2 5\n1 0\n1 2\n2 0\n1 0\n output: 3\n5\n2"], "Pid": "p02435", "ProblemText": "Task Description: Stack is a container of elements that are inserted and deleted according to LIFO (Last In First Out).\n\n For $n$ stack $S_i$ ($i = 0,1, . . . , n-1$), perform a sequence of the following operations.\n\npush($t$, $x$): Insert an integer $x$ to $S_t$.\n\ntop($t$): Report the value which should be deleted next from $S_t$. If $S_t$ is empty, do nothing.\n\npop($t$): Delete an element from $S_t$. If $S_t$ is empty, do nothing.\nIn the initial state, all stacks are empty.\nTask Constraint: $1 <= n <= 1,000$\n\n$1 <= q <= 200,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\n where the first digits 0,1 and 2 represent push, top and pop operations respectively.\nTask Output: For each top operation, print an integer in a line.\nTask Samples: input: 3 9\n0 0 1\n0 0 2\n0 0 3\n0 2 4\n0 2 5\n1 0\n1 2\n2 0\n1 0\n output: 3\n5\n2\n\n" }, { "title": "Queue", "content": "Queue is a container of elements that are inserted and deleted according to FIFO (First In First Out).\n\n For $n$ queues $Q_i$ ($i = 0,1, . . . , n-1$), perform a sequence of the following operations.\n\nenqueue($t$, $x$): Insert an integer $x$ to $Q_t$.\n\nfront($t$): Report the value which should be deleted next from $Q_t$. If $Q_t$ is empty, do nothing.\n\ndequeue($t$): Delete an element from $Q_t$. If $Q_t$ is empty, do nothing.\nIn the initial state, all queues are empty.", "constraint": "$1 <= n <= 1,000$\n\n$1 <= q <= 200,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\n where the first digits 0,1 and 2 represent enqueue, front and dequeue operations respectively.", "output": "For each front operation, print an integer in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 9\n0 0 1\n0 0 2\n0 0 3\n0 2 4\n0 2 5\n1 0\n1 2\n2 0\n1 0\n output: 1\n4\n2"], "Pid": "p02436", "ProblemText": "Task Description: Queue is a container of elements that are inserted and deleted according to FIFO (First In First Out).\n\n For $n$ queues $Q_i$ ($i = 0,1, . . . , n-1$), perform a sequence of the following operations.\n\nenqueue($t$, $x$): Insert an integer $x$ to $Q_t$.\n\nfront($t$): Report the value which should be deleted next from $Q_t$. If $Q_t$ is empty, do nothing.\n\ndequeue($t$): Delete an element from $Q_t$. If $Q_t$ is empty, do nothing.\nIn the initial state, all queues are empty.\nTask Constraint: $1 <= n <= 1,000$\n\n$1 <= q <= 200,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\n where the first digits 0,1 and 2 represent enqueue, front and dequeue operations respectively.\nTask Output: For each front operation, print an integer in a line.\nTask Samples: input: 3 9\n0 0 1\n0 0 2\n0 0 3\n0 2 4\n0 2 5\n1 0\n1 2\n2 0\n1 0\n output: 1\n4\n2\n\n" }, { "title": "Priority Queue", "content": "Priority queue is a container of elements which the element with the highest priority should be extracted first.\n\n For $n$ priority queues $Q_i$ ($i = 0,1, . . . , n-1$) of integers, perform a sequence of the following operations.\n\ninsert($t$, $x$): Insert $x$ to $Q_t$.\n\nget Max($t$): Report the maximum value in $Q_t$. If $Q_t$ is empty, do nothing.\n\ndelete Max($t$): Delete the maximum element from $Q_t$. If $Q_t$ is empty, do nothing.\nIn the initial state, all queues are empty.", "constraint": "$1 <= n <= 1,000$\n\n$1 <= q <= 200,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\n where the first digits 0,1 and 2 represent insert, get Max and delete Max operations respectively.", "output": "For each get Max operation, print an integer in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 10\n0 0 3\n0 0 9\n0 0 1\n1 0\n2 0\n1 0\n0 0 4\n1 0\n0 1 8\n1 1\n output: 9\n3\n4\n8"], "Pid": "p02437", "ProblemText": "Task Description: Priority queue is a container of elements which the element with the highest priority should be extracted first.\n\n For $n$ priority queues $Q_i$ ($i = 0,1, . . . , n-1$) of integers, perform a sequence of the following operations.\n\ninsert($t$, $x$): Insert $x$ to $Q_t$.\n\nget Max($t$): Report the maximum value in $Q_t$. If $Q_t$ is empty, do nothing.\n\ndelete Max($t$): Delete the maximum element from $Q_t$. If $Q_t$ is empty, do nothing.\nIn the initial state, all queues are empty.\nTask Constraint: $1 <= n <= 1,000$\n\n$1 <= q <= 200,000$\n\n$-1,000,000,000 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $t$\n\n where the first digits 0,1 and 2 represent insert, get Max and delete Max operations respectively.\nTask Output: For each get Max operation, print an integer in a line.\nTask Samples: input: 2 10\n0 0 3\n0 0 9\n0 0 1\n1 0\n2 0\n1 0\n0 0 4\n1 0\n0 1 8\n1 1\n output: 9\n3\n4\n8\n\n" }, { "title": "Splice", "content": "For $n$ lists $L_i$ $(i = 0,1, . . . , n-1)$, perform a sequence of the following operations.\n\ninsert($t$, $x$): Insert an integer $x$ at the end of $L_t$.\n\ndump($t$): Print all elements in $L_t$.\n\nsplice($s$, $t$):　Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.\n In the initial state, $L_i$ $(i = 0,1, . . . , n-1)$ are empty.", "constraint": "$1 <= n <= 1,000$\n\n$1 <= q <= 500,000$\n\nFor a splice operation, $s \\ne t$\n\nFor a splice operation, $L_s$ is not empty\n\nThe total number of elements printed by dump operations do not exceed 1,000,000\n\n$-1,000,000,000 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $s$ $t$\n\n where the first digits 0,1 and 2 represent insert, dump and splice operations respectively.", "output": "For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 10\n0 0 1\n0 0 2\n0 0 3\n0 1 4\n0 1 5\n2 1 0\n0 2 6\n1 0\n1 1\n1 2\n output: 1 2 3 4 5\n\n6"], "Pid": "p02438", "ProblemText": "Task Description: For $n$ lists $L_i$ $(i = 0,1, . . . , n-1)$, perform a sequence of the following operations.\n\ninsert($t$, $x$): Insert an integer $x$ at the end of $L_t$.\n\ndump($t$): Print all elements in $L_t$.\n\nsplice($s$, $t$):　Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.\n In the initial state, $L_i$ $(i = 0,1, . . . , n-1)$ are empty.\nTask Constraint: $1 <= n <= 1,000$\n\n$1 <= q <= 500,000$\n\nFor a splice operation, $s \\ne t$\n\nFor a splice operation, $L_s$ is not empty\n\nThe total number of elements printed by dump operations do not exceed 1,000,000\n\n$-1,000,000,000 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n \\; q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $t$ $x$\nor\n1 $t$\nor\n2 $s$ $t$\n\n where the first digits 0,1 and 2 represent insert, dump and splice operations respectively.\nTask Output: For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.\nTask Samples: input: 3 10\n0 0 1\n0 0 2\n0 0 3\n0 1 4\n0 1 5\n2 1 0\n0 2 6\n1 0\n1 1\n1 2\n output: 1 2 3 4 5\n\n6\n\n" }, { "title": "Min-Max", "content": "For given three integers $a, b, c$, print the minimum value and the maximum value.", "constraint": "$-1,000,000,000 <= a, b, c <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$a \\; b \\; c\\; $\n\n Three integers $a, b, c$ are given in a line.", "output": "Print the minimum and maximum values separated by a space in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 3\n output: 3 5"], "Pid": "p02439", "ProblemText": "Task Description: For given three integers $a, b, c$, print the minimum value and the maximum value.\nTask Constraint: $-1,000,000,000 <= a, b, c <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$a \\; b \\; c\\; $\n\n Three integers $a, b, c$ are given in a line.\nTask Output: Print the minimum and maximum values separated by a space in a line.\nTask Samples: input: 4 5 3\n output: 3 5\n\n" }, { "title": "Min-Max Element", "content": "Write a program which manipulates a sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ by the following operations:\n\nmin($b, e$): report the minimum element in $a_b, a_{b+1}, . . . , a_{e-1}$\n\nmax($b, e$): report the maximum element in $a_b, a_{b+1}, . . . , a_{e-1}$", "constraint": "$1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b < e <= n$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1, . . . , \\; a_{n-1}$\n$q$\n$com_1 \\; b_1 \\; e_1$\n$com_2 \\; b_2 \\; e_2$\n:\n$com_{q} \\; b_{q} \\; e_{q}$\n\nIn the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given in the following $q$ lines. $com_i$ denotes a type of query. 0 and 1 represents min($b, e$) and max($b, e$) respectively.", "output": "For each query, print the minimum element or the maximum element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n8 3 7 1 9 1 4\n3\n0 0 3\n0 1 5\n1 0 7\n output: 3\n1\n9"], "Pid": "p02440", "ProblemText": "Task Description: Write a program which manipulates a sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ by the following operations:\n\nmin($b, e$): report the minimum element in $a_b, a_{b+1}, . . . , a_{e-1}$\n\nmax($b, e$): report the maximum element in $a_b, a_{b+1}, . . . , a_{e-1}$\nTask Constraint: $1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b < e <= n$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1, . . . , \\; a_{n-1}$\n$q$\n$com_1 \\; b_1 \\; e_1$\n$com_2 \\; b_2 \\; e_2$\n:\n$com_{q} \\; b_{q} \\; e_{q}$\n\nIn the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given in the following $q$ lines. $com_i$ denotes a type of query. 0 and 1 represents min($b, e$) and max($b, e$) respectively.\nTask Output: For each query, print the minimum element or the maximum element in a line.\nTask Samples: input: 7\n8 3 7 1 9 1 4\n3\n0 0 3\n0 1 5\n1 0 7\n output: 3\n1\n9\n\n" }, { "title": "Count", "content": "For a given sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$, perform the following operations.\n\ncount($b, e, k$): print the number of the specific values $k$ in $a_b, a_{b+1}, . . . , a_{e-1}$.", "constraint": "$1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i, k_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b < e <= n$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1, . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; e_1 \\; k_1$\n$b_2 \\; e_2 \\; k_2$\n:\n$b_q \\; e_q \\; k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $b_i \\; b_e \\; k_i$ are given as queries.", "output": "For each query, print the number of specified values.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\n1 4 1 4 2 1 3 5 6\n3\n0 9 1\n1 6 1\n3 7 5\n output: 3\n2\n0"], "Pid": "p02441", "ProblemText": "Task Description: For a given sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$, perform the following operations.\n\ncount($b, e, k$): print the number of the specific values $k$ in $a_b, a_{b+1}, . . . , a_{e-1}$.\nTask Constraint: $1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i, k_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b < e <= n$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1, . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; e_1 \\; k_1$\n$b_2 \\; e_2 \\; k_2$\n:\n$b_q \\; e_q \\; k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $b_i \\; b_e \\; k_i$ are given as queries.\nTask Output: For each query, print the number of specified values.\nTask Samples: input: 9\n1 4 1 4 2 1 3 5 6\n3\n0 9 1\n1 6 1\n3 7 5\n output: 3\n2\n0\n\n" }, { "title": "Lexicographical Comparison", "content": "Compare given two sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}$ lexicographically.", "constraint": "$1 <= n, m <= 1,000$\n\n$0 <= a_i, b_i <= 1,000$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1, . . . , \\; a_{n-1}$\n$m$\n$b_0 \\; b_1, . . . , \\; b_{m-1}$\n\n The number of elements in $A$ and its elements $a_i$ are given in the first and second lines respectively.\n The number of elements in $B$ and its elements $b_i$ are given in the third and fourth lines respectively. All input are given in integers.", "output": "Print 1 $B$ is greater than $A$, otherwise 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3\n2\n2 4\n output: 1", "input: 4\n5 4 7 0\n5\n1 2 3 4 5\n output: 0", "input: 3\n1 1 2\n4\n1 1 2 2\n output: 1"], "Pid": "p02442", "ProblemText": "Task Description: Compare given two sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}$ lexicographically.\nTask Constraint: $1 <= n, m <= 1,000$\n\n$0 <= a_i, b_i <= 1,000$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1, . . . , \\; a_{n-1}$\n$m$\n$b_0 \\; b_1, . . . , \\; b_{m-1}$\n\n The number of elements in $A$ and its elements $a_i$ are given in the first and second lines respectively.\n The number of elements in $B$ and its elements $b_i$ are given in the third and fourth lines respectively. All input are given in integers.\nTask Output: Print 1 $B$ is greater than $A$, otherwise 0.\nTask Samples: input: 3\n1 2 3\n2\n2 4\n output: 1\ninput: 4\n5 4 7 0\n5\n1 2 3 4 5\n output: 0\ninput: 3\n1 1 2\n4\n1 1 2 2\n output: 1\n\n" }, { "title": "Reverse", "content": "Write a program which reads a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and reverse specified elements by a list of the following operation:\n\nreverse($b, e$): reverse the order of $a_b, a_{b+1}, . . . , a_{e-1}$", "constraint": "$1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b < e <= n$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; e_1$\n$b_2 \\; e_2$\n:\n$b_{q} \\; b_{q}$\n\n In the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by two integers $b_i \\; e_i$ in the following $q$ lines.", "output": "Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n1 2 3 4 5 6 7 8\n2\n1 6\n3 8\n output: 1 6 5 8 7 2 3 4"], "Pid": "p02443", "ProblemText": "Task Description: Write a program which reads a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and reverse specified elements by a list of the following operation:\n\nreverse($b, e$): reverse the order of $a_b, a_{b+1}, . . . , a_{e-1}$\nTask Constraint: $1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b < e <= n$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; e_1$\n$b_2 \\; e_2$\n:\n$b_{q} \\; b_{q}$\n\n In the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by two integers $b_i \\; e_i$ in the following $q$ lines.\nTask Output: Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element.\nTask Samples: input: 8\n1 2 3 4 5 6 7 8\n2\n1 6\n3 8\n output: 1 6 5 8 7 2 3 4\n\n" }, { "title": "Rotate", "content": "Write a program which reads a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and rotate specified elements by a list of the following operation: \n\nrotate($b, m, e$): For each integer $k$ ($0 <= k < (e - b)$), move element $b + k$ to the place of element $b + ((k + (e - m)) \\mod (e - b))$.", "constraint": "$1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b_i <= m_i < e_i <= n$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; m_1 \\; e_1$\n$b_2 \\; m_2 \\; e_2$\n:\n$b_{q} \\; m_{q} \\; e_{q}$\n\nIn the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by three integers $b_i \\; m_i \\; e_i$ in the following $q$ lines.", "output": "Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11\n1 2 3 4 5 6 7 8 9 10 11\n1\n2 6 9\n output: 1 2 7 8 9 3 4 5 6 10 11"], "Pid": "p02444", "ProblemText": "Task Description: Write a program which reads a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and rotate specified elements by a list of the following operation: \n\nrotate($b, m, e$): For each integer $k$ ($0 <= k < (e - b)$), move element $b + k$ to the place of element $b + ((k + (e - m)) \\mod (e - b))$.\nTask Constraint: $1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b_i <= m_i < e_i <= n$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; m_1 \\; e_1$\n$b_2 \\; m_2 \\; e_2$\n:\n$b_{q} \\; m_{q} \\; e_{q}$\n\nIn the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by three integers $b_i \\; m_i \\; e_i$ in the following $q$ lines.\nTask Output: Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element.\nTask Samples: input: 11\n1 2 3 4 5 6 7 8 9 10 11\n1\n2 6 9\n output: 1 2 7 8 9 3 4 5 6 10 11\n\n" }, { "title": "Swap", "content": "Write a program which reads a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and swap specified elements by a list of the following operation:\n\nswap Range($b, e, t$): For each integer $k$ ($0 <= k < (e - b)$, swap element $(b + k)$ and element $(t + k)$.", "constraint": "$1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b_i < e_i <= n$\n\n$0 <= t_i < t_i + (e_i - b_i) <= n$\n\nGiven swap ranges do not overlap each other", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; e_1 \\; t_1$\n$b_2 \\; e_2 \\; t_2$\n:\n$b_{q} \\; e_{q} \\; t_{q}$\n\n In the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by three integers $b_i \\; e_i \\; t_i$ in the following $q$ lines.", "output": "Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11\n1 2 3 4 5 6 7 8 9 10 11\n1\n1 4 7\n output: 1 8 9 10 5 6 7 2 3 4 11"], "Pid": "p02445", "ProblemText": "Task Description: Write a program which reads a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and swap specified elements by a list of the following operation:\n\nswap Range($b, e, t$): For each integer $k$ ($0 <= k < (e - b)$, swap element $(b + k)$ and element $(t + k)$.\nTask Constraint: $1 <= n <= 1,000$\n\n$-1,000,000,000 <= a_i <= 1,000,000,000$\n\n$1 <= q <= 1,000$\n\n$0 <= b_i < e_i <= n$\n\n$0 <= t_i < t_i + (e_i - b_i) <= n$\n\nGiven swap ranges do not overlap each other\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . , \\; a_{n-1}$\n$q$\n$b_1 \\; e_1 \\; t_1$\n$b_2 \\; e_2 \\; t_2$\n:\n$b_{q} \\; e_{q} \\; t_{q}$\n\n In the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by three integers $b_i \\; e_i \\; t_i$ in the following $q$ lines.\nTask Output: Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element.\nTask Samples: input: 11\n1 2 3 4 5 6 7 8 9 10 11\n1\n1 4 7\n output: 1 8 9 10 5 6 7 2 3 4 11\n\n" }, { "title": "Unique", "content": "For a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.", "constraint": "$1 <= n <= 100,000$\n\n$-1000,000,000 <= a_i <= 1,000,000,000$\n\n$a_0 <= a_1 <= ... <= a_{n-1}$", "input": "A sequence is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$", "output": "Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 2 4\n output: 1 2 4"], "Pid": "p02446", "ProblemText": "Task Description: For a sequence of integers $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.\nTask Constraint: $1 <= n <= 100,000$\n\n$-1000,000,000 <= a_i <= 1,000,000,000$\n\n$a_0 <= a_1 <= ... <= a_{n-1}$\nTask Input: A sequence is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\nTask Output: Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.\nTask Samples: input: 4\n1 2 2 4\n output: 1 2 4\n\n" }, { "title": "Sorting Pairs", "content": "Write a program which print coordinates $(x_i, y_i)$ of given $n$ points on the plane by the following criteria.\n\nfirst by $x$-coordinate\n\nin case of a tie, by $y$-coordinate", "constraint": "$1 <= n <= 100,000$\n\n$-1,000,000,000 <= x_i, y_i <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n$\n$x_0 \\; y_0$\n$x_1 \\; y_1$\n:\n$x_{n-1} \\; y_{n-1}$\n\n In the first line, the number of points $n$ is given. In the following $n$ lines, coordinates of each point are given.", "output": "Print coordinate of given points in order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n4 7\n5 5\n2 3\n6 8\n2 1\n output: 2 1\n2 3\n4 7\n5 5\n6 8"], "Pid": "p02447", "ProblemText": "Task Description: Write a program which print coordinates $(x_i, y_i)$ of given $n$ points on the plane by the following criteria.\n\nfirst by $x$-coordinate\n\nin case of a tie, by $y$-coordinate\nTask Constraint: $1 <= n <= 100,000$\n\n$-1,000,000,000 <= x_i, y_i <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n$\n$x_0 \\; y_0$\n$x_1 \\; y_1$\n:\n$x_{n-1} \\; y_{n-1}$\n\n In the first line, the number of points $n$ is given. In the following $n$ lines, coordinates of each point are given.\nTask Output: Print coordinate of given points in order.\nTask Samples: input: 5\n4 7\n5 5\n2 3\n6 8\n2 1\n output: 2 1\n2 3\n4 7\n5 5\n6 8\n\n" }, { "title": "Sorting Tuples", "content": "Write a program which reads $n$ items and sorts them. Each item has attributes $\\{value, weight, type, date, name\\}$ and they are represented by $\\{$ integer, integer, upper-case letter, integer, string $\\}$ respectively. Sort the items based on the following priorities.\n\nfirst by value (ascending)\n\nin case of a tie, by weight (ascending)\n\nin case of a tie, by type (ascending in lexicographic order)\n\nin case of a tie, by date (ascending)\n\nin case of a tie, by name (ascending in lexicographic order)", "constraint": "$1 <= n <= 100,000$\n\n$0 <= v_i <= 1,000,000,000$\n\n$0 <= w_i <= 1,000,000,000$\n\n$t_i$ is a upper-case letter\n\n$0 <= d_i <= 2,000,000,000,000$\n\n$1 <= $ size of $s_i <= 20$\n\n$s_i \\ne s_j$ if $(i \\ne j)$", "input": "The input is given in the following format.\n\n$n$\n$v_0 \\; w_0 \\; t_0 \\; d_0 \\; s_0$\n$v_1 \\; w_1 \\; t_1 \\; d_1 \\; s_1$\n:\n$v_{n-1} \\; w_{n-1} \\; t_{n-1} \\; d_{n-1} \\; s_{n-1}$\n\n In the first line, the number of items $n$. In the following $n$ lines, attributes of each item are given. $v_i \\; w_i \\; t_i \\; d_i \\; s_i$ represent value, weight, type, date and name of the $i$-th item respectively.", "output": "Print attributes of each item in order. Print an item in a line and adjacency attributes should be separated by a single space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n105 24 C 1500000000000 white\n100 23 C 1500000000000 blue\n105 23 A 1480000000000 pink\n110 25 B 1500000000000 black\n110 20 A 1300000000000 gree\n output: 100 23 C 1500000000000 blue\n105 23 A 1480000000000 pink\n105 24 C 1500000000000 white\n110 20 A 1300000000000 gree\n110 25 B 1500000000000 black"], "Pid": "p02448", "ProblemText": "Task Description: Write a program which reads $n$ items and sorts them. Each item has attributes $\\{value, weight, type, date, name\\}$ and they are represented by $\\{$ integer, integer, upper-case letter, integer, string $\\}$ respectively. Sort the items based on the following priorities.\n\nfirst by value (ascending)\n\nin case of a tie, by weight (ascending)\n\nin case of a tie, by type (ascending in lexicographic order)\n\nin case of a tie, by date (ascending)\n\nin case of a tie, by name (ascending in lexicographic order)\nTask Constraint: $1 <= n <= 100,000$\n\n$0 <= v_i <= 1,000,000,000$\n\n$0 <= w_i <= 1,000,000,000$\n\n$t_i$ is a upper-case letter\n\n$0 <= d_i <= 2,000,000,000,000$\n\n$1 <= $ size of $s_i <= 20$\n\n$s_i \\ne s_j$ if $(i \\ne j)$\nTask Input: The input is given in the following format.\n\n$n$\n$v_0 \\; w_0 \\; t_0 \\; d_0 \\; s_0$\n$v_1 \\; w_1 \\; t_1 \\; d_1 \\; s_1$\n:\n$v_{n-1} \\; w_{n-1} \\; t_{n-1} \\; d_{n-1} \\; s_{n-1}$\n\n In the first line, the number of items $n$. In the following $n$ lines, attributes of each item are given. $v_i \\; w_i \\; t_i \\; d_i \\; s_i$ represent value, weight, type, date and name of the $i$-th item respectively.\nTask Output: Print attributes of each item in order. Print an item in a line and adjacency attributes should be separated by a single space.\nTask Samples: input: 5\n105 24 C 1500000000000 white\n100 23 C 1500000000000 blue\n105 23 A 1480000000000 pink\n110 25 B 1500000000000 black\n110 20 A 1300000000000 gree\n output: 100 23 C 1500000000000 blue\n105 23 A 1480000000000 pink\n105 24 C 1500000000000 white\n110 20 A 1300000000000 gree\n110 25 B 1500000000000 black\n\n" }, { "title": "Permutation", "content": "For given a sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$, print the previous permutation and the next permutation in lexicographic order.", "constraint": "$1 <= n <= 9$\n\n$a_i$ consist of $1,2, ..., n$", "input": "A sequence is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$", "output": "Print the previous permutation, the given sequence and the next permutation in the 1st, 2nd and 3rd lines respectively.\n Separate adjacency elements by a space character. Note that if there is no permutation, print nothing in the corresponding line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 1 3\n output: 1 3 2\n2 1 3\n2 3 1", "input: 3\n3 2 1\n output: 3 1 2\n3 2 1"], "Pid": "p02449", "ProblemText": "Task Description: For given a sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$, print the previous permutation and the next permutation in lexicographic order.\nTask Constraint: $1 <= n <= 9$\n\n$a_i$ consist of $1,2, ..., n$\nTask Input: A sequence is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\nTask Output: Print the previous permutation, the given sequence and the next permutation in the 1st, 2nd and 3rd lines respectively.\n Separate adjacency elements by a space character. Note that if there is no permutation, print nothing in the corresponding line.\nTask Samples: input: 3\n2 1 3\n output: 1 3 2\n2 1 3\n2 3 1\ninput: 3\n3 2 1\n output: 3 1 2\n3 2 1\n\n" }, { "title": "Permutation Enumeration", "content": "For given an integer $n$, print all permutations of $\\{1,2, . . . , n\\}$ in lexicographic order.", "constraint": "$1 <= n <= 9$", "input": "An integer $n$ is given in a line.", "output": "Print each permutation in a line in order. Separate adjacency elements by a space character.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n output: 1 2\n2 1", "input: 3\n output: 1 2 3\n1 3 2\n2 1 3\n2 3 1\n3 1 2\n3 2 1"], "Pid": "p02450", "ProblemText": "Task Description: For given an integer $n$, print all permutations of $\\{1,2, . . . , n\\}$ in lexicographic order.\nTask Constraint: $1 <= n <= 9$\nTask Input: An integer $n$ is given in a line.\nTask Output: Print each permutation in a line in order. Separate adjacency elements by a space character.\nTask Samples: input: 2\n output: 1 2\n2 1\ninput: 3\n output: 1 2 3\n1 3 2\n2 1 3\n2 3 1\n3 1 2\n3 2 1\n\n" }, { "title": "Binary Search", "content": "For a given sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.", "constraint": "$1 <= n <= 100,000$\n\n$1 <= q <= 200,000$\n\n$0 <= a_0 <= a_1 <= ... <= a_{n-1} <= 1,000,000,000$\n $0 <= k_i <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$q$\n$k_1$\n$k_2$\n:\n$k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.", "output": "For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 2 4\n3\n2\n3\n5\n output: 1\n0\n0"], "Pid": "p02451", "ProblemText": "Task Description: For a given sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.\nTask Constraint: $1 <= n <= 100,000$\n\n$1 <= q <= 200,000$\n\n$0 <= a_0 <= a_1 <= ... <= a_{n-1} <= 1,000,000,000$\n $0 <= k_i <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$q$\n$k_1$\n$k_2$\n:\n$k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.\nTask Output: For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.\nTask Samples: input: 4\n1 2 2 4\n3\n2\n3\n5\n output: 1\n0\n0\n\n" }, { "title": "Includes", "content": "For given two sequneces $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$, determine whether all elements of $B$ are included in $A$. Note that, elements of $A$ and $B$ are sorted by ascending order respectively.", "constraint": "$1 <= n, m <= 200,000$\n\n$-1,000,000,000 <= a_0 < a_1 < ... < a_{n-1} <= 1,000,000,000$\n\n$-1,000,000,000 <= b_0 < b_1 < ... < b_{m-1} <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; , . . . , \\; b_{m-1}$\n\n The number of elements in $A$ and its elements $a_i$ are given in the first and second\n lines respectively.\n The number of elements in $B$ and its elements $b_i$ are given in the third and fourth\n lines respectively.", "output": "Print 1, if $A$ contains all elements of $B$, otherwise 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 3 4\n2\n2 4\n output: 1", "input: 4\n1 2 3 4\n3\n1 2 5\n output: 0"], "Pid": "p02452", "ProblemText": "Task Description: For given two sequneces $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$, determine whether all elements of $B$ are included in $A$. Note that, elements of $A$ and $B$ are sorted by ascending order respectively.\nTask Constraint: $1 <= n, m <= 200,000$\n\n$-1,000,000,000 <= a_0 < a_1 < ... < a_{n-1} <= 1,000,000,000$\n\n$-1,000,000,000 <= b_0 < b_1 < ... < b_{m-1} <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; , . . . , \\; b_{m-1}$\n\n The number of elements in $A$ and its elements $a_i$ are given in the first and second\n lines respectively.\n The number of elements in $B$ and its elements $b_i$ are given in the third and fourth\n lines respectively.\nTask Output: Print 1, if $A$ contains all elements of $B$, otherwise 0.\nTask Samples: input: 4\n1 2 3 4\n2\n2 4\n output: 1\ninput: 4\n1 2 3 4\n3\n1 2 5\n output: 0\n\n" }, { "title": "Lower Bound", "content": "For a given sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, find the lower bound for a specific value $k$ given as a query.\n lower bound: the place pointing to the first element greater than or equal to a specific value, or $n$ if there is no such element.", "constraint": "$1 <= n <= 100,000$\n\n$1 <= q <= 200,000$\n\n$0 <= a_0 <= a_1 <= ... <= a_{n-1} <= 1,000,000,000$\n $0 <= k_i <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$q$\n$k_1$\n$k_2$\n:\n$k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.", "output": "For each query, print the position $i$ ($i = 0,1, . . . , n$) of the lower bound in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 2 4\n3\n2\n3\n5\n output: 1\n3\n4"], "Pid": "p02453", "ProblemText": "Task Description: For a given sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, find the lower bound for a specific value $k$ given as a query.\n lower bound: the place pointing to the first element greater than or equal to a specific value, or $n$ if there is no such element.\nTask Constraint: $1 <= n <= 100,000$\n\n$1 <= q <= 200,000$\n\n$0 <= a_0 <= a_1 <= ... <= a_{n-1} <= 1,000,000,000$\n $0 <= k_i <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$q$\n$k_1$\n$k_2$\n:\n$k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.\nTask Output: For each query, print the position $i$ ($i = 0,1, . . . , n$) of the lower bound in a line.\nTask Samples: input: 4\n1 2 2 4\n3\n2\n3\n5\n output: 1\n3\n4\n\n" }, { "title": "Equal Range", "content": "For a given sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, print a pair of the lower bound and the upper bound for a specific value $k$ given as a query.\n lower bound: the place pointing to the first element greater than or equal to a specific value, or $n$ if there is no such element.\n\n upper bound: the place pointing to the first element greater than a specific value, or $n$ if there is no such element.", "constraint": "$1 <= n <= 100,000$\n\n$1 <= q <= 200,000$\n\n$0 <= a_0 <= a_1 <= ... <= a_{n-1} <= 1,000,000,000$\n $0 <= k_i <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$q$\n$k_1$\n$k_2$\n:\n$k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.", "output": "For each query, print the pari of the lower bound $l$ ($l = 0,1, . . . , n$) and upper bound $r$ ($r = 0,1, . . . , n$) separated by a space character in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 2 4\n3\n2\n3\n5\n output: 1 3\n3 3\n4 4"], "Pid": "p02454", "ProblemText": "Task Description: For a given sequence $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ which is sorted by ascending order, print a pair of the lower bound and the upper bound for a specific value $k$ given as a query.\n lower bound: the place pointing to the first element greater than or equal to a specific value, or $n$ if there is no such element.\n\n upper bound: the place pointing to the first element greater than a specific value, or $n$ if there is no such element.\nTask Constraint: $1 <= n <= 100,000$\n\n$1 <= q <= 200,000$\n\n$0 <= a_0 <= a_1 <= ... <= a_{n-1} <= 1,000,000,000$\n $0 <= k_i <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; , . . . , \\; a_{n-1}$\n$q$\n$k_1$\n$k_2$\n:\n$k_q$\n\nThe number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.\nTask Output: For each query, print the pari of the lower bound $l$ ($l = 0,1, . . . , n$) and upper bound $r$ ($r = 0,1, . . . , n$) separated by a space character in a line.\nTask Samples: input: 4\n1 2 2 4\n3\n2\n3\n5\n output: 1 3\n3 3\n4 4\n\n" }, { "title": "Set: Search", "content": "For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$ (0 or 1).", "constraint": "$1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\n\nwhere the first digits 0 and 1 represent insert and find operations respectively.", "output": "For each insert operation, print the number of elements in $S$. \n For each find operation, print the number of specified elements in $S$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n0 1\n0 2\n0 3\n0 2\n0 4\n1 3\n1 10\n output: 1\n2\n3\n3\n4\n1\n0"], "Pid": "p02455", "ProblemText": "Task Description: For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$ (0 or 1).\nTask Constraint: $1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\n\nwhere the first digits 0 and 1 represent insert and find operations respectively.\nTask Output: For each insert operation, print the number of elements in $S$. \n For each find operation, print the number of specified elements in $S$.\nTask Samples: input: 7\n0 1\n0 2\n0 3\n0 2\n0 4\n1 3\n1 10\n output: 1\n2\n3\n3\n4\n1\n0\n\n" }, { "title": "Set: Delete", "content": "For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$ (0 or 1).\n\ndelete($x$): Delete $x$ from $S$.", "constraint": "$1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\nor\n2 $x$\n\n where the first digits 0,1 and 2 represent insert, find and delete operations respectively.", "output": "For each insert operation, print the number of elements in $S$. \n For each find operation, print the number of specified elements in $S$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n0 1\n0 2\n0 3\n2 2\n1 1\n1 2\n1 3\n0 2\n output: 1\n2\n3\n1\n0\n1\n3"], "Pid": "p02456", "ProblemText": "Task Description: For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$ (0 or 1).\n\ndelete($x$): Delete $x$ from $S$.\nTask Constraint: $1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\nor\n2 $x$\n\n where the first digits 0,1 and 2 represent insert, find and delete operations respectively.\nTask Output: For each insert operation, print the number of elements in $S$. \n For each find operation, print the number of specified elements in $S$.\nTask Samples: input: 8\n0 1\n0 2\n0 3\n2 2\n1 1\n1 2\n1 3\n0 2\n output: 1\n2\n3\n1\n0\n1\n3\n\n" }, { "title": "Set: Range Search", "content": "For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$ (0 or 1).\n\ndelete($x$): Delete $x$ from $S$.\n\ndump($L$, $R$): Print elements $x$ in $S$ such that $L <= x <= R$.", "constraint": "$1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$\n\nThe total number of elements printed by dump operations does not exceed $1,000,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\nor\n2 $x$\nor\n3 $L$ $R$\n\nwhere the first digits 0,1,2 and 3 represent insert, find, delete and dump operations respectively.", "output": "For each insert operation, print the number of elements in $S$. \nFor each find operation, print the number of specified elements in $S$. \nFor each dump operation, print the corresponding elements in ascending order. Print an element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\n0 1\n0 2\n0 3\n2 2\n1 1\n1 2\n1 3\n0 4\n3 2 4\n output: 1\n2\n3\n1\n0\n1\n3\n3\n4"], "Pid": "p02457", "ProblemText": "Task Description: For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$ (0 or 1).\n\ndelete($x$): Delete $x$ from $S$.\n\ndump($L$, $R$): Print elements $x$ in $S$ such that $L <= x <= R$.\nTask Constraint: $1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$\n\nThe total number of elements printed by dump operations does not exceed $1,000,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\nor\n2 $x$\nor\n3 $L$ $R$\n\nwhere the first digits 0,1,2 and 3 represent insert, find, delete and dump operations respectively.\nTask Output: For each insert operation, print the number of elements in $S$. \nFor each find operation, print the number of specified elements in $S$. \nFor each dump operation, print the corresponding elements in ascending order. Print an element in a line.\nTask Samples: input: 9\n0 1\n0 2\n0 3\n2 2\n1 1\n1 2\n1 3\n0 4\n3 2 4\n output: 1\n2\n3\n1\n0\n1\n3\n3\n4\n\n" }, { "title": "Multi-Set", "content": "For a set $S$ of integers, perform a sequence of the following operations. Note that multiple elements can have equivalent values in $S$.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$.\n\ndelete($x$): Delete all $x$ from $S$.\n\ndump($L$, $R$): Print elements $x$ in $S$ such that $L <= x <= R$.", "constraint": "$1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$\n\nThe total number of elements printed by dump operations does not exceed $1,000,000$\n\nThe sum of numbers printed by find operations does not exceed $2,000,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\nor\n2 $x$\nor\n3 $L$ $R$\n\n where the first digits 0,1,2 and 3 represent insert, find, delete and dump operations respectively.", "output": "For each insert operation, print the number of elements in $S$. \n For each find operation, print the number of specified elements in $S$. \n For each dump operation, print the corresponding elements in ascending order. Print an element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\n0 1\n0 1\n0 2\n0 3\n2 2\n1 1\n1 2\n1 3\n0 4\n3 1 4\n output: 1\n2\n3\n4\n2\n0\n1\n4\n1\n1\n3\n4"], "Pid": "p02458", "ProblemText": "Task Description: For a set $S$ of integers, perform a sequence of the following operations. Note that multiple elements can have equivalent values in $S$.\n\ninsert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.\n\nfind($x$): Report the number of $x$ in $S$.\n\ndelete($x$): Delete all $x$ from $S$.\n\ndump($L$, $R$): Print elements $x$ in $S$ such that $L <= x <= R$.\nTask Constraint: $1 <= q <= 200,000$\n\n$0 <= x <= 1,000,000,000$\n\nThe total number of elements printed by dump operations does not exceed $1,000,000$\n\nThe sum of numbers printed by find operations does not exceed $2,000,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $x$\nor\n1 $x$\nor\n2 $x$\nor\n3 $L$ $R$\n\n where the first digits 0,1,2 and 3 represent insert, find, delete and dump operations respectively.\nTask Output: For each insert operation, print the number of elements in $S$. \n For each find operation, print the number of specified elements in $S$. \n For each dump operation, print the corresponding elements in ascending order. Print an element in a line.\nTask Samples: input: 10\n0 1\n0 1\n0 2\n0 3\n2 2\n1 1\n1 2\n1 3\n0 4\n3 1 4\n output: 1\n2\n3\n4\n2\n0\n1\n4\n1\n1\n3\n4\n\n" }, { "title": "Map: Search", "content": "For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$. If there is an element with $key$, replace the corresponding value with $x$.\n\nget($key$): Print the value with the specified $key$.", "constraint": "$1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consits of lower-case letter\n\nFor a get operation, the element with the specified key exists in $M$.", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\n\n where the first digits 0,1 and 2 represent insert and get operations respectively.", "output": "For each get operation, print an integer in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n0 blue 4\n0 red 1\n0 white 5\n1 red\n1 blue\n0 black 8\n1 black\n output: 1\n4\n8"], "Pid": "p02459", "ProblemText": "Task Description: For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$. If there is an element with $key$, replace the corresponding value with $x$.\n\nget($key$): Print the value with the specified $key$.\nTask Constraint: $1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consits of lower-case letter\n\nFor a get operation, the element with the specified key exists in $M$.\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\n\n where the first digits 0,1 and 2 represent insert and get operations respectively.\nTask Output: For each get operation, print an integer in a line.\nTask Samples: input: 7\n0 blue 4\n0 red 1\n0 white 5\n1 red\n1 blue\n0 black 8\n1 black\n output: 1\n4\n8\n\n" }, { "title": "Map: Delete", "content": "For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.\n\nget($key$): Print the value with the specified $key$. Print 0 if there is no such element.\n\ndelete($key$): Delete the element with the specified $key$.", "constraint": "$1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consits of lower case letters", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\nor\n2 $key$\n\n where the first digits 0,1 and 2 represent insert, get and delete operations respectively.", "output": "For each get operation, print an integer in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n0 blue 4\n0 red 1\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n output: 1\n4\n0\n0"], "Pid": "p02460", "ProblemText": "Task Description: For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.\n\nget($key$): Print the value with the specified $key$. Print 0 if there is no such element.\n\ndelete($key$): Delete the element with the specified $key$.\nTask Constraint: $1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consits of lower case letters\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\nor\n2 $key$\n\n where the first digits 0,1 and 2 represent insert, get and delete operations respectively.\nTask Output: For each get operation, print an integer in a line.\nTask Samples: input: 8\n0 blue 4\n0 red 1\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n output: 1\n4\n0\n0\n\n" }, { "title": "Map: Range Search", "content": "For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.\n\nget($key$): Print the value with the specified $key$. Print 0 if there is no such element. \n\ndelete($key$): Delete the element with the specified $key$.\n\ndump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order.", "constraint": "$1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consists of lower-case letters\n\n$L <= R$ in lexicographic order\n\nThe total number of elements printed by dump operations does not exceed $1,000,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\nor\n2 $key$\nor\n3 $L$ $R$\n\n where the first digits 0,1,2 and 3 represent insert, get, delete and dump operations.", "output": "For each get operation, print the corresponding value. \nFor each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements (a pair of key and value separated by a space character) in ascending order of the keys.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\n0 blue 4\n0 red 1\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n3 w z\n output: 1\n4\n0\n0\nwhite 5"], "Pid": "p02461", "ProblemText": "Task Description: For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.\n\nget($key$): Print the value with the specified $key$. Print 0 if there is no such element. \n\ndelete($key$): Delete the element with the specified $key$.\n\ndump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order.\nTask Constraint: $1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consists of lower-case letters\n\n$L <= R$ in lexicographic order\n\nThe total number of elements printed by dump operations does not exceed $1,000,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\nor\n2 $key$\nor\n3 $L$ $R$\n\n where the first digits 0,1,2 and 3 represent insert, get, delete and dump operations.\nTask Output: For each get operation, print the corresponding value. \nFor each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements (a pair of key and value separated by a space character) in ascending order of the keys.\nTask Samples: input: 9\n0 blue 4\n0 red 1\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n3 w z\n output: 1\n4\n0\n0\nwhite 5\n\n" }, { "title": "Multi-Map", "content": "For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that multiple elements can have equivalent keys.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.\n\nget($key$): Print all values with the specified $key$.\n\ndelete($key$): Delete all elements with the specified $key$.\n\ndump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order.", "constraint": "$1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consists of lower-case letters\n\n$L <= R$ in lexicographic order\n\nThe total number of elements printed by get operations does not exceed $500,000$\n\nThe total number of elements printed by dump operations does not exceed $500,000$", "input": "The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\nor\n2 $key$\nor\n3 $L$ $R$\n\n where the first digits 0,1,2 and 3 represent insert, get, delete and dump operations.", "output": "For each get operation, print the corresponding values in the order of insertions. \n For each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements in ascending order of the keys, in case of a tie, in the order of insertions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n3 w z\n output: 1\n6\n4\nwhite 5"], "Pid": "p02462", "ProblemText": "Task Description: For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that multiple elements can have equivalent keys.\n\ninsert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.\n\nget($key$): Print all values with the specified $key$.\n\ndelete($key$): Delete all elements with the specified $key$.\n\ndump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order.\nTask Constraint: $1 <= q <= 200,000$\n\n$1 <= x <= 1,000,000,000$\n\n$1 <= $ length of $key$ $ <= 20$ \n\n$key$ consists of lower-case letters\n\n$L <= R$ in lexicographic order\n\nThe total number of elements printed by get operations does not exceed $500,000$\n\nThe total number of elements printed by dump operations does not exceed $500,000$\nTask Input: The input is given in the following format.\n\n$q$\n$query_1$\n$query_2$\n:\n$query_q$\n\nEach query $query_i$ is given by\n\n0 $key$ $x$\nor\n1 $key$\nor\n2 $key$\nor\n3 $L$ $R$\n\n where the first digits 0,1,2 and 3 represent insert, get, delete and dump operations.\nTask Output: For each get operation, print the corresponding values in the order of insertions. \n For each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements in ascending order of the keys, in case of a tie, in the order of insertions.\nTask Samples: input: 10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n3 w z\n output: 1\n6\n4\nwhite 5\n\n" }, { "title": "Set Union", "content": "Find the union of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$.", "constraint": "$1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.", "output": "Print elements in the union in ascending order. Print an element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 5 8\n2\n5 9\n output: 1\n5\n8\n9"], "Pid": "p02463", "ProblemText": "Task Description: Find the union of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$.\nTask Constraint: $1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.\nTask Output: Print elements in the union in ascending order. Print an element in a line.\nTask Samples: input: 3\n1 5 8\n2\n5 9\n output: 1\n5\n8\n9\n\n" }, { "title": "Set Intersection", "content": "Find the intersection of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$.", "constraint": "$1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.", "output": "Print elements in the intersection in ascending order. Print an element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 5 8\n5\n2 3 5 9 11\n output: 2\n5"], "Pid": "p02464", "ProblemText": "Task Description: Find the intersection of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$.\nTask Constraint: $1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.\nTask Output: Print elements in the intersection in ascending order. Print an element in a line.\nTask Samples: input: 4\n1 2 5 8\n5\n2 3 5 9 11\n output: 2\n5\n\n" }, { "title": "Set Difference", "content": "Find the difference of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$, $A - B$.", "constraint": "$1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.", "output": "Print elements in the difference in ascending order. Print an element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 3 5 8\n2\n2 5\n output: 1\n3\n8"], "Pid": "p02465", "ProblemText": "Task Description: Find the difference of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$, $A - B$.\nTask Constraint: $1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.\nTask Output: Print elements in the difference in ascending order. Print an element in a line.\nTask Samples: input: 5\n1 2 3 5 8\n2\n2 5\n output: 1\n3\n8\n\n" }, { "title": "Set Symmetric Difference", "content": "Find the symmetric difference of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$.", "constraint": "$1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$", "input": "The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.", "output": "Print elements in the symmetric difference in ascending order. Print an element in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n1 2 3 4 5 6 7\n4\n2 4 6 8\n output: 1\n3\n5\n7\n8"], "Pid": "p02466", "ProblemText": "Task Description: Find the symmetric difference of two sets $A = \\{a_0, a_1, . . . , a_{n-1}\\}$ and $B = \\{b_0, b_1, . . . , b_{m-1}\\}$.\nTask Constraint: $1 <= n, m <= 200,000$\n\n$0 <= a_0 < a_1 < ... < a_{n-1} <= 10^9$\n\n$0 <= b_0 < b_1 < ... < b_{m-1} <= 10^9$\nTask Input: The input is given in the following format.\n\n$n$\n$a_0 \\; a_1 \\; . . . \\; a_{n-1}$\n$m$\n$b_0 \\; b_1 \\; . . . \\; b_{m-1}$\n\n Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.\nTask Output: Print elements in the symmetric difference in ascending order. Print an element in a line.\nTask Samples: input: 7\n1 2 3 4 5 6 7\n4\n2 4 6 8\n output: 1\n3\n5\n7\n8\n\n" }, { "title": "Prime Factorization", "content": "Factorize a given integer n.", "constraint": "2 <= n <= 10^9", "input": "n\n\nAn integer n is given in a line.", "output": "Print the given integer n and : . Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prime factor should be printed according to the number of times. Print a space before each prime factor.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12\n output: 12: 2 2 3", "input: 126\n output: 126: 2 3 3 7"], "Pid": "p02467", "ProblemText": "Task Description: Factorize a given integer n.\nTask Constraint: 2 <= n <= 10^9\nTask Input: n\n\nAn integer n is given in a line.\nTask Output: Print the given integer n and : . Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prime factor should be printed according to the number of times. Print a space before each prime factor.\nTask Samples: input: 12\n output: 12: 2 2 3\ninput: 126\n output: 126: 2 3 3 7\n\n" }, { "title": "Power", "content": "For given integers m and n, compute m^n (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.", "constraint": "1 <= m <= 100\n\n1 <= n <= 10^9", "input": "m n\n\nTwo integers m and n are given in a line.", "output": "Print m^n (mod 1,000,000,007) in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n output: 8", "input: 5 8\n output: 390625"], "Pid": "p02468", "ProblemText": "Task Description: For given integers m and n, compute m^n (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.\nTask Constraint: 1 <= m <= 100\n\n1 <= n <= 10^9\nTask Input: m n\n\nTwo integers m and n are given in a line.\nTask Output: Print m^n (mod 1,000,000,007) in a line.\nTask Samples: input: 2 3\n output: 8\ninput: 5 8\n output: 390625\n\n" }, { "title": "Least Common Multiple", "content": "Find the least common multiple (LCM) of given n integers.", "constraint": "2 <= n <= 10\n\n1 <= a_i <= 1000\n\nProduct of given integers a_i(i = 1,2, ... n) does not exceed 2^31-1", "input": "n\na_1 a_2 . . . a_n\n\nn is given in the first line. Then, n integers are given in the second line.", "output": "Print the least common multiple of the given integers in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 4 6\n output: 12", "input: 4\n1 2 3 5\n output: 30"], "Pid": "p02469", "ProblemText": "Task Description: Find the least common multiple (LCM) of given n integers.\nTask Constraint: 2 <= n <= 10\n\n1 <= a_i <= 1000\n\nProduct of given integers a_i(i = 1,2, ... n) does not exceed 2^31-1\nTask Input: n\na_1 a_2 . . . a_n\n\nn is given in the first line. Then, n integers are given in the second line.\nTask Output: Print the least common multiple of the given integers in a line.\nTask Samples: input: 3\n3 4 6\n output: 12\ninput: 4\n1 2 3 5\n output: 30\n\n" }, { "title": "Euler's Phi Function", "content": "For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n.", "constraint": "", "input": "n\n\nAn integer n (1 <= n <= 1000000000).", "output": "The number of totatives in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n output: 2", "input: 1000000\n output: 400000"], "Pid": "p02470", "ProblemText": "Task Description: For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n.\nTask Input: n\n\nAn integer n (1 <= n <= 1000000000).\nTask Output: The number of totatives in a line.\nTask Samples: input: 6\n output: 2\ninput: 1000000\n output: 400000\n\n" }, { "title": "", "content": "Given positive integers a and b, find the integer solution (x, y) to ax + by = gcd(a, b), where gcd(a, b) is the greatest common divisor of a and b.", "constraint": "1 <= a, b <= 10^9", "input": "a b\n\nTwo positive integers a and b are given separated by a space in a line.", "output": "Print two integers x and y separated by a space. If there are several pairs of such x and y, print that pair for which |x| + |y| is the minimal (primarily) and x <= y (secondarily).", "content_img": false, "lang": "", "error": false, "samples": ["input: 4 12\n output: 1 0", "input: 3 8\n output: 3 -1"], "Pid": "p02471", "ProblemText": "Task Description: Given positive integers a and b, find the integer solution (x, y) to ax + by = gcd(a, b), where gcd(a, b) is the greatest common divisor of a and b.\nTask Constraint: 1 <= a, b <= 10^9\nTask Input: a b\n\nTwo positive integers a and b are given separated by a space in a line.\nTask Output: Print two integers x and y separated by a space. If there are several pairs of such x and y, print that pair for which |x| + |y| is the minimal (primarily) and x <= y (secondarily).\nTask Samples: input: 4 12\n output: 1 0\ninput: 3 8\n output: 3 -1\n\n" }, { "title": "Addition of Big Integers", "content": "Given two integers $A$ and $B$, compute the sum, $A + B$.", "constraint": "$-1 * 10^{100000} <= A, B <= 10^{100000}$", "input": "Two integers $A$ and $B$ separated by a space character are given in a line.", "output": "Print the sum in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 8\n output: 13", "input: 100 25\n output: 125", "input: -1 1\n output: 0", "input: 12 -3\n output: 9"], "Pid": "p02472", "ProblemText": "Task Description: Given two integers $A$ and $B$, compute the sum, $A + B$.\nTask Constraint: $-1 * 10^{100000} <= A, B <= 10^{100000}$\nTask Input: Two integers $A$ and $B$ separated by a space character are given in a line.\nTask Output: Print the sum in a line.\nTask Samples: input: 5 8\n output: 13\ninput: 100 25\n output: 125\ninput: -1 1\n output: 0\ninput: 12 -3\n output: 9\n\n" }, { "title": "Difference of Big Integers", "content": "Given two integers $A$ and $B$, compute the difference, $A - B$.", "constraint": "$-1 * 10^{100000} <= A, B <= 10^{100000}$", "input": "Two integers $A$ and $B$ separated by a space character are given in a line.", "output": "Print the difference in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 8\n output: -3", "input: 100 25\n output: 75", "input: -1 -1\n output: 0", "input: 12 -3\n output: 15"], "Pid": "p02473", "ProblemText": "Task Description: Given two integers $A$ and $B$, compute the difference, $A - B$.\nTask Constraint: $-1 * 10^{100000} <= A, B <= 10^{100000}$\nTask Input: Two integers $A$ and $B$ separated by a space character are given in a line.\nTask Output: Print the difference in a line.\nTask Samples: input: 5 8\n output: -3\ninput: 100 25\n output: 75\ninput: -1 -1\n output: 0\ninput: 12 -3\n output: 15\n\n" }, { "title": "Multiplication of Big Integers", "content": "Given two integers $A$ and $B$, compute the product, $A * B$.", "constraint": "$-1 * 10^{1000} <= A, B <= 10^{1000}$", "input": "Two integers $A$ and $B$ separated by a space character are given in a line.", "output": "Print the product in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 8\n output: 40", "input: 100 25\n output: 2500", "input: -1 0\n output: 0", "input: 12 -3\n output: -36"], "Pid": "p02474", "ProblemText": "Task Description: Given two integers $A$ and $B$, compute the product, $A * B$.\nTask Constraint: $-1 * 10^{1000} <= A, B <= 10^{1000}$\nTask Input: Two integers $A$ and $B$ separated by a space character are given in a line.\nTask Output: Print the product in a line.\nTask Samples: input: 5 8\n output: 40\ninput: 100 25\n output: 2500\ninput: -1 0\n output: 0\ninput: 12 -3\n output: -36\n\n" }, { "title": "Division of Big Integers", "content": "Given two integers $A$ and $B$, compute the quotient, $\\frac{A}{B}$. Round down to the nearest decimal.", "constraint": "$-1 * 10^{1000} <= A, B <= 10^{1000}$\n\n$B \\ne 0$", "input": "Two integers $A$ and $B$ separated by a space character are given in a line.", "output": "Print the quotient in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 8\n output: 0", "input: 100 25\n output: 4", "input: -1 3\n output: 0", "input: 12 -3\n output: -4"], "Pid": "p02475", "ProblemText": "Task Description: Given two integers $A$ and $B$, compute the quotient, $\\frac{A}{B}$. Round down to the nearest decimal.\nTask Constraint: $-1 * 10^{1000} <= A, B <= 10^{1000}$\n\n$B \\ne 0$\nTask Input: Two integers $A$ and $B$ separated by a space character are given in a line.\nTask Output: Print the quotient in a line.\nTask Samples: input: 5 8\n output: 0\ninput: 100 25\n output: 4\ninput: -1 3\n output: 0\ninput: 12 -3\n output: -4\n\n" }, { "title": "Remainder of Big Integers", "content": "Given two integers $A$ and $B$, compute the remainder of $\\frac{A}{B}$.", "constraint": "$0 <= A, B <= 10^{1000}$\n\n$B \\ne 0$", "input": "Two integers $A$ and $B$ separated by a space character are given in a line.", "output": "Print the remainder in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 8\n output: 5", "input: 100 25\n output: 0"], "Pid": "p02476", "ProblemText": "Task Description: Given two integers $A$ and $B$, compute the remainder of $\\frac{A}{B}$.\nTask Constraint: $0 <= A, B <= 10^{1000}$\n\n$B \\ne 0$\nTask Input: Two integers $A$ and $B$ separated by a space character are given in a line.\nTask Output: Print the remainder in a line.\nTask Samples: input: 5 8\n output: 5\ninput: 100 25\n output: 0\n\n" }, { "title": "Multiplication of Big Integers II", "content": "Given two integers $A$ and $B$, compute the product, $A * B$.", "constraint": "$-1 * 10^{200000} <= A, B <= 10^{200000}$", "input": "Two integers $A$ and $B$ separated by a space character are given in a line.", "output": "Print the product in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 8\n output: 40", "input: 100 25\n output: 2500", "input: -1 0\n output: 0", "input: 12 -3\n output: -36"], "Pid": "p02477", "ProblemText": "Task Description: Given two integers $A$ and $B$, compute the product, $A * B$.\nTask Constraint: $-1 * 10^{200000} <= A, B <= 10^{200000}$\nTask Input: Two integers $A$ and $B$ separated by a space character are given in a line.\nTask Output: Print the product in a line.\nTask Samples: input: 5 8\n output: 40\ninput: 100 25\n output: 2500\ninput: -1 0\n output: 0\ninput: 12 -3\n output: -36\n\n" }, { "title": "", "content": "", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p02478", "ProblemText": "Task Description: \nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement You are given an integer K.\nPrint the string obtained by repeating the string ACL K times and concatenating them.\nFor example, if K = 3, print ACLACLACL.", "constraint": "1 <= K <= 5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print the string obtained by repeating the string ACL K times and concatenating them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 13 output: 1ACLACLACL"], "Pid": "p02534", "ProblemText": "Task Description: Problem Statement You are given an integer K.\nPrint the string obtained by repeating the string ACL K times and concatenating them.\nFor example, if K = 3, print ACLACLACL.\nTask Constraint: 1 <= K <= 5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print the string obtained by repeating the string ACL K times and concatenating them.\nTask Samples: input: 13 output: 1ACLACLACL\n\n" }, { "title": "", "content": "Problem Statement Snuke likes integers that are greater than or equal to A, and less than or equal to B.\nTakahashi likes integers that are greater than or equal to C, and less than or equal to D.\nDoes there exist an integer liked by both people?", "constraint": "0 <= A <= B <= 10^{18}\n0 <= C <= D <= 10^{18}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C D", "output": "Print Yes or No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 110 30 20 40 output: 1Yes\n\nFor example, both like 25.", "input: 210 20 30 40 output: 2No"], "Pid": "p02535", "ProblemText": "Task Description: Problem Statement Snuke likes integers that are greater than or equal to A, and less than or equal to B.\nTakahashi likes integers that are greater than or equal to C, and less than or equal to D.\nDoes there exist an integer liked by both people?\nTask Constraint: 0 <= A <= B <= 10^{18}\n0 <= C <= D <= 10^{18}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C D\nTask Output: Print Yes or No.\nTask Samples: input: 110 30 20 40 output: 1Yes\n\nFor example, both like 25.\ninput: 210 20 30 40 output: 2No\n\n" }, { "title": "", "content": "Problem Statement There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.\nRoad i connects City A_i and City B_i.\nSnuke can perform the following operation zero or more times:\n\nChoose two distinct cities that are not directly connected by a road, and build a new road between the two cities.\n\nAfter he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).\nWhat is the minimum number of roads he must build to achieve the goal?", "constraint": "2 <= N <= 100,000\n1 <= M <= 100,000\n1 <= A_i < B_i <= N\nNo two roads connect the same pair of cities.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_M B_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 13 1\n1 2 output 11\n\nInitially, there are three cities, and there is a road between City 1 and City 2.\nSnuke can achieve the goal by building one new road, for example, between City 1 and City 3.\nAfter that,\n\nWe can travel between 1 and 2 directly.\nWe can travel between 1 and 3 directly.\nWe can travel between 2 and 3 by following both roads (2 - 1 - 3)."], "Pid": "p02536", "ProblemText": "Task Description: Problem Statement There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.\nRoad i connects City A_i and City B_i.\nSnuke can perform the following operation zero or more times:\n\nChoose two distinct cities that are not directly connected by a road, and build a new road between the two cities.\n\nAfter he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).\nWhat is the minimum number of roads he must build to achieve the goal?\nTask Constraint: 2 <= N <= 100,000\n1 <= M <= 100,000\n1 <= A_i < B_i <= N\nNo two roads connect the same pair of cities.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_M B_M\nTask Output: Print the answer.\nTask Samples: input: 13 1\n1 2 output 11\n\nInitially, there are three cities, and there is a road between City 1 and City 2.\nSnuke can achieve the goal by building one new road, for example, between City 1 and City 3.\nAfter that,\n\nWe can travel between 1 and 2 directly.\nWe can travel between 1 and 3 directly.\nWe can travel between 2 and 3 by following both roads (2 - 1 - 3).\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence A_1, A_2, . . . , A_N and an integer K.\nPrint the maximum possible length of a sequence B that satisfies the following conditions:\n\nB is a (not necessarily continuous) subsequence of A.\nFor each pair of adjacents elements of B, the absolute difference of the elements is at most K.", "constraint": "1 <= N <= 300,000\n0 <= A_i <= 300,000\n0 <= K <= 300,000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1\nA_2\n:\nA_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 110 3\n1\n5\n4\n3\n8\n6\n9\n7\n2\n4 output: 17\n\nFor example, B = (1,4,3,6,9,7,4) satisfies the conditions.\n\nIt is a subsequence of A = (1,5,4,3,8,6,9,7,2,4).\nAll of the absolute differences between two adjacent elements (|1-4|, |4-3|, |3-6|, |6-9|, |9-7|, |7-4|) are at most K = 3."], "Pid": "p02537", "ProblemText": "Task Description: Problem Statement You are given a sequence A_1, A_2, . . . , A_N and an integer K.\nPrint the maximum possible length of a sequence B that satisfies the following conditions:\n\nB is a (not necessarily continuous) subsequence of A.\nFor each pair of adjacents elements of B, the absolute difference of the elements is at most K.\nTask Constraint: 1 <= N <= 300,000\n0 <= A_i <= 300,000\n0 <= K <= 300,000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1\nA_2\n:\nA_N\nTask Output: Print the answer.\nTask Samples: input: 110 3\n1\n5\n4\n3\n8\n6\n9\n7\n2\n4 output: 17\n\nFor example, B = (1,4,3,6,9,7,4) satisfies the conditions.\n\nIt is a subsequence of A = (1,5,4,3,8,6,9,7,2,4).\nAll of the absolute differences between two adjacent elements (|1-4|, |4-3|, |3-6|, |6-9|, |9-7|, |7-4|) are at most K = 3.\n\n" }, { "title": "", "content": "Problem Statement You have a string S of length N.\nInitially, all characters in S are 1s.\nYou will perform queries Q times.\nIn the i-th query, you are given two integers L_i, R_i and a character D_i (which is a digit).\nThen, you must replace all characters from the L_i-th to the R_i-th (inclusive) with D_i.\nAfter each query, read the string S as a decimal integer, and print its value modulo 998,244,353.", "constraint": "1 <= N, Q <= 200,000\n1 <= L_i <= R_i <= N\n1 <= D_i <= 9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN Q\nL_1 R_1 D_1\n:\nL_Q R_Q D_Q", "output": "Print Q lines.\nIn the i-th line print the value of S after the i-th query, modulo 998,244,353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 18 5\n3 6 2\n1 4 7\n3 8 3\n2 2 2\n4 5 1 output: 111222211\n77772211\n77333333\n72333333\n72311333", "input: 2200000 1\n123 456 7 output: 2641437905\n\nDon't forget to take the modulo."], "Pid": "p02538", "ProblemText": "Task Description: Problem Statement You have a string S of length N.\nInitially, all characters in S are 1s.\nYou will perform queries Q times.\nIn the i-th query, you are given two integers L_i, R_i and a character D_i (which is a digit).\nThen, you must replace all characters from the L_i-th to the R_i-th (inclusive) with D_i.\nAfter each query, read the string S as a decimal integer, and print its value modulo 998,244,353.\nTask Constraint: 1 <= N, Q <= 200,000\n1 <= L_i <= R_i <= N\n1 <= D_i <= 9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN Q\nL_1 R_1 D_1\n:\nL_Q R_Q D_Q\nTask Output: Print Q lines.\nIn the i-th line print the value of S after the i-th query, modulo 998,244,353.\nTask Samples: input: 18 5\n3 6 2\n1 4 7\n3 8 3\n2 2 2\n4 5 1 output: 111222211\n77772211\n77333333\n72333333\n72311333\ninput: 2200000 1\n123 456 7 output: 2641437905\n\nDon't forget to take the modulo.\n\n" }, { "title": "", "content": "Problem Statement There are 2N people numbered 1 through 2N.\nThe height of Person i is h_i.\nHow many ways are there to make N pairs of people such that the following conditions are satisfied?\nCompute the answer modulo 998,244,353.\n\nEach person is contained in exactly one pair.\nFor each pair, the heights of the two people in the pair are different.\n\nTwo ways are considered different if for some p and q, Person p and Person q are paired in one way and not in the other.", "constraint": "1 <= N <= 50,000\n1 <= h_i <= 100,000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nh_1\n:\nh_{2N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12\n1\n1\n2\n3 output: 12\n\nThere are two ways:\n\nForm the pair (Person 1, Person 3) and the pair (Person 2, Person 4).\nForm the pair (Person 1, Person 4) and the pair (Person 2, Person 3).", "input: 25\n30\n10\n20\n40\n20\n10\n10\n30\n50\n60 output: 2516"], "Pid": "p02539", "ProblemText": "Task Description: Problem Statement There are 2N people numbered 1 through 2N.\nThe height of Person i is h_i.\nHow many ways are there to make N pairs of people such that the following conditions are satisfied?\nCompute the answer modulo 998,244,353.\n\nEach person is contained in exactly one pair.\nFor each pair, the heights of the two people in the pair are different.\n\nTwo ways are considered different if for some p and q, Person p and Person q are paired in one way and not in the other.\nTask Constraint: 1 <= N <= 50,000\n1 <= h_i <= 100,000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nh_1\n:\nh_{2N}\nTask Output: Print the answer.\nTask Samples: input: 12\n1\n1\n2\n3 output: 12\n\nThere are two ways:\n\nForm the pair (Person 1, Person 3) and the pair (Person 2, Person 4).\nForm the pair (Person 1, Person 4) and the pair (Person 2, Person 3).\ninput: 25\n30\n10\n20\n40\n20\n10\n10\n30\n50\n60 output: 2516\n\n" }, { "title": "", "content": "Problem Statement There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \\dots, x_N) and (y_1, y_2, \\dots, y_N) are both permuations of (1,2, \\dots, N). For each k = 1,2, \\dots, N, find the answer to the following question: Rng is in City k.\nRng can perform the following move arbitrarily many times: move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in. How many cities (including City k) are reachable from City k?", "constraint": "1 <= N <= 200,000(x_1, x_2, \\dots, x_N) is a permutation of (1,2, \\dots, N).(y_1, y_2, \\dots, y_N) is a permutation of (1,2, \\dots, N).All values in input are integers.", "input": "Input is given from Standard Input in the following format: N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N", "output": "Print N lines. In i-th line print the answer to the question when k = i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 14\n1 4\n2 3\n3 1\n4 2 output: 11\n1\n2\n2\nRng can reach City 4 from City 3, or conversely City 3 from City 4.", "input: 27\n6 4\n4 3\n3 5\n7 1\n2 7\n5 2\n1 6 output: 23\n3\n1\n1\n2\n3\n2"], "Pid": "p02540", "ProblemText": "Task Description: Problem Statement There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \\dots, x_N) and (y_1, y_2, \\dots, y_N) are both permuations of (1,2, \\dots, N). For each k = 1,2, \\dots, N, find the answer to the following question: Rng is in City k.\nRng can perform the following move arbitrarily many times: move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in. How many cities (including City k) are reachable from City k?\nTask Constraint: 1 <= N <= 200,000(x_1, x_2, \\dots, x_N) is a permutation of (1,2, \\dots, N).(y_1, y_2, \\dots, y_N) is a permutation of (1,2, \\dots, N).All values in input are integers.\nTask Input: Input is given from Standard Input in the following format: N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\nTask Output: Print N lines. In i-th line print the answer to the question when k = i.\nTask Samples: input: 14\n1 4\n2 3\n3 1\n4 2 output: 11\n1\n2\n2\nRng can reach City 4 from City 3, or conversely City 3 from City 4.\ninput: 27\n6 4\n4 3\n3 5\n7 1\n2 7\n5 2\n1 6 output: 23\n3\n1\n1\n2\n3\n2\n\n" }, { "title": "", "content": "Problem Statement Given is an integer N.\nFind the minimum possible positive integer k such that (1+2+\\cdots+k) is a multiple of N.\nIt can be proved that such a positive integer k always exists.", "constraint": "1 <= N <= 10^{15}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 111 output: 110\n\n1+2+\\cdots+10=55 holds and 55 is indeed a multple of N=11.\nThere are no positive integers k <= 9 that satisfy the condition, so the answer is k = 10.", "input: 220200920 output: 21100144"], "Pid": "p02541", "ProblemText": "Task Description: Problem Statement Given is an integer N.\nFind the minimum possible positive integer k such that (1+2+\\cdots+k) is a multiple of N.\nIt can be proved that such a positive integer k always exists.\nTask Constraint: 1 <= N <= 10^{15}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer in a line.\nTask Samples: input: 111 output: 110\n\n1+2+\\cdots+10=55 holds and 55 is indeed a multple of N=11.\nThere are no positive integers k <= 9 that satisfy the condition, so the answer is k = 10.\ninput: 220200920 output: 21100144\n\n" }, { "title": "", "content": "Problem Statement There is a board with N rows and M columns.\nThe information of this board is represented by N strings S_1, S_2, \\ldots, S_N.\nSpecifically, the state of the square at the i-th row from the top and the j-th column from the left is represented as follows:\n\nS_{i, j}=. : the square is empty.\nS_{i, j}=# : an obstacle is placed on the square.\nS_{i, j}=o : a piece is placed on the square.\n\nYosupo repeats the following operation:\n\nChoose a piece and move it to its right adjecent square or its down adjacent square.\nMoving a piece to squares with another piece or an obstacle is prohibited.\nMoving a piece out of the board is also prohibited.\n\nYosupo wants to perform the operation as many times as possible.\nFind the maximum possible number of operations.", "constraint": "1 <= N <= 50\n1 <= M <= 50\nS_i is a string of length M consisting of ., # and o.\n1 <= ( the number of pieces )<= 100.\nIn other words, the number of pairs (i, j) that satisfy S_{i,j}=o is between 1 and 100, both inclusive.", "input": "Input is given from Standard Input in the following format:\nN M\nS_1\nS_2\n\\vdots\nS_N", "output": "Print the maximum possible number of operations in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\no..\n...\no.# output: 4\n\nYosupo can perform operations 4 times as follows:\no.. .o. ..o ... ...\n... -> ... -> ... -> ..o -> ..o\no.# o.# o.# o.# .o#", "input: 9 10\n.#....o#..\n.#..#..##o\n.....#o.##\n.###.#o..o\n#.#...##.#\n..#..#.###\n#o.....#..\n....###..o\no.......o# output: 24"], "Pid": "p02542", "ProblemText": "Task Description: Problem Statement There is a board with N rows and M columns.\nThe information of this board is represented by N strings S_1, S_2, \\ldots, S_N.\nSpecifically, the state of the square at the i-th row from the top and the j-th column from the left is represented as follows:\n\nS_{i, j}=. : the square is empty.\nS_{i, j}=# : an obstacle is placed on the square.\nS_{i, j}=o : a piece is placed on the square.\n\nYosupo repeats the following operation:\n\nChoose a piece and move it to its right adjecent square or its down adjacent square.\nMoving a piece to squares with another piece or an obstacle is prohibited.\nMoving a piece out of the board is also prohibited.\n\nYosupo wants to perform the operation as many times as possible.\nFind the maximum possible number of operations.\nTask Constraint: 1 <= N <= 50\n1 <= M <= 50\nS_i is a string of length M consisting of ., # and o.\n1 <= ( the number of pieces )<= 100.\nIn other words, the number of pairs (i, j) that satisfy S_{i,j}=o is between 1 and 100, both inclusive.\nTask Input: Input is given from Standard Input in the following format:\nN M\nS_1\nS_2\n\\vdots\nS_N\nTask Output: Print the maximum possible number of operations in a line.\nTask Samples: input: 3 3\no..\n...\no.# output: 4\n\nYosupo can perform operations 4 times as follows:\no.. .o. ..o ... ...\n... -> ... -> ... -> ..o -> ..o\no.# o.# o.# o.# .o#\ninput: 9 10\n.#....o#..\n.#..#..##o\n.....#o.##\n.###.#o..o\n#.#...##.#\n..#..#.###\n#o.....#..\n....###..o\no.......o# output: 24\n\n" }, { "title": "", "content": "Problem Statement There are N points on a number line, i-th of which is placed on coordinate X_i.\nThese points are numbered in the increasing order of coordinates.\nIn other words, for all i (1 <= i <= N-1), X_i < X_{i+1} holds.\nIn addition to that, an integer K is given.\nProcess Q queries.\nIn the i-th query, two integers L_i and R_i are given.\nHere, a set s of points is said to be a good set if it satisfies all of the following conditions.\nNote that the definition of good sets varies over queries.\n\nEach point in s is one of X_{L_i}, X_{L_i+1}, \\ldots, X_{R_i}.\nFor any two distinct points in s, the distance between them is greater than or equal to K.\nThe size of s is maximum among all sets that satisfy the aforementioned conditions.\n\nFor each query, find the size of the union of all good sets.", "constraint": "1 <= N <= 2 * 10^5\n1 <= K <= 10^9\n0 <= X_1 < X_2 < \\cdots < X_N <= 10^9\n1 <= Q <= 2 * 10^5\n1 <= L_i <= R_i <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nX_1 X_2 \\cdots X_N\nQ\nL_1 R_1\nL_2 R_2\n\\vdots\nL_Q R_Q", "output": "For each query, print the size of the union of all good sets in a line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 2 4 7 8\n2\n1 5\n1 2 output: 4\n2\n\nIn the first query, you can have at most 3 points in a good set.\nThere exist two good sets: \\{1,4,7\\} and \\{1,4,8\\}.\nTherefore, the size of the union of all good sets is |\\{1,4,7,8\\}|=4.\nIn the second query, you can have at most 1 point in a good set.\nThere exist two good sets: \\{1\\} and \\{2\\}.\nTherefore, the size of the union of all good sets is |\\{1,2\\}|=2.", "input: 15 220492538\n4452279 12864090 23146757 31318558 133073771 141315707 263239555 350278176 401243954 418305779 450172439 560311491 625900495 626194585 891960194\n5\n6 14\n1 8\n1 13\n7 12\n4 12 output: 4\n6\n11\n2\n3"], "Pid": "p02543", "ProblemText": "Task Description: Problem Statement There are N points on a number line, i-th of which is placed on coordinate X_i.\nThese points are numbered in the increasing order of coordinates.\nIn other words, for all i (1 <= i <= N-1), X_i < X_{i+1} holds.\nIn addition to that, an integer K is given.\nProcess Q queries.\nIn the i-th query, two integers L_i and R_i are given.\nHere, a set s of points is said to be a good set if it satisfies all of the following conditions.\nNote that the definition of good sets varies over queries.\n\nEach point in s is one of X_{L_i}, X_{L_i+1}, \\ldots, X_{R_i}.\nFor any two distinct points in s, the distance between them is greater than or equal to K.\nThe size of s is maximum among all sets that satisfy the aforementioned conditions.\n\nFor each query, find the size of the union of all good sets.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= K <= 10^9\n0 <= X_1 < X_2 < \\cdots < X_N <= 10^9\n1 <= Q <= 2 * 10^5\n1 <= L_i <= R_i <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nX_1 X_2 \\cdots X_N\nQ\nL_1 R_1\nL_2 R_2\n\\vdots\nL_Q R_Q\nTask Output: For each query, print the size of the union of all good sets in a line.\nTask Samples: input: 5 3\n1 2 4 7 8\n2\n1 5\n1 2 output: 4\n2\n\nIn the first query, you can have at most 3 points in a good set.\nThere exist two good sets: \\{1,4,7\\} and \\{1,4,8\\}.\nTherefore, the size of the union of all good sets is |\\{1,4,7,8\\}|=4.\nIn the second query, you can have at most 1 point in a good set.\nThere exist two good sets: \\{1\\} and \\{2\\}.\nTherefore, the size of the union of all good sets is |\\{1,2\\}|=2.\ninput: 15 220492538\n4452279 12864090 23146757 31318558 133073771 141315707 263239555 350278176 401243954 418305779 450172439 560311491 625900495 626194585 891960194\n5\n6 14\n1 8\n1 13\n7 12\n4 12 output: 4\n6\n11\n2\n3\n\n" }, { "title": "", "content": "Problem Statement Given are a permutation p_1, p_2, \\dots, p_N of (1,2, . . . , N) and an integer K. Maroon performs the following operation for i = 1,2, \\dots, N - K + 1 in this order:\n\nShuffle p_i, p_{i + 1}, \\dots, p_{i + K - 1} uniformly randomly.\n\nFind the expected value of the inversion number of the sequence after all the operations are performed, and print it modulo 998244353.\nMore specifically, from the constraints of this problem, it can be proved that the expected value is always a rational number, which can be represented as an irreducible fraction \\frac{P}{Q}, and that the integer R that satisfies R * Q \\equiv P \\pmod{998244353}, 0 <= R < 998244353 is uniquely determined. Print this R.\nHere, the inversion number of a sequence a_1, a_2, \\dots, a_N is defined to be the number of ordered pairs (i, j) that satisfy i < j, a_i > a_j.", "constraint": "2 <= N <= 200,000\n2 <= K <= N\n(p_1, p_2, \\dots, p_N) is a permutation of (1,2, \\dots, N).\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\np_1 p_2 . . . p_N", "output": "Print the expected value modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2 3 output: 1\n\nThe final sequence is one of (1,2,3), (2,1,3), (1,3,2), (2,3,1), each with probability \\frac{1}{4}.\nTheir inversion numbers are 0,1,1,2 respectively, so the expected value is 1.", "input: 10 3\n1 8 4 9 2 3 7 10 5 6 output: 164091855"], "Pid": "p02544", "ProblemText": "Task Description: Problem Statement Given are a permutation p_1, p_2, \\dots, p_N of (1,2, . . . , N) and an integer K. Maroon performs the following operation for i = 1,2, \\dots, N - K + 1 in this order:\n\nShuffle p_i, p_{i + 1}, \\dots, p_{i + K - 1} uniformly randomly.\n\nFind the expected value of the inversion number of the sequence after all the operations are performed, and print it modulo 998244353.\nMore specifically, from the constraints of this problem, it can be proved that the expected value is always a rational number, which can be represented as an irreducible fraction \\frac{P}{Q}, and that the integer R that satisfies R * Q \\equiv P \\pmod{998244353}, 0 <= R < 998244353 is uniquely determined. Print this R.\nHere, the inversion number of a sequence a_1, a_2, \\dots, a_N is defined to be the number of ordered pairs (i, j) that satisfy i < j, a_i > a_j.\nTask Constraint: 2 <= N <= 200,000\n2 <= K <= N\n(p_1, p_2, \\dots, p_N) is a permutation of (1,2, \\dots, N).\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\np_1 p_2 . . . p_N\nTask Output: Print the expected value modulo 998244353.\nTask Samples: input: 3 2\n1 2 3 output: 1\n\nThe final sequence is one of (1,2,3), (2,1,3), (1,3,2), (2,3,1), each with probability \\frac{1}{4}.\nTheir inversion numbers are 0,1,1,2 respectively, so the expected value is 1.\ninput: 10 3\n1 8 4 9 2 3 7 10 5 6 output: 164091855\n\n" }, { "title": "", "content": "Problem Statement Given are integer sequences A and B of length 3N. Each of these two sequences contains three copies of each of 1,2, \\dots, N.\nIn other words, A and B are both arrangements of (1,1,1,2,2,2, \\dots, N, N, N).\nTak can perform the following operation to the sequence A arbitrarily many times:\n\nPick a value from 1,2, \\dots, N and call it x. A contains exactly three copies of x. Remove the middle element of these three. After that, append x to the beginning or the end of A.\n\nCheck if he can turn A into B. If he can, print the minimum required number of operations to achieve that.", "constraint": "1 <= N <= 33\nA and B are both arrangements of (1,1,1,2,2,2, \\dots, N, N, N).\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{3N}\nB_1 B_2 . . . B_{3N}", "output": "If Tak can turn A into B, print the minimum required number of operations to achieve that. Otherwise, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3 1 1 3 2 2 1 3\n1 2 2 3 1 2 3 1 3 output: 4\n\nFor example, Tak can perform operations as follows:\n\n2 3 1 1 3 2 2 1 3 (The initial state)\n2 2 3 1 1 3 2 1 3 (Pick x = 2 and append it to the beginning)\n2 2 3 1 3 2 1 3 1 (Pick x = 1 and append it to the end)\n1 2 2 3 1 3 2 3 1 (Pick x = 1 and append it to the beginning)\n1 2 2 3 1 2 3 1 3 (Pick x = 3 and append it to the end)", "input: 3\n1 1 1 2 2 2 3 3 3\n1 1 1 2 2 2 3 3 3 output: 0", "input: 3\n2 3 3 1 1 1 2 2 3\n3 2 2 1 1 1 3 3 2 output: -1", "input: 8\n3 6 7 5 4 8 4 1 1 3 8 7 3 8 2 4 7 5 2 2 6 5 6 1\n7 5 8 1 3 6 7 5 4 8 1 3 3 8 2 4 2 6 5 6 1 4 7 2 output: 7"], "Pid": "p02545", "ProblemText": "Task Description: Problem Statement Given are integer sequences A and B of length 3N. Each of these two sequences contains three copies of each of 1,2, \\dots, N.\nIn other words, A and B are both arrangements of (1,1,1,2,2,2, \\dots, N, N, N).\nTak can perform the following operation to the sequence A arbitrarily many times:\n\nPick a value from 1,2, \\dots, N and call it x. A contains exactly three copies of x. Remove the middle element of these three. After that, append x to the beginning or the end of A.\n\nCheck if he can turn A into B. If he can, print the minimum required number of operations to achieve that.\nTask Constraint: 1 <= N <= 33\nA and B are both arrangements of (1,1,1,2,2,2, \\dots, N, N, N).\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{3N}\nB_1 B_2 . . . B_{3N}\nTask Output: If Tak can turn A into B, print the minimum required number of operations to achieve that. Otherwise, print -1.\nTask Samples: input: 3\n2 3 1 1 3 2 2 1 3\n1 2 2 3 1 2 3 1 3 output: 4\n\nFor example, Tak can perform operations as follows:\n\n2 3 1 1 3 2 2 1 3 (The initial state)\n2 2 3 1 1 3 2 1 3 (Pick x = 2 and append it to the beginning)\n2 2 3 1 3 2 1 3 1 (Pick x = 1 and append it to the end)\n1 2 2 3 1 3 2 3 1 (Pick x = 1 and append it to the beginning)\n1 2 2 3 1 2 3 1 3 (Pick x = 3 and append it to the end)\ninput: 3\n1 1 1 2 2 2 3 3 3\n1 1 1 2 2 2 3 3 3 output: 0\ninput: 3\n2 3 3 1 1 1 2 2 3\n3 2 2 1 1 1 3 3 2 output: -1\ninput: 8\n3 6 7 5 4 8 4 1 1 3 8 7 3 8 2 4 7 5 2 2 6 5 6 1\n7 5 8 1 3 6 7 5 4 8 1 3 3 8 2 4 2 6 5 6 1 4 7 2 output: 7\n\n" }, { "title": "", "content": "Problem Statement In the Kingdom of At Coder, people use a language called Taknese, which uses lowercase English letters.\nIn Taknese, the plural form of a noun is spelled based on the following rules:\n\nIf a noun's singular form does not end with s, append s to the end of the singular form.\nIf a noun's singular form ends with s, append es to the end of the singular form.\n\nYou are given the singular form S of a Taknese noun. Output its plural form.", "constraint": "S is a string of length 1 between 1000, inclusive.\nS contains only lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the plural form of the given Taknese word.", "content_img": false, "lang": "en", "error": false, "samples": ["input: apple output: apples\n\napple ends with e, so its plural form is apples.", "input: bus output: buses\n\nbus ends with s, so its plural form is buses.", "input: box output: boxs"], "Pid": "p02546", "ProblemText": "Task Description: Problem Statement In the Kingdom of At Coder, people use a language called Taknese, which uses lowercase English letters.\nIn Taknese, the plural form of a noun is spelled based on the following rules:\n\nIf a noun's singular form does not end with s, append s to the end of the singular form.\nIf a noun's singular form ends with s, append es to the end of the singular form.\n\nYou are given the singular form S of a Taknese noun. Output its plural form.\nTask Constraint: S is a string of length 1 between 1000, inclusive.\nS contains only lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the plural form of the given Taknese word.\nTask Samples: input: apple output: apples\n\napple ends with e, so its plural form is apples.\ninput: bus output: buses\n\nbus ends with s, so its plural form is buses.\ninput: box output: boxs\n\n" }, { "title": "", "content": "Problem Statement Tak performed the following action N times: rolling two dice.\nThe result of the i-th roll is D_{i, 1} and D_{i, 2}.\nCheck if doublets occurred at least three times in a row.\nSpecifically, check if there exists at lease one i such that D_{i, 1}=D_{i, 2}, D_{i+1,1}=D_{i+1,2} and D_{i+2,1}=D_{i+2,2} hold.", "constraint": "3 <= N <= 100\n1<= D_{i,j} <= 6\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nD_{1,1} D_{1,2}\n\\vdots\nD_{N, 1} D_{N, 2}", "output": "Print Yes if doublets occurred at least three times in a row. Print No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n6 6\n4 4\n3 3\n3 2 output: Yes\n\nFrom the second roll to the fourth roll, three doublets occurred in a row.", "input: 5\n1 1\n2 2\n3 4\n5 5\n6 6 output: No", "input: 6\n1 1\n2 2\n3 3\n4 4\n5 5\n6 6 output: Yes"], "Pid": "p02547", "ProblemText": "Task Description: Problem Statement Tak performed the following action N times: rolling two dice.\nThe result of the i-th roll is D_{i, 1} and D_{i, 2}.\nCheck if doublets occurred at least three times in a row.\nSpecifically, check if there exists at lease one i such that D_{i, 1}=D_{i, 2}, D_{i+1,1}=D_{i+1,2} and D_{i+2,1}=D_{i+2,2} hold.\nTask Constraint: 3 <= N <= 100\n1<= D_{i,j} <= 6\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nD_{1,1} D_{1,2}\n\\vdots\nD_{N, 1} D_{N, 2}\nTask Output: Print Yes if doublets occurred at least three times in a row. Print No otherwise.\nTask Samples: input: 5\n1 2\n6 6\n4 4\n3 3\n3 2 output: Yes\n\nFrom the second roll to the fourth roll, three doublets occurred in a row.\ninput: 5\n1 1\n2 2\n3 4\n5 5\n6 6 output: No\ninput: 6\n1 1\n2 2\n3 3\n4 4\n5 5\n6 6 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Given is a positive integer N.\nHow many tuples (A, B, C) of positive integers satisfy A * B + C = N?", "constraint": "2 <= N <= 10^6\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 3\n\nThere are 3 tuples of integers that satisfy A * B + C = 3: (A, B, C) = (1,1,2), (1,2,1), (2,1,1).", "input: 100 output: 473", "input: 1000000 output: 13969985"], "Pid": "p02548", "ProblemText": "Task Description: Problem Statement Given is a positive integer N.\nHow many tuples (A, B, C) of positive integers satisfy A * B + C = N?\nTask Constraint: 2 <= N <= 10^6\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 3 output: 3\n\nThere are 3 tuples of integers that satisfy A * B + C = 3: (A, B, C) = (1,1,2), (1,2,1), (2,1,1).\ninput: 100 output: 473\ninput: 1000000 output: 13969985\n\n" }, { "title": "", "content": "Problem Statement There are N cells arranged in a row, numbered 1,2, \\ldots, N from left to right.\nTak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.\nYou are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \\ldots, [L_K, R_K].\nLet S be the union of these K segments.\nHere, the segment [l, r] denotes the set consisting of all integers i that satisfy l <= i <= r.\n\n\bWhen you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.\n\nTo help Tak, find the number of ways to go to Cell N, modulo 998244353.", "constraint": "2 <= N <= 2 * 10^5\n1 <= K <= \\min(N, 10)\n1 <= L_i <= R_i <= N\n[L_i, R_i] and [L_j, R_j] do not intersect (i \\neq j) \nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nL_1 R_1\nL_2 R_2\n:\nL_K R_K", "output": "Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n1 1\n3 4 output: 4\n\nThe set S is the union of the segment [1,1] and the segment [3,4], therefore S = \\{ 1,3,4 \\} holds.\nThere are 4 possible ways to get to Cell 5:\n\n1 \\to 2 \\to 3 \\to 4 \\to 5,\n1 \\to 2 \\to 5,\n1 \\to 4 \\to 5 and\n1 \\to 5.", "input: 5 2\n3 3\n5 5 output: 0\n\nBecause S = \\{ 3,5 \\} holds, you cannot reach to Cell 5.\nPrint 0.", "input: 5 1\n1 2 output: 5", "input: 60 3\n5 8\n1 3\n10 15 output: 221823067\n\nNote that you have to print the answer modulo 998244353."], "Pid": "p02549", "ProblemText": "Task Description: Problem Statement There are N cells arranged in a row, numbered 1,2, \\ldots, N from left to right.\nTak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.\nYou are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \\ldots, [L_K, R_K].\nLet S be the union of these K segments.\nHere, the segment [l, r] denotes the set consisting of all integers i that satisfy l <= i <= r.\n\n\bWhen you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.\n\nTo help Tak, find the number of ways to go to Cell N, modulo 998244353.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= K <= \\min(N, 10)\n1 <= L_i <= R_i <= N\n[L_i, R_i] and [L_j, R_j] do not intersect (i \\neq j) \nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nL_1 R_1\nL_2 R_2\n:\nL_K R_K\nTask Output: Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.\nTask Samples: input: 5 2\n1 1\n3 4 output: 4\n\nThe set S is the union of the segment [1,1] and the segment [3,4], therefore S = \\{ 1,3,4 \\} holds.\nThere are 4 possible ways to get to Cell 5:\n\n1 \\to 2 \\to 3 \\to 4 \\to 5,\n1 \\to 2 \\to 5,\n1 \\to 4 \\to 5 and\n1 \\to 5.\ninput: 5 2\n3 3\n5 5 output: 0\n\nBecause S = \\{ 3,5 \\} holds, you cannot reach to Cell 5.\nPrint 0.\ninput: 5 1\n1 2 output: 5\ninput: 60 3\n5 8\n1 3\n10 15 output: 221823067\n\nNote that you have to print the answer modulo 998244353.\n\n" }, { "title": "", "content": "Problem Statement Let us denote by f(x, m) the remainder of the Euclidean division of x by m.\nLet A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M).\nFind \\displaystyle{\\sum_{i=1}^N A_i}.", "constraint": "1 <= N <= 10^{10}\n0 <= X < M <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X M", "output": "Print \\displaystyle{\\sum_{i=1}^N A_i}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 2 1001 output: 1369\n\nThe sequence A begins 2,4,16,256,471,620,\\ldots Therefore, the answer is 2+4+16+256+471+620=1369.", "input: 1000 2 16 output: 6\n\nThe sequence A begins 2,4,0,0,\\ldots Therefore, the answer is 6.", "input: 10000000000 10 99959 output: 492443256176507"], "Pid": "p02550", "ProblemText": "Task Description: Problem Statement Let us denote by f(x, m) the remainder of the Euclidean division of x by m.\nLet A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M).\nFind \\displaystyle{\\sum_{i=1}^N A_i}.\nTask Constraint: 1 <= N <= 10^{10}\n0 <= X < M <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X M\nTask Output: Print \\displaystyle{\\sum_{i=1}^N A_i}.\nTask Samples: input: 6 2 1001 output: 1369\n\nThe sequence A begins 2,4,16,256,471,620,\\ldots Therefore, the answer is 2+4+16+256+471+620=1369.\ninput: 1000 2 16 output: 6\n\nThe sequence A begins 2,4,0,0,\\ldots Therefore, the answer is 6.\ninput: 10000000000 10 99959 output: 492443256176507\n\n" }, { "title": "", "content": "Problem Statement There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.\nEach of the central (N-2) * (N-2) squares in the grid has a black stone on it.\nEach of the 2N - 1 squares on the bottom side and the right side has a white stone on it.\nQ queries are given. We ask you to process them in order.\nThere are two kinds of queries. Their input format and description are as follows:\n\n1 x: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone.\n2 x: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone.\n\nHow many black stones are there on the grid after processing all Q queries?", "constraint": "3 <= N <= 2* 10^5\n0 <= Q <= \\min(2N-4,2* 10^5)\n2 <= x <= N-1\nQueries are pairwise distinct.", "input": "Input is given from Standard Input in the following format:\nN Q\nQuery_1\n\\vdots\nQuery_Q", "output": "Print how many black stones there are on the grid after processing all Q queries.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n1 3\n2 3\n1 4\n2 2\n1 2 output: 1\n\nAfter each query, the grid changes in the following way:", "input: 200000 0 output: 39999200004", "input: 176527 15\n1 81279\n2 22308\n2 133061\n1 80744\n2 44603\n1 170938\n2 139754\n2 15220\n1 172794\n1 159290\n2 156968\n1 56426\n2 77429\n1 97459\n2 71282 output: 31159505795"], "Pid": "p02551", "ProblemText": "Task Description: Problem Statement There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.\nEach of the central (N-2) * (N-2) squares in the grid has a black stone on it.\nEach of the 2N - 1 squares on the bottom side and the right side has a white stone on it.\nQ queries are given. We ask you to process them in order.\nThere are two kinds of queries. Their input format and description are as follows:\n\n1 x: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone.\n2 x: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone.\n\nHow many black stones are there on the grid after processing all Q queries?\nTask Constraint: 3 <= N <= 2* 10^5\n0 <= Q <= \\min(2N-4,2* 10^5)\n2 <= x <= N-1\nQueries are pairwise distinct.\nTask Input: Input is given from Standard Input in the following format:\nN Q\nQuery_1\n\\vdots\nQuery_Q\nTask Output: Print how many black stones there are on the grid after processing all Q queries.\nTask Samples: input: 5 5\n1 3\n2 3\n1 4\n2 2\n1 2 output: 1\n\nAfter each query, the grid changes in the following way:\ninput: 200000 0 output: 39999200004\ninput: 176527 15\n1 81279\n2 22308\n2 133061\n1 80744\n2 44603\n1 170938\n2 139754\n2 15220\n1 172794\n1 159290\n2 156968\n1 56426\n2 77429\n1 97459\n2 71282 output: 31159505795\n\n" }, { "title": "", "content": "Problem Statement Given is an integer x that is greater than or equal to 0, and less than or equal to 1.\nOutput 1 if x is equal to 0, or 0 if x is equal to 1.", "constraint": "0 <= x <= 1\nx is an integer", "input": "Input is given from Standard Input in the following format:\nx", "output": "Print 1 if x is equal to 0, or 0 if x is equal to 1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11 output: 10", "input: 20 output: 21"], "Pid": "p02552", "ProblemText": "Task Description: Problem Statement Given is an integer x that is greater than or equal to 0, and less than or equal to 1.\nOutput 1 if x is equal to 0, or 0 if x is equal to 1.\nTask Constraint: 0 <= x <= 1\nx is an integer\nTask Input: Input is given from Standard Input in the following format:\nx\nTask Output: Print 1 if x is equal to 0, or 0 if x is equal to 1.\nTask Samples: input: 11 output: 10\ninput: 20 output: 21\n\n" }, { "title": "", "content": "Problem Statement Given are integers a, b, c and d.\nIf x and y are integers and a <= x <= b and c<= y <= d hold, what is the maximum possible value of x * y?", "constraint": "-10^9 <= a <= b <= 10^9\n-10^9 <= c <= d <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\na b c d", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 1 1 output: 2\n\nIf x = 1 and y = 1 then x * y = 1.\nIf x = 2 and y = 1 then x * y = 2.\nTherefore, the answer is 2.", "input: 3 5 -4 -2 output: -6\n\nThe answer can be negative.", "input: -1000000000 0 -1000000000 0 output: 1000000000000000000"], "Pid": "p02553", "ProblemText": "Task Description: Problem Statement Given are integers a, b, c and d.\nIf x and y are integers and a <= x <= b and c<= y <= d hold, what is the maximum possible value of x * y?\nTask Constraint: -10^9 <= a <= b <= 10^9\n-10^9 <= c <= d <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\na b c d\nTask Output: Print the answer.\nTask Samples: input: 1 2 1 1 output: 2\n\nIf x = 1 and y = 1 then x * y = 1.\nIf x = 2 and y = 1 then x * y = 2.\nTherefore, the answer is 2.\ninput: 3 5 -4 -2 output: -6\n\nThe answer can be negative.\ninput: -1000000000 0 -1000000000 0 output: 1000000000000000000\n\n" }, { "title": "", "content": "Problem Statement How many integer sequences A_1, A_2, \\ldots, A_N of length N satisfy all of the following conditions?\n\n0 <= A_i <= 9\nThere exists some i such that A_i=0 holds.\nThere exists some i such that A_i=9 holds.\n\nThe answer can be very large, so output it modulo 10^9 + 7.", "constraint": "1 <= N <= 10^6\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 2\n\nTwo sequences \\{0,9\\} and \\{9,0\\} satisfy all conditions.", "input: 1 output: 0", "input: 869121 output: 2511445"], "Pid": "p02554", "ProblemText": "Task Description: Problem Statement How many integer sequences A_1, A_2, \\ldots, A_N of length N satisfy all of the following conditions?\n\n0 <= A_i <= 9\nThere exists some i such that A_i=0 holds.\nThere exists some i such that A_i=9 holds.\n\nThe answer can be very large, so output it modulo 10^9 + 7.\nTask Constraint: 1 <= N <= 10^6\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer modulo 10^9 + 7.\nTask Samples: input: 2 output: 2\n\nTwo sequences \\{0,9\\} and \\{9,0\\} satisfy all conditions.\ninput: 1 output: 0\ninput: 869121 output: 2511445\n\n" }, { "title": "", "content": "Problem Statement Given is an integer S.\nFind how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S.\nThe answer can be very large, so output it modulo 10^9 + 7.", "constraint": "1 <= S <= 2000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 output: 3\n\n3 sequences satisfy the condition: \\{3,4\\}, \\{4,3\\} and \\{7\\}.", "input: 2 output: 0\n\nThere are no sequences that satisfy the condition.", "input: 1729 output: 294867501"], "Pid": "p02555", "ProblemText": "Task Description: Problem Statement Given is an integer S.\nFind how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S.\nThe answer can be very large, so output it modulo 10^9 + 7.\nTask Constraint: 1 <= S <= 2000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the answer.\nTask Samples: input: 7 output: 3\n\n3 sequences satisfy the condition: \\{3,4\\}, \\{4,3\\} and \\{7\\}.\ninput: 2 output: 0\n\nThere are no sequences that satisfy the condition.\ninput: 1729 output: 294867501\n\n" }, { "title": "", "content": "Problem Statement There are N points on the 2D plane, i-th of which is located on (x_i, y_i).\nThere can be multiple points that share the same coordinate.\nWhat is the maximum possible Manhattan distance between two distinct points?\nHere, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.", "constraint": "2 <= N <= 2 * 10^5\n1 <= x_i,y_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1\n2 4\n3 2 output: 4\n\nThe Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.", "input: 2\n1 1\n1 1 output: 0"], "Pid": "p02556", "ProblemText": "Task Description: Problem Statement There are N points on the 2D plane, i-th of which is located on (x_i, y_i).\nThere can be multiple points that share the same coordinate.\nWhat is the maximum possible Manhattan distance between two distinct points?\nHere, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= x_i,y_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\nTask Output: Print the answer.\nTask Samples: input: 3\n1 1\n2 4\n3 2 output: 4\n\nThe Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.\ninput: 2\n1 1\n1 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement Given are two sequences A and B, both of length N.\nA and B are each sorted in the ascending order.\nCheck if it is possible to reorder the terms of B so that for each i (1 <= i <= N) A_i \\neq B_i holds, and if it is possible, output any of the reorderings that achieve it.", "constraint": "1<= N <= 2 * 10^5\n1<= A_i,B_i <= N\nA and B are each sorted in the ascending order.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_N\nB_1 B_2 \\cdots B_N", "output": "If there exist no reorderings that satisfy the condition, print No.\nIf there exists a reordering that satisfies the condition, print Yes on the first line.\nAfter that, print a reordering of B on the second line, separating terms with a whitespace.\nIf there are multiple reorderings that satisfy the condition, you can print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 1 1 2 2 3\n1 1 1 2 2 3 output: Yes\n2 2 3 1 1 1", "input: 3\n1 1 2\n1 1 3 output: No", "input: 4\n1 1 2 3\n1 2 3 3 output: Yes\n3 3 1 2"], "Pid": "p02557", "ProblemText": "Task Description: Problem Statement Given are two sequences A and B, both of length N.\nA and B are each sorted in the ascending order.\nCheck if it is possible to reorder the terms of B so that for each i (1 <= i <= N) A_i \\neq B_i holds, and if it is possible, output any of the reorderings that achieve it.\nTask Constraint: 1<= N <= 2 * 10^5\n1<= A_i,B_i <= N\nA and B are each sorted in the ascending order.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_N\nB_1 B_2 \\cdots B_N\nTask Output: If there exist no reorderings that satisfy the condition, print No.\nIf there exists a reordering that satisfies the condition, print Yes on the first line.\nAfter that, print a reordering of B on the second line, separating terms with a whitespace.\nIf there are multiple reorderings that satisfy the condition, you can print any of them.\nTask Samples: input: 6\n1 1 1 2 2 3\n1 1 1 2 2 3 output: Yes\n2 2 3 1 1 1\ninput: 3\n1 1 2\n1 1 3 output: No\ninput: 4\n1 1 2 3\n1 2 3 3 output: Yes\n3 3 1 2\n\n" }, { "title": "", "content": "Problem Statement You are given an undirected graph with N vertices and 0 edges. Process Q queries of the following types.\n\n0 u v: Add an edge (u, v).\n1 u v: Print 1 if u and v are in the same connected component, 0 otherwise.", "constraint": "1 <= N <= 200,000\n1 <= Q <= 200,000\n0 <= u_i, v_i < N", "input": "Input is given from Standard Input in the following format:\nN Q\nt_1 u_1 v_1\nt_2 u_2 v_2\n:\nt_Q u_Q v_Q", "output": "For each query of the latter type, print the answer.", "content_img": false, "lang": "en", "error": true, "samples": ["input: 4 7\n1 0 1\n0 0 1\n0 2 3\n1 0 1\n1 1 2\n0 0 2\n1 1 3 output: 0\n1\n0\n1"], "Pid": "p02558", "ProblemText": "Task Description: Problem Statement You are given an undirected graph with N vertices and 0 edges. Process Q queries of the following types.\n\n0 u v: Add an edge (u, v).\n1 u v: Print 1 if u and v are in the same connected component, 0 otherwise.\nTask Constraint: 1 <= N <= 200,000\n1 <= Q <= 200,000\n0 <= u_i, v_i < N\nTask Input: Input is given from Standard Input in the following format:\nN Q\nt_1 u_1 v_1\nt_2 u_2 v_2\n:\nt_Q u_Q v_Q\nTask Output: For each query of the latter type, print the answer.\nTask Samples: input: 4 7\n1 0 1\n0 0 1\n0 2 3\n1 0 1\n1 1 2\n0 0 2\n1 1 3 output: 0\n1\n0\n1\n\n" }, { "title": "", "content": "Problem Statement You are given an array a_0, a_1, . . . , a_{N-1} of length N. Process Q queries of the following types.\n\n0 p x: a_p >=ts a_p + x\n1 l r: Print \\sum_{i = l}^{r - 1}{a_i}.", "constraint": "1 <= N, Q <= 500,000\n0 <= a_i, x <= 10^9\n0 <= p < N\n0 <= l_i < r_i <= N\nAll values in Input are integer.", "input": "Input is given from Standard Input in the following format:\nN Q\na_0 a_1 . . . a_{N - 1}\n\\textrm{Query}_0\n\\textrm{Query}_1\n:\n\\textrm{Query}_{Q - 1}", "output": "For each query of the latter type, print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n1 2 3 4 5\n1 0 5\n1 2 4\n0 3 10\n1 0 5\n1 0 3 output: 15\n7\n25\n6"], "Pid": "p02559", "ProblemText": "Task Description: Problem Statement You are given an array a_0, a_1, . . . , a_{N-1} of length N. Process Q queries of the following types.\n\n0 p x: a_p >=ts a_p + x\n1 l r: Print \\sum_{i = l}^{r - 1}{a_i}.\nTask Constraint: 1 <= N, Q <= 500,000\n0 <= a_i, x <= 10^9\n0 <= p < N\n0 <= l_i < r_i <= N\nAll values in Input are integer.\nTask Input: Input is given from Standard Input in the following format:\nN Q\na_0 a_1 . . . a_{N - 1}\n\\textrm{Query}_0\n\\textrm{Query}_1\n:\n\\textrm{Query}_{Q - 1}\nTask Output: For each query of the latter type, print the answer.\nTask Samples: input: 5 5\n1 2 3 4 5\n1 0 5\n1 2 4\n0 3 10\n1 0 5\n1 0 3 output: 15\n7\n25\n6\n\n" }, { "title": "", "content": "Problem Statement In this problem, you should process T testcases.\nFor each testcase, you are given four integers N, M, A, B.\nCalculate \\sum_{i = 0}^{N - 1} floor((A * i + B) / M).", "constraint": "1 <= T <= 100,000\n1 <= N, M <= 10^9\n0 <= A, B < M", "input": "Input is given from Standard Input in the following format:\nT\nN_0 M_0 A_0 B_0\nN_1 M_1 A_1 B_1\n:\nN_{T - 1} M_{T - 1} A_{T - 1} B_{T - 1}", "output": "Print the answer for each testcase.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n4 10 6 3\n6 5 4 3\n1 1 0 0\n31415 92653 58979 32384\n1000000000 1000000000 999999999 999999999 output: 3\n13\n0\n314095480\n499999999500000000"], "Pid": "p02560", "ProblemText": "Task Description: Problem Statement In this problem, you should process T testcases.\nFor each testcase, you are given four integers N, M, A, B.\nCalculate \\sum_{i = 0}^{N - 1} floor((A * i + B) / M).\nTask Constraint: 1 <= T <= 100,000\n1 <= N, M <= 10^9\n0 <= A, B < M\nTask Input: Input is given from Standard Input in the following format:\nT\nN_0 M_0 A_0 B_0\nN_1 M_1 A_1 B_1\n:\nN_{T - 1} M_{T - 1} A_{T - 1} B_{T - 1}\nTask Output: Print the answer for each testcase.\nTask Samples: input: 5\n4 10 6 3\n6 5 4 3\n1 1 0 0\n31415 92653 58979 32384\n1000000000 1000000000 999999999 999999999 output: 3\n13\n0\n314095480\n499999999500000000\n\n" }, { "title": "", "content": "Problem Statement You are given a grid of N rows and M columns. The square at the i-th row and j-th column will be denoted as (i, j).\nSome of the squares contain an object. All the remaining squares are empty.\nThe state of the grid is represented by strings S_1, S_2, \\cdots, S_N. The square (i, j) contains an object if S_{i, j}= # and is empty if S_{i, j}= . .\nConsider placing 1 * 2 tiles on the grid. Tiles can be placed vertically or horizontally to cover two adjacent empty squares.\nTiles must not stick out of the grid, and no two different tiles may intersect. Tiles cannot occupy the square with an object.\nCalculate the maximum number of tiles that can be placed and any configulation that acheives the maximum.", "constraint": "1 <= N <= 100\n1 <= M <= 100\nS_i is a string with length M consists of # and ..", "input": "Input is given from Standard Input in the following format:\nN M\nS_1\nS_2\n\\vdots\nS_N", "output": "Output On the first line, print the maximum number of tiles that can be placed.\nOn the next N lines, print a configulation that achieves the maximum.\nPrecisely, output the strings t_1, t_2, \\cdots, t_N constructed by the following way.\n\nt_i is initialized to S_i.\nFor each (i, j), if there is a tile that occupies (i, j) and (i+1, j), change t_{i, j}: =v, t_{i+1, j}: =^.\nFor each (i, j), if there is a tile that occupies (i, j) and (i, j+1), change t_{i, j}: =>, t_{i, j+1}: =<.\n\nSee samples for further information.\nYou may print any configulation that maximizes the number of tiles.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n#..\n..#\n... output: 3\n#><\nvv#\n^^.\n\nThe following output is also treated as a correct answer.\n3\n#><\nv.#\n^><"], "Pid": "p02561", "ProblemText": "Task Description: Problem Statement You are given a grid of N rows and M columns. The square at the i-th row and j-th column will be denoted as (i, j).\nSome of the squares contain an object. All the remaining squares are empty.\nThe state of the grid is represented by strings S_1, S_2, \\cdots, S_N. The square (i, j) contains an object if S_{i, j}= # and is empty if S_{i, j}= . .\nConsider placing 1 * 2 tiles on the grid. Tiles can be placed vertically or horizontally to cover two adjacent empty squares.\nTiles must not stick out of the grid, and no two different tiles may intersect. Tiles cannot occupy the square with an object.\nCalculate the maximum number of tiles that can be placed and any configulation that acheives the maximum.\nTask Constraint: 1 <= N <= 100\n1 <= M <= 100\nS_i is a string with length M consists of # and ..\nTask Input: Input is given from Standard Input in the following format:\nN M\nS_1\nS_2\n\\vdots\nS_N\nTask Output: Output On the first line, print the maximum number of tiles that can be placed.\nOn the next N lines, print a configulation that achieves the maximum.\nPrecisely, output the strings t_1, t_2, \\cdots, t_N constructed by the following way.\n\nt_i is initialized to S_i.\nFor each (i, j), if there is a tile that occupies (i, j) and (i+1, j), change t_{i, j}: =v, t_{i+1, j}: =^.\nFor each (i, j), if there is a tile that occupies (i, j) and (i, j+1), change t_{i, j}: =>, t_{i, j+1}: =<.\n\nSee samples for further information.\nYou may print any configulation that maximizes the number of tiles.\nTask Samples: input: 3 3\n#..\n..#\n... output: 3\n#><\nvv#\n^^.\n\nThe following output is also treated as a correct answer.\n3\n#><\nv.#\n^><\n\n" }, { "title": "", "content": "Problem Statement You are given a grid of N rows and M columns. The square at the i-th row and j-th column will be denoted as (i, j).\nA nonnegative integer A_{i, j} is written for each square (i, j).\nYou choose some of the squares so that each row and column contains at most K chosen squares.\nUnder this constraint, calculate the maximum value of the sum of the integers written on the chosen squares.\nAdditionally, calculate a way to choose squares that acheives the maximum.", "constraint": "1 <= N <= 50\n1 <= K <= N\n0 <= A_{i,j} <= 10^9\nAll values in Input are integer.", "input": "Input is given from Standard Input in the following format:\nN K\nA_{1,1} A_{1,2} \\cdots A_{1, N}\nA_{2,1} A_{2,2} \\cdots A_{2, N}\n\\vdots\nA_{N, 1} A_{N, 2} \\cdots A_{N, N}", "output": "Output On the first line, print the maximum value of the sum of the integers written on the chosen squares.\nOn the next N lines, print a way that achieves the maximum.\nPrecisely, output the strings t_1, t_2, \\cdots, t_N, that satisfies t_{i, j}=X if you choose (i, j) and t_{i, j}=. otherwise.\nYou may print any way to choose squares that maximizes the sum.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n5 3 2\n1 4 8\n7 6 9 output: 19\nX..\n..X\n.X.", "input: 3 2\n10 10 1\n10 10 1\n1 1 10 output: 50\nXX.\nXX.\n..X"], "Pid": "p02562", "ProblemText": "Task Description: Problem Statement You are given a grid of N rows and M columns. The square at the i-th row and j-th column will be denoted as (i, j).\nA nonnegative integer A_{i, j} is written for each square (i, j).\nYou choose some of the squares so that each row and column contains at most K chosen squares.\nUnder this constraint, calculate the maximum value of the sum of the integers written on the chosen squares.\nAdditionally, calculate a way to choose squares that acheives the maximum.\nTask Constraint: 1 <= N <= 50\n1 <= K <= N\n0 <= A_{i,j} <= 10^9\nAll values in Input are integer.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_{1,1} A_{1,2} \\cdots A_{1, N}\nA_{2,1} A_{2,2} \\cdots A_{2, N}\n\\vdots\nA_{N, 1} A_{N, 2} \\cdots A_{N, N}\nTask Output: Output On the first line, print the maximum value of the sum of the integers written on the chosen squares.\nOn the next N lines, print a way that achieves the maximum.\nPrecisely, output the strings t_1, t_2, \\cdots, t_N, that satisfies t_{i, j}=X if you choose (i, j) and t_{i, j}=. otherwise.\nYou may print any way to choose squares that maximizes the sum.\nTask Samples: input: 3 1\n5 3 2\n1 4 8\n7 6 9 output: 19\nX..\n..X\n.X.\ninput: 3 2\n10 10 1\n10 10 1\n1 1 10 output: 50\nXX.\nXX.\n..X\n\n" }, { "title": "", "content": "Problem Statement You are given two integer arrays a_0, a_1, . . . , a_{N - 1} and b_0, b_1, . . . , b_{M - 1}. Calculate the array c_0, c_1, . . . , c_{(N - 1) + (M - 1)}, defined by c_i = \\sum_{j = 0}^i a_j b_{i - j} \\bmod 998244353.", "constraint": "1 <= N, M <= 524288\n0 <= a_i, b_i < 998244353\nAll values in Input are integer.", "input": "Input is given from Standard Input in the following format:\nN M\na_0 a_1 . . . a_{N-1}\nb_0 b_1 . . . b_{M-1}", "output": "Print the answer in the following format:\nc_0 c_1 . . . c_{(N - 1) + (M - 1)}", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n1 2 3 4\n5 6 7 8 9 output: 5 16 34 60 70 70 59 36", "input: 1 1\n10000000\n10000000 output: 871938225"], "Pid": "p02563", "ProblemText": "Task Description: Problem Statement You are given two integer arrays a_0, a_1, . . . , a_{N - 1} and b_0, b_1, . . . , b_{M - 1}. Calculate the array c_0, c_1, . . . , c_{(N - 1) + (M - 1)}, defined by c_i = \\sum_{j = 0}^i a_j b_{i - j} \\bmod 998244353.\nTask Constraint: 1 <= N, M <= 524288\n0 <= a_i, b_i < 998244353\nAll values in Input are integer.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_0 a_1 . . . a_{N-1}\nb_0 b_1 . . . b_{M-1}\nTask Output: Print the answer in the following format:\nc_0 c_1 . . . c_{(N - 1) + (M - 1)}\nTask Samples: input: 4 5\n1 2 3 4\n5 6 7 8 9 output: 5 16 34 60 70 70 59 36\ninput: 1 1\n10000000\n10000000 output: 871938225\n\n" }, { "title": "", "content": "Problem Statement You are given a directed graph with N vertices and M edges, not necessarily simple. The i-th edge is oriented from the vertex a_i to the vertex b_i.\nDivide this graph into strongly connected components and print them in their topological order.", "constraint": "1 <= N <= 500,000\n1 <= M <= 500,000\n0 <= a_i, b_i < N", "input": "Input is given from Standard Input in the following format:\nN M\na_0 b_0\na_1 b_1\n:\na_{M - 1} b_{M - 1}", "output": "Print 1+K lines, where K is the number of strongly connected components.\nPrint K on the first line. \nPrint the information of each strongly connected component in next K lines in the following format, where l is the number of vertices in the strongly connected component and v_i is the index of the vertex in it.\nl v_0 v_1 . . . v_{l-1}\n\nHere, for each edge (a_i, b_i), b_i should not appear in earlier line than a_i.\nIf there are multiple correct output, print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 7\n1 4\n5 2\n3 0\n5 5\n4 1\n0 3\n4 2 output: 4\n1 5\n2 4 1\n1 2\n2 3 0"], "Pid": "p02564", "ProblemText": "Task Description: Problem Statement You are given a directed graph with N vertices and M edges, not necessarily simple. The i-th edge is oriented from the vertex a_i to the vertex b_i.\nDivide this graph into strongly connected components and print them in their topological order.\nTask Constraint: 1 <= N <= 500,000\n1 <= M <= 500,000\n0 <= a_i, b_i < N\nTask Input: Input is given from Standard Input in the following format:\nN M\na_0 b_0\na_1 b_1\n:\na_{M - 1} b_{M - 1}\nTask Output: Print 1+K lines, where K is the number of strongly connected components.\nPrint K on the first line. \nPrint the information of each strongly connected component in next K lines in the following format, where l is the number of vertices in the strongly connected component and v_i is the index of the vertex in it.\nl v_0 v_1 . . . v_{l-1}\n\nHere, for each edge (a_i, b_i), b_i should not appear in earlier line than a_i.\nIf there are multiple correct output, print any of them.\nTask Samples: input: 6 7\n1 4\n5 2\n3 0\n5 5\n4 1\n0 3\n4 2 output: 4\n1 5\n2 4 1\n1 2\n2 3 0\n\n" }, { "title": "", "content": "Problem Statement Consider placing N flags on a line. Flags are numbered through 1 to N.\nFlag i can be placed on the coordinate X_i or Y_i.\nFor any two different flags, the distance between them should be at least D.\nDecide whether it is possible to place all N flags. If it is possible, print such a configulation.", "constraint": "1 <= N <= 1000\n0 <= D <= 10^9\n0 <= X_i < Y_i <= 10^9\nAll values in Input are integer.", "input": "Input is given from Standard Input in the following format:\nN D\nX_1 Y_1\nX_2 Y_2\n\\vdots\nX_N Y_N", "output": "Print No if it is impossible to place N flags.\nIf it is possible, print Yes first.\nAfter that, print N lines. i-th line of them should contain the coodinate of flag i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 4\n2 5\n0 6 output: Yes\n4\n2\n0", "input: 3 3\n1 4\n2 5\n0 6 output: No"], "Pid": "p02565", "ProblemText": "Task Description: Problem Statement Consider placing N flags on a line. Flags are numbered through 1 to N.\nFlag i can be placed on the coordinate X_i or Y_i.\nFor any two different flags, the distance between them should be at least D.\nDecide whether it is possible to place all N flags. If it is possible, print such a configulation.\nTask Constraint: 1 <= N <= 1000\n0 <= D <= 10^9\n0 <= X_i < Y_i <= 10^9\nAll values in Input are integer.\nTask Input: Input is given from Standard Input in the following format:\nN D\nX_1 Y_1\nX_2 Y_2\n\\vdots\nX_N Y_N\nTask Output: Print No if it is impossible to place N flags.\nIf it is possible, print Yes first.\nAfter that, print N lines. i-th line of them should contain the coodinate of flag i.\nTask Samples: input: 3 2\n1 4\n2 5\n0 6 output: Yes\n4\n2\n0\ninput: 3 3\n1 4\n2 5\n0 6 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given a string of length N. Calculate the number of distinct substrings of S.", "constraint": "1 <= N <= 500,000\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abcbcba output: 21", "input: mississippi output: 53", "input: ababacaca output: 33", "input: aaaaa output: 5"], "Pid": "p02566", "ProblemText": "Task Description: Problem Statement You are given a string of length N. Calculate the number of distinct substrings of S.\nTask Constraint: 1 <= N <= 500,000\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the answer.\nTask Samples: input: abcbcba output: 21\ninput: mississippi output: 53\ninput: ababacaca output: 33\ninput: aaaaa output: 5\n\n" }, { "title": "", "content": "Problem Statement You are given an array a_0, a_1, . . . , a_{N-1} of length N. Process Q queries of the following types.\nThe type of i-th query is represented by T_i.\n\nT_i=1: You are given two integers X_i, V_i. Replace the value of A_{X_i} with V_i.\nT_i=2: You are given two integers L_i, R_i. Calculate the maximum value among A_{L_i}, A_{L_i+1}, \\cdots, A_{R_i}.\nT_i=3: You are given two integers X_i, V_i. Calculate the minimum j such that X_i <= j <= N, V_i <= A_j. If there is no such j, answer j=N+1 instead.", "constraint": "1 <= N <= 2 * 10^5\n0 <= A_i <= 10^9\n1 <= Q <= 2 * 10^5\n1 <= T_i <= 3\n1 <= X_i <= N, 0 <= V_i <= 10^9 (T_i=1,3)\n1 <= L_i <= R_i <= N (T_i=2)\nAll values in Input are integer.", "input": "Input is given from Standard Input in the following format:\nN Q\nA_1 A_2 \\cdots A_N\nFirst query\nSecond query\n\\vdots\nQ-th query\n\nEach query is given in the following format:\nIf T_i=1,3,\nT_i X_i V_i\n\nIf T_i=2,\nT_i L_i R_i", "output": "For each query with T_i=2,3, print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n1 2 3 2 1\n2 1 5\n3 2 3\n1 3 1\n2 2 4\n3 1 3 output: 3\n3\n2\n6\nFirst query: Print 3, which is the maximum of (A_1,A_2,A_3,A_4,A_5)=(1,2,3,2,1).\nSecond query: Since 3>A_2, j=2 does not satisfy the condition．Since 3 <= A_3, print j=3.\nThird query: Replace the value of A_3 with 1. It becomes A=(1,2,1,2,1).\nFourth query: Print 2, which is the maximum of (A_2,A_3,A_4)=(2,1,2).\nFifth query: Since there is no j that satisfies the condition, print j=N+1=6."], "Pid": "p02567", "ProblemText": "Task Description: Problem Statement You are given an array a_0, a_1, . . . , a_{N-1} of length N. Process Q queries of the following types.\nThe type of i-th query is represented by T_i.\n\nT_i=1: You are given two integers X_i, V_i. Replace the value of A_{X_i} with V_i.\nT_i=2: You are given two integers L_i, R_i. Calculate the maximum value among A_{L_i}, A_{L_i+1}, \\cdots, A_{R_i}.\nT_i=3: You are given two integers X_i, V_i. Calculate the minimum j such that X_i <= j <= N, V_i <= A_j. If there is no such j, answer j=N+1 instead.\nTask Constraint: 1 <= N <= 2 * 10^5\n0 <= A_i <= 10^9\n1 <= Q <= 2 * 10^5\n1 <= T_i <= 3\n1 <= X_i <= N, 0 <= V_i <= 10^9 (T_i=1,3)\n1 <= L_i <= R_i <= N (T_i=2)\nAll values in Input are integer.\nTask Input: Input is given from Standard Input in the following format:\nN Q\nA_1 A_2 \\cdots A_N\nFirst query\nSecond query\n\\vdots\nQ-th query\n\nEach query is given in the following format:\nIf T_i=1,3,\nT_i X_i V_i\n\nIf T_i=2,\nT_i L_i R_i\nTask Output: For each query with T_i=2,3, print the answer.\nTask Samples: input: 5 5\n1 2 3 2 1\n2 1 5\n3 2 3\n1 3 1\n2 2 4\n3 1 3 output: 3\n3\n2\n6\nFirst query: Print 3, which is the maximum of (A_1,A_2,A_3,A_4,A_5)=(1,2,3,2,1).\nSecond query: Since 3>A_2, j=2 does not satisfy the condition．Since 3 <= A_3, print j=3.\nThird query: Replace the value of A_3 with 1. It becomes A=(1,2,1,2,1).\nFourth query: Print 2, which is the maximum of (A_2,A_3,A_4)=(2,1,2).\nFifth query: Since there is no j that satisfies the condition, print j=N+1=6.\n\n" }, { "title": "", "content": "Problem Statement You are given an array a_0, a_1, . . . , a_{N-1} of length N. Process Q queries of the following types.\n\n0 l r b c: For each i = l, l+1, \\dots, {r - 1}, set a_i >=ts b * a_i + c.\n1 l r: Print \\sum_{i = l}^{r - 1} a_i \\bmod 998244353.", "constraint": "1 <= N, Q <= 500000\n0 <= a_i, c < 998244353\n1 <= b < 998244353\n0 <= l < r <= N\nAll values in Input are integer.", "input": "Input is given from Standard Input in the following format:\nN Q\na_0 a_1 . . . a_{N - 1}\n\\textrm{Query}_0\n\\textrm{Query}_1\n:\n\\textrm{Query}_{Q - 1}", "output": "For each query of the latter type, print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 7\n1 2 3 4 5\n1 0 5\n0 2 4 100 101\n1 0 3\n0 1 3 102 103\n1 2 5\n0 2 5 104 105\n1 0 5 output: 15\n404\n41511\n4317767"], "Pid": "p02568", "ProblemText": "Task Description: Problem Statement You are given an array a_0, a_1, . . . , a_{N-1} of length N. Process Q queries of the following types.\n\n0 l r b c: For each i = l, l+1, \\dots, {r - 1}, set a_i >=ts b * a_i + c.\n1 l r: Print \\sum_{i = l}^{r - 1} a_i \\bmod 998244353.\nTask Constraint: 1 <= N, Q <= 500000\n0 <= a_i, c < 998244353\n1 <= b < 998244353\n0 <= l < r <= N\nAll values in Input are integer.\nTask Input: Input is given from Standard Input in the following format:\nN Q\na_0 a_1 . . . a_{N - 1}\n\\textrm{Query}_0\n\\textrm{Query}_1\n:\n\\textrm{Query}_{Q - 1}\nTask Output: For each query of the latter type, print the answer.\nTask Samples: input: 5 7\n1 2 3 4 5\n1 0 5\n0 2 4 100 101\n1 0 3\n0 1 3 102 103\n1 2 5\n0 2 5 104 105\n1 0 5 output: 15\n404\n41511\n4317767\n\n" }, { "title": "", "content": "Problem Statement You are given a binary array A=(A_1, A_2, \\cdots, A_N) of length N. \nProcess Q queries of the following types. The i-th query is represented by three integers T_i, L_i, R_i.\n\nT_i=1: Replace the value of A_j with 1-A_j for each L_i <= j <= R_i.\nT_i=2: Calculate the inversion(*) of the array A_{L_i}, A_{L_i+1}, \\cdots, A_{R_i}．\n\nNote：The inversion of the array x_1, x_2, \\cdots, x_k is the number of the pair of integers i, j with 1 <= i < j <= k, x_i > x_j.", "constraint": "1 <= N <= 2 * 10^5\n0 <= A_i <= 1\n1 <= Q <= 2 * 10^5\n1 <= T_i <= 2\n1 <= L_i <= R_i <= N\nAll values in Input are integer.", "input": "Input is given from Standard Input in the following format:\nN Q\nA_1 A_2 \\cdots A_N\nT_1 L_1 R_1\nT_2 L_2 R_2\n\\vdots\nT_Q L_Q R_Q", "output": "For each query with T_i=2, print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n0 1 0 0 1\n2 1 5\n1 3 4\n2 2 5\n1 1 3\n2 1 2 output: 2\n0\n1\nFirst query: Print 2, which is the inversion of (A_1,A_2,A_3,A_4,A_5)=(0,1,0,0,1).\nSecond query: Replace the value of A_3 and A_4 with 1 and 1, respectively.\nThird query: Print 0, which is the inversion of (A_2,A_3,A_4,A_5)=(1,1,1,1).\nFourth query: Replace the value of A_1, A_2 and A_4 with 1,0 and 0, respectively.\nFifth query: Print 1, which is the inversion of (A_1,A_2)=(1,0)."], "Pid": "p02569", "ProblemText": "Task Description: Problem Statement You are given a binary array A=(A_1, A_2, \\cdots, A_N) of length N. \nProcess Q queries of the following types. The i-th query is represented by three integers T_i, L_i, R_i.\n\nT_i=1: Replace the value of A_j with 1-A_j for each L_i <= j <= R_i.\nT_i=2: Calculate the inversion(*) of the array A_{L_i}, A_{L_i+1}, \\cdots, A_{R_i}．\n\nNote：The inversion of the array x_1, x_2, \\cdots, x_k is the number of the pair of integers i, j with 1 <= i < j <= k, x_i > x_j.\nTask Constraint: 1 <= N <= 2 * 10^5\n0 <= A_i <= 1\n1 <= Q <= 2 * 10^5\n1 <= T_i <= 2\n1 <= L_i <= R_i <= N\nAll values in Input are integer.\nTask Input: Input is given from Standard Input in the following format:\nN Q\nA_1 A_2 \\cdots A_N\nT_1 L_1 R_1\nT_2 L_2 R_2\n\\vdots\nT_Q L_Q R_Q\nTask Output: For each query with T_i=2, print the answer.\nTask Samples: input: 5 5\n0 1 0 0 1\n2 1 5\n1 3 4\n2 2 5\n1 1 3\n2 1 2 output: 2\n0\n1\nFirst query: Print 2, which is the inversion of (A_1,A_2,A_3,A_4,A_5)=(0,1,0,0,1).\nSecond query: Replace the value of A_3 and A_4 with 1 and 1, respectively.\nThird query: Print 0, which is the inversion of (A_2,A_3,A_4,A_5)=(1,1,1,1).\nFourth query: Replace the value of A_1, A_2 and A_4 with 1,0 and 0, respectively.\nFifth query: Print 1, which is the inversion of (A_1,A_2)=(1,0).\n\n" }, { "title": "", "content": "Problem Statement Takahashi is meeting up with Aoki.\nThey have planned to meet at a place that is D meters away from Takahashi's house in T minutes from now.\nTakahashi will leave his house now and go straight to the place at a speed of S meters per minute.\nWill he arrive in time?", "constraint": "1 <= D <= 10000\n1 <= T <= 10000\n1 <= S <= 10000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nD T S", "output": "If Takahashi will reach the place in time, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1000 15 80 output: Yes\n\nIt takes 12.5 minutes to go 1000 meters to the place at a speed of 80 meters per minute. They have planned to meet in 15 minutes so he will arrive in time.", "input: 2000 20 100 output: Yes\n\nIt takes 20 minutes to go 2000 meters to the place at a speed of 100 meters per minute. They have planned to meet in 20 minutes so he will arrive just on time.", "input: 10000 1 1 output: No\n\nHe will be late."], "Pid": "p02570", "ProblemText": "Task Description: Problem Statement Takahashi is meeting up with Aoki.\nThey have planned to meet at a place that is D meters away from Takahashi's house in T minutes from now.\nTakahashi will leave his house now and go straight to the place at a speed of S meters per minute.\nWill he arrive in time?\nTask Constraint: 1 <= D <= 10000\n1 <= T <= 10000\n1 <= S <= 10000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nD T S\nTask Output: If Takahashi will reach the place in time, print Yes; otherwise, print No.\nTask Samples: input: 1000 15 80 output: Yes\n\nIt takes 12.5 minutes to go 1000 meters to the place at a speed of 80 meters per minute. They have planned to meet in 15 minutes so he will arrive in time.\ninput: 2000 20 100 output: Yes\n\nIt takes 20 minutes to go 2000 meters to the place at a speed of 100 meters per minute. They have planned to meet in 20 minutes so he will arrive just on time.\ninput: 10000 1 1 output: No\n\nHe will be late.\n\n" }, { "title": "", "content": "Problem Statement Given are two strings S and T.\nLet us change some of the characters in S so that T will be a substring of S.\nAt least how many characters do we need to change?\nHere, a substring is a consecutive subsequence. For example, xxx is a substring of yxxxy, but not a substring of xxyxx.", "constraint": "The lengths of S and T are each at least 1 and at most 1000.\nThe length of T is at most that of S.\nS and T consist of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS\nT", "output": "Print the minimum number of characters in S that need to be changed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: cabacc\nabc output: 1\n\nFor example, changing the fourth character a in S to c will match the second through fourth characters in S to T.\nSince S itself does not have T as its substring, this number of changes - one - is the minimum needed.", "input: codeforces\natcoder output: 6"], "Pid": "p02571", "ProblemText": "Task Description: Problem Statement Given are two strings S and T.\nLet us change some of the characters in S so that T will be a substring of S.\nAt least how many characters do we need to change?\nHere, a substring is a consecutive subsequence. For example, xxx is a substring of yxxxy, but not a substring of xxyxx.\nTask Constraint: The lengths of S and T are each at least 1 and at most 1000.\nThe length of T is at most that of S.\nS and T consist of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nT\nTask Output: Print the minimum number of characters in S that need to be changed.\nTask Samples: input: cabacc\nabc output: 1\n\nFor example, changing the fourth character a in S to c will match the second through fourth characters in S to T.\nSince S itself does not have T as its substring, this number of changes - one - is the minimum needed.\ninput: codeforces\natcoder output: 6\n\n" }, { "title": "", "content": "Problem Statement Given are N integers A_1, \\ldots, A_N.\nFind the sum of A_i * A_j over all pairs (i, j) such that 1<= i < j <= N, modulo (10^9+7).", "constraint": "2 <= N <= 2* 10^5\n0 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N", "output": "Print \\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} A_i A_j, modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 11\n\nWe have 1 * 2 + 1 * 3 + 2 * 3 = 11.", "input: 4\n141421356 17320508 22360679 244949 output: 437235829"], "Pid": "p02572", "ProblemText": "Task Description: Problem Statement Given are N integers A_1, \\ldots, A_N.\nFind the sum of A_i * A_j over all pairs (i, j) such that 1<= i < j <= N, modulo (10^9+7).\nTask Constraint: 2 <= N <= 2* 10^5\n0 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N\nTask Output: Print \\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} A_i A_j, modulo (10^9+7).\nTask Samples: input: 3\n1 2 3 output: 11\n\nWe have 1 * 2 + 1 * 3 + 2 * 3 = 11.\ninput: 4\n141421356 17320508 22360679 244949 output: 437235829\n\n" }, { "title": "", "content": "Problem Statement There are N persons called Person 1 through Person N.\nYou are given M facts that \"Person A_i and Person B_i are friends. \" The same fact may be given multiple times.\nIf X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.\nTakahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.\nAt least how many groups does he need to make?", "constraint": "2 <= N <= 2* 10^5\n0 <= M <= 2* 10^5\n1<= A_i,B_i<= N\nA_i \\neq B_i", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n\\vdots\nA_M B_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 2\n3 4\n5 1 output: 3\n\nDividing them into three groups such as \\{1,3\\}, \\{2,4\\}, and \\{5\\} achieves the goal.", "input: 4 10\n1 2\n2 1\n1 2\n2 1\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4 output: 4", "input: 10 4\n3 1\n4 1\n5 9\n2 6 output: 3"], "Pid": "p02573", "ProblemText": "Task Description: Problem Statement There are N persons called Person 1 through Person N.\nYou are given M facts that \"Person A_i and Person B_i are friends. \" The same fact may be given multiple times.\nIf X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.\nTakahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.\nAt least how many groups does he need to make?\nTask Constraint: 2 <= N <= 2* 10^5\n0 <= M <= 2* 10^5\n1<= A_i,B_i<= N\nA_i \\neq B_i\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n\\vdots\nA_M B_M\nTask Output: Print the answer.\nTask Samples: input: 5 3\n1 2\n3 4\n5 1 output: 3\n\nDividing them into three groups such as \\{1,3\\}, \\{2,4\\}, and \\{5\\} achieves the goal.\ninput: 4 10\n1 2\n2 1\n1 2\n2 1\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4 output: 4\ninput: 10 4\n3 1\n4 1\n5 9\n2 6 output: 3\n\n" }, { "title": "", "content": "Problem Statement We have N integers. The i-th number is A_i.\n\\{A_i\\} is said to be pairwise coprime when GCD(A_i, A_j)=1 holds for every pair (i, j) such that 1<= i < j <= N.\n\\{A_i\\} is said to be setwise coprime when \\{A_i\\} is not pairwise coprime but GCD(A_1, \\ldots, A_N)=1.\nDetermine if \\{A_i\\} is pairwise coprime, setwise coprime, or neither.\nHere, GCD(\\ldots) denotes greatest common divisor.", "constraint": "2 <= N <= 10^6\n1 <= A_i<= 10^6", "input": "Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N", "output": "If \\{A_i\\} is pairwise coprime, print pairwise coprime; if \\{A_i\\} is setwise coprime, print setwise coprime; if neither, print not coprime.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 4 5 output: pairwise coprime\n\nGCD(3,4)=GCD(3,5)=GCD(4,5)=1, so they are pairwise coprime.", "input: 3\n6 10 15 output: setwise coprime\n\nSince GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.", "input: 3\n6 10 16 output: not coprime\n\nGCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime."], "Pid": "p02574", "ProblemText": "Task Description: Problem Statement We have N integers. The i-th number is A_i.\n\\{A_i\\} is said to be pairwise coprime when GCD(A_i, A_j)=1 holds for every pair (i, j) such that 1<= i < j <= N.\n\\{A_i\\} is said to be setwise coprime when \\{A_i\\} is not pairwise coprime but GCD(A_1, \\ldots, A_N)=1.\nDetermine if \\{A_i\\} is pairwise coprime, setwise coprime, or neither.\nHere, GCD(\\ldots) denotes greatest common divisor.\nTask Constraint: 2 <= N <= 10^6\n1 <= A_i<= 10^6\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N\nTask Output: If \\{A_i\\} is pairwise coprime, print pairwise coprime; if \\{A_i\\} is setwise coprime, print setwise coprime; if neither, print not coprime.\nTask Samples: input: 3\n3 4 5 output: pairwise coprime\n\nGCD(3,4)=GCD(3,5)=GCD(4,5)=1, so they are pairwise coprime.\ninput: 3\n6 10 15 output: setwise coprime\n\nSince GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.\ninput: 3\n6 10 16 output: not coprime\n\nGCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime.\n\n" }, { "title": "", "content": "Problem Statement There is a grid of squares with H+1 horizontal rows and W vertical columns.\nYou will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \\ldots, B_i-th squares from the left in the i-th row from the top.\nFor each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case. ) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print -1 instead.", "constraint": "1 <= H,W <= 2* 10^5\n1 <= A_i <= B_i <= W", "input": "Input is given from Standard Input in the following format:\nH W\nA_1 B_1\nA_2 B_2\n:\nA_H B_H", "output": "Print H lines. The i-th line should contain the answer for the case k=i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n2 4\n1 1\n2 3\n2 4 output: 1\n3\n6\n-1\n\nLet (i,j) denote the square at the i-th row from the top and j-th column from the left.\nFor k=1, we need one move such as (1,1) → (2,1).\nFor k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).\nFor k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).\nFor k=4, it is impossible to reach any square in the fifth row from the top."], "Pid": "p02575", "ProblemText": "Task Description: Problem Statement There is a grid of squares with H+1 horizontal rows and W vertical columns.\nYou will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \\ldots, B_i-th squares from the left in the i-th row from the top.\nFor each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case. ) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print -1 instead.\nTask Constraint: 1 <= H,W <= 2* 10^5\n1 <= A_i <= B_i <= W\nTask Input: Input is given from Standard Input in the following format:\nH W\nA_1 B_1\nA_2 B_2\n:\nA_H B_H\nTask Output: Print H lines. The i-th line should contain the answer for the case k=i.\nTask Samples: input: 4 4\n2 4\n1 1\n2 3\n2 4 output: 1\n3\n6\n-1\n\nLet (i,j) denote the square at the i-th row from the top and j-th column from the left.\nFor k=1, we need one move such as (1,1) → (2,1).\nFor k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).\nFor k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).\nFor k=4, it is impossible to reach any square in the fifth row from the top.\n\n" }, { "title": "", "content": "Problem Statement Takahashi loves takoyaki - a ball-shaped snack.\nWith a takoyaki machine, he can make at most X pieces of takoyaki at a time, taking T minutes regardless of the number of pieces to make.\nHow long does it take to make N takoyaki?", "constraint": "1 <= N,X,T <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X T", "output": "Print an integer representing the minimum number of minutes needed to make N pieces of takoyaki.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 20 12 6 output: 12\n\nHe can make 12 pieces of takoyaki in the first 6 minutes and 8 more in the next 6 minutes, so he can make 20 in a total of 12 minutes.\nNote that being able to make 12 in 6 minutes does not mean he can make 2 in 1 minute.", "input: 1000 1 1000 output: 1000000\n\nIt seems to take a long time to make this kind of takoyaki."], "Pid": "p02576", "ProblemText": "Task Description: Problem Statement Takahashi loves takoyaki - a ball-shaped snack.\nWith a takoyaki machine, he can make at most X pieces of takoyaki at a time, taking T minutes regardless of the number of pieces to make.\nHow long does it take to make N takoyaki?\nTask Constraint: 1 <= N,X,T <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X T\nTask Output: Print an integer representing the minimum number of minutes needed to make N pieces of takoyaki.\nTask Samples: input: 20 12 6 output: 12\n\nHe can make 12 pieces of takoyaki in the first 6 minutes and 8 more in the next 6 minutes, so he can make 20 in a total of 12 minutes.\nNote that being able to make 12 in 6 minutes does not mean he can make 2 in 1 minute.\ninput: 1000 1 1000 output: 1000000\n\nIt seems to take a long time to make this kind of takoyaki.\n\n" }, { "title": "", "content": "Problem Statement An integer N is a multiple of 9 if and only if the sum of the digits in the decimal representation of N is a multiple of 9.\nDetermine whether N is a multiple of 9.", "constraint": "0 <= N < 10^{200000}\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If N is a multiple of 9, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 123456789 output: Yes\n\nThe sum of these digits is 1+2+3+4+5+6+7+8+9=45, which is a multiple of 9, so 123456789 is a multiple of 9.", "input: 0 output: Yes", "input: 31415926535897932384626433832795028841971693993751058209749445923078164062862089986280 output: No"], "Pid": "p02577", "ProblemText": "Task Description: Problem Statement An integer N is a multiple of 9 if and only if the sum of the digits in the decimal representation of N is a multiple of 9.\nDetermine whether N is a multiple of 9.\nTask Constraint: 0 <= N < 10^{200000}\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If N is a multiple of 9, print Yes; otherwise, print No.\nTask Samples: input: 123456789 output: Yes\n\nThe sum of these digits is 1+2+3+4+5+6+7+8+9=45, which is a multiple of 9, so 123456789 is a multiple of 9.\ninput: 0 output: Yes\ninput: 31415926535897932384626433832795028841971693993751058209749445923078164062862089986280 output: No\n\n" }, { "title": "", "content": "Problem Statement N persons are standing in a row. The height of the i-th person from the front is A_i.\nWe want to have each person stand on a stool of some heights - at least zero - so that the following condition is satisfied for every person:\nCondition: Nobody in front of the person is taller than the person. Here, the height of a person includes the stool.\nFind the minimum total height of the stools needed to meet this goal.", "constraint": "1 <= N <= 2* 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N", "output": "Print the minimum total height of the stools needed to meet the goal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 1 5 4 3 output: 4\n\nIf the persons stand on stools of heights 0,1,0,1, and 2, respectively, their heights will be 2,2,5,5, and 5, satisfying the condition.\nWe cannot meet the goal with a smaller total height of the stools.", "input: 5\n3 3 3 3 3 output: 0\n\nGiving a stool of height 0 to everyone will work."], "Pid": "p02578", "ProblemText": "Task Description: Problem Statement N persons are standing in a row. The height of the i-th person from the front is A_i.\nWe want to have each person stand on a stool of some heights - at least zero - so that the following condition is satisfied for every person:\nCondition: Nobody in front of the person is taller than the person. Here, the height of a person includes the stool.\nFind the minimum total height of the stools needed to meet this goal.\nTask Constraint: 1 <= N <= 2* 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N\nTask Output: Print the minimum total height of the stools needed to meet the goal.\nTask Samples: input: 5\n2 1 5 4 3 output: 4\n\nIf the persons stand on stools of heights 0,1,0,1, and 2, respectively, their heights will be 2,2,5,5, and 5, satisfying the condition.\nWe cannot meet the goal with a smaller total height of the stools.\ninput: 5\n3 3 3 3 3 output: 0\n\nGiving a stool of height 0 to everyone will work.\n\n" }, { "title": "", "content": "Problem Statement A maze is composed of a grid of H * W squares - H vertical, W horizontal.\nThe square at the i-th row from the top and the j-th column from the left - (i, j) - is a wall if S_{ij} is # and a road if S_{ij} is . .\nThere is a magician in (C_h, C_w). He can do the following two kinds of moves:\n\nMove A: Walk to a road square that is vertically or horizontally adjacent to the square he is currently in.\nMove B: Use magic to warp himself to a road square in the 5* 5 area centered at the square he is currently in.\n\nIn either case, he cannot go out of the maze.\nAt least how many times does he need to use the magic to reach (D_h, D_w)?", "constraint": "1 <= H,W <= 10^3\n1 <= C_h,D_h <= H\n1 <= C_w,D_w <= W\nS_{ij} is # or ..\nS_{C_h C_w} and S_{D_h D_w} are ..\n(C_h,C_w) \\neq (D_h,D_w)", "input": "Input is given from Standard Input in the following format:\nH W\nC_h C_w\nD_h D_w\nS_{11}\\ldots S_{1W}\n\\vdots\nS_{H1}\\ldots S_{HW}", "output": "Print the minimum number of times the magician needs to use the magic. If he cannot reach (D_h, D_w), print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n1 1\n4 4\n..#.\n..#.\n.#..\n.#.. output: 1\n\nFor example, by walking to (2,2) and then using the magic to travel to (4,4), just one use of magic is enough.\nNote that he cannot walk diagonally.", "input: 4 4\n1 4\n4 1\n.##.\n####\n####\n.##. output: -1\n\nHe cannot move from there.", "input: 4 4\n2 2\n3 3\n....\n....\n....\n.... output: 0\n\nNo use of magic is needed.", "input: 4 5\n1 2\n2 5\n#.###\n####.\n#..##\n#..## output: 2"], "Pid": "p02579", "ProblemText": "Task Description: Problem Statement A maze is composed of a grid of H * W squares - H vertical, W horizontal.\nThe square at the i-th row from the top and the j-th column from the left - (i, j) - is a wall if S_{ij} is # and a road if S_{ij} is . .\nThere is a magician in (C_h, C_w). He can do the following two kinds of moves:\n\nMove A: Walk to a road square that is vertically or horizontally adjacent to the square he is currently in.\nMove B: Use magic to warp himself to a road square in the 5* 5 area centered at the square he is currently in.\n\nIn either case, he cannot go out of the maze.\nAt least how many times does he need to use the magic to reach (D_h, D_w)?\nTask Constraint: 1 <= H,W <= 10^3\n1 <= C_h,D_h <= H\n1 <= C_w,D_w <= W\nS_{ij} is # or ..\nS_{C_h C_w} and S_{D_h D_w} are ..\n(C_h,C_w) \\neq (D_h,D_w)\nTask Input: Input is given from Standard Input in the following format:\nH W\nC_h C_w\nD_h D_w\nS_{11}\\ldots S_{1W}\n\\vdots\nS_{H1}\\ldots S_{HW}\nTask Output: Print the minimum number of times the magician needs to use the magic. If he cannot reach (D_h, D_w), print -1 instead.\nTask Samples: input: 4 4\n1 1\n4 4\n..#.\n..#.\n.#..\n.#.. output: 1\n\nFor example, by walking to (2,2) and then using the magic to travel to (4,4), just one use of magic is enough.\nNote that he cannot walk diagonally.\ninput: 4 4\n1 4\n4 1\n.##.\n####\n####\n.##. output: -1\n\nHe cannot move from there.\ninput: 4 4\n2 2\n3 3\n....\n....\n....\n.... output: 0\n\nNo use of magic is needed.\ninput: 4 5\n1 2\n2 5\n#.###\n####.\n#..##\n#..## output: 2\n\n" }, { "title": "", "content": "Problem Statement We have a two-dimensional grid with H * W squares. There are M targets to destroy in this grid - the position of the i-th target is <=ft(h_i, w_i \\right).\nTakahashi will choose one square in this grid, place a bomb there, and ignite it. The bomb will destroy all targets that are in the row or the column where the bomb is placed. It is possible to place the bomb at a square with a target.\nTakahashi is trying to maximize the number of targets to destroy. Find the maximum number of targets that can be destroyed.", "constraint": "All values in input are integers.\n1 <= H, W <= 3 * 10^5\n1 <= M <= \\min<=ft(H* W, 3 * 10^5\\right)\n1 <= h_i <= H\n1 <= w_i <= W\n<=ft(h_i, w_i\\right) \\neq <=ft(h_j, w_j\\right) <=ft(i \\neq j\\right)", "input": "Input is given from Standard Input in the following format:\nH W M\nh_1 w_1\n\\vdots\nh_M w_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 3\n2 2\n1 1\n1 3 output: 3\n\nWe can destroy all the targets by placing the bomb at <=ft(1,2\\right).", "input: 3 3 4\n3 3\n3 1\n1 1\n1 2 output: 3", "input: 5 5 10\n2 5\n4 3\n2 3\n5 5\n2 2\n5 4\n5 3\n5 1\n3 5\n1 4 output: 6"], "Pid": "p02580", "ProblemText": "Task Description: Problem Statement We have a two-dimensional grid with H * W squares. There are M targets to destroy in this grid - the position of the i-th target is <=ft(h_i, w_i \\right).\nTakahashi will choose one square in this grid, place a bomb there, and ignite it. The bomb will destroy all targets that are in the row or the column where the bomb is placed. It is possible to place the bomb at a square with a target.\nTakahashi is trying to maximize the number of targets to destroy. Find the maximum number of targets that can be destroyed.\nTask Constraint: All values in input are integers.\n1 <= H, W <= 3 * 10^5\n1 <= M <= \\min<=ft(H* W, 3 * 10^5\\right)\n1 <= h_i <= H\n1 <= w_i <= W\n<=ft(h_i, w_i\\right) \\neq <=ft(h_j, w_j\\right) <=ft(i \\neq j\\right)\nTask Input: Input is given from Standard Input in the following format:\nH W M\nh_1 w_1\n\\vdots\nh_M w_M\nTask Output: Print the answer.\nTask Samples: input: 2 3 3\n2 2\n1 1\n1 3 output: 3\n\nWe can destroy all the targets by placing the bomb at <=ft(1,2\\right).\ninput: 3 3 4\n3 3\n3 1\n1 1\n1 2 output: 3\ninput: 5 5 10\n2 5\n4 3\n2 3\n5 5\n2 2\n5 4\n5 3\n5 1\n3 5\n1 4 output: 6\n\n" }, { "title": "", "content": "Problem Statement We have 3N cards arranged in a row from left to right, where each card has an integer between 1 and N (inclusive) written on it. The integer written on the i-th card from the left is A_i.\nYou will do the following operation N-1 times:\n\nRearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain 1 point.\n\nAfter these N-1 operations, if the integers written on the remaining three cards are all equal, you will gain 1 additional point.\nFind the maximum number of points you can gain.", "constraint": "1 <= N <= 2000\n1 <= A_i <= N", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_{3N}", "output": "Print the maximum number of points you can gain.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2 1 2 2 1 output: 2\n\nLet us rearrange the five leftmost cards so that the integers written on the six cards will be 2\\ 2\\ 2\\ 1\\ 1\\ 1 from left to right.\nThen, remove the three leftmost cards, all of which have the same integer 2, gaining 1 point.\nNow, the integers written on the remaining cards are 1\\ 1\\ 1.\nSince these three cards have the same integer 1, we gain 1 more point.\nIn this way, we can gain 2 points - which is the maximum possible.", "input: 3\n1 1 2 2 3 3 3 2 1 output: 1", "input: 3\n1 1 2 2 2 3 3 3 1 output: 3"], "Pid": "p02581", "ProblemText": "Task Description: Problem Statement We have 3N cards arranged in a row from left to right, where each card has an integer between 1 and N (inclusive) written on it. The integer written on the i-th card from the left is A_i.\nYou will do the following operation N-1 times:\n\nRearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain 1 point.\n\nAfter these N-1 operations, if the integers written on the remaining three cards are all equal, you will gain 1 additional point.\nFind the maximum number of points you can gain.\nTask Constraint: 1 <= N <= 2000\n1 <= A_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_{3N}\nTask Output: Print the maximum number of points you can gain.\nTask Samples: input: 2\n1 2 1 2 2 1 output: 2\n\nLet us rearrange the five leftmost cards so that the integers written on the six cards will be 2\\ 2\\ 2\\ 1\\ 1\\ 1 from left to right.\nThen, remove the three leftmost cards, all of which have the same integer 2, gaining 1 point.\nNow, the integers written on the remaining cards are 1\\ 1\\ 1.\nSince these three cards have the same integer 1, we gain 1 more point.\nIn this way, we can gain 2 points - which is the maximum possible.\ninput: 3\n1 1 2 2 3 3 3 2 1 output: 1\ninput: 3\n1 1 2 2 2 3 3 3 1 output: 3\n\n" }, { "title": "", "content": "Problem Statement We have weather records at At Coder Town for some consecutive three days. A string of length 3, S, represents the records - if the i-th character is S, it means it was sunny on the i-th day; if that character is R, it means it was rainy on that day.\nFind the maximum number of consecutive rainy days in this period.", "constraint": "|S| = 3\nEach character of S is S or R.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the maximum number of consecutive rainy days in the period.", "content_img": false, "lang": "en", "error": false, "samples": ["input: RRS output: 2\n\nWe had rain on the 1-st and 2-nd days in the period. Here, the maximum number of consecutive rainy days is 2, so we should print 2.", "input: SSS output: 0\n\nIt was sunny throughout the period. We had no rainy days, so we should print 0.", "input: RSR output: 1\n\nWe had rain on the 1-st and 3-rd days - two \"streaks\" of one rainy day, so we should print 1."], "Pid": "p02582", "ProblemText": "Task Description: Problem Statement We have weather records at At Coder Town for some consecutive three days. A string of length 3, S, represents the records - if the i-th character is S, it means it was sunny on the i-th day; if that character is R, it means it was rainy on that day.\nFind the maximum number of consecutive rainy days in this period.\nTask Constraint: |S| = 3\nEach character of S is S or R.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the maximum number of consecutive rainy days in the period.\nTask Samples: input: RRS output: 2\n\nWe had rain on the 1-st and 2-nd days in the period. Here, the maximum number of consecutive rainy days is 2, so we should print 2.\ninput: SSS output: 0\n\nIt was sunny throughout the period. We had no rainy days, so we should print 0.\ninput: RSR output: 1\n\nWe had rain on the 1-st and 3-rd days - two \"streaks\" of one rainy day, so we should print 1.\n\n" }, { "title": "", "content": "Problem Statement We have sticks numbered 1, \\cdots, N. The length of Stick i (1 <= i <= N) is L_i.\nIn how many ways can we choose three of the sticks with different lengths that can form a triangle?\nThat is, find the number of triples of integers (i, j, k) (1 <= i < j < k <= N) that satisfy both of the following conditions:\n\nL_i, L_j, and L_k are all different.\nThere exists a triangle whose sides have lengths L_i, L_j, and L_k.", "constraint": "1 <= N <= 100\n1 <= L_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nL_1 L_2 \\cdots L_N", "output": "Print the number of ways to choose three of the sticks with different lengths that can form a triangle.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n4 4 9 7 5 output: 5\n\nThe following five triples (i, j, k) satisfy the conditions: (1,3,4), (1,4,5), (2,3,4), (2,4,5), and (3,4,5).", "input: 6\n4 5 4 3 3 5 output: 8\n\nWe have two sticks for each of the lengths 3,4, and 5. To satisfy the first condition, we have to choose one from each length.\nThere is a triangle whose sides have lengths 3,4, and 5, so we have 2 ^ 3 = 8 triples (i, j, k) that satisfy the conditions.", "input: 10\n9 4 6 1 9 6 10 6 6 8 output: 39", "input: 2\n1 1 output: 0\n\nNo triple (i, j, k) satisfies 1 <= i < j < k <= N, so we should print 0."], "Pid": "p02583", "ProblemText": "Task Description: Problem Statement We have sticks numbered 1, \\cdots, N. The length of Stick i (1 <= i <= N) is L_i.\nIn how many ways can we choose three of the sticks with different lengths that can form a triangle?\nThat is, find the number of triples of integers (i, j, k) (1 <= i < j < k <= N) that satisfy both of the following conditions:\n\nL_i, L_j, and L_k are all different.\nThere exists a triangle whose sides have lengths L_i, L_j, and L_k.\nTask Constraint: 1 <= N <= 100\n1 <= L_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nL_1 L_2 \\cdots L_N\nTask Output: Print the number of ways to choose three of the sticks with different lengths that can form a triangle.\nTask Samples: input: 5\n4 4 9 7 5 output: 5\n\nThe following five triples (i, j, k) satisfy the conditions: (1,3,4), (1,4,5), (2,3,4), (2,4,5), and (3,4,5).\ninput: 6\n4 5 4 3 3 5 output: 8\n\nWe have two sticks for each of the lengths 3,4, and 5. To satisfy the first condition, we have to choose one from each length.\nThere is a triangle whose sides have lengths 3,4, and 5, so we have 2 ^ 3 = 8 triples (i, j, k) that satisfy the conditions.\ninput: 10\n9 4 6 1 9 6 10 6 6 8 output: 39\ninput: 2\n1 1 output: 0\n\nNo triple (i, j, k) satisfies 1 <= i < j < k <= N, so we should print 0.\n\n" }, { "title": "", "content": "Problem Statement Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.\nMore specifically, in one move, he can go from coordinate x to x + D or x - D.\nHe wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.\nFind the minimum possible absolute value of the coordinate of the destination.", "constraint": "-10^{15} <= X <= 10^{15}\n1 <= K <= 10^{15}\n1 <= D <= 10^{15}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX K D", "output": "Print the minimum possible absolute value of the coordinate of the destination.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 2 4 output: 2\n\nTakahashi is now at coordinate 6. It is optimal to make the following moves:\n\nMove from coordinate 6 to (6 - 4 =) 2.\nMove from coordinate 2 to (2 - 4 =) -2.\n\nHere, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.", "input: 7 4 3 output: 1\n\nTakahashi is now at coordinate 7. It is optimal to make, for example, the following moves:\n\nMove from coordinate 7 to 4.\nMove from coordinate 4 to 7.\nMove from coordinate 7 to 4.\nMove from coordinate 4 to 1.\n\nHere, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.", "input: 10 1 2 output: 8", "input: 1000000000000000 1000000000000000 1000000000000000 output: 1000000000000000\n\nThe answer can be enormous."], "Pid": "p02584", "ProblemText": "Task Description: Problem Statement Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.\nMore specifically, in one move, he can go from coordinate x to x + D or x - D.\nHe wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.\nFind the minimum possible absolute value of the coordinate of the destination.\nTask Constraint: -10^{15} <= X <= 10^{15}\n1 <= K <= 10^{15}\n1 <= D <= 10^{15}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX K D\nTask Output: Print the minimum possible absolute value of the coordinate of the destination.\nTask Samples: input: 6 2 4 output: 2\n\nTakahashi is now at coordinate 6. It is optimal to make the following moves:\n\nMove from coordinate 6 to (6 - 4 =) 2.\nMove from coordinate 2 to (2 - 4 =) -2.\n\nHere, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.\ninput: 7 4 3 output: 1\n\nTakahashi is now at coordinate 7. It is optimal to make, for example, the following moves:\n\nMove from coordinate 7 to 4.\nMove from coordinate 4 to 7.\nMove from coordinate 7 to 4.\nMove from coordinate 4 to 1.\n\nHere, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.\ninput: 10 1 2 output: 8\ninput: 1000000000000000 1000000000000000 1000000000000000 output: 1000000000000000\n\nThe answer can be enormous.\n\n" }, { "title": "", "content": "Problem Statement Takahashi will play a game using a piece on an array of squares numbered 1,2, \\cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1,2, \\cdots, N: P_1, P_2, \\cdots, P_N.\nNow, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):\n\nIn one move, if the piece is now on Square i (1 <= i <= N), move it to Square P_i. Here, his score increases by C_{P_i}.\n\nHelp him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game. )", "constraint": "2 <= N <= 5000\n1 <= K <= 10^9\n1 <= P_i <= N\nP_i \\neq i\nP_1, P_2, \\cdots, P_N are all different.\n-10^9 <= C_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nP_1 P_2 \\cdots P_N\nC_1 C_2 \\cdots C_N", "output": "Print the maximum possible score at the end of the game.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n2 4 5 1 3\n3 4 -10 -8 8 output: 8\n\nWhen we start at some square of our choice and make at most two moves, we have the following options:\n\nIf we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.\nIf we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.\nIf we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.\nIf we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.\nIf we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.\n\nThe maximum score achieved is 8.", "input: 2 3\n2 1\n10 -7 output: 13", "input: 3 3\n3 1 2\n-1000 -2000 -3000 output: -1000\n\nWe have to make at least one move.", "input: 10 58\n9 1 6 7 8 4 3 2 10 5\n695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719 output: 29507023469\n\nThe absolute value of the answer may be enormous."], "Pid": "p02585", "ProblemText": "Task Description: Problem Statement Takahashi will play a game using a piece on an array of squares numbered 1,2, \\cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1,2, \\cdots, N: P_1, P_2, \\cdots, P_N.\nNow, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):\n\nIn one move, if the piece is now on Square i (1 <= i <= N), move it to Square P_i. Here, his score increases by C_{P_i}.\n\nHelp him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game. )\nTask Constraint: 2 <= N <= 5000\n1 <= K <= 10^9\n1 <= P_i <= N\nP_i \\neq i\nP_1, P_2, \\cdots, P_N are all different.\n-10^9 <= C_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nP_1 P_2 \\cdots P_N\nC_1 C_2 \\cdots C_N\nTask Output: Print the maximum possible score at the end of the game.\nTask Samples: input: 5 2\n2 4 5 1 3\n3 4 -10 -8 8 output: 8\n\nWhen we start at some square of our choice and make at most two moves, we have the following options:\n\nIf we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.\nIf we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.\nIf we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.\nIf we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.\nIf we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.\n\nThe maximum score achieved is 8.\ninput: 2 3\n2 1\n10 -7 output: 13\ninput: 3 3\n3 1 2\n-1000 -2000 -3000 output: -1000\n\nWe have to make at least one move.\ninput: 10 58\n9 1 6 7 8 4 3 2 10 5\n695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719 output: 29507023469\n\nThe absolute value of the answer may be enormous.\n\n" }, { "title": "", "content": "Problem Statement There are K items placed on a grid of squares with R rows and C columns. Let (i, j) denote the square at the i-th row (1 <= i <= R) and the j-th column (1 <= j <= C). The i-th item is at (r_i, c_i) and has the value v_i.\nTakahashi will begin at (1,1), the start, and get to (R, C), the goal. When he is at (i, j), he can move to (i + 1, j) or (i, j + 1) (but cannot move to a non-existent square).\nHe can pick up items on the squares he visits, including the start and the goal, but at most three for each row. It is allowed to ignore the item on a square he visits.\nFind the maximum possible sum of the values of items he picks up.", "constraint": "1 <= R, C <= 3000\n1 <= K <= \\min(2 * 10^5, R * C)\n1 <= r_i <= R\n1 <= c_i <= C\n(r_i, c_i) \\neq (r_j, c_j) (i \\neq j)\n1 <= v_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nR C K\nr_1 c_1 v_1\nr_2 c_2 v_2\n:\nr_K c_K v_K", "output": "Print the maximum possible sum of the values of items Takahashi picks up.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 3\n1 1 3\n2 1 4\n1 2 5 output: 8\n\nHe has two ways to get to the goal:\n\nVisit (1,1), (1,2), and (2,2), in this order. In this case, the total value of the items he can pick up is 3 + 5 = 8.\nVisit (1,1), (2,1), and (2,2), in this order. In this case, the total value of the items he can pick up is 3 + 4 = 7.\n\nThus, the maximum possible sum of the values of items he picks up is 8.", "input: 2 5 5\n1 1 3\n2 4 20\n1 2 1\n1 3 4\n1 4 2 output: 29\n\nWe have four items in the 1-st row. The optimal choices are as follows:\n\nVisit (1,1) (1,2), (1,3), (1,4), (2,4), and (2,5), in this order, and pick up all items except the one on (1,2). Then, the total value of the items he picks up will be 3 + 4 + 2 + 20 = 29.", "input: 4 5 10\n2 5 12\n1 5 12\n2 3 15\n1 2 20\n1 1 28\n2 4 26\n3 2 27\n4 5 21\n3 5 10\n1 3 10 output: 142"], "Pid": "p02586", "ProblemText": "Task Description: Problem Statement There are K items placed on a grid of squares with R rows and C columns. Let (i, j) denote the square at the i-th row (1 <= i <= R) and the j-th column (1 <= j <= C). The i-th item is at (r_i, c_i) and has the value v_i.\nTakahashi will begin at (1,1), the start, and get to (R, C), the goal. When he is at (i, j), he can move to (i + 1, j) or (i, j + 1) (but cannot move to a non-existent square).\nHe can pick up items on the squares he visits, including the start and the goal, but at most three for each row. It is allowed to ignore the item on a square he visits.\nFind the maximum possible sum of the values of items he picks up.\nTask Constraint: 1 <= R, C <= 3000\n1 <= K <= \\min(2 * 10^5, R * C)\n1 <= r_i <= R\n1 <= c_i <= C\n(r_i, c_i) \\neq (r_j, c_j) (i \\neq j)\n1 <= v_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nR C K\nr_1 c_1 v_1\nr_2 c_2 v_2\n:\nr_K c_K v_K\nTask Output: Print the maximum possible sum of the values of items Takahashi picks up.\nTask Samples: input: 2 2 3\n1 1 3\n2 1 4\n1 2 5 output: 8\n\nHe has two ways to get to the goal:\n\nVisit (1,1), (1,2), and (2,2), in this order. In this case, the total value of the items he can pick up is 3 + 5 = 8.\nVisit (1,1), (2,1), and (2,2), in this order. In this case, the total value of the items he can pick up is 3 + 4 = 7.\n\nThus, the maximum possible sum of the values of items he picks up is 8.\ninput: 2 5 5\n1 1 3\n2 4 20\n1 2 1\n1 3 4\n1 4 2 output: 29\n\nWe have four items in the 1-st row. The optimal choices are as follows:\n\nVisit (1,1) (1,2), (1,3), (1,4), (2,4), and (2,5), in this order, and pick up all items except the one on (1,2). Then, the total value of the items he picks up will be 3 + 4 + 2 + 20 = 29.\ninput: 4 5 10\n2 5 12\n1 5 12\n2 3 15\n1 2 20\n1 1 28\n2 4 26\n3 2 27\n4 5 21\n3 5 10\n1 3 10 output: 142\n\n" }, { "title": "", "content": "Problem Statement We have N strings of lowercase English letters: S_1, S_2, \\cdots, S_N.\nTakahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice.\nThe cost of using the string S_i once is C_i, and the cost of using it multiple times is C_i multiplied by that number of times.\nFind the minimum total cost needed to choose strings so that Takahashi can make a palindrome.\nIf there is no choice of strings in which he can make a palindrome, print -1.", "constraint": "1 <= N <= 50\n1 <= |S_i| <= 20\nS_i consists of lowercase English letters.\n1 <= C_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nS_1 C_1\nS_2 C_2\n:\nS_N C_N", "output": "Print the minimum total cost needed to choose strings so that Takahashi can make a palindrome, or -1 if there is no such choice.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nba 3\nabc 4\ncbaa 5 output: 7\n\nWe have ba, abc, and cbaa.\nFor example, we can use ba once and abc once for a cost of 7, then concatenate them in the order abc, ba to make a palindrome.\nAlso, we can use abc once and cbaa once for a cost of 9, then concatenate them in the order cbaa, abc to make a palindrome.\nWe cannot make a palindrome for a cost less than 7, so we should print 7.", "input: 2\nabcab 5\ncba 3 output: 11\n\nWe can choose abcab once and cba twice, then concatenate them in the order abcab, cba, cba to make a palindrome for a cost of 11.", "input: 4\nab 5\ncba 3\na 12\nab 10 output: 8\n\nWe can choose a once, which is already a palindrome, but it is cheaper to concatenate ab and cba.", "input: 2\nabc 1\nab 2 output: -1\n\nWe cannot make a palindrome, so we should print -1."], "Pid": "p02587", "ProblemText": "Task Description: Problem Statement We have N strings of lowercase English letters: S_1, S_2, \\cdots, S_N.\nTakahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice.\nThe cost of using the string S_i once is C_i, and the cost of using it multiple times is C_i multiplied by that number of times.\nFind the minimum total cost needed to choose strings so that Takahashi can make a palindrome.\nIf there is no choice of strings in which he can make a palindrome, print -1.\nTask Constraint: 1 <= N <= 50\n1 <= |S_i| <= 20\nS_i consists of lowercase English letters.\n1 <= C_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1 C_1\nS_2 C_2\n:\nS_N C_N\nTask Output: Print the minimum total cost needed to choose strings so that Takahashi can make a palindrome, or -1 if there is no such choice.\nTask Samples: input: 3\nba 3\nabc 4\ncbaa 5 output: 7\n\nWe have ba, abc, and cbaa.\nFor example, we can use ba once and abc once for a cost of 7, then concatenate them in the order abc, ba to make a palindrome.\nAlso, we can use abc once and cbaa once for a cost of 9, then concatenate them in the order cbaa, abc to make a palindrome.\nWe cannot make a palindrome for a cost less than 7, so we should print 7.\ninput: 2\nabcab 5\ncba 3 output: 11\n\nWe can choose abcab once and cba twice, then concatenate them in the order abcab, cba, cba to make a palindrome for a cost of 11.\ninput: 4\nab 5\ncba 3\na 12\nab 10 output: 8\n\nWe can choose a once, which is already a palindrome, but it is cheaper to concatenate ab and cba.\ninput: 2\nabc 1\nab 2 output: -1\n\nWe cannot make a palindrome, so we should print -1.\n\n" }, { "title": "", "content": "Problem Statement You are given N real values A_1, A_2, \\ldots, A_N.\nCompute the number of pairs of indices (i, j)\n such that i < j and the product A_i \\cdot A_j is integer.", "constraint": "2 <= N <= 200\\,000\n0 < A_i < 10^4\nA_i is given with at most 9 digits after the decimal.", "input": "Input is given from Standard Input in the following format.\nN\nA_1\nA_2\n\\vdots\nA_N", "output": "Print the number of pairs with integer product A_i \\cdot A_j (and i < j).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n7.5\n2.4\n17.000000001\n17\n16.000000000 output: 3\n\nThere are 3 pairs with integer product:\n\n7.5 \\cdot 2.4 = 18\n7.5 \\cdot 16 = 120\n17 \\cdot 16 = 272", "input: 11\n0.9\n1\n1\n1.25\n2.30000\n5\n70\n0.000000001\n9999.999999999\n0.999999999\n1.000000001 output: 8"], "Pid": "p02588", "ProblemText": "Task Description: Problem Statement You are given N real values A_1, A_2, \\ldots, A_N.\nCompute the number of pairs of indices (i, j)\n such that i < j and the product A_i \\cdot A_j is integer.\nTask Constraint: 2 <= N <= 200\\,000\n0 < A_i < 10^4\nA_i is given with at most 9 digits after the decimal.\nTask Input: Input is given from Standard Input in the following format.\nN\nA_1\nA_2\n\\vdots\nA_N\nTask Output: Print the number of pairs with integer product A_i \\cdot A_j (and i < j).\nTask Samples: input: 5\n7.5\n2.4\n17.000000001\n17\n16.000000000 output: 3\n\nThere are 3 pairs with integer product:\n\n7.5 \\cdot 2.4 = 18\n7.5 \\cdot 16 = 120\n17 \\cdot 16 = 272\ninput: 11\n0.9\n1\n1\n1.25\n2.30000\n5\n70\n0.000000001\n9999.999999999\n0.999999999\n1.000000001 output: 8\n\n" }, { "title": "", "content": "Problem Statement Limak can repeatedly remove one of the first two characters of a string,\n for example abcxyx \\rightarrow acxyx \\rightarrow cxyx \\rightarrow cyx.\nYou are given N different strings S_1, S_2, \\ldots, S_N.\nAmong N \\cdot (N-1) / 2 pairs (S_i, S_j),\n in how many pairs could Limak obtain one string from the other?", "constraint": "2 <= N <= 200\\,000\nS_i consists of lowercase English letters a-z.\nS_i \\neq S_j\n1 <= |S_i|\n|S_1| + |S_2| + \\ldots + |S_N| <= 10^6", "input": "Input is given from Standard Input in the following format.\nN\nS_1\nS_2\n\\vdots\nS_N", "output": "Print the number of unordered pairs (S_i, S_j)\n where i \\neq j and Limak can obtain one string from the other.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nabcxyx\ncyx\nabc output: 1\n\nThe only good pair is (abcxyx, cyx).", "input: 6\nb\na\nabc\nc\nd\nab output: 5\n\nThere are five good pairs: (b, abc), (a, abc), (abc, c), (b, ab), (a, ab)."], "Pid": "p02589", "ProblemText": "Task Description: Problem Statement Limak can repeatedly remove one of the first two characters of a string,\n for example abcxyx \\rightarrow acxyx \\rightarrow cxyx \\rightarrow cyx.\nYou are given N different strings S_1, S_2, \\ldots, S_N.\nAmong N \\cdot (N-1) / 2 pairs (S_i, S_j),\n in how many pairs could Limak obtain one string from the other?\nTask Constraint: 2 <= N <= 200\\,000\nS_i consists of lowercase English letters a-z.\nS_i \\neq S_j\n1 <= |S_i|\n|S_1| + |S_2| + \\ldots + |S_N| <= 10^6\nTask Input: Input is given from Standard Input in the following format.\nN\nS_1\nS_2\n\\vdots\nS_N\nTask Output: Print the number of unordered pairs (S_i, S_j)\n where i \\neq j and Limak can obtain one string from the other.\nTask Samples: input: 3\nabcxyx\ncyx\nabc output: 1\n\nThe only good pair is (abcxyx, cyx).\ninput: 6\nb\na\nabc\nc\nd\nab output: 5\n\nThere are five good pairs: (b, abc), (a, abc), (abc, c), (b, ab), (a, ab).\n\n" }, { "title": "", "content": "Problem Statement Let 's take a prime P = 200\\, 003.\nYou are given N integers A_1, A_2, \\ldots, A_N.\nFind the sum of ((A_i \\cdot A_j) \\bmod P) over all N \\cdot (N-1) / 2 unordered pairs of elements (i < j).\nPlease note that the sum isn't computed modulo P.", "constraint": "2 <= N <= 200\\,000\n0 <= A_i < P = 200\\,003\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format.\nN\nA_1 A_2 \\cdots A_N", "output": "Print one integer — the sum over ((A_i \\cdot A_j) \\bmod P).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2019 0 2020 200002 output: 474287\n\nThe non-zero products are:\n\n2019 \\cdot 2020 \\bmod P = 78320\n2019 \\cdot 200002 \\bmod P = 197984\n2020 \\cdot 200002 \\bmod P = 197983\n\nSo the answer is 0 + 78320 + 197984 + 0 + 0 + 197983 = 474287.", "input: 5\n1 1 2 2 100000 output: 600013"], "Pid": "p02590", "ProblemText": "Task Description: Problem Statement Let 's take a prime P = 200\\, 003.\nYou are given N integers A_1, A_2, \\ldots, A_N.\nFind the sum of ((A_i \\cdot A_j) \\bmod P) over all N \\cdot (N-1) / 2 unordered pairs of elements (i < j).\nPlease note that the sum isn't computed modulo P.\nTask Constraint: 2 <= N <= 200\\,000\n0 <= A_i < P = 200\\,003\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format.\nN\nA_1 A_2 \\cdots A_N\nTask Output: Print one integer — the sum over ((A_i \\cdot A_j) \\bmod P).\nTask Samples: input: 4\n2019 0 2020 200002 output: 474287\n\nThe non-zero products are:\n\n2019 \\cdot 2020 \\bmod P = 78320\n2019 \\cdot 200002 \\bmod P = 197984\n2020 \\cdot 200002 \\bmod P = 197983\n\nSo the answer is 0 + 78320 + 197984 + 0 + 0 + 197983 = 474287.\ninput: 5\n1 1 2 2 100000 output: 600013\n\n" }, { "title": "", "content": "Problem Statement Inspired by the tv series Stranger Things, bear Limak is going for a walk between two mirror worlds.\nThere are two perfect binary trees of height H,\n each with the standard numeration of vertices from 1 to 2^H-1.\nThe root is 1 and the children of x are 2 \\cdot x and 2 \\cdot x + 1.\nLet L denote the number of leaves in a single tree, L = 2^{H-1}.\nYou are given a permutation P_1, P_2, \\ldots, P_L of numbers 1 through L.\nIt describes L special edges that connect leaves of the two trees.\nThere is a special edge between vertex L+i-1 in the first tree and vertex L+P_i-1 in the second tree.\n\ndrawing for the first sample test, permutation P = (2,3,1,4), special edges in green\nLet's define product of a cycle as the product of numbers in its vertices.\nCompute the sum of products of all simple cycles that have exactly two special edges, modulo (10^9+7).\nA simple cycle is a cycle of length at least 3, without repeated vertices or edges.", "constraint": "2 <= H <= 18\n1 <= P_i <= L where L = 2^{H-1}\nP_i \\neq P_j (so this is a permutation)", "input": "Input is given from Standard Input in the following format (where L = 2^{H-1}).\nH\nP_1 P_2 \\cdots P_L", "output": "Output Compute the sum of products of simple cycles that have exactly two special edges.\nPrint the answer modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3 1 4 output: 121788\n\nThe following drawings show two valid cycles (but there are more!) with products\n 2 \\cdot 5 \\cdot 6 \\cdot 3 \\cdot 1 \\cdot 2 \\cdot 5 \\cdot 4 = 7200\n and 1 \\cdot 3 \\cdot 7 \\cdot 7 \\cdot 3 \\cdot 1 \\cdot 2 \\cdot 5 \\cdot 4 \\cdot 2 = 35280.\nThe third cycle is invalid because it doesn't have exactly two special edges.", "input: 2\n1 2 output: 36\n\nThe only simple cycle in the graph indeed has two special edges, and the product of vertices is\n 1 \\cdot 3 \\cdot 3 \\cdot 1 \\cdot 2 \\cdot 2 = 36.", "input: 5\n6 14 15 7 12 16 5 4 11 9 3 10 8 2 13 1 output: 10199246"], "Pid": "p02591", "ProblemText": "Task Description: Problem Statement Inspired by the tv series Stranger Things, bear Limak is going for a walk between two mirror worlds.\nThere are two perfect binary trees of height H,\n each with the standard numeration of vertices from 1 to 2^H-1.\nThe root is 1 and the children of x are 2 \\cdot x and 2 \\cdot x + 1.\nLet L denote the number of leaves in a single tree, L = 2^{H-1}.\nYou are given a permutation P_1, P_2, \\ldots, P_L of numbers 1 through L.\nIt describes L special edges that connect leaves of the two trees.\nThere is a special edge between vertex L+i-1 in the first tree and vertex L+P_i-1 in the second tree.\n\ndrawing for the first sample test, permutation P = (2,3,1,4), special edges in green\nLet's define product of a cycle as the product of numbers in its vertices.\nCompute the sum of products of all simple cycles that have exactly two special edges, modulo (10^9+7).\nA simple cycle is a cycle of length at least 3, without repeated vertices or edges.\nTask Constraint: 2 <= H <= 18\n1 <= P_i <= L where L = 2^{H-1}\nP_i \\neq P_j (so this is a permutation)\nTask Input: Input is given from Standard Input in the following format (where L = 2^{H-1}).\nH\nP_1 P_2 \\cdots P_L\nTask Output: Output Compute the sum of products of simple cycles that have exactly two special edges.\nPrint the answer modulo (10^9+7).\nTask Samples: input: 3\n2 3 1 4 output: 121788\n\nThe following drawings show two valid cycles (but there are more!) with products\n 2 \\cdot 5 \\cdot 6 \\cdot 3 \\cdot 1 \\cdot 2 \\cdot 5 \\cdot 4 = 7200\n and 1 \\cdot 3 \\cdot 7 \\cdot 7 \\cdot 3 \\cdot 1 \\cdot 2 \\cdot 5 \\cdot 4 \\cdot 2 = 35280.\nThe third cycle is invalid because it doesn't have exactly two special edges.\ninput: 2\n1 2 output: 36\n\nThe only simple cycle in the graph indeed has two special edges, and the product of vertices is\n 1 \\cdot 3 \\cdot 3 \\cdot 1 \\cdot 2 \\cdot 2 = 36.\ninput: 5\n6 14 15 7 12 16 5 4 11 9 3 10 8 2 13 1 output: 10199246\n\n" }, { "title": "", "content": "Problem Statement This is an output-only problem. You shouldn't read anything from the input.\nIn short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y).\nThere is no input in this problem, you just print a sequence of operations.\nImagine that there is a big array a[0], a[1], . . . , a[N-1] of length N.\nThe first two values are initially two non-negative integers A and B (which are unknown to you),\n the other elements are zeros.\nYour goal is to get the product A \\cdot B in a[2] at the end.\nYou are allowed operations of two types, with the following format (where 0 <= i, j, k < N):\n\n+ i j k — applies operation a[k] = a[i] + a[j].\n< i j k — applies operation a[k] = a[i] < a[j].\n That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0.\n\nYou can use at most Q operations.\nElements of a can't exceed V.\nIndices (i, j, k) don't have to be distinct.\nIt's allowed to modify any element of the array (including the first two).\nThe actual checker simulates the process for multiple pairs (A, B) within a single test.\nEach time, the checker chooses values A and B, creates the array a = [A, B, 0,0, \\ldots, 0],\n applies all your operations and ensures that a[2] = A \\cdot B. partial score: Partial Score\n800 points will be awarded for passing tests that satisfy A, B <= 10.\nAnother 1000 points will be awarded for passing all tests.", "constraint": "0 <= A, B <= 10^9\nN = Q = 200\\,000\nV = 10^{19} = 10\\,000\\,000\\,000\\,000\\,000\\,000", "input": "Input The Standard Input is empty.", "output": "In the first line, print the number of operations.\nEach operation should then be printed in a single line of format + i j k or < i j k.", "content_img": false, "lang": "en", "error": false, "samples": ["input: output: 4\n< 0 1 8\n+ 0 1 2\n+ 2 8 2\n+ 0 0 0\nIn the first sample test, the checker checks your sequence only for a pair (A, B) = (2,3).\nThe provided output is correct for this test:\n\nInitially, a[0] = 2, a[1] = 3, a[2] = a[3] = \\ldots = a[N-1] = 0.\n< 0 1 8 applies a[8] = 1 because a[0] < a[1].\n+ 0 1 2 applies a[2] = a[0] + a[1] = 5.\n+ 2 8 2 applies a[2] = a[2] + a[8] = 6.\n+ 0 0 0 applies a[0] = a[0] + a[0] = 4.\nAs required, at the end we have a[2] = 6 = A \\cdot B."], "Pid": "p02592", "ProblemText": "Task Description: Problem Statement This is an output-only problem. You shouldn't read anything from the input.\nIn short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y).\nThere is no input in this problem, you just print a sequence of operations.\nImagine that there is a big array a[0], a[1], . . . , a[N-1] of length N.\nThe first two values are initially two non-negative integers A and B (which are unknown to you),\n the other elements are zeros.\nYour goal is to get the product A \\cdot B in a[2] at the end.\nYou are allowed operations of two types, with the following format (where 0 <= i, j, k < N):\n\n+ i j k — applies operation a[k] = a[i] + a[j].\n< i j k — applies operation a[k] = a[i] < a[j].\n That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0.\n\nYou can use at most Q operations.\nElements of a can't exceed V.\nIndices (i, j, k) don't have to be distinct.\nIt's allowed to modify any element of the array (including the first two).\nThe actual checker simulates the process for multiple pairs (A, B) within a single test.\nEach time, the checker chooses values A and B, creates the array a = [A, B, 0,0, \\ldots, 0],\n applies all your operations and ensures that a[2] = A \\cdot B. partial score: Partial Score\n800 points will be awarded for passing tests that satisfy A, B <= 10.\nAnother 1000 points will be awarded for passing all tests.\nTask Constraint: 0 <= A, B <= 10^9\nN = Q = 200\\,000\nV = 10^{19} = 10\\,000\\,000\\,000\\,000\\,000\\,000\nTask Input: Input The Standard Input is empty.\nTask Output: In the first line, print the number of operations.\nEach operation should then be printed in a single line of format + i j k or < i j k.\nTask Samples: input: output: 4\n< 0 1 8\n+ 0 1 2\n+ 2 8 2\n+ 0 0 0\nIn the first sample test, the checker checks your sequence only for a pair (A, B) = (2,3).\nThe provided output is correct for this test:\n\nInitially, a[0] = 2, a[1] = 3, a[2] = a[3] = \\ldots = a[N-1] = 0.\n< 0 1 8 applies a[8] = 1 because a[0] < a[1].\n+ 0 1 2 applies a[2] = a[0] + a[1] = 5.\n+ 2 8 2 applies a[2] = a[2] + a[8] = 6.\n+ 0 0 0 applies a[0] = a[0] + a[0] = 4.\nAs required, at the end we have a[2] = 6 = A \\cdot B.\n\n" }, { "title": "", "content": "Problem Statement You are given positions (X_i, Y_i) of N enemy rooks on an infinite chessboard.\nNo two rooks attack each other (at most one rook per row or column).\nYou're going to replace one rook with a king and then move the king repeatedly to beat as many rooks as possible.\nYou can't enter a cell that is being attacked by a rook.\nAdditionally, you can't move diagonally to an empty cell (but you can beat a rook diagonally).\n(So this king moves like a superpawn that beats diagonally in 4 directions and moves horizontally/vertically in 4 directions. )\nFor each rook, consider replacing it with a king, and find the minimum possible number of moves\n needed to beat the maximum possible number of rooks.", "constraint": "2 <= N <= 200\\,000\n1 <= X_i, Y_i <= 10^6\nX_i \\neq X_j\nY_i \\neq Y_j\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format.\nN\nX_1 Y_1\nX_2 Y_2\n\\vdots\nX_N Y_N", "output": "Print N lines.\nThe i-th line is for scenario of replacing the rook at (X_i, Y_i) with your king.\nThis line should contain one integer: the minimum number of moves to beat M_i rooks\n where M_i denotes the maximum possible number of beaten rooks in this scenario (in infinite time).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 8\n6 10\n2 7\n4 4\n9 3\n5 1 output: 5\n0\n7\n5\n0\n0\n\nSee the drawing below.\nIf we replace rook 3 with a king, we can beat at most two other rooks.\nThe red path is one of optimal sequences of moves: beat rook 1,\n then keep going down and right until you can beat rook 4.\nThere are 7 steps and that's the third number in the output.\n\nx-coordinate increases from left to right,\n while y increases bottom to top.\nStarting from rook 2,5 or 6, we can't beat any other rook.\nThe optimal number of moves is 0.", "input: 5\n5 5\n100 100\n70 20\n81 70\n800 1 output: 985\n985\n1065\n1034\n0", "input: 10\n2 5\n4 4\n13 12\n12 13\n14 17\n17 19\n22 22\n16 18\n19 27\n25 26 output: 2\n2\n9\n9\n3\n3\n24\n5\n0\n25"], "Pid": "p02593", "ProblemText": "Task Description: Problem Statement You are given positions (X_i, Y_i) of N enemy rooks on an infinite chessboard.\nNo two rooks attack each other (at most one rook per row or column).\nYou're going to replace one rook with a king and then move the king repeatedly to beat as many rooks as possible.\nYou can't enter a cell that is being attacked by a rook.\nAdditionally, you can't move diagonally to an empty cell (but you can beat a rook diagonally).\n(So this king moves like a superpawn that beats diagonally in 4 directions and moves horizontally/vertically in 4 directions. )\nFor each rook, consider replacing it with a king, and find the minimum possible number of moves\n needed to beat the maximum possible number of rooks.\nTask Constraint: 2 <= N <= 200\\,000\n1 <= X_i, Y_i <= 10^6\nX_i \\neq X_j\nY_i \\neq Y_j\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format.\nN\nX_1 Y_1\nX_2 Y_2\n\\vdots\nX_N Y_N\nTask Output: Print N lines.\nThe i-th line is for scenario of replacing the rook at (X_i, Y_i) with your king.\nThis line should contain one integer: the minimum number of moves to beat M_i rooks\n where M_i denotes the maximum possible number of beaten rooks in this scenario (in infinite time).\nTask Samples: input: 6\n1 8\n6 10\n2 7\n4 4\n9 3\n5 1 output: 5\n0\n7\n5\n0\n0\n\nSee the drawing below.\nIf we replace rook 3 with a king, we can beat at most two other rooks.\nThe red path is one of optimal sequences of moves: beat rook 1,\n then keep going down and right until you can beat rook 4.\nThere are 7 steps and that's the third number in the output.\n\nx-coordinate increases from left to right,\n while y increases bottom to top.\nStarting from rook 2,5 or 6, we can't beat any other rook.\nThe optimal number of moves is 0.\ninput: 5\n5 5\n100 100\n70 20\n81 70\n800 1 output: 985\n985\n1065\n1034\n0\ninput: 10\n2 5\n4 4\n13 12\n12 13\n14 17\n17 19\n22 22\n16 18\n19 27\n25 26 output: 2\n2\n9\n9\n3\n3\n24\n5\n0\n25\n\n" }, { "title": "", "content": "Problem Statement You will turn on the air conditioner if, and only if, the temperature of the room is 30 degrees Celsius or above.\nThe current temperature of the room is X degrees Celsius. Will you turn on the air conditioner?", "constraint": "-40 <= X <= 40\nX is an integer.", "input": "Input is given from Standard Input in the following format:\nX", "output": "Print Yes if you will turn on the air conditioner; print No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 25 output: No", "input: 30 output: Yes"], "Pid": "p02594", "ProblemText": "Task Description: Problem Statement You will turn on the air conditioner if, and only if, the temperature of the room is 30 degrees Celsius or above.\nThe current temperature of the room is X degrees Celsius. Will you turn on the air conditioner?\nTask Constraint: -40 <= X <= 40\nX is an integer.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: Print Yes if you will turn on the air conditioner; print No otherwise.\nTask Samples: input: 25 output: No\ninput: 30 output: Yes\n\n" }, { "title": "", "content": "Problem Statement We have N points in the two-dimensional plane. The coordinates of the i-th point are (X_i, Y_i).\nAmong them, we are looking for the points such that the distance from the origin is at most D. How many such points are there?\nWe remind you that the distance between the origin and the point (p, q) can be represented as \\sqrt{p^2+q^2}.", "constraint": "1 <= N <= 2* 10^5\n0 <= D <= 2* 10^5\n|X_i|,|Y_i| <= 2* 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN D\nX_1 Y_1\n\\vdots\nX_N Y_N", "output": "Print an integer representing the number of points such that the distance from the origin is at most D.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n0 5\n-2 4\n3 4\n4 -4 output: 3\n\nThe distance between the origin and each of the given points is as follows:\n\n\\sqrt{0^2+5^2}=5\n\\sqrt{(-2)^2+4^2}=4.472\\ldots\n\\sqrt{3^2+4^2}=5\n\\sqrt{4^2+(-4)^2}=5.656\\ldots\n\nThus, we have three points such that the distance from the origin is at most 5.", "input: 12 3\n1 1\n1 1\n1 1\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3 output: 7\n\nMultiple points may exist at the same coordinates.", "input: 20 100000\n14309 -32939\n-56855 100340\n151364 25430\n103789 -113141\n147404 -136977\n-37006 -30929\n188810 -49557\n13419 70401\n-88280 165170\n-196399 137941\n-176527 -61904\n46659 115261\n-153551 114185\n98784 -6820\n94111 -86268\n-30401 61477\n-55056 7872\n5901 -163796\n138819 -185986\n-69848 -96669 output: 6"], "Pid": "p02595", "ProblemText": "Task Description: Problem Statement We have N points in the two-dimensional plane. The coordinates of the i-th point are (X_i, Y_i).\nAmong them, we are looking for the points such that the distance from the origin is at most D. How many such points are there?\nWe remind you that the distance between the origin and the point (p, q) can be represented as \\sqrt{p^2+q^2}.\nTask Constraint: 1 <= N <= 2* 10^5\n0 <= D <= 2* 10^5\n|X_i|,|Y_i| <= 2* 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN D\nX_1 Y_1\n\\vdots\nX_N Y_N\nTask Output: Print an integer representing the number of points such that the distance from the origin is at most D.\nTask Samples: input: 4 5\n0 5\n-2 4\n3 4\n4 -4 output: 3\n\nThe distance between the origin and each of the given points is as follows:\n\n\\sqrt{0^2+5^2}=5\n\\sqrt{(-2)^2+4^2}=4.472\\ldots\n\\sqrt{3^2+4^2}=5\n\\sqrt{4^2+(-4)^2}=5.656\\ldots\n\nThus, we have three points such that the distance from the origin is at most 5.\ninput: 12 3\n1 1\n1 1\n1 1\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3 output: 7\n\nMultiple points may exist at the same coordinates.\ninput: 20 100000\n14309 -32939\n-56855 100340\n151364 25430\n103789 -113141\n147404 -136977\n-37006 -30929\n188810 -49557\n13419 70401\n-88280 165170\n-196399 137941\n-176527 -61904\n46659 115261\n-153551 114185\n98784 -6820\n94111 -86268\n-30401 61477\n-55056 7872\n5901 -163796\n138819 -185986\n-69848 -96669 output: 6\n\n" }, { "title": "", "content": "Problem Statement Takahashi loves the number 7 and multiples of K.\nWhere is the first occurrence of a multiple of K in the sequence 7,77,777, \\ldots? (Also see Output and Sample Input/Output below. )\nIf the sequence contains no multiples of K, print -1 instead.", "constraint": "1 <= K <= 10^6\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print an integer representing the position of the first occurrence of a multiple of K. (For example, if the first occurrence is the fourth element of the sequence, print 4. )", "content_img": false, "lang": "en", "error": false, "samples": ["input: 101 output: 4\n\nNone of 7,77, and 777 is a multiple of 101, but 7777 is.", "input: 2 output: -1\n\nAll elements in the sequence are odd numbers; there are no multiples of 2.", "input: 999983 output: 999982"], "Pid": "p02596", "ProblemText": "Task Description: Problem Statement Takahashi loves the number 7 and multiples of K.\nWhere is the first occurrence of a multiple of K in the sequence 7,77,777, \\ldots? (Also see Output and Sample Input/Output below. )\nIf the sequence contains no multiples of K, print -1 instead.\nTask Constraint: 1 <= K <= 10^6\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print an integer representing the position of the first occurrence of a multiple of K. (For example, if the first occurrence is the fourth element of the sequence, print 4. )\nTask Samples: input: 101 output: 4\n\nNone of 7,77, and 777 is a multiple of 101, but 7777 is.\ninput: 2 output: -1\n\nAll elements in the sequence are odd numbers; there are no multiples of 2.\ninput: 999983 output: 999982\n\n" }, { "title": "", "content": "Problem Statement An altar enshrines N stones arranged in a row from left to right. The color of the i-th stone from the left (1 <= i <= N) is given to you as a character c_i; R stands for red and W stands for white.\nYou can do the following two kinds of operations any number of times in any order:\n\nChoose two stones (not necessarily adjacent) and swap them.\nChoose one stone and change its color (from red to white and vice versa).\n\nAccording to a fortune-teller, a white stone placed to the immediate left of a red stone will bring a disaster. At least how many operations are needed to reach a situation without such a white stone?", "constraint": "2 <= N <= 200000\nc_i is R or W.", "input": "Input is given from Standard Input in the following format:\nN\nc_{1}c_{2}. . . c_{N}", "output": "Print an integer representing the minimum number of operations needed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nWWRR output: 2\n\nFor example, the two operations below will achieve the objective.\n\nSwap the 1-st and 3-rd stones from the left, resulting in RWWR.\nChange the color of the 4-th stone from the left, resulting in RWWW.", "input: 2\nRR output: 0\n\nIt can be the case that no operation is needed.", "input: 8\nWRWWRWRR output: 3"], "Pid": "p02597", "ProblemText": "Task Description: Problem Statement An altar enshrines N stones arranged in a row from left to right. The color of the i-th stone from the left (1 <= i <= N) is given to you as a character c_i; R stands for red and W stands for white.\nYou can do the following two kinds of operations any number of times in any order:\n\nChoose two stones (not necessarily adjacent) and swap them.\nChoose one stone and change its color (from red to white and vice versa).\n\nAccording to a fortune-teller, a white stone placed to the immediate left of a red stone will bring a disaster. At least how many operations are needed to reach a situation without such a white stone?\nTask Constraint: 2 <= N <= 200000\nc_i is R or W.\nTask Input: Input is given from Standard Input in the following format:\nN\nc_{1}c_{2}. . . c_{N}\nTask Output: Print an integer representing the minimum number of operations needed.\nTask Samples: input: 4\nWWRR output: 2\n\nFor example, the two operations below will achieve the objective.\n\nSwap the 1-st and 3-rd stones from the left, resulting in RWWR.\nChange the color of the 4-th stone from the left, resulting in RWWW.\ninput: 2\nRR output: 0\n\nIt can be the case that no operation is needed.\ninput: 8\nWRWWRWRR output: 3\n\n" }, { "title": "", "content": "Problem Statement We have N logs of lengths A_1, A_2, \\cdots A_N.\nWe can cut these logs at most K times in total. When a log of length L is cut at a point whose distance from an end of the log is t (0 0:\n slightly modify the solution (randomly)\n if the solution gets worse:\n restore the solution\n\nFor example, in this problem, we can use the following modification: pick the date d and contest type q at random and change the type of contest to be held on day d to q.\nThe pseudo-code is as follows.\nt[1. . D] = compute an initial solution (by random generation, or by applying other methods such as greedy)\nwhile the remaining time > 0:\n pick d and q at random\n old = t[d] # Remember the original value so that we can restore it later\n t[d] = q\n if the solution gets worse:\n t[d] = old\n\nThe most important thing when using the local search method is the design of how to modify solutions.\n\nIf the amount of modification is too small, we will soon fall into a dead-end (local optimum) and, conversely, if the amount of modification is too large, the probability of finding an improving move becomes extremely small.\nIn order to increase the number of iterations, it is desirable to be able to quickly calculate the score after applying a modification.\n\nIn this problem C, we focus on the second point.\nThe score after the modification can, of course, be obtained by calculating the score from scratch.\nHowever, by focusing on only the parts that have been modified, it may be possible to quickly compute the difference between the scores before and after the modification.\nFrom another viewpoint, the impossibility of such a fast incremental calculation implies that a small modification to the solution affects a majority of the score calculation.\nIn such a case, we may need to redesign how to modify solutions, or there is a high possibility that the problem is not suitable for local search.\nLet's implement fast incremental score computation.\nIt's time to demonstrate the skills of algorithms and data structures you have developed in ABC and ARC!\nIn this kind of contest, where the objective is to find a better solution instead of the optimal one, a bug in a program does not result in a wrong answer, which may delay the discovery of the bug.\nFor early detection of bugs, it is a good idea to unit test functions you implemented complicated routines.\nFor example, if you implement fast incremental score calculation, it is a good idea to test that the scores computed by the fast implementation match the scores computed from scratch, as we will do in this problem C. next step: Next Step Let's go back to Problem A and implement the local search algorithm by utilizing the incremental score calculator you just implemented!\nFor this problem, the current modification \"pick the date d and contest type q at random and change the type of contest to be held on day d to q\" is actually not so good. By considering why it is not good, let's improve the modification operation.\nOne of the most powerful and widely used variant of the local search method is \"Simulated Annealing (SA)\", which makes it easier to reach a better solution by stochastically accepting worsening moves.\nFor more information about SA and other local search techniques, please refer to the editorial that will be published after the contest.", "constraint": "", "input": "Input is given from Standard Input in the form of the input of Problem A followed by the output of Problem A and the queries.\nD\nc_1 c_2 \\cdots c_{26}\ns_{1,1} s_{1,2} \\cdots s_{1,26}\n\\vdots\ns_{D, 1} s_{D, 2} \\cdots s_{D, 26}\nt_1\nt_2\n\\vdots\nt_D\nM\nd_1 q_1\nd_2 q_2\n\\vdots\nd_M q_M\nThe constraints and generation methods for the input part are the same as those for Problem A.\nFor each d=1, \\ldots, D, t_d is an integer generated independently and uniformly at random from {1,2, \\ldots, 26}.\nThe number of queries M is an integer satisfying 1<= M<= 10^5.\nFor each i=1, \\ldots, M, d_i is an integer generated independently and uniformly at random from {1,2, \\ldots, D}.\nFor each i=1, \\ldots, 26, q_i is an integer satisfying 1<= q_i<= 26 generated uniformly at random from the 25 values that differ from the type of contest on day d_i.", "output": "Let v_i be the final satisfaction at the end of day D on the schedule after applying the i-th query.\nPrint M integers v_i to Standard Output in the following format:\nv_1\nv_2\n\\vdots\nv_M", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\n6674 17707 13855 16407 12232 2886 11908 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\n1\n17\n13\n14\n13\n5\n1 7\n4 11\n3 4\n5 24\n4 19 output: 72882\n56634\n38425\n27930\n42884\n\nNote that this example is a small one for checking the problem specification. It does not satisfy the constraint D=365 and is never actually given as a test case."], "Pid": "p02620", "ProblemText": "Task Description: Problem Statement You will be given a contest schedule for D days and M queries of schedule modification.\nIn the i-th query, given integers d_i and q_i, change the type of contest to be held on day d_i to q_i, and then output the final satisfaction at the end of day D on the updated schedule.\nNote that we do not revert each query. That is, the i-th query is applied to the new schedule obtained by the (i-1)-th query. beginner's guide: Beginner's Guide\"Local search\" is a powerful method for finding a high-quality solution.\nIn this method, instead of constructing a solution from scratch, we try to find a better solution by slightly modifying the already found solution.\nIf the solution gets better, update it, and if it gets worse, restore it.\nBy repeating this process, the quality of the solution is gradually improved over time.\nThe pseudo-code is as follows.\nsolution = compute an initial solution (by random generation, or by applying other methods such as greedy)\nwhile the remaining time > 0:\n slightly modify the solution (randomly)\n if the solution gets worse:\n restore the solution\n\nFor example, in this problem, we can use the following modification: pick the date d and contest type q at random and change the type of contest to be held on day d to q.\nThe pseudo-code is as follows.\nt[1. . D] = compute an initial solution (by random generation, or by applying other methods such as greedy)\nwhile the remaining time > 0:\n pick d and q at random\n old = t[d] # Remember the original value so that we can restore it later\n t[d] = q\n if the solution gets worse:\n t[d] = old\n\nThe most important thing when using the local search method is the design of how to modify solutions.\n\nIf the amount of modification is too small, we will soon fall into a dead-end (local optimum) and, conversely, if the amount of modification is too large, the probability of finding an improving move becomes extremely small.\nIn order to increase the number of iterations, it is desirable to be able to quickly calculate the score after applying a modification.\n\nIn this problem C, we focus on the second point.\nThe score after the modification can, of course, be obtained by calculating the score from scratch.\nHowever, by focusing on only the parts that have been modified, it may be possible to quickly compute the difference between the scores before and after the modification.\nFrom another viewpoint, the impossibility of such a fast incremental calculation implies that a small modification to the solution affects a majority of the score calculation.\nIn such a case, we may need to redesign how to modify solutions, or there is a high possibility that the problem is not suitable for local search.\nLet's implement fast incremental score computation.\nIt's time to demonstrate the skills of algorithms and data structures you have developed in ABC and ARC!\nIn this kind of contest, where the objective is to find a better solution instead of the optimal one, a bug in a program does not result in a wrong answer, which may delay the discovery of the bug.\nFor early detection of bugs, it is a good idea to unit test functions you implemented complicated routines.\nFor example, if you implement fast incremental score calculation, it is a good idea to test that the scores computed by the fast implementation match the scores computed from scratch, as we will do in this problem C. next step: Next Step Let's go back to Problem A and implement the local search algorithm by utilizing the incremental score calculator you just implemented!\nFor this problem, the current modification \"pick the date d and contest type q at random and change the type of contest to be held on day d to q\" is actually not so good. By considering why it is not good, let's improve the modification operation.\nOne of the most powerful and widely used variant of the local search method is \"Simulated Annealing (SA)\", which makes it easier to reach a better solution by stochastically accepting worsening moves.\nFor more information about SA and other local search techniques, please refer to the editorial that will be published after the contest.\nTask Input: Input is given from Standard Input in the form of the input of Problem A followed by the output of Problem A and the queries.\nD\nc_1 c_2 \\cdots c_{26}\ns_{1,1} s_{1,2} \\cdots s_{1,26}\n\\vdots\ns_{D, 1} s_{D, 2} \\cdots s_{D, 26}\nt_1\nt_2\n\\vdots\nt_D\nM\nd_1 q_1\nd_2 q_2\n\\vdots\nd_M q_M\nThe constraints and generation methods for the input part are the same as those for Problem A.\nFor each d=1, \\ldots, D, t_d is an integer generated independently and uniformly at random from {1,2, \\ldots, 26}.\nThe number of queries M is an integer satisfying 1<= M<= 10^5.\nFor each i=1, \\ldots, M, d_i is an integer generated independently and uniformly at random from {1,2, \\ldots, D}.\nFor each i=1, \\ldots, 26, q_i is an integer satisfying 1<= q_i<= 26 generated uniformly at random from the 25 values that differ from the type of contest on day d_i.\nTask Output: Let v_i be the final satisfaction at the end of day D on the schedule after applying the i-th query.\nPrint M integers v_i to Standard Output in the following format:\nv_1\nv_2\n\\vdots\nv_M\nTask Samples: input: 5\n86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82\n19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424\n6674 17707 13855 16407 12232 2886 11908 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570\n6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256\n8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452\n19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192\n1\n17\n13\n14\n13\n5\n1 7\n4 11\n3 4\n5 24\n4 19 output: 72882\n56634\n38425\n27930\n42884\n\nNote that this example is a small one for checking the problem specification. It does not satisfy the constraint D=365 and is never actually given as a test case.\n\n" }, { "title": "", "content": "Problem Statement Given an integer a as input, print the value a + a^2 + a^3.", "constraint": "1 <= a <= 10\na is an integer.", "input": "Input is given from Standard Input in the following format:\na", "output": "Print the value a + a^2 + a^3 as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 14\n\nWhen a = 2, we have a + a^2 + a^3 = 2 + 2^2 + 2^3 = 2 + 4 + 8 = 14.\nPrint the answer as an input. Outputs such as 14.0 will be judged as incorrect.", "input: 10 output: 1110"], "Pid": "p02621", "ProblemText": "Task Description: Problem Statement Given an integer a as input, print the value a + a^2 + a^3.\nTask Constraint: 1 <= a <= 10\na is an integer.\nTask Input: Input is given from Standard Input in the following format:\na\nTask Output: Print the value a + a^2 + a^3 as an integer.\nTask Samples: input: 2 output: 14\n\nWhen a = 2, we have a + a^2 + a^3 = 2 + 2^2 + 2^3 = 2 + 4 + 8 = 14.\nPrint the answer as an input. Outputs such as 14.0 will be judged as incorrect.\ninput: 10 output: 1110\n\n" }, { "title": "", "content": "Problem Statement Given are strings S and T. Consider changing S to T by repeating the operation below. Find the minimum number of operations required to do so.\nOperation: Choose one character of S and replace it with a different character.", "constraint": "S and T have lengths between 1 and 2* 10^5 (inclusive).\nS and T consists of lowercase English letters.\nS and T have equal lengths.", "input": "Input is given from Standard Input in the following format:\nS\nT", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: cupofcoffee\ncupofhottea output: 4\n\nWe can achieve the objective in four operations, such as the following:\n\nFirst, replace the sixth character c with h.\nSecond, replace the eighth character f with t.\nThird, replace the ninth character f with t.\nFourth, replace the eleventh character e with a.", "input: abcde\nbcdea output: 5", "input: apple\napple output: 0\n\nNo operations may be needed to achieve the objective."], "Pid": "p02622", "ProblemText": "Task Description: Problem Statement Given are strings S and T. Consider changing S to T by repeating the operation below. Find the minimum number of operations required to do so.\nOperation: Choose one character of S and replace it with a different character.\nTask Constraint: S and T have lengths between 1 and 2* 10^5 (inclusive).\nS and T consists of lowercase English letters.\nS and T have equal lengths.\nTask Input: Input is given from Standard Input in the following format:\nS\nT\nTask Output: Print the answer.\nTask Samples: input: cupofcoffee\ncupofhottea output: 4\n\nWe can achieve the objective in four operations, such as the following:\n\nFirst, replace the sixth character c with h.\nSecond, replace the eighth character f with t.\nThird, replace the ninth character f with t.\nFourth, replace the eleventh character e with a.\ninput: abcde\nbcdea output: 5\ninput: apple\napple output: 0\n\nNo operations may be needed to achieve the objective.\n\n" }, { "title": "", "content": "Problem Statement We have two desks: A and B. Desk A has a vertical stack of N books on it, and Desk B similarly has M books on it.\nIt takes us A_i minutes to read the i-th book from the top on Desk A (1 <= i <= N), and B_i minutes to read the i-th book from the top on Desk B (1 <= i <= M).\nConsider the following action:\n\nChoose a desk with a book remaining, read the topmost book on that desk, and remove it from the desk.\n\nHow many books can we read at most by repeating this action so that it takes us at most K minutes in total? We ignore the time it takes to do anything other than reading.", "constraint": "1 <= N, M <= 200000\n1 <= K <= 10^9\n1 <= A_i, B_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M K\nA_1 A_2 \\ldots A_N\nB_1 B_2 \\ldots B_M", "output": "Print an integer representing the maximum number of books that can be read.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 240\n60 90 120\n80 150 80 150 output: 3\n\nIn this case, it takes us 60,90,120 minutes to read the 1-st, 2-nd, 3-rd books from the top on Desk A, and 80,150,80,150 minutes to read the 1-st, 2-nd, 3-rd, 4-th books from the top on Desk B, respectively.\nWe can read three books in 230 minutes, as shown below, and this is the maximum number of books we can read within 240 minutes.\n\nRead the topmost book on Desk A in 60 minutes, and remove that book from the desk.\nRead the topmost book on Desk B in 80 minutes, and remove that book from the desk.\nRead the topmost book on Desk A in 90 minutes, and remove that book from the desk.", "input: 3 4 730\n60 90 120\n80 150 80 150 output: 7", "input: 5 4 1\n1000000000 1000000000 1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000 1000000000 output: 0\n\nWatch out for integer overflows."], "Pid": "p02623", "ProblemText": "Task Description: Problem Statement We have two desks: A and B. Desk A has a vertical stack of N books on it, and Desk B similarly has M books on it.\nIt takes us A_i minutes to read the i-th book from the top on Desk A (1 <= i <= N), and B_i minutes to read the i-th book from the top on Desk B (1 <= i <= M).\nConsider the following action:\n\nChoose a desk with a book remaining, read the topmost book on that desk, and remove it from the desk.\n\nHow many books can we read at most by repeating this action so that it takes us at most K minutes in total? We ignore the time it takes to do anything other than reading.\nTask Constraint: 1 <= N, M <= 200000\n1 <= K <= 10^9\n1 <= A_i, B_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M K\nA_1 A_2 \\ldots A_N\nB_1 B_2 \\ldots B_M\nTask Output: Print an integer representing the maximum number of books that can be read.\nTask Samples: input: 3 4 240\n60 90 120\n80 150 80 150 output: 3\n\nIn this case, it takes us 60,90,120 minutes to read the 1-st, 2-nd, 3-rd books from the top on Desk A, and 80,150,80,150 minutes to read the 1-st, 2-nd, 3-rd, 4-th books from the top on Desk B, respectively.\nWe can read three books in 230 minutes, as shown below, and this is the maximum number of books we can read within 240 minutes.\n\nRead the topmost book on Desk A in 60 minutes, and remove that book from the desk.\nRead the topmost book on Desk B in 80 minutes, and remove that book from the desk.\nRead the topmost book on Desk A in 90 minutes, and remove that book from the desk.\ninput: 3 4 730\n60 90 120\n80 150 80 150 output: 7\ninput: 5 4 1\n1000000000 1000000000 1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000 1000000000 output: 0\n\nWatch out for integer overflows.\n\n" }, { "title": "", "content": "Problem Statement For a positive integer X, let f(X) be the number of positive divisors of X.\nGiven a positive integer N, find \\sum_{K=1}^N K* f(K).", "constraint": "1 <= N <= 10^7", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the value \\sum_{K=1}^N K* f(K).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 23\n\nWe have f(1)=1, f(2)=2, f(3)=2, and f(4)=3, so the answer is 1* 1 + 2* 2 + 3* 2 + 4* 3 =23.", "input: 100 output: 26879", "input: 10000000 output: 838627288460105\n\nWatch out for overflows."], "Pid": "p02624", "ProblemText": "Task Description: Problem Statement For a positive integer X, let f(X) be the number of positive divisors of X.\nGiven a positive integer N, find \\sum_{K=1}^N K* f(K).\nTask Constraint: 1 <= N <= 10^7\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the value \\sum_{K=1}^N K* f(K).\nTask Samples: input: 4 output: 23\n\nWe have f(1)=1, f(2)=2, f(3)=2, and f(4)=3, so the answer is 1* 1 + 2* 2 + 3* 2 + 4* 3 =23.\ninput: 100 output: 26879\ninput: 10000000 output: 838627288460105\n\nWatch out for overflows.\n\n" }, { "title": "", "content": "Problem Statement Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \\cdots, A_{N} and B_1, B_2, \\cdots, B_{N}, that satisfy all of the following conditions:\n\nA_i \\neq B_i, for every i such that 1<= i<= N.\nA_i \\neq A_j and B_i \\neq B_j, for every (i, j) such that 1<= i < j<= N.\n\nSince the count can be enormous, print it modulo (10^9+7).", "constraint": "1<= N <= M <= 5*10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the count modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 2\n\nA_1=1,A_2=2,B_1=2,B_2=1 and A_1=2,A_2=1,B_1=1,B_2=2 satisfy the conditions.", "input: 2 3 output: 18", "input: 141421 356237 output: 881613484"], "Pid": "p02625", "ProblemText": "Task Description: Problem Statement Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \\cdots, A_{N} and B_1, B_2, \\cdots, B_{N}, that satisfy all of the following conditions:\n\nA_i \\neq B_i, for every i such that 1<= i<= N.\nA_i \\neq A_j and B_i \\neq B_j, for every (i, j) such that 1<= i < j<= N.\n\nSince the count can be enormous, print it modulo (10^9+7).\nTask Constraint: 1<= N <= M <= 5*10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the count modulo (10^9+7).\nTask Samples: input: 2 2 output: 2\n\nA_1=1,A_2=2,B_1=2,B_2=1 and A_1=2,A_2=1,B_1=1,B_2=2 satisfy the conditions.\ninput: 2 3 output: 18\ninput: 141421 356237 output: 881613484\n\n" }, { "title": "", "content": "Problem Statement There are N piles of stones. The i-th pile has A_i stones.\nAoki and Takahashi are about to use them to play the following game:\n\nStarting with Aoki, the two players alternately do the following operation:\nOperation: Choose one pile of stones, and remove one or more stones from it.\nWhen a player is unable to do the operation, he loses, and the other player wins.\n\nWhen the two players play optimally, there are two possibilities in this game: the player who moves first always wins, or the player who moves second always wins, only depending on the initial number of stones in each pile.\nIn such a situation, Takahashi, the second player to act, is trying to guarantee his win by moving at least zero and at most (A_1 - 1) stones from the 1-st pile to the 2-nd pile before the game begins.\nIf this is possible, print the minimum number of stones to move to guarantee his victory; otherwise, print -1 instead.", "constraint": "2 <= N <= 300\n1 <= A_i <= 10^{12}", "input": "Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N", "output": "Print the minimum number of stones to move to guarantee Takahashi's win; otherwise, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n5 3 output: 1\n\nWithout moving stones, if Aoki first removes 2 stones from the 1-st pile, Takahashi cannot win in any way.\nIf Takahashi moves 1 stone from the 1-st pile to the 2-nd before the game begins so that both piles have 4 stones, Takahashi can always win by properly choosing his actions.", "input: 2\n3 5 output: -1\n\nIt is not allowed to move stones from the 2-nd pile to the 1-st.", "input: 3\n1 1 2 output: -1\n\nIt is not allowed to move all stones from the 1-st pile.", "input: 8\n10 9 8 7 6 5 4 3 output: 3", "input: 3\n4294967297 8589934593 12884901890 output: 1\n\nWatch out for overflows."], "Pid": "p02626", "ProblemText": "Task Description: Problem Statement There are N piles of stones. The i-th pile has A_i stones.\nAoki and Takahashi are about to use them to play the following game:\n\nStarting with Aoki, the two players alternately do the following operation:\nOperation: Choose one pile of stones, and remove one or more stones from it.\nWhen a player is unable to do the operation, he loses, and the other player wins.\n\nWhen the two players play optimally, there are two possibilities in this game: the player who moves first always wins, or the player who moves second always wins, only depending on the initial number of stones in each pile.\nIn such a situation, Takahashi, the second player to act, is trying to guarantee his win by moving at least zero and at most (A_1 - 1) stones from the 1-st pile to the 2-nd pile before the game begins.\nIf this is possible, print the minimum number of stones to move to guarantee his victory; otherwise, print -1 instead.\nTask Constraint: 2 <= N <= 300\n1 <= A_i <= 10^{12}\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 \\ldots A_N\nTask Output: Print the minimum number of stones to move to guarantee Takahashi's win; otherwise, print -1 instead.\nTask Samples: input: 2\n5 3 output: 1\n\nWithout moving stones, if Aoki first removes 2 stones from the 1-st pile, Takahashi cannot win in any way.\nIf Takahashi moves 1 stone from the 1-st pile to the 2-nd before the game begins so that both piles have 4 stones, Takahashi can always win by properly choosing his actions.\ninput: 2\n3 5 output: -1\n\nIt is not allowed to move stones from the 2-nd pile to the 1-st.\ninput: 3\n1 1 2 output: -1\n\nIt is not allowed to move all stones from the 1-st pile.\ninput: 8\n10 9 8 7 6 5 4 3 output: 3\ninput: 3\n4294967297 8589934593 12884901890 output: 1\n\nWatch out for overflows.\n\n" }, { "title": "", "content": "Problem Statement An uppercase or lowercase English letter \\alpha will be given as input.\nIf \\alpha is uppercase, print A; if it is lowercase, print a.", "constraint": "\\alpha is an uppercase (A - Z) or lowercase (a - z) English letter.", "input": "Input is given from Standard Input in the following format:\nα", "output": "If \\alpha is uppercase, print A; if it is lowercase, print a.", "content_img": false, "lang": "en", "error": false, "samples": ["input: B output: A\n\nB is uppercase, so we should print A.", "input: a output: a\n\na is lowercase, so we should print a."], "Pid": "p02627", "ProblemText": "Task Description: Problem Statement An uppercase or lowercase English letter \\alpha will be given as input.\nIf \\alpha is uppercase, print A; if it is lowercase, print a.\nTask Constraint: \\alpha is an uppercase (A - Z) or lowercase (a - z) English letter.\nTask Input: Input is given from Standard Input in the following format:\nα\nTask Output: If \\alpha is uppercase, print A; if it is lowercase, print a.\nTask Samples: input: B output: A\n\nB is uppercase, so we should print A.\ninput: a output: a\n\na is lowercase, so we should print a.\n\n" }, { "title": "", "content": "Problem Statement A shop sells N kinds of fruits, Fruit 1, \\ldots, N, at prices of p_1, \\ldots, p_N yen per item, respectively. (Yen is the currency of Japan. )\nHere, we will choose K kinds of fruits and buy one of each chosen kind. Find the minimum possible total price of those fruits.", "constraint": "1 <= K <= N <= 1000\n1 <= p_i <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\np_1 p_2 \\ldots p_N", "output": "Print an integer representing the minimum possible total price of fruits.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n50 100 80 120 80 output: 210\n\nThis shop sells Fruit 1,2,3,4, and 5 for 50 yen, 100 yen, 80 yen, 120 yen, and 80 yen, respectively.\nThe minimum total price for three kinds of fruits is 50 + 80 + 80 = 210 yen when choosing Fruit 1,3, and 5.", "input: 1 1\n1000 output: 1000"], "Pid": "p02628", "ProblemText": "Task Description: Problem Statement A shop sells N kinds of fruits, Fruit 1, \\ldots, N, at prices of p_1, \\ldots, p_N yen per item, respectively. (Yen is the currency of Japan. )\nHere, we will choose K kinds of fruits and buy one of each chosen kind. Find the minimum possible total price of those fruits.\nTask Constraint: 1 <= K <= N <= 1000\n1 <= p_i <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\np_1 p_2 \\ldots p_N\nTask Output: Print an integer representing the minimum possible total price of fruits.\nTask Samples: input: 5 3\n50 100 80 120 80 output: 210\n\nThis shop sells Fruit 1,2,3,4, and 5 for 50 yen, 100 yen, 80 yen, 120 yen, and 80 yen, respectively.\nThe minimum total price for three kinds of fruits is 50 + 80 + 80 = 210 yen when choosing Fruit 1,3, and 5.\ninput: 1 1\n1000 output: 1000\n\n" }, { "title": "", "content": "Problem Statement1000000000000001 dogs suddenly appeared under the roof of Roger's house, all of which he decided to keep. The dogs had been numbered 1 through 1000000000000001, but he gave them new names, as follows:\n\nthe dogs numbered 1,2, \\cdots, 26 were respectively given the names a, b, . . . , z;\nthe dogs numbered 27,28,29, \\cdots, 701,702 were respectively given the names aa, ab, ac, . . . , zy, zz;\nthe dogs numbered 703,704,705, \\cdots, 18277,18278 were respectively given the names aaa, aab, aac, . . . , zzy, zzz;\nthe dogs numbered 18279,18280,18281, \\cdots, 475253,475254 were respectively given the names aaaa, aaab, aaac, . . . , zzzy, zzzz;\nthe dogs numbered 475255,475256, \\cdots were respectively given the names aaaaa, aaaab, . . . ;\nand so on.\n\nTo sum it up, the dogs numbered 1,2, \\cdots were respectively given the following names:\na, b, . . . , z, aa, ab, . . . , az, ba, bb, . . . , bz, . . . , za, zb, . . . , zz, aaa, aab, . . . , aaz, aba, abb, . . . , abz, . . . , zzz, aaaa, . . .\nNow, Roger asks you:\n\"What is the name for the dog numbered N? \"", "constraint": "N is an integer.\n 1 <= N <= 1000000000000001", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer to Roger's question as a string consisting of lowercase English letters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: b", "input: 27 output: aa", "input: 123456789 output: jjddja"], "Pid": "p02629", "ProblemText": "Task Description: Problem Statement1000000000000001 dogs suddenly appeared under the roof of Roger's house, all of which he decided to keep. The dogs had been numbered 1 through 1000000000000001, but he gave them new names, as follows:\n\nthe dogs numbered 1,2, \\cdots, 26 were respectively given the names a, b, . . . , z;\nthe dogs numbered 27,28,29, \\cdots, 701,702 were respectively given the names aa, ab, ac, . . . , zy, zz;\nthe dogs numbered 703,704,705, \\cdots, 18277,18278 were respectively given the names aaa, aab, aac, . . . , zzy, zzz;\nthe dogs numbered 18279,18280,18281, \\cdots, 475253,475254 were respectively given the names aaaa, aaab, aaac, . . . , zzzy, zzzz;\nthe dogs numbered 475255,475256, \\cdots were respectively given the names aaaaa, aaaab, . . . ;\nand so on.\n\nTo sum it up, the dogs numbered 1,2, \\cdots were respectively given the following names:\na, b, . . . , z, aa, ab, . . . , az, ba, bb, . . . , bz, . . . , za, zb, . . . , zz, aaa, aab, . . . , aaz, aba, abb, . . . , abz, . . . , zzz, aaaa, . . .\nNow, Roger asks you:\n\"What is the name for the dog numbered N? \"\nTask Constraint: N is an integer.\n 1 <= N <= 1000000000000001\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer to Roger's question as a string consisting of lowercase English letters.\nTask Samples: input: 2 output: b\ninput: 27 output: aa\ninput: 123456789 output: jjddja\n\n" }, { "title": "", "content": "Problem Statement You have a sequence A composed of N positive integers: A_{1}, A_{2}, \\cdots, A_{N}.\nYou will now successively do the following Q operations:\n\nIn the i-th operation, you replace every element whose value is B_{i} with C_{i}.\n\nFor each i (1 <= i <= Q), find S_{i}: the sum of all elements in A just after the i-th operation.", "constraint": "All values in input are integers.\n 1 <= N, Q, A_{i}, B_{i}, C_{i} <= 10^{5} \n B_{i} \\neq C_{i}", "input": "Input is given from Standard Input in the following format:\nN\nA_{1} A_{2} \\cdots A_{N}\nQ\nB_{1} C_{1}\nB_{2} C_{2}\n\\vdots\nB_{Q} C_{Q}", "output": "Print Q integers S_{i} to Standard Output in the following format:\nS_{1}\nS_{2}\n\\vdots\nS_{Q}\n\nNote that S_{i} may not fit into a 32-bit integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 3 4\n3\n1 2\n3 4\n2 4 output: 11\n12\n16\n\nInitially, the sequence A is 1,2,3,4.\nAfter each operation, it becomes the following:\n\n2,2,3,4\n2,2,4,4\n4,4,4,4", "input: 4\n1 1 1 1\n3\n1 2\n2 1\n3 5 output: 8\n4\n4\n\nNote that the sequence A may not contain an element whose value is B_{i}.", "input: 2\n1 2\n3\n1 100\n2 100\n100 1000 output: 102\n200\n2000"], "Pid": "p02630", "ProblemText": "Task Description: Problem Statement You have a sequence A composed of N positive integers: A_{1}, A_{2}, \\cdots, A_{N}.\nYou will now successively do the following Q operations:\n\nIn the i-th operation, you replace every element whose value is B_{i} with C_{i}.\n\nFor each i (1 <= i <= Q), find S_{i}: the sum of all elements in A just after the i-th operation.\nTask Constraint: All values in input are integers.\n 1 <= N, Q, A_{i}, B_{i}, C_{i} <= 10^{5} \n B_{i} \\neq C_{i}\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{1} A_{2} \\cdots A_{N}\nQ\nB_{1} C_{1}\nB_{2} C_{2}\n\\vdots\nB_{Q} C_{Q}\nTask Output: Print Q integers S_{i} to Standard Output in the following format:\nS_{1}\nS_{2}\n\\vdots\nS_{Q}\n\nNote that S_{i} may not fit into a 32-bit integer.\nTask Samples: input: 4\n1 2 3 4\n3\n1 2\n3 4\n2 4 output: 11\n12\n16\n\nInitially, the sequence A is 1,2,3,4.\nAfter each operation, it becomes the following:\n\n2,2,3,4\n2,2,4,4\n4,4,4,4\ninput: 4\n1 1 1 1\n3\n1 2\n2 1\n3 5 output: 8\n4\n4\n\nNote that the sequence A may not contain an element whose value is B_{i}.\ninput: 2\n1 2\n3\n1 100\n2 100\n100 1000 output: 102\n200\n2000\n\n" }, { "title": "", "content": "Problem Statement There are N Snuke Cats numbered 1,2, \\ldots, N, where N is even.\nEach Snuke Cat wears a red scarf, on which his favorite non-negative integer is written.\nRecently, they learned the operation called xor (exclusive OR).\n\nWhat is xor?\n\nFor n non-negative integers x_1, x_2, \\ldots, x_n, their xor, x_1~\\textrm{xor}~x_2~\\textrm{xor}~\\ldots~\\textrm{xor}~x_n is defined as follows:\n\n When x_1~\\textrm{xor}~x_2~\\textrm{xor}~\\ldots~\\textrm{xor}~x_n is written in base two, the digit in the 2^k's place (k >= 0) is 1 if the number of integers among x_1, x_2, \\ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even. \n\nFor example, 3~\\textrm{xor}~5 = 6.\nThey wanted to use this operation quickly, so each of them calculated the xor of the integers written on their scarfs except his scarf.\nWe know that the xor calculated by Snuke Cat i, that is, the xor of the integers written on the scarfs except the scarf of Snuke Cat i is a_i.\nUsing this information, restore the integer written on the scarf of each Snuke Cat.", "constraint": "All values in input are integers.\n2 <= N <= 200000\nN is even.\n0 <= a_i <= 10^9\nThere exists a combination of integers on the scarfs that is consistent with the given information.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N", "output": "Print a line containing N integers separated with space.\nThe i-th of the integers from the left should represent the integer written on the scarf of Snuke Cat i.\nIf there are multiple possible solutions, you may print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n20 11 9 24 output: 26 5 7 22\n5~\\textrm{xor}~7~\\textrm{xor}~22 = 20\n26~\\textrm{xor}~7~\\textrm{xor}~22 = 11\n26~\\textrm{xor}~5~\\textrm{xor}~22 = 9\n26~\\textrm{xor}~5~\\textrm{xor}~7 = 24\n\nThus, this output is consistent with the given information."], "Pid": "p02631", "ProblemText": "Task Description: Problem Statement There are N Snuke Cats numbered 1,2, \\ldots, N, where N is even.\nEach Snuke Cat wears a red scarf, on which his favorite non-negative integer is written.\nRecently, they learned the operation called xor (exclusive OR).\n\nWhat is xor?\n\nFor n non-negative integers x_1, x_2, \\ldots, x_n, their xor, x_1~\\textrm{xor}~x_2~\\textrm{xor}~\\ldots~\\textrm{xor}~x_n is defined as follows:\n\n When x_1~\\textrm{xor}~x_2~\\textrm{xor}~\\ldots~\\textrm{xor}~x_n is written in base two, the digit in the 2^k's place (k >= 0) is 1 if the number of integers among x_1, x_2, \\ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even. \n\nFor example, 3~\\textrm{xor}~5 = 6.\nThey wanted to use this operation quickly, so each of them calculated the xor of the integers written on their scarfs except his scarf.\nWe know that the xor calculated by Snuke Cat i, that is, the xor of the integers written on the scarfs except the scarf of Snuke Cat i is a_i.\nUsing this information, restore the integer written on the scarf of each Snuke Cat.\nTask Constraint: All values in input are integers.\n2 <= N <= 200000\nN is even.\n0 <= a_i <= 10^9\nThere exists a combination of integers on the scarfs that is consistent with the given information.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N\nTask Output: Print a line containing N integers separated with space.\nThe i-th of the integers from the left should represent the integer written on the scarf of Snuke Cat i.\nIf there are multiple possible solutions, you may print any of them.\nTask Samples: input: 4\n20 11 9 24 output: 26 5 7 22\n5~\\textrm{xor}~7~\\textrm{xor}~22 = 20\n26~\\textrm{xor}~7~\\textrm{xor}~22 = 11\n26~\\textrm{xor}~5~\\textrm{xor}~22 = 9\n26~\\textrm{xor}~5~\\textrm{xor}~7 = 24\n\nThus, this output is consistent with the given information.\n\n" }, { "title": "", "content": "Problem Statement\nHow many strings can be obtained by applying the following operation on a string S exactly K times: \"choose one lowercase English letter and insert it somewhere\"?\nThe answer can be enormous, so print it modulo (10^9+7).", "constraint": "K is an integer between 1 and 10^6 (inclusive).\nS is a string of length between 1 and 10^6 (inclusive) consisting of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nK\nS", "output": "Print the number of strings satisfying the condition, modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\noof output: 575111451\n\nFor example, we can obtain proofend, moonwolf, and onionpuf, while we cannot obtain oofsix, oofelevennn, voxafolt, or fooooooo.", "input: 37564\nwhydidyoudesertme output: 318008117"], "Pid": "p02632", "ProblemText": "Task Description: Problem Statement\nHow many strings can be obtained by applying the following operation on a string S exactly K times: \"choose one lowercase English letter and insert it somewhere\"?\nThe answer can be enormous, so print it modulo (10^9+7).\nTask Constraint: K is an integer between 1 and 10^6 (inclusive).\nS is a string of length between 1 and 10^6 (inclusive) consisting of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nK\nS\nTask Output: Print the number of strings satisfying the condition, modulo (10^9+7).\nTask Samples: input: 5\noof output: 575111451\n\nFor example, we can obtain proofend, moonwolf, and onionpuf, while we cannot obtain oofsix, oofelevennn, voxafolt, or fooooooo.\ninput: 37564\nwhydidyoudesertme output: 318008117\n\n" }, { "title": "", "content": "Problem Statement Takahashi is standing on a two-dimensional plane, facing north. Find the minimum positive integer K such that Takahashi will be at the starting position again after he does the following action K times:\n\nGo one meter in the direction he is facing. Then, turn X degrees counter-clockwise.", "constraint": "1 <= X <= 179\nX is an integer.", "input": "Input is given from Standard Input in the following format:\nX", "output": "Print the number of times Takahashi will do the action before he is at the starting position again.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 90 output: 4\n\nTakahashi's path is a square.", "input: 1 output: 360"], "Pid": "p02633", "ProblemText": "Task Description: Problem Statement Takahashi is standing on a two-dimensional plane, facing north. Find the minimum positive integer K such that Takahashi will be at the starting position again after he does the following action K times:\n\nGo one meter in the direction he is facing. Then, turn X degrees counter-clockwise.\nTask Constraint: 1 <= X <= 179\nX is an integer.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: Print the number of times Takahashi will do the action before he is at the starting position again.\nTask Samples: input: 90 output: 4\n\nTakahashi's path is a square.\ninput: 1 output: 360\n\n" }, { "title": "", "content": "Problem Statement We have a grid with A horizontal rows and B vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:\n\nAssume that the grid currently has a horizontal rows and b vertical columns. Choose \"vertical\" or \"horizontal\".\nIf we choose \"vertical\", insert one row at the top of the grid, resulting in an (a+1) * b grid.\nIf we choose \"horizontal\", insert one column at the right end of the grid, resulting in an a * (b+1) grid.\nThen, paint one of the added squares black, and the other squares white.\n\nAssume the grid eventually has C horizontal rows and D vertical columns. Find the number of ways in which the squares can be painted in the end, modulo 998244353.", "constraint": "1 <= A <= C <= 3000\n1 <= B <= D <= 3000\nA, B, C, and D are integers.", "input": "Input is given from Standard Input in the following format:\nA B C D", "output": "Print the number of ways in which the squares can be painted in the end, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 2 2 output: 3\n\nAny two of the three squares other than the bottom-left square can be painted black.", "input: 2 1 3 4 output: 65", "input: 31 41 59 265 output: 387222020"], "Pid": "p02634", "ProblemText": "Task Description: Problem Statement We have a grid with A horizontal rows and B vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:\n\nAssume that the grid currently has a horizontal rows and b vertical columns. Choose \"vertical\" or \"horizontal\".\nIf we choose \"vertical\", insert one row at the top of the grid, resulting in an (a+1) * b grid.\nIf we choose \"horizontal\", insert one column at the right end of the grid, resulting in an a * (b+1) grid.\nThen, paint one of the added squares black, and the other squares white.\n\nAssume the grid eventually has C horizontal rows and D vertical columns. Find the number of ways in which the squares can be painted in the end, modulo 998244353.\nTask Constraint: 1 <= A <= C <= 3000\n1 <= B <= D <= 3000\nA, B, C, and D are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C D\nTask Output: Print the number of ways in which the squares can be painted in the end, modulo 998244353.\nTask Samples: input: 1 1 2 2 output: 3\n\nAny two of the three squares other than the bottom-left square can be painted black.\ninput: 2 1 3 4 output: 65\ninput: 31 41 59 265 output: 387222020\n\n" }, { "title": "", "content": "Problem Statement Given is a string S consisting of 0 and 1. Find the number of strings, modulo 998244353, that can result from applying the following operation on S between 0 and K times (inclusive):\n\nChoose a pair of integers i, j (1<= i < j<= |S|) such that the i-th and j-th characters of S are 0 and 1, respectively. Remove the j-th character from S and insert it to the immediate left of the i-th character.", "constraint": "1 <= |S| <= 300\n0 <= K <= 10^9\nS consists of 0 and 1.", "input": "Input is given from Standard Input in the following format:\nS K", "output": "Find the number of strings, modulo 998244353, that can result from applying the operation on S between 0 and K times (inclusive).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0101 1 output: 4\n\nFour strings, 0101,0110,1001, and 1010, can result.", "input: 01100110 2 output: 14", "input: 1101010010101101110111100011011111011000111101110101010010101010101 20 output: 113434815"], "Pid": "p02635", "ProblemText": "Task Description: Problem Statement Given is a string S consisting of 0 and 1. Find the number of strings, modulo 998244353, that can result from applying the following operation on S between 0 and K times (inclusive):\n\nChoose a pair of integers i, j (1<= i < j<= |S|) such that the i-th and j-th characters of S are 0 and 1, respectively. Remove the j-th character from S and insert it to the immediate left of the i-th character.\nTask Constraint: 1 <= |S| <= 300\n0 <= K <= 10^9\nS consists of 0 and 1.\nTask Input: Input is given from Standard Input in the following format:\nS K\nTask Output: Find the number of strings, modulo 998244353, that can result from applying the operation on S between 0 and K times (inclusive).\nTask Samples: input: 0101 1 output: 4\n\nFour strings, 0101,0110,1001, and 1010, can result.\ninput: 01100110 2 output: 14\ninput: 1101010010101101110111100011011111011000111101110101010010101010101 20 output: 113434815\n\n" }, { "title": "", "content": "Problem Statement Given is a string S consisting of 0 and 1. Find the number of strings, modulo 998244353, that can result from applying the following operation on S zero or more times:\n\nRemove the two characters at the beginning of S, erase one of them, and reinsert the other somewhere in S. This operation can be applied only when S has two or more characters.", "constraint": "1 <= |S| <= 300\nS consists of 0 and 1.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of strings, modulo 998244353, that can result from applying the operation on S zero or more times.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0001 output: 8\n\nEight strings, 0001,001,010,00,01,10,0, and 1, can result.", "input: 110001 output: 24", "input: 11101111011111000000000110000001111100011111000000001111111110000000111111111 output: 697354558"], "Pid": "p02636", "ProblemText": "Task Description: Problem Statement Given is a string S consisting of 0 and 1. Find the number of strings, modulo 998244353, that can result from applying the following operation on S zero or more times:\n\nRemove the two characters at the beginning of S, erase one of them, and reinsert the other somewhere in S. This operation can be applied only when S has two or more characters.\nTask Constraint: 1 <= |S| <= 300\nS consists of 0 and 1.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of strings, modulo 998244353, that can result from applying the operation on S zero or more times.\nTask Samples: input: 0001 output: 8\n\nEight strings, 0001,001,010,00,01,10,0, and 1, can result.\ninput: 110001 output: 24\ninput: 11101111011111000000000110000001111100011111000000001111111110000000111111111 output: 697354558\n\n" }, { "title": "", "content": "Problem Statement Given are an integer K and integers a_1, \\dots, a_K. Determine whether a sequence P satisfying below exists. If it exists, find the lexicographically smallest such sequence.\n\nEvery term in P is an integer between 1 and K (inclusive).\nFor each i=1, \\dots, K, P contains a_i occurrences of i.\nFor each term in P, there is a contiguous subsequence of length K that contains that term and is a permutation of 1, \\dots, K.", "constraint": "1 <= K <= 100\n1 <= a_i <= 1000 \\quad (1<= i<= K)\na_1 + \\dots + a_K<= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nK\na_1 a_2 \\dots a_K", "output": "If there is no sequence satisfying the conditions, print -1.\nOtherwise, print the lexicographically smallest sequence satisfying the conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 4 3 output: 2 1 3 2 2 3 1 2 3 \n\nFor example, the fifth term, which is 2, is in the subsequence (2,3,1) composed of the fifth, sixth, and seventh terms.", "input: 4\n3 2 3 2 output: 1 2 3 4 1 3 1 2 4 3", "input: 5\n3 1 4 1 5 output: -1"], "Pid": "p02637", "ProblemText": "Task Description: Problem Statement Given are an integer K and integers a_1, \\dots, a_K. Determine whether a sequence P satisfying below exists. If it exists, find the lexicographically smallest such sequence.\n\nEvery term in P is an integer between 1 and K (inclusive).\nFor each i=1, \\dots, K, P contains a_i occurrences of i.\nFor each term in P, there is a contiguous subsequence of length K that contains that term and is a permutation of 1, \\dots, K.\nTask Constraint: 1 <= K <= 100\n1 <= a_i <= 1000 \\quad (1<= i<= K)\na_1 + \\dots + a_K<= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nK\na_1 a_2 \\dots a_K\nTask Output: If there is no sequence satisfying the conditions, print -1.\nOtherwise, print the lexicographically smallest sequence satisfying the conditions.\nTask Samples: input: 3\n2 4 3 output: 2 1 3 2 2 3 1 2 3 \n\nFor example, the fifth term, which is 2, is in the subsequence (2,3,1) composed of the fifth, sixth, and seventh terms.\ninput: 4\n3 2 3 2 output: 1 2 3 4 1 3 1 2 4 3\ninput: 5\n3 1 4 1 5 output: -1\n\n" }, { "title": "", "content": "Problem Statement Given are integers N and K, and a prime number P. Find the number, modulo P, of directed graphs G with N vertices that satisfy below. Here, the vertices are distinguishable from each other.\n\nG is a tournament, that is, G contains no duplicated edges or self-loops, and exactly one of the edges u\\to v and v\\to u exists for any two vertices u and v.\nThe in-degree of every vertex in G is at most K.\nFor any four distinct vertices a, b, c, and d in G, it is not the case that all of the six edges a\\to b, b\\to c, c\\to a, a\\to d, b\\to d, and c\\to d exist simultaneously.", "constraint": "4 <= N <= 200\n\\frac{N-1}{2} <= K <= N-1\n10^8= 2) is Vertex <=ft[ \\frac{i}{2} \\right].\nEach vertex has one item in it. The item in Vertex i has a value of V_i and a weight of W_i.\nNow, process the following query Q times:\n\nGiven are a vertex v of the tree and a positive integer L.\n Let us choose some (possibly none) of the items in v and the ancestors of v so that their total weight is at most L.\n Find the maximum possible total value of the chosen items.\n\nHere, Vertex u is said to be an ancestor of Vertex v when u is an indirect parent of v, that is, there exists a sequence of vertices w_1, w_2, \\ldots, w_k (k>= 2) where w_1=v, w_k=u, and w_{i+1} is the parent of w_i for each i.", "constraint": "All values in input are integers.\n1 <= N < 2^{18}\n1 <= Q <= 10^5\n1 <= V_i <= 10^5\n1 <= W_i <= 10^5\nFor the values v and L given in each query, 1 <= v <= N and 1 <= L <= 10^5.", "input": "Input Let v_i and L_i be the values v and L given in the i-th query.\nThen, Input is given from Standard Input in the following format:\nN\nV_1 W_1\n:\nV_N W_N\nQ\nv_1 L_1\n:\nv_Q L_Q", "output": "For each integer i from 1 through Q,\nthe i-th line should contain the response to the i-th query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3\n3 4\n3\n1 1\n2 5\n3 5 output: 0\n3\n3\n\nIn the first query, we are given only one choice: the item with (V, W)=(1,2). Since L = 1, we cannot actually choose it, so our response should be 0.\nIn the second query, we are given two choices: the items with (V, W)=(1,2) and (V, W)=(2,3). Since L = 5, we can choose both of them, so our response should be 3.", "input: 15\n123 119\n129 120\n132 112\n126 109\n118 103\n115 109\n102 100\n130 120\n105 105\n132 115\n104 102\n107 107\n127 116\n121 104\n121 115\n8\n8 234\n9 244\n10 226\n11 227\n12 240\n13 237\n14 206\n15 227 output: 256\n255\n250\n247\n255\n259\n223\n253"], "Pid": "p02648", "ProblemText": "Task Description: Problem Statement We have a rooted binary tree with N vertices, where the vertices are numbered 1 to N.\nVertex 1 is the root, and the parent of Vertex i (i >= 2) is Vertex <=ft[ \\frac{i}{2} \\right].\nEach vertex has one item in it. The item in Vertex i has a value of V_i and a weight of W_i.\nNow, process the following query Q times:\n\nGiven are a vertex v of the tree and a positive integer L.\n Let us choose some (possibly none) of the items in v and the ancestors of v so that their total weight is at most L.\n Find the maximum possible total value of the chosen items.\n\nHere, Vertex u is said to be an ancestor of Vertex v when u is an indirect parent of v, that is, there exists a sequence of vertices w_1, w_2, \\ldots, w_k (k>= 2) where w_1=v, w_k=u, and w_{i+1} is the parent of w_i for each i.\nTask Constraint: All values in input are integers.\n1 <= N < 2^{18}\n1 <= Q <= 10^5\n1 <= V_i <= 10^5\n1 <= W_i <= 10^5\nFor the values v and L given in each query, 1 <= v <= N and 1 <= L <= 10^5.\nTask Input: Input Let v_i and L_i be the values v and L given in the i-th query.\nThen, Input is given from Standard Input in the following format:\nN\nV_1 W_1\n:\nV_N W_N\nQ\nv_1 L_1\n:\nv_Q L_Q\nTask Output: For each integer i from 1 through Q,\nthe i-th line should contain the response to the i-th query.\nTask Samples: input: 3\n1 2\n2 3\n3 4\n3\n1 1\n2 5\n3 5 output: 0\n3\n3\n\nIn the first query, we are given only one choice: the item with (V, W)=(1,2). Since L = 1, we cannot actually choose it, so our response should be 0.\nIn the second query, we are given two choices: the items with (V, W)=(1,2) and (V, W)=(2,3). Since L = 5, we can choose both of them, so our response should be 3.\ninput: 15\n123 119\n129 120\n132 112\n126 109\n118 103\n115 109\n102 100\n130 120\n105 105\n132 115\n104 102\n107 107\n127 116\n121 104\n121 115\n8\n8 234\n9 244\n10 226\n11 227\n12 240\n13 237\n14 206\n15 227 output: 256\n255\n250\n247\n255\n259\n223\n253\n\n" }, { "title": "", "content": "Problem Statement Given are N pairwise distinct non-negative integers A_1, A_2, \\ldots, A_N.\nFind the number of ways to choose a set of between 1 and K numbers (inclusive) from the given numbers so that the following two conditions are satisfied:\n\nThe bitwise AND of the chosen numbers is S.\nThe bitwise OR of the chosen numbers is T.", "constraint": "1 <= N <= 50\n1 <= K <= N\n0 <= A_i < 2^{18}\n0 <= S < 2^{18}\n0 <= T < 2^{18}\nA_i \\neq A_j (1 <= i < j <= N)", "input": "Input is given from Standard Input in the following format:\nN K S T\nA_1 A_2 . . . A_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 0 3\n1 2 3 output: 2\n\nThe conditions are satisfied when we choose \\{1,2\\} or \\{1,2,3\\}.", "input: 5 3 1 7\n3 4 9 1 5 output: 2", "input: 5 4 0 15\n3 4 9 1 5 output: 3"], "Pid": "p02649", "ProblemText": "Task Description: Problem Statement Given are N pairwise distinct non-negative integers A_1, A_2, \\ldots, A_N.\nFind the number of ways to choose a set of between 1 and K numbers (inclusive) from the given numbers so that the following two conditions are satisfied:\n\nThe bitwise AND of the chosen numbers is S.\nThe bitwise OR of the chosen numbers is T.\nTask Constraint: 1 <= N <= 50\n1 <= K <= N\n0 <= A_i < 2^{18}\n0 <= S < 2^{18}\n0 <= T < 2^{18}\nA_i \\neq A_j (1 <= i < j <= N)\nTask Input: Input is given from Standard Input in the following format:\nN K S T\nA_1 A_2 . . . A_N\nTask Output: Print the answer.\nTask Samples: input: 3 3 0 3\n1 2 3 output: 2\n\nThe conditions are satisfied when we choose \\{1,2\\} or \\{1,2,3\\}.\ninput: 5 3 1 7\n3 4 9 1 5 output: 2\ninput: 5 4 0 15\n3 4 9 1 5 output: 3\n\n" }, { "title": "", "content": "Problem Statement In a two-dimensional plane, we have a rectangle R whose vertices are (0,0), (W, 0), (0, H), and (W, H), where W and H are positive integers.\nHere, find the number of triangles \\Delta in the plane that satisfy all of the following conditions:\n\nEach vertex of \\Delta is a grid point, that is, has integer x- and y-coordinates.\n\\Delta and R shares no vertex.\nEach vertex of \\Delta lies on the perimeter of R, and all the vertices belong to different sides of R.\n\\Delta contains at most K grid points strictly within itself (excluding its perimeter and vertices).", "constraint": "1 <= W <= 10^5\n1 <= H <= 10^5\n0 <= K <= 10^5", "input": "Input is given from Standard Input in the following format:\nW H K", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 1 output: 12\n\nFor example, the triangle with the vertices (1,0), (0,2), and (2,2) contains just one grid point within itself and thus satisfies the condition.", "input: 5 4 5 output: 132", "input: 100 100 1000 output: 461316"], "Pid": "p02650", "ProblemText": "Task Description: Problem Statement In a two-dimensional plane, we have a rectangle R whose vertices are (0,0), (W, 0), (0, H), and (W, H), where W and H are positive integers.\nHere, find the number of triangles \\Delta in the plane that satisfy all of the following conditions:\n\nEach vertex of \\Delta is a grid point, that is, has integer x- and y-coordinates.\n\\Delta and R shares no vertex.\nEach vertex of \\Delta lies on the perimeter of R, and all the vertices belong to different sides of R.\n\\Delta contains at most K grid points strictly within itself (excluding its perimeter and vertices).\nTask Constraint: 1 <= W <= 10^5\n1 <= H <= 10^5\n0 <= K <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nW H K\nTask Output: Print the answer.\nTask Samples: input: 2 3 1 output: 12\n\nFor example, the triangle with the vertices (1,0), (0,2), and (2,2) contains just one grid point within itself and thus satisfies the condition.\ninput: 5 4 5 output: 132\ninput: 100 100 1000 output: 461316\n\n" }, { "title": "", "content": "Problem Statement There are two persons, numbered 0 and 1, and a variable x whose initial value is 0.\nThe two persons now play a game.\nThe game is played in N rounds. The following should be done in the i-th round (1 <= i <= N):\n\nPerson S_i does one of the following:\nReplace x with x \\oplus A_i, where \\oplus represents bitwise XOR.\nDo nothing.\n\nPerson 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \\neq 0 at the end of the game.\nDetermine whether x becomes 0 at the end of the game when the two persons play optimally.\nSolve T test cases for each input file.", "constraint": "1 <= T <= 100\n1 <= N <= 200\n1 <= A_i <= 10^{18}\nS is a string of length N consisting of 0 and 1.\nAll numbers in input are integers.", "input": "Input is given from Standard Input in the following format.\nThe first line is as follows:\nT\n\nThen, T test cases follow.\nEach test case is given in the following format:\nN\nA_1 A_2 \\cdots A_N\nS", "output": "For each test case, print a line containing 0 if x becomes 0 at the end of the game, and 1 otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2\n1 2\n10\n2\n1 1\n10\n6\n2 3 4 5 6 7\n111000 output: 1\n0\n0\n\nIn the first test case, if Person 1 replaces x with 0 \\oplus 1=1, we surely have x \\neq 0 at the end of the game, regardless of the choice of Person 0.\nIn the second test case, regardless of the choice of Person 1, Person 0 can make x=0 with a suitable choice."], "Pid": "p02651", "ProblemText": "Task Description: Problem Statement There are two persons, numbered 0 and 1, and a variable x whose initial value is 0.\nThe two persons now play a game.\nThe game is played in N rounds. The following should be done in the i-th round (1 <= i <= N):\n\nPerson S_i does one of the following:\nReplace x with x \\oplus A_i, where \\oplus represents bitwise XOR.\nDo nothing.\n\nPerson 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \\neq 0 at the end of the game.\nDetermine whether x becomes 0 at the end of the game when the two persons play optimally.\nSolve T test cases for each input file.\nTask Constraint: 1 <= T <= 100\n1 <= N <= 200\n1 <= A_i <= 10^{18}\nS is a string of length N consisting of 0 and 1.\nAll numbers in input are integers.\nTask Input: Input is given from Standard Input in the following format.\nThe first line is as follows:\nT\n\nThen, T test cases follow.\nEach test case is given in the following format:\nN\nA_1 A_2 \\cdots A_N\nS\nTask Output: For each test case, print a line containing 0 if x becomes 0 at the end of the game, and 1 otherwise.\nTask Samples: input: 3\n2\n1 2\n10\n2\n1 1\n10\n6\n2 3 4 5 6 7\n111000 output: 1\n0\n0\n\nIn the first test case, if Person 1 replaces x with 0 \\oplus 1=1, we surely have x \\neq 0 at the end of the game, regardless of the choice of Person 0.\nIn the second test case, regardless of the choice of Person 1, Person 0 can make x=0 with a suitable choice.\n\n" }, { "title": "", "content": "Problem Statement Given is a string S, where each character is 0,1, or ? .\nConsider making a string S' by replacing each occurrence of ? with 0 or 1 (we can choose the character for each ? independently).\nLet us define the unbalancedness of S' as follows:\n\n(The unbalancedness of S') = \\max \\{ The absolute difference between the number of occurrences of 0 and 1 between the l-th and r-th character of S (inclusive) : \\ 1 <= l <= r <= |S|\\}\n\nFind the minimum possible unbalancedness of S'.", "constraint": "1 <= |S| <= 10^6\nEach character of S is 0,1, or ?.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the minimum possible unbalancedness of S'.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0?? output: 1\n\nWe can make S'= 010 and achieve the minimum possible unbalancedness of 1.", "input: 0??0 output: 2", "input: ??00????0??0????0?0??00??1???11?1?1???1?11?111???1 output: 4"], "Pid": "p02652", "ProblemText": "Task Description: Problem Statement Given is a string S, where each character is 0,1, or ? .\nConsider making a string S' by replacing each occurrence of ? with 0 or 1 (we can choose the character for each ? independently).\nLet us define the unbalancedness of S' as follows:\n\n(The unbalancedness of S') = \\max \\{ The absolute difference between the number of occurrences of 0 and 1 between the l-th and r-th character of S (inclusive) : \\ 1 <= l <= r <= |S|\\}\n\nFind the minimum possible unbalancedness of S'.\nTask Constraint: 1 <= |S| <= 10^6\nEach character of S is 0,1, or ?.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the minimum possible unbalancedness of S'.\nTask Samples: input: 0?? output: 1\n\nWe can make S'= 010 and achieve the minimum possible unbalancedness of 1.\ninput: 0??0 output: 2\ninput: ??00????0??0????0?0??00??1???11?1?1???1?11?111???1 output: 4\n\n" }, { "title": "", "content": "Problem Statement Snuke has a string x of length N.\nInitially, every character in x is 0.\nSnuke can do the following two operations any number of times in any order:\n\nChoose A consecutive characters in x and replace each of them with 0.\nChoose B consecutive characters in x and replace each of them with 1.\n\nFind the number of different strings that x can be after Snuke finishes doing operations.\nThis count can be enormous, so compute it modulo (10^9+7).", "constraint": "1 <= N <= 5000\n1 <= A,B <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print the number of different strings that x can be after Snuke finishes doing operations, modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 3 output: 11\n\nFor example, x can be 0011 or 1111 in the end, but cannot be 0110.", "input: 10 7 2 output: 533", "input: 1000 100 10 output: 828178524"], "Pid": "p02653", "ProblemText": "Task Description: Problem Statement Snuke has a string x of length N.\nInitially, every character in x is 0.\nSnuke can do the following two operations any number of times in any order:\n\nChoose A consecutive characters in x and replace each of them with 0.\nChoose B consecutive characters in x and replace each of them with 1.\n\nFind the number of different strings that x can be after Snuke finishes doing operations.\nThis count can be enormous, so compute it modulo (10^9+7).\nTask Constraint: 1 <= N <= 5000\n1 <= A,B <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print the number of different strings that x can be after Snuke finishes doing operations, modulo (10^9+7).\nTask Samples: input: 4 2 3 output: 11\n\nFor example, x can be 0011 or 1111 in the end, but cannot be 0110.\ninput: 10 7 2 output: 533\ninput: 1000 100 10 output: 828178524\n\n" }, { "title": "", "content": "Problem Statement We have N lamps numbered 1 to N, and N buttons numbered 1 to N.\nInitially, Lamp 1,2, \\cdots, A are on, and the other lamps are off.\nSnuke and Ringo will play the following game.\nFirst, Ringo generates a permutation (p_1, p_2, \\cdots, p_N) of (1,2, \\cdots, N).\nThe permutation is chosen from all N! possible permutations with equal probability, without being informed to Snuke.\nThen, Snuke does the following operation any number of times he likes:\n\nChoose a lamp that is on at the moment. (The operation cannot be done if there is no such lamp. )\nLet Lamp i be the chosen lamp.\nPress Button i, which switches the state of Lamp p_i. That is, Lamp p_i will be turned off if it is on, and vice versa.\n\nAt every moment, Snuke knows which lamps are on.\nSnuke wins if all the lamps are on, and he will surrender when it turns out that he cannot win.\nWhat is the probability of winning when Snuke plays optimally?\nLet w be the probability of winning. Then, w * N! will be an integer.\nCompute w * N! modulo (10^9+7).", "constraint": "2 <= N <= 10^7\n1 <= A <= \\min(N-1,5000)", "input": "Input is given from Standard Input in the following format:\nN A", "output": "Print w * N! modulo (10^9+7), where w is the probability of Snuke's winning.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 output: 2\n\nFirst, Snuke will press Button 1.\nIf Lamp 1 turns off, he loses.\nOtherwise, he will press the button that he can now press.\nIf the remaining lamp turns on, he wins; if Lamp 1 turns off, he loses.\nThe probability of winning in this game is 1/3, so we should print (1/3)* 3!=2.", "input: 3 2 output: 3", "input: 8 4 output: 16776", "input: 9999999 4999 output: 90395416"], "Pid": "p02654", "ProblemText": "Task Description: Problem Statement We have N lamps numbered 1 to N, and N buttons numbered 1 to N.\nInitially, Lamp 1,2, \\cdots, A are on, and the other lamps are off.\nSnuke and Ringo will play the following game.\nFirst, Ringo generates a permutation (p_1, p_2, \\cdots, p_N) of (1,2, \\cdots, N).\nThe permutation is chosen from all N! possible permutations with equal probability, without being informed to Snuke.\nThen, Snuke does the following operation any number of times he likes:\n\nChoose a lamp that is on at the moment. (The operation cannot be done if there is no such lamp. )\nLet Lamp i be the chosen lamp.\nPress Button i, which switches the state of Lamp p_i. That is, Lamp p_i will be turned off if it is on, and vice versa.\n\nAt every moment, Snuke knows which lamps are on.\nSnuke wins if all the lamps are on, and he will surrender when it turns out that he cannot win.\nWhat is the probability of winning when Snuke plays optimally?\nLet w be the probability of winning. Then, w * N! will be an integer.\nCompute w * N! modulo (10^9+7).\nTask Constraint: 2 <= N <= 10^7\n1 <= A <= \\min(N-1,5000)\nTask Input: Input is given from Standard Input in the following format:\nN A\nTask Output: Print w * N! modulo (10^9+7), where w is the probability of Snuke's winning.\nTask Samples: input: 3 1 output: 2\n\nFirst, Snuke will press Button 1.\nIf Lamp 1 turns off, he loses.\nOtherwise, he will press the button that he can now press.\nIf the remaining lamp turns on, he wins; if Lamp 1 turns off, he loses.\nThe probability of winning in this game is 1/3, so we should print (1/3)* 3!=2.\ninput: 3 2 output: 3\ninput: 8 4 output: 16776\ninput: 9999999 4999 output: 90395416\n\n" }, { "title": "", "content": "Problem Statement We have N boxes numbered 1 to N, and M balls numbered 1 to M.\nCurrently, Ball i is in Box A_i.\nYou can do the following operation:\n\nChoose a box containing two or more balls, pick up one of the balls from that box, and put it into another box.\n\nSince the balls are very easy to break, you cannot move Ball i more than C_i times in total.\nWithin this limit, you can do the operation any number of times.\nYour objective is to have Ball i in Box B_i for every i (1 <= i <= M).\nDetermine whether this objective is achievable.\nIf it is, also find the minimum number of operations required to achieve it.", "constraint": "1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i,B_i <= N\n1 <= C_i <= 10^5\nIn the situation where the objective is achieved, every box contains one or more balls.\nThat is, for every i (1 <= i <= N), there exists j such that B_j=i.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1 C_1\nA_2 B_2 C_2\n\\vdots\nA_M B_M C_M", "output": "If the objective is unachievable, print -1; if it is achievable, print the minimum number of operations required to achieve it.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 1\n2 1 1\n1 3 2 output: 3\n\nWe can achieve the objective in three operations, as follows:\n\nPick up Ball 1 from Box 1 and put it into Box 2.\nPick up Ball 2 from Box 2 and put it into Box 1.\nPick up Ball 3 from Box 1 and put it into Box 3.", "input: 2 2\n1 2 1\n2 1 1 output: -1", "input: 5 5\n1 2 1\n2 1 1\n1 3 2\n4 5 1\n5 4 1 output: 6", "input: 1 1\n1 1 1 output: 0"], "Pid": "p02655", "ProblemText": "Task Description: Problem Statement We have N boxes numbered 1 to N, and M balls numbered 1 to M.\nCurrently, Ball i is in Box A_i.\nYou can do the following operation:\n\nChoose a box containing two or more balls, pick up one of the balls from that box, and put it into another box.\n\nSince the balls are very easy to break, you cannot move Ball i more than C_i times in total.\nWithin this limit, you can do the operation any number of times.\nYour objective is to have Ball i in Box B_i for every i (1 <= i <= M).\nDetermine whether this objective is achievable.\nIf it is, also find the minimum number of operations required to achieve it.\nTask Constraint: 1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i,B_i <= N\n1 <= C_i <= 10^5\nIn the situation where the objective is achieved, every box contains one or more balls.\nThat is, for every i (1 <= i <= N), there exists j such that B_j=i.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1 C_1\nA_2 B_2 C_2\n\\vdots\nA_M B_M C_M\nTask Output: If the objective is unachievable, print -1; if it is achievable, print the minimum number of operations required to achieve it.\nTask Samples: input: 3 3\n1 2 1\n2 1 1\n1 3 2 output: 3\n\nWe can achieve the objective in three operations, as follows:\n\nPick up Ball 1 from Box 1 and put it into Box 2.\nPick up Ball 2 from Box 2 and put it into Box 1.\nPick up Ball 3 from Box 1 and put it into Box 3.\ninput: 2 2\n1 2 1\n2 1 1 output: -1\ninput: 5 5\n1 2 1\n2 1 1\n1 3 2\n4 5 1\n5 4 1 output: 6\ninput: 1 1\n1 1 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement Snuke has X+Y balls.\nX of them have an integer A written on them, and the other Y of them have an integer B written on them.\nSnuke will divide these balls into some number of groups.\nHere, every ball should be contained in exactly one group, and every group should contain one or more balls.\nA group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C.\nFind the maximum possible number of good groups.\nSolve T test cases for each input file.", "constraint": "1 <= T <= 2 * 10^4\n1 <= A,X,B,Y,C <= 10^9\nA \\neq B", "input": "Input is given from Standard Input in the following format.\nThe first line is as follows:\nT\n\nThen, T test cases follow.\nEach test case is given in the following format:\nA X B Y C", "output": "For each test case, print a line containing the maximum possible number of good groups.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 3 4 4 5\n2 1 1 5 3\n3 1 4 2 5 output: 2\n2\n0\n\nIn the first test case, we can have two good groups by making the following groups: \\{3,3,4\\} and \\{3,4,4,4\\}.\nIn the second test case, we can have two good groups by making the following groups: \\{2,1\\}, \\{1,1,1\\}, and \\{1\\}."], "Pid": "p02656", "ProblemText": "Task Description: Problem Statement Snuke has X+Y balls.\nX of them have an integer A written on them, and the other Y of them have an integer B written on them.\nSnuke will divide these balls into some number of groups.\nHere, every ball should be contained in exactly one group, and every group should contain one or more balls.\nA group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C.\nFind the maximum possible number of good groups.\nSolve T test cases for each input file.\nTask Constraint: 1 <= T <= 2 * 10^4\n1 <= A,X,B,Y,C <= 10^9\nA \\neq B\nTask Input: Input is given from Standard Input in the following format.\nThe first line is as follows:\nT\n\nThen, T test cases follow.\nEach test case is given in the following format:\nA X B Y C\nTask Output: For each test case, print a line containing the maximum possible number of good groups.\nTask Samples: input: 3\n3 3 4 4 5\n2 1 1 5 3\n3 1 4 2 5 output: 2\n2\n0\n\nIn the first test case, we can have two good groups by making the following groups: \\{3,3,4\\} and \\{3,4,4,4\\}.\nIn the second test case, we can have two good groups by making the following groups: \\{2,1\\}, \\{1,1,1\\}, and \\{1\\}.\n\n" }, { "title": "", "content": "Problem Statement Compute A * B.", "constraint": "1 <= A <= 100\n1 <= B <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the value A * B as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5 output: 10\n\nWe have 2 * 5 = 10.", "input: 100 100 output: 10000"], "Pid": "p02657", "ProblemText": "Task Description: Problem Statement Compute A * B.\nTask Constraint: 1 <= A <= 100\n1 <= B <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the value A * B as an integer.\nTask Samples: input: 2 5 output: 10\n\nWe have 2 * 5 = 10.\ninput: 100 100 output: 10000\n\n" }, { "title": "", "content": "Problem Statement Given N integers A_1, . . . , A_N, compute A_1 * . . . * A_N.\nHowever, if the result exceeds 10^{18}, print -1 instead.", "constraint": "2 <= N <= 10^5\n0 <= A_i <= 10^{18}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N", "output": "Print the value A_1 * . . . * A_N as an integer, or -1 if the value exceeds 10^{18}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1000000000 1000000000 output: 1000000000000000000\n\nWe have 1000000000 * 1000000000 = 1000000000000000000.", "input: 3\n101 9901 999999000001 output: -1\n\nWe have 101 * 9901 * 999999000001 = 1000000000000000001, which exceeds 10^{18}, so we should print -1 instead.", "input: 31\n4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 output: 0"], "Pid": "p02658", "ProblemText": "Task Description: Problem Statement Given N integers A_1, . . . , A_N, compute A_1 * . . . * A_N.\nHowever, if the result exceeds 10^{18}, print -1 instead.\nTask Constraint: 2 <= N <= 10^5\n0 <= A_i <= 10^{18}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nTask Output: Print the value A_1 * . . . * A_N as an integer, or -1 if the value exceeds 10^{18}.\nTask Samples: input: 2\n1000000000 1000000000 output: 1000000000000000000\n\nWe have 1000000000 * 1000000000 = 1000000000000000000.\ninput: 3\n101 9901 999999000001 output: -1\n\nWe have 101 * 9901 * 999999000001 = 1000000000000000001, which exceeds 10^{18}, so we should print -1 instead.\ninput: 31\n4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 output: 0\n\n" }, { "title": "", "content": "Problem Statement Compute A * B, truncate its fractional part, and print the result as an integer.", "constraint": "0 <= A <= 10^{15}\n0 <= B < 10\nA is an integer.\nB is a number with two digits after the decimal point.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the answer as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 198 1.10 output: 217\n\nWe have 198 * 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.", "input: 1 0.01 output: 0", "input: 1000000000000000 9.99 output: 9990000000000000"], "Pid": "p02659", "ProblemText": "Task Description: Problem Statement Compute A * B, truncate its fractional part, and print the result as an integer.\nTask Constraint: 0 <= A <= 10^{15}\n0 <= B < 10\nA is an integer.\nB is a number with two digits after the decimal point.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the answer as an integer.\nTask Samples: input: 198 1.10 output: 217\n\nWe have 198 * 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.\ninput: 1 0.01 output: 0\ninput: 1000000000000000 9.99 output: 9990000000000000\n\n" }, { "title": "", "content": "Problem Statement\nGiven is a positive integer N. Consider repeatedly applying the operation below on N:\n\nFirst, choose a positive integer z satisfying all of the conditions below:\nz can be represented as z=p^e, where p is a prime number and e is a positive integer;\nz divides N;\nz is different from all integers chosen in previous operations.\nThen, replace N with N/z.\n\nFind the maximum number of times the operation can be applied.", "constraint": "All values in input are integers.\n1 <= N <= 10^{12}", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the maximum number of times the operation can be applied.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 24 output: 3\n\nWe can apply the operation three times by, for example, making the following choices:\n\nChoose z=2 (=2^1). (Now we have N=12.)\nChoose z=3 (=3^1). (Now we have N=4.)\nChoose z=4 (=2^2). (Now we have N=1.)", "input: 1 output: 0\n\nWe cannot apply the operation at all.", "input: 64 output: 3\n\nWe can apply the operation three times by, for example, making the following choices:\n\nChoose z=2 (=2^1). (Now we have N=32.)\nChoose z=4 (=2^2). (Now we have N=8.)\nChoose z=8 (=2^3). (Now we have N=1.)", "input: 1000000007 output: 1\n\nWe can apply the operation once by, for example, making the following choice:\n\nz=1000000007 (=1000000007^1). (Now we have N=1.)", "input: 997764507000 output: 7"], "Pid": "p02660", "ProblemText": "Task Description: Problem Statement\nGiven is a positive integer N. Consider repeatedly applying the operation below on N:\n\nFirst, choose a positive integer z satisfying all of the conditions below:\nz can be represented as z=p^e, where p is a prime number and e is a positive integer;\nz divides N;\nz is different from all integers chosen in previous operations.\nThen, replace N with N/z.\n\nFind the maximum number of times the operation can be applied.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^{12}\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the maximum number of times the operation can be applied.\nTask Samples: input: 24 output: 3\n\nWe can apply the operation three times by, for example, making the following choices:\n\nChoose z=2 (=2^1). (Now we have N=12.)\nChoose z=3 (=3^1). (Now we have N=4.)\nChoose z=4 (=2^2). (Now we have N=1.)\ninput: 1 output: 0\n\nWe cannot apply the operation at all.\ninput: 64 output: 3\n\nWe can apply the operation three times by, for example, making the following choices:\n\nChoose z=2 (=2^1). (Now we have N=32.)\nChoose z=4 (=2^2). (Now we have N=8.)\nChoose z=8 (=2^3). (Now we have N=1.)\ninput: 1000000007 output: 1\n\nWe can apply the operation once by, for example, making the following choice:\n\nz=1000000007 (=1000000007^1). (Now we have N=1.)\ninput: 997764507000 output: 7\n\n" }, { "title": "", "content": "Problem Statement There are N integers X_1, X_2, \\cdots, X_N, and we know that A_i <= X_i <= B_i.\nFind the number of different values that the median of X_1, X_2, \\cdots, X_N can take. note: Notes The median of X_1, X_2, \\cdots, X_N is defined as follows. Let x_1, x_2, \\cdots, x_N be the result of sorting X_1, X_2, \\cdots, X_N in ascending order.\n\nIf N is odd, the median is x_{(N+1)/2};\nif N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.", "constraint": "2 <= N <= 2 * 10^5\n1 <= A_i <= B_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2\n2 3 output: 3\n\nIf X_1 = 1 and X_2 = 2, the median is \\frac{3}{2};\nif X_1 = 1 and X_2 = 3, the median is 2;\nif X_1 = 2 and X_2 = 2, the median is 2;\nif X_1 = 2 and X_2 = 3, the median is \\frac{5}{2}.\nThus, the median can take three values: \\frac{3}{2}, 2, and \\frac{5}{2}.", "input: 3\n100 100\n10 10000\n1 1000000000 output: 9991"], "Pid": "p02661", "ProblemText": "Task Description: Problem Statement There are N integers X_1, X_2, \\cdots, X_N, and we know that A_i <= X_i <= B_i.\nFind the number of different values that the median of X_1, X_2, \\cdots, X_N can take. note: Notes The median of X_1, X_2, \\cdots, X_N is defined as follows. Let x_1, x_2, \\cdots, x_N be the result of sorting X_1, X_2, \\cdots, X_N in ascending order.\n\nIf N is odd, the median is x_{(N+1)/2};\nif N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= A_i <= B_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nTask Output: Print the answer.\nTask Samples: input: 2\n1 2\n2 3 output: 3\n\nIf X_1 = 1 and X_2 = 2, the median is \\frac{3}{2};\nif X_1 = 1 and X_2 = 3, the median is 2;\nif X_1 = 2 and X_2 = 2, the median is 2;\nif X_1 = 2 and X_2 = 3, the median is \\frac{5}{2}.\nThus, the median can take three values: \\frac{3}{2}, 2, and \\frac{5}{2}.\ninput: 3\n100 100\n10 10000\n1 1000000000 output: 9991\n\n" }, { "title": "", "content": "Problem Statement Given are a sequence of N positive integers A_1, A_2, \\ldots, A_N and another positive integer S.\nFor a non-empty subset T of the set \\{1,2, \\ldots , N \\}, let us define f(T) as follows:\n\nf(T) is the number of different non-empty subsets \\{x_1, x_2, \\ldots , x_k \\} of T such that A_{x_1}+A_{x_2}+\\cdots +A_{x_k} = S.\n\nFind the sum of f(T) over all 2^N-1 subsets T of \\{1,2, \\ldots , N \\}. Since the sum can be enormous, print it modulo 998244353.", "constraint": "All values in input are integers.\n1 <= N <= 3000\n1 <= S <= 3000\n1 <= A_i <= 3000", "input": "Input is given from Standard Input in the following format:\nN S\nA_1 A_2 . . . A_N", "output": "Print the sum of f(T) modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n2 2 4 output: 6\n\nFor each T, the value of f(T) is shown below. The sum of these values is 6.\n\nf(\\{1\\}) = 0\nf(\\{2\\}) = 0\nf(\\{3\\}) = 1 (One subset \\{3\\} satisfies the condition.)\nf(\\{1,2\\}) = 1 (\\{1,2\\})\nf(\\{2,3\\}) = 1 (\\{3\\})\nf(\\{1,3\\}) = 1 (\\{3\\})\nf(\\{1,2,3\\}) = 2 (\\{1,2\\}, \\{3\\})", "input: 5 8\n9 9 9 9 9 output: 0", "input: 10 10\n3 1 4 1 5 9 2 6 5 3 output: 3296"], "Pid": "p02662", "ProblemText": "Task Description: Problem Statement Given are a sequence of N positive integers A_1, A_2, \\ldots, A_N and another positive integer S.\nFor a non-empty subset T of the set \\{1,2, \\ldots , N \\}, let us define f(T) as follows:\n\nf(T) is the number of different non-empty subsets \\{x_1, x_2, \\ldots , x_k \\} of T such that A_{x_1}+A_{x_2}+\\cdots +A_{x_k} = S.\n\nFind the sum of f(T) over all 2^N-1 subsets T of \\{1,2, \\ldots , N \\}. Since the sum can be enormous, print it modulo 998244353.\nTask Constraint: All values in input are integers.\n1 <= N <= 3000\n1 <= S <= 3000\n1 <= A_i <= 3000\nTask Input: Input is given from Standard Input in the following format:\nN S\nA_1 A_2 . . . A_N\nTask Output: Print the sum of f(T) modulo 998244353.\nTask Samples: input: 3 4\n2 2 4 output: 6\n\nFor each T, the value of f(T) is shown below. The sum of these values is 6.\n\nf(\\{1\\}) = 0\nf(\\{2\\}) = 0\nf(\\{3\\}) = 1 (One subset \\{3\\} satisfies the condition.)\nf(\\{1,2\\}) = 1 (\\{1,2\\})\nf(\\{2,3\\}) = 1 (\\{3\\})\nf(\\{1,3\\}) = 1 (\\{3\\})\nf(\\{1,2,3\\}) = 2 (\\{1,2\\}, \\{3\\})\ninput: 5 8\n9 9 9 9 9 output: 0\ninput: 10 10\n3 1 4 1 5 9 2 6 5 3 output: 3296\n\n" }, { "title": "", "content": "Problem Statement In this problem, we use the 24-hour clock.\nTakahashi gets up exactly at the time H_1 : M_1 and goes to bed exactly at the time H_2 : M_2. (See Sample Inputs below for clarity. )\nHe has decided to study for K consecutive minutes while he is up.\nWhat is the length of the period in which he can start studying?", "constraint": "0 <= H_1, H_2 <= 23\n0 <= M_1, M_2 <= 59\nThe time H_1 : M_1 comes before the time H_2 : M_2.\nK >= 1\nTakahashi is up for at least K minutes.\nAll values in input are integers (without leading zeros).", "input": "Input is given from Standard Input in the following format:\nH_1 M_1 H_2 M_2 K", "output": "Print the length of the period in which he can start studying, as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 0 15 0 30 output: 270\n\nTakahashi gets up at exactly ten in the morning and goes to bed at exactly three in the afternoon.\nIt takes 30 minutes to do the study, so he can start it in the period between ten o'clock and half-past two. The length of this period is 270 minutes, so we should print 270.", "input: 10 0 12 0 120 output: 0\n\nTakahashi gets up at exactly ten in the morning and goes to bed at exactly noon. It takes 120 minutes to do the study, so he has to start it at exactly ten o'clock. Thus, we should print 0."], "Pid": "p02663", "ProblemText": "Task Description: Problem Statement In this problem, we use the 24-hour clock.\nTakahashi gets up exactly at the time H_1 : M_1 and goes to bed exactly at the time H_2 : M_2. (See Sample Inputs below for clarity. )\nHe has decided to study for K consecutive minutes while he is up.\nWhat is the length of the period in which he can start studying?\nTask Constraint: 0 <= H_1, H_2 <= 23\n0 <= M_1, M_2 <= 59\nThe time H_1 : M_1 comes before the time H_2 : M_2.\nK >= 1\nTakahashi is up for at least K minutes.\nAll values in input are integers (without leading zeros).\nTask Input: Input is given from Standard Input in the following format:\nH_1 M_1 H_2 M_2 K\nTask Output: Print the length of the period in which he can start studying, as an integer.\nTask Samples: input: 10 0 15 0 30 output: 270\n\nTakahashi gets up at exactly ten in the morning and goes to bed at exactly three in the afternoon.\nIt takes 30 minutes to do the study, so he can start it in the period between ten o'clock and half-past two. The length of this period is 270 minutes, so we should print 270.\ninput: 10 0 12 0 120 output: 0\n\nTakahashi gets up at exactly ten in the morning and goes to bed at exactly noon. It takes 120 minutes to do the study, so he has to start it at exactly ten o'clock. Thus, we should print 0.\n\n" }, { "title": "", "content": "Problem Statement For a string S consisting of the uppercase English letters P and D, let the doctoral and postdoctoral quotient of S be the total number of occurrences of D and PD in S as contiguous substrings. For example, if S = PPDDP, it contains two occurrences of D and one occurrence of PD as contiguous substrings, so the doctoral and postdoctoral quotient of S is 3.\nWe have a string T consisting of P, D, and ? .\nAmong the strings that can be obtained by replacing each ? in T with P or D, find one with the maximum possible doctoral and postdoctoral quotient.", "constraint": "1 <= |T| <= 2 * 10^5\nT consists of P, D, and ?.", "input": "Input is given from Standard Input in the following format:\nT", "output": "Print one string with the maximum possible doctoral and postdoctoral quotient among the strings that can be obtained by replacing each ? in T with P or D.\nIf there are multiple such strings, you may print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: PD?D??P output: PDPDPDP\n\nThis string contains three occurrences of D and three occurrences of PD as contiguous substrings, so its doctoral and postdoctoral quotient is 6, which is the maximum doctoral and postdoctoral quotient of a string obtained by replacing each ? in T with P or D.", "input: P?P? output: PDPD"], "Pid": "p02664", "ProblemText": "Task Description: Problem Statement For a string S consisting of the uppercase English letters P and D, let the doctoral and postdoctoral quotient of S be the total number of occurrences of D and PD in S as contiguous substrings. For example, if S = PPDDP, it contains two occurrences of D and one occurrence of PD as contiguous substrings, so the doctoral and postdoctoral quotient of S is 3.\nWe have a string T consisting of P, D, and ? .\nAmong the strings that can be obtained by replacing each ? in T with P or D, find one with the maximum possible doctoral and postdoctoral quotient.\nTask Constraint: 1 <= |T| <= 2 * 10^5\nT consists of P, D, and ?.\nTask Input: Input is given from Standard Input in the following format:\nT\nTask Output: Print one string with the maximum possible doctoral and postdoctoral quotient among the strings that can be obtained by replacing each ? in T with P or D.\nIf there are multiple such strings, you may print any of them.\nTask Samples: input: PD?D??P output: PDPDPDP\n\nThis string contains three occurrences of D and three occurrences of PD as contiguous substrings, so its doctoral and postdoctoral quotient is 6, which is the maximum doctoral and postdoctoral quotient of a string obtained by replacing each ? in T with P or D.\ninput: P?P? output: PDPD\n\n" }, { "title": "", "content": "Problem Statement Given is an integer sequence of length N+1: A_0, A_1, A_2, \\ldots, A_N. Is there a binary tree of depth N such that, for each d = 0,1, \\ldots, N, there are exactly A_d leaves at depth d? If such a tree exists, print the maximum possible number of vertices in such a tree; otherwise, print -1. note: Notes\nA binary tree is a rooted tree such that each vertex has at most two direct children.\nA leaf in a binary tree is a vertex with zero children.\nThe depth of a vertex v in a binary tree is the distance from the tree's root to v. (The root has the depth of 0. )\nThe depth of a binary tree is the maximum depth of a vertex in the tree.", "constraint": "0 <= N <= 10^5\n0 <= A_i <= 10^{8} (0 <= i <= N)\nA_N >= 1\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_0 A_1 A_2 \\cdots A_N", "output": "Print the answer as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 1 1 2 output: 7\n\nBelow is the tree with the maximum possible number of vertices. It has seven vertices, so we should print 7.", "input: 4\n0 0 1 0 2 output: 10", "input: 2\n0 3 1 output: -1", "input: 1\n1 1 output: -1", "input: 10\n0 0 1 1 2 3 5 8 13 21 34 output: 264"], "Pid": "p02665", "ProblemText": "Task Description: Problem Statement Given is an integer sequence of length N+1: A_0, A_1, A_2, \\ldots, A_N. Is there a binary tree of depth N such that, for each d = 0,1, \\ldots, N, there are exactly A_d leaves at depth d? If such a tree exists, print the maximum possible number of vertices in such a tree; otherwise, print -1. note: Notes\nA binary tree is a rooted tree such that each vertex has at most two direct children.\nA leaf in a binary tree is a vertex with zero children.\nThe depth of a vertex v in a binary tree is the distance from the tree's root to v. (The root has the depth of 0. )\nThe depth of a binary tree is the maximum depth of a vertex in the tree.\nTask Constraint: 0 <= N <= 10^5\n0 <= A_i <= 10^{8} (0 <= i <= N)\nA_N >= 1\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_0 A_1 A_2 \\cdots A_N\nTask Output: Print the answer as an integer.\nTask Samples: input: 3\n0 1 1 2 output: 7\n\nBelow is the tree with the maximum possible number of vertices. It has seven vertices, so we should print 7.\ninput: 4\n0 0 1 0 2 output: 10\ninput: 2\n0 3 1 output: -1\ninput: 1\n1 1 output: -1\ninput: 10\n0 0 1 1 2 3 5 8 13 21 34 output: 264\n\n" }, { "title": "", "content": "Problem Statement There are N towns numbered 1,2, \\cdots, N.\nSome roads are planned to be built so that each of them connects two distinct towns bidirectionally. Currently, there are no roads connecting towns.\nIn the planning of construction, each town chooses one town different from itself and requests the following: roads are built so that the chosen town is reachable from itself using one or more roads.\nThese requests from the towns are represented by an array P_1, P_2, \\cdots, P_N. If P_i = -1, it means that Town i has not chosen the request; if 1 <= P_i <= N, it means that Town i has chosen Town P_i.\nLet K be the number of towns i such that P_i = -1. There are (N-1)^K ways in which the towns can make the requests. For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo (10^9+7).", "constraint": "2 <= N <= 5000\nP_i = -1 or 1 <= P_i <= N.\nP_i \\neq i\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nP_1 P_2 \\cdots P_N", "output": "For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 1 -1 3 output: 8\n\nThere are three ways to make requests, as follows:\n\nChoose P_1 = 2, P_2 = 1, P_3 = 1, P_4 = 3. In this case, at least three roads - for example, (1,2),(1,3),(3,4) - are needed to meet the requests.\nChoose P_1 = 2, P_2 = 1, P_3 = 2, P_4 = 3. In this case, at least three roads - for example, (1,2),(1,3),(3,4) - are needed to meet the requests.\nChoose P_1 = 2, P_2 = 1, P_3 = 4, P_4 = 3. In this case, at least two roads - for example, (1,2),(3,4) - are needed to meet the requests.\n\nNote that it is not mandatory to connect Town i and Town P_i directly.\nThe sum of the above numbers is 8.", "input: 2\n2 1 output: 1\n\nThere may be just one fixed way to make requests.", "input: 10\n2 6 9 -1 6 9 -1 -1 -1 -1 output: 527841"], "Pid": "p02666", "ProblemText": "Task Description: Problem Statement There are N towns numbered 1,2, \\cdots, N.\nSome roads are planned to be built so that each of them connects two distinct towns bidirectionally. Currently, there are no roads connecting towns.\nIn the planning of construction, each town chooses one town different from itself and requests the following: roads are built so that the chosen town is reachable from itself using one or more roads.\nThese requests from the towns are represented by an array P_1, P_2, \\cdots, P_N. If P_i = -1, it means that Town i has not chosen the request; if 1 <= P_i <= N, it means that Town i has chosen Town P_i.\nLet K be the number of towns i such that P_i = -1. There are (N-1)^K ways in which the towns can make the requests. For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo (10^9+7).\nTask Constraint: 2 <= N <= 5000\nP_i = -1 or 1 <= P_i <= N.\nP_i \\neq i\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nP_1 P_2 \\cdots P_N\nTask Output: For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo (10^9+7).\nTask Samples: input: 4\n2 1 -1 3 output: 8\n\nThere are three ways to make requests, as follows:\n\nChoose P_1 = 2, P_2 = 1, P_3 = 1, P_4 = 3. In this case, at least three roads - for example, (1,2),(1,3),(3,4) - are needed to meet the requests.\nChoose P_1 = 2, P_2 = 1, P_3 = 2, P_4 = 3. In this case, at least three roads - for example, (1,2),(1,3),(3,4) - are needed to meet the requests.\nChoose P_1 = 2, P_2 = 1, P_3 = 4, P_4 = 3. In this case, at least two roads - for example, (1,2),(3,4) - are needed to meet the requests.\n\nNote that it is not mandatory to connect Town i and Town P_i directly.\nThe sum of the above numbers is 8.\ninput: 2\n2 1 output: 1\n\nThere may be just one fixed way to make requests.\ninput: 10\n2 6 9 -1 6 9 -1 -1 -1 -1 output: 527841\n\n" }, { "title": "", "content": "Problem Statement Takahashi has an empty string S and a variable x whose initial value is 0.\nAlso, we have a string T consisting of 0 and 1.\nNow, Takahashi will do the operation with the following two steps |T| times.\n\nInsert a 0 or a 1 at any position of S of his choice.\nThen, increment x by the sum of the digits in the odd positions (first, third, fifth, . . . ) of S. For example, if S is 01101, the digits in the odd positions are 0,1,1 from left to right, so x is incremented by 2.\n\nPrint the maximum possible final value of x in a sequence of operations such that S equals T in the end.", "constraint": "1 <= |T| <= 2 * 10^5\nT consists of 0 and 1.", "input": "Input is given from Standard Input in the following format:\nT", "output": "Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1101 output: 5\n\nBelow is one sequence of operations that maximizes the final value of x to 5.\n\nInsert a 1 at the beginning of S. S becomes 1, and x is incremented by 1.\nInsert a 0 to the immediate right of the first character of S. S becomes 10, and x is incremented by 1.\nInsert a 1 to the immediate right of the second character of S. S becomes 101, and x is incremented by 2.\nInsert a 1 at the beginning of S. S becomes 1101, and x is incremented by 1.", "input: 0111101101 output: 26"], "Pid": "p02667", "ProblemText": "Task Description: Problem Statement Takahashi has an empty string S and a variable x whose initial value is 0.\nAlso, we have a string T consisting of 0 and 1.\nNow, Takahashi will do the operation with the following two steps |T| times.\n\nInsert a 0 or a 1 at any position of S of his choice.\nThen, increment x by the sum of the digits in the odd positions (first, third, fifth, . . . ) of S. For example, if S is 01101, the digits in the odd positions are 0,1,1 from left to right, so x is incremented by 2.\n\nPrint the maximum possible final value of x in a sequence of operations such that S equals T in the end.\nTask Constraint: 1 <= |T| <= 2 * 10^5\nT consists of 0 and 1.\nTask Input: Input is given from Standard Input in the following format:\nT\nTask Output: Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.\nTask Samples: input: 1101 output: 5\n\nBelow is one sequence of operations that maximizes the final value of x to 5.\n\nInsert a 1 at the beginning of S. S becomes 1, and x is incremented by 1.\nInsert a 0 to the immediate right of the first character of S. S becomes 10, and x is incremented by 1.\nInsert a 1 to the immediate right of the second character of S. S becomes 101, and x is incremented by 2.\nInsert a 1 at the beginning of S. S becomes 1101, and x is incremented by 1.\ninput: 0111101101 output: 26\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Snuke came up with a game that uses a number sequence, as follows:\nPrepare a sequence of length M consisting of integers between 0 and 2^N-1 (inclusive): a = a_1, a_2, \\ldots, a_M.\nSnuke first does the operation below as many times as he likes:\n\nChoose a positive integer d, and for each i (1 <= i <= M), in binary, set the d-th least significant bit of a_i to 0. (Here the least significant bit is considered the 1-st least significant bit. )\n\nAfter Snuke finishes doing operations, Takahashi tries to sort a in ascending order by doing the operation below some number of times. Here a is said to be in ascending order when a_i <= a_{i + 1} for all i (1 <= i <= M - 1).\n\nChoose two adjacent elements of a: a_i and a_{i + 1}. If, in binary, these numbers differ in exactly one bit, swap a_i and a_{i + 1}.\n\nThere are 2^{NM} different sequences of length M consisting of integers between 0 and 2^N-1 that can be used in the game.\nHow many among them have the following property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations? Find the count modulo (10^9 + 7).", "constraint": "All values in input are integers.\n1 <= N <= 5000\n2 <= M <= 5000", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number, modulo (10^9 + 7), of sequences with the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5 output: 352\n\nConsider the case a = 1,3,1,3,1 for example.\n\nWhen the least significant bit of each element of a is set to 0, a = 0,2,0,2,0;\nWhen the second least significant bit of each element of a is set to 0, a = 1,1,1,1,1;\nWhen the least two significant bits of each element of a are set to 0, a = 0,0,0,0,0.\n\nIn all of the cases above and the case when Snuke does no operation to change a, we can sort the sequence by repeatedly swapping adjacent elements that differ in exactly one bit.\nThus, this sequence has the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.", "input: 2020 530 output: 823277409"], "Pid": "p02668", "ProblemText": "Task Description: Problem Statement Takahashi and Snuke came up with a game that uses a number sequence, as follows:\nPrepare a sequence of length M consisting of integers between 0 and 2^N-1 (inclusive): a = a_1, a_2, \\ldots, a_M.\nSnuke first does the operation below as many times as he likes:\n\nChoose a positive integer d, and for each i (1 <= i <= M), in binary, set the d-th least significant bit of a_i to 0. (Here the least significant bit is considered the 1-st least significant bit. )\n\nAfter Snuke finishes doing operations, Takahashi tries to sort a in ascending order by doing the operation below some number of times. Here a is said to be in ascending order when a_i <= a_{i + 1} for all i (1 <= i <= M - 1).\n\nChoose two adjacent elements of a: a_i and a_{i + 1}. If, in binary, these numbers differ in exactly one bit, swap a_i and a_{i + 1}.\n\nThere are 2^{NM} different sequences of length M consisting of integers between 0 and 2^N-1 that can be used in the game.\nHow many among them have the following property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations? Find the count modulo (10^9 + 7).\nTask Constraint: All values in input are integers.\n1 <= N <= 5000\n2 <= M <= 5000\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number, modulo (10^9 + 7), of sequences with the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.\nTask Samples: input: 2 5 output: 352\n\nConsider the case a = 1,3,1,3,1 for example.\n\nWhen the least significant bit of each element of a is set to 0, a = 0,2,0,2,0;\nWhen the second least significant bit of each element of a is set to 0, a = 1,1,1,1,1;\nWhen the least two significant bits of each element of a are set to 0, a = 0,0,0,0,0.\n\nIn all of the cases above and the case when Snuke does no operation to change a, we can sort the sequence by repeatedly swapping adjacent elements that differ in exactly one bit.\nThus, this sequence has the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.\ninput: 2020 530 output: 823277409\n\n" }, { "title": "", "content": "Problem Statement You start with the number 0 and you want to reach the number N.\nYou can change the number, paying a certain amount of coins, with the following operations:\n\nMultiply the number by 2, paying A coins.\nMultiply the number by 3, paying B coins.\nMultiply the number by 5, paying C coins.\nIncrease or decrease the number by 1, paying D coins.\n\nYou can perform these operations in arbitrary order and an arbitrary number of times.\nWhat is the minimum number of coins you need to reach N?\nYou have to solve T testcases.", "constraint": "1 <= T <= 10\n1 <= N <= 10^{18}\n1 <= A, B, C, D <= 10^9\nAll numbers N, A, B, C, D are integers.", "input": "Input The input is given from Standard Input. The first line of the input is\nT\n\nThen, T lines follow describing the T testcases.\nEach of the T lines has the format\nN A B C D", "output": "For each testcase, print the answer on Standard Output followed by a newline.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n11 1 2 4 8\n11 1 2 2 8\n32 10 8 5 4\n29384293847243 454353412 332423423 934923490 1\n900000000000000000 332423423 454353412 934923490 987654321 output: 20\n19\n26\n3821859835\n23441258666\n\nFor the first testcase, a sequence of moves that achieves the minimum cost of 20 is:\n\nInitially x = 0.\nPay 8 to increase by 1 (x = 1).\nPay 1 to multiply by 2 (x = 2).\nPay 1 to multiply by 2 (x = 4).\nPay 2 to multiply by 3 (x = 12).\nPay 8 to decrease by 1 (x = 11).\n\nFor the second testcase, a sequence of moves that achieves the minimum cost of 19 is:\n\nInitially x = 0.\nPay 8 to increase by 1 (x = 1).\nPay 1 to multiply by 2 (x = 2).\nPay 2 to multiply by 5 (x = 10).\nPay 8 to increase by 1 (x = 11)."], "Pid": "p02669", "ProblemText": "Task Description: Problem Statement You start with the number 0 and you want to reach the number N.\nYou can change the number, paying a certain amount of coins, with the following operations:\n\nMultiply the number by 2, paying A coins.\nMultiply the number by 3, paying B coins.\nMultiply the number by 5, paying C coins.\nIncrease or decrease the number by 1, paying D coins.\n\nYou can perform these operations in arbitrary order and an arbitrary number of times.\nWhat is the minimum number of coins you need to reach N?\nYou have to solve T testcases.\nTask Constraint: 1 <= T <= 10\n1 <= N <= 10^{18}\n1 <= A, B, C, D <= 10^9\nAll numbers N, A, B, C, D are integers.\nTask Input: Input The input is given from Standard Input. The first line of the input is\nT\n\nThen, T lines follow describing the T testcases.\nEach of the T lines has the format\nN A B C D\nTask Output: For each testcase, print the answer on Standard Output followed by a newline.\nTask Samples: input: 5\n11 1 2 4 8\n11 1 2 2 8\n32 10 8 5 4\n29384293847243 454353412 332423423 934923490 1\n900000000000000000 332423423 454353412 934923490 987654321 output: 20\n19\n26\n3821859835\n23441258666\n\nFor the first testcase, a sequence of moves that achieves the minimum cost of 20 is:\n\nInitially x = 0.\nPay 8 to increase by 1 (x = 1).\nPay 1 to multiply by 2 (x = 2).\nPay 1 to multiply by 2 (x = 4).\nPay 2 to multiply by 3 (x = 12).\nPay 8 to decrease by 1 (x = 11).\n\nFor the second testcase, a sequence of moves that achieves the minimum cost of 19 is:\n\nInitially x = 0.\nPay 8 to increase by 1 (x = 1).\nPay 1 to multiply by 2 (x = 2).\nPay 2 to multiply by 5 (x = 10).\nPay 8 to increase by 1 (x = 11).\n\n" }, { "title": "", "content": "Problem Statement Tonight, in your favourite cinema they are giving the movie Joker and all seats are occupied. In the cinema there are N rows with N seats each, forming an N* N square. We denote with 1,2, \\dots, N the viewers in the first row (from left to right); with N+1, \\dots, 2N the viewers in the second row (from left to right); and so on until the last row, whose viewers are denoted by N^2-N+1, \\dots, N^2.\nAt the end of the movie, the viewers go out of the cinema in a certain order: the i-th viewer leaving her seat is the one denoted by the number P_i. The viewer P_{i+1} waits until viewer P_i has left the cinema before leaving her seat.\nTo exit from the cinema, a viewer must move from seat to seat until she exits the square of seats (any side of the square is a valid exit). A viewer can move from a seat to one of its 4 adjacent seats (same row or same column).\nWhile leaving the cinema, it might be that a certain viewer x goes through a seat currently occupied by viewer y; in that case viewer y will hate viewer x forever. Each viewer chooses the way that minimizes the number of viewers that will hate her forever.\nCompute the number of pairs of viewers (x, y) such that y will hate x forever.", "constraint": "2 <= N <= 500\nThe sequence P_1, P_2, \\dots, P_{N^2} is a permutation of \\{1,2, \\dots, N^2\\}.", "input": "Input The input is given from Standard Input in the format\nN\nP_1 P_2 \\cdots P_{N^2}", "output": "If ans is the number of pairs of viewers described in the statement, you should print on Standard Output\nans", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 3 7 9 5 4 8 6 2 output: 1\n\nBefore the end of the movie, the viewers are arranged in the cinema as follows:\n1 2 3\n4 5 6\n7 8 9\n\nThe first four viewers leaving the cinema (1,3,7,9) can leave the cinema without going through any seat, so they will not be hated by anybody.\nThen, viewer 5 must go through one of the seats where viewers 2,4,6,8 are currently seated while leaving the cinema; hence he will be hated by at least one of those viewers.\nFinally the remaining viewers can leave the cinema (in the order 4,8,6,2) without going through any occupied seat (actually, they can leave the cinema without going through any seat at all).", "input: 4\n6 7 1 4 13 16 10 9 5 11 12 14 15 2 3 8 output: 3", "input: 6\n11 21 35 22 7 36 27 34 8 20 15 13 16 1 24 3 2 17 26 9 18 32 31 23 19 14 4 25 10 29 28 33 12 6 5 30 output: 11"], "Pid": "p02670", "ProblemText": "Task Description: Problem Statement Tonight, in your favourite cinema they are giving the movie Joker and all seats are occupied. In the cinema there are N rows with N seats each, forming an N* N square. We denote with 1,2, \\dots, N the viewers in the first row (from left to right); with N+1, \\dots, 2N the viewers in the second row (from left to right); and so on until the last row, whose viewers are denoted by N^2-N+1, \\dots, N^2.\nAt the end of the movie, the viewers go out of the cinema in a certain order: the i-th viewer leaving her seat is the one denoted by the number P_i. The viewer P_{i+1} waits until viewer P_i has left the cinema before leaving her seat.\nTo exit from the cinema, a viewer must move from seat to seat until she exits the square of seats (any side of the square is a valid exit). A viewer can move from a seat to one of its 4 adjacent seats (same row or same column).\nWhile leaving the cinema, it might be that a certain viewer x goes through a seat currently occupied by viewer y; in that case viewer y will hate viewer x forever. Each viewer chooses the way that minimizes the number of viewers that will hate her forever.\nCompute the number of pairs of viewers (x, y) such that y will hate x forever.\nTask Constraint: 2 <= N <= 500\nThe sequence P_1, P_2, \\dots, P_{N^2} is a permutation of \\{1,2, \\dots, N^2\\}.\nTask Input: Input The input is given from Standard Input in the format\nN\nP_1 P_2 \\cdots P_{N^2}\nTask Output: If ans is the number of pairs of viewers described in the statement, you should print on Standard Output\nans\nTask Samples: input: 3\n1 3 7 9 5 4 8 6 2 output: 1\n\nBefore the end of the movie, the viewers are arranged in the cinema as follows:\n1 2 3\n4 5 6\n7 8 9\n\nThe first four viewers leaving the cinema (1,3,7,9) can leave the cinema without going through any seat, so they will not be hated by anybody.\nThen, viewer 5 must go through one of the seats where viewers 2,4,6,8 are currently seated while leaving the cinema; hence he will be hated by at least one of those viewers.\nFinally the remaining viewers can leave the cinema (in the order 4,8,6,2) without going through any occupied seat (actually, they can leave the cinema without going through any seat at all).\ninput: 4\n6 7 1 4 13 16 10 9 5 11 12 14 15 2 3 8 output: 3\ninput: 6\n11 21 35 22 7 36 27 34 8 20 15 13 16 1 24 3 2 17 26 9 18 32 31 23 19 14 4 25 10 29 28 33 12 6 5 30 output: 11\n\n" }, { "title": "", "content": "Problem Statement There are 3^N people dancing in circle.\nWe denote with 0,1, \\dots, 3^{N}-1 the positions in the circle, starting from an arbitrary position and going around clockwise. Initially each position in the circle is occupied by one person.\nThe people are going to dance on two kinds of songs: salsa and rumba.\n\nWhen a salsa is played, the person in position i goes to position j, where j is the number obtained replacing all digits 1 with 2 and all digits 2 with 1 when reading i in base 3 (e. g. , the person in position 46 goes to position 65).\nWhen a rumba is played, the person in position i moves to position i+1 (with the identification 3^N = 0).\n\nYou are given a string T=T_1T_2\\cdots T_{|T|} such that T_i=S if the i-th song is a salsa and T_i=R if it is a rumba.\nAfter all the songs have been played, the person that initially was in position i is in position P_i.\nCompute the array P_0, P_1, \\dots, P_{3^N-1}.", "constraint": "1 <= N <= 12\n1 <= |T| <= 200,000\nT contains only the characters S and R.", "input": "Input is given from Standard Input in the following format:\nN\nT", "output": "Output You should print on Standard Output:\nP_0 P_1 \\cdots P_{3^N-1}", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\nSRS output: 2 0 1 \n\nBefore any song is played, the positions are: 0,1,2.\nWhen we say \"person i\", we mean \"the person that was initially in position i\".\n\nAfter the first salsa, the positions are: 0,2,1.\nAfter the rumba, the positions are: 1,0,2 (so, person 0 is in position 1, person 1 is in position 0 and person 2 is in position 2).\nAfter the second salsa, the positions are 2,0,1 (so, person 0 is in position 2, person 1 is in position 0 and person 2 is in position 1).", "input: 2\nRRSRSSSSR output: 3 8 1 0 5 7 6 2 4", "input: 3\nSRSRRSRRRSRRRR output: 23 9 22 8 3 7 20 24 19 5 18 4 17 12 16 2 6 1 14 0 13 26 21 25 11 15 10"], "Pid": "p02671", "ProblemText": "Task Description: Problem Statement There are 3^N people dancing in circle.\nWe denote with 0,1, \\dots, 3^{N}-1 the positions in the circle, starting from an arbitrary position and going around clockwise. Initially each position in the circle is occupied by one person.\nThe people are going to dance on two kinds of songs: salsa and rumba.\n\nWhen a salsa is played, the person in position i goes to position j, where j is the number obtained replacing all digits 1 with 2 and all digits 2 with 1 when reading i in base 3 (e. g. , the person in position 46 goes to position 65).\nWhen a rumba is played, the person in position i moves to position i+1 (with the identification 3^N = 0).\n\nYou are given a string T=T_1T_2\\cdots T_{|T|} such that T_i=S if the i-th song is a salsa and T_i=R if it is a rumba.\nAfter all the songs have been played, the person that initially was in position i is in position P_i.\nCompute the array P_0, P_1, \\dots, P_{3^N-1}.\nTask Constraint: 1 <= N <= 12\n1 <= |T| <= 200,000\nT contains only the characters S and R.\nTask Input: Input is given from Standard Input in the following format:\nN\nT\nTask Output: Output You should print on Standard Output:\nP_0 P_1 \\cdots P_{3^N-1}\nTask Samples: input: 1\nSRS output: 2 0 1 \n\nBefore any song is played, the positions are: 0,1,2.\nWhen we say \"person i\", we mean \"the person that was initially in position i\".\n\nAfter the first salsa, the positions are: 0,2,1.\nAfter the rumba, the positions are: 1,0,2 (so, person 0 is in position 1, person 1 is in position 0 and person 2 is in position 2).\nAfter the second salsa, the positions are 2,0,1 (so, person 0 is in position 2, person 1 is in position 0 and person 2 is in position 1).\ninput: 2\nRRSRSSSSR output: 3 8 1 0 5 7 6 2 4\ninput: 3\nSRSRRSRRRSRRRR output: 23 9 22 8 3 7 20 24 19 5 18 4 17 12 16 2 6 1 14 0 13 26 21 25 11 15 10\n\n" }, { "title": "", "content": "Problem Statement This is an interactive task.\nYou have to guess a secret password S.\nA password is a nonempty string whose length is at most L.\nThe characters of a password can be lowercase and uppercase english letters (a, b, . . . , z, A, B, . . . , Z) and digits (0,1, . . . , 9).\nIn order to guess the secret password S you can ask queries.\nA query is made of a valid password T, the answer to such query is the edit distance between S and T (the operations considered for the edit distance are: removal, insertion, substitution).\nYou can ask at most Q queries.\nNote: For a definition of edit distance (with operations: removal, insertion, substitution), see this wikipedia page. interaction: Interaction To ask a query, print on Standard Output (with a newline at the end)\n? T\n\nThe string T must be a valid password.\nThe answer ans to each query shall be read from Standard Input in the form:\nans\n\nAs soon as you have determined the hidden password S, you should print on Standard Output (with a newline at the end)\n! S\n\nand terminate your program. judgement: Judgement\nAfter each output, you must flush Standard Output. Otherwise you may get TLE.\nAfter you print (your guess of) the hidden password, the program must be terminated immediately. Otherwise, the behavior of the judge is undefined.\nIf the password you have determined is wrong, you will get WA.\nIf you ask a malformed query (for example because the string is not a valid password, or you forget to put ? ) or if your program crashes or if you ask more than Q queries, the behavior of the judge is undefined (it does not necessarily give WA).", "constraint": "L = 128\nQ = 850\nThe secret password S is chosen before the beginning of the interaction.", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p02672", "ProblemText": "Task Description: Problem Statement This is an interactive task.\nYou have to guess a secret password S.\nA password is a nonempty string whose length is at most L.\nThe characters of a password can be lowercase and uppercase english letters (a, b, . . . , z, A, B, . . . , Z) and digits (0,1, . . . , 9).\nIn order to guess the secret password S you can ask queries.\nA query is made of a valid password T, the answer to such query is the edit distance between S and T (the operations considered for the edit distance are: removal, insertion, substitution).\nYou can ask at most Q queries.\nNote: For a definition of edit distance (with operations: removal, insertion, substitution), see this wikipedia page. interaction: Interaction To ask a query, print on Standard Output (with a newline at the end)\n? T\n\nThe string T must be a valid password.\nThe answer ans to each query shall be read from Standard Input in the form:\nans\n\nAs soon as you have determined the hidden password S, you should print on Standard Output (with a newline at the end)\n! S\n\nand terminate your program. judgement: Judgement\nAfter each output, you must flush Standard Output. Otherwise you may get TLE.\nAfter you print (your guess of) the hidden password, the program must be terminated immediately. Otherwise, the behavior of the judge is undefined.\nIf the password you have determined is wrong, you will get WA.\nIf you ask a malformed query (for example because the string is not a valid password, or you forget to put ? ) or if your program crashes or if you ask more than Q queries, the behavior of the judge is undefined (it does not necessarily give WA).\nTask Constraint: L = 128\nQ = 850\nThe secret password S is chosen before the beginning of the interaction.\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement You are playing a game and your goal is to maximize your expected gain.\nAt the beginning of the game, a pawn is put, uniformly at random, at a position p\\in\\{1,2, \\dots, N\\}. The N positions are arranged on a circle (so that 1 is between N and 2).\nThe game consists of turns. At each turn you can either end the game, and get A_p dollars (where p is the current position of the pawn), or pay B_p dollar to keep playing.\nIf you decide to keep playing, the pawn is randomly moved to one of the two adjacent positions p-1, p+1 (with the identifications 0 = N and N+1=1).\nWhat is the expected gain of an optimal strategy?\nNote: The \"expected gain of an optimal strategy\" shall be defined as the supremum of the expected gain among all strategies such that the game ends in a finite number of turns.", "constraint": "2 <= N <= 200,000\n0 <= A_p <= 10^{12} for any p = 1,\\ldots, N\n0 <= B_p <= 100 for any p = 1, \\ldots, N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_N\nB_1 B_2 \\cdots B_N", "output": "Print a single real number, the expected gain of an optimal strategy. \nYour answer will be considered correct if its relative or absolute error does not exceed 10^{-10}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n4 2 6 3 5\n1 1 1 1 1 output: 4.700000000000", "input: 4\n100 0 100 0\n0 100 0 100 output: 50.000000000000", "input: 14\n4839 5400 6231 5800 6001 5200 6350 7133 7986 8012 7537 7013 6477 5912\n34 54 61 32 52 61 21 43 65 12 45 21 1 4 output: 7047.142857142857", "input: 10\n470606482521 533212137322 116718867454 746976621474 457112271419 815899162072 641324977314 88281100571 9231169966 455007126951\n26 83 30 59 100 88 84 91 54 61 output: 815899161079.400024414062"], "Pid": "p02673", "ProblemText": "Task Description: Problem Statement You are playing a game and your goal is to maximize your expected gain.\nAt the beginning of the game, a pawn is put, uniformly at random, at a position p\\in\\{1,2, \\dots, N\\}. The N positions are arranged on a circle (so that 1 is between N and 2).\nThe game consists of turns. At each turn you can either end the game, and get A_p dollars (where p is the current position of the pawn), or pay B_p dollar to keep playing.\nIf you decide to keep playing, the pawn is randomly moved to one of the two adjacent positions p-1, p+1 (with the identifications 0 = N and N+1=1).\nWhat is the expected gain of an optimal strategy?\nNote: The \"expected gain of an optimal strategy\" shall be defined as the supremum of the expected gain among all strategies such that the game ends in a finite number of turns.\nTask Constraint: 2 <= N <= 200,000\n0 <= A_p <= 10^{12} for any p = 1,\\ldots, N\n0 <= B_p <= 100 for any p = 1, \\ldots, N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_N\nB_1 B_2 \\cdots B_N\nTask Output: Print a single real number, the expected gain of an optimal strategy. \nYour answer will be considered correct if its relative or absolute error does not exceed 10^{-10}.\nTask Samples: input: 5\n4 2 6 3 5\n1 1 1 1 1 output: 4.700000000000\ninput: 4\n100 0 100 0\n0 100 0 100 output: 50.000000000000\ninput: 14\n4839 5400 6231 5800 6001 5200 6350 7133 7986 8012 7537 7013 6477 5912\n34 54 61 32 52 61 21 43 65 12 45 21 1 4 output: 7047.142857142857\ninput: 10\n470606482521 533212137322 116718867454 746976621474 457112271419 815899162072 641324977314 88281100571 9231169966 455007126951\n26 83 30 59 100 88 84 91 54 61 output: 815899161079.400024414062\n\n" }, { "title": "", "content": "Problem Statement There are N people (with different names) and K clubs. For each club you know the list of members (so you have K unordered lists). Each person can be a member of many clubs (and also 0 clubs) and two different clubs might have exactly the same members.\nThe value of the number K is the minimum possible such that the following property can be true for at least one configuration of clubs.\nIf every person changes her name (maintaining the property that all names are different) and you know the new K lists of members of the clubs (but you don't know which list corresponds to which club), you are sure that you would be able to match the old names with the new ones.\nCount the number of such configurations of clubs (or say that there are more than 1000).\nTwo configurations of clubs that can be obtained one from the other if the N people change their names are considered equal.\nFormal statement:\nA club is a (possibly empty) subset of \\{1, \\dots, N\\} (the subset identifies the members, assuming that the people are indexed by the numbers 1,2, \\dots, N).\nA configuration of clubs is an unordered collection of K clubs (not necessarily distinct).\nGiven a permutation \\sigma(1), \\dots, \\sigma(N) of \\{1, \\dots, N\\} and a configuration of clubs L=\\{C_1, C_2, \\dots, C_K\\}, we denote with \\sigma(L) the configuration of clubs \\{\\sigma(C_1), \\sigma(C_2), \\dots, \\sigma(C_K)\\} (if C is a club, \\sigma(C)=\\{\\sigma(x): \\, x\\in C\\}).\nA configuration of clubs L is name-preserving if for any pair of distinct permutations \\sigma\\not=\\tau, it holds \\sigma(L)\\not=\\tau(L).\nYou have to count the number of name-preserving configurations of clubs with the minimum possible number of clubs (so K is minimum). Two configurations L_1, L_2 such that L_2=\\sigma(L_1) (for some permutation \\sigma) are considered equal.\nIf there are more than 1000 such configurations, print -1.", "constraint": "2 <= N <= 2\\cdot10^{18}", "input": "Input The input is given from Standard Input in the format\nN", "output": "If ans is the number of configurations with the properties described in the statement, you should print on Standard Output\nans\n\nIf there are more than 1000 such configurations, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 1\n\nThe value of K is 1 and the unique name-preserving configuration of clubs is \\{\\{1\\}\\} (the configuration \\{\\{2\\}\\} is considered the same).", "input: 3 output: 1\n\nThe value of K is 2 and the unique (up to permutation) name-preserving configuration of clubs is \\{\\{1\\}, \\{1,2\\}\\}.", "input: 4 output: 7\n\nThe value of K is 3 and the name-preserving configurations of clubs with 3 clubs are:\n\n\\{\\{1\\}, \\{2\\}, \\{1,3\\}\\}\n\\{\\{1\\}, \\{1,2\\}, \\{2,3\\}\\}\n\\{\\{1,2\\}, \\{1,2\\}, \\{1,3\\}\\}\n\\{\\{1\\}, \\{1,2\\}, \\{1,2,3\\}\\}\n\\{\\{1\\}, \\{2,3\\}, \\{1,2,4\\}\\}\n\\{\\{1,2\\}, \\{1,3\\}, \\{1,2,4\\}\n\\{\\{1,2\\}, \\{1,2,3\\}, \\{2,3,4\\}\\}", "input: 13 output: 6", "input: 26 output: -1", "input: 123456789123456789 output: -1"], "Pid": "p02674", "ProblemText": "Task Description: Problem Statement There are N people (with different names) and K clubs. For each club you know the list of members (so you have K unordered lists). Each person can be a member of many clubs (and also 0 clubs) and two different clubs might have exactly the same members.\nThe value of the number K is the minimum possible such that the following property can be true for at least one configuration of clubs.\nIf every person changes her name (maintaining the property that all names are different) and you know the new K lists of members of the clubs (but you don't know which list corresponds to which club), you are sure that you would be able to match the old names with the new ones.\nCount the number of such configurations of clubs (or say that there are more than 1000).\nTwo configurations of clubs that can be obtained one from the other if the N people change their names are considered equal.\nFormal statement:\nA club is a (possibly empty) subset of \\{1, \\dots, N\\} (the subset identifies the members, assuming that the people are indexed by the numbers 1,2, \\dots, N).\nA configuration of clubs is an unordered collection of K clubs (not necessarily distinct).\nGiven a permutation \\sigma(1), \\dots, \\sigma(N) of \\{1, \\dots, N\\} and a configuration of clubs L=\\{C_1, C_2, \\dots, C_K\\}, we denote with \\sigma(L) the configuration of clubs \\{\\sigma(C_1), \\sigma(C_2), \\dots, \\sigma(C_K)\\} (if C is a club, \\sigma(C)=\\{\\sigma(x): \\, x\\in C\\}).\nA configuration of clubs L is name-preserving if for any pair of distinct permutations \\sigma\\not=\\tau, it holds \\sigma(L)\\not=\\tau(L).\nYou have to count the number of name-preserving configurations of clubs with the minimum possible number of clubs (so K is minimum). Two configurations L_1, L_2 such that L_2=\\sigma(L_1) (for some permutation \\sigma) are considered equal.\nIf there are more than 1000 such configurations, print -1.\nTask Constraint: 2 <= N <= 2\\cdot10^{18}\nTask Input: Input The input is given from Standard Input in the format\nN\nTask Output: If ans is the number of configurations with the properties described in the statement, you should print on Standard Output\nans\n\nIf there are more than 1000 such configurations, print -1.\nTask Samples: input: 2 output: 1\n\nThe value of K is 1 and the unique name-preserving configuration of clubs is \\{\\{1\\}\\} (the configuration \\{\\{2\\}\\} is considered the same).\ninput: 3 output: 1\n\nThe value of K is 2 and the unique (up to permutation) name-preserving configuration of clubs is \\{\\{1\\}, \\{1,2\\}\\}.\ninput: 4 output: 7\n\nThe value of K is 3 and the name-preserving configurations of clubs with 3 clubs are:\n\n\\{\\{1\\}, \\{2\\}, \\{1,3\\}\\}\n\\{\\{1\\}, \\{1,2\\}, \\{2,3\\}\\}\n\\{\\{1,2\\}, \\{1,2\\}, \\{1,3\\}\\}\n\\{\\{1\\}, \\{1,2\\}, \\{1,2,3\\}\\}\n\\{\\{1\\}, \\{2,3\\}, \\{1,2,4\\}\\}\n\\{\\{1,2\\}, \\{1,3\\}, \\{1,2,4\\}\n\\{\\{1,2\\}, \\{1,2,3\\}, \\{2,3,4\\}\\}\ninput: 13 output: 6\ninput: 26 output: -1\ninput: 123456789123456789 output: -1\n\n" }, { "title": "", "content": "Problem Statement\nThe cat Snuke wants to play a popular Japanese game called Åt Coder, so Iroha has decided to teach him Japanese.\nWhen counting pencils in Japanese, the counter word \"本\" follows the number. The pronunciation of this word varies depending on the number. Specifically, the pronunciation of \"本\" in the phrase \"N 本\" for a positive integer N not exceeding 999 is as follows:\n\nhon when the digit in the one's place of N is 2,4,5,7, or 9;\npon when the digit in the one's place of N is 0,1,6 or 8;\nbon when the digit in the one's place of N is 3.\n\nGiven N, print the pronunciation of \"本\" in the phrase \"N 本\".", "constraint": "N is a positive integer not exceeding 999.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 16 output: pon\n\nThe digit in the one's place of 16 is 6, so the \"本\" in \"16 本\" is pronounced pon.", "input: 2 output: hon", "input: 183 output: bon"], "Pid": "p02675", "ProblemText": "Task Description: Problem Statement\nThe cat Snuke wants to play a popular Japanese game called Åt Coder, so Iroha has decided to teach him Japanese.\nWhen counting pencils in Japanese, the counter word \"本\" follows the number. The pronunciation of this word varies depending on the number. Specifically, the pronunciation of \"本\" in the phrase \"N 本\" for a positive integer N not exceeding 999 is as follows:\n\nhon when the digit in the one's place of N is 2,4,5,7, or 9;\npon when the digit in the one's place of N is 0,1,6 or 8;\nbon when the digit in the one's place of N is 3.\n\nGiven N, print the pronunciation of \"本\" in the phrase \"N 本\".\nTask Constraint: N is a positive integer not exceeding 999.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 16 output: pon\n\nThe digit in the one's place of 16 is 6, so the \"本\" in \"16 本\" is pronounced pon.\ninput: 2 output: hon\ninput: 183 output: bon\n\n" }, { "title": "", "content": "Problem Statement\nWe have a string S consisting of lowercase English letters.\nIf the length of S is at most K, print S without change.\nIf the length of S exceeds K, extract the first K characters in S, append . . . to the end of them, and print the result.", "constraint": "K is an integer between 1 and 100 (inclusive).\nS is a string consisting of lowercase English letters.\nThe length of S is between 1 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format:\nK\nS", "output": "Print a string as stated in Problem Statement.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\nnikoandsolstice output: nikoand...\n\nnikoandsolstice has a length of 15, which exceeds K=7.\nWe should extract the first 7 characters in this string, append ... to the end of them, and print the result nikoand....", "input: 40\nferelibenterhominesidquodvoluntcredunt output: ferelibenterhominesidquodvoluntcredunt\n\nThe famous quote from Gaius Julius Caesar."], "Pid": "p02676", "ProblemText": "Task Description: Problem Statement\nWe have a string S consisting of lowercase English letters.\nIf the length of S is at most K, print S without change.\nIf the length of S exceeds K, extract the first K characters in S, append . . . to the end of them, and print the result.\nTask Constraint: K is an integer between 1 and 100 (inclusive).\nS is a string consisting of lowercase English letters.\nThe length of S is between 1 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nK\nS\nTask Output: Print a string as stated in Problem Statement.\nTask Samples: input: 7\nnikoandsolstice output: nikoand...\n\nnikoandsolstice has a length of 15, which exceeds K=7.\nWe should extract the first 7 characters in this string, append ... to the end of them, and print the result nikoand....\ninput: 40\nferelibenterhominesidquodvoluntcredunt output: ferelibenterhominesidquodvoluntcredunt\n\nThe famous quote from Gaius Julius Caesar.\n\n" }, { "title": "", "content": "Problem Statement\nConsider an analog clock whose hour and minute hands are A and B centimeters long, respectively.\nAn endpoint of the hour hand and an endpoint of the minute hand are fixed at the same point, around which each hand rotates clockwise at constant angular velocity. It takes the hour and minute hands 12 hours and 1 hour to make one full rotation, respectively.\nAt 0 o'clock, the two hands overlap each other. H hours and M minutes later, what is the distance in centimeters between the unfixed endpoints of the hands?", "constraint": "All values in input are integers.\n1 <= A, B <= 1000\n0 <= H <= 11\n0 <= M <= 59", "input": "Input is given from Standard Input in the following format:\nA B H M", "output": "Print the answer without units. Your output will be accepted when its absolute or relative error from the correct value is at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 9 0 output: 5.00000000000000000000\n\nThe two hands will be in the positions shown in the figure below, so the answer is 5 centimeters.", "input: 3 4 10 40 output: 4.56425719433005567605\n\nThe two hands will be in the positions shown in the figure below. Note that each hand always rotates at constant angular velocity."], "Pid": "p02677", "ProblemText": "Task Description: Problem Statement\nConsider an analog clock whose hour and minute hands are A and B centimeters long, respectively.\nAn endpoint of the hour hand and an endpoint of the minute hand are fixed at the same point, around which each hand rotates clockwise at constant angular velocity. It takes the hour and minute hands 12 hours and 1 hour to make one full rotation, respectively.\nAt 0 o'clock, the two hands overlap each other. H hours and M minutes later, what is the distance in centimeters between the unfixed endpoints of the hands?\nTask Constraint: All values in input are integers.\n1 <= A, B <= 1000\n0 <= H <= 11\n0 <= M <= 59\nTask Input: Input is given from Standard Input in the following format:\nA B H M\nTask Output: Print the answer without units. Your output will be accepted when its absolute or relative error from the correct value is at most 10^{-9}.\nTask Samples: input: 3 4 9 0 output: 5.00000000000000000000\n\nThe two hands will be in the positions shown in the figure below, so the answer is 5 centimeters.\ninput: 3 4 10 40 output: 4.56425719433005567605\n\nThe two hands will be in the positions shown in the figure below. Note that each hand always rotates at constant angular velocity.\n\n" }, { "title": "", "content": "Problem Statement\nThere is a cave.\nThe cave has N rooms and M passages. The rooms are numbered 1 to N, and the passages are numbered 1 to M. Passage i connects Room A_i and Room B_i bidirectionally. One can travel between any two rooms by traversing passages. Room 1 is a special room with an entrance from the outside.\nIt is dark in the cave, so we have decided to place a signpost in each room except Room 1. The signpost in each room will point to one of the rooms directly connected to that room with a passage.\nSince it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room 1.\n\nIf you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room 1 after traversing the minimum number of passages possible.\n\nDetermine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 2 * 10^5\n1 <= A_i, B_i <= N\\ (1 <= i <= M)\nA_i \\neq B_i\\ (1 <= i <= M)\nOne can travel between any two rooms by traversing passages.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_M B_M", "output": "If there is no way to place signposts satisfying the objective, print No.\nOtherwise, print N lines. The first line should contain Yes, and the i-th line (2 <= i <= N) should contain the integer representing the room indicated by the signpost in Room i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n1 2\n2 3\n3 4\n4 2 output: Yes\n1\n2\n2\n\nIf we place the signposts as described in the sample output, the following happens:\n\nStarting in Room 2, you will reach Room 1 after traversing one passage: (2) \\to 1. This is the minimum number of passages possible.\nStarting in Room 3, you will reach Room 1 after traversing two passages: (3) \\to 2 \\to 1. This is the minimum number of passages possible.\nStarting in Room 4, you will reach Room 1 after traversing two passages: (4) \\to 2 \\to 1. This is the minimum number of passages possible.\n\nThus, the objective is satisfied.", "input: 6 9\n3 4\n6 1\n2 4\n5 3\n4 6\n1 5\n6 2\n4 5\n5 6 output: Yes\n6\n5\n5\n1\n1\n\nIf there are multiple solutions, any of them will be accepted."], "Pid": "p02678", "ProblemText": "Task Description: Problem Statement\nThere is a cave.\nThe cave has N rooms and M passages. The rooms are numbered 1 to N, and the passages are numbered 1 to M. Passage i connects Room A_i and Room B_i bidirectionally. One can travel between any two rooms by traversing passages. Room 1 is a special room with an entrance from the outside.\nIt is dark in the cave, so we have decided to place a signpost in each room except Room 1. The signpost in each room will point to one of the rooms directly connected to that room with a passage.\nSince it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room 1.\n\nIf you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room 1 after traversing the minimum number of passages possible.\n\nDetermine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 2 * 10^5\n1 <= A_i, B_i <= N\\ (1 <= i <= M)\nA_i \\neq B_i\\ (1 <= i <= M)\nOne can travel between any two rooms by traversing passages.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_M B_M\nTask Output: If there is no way to place signposts satisfying the objective, print No.\nOtherwise, print N lines. The first line should contain Yes, and the i-th line (2 <= i <= N) should contain the integer representing the room indicated by the signpost in Room i.\nTask Samples: input: 4 4\n1 2\n2 3\n3 4\n4 2 output: Yes\n1\n2\n2\n\nIf we place the signposts as described in the sample output, the following happens:\n\nStarting in Room 2, you will reach Room 1 after traversing one passage: (2) \\to 1. This is the minimum number of passages possible.\nStarting in Room 3, you will reach Room 1 after traversing two passages: (3) \\to 2 \\to 1. This is the minimum number of passages possible.\nStarting in Room 4, you will reach Room 1 after traversing two passages: (4) \\to 2 \\to 1. This is the minimum number of passages possible.\n\nThus, the objective is satisfied.\ninput: 6 9\n3 4\n6 1\n2 4\n5 3\n4 6\n1 5\n6 2\n4 5\n5 6 output: Yes\n6\n5\n5\n1\n1\n\nIf there are multiple solutions, any of them will be accepted.\n\n" }, { "title": "", "content": "Problem Statement\nWe have caught N sardines. The deliciousness and fragrantness of the i-th sardine is A_i and B_i, respectively.\nWe will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time.\nThe i-th and j-th sardines (i \\neq j) are on bad terms if and only if A_i \\cdot A_j + B_i \\cdot B_j = 0.\nIn how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007.", "constraint": "All values in input are integers.\n1 <= N <= 2 * 10^5\n-10^{18} <= A_i, B_i <= 10^{18}", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_N B_N", "output": "Print the count modulo 1000000007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n-1 1\n2 -1 output: 5\n\nThere are five ways to choose the set of sardines, as follows:\n\nThe 1-st\nThe 1-st and 2-nd\nThe 2-nd\nThe 2-nd and 3-rd\nThe 3-rd", "input: 10\n3 2\n3 2\n-1 1\n2 -1\n-3 -9\n-8 12\n7 7\n8 1\n8 2\n8 4 output: 479"], "Pid": "p02679", "ProblemText": "Task Description: Problem Statement\nWe have caught N sardines. The deliciousness and fragrantness of the i-th sardine is A_i and B_i, respectively.\nWe will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time.\nThe i-th and j-th sardines (i \\neq j) are on bad terms if and only if A_i \\cdot A_j + B_i \\cdot B_j = 0.\nIn how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007.\nTask Constraint: All values in input are integers.\n1 <= N <= 2 * 10^5\n-10^{18} <= A_i, B_i <= 10^{18}\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_N B_N\nTask Output: Print the count modulo 1000000007.\nTask Samples: input: 3\n1 2\n-1 1\n2 -1 output: 5\n\nThere are five ways to choose the set of sardines, as follows:\n\nThe 1-st\nThe 1-st and 2-nd\nThe 2-nd\nThe 2-nd and 3-rd\nThe 3-rd\ninput: 10\n3 2\n3 2\n-1 1\n2 -1\n-3 -9\n-8 12\n7 7\n8 1\n8 2\n8 4 output: 479\n\n" }, { "title": "", "content": "Problem Statement\nThere is a grass field that stretches infinitely.\nIn this field, there is a negligibly small cow. Let (x, y) denote the point that is x\\ \\mathrm{cm} south and y\\ \\mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0,0).\nThere are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).\nWhat is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.", "constraint": "All values in input are integers between -10^9 and 10^9 (inclusive).\n1 <= N, M <= 1000\nA_i < B_i\\ (1 <= i <= N)\nE_j < F_j\\ (1 <= j <= M)\nThe point (0,0) does not lie on any of the given segments.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1 C_1\n:\nA_N B_N C_N\nD_1 E_1 F_1\n:\nD_M E_M F_M", "output": "If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in \\mathrm{cm^2}.\n(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite. )", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4 output: 13\n\nThe area of the region the cow can reach is 13\\ \\mathrm{cm^2}.", "input: 6 1\n-3 -1 -2\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4 output: INF\n\nThe area of the region the cow can reach is infinite."], "Pid": "p02680", "ProblemText": "Task Description: Problem Statement\nThere is a grass field that stretches infinitely.\nIn this field, there is a negligibly small cow. Let (x, y) denote the point that is x\\ \\mathrm{cm} south and y\\ \\mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0,0).\nThere are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).\nWhat is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.\nTask Constraint: All values in input are integers between -10^9 and 10^9 (inclusive).\n1 <= N, M <= 1000\nA_i < B_i\\ (1 <= i <= N)\nE_j < F_j\\ (1 <= j <= M)\nThe point (0,0) does not lie on any of the given segments.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1 C_1\n:\nA_N B_N C_N\nD_1 E_1 F_1\n:\nD_M E_M F_M\nTask Output: If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in \\mathrm{cm^2}.\n(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite. )\nTask Samples: input: 5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4 output: 13\n\nThe area of the region the cow can reach is 13\\ \\mathrm{cm^2}.\ninput: 6 1\n-3 -1 -2\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4 output: INF\n\nThe area of the region the cow can reach is infinite.\n\n" }, { "title": "", "content": "Problem Statement Takahashi wants to be a member of some web service.\nHe tried to register himself with the ID S, which turned out to be already used by another user.\nThus, he decides to register using a string obtained by appending one character at the end of S as his ID.\nHe is now trying to register with the ID T. Determine whether this string satisfies the property above.", "constraint": "S and T are strings consisting of lowercase English letters.\n1 <= |S| <= 10\n|T| = |S| + 1", "input": "Input is given from Standard Input in the following format:\nS\nT", "output": "If T satisfies the property in Problem Statement, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: chokudai\nchokudaiz output: Yes\n\nchokudaiz can be obtained by appending z at the end of chokudai.", "input: snuke\nsnekee output: No\n\nsnekee cannot be obtained by appending one character at the end of snuke.", "input: a\naa output: Yes"], "Pid": "p02681", "ProblemText": "Task Description: Problem Statement Takahashi wants to be a member of some web service.\nHe tried to register himself with the ID S, which turned out to be already used by another user.\nThus, he decides to register using a string obtained by appending one character at the end of S as his ID.\nHe is now trying to register with the ID T. Determine whether this string satisfies the property above.\nTask Constraint: S and T are strings consisting of lowercase English letters.\n1 <= |S| <= 10\n|T| = |S| + 1\nTask Input: Input is given from Standard Input in the following format:\nS\nT\nTask Output: If T satisfies the property in Problem Statement, print Yes; otherwise, print No.\nTask Samples: input: chokudai\nchokudaiz output: Yes\n\nchokudaiz can be obtained by appending z at the end of chokudai.\ninput: snuke\nsnekee output: No\n\nsnekee cannot be obtained by appending one character at the end of snuke.\ninput: a\naa output: Yes\n\n" }, { "title": "", "content": "Problem Statement We have A cards, each of which has an integer 1 written on it. Similarly, we also have B cards with 0s and C cards with -1s.\nWe will pick up K among these cards. What is the maximum possible sum of the numbers written on the cards chosen?", "constraint": "All values in input are integers.\n0 <= A, B, C\n1 <= K <= A + B + C <= 2 * 10^9", "input": "Input is given from Standard Input in the following format:\nA B C K", "output": "Print the maximum possible sum of the numbers written on the cards chosen.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 1 3 output: 2\n\nConsider picking up two cards with 1s and one card with a 0.\nIn this case, the sum of the numbers written on the cards is 2, which is the maximum possible value.", "input: 1 2 3 4 output: 0", "input: 2000000000 0 0 2000000000 output: 2000000000"], "Pid": "p02682", "ProblemText": "Task Description: Problem Statement We have A cards, each of which has an integer 1 written on it. Similarly, we also have B cards with 0s and C cards with -1s.\nWe will pick up K among these cards. What is the maximum possible sum of the numbers written on the cards chosen?\nTask Constraint: All values in input are integers.\n0 <= A, B, C\n1 <= K <= A + B + C <= 2 * 10^9\nTask Input: Input is given from Standard Input in the following format:\nA B C K\nTask Output: Print the maximum possible sum of the numbers written on the cards chosen.\nTask Samples: input: 2 1 1 3 output: 2\n\nConsider picking up two cards with 1s and one card with a 0.\nIn this case, the sum of the numbers written on the cards is 2, which is the maximum possible value.\ninput: 1 2 3 4 output: 0\ninput: 2000000000 0 0 2000000000 output: 2000000000\n\n" }, { "title": "", "content": "problem: Problem Takahashi, who is a novice in competitive programming, wants to learn M algorithms.\nInitially, his understanding level of each of the M algorithms is 0.\nTakahashi is visiting a bookstore, where he finds N books on algorithms.\nThe i-th book (1<= i<= N) is sold for C_i yen (the currency of Japan). If he buys and reads it, his understanding level of the j-th algorithm will increase by A_{i, j} for each j (1<= j<= M).\nThere is no other way to increase the understanding levels of the algorithms.\nTakahashi's objective is to make his understanding levels of all the M algorithms X or higher. Determine whether this objective is achievable. If it is achievable, find the minimum amount of money needed to achieve it.", "constraint": "All values in input are integers.\n1<= N, M<= 12\n1<= X<= 10^5\n1<= C_i <= 10^5\n0<= A_{i, j} <= 10^5", "input": "Input is given from Standard Input in the following format:\nN M X\nC_1 A_{1,1} A_{1,2} \\cdots A_{1, M}\nC_2 A_{2,1} A_{2,2} \\cdots A_{2, M}\n\\vdots\nC_N A_{N, 1} A_{N, 2} \\cdots A_{N, M}", "output": "If the objective is not achievable, print -1; otherwise, print the minimum amount of money needed to achieve it.", "content_img": false, "lang": "", "error": false, "samples": ["input: 3 3 10\n60 2 2 4\n70 8 7 9\n50 2 3 9 output: 120\n\nBuying the second and third books makes his understanding levels of all the algorithms 10 or higher, at the minimum cost possible.", "input: 3 3 10\n100 3 1 4\n100 1 5 9\n100 2 6 5 output: -1\n\nBuying all the books is still not enough to make his understanding levels of all the algorithms 10 or higher.", "input: 8 5 22\n100 3 7 5 3 1\n164 4 5 2 7 8\n334 7 2 7 2 9\n234 4 7 2 8 2\n541 5 4 3 3 6\n235 4 8 6 9 7\n394 3 6 1 6 2\n872 8 4 3 7 2 output: 1067"], "Pid": "p02683", "ProblemText": "Task Description: problem: Problem Takahashi, who is a novice in competitive programming, wants to learn M algorithms.\nInitially, his understanding level of each of the M algorithms is 0.\nTakahashi is visiting a bookstore, where he finds N books on algorithms.\nThe i-th book (1<= i<= N) is sold for C_i yen (the currency of Japan). If he buys and reads it, his understanding level of the j-th algorithm will increase by A_{i, j} for each j (1<= j<= M).\nThere is no other way to increase the understanding levels of the algorithms.\nTakahashi's objective is to make his understanding levels of all the M algorithms X or higher. Determine whether this objective is achievable. If it is achievable, find the minimum amount of money needed to achieve it.\nTask Constraint: All values in input are integers.\n1<= N, M<= 12\n1<= X<= 10^5\n1<= C_i <= 10^5\n0<= A_{i, j} <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nN M X\nC_1 A_{1,1} A_{1,2} \\cdots A_{1, M}\nC_2 A_{2,1} A_{2,2} \\cdots A_{2, M}\n\\vdots\nC_N A_{N, 1} A_{N, 2} \\cdots A_{N, M}\nTask Output: If the objective is not achievable, print -1; otherwise, print the minimum amount of money needed to achieve it.\nTask Samples: input: 3 3 10\n60 2 2 4\n70 8 7 9\n50 2 3 9 output: 120\n\nBuying the second and third books makes his understanding levels of all the algorithms 10 or higher, at the minimum cost possible.\ninput: 3 3 10\n100 3 1 4\n100 1 5 9\n100 2 6 5 output: -1\n\nBuying all the books is still not enough to make his understanding levels of all the algorithms 10 or higher.\ninput: 8 5 22\n100 3 7 5 3 1\n164 4 5 2 7 8\n334 7 2 7 2 9\n234 4 7 2 8 2\n541 5 4 3 3 6\n235 4 8 6 9 7\n394 3 6 1 6 2\n872 8 4 3 7 2 output: 1067\n\n" }, { "title": "", "content": "Problem Statement\nThe Kingdom of Takahashi has N towns, numbered 1 through N.\nThere is one teleporter in each town. The teleporter in Town i (1 <= i <= N) sends you to Town A_i.\nTakahashi, the king, loves the positive integer K. The selfish king wonders what town he will be in if he starts at Town 1 and uses a teleporter exactly K times from there.\nHelp the king by writing a program that answers this question.", "constraint": "2 <= N <= 2 * 10^5\n1 <= A_i <= N\n1 <= K <= 10^{18}", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\dots A_N", "output": "Print the integer representing the town the king will be in if he starts at Town 1 and uses a teleporter exactly K times from there.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n3 2 4 1 output: 4\n\nIf we start at Town 1 and use the teleporter 5 times, our travel will be as follows: 1 \\to 3 \\to 4 \\to 1 \\to 3 \\to 4.", "input: 6 727202214173249351\n6 5 2 5 3 2 output: 2"], "Pid": "p02684", "ProblemText": "Task Description: Problem Statement\nThe Kingdom of Takahashi has N towns, numbered 1 through N.\nThere is one teleporter in each town. The teleporter in Town i (1 <= i <= N) sends you to Town A_i.\nTakahashi, the king, loves the positive integer K. The selfish king wonders what town he will be in if he starts at Town 1 and uses a teleporter exactly K times from there.\nHelp the king by writing a program that answers this question.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= A_i <= N\n1 <= K <= 10^{18}\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\dots A_N\nTask Output: Print the integer representing the town the king will be in if he starts at Town 1 and uses a teleporter exactly K times from there.\nTask Samples: input: 4 5\n3 2 4 1 output: 4\n\nIf we start at Town 1 and use the teleporter 5 times, our travel will be as follows: 1 \\to 3 \\to 4 \\to 1 \\to 3 \\to 4.\ninput: 6 727202214173249351\n6 5 2 5 3 2 output: 2\n\n" }, { "title": "", "content": "Problem Statement There are N blocks arranged in a row. Let us paint these blocks.\nWe will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways.\nFind the number of ways to paint the blocks under the following conditions:\n\nFor each block, use one of the M colors, Color 1 through Color M, to paint it. It is not mandatory to use all the colors.\nThere may be at most K pairs of adjacent blocks that are painted in the same color.\n\nSince the count may be enormous, print it modulo 998244353.", "constraint": "All values in input are integers.\n1 <= N, M <= 2 * 10^5\n0 <= K <= N - 1", "input": "Input is given from Standard Input in the following format:\nN M K", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 1 output: 6\n\nThe following ways to paint the blocks satisfy the conditions: 112,121,122,211,212, and 221. Here, digits represent the colors of the blocks.", "input: 100 100 0 output: 73074801", "input: 60522 114575 7559 output: 479519525"], "Pid": "p02685", "ProblemText": "Task Description: Problem Statement There are N blocks arranged in a row. Let us paint these blocks.\nWe will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways.\nFind the number of ways to paint the blocks under the following conditions:\n\nFor each block, use one of the M colors, Color 1 through Color M, to paint it. It is not mandatory to use all the colors.\nThere may be at most K pairs of adjacent blocks that are painted in the same color.\n\nSince the count may be enormous, print it modulo 998244353.\nTask Constraint: All values in input are integers.\n1 <= N, M <= 2 * 10^5\n0 <= K <= N - 1\nTask Input: Input is given from Standard Input in the following format:\nN M K\nTask Output: Print the answer.\nTask Samples: input: 3 2 1 output: 6\n\nThe following ways to paint the blocks satisfy the conditions: 112,121,122,211,212, and 221. Here, digits represent the colors of the blocks.\ninput: 100 100 0 output: 73074801\ninput: 60522 114575 7559 output: 479519525\n\n" }, { "title": "", "content": "Problem Statement A bracket sequence is a string that is one of the following:\n\nAn empty string;\nThe concatenation of (, A, and ) in this order, for some bracket sequence A ;\nThe concatenation of A and B in this order, for some non-empty bracket sequences A and B /\n\nGiven are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?", "constraint": "1 <= N <= 10^6\nThe total length of the strings S_i is at most 10^6.\nS_i is a non-empty string consisting of ( and ).", "input": "Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N", "output": "If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n)\n(() output: Yes\n\nConcatenating (() and ) in this order forms a bracket sequence.", "input: 2\n)(\n() output: No", "input: 4\n((()))\n((((((\n))))))\n()()() output: Yes", "input: 3\n(((\n)\n) output: No"], "Pid": "p02686", "ProblemText": "Task Description: Problem Statement A bracket sequence is a string that is one of the following:\n\nAn empty string;\nThe concatenation of (, A, and ) in this order, for some bracket sequence A ;\nThe concatenation of A and B in this order, for some non-empty bracket sequences A and B /\n\nGiven are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?\nTask Constraint: 1 <= N <= 10^6\nThe total length of the strings S_i is at most 10^6.\nS_i is a non-empty string consisting of ( and ).\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N\nTask Output: If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.\nTask Samples: input: 2\n)\n(() output: Yes\n\nConcatenating (() and ) in this order forms a bracket sequence.\ninput: 2\n)(\n() output: No\ninput: 4\n((()))\n((((((\n))))))\n()()() output: Yes\ninput: 3\n(((\n)\n) output: No\n\n" }, { "title": "", "content": "Problem Statement At Coder Inc. holds a contest every Saturday.\nThere are two types of contests called ABC and ARC, and just one of them is held at a time.\nThe company holds these two types of contests alternately: an ARC follows an ABC and vice versa.\nGiven a string S representing the type of the contest held last week, print the string representing the type of the contest held this week.", "constraint": "S is ABC or ARC.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the string representing the type of the contest held this week.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ABC output: ARC\n\nThey held an ABC last week, so they will hold an ARC this week."], "Pid": "p02687", "ProblemText": "Task Description: Problem Statement At Coder Inc. holds a contest every Saturday.\nThere are two types of contests called ABC and ARC, and just one of them is held at a time.\nThe company holds these two types of contests alternately: an ARC follows an ABC and vice versa.\nGiven a string S representing the type of the contest held last week, print the string representing the type of the contest held this week.\nTask Constraint: S is ABC or ARC.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the string representing the type of the contest held this week.\nTask Samples: input: ABC output: ARC\n\nThey held an ABC last week, so they will hold an ARC this week.\n\n" }, { "title": "", "content": "Problem Statement N Snukes called Snuke 1, Snuke 2, . . . , Snuke N live in a town.\nThere are K kinds of snacks sold in this town, called Snack 1, Snack 2, . . . , Snack K. The following d_i Snukes have Snack i: Snuke A_{i, 1}, A_{i, 2}, \\cdots, A_{i, {d_i}}.\nTakahashi will walk around this town and make mischief on the Snukes who have no snacks. How many Snukes will fall victim to Takahashi's mischief?", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= K <= 100\n1 <= d_i <= N\n1 <= A_{i, 1} < \\cdots < A_{i, d_i} <= N", "input": "Input is given from Standard Input in the following format:\nN K\nd_1\nA_{1,1} \\cdots A_{1, d_1}\n\\vdots\nd_K\nA_{K, 1} \\cdots A_{K, d_K}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n2\n1 3\n1\n3 output: 1\nSnuke 1 has Snack 1.\nSnuke 2 has no snacks.\nSnuke 3 has Snack 1 and 2.\n\nThus, there will be one victim: Snuke 2.", "input: 3 3\n1\n3\n1\n3\n1\n3 output: 2"], "Pid": "p02688", "ProblemText": "Task Description: Problem Statement N Snukes called Snuke 1, Snuke 2, . . . , Snuke N live in a town.\nThere are K kinds of snacks sold in this town, called Snack 1, Snack 2, . . . , Snack K. The following d_i Snukes have Snack i: Snuke A_{i, 1}, A_{i, 2}, \\cdots, A_{i, {d_i}}.\nTakahashi will walk around this town and make mischief on the Snukes who have no snacks. How many Snukes will fall victim to Takahashi's mischief?\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= K <= 100\n1 <= d_i <= N\n1 <= A_{i, 1} < \\cdots < A_{i, d_i} <= N\nTask Input: Input is given from Standard Input in the following format:\nN K\nd_1\nA_{1,1} \\cdots A_{1, d_1}\n\\vdots\nd_K\nA_{K, 1} \\cdots A_{K, d_K}\nTask Output: Print the answer.\nTask Samples: input: 3 2\n2\n1 3\n1\n3 output: 1\nSnuke 1 has Snack 1.\nSnuke 2 has no snacks.\nSnuke 3 has Snack 1 and 2.\n\nThus, there will be one victim: Snuke 2.\ninput: 3 3\n1\n3\n1\n3\n1\n3 output: 2\n\n" }, { "title": "", "content": "Problem Statement There are N observatories in At Coder Hill, called Obs. 1, Obs. 2, . . . , Obs. N. The elevation of Obs. i is H_i.\nThere are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j.\nObs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road.\nNote that Obs. i is also good when no observatory can be reached from Obs. i using just one road.\nHow many good observatories are there?", "constraint": "2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= H_i <= 10^9\n1 <= A_i,B_i <= N\nA_i \\neq B_i\nMultiple roads may connect the same pair of observatories.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nH_1 H_2 . . . H_N\nA_1 B_1\nA_2 B_2\n:\nA_M B_M", "output": "Print the number of good observatories.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n1 2 3 4\n1 3\n2 3\n2 4 output: 2\n\nFrom Obs. 1, you can reach Obs. 3 using just one road. The elevation of Obs. 1 is not higher than that of Obs. 3, so Obs. 1 is not good.\nFrom Obs. 2, you can reach Obs. 3 and 4 using just one road. The elevation of Obs. 2 is not higher than that of Obs. 3, so Obs. 2 is not good.\nFrom Obs. 3, you can reach Obs. 1 and 2 using just one road. The elevation of Obs. 3 is higher than those of Obs. 1 and 2, so Obs. 3 is good.\nFrom Obs. 4, you can reach Obs. 2 using just one road. The elevation of Obs. 4 is higher than that of Obs. 2, so Obs. 4 is good.\nThus, the good observatories are Obs. 3 and 4, so there are two good observatories.", "input: 6 5\n8 6 9 1 2 1\n1 3\n4 2\n4 3\n4 6\n4 6 output: 3"], "Pid": "p02689", "ProblemText": "Task Description: Problem Statement There are N observatories in At Coder Hill, called Obs. 1, Obs. 2, . . . , Obs. N. The elevation of Obs. i is H_i.\nThere are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j.\nObs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road.\nNote that Obs. i is also good when no observatory can be reached from Obs. i using just one road.\nHow many good observatories are there?\nTask Constraint: 2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= H_i <= 10^9\n1 <= A_i,B_i <= N\nA_i \\neq B_i\nMultiple roads may connect the same pair of observatories.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nH_1 H_2 . . . H_N\nA_1 B_1\nA_2 B_2\n:\nA_M B_M\nTask Output: Print the number of good observatories.\nTask Samples: input: 4 3\n1 2 3 4\n1 3\n2 3\n2 4 output: 2\n\nFrom Obs. 1, you can reach Obs. 3 using just one road. The elevation of Obs. 1 is not higher than that of Obs. 3, so Obs. 1 is not good.\nFrom Obs. 2, you can reach Obs. 3 and 4 using just one road. The elevation of Obs. 2 is not higher than that of Obs. 3, so Obs. 2 is not good.\nFrom Obs. 3, you can reach Obs. 1 and 2 using just one road. The elevation of Obs. 3 is higher than those of Obs. 1 and 2, so Obs. 3 is good.\nFrom Obs. 4, you can reach Obs. 2 using just one road. The elevation of Obs. 4 is higher than that of Obs. 2, so Obs. 4 is good.\nThus, the good observatories are Obs. 3 and 4, so there are two good observatories.\ninput: 6 5\n8 6 9 1 2 1\n1 3\n4 2\n4 3\n4 6\n4 6 output: 3\n\n" }, { "title": "", "content": "Problem Statement Give a pair of integers (A, B) such that A^5-B^5 = X.\nIt is guaranteed that there exists such a pair for the given integer X.", "constraint": "1 <= X <= 10^9\nX is an integer.\nThere exists a pair of integers (A, B) satisfying the condition in Problem Statement.", "input": "Input is given from Standard Input in the following format:\nX", "output": "Print A and B, with space in between.\nIf there are multiple pairs of integers (A, B) satisfying the condition, you may print any of them.\nA B", "content_img": false, "lang": "en", "error": false, "samples": ["input: 33 output: 2 -1\n\nFor A=2 and B=-1, A^5-B^5 = 33.", "input: 1 output: 0 -1"], "Pid": "p02690", "ProblemText": "Task Description: Problem Statement Give a pair of integers (A, B) such that A^5-B^5 = X.\nIt is guaranteed that there exists such a pair for the given integer X.\nTask Constraint: 1 <= X <= 10^9\nX is an integer.\nThere exists a pair of integers (A, B) satisfying the condition in Problem Statement.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: Print A and B, with space in between.\nIf there are multiple pairs of integers (A, B) satisfying the condition, you may print any of them.\nA B\nTask Samples: input: 33 output: 2 -1\n\nFor A=2 and B=-1, A^5-B^5 = 33.\ninput: 1 output: 0 -1\n\n" }, { "title": "", "content": "Problem Statement\nYou are the top spy of At Coder Kingdom. To prevent the stolen secret from being handed to Al Debaran Kingdom, you have sneaked into the party where the transaction happens.\nThere are N attendees in the party, and they are given attendee numbers from 1 through N. The height of Attendee i is A_i.\nAccording to an examination beforehand, you know that a pair of attendees satisfying the condition below will make the transaction.\n\nThe absolute difference of their attendee numbers is equal to the sum of their heights.\n\nThere are \\frac{N(N-1)}{2} ways to choose two from the N attendees and make a pair. Among them, how many satisfy the condition above?\nP. S. : We cannot let you know the secret.", "constraint": "All values in input are integers.\n2 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\\ (1 <= i <= N)", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\dots A_N", "output": "Print the number of pairs satisfying the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n2 3 3 1 3 1 output: 3\nA_1 + A_4 = 3, so the pair of Attendee 1 and 4 satisfy the condition.\nA_2 + A_6 = 4, so the pair of Attendee 2 and 6 satisfy the condition.\nA_4 + A_6 = 2, so the pair of Attendee 4 and 6 satisfy the condition.\n\nNo other pair satisfies the condition, so you should print 3.", "input: 6\n5 2 4 2 8 8 output: 0\n\nNo pair satisfies the condition, so you should print 0.", "input: 32\n3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 output: 22"], "Pid": "p02691", "ProblemText": "Task Description: Problem Statement\nYou are the top spy of At Coder Kingdom. To prevent the stolen secret from being handed to Al Debaran Kingdom, you have sneaked into the party where the transaction happens.\nThere are N attendees in the party, and they are given attendee numbers from 1 through N. The height of Attendee i is A_i.\nAccording to an examination beforehand, you know that a pair of attendees satisfying the condition below will make the transaction.\n\nThe absolute difference of their attendee numbers is equal to the sum of their heights.\n\nThere are \\frac{N(N-1)}{2} ways to choose two from the N attendees and make a pair. Among them, how many satisfy the condition above?\nP. S. : We cannot let you know the secret.\nTask Constraint: All values in input are integers.\n2 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\\ (1 <= i <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\dots A_N\nTask Output: Print the number of pairs satisfying the condition.\nTask Samples: input: 6\n2 3 3 1 3 1 output: 3\nA_1 + A_4 = 3, so the pair of Attendee 1 and 4 satisfy the condition.\nA_2 + A_6 = 4, so the pair of Attendee 2 and 6 satisfy the condition.\nA_4 + A_6 = 2, so the pair of Attendee 4 and 6 satisfy the condition.\n\nNo other pair satisfies the condition, so you should print 3.\ninput: 6\n5 2 4 2 8 8 output: 0\n\nNo pair satisfies the condition, so you should print 0.\ninput: 32\n3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 output: 22\n\n" }, { "title": "", "content": "Problem Statement There is a game that involves three variables, denoted A, B, and C.\nAs the game progresses, there will be N events where you are asked to make a choice.\nEach of these choices is represented by a string s_i. If s_i is AB, you must add 1 to A or B then subtract 1 from the other; if s_i is AC, you must add 1 to A or C then subtract 1 from the other; if s_i is BC, you must add 1 to B or C then subtract 1 from the other.\nAfter each choice, none of A, B, and C should be negative.\nDetermine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices.", "constraint": "1 <= N <= 10^5\n0 <= A,B,C <= 10^9\nN, A, B, C are integers.\ns_i is AB, AC, or BC.", "input": "Input is given from Standard Input in the following format:\nN A B C\ns_1\ns_2\n:\ns_N", "output": "If it is possible to make N choices under the condition, print Yes; otherwise, print No.\nAlso, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (A, B, or C) to which you add 1 in the i-th choice.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 3 0\nAB\nAC output: Yes\nA\nC\n\nYou can successfully make two choices, as follows:\n\nIn the first choice, add 1 to A and subtract 1 from B. A becomes 2, and B becomes 2.\nIn the second choice, add 1 to C and subtract 1 from A. C becomes 1, and A becomes 1.", "input: 3 1 0 0\nAB\nBC\nAB output: No", "input: 1 0 9 0\nAC output: No", "input: 8 6 9 1\nAC\nBC\nAB\nBC\nAC\nBC\nAB\nAB output: Yes\nC\nB\nB\nC\nC\nB\nA\nA"], "Pid": "p02692", "ProblemText": "Task Description: Problem Statement There is a game that involves three variables, denoted A, B, and C.\nAs the game progresses, there will be N events where you are asked to make a choice.\nEach of these choices is represented by a string s_i. If s_i is AB, you must add 1 to A or B then subtract 1 from the other; if s_i is AC, you must add 1 to A or C then subtract 1 from the other; if s_i is BC, you must add 1 to B or C then subtract 1 from the other.\nAfter each choice, none of A, B, and C should be negative.\nDetermine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices.\nTask Constraint: 1 <= N <= 10^5\n0 <= A,B,C <= 10^9\nN, A, B, C are integers.\ns_i is AB, AC, or BC.\nTask Input: Input is given from Standard Input in the following format:\nN A B C\ns_1\ns_2\n:\ns_N\nTask Output: If it is possible to make N choices under the condition, print Yes; otherwise, print No.\nAlso, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (A, B, or C) to which you add 1 in the i-th choice.\nTask Samples: input: 2 1 3 0\nAB\nAC output: Yes\nA\nC\n\nYou can successfully make two choices, as follows:\n\nIn the first choice, add 1 to A and subtract 1 from B. A becomes 2, and B becomes 2.\nIn the second choice, add 1 to C and subtract 1 from A. C becomes 1, and A becomes 1.\ninput: 3 1 0 0\nAB\nBC\nAB output: No\ninput: 1 0 9 0\nAC output: No\ninput: 8 6 9 1\nAC\nBC\nAB\nBC\nAC\nBC\nAB\nAB output: Yes\nC\nB\nB\nC\nC\nB\nA\nA\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi the Jumbo will practice golf.\nHis objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).\nIf he can achieve the objective, print OK; if he cannot, print NG.", "constraint": "All values in input are integers.\n1 <= A <= B <= 1000\n1 <= K <= 1000", "input": "Input is given from Standard Input in the following format:\nK\nA B", "output": "If he can achieve the objective, print OK; if he cannot, print NG.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n500 600 output: OK\n\nAmong the multiples of 7, for example, 567 lies between 500 and 600.", "input: 4\n5 7 output: NG\n\nNo multiple of 4 lies between 5 and 7.", "input: 1\n11 11 output: OK"], "Pid": "p02693", "ProblemText": "Task Description: Problem Statement\nTakahashi the Jumbo will practice golf.\nHis objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).\nIf he can achieve the objective, print OK; if he cannot, print NG.\nTask Constraint: All values in input are integers.\n1 <= A <= B <= 1000\n1 <= K <= 1000\nTask Input: Input is given from Standard Input in the following format:\nK\nA B\nTask Output: If he can achieve the objective, print OK; if he cannot, print NG.\nTask Samples: input: 7\n500 600 output: OK\n\nAmong the multiples of 7, for example, 567 lies between 500 and 600.\ninput: 4\n5 7 output: NG\n\nNo multiple of 4 lies between 5 and 7.\ninput: 1\n11 11 output: OK\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi has a deposit of 100 yen (the currency of Japan) in At Coder Bank.\nThe bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded. )\nAssuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?", "constraint": "101 <= X <= 10^{18} \nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX", "output": "Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 103 output: 3\nThe balance after one year is 101 yen.\nThe balance after two years is 102 yen.\nThe balance after three years is 103 yen.\n\nThus, it takes three years for the balance to reach 103 yen or above.", "input: 1000000000000000000 output: 3760", "input: 1333333333 output: 1706"], "Pid": "p02694", "ProblemText": "Task Description: Problem Statement\nTakahashi has a deposit of 100 yen (the currency of Japan) in At Coder Bank.\nThe bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded. )\nAssuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?\nTask Constraint: 101 <= X <= 10^{18} \nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.\nTask Samples: input: 103 output: 3\nThe balance after one year is 101 yen.\nThe balance after two years is 102 yen.\nThe balance after three years is 103 yen.\n\nThus, it takes three years for the balance to reach 103 yen or above.\ninput: 1000000000000000000 output: 3760\ninput: 1333333333 output: 1706\n\n" }, { "title": "", "content": "Problem Statement Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).\nConsider a sequence A satisfying the following conditions:\n\nA is a sequence of N positive integers.\n1 <= A_1 <= A_2 <= \\cdots <= A_N <= M.\n\nLet us define a score of this sequence as follows:\n\nThe score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0. )\n\nFind the maximum possible score of A.", "constraint": "All values in input are integers.\n2 <= N <= 10\n1 <= M <= 10\n1 <= Q <= 50\n1 <= a_i < b_i <= N ( i = 1,2, ..., Q )\n0 <= c_i <= M - 1 ( i = 1,2, ..., Q )\n(a_i, b_i, c_i) \\neq (a_j, b_j, c_j) (where i \\neq j)\n1 <= d_i <= 10^5 ( i = 1,2, ..., Q )", "input": "Input is given from Standard Input in the following format:\nN M Q\na_1 b_1 c_1 d_1\n:\na_Q b_Q c_Q d_Q", "output": "Print the maximum possible score of A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 3\n1 3 3 100\n1 2 2 10\n2 3 2 10 output: 110\n\nWhen A = \\{1,3,4\\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.", "input: 4 6 10\n2 4 1 86568\n1 4 0 90629\n2 3 0 90310\n3 4 1 29211\n3 4 3 78537\n3 4 2 8580\n1 2 1 96263\n1 4 2 2156\n1 2 0 94325\n1 4 3 94328 output: 357500", "input: 10 10 1\n1 10 9 1 output: 1"], "Pid": "p02695", "ProblemText": "Task Description: Problem Statement Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).\nConsider a sequence A satisfying the following conditions:\n\nA is a sequence of N positive integers.\n1 <= A_1 <= A_2 <= \\cdots <= A_N <= M.\n\nLet us define a score of this sequence as follows:\n\nThe score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0. )\n\nFind the maximum possible score of A.\nTask Constraint: All values in input are integers.\n2 <= N <= 10\n1 <= M <= 10\n1 <= Q <= 50\n1 <= a_i < b_i <= N ( i = 1,2, ..., Q )\n0 <= c_i <= M - 1 ( i = 1,2, ..., Q )\n(a_i, b_i, c_i) \\neq (a_j, b_j, c_j) (where i \\neq j)\n1 <= d_i <= 10^5 ( i = 1,2, ..., Q )\nTask Input: Input is given from Standard Input in the following format:\nN M Q\na_1 b_1 c_1 d_1\n:\na_Q b_Q c_Q d_Q\nTask Output: Print the maximum possible score of A.\nTask Samples: input: 3 4 3\n1 3 3 100\n1 2 2 10\n2 3 2 10 output: 110\n\nWhen A = \\{1,3,4\\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.\ninput: 4 6 10\n2 4 1 86568\n1 4 0 90629\n2 3 0 90310\n3 4 1 29211\n3 4 3 78537\n3 4 2 8580\n1 2 1 96263\n1 4 2 2156\n1 2 0 94325\n1 4 3 94328 output: 357500\ninput: 10 10 1\n1 10 9 1 output: 1\n\n" }, { "title": "", "content": "Problem Statement Given are integers A, B, and N.\nFind the maximum possible value of floor(Ax/B) - A * floor(x/B) for a non-negative integer x not greater than N.\nHere floor(t) denotes the greatest integer not greater than the real number t.", "constraint": "1 <= A <= 10^{6}\n1 <= B <= 10^{12}\n1 <= N <= 10^{12}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B N", "output": "Print the maximum possible value of floor(Ax/B) - A * floor(x/B) for a non-negative integer x not greater than N, as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 7 4 output: 2\n\nWhen x=3, floor(Ax/B)-A*floor(x/B) = floor(15/7) - 5*floor(3/7) = 2. This is the maximum value possible.", "input: 11 10 9 output: 9"], "Pid": "p02696", "ProblemText": "Task Description: Problem Statement Given are integers A, B, and N.\nFind the maximum possible value of floor(Ax/B) - A * floor(x/B) for a non-negative integer x not greater than N.\nHere floor(t) denotes the greatest integer not greater than the real number t.\nTask Constraint: 1 <= A <= 10^{6}\n1 <= B <= 10^{12}\n1 <= N <= 10^{12}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B N\nTask Output: Print the maximum possible value of floor(Ax/B) - A * floor(x/B) for a non-negative integer x not greater than N, as an integer.\nTask Samples: input: 5 7 4 output: 2\n\nWhen x=3, floor(Ax/B)-A*floor(x/B) = floor(15/7) - 5*floor(3/7) = 2. This is the maximum value possible.\ninput: 11 10 9 output: 9\n\n" }, { "title": "", "content": "Problem Statement You are going to hold a competition of one-to-one game called At Coder Janken. (Janken is the Japanese name for Rock-paper-scissors. )\nN players will participate in this competition, and they are given distinct integers from 1 through N.\nThe arena has M playing fields for two players. You need to assign each playing field two distinct integers between 1 and N (inclusive).\nYou cannot assign the same integer to multiple playing fields.\nThe competition consists of N rounds, each of which proceeds as follows:\n\nFor each player, if there is a playing field that is assigned the player's integer, the player goes to that field and fight the other player who comes there.\nThen, each player adds 1 to its integer. If it becomes N+1, change it to 1.\n\nYou want to ensure that no player fights the same opponent more than once during the N rounds.\nPrint an assignment of integers to the playing fields satisfying this condition.\nIt can be proved that such an assignment always exists under the constraints given.", "constraint": "1 <= M\nM * 2 +1 <= N <= 200000", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print M lines in the format below.\nThe i-th line should contain the two integers a_i and b_i assigned to the i-th playing field.\na_1 b_1\na_2 b_2\n:\na_M b_M", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1 output: 2 3\n\nLet us call the four players A, B, C, and D, and assume that they are initially given the integers 1,2,3, and 4, respectively.\nThe 1-st round is fought by B and C, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 2,3,4, and 1, respectively.\nThe 2-nd round is fought by A and B, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 3,4,1, and 2, respectively.\nThe 3-rd round is fought by D and A, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 4,1,2, and 3, respectively.\nThe 4-th round is fought by C and D, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 1,2,3, and 4, respectively.\nNo player fights the same opponent more than once during the four rounds, so this solution will be accepted.", "input: 7 3 output: 1 6\n2 5\n3 4"], "Pid": "p02697", "ProblemText": "Task Description: Problem Statement You are going to hold a competition of one-to-one game called At Coder Janken. (Janken is the Japanese name for Rock-paper-scissors. )\nN players will participate in this competition, and they are given distinct integers from 1 through N.\nThe arena has M playing fields for two players. You need to assign each playing field two distinct integers between 1 and N (inclusive).\nYou cannot assign the same integer to multiple playing fields.\nThe competition consists of N rounds, each of which proceeds as follows:\n\nFor each player, if there is a playing field that is assigned the player's integer, the player goes to that field and fight the other player who comes there.\nThen, each player adds 1 to its integer. If it becomes N+1, change it to 1.\n\nYou want to ensure that no player fights the same opponent more than once during the N rounds.\nPrint an assignment of integers to the playing fields satisfying this condition.\nIt can be proved that such an assignment always exists under the constraints given.\nTask Constraint: 1 <= M\nM * 2 +1 <= N <= 200000\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print M lines in the format below.\nThe i-th line should contain the two integers a_i and b_i assigned to the i-th playing field.\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Samples: input: 4 1 output: 2 3\n\nLet us call the four players A, B, C, and D, and assume that they are initially given the integers 1,2,3, and 4, respectively.\nThe 1-st round is fought by B and C, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 2,3,4, and 1, respectively.\nThe 2-nd round is fought by A and B, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 3,4,1, and 2, respectively.\nThe 3-rd round is fought by D and A, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 4,1,2, and 3, respectively.\nThe 4-th round is fought by C and D, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 1,2,3, and 4, respectively.\nNo player fights the same opponent more than once during the four rounds, so this solution will be accepted.\ninput: 7 3 output: 1 6\n2 5\n3 4\n\n" }, { "title": "", "content": "Problem Statement We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i.\nVertex i has an integer a_i written on it.\nFor every integer k from 1 through N, solve the following problem:\n\nWe will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.\n\nHere, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , . . . , A_{i_M} with the greatest possible value of M such that 1 <= i_1 < i_2 < . . . < i_M <= L and A_{i_1} < A_{i_2} < . . . < A_{i_M}.", "constraint": "2 <= N <= 2 * 10^5\n1 <= a_i <= 10^9\n1 <= u_i , v_i <= N\nu_i \\neq v_i\nThe given graph is a tree.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nu_1 v_1\nu_2 v_2\n:\nu_{N-1} v_{N-1}", "output": "Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\n1 2 5 3 4 6 7 3 2 4\n1 2\n2 3\n3 4\n4 5\n3 6\n6 7\n1 8\n8 9\n9 10 output: 1\n2\n3\n3\n4\n4\n5\n2\n2\n3\n\nFor example, the sequence A obtained from the shortest path from Vertex 1 to Vertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4, A_5, with the length of 4."], "Pid": "p02698", "ProblemText": "Task Description: Problem Statement We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i.\nVertex i has an integer a_i written on it.\nFor every integer k from 1 through N, solve the following problem:\n\nWe will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.\n\nHere, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , . . . , A_{i_M} with the greatest possible value of M such that 1 <= i_1 < i_2 < . . . < i_M <= L and A_{i_1} < A_{i_2} < . . . < A_{i_M}.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= a_i <= 10^9\n1 <= u_i , v_i <= N\nu_i \\neq v_i\nThe given graph is a tree.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nu_1 v_1\nu_2 v_2\n:\nu_{N-1} v_{N-1}\nTask Output: Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.\nTask Samples: input: 10\n1 2 5 3 4 6 7 3 2 4\n1 2\n2 3\n3 4\n4 5\n3 6\n6 7\n1 8\n8 9\n9 10 output: 1\n2\n3\n3\n4\n4\n5\n2\n2\n3\n\nFor example, the sequence A obtained from the shortest path from Vertex 1 to Vertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4, A_5, with the length of 4.\n\n" }, { "title": "", "content": "Problem Statement There are S sheep and W wolves.\nIf the number of wolves is greater than or equal to that of sheep, the wolves will attack the sheep.\nIf the wolves will attack the sheep, print unsafe; otherwise, print safe.", "constraint": "1 <= S <= 100\n1 <= W <= 100", "input": "Input is given from Standard Input in the following format:\nS W", "output": "If the wolves will attack the sheep, print unsafe; otherwise, print safe.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 output: unsafe\n\nThere are four sheep and five wolves. The number of wolves is not less than that of sheep, so they will attack them.", "input: 100 2 output: safe\n\nMany a sheep drive away two wolves.", "input: 10 10 output: unsafe"], "Pid": "p02699", "ProblemText": "Task Description: Problem Statement There are S sheep and W wolves.\nIf the number of wolves is greater than or equal to that of sheep, the wolves will attack the sheep.\nIf the wolves will attack the sheep, print unsafe; otherwise, print safe.\nTask Constraint: 1 <= S <= 100\n1 <= W <= 100\nTask Input: Input is given from Standard Input in the following format:\nS W\nTask Output: If the wolves will attack the sheep, print unsafe; otherwise, print safe.\nTask Samples: input: 4 5 output: unsafe\n\nThere are four sheep and five wolves. The number of wolves is not less than that of sheep, so they will attack them.\ninput: 100 2 output: safe\n\nMany a sheep drive away two wolves.\ninput: 10 10 output: unsafe\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki will have a battle using their monsters.\nThe health and strength of Takahashi's monster are A and B, respectively, and those of Aoki's monster are C and D, respectively.\nThe two monsters will take turns attacking, in the order Takahashi's, Aoki's, Takahashi's, Aoki's, . . .\nHere, an attack decreases the opponent's health by the value equal to the attacker's strength.\nThe monsters keep attacking until the health of one monster becomes 0 or below. The person with the monster whose health becomes 0 or below loses, and the other person wins.\nIf Takahashi will win, print Yes; if he will lose, print No.", "constraint": "1 <= A,B,C,D <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C D", "output": "If Takahashi will win, print Yes; if he will lose, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 9 10 10 output: No\n\nFirst, Takahashi's monster attacks Aoki's monster, whose health is now 10-9=1.\nNext, Aoki's monster attacks Takahashi's monster, whose health is now 10-10=0.\nTakahashi's monster is the first to have 0 or less health, so Takahashi loses.", "input: 46 4 40 5 output: Yes"], "Pid": "p02700", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki will have a battle using their monsters.\nThe health and strength of Takahashi's monster are A and B, respectively, and those of Aoki's monster are C and D, respectively.\nThe two monsters will take turns attacking, in the order Takahashi's, Aoki's, Takahashi's, Aoki's, . . .\nHere, an attack decreases the opponent's health by the value equal to the attacker's strength.\nThe monsters keep attacking until the health of one monster becomes 0 or below. The person with the monster whose health becomes 0 or below loses, and the other person wins.\nIf Takahashi will win, print Yes; if he will lose, print No.\nTask Constraint: 1 <= A,B,C,D <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C D\nTask Output: If Takahashi will win, print Yes; if he will lose, print No.\nTask Samples: input: 10 9 10 10 output: No\n\nFirst, Takahashi's monster attacks Aoki's monster, whose health is now 10-9=1.\nNext, Aoki's monster attacks Takahashi's monster, whose health is now 10-10=0.\nTakahashi's monster is the first to have 0 or less health, so Takahashi loses.\ninput: 46 4 40 5 output: Yes\n\n" }, { "title": "", "content": "Problem Statement You drew lottery N times. In the i-th draw, you got an item of the kind represented by a string S_i.\nHow many kinds of items did you get?", "constraint": "1 <= N <= 2* 10^5\nS_i consists of lowercase English letters and has a length between 1 and 10 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N", "output": "Print the number of kinds of items you got.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\napple\norange\napple output: 2\n\nYou got two kinds of items: apple and orange.", "input: 5\ngrape\ngrape\ngrape\ngrape\ngrape output: 1", "input: 4\naaaa\na\naaa\naa output: 4"], "Pid": "p02701", "ProblemText": "Task Description: Problem Statement You drew lottery N times. In the i-th draw, you got an item of the kind represented by a string S_i.\nHow many kinds of items did you get?\nTask Constraint: 1 <= N <= 2* 10^5\nS_i consists of lowercase English letters and has a length between 1 and 10 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N\nTask Output: Print the number of kinds of items you got.\nTask Samples: input: 3\napple\norange\napple output: 2\n\nYou got two kinds of items: apple and orange.\ninput: 5\ngrape\ngrape\ngrape\ngrape\ngrape output: 1\ninput: 4\naaaa\na\naaa\naa output: 4\n\n" }, { "title": "", "content": "Problem Statement Given is a string S consisting of digits from 1 through 9.\nFind the number of pairs of integers (i, j) (1 <= i <= j <= |S|) that satisfy the following condition:\nCondition: In base ten, the i-th through j-th characters of S form an integer that is a multiple of 2019.", "constraint": "1 <= |S| <= 200000\nS is a string consisting of digits from 1 through 9.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of pairs of integers (i, j) (1 <= i <= j <= |S|) that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1817181712114 output: 3\n\nThree pairs - (1,5), (5,9), and (9,13) - satisfy the condition.", "input: 14282668646 output: 2", "input: 2119 output: 0\n\nNo pairs satisfy the condition."], "Pid": "p02702", "ProblemText": "Task Description: Problem Statement Given is a string S consisting of digits from 1 through 9.\nFind the number of pairs of integers (i, j) (1 <= i <= j <= |S|) that satisfy the following condition:\nCondition: In base ten, the i-th through j-th characters of S form an integer that is a multiple of 2019.\nTask Constraint: 1 <= |S| <= 200000\nS is a string consisting of digits from 1 through 9.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of pairs of integers (i, j) (1 <= i <= j <= |S|) that satisfy the condition.\nTask Samples: input: 1817181712114 output: 3\n\nThree pairs - (1,5), (5,9), and (9,13) - satisfy the condition.\ninput: 14282668646 output: 2\ninput: 2119 output: 0\n\nNo pairs satisfy the condition.\n\n" }, { "title": "", "content": "Problem Statement\nThere are N cities numbered 1 to N, connected by M railroads.\nYou are now at City 1, with 10^{100} gold coins and S silver coins in your pocket.\nThe i-th railroad connects City U_i and City V_i bidirectionally, and a one-way trip costs A_i silver coins and takes B_i minutes.\nYou cannot use gold coins to pay the fare.\nThere is an exchange counter in each city. At the exchange counter in City i, you can get C_i silver coins for 1 gold coin.\nThe transaction takes D_i minutes for each gold coin you give.\nYou can exchange any number of gold coins at each exchange counter.\nFor each t=2, . . . , N, find the minimum time needed to travel from City 1 to City t. You can ignore the time spent waiting for trains.", "constraint": "2 <= N <= 50\nN-1 <= M <= 100\n0 <= S <= 10^9\n1 <= A_i <= 50\n1 <= B_i,C_i,D_i <= 10^9\n1 <= U_i < V_i <= N\nThere is no pair i, j(i \\neq j) such that (U_i,V_i)=(U_j,V_j).\nEach city t=2,...,N can be reached from City 1 with some number of railroads.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M S\nU_1 V_1 A_1 B_1\n:\nU_M V_M A_M B_M\nC_1 D_1\n:\nC_N D_N", "output": "For each t=2, . . . , N in this order, print a line containing the minimum time needed to travel from City 1 to City t.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 1\n1 2 1 2\n1 3 2 4\n1 11\n1 2\n2 5 output: 2\n14\n\nThe railway network in this input is shown in the figure below.\nIn this figure, each city is labeled as follows:\n\nThe first line: the ID number i of the city (i for City i)\nThe second line: C_i / D_i\n\nSimilarly, each railroad is labeled as follows:\n\nThe first line: the ID number i of the railroad (i for the i-th railroad in input)\nThe second line: A_i / B_i\nYou can travel from City 1 to City 2 in 2 minutes, as follows:\n\nUse the 1-st railroad to move from City 1 to City 2 in 2 minutes.\nYou can travel from City 1 to City 3 in 14 minutes, as follows:\n\nUse the 1-st railroad to move from City 1 to City 2 in 2 minutes.\nAt the exchange counter in City 2, exchange 3 gold coins for 3 silver coins in 6 minutes.\nUse the 1-st railroad to move from City 2 to City 1 in 2 minutes.\nUse the 2-nd railroad to move from City 1 to City 3 in 4 minutes.", "input: 4 4 1\n1 2 1 5\n1 3 4 4\n2 4 2 2\n3 4 1 1\n3 1\n3 1\n5 2\n6 4 output: 5\n5\n7\n\nThe railway network in this input is shown in the figure below:\n\nYou can travel from City 1 to City 4 in 7 minutes, as follows:\n\nAt the exchange counter in City 1, exchange 2 gold coins for 6 silver coins in 2 minutes.\nUse the 2-nd railroad to move from City 1 to City 3 in 4 minutes.\nUse the 4-th railroad to move from City 3 to City 4 in 1 minutes.", "input: 6 5 1\n1 2 1 1\n1 3 2 1\n2 4 5 1\n3 5 11 1\n1 6 50 1\n1 10000\n1 3000\n1 700\n1 100\n1 1\n100 1 output: 1\n9003\n14606\n16510\n16576\n\nThe railway network in this input is shown in the figure below:\n\nYou can travel from City 1 to City 6 in 16576 minutes, as follows:\n\nUse the 1-st railroad to move from City 1 to City 2 in 1 minute.\nAt the exchange counter in City 2, exchange 3 gold coins for 3 silver coins in 9000 minutes.\nUse the 1-st railroad to move from City 2 to City 1 in 1 minute.\nUse the 2-nd railroad to move from City 1 to City 3 in 1 minute.\nAt the exchange counter in City 3, exchange 8 gold coins for 8 silver coins in 5600 minutes.\nUse the 2-nd railroad to move from City 3 to City 1 in 1 minute.\nUse the 1-st railroad to move from City 1 to City 2 in 1 minute.\nUse the 3-rd railroad to move from City 2 to City 4 in 1 minute.\nAt the exchange counter in City 4, exchange 19 gold coins for 19 silver coins in 1900 minutes.\nUse the 3-rd railroad to move from City 4 to City 2 in 1 minute.\nUse the 1-st railroad to move from City 2 to City 1 in 1 minute.\nUse the 2-nd railroad to move from City 1 to City 3 in 1 minute.\nUse the 4-th railroad to move from City 3 to City 5 in 1 minute.\nAt the exchange counter in City 5, exchange 63 gold coins for 63 silver coins in 63 minutes.\nUse the 4-th railroad to move from City 5 to City 3 in 1 minute.\nUse the 2-nd railroad to move from City 3 to City 1 in 1 minute.\nUse the 5-th railroad to move from City 1 to City 6 in 1 minute.", "input: 4 6 1000000000\n1 2 50 1\n1 3 50 5\n1 4 50 7\n2 3 50 2\n2 4 50 4\n3 4 50 3\n10 2\n4 4\n5 5\n7 7 output: 1\n3\n5\n\nThe railway network in this input is shown in the figure below:", "input: 2 1 0\n1 2 1 1\n1 1000000000\n1 1 output: 1000000001\n\nThe railway network in this input is shown in the figure below:\n\nYou can travel from City 1 to City 2 in 1000000001 minutes, as follows:\n\nAt the exchange counter in City 1, exchange 1 gold coin for 1 silver coin in 1000000000 minutes.\nUse the 1-st railroad to move from City 1 to City 2 in 1 minute."], "Pid": "p02703", "ProblemText": "Task Description: Problem Statement\nThere are N cities numbered 1 to N, connected by M railroads.\nYou are now at City 1, with 10^{100} gold coins and S silver coins in your pocket.\nThe i-th railroad connects City U_i and City V_i bidirectionally, and a one-way trip costs A_i silver coins and takes B_i minutes.\nYou cannot use gold coins to pay the fare.\nThere is an exchange counter in each city. At the exchange counter in City i, you can get C_i silver coins for 1 gold coin.\nThe transaction takes D_i minutes for each gold coin you give.\nYou can exchange any number of gold coins at each exchange counter.\nFor each t=2, . . . , N, find the minimum time needed to travel from City 1 to City t. You can ignore the time spent waiting for trains.\nTask Constraint: 2 <= N <= 50\nN-1 <= M <= 100\n0 <= S <= 10^9\n1 <= A_i <= 50\n1 <= B_i,C_i,D_i <= 10^9\n1 <= U_i < V_i <= N\nThere is no pair i, j(i \\neq j) such that (U_i,V_i)=(U_j,V_j).\nEach city t=2,...,N can be reached from City 1 with some number of railroads.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M S\nU_1 V_1 A_1 B_1\n:\nU_M V_M A_M B_M\nC_1 D_1\n:\nC_N D_N\nTask Output: For each t=2, . . . , N in this order, print a line containing the minimum time needed to travel from City 1 to City t.\nTask Samples: input: 3 2 1\n1 2 1 2\n1 3 2 4\n1 11\n1 2\n2 5 output: 2\n14\n\nThe railway network in this input is shown in the figure below.\nIn this figure, each city is labeled as follows:\n\nThe first line: the ID number i of the city (i for City i)\nThe second line: C_i / D_i\n\nSimilarly, each railroad is labeled as follows:\n\nThe first line: the ID number i of the railroad (i for the i-th railroad in input)\nThe second line: A_i / B_i\nYou can travel from City 1 to City 2 in 2 minutes, as follows:\n\nUse the 1-st railroad to move from City 1 to City 2 in 2 minutes.\nYou can travel from City 1 to City 3 in 14 minutes, as follows:\n\nUse the 1-st railroad to move from City 1 to City 2 in 2 minutes.\nAt the exchange counter in City 2, exchange 3 gold coins for 3 silver coins in 6 minutes.\nUse the 1-st railroad to move from City 2 to City 1 in 2 minutes.\nUse the 2-nd railroad to move from City 1 to City 3 in 4 minutes.\ninput: 4 4 1\n1 2 1 5\n1 3 4 4\n2 4 2 2\n3 4 1 1\n3 1\n3 1\n5 2\n6 4 output: 5\n5\n7\n\nThe railway network in this input is shown in the figure below:\n\nYou can travel from City 1 to City 4 in 7 minutes, as follows:\n\nAt the exchange counter in City 1, exchange 2 gold coins for 6 silver coins in 2 minutes.\nUse the 2-nd railroad to move from City 1 to City 3 in 4 minutes.\nUse the 4-th railroad to move from City 3 to City 4 in 1 minutes.\ninput: 6 5 1\n1 2 1 1\n1 3 2 1\n2 4 5 1\n3 5 11 1\n1 6 50 1\n1 10000\n1 3000\n1 700\n1 100\n1 1\n100 1 output: 1\n9003\n14606\n16510\n16576\n\nThe railway network in this input is shown in the figure below:\n\nYou can travel from City 1 to City 6 in 16576 minutes, as follows:\n\nUse the 1-st railroad to move from City 1 to City 2 in 1 minute.\nAt the exchange counter in City 2, exchange 3 gold coins for 3 silver coins in 9000 minutes.\nUse the 1-st railroad to move from City 2 to City 1 in 1 minute.\nUse the 2-nd railroad to move from City 1 to City 3 in 1 minute.\nAt the exchange counter in City 3, exchange 8 gold coins for 8 silver coins in 5600 minutes.\nUse the 2-nd railroad to move from City 3 to City 1 in 1 minute.\nUse the 1-st railroad to move from City 1 to City 2 in 1 minute.\nUse the 3-rd railroad to move from City 2 to City 4 in 1 minute.\nAt the exchange counter in City 4, exchange 19 gold coins for 19 silver coins in 1900 minutes.\nUse the 3-rd railroad to move from City 4 to City 2 in 1 minute.\nUse the 1-st railroad to move from City 2 to City 1 in 1 minute.\nUse the 2-nd railroad to move from City 1 to City 3 in 1 minute.\nUse the 4-th railroad to move from City 3 to City 5 in 1 minute.\nAt the exchange counter in City 5, exchange 63 gold coins for 63 silver coins in 63 minutes.\nUse the 4-th railroad to move from City 5 to City 3 in 1 minute.\nUse the 2-nd railroad to move from City 3 to City 1 in 1 minute.\nUse the 5-th railroad to move from City 1 to City 6 in 1 minute.\ninput: 4 6 1000000000\n1 2 50 1\n1 3 50 5\n1 4 50 7\n2 3 50 2\n2 4 50 4\n3 4 50 3\n10 2\n4 4\n5 5\n7 7 output: 1\n3\n5\n\nThe railway network in this input is shown in the figure below:\ninput: 2 1 0\n1 2 1 1\n1 1000000000\n1 1 output: 1000000001\n\nThe railway network in this input is shown in the figure below:\n\nYou can travel from City 1 to City 2 in 1000000001 minutes, as follows:\n\nAt the exchange counter in City 1, exchange 1 gold coin for 1 silver coin in 1000000000 minutes.\nUse the 1-st railroad to move from City 1 to City 2 in 1 minute.\n\n" }, { "title": "", "content": "Problem Statement Given are an integer N and arrays S, T, U, and V, each of length N.\nConstruct an N*N matrix a that satisfy the following conditions:\n\na_{i, j} is an integer.\n0 <= a_{i, j} < 2^{64}.\nIf S_{i} = 0, the bitwise AND of the elements in the i-th row is U_{i}.\nIf S_{i} = 1, the bitwise OR of the elements in the i-th row is U_{i}.\nIf T_{i} = 0, the bitwise AND of the elements in the i-th column is V_{i}.\nIf T_{i} = 1, the bitwise OR of the elements in the i-th column is V_{i}.\n\nHowever, there may be cases where no matrix satisfies the conditions.", "constraint": "All values in input are integers.\n 1 <= N <= 500 \n 0 <= S_{i} <= 1 \n 0 <= T_{i} <= 1 \n 0 <= U_{i} < 2^{64} \n 0 <= V_{i} < 2^{64}", "input": "Input is given from Standard Input in the following format:\nN\nS_{1} S_{2} . . . S_{N}\nT_{1} T_{2} . . . T_{N}\nU_{1} U_{2} . . . U_{N}\nV_{1} V_{2} . . . V_{N}", "output": "If there exists a matrix that satisfies the conditions, print one such matrix in the following format:\na_{1,1} . . . a_{1, N}\n:\na_{N, 1} . . . a_{N, N}\n\nNote that any matrix satisfying the conditions is accepted.\nIf no matrix satisfies the conditions, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 1\n1 0\n1 1\n1 0 output: 1 1\n1 0\n\nIn Sample Input 1, we need to find a matrix such that:\n\nthe bitwise AND of the elements in the 1-st row is 1;\nthe bitwise OR of the elements in the 2-nd row is 1;\nthe bitwise OR of the elements in the 1-st column is 1;\nthe bitwise AND of the elements in the 2-nd column is 0.", "input: 2\n1 1\n1 0\n15 15\n15 11 output: 15 11\n15 11"], "Pid": "p02704", "ProblemText": "Task Description: Problem Statement Given are an integer N and arrays S, T, U, and V, each of length N.\nConstruct an N*N matrix a that satisfy the following conditions:\n\na_{i, j} is an integer.\n0 <= a_{i, j} < 2^{64}.\nIf S_{i} = 0, the bitwise AND of the elements in the i-th row is U_{i}.\nIf S_{i} = 1, the bitwise OR of the elements in the i-th row is U_{i}.\nIf T_{i} = 0, the bitwise AND of the elements in the i-th column is V_{i}.\nIf T_{i} = 1, the bitwise OR of the elements in the i-th column is V_{i}.\n\nHowever, there may be cases where no matrix satisfies the conditions.\nTask Constraint: All values in input are integers.\n 1 <= N <= 500 \n 0 <= S_{i} <= 1 \n 0 <= T_{i} <= 1 \n 0 <= U_{i} < 2^{64} \n 0 <= V_{i} < 2^{64}\nTask Input: Input is given from Standard Input in the following format:\nN\nS_{1} S_{2} . . . S_{N}\nT_{1} T_{2} . . . T_{N}\nU_{1} U_{2} . . . U_{N}\nV_{1} V_{2} . . . V_{N}\nTask Output: If there exists a matrix that satisfies the conditions, print one such matrix in the following format:\na_{1,1} . . . a_{1, N}\n:\na_{N, 1} . . . a_{N, N}\n\nNote that any matrix satisfying the conditions is accepted.\nIf no matrix satisfies the conditions, print -1.\nTask Samples: input: 2\n0 1\n1 0\n1 1\n1 0 output: 1 1\n1 0\n\nIn Sample Input 1, we need to find a matrix such that:\n\nthe bitwise AND of the elements in the 1-st row is 1;\nthe bitwise OR of the elements in the 2-nd row is 1;\nthe bitwise OR of the elements in the 1-st column is 1;\nthe bitwise AND of the elements in the 2-nd column is 0.\ninput: 2\n1 1\n1 0\n15 15\n15 11 output: 15 11\n15 11\n\n" }, { "title": "", "content": "Problem Statement Print the circumference of a circle of radius R.", "constraint": "1 <= R <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nR", "output": "Print the circumference of the circle.\nYour output is considered correct if and only if its absolute or relative error from our answer is at most 10^{-2}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 output: 6.28318530717958623200\n\nSince we accept an absolute or relative error of at most 10^{-2}, 6.28 is also an acceptable output, but 6 is not.", "input: 73 output: 458.67252742410977361942"], "Pid": "p02705", "ProblemText": "Task Description: Problem Statement Print the circumference of a circle of radius R.\nTask Constraint: 1 <= R <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nR\nTask Output: Print the circumference of the circle.\nYour output is considered correct if and only if its absolute or relative error from our answer is at most 10^{-2}.\nTask Samples: input: 1 output: 6.28318530717958623200\n\nSince we accept an absolute or relative error of at most 10^{-2}, 6.28 is also an acceptable output, but 6 is not.\ninput: 73 output: 458.67252742410977361942\n\n" }, { "title": "", "content": "Problem Statement Takahashi has N days of summer vacation.\nHis teacher gave him M summer assignments. It will take A_i days for him to do the i-th assignment.\nHe cannot do multiple assignments on the same day, or hang out on a day he does an assignment.\nWhat is the maximum number of days Takahashi can hang out during the vacation if he finishes all the assignments during this vacation?\nIf Takahashi cannot finish all the assignments during the vacation, print -1 instead.", "constraint": "1 <= N <= 10^6\n1 <= M <= 10^4\n1 <= A_i <= 10^4", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 . . . A_M", "output": "Print the maximum number of days Takahashi can hang out during the vacation, or -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 41 2\n5 6 output: 30\n\nFor example, he can do the first assignment on the first 5 days, hang out on the next 30 days, and do the second assignment on the last 6 days of the vacation. In this way, he can safely spend 30 days hanging out.", "input: 10 2\n5 6 output: -1\n\nHe cannot finish his assignments.", "input: 11 2\n5 6 output: 0\n\nHe can finish his assignments, but he will have no time to hang out.", "input: 314 15\n9 26 5 35 8 9 79 3 23 8 46 2 6 43 3 output: 9"], "Pid": "p02706", "ProblemText": "Task Description: Problem Statement Takahashi has N days of summer vacation.\nHis teacher gave him M summer assignments. It will take A_i days for him to do the i-th assignment.\nHe cannot do multiple assignments on the same day, or hang out on a day he does an assignment.\nWhat is the maximum number of days Takahashi can hang out during the vacation if he finishes all the assignments during this vacation?\nIf Takahashi cannot finish all the assignments during the vacation, print -1 instead.\nTask Constraint: 1 <= N <= 10^6\n1 <= M <= 10^4\n1 <= A_i <= 10^4\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 . . . A_M\nTask Output: Print the maximum number of days Takahashi can hang out during the vacation, or -1.\nTask Samples: input: 41 2\n5 6 output: 30\n\nFor example, he can do the first assignment on the first 5 days, hang out on the next 30 days, and do the second assignment on the last 6 days of the vacation. In this way, he can safely spend 30 days hanging out.\ninput: 10 2\n5 6 output: -1\n\nHe cannot finish his assignments.\ninput: 11 2\n5 6 output: 0\n\nHe can finish his assignments, but he will have no time to hang out.\ninput: 314 15\n9 26 5 35 8 9 79 3 23 8 46 2 6 43 3 output: 9\n\n" }, { "title": "", "content": "Problem Statement A company has N members, who are assigned ID numbers 1, . . . , N.\nEvery member, except the member numbered 1, has exactly one immediate boss with a smaller ID number.\nWhen a person X is the immediate boss of a person Y, the person Y is said to be an immediate subordinate of the person X.\nYou are given the information that the immediate boss of the member numbered i is the member numbered A_i. For each member, find how many immediate subordinates it has.", "constraint": "2 <= N <= 2 * 10^5\n1 <= A_i < i", "input": "Input is given from Standard Input in the following format:\nN\nA_2 . . . A_N", "output": "For each of the members numbered 1,2, . . . , N, print the number of immediate subordinates it has, in its own line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 1 2 2 output: 2\n2\n0\n0\n0\n\nThe member numbered 1 has two immediate subordinates: the members numbered 2 and 3.\nThe member numbered 2 has two immediate subordinates: the members numbered 4 and 5.\nThe members numbered 3,4, and 5 do not have immediate subordinates.", "input: 10\n1 1 1 1 1 1 1 1 1 output: 9\n0\n0\n0\n0\n0\n0\n0\n0\n0", "input: 7\n1 2 3 4 5 6 output: 1\n1\n1\n1\n1\n1\n0"], "Pid": "p02707", "ProblemText": "Task Description: Problem Statement A company has N members, who are assigned ID numbers 1, . . . , N.\nEvery member, except the member numbered 1, has exactly one immediate boss with a smaller ID number.\nWhen a person X is the immediate boss of a person Y, the person Y is said to be an immediate subordinate of the person X.\nYou are given the information that the immediate boss of the member numbered i is the member numbered A_i. For each member, find how many immediate subordinates it has.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= A_i < i\nTask Input: Input is given from Standard Input in the following format:\nN\nA_2 . . . A_N\nTask Output: For each of the members numbered 1,2, . . . , N, print the number of immediate subordinates it has, in its own line.\nTask Samples: input: 5\n1 1 2 2 output: 2\n2\n0\n0\n0\n\nThe member numbered 1 has two immediate subordinates: the members numbered 2 and 3.\nThe member numbered 2 has two immediate subordinates: the members numbered 4 and 5.\nThe members numbered 3,4, and 5 do not have immediate subordinates.\ninput: 10\n1 1 1 1 1 1 1 1 1 output: 9\n0\n0\n0\n0\n0\n0\n0\n0\n0\ninput: 7\n1 2 3 4 5 6 output: 1\n1\n1\n1\n1\n1\n0\n\n" }, { "title": "", "content": "Problem Statement We have N+1 integers: 10^{100}, 10^{100}+1, . . . , 10^{100}+N.\nWe will choose K or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo (10^9+7).", "constraint": "1 <= N <= 2* 10^5\n1 <= K <= N+1\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the number of possible values of the sum, modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 10\n\nThe sum can take 10 values, as follows:\n\n(10^{100})+(10^{100}+1)=2* 10^{100}+1\n(10^{100})+(10^{100}+2)=2* 10^{100}+2\n(10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2* 10^{100}+3\n(10^{100}+1)+(10^{100}+3)=2* 10^{100}+4\n(10^{100}+2)+(10^{100}+3)=2* 10^{100}+5\n(10^{100})+(10^{100}+1)+(10^{100}+2)=3* 10^{100}+3\n(10^{100})+(10^{100}+1)+(10^{100}+3)=3* 10^{100}+4\n(10^{100})+(10^{100}+2)+(10^{100}+3)=3* 10^{100}+5\n(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3* 10^{100}+6\n(10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4* 10^{100}+6", "input: 200000 200001 output: 1\n\nWe must choose all of the integers, so the sum can take just 1 value.", "input: 141421 35623 output: 220280457"], "Pid": "p02708", "ProblemText": "Task Description: Problem Statement We have N+1 integers: 10^{100}, 10^{100}+1, . . . , 10^{100}+N.\nWe will choose K or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo (10^9+7).\nTask Constraint: 1 <= N <= 2* 10^5\n1 <= K <= N+1\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of possible values of the sum, modulo (10^9+7).\nTask Samples: input: 3 2 output: 10\n\nThe sum can take 10 values, as follows:\n\n(10^{100})+(10^{100}+1)=2* 10^{100}+1\n(10^{100})+(10^{100}+2)=2* 10^{100}+2\n(10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2* 10^{100}+3\n(10^{100}+1)+(10^{100}+3)=2* 10^{100}+4\n(10^{100}+2)+(10^{100}+3)=2* 10^{100}+5\n(10^{100})+(10^{100}+1)+(10^{100}+2)=3* 10^{100}+3\n(10^{100})+(10^{100}+1)+(10^{100}+3)=3* 10^{100}+4\n(10^{100})+(10^{100}+2)+(10^{100}+3)=3* 10^{100}+5\n(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3* 10^{100}+6\n(10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4* 10^{100}+6\ninput: 200000 200001 output: 1\n\nWe must choose all of the integers, so the sum can take just 1 value.\ninput: 141421 35623 output: 220280457\n\n" }, { "title": "", "content": "Problem Statement There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.\nYou can rearrange these children just one time in any order you like.\nWhen a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x * |x-y| happiness points.\nFind the maximum total happiness points the children can earn.", "constraint": "2 <= N <= 2000\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum total happiness points the children can earn.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 3 4 2 output: 20\n\nIf we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 * |1-3|+3 * |2-4|+4 * |3-1|+2 * |4-2|=20 happiness points in total.", "input: 6\n5 5 6 1 1 1 output: 58", "input: 6\n8 6 9 1 2 1 output: 85"], "Pid": "p02709", "ProblemText": "Task Description: Problem Statement There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.\nYou can rearrange these children just one time in any order you like.\nWhen a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x * |x-y| happiness points.\nFind the maximum total happiness points the children can earn.\nTask Constraint: 2 <= N <= 2000\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum total happiness points the children can earn.\nTask Samples: input: 4\n1 3 4 2 output: 20\n\nIf we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 * |1-3|+3 * |2-4|+4 * |3-1|+2 * |4-2|=20 happiness points in total.\ninput: 6\n5 5 6 1 1 1 output: 58\ninput: 6\n8 6 9 1 2 1 output: 85\n\n" }, { "title": "", "content": "Problem Statement\nWe have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i.\nAdditionally, each vertex is painted in a color, and the color of Vertex i is c_i. Here, the color of each vertex is represented by an integer between 1 and N (inclusive). The same integer corresponds to the same color; different integers correspond to different colors.\nFor each k=1,2, . . . , N, solve the following problem:\n\nFind the number of simple paths that visit a vertex painted in the color k one or more times.\n\nNote: The simple paths from Vertex u to v and from v to u are not distinguished.", "constraint": "1 <= N <= 2 * 10^5\n1 <= c_i <= N\n1 <= a_i,b_i <= N\nThe given graph is a tree.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nc_1 c_2 . . . c_N\na_1 b_1\n:\na_{N-1} b_{N-1}", "output": "Print the answers for k = 1,2, . . . , N in order, each in its own line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 1\n1 2\n2 3 output: 5\n4\n0\n\nLet P_{i,j} denote the simple path connecting Vertex i and j.\nThere are 5 simple paths that visit a vertex painted in the color 1 one or more times:\nP_{1,1}\\,,\\,\nP_{1,2}\\,,\\,\nP_{1,3}\\,,\\,\nP_{2,3}\\,,\\,\nP_{3,3} \nThere are 4 simple paths that visit a vertex painted in the color 2 one or more times:\nP_{1,2}\\,,\\,\nP_{1,3}\\,,\\,\nP_{2,2}\\,,\\,\nP_{2,3} \nThere are no simple paths that visit a vertex painted in the color 3 one or more times.", "input: 1\n1 output: 1", "input: 2\n1 2\n1 2 output: 2\n2", "input: 5\n1 2 3 4 5\n1 2\n2 3\n3 4\n3 5 output: 5\n8\n10\n5\n5", "input: 8\n2 7 2 5 4 1 7 5\n3 1\n1 2\n2 7\n4 5\n5 6\n6 8\n7 8 output: 18\n15\n0\n14\n23\n0\n23\n0"], "Pid": "p02710", "ProblemText": "Task Description: Problem Statement\nWe have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i.\nAdditionally, each vertex is painted in a color, and the color of Vertex i is c_i. Here, the color of each vertex is represented by an integer between 1 and N (inclusive). The same integer corresponds to the same color; different integers correspond to different colors.\nFor each k=1,2, . . . , N, solve the following problem:\n\nFind the number of simple paths that visit a vertex painted in the color k one or more times.\n\nNote: The simple paths from Vertex u to v and from v to u are not distinguished.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= c_i <= N\n1 <= a_i,b_i <= N\nThe given graph is a tree.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nc_1 c_2 . . . c_N\na_1 b_1\n:\na_{N-1} b_{N-1}\nTask Output: Print the answers for k = 1,2, . . . , N in order, each in its own line.\nTask Samples: input: 3\n1 2 1\n1 2\n2 3 output: 5\n4\n0\n\nLet P_{i,j} denote the simple path connecting Vertex i and j.\nThere are 5 simple paths that visit a vertex painted in the color 1 one or more times:\nP_{1,1}\\,,\\,\nP_{1,2}\\,,\\,\nP_{1,3}\\,,\\,\nP_{2,3}\\,,\\,\nP_{3,3} \nThere are 4 simple paths that visit a vertex painted in the color 2 one or more times:\nP_{1,2}\\,,\\,\nP_{1,3}\\,,\\,\nP_{2,2}\\,,\\,\nP_{2,3} \nThere are no simple paths that visit a vertex painted in the color 3 one or more times.\ninput: 1\n1 output: 1\ninput: 2\n1 2\n1 2 output: 2\n2\ninput: 5\n1 2 3 4 5\n1 2\n2 3\n3 4\n3 5 output: 5\n8\n10\n5\n5\ninput: 8\n2 7 2 5 4 1 7 5\n3 1\n1 2\n2 7\n4 5\n5 6\n6 8\n7 8 output: 18\n15\n0\n14\n23\n0\n23\n0\n\n" }, { "title": "", "content": "Problem Statement Given is a three-digit integer N. Does N contain the digit 7?\nIf so, print Yes; otherwise, print No.", "constraint": "100 <= N <= 999", "input": "Input is given from Standard Input in the following format:\nN", "output": "If N contains the digit 7, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 117 output: Yes\n\n117 contains 7 as its last digit.", "input: 123 output: No\n\n123 does not contain the digit 7.", "input: 777 output: Yes"], "Pid": "p02711", "ProblemText": "Task Description: Problem Statement Given is a three-digit integer N. Does N contain the digit 7?\nIf so, print Yes; otherwise, print No.\nTask Constraint: 100 <= N <= 999\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If N contains the digit 7, print Yes; otherwise, print No.\nTask Samples: input: 117 output: Yes\n\n117 contains 7 as its last digit.\ninput: 123 output: No\n\n123 does not contain the digit 7.\ninput: 777 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Let us define the Fizz Buzz sequence a_1, a_2, . . . as follows:\n\nIf both 3 and 5 divides i, a_i=\\mbox{Fizz Buzz}.\nIf the above does not hold but 3 divides i, a_i=\\mbox{Fizz}.\nIf none of the above holds but 5 divides i, a_i=\\mbox{Buzz}.\nIf none of the above holds, a_i=i.\n\nFind the sum of all numbers among the first N terms of the Fizz Buzz sequence.", "constraint": "1 <= N <= 10^6", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the sum of all numbers among the first N terms of the Fizz Buzz sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15 output: 60\n\nThe first 15 terms of the FizzBuzz sequence are:\n1,2,\\mbox{Fizz},4,\\mbox{Buzz},\\mbox{Fizz},7,8,\\mbox{Fizz},\\mbox{Buzz},11,\\mbox{Fizz},13,14,\\mbox{FizzBuzz}\nAmong them, numbers are 1,2,4,7,8,11,13,14, and the sum of them is 60.", "input: 1000000 output: 266666333332\n\nWatch out for overflow."], "Pid": "p02712", "ProblemText": "Task Description: Problem Statement Let us define the Fizz Buzz sequence a_1, a_2, . . . as follows:\n\nIf both 3 and 5 divides i, a_i=\\mbox{Fizz Buzz}.\nIf the above does not hold but 3 divides i, a_i=\\mbox{Fizz}.\nIf none of the above holds but 5 divides i, a_i=\\mbox{Buzz}.\nIf none of the above holds, a_i=i.\n\nFind the sum of all numbers among the first N terms of the Fizz Buzz sequence.\nTask Constraint: 1 <= N <= 10^6\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the sum of all numbers among the first N terms of the Fizz Buzz sequence.\nTask Samples: input: 15 output: 60\n\nThe first 15 terms of the FizzBuzz sequence are:\n1,2,\\mbox{Fizz},4,\\mbox{Buzz},\\mbox{Fizz},7,8,\\mbox{Fizz},\\mbox{Buzz},11,\\mbox{Fizz},13,14,\\mbox{FizzBuzz}\nAmong them, numbers are 1,2,4,7,8,11,13,14, and the sum of them is 60.\ninput: 1000000 output: 266666333332\n\nWatch out for overflow.\n\n" }, { "title": "", "content": "Problem Statement Find \\displaystyle{\\sum_{a=1}^{K}\\sum_{b=1}^{K}\\sum_{c=1}^{K} \\gcd(a, b, c)}.\nHere \\gcd(a, b, c) denotes the greatest common divisor of a, b, and c.", "constraint": "1 <= K <= 200\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print the value of \\displaystyle{\\sum_{a=1}^{K}\\sum_{b=1}^{K}\\sum_{c=1}^{K} \\gcd(a, b, c)}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 9\n\n\\gcd(1,1,1)+\\gcd(1,1,2)+\\gcd(1,2,1)+\\gcd(1,2,2)\n+\\gcd(2,1,1)+\\gcd(2,1,2)+\\gcd(2,2,1)+\\gcd(2,2,2)\n=1+1+1+1+1+1+1+2=9\nThus, the answer is 9.", "input: 200 output: 10813692"], "Pid": "p02713", "ProblemText": "Task Description: Problem Statement Find \\displaystyle{\\sum_{a=1}^{K}\\sum_{b=1}^{K}\\sum_{c=1}^{K} \\gcd(a, b, c)}.\nHere \\gcd(a, b, c) denotes the greatest common divisor of a, b, and c.\nTask Constraint: 1 <= K <= 200\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print the value of \\displaystyle{\\sum_{a=1}^{K}\\sum_{b=1}^{K}\\sum_{c=1}^{K} \\gcd(a, b, c)}.\nTask Samples: input: 2 output: 9\n\n\\gcd(1,1,1)+\\gcd(1,1,2)+\\gcd(1,2,1)+\\gcd(1,2,2)\n+\\gcd(2,1,1)+\\gcd(2,1,2)+\\gcd(2,2,1)+\\gcd(2,2,2)\n=1+1+1+1+1+1+1+2=9\nThus, the answer is 9.\ninput: 200 output: 10813692\n\n" }, { "title": "", "content": "Problem Statement We have a string S of length N consisting of R, G, and B.\nFind the number of triples (i, ~j, ~k)~(1 <= i < j < k <= N) that satisfy both of the following conditions:\n\nS_i \\neq S_j, S_i \\neq S_k, and S_j \\neq S_k.\nj - i \\neq k - j.", "constraint": "1 <= N <= 4000\nS is a string of length N consisting of R, G, and B.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the number of triplets in question.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nRRGB output: 1\n\nOnly the triplet (1,~3,~4) satisfies both conditions. The triplet (2,~3,~4) satisfies the first condition but not the second, so it does not count.", "input: 39\nRBRBGRBGGBBRRGBBRRRBGGBRBGBRBGBRBBBGBBB output: 1800"], "Pid": "p02714", "ProblemText": "Task Description: Problem Statement We have a string S of length N consisting of R, G, and B.\nFind the number of triples (i, ~j, ~k)~(1 <= i < j < k <= N) that satisfy both of the following conditions:\n\nS_i \\neq S_j, S_i \\neq S_k, and S_j \\neq S_k.\nj - i \\neq k - j.\nTask Constraint: 1 <= N <= 4000\nS is a string of length N consisting of R, G, and B.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the number of triplets in question.\nTask Samples: input: 4\nRRGB output: 1\n\nOnly the triplet (1,~3,~4) satisfies both conditions. The triplet (2,~3,~4) satisfies the first condition but not the second, so it does not count.\ninput: 39\nRBRBGRBGGBBRRGBBRRRBGGBRBGBRBGBRBBBGBBB output: 1800\n\n" }, { "title": "", "content": "Problem Statement Consider sequences \\{A_1, . . . , A_N\\} of length N consisting of integers between 1 and K (inclusive).\nThere are K^N such sequences. Find the sum of \\gcd(A_1, . . . , A_N) over all of them.\nSince this sum can be enormous, print the value modulo (10^9+7).\nHere \\gcd(A_1, . . . , A_N) denotes the greatest common divisor of A_1, . . . , A_N.", "constraint": "2 <= N <= 10^5\n1 <= K <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the sum of \\gcd(A_1, . . . , A_N) over all K^N sequences, modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 9\n\n\\gcd(1,1,1)+\\gcd(1,1,2)+\\gcd(1,2,1)+\\gcd(1,2,2)\n+\\gcd(2,1,1)+\\gcd(2,1,2)+\\gcd(2,2,1)+\\gcd(2,2,2)\n=1+1+1+1+1+1+1+2=9\nThus, the answer is 9.", "input: 3 200 output: 10813692", "input: 100000 100000 output: 742202979\n\nBe sure to print the sum modulo (10^9+7)."], "Pid": "p02715", "ProblemText": "Task Description: Problem Statement Consider sequences \\{A_1, . . . , A_N\\} of length N consisting of integers between 1 and K (inclusive).\nThere are K^N such sequences. Find the sum of \\gcd(A_1, . . . , A_N) over all of them.\nSince this sum can be enormous, print the value modulo (10^9+7).\nHere \\gcd(A_1, . . . , A_N) denotes the greatest common divisor of A_1, . . . , A_N.\nTask Constraint: 2 <= N <= 10^5\n1 <= K <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the sum of \\gcd(A_1, . . . , A_N) over all K^N sequences, modulo (10^9+7).\nTask Samples: input: 3 2 output: 9\n\n\\gcd(1,1,1)+\\gcd(1,1,2)+\\gcd(1,2,1)+\\gcd(1,2,2)\n+\\gcd(2,1,1)+\\gcd(2,1,2)+\\gcd(2,2,1)+\\gcd(2,2,2)\n=1+1+1+1+1+1+1+2=9\nThus, the answer is 9.\ninput: 3 200 output: 10813692\ninput: 100000 100000 output: 742202979\n\nBe sure to print the sum modulo (10^9+7).\n\n" }, { "title": "", "content": "Problem Statement Given is an integer sequence A_1, . . . , A_N of length N.\nWe will choose exactly <=ft\\lfloor \\frac{N}{2} \\right\\rfloor elements from this sequence so that no two adjacent elements are chosen.\nFind the maximum possible sum of the chosen elements.\nHere \\lfloor x \\rfloor denotes the greatest integer not greater than x.", "constraint": "2 <= N <= 2* 10^5\n|A_i|<= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N", "output": "Print the maximum possible sum of the chosen elements.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 2 3 4 5 6 output: 12\n\nChoosing 2,4, and 6 makes the sum 12, which is the maximum possible value.", "input: 5\n-1000 -100 -10 0 10 output: 0\n\nChoosing -10 and 10 makes the sum 0, which is the maximum possible value.", "input: 10\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 5000000000\n\nWatch out for overflow.", "input: 27\n18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49 output: 295"], "Pid": "p02716", "ProblemText": "Task Description: Problem Statement Given is an integer sequence A_1, . . . , A_N of length N.\nWe will choose exactly <=ft\\lfloor \\frac{N}{2} \\right\\rfloor elements from this sequence so that no two adjacent elements are chosen.\nFind the maximum possible sum of the chosen elements.\nHere \\lfloor x \\rfloor denotes the greatest integer not greater than x.\nTask Constraint: 2 <= N <= 2* 10^5\n|A_i|<= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nTask Output: Print the maximum possible sum of the chosen elements.\nTask Samples: input: 6\n1 2 3 4 5 6 output: 12\n\nChoosing 2,4, and 6 makes the sum 12, which is the maximum possible value.\ninput: 5\n-1000 -100 -10 0 10 output: 0\n\nChoosing -10 and 10 makes the sum 0, which is the maximum possible value.\ninput: 10\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 5000000000\n\nWatch out for overflow.\ninput: 27\n18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49 output: 295\n\n" }, { "title": "", "content": "Problem Statement\nWe have three boxes A, B, and C, each of which contains an integer.\nCurrently, the boxes A, B, and C contain the integers X, Y, and Z, respectively.\nWe will now do the operations below in order. Find the content of each box afterward. \n\nSwap the contents of the boxes A and B\nSwap the contents of the boxes A and C", "constraint": "1 <= X,Y,Z <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX Y Z", "output": "Print the integers contained in the boxes A, B, and C, in this order, with space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 3 output: 3 1 2\n\nAfter the contents of the boxes A and B are swapped, A, B, and C contain 2,1, and 3, respectively.\nThen, after the contents of A and C are swapped, A, B, and C contain 3,1, and 2, respectively.", "input: 100 100 100 output: 100 100 100", "input: 41 59 31 output: 31 41 59"], "Pid": "p02717", "ProblemText": "Task Description: Problem Statement\nWe have three boxes A, B, and C, each of which contains an integer.\nCurrently, the boxes A, B, and C contain the integers X, Y, and Z, respectively.\nWe will now do the operations below in order. Find the content of each box afterward. \n\nSwap the contents of the boxes A and B\nSwap the contents of the boxes A and C\nTask Constraint: 1 <= X,Y,Z <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y Z\nTask Output: Print the integers contained in the boxes A, B, and C, in this order, with space in between.\nTask Samples: input: 1 2 3 output: 3 1 2\n\nAfter the contents of the boxes A and B are swapped, A, B, and C contain 2,1, and 3, respectively.\nThen, after the contents of A and C are swapped, A, B, and C contain 3,1, and 2, respectively.\ninput: 100 100 100 output: 100 100 100\ninput: 41 59 31 output: 31 41 59\n\n" }, { "title": "", "content": "Problem Statement We have held a popularity poll for N items on sale. Item i received A_i votes.\nFrom these N items, we will select M as popular items. However, we cannot select an item with less than \\dfrac{1}{4M} of the total number of votes.\nIf M popular items can be selected, print Yes; otherwise, print No.", "constraint": "1 <= M <= N <= 100\n1 <= A_i <= 1000\nA_i are distinct.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 . . . A_N", "output": "If M popular items can be selected, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1\n5 4 2 1 output: Yes\n\nThere were 12 votes in total. The most popular item received 5 votes, and we can select it.", "input: 3 2\n380 19 1 output: No\n\nThere were 400 votes in total. The second and third most popular items received less than \\dfrac{1}{4* 2} of the total number of votes, so we cannot select them. Thus, we cannot select two popular items.", "input: 12 3\n4 56 78 901 2 345 67 890 123 45 6 789 output: Yes"], "Pid": "p02718", "ProblemText": "Task Description: Problem Statement We have held a popularity poll for N items on sale. Item i received A_i votes.\nFrom these N items, we will select M as popular items. However, we cannot select an item with less than \\dfrac{1}{4M} of the total number of votes.\nIf M popular items can be selected, print Yes; otherwise, print No.\nTask Constraint: 1 <= M <= N <= 100\n1 <= A_i <= 1000\nA_i are distinct.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 . . . A_N\nTask Output: If M popular items can be selected, print Yes; otherwise, print No.\nTask Samples: input: 4 1\n5 4 2 1 output: Yes\n\nThere were 12 votes in total. The most popular item received 5 votes, and we can select it.\ninput: 3 2\n380 19 1 output: No\n\nThere were 400 votes in total. The second and third most popular items received less than \\dfrac{1}{4* 2} of the total number of votes, so we cannot select them. Thus, we cannot select two popular items.\ninput: 12 3\n4 56 78 901 2 345 67 890 123 45 6 789 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Given any integer x, Aoki can do the operation below.\nOperation: Replace x with the absolute difference of x and K.\nYou are given the initial value of an integer N. Find the minimum possible value taken by N after Aoki does the operation zero or more times.", "constraint": "0 <= N <= 10^{18}\n1 <= K <= 10^{18}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the minimum possible value taken by N after Aoki does the operation zero or more times.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 4 output: 1\n\nInitially, N=7.\nAfter one operation, N becomes |7-4| = 3.\nAfter two operations, N becomes |3-4| = 1, which is the minimum value taken by N.", "input: 2 6 output: 2\n\nN=2 after zero operations is the minimum.", "input: 1000000000000000000 1 output: 0"], "Pid": "p02719", "ProblemText": "Task Description: Problem Statement Given any integer x, Aoki can do the operation below.\nOperation: Replace x with the absolute difference of x and K.\nYou are given the initial value of an integer N. Find the minimum possible value taken by N after Aoki does the operation zero or more times.\nTask Constraint: 0 <= N <= 10^{18}\n1 <= K <= 10^{18}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the minimum possible value taken by N after Aoki does the operation zero or more times.\nTask Samples: input: 7 4 output: 1\n\nInitially, N=7.\nAfter one operation, N becomes |7-4| = 3.\nAfter two operations, N becomes |3-4| = 1, which is the minimum value taken by N.\ninput: 2 6 output: 2\n\nN=2 after zero operations is the minimum.\ninput: 1000000000000000000 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement\nA positive integer X is said to be a lunlun number if and only if the following condition is satisfied:\n\nIn the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.\n\nFor example, 1234,1, and 334 are lunlun numbers, while none of 31415,119, or 13579 is.\nYou are given a positive integer K. Find the K-th smallest lunlun number.", "constraint": "1 <= K <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15 output: 23\n\nWe will list the 15 smallest lunlun numbers in ascending order:\n1,\n2,\n3,\n4,\n5,\n6,\n7,\n8,\n9,\n10,\n11,\n12,\n21,\n22,\n23.\nThus, the answer is 23.", "input: 1 output: 1", "input: 13 output: 21", "input: 100000 output: 3234566667\n\nNote that the answer may not fit into the 32-bit signed integer type."], "Pid": "p02720", "ProblemText": "Task Description: Problem Statement\nA positive integer X is said to be a lunlun number if and only if the following condition is satisfied:\n\nIn the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.\n\nFor example, 1234,1, and 334 are lunlun numbers, while none of 31415,119, or 13579 is.\nYou are given a positive integer K. Find the K-th smallest lunlun number.\nTask Constraint: 1 <= K <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print the answer.\nTask Samples: input: 15 output: 23\n\nWe will list the 15 smallest lunlun numbers in ascending order:\n1,\n2,\n3,\n4,\n5,\n6,\n7,\n8,\n9,\n10,\n11,\n12,\n21,\n22,\n23.\nThus, the answer is 23.\ninput: 1 output: 1\ninput: 13 output: 21\ninput: 100000 output: 3234566667\n\nNote that the answer may not fit into the 32-bit signed integer type.\n\n" }, { "title": "", "content": "Problem Statement Takahashi has decided to work on K days of his choice from the N days starting with tomorrow.\nYou are given an integer C and a string S. Takahashi will choose his workdays as follows:\n\nAfter working for a day, he will refrain from working on the subsequent C days.\nIf the i-th character of S is x, he will not work on Day i, where Day 1 is tomorrow, Day 2 is the day after tomorrow, and so on.\n\nFind all days on which Takahashi is bound to work.", "constraint": "1 <= N <= 2 * 10^5\n1 <= K <= N\n0 <= C <= N\nThe length of S is N.\nEach character of S is o or x.\nTakahashi can choose his workdays so that the conditions in Problem Statement are satisfied.", "input": "Input is given from Standard Input in the following format:\nN K C\nS", "output": "Print all days on which Takahashi is bound to work in ascending order, one per line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11 3 2\nooxxxoxxxoo output: 6\n\nTakahashi is going to work on 3 days out of the 11 days. After working for a day, he will refrain from working on the subsequent 2 days.\nThere are four possible choices for his workdays: Day 1,6,10, Day 1,6,11, Day 2,6,10, and Day 2,6,11.\nThus, he is bound to work on Day 6.", "input: 5 2 3\nooxoo output: 1\n5\n\nThere is only one possible choice for his workdays: Day 1,5.", "input: 5 1 0\nooooo output: There may be no days on which he is bound to work.", "input: 16 4 3\nooxxoxoxxxoxoxxo output: 11\n16"], "Pid": "p02721", "ProblemText": "Task Description: Problem Statement Takahashi has decided to work on K days of his choice from the N days starting with tomorrow.\nYou are given an integer C and a string S. Takahashi will choose his workdays as follows:\n\nAfter working for a day, he will refrain from working on the subsequent C days.\nIf the i-th character of S is x, he will not work on Day i, where Day 1 is tomorrow, Day 2 is the day after tomorrow, and so on.\n\nFind all days on which Takahashi is bound to work.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= K <= N\n0 <= C <= N\nThe length of S is N.\nEach character of S is o or x.\nTakahashi can choose his workdays so that the conditions in Problem Statement are satisfied.\nTask Input: Input is given from Standard Input in the following format:\nN K C\nS\nTask Output: Print all days on which Takahashi is bound to work in ascending order, one per line.\nTask Samples: input: 11 3 2\nooxxxoxxxoo output: 6\n\nTakahashi is going to work on 3 days out of the 11 days. After working for a day, he will refrain from working on the subsequent 2 days.\nThere are four possible choices for his workdays: Day 1,6,10, Day 1,6,11, Day 2,6,10, and Day 2,6,11.\nThus, he is bound to work on Day 6.\ninput: 5 2 3\nooxoo output: 1\n5\n\nThere is only one possible choice for his workdays: Day 1,5.\ninput: 5 1 0\nooooo output: There may be no days on which he is bound to work.\ninput: 16 4 3\nooxxoxoxxxoxoxxo output: 11\n16\n\n" }, { "title": "", "content": "Problem Statement Given is a positive integer N.\nWe will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.\n\nOperation: if K divides N, replace N with N/K; otherwise, replace N with N-K.\n\nIn how many choices of K will N become 1 in the end?", "constraint": "2 <= N <= 10^{12}\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of choices of K in which N becomes 1 in the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 output: 3\n\nThere are three choices of K in which N becomes 1 in the end: 2,5, and 6.\nIn each of these choices, N will change as follows:\n\nWhen K=2: 6 \\to 3 \\to 1\nWhen K=5: 6 \\to 1\nWhen K=6: 6 \\to 1", "input: 3141 output: 13", "input: 314159265358 output: 9"], "Pid": "p02722", "ProblemText": "Task Description: Problem Statement Given is a positive integer N.\nWe will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.\n\nOperation: if K divides N, replace N with N/K; otherwise, replace N with N-K.\n\nIn how many choices of K will N become 1 in the end?\nTask Constraint: 2 <= N <= 10^{12}\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of choices of K in which N becomes 1 in the end.\nTask Samples: input: 6 output: 3\n\nThere are three choices of K in which N becomes 1 in the end: 2,5, and 6.\nIn each of these choices, N will change as follows:\n\nWhen K=2: 6 \\to 3 \\to 1\nWhen K=5: 6 \\to 1\nWhen K=6: 6 \\to 1\ninput: 3141 output: 13\ninput: 314159265358 output: 9\n\n" }, { "title": "", "content": "Problem Statement A string of length 6 consisting of lowercase English letters is said to be coffee-like if and only if its 3-rd and 4-th characters are equal and its 5-th and 6-th characters are also equal.\nGiven a string S, determine whether it is coffee-like.", "constraint": "S is a string of length 6 consisting of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S is coffee-like, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: sippuu output: Yes\n\nIn sippuu, the 3-rd and 4-th characters are equal, and the 5-th and 6-th characters are also equal.", "input: iphone output: No", "input: coffee output: Yes"], "Pid": "p02723", "ProblemText": "Task Description: Problem Statement A string of length 6 consisting of lowercase English letters is said to be coffee-like if and only if its 3-rd and 4-th characters are equal and its 5-th and 6-th characters are also equal.\nGiven a string S, determine whether it is coffee-like.\nTask Constraint: S is a string of length 6 consisting of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S is coffee-like, print Yes; otherwise, print No.\nTask Samples: input: sippuu output: Yes\n\nIn sippuu, the 3-rd and 4-th characters are equal, and the 5-th and 6-th characters are also equal.\ninput: iphone output: No\ninput: coffee output: Yes\n\n" }, { "title": "", "content": "Problem Statement Takahashi loves gold coins. He gains 1000 happiness points for each 500-yen coin he has and gains 5 happiness points for each 5-yen coin he has. (Yen is the currency of Japan. )\nTakahashi has X yen. If he exchanges his money so that he will gain the most happiness points, how many happiness points will he earn?\n(We assume that there are six kinds of coins available: 500-yen, 100-yen, 50-yen, 10-yen, 5-yen, and 1-yen coins. )", "constraint": "0 <= X <= 10^9\nX is an integer.", "input": "Input is given from Standard Input in the following format:\nX", "output": "Print the maximum number of happiness points that can be earned.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1024 output: 2020\n\nBy exchanging his money so that he gets two 500-yen coins and four 5-yen coins, he gains 2020 happiness points, which is the maximum number of happiness points that can be earned.", "input: 0 output: 0\n\nHe is penniless - or yenless.", "input: 1000000000 output: 2000000000\n\nHe is a billionaire - in yen."], "Pid": "p02724", "ProblemText": "Task Description: Problem Statement Takahashi loves gold coins. He gains 1000 happiness points for each 500-yen coin he has and gains 5 happiness points for each 5-yen coin he has. (Yen is the currency of Japan. )\nTakahashi has X yen. If he exchanges his money so that he will gain the most happiness points, how many happiness points will he earn?\n(We assume that there are six kinds of coins available: 500-yen, 100-yen, 50-yen, 10-yen, 5-yen, and 1-yen coins. )\nTask Constraint: 0 <= X <= 10^9\nX is an integer.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: Print the maximum number of happiness points that can be earned.\nTask Samples: input: 1024 output: 2020\n\nBy exchanging his money so that he gets two 500-yen coins and four 5-yen coins, he gains 2020 happiness points, which is the maximum number of happiness points that can be earned.\ninput: 0 output: 0\n\nHe is penniless - or yenless.\ninput: 1000000000 output: 2000000000\n\nHe is a billionaire - in yen.\n\n" }, { "title": "", "content": "Problem Statement There is a circular pond with a perimeter of K meters, and N houses around them.\nThe i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.\nWhen traveling between these houses, you can only go around the pond.\nFind the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.", "constraint": "2 <= K <= 10^6\n2 <= N <= 2 * 10^5\n0 <= A_1 < ... < A_N < K\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nK N\nA_1 A_2 . . . A_N", "output": "Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 20 3\n5 10 15 output: 10\n\nIf you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.", "input: 20 3\n0 5 15 output: 10\n\nIf you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10."], "Pid": "p02725", "ProblemText": "Task Description: Problem Statement There is a circular pond with a perimeter of K meters, and N houses around them.\nThe i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.\nWhen traveling between these houses, you can only go around the pond.\nFind the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.\nTask Constraint: 2 <= K <= 10^6\n2 <= N <= 2 * 10^5\n0 <= A_1 < ... < A_N < K\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nK N\nA_1 A_2 . . . A_N\nTask Output: Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.\nTask Samples: input: 20 3\n5 10 15 output: 10\n\nIf you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.\ninput: 20 3\n0 5 15 output: 10\n\nIf you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.\n\n" }, { "title": "", "content": "Problem Statement\nWe have an undirected graph G with N vertices numbered 1 to N and N edges as follows:\n\nFor each i=1,2, . . . , N-1, there is an edge between Vertex i and Vertex i+1.\nThere is an edge between Vertex X and Vertex Y.\n\nFor each k=1,2, . . . , N-1, solve the problem below:\n\nFind the number of pairs of integers (i, j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j in G is k.", "constraint": "3 <= N <= 2 * 10^3\n1 <= X,Y <= N\nX+1 < Y\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X Y", "output": "For each k=1,2, . . . , N-1 in this order, print a line containing the answer to the problem.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 4 output: 5\n4\n1\n0\n\nThe graph in this input is as follows:\n\nThere are five pairs (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 1: (1,2)\\,,(2,3)\\,,(2,4)\\,,(3,4)\\,,(4,5).\n\nThere are four pairs (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 2: (1,3)\\,,(1,4)\\,,(2,5)\\,,(3,5).\n\nThere is one pair (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 3: (1,5).\n\nThere are no pairs (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 4.", "input: 3 1 3 output: 3\n0\n\nThe graph in this input is as follows:", "input: 7 3 7 output: 7\n8\n4\n2\n0\n0", "input: 10 4 8 output: 10\n12\n10\n8\n4\n1\n0\n0\n0"], "Pid": "p02726", "ProblemText": "Task Description: Problem Statement\nWe have an undirected graph G with N vertices numbered 1 to N and N edges as follows:\n\nFor each i=1,2, . . . , N-1, there is an edge between Vertex i and Vertex i+1.\nThere is an edge between Vertex X and Vertex Y.\n\nFor each k=1,2, . . . , N-1, solve the problem below:\n\nFind the number of pairs of integers (i, j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j in G is k.\nTask Constraint: 3 <= N <= 2 * 10^3\n1 <= X,Y <= N\nX+1 < Y\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X Y\nTask Output: For each k=1,2, . . . , N-1 in this order, print a line containing the answer to the problem.\nTask Samples: input: 5 2 4 output: 5\n4\n1\n0\n\nThe graph in this input is as follows:\n\nThere are five pairs (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 1: (1,2)\\,,(2,3)\\,,(2,4)\\,,(3,4)\\,,(4,5).\n\nThere are four pairs (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 2: (1,3)\\,,(1,4)\\,,(2,5)\\,,(3,5).\n\nThere is one pair (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 3: (1,5).\n\nThere are no pairs (i,j) (1 <= i < j <= N) such that the shortest distance between Vertex i and Vertex j is 4.\ninput: 3 1 3 output: 3\n0\n\nThe graph in this input is as follows:\ninput: 7 3 7 output: 7\n8\n4\n2\n0\n0\ninput: 10 4 8 output: 10\n12\n10\n8\n4\n1\n0\n0\n0\n\n" }, { "title": "", "content": "Problem Statement You are going to eat X red apples and Y green apples.\nYou have A red apples of deliciousness p_1, p_2, \\dots, p_A, B green apples of deliciousness q_1, q_2, \\dots, q_B, and C colorless apples of deliciousness r_1, r_2, \\dots, r_C.\nBefore eating a colorless apple, you can paint it red or green, and it will count as a red or green apple, respectively.\nFrom the apples above, you will choose the apples to eat while making the sum of the deliciousness of the eaten apples as large as possible.\nFind the maximum possible sum of the deliciousness of the eaten apples that can be achieved when optimally coloring zero or more colorless apples.", "constraint": "1 <= X <= A <= 10^5\n1 <= Y <= B <= 10^5\n1 <= C <= 10^5\n1 <= p_i <= 10^9\n1 <= q_i <= 10^9\n1 <= r_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX Y A B C\np_1 p_2 . . . p_A\nq_1 q_2 . . . q_B\nr_1 r_2 . . . r_C", "output": "Print the maximum possible sum of the deliciousness of the eaten apples.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 2 2 1\n2 4\n5 1\n3 output: 12\n\nThe maximum possible sum of the deliciousness of the eaten apples can be achieved as follows:\n\nEat the 2-nd red apple.\nEat the 1-st green apple.\nPaint the 1-st colorless apple green and eat it.", "input: 2 2 2 2 2\n8 6\n9 1\n2 1 output: 25", "input: 2 2 4 4 4\n11 12 13 14\n21 22 23 24\n1 2 3 4 output: 74"], "Pid": "p02727", "ProblemText": "Task Description: Problem Statement You are going to eat X red apples and Y green apples.\nYou have A red apples of deliciousness p_1, p_2, \\dots, p_A, B green apples of deliciousness q_1, q_2, \\dots, q_B, and C colorless apples of deliciousness r_1, r_2, \\dots, r_C.\nBefore eating a colorless apple, you can paint it red or green, and it will count as a red or green apple, respectively.\nFrom the apples above, you will choose the apples to eat while making the sum of the deliciousness of the eaten apples as large as possible.\nFind the maximum possible sum of the deliciousness of the eaten apples that can be achieved when optimally coloring zero or more colorless apples.\nTask Constraint: 1 <= X <= A <= 10^5\n1 <= Y <= B <= 10^5\n1 <= C <= 10^5\n1 <= p_i <= 10^9\n1 <= q_i <= 10^9\n1 <= r_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y A B C\np_1 p_2 . . . p_A\nq_1 q_2 . . . q_B\nr_1 r_2 . . . r_C\nTask Output: Print the maximum possible sum of the deliciousness of the eaten apples.\nTask Samples: input: 1 2 2 2 1\n2 4\n5 1\n3 output: 12\n\nThe maximum possible sum of the deliciousness of the eaten apples can be achieved as follows:\n\nEat the 2-nd red apple.\nEat the 1-st green apple.\nPaint the 1-st colorless apple green and eat it.\ninput: 2 2 2 2 2\n8 6\n9 1\n2 1 output: 25\ninput: 2 2 4 4 4\n11 12 13 14\n21 22 23 24\n1 2 3 4 output: 74\n\n" }, { "title": "", "content": "Problem Statement\nWe have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i.\nFor each k=1, . . . , N, solve the problem below:\n\nConsider writing a number on each vertex in the tree in the following manner:\nFirst, write 1 on Vertex k.\nThen, for each of the numbers 2, . . . , N in this order, write the number on the vertex chosen as follows:\nChoose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.\nFind the number of ways in which we can write the numbers on the vertices, modulo (10^9+7).", "constraint": "2 <= N <= 2 * 10^5\n1 <= a_i,b_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}", "output": "For each k=1,2, . . . , N in this order, print a line containing the answer to the problem.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n1 3 output: 2\n1\n1\n\nThe graph in this input is as follows:\n\nFor k=1, there are two ways in which we can write the numbers on the vertices, as follows:\n\nWriting 1,2,3 on Vertex 1,2,3, respectively\nWriting 1,3,2 on Vertex 1,2,3, respectively", "input: 2\n1 2 output: 1\n1\n\nThe graph in this input is as follows:", "input: 5\n1 2\n2 3\n3 4\n3 5 output: 2\n8\n12\n3\n3\n\nThe graph in this input is as follows:", "input: 8\n1 2\n2 3\n3 4\n3 5\n3 6\n6 7\n6 8 output: 40\n280\n840\n120\n120\n504\n72\n72\n\nThe graph in this input is as follows:"], "Pid": "p02728", "ProblemText": "Task Description: Problem Statement\nWe have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i.\nFor each k=1, . . . , N, solve the problem below:\n\nConsider writing a number on each vertex in the tree in the following manner:\nFirst, write 1 on Vertex k.\nThen, for each of the numbers 2, . . . , N in this order, write the number on the vertex chosen as follows:\nChoose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.\nFind the number of ways in which we can write the numbers on the vertices, modulo (10^9+7).\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= a_i,b_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nTask Output: For each k=1,2, . . . , N in this order, print a line containing the answer to the problem.\nTask Samples: input: 3\n1 2\n1 3 output: 2\n1\n1\n\nThe graph in this input is as follows:\n\nFor k=1, there are two ways in which we can write the numbers on the vertices, as follows:\n\nWriting 1,2,3 on Vertex 1,2,3, respectively\nWriting 1,3,2 on Vertex 1,2,3, respectively\ninput: 2\n1 2 output: 1\n1\n\nThe graph in this input is as follows:\ninput: 5\n1 2\n2 3\n3 4\n3 5 output: 2\n8\n12\n3\n3\n\nThe graph in this input is as follows:\ninput: 8\n1 2\n2 3\n3 4\n3 5\n3 6\n6 7\n6 8 output: 40\n280\n840\n120\n120\n504\n72\n72\n\nThe graph in this input is as follows:\n\n" }, { "title": "", "content": "Problem Statement\nWe have N+M balls, each of which has an integer written on it.\nIt is known that: \n\nThe numbers written on N of the balls are even.\nThe numbers written on M of the balls are odd.\n\nFind the number of ways to choose two of the N+M balls (disregarding order) so that the sum of the numbers written on them is even.\nIt can be shown that this count does not depend on the actual values written on the balls.", "constraint": "0 <= N,M <= 100\n2 <= N+M\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 output: 1\n\nFor example, let us assume that the numbers written on the three balls are 1,2,4.\n\nIf we choose the two balls with 1 and 2, the sum is odd;\nIf we choose the two balls with 1 and 4, the sum is odd;\nIf we choose the two balls with 2 and 4, the sum is even.\n\nThus, the answer is 1.", "input: 4 3 output: 9", "input: 1 1 output: 0", "input: 13 3 output: 81", "input: 0 3 output: 3"], "Pid": "p02729", "ProblemText": "Task Description: Problem Statement\nWe have N+M balls, each of which has an integer written on it.\nIt is known that: \n\nThe numbers written on N of the balls are even.\nThe numbers written on M of the balls are odd.\n\nFind the number of ways to choose two of the N+M balls (disregarding order) so that the sum of the numbers written on them is even.\nIt can be shown that this count does not depend on the actual values written on the balls.\nTask Constraint: 0 <= N,M <= 100\n2 <= N+M\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the answer.\nTask Samples: input: 2 1 output: 1\n\nFor example, let us assume that the numbers written on the three balls are 1,2,4.\n\nIf we choose the two balls with 1 and 2, the sum is odd;\nIf we choose the two balls with 1 and 4, the sum is odd;\nIf we choose the two balls with 2 and 4, the sum is even.\n\nThus, the answer is 1.\ninput: 4 3 output: 9\ninput: 1 1 output: 0\ninput: 13 3 output: 81\ninput: 0 3 output: 3\n\n" }, { "title": "", "content": "Problem Statement A string S of an odd length is said to be a strong palindrome if and only if all of the following conditions are satisfied:\n\nS is a palindrome.\nLet N be the length of S. The string formed by the 1-st through ((N-1)/2)-th characters of S is a palindrome.\nThe string consisting of the (N+3)/2-st through N-th characters of S is a palindrome.\n\nDetermine whether S is a strong palindrome.", "constraint": "S consists of lowercase English letters.\nThe length of S is an odd number between 3 and 99 (inclusive).", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S is a strong palindrome, print Yes;\notherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: akasaka output: Yes\nS is akasaka.\nThe string formed by the 1-st through the 3-rd characters is aka.\nThe string formed by the 5-th through the 7-th characters is aka.\nAll of these are palindromes, so S is a strong palindrome.", "input: level output: No", "input: atcoder output: No"], "Pid": "p02730", "ProblemText": "Task Description: Problem Statement A string S of an odd length is said to be a strong palindrome if and only if all of the following conditions are satisfied:\n\nS is a palindrome.\nLet N be the length of S. The string formed by the 1-st through ((N-1)/2)-th characters of S is a palindrome.\nThe string consisting of the (N+3)/2-st through N-th characters of S is a palindrome.\n\nDetermine whether S is a strong palindrome.\nTask Constraint: S consists of lowercase English letters.\nThe length of S is an odd number between 3 and 99 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S is a strong palindrome, print Yes;\notherwise, print No.\nTask Samples: input: akasaka output: Yes\nS is akasaka.\nThe string formed by the 1-st through the 3-rd characters is aka.\nThe string formed by the 5-th through the 7-th characters is aka.\nAll of these are palindromes, so S is a strong palindrome.\ninput: level output: No\ninput: atcoder output: No\n\n" }, { "title": "", "content": "Problem Statement Given is a positive integer L.\nFind the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L.", "constraint": "1 <= L <= 1000\nL is an integer.", "input": "Input is given from Standard Input in the following format:\nL", "output": "Print the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L.\nYour output is considered correct if its absolute or relative error from our answer is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 1.000000000000\n\nFor example, a rectangular cuboid whose dimensions are 0.8,1, and 1.2 has a volume of 0.96.\nOn the other hand, if the dimensions are 1,1, and 1, the volume of the rectangular cuboid is 1, which is greater.", "input: 999 output: 36926037.000000000000"], "Pid": "p02731", "ProblemText": "Task Description: Problem Statement Given is a positive integer L.\nFind the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L.\nTask Constraint: 1 <= L <= 1000\nL is an integer.\nTask Input: Input is given from Standard Input in the following format:\nL\nTask Output: Print the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L.\nYour output is considered correct if its absolute or relative error from our answer is at most 10^{-6}.\nTask Samples: input: 3 output: 1.000000000000\n\nFor example, a rectangular cuboid whose dimensions are 0.8,1, and 1.2 has a volume of 0.96.\nOn the other hand, if the dimensions are 1,1, and 1, the volume of the rectangular cuboid is 1, which is greater.\ninput: 999 output: 36926037.000000000000\n\n" }, { "title": "", "content": "Problem Statement\nWe have N balls. The i-th ball has an integer A_i written on it.\nFor each k=1,2, . . . , N, solve the following problem and print the answer. \n\nFind the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.", "constraint": "3 <= N <= 2 * 10^5\n1 <= A_i <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "For each k=1,2, . . . , N, print a line containing the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 1 2 1 2 output: 2\n2\n3\n2\n3\n\nConsider the case k=1 for example. The numbers written on the remaining balls are 1,2,1,2.\nFrom these balls, there are two ways to choose two distinct balls so that the integers written on them are equal.\nThus, the answer for k=1 is 2.", "input: 4\n1 2 3 4 output: 0\n0\n0\n0\n\nNo two balls have equal numbers written on them.", "input: 5\n3 3 3 3 3 output: 6\n6\n6\n6\n6\n\nAny two balls have equal numbers written on them.", "input: 8\n1 2 1 4 2 1 4 1 output: 5\n7\n5\n7\n7\n5\n7\n5"], "Pid": "p02732", "ProblemText": "Task Description: Problem Statement\nWe have N balls. The i-th ball has an integer A_i written on it.\nFor each k=1,2, . . . , N, solve the following problem and print the answer. \n\nFind the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.\nTask Constraint: 3 <= N <= 2 * 10^5\n1 <= A_i <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: For each k=1,2, . . . , N, print a line containing the answer.\nTask Samples: input: 5\n1 1 2 1 2 output: 2\n2\n3\n2\n3\n\nConsider the case k=1 for example. The numbers written on the remaining balls are 1,2,1,2.\nFrom these balls, there are two ways to choose two distinct balls so that the integers written on them are equal.\nThus, the answer for k=1 is 2.\ninput: 4\n1 2 3 4 output: 0\n0\n0\n0\n\nNo two balls have equal numbers written on them.\ninput: 5\n3 3 3 3 3 output: 6\n6\n6\n6\n6\n\nAny two balls have equal numbers written on them.\ninput: 8\n1 2 1 4 2 1 4 1 output: 5\n7\n5\n7\n7\n5\n7\n5\n\n" }, { "title": "", "content": "Problem Statement We have a chocolate bar partitioned into H horizontal rows and W vertical columns of squares.\nThe square (i, j) at the i-th row from the top and the j-th column from the left is dark if S_{i, j} is 0, and white if S_{i, j} is 1.\nWe will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.\nHow many times do we need to cut the bar so that every block after the cuts has K or less white squares?", "constraint": "1 <= H <= 10\n1 <= W <= 1000\n1 <= K <= H * W\nS_{i,j} is 0 or 1.", "input": "Input is given from Standard Input in the following format:\nH W K\nS_{1,1}S_{1,2}. . . S_{1, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}", "output": "Print the number of minimum times the bar needs to be cut so that every block after the cuts has K or less white squares.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 4\n11100\n10001\n00111 output: 2\n\nFor example, cutting between the 1-st and 2-nd rows and between the 3-rd and 4-th columns - as shown in the figure to the left - works.\nNote that we cannot cut the bar in the ways shown in the two figures to the right.", "input: 3 5 8\n11100\n10001\n00111 output: 0\n\nNo cut is needed.", "input: 4 10 4\n1110010010\n1000101110\n0011101001\n1101000111 output: 3"], "Pid": "p02733", "ProblemText": "Task Description: Problem Statement We have a chocolate bar partitioned into H horizontal rows and W vertical columns of squares.\nThe square (i, j) at the i-th row from the top and the j-th column from the left is dark if S_{i, j} is 0, and white if S_{i, j} is 1.\nWe will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.\nHow many times do we need to cut the bar so that every block after the cuts has K or less white squares?\nTask Constraint: 1 <= H <= 10\n1 <= W <= 1000\n1 <= K <= H * W\nS_{i,j} is 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nH W K\nS_{1,1}S_{1,2}. . . S_{1, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}\nTask Output: Print the number of minimum times the bar needs to be cut so that every block after the cuts has K or less white squares.\nTask Samples: input: 3 5 4\n11100\n10001\n00111 output: 2\n\nFor example, cutting between the 1-st and 2-nd rows and between the 3-rd and 4-th columns - as shown in the figure to the left - works.\nNote that we cannot cut the bar in the ways shown in the two figures to the right.\ninput: 3 5 8\n11100\n10001\n00111 output: 0\n\nNo cut is needed.\ninput: 4 10 4\n1110010010\n1000101110\n0011101001\n1101000111 output: 3\n\n" }, { "title": "", "content": "Problem Statement Given are a sequence of N integers A_1, A_2, \\ldots, A_N and a positive integer S.\nFor a pair of integers (L, R) such that 1<= L <= R <= N, let us define f(L, R) as follows:\n\nf(L, R) is the number of sequences of integers (x_1, x_2, \\ldots , x_k) such that L <= x_1 < x_2 < \\cdots < x_k <= R and A_{x_1}+A_{x_2}+\\cdots +A_{x_k} = S.\n\nFind the sum of f(L, R) over all pairs of integers (L, R) such that 1<= L <= R<= N. Since this sum can be enormous, print it modulo 998244353.", "constraint": "All values in input are integers.\n1 <= N <= 3000\n1 <= S <= 3000\n1 <= A_i <= 3000", "input": "Input is given from Standard Input in the following format:\nN S\nA_1 A_2 . . . A_N", "output": "Print the sum of f(L, R), modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n2 2 4 output: 5\n\nThe value of f(L, R) for each pair is as follows, for a total of 5.\n\nf(1,1) = 0\nf(1,2) = 1 (for the sequence (1,2))\nf(1,3) = 2 (for (1,2) and (3))\nf(2,2) = 0\nf(2,3) = 1 (for (3))\nf(3,3) = 1 (for (3))", "input: 5 8\n9 9 9 9 9 output: 0", "input: 10 10\n3 1 4 1 5 9 2 6 5 3 output: 152"], "Pid": "p02734", "ProblemText": "Task Description: Problem Statement Given are a sequence of N integers A_1, A_2, \\ldots, A_N and a positive integer S.\nFor a pair of integers (L, R) such that 1<= L <= R <= N, let us define f(L, R) as follows:\n\nf(L, R) is the number of sequences of integers (x_1, x_2, \\ldots , x_k) such that L <= x_1 < x_2 < \\cdots < x_k <= R and A_{x_1}+A_{x_2}+\\cdots +A_{x_k} = S.\n\nFind the sum of f(L, R) over all pairs of integers (L, R) such that 1<= L <= R<= N. Since this sum can be enormous, print it modulo 998244353.\nTask Constraint: All values in input are integers.\n1 <= N <= 3000\n1 <= S <= 3000\n1 <= A_i <= 3000\nTask Input: Input is given from Standard Input in the following format:\nN S\nA_1 A_2 . . . A_N\nTask Output: Print the sum of f(L, R), modulo 998244353.\nTask Samples: input: 3 4\n2 2 4 output: 5\n\nThe value of f(L, R) for each pair is as follows, for a total of 5.\n\nf(1,1) = 0\nf(1,2) = 1 (for the sequence (1,2))\nf(1,3) = 2 (for (1,2) and (3))\nf(2,2) = 0\nf(2,3) = 1 (for (3))\nf(3,3) = 1 (for (3))\ninput: 5 8\n9 9 9 9 9 output: 0\ninput: 10 10\n3 1 4 1 5 9 2 6 5 3 output: 152\n\n" }, { "title": "", "content": "Problem Statement Consider a grid with H rows and W columns of squares. Let (r, c) denote the square at the r-th row from the top and the c-th column from the left.\nEach square is painted black or white.\nThe grid is said to be good if and only if the following condition is satisfied:\n\nFrom (1,1), we can reach (H, W) by moving one square right or down repeatedly, while always being on a white square.\n\nNote that (1,1) and (H, W) must be white if the grid is good.\nYour task is to make the grid good by repeating the operation below. Find the minimum number of operations needed to complete the task. It can be proved that you can always complete the task in a finite number of operations.\n\nChoose four integers r_0, c_0, r_1, c_1(1 <= r_0 <= r_1 <= H, 1 <= c_0 <= c_1 <= W). For each pair r, c (r_0 <= r <= r_1, c_0 <= c <= c_1), invert the color of (r, c) - that is, from white to black and vice versa.", "constraint": "2 <= H, W <= 100", "input": "Input is given from Standard Input in the following format:\nH W\ns_{11} s_{12} \\cdots s_{1W}\ns_{21} s_{22} \\cdots s_{2W}\n \\vdots\ns_{H1} s_{H2} \\cdots s_{HW}\n\nHere s_{rc} represents the color of (r, c) - # stands for black, and . stands for white.", "output": "Print the minimum number of operations needed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n.##\n.#.\n##. output: 1\n\nDo the operation with (r_0, c_0, r_1, c_1) = (2,2,2,2) to change just the color of (2,2), and we are done.", "input: 2 2\n#.\n.# output: 2", "input: 4 4\n..##\n#...\n###.\n###. output: 0\n\nNo operation may be needed.", "input: 5 5\n.#.#.\n#.#.#\n.#.#.\n#.#.#\n.#.#. output: 4"], "Pid": "p02735", "ProblemText": "Task Description: Problem Statement Consider a grid with H rows and W columns of squares. Let (r, c) denote the square at the r-th row from the top and the c-th column from the left.\nEach square is painted black or white.\nThe grid is said to be good if and only if the following condition is satisfied:\n\nFrom (1,1), we can reach (H, W) by moving one square right or down repeatedly, while always being on a white square.\n\nNote that (1,1) and (H, W) must be white if the grid is good.\nYour task is to make the grid good by repeating the operation below. Find the minimum number of operations needed to complete the task. It can be proved that you can always complete the task in a finite number of operations.\n\nChoose four integers r_0, c_0, r_1, c_1(1 <= r_0 <= r_1 <= H, 1 <= c_0 <= c_1 <= W). For each pair r, c (r_0 <= r <= r_1, c_0 <= c <= c_1), invert the color of (r, c) - that is, from white to black and vice versa.\nTask Constraint: 2 <= H, W <= 100\nTask Input: Input is given from Standard Input in the following format:\nH W\ns_{11} s_{12} \\cdots s_{1W}\ns_{21} s_{22} \\cdots s_{2W}\n \\vdots\ns_{H1} s_{H2} \\cdots s_{HW}\n\nHere s_{rc} represents the color of (r, c) - # stands for black, and . stands for white.\nTask Output: Print the minimum number of operations needed.\nTask Samples: input: 3 3\n.##\n.#.\n##. output: 1\n\nDo the operation with (r_0, c_0, r_1, c_1) = (2,2,2,2) to change just the color of (2,2), and we are done.\ninput: 2 2\n#.\n.# output: 2\ninput: 4 4\n..##\n#...\n###.\n###. output: 0\n\nNo operation may be needed.\ninput: 5 5\n.#.#.\n#.#.#\n.#.#.\n#.#.#\n.#.#. output: 4\n\n" }, { "title": "", "content": "Problem Statement Given is a sequence of N digits a_1a_2\\ldots a_N, where each element is 1,2, or 3.\nLet x_{i, j} defined as follows:\n\nx_{1, j} : = a_j \\quad (1 <= j <= N)\nx_{i, j} : = | x_{i-1, j} - x_{i-1, j+1} | \\quad (2 <= i <= N and 1 <= j <= N+1-i)\n\nFind x_{N, 1}.", "constraint": "2 <= N <= 10^6\na_i = 1,2,3 (1 <= i <= N)", "input": "Input is given from Standard Input in the following format:\nN\na_1a_2\\ldotsa_N", "output": "Print x_{N, 1}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1231 output: 1\n\nx_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.\nx_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.\nx_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.\nFinally, x_{4,1} = |0-1| = 1, so the answer is 1.", "input: 10\n2311312312 output: 0"], "Pid": "p02736", "ProblemText": "Task Description: Problem Statement Given is a sequence of N digits a_1a_2\\ldots a_N, where each element is 1,2, or 3.\nLet x_{i, j} defined as follows:\n\nx_{1, j} : = a_j \\quad (1 <= j <= N)\nx_{i, j} : = | x_{i-1, j} - x_{i-1, j+1} | \\quad (2 <= i <= N and 1 <= j <= N+1-i)\n\nFind x_{N, 1}.\nTask Constraint: 2 <= N <= 10^6\na_i = 1,2,3 (1 <= i <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\na_1a_2\\ldotsa_N\nTask Output: Print x_{N, 1}.\nTask Samples: input: 4\n1231 output: 1\n\nx_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.\nx_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.\nx_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.\nFinally, x_{4,1} = |0-1| = 1, so the answer is 1.\ninput: 10\n2311312312 output: 0\n\n" }, { "title": "", "content": "Problem Statement Given are simple undirected graphs X, Y, Z, with N vertices each and M_1, M_2, M_3 edges, respectively.\nThe vertices in X, Y, Z are respectively called x_1, x_2, \\dots, x_N, y_1, y_2, \\dots, y_N, z_1, z_2, \\dots, z_N.\nThe edges in X, Y, Z are respectively (x_{a_i}, x_{b_i}), (y_{c_i}, y_{d_i}), (z_{e_i}, z_{f_i}).\nBased on X, Y, Z, we will build another undirected graph W with N^3 vertices.\nThere are N^3 ways to choose a vertex from each of the graphs X, Y, Z. Each of these choices corresponds to the vertices in W one-to-one. Let (x_i, y_j, z_k) denote the vertex in W corresponding to the choice of x_i, y_j, z_k.\nWe will span edges in W as follows:\n\nFor each edge (x_u, x_v) in X and each w, l, span an edge between (x_u, y_w, z_l) and (x_v, y_w, z_l).\nFor each edge (y_u, y_v) in Y and each w, l, span an edge between (x_w, y_u, z_l) and (x_w, y_v, z_l).\nFor each edge (z_u, z_v) in Z and each w, l, span an edge between (x_w, y_l, z_u) and (x_w, y_l, z_v).\n\nThen, let the weight of the vertex (x_i, y_j, z_k) in W be 1,000,000,000,000,000,000^{(i +j + k)} = 10^{18(i + j + k)}. Find the maximum possible total weight of the vertices in an independent set in W, and print that total weight modulo 998,244,353.", "constraint": "2 <= N <= 100,000\n1 <= M_1, M_2, M_3 <= 100,000\n1 <= a_i, b_i, c_i, d_i, e_i, f_i <= N\nX, Y, and Z are simple, that is, they have no self-loops and no multiple edges.", "input": "Input is given from Standard Input in the following format:\nN\nM_1\na_1 b_1\na_2 b_2\n\\vdots\na_{M_1} b_{M_1}\nM_2\nc_1 d_1\nc_2 d_2\n\\vdots\nc_{M_2} d_{M_2}\nM_3\ne_1 f_1\ne_2 f_2\n\\vdots\ne_{M_3} f_{M_3}", "output": "Print the maximum possible total weight of an independent set in W, modulo 998,244,353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1\n1 2\n1\n1 2\n1\n1 2 output: 46494701\n\nThe maximum possible total weight of an independent set is that of the set (x_2, y_1, z_1), (x_1, y_2, z_1), (x_1, y_1, z_2), (x_2, y_2, z_2). The output should be (3 * 10^{72} + 10^{108}) modulo 998,244,353, which is 46,494,701.", "input: 3\n3\n1 3\n1 2\n3 2\n2\n2 1\n2 3\n1\n2 1 output: 883188316", "input: 100000\n1\n1 2\n1\n99999 100000\n1\n1 100000 output: 318525248"], "Pid": "p02737", "ProblemText": "Task Description: Problem Statement Given are simple undirected graphs X, Y, Z, with N vertices each and M_1, M_2, M_3 edges, respectively.\nThe vertices in X, Y, Z are respectively called x_1, x_2, \\dots, x_N, y_1, y_2, \\dots, y_N, z_1, z_2, \\dots, z_N.\nThe edges in X, Y, Z are respectively (x_{a_i}, x_{b_i}), (y_{c_i}, y_{d_i}), (z_{e_i}, z_{f_i}).\nBased on X, Y, Z, we will build another undirected graph W with N^3 vertices.\nThere are N^3 ways to choose a vertex from each of the graphs X, Y, Z. Each of these choices corresponds to the vertices in W one-to-one. Let (x_i, y_j, z_k) denote the vertex in W corresponding to the choice of x_i, y_j, z_k.\nWe will span edges in W as follows:\n\nFor each edge (x_u, x_v) in X and each w, l, span an edge between (x_u, y_w, z_l) and (x_v, y_w, z_l).\nFor each edge (y_u, y_v) in Y and each w, l, span an edge between (x_w, y_u, z_l) and (x_w, y_v, z_l).\nFor each edge (z_u, z_v) in Z and each w, l, span an edge between (x_w, y_l, z_u) and (x_w, y_l, z_v).\n\nThen, let the weight of the vertex (x_i, y_j, z_k) in W be 1,000,000,000,000,000,000^{(i +j + k)} = 10^{18(i + j + k)}. Find the maximum possible total weight of the vertices in an independent set in W, and print that total weight modulo 998,244,353.\nTask Constraint: 2 <= N <= 100,000\n1 <= M_1, M_2, M_3 <= 100,000\n1 <= a_i, b_i, c_i, d_i, e_i, f_i <= N\nX, Y, and Z are simple, that is, they have no self-loops and no multiple edges.\nTask Input: Input is given from Standard Input in the following format:\nN\nM_1\na_1 b_1\na_2 b_2\n\\vdots\na_{M_1} b_{M_1}\nM_2\nc_1 d_1\nc_2 d_2\n\\vdots\nc_{M_2} d_{M_2}\nM_3\ne_1 f_1\ne_2 f_2\n\\vdots\ne_{M_3} f_{M_3}\nTask Output: Print the maximum possible total weight of an independent set in W, modulo 998,244,353.\nTask Samples: input: 2\n1\n1 2\n1\n1 2\n1\n1 2 output: 46494701\n\nThe maximum possible total weight of an independent set is that of the set (x_2, y_1, z_1), (x_1, y_2, z_1), (x_1, y_1, z_2), (x_2, y_2, z_2). The output should be (3 * 10^{72} + 10^{108}) modulo 998,244,353, which is 46,494,701.\ninput: 3\n3\n1 3\n1 2\n3 2\n2\n2 1\n2 3\n1\n2 1 output: 883188316\ninput: 100000\n1\n1 2\n1\n99999 100000\n1\n1 100000 output: 318525248\n\n" }, { "title": "", "content": "Problem Statement Given is a positive integer N.\nFind the number of permutations (P_1, P_2, \\cdots, P_{3N}) of (1,2, \\cdots, 3N) that can be generated through the procedure below.\nThis number can be enormous, so print it modulo a prime number M.\n\nMake N sequences A_1, A_2, \\cdots, A_N of length 3 each, using each of the integers 1 through 3N exactly once.\nLet P be an empty sequence, and do the following operation 3N times.\nAmong the elements that are at the beginning of one of the sequences A_i that is non-empty, let the smallest be x.\nRemove x from the sequence, and add x at the end of P.", "constraint": "1 <= N <= 2000\n10^8 <= M <= 10^9+7\nM is a prime number.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of permutations modulo M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 998244353 output: 6\n\nAll permutations of length 3 count.", "input: 2 998244353 output: 261", "input: 314 1000000007 output: 182908545"], "Pid": "p02738", "ProblemText": "Task Description: Problem Statement Given is a positive integer N.\nFind the number of permutations (P_1, P_2, \\cdots, P_{3N}) of (1,2, \\cdots, 3N) that can be generated through the procedure below.\nThis number can be enormous, so print it modulo a prime number M.\n\nMake N sequences A_1, A_2, \\cdots, A_N of length 3 each, using each of the integers 1 through 3N exactly once.\nLet P be an empty sequence, and do the following operation 3N times.\nAmong the elements that are at the beginning of one of the sequences A_i that is non-empty, let the smallest be x.\nRemove x from the sequence, and add x at the end of P.\nTask Constraint: 1 <= N <= 2000\n10^8 <= M <= 10^9+7\nM is a prime number.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of permutations modulo M.\nTask Samples: input: 1 998244353 output: 6\n\nAll permutations of length 3 count.\ninput: 2 998244353 output: 261\ninput: 314 1000000007 output: 182908545\n\n" }, { "title": "", "content": "Problem Statement Given are a positive integer N and a sequence of length 2^N consisting of 0s and 1s: A_0, A_1, \\ldots, A_{2^N-1}.\nDetermine whether there exists a closed curve C that satisfies the condition below for all 2^N sets S \\subseteq \\{0,1, \\ldots, N-1 \\}. If the answer is yes, construct one such closed curve.\n\nLet x = \\sum_{i \\in S} 2^i and B_S be the set of points \\{ (i+0.5,0.5) | i \\in S \\}.\nIf there is a way to continuously move the closed curve C without touching B_S so that every point on the closed curve has a negative y-coordinate, A_x = 1.\nIf there is no such way, A_x = 0.\n\nFor instruction on printing a closed curve, see Output below. note: Notes C is said to be a closed curve if and only if:\n\nC is a continuous function from [0,1] to \\mathbb{R}^2 such that C(0) = C(1).\n\nWe say that a closed curve C can be continuously moved without touching a set of points X so that it becomes a closed curve D if and only if:\n\nThere exists a function f : [0,1] * [0,1] \\rightarrow \\mathbb{R}^2 that satisfies all of the following.\nf is continuous.\nf(0, t) = C(t).\nf(1, t) = D(t).\nf(x, t) \\notin X.", "constraint": "1 <= N <= 8\nA_i = 0,1 \\quad (0 <= i <= 2^N-1)\nA_0 = 1", "input": "Input is given from Standard Input in the following format:\nN\nA_0A_1 \\cdots A_{2^N-1}", "output": "If there is no closed curve that satisfies the condition, print Impossible.\nIf such a closed curve exists, print Possible in the first line.\nThen, print one such curve in the following format:\nL\nx_0 y_0\nx_1 y_1\n:\nx_L y_L\n\nThis represents the closed polyline that passes (x_0, y_0), (x_1, y_1), \\ldots, (x_L, y_L) in this order.\nHere, all of the following must be satisfied:\n\n0 <= x_i <= N, 0 <= y_i <= 1, and x_i, y_i are integers. (0 <= i <= L)\n|x_i-x_{i+1}| + |y_i-y_{i+1}| = 1. (0 <= i <= L-1)\n(x_0, y_0) = (x_L, y_L).\n\nAdditionally, the length of the closed curve L must satisfy 0 <= L <= 250000.\nIt can be proved that, if there is a closed curve that satisfies the condition in Problem Statement, there is also a closed curve that can be expressed in this format.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n10 output: Possible\n4\n0 0\n0 1\n1 1\n1 0\n0 0\n\nWhen S = \\emptyset, we can move this curve so that every point on it has a negative y-coordinate.\n\nWhen S = \\{0\\}, we cannot do so.", "input: 2\n1000 output: Possible\n6\n1 0\n2 0\n2 1\n1 1\n0 1\n0 0\n1 0\n\nThe output represents the following curve:", "input: 2\n1001 output: Impossible", "input: 1\n11 output: Possible\n0\n1 1"], "Pid": "p02739", "ProblemText": "Task Description: Problem Statement Given are a positive integer N and a sequence of length 2^N consisting of 0s and 1s: A_0, A_1, \\ldots, A_{2^N-1}.\nDetermine whether there exists a closed curve C that satisfies the condition below for all 2^N sets S \\subseteq \\{0,1, \\ldots, N-1 \\}. If the answer is yes, construct one such closed curve.\n\nLet x = \\sum_{i \\in S} 2^i and B_S be the set of points \\{ (i+0.5,0.5) | i \\in S \\}.\nIf there is a way to continuously move the closed curve C without touching B_S so that every point on the closed curve has a negative y-coordinate, A_x = 1.\nIf there is no such way, A_x = 0.\n\nFor instruction on printing a closed curve, see Output below. note: Notes C is said to be a closed curve if and only if:\n\nC is a continuous function from [0,1] to \\mathbb{R}^2 such that C(0) = C(1).\n\nWe say that a closed curve C can be continuously moved without touching a set of points X so that it becomes a closed curve D if and only if:\n\nThere exists a function f : [0,1] * [0,1] \\rightarrow \\mathbb{R}^2 that satisfies all of the following.\nf is continuous.\nf(0, t) = C(t).\nf(1, t) = D(t).\nf(x, t) \\notin X.\nTask Constraint: 1 <= N <= 8\nA_i = 0,1 \\quad (0 <= i <= 2^N-1)\nA_0 = 1\nTask Input: Input is given from Standard Input in the following format:\nN\nA_0A_1 \\cdots A_{2^N-1}\nTask Output: If there is no closed curve that satisfies the condition, print Impossible.\nIf such a closed curve exists, print Possible in the first line.\nThen, print one such curve in the following format:\nL\nx_0 y_0\nx_1 y_1\n:\nx_L y_L\n\nThis represents the closed polyline that passes (x_0, y_0), (x_1, y_1), \\ldots, (x_L, y_L) in this order.\nHere, all of the following must be satisfied:\n\n0 <= x_i <= N, 0 <= y_i <= 1, and x_i, y_i are integers. (0 <= i <= L)\n|x_i-x_{i+1}| + |y_i-y_{i+1}| = 1. (0 <= i <= L-1)\n(x_0, y_0) = (x_L, y_L).\n\nAdditionally, the length of the closed curve L must satisfy 0 <= L <= 250000.\nIt can be proved that, if there is a closed curve that satisfies the condition in Problem Statement, there is also a closed curve that can be expressed in this format.\nTask Samples: input: 1\n10 output: Possible\n4\n0 0\n0 1\n1 1\n1 0\n0 0\n\nWhen S = \\emptyset, we can move this curve so that every point on it has a negative y-coordinate.\n\nWhen S = \\{0\\}, we cannot do so.\ninput: 2\n1000 output: Possible\n6\n1 0\n2 0\n2 1\n1 1\n0 1\n0 0\n1 0\n\nThe output represents the following curve:\ninput: 2\n1001 output: Impossible\ninput: 1\n11 output: Possible\n0\n1 1\n\n" }, { "title": "", "content": "Problem Statement There are N jewelry shops numbered 1 to N.\nShop i (1 <= i <= N) sells K_i kinds of jewels.\nThe j-th of these jewels (1 <= j <= K_i) has a size and price of S_{i, j} and P_{i, j}, respectively, and the shop has C_{i, j} jewels of this kind in stock.\nA jewelry box is said to be good if it satisfies all of the following conditions:\n\nFor each of the jewelry shops, the box contains one jewel purchased there.\nAll of the following M restrictions are met.\nRestriction i (1 <= i <= M): (The size of the jewel purchased at Shop V_i)<= (The size of the jewel purchased at Shop U_i)+W_i\n\nAnswer Q questions.\nIn the i-th question, given an integer A_i, find the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes. If it is impossible to make A_i good jewelry boxes, report that fact.", "constraint": "1 <= N <= 30\n1 <= K_i <= 30\n1 <= S_{i,j} <= 10^9\n1 <= P_{i,j} <= 30\n1 <= C_{i,j} <= 10^{12}\n0 <= M <= 50\n1 <= U_i,V_i <= N\nU_i \\neq V_i\n0 <= W_i <= 10^9\n1 <= Q <= 10^5\n1 <= A_i <= 3 * 10^{13}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nDescription of Shop 1\nDescription of Shop 2\n\\vdots\nDescription of Shop N\nM\nU_1 V_1 W_1\nU_2 V_2 W_2\n\\vdots\nU_M V_M W_M\nQ\nA_1\nA_2\n\\vdots\nA_Q\n\nThe description of Shop i (1 <= i <= N) is in the following format:\nK_i\nS_{i, 1} P_{i, 1} C_{i, 1}\nS_{i, 2} P_{i, 2} C_{i, 2}\n\\vdots\nS_{i, K_i} P_{i, K_i} C_{i, K_i}", "output": "Print Q lines.\nThe i-th line should contain the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes, or -1 if it is impossible to make them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2\n1 10 1\n3 1 1\n3\n1 10 1\n2 1 1\n3 10 1\n2\n1 1 1\n3 10 1\n2\n1 2 0\n2 3 0\n3\n1\n2\n3 output: 3\n42\n-1\n\nLet (i,j) represent the j-th jewel sold at Shop i.\nThe answer to each query is as follows:\n\nA_1=1: Making a box with (1,2),(2,2),(3,1) costs 1+1+1=3, which is optimal.\nA_2=2: Making a box with (1,1),(2,1),(3,1) and another with (1,2),(2,3),(3,2) costs (10+10+1)+(1+10+10)=42, which is optimal.\nA_3=3: We cannot make three good boxes.", "input: 5\n5\n86849520 30 272477201869\n968023357 28 539131386006\n478355090 8 194500792721\n298572419 6 894877901270\n203794105 25 594579473837\n5\n730211794 22 225797976416\n842538552 9 420531931830\n871332982 26 81253086754\n553846923 29 89734736118\n731788040 13 241088716205\n5\n903534485 22 140045153776\n187101906 8 145639722124\n513502442 9 227445343895\n499446330 6 719254728400\n564106748 20 333423097859\n5\n332809289 8 640911722470\n969492694 21 937931959818\n207959501 11 217019915462\n726936503 12 382527525674\n887971218 17 552919286358\n5\n444983655 13 487875689585\n855863581 6 625608576077\n885012925 10 105520979776\n980933856 1 711474069172\n653022356 19 977887412815\n10\n1 2 231274893\n2 3 829836076\n3 4 745221482\n4 5 935448462\n5 1 819308546\n3 5 815839350\n5 3 513188748\n3 1 968283437\n2 3 202352515\n4 3 292999238\n10\n510266667947\n252899314976\n510266667948\n374155726828\n628866122125\n628866122123\n1\n628866122124\n510266667949\n30000000000000 output: 26533866733244\n13150764378752\n26533866733296\n19456097795056\n-1\n33175436167096\n52\n33175436167152\n26533866733352\n-1"], "Pid": "p02740", "ProblemText": "Task Description: Problem Statement There are N jewelry shops numbered 1 to N.\nShop i (1 <= i <= N) sells K_i kinds of jewels.\nThe j-th of these jewels (1 <= j <= K_i) has a size and price of S_{i, j} and P_{i, j}, respectively, and the shop has C_{i, j} jewels of this kind in stock.\nA jewelry box is said to be good if it satisfies all of the following conditions:\n\nFor each of the jewelry shops, the box contains one jewel purchased there.\nAll of the following M restrictions are met.\nRestriction i (1 <= i <= M): (The size of the jewel purchased at Shop V_i)<= (The size of the jewel purchased at Shop U_i)+W_i\n\nAnswer Q questions.\nIn the i-th question, given an integer A_i, find the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes. If it is impossible to make A_i good jewelry boxes, report that fact.\nTask Constraint: 1 <= N <= 30\n1 <= K_i <= 30\n1 <= S_{i,j} <= 10^9\n1 <= P_{i,j} <= 30\n1 <= C_{i,j} <= 10^{12}\n0 <= M <= 50\n1 <= U_i,V_i <= N\nU_i \\neq V_i\n0 <= W_i <= 10^9\n1 <= Q <= 10^5\n1 <= A_i <= 3 * 10^{13}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nDescription of Shop 1\nDescription of Shop 2\n\\vdots\nDescription of Shop N\nM\nU_1 V_1 W_1\nU_2 V_2 W_2\n\\vdots\nU_M V_M W_M\nQ\nA_1\nA_2\n\\vdots\nA_Q\n\nThe description of Shop i (1 <= i <= N) is in the following format:\nK_i\nS_{i, 1} P_{i, 1} C_{i, 1}\nS_{i, 2} P_{i, 2} C_{i, 2}\n\\vdots\nS_{i, K_i} P_{i, K_i} C_{i, K_i}\nTask Output: Print Q lines.\nThe i-th line should contain the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes, or -1 if it is impossible to make them.\nTask Samples: input: 3\n2\n1 10 1\n3 1 1\n3\n1 10 1\n2 1 1\n3 10 1\n2\n1 1 1\n3 10 1\n2\n1 2 0\n2 3 0\n3\n1\n2\n3 output: 3\n42\n-1\n\nLet (i,j) represent the j-th jewel sold at Shop i.\nThe answer to each query is as follows:\n\nA_1=1: Making a box with (1,2),(2,2),(3,1) costs 1+1+1=3, which is optimal.\nA_2=2: Making a box with (1,1),(2,1),(3,1) and another with (1,2),(2,3),(3,2) costs (10+10+1)+(1+10+10)=42, which is optimal.\nA_3=3: We cannot make three good boxes.\ninput: 5\n5\n86849520 30 272477201869\n968023357 28 539131386006\n478355090 8 194500792721\n298572419 6 894877901270\n203794105 25 594579473837\n5\n730211794 22 225797976416\n842538552 9 420531931830\n871332982 26 81253086754\n553846923 29 89734736118\n731788040 13 241088716205\n5\n903534485 22 140045153776\n187101906 8 145639722124\n513502442 9 227445343895\n499446330 6 719254728400\n564106748 20 333423097859\n5\n332809289 8 640911722470\n969492694 21 937931959818\n207959501 11 217019915462\n726936503 12 382527525674\n887971218 17 552919286358\n5\n444983655 13 487875689585\n855863581 6 625608576077\n885012925 10 105520979776\n980933856 1 711474069172\n653022356 19 977887412815\n10\n1 2 231274893\n2 3 829836076\n3 4 745221482\n4 5 935448462\n5 1 819308546\n3 5 815839350\n5 3 513188748\n3 1 968283437\n2 3 202352515\n4 3 292999238\n10\n510266667947\n252899314976\n510266667948\n374155726828\n628866122125\n628866122123\n1\n628866122124\n510266667949\n30000000000000 output: 26533866733244\n13150764378752\n26533866733296\n19456097795056\n-1\n33175436167096\n52\n33175436167152\n26533866733352\n-1\n\n" }, { "title": "", "content": "Problem Statement Print the K-th element of the following sequence of length 32:\n1,1,1,2,1,2,1,5,2,2,1,5,1,2,1,14,1,5,1,5,2,2,1,15,2,2,5,4,1,4,1,51", "constraint": "1 <= K <= 32\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print the K-th element.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 output: 2\n\nThe 6-th element is 2.", "input: 27 output: 5\n\nThe 27-th element is 5."], "Pid": "p02741", "ProblemText": "Task Description: Problem Statement Print the K-th element of the following sequence of length 32:\n1,1,1,2,1,2,1,5,2,2,1,5,1,2,1,14,1,5,1,5,2,2,1,15,2,2,5,4,1,4,1,51\nTask Constraint: 1 <= K <= 32\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print the K-th element.\nTask Samples: input: 6 output: 2\n\nThe 6-th element is 2.\ninput: 27 output: 5\n\nThe 27-th element is 5.\n\n" }, { "title": "", "content": "Problem Statement We have a board with H horizontal rows and W vertical columns of squares.\nThere is a bishop at the top-left square on this board.\nHow many squares can this bishop reach by zero or more movements?\nHere the bishop can only move diagonally.\nMore formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:\n\nr_1 + c_1 = r_2 + c_2\nr_1 - c_1 = r_2 - c_2\n\nFor example, in the following figure, the bishop can move to any of the red squares in one move:", "constraint": "1 <= H, W <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nH \\ W", "output": "Print the number of squares the bishop can reach.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 output: 10\n\nThe bishop can reach the cyan squares in the following figure:", "input: 7 3 output: 11\n\nThe bishop can reach the cyan squares in the following figure:", "input: 1000000000 1000000000 output: 500000000000000000"], "Pid": "p02742", "ProblemText": "Task Description: Problem Statement We have a board with H horizontal rows and W vertical columns of squares.\nThere is a bishop at the top-left square on this board.\nHow many squares can this bishop reach by zero or more movements?\nHere the bishop can only move diagonally.\nMore formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:\n\nr_1 + c_1 = r_2 + c_2\nr_1 - c_1 = r_2 - c_2\n\nFor example, in the following figure, the bishop can move to any of the red squares in one move:\nTask Constraint: 1 <= H, W <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nH \\ W\nTask Output: Print the number of squares the bishop can reach.\nTask Samples: input: 4 5 output: 10\n\nThe bishop can reach the cyan squares in the following figure:\ninput: 7 3 output: 11\n\nThe bishop can reach the cyan squares in the following figure:\ninput: 1000000000 1000000000 output: 500000000000000000\n\n" }, { "title": "", "content": "Problem Statement Does \\sqrt{a} + \\sqrt{b} < \\sqrt{c} hold?", "constraint": "1 <= a, b, c <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\na \\ b \\ c", "output": "If \\sqrt{a} + \\sqrt{b} < \\sqrt{c}, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 9 output: No\n\n\\sqrt{2} + \\sqrt{3} < \\sqrt{9} does not hold.", "input: 2 3 10 output: Yes\n\n\\sqrt{2} + \\sqrt{3} < \\sqrt{10} holds."], "Pid": "p02743", "ProblemText": "Task Description: Problem Statement Does \\sqrt{a} + \\sqrt{b} < \\sqrt{c} hold?\nTask Constraint: 1 <= a, b, c <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\na \\ b \\ c\nTask Output: If \\sqrt{a} + \\sqrt{b} < \\sqrt{c}, print Yes; otherwise, print No.\nTask Samples: input: 2 3 9 output: No\n\n\\sqrt{2} + \\sqrt{3} < \\sqrt{9} does not hold.\ninput: 2 3 10 output: Yes\n\n\\sqrt{2} + \\sqrt{3} < \\sqrt{10} holds.\n\n" }, { "title": "", "content": "Problem Statement In this problem, we only consider strings consisting of lowercase English letters.\nStrings s and t are said to be isomorphic when the following conditions are satisfied:\n\n|s| = |t| holds.\nFor every pair i, j, one of the following holds:\ns_i = s_j and t_i = t_j.\ns_i \\neq s_j and t_i \\neq t_j.\n\nFor example, abcac and zyxzx are isomorphic, while abcac and ppppp are not.\nA string s is said to be in normal form when the following condition is satisfied:\n\nFor every string t that is isomorphic to s, s <= t holds. Here <= denotes lexicographic comparison.\n\nFor example, abcac is in normal form, but zyxzx is not since it is isomorphic to abcac, which is lexicographically smaller than zyxzx.\nYou are given an integer N.\nPrint all strings of length N that are in normal form, in lexicographically ascending order.", "constraint": "1 <= N <= 10\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Output Assume that there are K strings of length N that are in normal form: w_1, \\ldots, w_K in lexicographical order.\nOutput should be in the following format:\nw_1\n:\nw_K", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 output: a", "input: 2 output: aa\nab"], "Pid": "p02744", "ProblemText": "Task Description: Problem Statement In this problem, we only consider strings consisting of lowercase English letters.\nStrings s and t are said to be isomorphic when the following conditions are satisfied:\n\n|s| = |t| holds.\nFor every pair i, j, one of the following holds:\ns_i = s_j and t_i = t_j.\ns_i \\neq s_j and t_i \\neq t_j.\n\nFor example, abcac and zyxzx are isomorphic, while abcac and ppppp are not.\nA string s is said to be in normal form when the following condition is satisfied:\n\nFor every string t that is isomorphic to s, s <= t holds. Here <= denotes lexicographic comparison.\n\nFor example, abcac is in normal form, but zyxzx is not since it is isomorphic to abcac, which is lexicographically smaller than zyxzx.\nYou are given an integer N.\nPrint all strings of length N that are in normal form, in lexicographically ascending order.\nTask Constraint: 1 <= N <= 10\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Output Assume that there are K strings of length N that are in normal form: w_1, \\ldots, w_K in lexicographical order.\nOutput should be in the following format:\nw_1\n:\nw_K\nTask Samples: input: 1 output: a\ninput: 2 output: aa\nab\n\n" }, { "title": "", "content": "Problem Statement Snuke has a string s.\nFrom this string, Anuke, Bnuke, and Cnuke obtained strings a, b, and c, respectively, as follows:\n\nChoose a non-empty (contiguous) substring of s (possibly s itself). Then, replace some characters (possibly all or none) in it with ? s.\n\nFor example, if s is mississippi, we can choose the substring ssissip and replace its 1-st and 3-rd characters with ? to obtain ? s? ssip.\nYou are given the strings a, b, and c.\nFind the minimum possible length of s.", "constraint": "1 <= |a|, |b|, |c| <= 2000\na, b, and c consists of lowercase English letters and ?s.", "input": "Input is given from Standard Input in the following format:\na\nb\nc", "output": "Print the minimum possible length of s.", "content_img": false, "lang": "en", "error": false, "samples": ["input: a?c\nder\ncod output: 7\n\nFor example, s could be atcoder.", "input: atcoder\natcoder\n??????? output: 7\n\na, b, and c may not be distinct."], "Pid": "p02745", "ProblemText": "Task Description: Problem Statement Snuke has a string s.\nFrom this string, Anuke, Bnuke, and Cnuke obtained strings a, b, and c, respectively, as follows:\n\nChoose a non-empty (contiguous) substring of s (possibly s itself). Then, replace some characters (possibly all or none) in it with ? s.\n\nFor example, if s is mississippi, we can choose the substring ssissip and replace its 1-st and 3-rd characters with ? to obtain ? s? ssip.\nYou are given the strings a, b, and c.\nFind the minimum possible length of s.\nTask Constraint: 1 <= |a|, |b|, |c| <= 2000\na, b, and c consists of lowercase English letters and ?s.\nTask Input: Input is given from Standard Input in the following format:\na\nb\nc\nTask Output: Print the minimum possible length of s.\nTask Samples: input: a?c\nder\ncod output: 7\n\nFor example, s could be atcoder.\ninput: atcoder\natcoder\n??????? output: 7\n\na, b, and c may not be distinct.\n\n" }, { "title": "", "content": "Problem Statement For a non-negative integer K, we define a fractal of level K as follows:\n\nA fractal of level 0 is a grid with just one white square.\nWhen K > 0, a fractal of level K is a 3^K * 3^K grid. If we divide this grid into nine 3^{K-1} * 3^{K-1} subgrids:\nThe central subgrid consists of only black squares.\nEach of the other eight subgrids is a fractal of level K-1.\n\nFor example, a fractal of level 2 is as follows:\n\nIn a fractal of level 30, let (r, c) denote the square at the r-th row from the top and the c-th column from the left.\nYou are given Q quadruples of integers (a_i, b_i, c_i, d_i).\nFor each quadruple, find the distance from (a_i, b_i) to (c_i, d_i).\nHere the distance from (a, b) to (c, d) is the minimum integer n that satisfies the following condition:\n\nThere exists a sequence of white squares (x_0, y_0), \\ldots, (x_n, y_n) satisfying the following conditions:\n(x_0, y_0) = (a, b)\n(x_n, y_n) = (c, d)\nFor every i (0 <= i <= n-1), (x_i, y_i) and (x_{i+1}, y_{i+1}) share a side.", "constraint": "1 <= Q <= 10000\n1 <= a_i, b_i, c_i, d_i <= 3^{30}\n(a_i, b_i) \\neq (c_i, d_i)\n(a_i, b_i) and (c_i, d_i) are white squares.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nQ\na_1 \\ b_1 \\ c_1 \\ d_1\n:\na_Q \\ b_Q \\ c_Q \\ d_Q", "output": "Print Q lines.\nThe i-th line should contain the distance from (a_i, b_i) to (c_i, d_i).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4 2 7 4\n9 9 1 9 output: 5\n8"], "Pid": "p02746", "ProblemText": "Task Description: Problem Statement For a non-negative integer K, we define a fractal of level K as follows:\n\nA fractal of level 0 is a grid with just one white square.\nWhen K > 0, a fractal of level K is a 3^K * 3^K grid. If we divide this grid into nine 3^{K-1} * 3^{K-1} subgrids:\nThe central subgrid consists of only black squares.\nEach of the other eight subgrids is a fractal of level K-1.\n\nFor example, a fractal of level 2 is as follows:\n\nIn a fractal of level 30, let (r, c) denote the square at the r-th row from the top and the c-th column from the left.\nYou are given Q quadruples of integers (a_i, b_i, c_i, d_i).\nFor each quadruple, find the distance from (a_i, b_i) to (c_i, d_i).\nHere the distance from (a, b) to (c, d) is the minimum integer n that satisfies the following condition:\n\nThere exists a sequence of white squares (x_0, y_0), \\ldots, (x_n, y_n) satisfying the following conditions:\n(x_0, y_0) = (a, b)\n(x_n, y_n) = (c, d)\nFor every i (0 <= i <= n-1), (x_i, y_i) and (x_{i+1}, y_{i+1}) share a side.\nTask Constraint: 1 <= Q <= 10000\n1 <= a_i, b_i, c_i, d_i <= 3^{30}\n(a_i, b_i) \\neq (c_i, d_i)\n(a_i, b_i) and (c_i, d_i) are white squares.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nQ\na_1 \\ b_1 \\ c_1 \\ d_1\n:\na_Q \\ b_Q \\ c_Q \\ d_Q\nTask Output: Print Q lines.\nThe i-th line should contain the distance from (a_i, b_i) to (c_i, d_i).\nTask Samples: input: 2\n4 2 7 4\n9 9 1 9 output: 5\n8\n\n" }, { "title": "", "content": "Problem Statement\nA Hitachi string is a concatenation of one or more copies of the string hi.\nFor example, hi and hihi are Hitachi strings, while ha and hii are not.\nGiven a string S, determine whether S is a Hitachi string.", "constraint": "The length of S is between 1 and 10 (inclusive).\nS is a string consisting of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S is a Hitachi string, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: hihi output: Yes\n\nhihi is the concatenation of two copies of hi, so it is a Hitachi string.", "input: hi output: Yes", "input: ha output: No"], "Pid": "p02747", "ProblemText": "Task Description: Problem Statement\nA Hitachi string is a concatenation of one or more copies of the string hi.\nFor example, hi and hihi are Hitachi strings, while ha and hii are not.\nGiven a string S, determine whether S is a Hitachi string.\nTask Constraint: The length of S is between 1 and 10 (inclusive).\nS is a string consisting of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S is a Hitachi string, print Yes; otherwise, print No.\nTask Samples: input: hihi output: Yes\n\nhihi is the concatenation of two copies of hi, so it is a Hitachi string.\ninput: hi output: Yes\ninput: ha output: No\n\n" }, { "title": "", "content": "Problem Statement\nYou are visiting a large electronics store to buy a refrigerator and a microwave.\nThe store sells A kinds of refrigerators and B kinds of microwaves. The i-th refrigerator ( 1 <= i <= A ) is sold at a_i yen (the currency of Japan), and the j-th microwave ( 1 <= j <= B ) is sold at b_j yen.\nYou have M discount tickets. With the i-th ticket ( 1 <= i <= M ), you can get a discount of c_i yen from the total price when buying the x_i-th refrigerator and the y_i-th microwave together. Only one ticket can be used at a time.\nYou are planning to buy one refrigerator and one microwave. Find the minimum amount of money required.", "constraint": "All values in input are integers.\n 1 <= A <= 10^5 \n 1 <= B <= 10^5 \n 1 <= M <= 10^5 \n 1 <= a_i , b_i , c_i <= 10^5 \n 1 <= x_i <= A \n 1 <= y_i <= B \n c_i <= a_{x_i} + b_{y_i}", "input": "Input is given from Standard Input in the following format:\nA B M\na_1 a_2 . . . a_A\nb_1 b_2 . . . b_B\nx_1 y_1 c_1\n\\vdots\nx_M y_M c_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 1\n3 3\n3 3 3\n1 2 1 output: 5\n\nWith the ticket, you can get the 1-st refrigerator and the 2-nd microwave for 3+3-1=5 yen.", "input: 1 1 2\n10\n10\n1 1 5\n1 1 10 output: 10\n\nNote that you cannot use more than one ticket at a time.", "input: 2 2 1\n3 5\n3 5\n2 2 2 output: 6\n\nYou can get the 1-st refrigerator and the 1-st microwave for 6 yen, which is the minimum amount to pay in this case.\nNote that using a ticket is optional."], "Pid": "p02748", "ProblemText": "Task Description: Problem Statement\nYou are visiting a large electronics store to buy a refrigerator and a microwave.\nThe store sells A kinds of refrigerators and B kinds of microwaves. The i-th refrigerator ( 1 <= i <= A ) is sold at a_i yen (the currency of Japan), and the j-th microwave ( 1 <= j <= B ) is sold at b_j yen.\nYou have M discount tickets. With the i-th ticket ( 1 <= i <= M ), you can get a discount of c_i yen from the total price when buying the x_i-th refrigerator and the y_i-th microwave together. Only one ticket can be used at a time.\nYou are planning to buy one refrigerator and one microwave. Find the minimum amount of money required.\nTask Constraint: All values in input are integers.\n 1 <= A <= 10^5 \n 1 <= B <= 10^5 \n 1 <= M <= 10^5 \n 1 <= a_i , b_i , c_i <= 10^5 \n 1 <= x_i <= A \n 1 <= y_i <= B \n c_i <= a_{x_i} + b_{y_i}\nTask Input: Input is given from Standard Input in the following format:\nA B M\na_1 a_2 . . . a_A\nb_1 b_2 . . . b_B\nx_1 y_1 c_1\n\\vdots\nx_M y_M c_M\nTask Output: Print the answer.\nTask Samples: input: 2 3 1\n3 3\n3 3 3\n1 2 1 output: 5\n\nWith the ticket, you can get the 1-st refrigerator and the 2-nd microwave for 3+3-1=5 yen.\ninput: 1 1 2\n10\n10\n1 1 5\n1 1 10 output: 10\n\nNote that you cannot use more than one ticket at a time.\ninput: 2 2 1\n3 5\n3 5\n2 2 2 output: 6\n\nYou can get the 1-st refrigerator and the 1-st microwave for 6 yen, which is the minimum amount to pay in this case.\nNote that using a ticket is optional.\n\n" }, { "title": "", "content": "Problem Statement\nWe have a tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and Vertex b_i.\nTakahashi loves the number 3. He is seeking a permutation p_1, p_2, \\ldots , p_N of integers from 1 to N satisfying the following condition:\n\nFor every pair of vertices (i, j), if the distance between Vertex i and Vertex j is 3, the sum or product of p_i and p_j is a multiple of 3.\n\nHere the distance between Vertex i and Vertex j is the number of edges contained in the shortest path from Vertex i to Vertex j.\nHelp Takahashi by finding a permutation that satisfies the condition.", "constraint": "2<= N<= 2* 10^5\n1<= a_i, b_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n\\vdots\na_{N-1} b_{N-1}", "output": "If no permutation satisfies the condition, print -1.\nOtherwise, print a permutation satisfying the condition, with space in between.\nIf there are multiple solutions, you can print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n1 3\n3 4\n3 5 output: 1 2 5 4 3 \n\nThe distance between two vertices is 3 for the two pairs (2,4) and (2,5).\n\np_2 + p_4 = 6\np_2* p_5 = 6\n\nThus, this permutation satisfies the condition."], "Pid": "p02749", "ProblemText": "Task Description: Problem Statement\nWe have a tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and Vertex b_i.\nTakahashi loves the number 3. He is seeking a permutation p_1, p_2, \\ldots , p_N of integers from 1 to N satisfying the following condition:\n\nFor every pair of vertices (i, j), if the distance between Vertex i and Vertex j is 3, the sum or product of p_i and p_j is a multiple of 3.\n\nHere the distance between Vertex i and Vertex j is the number of edges contained in the shortest path from Vertex i to Vertex j.\nHelp Takahashi by finding a permutation that satisfies the condition.\nTask Constraint: 2<= N<= 2* 10^5\n1<= a_i, b_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n\\vdots\na_{N-1} b_{N-1}\nTask Output: If no permutation satisfies the condition, print -1.\nOtherwise, print a permutation satisfying the condition, with space in between.\nIf there are multiple solutions, you can print any of them.\nTask Samples: input: 5\n1 2\n1 3\n3 4\n3 5 output: 1 2 5 4 3 \n\nThe distance between two vertices is 3 for the two pairs (2,4) and (2,5).\n\np_2 + p_4 = 6\np_2* p_5 = 6\n\nThus, this permutation satisfies the condition.\n\n" }, { "title": "", "content": "Problem Statement There are N stores called Store 1, Store 2, \\cdots, Store N. Takahashi, who is at his house at time 0, is planning to visit some of these stores.\nIt takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.\nIf Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i * t + b_i units of time. (We assume that it takes no time other than waiting. )\nAll the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.\nTakahashi does not do shopping more than once in the same store.\nFind the maximum number of times he can do shopping before time T + 0.5.", "constraint": "All values in input are integers.\n1 <= N <= 2 * 10^5\n0 <= a_i <= 10^9\n0 <= b_i <= 10^9\n0 <= T <= 10^9", "input": "Input is given from Standard Input in the following format:\nN T\na_1 b_1\na_2 b_2\n\\vdots\na_N b_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 7\n2 0\n3 2\n0 3 output: 2\n\nHere is one possible way to visit stores:\n\nFrom time 0 to time 1: in 1 unit of time, he travels from his house to Store 1.\nFrom time 1 to time 3: for 2 units of time, he stands in a queue for Store 1 to do shopping.\nFrom time 3 to time 4: in 1 unit of time, he travels from Store 1 to Store 3.\nFrom time 4 to time 7: for 3 units of time, he stands in a queue for Store 3 to do shopping.\n\nIn this way, he can do shopping twice before time 7.5.", "input: 1 3\n0 3 output: 0", "input: 5 21600\n2 14\n3 22\n1 3\n1 10\n1 9 output: 5", "input: 7 57\n0 25\n3 10\n2 4\n5 15\n3 22\n2 14\n1 15 output: 3"], "Pid": "p02750", "ProblemText": "Task Description: Problem Statement There are N stores called Store 1, Store 2, \\cdots, Store N. Takahashi, who is at his house at time 0, is planning to visit some of these stores.\nIt takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.\nIf Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i * t + b_i units of time. (We assume that it takes no time other than waiting. )\nAll the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.\nTakahashi does not do shopping more than once in the same store.\nFind the maximum number of times he can do shopping before time T + 0.5.\nTask Constraint: All values in input are integers.\n1 <= N <= 2 * 10^5\n0 <= a_i <= 10^9\n0 <= b_i <= 10^9\n0 <= T <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN T\na_1 b_1\na_2 b_2\n\\vdots\na_N b_N\nTask Output: Print the answer.\nTask Samples: input: 3 7\n2 0\n3 2\n0 3 output: 2\n\nHere is one possible way to visit stores:\n\nFrom time 0 to time 1: in 1 unit of time, he travels from his house to Store 1.\nFrom time 1 to time 3: for 2 units of time, he stands in a queue for Store 1 to do shopping.\nFrom time 3 to time 4: in 1 unit of time, he travels from Store 1 to Store 3.\nFrom time 4 to time 7: for 3 units of time, he stands in a queue for Store 3 to do shopping.\n\nIn this way, he can do shopping twice before time 7.5.\ninput: 1 3\n0 3 output: 0\ninput: 5 21600\n2 14\n3 22\n1 3\n1 10\n1 9 output: 5\ninput: 7 57\n0 25\n3 10\n2 4\n5 15\n3 22\n2 14\n1 15 output: 3\n\n" }, { "title": "", "content": "Problem Statement\nWe have a grid with (2^N - 1) rows and (2^M-1) columns.\nYou are asked to write 0 or 1 in each of these squares.\nLet a_{i, j} be the number written in the square at the i-th row from the top and the j-th column from the left.\nFor a quadruple of integers (i_1, i_2, j_1, j_2) such that 1<= i_1 <= i_2<= 2^N-1,1<= j_1 <= j_2<= 2^M-1, let\nS(i_1, i_2, j_1, j_2) = \\displaystyle \\sum_{r=i_1}^{i_2}\\sum_{c=j_1}^{j_2}a_{r, c}.\nThen, let the oddness of the grid be the number of quadruples (i_1, i_2, j_1, j_2) such that S(i_1, i_2, j_1, j_2) is odd.\nFind a way to fill in the grid that maximizes its oddness.", "constraint": "N and M are integers between 1 and 10 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print numbers to write in the grid so that its oddness is maximized, in the following format:\na_{1,1}a_{1,2}\\cdots a_{1,2^M-1}\na_{2,1}a_{2,2}\\cdots a_{2,2^M-1}\n\\vdots\na_{2^N-1,1}a_{2^N-1,2}\\cdots a_{2^N-1,2^M-1}\n\nIf there are multiple solutions, you can print any of them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 output: 111\n\nFor this grid, S(1,1,1,1), S(1,1,2,2), S(1,1,3,3), and S(1,1,1,3) are odd, so it has the oddness of 4.\nWe cannot make the oddness 5 or higher, so this is one of the ways that maximize the oddness."], "Pid": "p02751", "ProblemText": "Task Description: Problem Statement\nWe have a grid with (2^N - 1) rows and (2^M-1) columns.\nYou are asked to write 0 or 1 in each of these squares.\nLet a_{i, j} be the number written in the square at the i-th row from the top and the j-th column from the left.\nFor a quadruple of integers (i_1, i_2, j_1, j_2) such that 1<= i_1 <= i_2<= 2^N-1,1<= j_1 <= j_2<= 2^M-1, let\nS(i_1, i_2, j_1, j_2) = \\displaystyle \\sum_{r=i_1}^{i_2}\\sum_{c=j_1}^{j_2}a_{r, c}.\nThen, let the oddness of the grid be the number of quadruples (i_1, i_2, j_1, j_2) such that S(i_1, i_2, j_1, j_2) is odd.\nFind a way to fill in the grid that maximizes its oddness.\nTask Constraint: N and M are integers between 1 and 10 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print numbers to write in the grid so that its oddness is maximized, in the following format:\na_{1,1}a_{1,2}\\cdots a_{1,2^M-1}\na_{2,1}a_{2,2}\\cdots a_{2,2^M-1}\n\\vdots\na_{2^N-1,1}a_{2^N-1,2}\\cdots a_{2^N-1,2^M-1}\n\nIf there are multiple solutions, you can print any of them.\nTask Samples: input: 1 2 output: 111\n\nFor this grid, S(1,1,1,1), S(1,1,2,2), S(1,1,3,3), and S(1,1,1,3) are odd, so it has the oddness of 4.\nWe cannot make the oddness 5 or higher, so this is one of the ways that maximize the oddness.\n\n" }, { "title": "", "content": "Problem Statement\nWe have a tree G with N vertices numbered 1 to N.\nThe i-th edge of G connects Vertex a_i and Vertex b_i.\nConsider adding zero or more edges in G, and let H be the graph resulted.\nFind the number of graphs H that satisfy the following conditions, modulo 998244353.\n\nH does not contain self-loops or multiple edges.\nThe diameters of G and H are equal.\nFor every pair of vertices in H that is not directly connected by an edge, the addition of an edge directly connecting them would reduce the diameter of the graph.", "constraint": "3 <= N <= 2 * 10^5 \n 1 <= a_i, b_i <= N \nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n\\vdots\na_{N-1} b_{N-1}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 6\n2 1\n5 2\n3 4\n2 3 output: 3\n\nFor example, adding the edges (1,5), (3,5) in G satisfies the conditions.", "input: 3\n1 2\n2 3 output: 1\n\nThe only graph H that satisfies the conditions is G.", "input: 9\n1 2\n2 3\n4 2\n1 7\n6 1\n2 5\n5 9\n6 8 output: 27", "input: 19\n2 4\n15 8\n1 16\n1 3\n12 19\n1 18\n7 11\n11 15\n12 9\n1 6\n7 14\n18 2\n13 12\n13 5\n16 13\n7 1\n11 10\n7 17 output: 78732"], "Pid": "p02752", "ProblemText": "Task Description: Problem Statement\nWe have a tree G with N vertices numbered 1 to N.\nThe i-th edge of G connects Vertex a_i and Vertex b_i.\nConsider adding zero or more edges in G, and let H be the graph resulted.\nFind the number of graphs H that satisfy the following conditions, modulo 998244353.\n\nH does not contain self-loops or multiple edges.\nThe diameters of G and H are equal.\nFor every pair of vertices in H that is not directly connected by an edge, the addition of an edge directly connecting them would reduce the diameter of the graph.\nTask Constraint: 3 <= N <= 2 * 10^5 \n 1 <= a_i, b_i <= N \nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n\\vdots\na_{N-1} b_{N-1}\nTask Output: Print the answer.\nTask Samples: input: 6\n1 6\n2 1\n5 2\n3 4\n2 3 output: 3\n\nFor example, adding the edges (1,5), (3,5) in G satisfies the conditions.\ninput: 3\n1 2\n2 3 output: 1\n\nThe only graph H that satisfies the conditions is G.\ninput: 9\n1 2\n2 3\n4 2\n1 7\n6 1\n2 5\n5 9\n6 8 output: 27\ninput: 19\n2 4\n15 8\n1 16\n1 3\n12 19\n1 18\n7 11\n11 15\n12 9\n1 6\n7 14\n18 2\n13 12\n13 5\n16 13\n7 1\n11 10\n7 17 output: 78732\n\n" }, { "title": "", "content": "Problem Statement In At Coder City, there are three stations numbered 1,2, and 3.\nEach of these stations is operated by one of the two railway companies, A and B. A string S of length 3 represents which company operates each station. If S_i is A, Company A operates Station i; if S_i is B, Company B operates Station i.\nTo improve the transportation condition, for each pair of a station operated by Company A and one operated by Company B, there will be a bus service connecting them.\nDetermine if there is a pair of stations that will be connected by a bus service.", "constraint": "Each character of S is A or B.\n|S| = 3", "input": "Input is given from Standard Input in the following format:\nS", "output": "If there is a pair of stations that will be connected by a bus service, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ABA output: Yes\n\nCompany A operates Station 1 and 3, while Company B operates Station 2.\nThere will be a bus service between Station 1 and 2, and between Station 2 and 3, so print Yes.", "input: BBA output: Yes\n\nCompany B operates Station 1 and 2, while Company A operates Station 3.\nThere will be a bus service between Station 1 and 3, and between Station 2 and 3, so print Yes.", "input: BBB output: No\n\nCompany B operates all the stations. Thus, there will be no bus service, so print No."], "Pid": "p02753", "ProblemText": "Task Description: Problem Statement In At Coder City, there are three stations numbered 1,2, and 3.\nEach of these stations is operated by one of the two railway companies, A and B. A string S of length 3 represents which company operates each station. If S_i is A, Company A operates Station i; if S_i is B, Company B operates Station i.\nTo improve the transportation condition, for each pair of a station operated by Company A and one operated by Company B, there will be a bus service connecting them.\nDetermine if there is a pair of stations that will be connected by a bus service.\nTask Constraint: Each character of S is A or B.\n|S| = 3\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If there is a pair of stations that will be connected by a bus service, print Yes; otherwise, print No.\nTask Samples: input: ABA output: Yes\n\nCompany A operates Station 1 and 3, while Company B operates Station 2.\nThere will be a bus service between Station 1 and 2, and between Station 2 and 3, so print Yes.\ninput: BBA output: Yes\n\nCompany B operates Station 1 and 2, while Company A operates Station 3.\nThere will be a bus service between Station 1 and 3, and between Station 2 and 3, so print Yes.\ninput: BBB output: No\n\nCompany B operates all the stations. Thus, there will be no bus service, so print No.\n\n" }, { "title": "", "content": "Problem Statement Takahashi has many red balls and blue balls. Now, he will place them in a row.\nInitially, there is no ball placed.\nTakahashi, who is very patient, will do the following operation 10^{100} times:\n\nPlace A blue balls at the end of the row of balls already placed. Then, place B red balls at the end of the row.\n\nHow many blue balls will be there among the first N balls in the row of balls made this way?", "constraint": "1 <= N <= 10^{18}\nA, B >= 0\n0 < A + B <= 10^{18}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print the number of blue balls that will be there among the first N balls in the row of balls.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 3 4 output: 4\n\nLet b denote a blue ball, and r denote a red ball. The first eight balls in the row will be bbbrrrrb, among which there are four blue balls.", "input: 8 0 4 output: 0\n\nHe placed only red balls from the beginning.", "input: 6 2 4 output: 2\n\nAmong bbrrrr, there are two blue balls."], "Pid": "p02754", "ProblemText": "Task Description: Problem Statement Takahashi has many red balls and blue balls. Now, he will place them in a row.\nInitially, there is no ball placed.\nTakahashi, who is very patient, will do the following operation 10^{100} times:\n\nPlace A blue balls at the end of the row of balls already placed. Then, place B red balls at the end of the row.\n\nHow many blue balls will be there among the first N balls in the row of balls made this way?\nTask Constraint: 1 <= N <= 10^{18}\nA, B >= 0\n0 < A + B <= 10^{18}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print the number of blue balls that will be there among the first N balls in the row of balls.\nTask Samples: input: 8 3 4 output: 4\n\nLet b denote a blue ball, and r denote a red ball. The first eight balls in the row will be bbbrrrrb, among which there are four blue balls.\ninput: 8 0 4 output: 0\n\nHe placed only red balls from the beginning.\ninput: 6 2 4 output: 2\n\nAmong bbrrrr, there are two blue balls.\n\n" }, { "title": "", "content": "Problem Statement Find the price of a product before tax such that, when the consumption tax rate is 8 percent and 10 percent, the amount of consumption tax levied on it is A yen and B yen, respectively. (Yen is the currency of Japan. )\nHere, the price before tax must be a positive integer, and the amount of consumption tax is rounded down to the nearest integer.\nIf multiple prices satisfy the condition, print the lowest such price; if no price satisfies the condition, print -1.", "constraint": "1 <= A <= B <= 100\nA and B are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "If there is a price that satisfies the condition, print an integer representing the lowest such price; otherwise, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 25\n\nIf the price of a product before tax is 25 yen, the amount of consumption tax levied on it is:\n\nWhen the consumption tax rate is 8 percent: \\lfloor 25 * 0.08 \\rfloor = \\lfloor 2 \\rfloor = 2 yen.\nWhen the consumption tax rate is 10 percent: \\lfloor 25 * 0.1 \\rfloor = \\lfloor 2.5 \\rfloor = 2 yen.\n\nThus, the price of 25 yen satisfies the condition. There are other possible prices, such as 26 yen, but print the minimum such price, 25.", "input: 8 10 output: 100\n\nIf the price of a product before tax is 100 yen, the amount of consumption tax levied on it is:\n\nWhen the consumption tax rate is 8 percent: \\lfloor 100 * 0.08 \\rfloor = 8 yen.\nWhen the consumption tax rate is 10 percent: \\lfloor 100 * 0.1 \\rfloor = 10 yen.", "input: 19 99 output: -1\n\nThere is no price before tax satisfying this condition, so print -1."], "Pid": "p02755", "ProblemText": "Task Description: Problem Statement Find the price of a product before tax such that, when the consumption tax rate is 8 percent and 10 percent, the amount of consumption tax levied on it is A yen and B yen, respectively. (Yen is the currency of Japan. )\nHere, the price before tax must be a positive integer, and the amount of consumption tax is rounded down to the nearest integer.\nIf multiple prices satisfy the condition, print the lowest such price; if no price satisfies the condition, print -1.\nTask Constraint: 1 <= A <= B <= 100\nA and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: If there is a price that satisfies the condition, print an integer representing the lowest such price; otherwise, print -1.\nTask Samples: input: 2 2 output: 25\n\nIf the price of a product before tax is 25 yen, the amount of consumption tax levied on it is:\n\nWhen the consumption tax rate is 8 percent: \\lfloor 25 * 0.08 \\rfloor = \\lfloor 2 \\rfloor = 2 yen.\nWhen the consumption tax rate is 10 percent: \\lfloor 25 * 0.1 \\rfloor = \\lfloor 2.5 \\rfloor = 2 yen.\n\nThus, the price of 25 yen satisfies the condition. There are other possible prices, such as 26 yen, but print the minimum such price, 25.\ninput: 8 10 output: 100\n\nIf the price of a product before tax is 100 yen, the amount of consumption tax levied on it is:\n\nWhen the consumption tax rate is 8 percent: \\lfloor 100 * 0.08 \\rfloor = 8 yen.\nWhen the consumption tax rate is 10 percent: \\lfloor 100 * 0.1 \\rfloor = 10 yen.\ninput: 19 99 output: -1\n\nThere is no price before tax satisfying this condition, so print -1.\n\n" }, { "title": "", "content": "Problem Statement Takahashi has a string S consisting of lowercase English letters.\nStarting with this string, he will produce a new one in the procedure given as follows.\nThe procedure consists of Q operations. In Operation i (1 <= i <= Q), an integer T_i is provided, which means the following:\nIf T_i = 1: reverse the string S.\nIf T_i = 2: An integer F_i and a lowercase English letter C_i are additionally provided.\n\nIf F_i = 1 : Add C_i to the beginning of the string S.\nIf F_i = 2 : Add C_i to the end of the string S.\n\nHelp Takahashi by finding the final string that results from the procedure.", "constraint": "1 <= |S| <= 10^5\nS consists of lowercase English letters.\n1 <= Q <= 2 * 10^5\nT_i = 1 or 2.\nF_i = 1 or 2, if provided.\nC_i is a lowercase English letter, if provided.", "input": "Input is given from Standard Input in the following format:\nS\nQ\nQuery_1\n:\nQuery_Q\n\nIn the 3-rd through the (Q+2)-th lines, Query_i is one of the following:\n1\n\nwhich means T_i = 1, and:\n2 F_i C_i\n\nwhich means T_i = 2.", "output": "Print the resulting string.", "content_img": false, "lang": "en", "error": false, "samples": ["input: a\n4\n2 1 p\n1\n2 2 c\n1 output: cpa\n\nThere will be Q = 4 operations. Initially, S is a.\nOperation 1: Add p at the beginning of S. S becomes pa.\nOperation 2: Reverse S. S becomes ap.\nOperation 3: Add c at the end of S. S becomes apc.\nOperation 4: Reverse S. S becomes cpa.\nThus, the resulting string is cpa.", "input: a\n6\n2 2 a\n2 1 b\n1\n2 2 c\n1\n1 output: aabc\n\nThere will be Q = 6 operations. Initially, S is a.\nOperation 1: S becomes aa.\nOperation 2: S becomes baa.\nOperation 3: S becomes aab.\nOperation 4: S becomes aabc.\nOperation 5: S becomes cbaa.\nOperation 6: S becomes aabc.\nThus, the resulting string is aabc.", "input: y\n1\n2 1 x output: xy"], "Pid": "p02756", "ProblemText": "Task Description: Problem Statement Takahashi has a string S consisting of lowercase English letters.\nStarting with this string, he will produce a new one in the procedure given as follows.\nThe procedure consists of Q operations. In Operation i (1 <= i <= Q), an integer T_i is provided, which means the following:\nIf T_i = 1: reverse the string S.\nIf T_i = 2: An integer F_i and a lowercase English letter C_i are additionally provided.\n\nIf F_i = 1 : Add C_i to the beginning of the string S.\nIf F_i = 2 : Add C_i to the end of the string S.\n\nHelp Takahashi by finding the final string that results from the procedure.\nTask Constraint: 1 <= |S| <= 10^5\nS consists of lowercase English letters.\n1 <= Q <= 2 * 10^5\nT_i = 1 or 2.\nF_i = 1 or 2, if provided.\nC_i is a lowercase English letter, if provided.\nTask Input: Input is given from Standard Input in the following format:\nS\nQ\nQuery_1\n:\nQuery_Q\n\nIn the 3-rd through the (Q+2)-th lines, Query_i is one of the following:\n1\n\nwhich means T_i = 1, and:\n2 F_i C_i\n\nwhich means T_i = 2.\nTask Output: Print the resulting string.\nTask Samples: input: a\n4\n2 1 p\n1\n2 2 c\n1 output: cpa\n\nThere will be Q = 4 operations. Initially, S is a.\nOperation 1: Add p at the beginning of S. S becomes pa.\nOperation 2: Reverse S. S becomes ap.\nOperation 3: Add c at the end of S. S becomes apc.\nOperation 4: Reverse S. S becomes cpa.\nThus, the resulting string is cpa.\ninput: a\n6\n2 2 a\n2 1 b\n1\n2 2 c\n1\n1 output: aabc\n\nThere will be Q = 6 operations. Initially, S is a.\nOperation 1: S becomes aa.\nOperation 2: S becomes baa.\nOperation 3: S becomes aab.\nOperation 4: S becomes aabc.\nOperation 5: S becomes cbaa.\nOperation 6: S becomes aabc.\nThus, the resulting string is aabc.\ninput: y\n1\n2 1 x output: xy\n\n" }, { "title": "", "content": "Problem Statement Takahashi has a string S of length N consisting of digits from 0 through 9.\nHe loves the prime number P. He wants to know how many non-empty (contiguous) substrings of S - there are N * (N + 1) / 2 of them - are divisible by P when regarded as integers written in base ten.\nHere substrings starting with a 0 also count, and substrings originated from different positions in S are distinguished, even if they are equal as strings or integers.\nCompute this count to help Takahashi.", "constraint": "1 <= N <= 2 * 10^5\nS consists of digits.\n|S| = N\n2 <= P <= 10000\nP is a prime number.", "input": "Input is given from Standard Input in the following format:\nN P\nS", "output": "Print the number of non-empty (contiguous) substrings of S that are divisible by P when regarded as an integer written in base ten.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n3543 output: 6\n\nHere S = 3543. There are ten non-empty (contiguous) substrings of S:\n3: divisible by 3.\n35: not divisible by 3.\n354: divisible by 3.\n3543: divisible by 3.\n5: not divisible by 3.\n54: divisible by 3.\n543: divisible by 3.\n4: not divisible by 3.\n43: not divisible by 3.\n3: divisible by 3.\nSix of these are divisible by 3, so print 6.", "input: 4 2\n2020 output: 10\n\nHere S = 2020. There are ten non-empty (contiguous) substrings of S, all of which are divisible by 2, so print 10.\nNote that substrings beginning with a 0 also count.", "input: 20 11\n33883322005544116655 output: 68"], "Pid": "p02757", "ProblemText": "Task Description: Problem Statement Takahashi has a string S of length N consisting of digits from 0 through 9.\nHe loves the prime number P. He wants to know how many non-empty (contiguous) substrings of S - there are N * (N + 1) / 2 of them - are divisible by P when regarded as integers written in base ten.\nHere substrings starting with a 0 also count, and substrings originated from different positions in S are distinguished, even if they are equal as strings or integers.\nCompute this count to help Takahashi.\nTask Constraint: 1 <= N <= 2 * 10^5\nS consists of digits.\n|S| = N\n2 <= P <= 10000\nP is a prime number.\nTask Input: Input is given from Standard Input in the following format:\nN P\nS\nTask Output: Print the number of non-empty (contiguous) substrings of S that are divisible by P when regarded as an integer written in base ten.\nTask Samples: input: 4 3\n3543 output: 6\n\nHere S = 3543. There are ten non-empty (contiguous) substrings of S:\n3: divisible by 3.\n35: not divisible by 3.\n354: divisible by 3.\n3543: divisible by 3.\n5: not divisible by 3.\n54: divisible by 3.\n543: divisible by 3.\n4: not divisible by 3.\n43: not divisible by 3.\n3: divisible by 3.\nSix of these are divisible by 3, so print 6.\ninput: 4 2\n2020 output: 10\n\nHere S = 2020. There are ten non-empty (contiguous) substrings of S, all of which are divisible by 2, so print 10.\nNote that substrings beginning with a 0 also count.\ninput: 20 11\n33883322005544116655 output: 68\n\n" }, { "title": "", "content": "Problem Statement There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.\nTakahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.\n\nChoose a robot and activate it. This operation cannot be done when there is a robot moving.\n\nWhile Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.\nHow many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.", "constraint": "1 <= N <= 2 * 10^5\n-10^9 <= X_i <= 10^9\n1 <= D_i <= 10^9\nX_i \\neq X_j (i \\neq j)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nX_1 D_1\n:\nX_N D_N", "output": "Print the number of possible sets of robots remaining on the number line, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 5\n3 3 output: 3\n\nThere are three possible sets of robots remaining on the number line: \\{1,2\\}, \\{1\\}, and \\{\\}.\nThese can be achieved as follows:\nIf Takahashi activates nothing, the robots \\{1,2\\} will remain.\nIf Takahashi activates Robot 1, it will activate Robot 2 while moving, after which there will be no robots on the number line. This state can also be reached by activating Robot 2 and then Robot 1.\nIf Takahashi activates Robot 2 and finishes doing the operation, the robot \\{1\\} will remain.", "input: 3\n6 5\n-1 10\n3 3 output: 5\n\nThere are five possible sets of robots remaining on the number line: \\{1,2,3\\}, \\{1,2\\}, \\{2\\}, \\{2,3\\}, and \\{\\}.", "input: 4\n7 10\n-10 3\n4 3\n-4 3 output: 16\n\nNone of the robots influences others.", "input: 20\n-8 1\n26 4\n0 5\n9 1\n19 4\n22 20\n28 27\n11 8\n-3 20\n-25 17\n10 4\n-18 27\n24 28\n-11 19\n2 27\n-2 18\n-1 12\n-24 29\n31 29\n29 7 output: 110\n\nRemember to print the count modulo 998244353."], "Pid": "p02758", "ProblemText": "Task Description: Problem Statement There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.\nTakahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.\n\nChoose a robot and activate it. This operation cannot be done when there is a robot moving.\n\nWhile Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.\nHow many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.\nTask Constraint: 1 <= N <= 2 * 10^5\n-10^9 <= X_i <= 10^9\n1 <= D_i <= 10^9\nX_i \\neq X_j (i \\neq j)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 D_1\n:\nX_N D_N\nTask Output: Print the number of possible sets of robots remaining on the number line, modulo 998244353.\nTask Samples: input: 2\n1 5\n3 3 output: 3\n\nThere are three possible sets of robots remaining on the number line: \\{1,2\\}, \\{1\\}, and \\{\\}.\nThese can be achieved as follows:\nIf Takahashi activates nothing, the robots \\{1,2\\} will remain.\nIf Takahashi activates Robot 1, it will activate Robot 2 while moving, after which there will be no robots on the number line. This state can also be reached by activating Robot 2 and then Robot 1.\nIf Takahashi activates Robot 2 and finishes doing the operation, the robot \\{1\\} will remain.\ninput: 3\n6 5\n-1 10\n3 3 output: 5\n\nThere are five possible sets of robots remaining on the number line: \\{1,2,3\\}, \\{1,2\\}, \\{2\\}, \\{2,3\\}, and \\{\\}.\ninput: 4\n7 10\n-10 3\n4 3\n-4 3 output: 16\n\nNone of the robots influences others.\ninput: 20\n-8 1\n26 4\n0 5\n9 1\n19 4\n22 20\n28 27\n11 8\n-3 20\n-25 17\n10 4\n-18 27\n24 28\n-11 19\n2 27\n-2 18\n-1 12\n-24 29\n31 29\n29 7 output: 110\n\nRemember to print the count modulo 998244353.\n\n" }, { "title": "", "content": "Problem Statement Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.\nAt least how many sheets of paper does he need?", "constraint": "N is an integer.\n1 <= N <= 100", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 output: 3\n\nBy printing the 1-st, 2-nd pages on the 1-st sheet, 3-rd and 4-th pages on the 2-nd sheet, and 5-th page on the 3-rd sheet, we can print all the data on 3 sheets of paper.", "input: 2 output: 1", "input: 100 output: 50"], "Pid": "p02759", "ProblemText": "Task Description: Problem Statement Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.\nAt least how many sheets of paper does he need?\nTask Constraint: N is an integer.\n1 <= N <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 5 output: 3\n\nBy printing the 1-st, 2-nd pages on the 1-st sheet, 3-rd and 4-th pages on the 2-nd sheet, and 5-th page on the 3-rd sheet, we can print all the data on 3 sheets of paper.\ninput: 2 output: 1\ninput: 100 output: 50\n\n" }, { "title": "", "content": "Problem Statement We have a bingo card with a 3*3 grid. The square at the i-th row from the top and the j-th column from the left contains the number A_{i, j}.\nThe MC will choose N numbers, b_1, b_2, \\cdots, b_N. If our bingo sheet contains some of those numbers, we will mark them on our sheet.\nDetermine whether we will have a bingo when the N numbers are chosen, that is, the sheet will contain three marked numbers in a row, column, or diagonal.", "constraint": "All values in input are integers.\n1 <= A_{i, j} <= 100\nA_{i_1, j_1} \\neq A_{i_2, j_2} ((i_1, j_1) \\neq (i_2, j_2))\n1 <= N <= 10\n1 <= b_i <= 100\nb_i \\neq b_j (i \\neq j)", "input": "Input is given from Standard Input in the following format:\nA_{1,1} A_{1,2} A_{1,3}\nA_{2,1} A_{2,2} A_{2,3}\nA_{3,1} A_{3,2} A_{3,3}\nN\nb_1\n\\vdots\nb_N", "output": "If we will have a bingo, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 84 97 66\n79 89 11\n61 59 7\n7\n89\n7\n87\n79\n24\n84\n30 output: Yes\n\nWe will mark A_{1,1}, A_{2,1}, A_{2,2}, A_{3,3}, and complete the diagonal from the top-left to the bottom-right.", "input: 41 7 46\n26 89 2\n78 92 8\n5\n6\n45\n16\n57\n17 output: No\n\nWe will mark nothing.", "input: 60 88 34\n92 41 43\n65 73 48\n10\n60\n43\n88\n11\n48\n73\n65\n41\n92\n34 output: Yes\n\nWe will mark all the squares."], "Pid": "p02760", "ProblemText": "Task Description: Problem Statement We have a bingo card with a 3*3 grid. The square at the i-th row from the top and the j-th column from the left contains the number A_{i, j}.\nThe MC will choose N numbers, b_1, b_2, \\cdots, b_N. If our bingo sheet contains some of those numbers, we will mark them on our sheet.\nDetermine whether we will have a bingo when the N numbers are chosen, that is, the sheet will contain three marked numbers in a row, column, or diagonal.\nTask Constraint: All values in input are integers.\n1 <= A_{i, j} <= 100\nA_{i_1, j_1} \\neq A_{i_2, j_2} ((i_1, j_1) \\neq (i_2, j_2))\n1 <= N <= 10\n1 <= b_i <= 100\nb_i \\neq b_j (i \\neq j)\nTask Input: Input is given from Standard Input in the following format:\nA_{1,1} A_{1,2} A_{1,3}\nA_{2,1} A_{2,2} A_{2,3}\nA_{3,1} A_{3,2} A_{3,3}\nN\nb_1\n\\vdots\nb_N\nTask Output: If we will have a bingo, print Yes; otherwise, print No.\nTask Samples: input: 84 97 66\n79 89 11\n61 59 7\n7\n89\n7\n87\n79\n24\n84\n30 output: Yes\n\nWe will mark A_{1,1}, A_{2,1}, A_{2,2}, A_{3,3}, and complete the diagonal from the top-left to the bottom-right.\ninput: 41 7 46\n26 89 2\n78 92 8\n5\n6\n45\n16\n57\n17 output: No\n\nWe will mark nothing.\ninput: 60 88 34\n92 41 43\n65 73 48\n10\n60\n43\n88\n11\n48\n73\n65\n41\n92\n34 output: Yes\n\nWe will mark all the squares.\n\n" }, { "title": "", "content": "Problem Statement If there is an integer not less than 0 satisfying the following conditions, print the smallest such integer; otherwise, print -1.\n\nThe integer has exactly N digits in base ten. (We assume 0 to be a 1-digit integer. For other integers, leading zeros are not allowed. )\nThe s_i-th digit from the left is c_i. <=ft(i = 1,2, \\cdots, M\\right)", "constraint": "All values in input are integers.\n1 <= N <= 3\n0 <= M <= 5\n1 <= s_i <= N\n0 <= c_i <= 9", "input": "Input is given from Standard Input in the following format:\nN M\ns_1 c_1\n\\vdots\ns_M c_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 7\n3 2\n1 7 output: 702\n\n702 satisfies the conditions - its 1-st and 3-rd digits are 7 and 2, respectively - while no non-negative integer less than 702 satisfies them.", "input: 3 2\n2 1\n2 3 output: -1", "input: 3 1\n1 0 output: -1"], "Pid": "p02761", "ProblemText": "Task Description: Problem Statement If there is an integer not less than 0 satisfying the following conditions, print the smallest such integer; otherwise, print -1.\n\nThe integer has exactly N digits in base ten. (We assume 0 to be a 1-digit integer. For other integers, leading zeros are not allowed. )\nThe s_i-th digit from the left is c_i. <=ft(i = 1,2, \\cdots, M\\right)\nTask Constraint: All values in input are integers.\n1 <= N <= 3\n0 <= M <= 5\n1 <= s_i <= N\n0 <= c_i <= 9\nTask Input: Input is given from Standard Input in the following format:\nN M\ns_1 c_1\n\\vdots\ns_M c_M\nTask Output: Print the answer.\nTask Samples: input: 3 3\n1 7\n3 2\n1 7 output: 702\n\n702 satisfies the conditions - its 1-st and 3-rd digits are 7 and 2, respectively - while no non-negative integer less than 702 satisfies them.\ninput: 3 2\n2 1\n2 3 output: -1\ninput: 3 1\n1 0 output: -1\n\n" }, { "title": "", "content": "Problem Statement An SNS has N users - User 1, User 2, \\cdots, User N.\nBetween these N users, there are some relationships - M friendships and K blockships.\nFor each i = 1,2, \\cdots, M, there is a bidirectional friendship between User A_i and User B_i.\nFor each i = 1,2, \\cdots, K, there is a bidirectional blockship between User C_i and User D_i.\nWe define User a to be a friend candidate for User b when all of the following four conditions are satisfied:\n\na \\neq b.\nThere is not a friendship between User a and User b.\nThere is not a blockship between User a and User b.\nThere exists a sequence c_0, c_1, c_2, \\cdots, c_L consisting of integers between 1 and N (inclusive) such that c_0 = a, c_L = b, and there is a friendship between User c_i and c_{i+1} for each i = 0,1, \\cdots, L - 1.\n\nFor each user i = 1,2, . . . N, how many friend candidates does it have?", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n0 <= M <= 10^5\n0 <= K <= 10^5\n1 <= A_i, B_i <= N\nA_i \\neq B_i\n1 <= C_i, D_i <= N\nC_i \\neq D_i\n(A_i, B_i) \\neq (A_j, B_j) (i \\neq j)\n(A_i, B_i) \\neq (B_j, A_j)\n(C_i, D_i) \\neq (C_j, D_j) (i \\neq j)\n(C_i, D_i) \\neq (D_j, C_j)\n(A_i, B_i) \\neq (C_j, D_j)\n(A_i, B_i) \\neq (D_j, C_j)", "input": "Input is given from Standard Input in the following format:\nN M K\nA_1 B_1\n\\vdots\nA_M B_M\nC_1 D_1\n\\vdots\nC_K D_K", "output": "Print the answers in order, with space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4 1\n2 1\n1 3\n3 2\n3 4\n4 1 output: 0 1 0 1\n\nThere is a friendship between User 2 and 3, and between 3 and 4. Also, there is no friendship or blockship between User 2 and 4. Thus, User 4 is a friend candidate for User 2.\nHowever, neither User 1 or 3 is a friend candidate for User 2, so User 2 has one friend candidate.", "input: 5 10 0\n1 2\n1 3\n1 4\n1 5\n3 2\n2 4\n2 5\n4 3\n5 3\n4 5 output: 0 0 0 0 0\n\nEveryone is a friend of everyone else and has no friend candidate.", "input: 10 9 3\n10 1\n6 7\n8 2\n2 5\n8 4\n7 3\n10 9\n6 4\n5 8\n2 6\n7 5\n3 1 output: 1 3 5 4 3 3 3 3 1 0"], "Pid": "p02762", "ProblemText": "Task Description: Problem Statement An SNS has N users - User 1, User 2, \\cdots, User N.\nBetween these N users, there are some relationships - M friendships and K blockships.\nFor each i = 1,2, \\cdots, M, there is a bidirectional friendship between User A_i and User B_i.\nFor each i = 1,2, \\cdots, K, there is a bidirectional blockship between User C_i and User D_i.\nWe define User a to be a friend candidate for User b when all of the following four conditions are satisfied:\n\na \\neq b.\nThere is not a friendship between User a and User b.\nThere is not a blockship between User a and User b.\nThere exists a sequence c_0, c_1, c_2, \\cdots, c_L consisting of integers between 1 and N (inclusive) such that c_0 = a, c_L = b, and there is a friendship between User c_i and c_{i+1} for each i = 0,1, \\cdots, L - 1.\n\nFor each user i = 1,2, . . . N, how many friend candidates does it have?\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n0 <= M <= 10^5\n0 <= K <= 10^5\n1 <= A_i, B_i <= N\nA_i \\neq B_i\n1 <= C_i, D_i <= N\nC_i \\neq D_i\n(A_i, B_i) \\neq (A_j, B_j) (i \\neq j)\n(A_i, B_i) \\neq (B_j, A_j)\n(C_i, D_i) \\neq (C_j, D_j) (i \\neq j)\n(C_i, D_i) \\neq (D_j, C_j)\n(A_i, B_i) \\neq (C_j, D_j)\n(A_i, B_i) \\neq (D_j, C_j)\nTask Input: Input is given from Standard Input in the following format:\nN M K\nA_1 B_1\n\\vdots\nA_M B_M\nC_1 D_1\n\\vdots\nC_K D_K\nTask Output: Print the answers in order, with space in between.\nTask Samples: input: 4 4 1\n2 1\n1 3\n3 2\n3 4\n4 1 output: 0 1 0 1\n\nThere is a friendship between User 2 and 3, and between 3 and 4. Also, there is no friendship or blockship between User 2 and 4. Thus, User 4 is a friend candidate for User 2.\nHowever, neither User 1 or 3 is a friend candidate for User 2, so User 2 has one friend candidate.\ninput: 5 10 0\n1 2\n1 3\n1 4\n1 5\n3 2\n2 4\n2 5\n4 3\n5 3\n4 5 output: 0 0 0 0 0\n\nEveryone is a friend of everyone else and has no friend candidate.\ninput: 10 9 3\n10 1\n6 7\n8 2\n2 5\n8 4\n7 3\n10 9\n6 4\n5 8\n2 6\n7 5\n3 1 output: 1 3 5 4 3 3 3 3 1 0\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N consisting of lowercase English letters.\nProcess Q queries of the following two types:\n\nType 1: change the i_q-th character of S to c_q. (Do nothing if the i_q-th character is already c_q. )\nType 2: answer the number of different characters occurring in the substring of S between the l_q-th and r_q-th characters (inclusive).", "constraint": "N, Q, i_q, l_q, and r_q are integers.\nS is a string consisting of lowercase English letters.\nc_q is a lowercase English letter.\n1 <= N <= 500000\n1 <= Q <= 20000\n|S| = N\n1 <= i_q <= N\n1 <= l_q <= r_q <= N\nThere is at least one query of type 2 in each testcase.", "input": "Input is given from Standard Input in the following format:\nN\nS\nQ\nQuery_1\n\\vdots\nQuery_Q\n\nHere, Query_i in the 4-th through (Q+3)-th lines is one of the following:\n1 i_q c_q\n\n2 l_q r_q", "output": "For each query of type 2, print a line containing the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\nabcdbbd\n6\n2 3 6\n1 5 z\n2 1 1\n1 4 a\n1 7 d\n2 1 7 output: 3\n1\n5\n\nIn the first query, cdbb contains three kinds of letters: b , c , and d, so we print 3.\nIn the second query, S is modified to abcdzbd.\nIn the third query, a contains one kind of letter: a, so we print 1.\nIn the fourth query, S is modified to abcazbd.\nIn the fifth query, S does not change and is still abcazbd.\nIn the sixth query, abcazbd contains five kinds of letters: a, b, c, d, and z, so we print 5."], "Pid": "p02763", "ProblemText": "Task Description: Problem Statement You are given a string S of length N consisting of lowercase English letters.\nProcess Q queries of the following two types:\n\nType 1: change the i_q-th character of S to c_q. (Do nothing if the i_q-th character is already c_q. )\nType 2: answer the number of different characters occurring in the substring of S between the l_q-th and r_q-th characters (inclusive).\nTask Constraint: N, Q, i_q, l_q, and r_q are integers.\nS is a string consisting of lowercase English letters.\nc_q is a lowercase English letter.\n1 <= N <= 500000\n1 <= Q <= 20000\n|S| = N\n1 <= i_q <= N\n1 <= l_q <= r_q <= N\nThere is at least one query of type 2 in each testcase.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nQ\nQuery_1\n\\vdots\nQuery_Q\n\nHere, Query_i in the 4-th through (Q+3)-th lines is one of the following:\n1 i_q c_q\n\n2 l_q r_q\nTask Output: For each query of type 2, print a line containing the answer.\nTask Samples: input: 7\nabcdbbd\n6\n2 3 6\n1 5 z\n2 1 1\n1 4 a\n1 7 d\n2 1 7 output: 3\n1\n5\n\nIn the first query, cdbb contains three kinds of letters: b , c , and d, so we print 3.\nIn the second query, S is modified to abcdzbd.\nIn the third query, a contains one kind of letter: a, so we print 1.\nIn the fourth query, S is modified to abcazbd.\nIn the fifth query, S does not change and is still abcazbd.\nIn the sixth query, abcazbd contains five kinds of letters: a, b, c, d, and z, so we print 5.\n\n" }, { "title": "", "content": "Problem Statement Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are <=ft(x_i, y_i\\right), and its hardness is c_i.\nTakahashi can use one heat source to grill the meat. If he puts the heat source at coordinates <=ft(X, Y\\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i * \\sqrt{<=ft(X - x_i\\right)^2 + <=ft(Y-y_i\\right)^2} seconds.\nTakahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.", "constraint": "All values in input are integers.\n1 <= N <= 60\n1 <= K <= N\n-1000 <= x_i , y_i <= 1000\n<=ft(x_i, y_i\\right) \\neq <=ft(x_j, y_j\\right) <=ft(i \\neq j \\right)\n1 <= c_i <= 100", "input": "Input is given from Standard Input in the following format:\nN K\nx_1 y_1 c_1\n\\vdots\nx_N y_N c_N", "output": "Print the answer.\nIt will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n-1 0 3\n0 0 3\n1 0 2\n1 1 40 output: 2.4\n\nIf we put the heat source at <=ft(-0.2,0\\right), the 1-st, 2-nd, and 3-rd pieces of meat will be ready to eat within 2.4 seconds. This is the optimal place to put the heat source.", "input: 10 5\n-879 981 26\n890 -406 81\n512 859 97\n362 -955 25\n128 553 17\n-885 763 2\n449 310 57\n-656 -204 11\n-270 76 40\n184 170 16 output: 7411.2252"], "Pid": "p02764", "ProblemText": "Task Description: Problem Statement Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are <=ft(x_i, y_i\\right), and its hardness is c_i.\nTakahashi can use one heat source to grill the meat. If he puts the heat source at coordinates <=ft(X, Y\\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i * \\sqrt{<=ft(X - x_i\\right)^2 + <=ft(Y-y_i\\right)^2} seconds.\nTakahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.\nTask Constraint: All values in input are integers.\n1 <= N <= 60\n1 <= K <= N\n-1000 <= x_i , y_i <= 1000\n<=ft(x_i, y_i\\right) \\neq <=ft(x_j, y_j\\right) <=ft(i \\neq j \\right)\n1 <= c_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN K\nx_1 y_1 c_1\n\\vdots\nx_N y_N c_N\nTask Output: Print the answer.\nIt will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.\nTask Samples: input: 4 3\n-1 0 3\n0 0 3\n1 0 2\n1 1 40 output: 2.4\n\nIf we put the heat source at <=ft(-0.2,0\\right), the 1-st, 2-nd, and 3-rd pieces of meat will be ready to eat within 2.4 seconds. This is the optimal place to put the heat source.\ninput: 10 5\n-879 981 26\n890 -406 81\n512 859 97\n362 -955 25\n128 553 17\n-885 763 2\n449 310 57\n-656 -204 11\n-270 76 40\n184 170 16 output: 7411.2252\n\n" }, { "title": "", "content": "Problem Statement Takahashi is a member of a programming competition site, But Coder.\nEach member of But Coder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 * (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.", "constraint": "All values in input are integers.\n1 <= N <= 100\n0 <= R <= 4111", "input": "Input is given from Standard Input in the following format:\nN R", "output": "Print his Inner Rating.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2919 output: 3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 * (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.", "input: 22 3051 output: 3051"], "Pid": "p02765", "ProblemText": "Task Description: Problem Statement Takahashi is a member of a programming competition site, But Coder.\nEach member of But Coder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 * (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n0 <= R <= 4111\nTask Input: Input is given from Standard Input in the following format:\nN R\nTask Output: Print his Inner Rating.\nTask Samples: input: 2 2919 output: 3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 * (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.\ninput: 22 3051 output: 3051\n\n" }, { "title": "", "content": "Problem Statement Given is an integer N. Find the number of digits that N has in base K. note: Notes For information on base-K representation, see Positional notation - Wikipedia.", "constraint": "All values in input are integers.\n1 <= N <= 10^9\n2 <= K <= 10", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the number of digits that N has in base K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11 2 output: 4\n\nIn binary, 11 is represented as 1011.", "input: 1010101 10 output: 7", "input: 314159265 3 output: 18"], "Pid": "p02766", "ProblemText": "Task Description: Problem Statement Given is an integer N. Find the number of digits that N has in base K. note: Notes For information on base-K representation, see Positional notation - Wikipedia.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^9\n2 <= K <= 10\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of digits that N has in base K.\nTask Samples: input: 11 2 output: 4\n\nIn binary, 11 is represented as 1011.\ninput: 1010101 10 output: 7\ninput: 314159265 3 output: 18\n\n" }, { "title": "", "content": "Problem Statement There are N people living on a number line.\nThe i-th person lives at coordinate X_i.\nYou are going to hold a meeting that all N people have to attend.\nThe meeting can be held at any integer coordinate. If you choose to hold the meeting at coordinate P, the i-th person will spend (X_i - P)^2 points of stamina to attend the meeting.\nFind the minimum total points of stamina the N people have to spend.", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= X_i <= 100", "input": "Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N", "output": "Print the minimum total stamina the N people have to spend.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 4 output: 5\n\nAssume the meeting is held at coordinate 2. In this case, the first person will spend (1 - 2)^2 points of stamina, and the second person will spend (4 - 2)^2 = 4 points of stamina, for a total of 5 points of stamina. This is the minimum total stamina that the 2 people have to spend.\nNote that you can hold the meeting only at an integer coordinate.", "input: 7\n14 14 2 13 56 2 37 output: 2354"], "Pid": "p02767", "ProblemText": "Task Description: Problem Statement There are N people living on a number line.\nThe i-th person lives at coordinate X_i.\nYou are going to hold a meeting that all N people have to attend.\nThe meeting can be held at any integer coordinate. If you choose to hold the meeting at coordinate P, the i-th person will spend (X_i - P)^2 points of stamina to attend the meeting.\nFind the minimum total points of stamina the N people have to spend.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= X_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N\nTask Output: Print the minimum total stamina the N people have to spend.\nTask Samples: input: 2\n1 4 output: 5\n\nAssume the meeting is held at coordinate 2. In this case, the first person will spend (1 - 2)^2 points of stamina, and the second person will spend (4 - 2)^2 = 4 points of stamina, for a total of 5 points of stamina. This is the minimum total stamina that the 2 people have to spend.\nNote that you can hold the meeting only at an integer coordinate.\ninput: 7\n14 14 2 13 56 2 37 output: 2354\n\n" }, { "title": "", "content": "Problem Statement Akari has n kinds of flowers, one of each kind.\nShe is going to choose one or more of these flowers to make a bouquet.\nHowever, she hates two numbers a and b, so the number of flowers in the bouquet cannot be a or b.\nHow many different bouquets are there that Akari can make?\nFind the count modulo (10^9 + 7).\nHere, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet.", "constraint": "All values in input are integers.\n2 <= n <= 10^9\n1 <= a < b <= \\textrm{min}(n, 2 * 10^5)", "input": "Input is given from Standard Input in the following format:\nn a b", "output": "Print the number of bouquets that Akari can make, modulo (10^9 + 7). (If there are no such bouquets, print 0. )", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1 3 output: 7\n\nIn this case, Akari can choose 2 or 4 flowers to make the bouquet.\nThere are 6 ways to choose 2 out of the 4 flowers, and 1 way to choose 4, so there are a total of 7 different bouquets that Akari can make.", "input: 1000000000 141421 173205 output: 34076506\n\nPrint the count modulo (10^9 + 7)."], "Pid": "p02768", "ProblemText": "Task Description: Problem Statement Akari has n kinds of flowers, one of each kind.\nShe is going to choose one or more of these flowers to make a bouquet.\nHowever, she hates two numbers a and b, so the number of flowers in the bouquet cannot be a or b.\nHow many different bouquets are there that Akari can make?\nFind the count modulo (10^9 + 7).\nHere, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet.\nTask Constraint: All values in input are integers.\n2 <= n <= 10^9\n1 <= a < b <= \\textrm{min}(n, 2 * 10^5)\nTask Input: Input is given from Standard Input in the following format:\nn a b\nTask Output: Print the number of bouquets that Akari can make, modulo (10^9 + 7). (If there are no such bouquets, print 0. )\nTask Samples: input: 4 1 3 output: 7\n\nIn this case, Akari can choose 2 or 4 flowers to make the bouquet.\nThere are 6 ways to choose 2 out of the 4 flowers, and 1 way to choose 4, so there are a total of 7 different bouquets that Akari can make.\ninput: 1000000000 141421 173205 output: 34076506\n\nPrint the count modulo (10^9 + 7).\n\n" }, { "title": "", "content": "Problem Statement There is a building with n rooms, numbered 1 to n.\nWe can move from any room to any other room in the building.\nLet us call the following event a move: a person in some room i goes to another room j~ (i \\neq j).\nInitially, there was one person in each room in the building.\nAfter that, we know that there were exactly k moves happened up to now.\nWe are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?\nFind the count modulo (10^9 + 7).", "constraint": "All values in input are integers.\n3 <= n <= 2 * 10^5\n2 <= k <= 10^9", "input": "Input is given from Standard Input in the following format:\nn k", "output": "Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 10\n\nLet c_1, c_2, and c_3 be the number of people in Room 1,2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):\n\n(0,0,3)\n(0,1,2)\n(0,2,1)\n(0,3,0)\n(1,0,2)\n(1,1,1)\n(1,2,0)\n(2,0,1)\n(2,1,0)\n(3,0,0)\n\nFor example, (c_1, c_2, c_3) will be (0,1,2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.", "input: 200000 1000000000 output: 607923868\n\nPrint the count modulo (10^9 + 7).", "input: 15 6 output: 22583772"], "Pid": "p02769", "ProblemText": "Task Description: Problem Statement There is a building with n rooms, numbered 1 to n.\nWe can move from any room to any other room in the building.\nLet us call the following event a move: a person in some room i goes to another room j~ (i \\neq j).\nInitially, there was one person in each room in the building.\nAfter that, we know that there were exactly k moves happened up to now.\nWe are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?\nFind the count modulo (10^9 + 7).\nTask Constraint: All values in input are integers.\n3 <= n <= 2 * 10^5\n2 <= k <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nn k\nTask Output: Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).\nTask Samples: input: 3 2 output: 10\n\nLet c_1, c_2, and c_3 be the number of people in Room 1,2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):\n\n(0,0,3)\n(0,1,2)\n(0,2,1)\n(0,3,0)\n(1,0,2)\n(1,1,1)\n(1,2,0)\n(2,0,1)\n(2,1,0)\n(3,0,0)\n\nFor example, (c_1, c_2, c_3) will be (0,1,2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.\ninput: 200000 1000000000 output: 607923868\n\nPrint the count modulo (10^9 + 7).\ninput: 15 6 output: 22583772\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of k numbers: d_0, d_1, . . . , d_{k - 1}.\nProcess the following q queries in order:\n\nThe i-th query contains three integers n_i, x_i, and m_i.\nLet a_0, a_1, . . . , a_{n_i - 1} be the following sequence of n_i numbers: \\begin{eqnarray} a_j = \\begin{cases} x_i & ( j = 0 ) \\\\ a_{j - 1} + d_{(j - 1)~\\textrm{mod}~k} & ( 0 < j <= n_i - 1 ) \\end{cases}\\end{eqnarray}\nPrint the number of j~(0 <= j < n_i - 1) such that (a_j~\\textrm{mod}~m_i) < (a_{j + 1}~\\textrm{mod}~m_i).\n\nHere (y~\\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0).", "constraint": "All values in input are integers.\n1 <= k, q <= 5000\n0 <= d_i <= 10^9\n2 <= n_i <= 10^9\n0 <= x_i <= 10^9\n2 <= m_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nk q\nd_0 d_1 . . . d_{k - 1}\nn_1 x_1 m_1\nn_2 x_2 m_2\n:\nn_q x_q m_q", "output": "Print q lines.\nThe i-th line should contain the response to the i-th query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n3 1 4\n5 3 2 output: 1\n\nFor the first query, the sequence {a_j} will be 3,6,7,11,14.\n\n(a_0~\\textrm{mod}~2) > (a_1~\\textrm{mod}~2)\n(a_1~\\textrm{mod}~2) < (a_2~\\textrm{mod}~2)\n(a_2~\\textrm{mod}~2) = (a_3~\\textrm{mod}~2)\n(a_3~\\textrm{mod}~2) > (a_4~\\textrm{mod}~2)\n\nThus, the response to this query should be 1.", "input: 7 3\n27 18 28 18 28 46 1000000000\n1000000000 1 7\n1000000000 2 10\n1000000000 3 12 output: 224489796\n214285714\n559523809"], "Pid": "p02770", "ProblemText": "Task Description: Problem Statement We have a sequence of k numbers: d_0, d_1, . . . , d_{k - 1}.\nProcess the following q queries in order:\n\nThe i-th query contains three integers n_i, x_i, and m_i.\nLet a_0, a_1, . . . , a_{n_i - 1} be the following sequence of n_i numbers: \\begin{eqnarray} a_j = \\begin{cases} x_i & ( j = 0 ) \\\\ a_{j - 1} + d_{(j - 1)~\\textrm{mod}~k} & ( 0 < j <= n_i - 1 ) \\end{cases}\\end{eqnarray}\nPrint the number of j~(0 <= j < n_i - 1) such that (a_j~\\textrm{mod}~m_i) < (a_{j + 1}~\\textrm{mod}~m_i).\n\nHere (y~\\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0).\nTask Constraint: All values in input are integers.\n1 <= k, q <= 5000\n0 <= d_i <= 10^9\n2 <= n_i <= 10^9\n0 <= x_i <= 10^9\n2 <= m_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nk q\nd_0 d_1 . . . d_{k - 1}\nn_1 x_1 m_1\nn_2 x_2 m_2\n:\nn_q x_q m_q\nTask Output: Print q lines.\nThe i-th line should contain the response to the i-th query.\nTask Samples: input: 3 1\n3 1 4\n5 3 2 output: 1\n\nFor the first query, the sequence {a_j} will be 3,6,7,11,14.\n\n(a_0~\\textrm{mod}~2) > (a_1~\\textrm{mod}~2)\n(a_1~\\textrm{mod}~2) < (a_2~\\textrm{mod}~2)\n(a_2~\\textrm{mod}~2) = (a_3~\\textrm{mod}~2)\n(a_3~\\textrm{mod}~2) > (a_4~\\textrm{mod}~2)\n\nThus, the response to this query should be 1.\ninput: 7 3\n27 18 28 18 28 46 1000000000\n1000000000 1 7\n1000000000 2 10\n1000000000 3 12 output: 224489796\n214285714\n559523809\n\n" }, { "title": "", "content": "Problem Statement\nA triple of numbers is said to be poor when two of those numbers are equal but the other number is different from those two numbers.\nYou will be given three integers A, B, and C. If this triple is poor, print Yes; otherwise, print No.", "constraint": "A, B, and C are all integers between 1 and 9 (inclusive).", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "If the given triple is poor, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 7 5 output: Yes\n\nA and C are equal, but B is different from those two numbers, so this triple is poor.", "input: 4 4 4 output: No\n\nA, B, and C are all equal, so this triple is not poor.", "input: 4 9 6 output: No", "input: 3 3 4 output: Yes"], "Pid": "p02771", "ProblemText": "Task Description: Problem Statement\nA triple of numbers is said to be poor when two of those numbers are equal but the other number is different from those two numbers.\nYou will be given three integers A, B, and C. If this triple is poor, print Yes; otherwise, print No.\nTask Constraint: A, B, and C are all integers between 1 and 9 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: If the given triple is poor, print Yes; otherwise, print No.\nTask Samples: input: 5 7 5 output: Yes\n\nA and C are equal, but B is different from those two numbers, so this triple is poor.\ninput: 4 4 4 output: No\n\nA, B, and C are all equal, so this triple is not poor.\ninput: 4 9 6 output: No\ninput: 3 3 4 output: Yes\n\n" }, { "title": "", "content": "Problem Statement\nYou are an immigration officer in the Kingdom of At Coder. The document carried by an immigrant has some number of integers written on it, and you need to check whether they meet certain criteria.\nAccording to the regulation, the immigrant should be allowed entry to the kingdom if and only if the following condition is satisfied:\n\nAll even numbers written on the document are divisible by 3 or 5.\n\nIf the immigrant should be allowed entry according to the regulation, output APPROVED; otherwise, print DENIED. note: Notes\n\nThe condition in the statement can be rephrased as \"If x is an even number written on the document, x is divisible by 3 or 5\".\nHere \"if\" and \"or\" are logical terms.", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= A_i <= 1000", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\dots A_N", "output": "If the immigrant should be allowed entry according to the regulation, print APPROVED; otherwise, print DENIED.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n6 7 9 10 31 output: APPROVED\n\nThe even numbers written on the document are 6 and 10.\nAll of them are divisible by 3 or 5, so the immigrant should be allowed entry.", "input: 3\n28 27 24 output: DENIED\n\n28 violates the condition, so the immigrant should not be allowed entry."], "Pid": "p02772", "ProblemText": "Task Description: Problem Statement\nYou are an immigration officer in the Kingdom of At Coder. The document carried by an immigrant has some number of integers written on it, and you need to check whether they meet certain criteria.\nAccording to the regulation, the immigrant should be allowed entry to the kingdom if and only if the following condition is satisfied:\n\nAll even numbers written on the document are divisible by 3 or 5.\n\nIf the immigrant should be allowed entry according to the regulation, output APPROVED; otherwise, print DENIED. note: Notes\n\nThe condition in the statement can be rephrased as \"If x is an even number written on the document, x is divisible by 3 or 5\".\nHere \"if\" and \"or\" are logical terms.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= A_i <= 1000\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\dots A_N\nTask Output: If the immigrant should be allowed entry according to the regulation, print APPROVED; otherwise, print DENIED.\nTask Samples: input: 5\n6 7 9 10 31 output: APPROVED\n\nThe even numbers written on the document are 6 and 10.\nAll of them are divisible by 3 or 5, so the immigrant should be allowed entry.\ninput: 3\n28 27 24 output: DENIED\n\n28 violates the condition, so the immigrant should not be allowed entry.\n\n" }, { "title": "", "content": "Problem Statement\nWe have N voting papers. The i-th vote (1 <= i <= N) has the string S_i written on it.\nPrint all strings that are written on the most number of votes, in lexicographical order.", "constraint": "1 <= N <= 2 * 10^5\nS_i (1 <= i <= N) are strings consisting of lowercase English letters.\nThe length of S_i (1 <= i <= N) is between 1 and 10 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N", "output": "Print all strings in question in lexicographical order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\nbeat\nvet\nbeet\nbed\nvet\nbet\nbeet output: beet\nvet\n\nbeet and vet are written on two sheets each, while beat, bed, and bet are written on one vote each. Thus, we should print the strings beet and vet.", "input: 8\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo output: buffalo", "input: 7\nbass\nbass\nkick\nkick\nbass\nkick\nkick output: kick", "input: 4\nushi\ntapu\nnichia\nkun output: kun\nnichia\ntapu\nushi"], "Pid": "p02773", "ProblemText": "Task Description: Problem Statement\nWe have N voting papers. The i-th vote (1 <= i <= N) has the string S_i written on it.\nPrint all strings that are written on the most number of votes, in lexicographical order.\nTask Constraint: 1 <= N <= 2 * 10^5\nS_i (1 <= i <= N) are strings consisting of lowercase English letters.\nThe length of S_i (1 <= i <= N) is between 1 and 10 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N\nTask Output: Print all strings in question in lexicographical order.\nTask Samples: input: 7\nbeat\nvet\nbeet\nbed\nvet\nbet\nbeet output: beet\nvet\n\nbeet and vet are written on two sheets each, while beat, bed, and bet are written on one vote each. Thus, we should print the strings beet and vet.\ninput: 8\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo\nbuffalo output: buffalo\ninput: 7\nbass\nbass\nkick\nkick\nbass\nkick\nkick output: kick\ninput: 4\nushi\ntapu\nnichia\nkun output: kun\nnichia\ntapu\nushi\n\n" }, { "title": "", "content": "Problem Statement\nWe have N integers A_1, A_2, . . . , A_N.\nThere are \\frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?", "constraint": "All values in input are integers.\n2 <= N <= 2 * 10^5\n1 <= K <= \\frac{N(N-1)}{2}\n-10^9 <= A_i <= 10^9\\ (1 <= i <= N)", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\dots A_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n3 3 -4 -2 output: -6\n\nThere are six ways to form a pair. The products of those pairs are 9, -12, -6, -12, -6,8.\nSorting those numbers in ascending order, we have -12, -12, -6, -6,8,9. The third number in this list is -6.", "input: 10 40\n5 4 3 2 -1 0 0 0 0 0 output: 6", "input: 30 413\n-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0 output: 448283280358331064"], "Pid": "p02774", "ProblemText": "Task Description: Problem Statement\nWe have N integers A_1, A_2, . . . , A_N.\nThere are \\frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?\nTask Constraint: All values in input are integers.\n2 <= N <= 2 * 10^5\n1 <= K <= \\frac{N(N-1)}{2}\n-10^9 <= A_i <= 10^9\\ (1 <= i <= N)\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\dots A_N\nTask Output: Print the answer.\nTask Samples: input: 4 3\n3 3 -4 -2 output: -6\n\nThere are six ways to form a pair. The products of those pairs are 9, -12, -6, -12, -6,8.\nSorting those numbers in ascending order, we have -12, -12, -6, -6,8,9. The third number in this list is -6.\ninput: 10 40\n5 4 3 2 -1 0 0 0 0 0 output: 6\ninput: 30 413\n-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0 output: 448283280358331064\n\n" }, { "title": "", "content": "Problem Statement\nIn the Kingdom of At Coder, only banknotes are used as currency. There are 10^{100}+1 kinds of banknotes, with the values of 1,10,10^2,10^3, \\dots, 10^{(10^{100})}. You have come shopping at a mall and are now buying a takoyaki machine with a value of N. (Takoyaki is the name of a Japanese snack. )\nTo make the payment, you will choose some amount of money which is at least N and give it to the clerk. Then, the clerk gives you back the change, which is the amount of money you give minus N.\nWhat will be the minimum possible number of total banknotes used by you and the clerk, when both choose the combination of banknotes to minimize this count?\nAssume that you have sufficient numbers of banknotes, and so does the clerk.", "constraint": "N is an integer between 1 and 10^{1,000,000} (inclusive).", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the minimum possible number of total banknotes used by you and the clerk.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 36 output: 8\n\nIf you give four banknotes of value 10 each, and the clerk gives you back four banknotes of value 1 each, a total of eight banknotes are used.\nThe payment cannot be made with less than eight banknotes in total, so the answer is 8.", "input: 91 output: 3\n\nIf you give two banknotes of value 100,1, and the clerk gives you back one banknote of value 10, a total of three banknotes are used.", "input: 314159265358979323846264338327950288419716939937551058209749445923078164062862089986280348253421170 output: 243"], "Pid": "p02775", "ProblemText": "Task Description: Problem Statement\nIn the Kingdom of At Coder, only banknotes are used as currency. There are 10^{100}+1 kinds of banknotes, with the values of 1,10,10^2,10^3, \\dots, 10^{(10^{100})}. You have come shopping at a mall and are now buying a takoyaki machine with a value of N. (Takoyaki is the name of a Japanese snack. )\nTo make the payment, you will choose some amount of money which is at least N and give it to the clerk. Then, the clerk gives you back the change, which is the amount of money you give minus N.\nWhat will be the minimum possible number of total banknotes used by you and the clerk, when both choose the combination of banknotes to minimize this count?\nAssume that you have sufficient numbers of banknotes, and so does the clerk.\nTask Constraint: N is an integer between 1 and 10^{1,000,000} (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the minimum possible number of total banknotes used by you and the clerk.\nTask Samples: input: 36 output: 8\n\nIf you give four banknotes of value 10 each, and the clerk gives you back four banknotes of value 1 each, a total of eight banknotes are used.\nThe payment cannot be made with less than eight banknotes in total, so the answer is 8.\ninput: 91 output: 3\n\nIf you give two banknotes of value 100,1, and the clerk gives you back one banknote of value 10, a total of three banknotes are used.\ninput: 314159265358979323846264338327950288419716939937551058209749445923078164062862089986280348253421170 output: 243\n\n" }, { "title": "", "content": "Problem Statement\nAfter being invaded by the Kingdom of Al Debaran, bombs are planted throughout our country, At Coder Kingdom.\nFortunately, our military team called ABC has managed to obtain a device that is a part of the system controlling the bombs.\nThere are N bombs, numbered 1 to N, planted in our country. Bomb i is planted at the coordinate A_i. It is currently activated if B_i=1, and deactivated if B_i=0.\nThe device has M cords numbered 1 to M. If we cut Cord j, the states of all the bombs planted between the coordinates L_j and R_j (inclusive) will be switched - from activated to deactivated, and vice versa.\nDetermine whether it is possible to deactivate all the bombs at the same time. If the answer is yes, output a set of cords that should be cut.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= A_i <= 10^9\\ (1 <= i <= N)\nA_i are pairwise distinct.\nB_i is 0 or 1. (1 <= i <= N)\n1 <= M <= 2 * 10^5\n1 <= L_j <= R_j <= 10^9\\ (1 <= j <= M)", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_N B_N\nL_1 R_1\n:\nL_M R_M", "output": "If it is impossible to deactivate all the bombs at the same time, print -1. If it is possible to do so, print a set of cords that should be cut, as follows:\nk\nc_1 c_2 \\dots c_k\n\nHere, k is the number of cords (possibly 0), and c_1, c_2, \\dots, c_k represent the cords that should be cut. 1 <= c_1 < c_2 < \\dots < c_k <= M must hold.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n5 1\n10 1\n8 0\n1 10\n4 5\n6 7\n8 9 output: 2\n1 4\n\nThere are two activated bombs at the coordinates 5,10, and one deactivated bomb at the coordinate 8.\nCutting Cord 1 switches the states of all the bombs planted between the coordinates 1 and 10, that is, all of the three bombs.\nCutting Cord 4 switches the states of all the bombs planted between the coordinates 8 and 9, that is, Bomb 3.\nThus, we can deactivate all the bombs by cutting Cord 1 and Cord 4.", "input: 4 2\n2 0\n3 1\n5 1\n7 0\n1 4\n4 7 output: -1\n\nCutting any set of cords will not deactivate all the bombs at the same time.", "input: 3 2\n5 0\n10 0\n8 0\n6 9\n66 99 output: 0\nAll the bombs are already deactivated, so we do not need to cut any cord.", "input: 12 20\n536130100 1\n150049660 1\n79245447 1\n132551741 0\n89484841 1\n328129089 0\n623467741 0\n248785745 0\n421631475 0\n498966877 0\n43768791 1\n112237273 0\n21499042 142460201\n58176487 384985131\n88563042 144788076\n120198276 497115965\n134867387 563350571\n211946499 458996604\n233934566 297258009\n335674184 555985828\n414601661 520203502\n101135608 501051309\n90972258 300372385\n255474956 630621190\n436210625 517850028\n145652401 192476406\n377607297 520655694\n244404406 304034433\n112237273 359737255\n392593015 463983307\n150586788 504362212\n54772353 83124235 output: 5\n1 7 8 9 11\n\nIf there are multiple sets of cords that deactivate all the bombs when cut, any of them can be printed."], "Pid": "p02776", "ProblemText": "Task Description: Problem Statement\nAfter being invaded by the Kingdom of Al Debaran, bombs are planted throughout our country, At Coder Kingdom.\nFortunately, our military team called ABC has managed to obtain a device that is a part of the system controlling the bombs.\nThere are N bombs, numbered 1 to N, planted in our country. Bomb i is planted at the coordinate A_i. It is currently activated if B_i=1, and deactivated if B_i=0.\nThe device has M cords numbered 1 to M. If we cut Cord j, the states of all the bombs planted between the coordinates L_j and R_j (inclusive) will be switched - from activated to deactivated, and vice versa.\nDetermine whether it is possible to deactivate all the bombs at the same time. If the answer is yes, output a set of cords that should be cut.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= A_i <= 10^9\\ (1 <= i <= N)\nA_i are pairwise distinct.\nB_i is 0 or 1. (1 <= i <= N)\n1 <= M <= 2 * 10^5\n1 <= L_j <= R_j <= 10^9\\ (1 <= j <= M)\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_N B_N\nL_1 R_1\n:\nL_M R_M\nTask Output: If it is impossible to deactivate all the bombs at the same time, print -1. If it is possible to do so, print a set of cords that should be cut, as follows:\nk\nc_1 c_2 \\dots c_k\n\nHere, k is the number of cords (possibly 0), and c_1, c_2, \\dots, c_k represent the cords that should be cut. 1 <= c_1 < c_2 < \\dots < c_k <= M must hold.\nTask Samples: input: 3 4\n5 1\n10 1\n8 0\n1 10\n4 5\n6 7\n8 9 output: 2\n1 4\n\nThere are two activated bombs at the coordinates 5,10, and one deactivated bomb at the coordinate 8.\nCutting Cord 1 switches the states of all the bombs planted between the coordinates 1 and 10, that is, all of the three bombs.\nCutting Cord 4 switches the states of all the bombs planted between the coordinates 8 and 9, that is, Bomb 3.\nThus, we can deactivate all the bombs by cutting Cord 1 and Cord 4.\ninput: 4 2\n2 0\n3 1\n5 1\n7 0\n1 4\n4 7 output: -1\n\nCutting any set of cords will not deactivate all the bombs at the same time.\ninput: 3 2\n5 0\n10 0\n8 0\n6 9\n66 99 output: 0\nAll the bombs are already deactivated, so we do not need to cut any cord.\ninput: 12 20\n536130100 1\n150049660 1\n79245447 1\n132551741 0\n89484841 1\n328129089 0\n623467741 0\n248785745 0\n421631475 0\n498966877 0\n43768791 1\n112237273 0\n21499042 142460201\n58176487 384985131\n88563042 144788076\n120198276 497115965\n134867387 563350571\n211946499 458996604\n233934566 297258009\n335674184 555985828\n414601661 520203502\n101135608 501051309\n90972258 300372385\n255474956 630621190\n436210625 517850028\n145652401 192476406\n377607297 520655694\n244404406 304034433\n112237273 359737255\n392593015 463983307\n150586788 504362212\n54772353 83124235 output: 5\n1 7 8 9 11\n\nIf there are multiple sets of cords that deactivate all the bombs when cut, any of them can be printed.\n\n" }, { "title": "", "content": "Problem Statement\nWe have A balls with the string S written on each of them and B balls with the string T written on each of them.\nFrom these balls, Takahashi chooses one with the string U written on it and throws it away.\nFind the number of balls with the string S and balls with the string T that we have now.", "constraint": "S, T, and U are strings consisting of lowercase English letters.\nThe lengths of S and T are each between 1 and 10 (inclusive).\nS \\not= T\nS=U or T=U.\n1 <= A,B <= 10\nA and B are integers.", "input": "Input is given from Standard Input in the following format:\nS T\nA B\nU", "output": "Print the answer, with space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: red blue\n3 4\nred output: 2 4\n\nTakahashi chose a ball with red written on it and threw it away.\nNow we have two balls with the string S and four balls with the string T.", "input: red blue\n5 5\nblue output: 5 4\n\nTakahashi chose a ball with blue written on it and threw it away.\nNow we have five balls with the string S and four balls with the string T."], "Pid": "p02777", "ProblemText": "Task Description: Problem Statement\nWe have A balls with the string S written on each of them and B balls with the string T written on each of them.\nFrom these balls, Takahashi chooses one with the string U written on it and throws it away.\nFind the number of balls with the string S and balls with the string T that we have now.\nTask Constraint: S, T, and U are strings consisting of lowercase English letters.\nThe lengths of S and T are each between 1 and 10 (inclusive).\nS \\not= T\nS=U or T=U.\n1 <= A,B <= 10\nA and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nS T\nA B\nU\nTask Output: Print the answer, with space in between.\nTask Samples: input: red blue\n3 4\nred output: 2 4\n\nTakahashi chose a ball with red written on it and threw it away.\nNow we have two balls with the string S and four balls with the string T.\ninput: red blue\n5 5\nblue output: 5 4\n\nTakahashi chose a ball with blue written on it and threw it away.\nNow we have five balls with the string S and four balls with the string T.\n\n" }, { "title": "", "content": "Problem Statement\nGiven is a string S. Replace every character in S with x and print the result.", "constraint": "S is a string consisting of lowercase English letters.\nThe length of S is between 1 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format:\nS", "output": "Replace every character in S with x and print the result.", "content_img": false, "lang": "en", "error": false, "samples": ["input: sardine output: xxxxxxx\n\nReplacing every character in S with x results in xxxxxxx.", "input: xxxx output: xxxx", "input: gone output: xxxx"], "Pid": "p02778", "ProblemText": "Task Description: Problem Statement\nGiven is a string S. Replace every character in S with x and print the result.\nTask Constraint: S is a string consisting of lowercase English letters.\nThe length of S is between 1 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Replace every character in S with x and print the result.\nTask Samples: input: sardine output: xxxxxxx\n\nReplacing every character in S with x results in xxxxxxx.\ninput: xxxx output: xxxx\ninput: gone output: xxxx\n\n" }, { "title": "", "content": "Problem Statement Given is a sequence of integers A_1, A_2, . . . , A_N.\nIf its elements are pairwise distinct, print YES; otherwise, print NO.", "constraint": "2 <= N <= 200000\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N", "output": "If the elements of the sequence are pairwise distinct, print YES; otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 6 1 4 5 output: YES\n\nThe elements are pairwise distinct.", "input: 6\n4 1 3 1 6 2 output: NO\n\nThe second and fourth elements are identical.", "input: 2\n10000000 10000000 output: NO"], "Pid": "p02779", "ProblemText": "Task Description: Problem Statement Given is a sequence of integers A_1, A_2, . . . , A_N.\nIf its elements are pairwise distinct, print YES; otherwise, print NO.\nTask Constraint: 2 <= N <= 200000\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nTask Output: If the elements of the sequence are pairwise distinct, print YES; otherwise, print NO.\nTask Samples: input: 5\n2 6 1 4 5 output: YES\n\nThe elements are pairwise distinct.\ninput: 6\n4 1 3 1 6 2 output: NO\n\nThe second and fourth elements are identical.\ninput: 2\n10000000 10000000 output: NO\n\n" }, { "title": "", "content": "Problem Statement We have N dice arranged in a line from left to right. The i-th die from the left shows p_i numbers from 1 to p_i with equal probability when thrown.\nWe will choose K adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this sum.", "constraint": "1 <= K <= N <= 200000\n1 <= p_i <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\np_1 . . . p_N", "output": "Print the maximum possible value of the expected value of the sum of the numbers shown.\nYour output will be considered correct when its absolute or relative error from our answer is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 2 2 4 5 output: 7.000000000000\n\nWhen we throw the third, fourth, and fifth dice from the left, the expected value of the sum of the numbers shown is 7. This is the maximum value we can achieve.", "input: 4 1\n6 6 6 6 output: 3.500000000000\n\nRegardless of which die we choose, the expected value of the number shown is 3.5.", "input: 10 4\n17 13 13 12 15 20 10 13 17 11 output: 32.000000000000"], "Pid": "p02780", "ProblemText": "Task Description: Problem Statement We have N dice arranged in a line from left to right. The i-th die from the left shows p_i numbers from 1 to p_i with equal probability when thrown.\nWe will choose K adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this sum.\nTask Constraint: 1 <= K <= N <= 200000\n1 <= p_i <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\np_1 . . . p_N\nTask Output: Print the maximum possible value of the expected value of the sum of the numbers shown.\nYour output will be considered correct when its absolute or relative error from our answer is at most 10^{-6}.\nTask Samples: input: 5 3\n1 2 2 4 5 output: 7.000000000000\n\nWhen we throw the third, fourth, and fifth dice from the left, the expected value of the sum of the numbers shown is 7. This is the maximum value we can achieve.\ninput: 4 1\n6 6 6 6 output: 3.500000000000\n\nRegardless of which die we choose, the expected value of the number shown is 3.5.\ninput: 10 4\n17 13 13 12 15 20 10 13 17 11 output: 32.000000000000\n\n" }, { "title": "", "content": "Problem Statement Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.", "constraint": "1 <= N < 10^{100}\n1 <= K <= 3", "input": "Input is given from Standard Input in the following format:\nN\nK", "output": "Print the count.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100\n1 output: 19\n\nThe following 19 integers satisfy the condition:\n\n1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100", "input: 25\n2 output: 14\n\nThe following 14 integers satisfy the condition:\n\n11,12,13,14,15,16,17,18,19,21,22,23,24,25", "input: 314159\n2 output: 937", "input: 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\n3 output: 117879300"], "Pid": "p02781", "ProblemText": "Task Description: Problem Statement Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.\nTask Constraint: 1 <= N < 10^{100}\n1 <= K <= 3\nTask Input: Input is given from Standard Input in the following format:\nN\nK\nTask Output: Print the count.\nTask Samples: input: 100\n1 output: 19\n\nThe following 19 integers satisfy the condition:\n\n1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100\ninput: 25\n2 output: 14\n\nThe following 14 integers satisfy the condition:\n\n11,12,13,14,15,16,17,18,19,21,22,23,24,25\ninput: 314159\n2 output: 937\ninput: 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\n3 output: 117879300\n\n" }, { "title": "", "content": "Problem Statement Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.\nLet us define a function f(r, c) as follows:\n\nf(r, c) : = (The number of paths from the point (0,0) to the point (r, c) that Snuke can trace by repeating the operation above)\n\nGiven are integers r_1, r_2, c_1, and c_2.\nFind the sum of f(i, j) over all pair of integers (i, j) such that r_1 <= i <= r_2 and c_1 <= j <= c_2, and compute this value modulo (10^9+7).", "constraint": "1 <= r_1 <= r_2 <= 10^6\n1 <= c_1 <= c_2 <= 10^6\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nr_1 c_1 r_2 c_2", "output": "Print the sum of f(i, j) modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 2 2 output: 14\n\nFor example, there are two paths from the point (0,0) to the point (1,1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.\nSimilarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.", "input: 314 159 2653 589 output: 602215194"], "Pid": "p02782", "ProblemText": "Task Description: Problem Statement Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.\nLet us define a function f(r, c) as follows:\n\nf(r, c) : = (The number of paths from the point (0,0) to the point (r, c) that Snuke can trace by repeating the operation above)\n\nGiven are integers r_1, r_2, c_1, and c_2.\nFind the sum of f(i, j) over all pair of integers (i, j) such that r_1 <= i <= r_2 and c_1 <= j <= c_2, and compute this value modulo (10^9+7).\nTask Constraint: 1 <= r_1 <= r_2 <= 10^6\n1 <= c_1 <= c_2 <= 10^6\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nr_1 c_1 r_2 c_2\nTask Output: Print the sum of f(i, j) modulo (10^9+7).\nTask Samples: input: 1 1 2 2 output: 14\n\nFor example, there are two paths from the point (0,0) to the point (1,1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.\nSimilarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.\ninput: 314 159 2653 589 output: 602215194\n\n" }, { "title": "", "content": "Problem Statement Serval is fighting with a monster.\nThe health of the monster is H.\nIn one attack, Serval can decrease the monster's health by A.\nThere is no other way to decrease the monster's health.\nServal wins when the monster's health becomes 0 or below.\nFind the number of attacks Serval needs to make before winning.", "constraint": "1 <= H <= 10^4\n1 <= A <= 10^4\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nH A", "output": "Print the number of attacks Serval needs to make before winning.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 4 output: 3\nAfter one attack, the monster's health will be 6.\nAfter two attacks, the monster's health will be 2.\nAfter three attacks, the monster's health will be -2.\n\nThus, Serval needs to make three attacks to win.", "input: 1 10000 output: 1", "input: 10000 1 output: 10000"], "Pid": "p02783", "ProblemText": "Task Description: Problem Statement Serval is fighting with a monster.\nThe health of the monster is H.\nIn one attack, Serval can decrease the monster's health by A.\nThere is no other way to decrease the monster's health.\nServal wins when the monster's health becomes 0 or below.\nFind the number of attacks Serval needs to make before winning.\nTask Constraint: 1 <= H <= 10^4\n1 <= A <= 10^4\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nH A\nTask Output: Print the number of attacks Serval needs to make before winning.\nTask Samples: input: 10 4 output: 3\nAfter one attack, the monster's health will be 6.\nAfter two attacks, the monster's health will be 2.\nAfter three attacks, the monster's health will be -2.\n\nThus, Serval needs to make three attacks to win.\ninput: 1 10000 output: 1\ninput: 10000 1 output: 10000\n\n" }, { "title": "", "content": "Problem Statement Raccoon is fighting with a monster.\nThe health of the monster is H.\nRaccoon can use N kinds of special moves. Using the i-th move decreases the monster's health by A_i.\nThere is no other way to decrease the monster's health.\nRaccoon wins when the monster's health becomes 0 or below.\nIf Raccoon can win without using the same move twice or more, print Yes; otherwise, print No.", "constraint": "1 <= H <= 10^9\n1 <= N <= 10^5\n1 <= A_i <= 10^4\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nH N\nA_1 A_2 . . . A_N", "output": "If Raccoon can win without using the same move twice or more, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 3\n4 5 6 output: Yes\n\nThe monster's health will become 0 or below after, for example, using the second and third moves.", "input: 20 3\n4 5 6 output: No", "input: 210 5\n31 41 59 26 53 output: Yes", "input: 211 5\n31 41 59 26 53 output: No"], "Pid": "p02784", "ProblemText": "Task Description: Problem Statement Raccoon is fighting with a monster.\nThe health of the monster is H.\nRaccoon can use N kinds of special moves. Using the i-th move decreases the monster's health by A_i.\nThere is no other way to decrease the monster's health.\nRaccoon wins when the monster's health becomes 0 or below.\nIf Raccoon can win without using the same move twice or more, print Yes; otherwise, print No.\nTask Constraint: 1 <= H <= 10^9\n1 <= N <= 10^5\n1 <= A_i <= 10^4\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nH N\nA_1 A_2 . . . A_N\nTask Output: If Raccoon can win without using the same move twice or more, print Yes; otherwise, print No.\nTask Samples: input: 10 3\n4 5 6 output: Yes\n\nThe monster's health will become 0 or below after, for example, using the second and third moves.\ninput: 20 3\n4 5 6 output: No\ninput: 210 5\n31 41 59 26 53 output: Yes\ninput: 211 5\n31 41 59 26 53 output: No\n\n" }, { "title": "", "content": "Problem Statement Fennec is fighting with N monsters.\nThe health of the i-th monster is H_i.\nFennec can do the following two actions:\n\nAttack: Fennec chooses one monster. That monster's health will decrease by 1.\nSpecial Move: Fennec chooses one monster. That monster's health will become 0.\n\nThere is no way other than Attack and Special Move to decrease the monsters' health.\nFennec wins when all the monsters' healths become 0 or below.\nFind the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.", "constraint": "1 <= N <= 2 * 10^5\n0 <= K <= 2 * 10^5\n1 <= H_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nH_1 . . . H_N", "output": "Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n4 1 5 output: 5\n\nBy using Special Move on the third monster, and doing Attack four times on the first monster and once on the second monster, Fennec can win with five Attacks.", "input: 8 9\n7 9 3 2 3 8 4 6 output: 0\n\nShe can use Special Move on all the monsters.", "input: 3 0\n1000000000 1000000000 1000000000 output: 3000000000\n\nWatch out for overflow."], "Pid": "p02785", "ProblemText": "Task Description: Problem Statement Fennec is fighting with N monsters.\nThe health of the i-th monster is H_i.\nFennec can do the following two actions:\n\nAttack: Fennec chooses one monster. That monster's health will decrease by 1.\nSpecial Move: Fennec chooses one monster. That monster's health will become 0.\n\nThere is no way other than Attack and Special Move to decrease the monsters' health.\nFennec wins when all the monsters' healths become 0 or below.\nFind the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.\nTask Constraint: 1 <= N <= 2 * 10^5\n0 <= K <= 2 * 10^5\n1 <= H_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nH_1 . . . H_N\nTask Output: Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.\nTask Samples: input: 3 1\n4 1 5 output: 5\n\nBy using Special Move on the third monster, and doing Attack four times on the first monster and once on the second monster, Fennec can win with five Attacks.\ninput: 8 9\n7 9 3 2 3 8 4 6 output: 0\n\nShe can use Special Move on all the monsters.\ninput: 3 0\n1000000000 1000000000 1000000000 output: 3000000000\n\nWatch out for overflow.\n\n" }, { "title": "", "content": "Problem Statement Caracal is fighting with a monster.\nThe health of the monster is H.\nCaracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens:\n\nIf the monster's health is 1, it drops to 0.\nIf the monster's health, X, is greater than 1, that monster disappears. Then, two new monsters appear, each with the health of \\lfloor X/2 \\rfloor.\n\n(\\lfloor r \\rfloor denotes the greatest integer not exceeding r. )\nCaracal wins when the healths of all existing monsters become 0 or below.\nFind the minimum number of attacks Caracal needs to make before winning.", "constraint": "1 <= H <= 10^{12}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nH", "output": "Find the minimum number of attacks Caracal needs to make before winning.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 3\n\nWhen Caracal attacks the initial monster, it disappears, and two monsters appear, each with the health of 1.\nThen, Caracal can attack each of these new monsters once and win with a total of three attacks.", "input: 4 output: 7", "input: 1000000000000 output: 1099511627775"], "Pid": "p02786", "ProblemText": "Task Description: Problem Statement Caracal is fighting with a monster.\nThe health of the monster is H.\nCaracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens:\n\nIf the monster's health is 1, it drops to 0.\nIf the monster's health, X, is greater than 1, that monster disappears. Then, two new monsters appear, each with the health of \\lfloor X/2 \\rfloor.\n\n(\\lfloor r \\rfloor denotes the greatest integer not exceeding r. )\nCaracal wins when the healths of all existing monsters become 0 or below.\nFind the minimum number of attacks Caracal needs to make before winning.\nTask Constraint: 1 <= H <= 10^{12}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nH\nTask Output: Find the minimum number of attacks Caracal needs to make before winning.\nTask Samples: input: 2 output: 3\n\nWhen Caracal attacks the initial monster, it disappears, and two monsters appear, each with the health of 1.\nThen, Caracal can attack each of these new monsters once and win with a total of three attacks.\ninput: 4 output: 7\ninput: 1000000000000 output: 1099511627775\n\n" }, { "title": "", "content": "Problem Statement Ibis is fighting with a monster.\nThe health of the monster is H.\nIbis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.\nThe same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.\nIbis wins when the health of the monster becomes 0 or below.\nFind the minimum total Magic Points that have to be consumed before winning.", "constraint": "1 <= H <= 10^4\n1 <= N <= 10^3\n1 <= A_i <= 10^4\n1 <= B_i <= 10^4\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nH N\nA_1 B_1\n:\nA_N B_N", "output": "Print the minimum total Magic Points that have to be consumed before winning.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 3\n8 3\n4 2\n2 1 output: 4\n\nFirst, let us cast the first spell to decrease the monster's health by 8, at the cost of 3 Magic Points. The monster's health is now 1.\nThen, cast the third spell to decrease the monster's health by 2, at the cost of 1 Magic Point. The monster's health is now -1.\nIn this way, we can win at the total cost of 4 Magic Points.", "input: 100 6\n1 1\n2 3\n3 9\n4 27\n5 81\n6 243 output: 100\n\nIt is optimal to cast the first spell 100 times.", "input: 9999 10\n540 7550\n691 9680\n700 9790\n510 7150\n415 5818\n551 7712\n587 8227\n619 8671\n588 8228\n176 2461 output: 139815"], "Pid": "p02787", "ProblemText": "Task Description: Problem Statement Ibis is fighting with a monster.\nThe health of the monster is H.\nIbis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.\nThe same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.\nIbis wins when the health of the monster becomes 0 or below.\nFind the minimum total Magic Points that have to be consumed before winning.\nTask Constraint: 1 <= H <= 10^4\n1 <= N <= 10^3\n1 <= A_i <= 10^4\n1 <= B_i <= 10^4\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nH N\nA_1 B_1\n:\nA_N B_N\nTask Output: Print the minimum total Magic Points that have to be consumed before winning.\nTask Samples: input: 9 3\n8 3\n4 2\n2 1 output: 4\n\nFirst, let us cast the first spell to decrease the monster's health by 8, at the cost of 3 Magic Points. The monster's health is now 1.\nThen, cast the third spell to decrease the monster's health by 2, at the cost of 1 Magic Point. The monster's health is now -1.\nIn this way, we can win at the total cost of 4 Magic Points.\ninput: 100 6\n1 1\n2 3\n3 9\n4 27\n5 81\n6 243 output: 100\n\nIt is optimal to cast the first spell 100 times.\ninput: 9999 10\n540 7550\n691 9680\n700 9790\n510 7150\n415 5818\n551 7712\n587 8227\n619 8671\n588 8228\n176 2461 output: 139815\n\n" }, { "title": "", "content": "Problem Statement Silver Fox is fighting with N monsters.\nThe monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.\nSilver Fox can use bombs to attack the monsters.\nUsing a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.\nThere is no way other than bombs to decrease the monster's health.\nSilver Fox wins when all the monsters' healths become 0 or below.\nFind the minimum number of bombs needed to win.", "constraint": "1 <= N <= 2 * 10^5\n0 <= D <= 10^9\n1 <= A <= 10^9\n0 <= X_i <= 10^9\n1 <= H_i <= 10^9\nX_i are distinct.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN D A\nX_1 H_1\n:\nX_N H_N", "output": "Print the minimum number of bombs needed to win.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 2\n1 2\n5 4\n9 2 output: 2\n\nFirst, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.\nThen, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.\nNow, all the monsters' healths are 0.\nWe cannot make all the monsters' health drop to 0 or below with just one bomb.", "input: 9 4 1\n1 5\n2 4\n3 3\n4 2\n5 1\n6 2\n7 3\n8 4\n9 5 output: 5\n\nWe should use five bombs at the coordinate 5.", "input: 3 0 1\n300000000 1000000000\n100000000 1000000000\n200000000 1000000000 output: 3000000000\n\nWatch out for overflow."], "Pid": "p02788", "ProblemText": "Task Description: Problem Statement Silver Fox is fighting with N monsters.\nThe monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.\nSilver Fox can use bombs to attack the monsters.\nUsing a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.\nThere is no way other than bombs to decrease the monster's health.\nSilver Fox wins when all the monsters' healths become 0 or below.\nFind the minimum number of bombs needed to win.\nTask Constraint: 1 <= N <= 2 * 10^5\n0 <= D <= 10^9\n1 <= A <= 10^9\n0 <= X_i <= 10^9\n1 <= H_i <= 10^9\nX_i are distinct.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN D A\nX_1 H_1\n:\nX_N H_N\nTask Output: Print the minimum number of bombs needed to win.\nTask Samples: input: 3 3 2\n1 2\n5 4\n9 2 output: 2\n\nFirst, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.\nThen, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.\nNow, all the monsters' healths are 0.\nWe cannot make all the monsters' health drop to 0 or below with just one bomb.\ninput: 9 4 1\n1 5\n2 4\n3 3\n4 2\n5 1\n6 2\n7 3\n8 4\n9 5 output: 5\n\nWe should use five bombs at the coordinate 5.\ninput: 3 0 1\n300000000 1000000000\n100000000 1000000000\n200000000 1000000000 output: 3000000000\n\nWatch out for overflow.\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi is participating in a programming contest, AXC001. He has just submitted his code to Problem A.\nThe problem has N test cases, all of which must be passed to get an AC verdict.\nTakahashi's submission has passed M cases out of the N test cases.\nDetermine whether Takahashi's submission gets an AC.", "constraint": "1 <= N <= 100\n0 <= M <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "If Takahashi's submission gets an AC, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 output: Yes\n\nAll three test cases have been passed, so his submission gets an AC.", "input: 3 2 output: No\n\nOnly two out of the three test cases have been passed, so his submission does not get an AC.", "input: 1 1 output: Yes"], "Pid": "p02789", "ProblemText": "Task Description: Problem Statement\nTakahashi is participating in a programming contest, AXC001. He has just submitted his code to Problem A.\nThe problem has N test cases, all of which must be passed to get an AC verdict.\nTakahashi's submission has passed M cases out of the N test cases.\nDetermine whether Takahashi's submission gets an AC.\nTask Constraint: 1 <= N <= 100\n0 <= M <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: If Takahashi's submission gets an AC, print Yes; otherwise, print No.\nTask Samples: input: 3 3 output: Yes\n\nAll three test cases have been passed, so his submission gets an AC.\ninput: 3 2 output: No\n\nOnly two out of the three test cases have been passed, so his submission does not get an AC.\ninput: 1 1 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Given are 1-digit positive integers a and b. Consider these two strings: the concatenation of b copies of the digit a, and the concatenation of a copies of the digit b. Which of these is lexicographically smaller?", "constraint": "1 <= a <= 9\n1 <= b <= 9\na and b are integers.", "input": "Input is given from Standard Input in the following format:\na b", "output": "Print the lexicographically smaller of the two strings. (If the two strings are equal, print one of them. )", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 output: 3333\n\nWe have two strings 444 and 3333. Between them, 3333 is the lexicographically smaller.", "input: 7 7 output: 7777777"], "Pid": "p02790", "ProblemText": "Task Description: Problem Statement Given are 1-digit positive integers a and b. Consider these two strings: the concatenation of b copies of the digit a, and the concatenation of a copies of the digit b. Which of these is lexicographically smaller?\nTask Constraint: 1 <= a <= 9\n1 <= b <= 9\na and b are integers.\nTask Input: Input is given from Standard Input in the following format:\na b\nTask Output: Print the lexicographically smaller of the two strings. (If the two strings are equal, print one of them. )\nTask Samples: input: 4 3 output: 3333\n\nWe have two strings 444 and 3333. Between them, 3333 is the lexicographically smaller.\ninput: 7 7 output: 7777777\n\n" }, { "title": "", "content": "Problem Statement\nGiven is a permutation P_1, \\ldots, P_N of 1, \\ldots, N.\nFind the number of integers i (1 <= i <= N) that satisfy the following condition: \n\nFor any integer j (1 <= j <= i), P_i <= P_j.", "constraint": "1 <= N <= 2 * 10^5\nP_1, \\ldots, P_N is a permutation of 1, \\ldots, N. \nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nP_1 . . . P_N", "output": "Print the number of integers i that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n4 2 5 1 3 output: 3\n\ni=1,2, and 4 satisfy the condition, but i=3 does not - for example, P_i > P_j holds for j = 1.\nSimilarly, i=5 does not satisfy the condition, either. Thus, there are three integers that satisfy the condition.", "input: 4\n4 3 2 1 output: 4\n\nAll integers i (1 <= i <= N) satisfy the condition.", "input: 6\n1 2 3 4 5 6 output: 1\n\nOnly i=1 satisfies the condition.", "input: 8\n5 7 4 2 6 8 1 3 output: 4", "input: 1\n1 output: 1"], "Pid": "p02791", "ProblemText": "Task Description: Problem Statement\nGiven is a permutation P_1, \\ldots, P_N of 1, \\ldots, N.\nFind the number of integers i (1 <= i <= N) that satisfy the following condition: \n\nFor any integer j (1 <= j <= i), P_i <= P_j.\nTask Constraint: 1 <= N <= 2 * 10^5\nP_1, \\ldots, P_N is a permutation of 1, \\ldots, N. \nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nP_1 . . . P_N\nTask Output: Print the number of integers i that satisfy the condition.\nTask Samples: input: 5\n4 2 5 1 3 output: 3\n\ni=1,2, and 4 satisfy the condition, but i=3 does not - for example, P_i > P_j holds for j = 1.\nSimilarly, i=5 does not satisfy the condition, either. Thus, there are three integers that satisfy the condition.\ninput: 4\n4 3 2 1 output: 4\n\nAll integers i (1 <= i <= N) satisfy the condition.\ninput: 6\n1 2 3 4 5 6 output: 1\n\nOnly i=1 satisfies the condition.\ninput: 8\n5 7 4 2 6 8 1 3 output: 4\ninput: 1\n1 output: 1\n\n" }, { "title": "", "content": "Problem Statement\nGiven is a positive integer N.\nFind the number of pairs (A, B) of positive integers not greater than N that satisfy the following condition:\n\nWhen A and B are written in base ten without leading zeros, the last digit of A is equal to the first digit of B, and the first digit of A is equal to the last digit of B.", "constraint": "1 <= N <= 2 * 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 25 output: 17\n\nThe following 17 pairs satisfy the condition: (1,1), (1,11), (2,2), (2,22), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (11,1), (11,11), (12,21), (21,12), (22,2), and (22,22).", "input: 1 output: 1", "input: 100 output: 108", "input: 2020 output: 40812", "input: 200000 output: 400000008"], "Pid": "p02792", "ProblemText": "Task Description: Problem Statement\nGiven is a positive integer N.\nFind the number of pairs (A, B) of positive integers not greater than N that satisfy the following condition:\n\nWhen A and B are written in base ten without leading zeros, the last digit of A is equal to the first digit of B, and the first digit of A is equal to the last digit of B.\nTask Constraint: 1 <= N <= 2 * 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 25 output: 17\n\nThe following 17 pairs satisfy the condition: (1,1), (1,11), (2,2), (2,22), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (11,1), (11,11), (12,21), (21,12), (22,2), and (22,22).\ninput: 1 output: 1\ninput: 100 output: 108\ninput: 2020 output: 40812\ninput: 200000 output: 400000008\n\n" }, { "title": "", "content": "Problem Statement Given are N positive integers A_1, . . . , A_N.\nConsider positive integers B_1, . . . , B_N that satisfy the following condition.\nCondition: For any i, j such that 1 <= i < j <= N, A_i B_i = A_j B_j holds.\nFind the minimum possible value of B_1 + . . . + B_N for such B_1, . . . , B_N.\nSince the answer can be enormous, print the sum modulo (10^9 +7).", "constraint": "1 <= N <= 10^4\n1 <= A_i <= 10^6\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N", "output": "Print the minimum possible value of B_1 + . . . + B_N for B_1, . . . , B_N that satisfy the condition, modulo (10^9 +7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3 4 output: 13\n\nLet B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.", "input: 5\n12 12 12 12 12 output: 5\n\nWe can let all B_i be 1.", "input: 3\n1000000 999999 999998 output: 996989508\n\nPrint the sum modulo (10^9+7)."], "Pid": "p02793", "ProblemText": "Task Description: Problem Statement Given are N positive integers A_1, . . . , A_N.\nConsider positive integers B_1, . . . , B_N that satisfy the following condition.\nCondition: For any i, j such that 1 <= i < j <= N, A_i B_i = A_j B_j holds.\nFind the minimum possible value of B_1 + . . . + B_N for such B_1, . . . , B_N.\nSince the answer can be enormous, print the sum modulo (10^9 +7).\nTask Constraint: 1 <= N <= 10^4\n1 <= A_i <= 10^6\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nTask Output: Print the minimum possible value of B_1 + . . . + B_N for B_1, . . . , B_N that satisfy the condition, modulo (10^9 +7).\nTask Samples: input: 3\n2 3 4 output: 13\n\nLet B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.\ninput: 5\n12 12 12 12 12 output: 5\n\nWe can let all B_i be 1.\ninput: 3\n1000000 999999 999998 output: 996989508\n\nPrint the sum modulo (10^9+7).\n\n" }, { "title": "", "content": "Problem Statement\nWe have a tree with N vertices numbered 1 to N.\nThe i-th edge in this tree connects Vertex a_i and Vertex b_i.\nConsider painting each of these edges white or black. There are 2^{N-1} such ways to paint the edges. Among them, how many satisfy all of the following M restrictions? \n\nThe i-th (1 <= i <= M) restriction is represented by two integers u_i and v_i, which mean that the path connecting Vertex u_i and Vertex v_i must contain at least one edge painted black.", "constraint": "2 <= N <= 50\n1 <= a_i,b_i <= N\nThe graph given in input is a tree.\n1 <= M <= \\min(20,\\frac{N(N-1)}{2})\n1 <= u_i < v_i <= N\nIf i \\not= j, either u_i \\not=u_j or v_i\\not=v_j\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nM\nu_1 v_1\n:\nu_M v_M", "output": "Print the number of ways to paint the edges that satisfy all of the M conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3\n1\n1 3 output: 3\n\nThe tree in this input is shown below:\n\nAll of the M restrictions will be satisfied if Edge 1 and 2 are respectively painted (white, black), (black, white), or (black, black), so the answer is 3.", "input: 2\n1 2\n1\n1 2 output: 1\n\nThe tree in this input is shown below:\n\nAll of the M restrictions will be satisfied only if Edge 1 is painted black, so the answer is 1.", "input: 5\n1 2\n3 2\n3 4\n5 3\n3\n1 3\n2 4\n2 5 output: 9\n\nThe tree in this input is shown below:", "input: 8\n1 2\n2 3\n4 3\n2 5\n6 3\n6 7\n8 6\n5\n2 7\n3 5\n1 6\n2 8\n7 8 output: 62\n\nThe tree in this input is shown below:"], "Pid": "p02794", "ProblemText": "Task Description: Problem Statement\nWe have a tree with N vertices numbered 1 to N.\nThe i-th edge in this tree connects Vertex a_i and Vertex b_i.\nConsider painting each of these edges white or black. There are 2^{N-1} such ways to paint the edges. Among them, how many satisfy all of the following M restrictions? \n\nThe i-th (1 <= i <= M) restriction is represented by two integers u_i and v_i, which mean that the path connecting Vertex u_i and Vertex v_i must contain at least one edge painted black.\nTask Constraint: 2 <= N <= 50\n1 <= a_i,b_i <= N\nThe graph given in input is a tree.\n1 <= M <= \\min(20,\\frac{N(N-1)}{2})\n1 <= u_i < v_i <= N\nIf i \\not= j, either u_i \\not=u_j or v_i\\not=v_j\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nM\nu_1 v_1\n:\nu_M v_M\nTask Output: Print the number of ways to paint the edges that satisfy all of the M conditions.\nTask Samples: input: 3\n1 2\n2 3\n1\n1 3 output: 3\n\nThe tree in this input is shown below:\n\nAll of the M restrictions will be satisfied if Edge 1 and 2 are respectively painted (white, black), (black, white), or (black, black), so the answer is 3.\ninput: 2\n1 2\n1\n1 2 output: 1\n\nThe tree in this input is shown below:\n\nAll of the M restrictions will be satisfied only if Edge 1 is painted black, so the answer is 1.\ninput: 5\n1 2\n3 2\n3 4\n5 3\n3\n1 3\n2 4\n2 5 output: 9\n\nThe tree in this input is shown below:\ninput: 8\n1 2\n2 3\n4 3\n2 5\n6 3\n6 7\n8 6\n5\n2 7\n3 5\n1 6\n2 8\n7 8 output: 62\n\nThe tree in this input is shown below:\n\n" }, { "title": "", "content": "Problem Statement We have a grid with H rows and W columns, where all the squares are initially white.\nYou will perform some number of painting operations on the grid.\nIn one operation, you can do one of the following two actions:\n\nChoose one row, then paint all the squares in that row black.\nChoose one column, then paint all the squares in that column black.\n\nAt least how many operations do you need in order to have N or more black squares in the grid?\nIt is guaranteed that, under the conditions in Constraints, having N or more black squares is always possible by performing some number of operations.", "constraint": "1 <= H <= 100\n1 <= W <= 100\n1 <= N <= H * W\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nH\nW\nN", "output": "Print the minimum number of operations needed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n7\n10 output: 2\n\nYou can have 14 black squares in the grid by performing the \"row\" operation twice, on different rows.", "input: 14\n12\n112 output: 8", "input: 2\n100\n200 output: 2"], "Pid": "p02795", "ProblemText": "Task Description: Problem Statement We have a grid with H rows and W columns, where all the squares are initially white.\nYou will perform some number of painting operations on the grid.\nIn one operation, you can do one of the following two actions:\n\nChoose one row, then paint all the squares in that row black.\nChoose one column, then paint all the squares in that column black.\n\nAt least how many operations do you need in order to have N or more black squares in the grid?\nIt is guaranteed that, under the conditions in Constraints, having N or more black squares is always possible by performing some number of operations.\nTask Constraint: 1 <= H <= 100\n1 <= W <= 100\n1 <= N <= H * W\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nH\nW\nN\nTask Output: Print the minimum number of operations needed.\nTask Samples: input: 3\n7\n10 output: 2\n\nYou can have 14 black squares in the grid by performing the \"row\" operation twice, on different rows.\ninput: 14\n12\n112 output: 8\ninput: 2\n100\n200 output: 2\n\n" }, { "title": "", "content": "Problem Statement In a factory, there are N robots placed on a number line.\nRobot i is placed at coordinate X_i and can extend its arms of length L_i in both directions, positive and negative.\nWe want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect.\nHere, for each i (1 <= i <= N), the movable range of arms of Robot i is the part of the number line between the coordinates X_i - L_i and X_i + L_i, excluding the endpoints.\nFind the maximum number of robots that we can keep.", "constraint": "1 <= N <= 100,000\n0 <= X_i <= 10^9 (1 <= i <= N)\n1 <= L_i <= 10^9 (1 <= i <= N)\nIf i \\neq j, X_i \\neq X_j.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nX_1 L_1\nX_2 L_2\n\\vdots\nX_N L_N", "output": "Print the maximum number of robots that we can keep.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 4\n4 3\n9 3\n100 5 output: 3\n\nBy removing Robot 2, we can keep the other three robots.", "input: 2\n8 20\n1 10 output: 1", "input: 5\n10 1\n2 1\n4 1\n6 1\n8 1 output: 5"], "Pid": "p02796", "ProblemText": "Task Description: Problem Statement In a factory, there are N robots placed on a number line.\nRobot i is placed at coordinate X_i and can extend its arms of length L_i in both directions, positive and negative.\nWe want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect.\nHere, for each i (1 <= i <= N), the movable range of arms of Robot i is the part of the number line between the coordinates X_i - L_i and X_i + L_i, excluding the endpoints.\nFind the maximum number of robots that we can keep.\nTask Constraint: 1 <= N <= 100,000\n0 <= X_i <= 10^9 (1 <= i <= N)\n1 <= L_i <= 10^9 (1 <= i <= N)\nIf i \\neq j, X_i \\neq X_j.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 L_1\nX_2 L_2\n\\vdots\nX_N L_N\nTask Output: Print the maximum number of robots that we can keep.\nTask Samples: input: 4\n2 4\n4 3\n9 3\n100 5 output: 3\n\nBy removing Robot 2, we can keep the other three robots.\ninput: 2\n8 20\n1 10 output: 1\ninput: 5\n10 1\n2 1\n4 1\n6 1\n8 1 output: 5\n\n" }, { "title": "", "content": "Problem Statement Given are three integers N, K, and S.\nFind a sequence A_1, A_2, . . . , A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below.\nWe can prove that, under the conditions in Constraints, such a sequence always exists.\n\nThere are exactly K pairs (l, r) of integers such that 1 <= l <= r <= N and A_l + A_{l + 1} + \\cdots + A_r = S.", "constraint": "1 <= N <= 10^5\n0 <= K <= N\n1 <= S <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K S", "output": "Print a sequence satisfying the condition, in the following format:\nA_1 A_2 . . . A_N", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 3 output: 1 2 3 4\n\nTwo pairs (l, r) = (1,2) and (3,3) satisfy the condition in the statement.", "input: 5 3 100 output: 50 50 50 30 70"], "Pid": "p02797", "ProblemText": "Task Description: Problem Statement Given are three integers N, K, and S.\nFind a sequence A_1, A_2, . . . , A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below.\nWe can prove that, under the conditions in Constraints, such a sequence always exists.\n\nThere are exactly K pairs (l, r) of integers such that 1 <= l <= r <= N and A_l + A_{l + 1} + \\cdots + A_r = S.\nTask Constraint: 1 <= N <= 10^5\n0 <= K <= N\n1 <= S <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K S\nTask Output: Print a sequence satisfying the condition, in the following format:\nA_1 A_2 . . . A_N\nTask Samples: input: 4 2 3 output: 1 2 3 4\n\nTwo pairs (l, r) = (1,2) and (3,3) satisfy the condition in the statement.\ninput: 5 3 100 output: 50 50 50 30 70\n\n" }, { "title": "", "content": "Problem Statement We have N cards numbered 1,2, . . . , N.\nCard i (1 <= i <= N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side.\nInitially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.\nDetermine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 <= i <= N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.\n\nChoose an integer i (1 <= i <= N - 1).\nSwap the i-th and (i+1)-th cards from the left, then flip these two cards.", "constraint": "1 <= N <= 18\n1 <= A_i, B_i <= 50 (1 <= i <= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N", "output": "If it is impossible to have a non-decreasing sequence, print -1.\nIf it is possible, print the minimum number of operations required to achieve it.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 4 3\n3 2 3 output: 1\n\nBy doing the operation once with i = 1, we have a sequence [2,3,3] facing up, which is non-decreasing.", "input: 2\n2 1\n1 2 output: -1\n\nAfter any number of operations, we have the sequence [2,1] facing up, which is not non-decreasing.", "input: 4\n1 2 3 4\n5 6 7 8 output: 0\n\nNo operation may be required.", "input: 5\n28 15 22 43 31\n20 22 43 33 32 output: -1", "input: 5\n4 46 6 38 43\n33 15 18 27 37 output: 3"], "Pid": "p02798", "ProblemText": "Task Description: Problem Statement We have N cards numbered 1,2, . . . , N.\nCard i (1 <= i <= N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side.\nInitially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.\nDetermine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 <= i <= N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.\n\nChoose an integer i (1 <= i <= N - 1).\nSwap the i-th and (i+1)-th cards from the left, then flip these two cards.\nTask Constraint: 1 <= N <= 18\n1 <= A_i, B_i <= 50 (1 <= i <= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N\nTask Output: If it is impossible to have a non-decreasing sequence, print -1.\nIf it is possible, print the minimum number of operations required to achieve it.\nTask Samples: input: 3\n3 4 3\n3 2 3 output: 1\n\nBy doing the operation once with i = 1, we have a sequence [2,3,3] facing up, which is non-decreasing.\ninput: 2\n2 1\n1 2 output: -1\n\nAfter any number of operations, we have the sequence [2,1] facing up, which is not non-decreasing.\ninput: 4\n1 2 3 4\n5 6 7 8 output: 0\n\nNo operation may be required.\ninput: 5\n28 15 22 43 31\n20 22 43 33 32 output: -1\ninput: 5\n4 46 6 38 43\n33 15 18 27 37 output: 3\n\n" }, { "title": "", "content": "Problem Statement We have a connected undirected graph with N vertices and M edges.\nEdge i in this graph (1 <= i <= M) connects Vertex U_i and Vertex V_i bidirectionally.\nWe are additionally given N integers D_1, D_2, . . . , D_N.\nDetermine whether the conditions below can be satisfied by assigning a color - white or black - to each vertex and an integer weight between 1 and 10^9 (inclusive) to each edge in this graph.\nIf the answer is yes, find one such assignment of colors and integers, too.\n\nThere is at least one vertex assigned white and at least one vertex assigned black.\nFor each vertex v (1 <= v <= N), the following holds.\nThe minimum cost to travel from Vertex v to a vertex whose color assigned is different from that of Vertex v by traversing the edges is equal to D_v.\n\nHere, the cost of traversing the edges is the sum of the weights of the edges traversed.", "constraint": "2 <= N <= 100,000\n1 <= M <= 200,000\n1 <= D_i <= 10^9\n1 <= U_i, V_i <= N\nThe given graph is connected and has no self-loops or multiple edges.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nD_1 D_2 . . . D_N\nU_1 V_1\nU_2 V_2\n\\vdots\nU_M V_M", "output": "If there is no assignment satisfying the conditions, print a single line containing -1.\nIf such an assignment exists, print one such assignment in the following format:\nS\nC_1\nC_2\n\\vdots\nC_M\n\nHere,\n\nthe first line should contain the string S of length N. Its i-th character (1 <= i <= N) should be W if Vertex i is assigned white and B if it is assigned black.\nThe (i + 1)-th line (1 <= i <= M) should contain the integer weight C_i assigned to Edge i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n3 4 3 5 7\n1 2\n1 3\n3 2\n4 2\n4 5 output: BWWBB\n4\n3\n1\n5\n2\n\nAssume that we assign the colors and integers as the sample output, and let us consider Vertex 5, for example. To travel from Vertex 5, which is assigned black, to a vertex that is assigned white with the minimum cost, we should make these moves: Vertex 5 \\to Vertex 4 \\to Vertex 2. The total cost of these moves is 7, which satisfies the condition. We can also verify that the condition is satisfied for other vertices.", "input: 5 7\n1 2 3 4 5\n1 2\n1 3\n1 4\n2 3\n2 5\n3 5\n4 5 output: -1", "input: 4 6\n1 1 1 1\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4 output: BBBW\n1\n1\n1\n2\n1\n1"], "Pid": "p02799", "ProblemText": "Task Description: Problem Statement We have a connected undirected graph with N vertices and M edges.\nEdge i in this graph (1 <= i <= M) connects Vertex U_i and Vertex V_i bidirectionally.\nWe are additionally given N integers D_1, D_2, . . . , D_N.\nDetermine whether the conditions below can be satisfied by assigning a color - white or black - to each vertex and an integer weight between 1 and 10^9 (inclusive) to each edge in this graph.\nIf the answer is yes, find one such assignment of colors and integers, too.\n\nThere is at least one vertex assigned white and at least one vertex assigned black.\nFor each vertex v (1 <= v <= N), the following holds.\nThe minimum cost to travel from Vertex v to a vertex whose color assigned is different from that of Vertex v by traversing the edges is equal to D_v.\n\nHere, the cost of traversing the edges is the sum of the weights of the edges traversed.\nTask Constraint: 2 <= N <= 100,000\n1 <= M <= 200,000\n1 <= D_i <= 10^9\n1 <= U_i, V_i <= N\nThe given graph is connected and has no self-loops or multiple edges.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nD_1 D_2 . . . D_N\nU_1 V_1\nU_2 V_2\n\\vdots\nU_M V_M\nTask Output: If there is no assignment satisfying the conditions, print a single line containing -1.\nIf such an assignment exists, print one such assignment in the following format:\nS\nC_1\nC_2\n\\vdots\nC_M\n\nHere,\n\nthe first line should contain the string S of length N. Its i-th character (1 <= i <= N) should be W if Vertex i is assigned white and B if it is assigned black.\nThe (i + 1)-th line (1 <= i <= M) should contain the integer weight C_i assigned to Edge i.\nTask Samples: input: 5 5\n3 4 3 5 7\n1 2\n1 3\n3 2\n4 2\n4 5 output: BWWBB\n4\n3\n1\n5\n2\n\nAssume that we assign the colors and integers as the sample output, and let us consider Vertex 5, for example. To travel from Vertex 5, which is assigned black, to a vertex that is assigned white with the minimum cost, we should make these moves: Vertex 5 \\to Vertex 4 \\to Vertex 2. The total cost of these moves is 7, which satisfies the condition. We can also verify that the condition is satisfied for other vertices.\ninput: 5 7\n1 2 3 4 5\n1 2\n1 3\n1 4\n2 3\n2 5\n3 5\n4 5 output: -1\ninput: 4 6\n1 1 1 1\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4 output: BBBW\n1\n1\n1\n2\n1\n1\n\n" }, { "title": "", "content": "Problem Statement We have an H * W grid, where each square is painted white or black in the initial state.\nGiven are strings A_1, A_2, . . . , A_H representing the colors of the squares in the initial state.\nFor each pair (i, j) (1 <= i <= H, 1 <= j <= W), if the j-th character of A_i is . , the square at the i-th row and j-th column is painted white; if that character is #, that square is painted black.\nAmong the 2^{HW} ways for each square in the grid to be painted white or black, how many can be obtained from the initial state by performing the operations below any number of times (possibly zero) in any order? Find this count modulo 998,244,353.\n\nChoose one row, then paint all the squares in that row white.\nChoose one row, then paint all the squares in that row black.\nChoose one column, then paint all the squares in that column white.\nChoose one column, then paint all the squares in that column black.", "constraint": "1 <= H, W <= 10\n|A_i| = W (1 <= i <= H)\nAll strings A_i consist of . and #.\nH and W are integers.", "input": "Input is given from Standard Input in the following format:\nH W\nA_1\nA_2\n\\vdots\nA_H", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n#.\n.# output: 15\n\nFor example, if we paint the second row black, the grid becomes:\n#.\n##", "input: 3 3\n...\n...\n... output: 230", "input: 2 4\n#...\n...# output: 150", "input: 6 7\n.......\n.......\n.#.....\n..#....\n.#.#...\n....... output: 203949910"], "Pid": "p02800", "ProblemText": "Task Description: Problem Statement We have an H * W grid, where each square is painted white or black in the initial state.\nGiven are strings A_1, A_2, . . . , A_H representing the colors of the squares in the initial state.\nFor each pair (i, j) (1 <= i <= H, 1 <= j <= W), if the j-th character of A_i is . , the square at the i-th row and j-th column is painted white; if that character is #, that square is painted black.\nAmong the 2^{HW} ways for each square in the grid to be painted white or black, how many can be obtained from the initial state by performing the operations below any number of times (possibly zero) in any order? Find this count modulo 998,244,353.\n\nChoose one row, then paint all the squares in that row white.\nChoose one row, then paint all the squares in that row black.\nChoose one column, then paint all the squares in that column white.\nChoose one column, then paint all the squares in that column black.\nTask Constraint: 1 <= H, W <= 10\n|A_i| = W (1 <= i <= H)\nAll strings A_i consist of . and #.\nH and W are integers.\nTask Input: Input is given from Standard Input in the following format:\nH W\nA_1\nA_2\n\\vdots\nA_H\nTask Output: Print the answer.\nTask Samples: input: 2 2\n#.\n.# output: 15\n\nFor example, if we paint the second row black, the grid becomes:\n#.\n##\ninput: 3 3\n...\n...\n... output: 230\ninput: 2 4\n#...\n...# output: 150\ninput: 6 7\n.......\n.......\n.#.....\n..#....\n.#.#...\n....... output: 203949910\n\n" }, { "title": "", "content": "Problem Statement Given is a lowercase English letter C that is not z. Print the letter that follows C in alphabetical order.", "constraint": "C is a lowercase English letter that is not z.", "input": "Input is given from Standard Input in the following format:\nC", "output": "Print the letter that follows C in alphabetical order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: a output: b\n\na is followed by b.", "input: y output: z\n\ny is followed by z."], "Pid": "p02801", "ProblemText": "Task Description: Problem Statement Given is a lowercase English letter C that is not z. Print the letter that follows C in alphabetical order.\nTask Constraint: C is a lowercase English letter that is not z.\nTask Input: Input is given from Standard Input in the following format:\nC\nTask Output: Print the letter that follows C in alphabetical order.\nTask Samples: input: a output: b\n\na is followed by b.\ninput: y output: z\n\ny is followed by z.\n\n" }, { "title": "", "content": "Problem Statement Takahashi participated in a contest on At Coder.\nThe contest had N problems.\nTakahashi made M submissions during the contest.\nThe i-th submission was made for the p_i-th problem and received the verdict S_i (AC or WA).\nThe number of Takahashi's correct answers is the number of problems on which he received an AC once or more.\nThe number of Takahashi's penalties is the sum of the following count for the problems on which he received an AC once or more: the number of WAs received before receiving an AC for the first time on that problem.\nFind the numbers of Takahashi's correct answers and penalties.", "constraint": "N, M, and p_i are integers.\n1 <= N <= 10^5\n0 <= M <= 10^5\n1 <= p_i <= N\nS_i is AC or WA.", "input": "Input is given from Standard Input in the following format:\nN M\np_1 S_1\n:\np_M S_M", "output": "Print the number of Takahashi's correct answers and the number of Takahashi's penalties.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5\n1 WA\n1 AC\n2 WA\n2 AC\n2 WA output: 2 2\n\nIn his second submission, he received an AC on the first problem for the first time. Before this, he received one WA on this problem.\nIn his fourth submission, he received an AC on the second problem for the first time. Before this, he received one WA on this problem.\nThus, he has two correct answers and two penalties.", "input: 100000 3\n7777 AC\n7777 AC\n7777 AC output: 1 0\n\nNote that it is pointless to get an AC more than once on the same problem.", "input: 6 0 output: 0 0"], "Pid": "p02802", "ProblemText": "Task Description: Problem Statement Takahashi participated in a contest on At Coder.\nThe contest had N problems.\nTakahashi made M submissions during the contest.\nThe i-th submission was made for the p_i-th problem and received the verdict S_i (AC or WA).\nThe number of Takahashi's correct answers is the number of problems on which he received an AC once or more.\nThe number of Takahashi's penalties is the sum of the following count for the problems on which he received an AC once or more: the number of WAs received before receiving an AC for the first time on that problem.\nFind the numbers of Takahashi's correct answers and penalties.\nTask Constraint: N, M, and p_i are integers.\n1 <= N <= 10^5\n0 <= M <= 10^5\n1 <= p_i <= N\nS_i is AC or WA.\nTask Input: Input is given from Standard Input in the following format:\nN M\np_1 S_1\n:\np_M S_M\nTask Output: Print the number of Takahashi's correct answers and the number of Takahashi's penalties.\nTask Samples: input: 2 5\n1 WA\n1 AC\n2 WA\n2 AC\n2 WA output: 2 2\n\nIn his second submission, he received an AC on the first problem for the first time. Before this, he received one WA on this problem.\nIn his fourth submission, he received an AC on the second problem for the first time. Before this, he received one WA on this problem.\nThus, he has two correct answers and two penalties.\ninput: 100000 3\n7777 AC\n7777 AC\n7777 AC output: 1 0\n\nNote that it is pointless to get an AC more than once on the same problem.\ninput: 6 0 output: 0 0\n\n" }, { "title": "", "content": "Problem Statement Takahashi has a maze, which is a grid of H * W squares with H horizontal rows and W vertical columns.\nThe square at the i-th row from the top and the j-th column is a \"wall\" square if S_{ij} is #, and a \"road\" square if S_{ij} is . .\nFrom a road square, you can move to a horizontally or vertically adjacent road square.\nYou cannot move out of the maze, move to a wall square, or move diagonally.\nTakahashi will choose a starting square and a goal square, which can be any road squares, and give the maze to Aoki.\nAoki will then travel from the starting square to the goal square, in the minimum number of moves required.\nIn this situation, find the maximum possible number of moves Aoki has to make.", "constraint": "1 <= H,W <= 20\nS_{ij} is . or #.\nS contains at least two occurrences of ..\nAny road square can be reached from any road square in zero or more moves.", "input": "Input is given from Standard Input in the following format:\nH W\nS_{11}. . . S_{1W}\n:\nS_{H1}. . . S_{HW}", "output": "Print the maximum possible number of moves Aoki has to make.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n...\n...\n... output: 4\n\nIf Takahashi chooses the top-left square as the starting square and the bottom-right square as the goal square, Aoki has to make four moves.", "input: 3 5\n...#.\n.#.#.\n.#... output: 10\n\nIf Takahashi chooses the bottom-left square as the starting square and the top-right square as the goal square, Aoki has to make ten moves."], "Pid": "p02803", "ProblemText": "Task Description: Problem Statement Takahashi has a maze, which is a grid of H * W squares with H horizontal rows and W vertical columns.\nThe square at the i-th row from the top and the j-th column is a \"wall\" square if S_{ij} is #, and a \"road\" square if S_{ij} is . .\nFrom a road square, you can move to a horizontally or vertically adjacent road square.\nYou cannot move out of the maze, move to a wall square, or move diagonally.\nTakahashi will choose a starting square and a goal square, which can be any road squares, and give the maze to Aoki.\nAoki will then travel from the starting square to the goal square, in the minimum number of moves required.\nIn this situation, find the maximum possible number of moves Aoki has to make.\nTask Constraint: 1 <= H,W <= 20\nS_{ij} is . or #.\nS contains at least two occurrences of ..\nAny road square can be reached from any road square in zero or more moves.\nTask Input: Input is given from Standard Input in the following format:\nH W\nS_{11}. . . S_{1W}\n:\nS_{H1}. . . S_{HW}\nTask Output: Print the maximum possible number of moves Aoki has to make.\nTask Samples: input: 3 3\n...\n...\n... output: 4\n\nIf Takahashi chooses the top-left square as the starting square and the bottom-right square as the goal square, Aoki has to make four moves.\ninput: 3 5\n...#.\n.#.#.\n.#... output: 10\n\nIf Takahashi chooses the bottom-left square as the starting square and the top-right square as the goal square, Aoki has to make ten moves.\n\n" }, { "title": "", "content": "Problem Statement For a finite set of integers X, let f(X)=\\max X - \\min X.\nGiven are N integers A_1, . . . , A_N.\nWe will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.\nSince the answer can be enormous, print it \\bmod (10^9+7).", "constraint": "1 <= N <= 10^5\n1 <= K <= N\n|A_i| <= 10^9", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 . . . A_N", "output": "Print the answer \\bmod (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n1 1 3 4 output: 11\n\nThere are six ways to choose S: \\{1,1\\},\\{1,3\\},\\{1,4\\},\\{1,3\\},\\{1,4\\}, \\{3,4\\} (we distinguish the two 1s). The value of f(S) for these choices are 0,2,3,2,3,1, respectively, for the total of 11.", "input: 6 3\n10 10 10 -10 -10 -10 output: 360\n\nThere are 20 ways to choose S. In 18 of them, f(S)=20, and in 2 of them, f(S)=0.", "input: 3 1\n1 1 1 output: 0", "input: 10 6\n1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0 output: 999998537\n\nPrint the sum \\bmod (10^9+7)."], "Pid": "p02804", "ProblemText": "Task Description: Problem Statement For a finite set of integers X, let f(X)=\\max X - \\min X.\nGiven are N integers A_1, . . . , A_N.\nWe will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.\nSince the answer can be enormous, print it \\bmod (10^9+7).\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= N\n|A_i| <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 . . . A_N\nTask Output: Print the answer \\bmod (10^9+7).\nTask Samples: input: 4 2\n1 1 3 4 output: 11\n\nThere are six ways to choose S: \\{1,1\\},\\{1,3\\},\\{1,4\\},\\{1,3\\},\\{1,4\\}, \\{3,4\\} (we distinguish the two 1s). The value of f(S) for these choices are 0,2,3,2,3,1, respectively, for the total of 11.\ninput: 6 3\n10 10 10 -10 -10 -10 output: 360\n\nThere are 20 ways to choose S. In 18 of them, f(S)=20, and in 2 of them, f(S)=0.\ninput: 3 1\n1 1 1 output: 0\ninput: 10 6\n1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0 output: 999998537\n\nPrint the sum \\bmod (10^9+7).\n\n" }, { "title": "", "content": "Problem Statement Given are N points (x_i, y_i) in a two-dimensional plane.\nFind the minimum radius of a circle such that all the points are inside or on it.", "constraint": "2 <= N <= 50\n0 <= x_i <= 1000\n0 <= y_i <= 1000\nThe given N points are all different.\nThe values in input are all integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print the minimum radius of a circle such that all the N points are inside or on it.\nYour output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0\n1 0 output: 0.500000000000000000\n\nBoth points are contained in the circle centered at (0.5,0) with a radius of 0.5.", "input: 3\n0 0\n0 1\n1 0 output: 0.707106781186497524", "input: 10\n10 9\n5 9\n2 0\n0 0\n2 7\n3 3\n2 5\n10 0\n3 7\n1 9 output: 6.726812023536805158\n\nIf the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct."], "Pid": "p02805", "ProblemText": "Task Description: Problem Statement Given are N points (x_i, y_i) in a two-dimensional plane.\nFind the minimum radius of a circle such that all the points are inside or on it.\nTask Constraint: 2 <= N <= 50\n0 <= x_i <= 1000\n0 <= y_i <= 1000\nThe given N points are all different.\nThe values in input are all integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print the minimum radius of a circle such that all the N points are inside or on it.\nYour output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.\nTask Samples: input: 2\n0 0\n1 0 output: 0.500000000000000000\n\nBoth points are contained in the circle centered at (0.5,0) with a radius of 0.5.\ninput: 3\n0 0\n0 1\n1 0 output: 0.707106781186497524\ninput: 10\n10 9\n5 9\n2 0\n0 0\n2 7\n3 3\n2 5\n10 0\n3 7\n1 9 output: 6.726812023536805158\n\nIf the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.\n\n" }, { "title": "", "content": "Problem Statement\nNiwango created a playlist of N songs.\nThe title and the duration of the i-th song are s_i and t_i seconds, respectively.\nIt is guaranteed that s_1, \\ldots, s_N are all distinct.\nNiwango was doing some work while playing this playlist. (That is, all the songs were played once, in the order they appear in the playlist, without any pause in between. )\nHowever, he fell asleep during his work, and he woke up after all the songs were played.\nAccording to his record, it turned out that he fell asleep at the very end of the song titled X.\nFind the duration of time when some song was played while Niwango was asleep.", "constraint": "1 <= N <= 50\ns_i and X are strings of length between 1 and 100 (inclusive) consisting of lowercase English letters.\ns_1,\\ldots,s_N are distinct.\nThere exists an integer i such that s_i = X.\n1 <= t_i <= 1000\nt_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\ns_1 t_1\n\\vdots\ns_{N} t_N\nX", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\ndwango 2\nsixth 5\nprelims 25\ndwango output: 30\nWhile Niwango was asleep, two songs were played: sixth and prelims.\nThe answer is the total duration of these songs, 30.", "input: 1\nabcde 1000\nabcde output: 0\nNo songs were played while Niwango was asleep.\nIn such a case, the total duration of songs is 0.", "input: 15\nypnxn 279\nkgjgwx 464\nqquhuwq 327\nrxing 549\npmuduhznoaqu 832\ndagktgdarveusju 595\nwunfagppcoi 200\ndhavrncwfw 720\njpcmigg 658\nwrczqxycivdqn 639\nmcmkkbnjfeod 992\nhtqvkgkbhtytsz 130\ntwflegsjz 467\ndswxxrxuzzfhkp 989\nszfwtzfpnscgue 958\npmuduhznoaqu output: 6348"], "Pid": "p02806", "ProblemText": "Task Description: Problem Statement\nNiwango created a playlist of N songs.\nThe title and the duration of the i-th song are s_i and t_i seconds, respectively.\nIt is guaranteed that s_1, \\ldots, s_N are all distinct.\nNiwango was doing some work while playing this playlist. (That is, all the songs were played once, in the order they appear in the playlist, without any pause in between. )\nHowever, he fell asleep during his work, and he woke up after all the songs were played.\nAccording to his record, it turned out that he fell asleep at the very end of the song titled X.\nFind the duration of time when some song was played while Niwango was asleep.\nTask Constraint: 1 <= N <= 50\ns_i and X are strings of length between 1 and 100 (inclusive) consisting of lowercase English letters.\ns_1,\\ldots,s_N are distinct.\nThere exists an integer i such that s_i = X.\n1 <= t_i <= 1000\nt_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\ns_1 t_1\n\\vdots\ns_{N} t_N\nX\nTask Output: Print the answer.\nTask Samples: input: 3\ndwango 2\nsixth 5\nprelims 25\ndwango output: 30\nWhile Niwango was asleep, two songs were played: sixth and prelims.\nThe answer is the total duration of these songs, 30.\ninput: 1\nabcde 1000\nabcde output: 0\nNo songs were played while Niwango was asleep.\nIn such a case, the total duration of songs is 0.\ninput: 15\nypnxn 279\nkgjgwx 464\nqquhuwq 327\nrxing 549\npmuduhznoaqu 832\ndagktgdarveusju 595\nwunfagppcoi 200\ndhavrncwfw 720\njpcmigg 658\nwrczqxycivdqn 639\nmcmkkbnjfeod 992\nhtqvkgkbhtytsz 130\ntwflegsjz 467\ndswxxrxuzzfhkp 989\nszfwtzfpnscgue 958\npmuduhznoaqu output: 6348\n\n" }, { "title": "", "content": "Problem Statement\nThere are N slimes standing on a number line.\nThe i-th slime from the left is at position x_i.\nIt is guaruanteed that 1 <= x_1 < x_2 < \\ldots < x_N <= 10^{9}.\nNiwango will perform N-1 operations. The i-th operation consists of the following procedures:\n\nChoose an integer k between 1 and N-i (inclusive) with equal probability.\nMove the k-th slime from the left, to the position of the neighboring slime to the right.\nFuse the two slimes at the same position into one slime.\n\nFind the total distance traveled by the slimes multiplied by (N-1)! (we can show that this value is an integer), modulo (10^{9}+7). If a slime is born by a fuse and that slime moves, we count it as just one slime. tasks: Subtasks\n\n400 points will be awarded for passing the test cases satisfying N <= 2000.", "constraint": "2 <= N <= 10^{5}\n1 <= x_1 < x_2 < \\ldots < x_N <= 10^{9}\nx_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 x_2 \\ldots x_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 5\nWith probability \\frac{1}{2}, the leftmost slime is chosen in the first operation, in which case the total distance traveled is 2.\nWith probability \\frac{1}{2}, the middle slime is chosen in the first operation, in which case the total distance traveled is 3.\nThe answer is the expected total distance traveled, 2.5, multiplied by 2!, which is 5.", "input: 12\n161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932 output: 750927044\nFind the expected value multiplied by (N-1)!, modulo (10^9+7)."], "Pid": "p02807", "ProblemText": "Task Description: Problem Statement\nThere are N slimes standing on a number line.\nThe i-th slime from the left is at position x_i.\nIt is guaruanteed that 1 <= x_1 < x_2 < \\ldots < x_N <= 10^{9}.\nNiwango will perform N-1 operations. The i-th operation consists of the following procedures:\n\nChoose an integer k between 1 and N-i (inclusive) with equal probability.\nMove the k-th slime from the left, to the position of the neighboring slime to the right.\nFuse the two slimes at the same position into one slime.\n\nFind the total distance traveled by the slimes multiplied by (N-1)! (we can show that this value is an integer), modulo (10^{9}+7). If a slime is born by a fuse and that slime moves, we count it as just one slime. tasks: Subtasks\n\n400 points will be awarded for passing the test cases satisfying N <= 2000.\nTask Constraint: 2 <= N <= 10^{5}\n1 <= x_1 < x_2 < \\ldots < x_N <= 10^{9}\nx_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 x_2 \\ldots x_N\nTask Output: Print the answer.\nTask Samples: input: 3\n1 2 3 output: 5\nWith probability \\frac{1}{2}, the leftmost slime is chosen in the first operation, in which case the total distance traveled is 2.\nWith probability \\frac{1}{2}, the middle slime is chosen in the first operation, in which case the total distance traveled is 3.\nThe answer is the expected total distance traveled, 2.5, multiplied by 2!, which is 5.\ninput: 12\n161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932 output: 750927044\nFind the expected value multiplied by (N-1)!, modulo (10^9+7).\n\n" }, { "title": "", "content": "Problem Statement\nThere are N children, numbered 1,2, \\ldots, N.\nIn the next K days, we will give them some cookies.\nIn the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently. )\nLet us define the happiness of the children as c_1 * c_2 * \\ldots * c_N, where c_i is the number of cookies received by Child i in the K days.\nFind the expected happiness multiplied by \\binom{N}{a_1} * \\binom{N}{a_2} * \\ldots * \\binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7). note: Notes\n\\binom{n}{k} denotes the number of possible choices of k objects out of given distinct n objects, disregarding order.", "constraint": "1 <= N <= 1000\n1 <= K <= 20\n1 <= a_i <= N", "input": "Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\ldots a_K", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n3 2 output: 12\nOn the first day, all the children 1,2, and 3 receive one cookie.\nOn the second day, two out of the three children 1,2, and 3 receive one cookie.\nTheir happiness is 4 in any case, so the expected happiness is 4. Print this value multiplied by \\binom{3}{3} * \\binom{3}{2}, which is 12.", "input: 856 16\n399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63 output: 337587117\nFind the expected value multiplied by \\binom{N}{a_1} * \\binom{N}{a_2} * \\ldots * \\binom{N}{a_K}, modulo (10^9+7)."], "Pid": "p02808", "ProblemText": "Task Description: Problem Statement\nThere are N children, numbered 1,2, \\ldots, N.\nIn the next K days, we will give them some cookies.\nIn the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently. )\nLet us define the happiness of the children as c_1 * c_2 * \\ldots * c_N, where c_i is the number of cookies received by Child i in the K days.\nFind the expected happiness multiplied by \\binom{N}{a_1} * \\binom{N}{a_2} * \\ldots * \\binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7). note: Notes\n\\binom{n}{k} denotes the number of possible choices of k objects out of given distinct n objects, disregarding order.\nTask Constraint: 1 <= N <= 1000\n1 <= K <= 20\n1 <= a_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\ldots a_K\nTask Output: Print the answer.\nTask Samples: input: 3 2\n3 2 output: 12\nOn the first day, all the children 1,2, and 3 receive one cookie.\nOn the second day, two out of the three children 1,2, and 3 receive one cookie.\nTheir happiness is 4 in any case, so the expected happiness is 4. Print this value multiplied by \\binom{3}{3} * \\binom{3}{2}, which is 12.\ninput: 856 16\n399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63 output: 337587117\nFind the expected value multiplied by \\binom{N}{a_1} * \\binom{N}{a_2} * \\ldots * \\binom{N}{a_K}, modulo (10^9+7).\n\n" }, { "title": "", "content": "Problem Statement\nNiwango has N cards, numbered 1,2, \\ldots, N.\nHe will now arrange these cards in a row.\nNiwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below.\nTo help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.\n\nTo the immediate right of Card 1 (if any) is NOT Card a_1.\nTo the immediate right of Card 2 (if any) is NOT Card a_2.\n\\vdots\nTo the immediate right of Card N (if any) is NOT Card a_N.", "constraint": "2 <= N <= 10^{5}\n1 <= a_i <= N\na_i \\neq i", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N", "output": "If no arrangements satisfy the conditions, print -1. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:\nb_1 b_2 \\ldots b_N\n\nHere, b_i represents the i-th card from the left.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 3 4 1 output: 1 3 2 4\nThe arrangement (1,2,3,4) is lexicographically smaller than (1,3,2,4), but is invalid, since it violates the condition \"to the immediate right of Card 1 is not Card 2.\"", "input: 2\n2 1 output: -1\nIf no arrangements satisfy the conditions, print -1.", "input: 13\n2 3 4 5 6 7 8 9 10 11 12 13 12 output: 1 3 2 4 6 5 7 9 8 10 12 11 13"], "Pid": "p02809", "ProblemText": "Task Description: Problem Statement\nNiwango has N cards, numbered 1,2, \\ldots, N.\nHe will now arrange these cards in a row.\nNiwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below.\nTo help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.\n\nTo the immediate right of Card 1 (if any) is NOT Card a_1.\nTo the immediate right of Card 2 (if any) is NOT Card a_2.\n\\vdots\nTo the immediate right of Card N (if any) is NOT Card a_N.\nTask Constraint: 2 <= N <= 10^{5}\n1 <= a_i <= N\na_i \\neq i\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N\nTask Output: If no arrangements satisfy the conditions, print -1. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:\nb_1 b_2 \\ldots b_N\n\nHere, b_i represents the i-th card from the left.\nTask Samples: input: 4\n2 3 4 1 output: 1 3 2 4\nThe arrangement (1,2,3,4) is lexicographically smaller than (1,3,2,4), but is invalid, since it violates the condition \"to the immediate right of Card 1 is not Card 2.\"\ninput: 2\n2 1 output: -1\nIf no arrangements satisfy the conditions, print -1.\ninput: 13\n2 3 4 5 6 7 8 9 10 11 12 13 12 output: 1 3 2 4 6 5 7 9 8 10 12 11 13\n\n" }, { "title": "", "content": "Problem Statement\nNiwango bought a piece of land that can be represented as a half-open interval [0, X).\nNiwango will lay out N vinyl sheets on this land. The sheets are numbered 1,2, \\ldots, N, and they are distinguishable.\nFor Sheet i, he can choose an integer j such that 0 <= j <= X - L_i and cover [j, j + L_i) with this sheet.\nFind the number of ways to cover the land with the sheets such that no point in [0, X) remains uncovered, modulo (10^9+7).\nWe consider two ways to cover the land different if and only if there is an integer i (1 <= i <= N) such that the region covered by Sheet i is different.", "constraint": "1 <= N <= 100\n1 <= L_i <= X <= 500\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X\nL_1 L_2 \\ldots L_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 1 2 output: 10\nIf we ignore whether the whole interval is covered, there are 18 ways to lay out the sheets.\nAmong them, there are 4 ways that leave [0,1) uncovered, and 4 ways that leave [2,3) uncovered.\nEach of the other ways covers the whole interval [0,3), so the answer is 10.", "input: 18 477\n324 31 27 227 9 21 41 29 50 34 2 362 92 11 13 17 183 119 output: 134796357\nFind the number of ways modulo (10^9+7)."], "Pid": "p02810", "ProblemText": "Task Description: Problem Statement\nNiwango bought a piece of land that can be represented as a half-open interval [0, X).\nNiwango will lay out N vinyl sheets on this land. The sheets are numbered 1,2, \\ldots, N, and they are distinguishable.\nFor Sheet i, he can choose an integer j such that 0 <= j <= X - L_i and cover [j, j + L_i) with this sheet.\nFind the number of ways to cover the land with the sheets such that no point in [0, X) remains uncovered, modulo (10^9+7).\nWe consider two ways to cover the land different if and only if there is an integer i (1 <= i <= N) such that the region covered by Sheet i is different.\nTask Constraint: 1 <= N <= 100\n1 <= L_i <= X <= 500\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X\nL_1 L_2 \\ldots L_N\nTask Output: Print the answer.\nTask Samples: input: 3 3\n1 1 2 output: 10\nIf we ignore whether the whole interval is covered, there are 18 ways to lay out the sheets.\nAmong them, there are 4 ways that leave [0,1) uncovered, and 4 ways that leave [2,3) uncovered.\nEach of the other ways covers the whole interval [0,3), so the answer is 10.\ninput: 18 477\n324 31 27 227 9 21 41 29 50 34 2 362 92 11 13 17 183 119 output: 134796357\nFind the number of ways modulo (10^9+7).\n\n" }, { "title": "", "content": "Problem Statement Takahashi has K 500-yen coins. (Yen is the currency of Japan. )\nIf these coins add up to X yen or more, print Yes; otherwise, print No.", "constraint": "1 <= K <= 100\n1 <= X <= 10^5", "input": "Input is given from Standard Input in the following format:\nK X", "output": "If the coins add up to X yen or more, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 900 output: Yes\n\nTwo 500-yen coins add up to 1000 yen, which is not less than X = 900 yen.", "input: 1 501 output: No\n\nOne 500-yen coin is worth 500 yen, which is less than X = 501 yen.", "input: 4 2000 output: Yes\n\nFour 500-yen coins add up to 2000 yen, which is not less than X = 2000 yen."], "Pid": "p02811", "ProblemText": "Task Description: Problem Statement Takahashi has K 500-yen coins. (Yen is the currency of Japan. )\nIf these coins add up to X yen or more, print Yes; otherwise, print No.\nTask Constraint: 1 <= K <= 100\n1 <= X <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nK X\nTask Output: If the coins add up to X yen or more, print Yes; otherwise, print No.\nTask Samples: input: 2 900 output: Yes\n\nTwo 500-yen coins add up to 1000 yen, which is not less than X = 900 yen.\ninput: 1 501 output: No\n\nOne 500-yen coin is worth 500 yen, which is less than X = 501 yen.\ninput: 4 2000 output: Yes\n\nFour 500-yen coins add up to 2000 yen, which is not less than X = 2000 yen.\n\n" }, { "title": "", "content": "Problem Statement We have a string S of length N consisting of uppercase English letters.\nHow many times does ABC occur in S as contiguous subsequences (see Sample Inputs and Outputs)?", "constraint": "3 <= N <= 50\nS consists of uppercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print number of occurrences of ABC in S as contiguous subsequences.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\nZABCDBABCQ output: 2\n\nTwo contiguous subsequences of S are equal to ABC: the 2-nd through 4-th characters, and the 7-th through 9-th characters.", "input: 19\nTHREEONEFOURONEFIVE output: 0\n\nNo contiguous subsequences of S are equal to ABC.", "input: 33\nABCCABCBABCCABACBCBBABCBCBCBCABCB output: 5"], "Pid": "p02812", "ProblemText": "Task Description: Problem Statement We have a string S of length N consisting of uppercase English letters.\nHow many times does ABC occur in S as contiguous subsequences (see Sample Inputs and Outputs)?\nTask Constraint: 3 <= N <= 50\nS consists of uppercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print number of occurrences of ABC in S as contiguous subsequences.\nTask Samples: input: 10\nZABCDBABCQ output: 2\n\nTwo contiguous subsequences of S are equal to ABC: the 2-nd through 4-th characters, and the 7-th through 9-th characters.\ninput: 19\nTHREEONEFOURONEFIVE output: 0\n\nNo contiguous subsequences of S are equal to ABC.\ninput: 33\nABCCABCBABCCABACBCBBABCBCBCBCABCB output: 5\n\n" }, { "title": "", "content": "Problem Statement We have two permutations P and Q of size N (that is, P and Q are both rearrangements of (1, ~2, ~. . . , ~N)).\nThere are N! possible permutations of size N. Among them, let P and Q be the a-th and b-th lexicographically smallest permutations, respectively. Find |a - b|. note: Notes For two sequences X and Y, X is said to be lexicographically smaller than Y if and only if there exists an integer k such that X_i = Y_i~(1 <= i < k) and X_k < Y_k.", "constraint": "2 <= N <= 8\nP and Q are permutations of size N.", "input": "Input is given from Standard Input in the following format:\nN\nP_1 P_2 . . . P_N\nQ_1 Q_2 . . . Q_N", "output": "Print |a - b|.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 3 2\n3 1 2 output: 3\n\nThere are 6 permutations of size 3: (1,~2,~3), (1,~3,~2), (2,~1,~3), (2,~3,~1), (3,~1,~2), and (3,~2,~1). Among them, (1,~3,~2) and (3,~1,~2) come 2-nd and 5-th in lexicographical order, so the answer is |2 - 5| = 3.", "input: 8\n7 3 5 4 2 1 6 8\n3 8 2 5 4 6 7 1 output: 17517", "input: 3\n1 2 3\n1 2 3 output: 0"], "Pid": "p02813", "ProblemText": "Task Description: Problem Statement We have two permutations P and Q of size N (that is, P and Q are both rearrangements of (1, ~2, ~. . . , ~N)).\nThere are N! possible permutations of size N. Among them, let P and Q be the a-th and b-th lexicographically smallest permutations, respectively. Find |a - b|. note: Notes For two sequences X and Y, X is said to be lexicographically smaller than Y if and only if there exists an integer k such that X_i = Y_i~(1 <= i < k) and X_k < Y_k.\nTask Constraint: 2 <= N <= 8\nP and Q are permutations of size N.\nTask Input: Input is given from Standard Input in the following format:\nN\nP_1 P_2 . . . P_N\nQ_1 Q_2 . . . Q_N\nTask Output: Print |a - b|.\nTask Samples: input: 3\n1 3 2\n3 1 2 output: 3\n\nThere are 6 permutations of size 3: (1,~2,~3), (1,~3,~2), (2,~1,~3), (2,~3,~1), (3,~1,~2), and (3,~2,~1). Among them, (1,~3,~2) and (3,~1,~2) come 2-nd and 5-th in lexicographical order, so the answer is |2 - 5| = 3.\ninput: 8\n7 3 5 4 2 1 6 8\n3 8 2 5 4 6 7 1 output: 17517\ninput: 3\n1 2 3\n1 2 3 output: 0\n\n" }, { "title": "", "content": "Problem Statement Given are a sequence A= {a_1, a_2, . . . . . . a_N} of N positive even numbers, and an integer M.\nLet a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 <= k <= N):\n\nThere exists a non-negative integer p such that X= a_k * (p+0.5).\n\nFind the number of semi-common multiples of A among the integers between 1 and M (inclusive).", "constraint": "1 <= N <= 10^5\n1 <= M <= 10^9\n2 <= a_i <= 10^9\na_i is an even number.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 a_2 . . . a_N", "output": "Print the number of semi-common multiples of A among the integers between 1 and M (inclusive).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 50\n6 10 output: 2\n15 = 6 * 2.5 \n15 = 10 * 1.5 \n45 = 6 * 7.5 \n45 = 10 * 4.5 \n\nThus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.", "input: 3 100\n14 22 40 output: 0\n\nThe answer can be 0.", "input: 5 1000000000\n6 6 2 6 2 output: 166666667"], "Pid": "p02814", "ProblemText": "Task Description: Problem Statement Given are a sequence A= {a_1, a_2, . . . . . . a_N} of N positive even numbers, and an integer M.\nLet a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 <= k <= N):\n\nThere exists a non-negative integer p such that X= a_k * (p+0.5).\n\nFind the number of semi-common multiples of A among the integers between 1 and M (inclusive).\nTask Constraint: 1 <= N <= 10^5\n1 <= M <= 10^9\n2 <= a_i <= 10^9\na_i is an even number.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 a_2 . . . a_N\nTask Output: Print the number of semi-common multiples of A among the integers between 1 and M (inclusive).\nTask Samples: input: 2 50\n6 10 output: 2\n15 = 6 * 2.5 \n15 = 10 * 1.5 \n45 = 6 * 7.5 \n45 = 10 * 4.5 \n\nThus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.\ninput: 3 100\n14 22 40 output: 0\n\nThe answer can be 0.\ninput: 5 1000000000\n6 6 2 6 2 output: 166666667\n\n" }, { "title": "", "content": "Problem Statement For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:\nConsider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.\n\nChange S_i (from 0 to 1 or vice versa). The cost of this operation is D * C_i, where D is the number of integers j such that S_j \\neq T_j (1 <= j <= N) just before this change.\n\nThere are 2^N * (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).", "constraint": "1 <= N <= 2 * 10^5\n1 <= C_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nC_1 C_2 \\cdots C_N", "output": "Print the sum of f(S, T), modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n1000000000 output: 999999993\n\nThere are two pairs (S, T) of different sequences of length 2 consisting of 0 and 1, as follows:\n\nS = (0), T = (1): by changing S_1 to 1, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.\nS = (1), T = (0): by changing S_1 to 0, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.\n\nThe sum of these is 2000000000, and we should print it modulo (10^9+7), that is, 999999993.", "input: 2\n5 8 output: 124\n\nThere are 12 pairs (S, T) of different sequences of length 3 consisting of 0 and 1, which include:\n\nS = (0,1), T = (1,0)\n\nIn this case, if we first change S_1 to 1 then change S_2 to 0, the total cost is 5 * 2 + 8 = 18. We cannot have S = T at a smaller cost, so f(S, T) = 18.", "input: 5\n52 67 72 25 79 output: 269312"], "Pid": "p02815", "ProblemText": "Task Description: Problem Statement For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:\nConsider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.\n\nChange S_i (from 0 to 1 or vice versa). The cost of this operation is D * C_i, where D is the number of integers j such that S_j \\neq T_j (1 <= j <= N) just before this change.\n\nThere are 2^N * (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= C_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nC_1 C_2 \\cdots C_N\nTask Output: Print the sum of f(S, T), modulo (10^9+7).\nTask Samples: input: 1\n1000000000 output: 999999993\n\nThere are two pairs (S, T) of different sequences of length 2 consisting of 0 and 1, as follows:\n\nS = (0), T = (1): by changing S_1 to 1, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.\nS = (1), T = (0): by changing S_1 to 0, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.\n\nThe sum of these is 2000000000, and we should print it modulo (10^9+7), that is, 999999993.\ninput: 2\n5 8 output: 124\n\nThere are 12 pairs (S, T) of different sequences of length 3 consisting of 0 and 1, which include:\n\nS = (0,1), T = (1,0)\n\nIn this case, if we first change S_1 to 1 then change S_2 to 0, the total cost is 5 * 2 + 8 = 18. We cannot have S = T at a smaller cost, so f(S, T) = 18.\ninput: 5\n52 67 72 25 79 output: 269312\n\n" }, { "title": "", "content": "Problem Statement Given are two sequences a=\\{a_0, \\ldots, a_{N-1}\\} and b=\\{b_0, \\ldots, b_{N-1}\\} of N non-negative integers each.\nSnuke will choose an integer k such that 0 <= k < N and an integer x not less than 0, to make a new sequence of length N, a'=\\{a_0', \\ldots, a_{N-1}'\\}, as follows:\n\na_i'= a_{i+k \\mod N}\\ XOR \\ x\n\nFind all pairs (k, x) such that a' will be equal to b.\n\nWhat is \\mbox{ XOR }?\n\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )", "constraint": "1 <= N <= 2 * 10^5\n0 <= a_i,b_i < 2^{30}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_0 a_1 . . . a_{N-1}\nb_0 b_1 . . . b_{N-1}", "output": "Print all pairs (k, x) such that a' and b will be equal, using one line for each pair, in ascending order of k (ascending order of x for pairs with the same k).\nIf there are no such pairs, the output should be empty.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 2 1\n1 2 3 output: 1 3\n\nIf (k,x)=(1,3),\na_0'=(a_1\\ XOR \\ 3)=1\na_1'=(a_2\\ XOR \\ 3)=2\na_2'=(a_0\\ XOR \\ 3)=3\nand we have a' = b.", "input: 5\n0 0 0 0 0\n2 2 2 2 2 output: 0 2\n1 2\n2 2\n3 2\n4 2", "input: 6\n0 1 3 7 6 4\n1 5 4 6 2 3 output: 2 2\n5 5", "input: 2\n1 2\n0 0 output: No pairs may satisfy the condition."], "Pid": "p02816", "ProblemText": "Task Description: Problem Statement Given are two sequences a=\\{a_0, \\ldots, a_{N-1}\\} and b=\\{b_0, \\ldots, b_{N-1}\\} of N non-negative integers each.\nSnuke will choose an integer k such that 0 <= k < N and an integer x not less than 0, to make a new sequence of length N, a'=\\{a_0', \\ldots, a_{N-1}'\\}, as follows:\n\na_i'= a_{i+k \\mod N}\\ XOR \\ x\n\nFind all pairs (k, x) such that a' will be equal to b.\n\nWhat is \\mbox{ XOR }?\n\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )\nTask Constraint: 1 <= N <= 2 * 10^5\n0 <= a_i,b_i < 2^{30}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_0 a_1 . . . a_{N-1}\nb_0 b_1 . . . b_{N-1}\nTask Output: Print all pairs (k, x) such that a' and b will be equal, using one line for each pair, in ascending order of k (ascending order of x for pairs with the same k).\nIf there are no such pairs, the output should be empty.\nTask Samples: input: 3\n0 2 1\n1 2 3 output: 1 3\n\nIf (k,x)=(1,3),\na_0'=(a_1\\ XOR \\ 3)=1\na_1'=(a_2\\ XOR \\ 3)=2\na_2'=(a_0\\ XOR \\ 3)=3\nand we have a' = b.\ninput: 5\n0 0 0 0 0\n2 2 2 2 2 output: 0 2\n1 2\n2 2\n3 2\n4 2\ninput: 6\n0 1 3 7 6 4\n1 5 4 6 2 3 output: 2 2\n5 5\ninput: 2\n1 2\n0 0 output: No pairs may satisfy the condition.\n\n" }, { "title": "", "content": "Problem Statement Given are two strings S and T consisting of lowercase English letters. Concatenate T and S in this order, without space in between, and print the resulting string.", "constraint": "S and T are strings consisting of lowercase English letters.\nThe lengths of S and T are between 1 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format:\nS T", "output": "Print the resulting string.", "content_img": false, "lang": "en", "error": false, "samples": ["input: oder atc output: atcoder\n\nWhen S = oder and T = atc, concatenating T and S in this order results in atcoder.", "input: humu humu output: humuhumu"], "Pid": "p02817", "ProblemText": "Task Description: Problem Statement Given are two strings S and T consisting of lowercase English letters. Concatenate T and S in this order, without space in between, and print the resulting string.\nTask Constraint: S and T are strings consisting of lowercase English letters.\nThe lengths of S and T are between 1 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nS T\nTask Output: Print the resulting string.\nTask Samples: input: oder atc output: atcoder\n\nWhen S = oder and T = atc, concatenating T and S in this order results in atcoder.\ninput: humu humu output: humuhumu\n\n" }, { "title": "", "content": "Problem Statement Takahashi has A cookies, and Aoki has B cookies.\nTakahashi will do the following action K times:\n\nIf Takahashi has one or more cookies, eat one of his cookies.\nOtherwise, if Aoki has one or more cookies, eat one of Aoki's cookies.\nIf they both have no cookies, do nothing.\n\nIn the end, how many cookies will Takahashi and Aoki have, respectively?", "constraint": "0 <= A <= 10^{12}\n0 <= B <= 10^{12}\n0 <= K <= 10^{12}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B K", "output": "Print the numbers of Takahashi's and Aoki's cookies after K actions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 3 output: 0 2\n\nTakahashi will do the following:\n\nHe has two cookies, so he eats one of them.\nNow he has one cookie left, and he eats it.\nNow he has no cookies left, but Aoki has three, so Takahashi eats one of them.\n\nThus, in the end, Takahashi will have 0 cookies, and Aoki will have 2.", "input: 500000000000 500000000000 1000000000000 output: 0 0\n\nWatch out for overflows."], "Pid": "p02818", "ProblemText": "Task Description: Problem Statement Takahashi has A cookies, and Aoki has B cookies.\nTakahashi will do the following action K times:\n\nIf Takahashi has one or more cookies, eat one of his cookies.\nOtherwise, if Aoki has one or more cookies, eat one of Aoki's cookies.\nIf they both have no cookies, do nothing.\n\nIn the end, how many cookies will Takahashi and Aoki have, respectively?\nTask Constraint: 0 <= A <= 10^{12}\n0 <= B <= 10^{12}\n0 <= K <= 10^{12}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B K\nTask Output: Print the numbers of Takahashi's and Aoki's cookies after K actions.\nTask Samples: input: 2 3 3 output: 0 2\n\nTakahashi will do the following:\n\nHe has two cookies, so he eats one of them.\nNow he has one cookie left, and he eats it.\nNow he has no cookies left, but Aoki has three, so Takahashi eats one of them.\n\nThus, in the end, Takahashi will have 0 cookies, and Aoki will have 2.\ninput: 500000000000 500000000000 1000000000000 output: 0 0\n\nWatch out for overflows.\n\n" }, { "title": "", "content": "Problem Statement\nFind the minimum prime number greater than or equal to X. note: Notes\nA prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.\nFor example, 2,3, and 5 are prime numbers, while 4 and 6 are not.", "constraint": "2 <= X <= 10^5 \nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX", "output": "Print the minimum prime number greater than or equal to X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 20 output: 23\n\nThe minimum prime number greater than or equal to 20 is 23.", "input: 2 output: 2\n\nX itself can be a prime number.", "input: 99992 output: 100003"], "Pid": "p02819", "ProblemText": "Task Description: Problem Statement\nFind the minimum prime number greater than or equal to X. note: Notes\nA prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.\nFor example, 2,3, and 5 are prime numbers, while 4 and 6 are not.\nTask Constraint: 2 <= X <= 10^5 \nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: Print the minimum prime number greater than or equal to X.\nTask Samples: input: 20 output: 23\n\nThe minimum prime number greater than or equal to 20 is 23.\ninput: 2 output: 2\n\nX itself can be a prime number.\ninput: 99992 output: 100003\n\n" }, { "title": "", "content": "Problem Statement At an arcade, Takahashi is playing a game called RPS Battle, which is played as follows:\n\nThe player plays N rounds of Rock Paper Scissors against the machine. (See Notes for the description of Rock Paper Scissors. A draw also counts as a round. )\nEach time the player wins a round, depending on which hand he/she uses, he/she earns the following score (no points for a draw or a loss):\nR points for winning with Rock;\nS points for winning with Scissors;\nP points for winning with Paper.\nHowever, in the i-th round, the player cannot use the hand he/she used in the (i-K)-th round. (In the first K rounds, the player can use any hand. )\n\nBefore the start of the game, the machine decides the hand it will play in each round. With supernatural power, Takahashi managed to read all of those hands.\nThe information Takahashi obtained is given as a string T. If the i-th character of T (1 <= i <= N) is r, the machine will play Rock in the i-th round. Similarly, p and s stand for Paper and Scissors, respectively.\nWhat is the maximum total score earned in the game by adequately choosing the hand to play in each round? note: Notes In this problem, Rock Paper Scissors can be thought of as a two-player game, in which each player simultaneously forms Rock, Paper, or Scissors with a hand.\n\nIf a player chooses Rock and the other chooses Scissors, the player choosing Rock wins;\nif a player chooses Scissors and the other chooses Paper, the player choosing Scissors wins;\nif a player chooses Paper and the other chooses Rock, the player choosing Paper wins;\nif both players play the same hand, it is a draw.", "constraint": "2 <= N <= 10^5\n1 <= K <= N-1\n1 <= R,S,P <= 10^4\nN,K,R,S, and P are all integers.\n|T| = N\nT consists of r, p, and s.", "input": "Input is given from Standard Input in the following format:\nN K\nR S P\nT", "output": "Print the maximum total score earned in the game.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n8 7 6\nrsrpr output: 27\n\nThe machine will play {Rock, Scissors, Rock, Paper, Rock}.\nWe can, for example, play {Paper, Rock, Rock, Scissors, Paper} against it to earn 27 points.\nWe cannot earn more points, so the answer is 27.", "input: 7 1\n100 10 1\nssssppr output: 211", "input: 30 5\n325 234 123\nrspsspspsrpspsppprpsprpssprpsr output: 4996"], "Pid": "p02820", "ProblemText": "Task Description: Problem Statement At an arcade, Takahashi is playing a game called RPS Battle, which is played as follows:\n\nThe player plays N rounds of Rock Paper Scissors against the machine. (See Notes for the description of Rock Paper Scissors. A draw also counts as a round. )\nEach time the player wins a round, depending on which hand he/she uses, he/she earns the following score (no points for a draw or a loss):\nR points for winning with Rock;\nS points for winning with Scissors;\nP points for winning with Paper.\nHowever, in the i-th round, the player cannot use the hand he/she used in the (i-K)-th round. (In the first K rounds, the player can use any hand. )\n\nBefore the start of the game, the machine decides the hand it will play in each round. With supernatural power, Takahashi managed to read all of those hands.\nThe information Takahashi obtained is given as a string T. If the i-th character of T (1 <= i <= N) is r, the machine will play Rock in the i-th round. Similarly, p and s stand for Paper and Scissors, respectively.\nWhat is the maximum total score earned in the game by adequately choosing the hand to play in each round? note: Notes In this problem, Rock Paper Scissors can be thought of as a two-player game, in which each player simultaneously forms Rock, Paper, or Scissors with a hand.\n\nIf a player chooses Rock and the other chooses Scissors, the player choosing Rock wins;\nif a player chooses Scissors and the other chooses Paper, the player choosing Scissors wins;\nif a player chooses Paper and the other chooses Rock, the player choosing Paper wins;\nif both players play the same hand, it is a draw.\nTask Constraint: 2 <= N <= 10^5\n1 <= K <= N-1\n1 <= R,S,P <= 10^4\nN,K,R,S, and P are all integers.\n|T| = N\nT consists of r, p, and s.\nTask Input: Input is given from Standard Input in the following format:\nN K\nR S P\nT\nTask Output: Print the maximum total score earned in the game.\nTask Samples: input: 5 2\n8 7 6\nrsrpr output: 27\n\nThe machine will play {Rock, Scissors, Rock, Paper, Rock}.\nWe can, for example, play {Paper, Rock, Rock, Scissors, Paper} against it to earn 27 points.\nWe cannot earn more points, so the answer is 27.\ninput: 7 1\n100 10 1\nssssppr output: 211\ninput: 30 5\n325 234 123\nrspsspspsrpspsppprpsprpssprpsr output: 4996\n\n" }, { "title": "", "content": "Problem Statement Takahashi has come to a party as a special guest.\nThere are N ordinary guests at the party. The i-th ordinary guest has a power of A_i.\nTakahashi has decided to perform M handshakes to increase the happiness of the party (let the current happiness be 0).\nA handshake will be performed as follows:\n\nTakahashi chooses one (ordinary) guest x for his left hand and another guest y for his right hand (x and y can be the same).\nThen, he shakes the left hand of Guest x and the right hand of Guest y simultaneously to increase the happiness by A_x+A_y.\n\nHowever, Takahashi should not perform the same handshake more than once. Formally, the following condition must hold:\n\nAssume that, in the k-th handshake, Takahashi shakes the left hand of Guest x_k and the right hand of Guest y_k. Then, there is no pair p, q (1 <= p < q <= M) such that (x_p, y_p)=(x_q, y_q).\n\nWhat is the maximum possible happiness after M handshakes?", "constraint": "1 <= N <= 10^5\n1 <= M <= N^2\n1 <= A_i <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N", "output": "Print the maximum possible happiness after M handshakes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n10 14 19 34 33 output: 202\n\nLet us say that Takahashi performs the following handshakes:\n\nIn the first handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 4.\nIn the second handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 5.\nIn the third handshake, Takahashi shakes the left hand of Guest 5 and the right hand of Guest 4.\n\nThen, we will have the happiness of (34+34)+(34+33)+(33+34)=202.\nWe cannot achieve the happiness of 203 or greater, so the answer is 202.", "input: 9 14\n1 3 5 110 24 21 34 5 3 output: 1837", "input: 9 73\n67597 52981 5828 66249 75177 64141 40773 79105 16076 output: 8128170"], "Pid": "p02821", "ProblemText": "Task Description: Problem Statement Takahashi has come to a party as a special guest.\nThere are N ordinary guests at the party. The i-th ordinary guest has a power of A_i.\nTakahashi has decided to perform M handshakes to increase the happiness of the party (let the current happiness be 0).\nA handshake will be performed as follows:\n\nTakahashi chooses one (ordinary) guest x for his left hand and another guest y for his right hand (x and y can be the same).\nThen, he shakes the left hand of Guest x and the right hand of Guest y simultaneously to increase the happiness by A_x+A_y.\n\nHowever, Takahashi should not perform the same handshake more than once. Formally, the following condition must hold:\n\nAssume that, in the k-th handshake, Takahashi shakes the left hand of Guest x_k and the right hand of Guest y_k. Then, there is no pair p, q (1 <= p < q <= M) such that (x_p, y_p)=(x_q, y_q).\n\nWhat is the maximum possible happiness after M handshakes?\nTask Constraint: 1 <= N <= 10^5\n1 <= M <= N^2\n1 <= A_i <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N\nTask Output: Print the maximum possible happiness after M handshakes.\nTask Samples: input: 5 3\n10 14 19 34 33 output: 202\n\nLet us say that Takahashi performs the following handshakes:\n\nIn the first handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 4.\nIn the second handshake, Takahashi shakes the left hand of Guest 4 and the right hand of Guest 5.\nIn the third handshake, Takahashi shakes the left hand of Guest 5 and the right hand of Guest 4.\n\nThen, we will have the happiness of (34+34)+(34+33)+(33+34)=202.\nWe cannot achieve the happiness of 203 or greater, so the answer is 202.\ninput: 9 14\n1 3 5 110 24 21 34 5 3 output: 1837\ninput: 9 73\n67597 52981 5828 66249 75177 64141 40773 79105 16076 output: 8128170\n\n" }, { "title": "", "content": "Problem Statement Given is a tree T with N vertices. The i-th edge connects Vertex A_i and B_i (1 <= A_i, B_i <= N).\nNow, each vertex is painted black with probability 1/2 and white with probability 1/2, which is chosen independently from other vertices. Then, let S be the smallest subtree (connected subgraph) of T containing all the vertices painted black. (If no vertex is painted black, S is the empty graph. )\nLet the holeyness of S be the number of white vertices contained in S. Find the expected holeyness of S.\nSince the answer is a rational number, we ask you to print it \\bmod 10^9+7, as described in Notes. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers, and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.", "constraint": "2 <= N <= 2 * 10^5\n1 <= A_i,B_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_{N-1} B_{N-1}", "output": "Print the expected holeyness of S, \\bmod 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3 output: 125000001\n\nIf the vertices 1,2,3 are painted black, white, black, respectively, the holeyness of S is 1.\nOtherwise, the holeyness is 0, so the expected holeyness is 1/8.\nSince 8 * 125000001 \\equiv 1 \\pmod{10^9+7}, we should print 125000001.", "input: 4\n1 2\n2 3\n3 4 output: 375000003\n\nThe expected holeyness is 3/8.\nSince 8 * 375000003 \\equiv 3 \\pmod{10^9+7}, we should print 375000003.", "input: 4\n1 2\n1 3\n1 4 output: 250000002\n\nThe expected holeyness is 1/4.", "input: 7\n4 7\n3 1\n2 6\n5 2\n7 1\n2 7 output: 570312505"], "Pid": "p02822", "ProblemText": "Task Description: Problem Statement Given is a tree T with N vertices. The i-th edge connects Vertex A_i and B_i (1 <= A_i, B_i <= N).\nNow, each vertex is painted black with probability 1/2 and white with probability 1/2, which is chosen independently from other vertices. Then, let S be the smallest subtree (connected subgraph) of T containing all the vertices painted black. (If no vertex is painted black, S is the empty graph. )\nLet the holeyness of S be the number of white vertices contained in S. Find the expected holeyness of S.\nSince the answer is a rational number, we ask you to print it \\bmod 10^9+7, as described in Notes. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers, and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= A_i,B_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_{N-1} B_{N-1}\nTask Output: Print the expected holeyness of S, \\bmod 10^9+7.\nTask Samples: input: 3\n1 2\n2 3 output: 125000001\n\nIf the vertices 1,2,3 are painted black, white, black, respectively, the holeyness of S is 1.\nOtherwise, the holeyness is 0, so the expected holeyness is 1/8.\nSince 8 * 125000001 \\equiv 1 \\pmod{10^9+7}, we should print 125000001.\ninput: 4\n1 2\n2 3\n3 4 output: 375000003\n\nThe expected holeyness is 3/8.\nSince 8 * 375000003 \\equiv 3 \\pmod{10^9+7}, we should print 375000003.\ninput: 4\n1 2\n1 3\n1 4 output: 250000002\n\nThe expected holeyness is 1/4.\ninput: 7\n4 7\n3 1\n2 6\n5 2\n7 1\n2 7 output: 570312505\n\n" }, { "title": "", "content": "Problem Statement2N players are running a competitive table tennis training on N tables numbered from 1 to N.\nThe training consists of rounds.\nIn each round, the players form N pairs, one pair per table.\nIn each pair, competitors play a match against each other.\nAs a result, one of them wins and the other one loses.\nThe winner of the match on table X plays on table X-1 in the next round,\nexcept for the winner of the match on table 1 who stays at table 1.\nSimilarly, the loser of the match on table X plays on table X+1 in the next round,\nexcept for the loser of the match on table N who stays at table N.\nTwo friends are playing their first round matches on distinct tables A and B.\nLet's assume that the friends are strong enough to win or lose any match at will.\nWhat is the smallest number of rounds after which the friends can get to play a match against each other?", "constraint": "2 <= N <= 10^{18}\n1 <= A < B <= N\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print the smallest number of rounds after which the friends can get to play a match against each other.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 4 output: 1\n\nIf the first friend loses their match and the second friend wins their match, they will both move to table 3 and play each other in the next round.", "input: 5 2 3 output: 2\n\nIf both friends win two matches in a row, they will both move to table 1."], "Pid": "p02823", "ProblemText": "Task Description: Problem Statement2N players are running a competitive table tennis training on N tables numbered from 1 to N.\nThe training consists of rounds.\nIn each round, the players form N pairs, one pair per table.\nIn each pair, competitors play a match against each other.\nAs a result, one of them wins and the other one loses.\nThe winner of the match on table X plays on table X-1 in the next round,\nexcept for the winner of the match on table 1 who stays at table 1.\nSimilarly, the loser of the match on table X plays on table X+1 in the next round,\nexcept for the loser of the match on table N who stays at table N.\nTwo friends are playing their first round matches on distinct tables A and B.\nLet's assume that the friends are strong enough to win or lose any match at will.\nWhat is the smallest number of rounds after which the friends can get to play a match against each other?\nTask Constraint: 2 <= N <= 10^{18}\n1 <= A < B <= N\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print the smallest number of rounds after which the friends can get to play a match against each other.\nTask Samples: input: 5 2 4 output: 1\n\nIf the first friend loses their match and the second friend wins their match, they will both move to table 3 and play each other in the next round.\ninput: 5 2 3 output: 2\n\nIf both friends win two matches in a row, they will both move to table 1.\n\n" }, { "title": "", "content": "Problem Statement N problems are proposed for an upcoming contest. Problem i has an initial integer score of A_i points.\nM judges are about to vote for problems they like. Each judge will choose exactly V problems, independently from the other judges,\nand increase the score of each chosen problem by 1.\nAfter all M judges cast their vote, the problems will be sorted in non-increasing order of score, and the first P problems will be chosen for the problemset.\nProblems with the same score can be ordered arbitrarily, this order is decided by the chief judge.\nHow many problems out of the given N have a chance to be chosen for the problemset?", "constraint": "2 <= N <= 10^5\n1 <= M <= 10^9\n1 <= V <= N - 1\n1 <= P <= N - 1\n0 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN M V P\nA_1 A_2 . . . A_N", "output": "Print the number of problems that have a chance to be chosen for the problemset.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 1 2 2\n2 1 1 3 0 2 output: 5\n\nIf the only judge votes for problems 2 and 5, the scores will be 2 2 1 3 1 2.\nThe problemset will consist of problem 4 and one of problems 1,2, or 6.\nIf the only judge votes for problems 3 and 4, the scores will be 2 1 2 4 0 2.\nThe problemset will consist of problem 4 and one of problems 1,3, or 6.\nThus, problems 1,2,3,4, and 6 have a chance to be chosen for the problemset. On the contrary, there is no way for problem 5 to be chosen.", "input: 6 1 5 2\n2 1 1 3 0 2 output: 3\n\nOnly problems 1,4, and 6 have a chance to be chosen.", "input: 10 4 8 5\n7 2 3 6 1 6 5 4 6 5 output: 8"], "Pid": "p02824", "ProblemText": "Task Description: Problem Statement N problems are proposed for an upcoming contest. Problem i has an initial integer score of A_i points.\nM judges are about to vote for problems they like. Each judge will choose exactly V problems, independently from the other judges,\nand increase the score of each chosen problem by 1.\nAfter all M judges cast their vote, the problems will be sorted in non-increasing order of score, and the first P problems will be chosen for the problemset.\nProblems with the same score can be ordered arbitrarily, this order is decided by the chief judge.\nHow many problems out of the given N have a chance to be chosen for the problemset?\nTask Constraint: 2 <= N <= 10^5\n1 <= M <= 10^9\n1 <= V <= N - 1\n1 <= P <= N - 1\n0 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN M V P\nA_1 A_2 . . . A_N\nTask Output: Print the number of problems that have a chance to be chosen for the problemset.\nTask Samples: input: 6 1 2 2\n2 1 1 3 0 2 output: 5\n\nIf the only judge votes for problems 2 and 5, the scores will be 2 2 1 3 1 2.\nThe problemset will consist of problem 4 and one of problems 1,2, or 6.\nIf the only judge votes for problems 3 and 4, the scores will be 2 1 2 4 0 2.\nThe problemset will consist of problem 4 and one of problems 1,3, or 6.\nThus, problems 1,2,3,4, and 6 have a chance to be chosen for the problemset. On the contrary, there is no way for problem 5 to be chosen.\ninput: 6 1 5 2\n2 1 1 3 0 2 output: 3\n\nOnly problems 1,4, and 6 have a chance to be chosen.\ninput: 10 4 8 5\n7 2 3 6 1 6 5 4 6 5 output: 8\n\n" }, { "title": "", "content": "Problem Statement Let us consider a grid of squares with N rows and N columns. You want to put some domino pieces on this grid.\nEach domino piece covers two squares that have a common side. Each square can be covered by at most one piece.\nFor each row of the grid, let's define its quality as the number of domino pieces that cover at least one square in this row.\nWe define the quality of each column similarly.\nFind a way to put at least one domino piece on the grid so that the quality of every row is equal to the quality of every column,\nor determine that such a placement doesn't exist.", "constraint": "2 <= N <= 1000", "input": "Input is given from Standard Input in the following format:\nN", "output": "If the required domino placement doesn't exist, print a single integer -1.\nOtherwise, output your placement as N strings of N characters each.\nIf a square is not covered, the corresponding character must be . (a dot).\nOtherwise, it must contain a lowercase English letter.\nSquares covered by the same domino piece must contain the same letter.\nIf two squares have a common side but belong to different pieces, they must contain different letters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 output: aabb..\nb..zz.\nba....\n.a..aa\n..a..b\n..a..b\n\nThe quality of every row and every column is 2.", "input: 2 output: -1"], "Pid": "p02825", "ProblemText": "Task Description: Problem Statement Let us consider a grid of squares with N rows and N columns. You want to put some domino pieces on this grid.\nEach domino piece covers two squares that have a common side. Each square can be covered by at most one piece.\nFor each row of the grid, let's define its quality as the number of domino pieces that cover at least one square in this row.\nWe define the quality of each column similarly.\nFind a way to put at least one domino piece on the grid so that the quality of every row is equal to the quality of every column,\nor determine that such a placement doesn't exist.\nTask Constraint: 2 <= N <= 1000\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If the required domino placement doesn't exist, print a single integer -1.\nOtherwise, output your placement as N strings of N characters each.\nIf a square is not covered, the corresponding character must be . (a dot).\nOtherwise, it must contain a lowercase English letter.\nSquares covered by the same domino piece must contain the same letter.\nIf two squares have a common side but belong to different pieces, they must contain different letters.\nTask Samples: input: 6 output: aabb..\nb..zz.\nba....\n.a..aa\n..a..b\n..a..b\n\nThe quality of every row and every column is 2.\ninput: 2 output: -1\n\n" }, { "title": "", "content": "Problem Statement N problems have been chosen by the judges, now it's time to assign scores to them!\nProblem i must get an integer score A_i between 1 and N, inclusive.\nThe problems have already been sorted by difficulty: A_1 <= A_2 <= \\ldots <= A_N must hold.\nDifferent problems can have the same score, though.\nBeing an ICPC fan, you want contestants who solve more problems to be ranked higher.\nThat's why, for any k (1 <= k <= N-1), you want the sum of scores of any k problems to be strictly less than the sum of scores of any k+1 problems.\nHow many ways to assign scores do you have? Find this number modulo the given prime M.", "constraint": "2 <= N <= 5000\n9 * 10^8 < M < 10^9\nM is a prime.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of ways to assign scores to the problems, modulo M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 998244353 output: 3\n\nThe possible assignments are (1,1), (1,2), (2,2).", "input: 3 998244353 output: 7\n\nThe possible assignments are (1,1,1), (1,2,2), (1,3,3), (2,2,2), (2,2,3), (2,3,3), (3,3,3).", "input: 6 966666661 output: 66", "input: 96 925309799 output: 83779"], "Pid": "p02826", "ProblemText": "Task Description: Problem Statement N problems have been chosen by the judges, now it's time to assign scores to them!\nProblem i must get an integer score A_i between 1 and N, inclusive.\nThe problems have already been sorted by difficulty: A_1 <= A_2 <= \\ldots <= A_N must hold.\nDifferent problems can have the same score, though.\nBeing an ICPC fan, you want contestants who solve more problems to be ranked higher.\nThat's why, for any k (1 <= k <= N-1), you want the sum of scores of any k problems to be strictly less than the sum of scores of any k+1 problems.\nHow many ways to assign scores do you have? Find this number modulo the given prime M.\nTask Constraint: 2 <= N <= 5000\n9 * 10^8 < M < 10^9\nM is a prime.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of ways to assign scores to the problems, modulo M.\nTask Samples: input: 2 998244353 output: 3\n\nThe possible assignments are (1,1), (1,2), (2,2).\ninput: 3 998244353 output: 7\n\nThe possible assignments are (1,1,1), (1,2,2), (1,3,3), (2,2,2), (2,2,3), (2,3,3), (3,3,3).\ninput: 6 966666661 output: 66\ninput: 96 925309799 output: 83779\n\n" }, { "title": "", "content": "Problem Statement A balancing network is an abstract device built up of N wires, thought of as running from left to right,\nand M balancers that connect pairs of wires. The wires are numbered from 1 to N from top to bottom,\nand the balancers are numbered from 1 to M from left to right.\nBalancer i connects wires x_i and y_i (x_i < y_i).\n\nEach balancer must be in one of two states: up or down.\nConsider a token that starts moving to the right along some wire at a point to the left of all balancers.\nDuring the process, the token passes through each balancer exactly once.\nWhenever the token encounters balancer i, the following happens:\n\nIf the token is moving along wire x_i and balancer i is in the down state, the token moves down to wire y_i and continues moving to the right.\nIf the token is moving along wire y_i and balancer i is in the up state, the token moves up to wire x_i and continues moving to the right.\nOtherwise, the token doesn't change the wire it's moving along.\n\nLet a state of the balancing network be a string of length M, describing the states of all balancers.\nThe i-th character is ^ if balancer i is in the up state, and v if balancer i is in the down state.\nA state of the balancing network is called uniforming if a wire w exists such that, regardless of the starting wire,\nthe token will always end up at wire w and run to infinity along it. Any other state is called non-uniforming.\nYou are given an integer T (1 <= T <= 2). Answer the following question:\n\nIf T = 1, find any uniforming state of the network or determine that it doesn't exist.\nIf T = 2, find any non-uniforming state of the network or determine that it doesn't exist.\n\nNote that if you answer just one kind of questions correctly, you can get partial score. partial score: Partial Score\n800 points will be awarded for passing the testset satisfying T = 1.\n800 points will be awarded for passing the testset satisfying T = 2.", "constraint": "2 <= N <= 50000\n1 <= M <= 100000\n1 <= T <= 2\n1 <= x_i < y_i <= N\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M T\nx_1 y_1\nx_2 y_2\n:\nx_M y_M", "output": "Print any uniforming state of the given network if T = 1, or any non-uniforming state if T = 2. If the required state doesn't exist, output -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 1\n1 3\n2 4\n1 2\n3 4\n2 3 output: ^^^^^\n\nThis state is uniforming: regardless of the starting wire, the token ends up at wire 1.", "input: 4 5 2\n1 3\n2 4\n1 2\n3 4\n2 3 output: v^^^^\n\nThis state is non-uniforming: depending on the starting wire, the token might end up at wire 1 or wire 2.", "input: 3 1 1\n1 2 output: -1\n\nA uniforming state doesn't exist.", "input: 2 1 2\n1 2 output: -1\n\nA non-uniforming state doesn't exist."], "Pid": "p02827", "ProblemText": "Task Description: Problem Statement A balancing network is an abstract device built up of N wires, thought of as running from left to right,\nand M balancers that connect pairs of wires. The wires are numbered from 1 to N from top to bottom,\nand the balancers are numbered from 1 to M from left to right.\nBalancer i connects wires x_i and y_i (x_i < y_i).\n\nEach balancer must be in one of two states: up or down.\nConsider a token that starts moving to the right along some wire at a point to the left of all balancers.\nDuring the process, the token passes through each balancer exactly once.\nWhenever the token encounters balancer i, the following happens:\n\nIf the token is moving along wire x_i and balancer i is in the down state, the token moves down to wire y_i and continues moving to the right.\nIf the token is moving along wire y_i and balancer i is in the up state, the token moves up to wire x_i and continues moving to the right.\nOtherwise, the token doesn't change the wire it's moving along.\n\nLet a state of the balancing network be a string of length M, describing the states of all balancers.\nThe i-th character is ^ if balancer i is in the up state, and v if balancer i is in the down state.\nA state of the balancing network is called uniforming if a wire w exists such that, regardless of the starting wire,\nthe token will always end up at wire w and run to infinity along it. Any other state is called non-uniforming.\nYou are given an integer T (1 <= T <= 2). Answer the following question:\n\nIf T = 1, find any uniforming state of the network or determine that it doesn't exist.\nIf T = 2, find any non-uniforming state of the network or determine that it doesn't exist.\n\nNote that if you answer just one kind of questions correctly, you can get partial score. partial score: Partial Score\n800 points will be awarded for passing the testset satisfying T = 1.\n800 points will be awarded for passing the testset satisfying T = 2.\nTask Constraint: 2 <= N <= 50000\n1 <= M <= 100000\n1 <= T <= 2\n1 <= x_i < y_i <= N\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M T\nx_1 y_1\nx_2 y_2\n:\nx_M y_M\nTask Output: Print any uniforming state of the given network if T = 1, or any non-uniforming state if T = 2. If the required state doesn't exist, output -1.\nTask Samples: input: 4 5 1\n1 3\n2 4\n1 2\n3 4\n2 3 output: ^^^^^\n\nThis state is uniforming: regardless of the starting wire, the token ends up at wire 1.\ninput: 4 5 2\n1 3\n2 4\n1 2\n3 4\n2 3 output: v^^^^\n\nThis state is non-uniforming: depending on the starting wire, the token might end up at wire 1 or wire 2.\ninput: 3 1 1\n1 2 output: -1\n\nA uniforming state doesn't exist.\ninput: 2 1 2\n1 2 output: -1\n\nA non-uniforming state doesn't exist.\n\n" }, { "title": "", "content": "Problem Statement Let us consider a grid of squares with N rows and N columns.\nArbok has cut out some part of the grid so that, for each i = 1,2, \\ldots, N, the bottommost h_i squares are remaining in the i-th column from the left.\nNow, he wants to place rooks into some of the remaining squares.\nA rook is a chess piece that occupies one square and can move horizontally or vertically, through any number of unoccupied squares.\nA rook can not move through squares that have been cut out by Arbok.\nLet's say that a square is covered if it either contains a rook, or a rook can be moved to this square in one move.\nFind the number of ways to place rooks into some of the remaining squares so that every remaining square is covered, modulo 998244353.", "constraint": "1 <= N <= 400\n1 <= h_i <= N\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nh_1 h_2 . . . h_N", "output": "Print the number of ways to place rooks into some of the remaining squares so that every remaining square is covered, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n2 2 output: 11\n\nAny placement with at least two rooks is fine. There are 11 such placements.", "input: 3\n2 1 2 output: 17\n\nThe following 17 rook placements satisfy the conditions (R denotes a rook, * denotes an empty square):\nR * * R * * R R R R R R \n**R R** R*R R** *R* **R \nR * R * * R * R * * R R \nR*R *RR RR* R*R RRR RR* \nR R R R R * * R R R \nR*R *RR RRR RRR RRR", "input: 4\n1 2 4 1 output: 201", "input: 10\n4 7 4 8 4 6 8 2 3 6 output: 263244071"], "Pid": "p02828", "ProblemText": "Task Description: Problem Statement Let us consider a grid of squares with N rows and N columns.\nArbok has cut out some part of the grid so that, for each i = 1,2, \\ldots, N, the bottommost h_i squares are remaining in the i-th column from the left.\nNow, he wants to place rooks into some of the remaining squares.\nA rook is a chess piece that occupies one square and can move horizontally or vertically, through any number of unoccupied squares.\nA rook can not move through squares that have been cut out by Arbok.\nLet's say that a square is covered if it either contains a rook, or a rook can be moved to this square in one move.\nFind the number of ways to place rooks into some of the remaining squares so that every remaining square is covered, modulo 998244353.\nTask Constraint: 1 <= N <= 400\n1 <= h_i <= N\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nh_1 h_2 . . . h_N\nTask Output: Print the number of ways to place rooks into some of the remaining squares so that every remaining square is covered, modulo 998244353.\nTask Samples: input: 2\n2 2 output: 11\n\nAny placement with at least two rooks is fine. There are 11 such placements.\ninput: 3\n2 1 2 output: 17\n\nThe following 17 rook placements satisfy the conditions (R denotes a rook, * denotes an empty square):\nR * * R * * R R R R R R \n**R R** R*R R** *R* **R \nR * R * * R * R * * R R \nR*R *RR RR* R*R RRR RR* \nR R R R R * * R R R \nR*R *RR RRR RRR RRR\ninput: 4\n1 2 4 1 output: 201\ninput: 10\n4 7 4 8 4 6 8 2 3 6 output: 263244071\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi is solving quizzes. He has easily solved all but the last one.\nThe last quiz has three choices: 1,2, and 3.\nWith his supernatural power, Takahashi has found out that the choices A and B are both wrong.\nPrint the correct choice for this problem.", "constraint": "Each of the numbers A and B is 1,2, or 3.\nA and B are different.", "input": "Input is given from Standard Input in the following format:\nA\nB", "output": "Print the correct choice.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 output: 2\n\nWhen we know 3 and 1 are both wrong, the correct choice is 2.", "input: 1\n2 output: 3"], "Pid": "p02829", "ProblemText": "Task Description: Problem Statement\nTakahashi is solving quizzes. He has easily solved all but the last one.\nThe last quiz has three choices: 1,2, and 3.\nWith his supernatural power, Takahashi has found out that the choices A and B are both wrong.\nPrint the correct choice for this problem.\nTask Constraint: Each of the numbers A and B is 1,2, or 3.\nA and B are different.\nTask Input: Input is given from Standard Input in the following format:\nA\nB\nTask Output: Print the correct choice.\nTask Samples: input: 3\n1 output: 2\n\nWhen we know 3 and 1 are both wrong, the correct choice is 2.\ninput: 1\n2 output: 3\n\n" }, { "title": "", "content": "Problem Statement Given are strings s and t of length N each, both consisting of lowercase English letters.\nLet us form a new string by alternating the characters of S and the characters of T, as follows: the first character of S, the first character of T, the second character of S, the second character of T, . . . , the N-th character of S, the N-th character of T. Print this new string.", "constraint": "1 <= N <= 100\n|S| = |T| = N\nS and T are strings consisting of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\nS T", "output": "Print the string formed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\nip cc output: icpc", "input: 8\nhmhmnknk uuuuuuuu output: humuhumunukunuku", "input: 5\naaaaa aaaaa output: aaaaaaaaaa"], "Pid": "p02830", "ProblemText": "Task Description: Problem Statement Given are strings s and t of length N each, both consisting of lowercase English letters.\nLet us form a new string by alternating the characters of S and the characters of T, as follows: the first character of S, the first character of T, the second character of S, the second character of T, . . . , the N-th character of S, the N-th character of T. Print this new string.\nTask Constraint: 1 <= N <= 100\n|S| = |T| = N\nS and T are strings consisting of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\nS T\nTask Output: Print the string formed.\nTask Samples: input: 2\nip cc output: icpc\ninput: 8\nhmhmnknk uuuuuuuu output: humuhumunukunuku\ninput: 5\naaaaa aaaaa output: aaaaaaaaaa\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi is organizing a party.\nAt the party, each guest will receive one or more snack pieces.\nTakahashi predicts that the number of guests at this party will be A or B.\nFind the minimum number of pieces that can be evenly distributed to the guests in both of the cases predicted.\nWe assume that a piece cannot be divided and distributed to multiple guests.", "constraint": "1 <= A, B <= 10^5\nA \\neq B\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the minimum number of pieces that can be evenly distributed to the guests in both of the cases with A guests and B guests.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 output: 6\n\nWhen we have six snack pieces, each guest can take three pieces if we have two guests, and each guest can take two if we have three guests.", "input: 123 456 output: 18696", "input: 100000 99999 output: 9999900000"], "Pid": "p02831", "ProblemText": "Task Description: Problem Statement\nTakahashi is organizing a party.\nAt the party, each guest will receive one or more snack pieces.\nTakahashi predicts that the number of guests at this party will be A or B.\nFind the minimum number of pieces that can be evenly distributed to the guests in both of the cases predicted.\nWe assume that a piece cannot be divided and distributed to multiple guests.\nTask Constraint: 1 <= A, B <= 10^5\nA \\neq B\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the minimum number of pieces that can be evenly distributed to the guests in both of the cases with A guests and B guests.\nTask Samples: input: 2 3 output: 6\n\nWhen we have six snack pieces, each guest can take three pieces if we have two guests, and each guest can take two if we have three guests.\ninput: 123 456 output: 18696\ninput: 100000 99999 output: 9999900000\n\n" }, { "title": "", "content": "Problem Statement We have N bricks arranged in a row from left to right.\nThe i-th brick from the left (1 <= i <= N) has an integer a_i written on it.\nAmong them, you can break at most N-1 bricks of your choice.\nLet us say there are K bricks remaining. Snuke will be satisfied if, for each integer i (1 <= i <= K), the i-th of those brick from the left has the integer i written on it.\nFind the minimum number of bricks you need to break to satisfy Snuke's desire. If his desire is unsatisfiable, print -1 instead.", "constraint": "All values in input are integers.\n1 <= N <= 200000\n1 <= a_i <= N", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum number of bricks that need to be broken to satisfy Snuke's desire, or print -1 if his desire is unsatisfiable.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 1 2 output: 1\n\nIf we break the leftmost brick, the remaining bricks have integers 1 and 2 written on them from left to right, in which case Snuke will be satisfied.", "input: 3\n2 2 2 output: -1\n\nIn this case, there is no way to break some of the bricks to satisfy Snuke's desire.", "input: 10\n3 1 4 1 5 9 2 6 5 3 output: 7", "input: 1\n1 output: 0\n\nThere may be no need to break the bricks at all."], "Pid": "p02832", "ProblemText": "Task Description: Problem Statement We have N bricks arranged in a row from left to right.\nThe i-th brick from the left (1 <= i <= N) has an integer a_i written on it.\nAmong them, you can break at most N-1 bricks of your choice.\nLet us say there are K bricks remaining. Snuke will be satisfied if, for each integer i (1 <= i <= K), the i-th of those brick from the left has the integer i written on it.\nFind the minimum number of bricks you need to break to satisfy Snuke's desire. If his desire is unsatisfiable, print -1 instead.\nTask Constraint: All values in input are integers.\n1 <= N <= 200000\n1 <= a_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum number of bricks that need to be broken to satisfy Snuke's desire, or print -1 if his desire is unsatisfiable.\nTask Samples: input: 3\n2 1 2 output: 1\n\nIf we break the leftmost brick, the remaining bricks have integers 1 and 2 written on them from left to right, in which case Snuke will be satisfied.\ninput: 3\n2 2 2 output: -1\n\nIn this case, there is no way to break some of the bricks to satisfy Snuke's desire.\ninput: 10\n3 1 4 1 5 9 2 6 5 3 output: 7\ninput: 1\n1 output: 0\n\nThere may be no need to break the bricks at all.\n\n" }, { "title": "", "content": "Problem Statement For an integer n not less than 0, let us define f(n) as follows:\n\nf(n) = 1 (if n < 2)\nf(n) = n f(n-2) (if n >= 2)\n\nGiven is an integer N. Find the number of trailing zeros in the decimal notation of f(N).", "constraint": "0 <= N <= 10^{18}", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of trailing zeros in the decimal notation of f(N).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12 output: 1\n\nf(12) = 12 * 10 * 8 * 6 * 4 * 2 = 46080, which has one trailing zero.", "input: 5 output: 0\n\nf(5) = 5 * 3 * 1 = 15, which has no trailing zeros.", "input: 1000000000000000000 output: 124999999999999995"], "Pid": "p02833", "ProblemText": "Task Description: Problem Statement For an integer n not less than 0, let us define f(n) as follows:\n\nf(n) = 1 (if n < 2)\nf(n) = n f(n-2) (if n >= 2)\n\nGiven is an integer N. Find the number of trailing zeros in the decimal notation of f(N).\nTask Constraint: 0 <= N <= 10^{18}\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of trailing zeros in the decimal notation of f(N).\nTask Samples: input: 12 output: 1\n\nf(12) = 12 * 10 * 8 * 6 * 4 * 2 = 46080, which has one trailing zero.\ninput: 5 output: 0\n\nf(5) = 5 * 3 * 1 = 15, which has no trailing zeros.\ninput: 1000000000000000000 output: 124999999999999995\n\n" }, { "title": "", "content": "Problem Statement We have a tree with N vertices. The i-th edge connects Vertex A_i and B_i bidirectionally.\nTakahashi is standing at Vertex u, and Aoki is standing at Vertex v.\nNow, they will play a game of tag as follows:\n1. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Takahashi moves to a vertex of his choice that is adjacent to his current vertex.\n2. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Aoki moves to a vertex of his choice that is adjacent to his current vertex.\n3. Go back to step 1.\nTakahashi performs his moves so that the game ends as late as possible, while Aoki performs his moves so that the game ends as early as possible.\nFind the number of moves Aoki will perform before the end of the game if both Takahashi and Aoki know each other's position and strategy.\nIt can be proved that the game is bound to end.", "constraint": "2 <= N <= 10^5\n1 <= u,v <= N\nu \\neq v\n1 <= A_i,B_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN u v\nA_1 B_1\n:\nA_{N-1} B_{N-1}", "output": "Print the number of moves Aoki will perform before the end of the game.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 1\n1 2\n2 3\n3 4\n3 5 output: 2\n\nIf both players play optimally, the game will progress as follows:\n\nTakahashi moves to Vertex 3.\nAoki moves to Vertex 2.\nTakahashi moves to Vertex 5.\nAoki moves to Vertex 3.\nTakahashi moves to Vertex 3.\n\nHere, Aoki performs two moves.\nNote that, in each move, it is prohibited to stay at the current vertex.", "input: 5 4 5\n1 2\n1 3\n1 4\n1 5 output: 1", "input: 2 1 2\n1 2 output: 0", "input: 9 6 1\n1 2\n2 3\n3 4\n4 5\n5 6\n4 7\n7 8\n8 9 output: 5"], "Pid": "p02834", "ProblemText": "Task Description: Problem Statement We have a tree with N vertices. The i-th edge connects Vertex A_i and B_i bidirectionally.\nTakahashi is standing at Vertex u, and Aoki is standing at Vertex v.\nNow, they will play a game of tag as follows:\n1. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Takahashi moves to a vertex of his choice that is adjacent to his current vertex.\n2. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Aoki moves to a vertex of his choice that is adjacent to his current vertex.\n3. Go back to step 1.\nTakahashi performs his moves so that the game ends as late as possible, while Aoki performs his moves so that the game ends as early as possible.\nFind the number of moves Aoki will perform before the end of the game if both Takahashi and Aoki know each other's position and strategy.\nIt can be proved that the game is bound to end.\nTask Constraint: 2 <= N <= 10^5\n1 <= u,v <= N\nu \\neq v\n1 <= A_i,B_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN u v\nA_1 B_1\n:\nA_{N-1} B_{N-1}\nTask Output: Print the number of moves Aoki will perform before the end of the game.\nTask Samples: input: 5 4 1\n1 2\n2 3\n3 4\n3 5 output: 2\n\nIf both players play optimally, the game will progress as follows:\n\nTakahashi moves to Vertex 3.\nAoki moves to Vertex 2.\nTakahashi moves to Vertex 5.\nAoki moves to Vertex 3.\nTakahashi moves to Vertex 3.\n\nHere, Aoki performs two moves.\nNote that, in each move, it is prohibited to stay at the current vertex.\ninput: 5 4 5\n1 2\n1 3\n1 4\n1 5 output: 1\ninput: 2 1 2\n1 2 output: 0\ninput: 9 6 1\n1 2\n2 3\n3 4\n4 5\n5 6\n4 7\n7 8\n8 9 output: 5\n\n" }, { "title": "", "content": "Problem Statement Given are three integers A_1, A_2, and A_3.\nIf A_1+A_2+A_3 is greater than or equal to 22, print bust; otherwise, print win.", "constraint": "1 <= A_i <= 13 \\ \\ (i=1,2,3)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA_1 A_2 A_3", "output": "If A_1+A_2+A_3 is greater than or equal to 22, print bust; otherwise, print win.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 7 9 output: win\n\n5+7+9=21, so print win.", "input: 13 7 2 output: bust\n\n13+7+2=22, so print bust."], "Pid": "p02835", "ProblemText": "Task Description: Problem Statement Given are three integers A_1, A_2, and A_3.\nIf A_1+A_2+A_3 is greater than or equal to 22, print bust; otherwise, print win.\nTask Constraint: 1 <= A_i <= 13 \\ \\ (i=1,2,3)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA_1 A_2 A_3\nTask Output: If A_1+A_2+A_3 is greater than or equal to 22, print bust; otherwise, print win.\nTask Samples: input: 5 7 9 output: win\n\n5+7+9=21, so print win.\ninput: 13 7 2 output: bust\n\n13+7+2=22, so print bust.\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi loves palindromes. Non-palindromic strings are unacceptable to him. Each time he hugs a string, he can change one of its characters to any character of his choice.\nGiven is a string S. Find the minimum number of hugs needed to make S palindromic.", "constraint": "S is a string consisting of lowercase English letters.\nThe length of S is between 1 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the minimum number of hugs needed to make S palindromic.", "content_img": false, "lang": "en", "error": false, "samples": ["input: redcoder output: 1\n\nFor example, we can change the fourth character to o and get a palindrome redooder.", "input: vvvvvv output: 0\n\nWe might need no hugs at all.", "input: abcdabc output: 2"], "Pid": "p02836", "ProblemText": "Task Description: Problem Statement\nTakahashi loves palindromes. Non-palindromic strings are unacceptable to him. Each time he hugs a string, he can change one of its characters to any character of his choice.\nGiven is a string S. Find the minimum number of hugs needed to make S palindromic.\nTask Constraint: S is a string consisting of lowercase English letters.\nThe length of S is between 1 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the minimum number of hugs needed to make S palindromic.\nTask Samples: input: redcoder output: 1\n\nFor example, we can change the fourth character to o and get a palindrome redooder.\ninput: vvvvvv output: 0\n\nWe might need no hugs at all.\ninput: abcdabc output: 2\n\n" }, { "title": "", "content": "Problem Statement There are N people numbered 1 to N. Each of them is either an honest person whose testimonies are always correct or an unkind person whose testimonies may be correct or not.\nPerson i gives A_i testimonies. The j-th testimony by Person i is represented by two integers x_{ij} and y_{ij}. If y_{ij} = 1, the testimony says Person x_{ij} is honest; if y_{ij} = 0, it says Person x_{ij} is unkind.\nHow many honest persons can be among those N people at most?", "constraint": "All values in input are integers.\n1 <= N <= 15\n0 <= A_i <= N - 1\n1 <= x_{ij} <= N\nx_{ij} \\neq i\nx_{ij_1} \\neq x_{ij_2} (j_1 \\neq j_2)\ny_{ij} = 0,1", "input": "Input is given from Standard Input in the following format:\nN\nA_1\nx_{11} y_{11}\nx_{12} y_{12}\n:\nx_{1A_1} y_{1A_1}\nA_2\nx_{21} y_{21}\nx_{22} y_{22}\n:\nx_{2A_2} y_{2A_2}\n:\nA_N\nx_{N1} y_{N1}\nx_{N2} y_{N2}\n:\nx_{NA_N} y_{NA_N}", "output": "Print the maximum possible number of honest persons among the N people.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1\n2 1\n1\n1 1\n1\n2 0 output: 2\n\nIf Person 1 and Person 2 are honest and Person 3 is unkind, we have two honest persons without inconsistencies, which is the maximum possible number of honest persons.", "input: 3\n2\n2 1\n3 0\n2\n3 1\n1 0\n2\n1 1\n2 0 output: 0\n\nAssuming that one or more of them are honest immediately leads to a contradiction.", "input: 2\n1\n2 0\n1\n1 0 output: 1"], "Pid": "p02837", "ProblemText": "Task Description: Problem Statement There are N people numbered 1 to N. Each of them is either an honest person whose testimonies are always correct or an unkind person whose testimonies may be correct or not.\nPerson i gives A_i testimonies. The j-th testimony by Person i is represented by two integers x_{ij} and y_{ij}. If y_{ij} = 1, the testimony says Person x_{ij} is honest; if y_{ij} = 0, it says Person x_{ij} is unkind.\nHow many honest persons can be among those N people at most?\nTask Constraint: All values in input are integers.\n1 <= N <= 15\n0 <= A_i <= N - 1\n1 <= x_{ij} <= N\nx_{ij} \\neq i\nx_{ij_1} \\neq x_{ij_2} (j_1 \\neq j_2)\ny_{ij} = 0,1\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\nx_{11} y_{11}\nx_{12} y_{12}\n:\nx_{1A_1} y_{1A_1}\nA_2\nx_{21} y_{21}\nx_{22} y_{22}\n:\nx_{2A_2} y_{2A_2}\n:\nA_N\nx_{N1} y_{N1}\nx_{N2} y_{N2}\n:\nx_{NA_N} y_{NA_N}\nTask Output: Print the maximum possible number of honest persons among the N people.\nTask Samples: input: 3\n1\n2 1\n1\n1 1\n1\n2 0 output: 2\n\nIf Person 1 and Person 2 are honest and Person 3 is unkind, we have two honest persons without inconsistencies, which is the maximum possible number of honest persons.\ninput: 3\n2\n2 1\n3 0\n2\n3 1\n1 0\n2\n1 1\n2 0 output: 0\n\nAssuming that one or more of them are honest immediately leads to a contradiction.\ninput: 2\n1\n2 0\n1\n1 0 output: 1\n\n" }, { "title": "", "content": "Problem Statement We have N integers. The i-th integer is A_i.\nFind \\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\mbox{ XOR } A_j), modulo (10^9+7).\n\nWhat is \\mbox{ XOR }?\n\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )", "constraint": "2 <= N <= 3 * 10^5\n0 <= A_i < 2^{60}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the value \\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\mbox{ XOR } A_j), modulo (10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 6\n\nWe have (1\\mbox{ XOR } 2)+(1\\mbox{ XOR } 3)+(2\\mbox{ XOR } 3)=3+2+1=6.", "input: 10\n3 1 4 1 5 9 2 6 5 3 output: 237", "input: 10\n3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820 output: 103715602\n\nPrint the sum modulo (10^9+7)."], "Pid": "p02838", "ProblemText": "Task Description: Problem Statement We have N integers. The i-th integer is A_i.\nFind \\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\mbox{ XOR } A_j), modulo (10^9+7).\n\nWhat is \\mbox{ XOR }?\n\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )\nTask Constraint: 2 <= N <= 3 * 10^5\n0 <= A_i < 2^{60}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the value \\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\mbox{ XOR } A_j), modulo (10^9+7).\nTask Samples: input: 3\n1 2 3 output: 6\n\nWe have (1\\mbox{ XOR } 2)+(1\\mbox{ XOR } 3)+(2\\mbox{ XOR } 3)=3+2+1=6.\ninput: 10\n3 1 4 1 5 9 2 6 5 3 output: 237\ninput: 10\n3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820 output: 103715602\n\nPrint the sum modulo (10^9+7).\n\n" }, { "title": "", "content": "Problem Statement We have a grid with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nThe square (i, j) has two numbers A_{ij} and B_{ij} written on it.\nFirst, for each square, Takahashi paints one of the written numbers red and the other blue.\nThen, he travels from the square (1,1) to the square (H, W). In one move, he can move from a square (i, j) to the square (i+1, j) or the square (i, j+1). He must not leave the grid.\nLet the unbalancedness be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares (1,1) and (H, W).\nTakahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it.\nFind the minimum unbalancedness possible.", "constraint": "2 <= H <= 80\n2 <= W <= 80\n0 <= A_{ij} <= 80\n0 <= B_{ij} <= 80\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nH W\nA_{11} A_{12} \\ldots A_{1W}\n:\nA_{H1} A_{H2} \\ldots A_{HW}\nB_{11} B_{12} \\ldots B_{1W}\n:\nB_{H1} B_{H2} \\ldots B_{HW}", "output": "Print the minimum unbalancedness possible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n1 2\n3 4\n3 4\n2 1 output: 0\n\nBy painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are 3+3+1=7 and 1+2+4=7, respectively, for the unbalancedness of 0.", "input: 2 3\n1 10 80\n80 10 1\n1 2 3\n4 5 6 output: 2"], "Pid": "p02839", "ProblemText": "Task Description: Problem Statement We have a grid with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nThe square (i, j) has two numbers A_{ij} and B_{ij} written on it.\nFirst, for each square, Takahashi paints one of the written numbers red and the other blue.\nThen, he travels from the square (1,1) to the square (H, W). In one move, he can move from a square (i, j) to the square (i+1, j) or the square (i, j+1). He must not leave the grid.\nLet the unbalancedness be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares (1,1) and (H, W).\nTakahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it.\nFind the minimum unbalancedness possible.\nTask Constraint: 2 <= H <= 80\n2 <= W <= 80\n0 <= A_{ij} <= 80\n0 <= B_{ij} <= 80\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nH W\nA_{11} A_{12} \\ldots A_{1W}\n:\nA_{H1} A_{H2} \\ldots A_{HW}\nB_{11} B_{12} \\ldots B_{1W}\n:\nB_{H1} B_{H2} \\ldots B_{HW}\nTask Output: Print the minimum unbalancedness possible.\nTask Samples: input: 2 2\n1 2\n3 4\n3 4\n2 1 output: 0\n\nBy painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are 3+3+1=7 and 1+2+4=7, respectively, for the unbalancedness of 0.\ninput: 2 3\n1 10 80\n80 10 1\n1 2 3\n4 5 6 output: 2\n\n" }, { "title": "", "content": "Problem Statement We have an integer sequence A of length N, where A_1 = X, A_{i+1} = A_i + D (1 <= i < N ) holds.\nTakahashi will take some (possibly all or none) of the elements in this sequence, and Aoki will take all of the others.\nLet S and T be the sum of the numbers taken by Takahashi and Aoki, respectively. How many possible values of S - T are there?", "constraint": "-10^8 <= X, D <= 10^8\n1 <= N <= 2 * 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X D", "output": "Print the number of possible values of S - T.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 2 output: 8\n\nA is (4,6,8).\nThere are eight ways for (Takahashi, Aoki) to take the elements: ((), (4,6,8)), ((4), (6,8)), ((6), (4,8)), ((8), (4,6))), ((4,6), (8))), ((4,8), (6))), ((6,8), (4))), and ((4,6,8), ()).\nThe values of S - T in these ways are -18, -10, -6, -2,2,6,10, and 18, respectively, so there are eight possible values of S - T.", "input: 2 3 -3 output: 2\n\nA is (3,0). There are two possible values of S - T: -3 and 3.", "input: 100 14 20 output: 49805"], "Pid": "p02840", "ProblemText": "Task Description: Problem Statement We have an integer sequence A of length N, where A_1 = X, A_{i+1} = A_i + D (1 <= i < N ) holds.\nTakahashi will take some (possibly all or none) of the elements in this sequence, and Aoki will take all of the others.\nLet S and T be the sum of the numbers taken by Takahashi and Aoki, respectively. How many possible values of S - T are there?\nTask Constraint: -10^8 <= X, D <= 10^8\n1 <= N <= 2 * 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X D\nTask Output: Print the number of possible values of S - T.\nTask Samples: input: 3 4 2 output: 8\n\nA is (4,6,8).\nThere are eight ways for (Takahashi, Aoki) to take the elements: ((), (4,6,8)), ((4), (6,8)), ((6), (4,8)), ((8), (4,6))), ((4,6), (8))), ((4,8), (6))), ((6,8), (4))), and ((4,6,8), ()).\nThe values of S - T in these ways are -18, -10, -6, -2,2,6,10, and 18, respectively, so there are eight possible values of S - T.\ninput: 2 3 -3 output: 2\n\nA is (3,0). There are two possible values of S - T: -3 and 3.\ninput: 100 14 20 output: 49805\n\n" }, { "title": "", "content": "Problem Statement\nIn this problem, a date is written as Y-M-D. For example, 2019-11-30 means November 30,2019.\nIntegers M_1, D_1, M_2, and D_2 will be given as input.\nIt is known that the date 2019-M_2-D_2 follows 2019-M_1-D_1.\nDetermine whether the date 2019-M_1-D_1 is the last day of a month.", "constraint": "Both 2019-M_1-D_1 and 2019-M_2-D_2 are valid dates in the Gregorian calendar.\nThe date 2019-M_2-D_2 follows 2019-M_1-D_1.", "input": "Input is given from Standard Input in the following format:\nM_1 D_1\nM_2 D_2", "output": "If the date 2019-M_1-D_1 is the last day of a month, print 1; otherwise, print 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11 16\n11 17 output: 0\n\nNovember 16 is not the last day of a month.", "input: 11 30\n12 1 output: 1\n\nNovember 30 is the last day of November."], "Pid": "p02841", "ProblemText": "Task Description: Problem Statement\nIn this problem, a date is written as Y-M-D. For example, 2019-11-30 means November 30,2019.\nIntegers M_1, D_1, M_2, and D_2 will be given as input.\nIt is known that the date 2019-M_2-D_2 follows 2019-M_1-D_1.\nDetermine whether the date 2019-M_1-D_1 is the last day of a month.\nTask Constraint: Both 2019-M_1-D_1 and 2019-M_2-D_2 are valid dates in the Gregorian calendar.\nThe date 2019-M_2-D_2 follows 2019-M_1-D_1.\nTask Input: Input is given from Standard Input in the following format:\nM_1 D_1\nM_2 D_2\nTask Output: If the date 2019-M_1-D_1 is the last day of a month, print 1; otherwise, print 0.\nTask Samples: input: 11 16\n11 17 output: 0\n\nNovember 16 is not the last day of a month.\ninput: 11 30\n12 1 output: 1\n\nNovember 30 is the last day of November.\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi bought a piece of apple pie at ABC Confiserie. According to his memory, he paid N yen (the currency of Japan) for it.\nThe consumption tax rate for foods in this shop is 8 percent. That is, to buy an apple pie priced at X yen before tax, you have to pay X * 1.08 yen (rounded down to the nearest integer).\nTakahashi forgot the price of his apple pie before tax, X, and wants to know it again. Write a program that takes N as input and finds X. We assume X is an integer.\nIf there are multiple possible values for X, find any one of them. Also, Takahashi's memory of N, the amount he paid, may be incorrect. If no value could be X, report that fact.", "constraint": "1 <= N <= 50000\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If there are values that could be X, the price of the apple pie before tax, print any one of them.\nIf there are multiple such values, printing any one of them will be accepted.\nIf no value could be X, print : (.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 432 output: 400\n\nIf the apple pie is priced at 400 yen before tax, you have to pay 400 * 1.08 = 432 yen to buy one.\nOtherwise, the amount you have to pay will not be 432 yen.", "input: 1079 output: :(\n\nThere is no possible price before tax for which you have to pay 1079 yen with tax.", "input: 1001 output: 927\n\nIf the apple pie is priced 927 yen before tax, by rounding down 927 * 1.08 = 1001.16, you have to pay 1001 yen."], "Pid": "p02842", "ProblemText": "Task Description: Problem Statement\nTakahashi bought a piece of apple pie at ABC Confiserie. According to his memory, he paid N yen (the currency of Japan) for it.\nThe consumption tax rate for foods in this shop is 8 percent. That is, to buy an apple pie priced at X yen before tax, you have to pay X * 1.08 yen (rounded down to the nearest integer).\nTakahashi forgot the price of his apple pie before tax, X, and wants to know it again. Write a program that takes N as input and finds X. We assume X is an integer.\nIf there are multiple possible values for X, find any one of them. Also, Takahashi's memory of N, the amount he paid, may be incorrect. If no value could be X, report that fact.\nTask Constraint: 1 <= N <= 50000\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If there are values that could be X, the price of the apple pie before tax, print any one of them.\nIf there are multiple such values, printing any one of them will be accepted.\nIf no value could be X, print : (.\nTask Samples: input: 432 output: 400\n\nIf the apple pie is priced at 400 yen before tax, you have to pay 400 * 1.08 = 432 yen to buy one.\nOtherwise, the amount you have to pay will not be 432 yen.\ninput: 1079 output: :(\n\nThere is no possible price before tax for which you have to pay 1079 yen with tax.\ninput: 1001 output: 927\n\nIf the apple pie is priced 927 yen before tax, by rounding down 927 * 1.08 = 1001.16, you have to pay 1001 yen.\n\n" }, { "title": "", "content": "Problem Statement\nAt Coder Mart sells 1000000 of each of the six items below:\n\nRiceballs, priced at 100 yen (the currency of Japan) each\nSandwiches, priced at 101 yen each\nCookies, priced at 102 yen each\nCakes, priced at 103 yen each\nCandies, priced at 104 yen each\nComputers, priced at 105 yen each\n\nTakahashi wants to buy some of them that cost exactly X yen in total.\nDetermine whether this is possible.\n(Ignore consumption tax. )", "constraint": "1 <= X <= 100000\nX is an integer.", "input": "Input is given from Standard Input in the following format:\nX", "output": "If it is possible to buy some set of items that cost exactly X yen in total, print 1; otherwise, print 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 615 output: 1\n\nFor example, we can buy one of each kind of item, which will cost 100+101+102+103+104+105=615 yen in total.", "input: 217 output: 0\n\nNo set of items costs 217 yen in total."], "Pid": "p02843", "ProblemText": "Task Description: Problem Statement\nAt Coder Mart sells 1000000 of each of the six items below:\n\nRiceballs, priced at 100 yen (the currency of Japan) each\nSandwiches, priced at 101 yen each\nCookies, priced at 102 yen each\nCakes, priced at 103 yen each\nCandies, priced at 104 yen each\nComputers, priced at 105 yen each\n\nTakahashi wants to buy some of them that cost exactly X yen in total.\nDetermine whether this is possible.\n(Ignore consumption tax. )\nTask Constraint: 1 <= X <= 100000\nX is an integer.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: If it is possible to buy some set of items that cost exactly X yen in total, print 1; otherwise, print 0.\nTask Samples: input: 615 output: 1\n\nFor example, we can buy one of each kind of item, which will cost 100+101+102+103+104+105=615 yen in total.\ninput: 217 output: 0\n\nNo set of items costs 217 yen in total.\n\n" }, { "title": "", "content": "Problem Statement\nAt Coder Inc. has decided to lock the door of its office with a 3-digit PIN code.\nThe company has an N-digit lucky number, S. Takahashi, the president, will erase N-3 digits from S and concatenate the remaining 3 digits without changing the order to set the PIN code.\nHow many different PIN codes can he set this way?\nBoth the lucky number and the PIN code may begin with a 0.", "constraint": "4 <= N <= 30000\nS is a string of length N consisting of digits.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the number of different PIN codes Takahashi can set.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0224 output: 3\n\nTakahashi has the following options:\n\nErase the first digit of S and set 224.\nErase the second digit of S and set 024.\nErase the third digit of S and set 024.\nErase the fourth digit of S and set 022.\n\nThus, he can set three different PIN codes: 022,024, and 224.", "input: 6\n123123 output: 17", "input: 19\n3141592653589793238 output: 329"], "Pid": "p02844", "ProblemText": "Task Description: Problem Statement\nAt Coder Inc. has decided to lock the door of its office with a 3-digit PIN code.\nThe company has an N-digit lucky number, S. Takahashi, the president, will erase N-3 digits from S and concatenate the remaining 3 digits without changing the order to set the PIN code.\nHow many different PIN codes can he set this way?\nBoth the lucky number and the PIN code may begin with a 0.\nTask Constraint: 4 <= N <= 30000\nS is a string of length N consisting of digits.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the number of different PIN codes Takahashi can set.\nTask Samples: input: 4\n0224 output: 3\n\nTakahashi has the following options:\n\nErase the first digit of S and set 224.\nErase the second digit of S and set 024.\nErase the third digit of S and set 024.\nErase the fourth digit of S and set 022.\n\nThus, he can set three different PIN codes: 022,024, and 224.\ninput: 6\n123123 output: 17\ninput: 19\n3141592653589793238 output: 329\n\n" }, { "title": "", "content": "Problem Statement\nN people are standing in a queue, numbered 1,2,3, . . . , N from front to back. Each person wears a hat, which is red, blue, or green.\nThe person numbered i says:\n\n\"In front of me, exactly A_i people are wearing hats with the same color as mine. \"\n\nAssuming that all these statements are correct, find the number of possible combinations of colors of the N people's hats.\nSince the count can be enormous, compute it modulo 1000000007.", "constraint": "1 <= N <= 100000\n0 <= A_i <= N-1\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 A_3 . . . A_N", "output": "Print the number of possible combinations of colors of the N people's hats, modulo 1000000007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n0 1 2 3 4 5 output: 3\n\nWe have three possible combinations, as follows:\n\nRed, Red, Red, Red, Red, Red\nBlue, Blue, Blue, Blue, Blue, Blue\nGreen, Green, Green, Green, Green, Green", "input: 3\n0 0 0 output: 6", "input: 54\n0 0 1 0 1 2 1 2 3 2 3 3 4 4 5 4 6 5 7 8 5 6 6 7 7 8 8 9 9 10 10 11 9 12 10 13 14 11 11 12 12 13 13 14 14 15 15 15 16 16 16 17 17 17 output: 115295190"], "Pid": "p02845", "ProblemText": "Task Description: Problem Statement\nN people are standing in a queue, numbered 1,2,3, . . . , N from front to back. Each person wears a hat, which is red, blue, or green.\nThe person numbered i says:\n\n\"In front of me, exactly A_i people are wearing hats with the same color as mine. \"\n\nAssuming that all these statements are correct, find the number of possible combinations of colors of the N people's hats.\nSince the count can be enormous, compute it modulo 1000000007.\nTask Constraint: 1 <= N <= 100000\n0 <= A_i <= N-1\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 A_3 . . . A_N\nTask Output: Print the number of possible combinations of colors of the N people's hats, modulo 1000000007.\nTask Samples: input: 6\n0 1 2 3 4 5 output: 3\n\nWe have three possible combinations, as follows:\n\nRed, Red, Red, Red, Red, Red\nBlue, Blue, Blue, Blue, Blue, Blue\nGreen, Green, Green, Green, Green, Green\ninput: 3\n0 0 0 output: 6\ninput: 54\n0 0 1 0 1 2 1 2 3 2 3 3 4 4 5 4 6 5 7 8 5 6 6 7 7 8 8 9 9 10 10 11 9 12 10 13 14 11 11 12 12 13 13 14 14 15 15 15 16 16 16 17 17 17 output: 115295190\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi and Aoki are training for long-distance races in an infinitely long straight course running from west to east.\nThey start simultaneously at the same point and moves as follows towards the east:\n\nTakahashi runs A_1 meters per minute for the first T_1 minutes, then runs at A_2 meters per minute for the subsequent T_2 minutes, and alternates between these two modes forever.\nAoki runs B_1 meters per minute for the first T_1 minutes, then runs at B_2 meters per minute for the subsequent T_2 minutes, and alternates between these two modes forever.\n\nHow many times will Takahashi and Aoki meet each other, that is, come to the same point? We do not count the start of the run. If they meet infinitely many times, report that fact.", "constraint": "1 <= T_i <= 100000\n1 <= A_i <= 10^{10}\n1 <= B_i <= 10^{10}\nA_1 \\neq B_1\nA_2 \\neq B_2\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nT_1 T_2\nA_1 A_2\nB_1 B_2", "output": "Print the number of times Takahashi and Aoki will meet each other.\nIf they meet infinitely many times, print infinity instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2\n10 10\n12 4 output: 1\n\nThey will meet just once, \\frac{4}{3} minutes after they start, at \\frac{40}{3} meters from where they start.", "input: 100 1\n101 101\n102 1 output: infinity\n\nThey will meet 101,202,303,404,505,606, ... minutes after they start, that is, they will meet infinitely many times.", "input: 12000 15700\n3390000000 3810000000\n5550000000 2130000000 output: 113\n\nThe values in input may not fit into a 32-bit integer type."], "Pid": "p02846", "ProblemText": "Task Description: Problem Statement\nTakahashi and Aoki are training for long-distance races in an infinitely long straight course running from west to east.\nThey start simultaneously at the same point and moves as follows towards the east:\n\nTakahashi runs A_1 meters per minute for the first T_1 minutes, then runs at A_2 meters per minute for the subsequent T_2 minutes, and alternates between these two modes forever.\nAoki runs B_1 meters per minute for the first T_1 minutes, then runs at B_2 meters per minute for the subsequent T_2 minutes, and alternates between these two modes forever.\n\nHow many times will Takahashi and Aoki meet each other, that is, come to the same point? We do not count the start of the run. If they meet infinitely many times, report that fact.\nTask Constraint: 1 <= T_i <= 100000\n1 <= A_i <= 10^{10}\n1 <= B_i <= 10^{10}\nA_1 \\neq B_1\nA_2 \\neq B_2\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nT_1 T_2\nA_1 A_2\nB_1 B_2\nTask Output: Print the number of times Takahashi and Aoki will meet each other.\nIf they meet infinitely many times, print infinity instead.\nTask Samples: input: 1 2\n10 10\n12 4 output: 1\n\nThey will meet just once, \\frac{4}{3} minutes after they start, at \\frac{40}{3} meters from where they start.\ninput: 100 1\n101 101\n102 1 output: infinity\n\nThey will meet 101,202,303,404,505,606, ... minutes after they start, that is, they will meet infinitely many times.\ninput: 12000 15700\n3390000000 3810000000\n5550000000 2130000000 output: 113\n\nThe values in input may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement Given is a string S representing the day of the week today.\nS is SUN, MON, TUE, WED, THU, FRI, or SAT, for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday, respectively.\nAfter how many days is the next Sunday (tomorrow or later)?", "constraint": "S is SUN, MON, TUE, WED, THU, FRI, or SAT.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of days before the next Sunday.", "content_img": false, "lang": "en", "error": false, "samples": ["input: SAT output: 1\n\nIt is Saturday today, and tomorrow will be Sunday.", "input: SUN output: 7\n\nIt is Sunday today, and seven days later, it will be Sunday again."], "Pid": "p02847", "ProblemText": "Task Description: Problem Statement Given is a string S representing the day of the week today.\nS is SUN, MON, TUE, WED, THU, FRI, or SAT, for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday, respectively.\nAfter how many days is the next Sunday (tomorrow or later)?\nTask Constraint: S is SUN, MON, TUE, WED, THU, FRI, or SAT.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of days before the next Sunday.\nTask Samples: input: SAT output: 1\n\nIt is Saturday today, and tomorrow will be Sunday.\ninput: SUN output: 7\n\nIt is Sunday today, and seven days later, it will be Sunday again.\n\n" }, { "title": "", "content": "Problem Statement We have a string S consisting of uppercase English letters. Additionally, an integer N will be given.\nShift each character of S by N in alphabetical order (see below), and print the resulting string.\nWe assume that A follows Z. For example, shifting A by 2 results in C (A \\to B \\to C), and shifting Y by 3 results in B (Y \\to Z \\to A \\to B).", "constraint": "0 <= N <= 26\n1 <= |S| <= 10^4\nS consists of uppercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the string resulting from shifting each character of S by N in alphabetical order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\nABCXYZ output: CDEZAB\n\nNote that A follows Z.", "input: 0\nABCXYZ output: ABCXYZ", "input: 13\nABCDEFGHIJKLMNOPQRSTUVWXYZ output: NOPQRSTUVWXYZABCDEFGHIJKLM"], "Pid": "p02848", "ProblemText": "Task Description: Problem Statement We have a string S consisting of uppercase English letters. Additionally, an integer N will be given.\nShift each character of S by N in alphabetical order (see below), and print the resulting string.\nWe assume that A follows Z. For example, shifting A by 2 results in C (A \\to B \\to C), and shifting Y by 3 results in B (Y \\to Z \\to A \\to B).\nTask Constraint: 0 <= N <= 26\n1 <= |S| <= 10^4\nS consists of uppercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the string resulting from shifting each character of S by N in alphabetical order.\nTask Samples: input: 2\nABCXYZ output: CDEZAB\n\nNote that A follows Z.\ninput: 0\nABCXYZ output: ABCXYZ\ninput: 13\nABCDEFGHIJKLMNOPQRSTUVWXYZ output: NOPQRSTUVWXYZABCDEFGHIJKLM\n\n" }, { "title": "", "content": "Problem Statement Takahashi has come to an integer shop to buy an integer.\nThe shop sells the integers from 1 through 10^9. The integer N is sold for A * N + B * d(N) yen (the currency of Japan), where d(N) is the number of digits in the decimal notation of N.\nFind the largest integer that Takahashi can buy when he has X yen. If no integer can be bought, print 0.", "constraint": "All values in input are integers.\n1 <= A <= 10^9\n1 <= B <= 10^9\n1 <= X <= 10^{18}", "input": "Input is given from Standard Input in the following format:\nA B X", "output": "Print the greatest integer that Takahashi can buy. If no integer can be bought, print 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 7 100 output: 9\n\nThe integer 9 is sold for 10 * 9 + 7 * 1 = 97 yen, and this is the greatest integer that can be bought.\nSome of the other integers are sold for the following prices:\n\n10: 10 * 10 + 7 * 2 = 114 yen\n100: 10 * 100 + 7 * 3 = 1021 yen\n12345: 10 * 12345 + 7 * 5 = 123485 yen", "input: 2 1 100000000000 output: 1000000000\n\nHe can buy the largest integer that is sold. Note that input may not fit into a 32-bit integer type.", "input: 1000000000 1000000000 100 output: 0", "input: 1234 56789 314159265 output: 254309"], "Pid": "p02849", "ProblemText": "Task Description: Problem Statement Takahashi has come to an integer shop to buy an integer.\nThe shop sells the integers from 1 through 10^9. The integer N is sold for A * N + B * d(N) yen (the currency of Japan), where d(N) is the number of digits in the decimal notation of N.\nFind the largest integer that Takahashi can buy when he has X yen. If no integer can be bought, print 0.\nTask Constraint: All values in input are integers.\n1 <= A <= 10^9\n1 <= B <= 10^9\n1 <= X <= 10^{18}\nTask Input: Input is given from Standard Input in the following format:\nA B X\nTask Output: Print the greatest integer that Takahashi can buy. If no integer can be bought, print 0.\nTask Samples: input: 10 7 100 output: 9\n\nThe integer 9 is sold for 10 * 9 + 7 * 1 = 97 yen, and this is the greatest integer that can be bought.\nSome of the other integers are sold for the following prices:\n\n10: 10 * 10 + 7 * 2 = 114 yen\n100: 10 * 100 + 7 * 3 = 1021 yen\n12345: 10 * 12345 + 7 * 5 = 123485 yen\ninput: 2 1 100000000000 output: 1000000000\n\nHe can buy the largest integer that is sold. Note that input may not fit into a 32-bit integer type.\ninput: 1000000000 1000000000 100 output: 0\ninput: 1234 56789 314159265 output: 254309\n\n" }, { "title": "", "content": "Problem Statement\nGiven is a tree G with N vertices.\nThe vertices are numbered 1 through N, and the i-th edge connects Vertex a_i and Vertex b_i.\nConsider painting the edges in G with some number of colors.\nWe want to paint them so that, for each vertex, the colors of the edges incident to that vertex are all different.\nAmong the colorings satisfying the condition above, construct one that uses the minimum number of colors.", "constraint": "2 <= N <= 10^5\n 1 <= a_i < b_i <= N\nAll values in input are integers.\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n\\vdots\na_{N-1} b_{N-1}", "output": "Print N lines.\nThe first line should contain K, the number of colors used.\nThe (i+1)-th line (1 <= i <= N-1) should contain c_i, the integer representing the color of the i-th edge, where 1 <= c_i <= K must hold.\nIf there are multiple colorings with the minimum number of colors that satisfy the condition, printing any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3 output: 2\n1\n2", "input: 8\n1 2\n2 3\n2 4\n2 5\n4 7\n5 6\n6 8 output: 4\n1\n2\n3\n4\n1\n1\n2", "input: 6\n1 2\n1 3\n1 4\n1 5\n1 6 output: 5\n1\n2\n3\n4\n5"], "Pid": "p02850", "ProblemText": "Task Description: Problem Statement\nGiven is a tree G with N vertices.\nThe vertices are numbered 1 through N, and the i-th edge connects Vertex a_i and Vertex b_i.\nConsider painting the edges in G with some number of colors.\nWe want to paint them so that, for each vertex, the colors of the edges incident to that vertex are all different.\nAmong the colorings satisfying the condition above, construct one that uses the minimum number of colors.\nTask Constraint: 2 <= N <= 10^5\n 1 <= a_i < b_i <= N\nAll values in input are integers.\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n\\vdots\na_{N-1} b_{N-1}\nTask Output: Print N lines.\nThe first line should contain K, the number of colors used.\nThe (i+1)-th line (1 <= i <= N-1) should contain c_i, the integer representing the color of the i-th edge, where 1 <= c_i <= K must hold.\nIf there are multiple colorings with the minimum number of colors that satisfy the condition, printing any of them will be accepted.\nTask Samples: input: 3\n1 2\n2 3 output: 2\n1\n2\ninput: 8\n1 2\n2 3\n2 4\n2 5\n4 7\n5 6\n6 8 output: 4\n1\n2\n3\n4\n1\n1\n2\ninput: 6\n1 2\n1 3\n1 4\n1 5\n1 6 output: 5\n1\n2\n3\n4\n5\n\n" }, { "title": "", "content": "Problem Statement Given are a sequence of N positive integers A_1, A_2, \\ldots, A_N, and a positive integer K.\nFind the number of non-empty contiguous subsequences in A such that the remainder when dividing the sum of its elements by K is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences.", "constraint": "All values in input are integers.\n1 <= N <= 2* 10^5\n1 <= K <= 10^9\n1 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\cdots A_N", "output": "Print the number of subsequences that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n1 4 2 3 5 output: 4\n\nFour sequences satisfy the condition: (1), (4,2), (1,4,2), and (5).", "input: 8 4\n4 2 4 2 4 2 4 2 output: 7\n\n(4,2) is counted four times, and (2,4) is counted three times.", "input: 10 7\n14 15 92 65 35 89 79 32 38 46 output: 8"], "Pid": "p02851", "ProblemText": "Task Description: Problem Statement Given are a sequence of N positive integers A_1, A_2, \\ldots, A_N, and a positive integer K.\nFind the number of non-empty contiguous subsequences in A such that the remainder when dividing the sum of its elements by K is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences.\nTask Constraint: All values in input are integers.\n1 <= N <= 2* 10^5\n1 <= K <= 10^9\n1 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\cdots A_N\nTask Output: Print the number of subsequences that satisfy the condition.\nTask Samples: input: 5 4\n1 4 2 3 5 output: 4\n\nFour sequences satisfy the condition: (1), (4,2), (1,4,2), and (5).\ninput: 8 4\n4 2 4 2 4 2 4 2 output: 7\n\n(4,2) is counted four times, and (2,4) is counted three times.\ninput: 10 7\n14 15 92 65 35 89 79 32 38 46 output: 8\n\n" }, { "title": "", "content": "Problem Statement Takahashi is playing a board game called Sugoroku.\nOn the board, there are N + 1 squares numbered 0 to N. Takahashi starts at Square 0, and he has to stop exactly at Square N to win the game.\nThe game uses a roulette with the M numbers from 1 to M. In each turn, Takahashi spins the roulette. If the number x comes up when he is at Square s, he moves to Square s+x. If this makes him go beyond Square N, he loses the game.\nAdditionally, some of the squares are Game Over Squares. He also loses the game if he stops at one of those squares. You are given a string S of length N + 1, representing which squares are Game Over Squares. For each i (0 <= i <= N), Square i is a Game Over Square if S[i] = 1 and not if S[i] = 0.\nFind the sequence of numbers coming up in the roulette in which Takahashi can win the game in the fewest number of turns possible. If there are multiple such sequences, find the lexicographically smallest such sequence. If Takahashi cannot win the game, print -1.", "constraint": "1 <= N <= 10^5\n1 <= M <= 10^5\n|S| = N + 1\nS consists of 0 and 1.\nS[0] = 0\nS[N] = 0", "input": "Input is given from Standard Input in the following format:\nN M\nS", "output": "If Takahashi can win the game, print the lexicographically smallest sequence among the shortest sequences of numbers coming up in the roulette in which Takahashi can win the game, with spaces in between.\nIf Takahashi cannot win the game, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 3\n0001000100 output: 1 3 2 3\n\nIf the numbers 1,3,2,3 come up in this order, Takahashi can reach Square 9 via Square 1,4, and 6. He cannot reach Square 9 in three or fewer turns, and this is the lexicographically smallest sequence in which he reaches Square 9 in four turns.", "input: 5 4\n011110 output: -1\n\nTakahashi cannot reach Square 5.", "input: 6 6\n0101010 output: 6"], "Pid": "p02852", "ProblemText": "Task Description: Problem Statement Takahashi is playing a board game called Sugoroku.\nOn the board, there are N + 1 squares numbered 0 to N. Takahashi starts at Square 0, and he has to stop exactly at Square N to win the game.\nThe game uses a roulette with the M numbers from 1 to M. In each turn, Takahashi spins the roulette. If the number x comes up when he is at Square s, he moves to Square s+x. If this makes him go beyond Square N, he loses the game.\nAdditionally, some of the squares are Game Over Squares. He also loses the game if he stops at one of those squares. You are given a string S of length N + 1, representing which squares are Game Over Squares. For each i (0 <= i <= N), Square i is a Game Over Square if S[i] = 1 and not if S[i] = 0.\nFind the sequence of numbers coming up in the roulette in which Takahashi can win the game in the fewest number of turns possible. If there are multiple such sequences, find the lexicographically smallest such sequence. If Takahashi cannot win the game, print -1.\nTask Constraint: 1 <= N <= 10^5\n1 <= M <= 10^5\n|S| = N + 1\nS consists of 0 and 1.\nS[0] = 0\nS[N] = 0\nTask Input: Input is given from Standard Input in the following format:\nN M\nS\nTask Output: If Takahashi can win the game, print the lexicographically smallest sequence among the shortest sequences of numbers coming up in the roulette in which Takahashi can win the game, with spaces in between.\nIf Takahashi cannot win the game, print -1.\nTask Samples: input: 9 3\n0001000100 output: 1 3 2 3\n\nIf the numbers 1,3,2,3 come up in this order, Takahashi can reach Square 9 via Square 1,4, and 6. He cannot reach Square 9 in three or fewer turns, and this is the lexicographically smallest sequence in which he reaches Square 9 in four turns.\ninput: 5 4\n011110 output: -1\n\nTakahashi cannot reach Square 5.\ninput: 6 6\n0101010 output: 6\n\n" }, { "title": "", "content": "Problem Statement\nWe held two competitions: Coding Contest and Robot Maneuver.\nIn each competition, the contestants taking the 3-rd, 2-nd, and 1-st places receive 100000,200000, and 300000 yen (the currency of Japan), respectively. Furthermore, a contestant taking the first place in both competitions receives an additional 400000 yen.\nDISCO-Kun took the X-th place in Coding Contest and the Y-th place in Robot Maneuver.\nFind the total amount of money he earned.", "constraint": "1 <= X <= 205\n1 <= Y <= 205\nX and Y are integers.", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "Print the amount of money DISCO-Kun earned, as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 output: 1000000\n\nIn this case, he earned 300000 yen in Coding Contest and another 300000 yen in Robot Maneuver. Furthermore, as he won both competitions, he got an additional 400000 yen.\nIn total, he made 300000 + 300000 + 400000 = 1000000 yen.", "input: 3 101 output: 100000\n\nIn this case, he earned 100000 yen in Coding Contest.", "input: 4 4 output: 0\n\nIn this case, unfortunately, he was the highest-ranked contestant without prize money in both competitions."], "Pid": "p02853", "ProblemText": "Task Description: Problem Statement\nWe held two competitions: Coding Contest and Robot Maneuver.\nIn each competition, the contestants taking the 3-rd, 2-nd, and 1-st places receive 100000,200000, and 300000 yen (the currency of Japan), respectively. Furthermore, a contestant taking the first place in both competitions receives an additional 400000 yen.\nDISCO-Kun took the X-th place in Coding Contest and the Y-th place in Robot Maneuver.\nFind the total amount of money he earned.\nTask Constraint: 1 <= X <= 205\n1 <= Y <= 205\nX and Y are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: Print the amount of money DISCO-Kun earned, as an integer.\nTask Samples: input: 1 1 output: 1000000\n\nIn this case, he earned 300000 yen in Coding Contest and another 300000 yen in Robot Maneuver. Furthermore, as he won both competitions, he got an additional 400000 yen.\nIn total, he made 300000 + 300000 + 400000 = 1000000 yen.\ninput: 3 101 output: 100000\n\nIn this case, he earned 100000 yen in Coding Contest.\ninput: 4 4 output: 0\n\nIn this case, unfortunately, he was the highest-ranked contestant without prize money in both competitions.\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi, who works at DISCO, is standing before an iron bar.\nThe bar has N-1 notches, which divide the bar into N sections. The i-th section from the left has a length of A_i millimeters.\nTakahashi wanted to choose a notch and cut the bar at that point into two parts with the same length.\nHowever, this may not be possible as is, so he will do the following operations some number of times before he does the cut:\n\nChoose one section and expand it, increasing its length by 1 millimeter. Doing this operation once costs 1 yen (the currency of Japan).\nChoose one section of length at least 2 millimeters and shrink it, decreasing its length by 1 millimeter. Doing this operation once costs 1 yen.\n\nFind the minimum amount of money needed before cutting the bar into two parts with the same length.", "constraint": "2 <= N <= 200000\n1 <= A_i <= 2020202020\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 A_3 . . . A_N", "output": "Print an integer representing the minimum amount of money needed before cutting the bar into two parts with the same length.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 4 3 output: 3\n\nThe initial lengths of the sections are [2,4,3] (in millimeters). Takahashi can cut the bar equally after doing the following operations for 3 yen:\n\nShrink the second section from the left. The lengths of the sections are now [2,3,3].\nShrink the first section from the left. The lengths of the sections are now [1,3,3].\nShrink the second section from the left. The lengths of the sections are now [1,2,3], and we can cut the bar at the second notch from the left into two parts of length 3 each.", "input: 12\n100 104 102 105 103 103 101 105 104 102 104 101 output: 0"], "Pid": "p02854", "ProblemText": "Task Description: Problem Statement\nTakahashi, who works at DISCO, is standing before an iron bar.\nThe bar has N-1 notches, which divide the bar into N sections. The i-th section from the left has a length of A_i millimeters.\nTakahashi wanted to choose a notch and cut the bar at that point into two parts with the same length.\nHowever, this may not be possible as is, so he will do the following operations some number of times before he does the cut:\n\nChoose one section and expand it, increasing its length by 1 millimeter. Doing this operation once costs 1 yen (the currency of Japan).\nChoose one section of length at least 2 millimeters and shrink it, decreasing its length by 1 millimeter. Doing this operation once costs 1 yen.\n\nFind the minimum amount of money needed before cutting the bar into two parts with the same length.\nTask Constraint: 2 <= N <= 200000\n1 <= A_i <= 2020202020\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 A_3 . . . A_N\nTask Output: Print an integer representing the minimum amount of money needed before cutting the bar into two parts with the same length.\nTask Samples: input: 3\n2 4 3 output: 3\n\nThe initial lengths of the sections are [2,4,3] (in millimeters). Takahashi can cut the bar equally after doing the following operations for 3 yen:\n\nShrink the second section from the left. The lengths of the sections are now [2,3,3].\nShrink the first section from the left. The lengths of the sections are now [1,3,3].\nShrink the second section from the left. The lengths of the sections are now [1,2,3], and we can cut the bar at the second notch from the left into two parts of length 3 each.\ninput: 12\n100 104 102 105 103 103 101 105 104 102 104 101 output: 0\n\n" }, { "title": "", "content": "Problem Statement\nChokudai made a rectangular cake for contestants in DDCC 2020 Finals.\nThe cake has H - 1 horizontal notches and W - 1 vertical notches, which divide the cake into H * W equal sections. K of these sections has a strawberry on top of each of them.\nThe positions of the strawberries are given to you as H * W characters s_{i, j} (1 <= i <= H, 1 <= j <= W). If s_{i, j} is #, the section at the i-th row from the top and the j-th column from the left contains a strawberry; if s_{i, j} is . , the section does not contain one. There are exactly K occurrences of #s.\nTakahashi wants to cut this cake into K pieces and serve them to the contestants. Each of these pieces must satisfy the following conditions:\n\nHas a rectangular shape.\nContains exactly one strawberry.\n\nOne possible way to cut the cake is shown below:\n\nFind one way to cut the cake and satisfy the condition. We can show that this is always possible, regardless of the number and positions of the strawberries.", "constraint": "1 <= H <= 300\n1 <= W <= 300\n1 <= K <= H * W\ns_{i, j} is # or ..\nThere are exactly K occurrences of # in s.", "input": "Input is given from Standard Input in the following format:\nH W K\ns_{1,1} s_{1,2} \\cdots s_{1, W}\ns_{2,1} s_{2,2} \\cdots s_{2, W}\n:\ns_{H, 1} s_{H, 2} \\cdots s_{H, W}", "output": "Assign the numbers 1,2,3, \\dots, K to the K pieces obtained after the cut, in any order. Then, let a_{i, j} be the number representing the piece containing the section at the i-th row from the top and the j-th column from the left of the cake. Output should be in the following format:\na_{1,1} \\ a_{1,2} \\ \\cdots \\ a_{1, W}\na_{2,1} \\ a_{2,2} \\ \\cdots \\ a_{2, W}\n:\na_{H, 1} \\ a_{H, 2} \\ \\cdots \\ a_{H, W}\n\nIf multiple solutions exist, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 5\n#.#\n.#.\n#.# output: 1 2 2\n1 3 4\n5 5 4\n\nOne way to cut this cake is shown below:", "input: 3 7 7\n#...#.#\n..#...#\n.#..#.. output: 1 1 2 2 3 4 4\n6 6 2 2 3 5 5\n6 6 7 7 7 7 7\n\nOne way to cut this cake is shown below:", "input: 13 21 106\n.....................\n.####.####.####.####.\n..#.#..#.#.#....#....\n..#.#..#.#.#....#....\n..#.#..#.#.#....#....\n.####.####.####.####.\n.....................\n.####.####.####.####.\n....#.#..#....#.#..#.\n.####.#..#.####.#..#.\n.#....#..#.#....#..#.\n.####.####.####.####.\n..................... output: 12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50\n12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50\n12 12 56 89 89 89 60 104 82 31 31 46 13 24 35 35 61 61 39 50 50\n12 12 67 67 100 100 60 9 9 42 42 57 13 24 6 72 72 72 72 72 72\n12 12 78 5 5 5 20 20 20 53 68 68 90 24 6 83 83 83 83 83 83\n16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21\n16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21\n32 32 43 54 65 65 80 11 106 95 22 22 33 44 55 55 70 1 96 85 85\n32 32 43 54 76 76 91 11 106 84 84 4 99 66 66 66 81 1 96 74 74\n14 14 3 98 87 87 102 11 73 73 73 4 99 88 77 77 92 92 63 63 63\n25 25 3 98 87 87 7 29 62 62 62 15 99 88 77 77 103 19 30 52 52\n36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41\n36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41"], "Pid": "p02855", "ProblemText": "Task Description: Problem Statement\nChokudai made a rectangular cake for contestants in DDCC 2020 Finals.\nThe cake has H - 1 horizontal notches and W - 1 vertical notches, which divide the cake into H * W equal sections. K of these sections has a strawberry on top of each of them.\nThe positions of the strawberries are given to you as H * W characters s_{i, j} (1 <= i <= H, 1 <= j <= W). If s_{i, j} is #, the section at the i-th row from the top and the j-th column from the left contains a strawberry; if s_{i, j} is . , the section does not contain one. There are exactly K occurrences of #s.\nTakahashi wants to cut this cake into K pieces and serve them to the contestants. Each of these pieces must satisfy the following conditions:\n\nHas a rectangular shape.\nContains exactly one strawberry.\n\nOne possible way to cut the cake is shown below:\n\nFind one way to cut the cake and satisfy the condition. We can show that this is always possible, regardless of the number and positions of the strawberries.\nTask Constraint: 1 <= H <= 300\n1 <= W <= 300\n1 <= K <= H * W\ns_{i, j} is # or ..\nThere are exactly K occurrences of # in s.\nTask Input: Input is given from Standard Input in the following format:\nH W K\ns_{1,1} s_{1,2} \\cdots s_{1, W}\ns_{2,1} s_{2,2} \\cdots s_{2, W}\n:\ns_{H, 1} s_{H, 2} \\cdots s_{H, W}\nTask Output: Assign the numbers 1,2,3, \\dots, K to the K pieces obtained after the cut, in any order. Then, let a_{i, j} be the number representing the piece containing the section at the i-th row from the top and the j-th column from the left of the cake. Output should be in the following format:\na_{1,1} \\ a_{1,2} \\ \\cdots \\ a_{1, W}\na_{2,1} \\ a_{2,2} \\ \\cdots \\ a_{2, W}\n:\na_{H, 1} \\ a_{H, 2} \\ \\cdots \\ a_{H, W}\n\nIf multiple solutions exist, any of them will be accepted.\nTask Samples: input: 3 3 5\n#.#\n.#.\n#.# output: 1 2 2\n1 3 4\n5 5 4\n\nOne way to cut this cake is shown below:\ninput: 3 7 7\n#...#.#\n..#...#\n.#..#.. output: 1 1 2 2 3 4 4\n6 6 2 2 3 5 5\n6 6 7 7 7 7 7\n\nOne way to cut this cake is shown below:\ninput: 13 21 106\n.....................\n.####.####.####.####.\n..#.#..#.#.#....#....\n..#.#..#.#.#....#....\n..#.#..#.#.#....#....\n.####.####.####.####.\n.....................\n.####.####.####.####.\n....#.#..#....#.#..#.\n.####.#..#.####.#..#.\n.#....#..#.#....#..#.\n.####.####.####.####.\n..................... output: 12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50\n12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50\n12 12 56 89 89 89 60 104 82 31 31 46 13 24 35 35 61 61 39 50 50\n12 12 67 67 100 100 60 9 9 42 42 57 13 24 6 72 72 72 72 72 72\n12 12 78 5 5 5 20 20 20 53 68 68 90 24 6 83 83 83 83 83 83\n16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21\n16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21\n32 32 43 54 65 65 80 11 106 95 22 22 33 44 55 55 70 1 96 85 85\n32 32 43 54 76 76 91 11 106 84 84 4 99 66 66 66 81 1 96 74 74\n14 14 3 98 87 87 102 11 73 73 73 4 99 88 77 77 92 92 63 63 63\n25 25 3 98 87 87 7 29 62 62 62 15 99 88 77 77 103 19 30 52 52\n36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41\n36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41\n\n" }, { "title": "", "content": "Problem Statement\nN programmers are going to participate in the preliminary stage of DDCC 20XX. Due to the size of the venue, however, at most 9 contestants can participate in the finals.\nThe preliminary stage consists of several rounds, which will take place as follows:\n\nAll the N contestants will participate in the first round.\nWhen X contestants participate in some round, the number of contestants advancing to the next round will be decided as follows:\nThe organizer will choose two consecutive digits in the decimal notation of X, and replace them with the sum of these digits. The number resulted will be the number of contestants advancing to the next round.\nFor example, when X = 2378, the number of contestants advancing to the next round will be 578 (if 2 and 3 are chosen), 2108 (if 3 and 7 are chosen), or 2315 (if 7 and 8 are chosen).\nWhen X = 100, the number of contestants advancing to the next round will be 10, no matter which two digits are chosen.\nThe preliminary stage ends when 9 or fewer contestants remain.\n\nRingo, the chief organizer, wants to hold as many rounds as possible.\nFind the maximum possible number of rounds in the preliminary stage.\nSince the number of contestants, N, can be enormous, it is given to you as two integer sequences d_1, \\ldots, d_M and c_1, \\ldots, c_M, which means the following: the decimal notation of N consists of c_1 + c_2 + \\ldots + c_M digits, whose first c_1 digits are all d_1, the following c_2 digits are all d_2, \\ldots, and the last c_M digits are all d_M.", "constraint": "1 <= M <= 200000\n0 <= d_i <= 9\nd_1 \\neq 0\nd_i \\neq d_{i+1}\nc_i >= 1\n2 <= c_1 + \\ldots + c_M <= 10^{15}", "input": "Input is given from Standard Input in the following format:\nM\nd_1 c_1\nd_2 c_2\n:\nd_M c_M", "output": "Print the maximum possible number of rounds in the preliminary stage.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n2 2\n9 1 output: 3\n\nIn this case, N = 229 contestants will participate in the first round. One possible progression of the preliminary stage is as follows:\n\n229 contestants participate in Round 1,49 contestants participate in Round 2,13 contestants participate in Round 3, and 4 contestants advance to the finals.\n\nHere, three rounds take place in the preliminary stage, which is the maximum possible number.", "input: 3\n1 1\n0 8\n7 1 output: 9\n\nIn this case, 1000000007 will participate in the first round."], "Pid": "p02856", "ProblemText": "Task Description: Problem Statement\nN programmers are going to participate in the preliminary stage of DDCC 20XX. Due to the size of the venue, however, at most 9 contestants can participate in the finals.\nThe preliminary stage consists of several rounds, which will take place as follows:\n\nAll the N contestants will participate in the first round.\nWhen X contestants participate in some round, the number of contestants advancing to the next round will be decided as follows:\nThe organizer will choose two consecutive digits in the decimal notation of X, and replace them with the sum of these digits. The number resulted will be the number of contestants advancing to the next round.\nFor example, when X = 2378, the number of contestants advancing to the next round will be 578 (if 2 and 3 are chosen), 2108 (if 3 and 7 are chosen), or 2315 (if 7 and 8 are chosen).\nWhen X = 100, the number of contestants advancing to the next round will be 10, no matter which two digits are chosen.\nThe preliminary stage ends when 9 or fewer contestants remain.\n\nRingo, the chief organizer, wants to hold as many rounds as possible.\nFind the maximum possible number of rounds in the preliminary stage.\nSince the number of contestants, N, can be enormous, it is given to you as two integer sequences d_1, \\ldots, d_M and c_1, \\ldots, c_M, which means the following: the decimal notation of N consists of c_1 + c_2 + \\ldots + c_M digits, whose first c_1 digits are all d_1, the following c_2 digits are all d_2, \\ldots, and the last c_M digits are all d_M.\nTask Constraint: 1 <= M <= 200000\n0 <= d_i <= 9\nd_1 \\neq 0\nd_i \\neq d_{i+1}\nc_i >= 1\n2 <= c_1 + \\ldots + c_M <= 10^{15}\nTask Input: Input is given from Standard Input in the following format:\nM\nd_1 c_1\nd_2 c_2\n:\nd_M c_M\nTask Output: Print the maximum possible number of rounds in the preliminary stage.\nTask Samples: input: 2\n2 2\n9 1 output: 3\n\nIn this case, N = 229 contestants will participate in the first round. One possible progression of the preliminary stage is as follows:\n\n229 contestants participate in Round 1,49 contestants participate in Round 2,13 contestants participate in Round 3, and 4 contestants advance to the finals.\n\nHere, three rounds take place in the preliminary stage, which is the maximum possible number.\ninput: 3\n1 1\n0 8\n7 1 output: 9\n\nIn this case, 1000000007 will participate in the first round.\n\n" }, { "title": "", "content": "Problem Statement\nThis is an interactive task.\nWe have 2N balls arranged in a row, numbered 1,2,3, . . . , 2N from left to right, where N is an odd number. Among them, there are N red balls and N blue balls.\nWhile blindfolded, you are challenged to guess the color of every ball correctly, by asking at most 210 questions of the following form:\n\nYou choose any N of the 2N balls and ask whether there are more red balls than blue balls or not among those N balls.\n\nNow, let us begin. note: Notice\n\nFlush Standard Output each time you print something. Failure to do so may result in TLE.\nImmediately terminate your program after printing your guess (or receiving the -1 response). Otherwise, the verdict will be indeterminate.\nIf your program prints something invalid, the verdict will be indeterminate. Sample Input and Output\nInput\nOutput\n3\n? 1 2 3\nRed\n? 2 4 6\nBlue\n! RRBBRB\nIn this sample, N = 3, and the colors of Ball 1,2,3,4,5,6 are red, red, blue, blue, red, blue, respectively.\n\nIn the first question, there are two red balls and one blue ball among the balls 1,2,3, so the judge returns Red.\nIn the second question, there are one red ball and two blue balls among the balls 2,4,6, so the judge returns Blue.", "constraint": "1 <= N <= 99\nN is an odd number.", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p02857", "ProblemText": "Task Description: Problem Statement\nThis is an interactive task.\nWe have 2N balls arranged in a row, numbered 1,2,3, . . . , 2N from left to right, where N is an odd number. Among them, there are N red balls and N blue balls.\nWhile blindfolded, you are challenged to guess the color of every ball correctly, by asking at most 210 questions of the following form:\n\nYou choose any N of the 2N balls and ask whether there are more red balls than blue balls or not among those N balls.\n\nNow, let us begin. note: Notice\n\nFlush Standard Output each time you print something. Failure to do so may result in TLE.\nImmediately terminate your program after printing your guess (or receiving the -1 response). Otherwise, the verdict will be indeterminate.\nIf your program prints something invalid, the verdict will be indeterminate. Sample Input and Output\nInput\nOutput\n3\n? 1 2 3\nRed\n? 2 4 6\nBlue\n! RRBBRB\nIn this sample, N = 3, and the colors of Ball 1,2,3,4,5,6 are red, red, blue, blue, red, blue, respectively.\n\nIn the first question, there are two red balls and one blue ball among the balls 1,2,3, so the judge returns Red.\nIn the second question, there are one red ball and two blue balls among the balls 2,4,6, so the judge returns Blue.\nTask Constraint: 1 <= N <= 99\nN is an odd number.\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement\nIn 2937, DISCO creates a new universe called DISCOSMOS to celebrate its 1000-th anniversary.\nDISCOSMOS can be described as an H * W grid. Let (i, j) (1 <= i <= H, 1 <= j <= W) denote the square at the i-th row from the top and the j-th column from the left.\nAt time 0, one robot will be placed onto each square. Each robot is one of the following three types:\n\nType-H: Does not move at all.\nType-R: If a robot of this type is in (i, j) at time t, it will be in (i, j+1) at time t+1. If it is in (i, W) at time t, however, it will be instead in (i, 1) at time t+1. (The robots do not collide with each other. )\nType-D: If a robot of this type is in (i, j) at time t, it will be in (i+1, j) at time t+1. If it is in (H, j) at time t, however, it will be instead in (1, j) at time t+1.\n\nThere are 3^{H * W} possible ways to place these robots. In how many of them will every square be occupied by one robot at times 0, T, 2T, 3T, 4T, and all subsequent multiples of T?\nSince the count can be enormous, compute it modulo (10^9 + 7).", "constraint": "1 <= H <= 10^9\n1 <= W <= 10^9\n1 <= T <= 10^9\nH, W, T are all integers.", "input": "Input is given from Standard Input in the following format:\nH W T", "output": "Print the number of ways to place the robots that satisfy the condition, modulo (10^9 + 7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 1 output: 9\n\nShown below are some of the ways to place the robots that satisfy the condition, where ., >, and v stand for Type-H, Type-R, and Type-D, respectively:\n>> .. vv\n.. .. vv", "input: 869 120 1001 output: 672919729"], "Pid": "p02858", "ProblemText": "Task Description: Problem Statement\nIn 2937, DISCO creates a new universe called DISCOSMOS to celebrate its 1000-th anniversary.\nDISCOSMOS can be described as an H * W grid. Let (i, j) (1 <= i <= H, 1 <= j <= W) denote the square at the i-th row from the top and the j-th column from the left.\nAt time 0, one robot will be placed onto each square. Each robot is one of the following three types:\n\nType-H: Does not move at all.\nType-R: If a robot of this type is in (i, j) at time t, it will be in (i, j+1) at time t+1. If it is in (i, W) at time t, however, it will be instead in (i, 1) at time t+1. (The robots do not collide with each other. )\nType-D: If a robot of this type is in (i, j) at time t, it will be in (i+1, j) at time t+1. If it is in (H, j) at time t, however, it will be instead in (1, j) at time t+1.\n\nThere are 3^{H * W} possible ways to place these robots. In how many of them will every square be occupied by one robot at times 0, T, 2T, 3T, 4T, and all subsequent multiples of T?\nSince the count can be enormous, compute it modulo (10^9 + 7).\nTask Constraint: 1 <= H <= 10^9\n1 <= W <= 10^9\n1 <= T <= 10^9\nH, W, T are all integers.\nTask Input: Input is given from Standard Input in the following format:\nH W T\nTask Output: Print the number of ways to place the robots that satisfy the condition, modulo (10^9 + 7).\nTask Samples: input: 2 2 1 output: 9\n\nShown below are some of the ways to place the robots that satisfy the condition, where ., >, and v stand for Type-H, Type-R, and Type-D, respectively:\n>> .. vv\n.. .. vv\ninput: 869 120 1001 output: 672919729\n\n" }, { "title": "", "content": "Problem Statement Given is an integer r.\nHow many times is the area of a circle of radius r larger than the area of a circle of radius 1?\nIt can be proved that the answer is always an integer under the constraints given.", "constraint": "1 <= r <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nr", "output": "Print the area of a circle of radius r, divided by the area of a circle of radius 1, as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 4\n\nThe area of a circle of radius 2 is 4 times larger than the area of a circle of radius 1.\nNote that output must be an integer - for example, 4.0 will not be accepted.", "input: 100 output: 10000"], "Pid": "p02859", "ProblemText": "Task Description: Problem Statement Given is an integer r.\nHow many times is the area of a circle of radius r larger than the area of a circle of radius 1?\nIt can be proved that the answer is always an integer under the constraints given.\nTask Constraint: 1 <= r <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nr\nTask Output: Print the area of a circle of radius r, divided by the area of a circle of radius 1, as an integer.\nTask Samples: input: 2 output: 4\n\nThe area of a circle of radius 2 is 4 times larger than the area of a circle of radius 1.\nNote that output must be an integer - for example, 4.0 will not be accepted.\ninput: 100 output: 10000\n\n" }, { "title": "", "content": "Problem Statement Given are a positive integer N and a string S of length N consisting of lowercase English letters.\nDetermine whether the string is a concatenation of two copies of some string.\nThat is, determine whether there is a string T such that S = T + T.", "constraint": "1 <= N <= 100\nS consists of lowercase English letters.\n|S| = N", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "If S is a concatenation of two copies of some string, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\nabcabc output: Yes\n\nLet T = abc, and S = T + T.", "input: 6\nabcadc output: No", "input: 1\nz output: No"], "Pid": "p02860", "ProblemText": "Task Description: Problem Statement Given are a positive integer N and a string S of length N consisting of lowercase English letters.\nDetermine whether the string is a concatenation of two copies of some string.\nThat is, determine whether there is a string T such that S = T + T.\nTask Constraint: 1 <= N <= 100\nS consists of lowercase English letters.\n|S| = N\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: If S is a concatenation of two copies of some string, print Yes; otherwise, print No.\nTask Samples: input: 6\nabcabc output: Yes\n\nLet T = abc, and S = T + T.\ninput: 6\nabcadc output: No\ninput: 1\nz output: No\n\n" }, { "title": "", "content": "Problem Statement There are N towns in a coordinate plane. Town i is located at coordinates (x_i, y_i). The distance between Town i and Town j is \\sqrt{<=ft(x_i-x_j\\right)^2+<=ft(y_i-y_j\\right)^2}.\nThere are N! possible paths to visit all of these towns once. Let the length of a path be the distance covered when we start at the first town in the path, visit the second, third, \\dots, towns, and arrive at the last town (assume that we travel in a straight line from a town to another). Compute the average length of these N! paths.", "constraint": "2 <= N <= 8\n-1000 <= x_i <= 1000\n-1000 <= y_i <= 1000\n<=ft(x_i, y_i\\right) \\neq <=ft(x_j, y_j\\right) (if i \\neq j)\n(Added 21:12 JST) All values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print the average length of the paths.\nYour output will be judges as correct when the absolute difference from the judge's output is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0\n1 0\n0 1 output: 2.2761423749\n\nThere are six paths to visit the towns: 1 → 2 → 3,1 → 3 → 2,2 → 1 → 3,2 → 3 → 1,3 → 1 → 2, and 3 → 2 → 1.\nThe length of the path 1 → 2 → 3 is \\sqrt{<=ft(0-1\\right)^2+<=ft(0-0\\right)^2} + \\sqrt{<=ft(1-0\\right)^2+<=ft(0-1\\right)^2} = 1+\\sqrt{2}.\nBy calculating the lengths of the other paths in this way, we see that the average length of all routes is:\n\\frac{<=ft(1+\\sqrt{2}\\right)+<=ft(1+\\sqrt{2}\\right)+<=ft(2\\right)+<=ft(1+\\sqrt{2}\\right)+<=ft(2\\right)+<=ft(1+\\sqrt{2}\\right)}{6} = 2.276142...", "input: 2\n-879 981\n-866 890 output: 91.9238815543\n\nThere are two paths to visit the towns: 1 → 2 and 2 → 1. These paths have the same length.", "input: 8\n-406 10\n512 859\n494 362\n-955 -475\n128 553\n-986 -885\n763 77\n449 310 output: 7641.9817824387"], "Pid": "p02861", "ProblemText": "Task Description: Problem Statement There are N towns in a coordinate plane. Town i is located at coordinates (x_i, y_i). The distance between Town i and Town j is \\sqrt{<=ft(x_i-x_j\\right)^2+<=ft(y_i-y_j\\right)^2}.\nThere are N! possible paths to visit all of these towns once. Let the length of a path be the distance covered when we start at the first town in the path, visit the second, third, \\dots, towns, and arrive at the last town (assume that we travel in a straight line from a town to another). Compute the average length of these N! paths.\nTask Constraint: 2 <= N <= 8\n-1000 <= x_i <= 1000\n-1000 <= y_i <= 1000\n<=ft(x_i, y_i\\right) \\neq <=ft(x_j, y_j\\right) (if i \\neq j)\n(Added 21:12 JST) All values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print the average length of the paths.\nYour output will be judges as correct when the absolute difference from the judge's output is at most 10^{-6}.\nTask Samples: input: 3\n0 0\n1 0\n0 1 output: 2.2761423749\n\nThere are six paths to visit the towns: 1 → 2 → 3,1 → 3 → 2,2 → 1 → 3,2 → 3 → 1,3 → 1 → 2, and 3 → 2 → 1.\nThe length of the path 1 → 2 → 3 is \\sqrt{<=ft(0-1\\right)^2+<=ft(0-0\\right)^2} + \\sqrt{<=ft(1-0\\right)^2+<=ft(0-1\\right)^2} = 1+\\sqrt{2}.\nBy calculating the lengths of the other paths in this way, we see that the average length of all routes is:\n\\frac{<=ft(1+\\sqrt{2}\\right)+<=ft(1+\\sqrt{2}\\right)+<=ft(2\\right)+<=ft(1+\\sqrt{2}\\right)+<=ft(2\\right)+<=ft(1+\\sqrt{2}\\right)}{6} = 2.276142...\ninput: 2\n-879 981\n-866 890 output: 91.9238815543\n\nThere are two paths to visit the towns: 1 → 2 and 2 → 1. These paths have the same length.\ninput: 8\n-406 10\n512 859\n494 362\n-955 -475\n128 553\n-986 -885\n763 77\n449 310 output: 7641.9817824387\n\n" }, { "title": "", "content": "Problem Statement There is a knight - the chess piece - at the origin (0,0) of a two-dimensional grid.\nWhen the knight is at the square (i, j), it can be moved to either (i+1, j+2) or (i+2, j+1).\nIn how many ways can the knight reach the square (X, Y)?\nFind the number of ways modulo 10^9 + 7.", "constraint": "1 <= X <= 10^6\n1 <= Y <= 10^6\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "Print the number of ways for the knight to reach (X, Y) from (0,0), modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 output: 2\n\nThere are two ways: (0,0) \\to (1,2) \\to (3,3) and (0,0) \\to (2,1) \\to (3,3).", "input: 2 2 output: 0\n\nThe knight cannot reach (2,2).", "input: 999999 999999 output: 151840682\n\nPrint the number of ways modulo 10^9 + 7."], "Pid": "p02862", "ProblemText": "Task Description: Problem Statement There is a knight - the chess piece - at the origin (0,0) of a two-dimensional grid.\nWhen the knight is at the square (i, j), it can be moved to either (i+1, j+2) or (i+2, j+1).\nIn how many ways can the knight reach the square (X, Y)?\nFind the number of ways modulo 10^9 + 7.\nTask Constraint: 1 <= X <= 10^6\n1 <= Y <= 10^6\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: Print the number of ways for the knight to reach (X, Y) from (0,0), modulo 10^9 + 7.\nTask Samples: input: 3 3 output: 2\n\nThere are two ways: (0,0) \\to (1,2) \\to (3,3) and (0,0) \\to (2,1) \\to (3,3).\ninput: 2 2 output: 0\n\nThe knight cannot reach (2,2).\ninput: 999999 999999 output: 151840682\n\nPrint the number of ways modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement Takahashi is at an all-you-can-eat restaurant.\nThe restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.\nThe restaurant has the following rules:\n\nYou can only order one dish at a time. The dish ordered will be immediately served and ready to eat.\nYou cannot order the same kind of dish more than once.\nUntil you finish eating the dish already served, you cannot order a new dish.\nAfter T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.\n\nLet Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.\nWhat is the maximum possible happiness achieved by making optimal choices?", "constraint": "2 <= N <= 3000\n1 <= T <= 3000\n1 <= A_i <= 3000\n1 <= B_i <= 3000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN T\nA_1 B_1\n:\nA_N B_N", "output": "Print the maximum possible happiness Takahashi can achieve.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 60\n10 10\n100 100 output: 110\n\nBy ordering the first and second dishes in this order, Takahashi's happiness will be 110.\nNote that, if we manage to order a dish in time, we can spend any amount of time to eat it.", "input: 3 60\n10 10\n10 20\n10 30 output: 60\n\nTakahashi can eat all the dishes within 60 minutes.", "input: 3 60\n30 10\n30 20\n30 30 output: 50\n\nBy ordering the second and third dishes in this order, Takahashi's happiness will be 50.\nWe cannot order three dishes, in whatever order we place them.", "input: 10 100\n15 23\n20 18\n13 17\n24 12\n18 29\n19 27\n23 21\n18 20\n27 15\n22 25 output: 145"], "Pid": "p02863", "ProblemText": "Task Description: Problem Statement Takahashi is at an all-you-can-eat restaurant.\nThe restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.\nThe restaurant has the following rules:\n\nYou can only order one dish at a time. The dish ordered will be immediately served and ready to eat.\nYou cannot order the same kind of dish more than once.\nUntil you finish eating the dish already served, you cannot order a new dish.\nAfter T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.\n\nLet Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.\nWhat is the maximum possible happiness achieved by making optimal choices?\nTask Constraint: 2 <= N <= 3000\n1 <= T <= 3000\n1 <= A_i <= 3000\n1 <= B_i <= 3000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN T\nA_1 B_1\n:\nA_N B_N\nTask Output: Print the maximum possible happiness Takahashi can achieve.\nTask Samples: input: 2 60\n10 10\n100 100 output: 110\n\nBy ordering the first and second dishes in this order, Takahashi's happiness will be 110.\nNote that, if we manage to order a dish in time, we can spend any amount of time to eat it.\ninput: 3 60\n10 10\n10 20\n10 30 output: 60\n\nTakahashi can eat all the dishes within 60 minutes.\ninput: 3 60\n30 10\n30 20\n30 30 output: 50\n\nBy ordering the second and third dishes in this order, Takahashi's happiness will be 50.\nWe cannot order three dishes, in whatever order we place them.\ninput: 10 100\n15 23\n20 18\n13 17\n24 12\n18 29\n19 27\n23 21\n18 20\n27 15\n22 25 output: 145\n\n" }, { "title": "", "content": "Problem Statement We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns.\nThe current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squares in that column.\nBefore starting to work, you can choose at most K columns (possibly zero) and change the values of H_i for these columns to any integers of your choice between 0 and 10^9 (inclusive).\nDifferent values can be chosen for different columns.\nThen, you will create the modified artwork by repeating the following operation:\n\nChoose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted. )\n\nFind the minimum number of times you need to perform this operation.", "constraint": "1 <= N <= 300\n0 <= K <= N\n0 <= H_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nH_1 H_2 . . . H_N", "output": "Print the minimum number of operations required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1\n2 3 4 1 output: 3\n\nFor example, by changing the value of H_3 to 2, you can create the modified artwork by the following three operations:\n\nPaint black the 1-st through 4-th squares from the left in the 1-st row from the bottom.\nPaint black the 1-st through 3-rd squares from the left in the 2-nd row from the bottom.\nPaint black the 2-nd square from the left in the 3-rd row from the bottom.", "input: 6 2\n8 6 9 1 2 1 output: 7", "input: 10 0\n1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 output: 4999999996"], "Pid": "p02864", "ProblemText": "Task Description: Problem Statement We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns.\nThe current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squares in that column.\nBefore starting to work, you can choose at most K columns (possibly zero) and change the values of H_i for these columns to any integers of your choice between 0 and 10^9 (inclusive).\nDifferent values can be chosen for different columns.\nThen, you will create the modified artwork by repeating the following operation:\n\nChoose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted. )\n\nFind the minimum number of times you need to perform this operation.\nTask Constraint: 1 <= N <= 300\n0 <= K <= N\n0 <= H_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nH_1 H_2 . . . H_N\nTask Output: Print the minimum number of operations required.\nTask Samples: input: 4 1\n2 3 4 1 output: 3\n\nFor example, by changing the value of H_3 to 2, you can create the modified artwork by the following three operations:\n\nPaint black the 1-st through 4-th squares from the left in the 1-st row from the bottom.\nPaint black the 1-st through 3-rd squares from the left in the 2-nd row from the bottom.\nPaint black the 2-nd square from the left in the 3-rd row from the bottom.\ninput: 6 2\n8 6 9 1 2 1 output: 7\ninput: 10 0\n1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 output: 4999999996\n\n" }, { "title": "", "content": "Problem Statement How many ways are there to choose two distinct positive integers totaling N, disregarding the order?", "constraint": "1 <= N <= 10^6\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 1\n\nThere is only one way to choose two distinct integers totaling 4: to choose 1 and 3. (Choosing 3 and 1 is not considered different from this.)", "input: 999999 output: 499999"], "Pid": "p02865", "ProblemText": "Task Description: Problem Statement How many ways are there to choose two distinct positive integers totaling N, disregarding the order?\nTask Constraint: 1 <= N <= 10^6\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 4 output: 1\n\nThere is only one way to choose two distinct integers totaling 4: to choose 1 and 3. (Choosing 3 and 1 is not considered different from this.)\ninput: 999999 output: 499999\n\n" }, { "title": "", "content": "Problem Statement Given is an integer sequence D_1, . . . , D_N of N elements. Find the number, modulo 998244353, of trees with N vertices numbered 1 to N that satisfy the following condition:\n\nFor every integer i from 1 to N, the distance between Vertex 1 and Vertex i is D_i. note: Notes\nA tree of N vertices is a connected undirected graph with N vertices and N-1 edges, and the distance between two vertices are the number of edges in the shortest path between them.\nTwo trees are considered different if and only if there are two vertices x and y such that there is an edge between x and y in one of those trees and not in the other.", "constraint": "1 <= N <= 10^5\n0 <= D_i <= N-1", "input": "Input is given from Standard Input in the following format:\nN\nD_1 D_2 . . . D_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 1 1 2 output: 2\n\nFor example, a tree with edges (1,2), (1,3), and (2,4) satisfies the condition.", "input: 4\n1 1 1 1 output: 0", "input: 7\n0 3 2 1 2 2 1 output: 24"], "Pid": "p02866", "ProblemText": "Task Description: Problem Statement Given is an integer sequence D_1, . . . , D_N of N elements. Find the number, modulo 998244353, of trees with N vertices numbered 1 to N that satisfy the following condition:\n\nFor every integer i from 1 to N, the distance between Vertex 1 and Vertex i is D_i. note: Notes\nA tree of N vertices is a connected undirected graph with N vertices and N-1 edges, and the distance between two vertices are the number of edges in the shortest path between them.\nTwo trees are considered different if and only if there are two vertices x and y such that there is an edge between x and y in one of those trees and not in the other.\nTask Constraint: 1 <= N <= 10^5\n0 <= D_i <= N-1\nTask Input: Input is given from Standard Input in the following format:\nN\nD_1 D_2 . . . D_N\nTask Output: Print the answer.\nTask Samples: input: 4\n0 1 1 2 output: 2\n\nFor example, a tree with edges (1,2), (1,3), and (2,4) satisfies the condition.\ninput: 4\n1 1 1 1 output: 0\ninput: 7\n0 3 2 1 2 2 1 output: 24\n\n" }, { "title": "", "content": "Problem Statement Given are two integer sequences of N elements each: A_1, . . . , A_N and B_1, . . . , B_N.\nDetermine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i <= B_i holds:\n\nChoose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.", "constraint": "2 <= N <= 10^5\n1 <= A_i,B_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N", "output": "If the objective is achievable, print Yes; if it is not, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 3 2\n1 2 3 output: Yes\n\nWe should swap the values of A_2 and A_3.", "input: 3\n1 2 3\n2 2 2 output: No", "input: 6\n3 1 2 6 3 4\n2 2 8 3 4 3 output: Yes"], "Pid": "p02867", "ProblemText": "Task Description: Problem Statement Given are two integer sequences of N elements each: A_1, . . . , A_N and B_1, . . . , B_N.\nDetermine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i <= B_i holds:\n\nChoose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.\nTask Constraint: 2 <= N <= 10^5\n1 <= A_i,B_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N\nTask Output: If the objective is achievable, print Yes; if it is not, print No.\nTask Samples: input: 3\n1 3 2\n1 2 3 output: Yes\n\nWe should swap the values of A_2 and A_3.\ninput: 3\n1 2 3\n2 2 2 output: No\ninput: 6\n3 1 2 6 3 4\n2 2 8 3 4 3 output: Yes\n\n" }, { "title": "", "content": "Problem Statement We have N points numbered 1 to N arranged in a line in this order.\nTakahashi decides to make an undirected graph, using these points as the vertices.\nIn the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph.\nThe i-th operation is as follows:\n\nThe operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i <= s < t <= R_i, add an edge of length C_i between Vertex s and Vertex t.\n\nThe integers L_1, . . . , L_M, R_1, . . . , R_M, C_1, . . . , C_M are all given as input.\nTakahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.", "constraint": "2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= L_i < R_i <= N\n1 <= C_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN M\nL_1 R_1 C_1\n:\nL_M R_M C_M", "output": "Print the length of the shortest path from Vertex 1 to Vertex N in the final graph.\nIf there is no shortest path, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n1 3 2\n2 4 3\n1 4 6 output: 5\n\nWe have an edge of length 2 between Vertex 1 and Vertex 2, and an edge of length 3 between Vertex 2 and Vertex 4, so there is a path of length 5 between Vertex 1 and Vertex 4.", "input: 4 2\n1 2 1\n3 4 2 output: -1", "input: 10 7\n1 5 18\n3 4 8\n1 3 5\n4 7 10\n5 9 8\n6 10 5\n8 10 3 output: 28"], "Pid": "p02868", "ProblemText": "Task Description: Problem Statement We have N points numbered 1 to N arranged in a line in this order.\nTakahashi decides to make an undirected graph, using these points as the vertices.\nIn the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph.\nThe i-th operation is as follows:\n\nThe operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i <= s < t <= R_i, add an edge of length C_i between Vertex s and Vertex t.\n\nThe integers L_1, . . . , L_M, R_1, . . . , R_M, C_1, . . . , C_M are all given as input.\nTakahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.\nTask Constraint: 2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= L_i < R_i <= N\n1 <= C_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN M\nL_1 R_1 C_1\n:\nL_M R_M C_M\nTask Output: Print the length of the shortest path from Vertex 1 to Vertex N in the final graph.\nIf there is no shortest path, print -1 instead.\nTask Samples: input: 4 3\n1 3 2\n2 4 3\n1 4 6 output: 5\n\nWe have an edge of length 2 between Vertex 1 and Vertex 2, and an edge of length 3 between Vertex 2 and Vertex 4, so there is a path of length 5 between Vertex 1 and Vertex 4.\ninput: 4 2\n1 2 1\n3 4 2 output: -1\ninput: 10 7\n1 5 18\n3 4 8\n1 3 5\n4 7 10\n5 9 8\n6 10 5\n8 10 3 output: 28\n\n" }, { "title": "", "content": "Problem Statement Given are positive integers N and K.\nDetermine if the 3N integers K, K+1, . . . , K+3N-1 can be partitioned into N triples (a_1, b_1, c_1), . . . , (a_N, b_N, c_N) so that the condition below is satisfied. Any of the integers K, K+1, . . . , K+3N-1 must appear in exactly one of those triples.\n\nFor every integer i from 1 to N, a_i + b_i <= c_i holds.\n\nIf the answer is yes, construct one such partition.", "constraint": "1 <= N <= 10^5\n1 <= K <= 10^9", "input": "Input is given from Standard Input in the following format:\nN K", "output": "If it is impossible to partition the integers satisfying the condition, print -1. If it is possible, print N triples in the following format:\na_1 b_1 c_1\n:\na_N b_N c_N", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 output: 1 2 3", "input: 3 3 output: -1"], "Pid": "p02869", "ProblemText": "Task Description: Problem Statement Given are positive integers N and K.\nDetermine if the 3N integers K, K+1, . . . , K+3N-1 can be partitioned into N triples (a_1, b_1, c_1), . . . , (a_N, b_N, c_N) so that the condition below is satisfied. Any of the integers K, K+1, . . . , K+3N-1 must appear in exactly one of those triples.\n\nFor every integer i from 1 to N, a_i + b_i <= c_i holds.\n\nIf the answer is yes, construct one such partition.\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: If it is impossible to partition the integers satisfying the condition, print -1. If it is possible, print N triples in the following format:\na_1 b_1 c_1\n:\na_N b_N c_N\nTask Samples: input: 1 1 output: 1 2 3\ninput: 3 3 output: -1\n\n" }, { "title": "", "content": "Problem Statement In a two-dimensional plane, there is a square frame whose vertices are at coordinates (0,0), (N, 0), (0, N), and (N, N).\nThe frame is made of mirror glass. A ray of light striking an edge of the frame (but not a vertex) will be reflected so that the angle of incidence is equal to the angle of reflection.\nA ray of light striking a vertex of the frame will be reflected in the direction opposite to the direction it is coming from.\nWe will define the path for a grid point (a point with integer coordinates) (i, j) (0= 1.\nGraph creation: The algorithm for generating the map graph based on a random seed is specified in the following pseudo-code. For further details, please see the sample code below.\n Pseudo code: Map graph generator \n\n Input: |V|, |E|, \\mathrm{Max Degree}=5\n 2d vertex grid:\n\n First, find the largest integer R>0 such that |V| = R^{2} + r, with r being the smallest possible non-negative integer.\n Then we plot points (x, y) on the 2d vertex grid (0 <= x, y < R).\n For each point (x, y) add a uniform random offset dx, dy \\in [0,1] , giving the final vertex position (x + dx, y + dy)\\in [0, R] * [0, R].\n Finally, add the remaining r vertices at a uniform random position (x, y) with 0 <= x, y <= R.\n Vertex labels u \\in V are assigned by random shuffling. The shop is the vertex u=1.\n How we create Highways:\n\n To generate a highway network, we create a complete graph G_{\\text{comp}} on the vertex set u \\in V, assigning each vertex pair u, v \\in V * V the Euclidean distance W_{u, v} as an edge weight.\n Next, we construct a minimum spanning tree of G_{\\text{comp}}. The |V|-1 edges of the minimum spanning tree are the highway network of the graph G. We assign each of those edges <=ft\\{ u, v \\right\\} an edge weight d_{u, v} <=ftarrow \\lceil 2 * W_{u, v} \\rceil .\n \n How we add side roads:\n\n To create a network of side roads, we successively add |E|-(|V|-1) edges to the graph G as follows:\n \n Update \\mathrm{cost}(u, v). \n Among the vertex pairs <=ft( u, v \\right) \\in V* V, not yet connected by an edge, select a pair with minimal \\mathrm{cost}(u, v).\n Assign the edge weight d_{u, v} <=ftarrow \\lceil 4 * W_{u, v} \\rceil .\n\n Here, \\mathrm{cost}(u, v) is essentially based on the Euclidean distance of vertices, giving preference to connecting nearby vertices with low degree. In addition, preference is given to side roads along the rectangular grid, to avoid too many bridges. The detailed definitions are as follows:\n \n Define \\mathrm{degree}(u), the degree of vertex u\\in V as the number of incident edges. \n Define \\mathrm{color}(u) for each vertex u\\in V according to its original position (x, y) on the vertex grid as:\n \n If x+y is even : \\mathrm{color}(u) = 0 \n If x+y is odd : \\mathrm{color}(u) = 1 \n For the remaining r vertices : Assign a color \\mathrm{color}(u) \\in <=ft\\{0,1\\right\\} at random. \n Define a factor f(u, v) as follows:\n \n If \\mathrm{color}(u) and \\mathrm{color}(v) are the same : Set \\mathrm{f}(u, v) = 5 \n If \\mathrm{color}(u) and \\mathrm{color}(v) are different : Set \\mathrm{f}(u, v) = 1 \n Define a factor g(u) as follows:\n \n If \\mathrm{degree}(u) < \\mathrm{Max Degree} : Set g(u)=1 \n If \\mathrm{degree}(u) >= \\mathrm{Max Degree} : Set g(u)=\\infty \n Finally, the cost is defined as follows:\n \n \\mathrm{cost}(u, v) = W_{u, v}* \\mathrm{degree}(u) * \\mathrm{degree}(v) * f(u, v) * g(u) * g(v). \n How we assign order frequencies: \n\n Assign each vertex u \\in V an order frequency f_u \\in <=ft\\{0,1,2\\right\\}.\n Init the order frequency of the shop vertex: f_1 <=ftarrow 0. \n Init the order frequency of the other vertices: f_u <=ftarrow 1\n Now determine vertices with order frequency 2. For this draw a uniform random center point c=(c_x, c_y)\\in [R/4,3R/4]*[R/4,3R/4] and then for all vertices u=2, . . . , |V| do: \n \n If \\mathrm{Euclidean Distance}(c, u)<= R/8 + \\mathrm{uniform Random}[0, R/8]: f_{u} <=ftarrow 2 specification of car locations and moves: : Specification of Car Locations and Moves:\nIn order to make deliveries you will operate a delivery car, which can take positions and make moves as specified below.\nCar position: A car can generally take two types of position:\n\non a vertex u \\in V.\non an edge <=ft\\{ u, v \\right\\} \\in E. More specifically, it is located at a distance x (0 < x < d_{u, v}) from u to v .\n\nCar move: At each step 0 <= t < T_{\\text{max}} you have to choose one of the following actions in order to control your delivery car.\n\nstay: stay at the current position.\nmove w: Take one step towards vertex w \\in V.\n\nIn case of choosing move w, w must obey the following constraints. A failure to obey these constraints results in a wrong answer WA.\n\n w must be a vertex, i. e. , w \\in V.\n If the car is on vertex u \\in V, there must be an edge connecting u and v, i. e. , <=ft\\{ u, w \\right\\} \\in E.\n If the car is on the edge <=ft\\{ u, v \\right\\} \\in E, w must either be w = u or w = v. orders, deliveries, and constraints: : Orders, Deliveries, and Constraints:\n\nOrders: Throughout the contest each order is characterized by three quantities: A unique order ID, a vertex v \\in V indicating the order destination, and the order time t at which the order appeared. For the detailed format see below.\nOrder generation: At each time 0 <= t <= T_{\\text{last}} = 0.95 * T_{\\text{max}} up to one new order can appear with probability p_{\\text{order}}(t). In case there is an order, the order destination i is chosen from the vertex set V with probability proportional to the order frequency f_i. For details, see the pseudo-code below or the sample code further below.\n Pseudo code: Order generation \n\n Input: Last order time T_{\\text{last}} and average order probability p_{\\text{order}}(t). \n Init: \\mathrm{ID} <=ftarrow 0. \n For each step t = 0, . . . , T_{\\text{last}} do:\n \n Generate a uniform random number r \\in [0,1] . \n If r <= p_{\\text{order}}(t) :\n \n Select a vertex position u \\in V at random with probability proportional to the order frequency f_{u} of the vertex. \n \\mathrm{ID} <=ftarrow \\mathrm{ID} + 1 \n place order (new order ID, order time t, vertex position\n u \\in V )\n Else: place no order\n Note: The average order probability is defined as follows:\n\n p_{\\text{order}}(t) =\n\\begin{cases}\nt / T_{\\text{peak}}, &\n\\text{if } 0<= t < T_{\\text{peak}}, \\\\\n(T_{\\text{last}} - t) / (T_{\\text{last}}- T_{\\text{peak}}), &\n\\text{if } T_{\\text{peak}} <= t < T_{\\text{last}}, \\\\\n0, &\n\\text{if } T_{\\text{last}} <= t,\n\\end{cases}\n\nwhere T_{\\text{last}}: =0.95 * T_{\\max} and T_{\\text{peak}} is drawn randomly uniform from the interval [0, T_{\\text{last}}].\n Note: The value of T_{\\text{peak}} will not be given as an input. \nDelivery: To deliver an order, the contestant must do the following steps after the order has been placed:\n(1st) Move the car onto the shop: Note: When moving a car onto the shop, all orders with order time less than or equal to the current time, will be transfered into the car. On the other hand, orders which have not appeared yet, cannot be placed into the car.\n(2nd) Move the car to the customer position: To finalize a delivery, move the car onto the vertex of the customer position. Note: Orders which have not been transfered into the car yet, will not be delivered, even if you arrive at the customer position.\n\nConstraints: Throughout the contest, we assume each order has a unique \\text{ID} and should be delivered to the corresponding customer. It is further assumed that an unlimited number of orders can be placed in the car. scoring: Scoring\n\n During the contest the total score of a submission is determined by summing the score of the submission with respect to 30 input cases.\n After the contest a system test will be performed. To this end, the contestant's last submission will be scored by summing the score of the submission on 100 previously unseen input cases.\n For each input case, the score is calculated as follows:\n\n \\text{Score} =\n \\sum_{i \\in D} {(T_{\\text{max}})}^{2} - {(\\mathrm{waiting Time}_i)}^{2}, \n\nHere we use the following definitions:\n\n D : the set of orders delivered until t=T_{\\text{max}}\n the waiting time of the ith order: \\mathrm{waiting Time}_i = \\mathrm{delivered Time}_i - \\mathrm{ordered Time}_i.\nNote that an input case giving the output WA will receive 0 points. particulars of problem a: Particulars of Problem A\nIn problem A we pass all orders which appear at time 0 <= t < 0.95 * T_{\\text{max}} as an input to the contestant code. The task is to provide an algorithm which optimizes the moves of the car such that the above score becomes maximal. requirements: Requirements\n\n All inputs are of non-negative integer value. \n T_{\\text{max}} = 10000\n 200 <= |V| <= 400 \n 1.5 |V| <= |E| <= 2 |V|\n1 <= u_{i}, v_{i} <= |V| (1 <= i <= |E|)\n1 <= d_{u_i, v_i} <= \\lceil 4\\sqrt{2|V|} \\rceil (1 <= i <= |E|)\nThe given graph has no self-loops / multiple edges and is guaranteed to be connected.\n0 <= N_{\\text{new}} <= 1\n1 <= \\mathrm{new\\_id}_{i} <= T_{\\text{last}}+1 (1 <= i <= N_{\\text{new}}). Note: If all orders are generated by the order generation rule as explained above, the total number of orders is at most T_{\\text{last}}+1. Therefore, the possible range of \\mathrm{new\\_id}_{i} should be from 1 to T_{\\text{last}}+1.\n2 <= \\mathrm{dst}_i <= |V| (1 <= i <= N_{\\text{new}})\nThe order IDs \\mathrm{new\\_{id}}_i are unique. explanation: Explanation\nThe example operates on a graph with |V| = 5 vertices, |E| = 7 edges, and T_{\\text{max}} = 4 time steps. We now describe the orders which have occured and the movement of the car.\nTime t=0\nAt time t=0 an order is placed at the shop. This order has ID= 1 and should be delivered to vertex 2. Because your car is currently at vertex one, the order will be automatically transfered into your car. In this way, when your car is at the shop, all orders which have been made at present and before, will automatically be loaded into your car.\nTime 0 → 1\nYou choose to move towards vertex move 2. You will now move one step towards vertex 2.\nTime t=1\nA new order has appeared. It has ID =2 and shall be delivered at vertex 5.\nTime 1 → 2\nYou decided to stay. You can now stay on the edge where you are.\nTime t=2\nA new order has appeared. It has ID =3 and shall be delivered at vertex 4.\nTime 2 → 3\nYou decided to move move 1 back to vertex 1.\nYou are approaching one step towards vertex 1.\nDoing a U-turn in this way is explicitly allowed.\nTime t=3\nNew orders have not occurred. Now that you are at the vertex 1 (store), the orders with order ID 2,3 are loaded into your car. In a similar way, whenever you return to the store, all the orders that have already been placed are loaded into your car automatically.\nTime 3 → 4\nBeing at vertex 1 you choose move 5. You are moving your car one step towards vertex 5. You arrive at vertex 5.\nTime t=4\nSince you arrived at vertex 5, the order with order ID 2 can be delivered. sample code a: Sample Code A\nA software toolkit for generation of input samples, scoring and testing on a local contestant environment, and sample codes for beginners\nis provided through the following link. In addition we provide software for visualizing the contestants results.", "constraint": "orders, deliveries, and constraints:\norders: throughout the contest each order is characterized by three quantities: a unique order id, a vertex v \\in v indicating the order destination, and the order time t at which the order appeared. for the detailed format see below.\norder generation: at each time 0 <= t <= t_{\\text{last}} = 0.95 * t_{\\text{max}} up to one new order can appear with probability p_{\\text{order}}(t). in case there is an order, the order destination i is chosen from the vertex set v with probability proportional to the order frequency f_i. for details, see the zpseudo-code below or the sample code further below.\n pseudo code: order generation \n input: last order time t_{\\text{last}} and average order probability p_{\\text{order}}(t). \n init: \\mathrm{id} (arrow 0. \n for each step t = 0, . . . , t_{\\text{last}} do:\n \n generate a uniform random number r \\in [0,1] . \n if r <= p_{\\text{order}}(t) :\n \n select a vertex position u \\in v at random with probability proportional to the order frequency f_{u} of the vertex. \n \\mathrm{id} (arrow \\mathrm{id} + 1 \n place order (new order id, order time t, vertex position\n u \\in v )\n else: place no order\n note: the average order probability is defined as follows:\n p_{\\text{order}}(t) =\n\\begin{cases}\nt / t_{\\text{peak}}, &\n\\text{if } 0<= t < t_{\\text{peak}}, \\\\\n(t_{\\text{last}} - t) / (t_{\\text{last}}- t_{\\text{peak}}), &\n\\text{if } t_{\\text{peak}} <= t < t_{\\text{last}}, \\\\\n0, &\n\\text{if } t_{\\text{last}} <= t,\n\\end{cases}\nwhere t_{\\text{last}}: =0.95 * t_{\\max} and t_{\\text{peak}} is drawn randomly uniform from the interval [0, t_{\\text{last}}].\n note: the value of t_{\\text{peak}} will not be given as an input. \ndelivery: to deliver an order, the contestant must do the following steps after the order has been placed:\n(1st) move the car onto the shop: note: when moving a car onto the shop, all orders with order time less than or equal to the current time, will be transfered into the car. on the other hand, orders which have not appeared yet, cannot be placed into the car.\n(2nd) move the car to the customer position: to finalize a delivery, move the car onto the vertex of the customer position. note: orders which have not been transfered into the car yet, will not be delivered, even if you arrive at the customer position.\nconstraints: throughout the contest, we assume each order has a unique \\text{id} and should be delivered to the corresponding customer. it is further assumed that an unlimited number of orders can be placed in the car.", "input": "Input Format\nInput is provided in the following form:\n|V| |E|\nu_{1} v_{1} d_{u_{1}, v_{1}}\nu_{2} v_{2} d_{u_{2}, v_{2}}\n:\nu_{|E|} v_{|E|} d_{u_{|E|}, v_{|E|}}\nT_{\\text{max}}\n\\mathrm{info}_{0}\n\\mathrm{info}_{1}\n:\n\\mathrm{info}_{T_{\\text{max}}-1}\n In the first line |V| denotes the number of vertices, while |E| denotes the number of edges.\n The following |E| lines denote the edges of the graph. In particular, in the ith line u_{i} and v_{i} denote the edge connecting u_{i} and v_{i} and d_{u_{i}, v_{i}} the corresponding distance.\n The following line denotes the number of steps T_{\\text{max}}.\n\nIn the following line, \\mathrm{info}_t is information about the order from the customer that occurs at time t. \\mathrm{info}_t is given in the form:\nN_{\\text{new}}\n\\mathrm{new\\_id}_1 \\mathrm{dst}_1\n\\mathrm{new\\_id}_2 \\mathrm{dst}_2\n\\vdots\n\\mathrm{new\\_id}_{N_{\\text{new}}} \\mathrm{dst}_{N_{\\text{new}}}\n N_{\\text{new}} represents the number of new orders which appear at time t.\n The next N_{\\text{new}} lines give the newly generated order information. The i-th order information indicates that the order ID \\mathrm{new\\_{id}}_i of the new order, while \\mathrm{dst}_i\ndenotes the vertex to which the customer wishes the order to be delivered.\n Note: If N_{\\text{new}}=0, there are no new lines.", "output": "Format\nThe Output expects T_{\\text{max}} integers in the format specified below.\n\\mathrm{command}_{0}\n\\mathrm{command}_{1}\n:\n\\mathrm{command}_{T_{\\text{max}}-1}\n\nIn particular, \\mathrm{command}_{i} shall specify the movement of the delivery car by using one of the following two options:\n1) stay, if the car shall not move:\n-1\n\n2) move w, if the car shall be moved one step towards the neighboring vertex w\nw\n\nNote that in case of 2) w has to satisfy the following conditions:\n\nw \\in V\nIf the car is at vertex u: <=ft\\{ u, w \\right\\} \\in E .\nIf the car is on the edge <=ft\\{ u, v \\right\\}, w must either satisfy u = w or v = w.", "content_img": false, "lang": "en", "error": false, "samples": ["input: Input Example\n5 7\n1 2 5\n5 3 4\n2 4 8\n1 5 1\n2 3 3\n4 5 3\n4 3 9\n4\n1\n1 2\n1\n2 5\n1\n3 4\n0\n\nNote that this input is an example of small size and does not meet the constraints of the contest. output: Output Example\n2\n-1\n1\n5"], "Pid": "p02871", "ProblemText": "Task Description: Problem Setting overview: Overview\n\nConcept: In this programming contest, you will run a delivery service. Customers will place orders with your shop. Each order has a unique \\text{ID} and should be delivered to the corresponding customer. Your delivery service has one car. The car will fetch the ordered item from the shop and deliver it to the customer.\nScore: Your goal is to deliver as many items as possible, as quickly as possible in a given amount of time T_{\\text{max}}. (Orders are expected until 0.95 * T_{\\text{max}}).\nConstraint: In this contest there is no constraint on the number of items you can place in the car. However, an item can only be loaded in the car, by fetching it from the shop, after the order has been placed.\nProblem A/B: In problem A all order positions and times are given to the contestant in advance and the contestant algorithm shall optimize the moves of the car to make as many deliveries as possible as fast as possible. On the other hand, in problem B orders appear online, that is new orders appear, while you move your car to make as many deliveries as possible as fast as possible. specification of time and space: : Specification of Time and Space:\n\nTime: In this contest we model the progress of time by integer values 0 <= t < T_{\\text{max}}.\nMap: In this contest we model a map by a simple, undirected, and connected graph G=(V, E), consisting of a set of vertices V and a set of edges E\nShop and customer locations: The vertices u \\in V are labeled from 1 to |V| and the vertex u=1 denotes the location of your shop, while vertices u = 2, . . . , |V| denote locations of potential customers. Here, |V| denotes the number of elements of the set V.\nStreets: Each edge <=ft\\{ u, v \\right\\} \\in E represents a street connecting the vertices u, v \\in V. The corresponding length is given by an integer edge weight d_{u, v} >= 1.\nGraph creation: The algorithm for generating the map graph based on a random seed is specified in the following pseudo-code. For further details, please see the sample code below.\n Pseudo code: Map graph generator \n\n Input: |V|, |E|, \\mathrm{Max Degree}=5\n 2d vertex grid:\n\n First, find the largest integer R>0 such that |V| = R^{2} + r, with r being the smallest possible non-negative integer.\n Then we plot points (x, y) on the 2d vertex grid (0 <= x, y < R).\n For each point (x, y) add a uniform random offset dx, dy \\in [0,1] , giving the final vertex position (x + dx, y + dy)\\in [0, R] * [0, R].\n Finally, add the remaining r vertices at a uniform random position (x, y) with 0 <= x, y <= R.\n Vertex labels u \\in V are assigned by random shuffling. The shop is the vertex u=1.\n How we create Highways:\n\n To generate a highway network, we create a complete graph G_{\\text{comp}} on the vertex set u \\in V, assigning each vertex pair u, v \\in V * V the Euclidean distance W_{u, v} as an edge weight.\n Next, we construct a minimum spanning tree of G_{\\text{comp}}. The |V|-1 edges of the minimum spanning tree are the highway network of the graph G. We assign each of those edges <=ft\\{ u, v \\right\\} an edge weight d_{u, v} <=ftarrow \\lceil 2 * W_{u, v} \\rceil .\n \n How we add side roads:\n\n To create a network of side roads, we successively add |E|-(|V|-1) edges to the graph G as follows:\n \n Update \\mathrm{cost}(u, v). \n Among the vertex pairs <=ft( u, v \\right) \\in V* V, not yet connected by an edge, select a pair with minimal \\mathrm{cost}(u, v).\n Assign the edge weight d_{u, v} <=ftarrow \\lceil 4 * W_{u, v} \\rceil .\n\n Here, \\mathrm{cost}(u, v) is essentially based on the Euclidean distance of vertices, giving preference to connecting nearby vertices with low degree. In addition, preference is given to side roads along the rectangular grid, to avoid too many bridges. The detailed definitions are as follows:\n \n Define \\mathrm{degree}(u), the degree of vertex u\\in V as the number of incident edges. \n Define \\mathrm{color}(u) for each vertex u\\in V according to its original position (x, y) on the vertex grid as:\n \n If x+y is even : \\mathrm{color}(u) = 0 \n If x+y is odd : \\mathrm{color}(u) = 1 \n For the remaining r vertices : Assign a color \\mathrm{color}(u) \\in <=ft\\{0,1\\right\\} at random. \n Define a factor f(u, v) as follows:\n \n If \\mathrm{color}(u) and \\mathrm{color}(v) are the same : Set \\mathrm{f}(u, v) = 5 \n If \\mathrm{color}(u) and \\mathrm{color}(v) are different : Set \\mathrm{f}(u, v) = 1 \n Define a factor g(u) as follows:\n \n If \\mathrm{degree}(u) < \\mathrm{Max Degree} : Set g(u)=1 \n If \\mathrm{degree}(u) >= \\mathrm{Max Degree} : Set g(u)=\\infty \n Finally, the cost is defined as follows:\n \n \\mathrm{cost}(u, v) = W_{u, v}* \\mathrm{degree}(u) * \\mathrm{degree}(v) * f(u, v) * g(u) * g(v). \n How we assign order frequencies: \n\n Assign each vertex u \\in V an order frequency f_u \\in <=ft\\{0,1,2\\right\\}.\n Init the order frequency of the shop vertex: f_1 <=ftarrow 0. \n Init the order frequency of the other vertices: f_u <=ftarrow 1\n Now determine vertices with order frequency 2. For this draw a uniform random center point c=(c_x, c_y)\\in [R/4,3R/4]*[R/4,3R/4] and then for all vertices u=2, . . . , |V| do: \n \n If \\mathrm{Euclidean Distance}(c, u)<= R/8 + \\mathrm{uniform Random}[0, R/8]: f_{u} <=ftarrow 2 specification of car locations and moves: : Specification of Car Locations and Moves:\nIn order to make deliveries you will operate a delivery car, which can take positions and make moves as specified below.\nCar position: A car can generally take two types of position:\n\non a vertex u \\in V.\non an edge <=ft\\{ u, v \\right\\} \\in E. More specifically, it is located at a distance x (0 < x < d_{u, v}) from u to v .\n\nCar move: At each step 0 <= t < T_{\\text{max}} you have to choose one of the following actions in order to control your delivery car.\n\nstay: stay at the current position.\nmove w: Take one step towards vertex w \\in V.\n\nIn case of choosing move w, w must obey the following constraints. A failure to obey these constraints results in a wrong answer WA.\n\n w must be a vertex, i. e. , w \\in V.\n If the car is on vertex u \\in V, there must be an edge connecting u and v, i. e. , <=ft\\{ u, w \\right\\} \\in E.\n If the car is on the edge <=ft\\{ u, v \\right\\} \\in E, w must either be w = u or w = v. orders, deliveries, and constraints: : Orders, Deliveries, and Constraints:\n\nOrders: Throughout the contest each order is characterized by three quantities: A unique order ID, a vertex v \\in V indicating the order destination, and the order time t at which the order appeared. For the detailed format see below.\nOrder generation: At each time 0 <= t <= T_{\\text{last}} = 0.95 * T_{\\text{max}} up to one new order can appear with probability p_{\\text{order}}(t). In case there is an order, the order destination i is chosen from the vertex set V with probability proportional to the order frequency f_i. For details, see the pseudo-code below or the sample code further below.\n Pseudo code: Order generation \n\n Input: Last order time T_{\\text{last}} and average order probability p_{\\text{order}}(t). \n Init: \\mathrm{ID} <=ftarrow 0. \n For each step t = 0, . . . , T_{\\text{last}} do:\n \n Generate a uniform random number r \\in [0,1] . \n If r <= p_{\\text{order}}(t) :\n \n Select a vertex position u \\in V at random with probability proportional to the order frequency f_{u} of the vertex. \n \\mathrm{ID} <=ftarrow \\mathrm{ID} + 1 \n place order (new order ID, order time t, vertex position\n u \\in V )\n Else: place no order\n Note: The average order probability is defined as follows:\n\n p_{\\text{order}}(t) =\n\\begin{cases}\nt / T_{\\text{peak}}, &\n\\text{if } 0<= t < T_{\\text{peak}}, \\\\\n(T_{\\text{last}} - t) / (T_{\\text{last}}- T_{\\text{peak}}), &\n\\text{if } T_{\\text{peak}} <= t < T_{\\text{last}}, \\\\\n0, &\n\\text{if } T_{\\text{last}} <= t,\n\\end{cases}\n\nwhere T_{\\text{last}}: =0.95 * T_{\\max} and T_{\\text{peak}} is drawn randomly uniform from the interval [0, T_{\\text{last}}].\n Note: The value of T_{\\text{peak}} will not be given as an input. \nDelivery: To deliver an order, the contestant must do the following steps after the order has been placed:\n(1st) Move the car onto the shop: Note: When moving a car onto the shop, all orders with order time less than or equal to the current time, will be transfered into the car. On the other hand, orders which have not appeared yet, cannot be placed into the car.\n(2nd) Move the car to the customer position: To finalize a delivery, move the car onto the vertex of the customer position. Note: Orders which have not been transfered into the car yet, will not be delivered, even if you arrive at the customer position.\n\nConstraints: Throughout the contest, we assume each order has a unique \\text{ID} and should be delivered to the corresponding customer. It is further assumed that an unlimited number of orders can be placed in the car. scoring: Scoring\n\n During the contest the total score of a submission is determined by summing the score of the submission with respect to 30 input cases.\n After the contest a system test will be performed. To this end, the contestant's last submission will be scored by summing the score of the submission on 100 previously unseen input cases.\n For each input case, the score is calculated as follows:\n\n \\text{Score} =\n \\sum_{i \\in D} {(T_{\\text{max}})}^{2} - {(\\mathrm{waiting Time}_i)}^{2}, \n\nHere we use the following definitions:\n\n D : the set of orders delivered until t=T_{\\text{max}}\n the waiting time of the ith order: \\mathrm{waiting Time}_i = \\mathrm{delivered Time}_i - \\mathrm{ordered Time}_i.\nNote that an input case giving the output WA will receive 0 points. particulars of problem a: Particulars of Problem A\nIn problem A we pass all orders which appear at time 0 <= t < 0.95 * T_{\\text{max}} as an input to the contestant code. The task is to provide an algorithm which optimizes the moves of the car such that the above score becomes maximal. requirements: Requirements\n\n All inputs are of non-negative integer value. \n T_{\\text{max}} = 10000\n 200 <= |V| <= 400 \n 1.5 |V| <= |E| <= 2 |V|\n1 <= u_{i}, v_{i} <= |V| (1 <= i <= |E|)\n1 <= d_{u_i, v_i} <= \\lceil 4\\sqrt{2|V|} \\rceil (1 <= i <= |E|)\nThe given graph has no self-loops / multiple edges and is guaranteed to be connected.\n0 <= N_{\\text{new}} <= 1\n1 <= \\mathrm{new\\_id}_{i} <= T_{\\text{last}}+1 (1 <= i <= N_{\\text{new}}). Note: If all orders are generated by the order generation rule as explained above, the total number of orders is at most T_{\\text{last}}+1. Therefore, the possible range of \\mathrm{new\\_id}_{i} should be from 1 to T_{\\text{last}}+1.\n2 <= \\mathrm{dst}_i <= |V| (1 <= i <= N_{\\text{new}})\nThe order IDs \\mathrm{new\\_{id}}_i are unique. explanation: Explanation\nThe example operates on a graph with |V| = 5 vertices, |E| = 7 edges, and T_{\\text{max}} = 4 time steps. We now describe the orders which have occured and the movement of the car.\nTime t=0\nAt time t=0 an order is placed at the shop. This order has ID= 1 and should be delivered to vertex 2. Because your car is currently at vertex one, the order will be automatically transfered into your car. In this way, when your car is at the shop, all orders which have been made at present and before, will automatically be loaded into your car.\nTime 0 → 1\nYou choose to move towards vertex move 2. You will now move one step towards vertex 2.\nTime t=1\nA new order has appeared. It has ID =2 and shall be delivered at vertex 5.\nTime 1 → 2\nYou decided to stay. You can now stay on the edge where you are.\nTime t=2\nA new order has appeared. It has ID =3 and shall be delivered at vertex 4.\nTime 2 → 3\nYou decided to move move 1 back to vertex 1.\nYou are approaching one step towards vertex 1.\nDoing a U-turn in this way is explicitly allowed.\nTime t=3\nNew orders have not occurred. Now that you are at the vertex 1 (store), the orders with order ID 2,3 are loaded into your car. In a similar way, whenever you return to the store, all the orders that have already been placed are loaded into your car automatically.\nTime 3 → 4\nBeing at vertex 1 you choose move 5. You are moving your car one step towards vertex 5. You arrive at vertex 5.\nTime t=4\nSince you arrived at vertex 5, the order with order ID 2 can be delivered. sample code a: Sample Code A\nA software toolkit for generation of input samples, scoring and testing on a local contestant environment, and sample codes for beginners\nis provided through the following link. In addition we provide software for visualizing the contestants results.\nTask Constraint: orders, deliveries, and constraints:\norders: throughout the contest each order is characterized by three quantities: a unique order id, a vertex v \\in v indicating the order destination, and the order time t at which the order appeared. for the detailed format see below.\norder generation: at each time 0 <= t <= t_{\\text{last}} = 0.95 * t_{\\text{max}} up to one new order can appear with probability p_{\\text{order}}(t). in case there is an order, the order destination i is chosen from the vertex set v with probability proportional to the order frequency f_i. for details, see the zpseudo-code below or the sample code further below.\n pseudo code: order generation \n input: last order time t_{\\text{last}} and average order probability p_{\\text{order}}(t). \n init: \\mathrm{id} (arrow 0. \n for each step t = 0, . . . , t_{\\text{last}} do:\n \n generate a uniform random number r \\in [0,1] . \n if r <= p_{\\text{order}}(t) :\n \n select a vertex position u \\in v at random with probability proportional to the order frequency f_{u} of the vertex. \n \\mathrm{id} (arrow \\mathrm{id} + 1 \n place order (new order id, order time t, vertex position\n u \\in v )\n else: place no order\n note: the average order probability is defined as follows:\n p_{\\text{order}}(t) =\n\\begin{cases}\nt / t_{\\text{peak}}, &\n\\text{if } 0<= t < t_{\\text{peak}}, \\\\\n(t_{\\text{last}} - t) / (t_{\\text{last}}- t_{\\text{peak}}), &\n\\text{if } t_{\\text{peak}} <= t < t_{\\text{last}}, \\\\\n0, &\n\\text{if } t_{\\text{last}} <= t,\n\\end{cases}\nwhere t_{\\text{last}}: =0.95 * t_{\\max} and t_{\\text{peak}} is drawn randomly uniform from the interval [0, t_{\\text{last}}].\n note: the value of t_{\\text{peak}} will not be given as an input. \ndelivery: to deliver an order, the contestant must do the following steps after the order has been placed:\n(1st) move the car onto the shop: note: when moving a car onto the shop, all orders with order time less than or equal to the current time, will be transfered into the car. on the other hand, orders which have not appeared yet, cannot be placed into the car.\n(2nd) move the car to the customer position: to finalize a delivery, move the car onto the vertex of the customer position. note: orders which have not been transfered into the car yet, will not be delivered, even if you arrive at the customer position.\nconstraints: throughout the contest, we assume each order has a unique \\text{id} and should be delivered to the corresponding customer. it is further assumed that an unlimited number of orders can be placed in the car.\nTask Input: Input Format\nInput is provided in the following form:\n|V| |E|\nu_{1} v_{1} d_{u_{1}, v_{1}}\nu_{2} v_{2} d_{u_{2}, v_{2}}\n:\nu_{|E|} v_{|E|} d_{u_{|E|}, v_{|E|}}\nT_{\\text{max}}\n\\mathrm{info}_{0}\n\\mathrm{info}_{1}\n:\n\\mathrm{info}_{T_{\\text{max}}-1}\n In the first line |V| denotes the number of vertices, while |E| denotes the number of edges.\n The following |E| lines denote the edges of the graph. In particular, in the ith line u_{i} and v_{i} denote the edge connecting u_{i} and v_{i} and d_{u_{i}, v_{i}} the corresponding distance.\n The following line denotes the number of steps T_{\\text{max}}.\n\nIn the following line, \\mathrm{info}_t is information about the order from the customer that occurs at time t. \\mathrm{info}_t is given in the form:\nN_{\\text{new}}\n\\mathrm{new\\_id}_1 \\mathrm{dst}_1\n\\mathrm{new\\_id}_2 \\mathrm{dst}_2\n\\vdots\n\\mathrm{new\\_id}_{N_{\\text{new}}} \\mathrm{dst}_{N_{\\text{new}}}\n N_{\\text{new}} represents the number of new orders which appear at time t.\n The next N_{\\text{new}} lines give the newly generated order information. The i-th order information indicates that the order ID \\mathrm{new\\_{id}}_i of the new order, while \\mathrm{dst}_i\ndenotes the vertex to which the customer wishes the order to be delivered.\n Note: If N_{\\text{new}}=0, there are no new lines.\nTask Output: Format\nThe Output expects T_{\\text{max}} integers in the format specified below.\n\\mathrm{command}_{0}\n\\mathrm{command}_{1}\n:\n\\mathrm{command}_{T_{\\text{max}}-1}\n\nIn particular, \\mathrm{command}_{i} shall specify the movement of the delivery car by using one of the following two options:\n1) stay, if the car shall not move:\n-1\n\n2) move w, if the car shall be moved one step towards the neighboring vertex w\nw\n\nNote that in case of 2) w has to satisfy the following conditions:\n\nw \\in V\nIf the car is at vertex u: <=ft\\{ u, w \\right\\} \\in E .\nIf the car is on the edge <=ft\\{ u, v \\right\\}, w must either satisfy u = w or v = w.\nTask Samples: input: Input Example\n5 7\n1 2 5\n5 3 4\n2 4 8\n1 5 1\n2 3 3\n4 5 3\n4 3 9\n4\n1\n1 2\n1\n2 5\n1\n3 4\n0\n\nNote that this input is an example of small size and does not meet the constraints of the contest. output: Output Example\n2\n-1\n1\n5\n\n" }, { "title": "problem setting", "content": "Problem Setting overview: Overview\n\nConcept: In this programming contest, you will run a delivery service. Customers will place orders with your shop. Each order has a unique \\text{ID} and should be delivered to the corresponding customer. Your delivery service has one car. The car will fetch the ordered item from the shop and deliver it to the customer.\nScore: Your goal is to deliver as many items as possible, as quickly as possible in a given amount of time T_{\\text{max}}. (Orders are expected until 0.95 * T_{\\text{max}}).\nConstraint: In this contest there is no constraint on the number of items you can place in the car. However, an item can only be loaded in the car, by fetching it from the shop, after the order has been placed.\nProblem A/B: In problem A all order positions and times are given to the contestant in advance and the contestant algorithm shall optimize the moves of the car to make as many deliveries as possible as fast as possible. On the other hand, in problem B orders appear online, that is new orders appear, while you move your car to make as many deliveries as possible as fast as possible. specification of time and space: : Specification of Time and Space:\n\nTime: In this contest we model the progress of time by integer values 0 <= t < T_{\\text{max}}.\nMap: In this contest we model a map by a simple, undirected, and connected graph G=(V, E), consisting of a set of vertices V and a set of edges E\nShop and customer locations: The vertices u \\in V are labeled from 1 to |V| and the vertex u=1 denotes the location of your shop, while vertices u = 2, . . . , |V| denote locations of potential customers. Here, |V| denotes the number of elements of the set V.\nStreets: Each edge <=ft\\{ u, v \\right\\} \\in E represents a street connecting the vertices u, v \\in V. The corresponding length is given by an integer edge weight d_{u, v} >= 1.\nGraph creation: The algorithm for generating the map graph based on a random seed is specified in the following pseudo-code. For further details, please see the sample code below.\n Pseudo code: Map graph generator \n\n Input: |V|, |E|, \\mathrm{Max Degree}=5\n 2d vertex grid:\n\n First, find the largest integer R>0 such that |V| = R^{2} + r, with r being the smallest possible non-negative integer.\n Then we plot points (x, y) on the 2d vertex grid (0 <= x, y < R).\n For each point (x, y) add a uniform random offset dx, dy \\in [0,1] , giving the final vertex position (x + dx, y + dy)\\in [0, R] * [0, R].\n Finally, add the remaining r vertices at a uniform random position (x, y) with 0 <= x, y <= R.\n Vertex labels u \\in V are assigned by random shuffling. The shop is the vertex u=1.\n How we create Highways:\n\n To generate a highway network, we create a complete graph G_{\\text{comp}} on the vertex set u \\in V, assigning each vertex pair u, v \\in V * V the Euclidean distance W_{u, v} as an edge weight.\n Next, we construct a minimum spanning tree of G_{\\text{comp}}. The |V|-1 edges of the minimum spanning tree are the highway network of the graph G. We assign each of those edges <=ft\\{ u, v \\right\\} an edge weight d_{u, v} <=ftarrow \\lceil 2 * W_{u, v} \\rceil .\n \n How we add side roads:\n\n To create a network of side roads, we successively add |E|-(|V|-1) edges to the graph G as follows:\n \n Update \\mathrm{cost}(u, v). \n Among the vertex pairs <=ft( u, v \\right) \\in V* V, not yet connected by an edge, select a pair with minimal \\mathrm{cost}(u, v).\n Assign the edge weight d_{u, v} <=ftarrow \\lceil 4 * W_{u, v} \\rceil .\n\n Here, \\mathrm{cost}(u, v) is essentially based on the Euclidean distance of vertices, giving preference to connecting nearby vertices with low degree. In addition, preference is given to side roads along the rectangular grid, to avoid too many bridges. The detailed definitions are as follows:\n \n Define \\mathrm{degree}(u), the degree of vertex u\\in V as the number of incident edges. \n Define \\mathrm{color}(u) for each vertex u\\in V according to its original position (x, y) on the vertex grid as:\n \n If x+y is even : \\mathrm{color}(u) = 0 \n If x+y is odd : \\mathrm{color}(u) = 1 \n For the remaining r vertices : Assign a color \\mathrm{color}(u) \\in <=ft\\{0,1\\right\\} at random. \n Define a factor f(u, v) as follows:\n \n If \\mathrm{color}(u) and \\mathrm{color}(v) are the same : Set \\mathrm{f}(u, v) = 5 \n If \\mathrm{color}(u) and \\mathrm{color}(v) are different : Set \\mathrm{f}(u, v) = 1 \n Define a factor g(u) as follows:\n \n If \\mathrm{degree}(u) < \\mathrm{Max Degree} : Set g(u)=1 \n If \\mathrm{degree}(u) >= \\mathrm{Max Degree} : Set g(u)=\\infty \n Finally, the cost is defined as follows:\n \n \\mathrm{cost}(u, v) = W_{u, v}* \\mathrm{degree}(u) * \\mathrm{degree}(v) * f(u, v) * g(u) * g(v). \n How we assign order frequencies: \n\n Assign each vertex u \\in V an order frequency f_u \\in <=ft\\{0,1,2\\right\\}.\n Init the order frequency of the shop vertex: f_1 <=ftarrow 0. \n Init the order frequency of the other vertices: f_u <=ftarrow 1\n Now determine vertices with order frequency 2. For this draw a uniform random center point c=(c_x, c_y)\\in [R/4,3R/4]*[R/4,3R/4] and then for all vertices u=2, . . . , |V| do: \n \n If \\mathrm{Euclidean Distance}(c, u)<= R/8 + \\mathrm{uniform Random}[0, R/8]: f_{u} <=ftarrow 2 specification of car locations and moves: : Specification of Car Locations and Moves:\nIn order to make deliveries you will operate a delivery car, which can take positions and make moves as specified below.\nCar position: A car can generally take two types of position:\n\non a vertex u \\in V.\non an edge <=ft\\{ u, v \\right\\} \\in E. More specifically, it is located at a distance x (0 < x < d_{u, v}) from u to v .\n\nCar move: At each step 0 <= t < T_{\\text{max}} you have to choose one of the following actions in order to control your delivery car.\n\nstay: stay at the current position.\nmove w: Take one step towards vertex w \\in V.\n\nIn case of choosing move w, w must obey the following constraints. A failure to obey these constraints results in a wrong answer WA.\n\n w must be a vertex, i. e. , w \\in V.\n If the car is on vertex u \\in V, there must be an edge connecting u and v, i. e. , <=ft\\{ u, w \\right\\} \\in E.\n If the car is on the edge <=ft\\{ u, v \\right\\} \\in E, w must either be w = u or w = v. orders, deliveries, and constraints: : Orders, Deliveries, and Constraints:\n\nOrders: Throughout the contest each order is characterized by three quantities: A unique order ID, a vertex v \\in V indicating the order destination, and the order time t at which the order appeared. For the detailed format see below.\nOrder generation: At each time 0 <= t <= T_{\\text{last}} = 0.95 * T_{\\text{max}} up to one new order can appear with probability p_{\\text{order}}(t). In case there is an order, the order destination i is chosen from the vertex set V with probability proportional to the order frequency f_i. For details, see the pseudo-code below or the sample code further below.\n Pseudo code: Order generation \n\n Input: Last order time T_{\\text{last}} and average order probability p_{\\text{order}}(t). \n Init: \\mathrm{ID} <=ftarrow 0. \n For each step t = 0, . . . , T_{\\text{last}} do:\n \n Generate a uniform random number r \\in [0,1] . \n If r <= p_{\\text{order}}(t) :\n \n Select a vertex position u \\in V at random with probability proportional to the order frequency f_{u} of the vertex. \n \\mathrm{ID} <=ftarrow \\mathrm{ID} + 1 \n place order (new order ID, order time t, vertex position\n u \\in V )\n Else: place no order\n Note: The average order probability is defined as follows:\n\n p_{\\text{order}}(t) =\n\\begin{cases}\nt / T_{\\text{peak}}, &\n\\text{if } 0<= t < T_{\\text{peak}}, \\\\\n(T_{\\text{last}} - t) / (T_{\\text{last}}- T_{\\text{peak}}), &\n\\text{if } T_{\\text{peak}} <= t < T_{\\text{last}}, \\\\\n0, &\n\\text{if } T_{\\text{last}} <= t,\n\\end{cases}\n\nwhere T_{\\text{last}}: =0.95 * T_{\\max} and T_{\\text{peak}} is drawn randomly uniform from the interval [0, T_{\\text{last}}].\n Note: The value of T_{\\text{peak}} will not be given as an input. \nDelivery: To deliver an order, the contestant must do the following steps after the order has been placed:\n(1st) Move the car onto the shop: Note: When moving a car onto the shop, all orders with order time less than or equal to the current time, will be transfered into the car. On the other hand, orders which have not appeared yet, cannot be placed into the car.\n(2nd) Move the car to the customer position: To finalize a delivery, move the car onto the vertex of the customer position. Note: Orders which have not been transfered into the car yet, will not be delivered, even if you arrive at the customer position.\n\nConstraints: Throughout the contest, we assume each order has a unique \\text{ID} and should be delivered to the corresponding customer. It is further assumed that an unlimited number of orders can be placed in the car. scoring: Scoring\n\n During the contest the total score of a submission is determined by summing the score of the submission with respect to 30 input cases.\n After the contest a system test will be performed. To this end, the contestant's last submission will be scored by summing the score of the submission on 100 previously unseen input cases.\n For each input case, the score is calculated as follows:\n\n \\text{Score} =\n \\sum_{i \\in D} {(T_{\\text{max}})}^{2} - {(\\mathrm{waiting Time}_i)}^{2}, \n\nHere we use the following definitions:\n\n D : the set of orders delivered until t=T_{\\text{max}}\n the waiting time of the ith order: \\mathrm{waiting Time}_i = \\mathrm{delivered Time}_i - \\mathrm{ordered Time}_i.\nNote that an input case giving the output WA will receive 0 points. particulars of problem b: : Particulars of Problem B:\n\nProblem B is an interactive contest, where the contestant code successively receives updates on newly generated and delivered orders from a host code, while simultaneously servicing the customer by moving the car to a neighboring position in every step t=0, . . . , T_{\\max}-1. The precise flow which details the interaction of the contestant and host code is shown below.\n\nContestant Code\nHost Code\nGenerate and output graph G\n+\n\nTime t: Generate and output new orders\n+\n\nTime t: If on shop, output orders loaded into car\n+\nTime t: Determine and output a move\n\n+\n\nCheck feasibility of move; If move unfeasible: output NG, If feasible: output OK\n+\n\nTime t+1: update and output information on delivered items (if any)\n\nNote: The host code outputs the graph only once. The processes marked by a \"+\" on the left side of the table are repeated iteratively for integers t in t = 0, . . . , T_{\\max} - 1. sample code b: Sample Code B\nA software toolkit for generation of input samples, scoring and testing on a local contestant environment, and sample codes for beginners\nis provided through the following link. In addition we provide software for visualizing the contestants results. Input/Output Example\n\nTime\nContestant\nHost Code\nExplanation\n5 7\n1 2 5\n5 3 4\n2 4 8\n1 5 1\n2 3 3\n4 5 3\n4 3 9\n0 1 1 5 5\n500\n At first, the host code provides the graph data through the standard input. In this example, the graph has |V| = 5 vertices and | E | = 7 edges. Next, the order frequency for each vertex is given in one line. Finally, T_{\\max} is given.\n\n0 \\rightarrow 1\n\n1\n1 5\n1\n1\n At time t=0 we get one order. This order has ID= 1 and should be delivered to vertex 5. Because your car is currently at vertex one, the order will be automatically transfered into your car. In this way, when your car is at the shop, all orders which have been made at present and before, will automatically be loaded into your car.\n2\n\nYou decided to move one step towards vertex.\n\nOK\n0\nThe first line indicates that your move was feasible. The second line shows that no orders have been delivered.\n1 \\rightarrow 2\n\n1\n2 2\n0\n One new order (ID =2, delivery vertex =2) has occured. Your car is on the edge between vertex 1 and 2, so zero orders have been transfered to your car.\n-1\n\nYou decided to keep your car in the same position.\n\nOK\n0\n Your move was valid. No orders will be delivered, because you are not at a delivery item position.\n2 \\rightarrow 3\n\n1\n3 4\n0\nA new order (ID =3, delivery vertex =4) has appeared. \n1\n\nYou decided to move back one step towards vertex 1. In this way you are allowed to perform a U-turn.\n\nOK\n0\nNo orders have been delivered.\n3 \\rightarrow 4\n\n0\n2\n2\n3\nSince the car has returned to the store, products corresponding to order ID 2 and 3 are loaded onto the car.\n5\n\nThe contestant has decided to move one step towards vertex 5.\n\nOK\n1\n1\nSince you arrived at vertex 5, the order with ID 1 was delivered.\n4 \\rightarrow 5\n\n0\n0\nThere is no new order. \n5\n\nThe contestant decides to move one step towards vertex 5.\n\nNG\nThe input was invalid and you should terminate your program.", "constraint": "I/O Constraints\n\n All numbers given through the standard input are integers. \n All outputs must be integers \n T_{\\text{max}} = 10000 \n 200 <= |V| <= 400 \n 1.5 |V| <= |E| <= 2|V|\n1 <= u_{i}, v_{i} <= |V| (1 <= i <= |E|)\n1 <= d_{u_i, v_i} <= \\lceil 4\\sqrt{2|V|} \\rceil (1 <= i <= |E|)\nThe given graph has no self-loops, no multiple edges and is guaranteed to be connected.\n f_1 = 0 \n f_i \\in <=ft\\{ 1,2 \\right\\} (2 <= i <= |V|) \n \\mathrm{verdict} \\in <=ft\\{ \\text{\"OK\"}, \\text{\"NG\"} \\right\\} \n0 <= N_{\\text{new}} <= 1\n1 <= \\mathrm{new\\_id}_{i} <= T_{\\text{last}}+1 (1 <= i <= N_{\\text{new}}). Note: If all orders are generated by the order generation rule as explained above, the total number of orders is at most T_{\\text{last}}+1. Therefore, the possible range of \\mathrm{new\\_id}_{i} should be from 1 to T_{\\text{last}}+1.\nThe order IDs \\mathrm{new\\_{id}}_i are unique. \n2 <= \\mathrm{dst}_i <= |V| (1 <= i <= N_{\\text{new}})\n The integer which the contestant outputs to the standard output at time t must either be -1 or 1 <= w <= |V|", "input": "", "output": "Using the Standard Output\nWhen returning your move instruction to the standard output, please use the flush command. As an example, consider the case where you want to output -1. This is how to do it in some of the major programming languages.\nC++\n\nstd: : cout << \"-1\" << std: : endl;\n\nJava\n\nSystem. out. println(\"-1\");\n\nPython 3.4\n\nprint(\"-1\", flush=True)", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p02872", "ProblemText": "Task Description: Problem Setting overview: Overview\n\nConcept: In this programming contest, you will run a delivery service. Customers will place orders with your shop. Each order has a unique \\text{ID} and should be delivered to the corresponding customer. Your delivery service has one car. The car will fetch the ordered item from the shop and deliver it to the customer.\nScore: Your goal is to deliver as many items as possible, as quickly as possible in a given amount of time T_{\\text{max}}. (Orders are expected until 0.95 * T_{\\text{max}}).\nConstraint: In this contest there is no constraint on the number of items you can place in the car. However, an item can only be loaded in the car, by fetching it from the shop, after the order has been placed.\nProblem A/B: In problem A all order positions and times are given to the contestant in advance and the contestant algorithm shall optimize the moves of the car to make as many deliveries as possible as fast as possible. On the other hand, in problem B orders appear online, that is new orders appear, while you move your car to make as many deliveries as possible as fast as possible. specification of time and space: : Specification of Time and Space:\n\nTime: In this contest we model the progress of time by integer values 0 <= t < T_{\\text{max}}.\nMap: In this contest we model a map by a simple, undirected, and connected graph G=(V, E), consisting of a set of vertices V and a set of edges E\nShop and customer locations: The vertices u \\in V are labeled from 1 to |V| and the vertex u=1 denotes the location of your shop, while vertices u = 2, . . . , |V| denote locations of potential customers. Here, |V| denotes the number of elements of the set V.\nStreets: Each edge <=ft\\{ u, v \\right\\} \\in E represents a street connecting the vertices u, v \\in V. The corresponding length is given by an integer edge weight d_{u, v} >= 1.\nGraph creation: The algorithm for generating the map graph based on a random seed is specified in the following pseudo-code. For further details, please see the sample code below.\n Pseudo code: Map graph generator \n\n Input: |V|, |E|, \\mathrm{Max Degree}=5\n 2d vertex grid:\n\n First, find the largest integer R>0 such that |V| = R^{2} + r, with r being the smallest possible non-negative integer.\n Then we plot points (x, y) on the 2d vertex grid (0 <= x, y < R).\n For each point (x, y) add a uniform random offset dx, dy \\in [0,1] , giving the final vertex position (x + dx, y + dy)\\in [0, R] * [0, R].\n Finally, add the remaining r vertices at a uniform random position (x, y) with 0 <= x, y <= R.\n Vertex labels u \\in V are assigned by random shuffling. The shop is the vertex u=1.\n How we create Highways:\n\n To generate a highway network, we create a complete graph G_{\\text{comp}} on the vertex set u \\in V, assigning each vertex pair u, v \\in V * V the Euclidean distance W_{u, v} as an edge weight.\n Next, we construct a minimum spanning tree of G_{\\text{comp}}. The |V|-1 edges of the minimum spanning tree are the highway network of the graph G. We assign each of those edges <=ft\\{ u, v \\right\\} an edge weight d_{u, v} <=ftarrow \\lceil 2 * W_{u, v} \\rceil .\n \n How we add side roads:\n\n To create a network of side roads, we successively add |E|-(|V|-1) edges to the graph G as follows:\n \n Update \\mathrm{cost}(u, v). \n Among the vertex pairs <=ft( u, v \\right) \\in V* V, not yet connected by an edge, select a pair with minimal \\mathrm{cost}(u, v).\n Assign the edge weight d_{u, v} <=ftarrow \\lceil 4 * W_{u, v} \\rceil .\n\n Here, \\mathrm{cost}(u, v) is essentially based on the Euclidean distance of vertices, giving preference to connecting nearby vertices with low degree. In addition, preference is given to side roads along the rectangular grid, to avoid too many bridges. The detailed definitions are as follows:\n \n Define \\mathrm{degree}(u), the degree of vertex u\\in V as the number of incident edges. \n Define \\mathrm{color}(u) for each vertex u\\in V according to its original position (x, y) on the vertex grid as:\n \n If x+y is even : \\mathrm{color}(u) = 0 \n If x+y is odd : \\mathrm{color}(u) = 1 \n For the remaining r vertices : Assign a color \\mathrm{color}(u) \\in <=ft\\{0,1\\right\\} at random. \n Define a factor f(u, v) as follows:\n \n If \\mathrm{color}(u) and \\mathrm{color}(v) are the same : Set \\mathrm{f}(u, v) = 5 \n If \\mathrm{color}(u) and \\mathrm{color}(v) are different : Set \\mathrm{f}(u, v) = 1 \n Define a factor g(u) as follows:\n \n If \\mathrm{degree}(u) < \\mathrm{Max Degree} : Set g(u)=1 \n If \\mathrm{degree}(u) >= \\mathrm{Max Degree} : Set g(u)=\\infty \n Finally, the cost is defined as follows:\n \n \\mathrm{cost}(u, v) = W_{u, v}* \\mathrm{degree}(u) * \\mathrm{degree}(v) * f(u, v) * g(u) * g(v). \n How we assign order frequencies: \n\n Assign each vertex u \\in V an order frequency f_u \\in <=ft\\{0,1,2\\right\\}.\n Init the order frequency of the shop vertex: f_1 <=ftarrow 0. \n Init the order frequency of the other vertices: f_u <=ftarrow 1\n Now determine vertices with order frequency 2. For this draw a uniform random center point c=(c_x, c_y)\\in [R/4,3R/4]*[R/4,3R/4] and then for all vertices u=2, . . . , |V| do: \n \n If \\mathrm{Euclidean Distance}(c, u)<= R/8 + \\mathrm{uniform Random}[0, R/8]: f_{u} <=ftarrow 2 specification of car locations and moves: : Specification of Car Locations and Moves:\nIn order to make deliveries you will operate a delivery car, which can take positions and make moves as specified below.\nCar position: A car can generally take two types of position:\n\non a vertex u \\in V.\non an edge <=ft\\{ u, v \\right\\} \\in E. More specifically, it is located at a distance x (0 < x < d_{u, v}) from u to v .\n\nCar move: At each step 0 <= t < T_{\\text{max}} you have to choose one of the following actions in order to control your delivery car.\n\nstay: stay at the current position.\nmove w: Take one step towards vertex w \\in V.\n\nIn case of choosing move w, w must obey the following constraints. A failure to obey these constraints results in a wrong answer WA.\n\n w must be a vertex, i. e. , w \\in V.\n If the car is on vertex u \\in V, there must be an edge connecting u and v, i. e. , <=ft\\{ u, w \\right\\} \\in E.\n If the car is on the edge <=ft\\{ u, v \\right\\} \\in E, w must either be w = u or w = v. orders, deliveries, and constraints: : Orders, Deliveries, and Constraints:\n\nOrders: Throughout the contest each order is characterized by three quantities: A unique order ID, a vertex v \\in V indicating the order destination, and the order time t at which the order appeared. For the detailed format see below.\nOrder generation: At each time 0 <= t <= T_{\\text{last}} = 0.95 * T_{\\text{max}} up to one new order can appear with probability p_{\\text{order}}(t). In case there is an order, the order destination i is chosen from the vertex set V with probability proportional to the order frequency f_i. For details, see the pseudo-code below or the sample code further below.\n Pseudo code: Order generation \n\n Input: Last order time T_{\\text{last}} and average order probability p_{\\text{order}}(t). \n Init: \\mathrm{ID} <=ftarrow 0. \n For each step t = 0, . . . , T_{\\text{last}} do:\n \n Generate a uniform random number r \\in [0,1] . \n If r <= p_{\\text{order}}(t) :\n \n Select a vertex position u \\in V at random with probability proportional to the order frequency f_{u} of the vertex. \n \\mathrm{ID} <=ftarrow \\mathrm{ID} + 1 \n place order (new order ID, order time t, vertex position\n u \\in V )\n Else: place no order\n Note: The average order probability is defined as follows:\n\n p_{\\text{order}}(t) =\n\\begin{cases}\nt / T_{\\text{peak}}, &\n\\text{if } 0<= t < T_{\\text{peak}}, \\\\\n(T_{\\text{last}} - t) / (T_{\\text{last}}- T_{\\text{peak}}), &\n\\text{if } T_{\\text{peak}} <= t < T_{\\text{last}}, \\\\\n0, &\n\\text{if } T_{\\text{last}} <= t,\n\\end{cases}\n\nwhere T_{\\text{last}}: =0.95 * T_{\\max} and T_{\\text{peak}} is drawn randomly uniform from the interval [0, T_{\\text{last}}].\n Note: The value of T_{\\text{peak}} will not be given as an input. \nDelivery: To deliver an order, the contestant must do the following steps after the order has been placed:\n(1st) Move the car onto the shop: Note: When moving a car onto the shop, all orders with order time less than or equal to the current time, will be transfered into the car. On the other hand, orders which have not appeared yet, cannot be placed into the car.\n(2nd) Move the car to the customer position: To finalize a delivery, move the car onto the vertex of the customer position. Note: Orders which have not been transfered into the car yet, will not be delivered, even if you arrive at the customer position.\n\nConstraints: Throughout the contest, we assume each order has a unique \\text{ID} and should be delivered to the corresponding customer. It is further assumed that an unlimited number of orders can be placed in the car. scoring: Scoring\n\n During the contest the total score of a submission is determined by summing the score of the submission with respect to 30 input cases.\n After the contest a system test will be performed. To this end, the contestant's last submission will be scored by summing the score of the submission on 100 previously unseen input cases.\n For each input case, the score is calculated as follows:\n\n \\text{Score} =\n \\sum_{i \\in D} {(T_{\\text{max}})}^{2} - {(\\mathrm{waiting Time}_i)}^{2}, \n\nHere we use the following definitions:\n\n D : the set of orders delivered until t=T_{\\text{max}}\n the waiting time of the ith order: \\mathrm{waiting Time}_i = \\mathrm{delivered Time}_i - \\mathrm{ordered Time}_i.\nNote that an input case giving the output WA will receive 0 points. particulars of problem b: : Particulars of Problem B:\n\nProblem B is an interactive contest, where the contestant code successively receives updates on newly generated and delivered orders from a host code, while simultaneously servicing the customer by moving the car to a neighboring position in every step t=0, . . . , T_{\\max}-1. The precise flow which details the interaction of the contestant and host code is shown below.\n\nContestant Code\nHost Code\nGenerate and output graph G\n+\n\nTime t: Generate and output new orders\n+\n\nTime t: If on shop, output orders loaded into car\n+\nTime t: Determine and output a move\n\n+\n\nCheck feasibility of move; If move unfeasible: output NG, If feasible: output OK\n+\n\nTime t+1: update and output information on delivered items (if any)\n\nNote: The host code outputs the graph only once. The processes marked by a \"+\" on the left side of the table are repeated iteratively for integers t in t = 0, . . . , T_{\\max} - 1. sample code b: Sample Code B\nA software toolkit for generation of input samples, scoring and testing on a local contestant environment, and sample codes for beginners\nis provided through the following link. In addition we provide software for visualizing the contestants results. Input/Output Example\n\nTime\nContestant\nHost Code\nExplanation\n5 7\n1 2 5\n5 3 4\n2 4 8\n1 5 1\n2 3 3\n4 5 3\n4 3 9\n0 1 1 5 5\n500\n At first, the host code provides the graph data through the standard input. In this example, the graph has |V| = 5 vertices and | E | = 7 edges. Next, the order frequency for each vertex is given in one line. Finally, T_{\\max} is given.\n\n0 \\rightarrow 1\n\n1\n1 5\n1\n1\n At time t=0 we get one order. This order has ID= 1 and should be delivered to vertex 5. Because your car is currently at vertex one, the order will be automatically transfered into your car. In this way, when your car is at the shop, all orders which have been made at present and before, will automatically be loaded into your car.\n2\n\nYou decided to move one step towards vertex.\n\nOK\n0\nThe first line indicates that your move was feasible. The second line shows that no orders have been delivered.\n1 \\rightarrow 2\n\n1\n2 2\n0\n One new order (ID =2, delivery vertex =2) has occured. Your car is on the edge between vertex 1 and 2, so zero orders have been transfered to your car.\n-1\n\nYou decided to keep your car in the same position.\n\nOK\n0\n Your move was valid. No orders will be delivered, because you are not at a delivery item position.\n2 \\rightarrow 3\n\n1\n3 4\n0\nA new order (ID =3, delivery vertex =4) has appeared. \n1\n\nYou decided to move back one step towards vertex 1. In this way you are allowed to perform a U-turn.\n\nOK\n0\nNo orders have been delivered.\n3 \\rightarrow 4\n\n0\n2\n2\n3\nSince the car has returned to the store, products corresponding to order ID 2 and 3 are loaded onto the car.\n5\n\nThe contestant has decided to move one step towards vertex 5.\n\nOK\n1\n1\nSince you arrived at vertex 5, the order with ID 1 was delivered.\n4 \\rightarrow 5\n\n0\n0\nThere is no new order. \n5\n\nThe contestant decides to move one step towards vertex 5.\n\nNG\nThe input was invalid and you should terminate your program.\nTask Constraint: I/O Constraints\n\n All numbers given through the standard input are integers. \n All outputs must be integers \n T_{\\text{max}} = 10000 \n 200 <= |V| <= 400 \n 1.5 |V| <= |E| <= 2|V|\n1 <= u_{i}, v_{i} <= |V| (1 <= i <= |E|)\n1 <= d_{u_i, v_i} <= \\lceil 4\\sqrt{2|V|} \\rceil (1 <= i <= |E|)\nThe given graph has no self-loops, no multiple edges and is guaranteed to be connected.\n f_1 = 0 \n f_i \\in <=ft\\{ 1,2 \\right\\} (2 <= i <= |V|) \n \\mathrm{verdict} \\in <=ft\\{ \\text{\"OK\"}, \\text{\"NG\"} \\right\\} \n0 <= N_{\\text{new}} <= 1\n1 <= \\mathrm{new\\_id}_{i} <= T_{\\text{last}}+1 (1 <= i <= N_{\\text{new}}). Note: If all orders are generated by the order generation rule as explained above, the total number of orders is at most T_{\\text{last}}+1. Therefore, the possible range of \\mathrm{new\\_id}_{i} should be from 1 to T_{\\text{last}}+1.\nThe order IDs \\mathrm{new\\_{id}}_i are unique. \n2 <= \\mathrm{dst}_i <= |V| (1 <= i <= N_{\\text{new}})\n The integer which the contestant outputs to the standard output at time t must either be -1 or 1 <= w <= |V|\nTask Input: \nTask Output: Using the Standard Output\nWhen returning your move instruction to the standard output, please use the flush command. As an example, consider the case where you want to output -1. This is how to do it in some of the major programming languages.\nC++\n\nstd: : cout << \"-1\" << std: : endl;\n\nJava\n\nSystem. out. println(\"-1\");\n\nPython 3.4\n\nprint(\"-1\", flush=True)\n\n" }, { "title": "", "content": "Problem Statement Given is a string S of length N-1.\nEach character in S is < or >.\nA sequence of N non-negative integers, a_1, a_2, \\cdots, a_N, is said to be good when the following condition is satisfied for all i (1 <= i <= N-1):\n\nIf S_i= <: a_i: a_i>a_{i+1}\n\nFind the minimum possible sum of the elements of a good sequence of N non-negative integers.", "constraint": "2 <= N <= 5 * 10^5\nS is a string of length N-1 consisting of < and >.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Find the minimum possible sum of the elements of a good sequence of N non-negative integers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: <>> output: 3\n\na=(0,2,1,0) is a good sequence whose sum is 3.\nThere is no good sequence whose sum is less than 3.", "input: <>>><<><<<<<>>>< output: 28"], "Pid": "p02873", "ProblemText": "Task Description: Problem Statement Given is a string S of length N-1.\nEach character in S is < or >.\nA sequence of N non-negative integers, a_1, a_2, \\cdots, a_N, is said to be good when the following condition is satisfied for all i (1 <= i <= N-1):\n\nIf S_i= <: a_i: a_i>a_{i+1}\n\nFind the minimum possible sum of the elements of a good sequence of N non-negative integers.\nTask Constraint: 2 <= N <= 5 * 10^5\nS is a string of length N-1 consisting of < and >.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Find the minimum possible sum of the elements of a good sequence of N non-negative integers.\nTask Samples: input: <>> output: 3\n\na=(0,2,1,0) is a good sequence whose sum is 3.\nThere is no good sequence whose sum is less than 3.\ninput: <>>><<><<<<<>>>< output: 28\n\n" }, { "title": "", "content": "Problem Statement10^9 contestants, numbered 1 to 10^9, will compete in a competition.\nThere will be two contests in this competition.\nThe organizer prepared N problems, numbered 1 to N, to use in these contests.\nWhen Problem i is presented in a contest, it will be solved by all contestants from Contestant L_i to Contestant R_i (inclusive), and will not be solved by any other contestants.\nThe organizer will use these N problems in the two contests.\nEach problem must be used in exactly one of the contests, and each contest must have at least one problem.\nThe joyfulness of each contest is the number of contestants who will solve all the problems in the contest.\nFind the maximum possible total joyfulness of the two contests.", "constraint": "2 <= N <= 10^5\n1 <= L_i <= R_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nL_1 R_1\nL_2 R_2\n\\vdots\nL_N R_N", "output": "Print the maximum possible total joyfulness of the two contests.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n4 7\n1 4\n5 8\n2 5 output: 6\n\nThe optimal choice is:\n\nUse Problem 1 and 3 in the first contest. Contestant 5,6, and 7 will solve both of them, so the joyfulness of this contest is 3.\nUse Problem 2 and 4 in the second contest. Contestant 2,3, and 4 will solve both of them, so the joyfulness of this contest is 3.\nThe total joyfulness of these two contests is 6. We cannot make the total joyfulness greater than 6.", "input: 4\n1 20\n2 19\n3 18\n4 17 output: 34", "input: 10\n457835016 996058008\n456475528 529149798\n455108441 512701454\n455817105 523506955\n457368248 814532746\n455073228 459494089\n456651538 774276744\n457667152 974637457\n457293701 800549465\n456580262 636471526 output: 540049931"], "Pid": "p02874", "ProblemText": "Task Description: Problem Statement10^9 contestants, numbered 1 to 10^9, will compete in a competition.\nThere will be two contests in this competition.\nThe organizer prepared N problems, numbered 1 to N, to use in these contests.\nWhen Problem i is presented in a contest, it will be solved by all contestants from Contestant L_i to Contestant R_i (inclusive), and will not be solved by any other contestants.\nThe organizer will use these N problems in the two contests.\nEach problem must be used in exactly one of the contests, and each contest must have at least one problem.\nThe joyfulness of each contest is the number of contestants who will solve all the problems in the contest.\nFind the maximum possible total joyfulness of the two contests.\nTask Constraint: 2 <= N <= 10^5\n1 <= L_i <= R_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nL_1 R_1\nL_2 R_2\n\\vdots\nL_N R_N\nTask Output: Print the maximum possible total joyfulness of the two contests.\nTask Samples: input: 4\n4 7\n1 4\n5 8\n2 5 output: 6\n\nThe optimal choice is:\n\nUse Problem 1 and 3 in the first contest. Contestant 5,6, and 7 will solve both of them, so the joyfulness of this contest is 3.\nUse Problem 2 and 4 in the second contest. Contestant 2,3, and 4 will solve both of them, so the joyfulness of this contest is 3.\nThe total joyfulness of these two contests is 6. We cannot make the total joyfulness greater than 6.\ninput: 4\n1 20\n2 19\n3 18\n4 17 output: 34\ninput: 10\n457835016 996058008\n456475528 529149798\n455108441 512701454\n455817105 523506955\n457368248 814532746\n455073228 459494089\n456651538 774276744\n457667152 974637457\n457293701 800549465\n456580262 636471526 output: 540049931\n\n" }, { "title": "", "content": "Problem Statement Given is a positive even number N.\nFind the number of strings s of length N consisting of A, B, and C that satisfy the following condition:\n\ns can be converted to the empty string by repeating the following operation:\nChoose two consecutive characters in s and erase them. However, choosing AB or BA is not allowed.\n\nFor example, ABBC satisfies the condition for N=4, because we can convert it as follows: ABBC → (erase BB) → AC → (erase AC) → (empty).\nThe answer can be enormous, so compute the count modulo 998244353.", "constraint": "2 <= N <= 10^7\nN is an even number.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of strings that satisfy the conditions, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 7\n\nExcept AB and BA, all possible strings satisfy the conditions.", "input: 10 output: 50007", "input: 1000000 output: 210055358"], "Pid": "p02875", "ProblemText": "Task Description: Problem Statement Given is a positive even number N.\nFind the number of strings s of length N consisting of A, B, and C that satisfy the following condition:\n\ns can be converted to the empty string by repeating the following operation:\nChoose two consecutive characters in s and erase them. However, choosing AB or BA is not allowed.\n\nFor example, ABBC satisfies the condition for N=4, because we can convert it as follows: ABBC → (erase BB) → AC → (erase AC) → (empty).\nThe answer can be enormous, so compute the count modulo 998244353.\nTask Constraint: 2 <= N <= 10^7\nN is an even number.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of strings that satisfy the conditions, modulo 998244353.\nTask Samples: input: 2 output: 7\n\nExcept AB and BA, all possible strings satisfy the conditions.\ninput: 10 output: 50007\ninput: 1000000 output: 210055358\n\n" }, { "title": "", "content": "Problem Statement We have N balance beams numbered 1 to N.\nThe length of each beam is 1 meters.\nSnuke walks on Beam i at a speed of 1/A_i meters per second, and Ringo walks on Beam i at a speed of 1/B_i meters per second.\nSnuke and Ringo will play the following game:\n\nFirst, Snuke connects the N beams in any order of his choice and makes a long beam of length N meters.\nThen, Snuke starts at the left end of the long beam. At the same time, Ringo starts at a point chosen uniformly at random on the long beam. Both of them walk to the right end of the long beam.\nSnuke wins if and only if he catches up to Ringo before Ringo reaches the right end of the long beam. That is, Snuke wins if there is a moment when Snuke and Ringo stand at the same position, and Ringo wins otherwise.\n\nFind the probability that Snuke wins when Snuke arranges the N beams so that the probability of his winning is maximized.\nThis probability is a rational number, so we ask you to represent it as an irreducible fraction P/Q (to represent 0, use P=0, Q=1).", "constraint": "1 <= N <= 10^5\n1 <= A_i,B_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N", "output": "Print the numerator and denominator of the irreducible fraction that represents the maximum probability of Snuke's winning.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 2\n1 2 output: 1 4\n\nWhen the beams are connected in the order 2,1 from left to right, the probability of Snuke's winning is 1/4, which is the maximum possible value.", "input: 4\n1 5\n4 7\n2 1\n8 4 output: 1 2", "input: 3\n4 1\n5 2\n6 3 output: 0 1", "input: 10\n866111664 178537096\n705445072 318106937\n472381277 579910117\n353498483 865935868\n383133839 231371336\n378371075 681212831\n304570952 16537461\n955719384 267238505\n844917655 218662351\n550309930 62731178 output: 697461712 2899550585"], "Pid": "p02876", "ProblemText": "Task Description: Problem Statement We have N balance beams numbered 1 to N.\nThe length of each beam is 1 meters.\nSnuke walks on Beam i at a speed of 1/A_i meters per second, and Ringo walks on Beam i at a speed of 1/B_i meters per second.\nSnuke and Ringo will play the following game:\n\nFirst, Snuke connects the N beams in any order of his choice and makes a long beam of length N meters.\nThen, Snuke starts at the left end of the long beam. At the same time, Ringo starts at a point chosen uniformly at random on the long beam. Both of them walk to the right end of the long beam.\nSnuke wins if and only if he catches up to Ringo before Ringo reaches the right end of the long beam. That is, Snuke wins if there is a moment when Snuke and Ringo stand at the same position, and Ringo wins otherwise.\n\nFind the probability that Snuke wins when Snuke arranges the N beams so that the probability of his winning is maximized.\nThis probability is a rational number, so we ask you to represent it as an irreducible fraction P/Q (to represent 0, use P=0, Q=1).\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i,B_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N\nTask Output: Print the numerator and denominator of the irreducible fraction that represents the maximum probability of Snuke's winning.\nTask Samples: input: 2\n3 2\n1 2 output: 1 4\n\nWhen the beams are connected in the order 2,1 from left to right, the probability of Snuke's winning is 1/4, which is the maximum possible value.\ninput: 4\n1 5\n4 7\n2 1\n8 4 output: 1 2\ninput: 3\n4 1\n5 2\n6 3 output: 0 1\ninput: 10\n866111664 178537096\n705445072 318106937\n472381277 579910117\n353498483 865935868\n383133839 231371336\n378371075 681212831\n304570952 16537461\n955719384 267238505\n844917655 218662351\n550309930 62731178 output: 697461712 2899550585\n\n" }, { "title": "", "content": "Problem Statement Snuke has a sequence of N integers x_1, x_2, \\cdots, x_N.\nInitially, all the elements are 0.\nHe can do the following two kinds of operations any number of times in any order:\n\nOperation 1: choose an integer k (1 <= k <= N) and a non-decreasing sequence of k non-negative integers c_1, c_2, \\cdots, c_k.\nThen, for each i (1 <= i <= k), replace x_i with x_i+c_i.\nOperation 2: choose an integer k (1 <= k <= N) and a non-increasing sequence of k non-negative integers c_1, c_2, \\cdots, c_k.\nThen, for each i (1 <= i <= k), replace x_{N-k+i} with x_{N-k+i}+c_i.\n\nHis objective is to have x_i=A_i for all i.\nFind the minimum number of operations required to achieve it.", "constraint": "1 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_N", "output": "Print the minimum number of operations required to achieve Snuke's objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 1 2 1 output: 3\n\nOne way to achieve the objective in three operations is shown below.\nThe objective cannot be achieved in less than three operations.\n\nDo Operation 1 and choose k=2,c=(1,2). Now we have x=(1,2,0,0,0).\nDo Operation 1 and choose k=3,c=(0,0,1). Now we have x=(1,2,1,0,0).\nDo Operation 2 and choose k=2,c=(2,1). Now we have x=(1,2,1,2,1).", "input: 5\n2 1 2 1 2 output: 2", "input: 15\n541962451 761940280 182215520 378290929 211514670 802103642 28942109 641621418 380343684 526398645 81993818 14709769 139483158 444795625 40343083 output: 7"], "Pid": "p02877", "ProblemText": "Task Description: Problem Statement Snuke has a sequence of N integers x_1, x_2, \\cdots, x_N.\nInitially, all the elements are 0.\nHe can do the following two kinds of operations any number of times in any order:\n\nOperation 1: choose an integer k (1 <= k <= N) and a non-decreasing sequence of k non-negative integers c_1, c_2, \\cdots, c_k.\nThen, for each i (1 <= i <= k), replace x_i with x_i+c_i.\nOperation 2: choose an integer k (1 <= k <= N) and a non-increasing sequence of k non-negative integers c_1, c_2, \\cdots, c_k.\nThen, for each i (1 <= i <= k), replace x_{N-k+i} with x_{N-k+i}+c_i.\n\nHis objective is to have x_i=A_i for all i.\nFind the minimum number of operations required to achieve it.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\cdots A_N\nTask Output: Print the minimum number of operations required to achieve Snuke's objective.\nTask Samples: input: 5\n1 2 1 2 1 output: 3\n\nOne way to achieve the objective in three operations is shown below.\nThe objective cannot be achieved in less than three operations.\n\nDo Operation 1 and choose k=2,c=(1,2). Now we have x=(1,2,0,0,0).\nDo Operation 1 and choose k=3,c=(0,0,1). Now we have x=(1,2,1,0,0).\nDo Operation 2 and choose k=2,c=(2,1). Now we have x=(1,2,1,2,1).\ninput: 5\n2 1 2 1 2 output: 2\ninput: 15\n541962451 761940280 182215520 378290929 211514670 802103642 28942109 641621418 380343684 526398645 81993818 14709769 139483158 444795625 40343083 output: 7\n\n" }, { "title": "", "content": "Problem Statement We have two indistinguishable pieces placed on a number line.\nBoth pieces are initially at coordinate 0. (They can occupy the same position. )\nWe can do the following two kinds of operations:\n\nChoose a piece and move it to the right (the positive direction) by 1.\nMove the piece with the smaller coordinate to the position of the piece with the greater coordinate.\nIf two pieces already occupy the same position, nothing happens, but it still counts as doing one operation.\n\nWe want to do a total of N operations of these kinds in some order so that one of the pieces will be at coordinate A and the other at coordinate B.\nFind the number of ways to move the pieces to achieve it.\nThe answer can be enormous, so compute the count modulo 998244353.\nTwo ways to move the pieces are considered different if and only if there exists an integer i (1 <= i <= N) such that the set of the coordinates occupied by the pieces after the i-th operation is different in those two ways.", "constraint": "1 <= N <= 10^7\n0 <= A <= B <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print the number of ways to move the pieces to achieve our objective, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1 3 output: 4\n\nShown below are the four ways to move the pieces, where (x,y) represents the state where the two pieces are at coordinates x and y.\n\n(0,0)→(0,0)→(0,1)→(0,2)→(0,3)→(1,3)\n(0,0)→(0,0)→(0,1)→(0,2)→(1,2)→(1,3)\n(0,0)→(0,0)→(0,1)→(1,1)→(1,2)→(1,3)\n(0,0)→(0,1)→(1,1)→(1,1)→(1,2)→(1,3)", "input: 10 0 0 output: 1", "input: 10 4 6 output: 197", "input: 1000000 100000 200000 output: 758840509"], "Pid": "p02878", "ProblemText": "Task Description: Problem Statement We have two indistinguishable pieces placed on a number line.\nBoth pieces are initially at coordinate 0. (They can occupy the same position. )\nWe can do the following two kinds of operations:\n\nChoose a piece and move it to the right (the positive direction) by 1.\nMove the piece with the smaller coordinate to the position of the piece with the greater coordinate.\nIf two pieces already occupy the same position, nothing happens, but it still counts as doing one operation.\n\nWe want to do a total of N operations of these kinds in some order so that one of the pieces will be at coordinate A and the other at coordinate B.\nFind the number of ways to move the pieces to achieve it.\nThe answer can be enormous, so compute the count modulo 998244353.\nTwo ways to move the pieces are considered different if and only if there exists an integer i (1 <= i <= N) such that the set of the coordinates occupied by the pieces after the i-th operation is different in those two ways.\nTask Constraint: 1 <= N <= 10^7\n0 <= A <= B <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print the number of ways to move the pieces to achieve our objective, modulo 998244353.\nTask Samples: input: 5 1 3 output: 4\n\nShown below are the four ways to move the pieces, where (x,y) represents the state where the two pieces are at coordinates x and y.\n\n(0,0)→(0,0)→(0,1)→(0,2)→(0,3)→(1,3)\n(0,0)→(0,0)→(0,1)→(0,2)→(1,2)→(1,3)\n(0,0)→(0,0)→(0,1)→(1,1)→(1,2)→(1,3)\n(0,0)→(0,1)→(1,1)→(1,1)→(1,2)→(1,3)\ninput: 10 0 0 output: 1\ninput: 10 4 6 output: 197\ninput: 1000000 100000 200000 output: 758840509\n\n" }, { "title": "", "content": "Problem Statement Having learned the multiplication table, Takahashi can multiply two integers between 1 and 9 (inclusive) together. He cannot do any other calculation.\nGiven are two integers A and B.\nIf Takahashi can calculate A * B, print the result; if he cannot, print -1 instead.", "constraint": "1 <= A <= 20\n1 <= B <= 20\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "If Takahashi can calculate A * B, print the result; if he cannot, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5 output: 10\n\n2 * 5 = 10.", "input: 5 10 output: -1\n\n5* 10 = 50, but Takahashi cannot do this calculation, so print -1 instead.", "input: 9 9 output: 81"], "Pid": "p02879", "ProblemText": "Task Description: Problem Statement Having learned the multiplication table, Takahashi can multiply two integers between 1 and 9 (inclusive) together. He cannot do any other calculation.\nGiven are two integers A and B.\nIf Takahashi can calculate A * B, print the result; if he cannot, print -1 instead.\nTask Constraint: 1 <= A <= 20\n1 <= B <= 20\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: If Takahashi can calculate A * B, print the result; if he cannot, print -1.\nTask Samples: input: 2 5 output: 10\n\n2 * 5 = 10.\ninput: 5 10 output: -1\n\n5* 10 = 50, but Takahashi cannot do this calculation, so print -1 instead.\ninput: 9 9 output: 81\n\n" }, { "title": "", "content": "Problem Statement Having learned the multiplication table, Takahashi can multiply two integers between 1 and 9 (inclusive) together.\nGiven an integer N, determine whether N can be represented as the product of two integers between 1 and 9. If it can, print Yes; if it cannot, print No.", "constraint": "1 <= N <= 100\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If N can be represented as the product of two integers between 1 and 9 (inclusive), print Yes; if it cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 output: Yes\n\n10 can be represented as, for example, 2 * 5.", "input: 50 output: No\n\n50 cannot be represented as the product of two integers between 1 and 9.", "input: 81 output: Yes"], "Pid": "p02880", "ProblemText": "Task Description: Problem Statement Having learned the multiplication table, Takahashi can multiply two integers between 1 and 9 (inclusive) together.\nGiven an integer N, determine whether N can be represented as the product of two integers between 1 and 9. If it can, print Yes; if it cannot, print No.\nTask Constraint: 1 <= N <= 100\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If N can be represented as the product of two integers between 1 and 9 (inclusive), print Yes; if it cannot, print No.\nTask Samples: input: 10 output: Yes\n\n10 can be represented as, for example, 2 * 5.\ninput: 50 output: No\n\n50 cannot be represented as the product of two integers between 1 and 9.\ninput: 81 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Takahashi is standing on a multiplication table with infinitely many rows and columns.\nThe square (i, j) contains the integer i * j. Initially, Takahashi is standing at (1,1).\nIn one move, he can move from (i, j) to either (i+1, j) or (i, j+1).\nGiven an integer N, find the minimum number of moves needed to reach a square that contains N.", "constraint": "2 <= N <= 10^{12}\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the minimum number of moves needed to reach a square that contains the integer N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 output: 5\n\n(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.", "input: 50 output: 13\n\n(5,10) can be reached in 13 moves.", "input: 10000000019 output: 10000000018\n\nBoth input and output may be enormous."], "Pid": "p02881", "ProblemText": "Task Description: Problem Statement Takahashi is standing on a multiplication table with infinitely many rows and columns.\nThe square (i, j) contains the integer i * j. Initially, Takahashi is standing at (1,1).\nIn one move, he can move from (i, j) to either (i+1, j) or (i, j+1).\nGiven an integer N, find the minimum number of moves needed to reach a square that contains N.\nTask Constraint: 2 <= N <= 10^{12}\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the minimum number of moves needed to reach a square that contains the integer N.\nTask Samples: input: 10 output: 5\n\n(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.\ninput: 50 output: 13\n\n(5,10) can be reached in 13 moves.\ninput: 10000000019 output: 10000000018\n\nBoth input and output may be enormous.\n\n" }, { "title": "", "content": "Problem Statement Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side a~\\mathrm{cm} and whose height is b~\\mathrm{cm}. (The thickness of the bottle can be ignored. )\nWe will pour x~\\mathrm{cm}^3 of water into the bottle, and gradually tilt the bottle around one of the sides of the base.\nWhen will the water be spilled? More formally, find the maximum angle in which we can tilt the bottle without spilling any water.", "constraint": "All values in input are integers.\n1 <= a <= 100\n1 <= b <= 100\n1 <= x <= a^2b", "input": "Input is given from Standard Input in the following format:\na b x", "output": "Print the maximum angle in which we can tilt the bottle without spilling any water, in degrees.\nYour output will be judged as correct when the absolute or relative error from the judge's output is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 4 output: 45.0000000000\n\nThis bottle has a cubic shape, and it is half-full. The water gets spilled when we tilt the bottle more than 45 degrees.", "input: 12 21 10 output: 89.7834636934\n\nThis bottle is almost empty. When the water gets spilled, the bottle is nearly horizontal.", "input: 3 1 8 output: 4.2363947991\n\nThis bottle is almost full. When the water gets spilled, the bottle is still nearly vertical."], "Pid": "p02882", "ProblemText": "Task Description: Problem Statement Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side a~\\mathrm{cm} and whose height is b~\\mathrm{cm}. (The thickness of the bottle can be ignored. )\nWe will pour x~\\mathrm{cm}^3 of water into the bottle, and gradually tilt the bottle around one of the sides of the base.\nWhen will the water be spilled? More formally, find the maximum angle in which we can tilt the bottle without spilling any water.\nTask Constraint: All values in input are integers.\n1 <= a <= 100\n1 <= b <= 100\n1 <= x <= a^2b\nTask Input: Input is given from Standard Input in the following format:\na b x\nTask Output: Print the maximum angle in which we can tilt the bottle without spilling any water, in degrees.\nYour output will be judged as correct when the absolute or relative error from the judge's output is at most 10^{-6}.\nTask Samples: input: 2 2 4 output: 45.0000000000\n\nThis bottle has a cubic shape, and it is half-full. The water gets spilled when we tilt the bottle more than 45 degrees.\ninput: 12 21 10 output: 89.7834636934\n\nThis bottle is almost empty. When the water gets spilled, the bottle is nearly horizontal.\ninput: 3 1 8 output: 4.2363947991\n\nThis bottle is almost full. When the water gets spilled, the bottle is still nearly vertical.\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi will take part in an eating contest. Teams of N members will compete in this contest, and Takahashi's team consists of N players numbered 1 through N from youngest to oldest. The consumption coefficient of Member i is A_i.\nIn the contest, N foods numbered 1 through N will be presented, and the difficulty of Food i is F_i. The details of the contest are as follows:\n\nA team should assign one member to each food, and should not assign the same member to multiple foods.\nIt will take x * y seconds for a member to finish the food, where x is the consumption coefficient of the member and y is the difficulty of the dish.\nThe score of a team is the longest time it takes for an individual member to finish the food.\n\nBefore the contest, Takahashi's team decided to do some training. In one set of training, a member can reduce his/her consumption coefficient by 1, as long as it does not go below 0. However, for financial reasons, the N members can do at most K sets of training in total.\nWhat is the minimum possible score of the team, achieved by choosing the amounts of members' training and allocating the dishes optimally?", "constraint": "All values in input are integers.\n1 <= N <= 2 * 10^5\n0 <= K <= 10^{18}\n1 <= A_i <= 10^6\\ (1 <= i <= N)\n1 <= F_i <= 10^6\\ (1 <= i <= N)", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nF_1 F_2 . . . F_N", "output": "Print the minimum possible score of the team.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n4 2 1\n2 3 1 output: 2\n\nThey can achieve the score of 2, as follows:\n\nMember 1 does 4 sets of training and eats Food 2 in (4-4) * 3 = 0 seconds.\nMember 2 does 1 set of training and eats Food 3 in (2-1) * 1 = 1 second.\nMember 3 does 0 sets of training and eats Food 1 in (1-0) * 2 = 2 seconds.\n\nThey cannot achieve a score of less than 2, so the answer is 2.", "input: 3 8\n4 2 1\n2 3 1 output: 0\n\nThey can choose not to do exactly K sets of training.", "input: 11 14\n3 1 4 1 5 9 2 6 5 3 5\n8 9 7 9 3 2 3 8 4 6 2 output: 12"], "Pid": "p02883", "ProblemText": "Task Description: Problem Statement\nTakahashi will take part in an eating contest. Teams of N members will compete in this contest, and Takahashi's team consists of N players numbered 1 through N from youngest to oldest. The consumption coefficient of Member i is A_i.\nIn the contest, N foods numbered 1 through N will be presented, and the difficulty of Food i is F_i. The details of the contest are as follows:\n\nA team should assign one member to each food, and should not assign the same member to multiple foods.\nIt will take x * y seconds for a member to finish the food, where x is the consumption coefficient of the member and y is the difficulty of the dish.\nThe score of a team is the longest time it takes for an individual member to finish the food.\n\nBefore the contest, Takahashi's team decided to do some training. In one set of training, a member can reduce his/her consumption coefficient by 1, as long as it does not go below 0. However, for financial reasons, the N members can do at most K sets of training in total.\nWhat is the minimum possible score of the team, achieved by choosing the amounts of members' training and allocating the dishes optimally?\nTask Constraint: All values in input are integers.\n1 <= N <= 2 * 10^5\n0 <= K <= 10^{18}\n1 <= A_i <= 10^6\\ (1 <= i <= N)\n1 <= F_i <= 10^6\\ (1 <= i <= N)\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nF_1 F_2 . . . F_N\nTask Output: Print the minimum possible score of the team.\nTask Samples: input: 3 5\n4 2 1\n2 3 1 output: 2\n\nThey can achieve the score of 2, as follows:\n\nMember 1 does 4 sets of training and eats Food 2 in (4-4) * 3 = 0 seconds.\nMember 2 does 1 set of training and eats Food 3 in (2-1) * 1 = 1 second.\nMember 3 does 0 sets of training and eats Food 1 in (1-0) * 2 = 2 seconds.\n\nThey cannot achieve a score of less than 2, so the answer is 2.\ninput: 3 8\n4 2 1\n2 3 1 output: 0\n\nThey can choose not to do exactly K sets of training.\ninput: 11 14\n3 1 4 1 5 9 2 6 5 3 5\n8 9 7 9 3 2 3 8 4 6 2 output: 12\n\n" }, { "title": "", "content": "Problem Statement There is a cave consisting of N rooms and M one-directional passages. The rooms are numbered 1 through N.\nTakahashi is now in Room 1, and Room N has the exit. The i-th passage connects Room s_i and Room t_i (s_i < t_i) and can only be traversed in the direction from Room s_i to Room t_i. It is known that, for each room except Room N, there is at least one passage going from that room.\nTakahashi will escape from the cave. Each time he reaches a room (assume that he has reached Room 1 at the beginning), he will choose a passage uniformly at random from the ones going from that room and take that passage.\nAoki, a friend of Takahashi's, can block one of the passages (or do nothing) before Takahashi leaves Room 1. However, it is not allowed to block a passage so that Takahashi is potentially unable to reach Room N.\nLet E be the expected number of passages Takahashi takes before he reaches Room N. Find the value of E when Aoki makes a choice that minimizes E.", "constraint": "2 <= N <= 600\nN-1 <= M <= \\frac{N(N-1)}{2}\ns_i < t_i\nIf i != j, (s_i, t_i) \\neq (s_j, t_j). (Added 21:23 JST)\nFor every v = 1,2, ..., N-1, there exists i such that v = s_i.", "input": "Input is given from Standard Input in the following format:\nN M\ns_1 t_1\n:\ns_M t_M", "output": "Print the value of E when Aoki makes a choice that minimizes E.\nYour output will be judged as correct when the absolute or relative error from the judge's output is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n1 4\n2 3\n1 3\n1 2\n3 4\n2 4 output: 1.5000000000\n\nIf Aoki blocks the passage from Room 1 to Room 2, Takahashi will go along the path 1 → 3 → 4 with probability \\frac{1}{2} and 1 → 4 with probability \\frac{1}{2}. E = 1.5 here, and this is the minimum possible value of E.", "input: 3 2\n1 2\n2 3 output: 2.0000000000\n\nBlocking any one passage makes Takahashi unable to reach Room N, so Aoki cannot block a passage.", "input: 10 33\n3 7\n5 10\n8 9\n1 10\n4 6\n2 5\n1 7\n6 10\n1 4\n1 3\n8 10\n1 5\n2 6\n6 9\n5 6\n5 8\n3 6\n4 8\n2 7\n2 9\n6 7\n1 2\n5 9\n6 8\n9 10\n3 9\n7 8\n4 5\n2 10\n5 7\n3 5\n4 7\n4 9 output: 3.0133333333"], "Pid": "p02884", "ProblemText": "Task Description: Problem Statement There is a cave consisting of N rooms and M one-directional passages. The rooms are numbered 1 through N.\nTakahashi is now in Room 1, and Room N has the exit. The i-th passage connects Room s_i and Room t_i (s_i < t_i) and can only be traversed in the direction from Room s_i to Room t_i. It is known that, for each room except Room N, there is at least one passage going from that room.\nTakahashi will escape from the cave. Each time he reaches a room (assume that he has reached Room 1 at the beginning), he will choose a passage uniformly at random from the ones going from that room and take that passage.\nAoki, a friend of Takahashi's, can block one of the passages (or do nothing) before Takahashi leaves Room 1. However, it is not allowed to block a passage so that Takahashi is potentially unable to reach Room N.\nLet E be the expected number of passages Takahashi takes before he reaches Room N. Find the value of E when Aoki makes a choice that minimizes E.\nTask Constraint: 2 <= N <= 600\nN-1 <= M <= \\frac{N(N-1)}{2}\ns_i < t_i\nIf i != j, (s_i, t_i) \\neq (s_j, t_j). (Added 21:23 JST)\nFor every v = 1,2, ..., N-1, there exists i such that v = s_i.\nTask Input: Input is given from Standard Input in the following format:\nN M\ns_1 t_1\n:\ns_M t_M\nTask Output: Print the value of E when Aoki makes a choice that minimizes E.\nYour output will be judged as correct when the absolute or relative error from the judge's output is at most 10^{-6}.\nTask Samples: input: 4 6\n1 4\n2 3\n1 3\n1 2\n3 4\n2 4 output: 1.5000000000\n\nIf Aoki blocks the passage from Room 1 to Room 2, Takahashi will go along the path 1 → 3 → 4 with probability \\frac{1}{2} and 1 → 4 with probability \\frac{1}{2}. E = 1.5 here, and this is the minimum possible value of E.\ninput: 3 2\n1 2\n2 3 output: 2.0000000000\n\nBlocking any one passage makes Takahashi unable to reach Room N, so Aoki cannot block a passage.\ninput: 10 33\n3 7\n5 10\n8 9\n1 10\n4 6\n2 5\n1 7\n6 10\n1 4\n1 3\n8 10\n1 5\n2 6\n6 9\n5 6\n5 8\n3 6\n4 8\n2 7\n2 9\n6 7\n1 2\n5 9\n6 8\n9 10\n3 9\n7 8\n4 5\n2 10\n5 7\n3 5\n4 7\n4 9 output: 3.0133333333\n\n" }, { "title": "", "content": "Problem Statement The window of Takahashi's room has a width of A. There are two curtains hung over the window, each of which has a horizontal length of B. (Vertically, the curtains are long enough to cover the whole window. )\nWe will close the window so as to minimize the total horizontal length of the uncovered part of the window.\nFind the total horizontal length of the uncovered parts of the window then.", "constraint": "1 <= A <= 100\n1 <= B <= 100\nA and B are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the total horizontal length of the uncovered parts of the window.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12 4 output: 4\n\nWe have a window with a horizontal length of 12, and two curtains, each of length 4, that cover both ends of the window, for example. The uncovered part has a horizontal length of 4.", "input: 20 15 output: 0\n\nIf the window is completely covered, print 0.", "input: 20 30 output: 0\n\nEach curtain may be longer than the window."], "Pid": "p02885", "ProblemText": "Task Description: Problem Statement The window of Takahashi's room has a width of A. There are two curtains hung over the window, each of which has a horizontal length of B. (Vertically, the curtains are long enough to cover the whole window. )\nWe will close the window so as to minimize the total horizontal length of the uncovered part of the window.\nFind the total horizontal length of the uncovered parts of the window then.\nTask Constraint: 1 <= A <= 100\n1 <= B <= 100\nA and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the total horizontal length of the uncovered parts of the window.\nTask Samples: input: 12 4 output: 4\n\nWe have a window with a horizontal length of 12, and two curtains, each of length 4, that cover both ends of the window, for example. The uncovered part has a horizontal length of 4.\ninput: 20 15 output: 0\n\nIf the window is completely covered, print 0.\ninput: 20 30 output: 0\n\nEach curtain may be longer than the window.\n\n" }, { "title": "", "content": "Problem Statement It's now the season of TAKOYAKI FESTIVAL!\nThis year, N takoyaki (a ball-shaped food with a piece of octopus inside) will be served. The deliciousness of the i-th takoyaki is d_i.\nAs is commonly known, when you eat two takoyaki of deliciousness x and y together, you restore x * y health points.\nThere are \\frac{N * (N - 1)}{2} ways to choose two from the N takoyaki served in the festival. For each of these choices, find the health points restored from eating the two takoyaki, then compute the sum of these \\frac{N * (N - 1)}{2} values.", "constraint": "All values in input are integers.\n2 <= N <= 50\n0 <= d_i <= 100", "input": "Input is given from Standard Input in the following format:\nN\nd_1 d_2 . . . d_N", "output": "Print the sum of the health points restored from eating two takoyaki over all possible choices of two takoyaki from the N takoyaki served.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 1 2 output: 11\n\nThere are three possible choices:\n\nEat the first and second takoyaki. You will restore 3 health points.\nEat the second and third takoyaki. You will restore 2 health points.\nEat the first and third takoyaki. You will restore 6 health points.\n\nThe sum of these values is 11.", "input: 7\n5 0 7 8 3 3 2 output: 312"], "Pid": "p02886", "ProblemText": "Task Description: Problem Statement It's now the season of TAKOYAKI FESTIVAL!\nThis year, N takoyaki (a ball-shaped food with a piece of octopus inside) will be served. The deliciousness of the i-th takoyaki is d_i.\nAs is commonly known, when you eat two takoyaki of deliciousness x and y together, you restore x * y health points.\nThere are \\frac{N * (N - 1)}{2} ways to choose two from the N takoyaki served in the festival. For each of these choices, find the health points restored from eating the two takoyaki, then compute the sum of these \\frac{N * (N - 1)}{2} values.\nTask Constraint: All values in input are integers.\n2 <= N <= 50\n0 <= d_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nd_1 d_2 . . . d_N\nTask Output: Print the sum of the health points restored from eating two takoyaki over all possible choices of two takoyaki from the N takoyaki served.\nTask Samples: input: 3\n3 1 2 output: 11\n\nThere are three possible choices:\n\nEat the first and second takoyaki. You will restore 3 health points.\nEat the second and third takoyaki. You will restore 2 health points.\nEat the first and third takoyaki. You will restore 6 health points.\n\nThe sum of these values is 11.\ninput: 7\n5 0 7 8 3 3 2 output: 312\n\n" }, { "title": "", "content": "Problem Statement There are N slimes lining up from left to right. The colors of these slimes will be given as a string S of length N consisting of lowercase English letters. The i-th slime from the left has the color that corresponds to the i-th character of S.\nAdjacent slimes with the same color will fuse into one larger slime without changing the color. If there were a slime adjacent to this group of slimes before fusion, that slime is now adjacent to the new larger slime.\nUltimately, how many slimes will be there?", "constraint": "1 <= N <= 10^5\n|S| = N\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the final number of slimes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10\naabbbbaaca output: 5\n\nUltimately, these slimes will fuse into abaca.", "input: 5\naaaaa output: 1\n\nAll the slimes will fuse into one.", "input: 20\nxxzaffeeeeddfkkkkllq output: 10"], "Pid": "p02887", "ProblemText": "Task Description: Problem Statement There are N slimes lining up from left to right. The colors of these slimes will be given as a string S of length N consisting of lowercase English letters. The i-th slime from the left has the color that corresponds to the i-th character of S.\nAdjacent slimes with the same color will fuse into one larger slime without changing the color. If there were a slime adjacent to this group of slimes before fusion, that slime is now adjacent to the new larger slime.\nUltimately, how many slimes will be there?\nTask Constraint: 1 <= N <= 10^5\n|S| = N\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the final number of slimes.\nTask Samples: input: 10\naabbbbaaca output: 5\n\nUltimately, these slimes will fuse into abaca.\ninput: 5\naaaaa output: 1\n\nAll the slimes will fuse into one.\ninput: 20\nxxzaffeeeeddfkkkkllq output: 10\n\n" }, { "title": "", "content": "Problem Statement Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.\nHe is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:\n\na < b + c\nb < c + a\nc < a + b\n\nHow many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.", "constraint": "", "input": "Input is given from Standard Input in the following format:\nN\nL_1 L_2 . . . L_N", "output": "Print the number of different triangles that can be formed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 4 2 1 output: 1\n\nOnly one triangle can be formed: the triangle formed by the first, second, and third sticks.", "input: 3\n1 1000 1 output: 0\n\nNo triangles can be formed.", "input: 7\n218 786 704 233 645 728 389 output: 23"], "Pid": "p02888", "ProblemText": "Task Description: Problem Statement Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.\nHe is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:\n\na < b + c\nb < c + a\nc < a + b\n\nHow many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.\nTask Input: Input is given from Standard Input in the following format:\nN\nL_1 L_2 . . . L_N\nTask Output: Print the number of different triangles that can be formed.\nTask Samples: input: 4\n3 4 2 1 output: 1\n\nOnly one triangle can be formed: the triangle formed by the first, second, and third sticks.\ninput: 3\n1 1000 1 output: 0\n\nNo triangles can be formed.\ninput: 7\n218 786 704 233 645 728 389 output: 23\n\n" }, { "title": "", "content": "Problem Statement There are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.\nTakahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each unit distance traveled. When visiting a town while traveling, he can full the tank (or choose not to do so). Travel that results in the tank becoming empty halfway on the road cannot be done.\nProcess the following Q queries:\n\nThe tank is now full. Find the minimum number of times he needs to full his tank while traveling from Town s_i to Town t_i. If Town t_i is unreachable, print -1.", "constraint": "All values in input are integers.\n2 <= N <= 300\n0 <= M <= \\frac{N(N-1)}{2}\n1 <= L <= 10^9\n1 <= A_i, B_i <= N\nA_i \\neq B_i\n<=ft(A_i, B_i\\right) \\neq <=ft(A_j, B_j\\right) (if i \\neq j)\n<=ft(A_i, B_i\\right) \\neq <=ft(B_j, A_j\\right) (if i \\neq j)\n1 <= C_i <= 10^9\n1 <= Q <= N<=ft(N-1\\right)\n1 <= s_i, t_i <= N\ns_i \\neq t_i\n<=ft(s_i, t_i\\right) \\neq <=ft(s_j, t_j\\right) (if i \\neq j)", "input": "Input is given from Standard Input in the following format:\nN M L\nA_1 B_1 C_1\n:\nA_M B_M C_M\nQ\ns_1 t_1\n:\ns_Q t_Q", "output": "Print Q lines.\nThe i-th line should contain the minimum number of times the tank needs to be fulled while traveling from Town s_i to Town t_i. If Town t_i is unreachable, the line should contain -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 5\n1 2 3\n2 3 3\n2\n3 2\n1 3 output: 0\n1\n\nTo travel from Town 3 to Town 2, we can use the second road to reach Town 2 without fueling the tank on the way.\nTo travel from Town 1 to Town 3, we can first use the first road to get to Town 2, full the tank, and use the second road to reach Town 3.", "input: 4 0 1\n1\n2 1 output: -1\n\nThere may be no road at all.", "input: 5 4 4\n1 2 2\n2 3 2\n3 4 3\n4 5 2\n20\n2 1\n3 1\n4 1\n5 1\n1 2\n3 2\n4 2\n5 2\n1 3\n2 3\n4 3\n5 3\n1 4\n2 4\n3 4\n5 4\n1 5\n2 5\n3 5\n4 5 output: 0\n0\n1\n2\n0\n0\n1\n2\n0\n0\n0\n1\n1\n1\n0\n0\n2\n2\n1\n0"], "Pid": "p02889", "ProblemText": "Task Description: Problem Statement There are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.\nTakahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each unit distance traveled. When visiting a town while traveling, he can full the tank (or choose not to do so). Travel that results in the tank becoming empty halfway on the road cannot be done.\nProcess the following Q queries:\n\nThe tank is now full. Find the minimum number of times he needs to full his tank while traveling from Town s_i to Town t_i. If Town t_i is unreachable, print -1.\nTask Constraint: All values in input are integers.\n2 <= N <= 300\n0 <= M <= \\frac{N(N-1)}{2}\n1 <= L <= 10^9\n1 <= A_i, B_i <= N\nA_i \\neq B_i\n<=ft(A_i, B_i\\right) \\neq <=ft(A_j, B_j\\right) (if i \\neq j)\n<=ft(A_i, B_i\\right) \\neq <=ft(B_j, A_j\\right) (if i \\neq j)\n1 <= C_i <= 10^9\n1 <= Q <= N<=ft(N-1\\right)\n1 <= s_i, t_i <= N\ns_i \\neq t_i\n<=ft(s_i, t_i\\right) \\neq <=ft(s_j, t_j\\right) (if i \\neq j)\nTask Input: Input is given from Standard Input in the following format:\nN M L\nA_1 B_1 C_1\n:\nA_M B_M C_M\nQ\ns_1 t_1\n:\ns_Q t_Q\nTask Output: Print Q lines.\nThe i-th line should contain the minimum number of times the tank needs to be fulled while traveling from Town s_i to Town t_i. If Town t_i is unreachable, the line should contain -1 instead.\nTask Samples: input: 3 2 5\n1 2 3\n2 3 3\n2\n3 2\n1 3 output: 0\n1\n\nTo travel from Town 3 to Town 2, we can use the second road to reach Town 2 without fueling the tank on the way.\nTo travel from Town 1 to Town 3, we can first use the first road to get to Town 2, full the tank, and use the second road to reach Town 3.\ninput: 4 0 1\n1\n2 1 output: -1\n\nThere may be no road at all.\ninput: 5 4 4\n1 2 2\n2 3 2\n3 4 3\n4 5 2\n20\n2 1\n3 1\n4 1\n5 1\n1 2\n3 2\n4 2\n5 2\n1 3\n2 3\n4 3\n5 3\n1 4\n2 4\n3 4\n5 4\n1 5\n2 5\n3 5\n4 5 output: 0\n0\n1\n2\n0\n0\n1\n2\n0\n0\n0\n1\n1\n1\n0\n0\n2\n2\n1\n0\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi has N cards. The i-th of these cards has an integer A_i written on it.\nTakahashi will choose an integer K, and then repeat the following operation some number of times:\n\nChoose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear. )\n\nFor each K = 1,2, \\ldots, N, find the maximum number of times Takahashi can do the operation.", "constraint": "1 <= N <= 3 * 10^5 \n 1 <= A_i <= N \nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\ldots A_N", "output": "Print N integers.\nThe t-th (1 <= t <= N) of them should be the answer for the case K=t.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 1 2 output: 3\n1\n0\n\nFor K = 1, we can do the operation as follows:\n\nChoose the first card to eat.\nChoose the second card to eat.\nChoose the third card to eat.\n\nFor K = 2, we can do the operation as follows:\n\nChoose the first and second cards to eat.\n\nFor K = 3, we cannot do the operation at all. Note that we cannot choose the first and third cards at the same time.", "input: 5\n1 2 3 4 5 output: 5\n2\n1\n1\n1", "input: 4\n1 3 3 3 output: 4\n1\n0\n0"], "Pid": "p02890", "ProblemText": "Task Description: Problem Statement\nTakahashi has N cards. The i-th of these cards has an integer A_i written on it.\nTakahashi will choose an integer K, and then repeat the following operation some number of times:\n\nChoose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear. )\n\nFor each K = 1,2, \\ldots, N, find the maximum number of times Takahashi can do the operation.\nTask Constraint: 1 <= N <= 3 * 10^5 \n 1 <= A_i <= N \nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\ldots A_N\nTask Output: Print N integers.\nThe t-th (1 <= t <= N) of them should be the answer for the case K=t.\nTask Samples: input: 3\n2 1 2 output: 3\n1\n0\n\nFor K = 1, we can do the operation as follows:\n\nChoose the first card to eat.\nChoose the second card to eat.\nChoose the third card to eat.\n\nFor K = 2, we can do the operation as follows:\n\nChoose the first and second cards to eat.\n\nFor K = 3, we cannot do the operation at all. Note that we cannot choose the first and third cards at the same time.\ninput: 5\n1 2 3 4 5 output: 5\n2\n1\n1\n1\ninput: 4\n1 3 3 3 output: 4\n1\n0\n0\n\n" }, { "title": "", "content": "Problem Statement Given is a string S. Let T be the concatenation of K copies of S.\nWe can repeatedly perform the following operation: choose a character in T and replace it with a different character.\nFind the minimum number of operations required to satisfy the following condition: any two adjacent characters in T are different.", "constraint": "1 <= |S| <= 100\nS consists of lowercase English letters.\n1 <= K <= 10^9\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nS\nK", "output": "Print the minimum number of operations required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: issii\n2 output: 4\n\nT is issiiissii. For example, we can rewrite it into ispiqisyhi, and now any two adjacent characters are different.", "input: qq\n81 output: 81", "input: cooooooooonteeeeeeeeeest\n999993333 output: 8999939997"], "Pid": "p02891", "ProblemText": "Task Description: Problem Statement Given is a string S. Let T be the concatenation of K copies of S.\nWe can repeatedly perform the following operation: choose a character in T and replace it with a different character.\nFind the minimum number of operations required to satisfy the following condition: any two adjacent characters in T are different.\nTask Constraint: 1 <= |S| <= 100\nS consists of lowercase English letters.\n1 <= K <= 10^9\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nS\nK\nTask Output: Print the minimum number of operations required.\nTask Samples: input: issii\n2 output: 4\n\nT is issiiissii. For example, we can rewrite it into ispiqisyhi, and now any two adjacent characters are different.\ninput: qq\n81 output: 81\ninput: cooooooooonteeeeeeeeeest\n999993333 output: 8999939997\n\n" }, { "title": "", "content": "Problem Statement Given is a connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the edges are described by a grid of characters S.\nIf S_{i, j} is 1, there is an edge connecting Vertex i and j; otherwise, there is no such edge.\nDetermine whether it is possible to divide the vertices into non-empty sets V_1, \\dots, V_k such that the following condition is satisfied. If the answer is yes, find the maximum possible number of sets, k, in such a division.\n\nEvery edge connects two vertices belonging to two \"adjacent\" sets. More formally, for every edge (i, j), there exists 1<= t<= k-1 such that i\\in V_t, j\\in V_{t+1} or i\\in V_{t+1}, j\\in V_t holds.", "constraint": "2 <= N <= 200\nS_{i,j} is 0 or 1.\nS_{i,i} is 0.\nS_{i,j}=S_{j,i}\nThe given graph is connected.\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN\nS_{1,1}. . . S_{1, N}\n:\nS_{N, 1}. . . S_{N, N}", "output": "If it is impossible to divide the vertices into sets so that the condition is satisfied, print -1.\nOtherwise, print the maximum possible number of sets, k, in a division that satisfies the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n01\n10 output: 2\n\nWe can put Vertex 1 in V_1 and Vertex 2 in V_2.", "input: 3\n011\n101\n110 output: -1", "input: 6\n010110\n101001\n010100\n101000\n100000\n010000 output: 4"], "Pid": "p02892", "ProblemText": "Task Description: Problem Statement Given is a connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the edges are described by a grid of characters S.\nIf S_{i, j} is 1, there is an edge connecting Vertex i and j; otherwise, there is no such edge.\nDetermine whether it is possible to divide the vertices into non-empty sets V_1, \\dots, V_k such that the following condition is satisfied. If the answer is yes, find the maximum possible number of sets, k, in such a division.\n\nEvery edge connects two vertices belonging to two \"adjacent\" sets. More formally, for every edge (i, j), there exists 1<= t<= k-1 such that i\\in V_t, j\\in V_{t+1} or i\\in V_{t+1}, j\\in V_t holds.\nTask Constraint: 2 <= N <= 200\nS_{i,j} is 0 or 1.\nS_{i,i} is 0.\nS_{i,j}=S_{j,i}\nThe given graph is connected.\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nS_{1,1}. . . S_{1, N}\n:\nS_{N, 1}. . . S_{N, N}\nTask Output: If it is impossible to divide the vertices into sets so that the condition is satisfied, print -1.\nOtherwise, print the maximum possible number of sets, k, in a division that satisfies the condition.\nTask Samples: input: 2\n01\n10 output: 2\n\nWe can put Vertex 1 in V_1 and Vertex 2 in V_2.\ninput: 3\n011\n101\n110 output: -1\ninput: 6\n010110\n101001\n010100\n101000\n100000\n010000 output: 4\n\n" }, { "title": "", "content": "Problem Statement Given are integers N and X. For each integer k between 0 and X (inclusive), find the answer to the following question, then compute the sum of all those answers, modulo 998244353.\n\nLet us repeat the following operation on the integer k. Operation: if the integer is currently odd, subtract 1 from it and divide it by 2; otherwise, divide it by 2 and add 2^{N-1} to it. How many operations need to be performed until k returns to its original value? (The answer is considered to be 0 if k never returns to its original value. )", "constraint": "1 <= N <= 2* 10^5\n0 <= X < 2^N\nX is given in binary and has exactly N digits. (In case X has less than N digits, it is given with leading zeroes.)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nX", "output": "Print the sum of the answers to the questions for the integers between 0 and X (inclusive), modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n111 output: 40\n\nFor example, for k=3, the operation changes k as follows: 1,0,4,6,7,3. Therefore the answer for k=3 is 6.", "input: 6\n110101 output: 616", "input: 30\n001110011011011101010111011100 output: 549320998"], "Pid": "p02893", "ProblemText": "Task Description: Problem Statement Given are integers N and X. For each integer k between 0 and X (inclusive), find the answer to the following question, then compute the sum of all those answers, modulo 998244353.\n\nLet us repeat the following operation on the integer k. Operation: if the integer is currently odd, subtract 1 from it and divide it by 2; otherwise, divide it by 2 and add 2^{N-1} to it. How many operations need to be performed until k returns to its original value? (The answer is considered to be 0 if k never returns to its original value. )\nTask Constraint: 1 <= N <= 2* 10^5\n0 <= X < 2^N\nX is given in binary and has exactly N digits. (In case X has less than N digits, it is given with leading zeroes.)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nX\nTask Output: Print the sum of the answers to the questions for the integers between 0 and X (inclusive), modulo 998244353.\nTask Samples: input: 3\n111 output: 40\n\nFor example, for k=3, the operation changes k as follows: 1,0,4,6,7,3. Therefore the answer for k=3 is 6.\ninput: 6\n110101 output: 616\ninput: 30\n001110011011011101010111011100 output: 549320998\n\n" }, { "title": "", "content": "Problem Statement Given are N points on the circumference of a circle centered at (0,0) in an xy-plane.\nThe coordinates of the i-th point are (\\cos(\\frac{2\\pi T_i}{L}), \\sin(\\frac{2\\pi T_i}{L})).\nThree distinct points will be chosen uniformly at random from these N points.\nFind the expected x- and y-coordinates of the center of the circle inscribed in the triangle formed by the chosen points.", "constraint": "3 <= N <= 3000\nN <= L <= 10^9\n0 <= T_i <= L-1\nT_i= 0) is 1 if the number of integers among x_1, x_2, \\ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even. \n\nFor example, 3 \\oplus 5 = 6.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n0 <= A_i < 2^{60}\\ (1 <= i <= N)", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum possible beauty of the painting.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 6 5 output: 12\n\nIf we paint 3,6,5 in blue, red, blue, respectively, the beauty will be (6) + (3 \\oplus 5) = 12.\nThere is no way to paint the integers resulting in greater beauty than 12, so the answer is 12.", "input: 4\n23 36 66 65 output: 188", "input: 20\n1008288677408720767 539403903321871999 1044301017184589821 215886900497862655 504277496111605629 972104334925272829 792625803473366909 972333547668684797 467386965442856573 755861732751878143 1151846447448561405 467257771752201853 683930041385277311 432010719984459389 319104378117934975 611451291444233983 647509226592964607 251832107792119421 827811265410084479 864032478037725181 output: 2012721721873704572\n\nA_i and the answer may not fit into a 32-bit integer type."], "Pid": "p02914", "ProblemText": "Task Description: Problem Statement\nWe have N non-negative integers: A_1, A_2, . . . , A_N.\nConsider painting at least one and at most N-1 integers among them in red, and painting the rest in blue.\nLet the beauty of the painting be the \\mbox{XOR} of the integers painted in red, plus the \\mbox{XOR} of the integers painted in blue.\nFind the maximum possible beauty of the painting.\n\nWhat is \\mbox{XOR}?\n\nThe bitwise \\mbox{XOR} x_1 \\oplus x_2 \\oplus \\ldots \\oplus x_n of n non-negative integers x_1, x_2, \\ldots, x_n is defined as follows:\n\n When x_1 \\oplus x_2 \\oplus \\ldots \\oplus x_n is written in base two, the digit in the 2^k's place (k >= 0) is 1 if the number of integers among x_1, x_2, \\ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even. \n\nFor example, 3 \\oplus 5 = 6.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n0 <= A_i < 2^{60}\\ (1 <= i <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum possible beauty of the painting.\nTask Samples: input: 3\n3 6 5 output: 12\n\nIf we paint 3,6,5 in blue, red, blue, respectively, the beauty will be (6) + (3 \\oplus 5) = 12.\nThere is no way to paint the integers resulting in greater beauty than 12, so the answer is 12.\ninput: 4\n23 36 66 65 output: 188\ninput: 20\n1008288677408720767 539403903321871999 1044301017184589821 215886900497862655 504277496111605629 972104334925272829 792625803473366909 972333547668684797 467386965442856573 755861732751878143 1151846447448561405 467257771752201853 683930041385277311 432010719984459389 319104378117934975 611451291444233983 647509226592964607 251832107792119421 827811265410084479 864032478037725181 output: 2012721721873704572\n\nA_i and the answer may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement Takahashi is going to set a 3-character password.\nHow many possible passwords are there if each of its characters must be a digit between 1 and N (inclusive)?", "constraint": "1 <= N <= 9\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of possible passwords.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 8\n\nThere are eight possible passwords: 111,112,121,122,211,212,221, and 222.", "input: 1 output: 1\n\nThere is only one possible password if you can only use one kind of character."], "Pid": "p02915", "ProblemText": "Task Description: Problem Statement Takahashi is going to set a 3-character password.\nHow many possible passwords are there if each of its characters must be a digit between 1 and N (inclusive)?\nTask Constraint: 1 <= N <= 9\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of possible passwords.\nTask Samples: input: 2 output: 8\n\nThere are eight possible passwords: 111,112,121,122,211,212,221, and 222.\ninput: 1 output: 1\n\nThere is only one possible password if you can only use one kind of character.\n\n" }, { "title": "", "content": "Problem Statement Takahashi went to an all-you-can-eat buffet with N kinds of dishes and ate all of them (Dish 1, Dish 2, \\ldots, Dish N) once.\nThe i-th dish (1 <= i <= N) he ate was Dish A_i.\nWhen he eats Dish i (1 <= i <= N), he gains B_i satisfaction points.\nAdditionally, when he eats Dish i+1 just after eating Dish i (1 <= i <= N - 1), he gains C_i more satisfaction points.\nFind the sum of the satisfaction points he gained.", "constraint": "All values in input are integers.\n2 <= N <= 20\n1 <= A_i <= N\nA_1, A_2, ..., A_N are all different.\n1 <= B_i <= 50\n1 <= C_i <= 50", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N\nC_1 C_2 . . . C_{N-1}", "output": "Print the sum of the satisfaction points Takahashi gained, as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 1 2\n2 5 4\n3 6 output: 14\n\nTakahashi gained 14 satisfaction points in total, as follows:\n\nFirst, he ate Dish 3 and gained 4 satisfaction points.\nNext, he ate Dish 1 and gained 2 satisfaction points.\nLastly, he ate Dish 2 and gained 5 + 3 = 8 satisfaction points.", "input: 4\n2 3 4 1\n13 5 8 24\n45 9 15 output: 74", "input: 2\n1 2\n50 50\n50 output: 150"], "Pid": "p02916", "ProblemText": "Task Description: Problem Statement Takahashi went to an all-you-can-eat buffet with N kinds of dishes and ate all of them (Dish 1, Dish 2, \\ldots, Dish N) once.\nThe i-th dish (1 <= i <= N) he ate was Dish A_i.\nWhen he eats Dish i (1 <= i <= N), he gains B_i satisfaction points.\nAdditionally, when he eats Dish i+1 just after eating Dish i (1 <= i <= N - 1), he gains C_i more satisfaction points.\nFind the sum of the satisfaction points he gained.\nTask Constraint: All values in input are integers.\n2 <= N <= 20\n1 <= A_i <= N\nA_1, A_2, ..., A_N are all different.\n1 <= B_i <= 50\n1 <= C_i <= 50\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N\nC_1 C_2 . . . C_{N-1}\nTask Output: Print the sum of the satisfaction points Takahashi gained, as an integer.\nTask Samples: input: 3\n3 1 2\n2 5 4\n3 6 output: 14\n\nTakahashi gained 14 satisfaction points in total, as follows:\n\nFirst, he ate Dish 3 and gained 4 satisfaction points.\nNext, he ate Dish 1 and gained 2 satisfaction points.\nLastly, he ate Dish 2 and gained 5 + 3 = 8 satisfaction points.\ninput: 4\n2 3 4 1\n13 5 8 24\n45 9 15 output: 74\ninput: 2\n1 2\n50 50\n50 output: 150\n\n" }, { "title": "", "content": "Problem Statement There is an integer sequence A of length N whose values are unknown.\nGiven is an integer sequence B of length N-1 which is known to satisfy the following:\n B_i >= \\max(A_i, A_{i+1}) \nFind the maximum possible sum of the elements of A.", "constraint": "All values in input are integers.\n2 <= N <= 100\n0 <= B_i <= 10^5", "input": "Input is given from Standard Input in the following format:\nN\nB_1 B_2 . . . B_{N-1}", "output": "Print the maximum possible sum of the elements of A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 5 output: 9\n\nA can be, for example, ( 2 , 1 , 5 ), ( -1 , -2 , -3 ), or ( 2 , 2 , 5 ). Among those candidates, A = ( 2 , 2 , 5 ) has the maximum possible sum.", "input: 2\n3 output: 6", "input: 6\n0 153 10 10 23 output: 53"], "Pid": "p02917", "ProblemText": "Task Description: Problem Statement There is an integer sequence A of length N whose values are unknown.\nGiven is an integer sequence B of length N-1 which is known to satisfy the following:\n B_i >= \\max(A_i, A_{i+1}) \nFind the maximum possible sum of the elements of A.\nTask Constraint: All values in input are integers.\n2 <= N <= 100\n0 <= B_i <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nN\nB_1 B_2 . . . B_{N-1}\nTask Output: Print the maximum possible sum of the elements of A.\nTask Samples: input: 3\n2 5 output: 9\n\nA can be, for example, ( 2 , 1 , 5 ), ( -1 , -2 , -3 ), or ( 2 , 2 , 5 ). Among those candidates, A = ( 2 , 2 , 5 ) has the maximum possible sum.\ninput: 2\n3 output: 6\ninput: 6\n0 153 10 10 23 output: 53\n\n" }, { "title": "", "content": "Problem Statement There are N people standing in a queue from west to east.\nGiven is a string S of length N representing the directions of the people.\nThe i-th person from the west is facing west if the i-th character of S is L, and east if that character of S is R.\nA person is happy if the person in front of him/her is facing the same direction.\nIf no person is standing in front of a person, however, he/she is not happy.\nYou can perform the following operation any number of times between 0 and K (inclusive):\nOperation: Choose integers l and r such that 1 <= l <= r <= N, and rotate by 180 degrees the part of the queue: the l-th, (l+1)-th, . . . , r-th persons. That is, for each i = 0,1, . . . , r-l, the (l + i)-th person from the west will stand the (r - i)-th from the west after the operation, facing east if he/she is facing west now, and vice versa.\nWhat is the maximum possible number of happy people you can have?", "constraint": "N is an integer satisfying 1 <= N <= 10^5.\nK is an integer satisfying 1 <= K <= 10^5.\n|S| = N\nEach character of S is L or R.", "input": "Input is given from Standard Input in the following format:\nN K\nS", "output": "Print the maximum possible number of happy people after at most K operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 1\nLRLRRL output: 3\n\nIf we choose (l, r) = (2,5), we have LLLRLL, where the 2-nd, 3-rd, and 6-th persons from the west are happy.", "input: 13 3\nLRRLRLRRLRLLR output: 9", "input: 10 1\nLLLLLRRRRR output: 9", "input: 9 2\nRRRLRLRLL output: 7"], "Pid": "p02918", "ProblemText": "Task Description: Problem Statement There are N people standing in a queue from west to east.\nGiven is a string S of length N representing the directions of the people.\nThe i-th person from the west is facing west if the i-th character of S is L, and east if that character of S is R.\nA person is happy if the person in front of him/her is facing the same direction.\nIf no person is standing in front of a person, however, he/she is not happy.\nYou can perform the following operation any number of times between 0 and K (inclusive):\nOperation: Choose integers l and r such that 1 <= l <= r <= N, and rotate by 180 degrees the part of the queue: the l-th, (l+1)-th, . . . , r-th persons. That is, for each i = 0,1, . . . , r-l, the (l + i)-th person from the west will stand the (r - i)-th from the west after the operation, facing east if he/she is facing west now, and vice versa.\nWhat is the maximum possible number of happy people you can have?\nTask Constraint: N is an integer satisfying 1 <= N <= 10^5.\nK is an integer satisfying 1 <= K <= 10^5.\n|S| = N\nEach character of S is L or R.\nTask Input: Input is given from Standard Input in the following format:\nN K\nS\nTask Output: Print the maximum possible number of happy people after at most K operations.\nTask Samples: input: 6 1\nLRLRRL output: 3\n\nIf we choose (l, r) = (2,5), we have LLLRLL, where the 2-nd, 3-rd, and 6-th persons from the west are happy.\ninput: 13 3\nLRRLRLRRLRLLR output: 9\ninput: 10 1\nLLLLLRRRRR output: 9\ninput: 9 2\nRRRLRLRLL output: 7\n\n" }, { "title": "", "content": "Problem Statement\nGiven is a permutation P of \\{1,2, \\ldots, N\\}.\nFor a pair (L, R) (1 <= L < R <= N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \\ldots, P_R.\nFind \\displaystyle \\sum_{L=1}^{N-1} \\sum_{R=L+1}^{N} X_{L, R}.", "constraint": "2 <= N <= 10^5 \n 1 <= P_i <= N \n P_i \\neq P_j (i \\neq j)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nP_1 P_2 \\ldots P_N", "output": "Print \\displaystyle \\sum_{L=1}^{N-1} \\sum_{R=L+1}^{N} X_{L, R}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3 1 output: 5\n\nX_{1,2} = 2, X_{1,3} = 2, and X_{2,3} = 1, so the sum is 2 + 2 + 1 = 5.", "input: 5\n1 2 3 4 5 output: 30", "input: 8\n8 2 7 3 4 5 6 1 output: 136"], "Pid": "p02919", "ProblemText": "Task Description: Problem Statement\nGiven is a permutation P of \\{1,2, \\ldots, N\\}.\nFor a pair (L, R) (1 <= L < R <= N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \\ldots, P_R.\nFind \\displaystyle \\sum_{L=1}^{N-1} \\sum_{R=L+1}^{N} X_{L, R}.\nTask Constraint: 2 <= N <= 10^5 \n 1 <= P_i <= N \n P_i \\neq P_j (i \\neq j)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nP_1 P_2 \\ldots P_N\nTask Output: Print \\displaystyle \\sum_{L=1}^{N-1} \\sum_{R=L+1}^{N} X_{L, R}.\nTask Samples: input: 3\n2 3 1 output: 5\n\nX_{1,2} = 2, X_{1,3} = 2, and X_{2,3} = 1, so the sum is 2 + 2 + 1 = 5.\ninput: 5\n1 2 3 4 5 output: 30\ninput: 8\n8 2 7 3 4 5 6 1 output: 136\n\n" }, { "title": "", "content": "Problem Statement We have one slime.\nYou can set the health of this slime to any integer value of your choice.\nA slime reproduces every second by spawning another slime that has strictly less health. You can freely choose the health of each new slime. The first reproduction of our slime will happen in one second.\nDetermine if it is possible to set the healths of our first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals a multiset S.\nHere S is a multiset containing 2^N (possibly duplicated) integers: S_1, ~S_2, ~. . . , ~S_{2^N}.", "constraint": "All values in input are integers.\n1 <= N <= 18\n1 <= S_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nS_1 S_2 . . . S_{2^N}", "output": "If it is possible to set the healths of the first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals S, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4 2 3 1 output: Yes\n\nWe will show one way to make the multiset of the healths of the slimes that will exist in 2 seconds equal to S.\nFirst, set the health of the first slime to 4.\nBy letting the first slime spawn a slime whose health is 3, the healths of the slimes that exist in 1 second can be 4,~3.\nThen, by letting the first slime spawn a slime whose health is 2, and letting the second slime spawn a slime whose health is 1, the healths of the slimes that exist in 2 seconds can be 4,~3,~2,~1, which is equal to S as multisets.", "input: 2\n1 2 3 1 output: Yes\n\nS may contain multiple instances of the same integer.", "input: 1\n1 1 output: No", "input: 5\n4 3 5 3 1 2 7 8 7 4 6 3 7 2 3 6 2 7 3 2 6 7 3 4 6 7 3 4 2 5 2 3 output: No"], "Pid": "p02920", "ProblemText": "Task Description: Problem Statement We have one slime.\nYou can set the health of this slime to any integer value of your choice.\nA slime reproduces every second by spawning another slime that has strictly less health. You can freely choose the health of each new slime. The first reproduction of our slime will happen in one second.\nDetermine if it is possible to set the healths of our first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals a multiset S.\nHere S is a multiset containing 2^N (possibly duplicated) integers: S_1, ~S_2, ~. . . , ~S_{2^N}.\nTask Constraint: All values in input are integers.\n1 <= N <= 18\n1 <= S_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1 S_2 . . . S_{2^N}\nTask Output: If it is possible to set the healths of the first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals S, print Yes; otherwise, print No.\nTask Samples: input: 2\n4 2 3 1 output: Yes\n\nWe will show one way to make the multiset of the healths of the slimes that will exist in 2 seconds equal to S.\nFirst, set the health of the first slime to 4.\nBy letting the first slime spawn a slime whose health is 3, the healths of the slimes that exist in 1 second can be 4,~3.\nThen, by letting the first slime spawn a slime whose health is 2, and letting the second slime spawn a slime whose health is 1, the healths of the slimes that exist in 2 seconds can be 4,~3,~2,~1, which is equal to S as multisets.\ninput: 2\n1 2 3 1 output: Yes\n\nS may contain multiple instances of the same integer.\ninput: 1\n1 1 output: No\ninput: 5\n4 3 5 3 1 2 7 8 7 4 6 3 7 2 3 6 2 7 3 2 6 7 3 4 6 7 3 4 2 5 2 3 output: No\n\n" }, { "title": "", "content": "Problem Statement You will be given a string S of length 3 representing the weather forecast for three days in the past.\nThe i-th character (1 <= i <= 3) of S represents the forecast for the i-th day. S, C, and R stand for sunny, cloudy, and rainy, respectively.\nYou will also be given a string T of length 3 representing the actual weather on those three days.\nThe i-th character (1 <= i <= 3) of S represents the actual weather on the i-th day. S, C, and R stand for sunny, cloudy, and rainy, respectively.\nPrint the number of days for which the forecast was correct.", "constraint": "S and T are strings of length 3 each.\nS and T consist of S, C, and R.", "input": "Input is given from Standard Input in the following format:\nS\nT", "output": "Print the number of days for which the forecast was correct.", "content_img": false, "lang": "en", "error": false, "samples": ["input: CSS\nCSR output: 2\nFor the first day, it was forecast to be cloudy, and it was indeed cloudy.\nFor the second day, it was forecast to be sunny, and it was indeed sunny.\nFor the third day, it was forecast to be sunny, but it was rainy.\n\nThus, the forecast was correct for two days in this case.", "input: SSR\nSSR output: 3", "input: RRR\nSSS output: 0"], "Pid": "p02921", "ProblemText": "Task Description: Problem Statement You will be given a string S of length 3 representing the weather forecast for three days in the past.\nThe i-th character (1 <= i <= 3) of S represents the forecast for the i-th day. S, C, and R stand for sunny, cloudy, and rainy, respectively.\nYou will also be given a string T of length 3 representing the actual weather on those three days.\nThe i-th character (1 <= i <= 3) of S represents the actual weather on the i-th day. S, C, and R stand for sunny, cloudy, and rainy, respectively.\nPrint the number of days for which the forecast was correct.\nTask Constraint: S and T are strings of length 3 each.\nS and T consist of S, C, and R.\nTask Input: Input is given from Standard Input in the following format:\nS\nT\nTask Output: Print the number of days for which the forecast was correct.\nTask Samples: input: CSS\nCSR output: 2\nFor the first day, it was forecast to be cloudy, and it was indeed cloudy.\nFor the second day, it was forecast to be sunny, and it was indeed sunny.\nFor the third day, it was forecast to be sunny, but it was rainy.\n\nThus, the forecast was correct for two days in this case.\ninput: SSR\nSSR output: 3\ninput: RRR\nSSS output: 0\n\n" }, { "title": "", "content": "Problem Statement Takahashi's house has only one socket.\nTakahashi wants to extend it with some number of power strips, each with A sockets, into B or more empty sockets.\nOne power strip with A sockets can extend one empty socket into A empty sockets.\nFind the minimum number of power strips required.", "constraint": "All values in input are integers.\n2 <= A <= 20\n1 <= B <= 20", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the minimum number of power strips required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 10 output: 3\n\n3 power strips, each with 4 sockets, extend the socket into 10 empty sockets.", "input: 8 9 output: 2\n\n2 power strips, each with 8 sockets, extend the socket into 15 empty sockets.", "input: 8 8 output: 1"], "Pid": "p02922", "ProblemText": "Task Description: Problem Statement Takahashi's house has only one socket.\nTakahashi wants to extend it with some number of power strips, each with A sockets, into B or more empty sockets.\nOne power strip with A sockets can extend one empty socket into A empty sockets.\nFind the minimum number of power strips required.\nTask Constraint: All values in input are integers.\n2 <= A <= 20\n1 <= B <= 20\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the minimum number of power strips required.\nTask Samples: input: 4 10 output: 3\n\n3 power strips, each with 4 sockets, extend the socket into 10 empty sockets.\ninput: 8 9 output: 2\n\n2 power strips, each with 8 sockets, extend the socket into 15 empty sockets.\ninput: 8 8 output: 1\n\n" }, { "title": "", "content": "Problem Statement There are N squares arranged in a row from left to right.\nThe height of the i-th square from the left is H_i.\nYou will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.\nFind the maximum number of times you can move.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= H_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nH_1 H_2 . . . H_N", "output": "Print the maximum number of times you can move.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n10 4 8 7 3 output: 2\n\nBy landing on the third square from the left, you can move to the right twice.", "input: 7\n4 4 5 6 6 5 5 output: 3\n\nBy landing on the fourth square from the left, you can move to the right three times.", "input: 4\n1 2 3 4 output: 0"], "Pid": "p02923", "ProblemText": "Task Description: Problem Statement There are N squares arranged in a row from left to right.\nThe height of the i-th square from the left is H_i.\nYou will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.\nFind the maximum number of times you can move.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= H_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nH_1 H_2 . . . H_N\nTask Output: Print the maximum number of times you can move.\nTask Samples: input: 5\n10 4 8 7 3 output: 2\n\nBy landing on the third square from the left, you can move to the right twice.\ninput: 7\n4 4 5 6 6 5 5 output: 3\n\nBy landing on the fourth square from the left, you can move to the right three times.\ninput: 4\n1 2 3 4 output: 0\n\n" }, { "title": "", "content": "Problem Statement For an integer N, we will choose a permutation \\{P_1, P_2, . . . , P_N\\} of \\{1,2, . . . , N\\}.\nThen, for each i=1,2, . . . , N, let M_i be the remainder when i is divided by P_i.\nFind the maximum possible value of M_1 + M_2 + \\cdots + M_N.", "constraint": "N is an integer satisfying 1 <= N <= 10^9.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the maximum possible value of M_1 + M_2 + \\cdots + M_N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 1\n\nWhen the permutation \\{P_1, P_2\\} = \\{2,1\\} is chosen, M_1 + M_2 = 1 + 0 = 1.", "input: 13 output: 78", "input: 1 output: 0"], "Pid": "p02924", "ProblemText": "Task Description: Problem Statement For an integer N, we will choose a permutation \\{P_1, P_2, . . . , P_N\\} of \\{1,2, . . . , N\\}.\nThen, for each i=1,2, . . . , N, let M_i be the remainder when i is divided by P_i.\nFind the maximum possible value of M_1 + M_2 + \\cdots + M_N.\nTask Constraint: N is an integer satisfying 1 <= N <= 10^9.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the maximum possible value of M_1 + M_2 + \\cdots + M_N.\nTask Samples: input: 2 output: 1\n\nWhen the permutation \\{P_1, P_2\\} = \\{2,1\\} is chosen, M_1 + M_2 = 1 + 0 = 1.\ninput: 13 output: 78\ninput: 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement N players will participate in a tennis tournament. We will call them Player 1, Player 2, \\ldots, Player N.\nThe tournament is round-robin format, and there will be N(N-1)/2 matches in total.\nIs it possible to schedule these matches so that all of the following conditions are satisfied? If the answer is yes, also find the minimum number of days required.\n\nEach player plays at most one matches in a day.\nEach player i (1 <= i <= N) plays one match against Player A_{i, 1}, A_{i, 2}, \\ldots, A_{i, N-1} in this order.", "constraint": "3 <= N <= 1000\n1 <= A_{i, j} <= N\nA_{i, j} \\neq i\nA_{i, 1}, A_{i, 2}, \\ldots, A_{i, N-1} are all different.", "input": "Input is given from Standard Input in the following format:\nN\nA_{1,1} A_{1,2} \\ldots A_{1, N-1}\nA_{2,1} A_{2,2} \\ldots A_{2, N-1}\n:\nA_{N, 1} A_{N, 2} \\ldots A_{N, N-1}", "output": "If it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3\n1 3\n1 2 output: 3\n\nAll the conditions can be satisfied if the matches are scheduled for three days as follows:\n\nDay 1: Player 1 vs Player 2\nDay 2: Player 1 vs Player 3\nDay 3: Player 2 vs Player 3\n\nThis is the minimum number of days required.", "input: 4\n2 3 4\n1 3 4\n4 1 2\n3 1 2 output: 4\n\nAll the conditions can be satisfied if the matches are scheduled for four days as follows:\n\nDay 1: Player 1 vs Player 2, Player 3 vs Player 4\nDay 2: Player 1 vs Player 3\nDay 3: Player 1 vs Player 4, Player 2 vs Player 3\nDay 4: Player 2 vs Player 4\n\nThis is the minimum number of days required.", "input: 3\n2 3\n3 1\n1 2 output: -1\n\nAny scheduling of the matches violates some condition."], "Pid": "p02925", "ProblemText": "Task Description: Problem Statement N players will participate in a tennis tournament. We will call them Player 1, Player 2, \\ldots, Player N.\nThe tournament is round-robin format, and there will be N(N-1)/2 matches in total.\nIs it possible to schedule these matches so that all of the following conditions are satisfied? If the answer is yes, also find the minimum number of days required.\n\nEach player plays at most one matches in a day.\nEach player i (1 <= i <= N) plays one match against Player A_{i, 1}, A_{i, 2}, \\ldots, A_{i, N-1} in this order.\nTask Constraint: 3 <= N <= 1000\n1 <= A_{i, j} <= N\nA_{i, j} \\neq i\nA_{i, 1}, A_{i, 2}, \\ldots, A_{i, N-1} are all different.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{1,1} A_{1,2} \\ldots A_{1, N-1}\nA_{2,1} A_{2,2} \\ldots A_{2, N-1}\n:\nA_{N, 1} A_{N, 2} \\ldots A_{N, N-1}\nTask Output: If it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print -1.\nTask Samples: input: 3\n2 3\n1 3\n1 2 output: 3\n\nAll the conditions can be satisfied if the matches are scheduled for three days as follows:\n\nDay 1: Player 1 vs Player 2\nDay 2: Player 1 vs Player 3\nDay 3: Player 2 vs Player 3\n\nThis is the minimum number of days required.\ninput: 4\n2 3 4\n1 3 4\n4 1 2\n3 1 2 output: 4\n\nAll the conditions can be satisfied if the matches are scheduled for four days as follows:\n\nDay 1: Player 1 vs Player 2, Player 3 vs Player 4\nDay 2: Player 1 vs Player 3\nDay 3: Player 1 vs Player 4, Player 2 vs Player 3\nDay 4: Player 2 vs Player 4\n\nThis is the minimum number of days required.\ninput: 3\n2 3\n3 1\n1 2 output: -1\n\nAny scheduling of the matches violates some condition.\n\n" }, { "title": "", "content": "Problem Statement\nE869120 is initially standing at the origin (0,0) in a two-dimensional plane.\nHe has N engines, which can be used as follows:\n\nWhen E869120 uses the i-th engine, his X- and Y-coordinate change by x_i and y_i, respectively. In other words, if E869120 uses the i-th engine from coordinates (X, Y), he will move to the coordinates (X + x_i, Y + y_i).\nE869120 can use these engines in any order, but each engine can be used at most once. He may also choose not to use some of the engines.\n\nHe wants to go as far as possible from the origin.\nLet (X, Y) be his final coordinates. Find the maximum possible value of \\sqrt{X^2 + Y^2}, the distance from the origin.", "constraint": "1 <= N <= 100\n-1 \\ 000 \\ 000 <= x_i <= 1 \\ 000 \\ 000\n-1 \\ 000 \\ 000 <= y_i <= 1 \\ 000 \\ 000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n : :\nx_N y_N", "output": "Print the maximum possible final distance from the origin, as a real value.\nYour output is considered correct when the relative or absolute error from the true answer is at most 10^{-10}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 10\n5 -5\n-5 -5 output: 10.000000000000000000000000000000000000000000000000\n\nThe final distance from the origin can be 10 if we use the engines in one of the following three ways:\n\nUse Engine 1 to move to (0,10).\nUse Engine 2 to move to (5, -5), and then use Engine 3 to move to (0, -10).\nUse Engine 3 to move to (-5, -5), and then use Engine 2 to move to (0, -10).\n\nThe distance cannot be greater than 10, so the maximum possible distance is 10.", "input: 5\n1 1\n1 0\n0 1\n-1 0\n0 -1 output: 2.828427124746190097603377448419396157139343750753\n\nThe maximum possible final distance is 2 \\sqrt{2} = 2.82842....\nOne of the ways to achieve it is:\n\nUse Engine 1 to move to (1,1), and then use Engine 2 to move to (2,1), and finally use Engine 3 to move to (2,2).", "input: 5\n1 1\n2 2\n3 3\n4 4\n5 5 output: 21.213203435596425732025330863145471178545078130654\n\nIf we use all the engines in the order 1 \\rightarrow 2 \\rightarrow 3 \\rightarrow 4 \\rightarrow 5, we will end up at (15,15), with the distance 15 \\sqrt{2} = 21.2132... from the origin.", "input: 3\n0 0\n0 1\n1 0 output: 1.414213562373095048801688724209698078569671875376\n\nThere can be useless engines with (x_i, y_i) = (0,0).", "input: 1\n90447 91000 output: 128303.000000000000000000000000000000000000000000000000\n\nNote that there can be only one engine.", "input: 2\n96000 -72000\n-72000 54000 output: 120000.000000000000000000000000000000000000000000000000\n\nThere can be only two engines, too.", "input: 10\n1 2\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n17 18\n19 20 output: 148.660687473185055226120082139313966514489855137208"], "Pid": "p02926", "ProblemText": "Task Description: Problem Statement\nE869120 is initially standing at the origin (0,0) in a two-dimensional plane.\nHe has N engines, which can be used as follows:\n\nWhen E869120 uses the i-th engine, his X- and Y-coordinate change by x_i and y_i, respectively. In other words, if E869120 uses the i-th engine from coordinates (X, Y), he will move to the coordinates (X + x_i, Y + y_i).\nE869120 can use these engines in any order, but each engine can be used at most once. He may also choose not to use some of the engines.\n\nHe wants to go as far as possible from the origin.\nLet (X, Y) be his final coordinates. Find the maximum possible value of \\sqrt{X^2 + Y^2}, the distance from the origin.\nTask Constraint: 1 <= N <= 100\n-1 \\ 000 \\ 000 <= x_i <= 1 \\ 000 \\ 000\n-1 \\ 000 \\ 000 <= y_i <= 1 \\ 000 \\ 000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n : :\nx_N y_N\nTask Output: Print the maximum possible final distance from the origin, as a real value.\nYour output is considered correct when the relative or absolute error from the true answer is at most 10^{-10}.\nTask Samples: input: 3\n0 10\n5 -5\n-5 -5 output: 10.000000000000000000000000000000000000000000000000\n\nThe final distance from the origin can be 10 if we use the engines in one of the following three ways:\n\nUse Engine 1 to move to (0,10).\nUse Engine 2 to move to (5, -5), and then use Engine 3 to move to (0, -10).\nUse Engine 3 to move to (-5, -5), and then use Engine 2 to move to (0, -10).\n\nThe distance cannot be greater than 10, so the maximum possible distance is 10.\ninput: 5\n1 1\n1 0\n0 1\n-1 0\n0 -1 output: 2.828427124746190097603377448419396157139343750753\n\nThe maximum possible final distance is 2 \\sqrt{2} = 2.82842....\nOne of the ways to achieve it is:\n\nUse Engine 1 to move to (1,1), and then use Engine 2 to move to (2,1), and finally use Engine 3 to move to (2,2).\ninput: 5\n1 1\n2 2\n3 3\n4 4\n5 5 output: 21.213203435596425732025330863145471178545078130654\n\nIf we use all the engines in the order 1 \\rightarrow 2 \\rightarrow 3 \\rightarrow 4 \\rightarrow 5, we will end up at (15,15), with the distance 15 \\sqrt{2} = 21.2132... from the origin.\ninput: 3\n0 0\n0 1\n1 0 output: 1.414213562373095048801688724209698078569671875376\n\nThere can be useless engines with (x_i, y_i) = (0,0).\ninput: 1\n90447 91000 output: 128303.000000000000000000000000000000000000000000000000\n\nNote that there can be only one engine.\ninput: 2\n96000 -72000\n-72000 54000 output: 120000.000000000000000000000000000000000000000000000000\n\nThere can be only two engines, too.\ninput: 10\n1 2\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n17 18\n19 20 output: 148.660687473185055226120082139313966514489855137208\n\n" }, { "title": "", "content": "Problem Statement Today is August 24, one of the five Product Days in a year.\nA date m-d (m is the month, d is the date) is called a Product Day when d is a two-digit number, and all of the following conditions are satisfied (here d_{10} is the tens digit of the day and d_1 is the ones digit of the day):\n\nd_1 >= 2\nd_{10} >= 2\nd_1 * d_{10} = m\n\nTakahashi wants more Product Days, and he made a new calendar called Takahashi Calendar where a year consists of M month from Month 1 to Month M, and each month consists of D days from Day 1 to Day D.\nIn Takahashi Calendar, how many Product Days does a year have?", "constraint": "All values in input are integers.\n1 <= M <= 100\n1 <= D <= 99", "input": "Input is given from Standard Input in the following format:\nM D", "output": "Print the number of Product Days in a year in Takahashi Calender.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15 40 output: 10\n\nThere are 10 Product Days in a year, as follows (m-d denotes Month m, Day d):\n\n4-22\n6-23\n6-32\n8-24\n9-33\n10-25\n12-26\n12-34\n14-27\n15-35", "input: 12 31 output: 5", "input: 1 1 output: 0"], "Pid": "p02927", "ProblemText": "Task Description: Problem Statement Today is August 24, one of the five Product Days in a year.\nA date m-d (m is the month, d is the date) is called a Product Day when d is a two-digit number, and all of the following conditions are satisfied (here d_{10} is the tens digit of the day and d_1 is the ones digit of the day):\n\nd_1 >= 2\nd_{10} >= 2\nd_1 * d_{10} = m\n\nTakahashi wants more Product Days, and he made a new calendar called Takahashi Calendar where a year consists of M month from Month 1 to Month M, and each month consists of D days from Day 1 to Day D.\nIn Takahashi Calendar, how many Product Days does a year have?\nTask Constraint: All values in input are integers.\n1 <= M <= 100\n1 <= D <= 99\nTask Input: Input is given from Standard Input in the following format:\nM D\nTask Output: Print the number of Product Days in a year in Takahashi Calender.\nTask Samples: input: 15 40 output: 10\n\nThere are 10 Product Days in a year, as follows (m-d denotes Month m, Day d):\n\n4-22\n6-23\n6-32\n8-24\n9-33\n10-25\n12-26\n12-34\n14-27\n15-35\ninput: 12 31 output: 5\ninput: 1 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of N integers A~=~A_0, ~A_1, ~. . . , ~A_{N - 1}.\nLet B be a sequence of K * N integers obtained by concatenating K copies of A. For example, if A~=~1, ~3, ~2 and K~=~2, B~=~1, ~3, ~2, ~1, ~3, ~2.\nFind the inversion number of B, modulo 10^9 + 7.\nHere the inversion number of B is defined as the number of ordered pairs of integers (i, ~j)~(0 <= i < j <= K * N - 1) such that B_i > B_j.", "constraint": "All values in input are integers.\n1 <= N <= 2000\n1 <= K <= 10^9\n1 <= A_i <= 2000", "input": "Input is given from Standard Input in the following format:\nN K\nA_0 A_1 . . . A_{N - 1}", "output": "Print the inversion number of B, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n2 1 output: 3\n\nIn this case, B~=~2,~1,~2,~1. We have:\n\nB_0 > B_1\nB_0 > B_3\nB_2 > B_3\n\nThus, the inversion number of B is 3.", "input: 3 5\n1 1 1 output: 0\n\nA may contain multiple occurrences of the same number.", "input: 10 998244353\n10 9 8 7 5 6 3 4 2 1 output: 185297239\n\nBe sure to print the output modulo 10^9 + 7."], "Pid": "p02928", "ProblemText": "Task Description: Problem Statement We have a sequence of N integers A~=~A_0, ~A_1, ~. . . , ~A_{N - 1}.\nLet B be a sequence of K * N integers obtained by concatenating K copies of A. For example, if A~=~1, ~3, ~2 and K~=~2, B~=~1, ~3, ~2, ~1, ~3, ~2.\nFind the inversion number of B, modulo 10^9 + 7.\nHere the inversion number of B is defined as the number of ordered pairs of integers (i, ~j)~(0 <= i < j <= K * N - 1) such that B_i > B_j.\nTask Constraint: All values in input are integers.\n1 <= N <= 2000\n1 <= K <= 10^9\n1 <= A_i <= 2000\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_0 A_1 . . . A_{N - 1}\nTask Output: Print the inversion number of B, modulo 10^9 + 7.\nTask Samples: input: 2 2\n2 1 output: 3\n\nIn this case, B~=~2,~1,~2,~1. We have:\n\nB_0 > B_1\nB_0 > B_3\nB_2 > B_3\n\nThus, the inversion number of B is 3.\ninput: 3 5\n1 1 1 output: 0\n\nA may contain multiple occurrences of the same number.\ninput: 10 998244353\n10 9 8 7 5 6 3 4 2 1 output: 185297239\n\nBe sure to print the output modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement There are 2N squares arranged from left to right. You are given a string of length 2N representing the color of each of the squares.\nThe color of the i-th square from the left is black if the i-th character of S is B, and white if that character is W.\nYou will perform the following operation exactly N times: choose two distinct squares, then invert the colors of these squares and the squares between them. Here, to invert the color of a square is to make it white if it is black, and vice versa. \nThroughout this process, you cannot choose the same square twice or more. That is, each square has to be chosen exactly once.\nFind the number of ways to make all the squares white at the end of the process, modulo 10^9+7.\nTwo ways to make the squares white are considered different if and only if there exists i (1 <= i <= N) such that the pair of the squares chosen in the i-th operation is different.", "constraint": "1 <= N <= 10^5\n|S| = 2N\nEach character of S is B or W.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the number of ways to make all the squares white at the end of the process, modulo 10^9+7. If there are no such ways, print 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\nBWWB output: 4\n\nThere are four ways to make all the squares white, as follows:\n\nChoose Squares 1,3 in the first operation, and choose Squares 2,4 in the second operation.\nChoose Squares 2,4 in the first operation, and choose Squares 1,3 in the second operation.\nChoose Squares 1,4 in the first operation, and choose Squares 2,3 in the second operation.\nChoose Squares 2,3 in the first operation, and choose Squares 1,4 in the second operation.", "input: 4\nBWBBWWWB output: 288", "input: 5\nWWWWWWWWWW output: 0"], "Pid": "p02929", "ProblemText": "Task Description: Problem Statement There are 2N squares arranged from left to right. You are given a string of length 2N representing the color of each of the squares.\nThe color of the i-th square from the left is black if the i-th character of S is B, and white if that character is W.\nYou will perform the following operation exactly N times: choose two distinct squares, then invert the colors of these squares and the squares between them. Here, to invert the color of a square is to make it white if it is black, and vice versa. \nThroughout this process, you cannot choose the same square twice or more. That is, each square has to be chosen exactly once.\nFind the number of ways to make all the squares white at the end of the process, modulo 10^9+7.\nTwo ways to make the squares white are considered different if and only if there exists i (1 <= i <= N) such that the pair of the squares chosen in the i-th operation is different.\nTask Constraint: 1 <= N <= 10^5\n|S| = 2N\nEach character of S is B or W.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the number of ways to make all the squares white at the end of the process, modulo 10^9+7. If there are no such ways, print 0.\nTask Samples: input: 2\nBWWB output: 4\n\nThere are four ways to make all the squares white, as follows:\n\nChoose Squares 1,3 in the first operation, and choose Squares 2,4 in the second operation.\nChoose Squares 2,4 in the first operation, and choose Squares 1,3 in the second operation.\nChoose Squares 1,4 in the first operation, and choose Squares 2,3 in the second operation.\nChoose Squares 2,3 in the first operation, and choose Squares 1,4 in the second operation.\ninput: 4\nBWBBWWWB output: 288\ninput: 5\nWWWWWWWWWW output: 0\n\n" }, { "title": "", "content": "Problem Statement\nAt Coder's head office consists of N rooms numbered 1 to N. For any two rooms, there is a direct passage connecting these rooms.\nFor security reasons, Takahashi the president asked you to set a level for every passage, which is a positive integer and must satisfy the following condition:\n\nFor each room i\\ (1 <= i <= N), if we leave Room i, pass through some passages whose levels are all equal and get back to Room i, the number of times we pass through a passage is always even.\n\nYour task is to set levels to the passages so that the highest level of a passage is minimized.", "constraint": "N is an integer between 2 and 500 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print one way to set levels to the passages so that the objective is achieved, as follows:\na_{1,2} a_{1,3} . . . a_{1, N}\na_{2,3} . . . a_{2, N}\n.\n.\n.\na_{N-1, N}\n\nHere a_{i, j} is the level of the passage connecting Room i and Room j.\nIf there are multiple solutions, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 1 2\n1\n\nThe following image describes this output:\n\nFor example, if we leave Room 2, traverse the path 2 \\to 3 \\to 2 \\to 3 \\to 2 \\to 1 \\to 2 while only passing passages of level 1 and get back to Room 2, we pass through a passage six times."], "Pid": "p02930", "ProblemText": "Task Description: Problem Statement\nAt Coder's head office consists of N rooms numbered 1 to N. For any two rooms, there is a direct passage connecting these rooms.\nFor security reasons, Takahashi the president asked you to set a level for every passage, which is a positive integer and must satisfy the following condition:\n\nFor each room i\\ (1 <= i <= N), if we leave Room i, pass through some passages whose levels are all equal and get back to Room i, the number of times we pass through a passage is always even.\n\nYour task is to set levels to the passages so that the highest level of a passage is minimized.\nTask Constraint: N is an integer between 2 and 500 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print one way to set levels to the passages so that the objective is achieved, as follows:\na_{1,2} a_{1,3} . . . a_{1, N}\na_{2,3} . . . a_{2, N}\n.\n.\n.\na_{N-1, N}\n\nHere a_{i, j} is the level of the passage connecting Room i and Room j.\nIf there are multiple solutions, any of them will be accepted.\nTask Samples: input: 3 output: 1 2\n1\n\nThe following image describes this output:\n\nFor example, if we leave Room 2, traverse the path 2 \\to 3 \\to 2 \\to 3 \\to 2 \\to 1 \\to 2 while only passing passages of level 1 and get back to Room 2, we pass through a passage six times.\n\n" }, { "title": "", "content": "Problem Statement There are N cards placed on a grid with H rows and W columns of squares.\nThe i-th card has an integer A_i written on it, and it is placed on the square at the R_i-th row from the top and the C_i-th column from the left.\nMultiple cards may be placed on the same square.\nYou will first pick up at most one card from each row.\nThen, you will pick up at most one card from each column.\nFind the maximum possible sum of the integers written on the picked cards.", "constraint": "All values are integers.\n1 <= N <= 10^5\n1 <= H, W <= 10^5\n1 <= A_i <= 10^5\n1 <= R_i <= H\n1 <= C_i <= W", "input": "Input is given from Standard Input in the following format:\nN H W\nR_1 C_1 A_1\nR_2 C_2 A_2\n\\vdots\nR_N C_N A_N", "output": "Print the maximum possible sum of the integers written on the picked cards.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 2 2\n2 2 2\n1 1 8\n1 1 5\n1 2 9\n1 2 7\n2 1 4 output: 28\n\nThe sum of the integers written on the picked cards will be 28, the maximum value possible, if you pick up cards as follows:\n\nPick up the fourth card from the first row.\nPick up the sixth card from the second row.\nPick up the second card from the first column.\nPick up the fifth card from the second column.", "input: 13 5 6\n1 3 35902\n4 6 19698\n4 6 73389\n3 6 3031\n3 1 4771\n1 4 4784\n2 1 36357\n2 1 24830\n5 6 50219\n4 6 22645\n1 2 30739\n1 4 68417\n1 5 78537 output: 430590", "input: 1 100000 100000\n1 1 1 output: 1"], "Pid": "p02931", "ProblemText": "Task Description: Problem Statement There are N cards placed on a grid with H rows and W columns of squares.\nThe i-th card has an integer A_i written on it, and it is placed on the square at the R_i-th row from the top and the C_i-th column from the left.\nMultiple cards may be placed on the same square.\nYou will first pick up at most one card from each row.\nThen, you will pick up at most one card from each column.\nFind the maximum possible sum of the integers written on the picked cards.\nTask Constraint: All values are integers.\n1 <= N <= 10^5\n1 <= H, W <= 10^5\n1 <= A_i <= 10^5\n1 <= R_i <= H\n1 <= C_i <= W\nTask Input: Input is given from Standard Input in the following format:\nN H W\nR_1 C_1 A_1\nR_2 C_2 A_2\n\\vdots\nR_N C_N A_N\nTask Output: Print the maximum possible sum of the integers written on the picked cards.\nTask Samples: input: 6 2 2\n2 2 2\n1 1 8\n1 1 5\n1 2 9\n1 2 7\n2 1 4 output: 28\n\nThe sum of the integers written on the picked cards will be 28, the maximum value possible, if you pick up cards as follows:\n\nPick up the fourth card from the first row.\nPick up the sixth card from the second row.\nPick up the second card from the first column.\nPick up the fifth card from the second column.\ninput: 13 5 6\n1 3 35902\n4 6 19698\n4 6 73389\n3 6 3031\n3 1 4771\n1 4 4784\n2 1 36357\n2 1 24830\n5 6 50219\n4 6 22645\n1 2 30739\n1 4 68417\n1 5 78537 output: 430590\ninput: 1 100000 100000\n1 1 1 output: 1\n\n" }, { "title": "", "content": "Problem Statement\nFind the number of sequences of N non-negative integers A_1, A_2, . . . , A_N that satisfy the following conditions:\n\nL <= A_1 + A_2 + . . . + A_N <= R\nWhen the N elements are sorted in non-increasing order, the M-th and (M+1)-th elements are equal.\n\nSince the answer can be enormous, print it modulo 10^9+7.", "constraint": "All values in input are integers.\n1 <= M < N <= 3 * 10^5\n1 <= L <= R <= 3 * 10^5", "input": "Input is given from Standard Input in the following format:\nN M L R", "output": "Print the number of sequences of N non-negative integers, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 3 7 output: 105\n\nThe sequences of non-negative integers that satisfy the conditions are:\n\\begin{eqnarray} &(1,1,1,0), (1,1,1,1), (2,1,1,0), (2,1,1,1), (2,2,2,0), (2,2,2,1), \\\\ &(3,0,0,0), (3,1,1,0), (3,1,1,1), (3,2,2,0), (4,0,0,0), (4,1,1,0), \\\\ &(4,1,1,1), (5,0,0,0), (5,1,1,0), (6,0,0,0), (7,0,0,0)\\end{eqnarray}\nand their permutations, for a total of 105 sequences.", "input: 2 1 4 8 output: 3\n\nThe three sequences that satisfy the conditions are (2,2), (3,3), and (4,4).", "input: 141592 6535 89793 238462 output: 933832916"], "Pid": "p02932", "ProblemText": "Task Description: Problem Statement\nFind the number of sequences of N non-negative integers A_1, A_2, . . . , A_N that satisfy the following conditions:\n\nL <= A_1 + A_2 + . . . + A_N <= R\nWhen the N elements are sorted in non-increasing order, the M-th and (M+1)-th elements are equal.\n\nSince the answer can be enormous, print it modulo 10^9+7.\nTask Constraint: All values in input are integers.\n1 <= M < N <= 3 * 10^5\n1 <= L <= R <= 3 * 10^5\nTask Input: Input is given from Standard Input in the following format:\nN M L R\nTask Output: Print the number of sequences of N non-negative integers, modulo 10^9+7.\nTask Samples: input: 4 2 3 7 output: 105\n\nThe sequences of non-negative integers that satisfy the conditions are:\n\\begin{eqnarray} &(1,1,1,0), (1,1,1,1), (2,1,1,0), (2,1,1,1), (2,2,2,0), (2,2,2,1), \\\\ &(3,0,0,0), (3,1,1,0), (3,1,1,1), (3,2,2,0), (4,0,0,0), (4,1,1,0), \\\\ &(4,1,1,1), (5,0,0,0), (5,1,1,0), (6,0,0,0), (7,0,0,0)\\end{eqnarray}\nand their permutations, for a total of 105 sequences.\ninput: 2 1 4 8 output: 3\n\nThe three sequences that satisfy the conditions are (2,2), (3,3), and (4,4).\ninput: 141592 6535 89793 238462 output: 933832916\n\n" }, { "title": "", "content": "Problem Statement You will be given an integer a and a string s consisting of lowercase English letters as input.\nWrite a program that prints s if a is not less than 3200 and prints red if a is less than 3200.", "constraint": "2800 <= a < 5000\ns is a string of length between 1 and 10 (inclusive).\nEach character of s is a lowercase English letter.", "input": "Input is given from Standard Input in the following format:\na\ns", "output": "If a is not less than 3200, print s; if a is less than 3200, print red.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3200\npink output: pink\n\na = 3200 is not less than 3200, so we print s = pink.", "input: 3199\npink output: red\n\na = 3199 is less than 3200, so we print red.", "input: 4049\nred output: red\n\na = 4049 is not less than 3200, so we print s = red."], "Pid": "p02933", "ProblemText": "Task Description: Problem Statement You will be given an integer a and a string s consisting of lowercase English letters as input.\nWrite a program that prints s if a is not less than 3200 and prints red if a is less than 3200.\nTask Constraint: 2800 <= a < 5000\ns is a string of length between 1 and 10 (inclusive).\nEach character of s is a lowercase English letter.\nTask Input: Input is given from Standard Input in the following format:\na\ns\nTask Output: If a is not less than 3200, print s; if a is less than 3200, print red.\nTask Samples: input: 3200\npink output: pink\n\na = 3200 is not less than 3200, so we print s = pink.\ninput: 3199\npink output: red\n\na = 3199 is less than 3200, so we print red.\ninput: 4049\nred output: red\n\na = 4049 is not less than 3200, so we print s = red.\n\n" }, { "title": "", "content": "Problem Statement Given is a sequence of N integers A_1, \\ldots, A_N.\nFind the (multiplicative) inverse of the sum of the inverses of these numbers, \\frac{1}{\\frac{1}{A_1} + \\ldots + \\frac{1}{A_N}}.", "constraint": "1 <= N <= 100\n1 <= A_i <= 1000", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\ldots A_N", "output": "Print a decimal number (or an integer) representing the value of \\frac{1}{\\frac{1}{A_1} + \\ldots + \\frac{1}{A_N}}.\nYour output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n10 30 output: 7.5\n\n\\frac{1}{\\frac{1}{10} + \\frac{1}{30}} = \\frac{1}{\\frac{4}{30}} = \\frac{30}{4} = 7.5.\nPrinting 7.50001,7.49999, and so on will also be accepted.", "input: 3\n200 200 200 output: 66.66666666666667\n\n\\frac{1}{\\frac{1}{200} + \\frac{1}{200} + \\frac{1}{200}} = \\frac{1}{\\frac{3}{200}} = \\frac{200}{3} = 66.6666....\nPrinting 6.66666e+1 and so on will also be accepted.", "input: 1\n1000 output: 1000\n\n\\frac{1}{\\frac{1}{1000}} = 1000.\nPrinting +1000.0 and so on will also be accepted."], "Pid": "p02934", "ProblemText": "Task Description: Problem Statement Given is a sequence of N integers A_1, \\ldots, A_N.\nFind the (multiplicative) inverse of the sum of the inverses of these numbers, \\frac{1}{\\frac{1}{A_1} + \\ldots + \\frac{1}{A_N}}.\nTask Constraint: 1 <= N <= 100\n1 <= A_i <= 1000\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\ldots A_N\nTask Output: Print a decimal number (or an integer) representing the value of \\frac{1}{\\frac{1}{A_1} + \\ldots + \\frac{1}{A_N}}.\nYour output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.\nTask Samples: input: 2\n10 30 output: 7.5\n\n\\frac{1}{\\frac{1}{10} + \\frac{1}{30}} = \\frac{1}{\\frac{4}{30}} = \\frac{30}{4} = 7.5.\nPrinting 7.50001,7.49999, and so on will also be accepted.\ninput: 3\n200 200 200 output: 66.66666666666667\n\n\\frac{1}{\\frac{1}{200} + \\frac{1}{200} + \\frac{1}{200}} = \\frac{1}{\\frac{3}{200}} = \\frac{200}{3} = 66.6666....\nPrinting 6.66666e+1 and so on will also be accepted.\ninput: 1\n1000 output: 1000\n\n\\frac{1}{\\frac{1}{1000}} = 1000.\nPrinting +1000.0 and so on will also be accepted.\n\n" }, { "title": "", "content": "Problem Statement You have a pot and N ingredients. Each ingredient has a real number parameter called value, and the value of the i-th ingredient (1 <= i <= N) is v_i.\nWhen you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be (x + y) / 2 where x and y are the values of the ingredients consumed, and you can put this ingredient again in the pot.\nAfter you compose ingredients in this way N-1 times, you will end up with one ingredient. Find the maximum possible value of this ingredient.", "constraint": "2 <= N <= 50\n1 <= v_i <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nv_1 v_2 \\ldots v_N", "output": "Print a decimal number (or an integer) representing the maximum possible value of the last ingredient remaining.\nYour output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 4 output: 3.5\n\nIf you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values 3 and 4 is (3 + 4) / 2 = 3.5.\nPrinting 3.50001,3.49999, and so on will also be accepted.", "input: 3\n500 300 200 output: 375\n\nYou start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices:\n\nUse the ingredients of values 500 and 300 to produce an ingredient of value (500 + 300) / 2 = 400. The next composition will use this ingredient and the ingredient of value 200, resulting in an ingredient of value (400 + 200) / 2 = 300.\nUse the ingredients of values 500 and 200 to produce an ingredient of value (500 + 200) / 2 = 350. The next composition will use this ingredient and the ingredient of value 300, resulting in an ingredient of value (350 + 300) / 2 = 325.\nUse the ingredients of values 300 and 200 to produce an ingredient of value (300 + 200) / 2 = 250. The next composition will use this ingredient and the ingredient of value 500, resulting in an ingredient of value (250 + 500) / 2 = 375.\n\nThus, the maximum possible value of the last ingredient remaining is 375.\nPrinting 375.0 and so on will also be accepted.", "input: 5\n138 138 138 138 138 output: 138"], "Pid": "p02935", "ProblemText": "Task Description: Problem Statement You have a pot and N ingredients. Each ingredient has a real number parameter called value, and the value of the i-th ingredient (1 <= i <= N) is v_i.\nWhen you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be (x + y) / 2 where x and y are the values of the ingredients consumed, and you can put this ingredient again in the pot.\nAfter you compose ingredients in this way N-1 times, you will end up with one ingredient. Find the maximum possible value of this ingredient.\nTask Constraint: 2 <= N <= 50\n1 <= v_i <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nv_1 v_2 \\ldots v_N\nTask Output: Print a decimal number (or an integer) representing the maximum possible value of the last ingredient remaining.\nYour output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.\nTask Samples: input: 2\n3 4 output: 3.5\n\nIf you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values 3 and 4 is (3 + 4) / 2 = 3.5.\nPrinting 3.50001,3.49999, and so on will also be accepted.\ninput: 3\n500 300 200 output: 375\n\nYou start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices:\n\nUse the ingredients of values 500 and 300 to produce an ingredient of value (500 + 300) / 2 = 400. The next composition will use this ingredient and the ingredient of value 200, resulting in an ingredient of value (400 + 200) / 2 = 300.\nUse the ingredients of values 500 and 200 to produce an ingredient of value (500 + 200) / 2 = 350. The next composition will use this ingredient and the ingredient of value 300, resulting in an ingredient of value (350 + 300) / 2 = 325.\nUse the ingredients of values 300 and 200 to produce an ingredient of value (300 + 200) / 2 = 250. The next composition will use this ingredient and the ingredient of value 500, resulting in an ingredient of value (250 + 500) / 2 = 375.\n\nThus, the maximum possible value of the last ingredient remaining is 375.\nPrinting 375.0 and so on will also be accepted.\ninput: 5\n138 138 138 138 138 output: 138\n\n" }, { "title": "", "content": "Problem Statement Given is a rooted tree with N vertices numbered 1 to N.\nThe root is Vertex 1, and the i-th edge (1 <= i <= N - 1) connects Vertex a_i and b_i.\nEach of the vertices has a counter installed. Initially, the counters on all the vertices have the value 0.\nNow, the following Q operations will be performed:\n\nOperation j (1 <= j <= Q): Increment by x_j the counter on every vertex contained in the subtree rooted at Vertex p_j.\n\nFind the value of the counter on each vertex after all operations.", "constraint": "2 <= N <= 2 * 10^5\n1 <= Q <= 2 * 10^5\n1 <= a_i < b_i <= N\n1 <= p_j <= N\n1 <= x_j <= 10^4\nThe given graph is a tree.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN Q\na_1 b_1\n:\na_{N-1} b_{N-1}\np_1 x_1\n:\np_Q x_Q", "output": "Print the values of the counters on Vertex 1,2, \\ldots, N after all operations, in this order, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n1 2\n2 3\n2 4\n2 10\n1 100\n3 1 output: 100 110 111 110\n\nThe tree in this input is as follows:\n\nEach operation changes the values of the counters on the vertices as follows:\n\nOperation 1: Increment by 10 the counter on every vertex contained in the subtree rooted at Vertex 2, that is, Vertex 2,3,4. The values of the counters on Vertex 1,2,3,4 are now 0,10,10,10, respectively.\nOperation 2: Increment by 100 the counter on every vertex contained in the subtree rooted at Vertex 1, that is, Vertex 1,2,3,4. The values of the counters on Vertex 1,2,3,4 are now 100,110,110,110, respectively.\nOperation 3: Increment by 1 the counter on every vertex contained in the subtree rooted at Vertex 3, that is, Vertex 3. The values of the counters on Vertex 1,2,3,4 are now 100,110,111,110, respectively.", "input: 6 2\n1 2\n1 3\n2 4\n3 6\n2 5\n1 10\n1 10 output: 20 20 20 20 20 20"], "Pid": "p02936", "ProblemText": "Task Description: Problem Statement Given is a rooted tree with N vertices numbered 1 to N.\nThe root is Vertex 1, and the i-th edge (1 <= i <= N - 1) connects Vertex a_i and b_i.\nEach of the vertices has a counter installed. Initially, the counters on all the vertices have the value 0.\nNow, the following Q operations will be performed:\n\nOperation j (1 <= j <= Q): Increment by x_j the counter on every vertex contained in the subtree rooted at Vertex p_j.\n\nFind the value of the counter on each vertex after all operations.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= Q <= 2 * 10^5\n1 <= a_i < b_i <= N\n1 <= p_j <= N\n1 <= x_j <= 10^4\nThe given graph is a tree.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN Q\na_1 b_1\n:\na_{N-1} b_{N-1}\np_1 x_1\n:\np_Q x_Q\nTask Output: Print the values of the counters on Vertex 1,2, \\ldots, N after all operations, in this order, with spaces in between.\nTask Samples: input: 4 3\n1 2\n2 3\n2 4\n2 10\n1 100\n3 1 output: 100 110 111 110\n\nThe tree in this input is as follows:\n\nEach operation changes the values of the counters on the vertices as follows:\n\nOperation 1: Increment by 10 the counter on every vertex contained in the subtree rooted at Vertex 2, that is, Vertex 2,3,4. The values of the counters on Vertex 1,2,3,4 are now 0,10,10,10, respectively.\nOperation 2: Increment by 100 the counter on every vertex contained in the subtree rooted at Vertex 1, that is, Vertex 1,2,3,4. The values of the counters on Vertex 1,2,3,4 are now 100,110,110,110, respectively.\nOperation 3: Increment by 1 the counter on every vertex contained in the subtree rooted at Vertex 3, that is, Vertex 3. The values of the counters on Vertex 1,2,3,4 are now 100,110,111,110, respectively.\ninput: 6 2\n1 2\n1 3\n2 4\n3 6\n2 5\n1 10\n1 10 output: 20 20 20 20 20 20\n\n" }, { "title": "", "content": "Problem Statement Given are two strings s and t consisting of lowercase English letters. Determine if there exists an integer i satisfying the following condition, and find the minimum such i if it exists.\n\nLet s' be the concatenation of 10^{100} copies of s. t is a subsequence of the string {s'}_1{s'}_2\\ldots{s'}_i (the first i characters in s'). note: Notes\nA subsequence of a string a is a string obtained by deleting zero or more characters from a and concatenating the remaining characters without changing the relative order. For example, the subsequences of contest include net, c, and contest.", "constraint": "1 <= |s| <= 10^5\n1 <= |t| <= 10^5\ns and t consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\ns\nt", "output": "If there exists an integer i satisfying the following condition, print the minimum such i; otherwise, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: contest\nson output: 10\n\nt = son is a subsequence of the string contestcon (the first 10 characters in s' = contestcontestcontest...), so i = 10 satisfies the condition.\nOn the other hand, t is not a subsequence of the string contestco (the first 9 characters in s'), so i = 9 does not satisfy the condition.\nSimilarly, any integer less than 9 does not satisfy the condition, either. Thus, the minimum integer i satisfying the condition is 10.", "input: contest\nprogramming output: -1\n\nt = programming is not a substring of s' = contestcontestcontest.... Thus, there is no integer i satisfying the condition.", "input: contest\nsentence output: 33\n\nNote that the answer may not fit into a 32-bit integer type, though we cannot put such a case here."], "Pid": "p02937", "ProblemText": "Task Description: Problem Statement Given are two strings s and t consisting of lowercase English letters. Determine if there exists an integer i satisfying the following condition, and find the minimum such i if it exists.\n\nLet s' be the concatenation of 10^{100} copies of s. t is a subsequence of the string {s'}_1{s'}_2\\ldots{s'}_i (the first i characters in s'). note: Notes\nA subsequence of a string a is a string obtained by deleting zero or more characters from a and concatenating the remaining characters without changing the relative order. For example, the subsequences of contest include net, c, and contest.\nTask Constraint: 1 <= |s| <= 10^5\n1 <= |t| <= 10^5\ns and t consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\ns\nt\nTask Output: If there exists an integer i satisfying the following condition, print the minimum such i; otherwise, print -1.\nTask Samples: input: contest\nson output: 10\n\nt = son is a subsequence of the string contestcon (the first 10 characters in s' = contestcontestcontest...), so i = 10 satisfies the condition.\nOn the other hand, t is not a subsequence of the string contestco (the first 9 characters in s'), so i = 9 does not satisfy the condition.\nSimilarly, any integer less than 9 does not satisfy the condition, either. Thus, the minimum integer i satisfying the condition is 10.\ninput: contest\nprogramming output: -1\n\nt = programming is not a substring of s' = contestcontestcontest.... Thus, there is no integer i satisfying the condition.\ninput: contest\nsentence output: 33\n\nNote that the answer may not fit into a 32-bit integer type, though we cannot put such a case here.\n\n" }, { "title": "", "content": "Problem Statement Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L <= x <= y <= R) such that the remainder when y is divided by x is equal to y \\mbox{ XOR } x.\n\nWhat is \\mbox{ XOR }?\n\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )", "constraint": "1 <= L <= R <= 10^{18}", "input": "Input is given from Standard Input in the following format:\nL R", "output": "Print the number of pairs of integers (x, y) (L <= x <= y <= R) satisfying the condition, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 output: 3\n\nThree pairs satisfy the condition: (2,2), (2,3), and (3,3).", "input: 10 100 output: 604", "input: 1 1000000000000000000 output: 68038601\n\nBe sure to compute the number modulo 10^9 + 7."], "Pid": "p02938", "ProblemText": "Task Description: Problem Statement Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L <= x <= y <= R) such that the remainder when y is divided by x is equal to y \\mbox{ XOR } x.\n\nWhat is \\mbox{ XOR }?\n\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )\nTask Constraint: 1 <= L <= R <= 10^{18}\nTask Input: Input is given from Standard Input in the following format:\nL R\nTask Output: Print the number of pairs of integers (x, y) (L <= x <= y <= R) satisfying the condition, modulo 10^9 + 7.\nTask Samples: input: 2 3 output: 3\n\nThree pairs satisfy the condition: (2,2), (2,3), and (3,3).\ninput: 10 100 output: 604\ninput: 1 1000000000000000000 output: 68038601\n\nBe sure to compute the number modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement Given is a string S consisting of lowercase English letters. Find the maximum positive integer K that satisfies the following condition:\n\nThere exists a partition of S into K non-empty strings S=S_1S_2. . . S_K such that S_i \\neq S_{i+1} (1 <= i <= K-1).\n\nHere S_1S_2. . . S_K represents the concatenation of S_1, S_2, . . . , S_K in this order.", "constraint": "1 <= |S| <= 2 * 10^5\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the maximum positive integer K that satisfies the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aabbaa output: 4\n\nWe can, for example, divide S into four strings aa, b, ba, and a.", "input: aaaccacabaababc output: 12"], "Pid": "p02939", "ProblemText": "Task Description: Problem Statement Given is a string S consisting of lowercase English letters. Find the maximum positive integer K that satisfies the following condition:\n\nThere exists a partition of S into K non-empty strings S=S_1S_2. . . S_K such that S_i \\neq S_{i+1} (1 <= i <= K-1).\n\nHere S_1S_2. . . S_K represents the concatenation of S_1, S_2, . . . , S_K in this order.\nTask Constraint: 1 <= |S| <= 2 * 10^5\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the maximum positive integer K that satisfies the condition.\nTask Samples: input: aabbaa output: 4\n\nWe can, for example, divide S into four strings aa, b, ba, and a.\ninput: aaaccacabaababc output: 12\n\n" }, { "title": "", "content": "Problem Statement We have 3N colored balls with IDs from 1 to 3N.\nA string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is R, green if S_i is G, and blue if S_i is B. There are N red balls, N green balls, and N blue balls.\nTakahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball.\nThe people want balls with IDs close to each other, so he will additionally satisfy the following condition:\n\nLet a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.\nThen, \\sum_j (c_j-a_j) should be as small as possible.\n\nFind the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353.\nWe consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.", "constraint": "1 <= N <= 10^5\n|S|=3N\nS consists of R, G, and B, and each of these characters occurs N times in S.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nRRRGGGBBB output: 216\n\nThe minimum value of \\sum_j (c_j-a_j) is 18 when the balls are, for example, distributed as follows:\n\nThe first person gets Ball 1,5, and 9.\nThe second person gets Ball 2,4, and 8.\nThe third person gets Ball 3,6, and 7.", "input: 5\nBBRGRRGRGGRBBGB output: 960"], "Pid": "p02940", "ProblemText": "Task Description: Problem Statement We have 3N colored balls with IDs from 1 to 3N.\nA string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is R, green if S_i is G, and blue if S_i is B. There are N red balls, N green balls, and N blue balls.\nTakahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball.\nThe people want balls with IDs close to each other, so he will additionally satisfy the following condition:\n\nLet a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.\nThen, \\sum_j (c_j-a_j) should be as small as possible.\n\nFind the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353.\nWe consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.\nTask Constraint: 1 <= N <= 10^5\n|S|=3N\nS consists of R, G, and B, and each of these characters occurs N times in S.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.\nTask Samples: input: 3\nRRRGGGBBB output: 216\n\nThe minimum value of \\sum_j (c_j-a_j) is 18 when the balls are, for example, distributed as follows:\n\nThe first person gets Ball 1,5, and 9.\nThe second person gets Ball 2,4, and 8.\nThe third person gets Ball 3,6, and 7.\ninput: 5\nBBRGRRGRGGRBBGB output: 960\n\n" }, { "title": "", "content": "Problem Statement There are N positive integers arranged in a circle.\nNow, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:\n\nChoose an integer i such that 1 <= i <= N.\nLet a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.\n\nHere the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.\nDetermine if Takahashi can achieve his objective.\nIf the answer is yes, find the minimum number of operations required.", "constraint": "3 <= N <= 2 * 10^5\n1 <= A_i, B_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N", "output": "Print the minimum number of operations required, or -1 if the objective cannot be achieved.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1 1\n13 5 7 output: 4\n\nTakahashi can achieve his objective by, for example, performing the following operations:\n\nReplace the second number with 3.\nReplace the second number with 5.\nReplace the third number with 7.\nReplace the first number with 13.", "input: 4\n1 2 3 4\n2 3 4 5 output: -1", "input: 5\n5 6 5 2 1\n9817 1108 6890 4343 8704 output: 25"], "Pid": "p02941", "ProblemText": "Task Description: Problem Statement There are N positive integers arranged in a circle.\nNow, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:\n\nChoose an integer i such that 1 <= i <= N.\nLet a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.\n\nHere the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.\nDetermine if Takahashi can achieve his objective.\nIf the answer is yes, find the minimum number of operations required.\nTask Constraint: 3 <= N <= 2 * 10^5\n1 <= A_i, B_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N\nTask Output: Print the minimum number of operations required, or -1 if the objective cannot be achieved.\nTask Samples: input: 3\n1 1 1\n13 5 7 output: 4\n\nTakahashi can achieve his objective by, for example, performing the following operations:\n\nReplace the second number with 3.\nReplace the second number with 5.\nReplace the third number with 7.\nReplace the first number with 13.\ninput: 4\n1 2 3 4\n2 3 4 5 output: -1\ninput: 5\n5 6 5 2 1\n9817 1108 6890 4343 8704 output: 25\n\n" }, { "title": "", "content": "Problem Statement We have a grid with N rows and M columns of squares.\nEach integer from 1 to NM is written in this grid once.\nThe number written in the square at the i-th row from the top and the j-th column from the left is A_{ij}.\nYou need to rearrange these numbers as follows:\n\nFirst, for each of the N rows, rearrange the numbers written in it as you like.\nSecond, for each of the M columns, rearrange the numbers written in it as you like.\nFinally, for each of the N rows, rearrange the numbers written in it as you like.\n\nAfter rearranging the numbers, you want the number written in the square at the i-th row from the top and the j-th column from the left to be M* (i-1)+j.\nConstruct one such way to rearrange the numbers. The constraints guarantee that it is always possible to achieve the objective.", "constraint": "1 <= N,M <= 100\n1 <= A_{ij} <= NM\nA_{ij} are distinct.", "input": "Input is given from Standard Input in the following format:\nN M\nA_{11} A_{12} . . . A_{1M}\n:\nA_{N1} A_{N2} . . . A_{NM}", "output": "Print one way to rearrange the numbers in the following format:\nB_{11} B_{12} . . . B_{1M}\n:\nB_{N1} B_{N2} . . . B_{NM}\nC_{11} C_{12} . . . C_{1M}\n:\nC_{N1} C_{N2} . . . C_{NM}\n\nHere B_{ij} is the number written in the square at the i-th row from the top and the j-th column from the left after Step 1, and C_{ij} is the number written in that square after Step 2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n2 6\n4 3\n1 5 output: 2 6 \n4 3 \n5 1 \n2 1 \n4 3 \n5 6", "input: 3 4\n1 4 7 10\n2 5 8 11\n3 6 9 12 output: 1 4 7 10 \n5 8 11 2 \n9 12 3 6 \n1 4 3 2 \n5 8 7 6 \n9 12 11 10"], "Pid": "p02942", "ProblemText": "Task Description: Problem Statement We have a grid with N rows and M columns of squares.\nEach integer from 1 to NM is written in this grid once.\nThe number written in the square at the i-th row from the top and the j-th column from the left is A_{ij}.\nYou need to rearrange these numbers as follows:\n\nFirst, for each of the N rows, rearrange the numbers written in it as you like.\nSecond, for each of the M columns, rearrange the numbers written in it as you like.\nFinally, for each of the N rows, rearrange the numbers written in it as you like.\n\nAfter rearranging the numbers, you want the number written in the square at the i-th row from the top and the j-th column from the left to be M* (i-1)+j.\nConstruct one such way to rearrange the numbers. The constraints guarantee that it is always possible to achieve the objective.\nTask Constraint: 1 <= N,M <= 100\n1 <= A_{ij} <= NM\nA_{ij} are distinct.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_{11} A_{12} . . . A_{1M}\n:\nA_{N1} A_{N2} . . . A_{NM}\nTask Output: Print one way to rearrange the numbers in the following format:\nB_{11} B_{12} . . . B_{1M}\n:\nB_{N1} B_{N2} . . . B_{NM}\nC_{11} C_{12} . . . C_{1M}\n:\nC_{N1} C_{N2} . . . C_{NM}\n\nHere B_{ij} is the number written in the square at the i-th row from the top and the j-th column from the left after Step 1, and C_{ij} is the number written in that square after Step 2.\nTask Samples: input: 3 2\n2 6\n4 3\n1 5 output: 2 6 \n4 3 \n5 1 \n2 1 \n4 3 \n5 6\ninput: 3 4\n1 4 7 10\n2 5 8 11\n3 6 9 12 output: 1 4 7 10 \n5 8 11 2 \n9 12 3 6 \n1 4 3 2 \n5 8 7 6 \n9 12 11 10\n\n" }, { "title": "", "content": "Problem Statement Takahashi has a string S of length N consisting of lowercase English letters.\nOn this string, he will perform the following operation K times:\n\nLet T be the string obtained by reversing S, and U be the string obtained by concatenating S and T in this order.\nLet S' be some contiguous substring of U with length N, and replace S with S'.\n\nAmong the strings that can be the string S after the K operations, find the lexicographically smallest possible one.", "constraint": "1 <= N <= 5000\n1 <= K <= 10^9\n|S|=N\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nN K\nS", "output": "Print the lexicographically smallest possible string that can be the string S after the K operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1\nbacba output: aabca\n\nWhen S=bacba, T=abcab, U=bacbaabcab, and the optimal choice of S' is S'=aabca.", "input: 10 2\nbbaabbbaab output: aaaabbaabb"], "Pid": "p02943", "ProblemText": "Task Description: Problem Statement Takahashi has a string S of length N consisting of lowercase English letters.\nOn this string, he will perform the following operation K times:\n\nLet T be the string obtained by reversing S, and U be the string obtained by concatenating S and T in this order.\nLet S' be some contiguous substring of U with length N, and replace S with S'.\n\nAmong the strings that can be the string S after the K operations, find the lexicographically smallest possible one.\nTask Constraint: 1 <= N <= 5000\n1 <= K <= 10^9\n|S|=N\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN K\nS\nTask Output: Print the lexicographically smallest possible string that can be the string S after the K operations.\nTask Samples: input: 5 1\nbacba output: aabca\n\nWhen S=bacba, T=abcab, U=bacbaabcab, and the optimal choice of S' is S'=aabca.\ninput: 10 2\nbbaabbbaab output: aaaabbaabb\n\n" }, { "title": "", "content": "Problem Statement For a sequence S of positive integers and positive integers k and l, S is said to belong to level (k, l) when one of the following conditions is satisfied:\n\nThe length of S is 1, and its only element is k.\nThere exist sequences T_1, T_2, . . . , T_m (m >= l) belonging to level (k-1, l) such that the concatenation of T_1, T_2, . . . , T_m in this order coincides with S.\n\nNote that the second condition has no effect when k=1, that is, a sequence belongs to level (1, l) only if the first condition is satisfied.\nGiven are a sequence of positive integers A_1, A_2, . . . , A_N and a positive integer L.\nFind the number of subsequences A_i, A_{i+1}, . . . , A_j (1 <= i <= j <= N) that satisfy the following condition:\n\nThere exists a positive integer K such that the sequence A_i, A_{i+1}, . . . , A_j belongs to level (K, L).", "constraint": "1 <= N <= 2 * 10^5\n2 <= L <= N\n1 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN L\nA_1 A_2 . . . A_N", "output": "Print the number of subsequences A_i, A_{i+1}, . . . , A_j (1 <= i <= j <= N) that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 3\n2 1 1 1 1 1 1 2 3 output: 22\n\nFor example, both of the sequences (1,1,1) and (2) belong to level (2,3), so the sequence (2,1,1,1,1,1,1) belong to level (3,3).", "input: 9 2\n2 1 1 1 1 1 1 2 3 output: 41", "input: 15 3\n4 3 2 1 1 1 2 3 2 2 1 1 1 2 2 output: 31"], "Pid": "p02944", "ProblemText": "Task Description: Problem Statement For a sequence S of positive integers and positive integers k and l, S is said to belong to level (k, l) when one of the following conditions is satisfied:\n\nThe length of S is 1, and its only element is k.\nThere exist sequences T_1, T_2, . . . , T_m (m >= l) belonging to level (k-1, l) such that the concatenation of T_1, T_2, . . . , T_m in this order coincides with S.\n\nNote that the second condition has no effect when k=1, that is, a sequence belongs to level (1, l) only if the first condition is satisfied.\nGiven are a sequence of positive integers A_1, A_2, . . . , A_N and a positive integer L.\nFind the number of subsequences A_i, A_{i+1}, . . . , A_j (1 <= i <= j <= N) that satisfy the following condition:\n\nThere exists a positive integer K such that the sequence A_i, A_{i+1}, . . . , A_j belongs to level (K, L).\nTask Constraint: 1 <= N <= 2 * 10^5\n2 <= L <= N\n1 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN L\nA_1 A_2 . . . A_N\nTask Output: Print the number of subsequences A_i, A_{i+1}, . . . , A_j (1 <= i <= j <= N) that satisfy the condition.\nTask Samples: input: 9 3\n2 1 1 1 1 1 1 2 3 output: 22\n\nFor example, both of the sequences (1,1,1) and (2) belong to level (2,3), so the sequence (2,1,1,1,1,1,1) belong to level (3,3).\ninput: 9 2\n2 1 1 1 1 1 1 2 3 output: 41\ninput: 15 3\n4 3 2 1 1 1 2 3 2 2 1 1 1 2 2 output: 31\n\n" }, { "title": "", "content": "Problem Statement We have two integers: A and B.\nPrint the largest number among A + B, A - B, and A * B.", "constraint": "All values in input are integers.\n-100 <= A,\\ B <= 100", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the largest number among A + B, A - B, and A * B.", "content_img": false, "lang": "en", "error": false, "samples": ["input: -13 3 output: -10\n\nThe largest number among A + B = -10, A - B = -16, and A * B = -39 is -10.", "input: 1 -33 output: 34\n\nThe largest number among A + B = -32, A - B = 34, and A * B = -33 is 34.", "input: 13 3 output: 39\n\nThe largest number among A + B = 16, A - B = 10, and A * B = 39 is 39."], "Pid": "p02945", "ProblemText": "Task Description: Problem Statement We have two integers: A and B.\nPrint the largest number among A + B, A - B, and A * B.\nTask Constraint: All values in input are integers.\n-100 <= A,\\ B <= 100\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the largest number among A + B, A - B, and A * B.\nTask Samples: input: -13 3 output: -10\n\nThe largest number among A + B = -10, A - B = -16, and A * B = -39 is -10.\ninput: 1 -33 output: 34\n\nThe largest number among A + B = -32, A - B = 34, and A * B = -33 is 34.\ninput: 13 3 output: 39\n\nThe largest number among A + B = 16, A - B = 10, and A * B = 39 is 39.\n\n" }, { "title": "", "content": "Problem Statement There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \\ldots, 999999,1000000.\nAmong them, some K consecutive stones are painted black, and the others are painted white.\nAdditionally, we know that the stone at coordinate X is painted black.\nPrint all coordinates that potentially contain a stone painted black, in ascending order.", "constraint": "1 <= K <= 100\n0 <= X <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nK X", "output": "Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 7 output: 5 6 7 8 9\n\nWe know that there are three stones painted black, and the stone at coordinate 7 is painted black. There are three possible cases:\n\nThe three stones painted black are placed at coordinates 5,6, and 7.\nThe three stones painted black are placed at coordinates 6,7, and 8.\nThe three stones painted black are placed at coordinates 7,8, and 9.\n\nThus, five coordinates potentially contain a stone painted black: 5,6,7,8, and 9.", "input: 4 0 output: -3 -2 -1 0 1 2 3\n\nNegative coordinates can also contain a stone painted black.", "input: 1 100 output: 100"], "Pid": "p02946", "ProblemText": "Task Description: Problem Statement There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \\ldots, 999999,1000000.\nAmong them, some K consecutive stones are painted black, and the others are painted white.\nAdditionally, we know that the stone at coordinate X is painted black.\nPrint all coordinates that potentially contain a stone painted black, in ascending order.\nTask Constraint: 1 <= K <= 100\n0 <= X <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nK X\nTask Output: Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.\nTask Samples: input: 3 7 output: 5 6 7 8 9\n\nWe know that there are three stones painted black, and the stone at coordinate 7 is painted black. There are three possible cases:\n\nThe three stones painted black are placed at coordinates 5,6, and 7.\nThe three stones painted black are placed at coordinates 6,7, and 8.\nThe three stones painted black are placed at coordinates 7,8, and 9.\n\nThus, five coordinates potentially contain a stone painted black: 5,6,7,8, and 9.\ninput: 4 0 output: -3 -2 -1 0 1 2 3\n\nNegative coordinates can also contain a stone painted black.\ninput: 1 100 output: 100\n\n" }, { "title": "", "content": "Problem Statement We will call a string obtained by arranging the characters contained in a string a in some order, an anagram of a.\nFor example, greenbin is an anagram of beginner. As seen here, when the same character occurs multiple times, that character must be used that number of times.\nGiven are N strings s_1, s_2, \\ldots, s_N. Each of these strings has a length of 10 and consists of lowercase English characters. Additionally, all of these strings are distinct. Find the number of pairs of integers i, j (1 <= i < j <= N) such that s_i is an anagram of s_j.", "constraint": "2 <= N <= 10^5\ns_i is a string of length 10.\nEach character in s_i is a lowercase English letter.\ns_1, s_2, \\ldots, s_N are all distinct.", "input": "Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N", "output": "Print the number of pairs of integers i, j (1 <= i < j <= N) such that s_i is an anagram of s_j.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nacornistnt\npeanutbomb\nconstraint output: 1\n\ns_1 = acornistnt is an anagram of s_3 = constraint. There are no other pairs i, j such that s_i is an anagram of s_j, so the answer is 1.", "input: 2\noneplustwo\nninemodsix output: 0\n\nIf there is no pair i, j such that s_i is an anagram of s_j, print 0.", "input: 5\nabaaaaaaaa\noneplustwo\naaaaaaaaba\ntwoplusone\naaaabaaaaa output: 4\n\nNote that the answer may not fit into a 32-bit integer type, though we cannot put such a case here."], "Pid": "p02947", "ProblemText": "Task Description: Problem Statement We will call a string obtained by arranging the characters contained in a string a in some order, an anagram of a.\nFor example, greenbin is an anagram of beginner. As seen here, when the same character occurs multiple times, that character must be used that number of times.\nGiven are N strings s_1, s_2, \\ldots, s_N. Each of these strings has a length of 10 and consists of lowercase English characters. Additionally, all of these strings are distinct. Find the number of pairs of integers i, j (1 <= i < j <= N) such that s_i is an anagram of s_j.\nTask Constraint: 2 <= N <= 10^5\ns_i is a string of length 10.\nEach character in s_i is a lowercase English letter.\ns_1, s_2, \\ldots, s_N are all distinct.\nTask Input: Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N\nTask Output: Print the number of pairs of integers i, j (1 <= i < j <= N) such that s_i is an anagram of s_j.\nTask Samples: input: 3\nacornistnt\npeanutbomb\nconstraint output: 1\n\ns_1 = acornistnt is an anagram of s_3 = constraint. There are no other pairs i, j such that s_i is an anagram of s_j, so the answer is 1.\ninput: 2\noneplustwo\nninemodsix output: 0\n\nIf there is no pair i, j such that s_i is an anagram of s_j, print 0.\ninput: 5\nabaaaaaaaa\noneplustwo\naaaaaaaaba\ntwoplusone\naaaabaaaaa output: 4\n\nNote that the answer may not fit into a 32-bit integer type, though we cannot put such a case here.\n\n" }, { "title": "", "content": "Problem Statement There are N one-off jobs available. If you take the i-th job and complete it, you will earn the reward of B_i after A_i days from the day you do it.\nYou can take and complete at most one of these jobs in a day.\nHowever, you cannot retake a job that you have already done.\nFind the maximum total reward that you can earn no later than M days from today.\nYou can already start working today.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i <= 10^5\n1 <= B_i <= 10^4", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N", "output": "Print the maximum total reward that you can earn no later than M days from today.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n4 3\n4 1\n2 2 output: 5\n\nYou can earn the total reward of 5 by taking the jobs as follows:\n\nTake and complete the first job today. You will earn the reward of 3 after four days from today.\nTake and complete the third job tomorrow. You will earn the reward of 2 after two days from tomorrow, that is, after three days from today.", "input: 5 3\n1 2\n1 3\n1 4\n2 1\n2 3 output: 10", "input: 1 1\n2 1 output: 0"], "Pid": "p02948", "ProblemText": "Task Description: Problem Statement There are N one-off jobs available. If you take the i-th job and complete it, you will earn the reward of B_i after A_i days from the day you do it.\nYou can take and complete at most one of these jobs in a day.\nHowever, you cannot retake a job that you have already done.\nFind the maximum total reward that you can earn no later than M days from today.\nYou can already start working today.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i <= 10^5\n1 <= B_i <= 10^4\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N\nTask Output: Print the maximum total reward that you can earn no later than M days from today.\nTask Samples: input: 3 4\n4 3\n4 1\n2 2 output: 5\n\nYou can earn the total reward of 5 by taking the jobs as follows:\n\nTake and complete the first job today. You will earn the reward of 3 after four days from today.\nTake and complete the third job tomorrow. You will earn the reward of 2 after two days from tomorrow, that is, after three days from today.\ninput: 5 3\n1 2\n1 3\n1 4\n2 1\n2 3 output: 10\ninput: 1 1\n2 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement There is a directed graph with N vertices numbered 1 to N and M edges.\nThe i-th edge is directed from Vertex A_i to Vertex B_i, and there are C_i coins \bplaced along that edge.\nAdditionally, there is a button on Vertex N.\nWe will play a game on this graph.\nYou start the game on Vertex 1 with zero coins, and head for Vertex N by traversing the edges while collecting coins.\nIt takes one minute to traverse an edge, and you can collect the coins placed along the edge each time you traverse it.\nAs usual in games, even if you traverse an edge once and collect the coins, the same number of coins will reappear next time you traverse that edge, which you can collect again.\nWhen you reach Vertex N, you can end the game by pressing the button. (You can also choose to leave Vertex N without pressing the button and continue traveling. )\nHowever, when you end the game, you will be asked to pay T * P coins, where T is the number of minutes elapsed since the start of the game. If you have less than T * P coins, you will have to pay all of your coins instead.\nYour score will be the number of coins you have after this payment.\nDetermine if there exists a maximum value of the score that can be obtained. If the answer is yes, find that maximum value.", "constraint": "2 <= N <= 2500\n1 <= M <= 5000\n1 <= A_i, B_i <= N\n1 <= C_i <= 10^5\n0 <= P <= 10^5\nAll values in input are integers.\nVertex N can be reached from Vertex 1.", "input": "Input is given from Standard Input in the following format:\nN M P\nA_1 B_1 C_1\n:\nA_M B_M C_M", "output": "If there exists a maximum value of the score that can be obtained, print that maximum value; otherwise, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 10\n1 2 20\n2 3 30\n1 3 45 output: 35\nThere are two ways to travel from Vertex 1 to Vertex 3:\n\nVertex 1 \\rightarrow 2 \\rightarrow 3: You collect 20 + 30 = 50 coins on the way. After two minutes from the start of the game, you press the button, pay 2 * 10 = 20 coins, and you have 50 - 20 = 30 coins left.\nVertex 1 \\rightarrow 2: You collect 45 coins on the way. After one minute from the start of the game, you press the button, pay 1 * 10 = 10 coins, and you have 45 - 10 = 35 coins left.\n\nThus, the maximum score that can be obtained is 35.", "input: 2 2 10\n1 2 100\n2 2 100 output: -1\nThe edge extending from Vertex 1 takes you to Vertex 2. If you then traverse the edge extending from Vertex 2 to itself t times and press the button, your score will be 90 + 90t. Thus, you can infinitely increase your score, which means there is no maximum value of the score that can be obtained.", "input: 4 5 10\n1 2 1\n1 4 1\n3 4 1\n2 2 100\n3 3 100 output: 0\nThere is no way to travel from Vertex 1 to Vertex 4 other than traversing the edge leading from Vertex 1 to Vertex 4 directly. You will pick up one coin along this edge, but after being asked to paying 10 coins, your score will be 0.\nNote that you can collect an infinite number of coins if you traverse the edge leading from Vertex 1 to Vertex 2, but this is pointless since you can no longer reach Vertex 4 and end the game."], "Pid": "p02949", "ProblemText": "Task Description: Problem Statement There is a directed graph with N vertices numbered 1 to N and M edges.\nThe i-th edge is directed from Vertex A_i to Vertex B_i, and there are C_i coins \bplaced along that edge.\nAdditionally, there is a button on Vertex N.\nWe will play a game on this graph.\nYou start the game on Vertex 1 with zero coins, and head for Vertex N by traversing the edges while collecting coins.\nIt takes one minute to traverse an edge, and you can collect the coins placed along the edge each time you traverse it.\nAs usual in games, even if you traverse an edge once and collect the coins, the same number of coins will reappear next time you traverse that edge, which you can collect again.\nWhen you reach Vertex N, you can end the game by pressing the button. (You can also choose to leave Vertex N without pressing the button and continue traveling. )\nHowever, when you end the game, you will be asked to pay T * P coins, where T is the number of minutes elapsed since the start of the game. If you have less than T * P coins, you will have to pay all of your coins instead.\nYour score will be the number of coins you have after this payment.\nDetermine if there exists a maximum value of the score that can be obtained. If the answer is yes, find that maximum value.\nTask Constraint: 2 <= N <= 2500\n1 <= M <= 5000\n1 <= A_i, B_i <= N\n1 <= C_i <= 10^5\n0 <= P <= 10^5\nAll values in input are integers.\nVertex N can be reached from Vertex 1.\nTask Input: Input is given from Standard Input in the following format:\nN M P\nA_1 B_1 C_1\n:\nA_M B_M C_M\nTask Output: If there exists a maximum value of the score that can be obtained, print that maximum value; otherwise, print -1.\nTask Samples: input: 3 3 10\n1 2 20\n2 3 30\n1 3 45 output: 35\nThere are two ways to travel from Vertex 1 to Vertex 3:\n\nVertex 1 \\rightarrow 2 \\rightarrow 3: You collect 20 + 30 = 50 coins on the way. After two minutes from the start of the game, you press the button, pay 2 * 10 = 20 coins, and you have 50 - 20 = 30 coins left.\nVertex 1 \\rightarrow 2: You collect 45 coins on the way. After one minute from the start of the game, you press the button, pay 1 * 10 = 10 coins, and you have 45 - 10 = 35 coins left.\n\nThus, the maximum score that can be obtained is 35.\ninput: 2 2 10\n1 2 100\n2 2 100 output: -1\nThe edge extending from Vertex 1 takes you to Vertex 2. If you then traverse the edge extending from Vertex 2 to itself t times and press the button, your score will be 90 + 90t. Thus, you can infinitely increase your score, which means there is no maximum value of the score that can be obtained.\ninput: 4 5 10\n1 2 1\n1 4 1\n3 4 1\n2 2 100\n3 3 100 output: 0\nThere is no way to travel from Vertex 1 to Vertex 4 other than traversing the edge leading from Vertex 1 to Vertex 4 directly. You will pick up one coin along this edge, but after being asked to paying 10 coins, your score will be 0.\nNote that you can collect an infinite number of coins if you traverse the edge leading from Vertex 1 to Vertex 2, but this is pointless since you can no longer reach Vertex 4 and end the game.\n\n" }, { "title": "", "content": "Problem Statement Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n\nFor each i (0 <= i <= p-1), b_i is an integer such that 0 <= b_i <= p-1.\nFor each i (0 <= i <= p-1), f(i) \\equiv a_i \\pmod p.", "constraint": "2 <= p <= 2999\np is a prime number.\n0 <= a_i <= 1", "input": "Input is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}", "output": "Print b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 0 output: 1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n\nf(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\nf(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2", "input: 3\n0 0 0 output: 0 0 0\n\nf(x) = 0 is also valid.", "input: 5\n0 1 0 1 0 output: 0 2 0 1 3"], "Pid": "p02950", "ProblemText": "Task Description: Problem Statement Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n\nFor each i (0 <= i <= p-1), b_i is an integer such that 0 <= b_i <= p-1.\nFor each i (0 <= i <= p-1), f(i) \\equiv a_i \\pmod p.\nTask Constraint: 2 <= p <= 2999\np is a prime number.\n0 <= a_i <= 1\nTask Input: Input is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\nTask Output: Print b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\nTask Samples: input: 2\n1 0 output: 1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n\nf(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\nf(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2\ninput: 3\n0 0 0 output: 0 0 0\n\nf(x) = 0 is also valid.\ninput: 5\n0 1 0 1 0 output: 0 2 0 1 3\n\n" }, { "title": "", "content": "Problem Statement We have two bottles for holding water.\nBottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.\nBottle 2 contains C milliliters of water.\nWe will transfer water from Bottle 2 to Bottle 1 as much as possible.\nHow much amount of water will remain in Bottle 2?", "constraint": "All values in input are integers.\n1 <= B <= A <= 20\n1 <= C <= 20", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 4 3 output: 1\n\nWe will transfer two milliliters of water from Bottle 2 to Bottle 1, and one milliliter of water will remain in Bottle 2.", "input: 8 3 9 output: 4", "input: 12 3 7 output: 0"], "Pid": "p02951", "ProblemText": "Task Description: Problem Statement We have two bottles for holding water.\nBottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.\nBottle 2 contains C milliliters of water.\nWe will transfer water from Bottle 2 to Bottle 1 as much as possible.\nHow much amount of water will remain in Bottle 2?\nTask Constraint: All values in input are integers.\n1 <= B <= A <= 20\n1 <= C <= 20\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.\nTask Samples: input: 6 4 3 output: 1\n\nWe will transfer two milliliters of water from Bottle 2 to Bottle 1, and one milliliter of water will remain in Bottle 2.\ninput: 8 3 9 output: 4\ninput: 12 3 7 output: 0\n\n" }, { "title": "", "content": "Problem Statement Given is an integer N. Find the number of positive integers less than or equal to N that have an odd number of digits (in base ten without leading zeros).", "constraint": "1 <= N <= 10^5", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of positive integers less than or equal to N that have an odd number of digits.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11 output: 9\n\nAmong the positive integers less than or equal to 11, nine integers have an odd number of digits: 1,2, \\ldots, 9.", "input: 136 output: 46\n\nIn addition to 1,2, \\ldots, 9, another 37 integers also have an odd number of digits: 100,101, \\ldots, 136.", "input: 100000 output: 90909"], "Pid": "p02952", "ProblemText": "Task Description: Problem Statement Given is an integer N. Find the number of positive integers less than or equal to N that have an odd number of digits (in base ten without leading zeros).\nTask Constraint: 1 <= N <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of positive integers less than or equal to N that have an odd number of digits.\nTask Samples: input: 11 output: 9\n\nAmong the positive integers less than or equal to 11, nine integers have an odd number of digits: 1,2, \\ldots, 9.\ninput: 136 output: 46\n\nIn addition to 1,2, \\ldots, 9, another 37 integers also have an odd number of digits: 100,101, \\ldots, 136.\ninput: 100000 output: 90909\n\n" }, { "title": "", "content": "Problem Statement There are N squares arranged in a row from left to right. The height of the i-th square from the left is H_i.\nFor each square, you will perform either of the following operations once:\n\nDecrease the height of the square by 1.\nDo nothing.\n\nDetermine if it is possible to perform the operations so that the heights of the squares are non-decreasing from left to right.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= H_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nH_1 H_2 . . . H_N", "output": "If it is possible to perform the operations so that the heights of the squares are non-decreasing from left to right, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 1 1 3 output: Yes\n\nYou can achieve the objective by decreasing the height of only the second square from the left by 1.", "input: 4\n1 3 2 1 output: No", "input: 5\n1 2 3 4 5 output: Yes", "input: 1\n1000000000 output: Yes"], "Pid": "p02953", "ProblemText": "Task Description: Problem Statement There are N squares arranged in a row from left to right. The height of the i-th square from the left is H_i.\nFor each square, you will perform either of the following operations once:\n\nDecrease the height of the square by 1.\nDo nothing.\n\nDetermine if it is possible to perform the operations so that the heights of the squares are non-decreasing from left to right.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= H_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nH_1 H_2 . . . H_N\nTask Output: If it is possible to perform the operations so that the heights of the squares are non-decreasing from left to right, print Yes; otherwise, print No.\nTask Samples: input: 5\n1 2 1 1 3 output: Yes\n\nYou can achieve the objective by decreasing the height of only the second square from the left by 1.\ninput: 4\n1 3 2 1 output: No\ninput: 5\n1 2 3 4 5 output: Yes\ninput: 1\n1000000000 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Given is a string S consisting of L and R.\nLet N be the length of S. There are N squares arranged from left to right, and the i-th character of S from the left is written on the i-th square from the left.\nThe character written on the leftmost square is always R, and the character written on the rightmost square is always L.\nInitially, one child is standing on each square.\nEach child will perform the move below 10^{100} times:\n\nMove one square in the direction specified by the character written in the square on which the child is standing. L denotes left, and R denotes right.\n\nFind the number of children standing on each square after the children performed the moves.", "constraint": "S is a string of length between 2 and 10^5 (inclusive).\nEach character of S is L or R.\nThe first and last characters of S are R and L, respectively.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of children standing on each square after the children performed the moves, in order from left to right.", "content_img": false, "lang": "en", "error": false, "samples": ["input: RRLRL output: 0 1 2 1 1\nAfter each child performed one move, the number of children standing on each square is 0,2,1,1,1 from left to right.\nAfter each child performed two moves, the number of children standing on each square is 0,1,2,1,1 from left to right.\nAfter each child performed 10^{100} moves, the number of children standing on each square is 0,1,2,1,1 from left to right.", "input: RRLLLLRLRRLL output: 0 3 3 0 0 0 1 1 0 2 2 0", "input: RRRLLRLLRRRLLLLL output: 0 0 3 2 0 2 1 0 0 0 4 4 0 0 0 0"], "Pid": "p02954", "ProblemText": "Task Description: Problem Statement Given is a string S consisting of L and R.\nLet N be the length of S. There are N squares arranged from left to right, and the i-th character of S from the left is written on the i-th square from the left.\nThe character written on the leftmost square is always R, and the character written on the rightmost square is always L.\nInitially, one child is standing on each square.\nEach child will perform the move below 10^{100} times:\n\nMove one square in the direction specified by the character written in the square on which the child is standing. L denotes left, and R denotes right.\n\nFind the number of children standing on each square after the children performed the moves.\nTask Constraint: S is a string of length between 2 and 10^5 (inclusive).\nEach character of S is L or R.\nThe first and last characters of S are R and L, respectively.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of children standing on each square after the children performed the moves, in order from left to right.\nTask Samples: input: RRLRL output: 0 1 2 1 1\nAfter each child performed one move, the number of children standing on each square is 0,2,1,1,1 from left to right.\nAfter each child performed two moves, the number of children standing on each square is 0,1,2,1,1 from left to right.\nAfter each child performed 10^{100} moves, the number of children standing on each square is 0,1,2,1,1 from left to right.\ninput: RRLLLLRLRRLL output: 0 3 3 0 0 0 1 1 0 2 2 0\ninput: RRRLLRLLRRRLLLLL output: 0 0 3 2 0 2 1 0 0 0 4 4 0 0 0 0\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of N integers: A_1, A_2, \\cdots, A_N.\nYou can perform the following operation between 0 and K times (inclusive):\n\nChoose two integers i and j such that i \\neq j, each between 1 and N (inclusive). Add 1 to A_i and -1 to A_j, possibly producing a negative element.\n\nCompute the maximum possible positive integer that divides every element of A after the operations. Here a positive integer x divides an integer y if and only if there exists an integer z such that y = xz.", "constraint": "2 <= N <= 500\n1 <= A_i <= 10^6\n0 <= K <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\cdots A_{N-1} A_{N}", "output": "Print the maximum possible positive integer that divides every element of A after the operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n8 20 output: 7\n\n7 will divide every element of A if, for example, we perform the following operation:\n\nChoose i = 2, j = 1. A becomes (7,21).\n\nWe cannot reach the situation where 8 or greater integer divides every element of A.", "input: 2 10\n3 5 output: 8\n\nConsider performing the following five operations:\n\nChoose i = 2, j = 1. A becomes (2,6).\nChoose i = 2, j = 1. A becomes (1,7).\nChoose i = 2, j = 1. A becomes (0,8).\nChoose i = 2, j = 1. A becomes (-1,9).\nChoose i = 1, j = 2. A becomes (0,8).\n\nThen, 0 = 8 * 0 and 8 = 8 * 1, so 8 divides every element of A. We cannot reach the situation where 9 or greater integer divides every element of A.", "input: 4 5\n10 1 2 22 output: 7", "input: 8 7\n1 7 5 6 8 2 6 5 output: 5"], "Pid": "p02955", "ProblemText": "Task Description: Problem Statement We have a sequence of N integers: A_1, A_2, \\cdots, A_N.\nYou can perform the following operation between 0 and K times (inclusive):\n\nChoose two integers i and j such that i \\neq j, each between 1 and N (inclusive). Add 1 to A_i and -1 to A_j, possibly producing a negative element.\n\nCompute the maximum possible positive integer that divides every element of A after the operations. Here a positive integer x divides an integer y if and only if there exists an integer z such that y = xz.\nTask Constraint: 2 <= N <= 500\n1 <= A_i <= 10^6\n0 <= K <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 \\cdots A_{N-1} A_{N}\nTask Output: Print the maximum possible positive integer that divides every element of A after the operations.\nTask Samples: input: 2 3\n8 20 output: 7\n\n7 will divide every element of A if, for example, we perform the following operation:\n\nChoose i = 2, j = 1. A becomes (7,21).\n\nWe cannot reach the situation where 8 or greater integer divides every element of A.\ninput: 2 10\n3 5 output: 8\n\nConsider performing the following five operations:\n\nChoose i = 2, j = 1. A becomes (2,6).\nChoose i = 2, j = 1. A becomes (1,7).\nChoose i = 2, j = 1. A becomes (0,8).\nChoose i = 2, j = 1. A becomes (-1,9).\nChoose i = 1, j = 2. A becomes (0,8).\n\nThen, 0 = 8 * 0 and 8 = 8 * 1, so 8 divides every element of A. We cannot reach the situation where 9 or greater integer divides every element of A.\ninput: 4 5\n10 1 2 22 output: 7\ninput: 8 7\n1 7 5 6 8 2 6 5 output: 5\n\n" }, { "title": "", "content": "Problem Statement We have a set S of N points in a two-dimensional plane. The coordinates of the i-th point are (x_i, y_i). The N points have distinct x-coordinates and distinct y-coordinates.\nFor a non-empty subset T of S, let f(T) be the number of points contained in the smallest rectangle, whose sides are parallel to the coordinate axes, that contains all the points in T. More formally, we define f(T) as follows:\n\nf(T) : = (the number of integers i (1 <= i <= N) such that a <= x_i <= b and c <= y_i <= d, where a, b, c, and d are the minimum x-coordinate, the maximum x-coordinate, the minimum y-coordinate, and the maximum y-coordinate of the points in T)\n\nFind the sum of f(T) over all non-empty subset T of S. Since it can be enormous, print the sum modulo 998244353.", "constraint": "1 <= N <= 2 * 10^5\n-10^9 <= x_i, y_i <= 10^9\nx_i \\neq x_j (i \\neq j)\ny_i \\neq y_j (i \\neq j)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print the sum of f(T) over all non-empty subset T of S, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-1 3\n2 1\n3 -2 output: 13\n\nLet the first, second, and third points be P_1, P_2, and P_3, respectively. S = \\{P_1, P_2, P_3\\} has seven non-empty subsets, and f has the following values for each of them:\n\nf(\\{P_1\\}) = 1\nf(\\{P_2\\}) = 1\nf(\\{P_3\\}) = 1\nf(\\{P_1, P_2\\}) = 2\nf(\\{P_2, P_3\\}) = 2\nf(\\{P_3, P_1\\}) = 3\nf(\\{P_1, P_2, P_3\\}) = 3\n\nThe sum of these is 13.", "input: 4\n1 4\n2 1\n3 3\n4 2 output: 34", "input: 10\n19 -11\n-3 -12\n5 3\n3 -15\n8 -14\n-9 -20\n10 -9\n0 2\n-7 17\n6 -6 output: 7222\n\nBe sure to print the sum modulo 998244353."], "Pid": "p02956", "ProblemText": "Task Description: Problem Statement We have a set S of N points in a two-dimensional plane. The coordinates of the i-th point are (x_i, y_i). The N points have distinct x-coordinates and distinct y-coordinates.\nFor a non-empty subset T of S, let f(T) be the number of points contained in the smallest rectangle, whose sides are parallel to the coordinate axes, that contains all the points in T. More formally, we define f(T) as follows:\n\nf(T) : = (the number of integers i (1 <= i <= N) such that a <= x_i <= b and c <= y_i <= d, where a, b, c, and d are the minimum x-coordinate, the maximum x-coordinate, the minimum y-coordinate, and the maximum y-coordinate of the points in T)\n\nFind the sum of f(T) over all non-empty subset T of S. Since it can be enormous, print the sum modulo 998244353.\nTask Constraint: 1 <= N <= 2 * 10^5\n-10^9 <= x_i, y_i <= 10^9\nx_i \\neq x_j (i \\neq j)\ny_i \\neq y_j (i \\neq j)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print the sum of f(T) over all non-empty subset T of S, modulo 998244353.\nTask Samples: input: 3\n-1 3\n2 1\n3 -2 output: 13\n\nLet the first, second, and third points be P_1, P_2, and P_3, respectively. S = \\{P_1, P_2, P_3\\} has seven non-empty subsets, and f has the following values for each of them:\n\nf(\\{P_1\\}) = 1\nf(\\{P_2\\}) = 1\nf(\\{P_3\\}) = 1\nf(\\{P_1, P_2\\}) = 2\nf(\\{P_2, P_3\\}) = 2\nf(\\{P_3, P_1\\}) = 3\nf(\\{P_1, P_2, P_3\\}) = 3\n\nThe sum of these is 13.\ninput: 4\n1 4\n2 1\n3 3\n4 2 output: 34\ninput: 10\n19 -11\n-3 -12\n5 3\n3 -15\n8 -14\n-9 -20\n10 -9\n0 2\n-7 17\n6 -6 output: 7222\n\nBe sure to print the sum modulo 998244353.\n\n" }, { "title": "", "content": "Problem Statement We have two distinct integers A and B.\nPrint the integer K such that |A - K| = |B - K|.\nIf such an integer does not exist, print IMPOSSIBLE instead.", "constraint": "All values in input are integers.\n0 <= A,\\ B <= 10^9\nA and B are distinct.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the integer K satisfying the condition.\nIf such an integer does not exist, print IMPOSSIBLE instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 16 output: 9\n\n|2 - 9| = 7 and |16 - 9| = 7, so 9 satisfies the condition.", "input: 0 3 output: IMPOSSIBLE\n\nNo integer satisfies the condition.", "input: 998244353 99824435 output: 549034394"], "Pid": "p02957", "ProblemText": "Task Description: Problem Statement We have two distinct integers A and B.\nPrint the integer K such that |A - K| = |B - K|.\nIf such an integer does not exist, print IMPOSSIBLE instead.\nTask Constraint: All values in input are integers.\n0 <= A,\\ B <= 10^9\nA and B are distinct.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the integer K satisfying the condition.\nIf such an integer does not exist, print IMPOSSIBLE instead.\nTask Samples: input: 2 16 output: 9\n\n|2 - 9| = 7 and |16 - 9| = 7, so 9 satisfies the condition.\ninput: 0 3 output: IMPOSSIBLE\n\nNo integer satisfies the condition.\ninput: 998244353 99824435 output: 549034394\n\n" }, { "title": "", "content": "Problem Statement We have a sequence p = {p_1, \\ p_2, \\ . . . , \\ p_N} which is a permutation of {1, \\ 2, \\ . . . , \\ N}.\nYou can perform the following operation at most once: choose integers i and j (1 <= i < j <= N), and swap p_i and p_j. Note that you can also choose not to perform it.\nPrint YES if you can sort p in ascending order in this way, and NO otherwise.", "constraint": "All values in input are integers.\n2 <= N <= 50\np is a permutation of {1,\\ 2,\\ ...,\\ N}.", "input": "Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N", "output": "Print YES if you can sort p in ascending order in the way stated in the problem statement, and NO otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n5 2 3 4 1 output: YES\n\nYou can sort p in ascending order by swapping p_1 and p_5.", "input: 5\n2 4 3 5 1 output: NO\n\nIn this case, swapping any two elements does not sort p in ascending order.", "input: 7\n1 2 3 4 5 6 7 output: YES\n\np is already sorted in ascending order, so no operation is needed."], "Pid": "p02958", "ProblemText": "Task Description: Problem Statement We have a sequence p = {p_1, \\ p_2, \\ . . . , \\ p_N} which is a permutation of {1, \\ 2, \\ . . . , \\ N}.\nYou can perform the following operation at most once: choose integers i and j (1 <= i < j <= N), and swap p_i and p_j. Note that you can also choose not to perform it.\nPrint YES if you can sort p in ascending order in this way, and NO otherwise.\nTask Constraint: All values in input are integers.\n2 <= N <= 50\np is a permutation of {1,\\ 2,\\ ...,\\ N}.\nTask Input: Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N\nTask Output: Print YES if you can sort p in ascending order in the way stated in the problem statement, and NO otherwise.\nTask Samples: input: 5\n5 2 3 4 1 output: YES\n\nYou can sort p in ascending order by swapping p_1 and p_5.\ninput: 5\n2 4 3 5 1 output: NO\n\nIn this case, swapping any two elements does not sort p in ascending order.\ninput: 7\n1 2 3 4 5 6 7 output: YES\n\np is already sorted in ascending order, so no operation is needed.\n\n" }, { "title": "", "content": "Problem Statement There are N+1 towns. The i-th town is being attacked by A_i monsters.\nWe have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.\nWhat is the maximum total number of monsters the heroes can cooperate to defeat?", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N+1}\nB_1 B_2 . . . B_N", "output": "Print the maximum total number of monsters the heroes can defeat.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 5 2\n4 5 output: 9\n\nIf the heroes choose the monsters to defeat as follows, they can defeat nine monsters in total, which is the maximum result.\n\nThe first hero defeats two monsters attacking the first town and two monsters attacking the second town.\nThe second hero defeats three monsters attacking the second town and two monsters attacking the third town.", "input: 3\n5 6 3 8\n5 100 8 output: 22", "input: 2\n100 1 1\n1 100 output: 3"], "Pid": "p02959", "ProblemText": "Task Description: Problem Statement There are N+1 towns. The i-th town is being attacked by A_i monsters.\nWe have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.\nWhat is the maximum total number of monsters the heroes can cooperate to defeat?\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N+1}\nB_1 B_2 . . . B_N\nTask Output: Print the maximum total number of monsters the heroes can defeat.\nTask Samples: input: 2\n3 5 2\n4 5 output: 9\n\nIf the heroes choose the monsters to defeat as follows, they can defeat nine monsters in total, which is the maximum result.\n\nThe first hero defeats two monsters attacking the first town and two monsters attacking the second town.\nThe second hero defeats three monsters attacking the second town and two monsters attacking the third town.\ninput: 3\n5 6 3 8\n5 100 8 output: 22\ninput: 2\n100 1 1\n1 100 output: 3\n\n" }, { "title": "", "content": "Problem Statement Given is a string S. Each character in S is either a digit (0, . . . , 9) or ? .\nAmong the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.\nSince the answer can be enormous, print the count modulo 10^9+7.", "constraint": "S is a string consisting of digits (0, ..., 9) and ?.\n1 <= |S| <= 10^5", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of integers satisfying the condition, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ??2??5 output: 768\n\nFor example, 482305,002865, and 972665 satisfy the condition.", "input: ?44 output: 1\n\nOnly 044 satisfies the condition.", "input: 7?4 output: 0\n\nWe may not be able to produce an integer satisfying the condition.", "input: ?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76??? output: 153716888"], "Pid": "p02960", "ProblemText": "Task Description: Problem Statement Given is a string S. Each character in S is either a digit (0, . . . , 9) or ? .\nAmong the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.\nSince the answer can be enormous, print the count modulo 10^9+7.\nTask Constraint: S is a string consisting of digits (0, ..., 9) and ?.\n1 <= |S| <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of integers satisfying the condition, modulo 10^9+7.\nTask Samples: input: ??2??5 output: 768\n\nFor example, 482305,002865, and 972665 satisfy the condition.\ninput: ?44 output: 1\n\nOnly 044 satisfies the condition.\ninput: 7?4 output: 0\n\nWe may not be able to produce an integer satisfying the condition.\ninput: ?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76??? output: 153716888\n\n" }, { "title": "", "content": "Problem Statement Jumbo Takahashi will play golf on an infinite two-dimensional grid.\nThe ball is initially at the origin (0,0), and the goal is a grid point (a point with integer coordinates) (X, Y). In one stroke, Jumbo Takahashi can perform the following operation:\n\nChoose a grid point whose Manhattan distance from the current position of the ball is K, and send the ball to that point.\n\nThe game is finished when the ball reaches the goal, and the score will be the number of strokes so far. Jumbo Takahashi wants to finish the game with the lowest score possible.\nDetermine if the game can be finished. If the answer is yes, find one way to bring the ball to the goal with the lowest score possible.\nWhat is Manhattan distance?\nThe Manhattan distance between two points (x_1, y_1) and (x_2, y_2) is defined as |x_1-x_2|+|y_1-y_2|.", "constraint": "", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\nc_{11} c_{12} . . . c_{1{b_1}}\n:\na_M b_M\nc_{M1} c_{M2} . . . c_{M{b_M}}", "output": "Print the minimum cost required to unlock all the treasure boxes. If it is impossible to unlock all of them, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12 1\n100000 1\n2 output: -1", "input: 2 3\n10 1\n1\n15 1\n2\n30 2\n1 2 output: 25", "input: 4 6\n67786 3\n1 3 4\n3497 1\n2\n44908 3\n2 3 4\n2156 3\n2 3 4\n26230 1\n2\n86918 1\n3 output: 69942"], "Pid": "p02961", "ProblemText": "Task Description: Problem Statement Jumbo Takahashi will play golf on an infinite two-dimensional grid.\nThe ball is initially at the origin (0,0), and the goal is a grid point (a point with integer coordinates) (X, Y). In one stroke, Jumbo Takahashi can perform the following operation:\n\nChoose a grid point whose Manhattan distance from the current position of the ball is K, and send the ball to that point.\n\nThe game is finished when the ball reaches the goal, and the score will be the number of strokes so far. Jumbo Takahashi wants to finish the game with the lowest score possible.\nDetermine if the game can be finished. If the answer is yes, find one way to bring the ball to the goal with the lowest score possible.\nWhat is Manhattan distance?\nThe Manhattan distance between two points (x_1, y_1) and (x_2, y_2) is defined as |x_1-x_2|+|y_1-y_2|.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\nc_{11} c_{12} . . . c_{1{b_1}}\n:\na_M b_M\nc_{M1} c_{M2} . . . c_{M{b_M}}\nTask Output: Print the minimum cost required to unlock all the treasure boxes. If it is impossible to unlock all of them, print -1.\nTask Samples: input: 12 1\n100000 1\n2 output: -1\ninput: 2 3\n10 1\n1\n15 1\n2\n30 2\n1 2 output: 25\ninput: 4 6\n67786 3\n1 3 4\n3497 1\n2\n44908 3\n2 3 4\n2156 3\n2 3 4\n26230 1\n2\n86918 1\n3 output: 69942\n\n" }, { "title": "", "content": "Problem Statement Given are two strings s and t consisting of lowercase English letters. Determine if the number of non-negative integers i satisfying the following condition is finite, and find the maximum value of such i if the number is finite.\n\nThere exists a non-negative integer j such that the concatenation of i copies of t is a substring of the concatenation of j copies of s. note: Notes\n\nA string a is a substring of another string b if and only if there exists an integer x (0 <= x <= |b| - |a|) such that, for any y (1 <= y <= |a|), a_y = b_{x+y} holds.\nWe assume that the concatenation of zero copies of any string is the empty string. From the definition above, the empty string is a substring of any string. Thus, for any two strings s and t, i = 0 satisfies the condition in the problem statement.", "constraint": "1 <= |s| <= 5 * 10^5\n1 <= |t| <= 5 * 10^5\ns and t consist of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\ns\nt", "output": "If the number of non-negative integers i satisfying the following condition is finite, print the maximum value of such i; if the number is infinite, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abcabab\nab output: 3\n\nThe concatenation of three copies of t, ababab, is a substring of the concatenation of two copies of s, abcabababcabab, so i = 3 satisfies the condition.\nOn the other hand, the concatenation of four copies of t, abababab, is not a substring of the concatenation of any number of copies of s, so i = 4 does not satisfy the condition.\nSimilarly, any integer greater than 4 does not satisfy the condition, either. Thus, the number of non-negative integers i satisfying the condition is finite, and the maximum value of such i is 3.", "input: aa\naaaaaaa output: -1\n\nFor any non-negative integer i, the concatenation of i copies of t is a substring of the concatenation of 4i copies of s. Thus, there are infinitely many non-negative integers i that satisfy the condition.", "input: aba\nbaaab output: 0\n\nAs stated in Notes, i = 0 always satisfies the condition."], "Pid": "p02962", "ProblemText": "Task Description: Problem Statement Given are two strings s and t consisting of lowercase English letters. Determine if the number of non-negative integers i satisfying the following condition is finite, and find the maximum value of such i if the number is finite.\n\nThere exists a non-negative integer j such that the concatenation of i copies of t is a substring of the concatenation of j copies of s. note: Notes\n\nA string a is a substring of another string b if and only if there exists an integer x (0 <= x <= |b| - |a|) such that, for any y (1 <= y <= |a|), a_y = b_{x+y} holds.\nWe assume that the concatenation of zero copies of any string is the empty string. From the definition above, the empty string is a substring of any string. Thus, for any two strings s and t, i = 0 satisfies the condition in the problem statement.\nTask Constraint: 1 <= |s| <= 5 * 10^5\n1 <= |t| <= 5 * 10^5\ns and t consist of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\ns\nt\nTask Output: If the number of non-negative integers i satisfying the following condition is finite, print the maximum value of such i; if the number is infinite, print -1.\nTask Samples: input: abcabab\nab output: 3\n\nThe concatenation of three copies of t, ababab, is a substring of the concatenation of two copies of s, abcabababcabab, so i = 3 satisfies the condition.\nOn the other hand, the concatenation of four copies of t, abababab, is not a substring of the concatenation of any number of copies of s, so i = 4 does not satisfy the condition.\nSimilarly, any integer greater than 4 does not satisfy the condition, either. Thus, the number of non-negative integers i satisfying the condition is finite, and the maximum value of such i is 3.\ninput: aa\naaaaaaa output: -1\n\nFor any non-negative integer i, the concatenation of i copies of t is a substring of the concatenation of 4i copies of s. Thus, there are infinitely many non-negative integers i that satisfy the condition.\ninput: aba\nbaaab output: 0\n\nAs stated in Notes, i = 0 always satisfies the condition.\n\n" }, { "title": "", "content": "Problem Statement Given is an integer S.\nFind a combination of six integers X_1, Y_1, X_2, Y_2, X_3, and Y_3 that satisfies all of the following conditions:\n\n0 <= X_1, Y_1, X_2, Y_2, X_3, Y_3 <= 10^9\nThe area of the triangle in a two-dimensional plane whose vertices are (X_1, Y_1), (X_2, Y_2), and (X_3, Y_3) is S/2.\n\nWe can prove that there always exist six integers that satisfy the conditions under the constraints of this problem.", "constraint": "1 <= S <= 10^{18}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print six integers X_1, Y_1, X_2, Y_2, X_3, and Y_3 that satisfy the conditions, in this order, with spaces in between.\nIf multiple solutions exist, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 1 0 2 2 0 1\n\nThe area of the triangle in a two-dimensional plane whose vertices are (1,0),(2,2), and (0,1) is 3/2.\nPrinting 3 0 3 1 0 1 or 1 0 0 1 2 2 will also be accepted.", "input: 100 output: 0 0 10 0 0 10", "input: 311114770564041497 output: 314159265 358979323 846264338 327950288 419716939 937510582"], "Pid": "p02963", "ProblemText": "Task Description: Problem Statement Given is an integer S.\nFind a combination of six integers X_1, Y_1, X_2, Y_2, X_3, and Y_3 that satisfies all of the following conditions:\n\n0 <= X_1, Y_1, X_2, Y_2, X_3, Y_3 <= 10^9\nThe area of the triangle in a two-dimensional plane whose vertices are (X_1, Y_1), (X_2, Y_2), and (X_3, Y_3) is S/2.\n\nWe can prove that there always exist six integers that satisfy the conditions under the constraints of this problem.\nTask Constraint: 1 <= S <= 10^{18}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print six integers X_1, Y_1, X_2, Y_2, X_3, and Y_3 that satisfy the conditions, in this order, with spaces in between.\nIf multiple solutions exist, any of them will be accepted.\nTask Samples: input: 3 output: 1 0 2 2 0 1\n\nThe area of the triangle in a two-dimensional plane whose vertices are (1,0),(2,2), and (0,1) is 3/2.\nPrinting 3 0 3 1 0 1 or 1 0 0 1 2 2 will also be accepted.\ninput: 100 output: 0 0 10 0 0 10\ninput: 311114770564041497 output: 314159265 358979323 846264338 327950288 419716939 937510582\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of N * K integers: X=(X_0, X_1, \\cdots, X_{N * K-1}).\nIts elements are represented by another sequence of N integers: A=(A_0, A_1, \\cdots, A_{N-1}). For each pair i, j (0 <= i <= K-1, \\ 0 <= j <= N-1), X_{i * N + j}=A_j holds.\nSnuke has an integer sequence s, which is initially empty.\nFor each i=0,1,2, \\cdots, N * K-1, in this order, he will perform the following operation:\n\nIf s does not contain X_i: add X_i to the end of s.\nIf s does contain X_i: repeatedly delete the element at the end of s until s no longer contains X_i. Note that, in this case, we do not add X_i to the end of s.\n\nFind the elements of s after Snuke finished the operations.", "constraint": "1 <= N <= 2 * 10^5\n1 <= K <= 10^{12}\n1 <= A_i <= 2 * 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_0 A_1 \\cdots A_{N-1}", "output": "Print the elements of s after Snuke finished the operations, in order from beginning to end, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2 3 output: 2 3\n\nIn this case, X=(1,2,3,1,2,3).\nWe will perform the operations as follows:\n\ni=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).\ni=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).\ni=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).\ni=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)→(1,2)→(1)→().\ni=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).\ni=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).", "input: 5 10\n1 2 3 2 3 output: 3", "input: 6 1000000000000\n1 1 2 2 3 3 output: s may be empty in the end.", "input: 11 97\n3 1 4 1 5 9 2 6 5 3 5 output: 9 2 6"], "Pid": "p02964", "ProblemText": "Task Description: Problem Statement We have a sequence of N * K integers: X=(X_0, X_1, \\cdots, X_{N * K-1}).\nIts elements are represented by another sequence of N integers: A=(A_0, A_1, \\cdots, A_{N-1}). For each pair i, j (0 <= i <= K-1, \\ 0 <= j <= N-1), X_{i * N + j}=A_j holds.\nSnuke has an integer sequence s, which is initially empty.\nFor each i=0,1,2, \\cdots, N * K-1, in this order, he will perform the following operation:\n\nIf s does not contain X_i: add X_i to the end of s.\nIf s does contain X_i: repeatedly delete the element at the end of s until s no longer contains X_i. Note that, in this case, we do not add X_i to the end of s.\n\nFind the elements of s after Snuke finished the operations.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= K <= 10^{12}\n1 <= A_i <= 2 * 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_0 A_1 \\cdots A_{N-1}\nTask Output: Print the elements of s after Snuke finished the operations, in order from beginning to end, with spaces in between.\nTask Samples: input: 3 2\n1 2 3 output: 2 3\n\nIn this case, X=(1,2,3,1,2,3).\nWe will perform the operations as follows:\n\ni=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).\ni=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).\ni=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).\ni=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)→(1,2)→(1)→().\ni=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).\ni=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).\ninput: 5 10\n1 2 3 2 3 output: 3\ninput: 6 1000000000000\n1 1 2 2 3 3 output: s may be empty in the end.\ninput: 11 97\n3 1 4 1 5 9 2 6 5 3 5 output: 9 2 6\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of N integers: x=(x_0, x_1, \\cdots, x_{N-1}).\nInitially, x_i=0 for each i (0 <= i <= N-1).\nSnuke will perform the following operation exactly M times:\n\nChoose two distinct indices i, j (0 <= i, j <= N-1, \\ i \\neq j).\nThen, replace x_i with x_i+2 and x_j with x_j+1.\n\nFind the number of different sequences that can result after M operations.\nSince it can be enormous, compute the count modulo 998244353.", "constraint": "2 <= N <= 10^6\n1 <= M <= 5 * 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of different sequences that can result after M operations, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 3\n\nAfter two operations, there are three possible outcomes:\n\nx=(2,4)\nx=(3,3)\nx=(4,2)\n\nFor example, x=(3,3) can result after the following sequence of operations:\n\nFirst, choose i=0,j=1, changing x from (0,0) to (2,1).\nSecond, choose i=1,j=0, changing x from (2,1) to (3,3).", "input: 3 2 output: 19", "input: 10 10 output: 211428932", "input: 100000 50000 output: 3463133"], "Pid": "p02965", "ProblemText": "Task Description: Problem Statement We have a sequence of N integers: x=(x_0, x_1, \\cdots, x_{N-1}).\nInitially, x_i=0 for each i (0 <= i <= N-1).\nSnuke will perform the following operation exactly M times:\n\nChoose two distinct indices i, j (0 <= i, j <= N-1, \\ i \\neq j).\nThen, replace x_i with x_i+2 and x_j with x_j+1.\n\nFind the number of different sequences that can result after M operations.\nSince it can be enormous, compute the count modulo 998244353.\nTask Constraint: 2 <= N <= 10^6\n1 <= M <= 5 * 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of different sequences that can result after M operations, modulo 998244353.\nTask Samples: input: 2 2 output: 3\n\nAfter two operations, there are three possible outcomes:\n\nx=(2,4)\nx=(3,3)\nx=(4,2)\n\nFor example, x=(3,3) can result after the following sequence of operations:\n\nFirst, choose i=0,j=1, changing x from (0,0) to (2,1).\nSecond, choose i=1,j=0, changing x from (2,1) to (3,3).\ninput: 3 2 output: 19\ninput: 10 10 output: 211428932\ninput: 100000 50000 output: 3463133\n\n" }, { "title": "", "content": "Problem Statement We have a weighted directed graph with N vertices numbered 0 to N-1.\nThe graph initially has N-1 edges. The i-th edge (0 <= i <= N-2) is directed from Vertex i to Vertex i+1 and has a weight of 0.\nSnuke will now add a new edge (i → j) for every pair i, j (0 <= i, j <= N-1, \\ i \\neq j).\nThe weight of the edge will be -1 if i < j, and 1 otherwise.\nRingo is a boy. A negative cycle (a cycle whose total weight is negative) in a graph makes him sad.\nHe will delete some of the edges added by Snuke so that the graph will no longer contain a negative cycle.\nThe cost of deleting the edge (i → j) is A_{i, j}. He cannot delete edges that have been present from the beginning.\nFind the minimum total cost required to achieve Ringo's objective.", "constraint": "3 <= N <= 500\n1 <= A_{i,j} <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_{0,1} A_{0,2} A_{0,3} \\cdots A_{0, N-1}\nA_{1,0} A_{1,2} A_{1,3} \\cdots A_{1, N-1}\nA_{2,0} A_{2,1} A_{2,3} \\cdots A_{2, N-1}\n\\vdots\nA_{N-1,0} A_{N-1,1} A_{N-1,2} \\cdots A_{N-1, N-2}", "output": "Print the minimum total cost required to achieve Ringo's objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 1\n1 4\n3 3 output: 2\n\nIf we delete the edge (0 → 1) added by Snuke, the graph will no longer contain a negative cycle.\nThe cost will be 2 in this case, which is the minimum possible.", "input: 4\n1 1 1\n1 1 1\n1 1 1\n1 1 1 output: 2\n\nIf we delete the edges (1 → 2) and (3 → 0) added by Snuke, the graph will no longer contain a negative cycle.\nThe cost will be 1+1=2 in this case, which is the minimum possible.", "input: 10\n190587 2038070 142162180 88207341 215145790 38 2 5 20\n32047998 21426 4177178 52 734621629 2596 102224223 5 1864\n41 481241221 1518272 51 772 146 8805349 3243297 449\n918151 126080576 5186563 46354 6646 491776 5750138 2897 161\n3656 7551068 2919714 43035419 495 3408 26 3317 2698\n455357 3 12 1857 5459 7870 4123856 2402 258\n3 25700 16191 102120 971821039 52375 40449 20548149 16186673\n2 16 130300357 18 6574485 29175 179 1693 2681\n99 833 131 2 414045824 57357 56 302669472 95\n8408 7 1266941 60620177 129747 41382505 38966 187 5151064 output: 2280211"], "Pid": "p02966", "ProblemText": "Task Description: Problem Statement We have a weighted directed graph with N vertices numbered 0 to N-1.\nThe graph initially has N-1 edges. The i-th edge (0 <= i <= N-2) is directed from Vertex i to Vertex i+1 and has a weight of 0.\nSnuke will now add a new edge (i → j) for every pair i, j (0 <= i, j <= N-1, \\ i \\neq j).\nThe weight of the edge will be -1 if i < j, and 1 otherwise.\nRingo is a boy. A negative cycle (a cycle whose total weight is negative) in a graph makes him sad.\nHe will delete some of the edges added by Snuke so that the graph will no longer contain a negative cycle.\nThe cost of deleting the edge (i → j) is A_{i, j}. He cannot delete edges that have been present from the beginning.\nFind the minimum total cost required to achieve Ringo's objective.\nTask Constraint: 3 <= N <= 500\n1 <= A_{i,j} <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{0,1} A_{0,2} A_{0,3} \\cdots A_{0, N-1}\nA_{1,0} A_{1,2} A_{1,3} \\cdots A_{1, N-1}\nA_{2,0} A_{2,1} A_{2,3} \\cdots A_{2, N-1}\n\\vdots\nA_{N-1,0} A_{N-1,1} A_{N-1,2} \\cdots A_{N-1, N-2}\nTask Output: Print the minimum total cost required to achieve Ringo's objective.\nTask Samples: input: 3\n2 1\n1 4\n3 3 output: 2\n\nIf we delete the edge (0 → 1) added by Snuke, the graph will no longer contain a negative cycle.\nThe cost will be 2 in this case, which is the minimum possible.\ninput: 4\n1 1 1\n1 1 1\n1 1 1\n1 1 1 output: 2\n\nIf we delete the edges (1 → 2) and (3 → 0) added by Snuke, the graph will no longer contain a negative cycle.\nThe cost will be 1+1=2 in this case, which is the minimum possible.\ninput: 10\n190587 2038070 142162180 88207341 215145790 38 2 5 20\n32047998 21426 4177178 52 734621629 2596 102224223 5 1864\n41 481241221 1518272 51 772 146 8805349 3243297 449\n918151 126080576 5186563 46354 6646 491776 5750138 2897 161\n3656 7551068 2919714 43035419 495 3408 26 3317 2698\n455357 3 12 1857 5459 7870 4123856 2402 258\n3 25700 16191 102120 971821039 52375 40449 20548149 16186673\n2 16 130300357 18 6574485 29175 179 1693 2681\n99 833 131 2 414045824 57357 56 302669472 95\n8408 7 1266941 60620177 129747 41382505 38966 187 5151064 output: 2280211\n\n" }, { "title": "", "content": "Problem Statement Given is a string S consisting of A, B, and C.\nConsider the (not necessarily contiguous) subsequences x of S that satisfy all of the following conditions:\n\nA, B, and C all occur the same number of times in x.\nNo two adjacent characters in x are the same.\n\nAmong these subsequences, find one of the longest. Here a subsequence of S is a string obtained by deleting zero or more characters from S.", "constraint": "1 <= |S| <= 10^6\nS consists of A,B, and C.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print one longest subsequence that satisfies the conditions.\nIf multiple solutions exist, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ABBCBCAB output: ACBCAB\n\nConsider the subsequence ACBCAB of S. It satisfies the conditions and is one of the longest with these properties, along with ABCBCA.\nOn the other hand, the subsequences ABCBCAB and ABBCCA do not satisfy the conditions.", "input: ABABABABACACACAC output: BABCAC", "input: ABCABACBCBABABACBCBCBCBCBCAB output: ACABACABABACBCBCBCBCA", "input: AAA output: \nIt is possible that only the empty string satisfies the condition."], "Pid": "p02967", "ProblemText": "Task Description: Problem Statement Given is a string S consisting of A, B, and C.\nConsider the (not necessarily contiguous) subsequences x of S that satisfy all of the following conditions:\n\nA, B, and C all occur the same number of times in x.\nNo two adjacent characters in x are the same.\n\nAmong these subsequences, find one of the longest. Here a subsequence of S is a string obtained by deleting zero or more characters from S.\nTask Constraint: 1 <= |S| <= 10^6\nS consists of A,B, and C.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print one longest subsequence that satisfies the conditions.\nIf multiple solutions exist, any of them will be accepted.\nTask Samples: input: ABBCBCAB output: ACBCAB\n\nConsider the subsequence ACBCAB of S. It satisfies the conditions and is one of the longest with these properties, along with ABCBCA.\nOn the other hand, the subsequences ABCBCAB and ABBCCA do not satisfy the conditions.\ninput: ABABABABACACACAC output: BABCAC\ninput: ABCABACBCBABABACBCBCBCBCBCAB output: ACABACABABACBCBCBCBCA\ninput: AAA output: \nIt is possible that only the empty string satisfies the condition.\n\n" }, { "title": "", "content": "Problem Statement Given is an integer N.\nHow many permutations (P_0, P_1, \\cdots, P_{2N-1}) of (0,1, \\cdots, 2N-1) satisfy the following condition?\n\nFor each i (0 <= i <= 2N-1), N^2 <= i^2+P_i^2 <= (2N)^2 holds.\n\nSince the number can be enormous, compute it modulo M.", "constraint": "1 <= N <= 250\n2 <= M <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of permutations that satisfy the condition, modulo M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 998244353 output: 4\n\nFour permutations satisfy the condition:\n\n(2,3,0,1)\n(2,3,1,0)\n(3,2,0,1)\n(3,2,1,0)", "input: 10 998244353 output: 53999264", "input: 200 998244353 output: 112633322"], "Pid": "p02968", "ProblemText": "Task Description: Problem Statement Given is an integer N.\nHow many permutations (P_0, P_1, \\cdots, P_{2N-1}) of (0,1, \\cdots, 2N-1) satisfy the following condition?\n\nFor each i (0 <= i <= 2N-1), N^2 <= i^2+P_i^2 <= (2N)^2 holds.\n\nSince the number can be enormous, compute it modulo M.\nTask Constraint: 1 <= N <= 250\n2 <= M <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of permutations that satisfy the condition, modulo M.\nTask Samples: input: 2 998244353 output: 4\n\nFour permutations satisfy the condition:\n\n(2,3,0,1)\n(2,3,1,0)\n(3,2,0,1)\n(3,2,1,0)\ninput: 10 998244353 output: 53999264\ninput: 200 998244353 output: 112633322\n\n" }, { "title": "", "content": "Problem Statement It is known that the area of a regular dodecagon inscribed in a circle of radius a is 3a^2.\nGiven an integer r, find the area of a regular dodecagon inscribed in a circle of radius r.", "constraint": "1 <= r <= 100\nr is an integer.", "input": "Input is given from Standard Input in the following format:\nr", "output": "Print an integer representing the area of the regular dodecagon.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 48\n\nThe area of the regular dodecagon is 3 * 4^2 = 48.", "input: 15 output: 675", "input: 80 output: 19200"], "Pid": "p02969", "ProblemText": "Task Description: Problem Statement It is known that the area of a regular dodecagon inscribed in a circle of radius a is 3a^2.\nGiven an integer r, find the area of a regular dodecagon inscribed in a circle of radius r.\nTask Constraint: 1 <= r <= 100\nr is an integer.\nTask Input: Input is given from Standard Input in the following format:\nr\nTask Output: Print an integer representing the area of the regular dodecagon.\nTask Samples: input: 4 output: 48\n\nThe area of the regular dodecagon is 3 * 4^2 = 48.\ninput: 15 output: 675\ninput: 80 output: 19200\n\n" }, { "title": "", "content": "Problem Statement There are N apple trees in a row. People say that one of them will bear golden apples.\nWe want to deploy some number of inspectors so that each of these trees will be inspected.\nEach inspector will be deployed under one of the trees. For convenience, we will assign numbers from 1 through N to the trees. An inspector deployed under the i-th tree (1 <= i <= N) will inspect the trees with numbers between i-D and i+D (inclusive).\nFind the minimum number of inspectors that we need to deploy to achieve the objective.", "constraint": "All values in input are integers.\n1 <= N <= 20\n1 <= D <= 20", "input": "Input is given from Standard Input in the following format:\nN D", "output": "Print the minimum number of inspectors that we need to deploy to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 2 output: 2\n\nWe can achieve the objective by, for example, placing an inspector under Tree 3 and Tree 4.", "input: 14 3 output: 2", "input: 20 4 output: 3"], "Pid": "p02970", "ProblemText": "Task Description: Problem Statement There are N apple trees in a row. People say that one of them will bear golden apples.\nWe want to deploy some number of inspectors so that each of these trees will be inspected.\nEach inspector will be deployed under one of the trees. For convenience, we will assign numbers from 1 through N to the trees. An inspector deployed under the i-th tree (1 <= i <= N) will inspect the trees with numbers between i-D and i+D (inclusive).\nFind the minimum number of inspectors that we need to deploy to achieve the objective.\nTask Constraint: All values in input are integers.\n1 <= N <= 20\n1 <= D <= 20\nTask Input: Input is given from Standard Input in the following format:\nN D\nTask Output: Print the minimum number of inspectors that we need to deploy to achieve the objective.\nTask Samples: input: 6 2 output: 2\n\nWe can achieve the objective by, for example, placing an inspector under Tree 3 and Tree 4.\ninput: 14 3 output: 2\ninput: 20 4 output: 3\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence of length N: A_1, A_2, . . . , A_N.\nFor each integer i between 1 and N (inclusive), answer the following question:\n\nFind the maximum value among the N-1 elements other than A_i in the sequence.", "constraint": "2 <= N <= 200000\n1 <= A_i <= 200000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print N lines. The i-th line (1 <= i <= N) should contain the maximum value among the N-1 elements other than A_i in the sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1\n4\n3 output: 4\n3\n4\nThe maximum value among the two elements other than A_1, that is, A_2 = 4 and A_3 = 3, is 4.\nThe maximum value among the two elements other than A_2, that is, A_1 = 1 and A_3 = 3, is 3.\nThe maximum value among the two elements other than A_3, that is, A_1 = 1 and A_2 = 4, is 4.", "input: 2\n5\n5 output: 5\n5"], "Pid": "p02971", "ProblemText": "Task Description: Problem Statement You are given a sequence of length N: A_1, A_2, . . . , A_N.\nFor each integer i between 1 and N (inclusive), answer the following question:\n\nFind the maximum value among the N-1 elements other than A_i in the sequence.\nTask Constraint: 2 <= N <= 200000\n1 <= A_i <= 200000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print N lines. The i-th line (1 <= i <= N) should contain the maximum value among the N-1 elements other than A_i in the sequence.\nTask Samples: input: 3\n1\n4\n3 output: 4\n3\n4\nThe maximum value among the two elements other than A_1, that is, A_2 = 4 and A_3 = 3, is 4.\nThe maximum value among the two elements other than A_2, that is, A_1 = 1 and A_3 = 3, is 3.\nThe maximum value among the two elements other than A_3, that is, A_1 = 1 and A_2 = 4, is 4.\ninput: 2\n5\n5 output: 5\n5\n\n" }, { "title": "", "content": "Problem Statement There are N empty boxes arranged in a row from left to right.\nThe integer i is written on the i-th box from the left (1 <= i <= N).\nFor each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.\nWe say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:\n\nFor every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.\n\nDoes there exist a good set of choices? If the answer is yes, find one good set of choices.", "constraint": "All values in input are integers.\n1 <= N <= 2 * 10^5\na_i is 0 or 1.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "If a good set of choices does not exist, print -1.\nIf a good set of choices exists, print one such set of choices in the following format:\nM\nb_1 b_2 . . . b_M\n\nwhere M denotes the number of boxes that will contain a ball, and b_1, \\ b_2, \\ . . . , \\ b_M are the integers written on these boxes, in any order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 0 0 output: 1\n1\n\nConsider putting a ball only in the box with 1 written on it.\n\nThere are three boxes with multiples of 1 written on them: the boxes with 1,2, and 3. The total number of balls contained in these boxes is 1.\nThere is only one box with a multiple of 2 written on it: the box with 2. The total number of balls contained in these boxes is 0.\nThere is only one box with a multiple of 3 written on it: the box with 3. The total number of balls contained in these boxes is 0.\n\nThus, the condition is satisfied, so this set of choices is good.", "input: 5\n0 0 0 0 0 output: 0\n\nPutting nothing in the boxes can be a good set of choices."], "Pid": "p02972", "ProblemText": "Task Description: Problem Statement There are N empty boxes arranged in a row from left to right.\nThe integer i is written on the i-th box from the left (1 <= i <= N).\nFor each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.\nWe say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:\n\nFor every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.\n\nDoes there exist a good set of choices? If the answer is yes, find one good set of choices.\nTask Constraint: All values in input are integers.\n1 <= N <= 2 * 10^5\na_i is 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: If a good set of choices does not exist, print -1.\nIf a good set of choices exists, print one such set of choices in the following format:\nM\nb_1 b_2 . . . b_M\n\nwhere M denotes the number of boxes that will contain a ball, and b_1, \\ b_2, \\ . . . , \\ b_M are the integers written on these boxes, in any order.\nTask Samples: input: 3\n1 0 0 output: 1\n1\n\nConsider putting a ball only in the box with 1 written on it.\n\nThere are three boxes with multiples of 1 written on them: the boxes with 1,2, and 3. The total number of balls contained in these boxes is 1.\nThere is only one box with a multiple of 2 written on it: the box with 2. The total number of balls contained in these boxes is 0.\nThere is only one box with a multiple of 3 written on it: the box with 3. The total number of balls contained in these boxes is 0.\n\nThus, the condition is satisfied, so this set of choices is good.\ninput: 5\n0 0 0 0 0 output: 0\n\nPutting nothing in the boxes can be a good set of choices.\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence with N integers: A = \\{ A_1, A_2, \\cdots, A_N \\}.\nFor each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:\n\nIf A_i and A_j (i < j) are painted with the same color, A_i < A_j.\n\nFind the minimum number of colors required to satisfy the condition.", "constraint": "1 <= N <= 10^5\n0 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print the minimum number of colors required to satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2\n1\n4\n5\n3 output: 2\n\nWe can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1,4, and 5 blue.", "input: 4\n0\n0\n0\n0 output: 4\n\nWe have to paint all the integers with distinct colors."], "Pid": "p02973", "ProblemText": "Task Description: Problem Statement You are given a sequence with N integers: A = \\{ A_1, A_2, \\cdots, A_N \\}.\nFor each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:\n\nIf A_i and A_j (i < j) are painted with the same color, A_i < A_j.\n\nFind the minimum number of colors required to satisfy the condition.\nTask Constraint: 1 <= N <= 10^5\n0 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print the minimum number of colors required to satisfy the condition.\nTask Samples: input: 5\n2\n1\n4\n5\n3 output: 2\n\nWe can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1,4, and 5 blue.\ninput: 4\n0\n0\n0\n0 output: 4\n\nWe have to paint all the integers with distinct colors.\n\n" }, { "title": "", "content": "Problem Statement Let us define the oddness of a permutation p = {p_1, \\ p_2, \\ . . . , \\ p_n} of {1, \\ 2, \\ . . . , \\ n} as \\sum_{i = 1}^n |i - p_i|.\nFind the number of permutations of {1, \\ 2, \\ . . . , \\ n} of oddness k, modulo 10^9+7.", "constraint": "All values in input are integers.\n1 <= n <= 50\n0 <= k <= n^2", "input": "Input is given from Standard Input in the following format:\nn k", "output": "Print the number of permutations of {1, \\ 2, \\ . . . , \\ n} of oddness k, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 2\n\nThere are six permutations of {1,\\ 2,\\ 3}. Among them, two have oddness of 2: {2,\\ 1,\\ 3} and {1,\\ 3,\\ 2}.", "input: 39 14 output: 74764168"], "Pid": "p02974", "ProblemText": "Task Description: Problem Statement Let us define the oddness of a permutation p = {p_1, \\ p_2, \\ . . . , \\ p_n} of {1, \\ 2, \\ . . . , \\ n} as \\sum_{i = 1}^n |i - p_i|.\nFind the number of permutations of {1, \\ 2, \\ . . . , \\ n} of oddness k, modulo 10^9+7.\nTask Constraint: All values in input are integers.\n1 <= n <= 50\n0 <= k <= n^2\nTask Input: Input is given from Standard Input in the following format:\nn k\nTask Output: Print the number of permutations of {1, \\ 2, \\ . . . , \\ n} of oddness k, modulo 10^9+7.\nTask Samples: input: 3 2 output: 2\n\nThere are six permutations of {1,\\ 2,\\ 3}. Among them, two have oddness of 2: {2,\\ 1,\\ 3} and {1,\\ 3,\\ 2}.\ninput: 39 14 output: 74764168\n\n" }, { "title": "", "content": "Problem Statement Snuke has N hats. The i-th hat has an integer a_i written on it.\nThere are N camels standing in a circle.\nSnuke will put one of his hats on each of these camels.\nIf there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print Yes; otherwise, print No.\n\nThe bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself.\nWhat is XOR?\n\nThe bitwise XOR x_1 \\oplus x_2 \\oplus \\ldots \\oplus x_n of n non-negative integers x_1, x_2, \\ldots, x_n is defined as follows:\n\n- When x_1 \\oplus x_2 \\oplus \\ldots \\oplus x_n is written in base two, the digit in the 2^k's place (k >= 0) is 1 if the number of integers among x_1, x_2, \\ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even.\n\nFor example, 3 \\oplus 5 = 6.", "constraint": "All values in input are integers.\n3 <= N <= 10^{5}\n0 <= a_i <= 10^{9}", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: Yes\nIf we put the hats with 1,2, and 3 in this order, clockwise, the condition will be satisfied for every camel, so the answer is Yes.", "input: 4\n1 2 4 8 output: No\nThere is no such way to distribute the hats; the answer is No."], "Pid": "p02975", "ProblemText": "Task Description: Problem Statement Snuke has N hats. The i-th hat has an integer a_i written on it.\nThere are N camels standing in a circle.\nSnuke will put one of his hats on each of these camels.\nIf there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print Yes; otherwise, print No.\n\nThe bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself.\nWhat is XOR?\n\nThe bitwise XOR x_1 \\oplus x_2 \\oplus \\ldots \\oplus x_n of n non-negative integers x_1, x_2, \\ldots, x_n is defined as follows:\n\n- When x_1 \\oplus x_2 \\oplus \\ldots \\oplus x_n is written in base two, the digit in the 2^k's place (k >= 0) is 1 if the number of integers among x_1, x_2, \\ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even.\n\nFor example, 3 \\oplus 5 = 6.\nTask Constraint: All values in input are integers.\n3 <= N <= 10^{5}\n0 <= a_i <= 10^{9}\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_{N}\nTask Output: Print the answer.\nTask Samples: input: 3\n1 2 3 output: Yes\nIf we put the hats with 1,2, and 3 in this order, clockwise, the condition will be satisfied for every camel, so the answer is Yes.\ninput: 4\n1 2 4 8 output: No\nThere is no such way to distribute the hats; the answer is No.\n\n" }, { "title": "", "content": "Problem Statement You are given a simple connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex A_i and Vertex B_i.\nTakahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph.\nDetermine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph. note: Notes An undirected graph is said to be simple when it contains no self-loops or multiple edges.", "constraint": "2 <= N <= 10^5\nN-1 <= M <= 10^5\n1 <= A_i,B_i <= N (1<= i<= M)\nThe given graph is simple and connected.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_M B_M", "output": "If it is impossible to assign directions\b to satisfy the requirement, print -1.\nOtherwise, print an assignment of directions that satisfies the requirement, in the following format:\nC_1 D_1\n:\nC_M D_M\n\nHere each pair (C_i, D_i) means that there is an edge directed from Vertex C_i to Vertex D_i. The edges may be printed in any order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n1 2\n2 3\n3 4\n4 1 output: 1 2\n1 4\n3 2\n3 4\n\nAfter this assignment of directions, Vertex 1 and 3 will each have two outgoing edges, and Vertex 2 and 4 will each have zero outgoing edges.", "input: 5 5\n1 2\n2 3\n3 4\n2 5\n4 5 output: -1"], "Pid": "p02976", "ProblemText": "Task Description: Problem Statement You are given a simple connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex A_i and Vertex B_i.\nTakahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph.\nDetermine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph. note: Notes An undirected graph is said to be simple when it contains no self-loops or multiple edges.\nTask Constraint: 2 <= N <= 10^5\nN-1 <= M <= 10^5\n1 <= A_i,B_i <= N (1<= i<= M)\nThe given graph is simple and connected.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_M B_M\nTask Output: If it is impossible to assign directions\b to satisfy the requirement, print -1.\nOtherwise, print an assignment of directions that satisfies the requirement, in the following format:\nC_1 D_1\n:\nC_M D_M\n\nHere each pair (C_i, D_i) means that there is an edge directed from Vertex C_i to Vertex D_i. The edges may be printed in any order.\nTask Samples: input: 4 4\n1 2\n2 3\n3 4\n4 1 output: 1 2\n1 4\n3 2\n3 4\n\nAfter this assignment of directions, Vertex 1 and 3 will each have two outgoing edges, and Vertex 2 and 4 will each have zero outgoing edges.\ninput: 5 5\n1 2\n2 3\n3 4\n2 5\n4 5 output: -1\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N. Determine if there exists a tree with 2N vertices numbered 1 to 2N satisfying the following condition, and show one such tree if the answer is yes.\n\nAssume that, for each integer i between 1 and N (inclusive), Vertex i and N+i have the weight i. Then, for each integer i between 1 and N, the bitwise XOR of the weights of the vertices on the path between Vertex i and N+i (including themselves) is i.", "constraint": "N is an integer.\n1 <= N <= 10^{5}", "input": "Input is given from Standard Input in the following format:\nN", "output": "If there exists a tree satisfying the condition in the statement, print Yes; otherwise, print No.\nThen, if such a tree exists, print the 2N-1 edges of such a tree in the subsequent 2N-1 lines, in the following format:\na_{1} b_{1}\n\\vdots\na_{2N-1} b_{2N-1}\n\nHere each pair (a_i, b_i) means that there is an edge connecting Vertex a_i and b_i. The edges may be printed in any order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: Yes\n1 2\n2 3\n3 4\n4 5\n5 6\nThe sample output represents the following graph:", "input: 1 output: No\nThere is no tree satisfying the condition."], "Pid": "p02977", "ProblemText": "Task Description: Problem Statement You are given an integer N. Determine if there exists a tree with 2N vertices numbered 1 to 2N satisfying the following condition, and show one such tree if the answer is yes.\n\nAssume that, for each integer i between 1 and N (inclusive), Vertex i and N+i have the weight i. Then, for each integer i between 1 and N, the bitwise XOR of the weights of the vertices on the path between Vertex i and N+i (including themselves) is i.\nTask Constraint: N is an integer.\n1 <= N <= 10^{5}\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If there exists a tree satisfying the condition in the statement, print Yes; otherwise, print No.\nThen, if such a tree exists, print the 2N-1 edges of such a tree in the subsequent 2N-1 lines, in the following format:\na_{1} b_{1}\n\\vdots\na_{2N-1} b_{2N-1}\n\nHere each pair (a_i, b_i) means that there is an edge connecting Vertex a_i and b_i. The edges may be printed in any order.\nTask Samples: input: 3 output: Yes\n1 2\n2 3\n3 4\n4 5\n5 6\nThe sample output represents the following graph:\ninput: 1 output: No\nThere is no tree satisfying the condition.\n\n" }, { "title": "", "content": "Problem Statement There is a stack of N cards, each of which has a non-negative integer written on it. The integer written on the i-th card from the top is A_i.\nSnuke will repeat the following operation until two cards remain:\n\nChoose three consecutive cards from the stack.\nEat the middle card of the three.\nFor each of the other two cards, replace the integer written on it by the sum of that integer and the integer written on the card eaten.\nReturn the two cards to the original position in the stack, without swapping them.\n\nFind the minimum possible sum of the integers written on the last two cards remaining.", "constraint": "2 <= N <= 18\n0 <= A_i <= 10^9 (1<= i<= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the minimum possible sum of the integers written on the last two cards remaining.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 1 4 2 output: 16\n\nWe can minimize the sum of the integers written on the last two cards remaining by doing as follows:\n\nInitially, the integers written on the cards are 3,1,4, and 2 from top to bottom.\nChoose the first, second, and third card from the top. Eat the second card with 1 written on it, add 1 to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now 4,5, and 2 from top to bottom.\nChoose the first, second, and third card from the top. Eat the second card with 5 written on it, add 5 to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now 9 and 7 from top to bottom.\nThe sum of the integers written on the last two cards remaining is 16.", "input: 6\n5 2 4 1 6 9 output: 51", "input: 10\n3 1 4 1 5 9 2 6 5 3 output: 115"], "Pid": "p02978", "ProblemText": "Task Description: Problem Statement There is a stack of N cards, each of which has a non-negative integer written on it. The integer written on the i-th card from the top is A_i.\nSnuke will repeat the following operation until two cards remain:\n\nChoose three consecutive cards from the stack.\nEat the middle card of the three.\nFor each of the other two cards, replace the integer written on it by the sum of that integer and the integer written on the card eaten.\nReturn the two cards to the original position in the stack, without swapping them.\n\nFind the minimum possible sum of the integers written on the last two cards remaining.\nTask Constraint: 2 <= N <= 18\n0 <= A_i <= 10^9 (1<= i<= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the minimum possible sum of the integers written on the last two cards remaining.\nTask Samples: input: 4\n3 1 4 2 output: 16\n\nWe can minimize the sum of the integers written on the last two cards remaining by doing as follows:\n\nInitially, the integers written on the cards are 3,1,4, and 2 from top to bottom.\nChoose the first, second, and third card from the top. Eat the second card with 1 written on it, add 1 to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now 4,5, and 2 from top to bottom.\nChoose the first, second, and third card from the top. Eat the second card with 5 written on it, add 5 to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now 9 and 7 from top to bottom.\nThe sum of the integers written on the last two cards remaining is 16.\ninput: 6\n5 2 4 1 6 9 output: 51\ninput: 10\n3 1 4 1 5 9 2 6 5 3 output: 115\n\n" }, { "title": "", "content": "Problem Statement There is a blackboard on which all integers from -10^{18} through 10^{18} are written, each of them appearing once. Takahashi will repeat the following sequence of operations any number of times he likes, possibly zero:\n\nChoose an integer between 1 and N (inclusive) that is written on the blackboard. Let x be the chosen integer, and erase x.\nIf x-2 is not written on the blackboard, write x-2 on the blackboard.\nIf x+K is not written on the blackboard, write x+K on the blackboard.\n\nFind the number of possible sets of integers written on the blackboard after some number of operations, modulo M.\nWe consider two sets different when there exists an integer contained in only one of the sets.", "constraint": "1 <= K<= N <= 150\n10^8<= M<= 10^9\nN, K, and M are integers.", "input": "Input is given from Standard Input in the following format:\nN K M", "output": "Print the number of possible sets of integers written on the blackboard after some number of operations, modulo M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 998244353 output: 7\n\nEvery set containing all integers less than 1, all integers greater than 3, and at least one of the three integers 1,2, and 3 satisfies the condition. There are seven such sets.", "input: 6 3 998244353 output: 61", "input: 9 4 702443618 output: 312", "input: 17 7 208992811 output: 128832", "input: 123 45 678901234 output: 256109226"], "Pid": "p02979", "ProblemText": "Task Description: Problem Statement There is a blackboard on which all integers from -10^{18} through 10^{18} are written, each of them appearing once. Takahashi will repeat the following sequence of operations any number of times he likes, possibly zero:\n\nChoose an integer between 1 and N (inclusive) that is written on the blackboard. Let x be the chosen integer, and erase x.\nIf x-2 is not written on the blackboard, write x-2 on the blackboard.\nIf x+K is not written on the blackboard, write x+K on the blackboard.\n\nFind the number of possible sets of integers written on the blackboard after some number of operations, modulo M.\nWe consider two sets different when there exists an integer contained in only one of the sets.\nTask Constraint: 1 <= K<= N <= 150\n10^8<= M<= 10^9\nN, K, and M are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K M\nTask Output: Print the number of possible sets of integers written on the blackboard after some number of operations, modulo M.\nTask Samples: input: 3 1 998244353 output: 7\n\nEvery set containing all integers less than 1, all integers greater than 3, and at least one of the three integers 1,2, and 3 satisfies the condition. There are seven such sets.\ninput: 6 3 998244353 output: 61\ninput: 9 4 702443618 output: 312\ninput: 17 7 208992811 output: 128832\ninput: 123 45 678901234 output: 256109226\n\n" }, { "title": "", "content": "Problem Statement We have a square grid with N rows and M columns. Takahashi will write an integer in each of the squares, as follows:\n\nFirst, write 0 in every square.\nFor each i=1,2, . . . , N, choose an integer k_i (0<= k_i<= M), and add 1 to each of the leftmost k_i squares in the i-th row.\nFor each j=1,2, . . . , M, choose an integer l_j (0<= l_j<= N), and add 1 to each of the topmost l_j squares in the j-th column.\n\nNow we have a grid where each square contains 0,1, or 2. Find the number of different grids that can be made this way, modulo 998244353.\nWe consider two grids different when there exists a square with different integers.", "constraint": "1 <= N,M <= 5* 10^5\nN and M are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of different grids that can be made, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 output: 8\n\nLet (a,b) denote the grid where the square to the left contains a and the square to the right contains b. Eight grids can be made: (0,0),(0,1),(1,0),(1,1),(1,2),(2,0),(2,1), and (2,2).", "input: 2 3 output: 234", "input: 10 7 output: 995651918", "input: 314159 265358 output: 70273732"], "Pid": "p02980", "ProblemText": "Task Description: Problem Statement We have a square grid with N rows and M columns. Takahashi will write an integer in each of the squares, as follows:\n\nFirst, write 0 in every square.\nFor each i=1,2, . . . , N, choose an integer k_i (0<= k_i<= M), and add 1 to each of the leftmost k_i squares in the i-th row.\nFor each j=1,2, . . . , M, choose an integer l_j (0<= l_j<= N), and add 1 to each of the topmost l_j squares in the j-th column.\n\nNow we have a grid where each square contains 0,1, or 2. Find the number of different grids that can be made this way, modulo 998244353.\nWe consider two grids different when there exists a square with different integers.\nTask Constraint: 1 <= N,M <= 5* 10^5\nN and M are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of different grids that can be made, modulo 998244353.\nTask Samples: input: 1 2 output: 8\n\nLet (a,b) denote the grid where the square to the left contains a and the square to the right contains b. Eight grids can be made: (0,0),(0,1),(1,0),(1,1),(1,2),(2,0),(2,1), and (2,2).\ninput: 2 3 output: 234\ninput: 10 7 output: 995651918\ninput: 314159 265358 output: 70273732\n\n" }, { "title": "", "content": "Problem Statement N of us are going on a trip, by train or taxi.\nThe train will cost each of us A yen (the currency of Japan).\nThe taxi will cost us a total of B yen.\nHow much is our minimum total travel expense?", "constraint": "All values in input are integers.\n1 <= N <= 20\n1 <= A <= 50\n1 <= B <= 50", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print an integer representing the minimum total travel expense.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 9 output: 8\n\nThe train will cost us 4 * 2 = 8 yen, and the taxi will cost us 9 yen, so the minimum total travel expense is 8 yen.", "input: 4 2 7 output: 7", "input: 4 2 8 output: 8"], "Pid": "p02981", "ProblemText": "Task Description: Problem Statement N of us are going on a trip, by train or taxi.\nThe train will cost each of us A yen (the currency of Japan).\nThe taxi will cost us a total of B yen.\nHow much is our minimum total travel expense?\nTask Constraint: All values in input are integers.\n1 <= N <= 20\n1 <= A <= 50\n1 <= B <= 50\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print an integer representing the minimum total travel expense.\nTask Samples: input: 4 2 9 output: 8\n\nThe train will cost us 4 * 2 = 8 yen, and the taxi will cost us 9 yen, so the minimum total travel expense is 8 yen.\ninput: 4 2 7 output: 7\ninput: 4 2 8 output: 8\n\n" }, { "title": "", "content": "Problem Statement There are N points in a D-dimensional space.\nThe coordinates of the i-th point are (X_{i1}, X_{i2}, . . . , X_{i D}).\nThe distance between two points with coordinates (y_1, y_2, . . . , y_D) and (z_1, z_2, . . . , z_D) is \\sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + . . . + (y_D - z_D)^2}.\nHow many pairs (i, j) (i < j) are there such that the distance between the i-th point and the j-th point is an integer?", "constraint": "All values in input are integers.\n2 <= N <= 10\n1 <= D <= 10\n-20 <= X_{ij} <= 20\nNo two given points have the same coordinates. That is, if i \\neq j, there exists k such that X_{ik} \\neq X_{jk}.", "input": "Input is given from Standard Input in the following format:\nN D\nX_{11} X_{12} . . . X_{1D}\nX_{21} X_{22} . . . X_{2D}\n\\vdots\nX_{N1} X_{N2} . . . X_{ND}", "output": "Print the number of pairs (i, j) (i < j) such that the distance between the i-th point and the j-th point is an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n5 5\n-2 8 output: 1\n\nThe number of pairs with an integer distance is one, as follows:\n\nThe distance between the first point and the second point is \\sqrt{|1-5|^2 + |2-5|^2} = 5, which is an integer.\nThe distance between the second point and the third point is \\sqrt{|5-(-2)|^2 + |5-8|^2} = \\sqrt{58}, which is not an integer.\nThe distance between the third point and the first point is \\sqrt{|-2-1|^2+|8-2|^2} = 3\\sqrt{5}, which is not an integer.", "input: 3 4\n-3 7 8 2\n-12 1 10 2\n-2 8 9 3 output: 2", "input: 5 1\n1\n2\n3\n4\n5 output: 10"], "Pid": "p02982", "ProblemText": "Task Description: Problem Statement There are N points in a D-dimensional space.\nThe coordinates of the i-th point are (X_{i1}, X_{i2}, . . . , X_{i D}).\nThe distance between two points with coordinates (y_1, y_2, . . . , y_D) and (z_1, z_2, . . . , z_D) is \\sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + . . . + (y_D - z_D)^2}.\nHow many pairs (i, j) (i < j) are there such that the distance between the i-th point and the j-th point is an integer?\nTask Constraint: All values in input are integers.\n2 <= N <= 10\n1 <= D <= 10\n-20 <= X_{ij} <= 20\nNo two given points have the same coordinates. That is, if i \\neq j, there exists k such that X_{ik} \\neq X_{jk}.\nTask Input: Input is given from Standard Input in the following format:\nN D\nX_{11} X_{12} . . . X_{1D}\nX_{21} X_{22} . . . X_{2D}\n\\vdots\nX_{N1} X_{N2} . . . X_{ND}\nTask Output: Print the number of pairs (i, j) (i < j) such that the distance between the i-th point and the j-th point is an integer.\nTask Samples: input: 3 2\n1 2\n5 5\n-2 8 output: 1\n\nThe number of pairs with an integer distance is one, as follows:\n\nThe distance between the first point and the second point is \\sqrt{|1-5|^2 + |2-5|^2} = 5, which is an integer.\nThe distance between the second point and the third point is \\sqrt{|5-(-2)|^2 + |5-8|^2} = \\sqrt{58}, which is not an integer.\nThe distance between the third point and the first point is \\sqrt{|-2-1|^2+|8-2|^2} = 3\\sqrt{5}, which is not an integer.\ninput: 3 4\n-3 7 8 2\n-12 1 10 2\n-2 8 9 3 output: 2\ninput: 5 1\n1\n2\n3\n4\n5 output: 10\n\n" }, { "title": "", "content": "Problem Statement You are given two non-negative integers L and R.\nWe will choose two integers i and j such that L <= i < j <= R.\nFind the minimum possible value of (i * j) \\mbox{ mod } 2019.", "constraint": "All values in input are integers.\n0 <= L < R <= 2 * 10^9", "input": "Input is given from Standard Input in the following format:\nL R", "output": "Print the minimum possible value of (i * j) \\mbox{ mod } 2019 when i and j are chosen under the given condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2020 2040 output: 2\n\nWhen (i, j) = (2020,2021), (i * j) \\mbox{ mod } 2019 = 2.", "input: 4 5 output: 20\n\nWe have only one choice: (i, j) = (4,5)."], "Pid": "p02983", "ProblemText": "Task Description: Problem Statement You are given two non-negative integers L and R.\nWe will choose two integers i and j such that L <= i < j <= R.\nFind the minimum possible value of (i * j) \\mbox{ mod } 2019.\nTask Constraint: All values in input are integers.\n0 <= L < R <= 2 * 10^9\nTask Input: Input is given from Standard Input in the following format:\nL R\nTask Output: Print the minimum possible value of (i * j) \\mbox{ mod } 2019 when i and j are chosen under the given condition.\nTask Samples: input: 2020 2040 output: 2\n\nWhen (i, j) = (2020,2021), (i * j) \\mbox{ mod } 2019 = 2.\ninput: 4 5 output: 20\n\nWe have only one choice: (i, j) = (4,5).\n\n" }, { "title": "", "content": "Problem Statement There are N mountains in a circle, called Mountain 1, Mountain 2, . . . , Mountain N in clockwise order. N is an odd number.\nBetween these mountains, there are N dams, called Dam 1, Dam 2, . . . , Dam N. Dam i (1 <= i <= N) is located between Mountain i and i+1 (Mountain N+1 is Mountain 1).\nWhen Mountain i (1 <= i <= N) receives 2x liters of rain, Dam i-1 and Dam i each accumulates x liters of water (Dam 0 is Dam N).\nOne day, each of the mountains received a non-negative even number of liters of rain.\nAs a result, Dam i (1 <= i <= N) accumulated a total of A_i liters of water.\nFind the amount of rain each of the mountains received. We can prove that the solution is unique under the constraints of this problem.", "constraint": "All values in input are integers.\n3 <= N <= 10^5-1\nN is an odd number.\n0 <= A_i <= 10^9\nThe situation represented by input can occur when each of the mountains receives a non-negative even number of liters of rain.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print N integers representing the number of liters of rain Mountain 1, Mountain 2, . . . , Mountain N received, in this order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 2 4 output: 4 0 4\n\nIf we assume Mountain 1,2, and 3 received 4,0, and 4 liters of rain, respectively, it is consistent with this input, as follows:\n\nDam 1 should have accumulated \\frac{4}{2} + \\frac{0}{2} = 2 liters of water.\nDam 2 should have accumulated \\frac{0}{2} + \\frac{4}{2} = 2 liters of water.\nDam 3 should have accumulated \\frac{4}{2} + \\frac{4}{2} = 4 liters of water.", "input: 5\n3 8 7 5 5 output: 2 4 12 2 8", "input: 3\n1000000000 1000000000 0 output: 0 2000000000 0"], "Pid": "p02984", "ProblemText": "Task Description: Problem Statement There are N mountains in a circle, called Mountain 1, Mountain 2, . . . , Mountain N in clockwise order. N is an odd number.\nBetween these mountains, there are N dams, called Dam 1, Dam 2, . . . , Dam N. Dam i (1 <= i <= N) is located between Mountain i and i+1 (Mountain N+1 is Mountain 1).\nWhen Mountain i (1 <= i <= N) receives 2x liters of rain, Dam i-1 and Dam i each accumulates x liters of water (Dam 0 is Dam N).\nOne day, each of the mountains received a non-negative even number of liters of rain.\nAs a result, Dam i (1 <= i <= N) accumulated a total of A_i liters of water.\nFind the amount of rain each of the mountains received. We can prove that the solution is unique under the constraints of this problem.\nTask Constraint: All values in input are integers.\n3 <= N <= 10^5-1\nN is an odd number.\n0 <= A_i <= 10^9\nThe situation represented by input can occur when each of the mountains receives a non-negative even number of liters of rain.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print N integers representing the number of liters of rain Mountain 1, Mountain 2, . . . , Mountain N received, in this order.\nTask Samples: input: 3\n2 2 4 output: 4 0 4\n\nIf we assume Mountain 1,2, and 3 received 4,0, and 4 liters of rain, respectively, it is consistent with this input, as follows:\n\nDam 1 should have accumulated \\frac{4}{2} + \\frac{0}{2} = 2 liters of water.\nDam 2 should have accumulated \\frac{0}{2} + \\frac{4}{2} = 2 liters of water.\nDam 3 should have accumulated \\frac{4}{2} + \\frac{4}{2} = 4 liters of water.\ninput: 5\n3 8 7 5 5 output: 2 4 12 2 8\ninput: 3\n1000000000 1000000000 0 output: 0 2000000000 0\n\n" }, { "title": "", "content": "Problem Statement You are given a tree with N vertices and N-1 edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and b_i.\nYou have coloring materials of K colors.\nFor each vertex in the tree, you will choose one of the K colors to paint it, so that the following condition is satisfied:\n\nIf the distance between two different vertices x and y is less than or equal to two, x and y have different colors.\n\nHow many ways are there to paint the tree? Find the count modulo 1\\ 000\\ 000\\ 007.\n\nWhat is tree?\nA tree is a kind of graph. For detail, please see: Wikipedia \"Tree (graph theory)\"", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p02985", "ProblemText": "Task Description: Problem Statement You are given a tree with N vertices and N-1 edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and b_i.\nYou have coloring materials of K colors.\nFor each vertex in the tree, you will choose one of the K colors to paint it, so that the following condition is satisfied:\n\nIf the distance between two different vertices x and y is less than or equal to two, x and y have different colors.\n\nHow many ways are there to paint the tree? Find the count modulo 1\\ 000\\ 000\\ 007.\n\nWhat is tree?\nA tree is a kind of graph. For detail, please see: Wikipedia \"Tree (graph theory)\"\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices numbered 1 to N.\nThe i-th edge in this tree connects Vertex a_i and Vertex b_i, and the color and length of that edge are c_i and d_i, respectively.\nHere the color of each edge is represented by an integer between 1 and N-1 (inclusive). The same integer corresponds to the same color, and different integers correspond to different colors.\nAnswer the following Q queries:\n\nQuery j (1 <= j <= Q): assuming that the length of every edge whose color is x_j is changed to y_j, find the distance between Vertex u_j and Vertex v_j. (The changes of the lengths of edges do not affect the subsequent queries. )", "constraint": "2 <= N <= 10^5\n1 <= Q <= 10^5\n1 <= a_i, b_i <= N\n1 <= c_i <= N-1\n1 <= d_i <= 10^4\n1 <= x_j <= N-1\n1 <= y_j <= 10^4\n1 <= u_j < v_j <= N\nThe given graph is a tree.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN Q\na_1 b_1 c_1 d_1\n:\na_{N-1} b_{N-1} c_{N-1} d_{N-1}\nx_1 y_1 u_1 v_1\n:\nx_Q y_Q u_Q v_Q", "output": "Print Q lines. The j-th line (1 <= j <= Q) should contain the answer to Query j.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 2 1 10\n1 3 2 20\n2 4 4 30\n5 2 1 40\n1 100 1 4\n1 100 1 5\n3 1000 3 4 output: 130\n200\n60\n\nThe graph in this input is as follows:\n\nHere the edges of Color 1 are shown as solid red lines, the edge of Color 2 is shown as a bold green line, and the edge of Color 4 is shown as a blue dashed line.\n\nQuery 1: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 4 is 100 + 30 = 130.\nQuery 2: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 5 is 100 + 100 = 200.\nQuery 3: Assuming that the length of every edge whose color is 3 is changed to 1000 (there is no such edge), the distance between Vertex 3 and Vertex 4 is 20 + 10 + 30 = 60. Note that the edges of Color 1 now have their original lengths."], "Pid": "p02986", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices numbered 1 to N.\nThe i-th edge in this tree connects Vertex a_i and Vertex b_i, and the color and length of that edge are c_i and d_i, respectively.\nHere the color of each edge is represented by an integer between 1 and N-1 (inclusive). The same integer corresponds to the same color, and different integers correspond to different colors.\nAnswer the following Q queries:\n\nQuery j (1 <= j <= Q): assuming that the length of every edge whose color is x_j is changed to y_j, find the distance between Vertex u_j and Vertex v_j. (The changes of the lengths of edges do not affect the subsequent queries. )\nTask Constraint: 2 <= N <= 10^5\n1 <= Q <= 10^5\n1 <= a_i, b_i <= N\n1 <= c_i <= N-1\n1 <= d_i <= 10^4\n1 <= x_j <= N-1\n1 <= y_j <= 10^4\n1 <= u_j < v_j <= N\nThe given graph is a tree.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN Q\na_1 b_1 c_1 d_1\n:\na_{N-1} b_{N-1} c_{N-1} d_{N-1}\nx_1 y_1 u_1 v_1\n:\nx_Q y_Q u_Q v_Q\nTask Output: Print Q lines. The j-th line (1 <= j <= Q) should contain the answer to Query j.\nTask Samples: input: 5 3\n1 2 1 10\n1 3 2 20\n2 4 4 30\n5 2 1 40\n1 100 1 4\n1 100 1 5\n3 1000 3 4 output: 130\n200\n60\n\nThe graph in this input is as follows:\n\nHere the edges of Color 1 are shown as solid red lines, the edge of Color 2 is shown as a bold green line, and the edge of Color 4 is shown as a blue dashed line.\n\nQuery 1: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 4 is 100 + 30 = 130.\nQuery 2: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 5 is 100 + 100 = 200.\nQuery 3: Assuming that the length of every edge whose color is 3 is changed to 1000 (there is no such edge), the distance between Vertex 3 and Vertex 4 is 20 + 10 + 30 = 60. Note that the edges of Color 1 now have their original lengths.\n\n" }, { "title": "", "content": "Problem Statement You are given a 4-character string S consisting of uppercase English letters.\nDetermine if S consists of exactly two kinds of characters which both appear twice in S.", "constraint": "The length of S is 4.\nS consists of uppercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S consists of exactly two kinds of characters which both appear twice in S, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ASSA output: Yes\n\nS consists of A and S which both appear twice in S.", "input: STOP output: No", "input: FFEE output: Yes", "input: FREE output: No"], "Pid": "p02987", "ProblemText": "Task Description: Problem Statement You are given a 4-character string S consisting of uppercase English letters.\nDetermine if S consists of exactly two kinds of characters which both appear twice in S.\nTask Constraint: The length of S is 4.\nS consists of uppercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S consists of exactly two kinds of characters which both appear twice in S, print Yes; otherwise, print No.\nTask Samples: input: ASSA output: Yes\n\nS consists of A and S which both appear twice in S.\ninput: STOP output: No\ninput: FFEE output: Yes\ninput: FREE output: No\n\n" }, { "title": "", "content": "Problem Statement We have a permutation p = {p_1, \\ p_2, \\ . . . , \\ p_n} of {1, \\ 2, \\ . . . , \\ n}.\nPrint the number of elements p_i (1 < i < n) that satisfy the following condition:\n\np_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.", "constraint": "All values in input are integers.\n3 <= n <= 20\np is a permutation of {1,\\ 2,\\ ...,\\ n}.", "input": "Input is given from Standard Input in the following format:\nn\np_1 p_2 . . . p_n", "output": "Print the number of elements p_i (1 < i < n) that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 3 5 4 2 output: 2\n\np_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.", "input: 9\n9 6 3 2 5 8 7 4 1 output: 5"], "Pid": "p02988", "ProblemText": "Task Description: Problem Statement We have a permutation p = {p_1, \\ p_2, \\ . . . , \\ p_n} of {1, \\ 2, \\ . . . , \\ n}.\nPrint the number of elements p_i (1 < i < n) that satisfy the following condition:\n\np_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.\nTask Constraint: All values in input are integers.\n3 <= n <= 20\np is a permutation of {1,\\ 2,\\ ...,\\ n}.\nTask Input: Input is given from Standard Input in the following format:\nn\np_1 p_2 . . . p_n\nTask Output: Print the number of elements p_i (1 < i < n) that satisfy the condition.\nTask Samples: input: 5\n1 3 5 4 2 output: 2\n\np_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.\ninput: 9\n9 6 3 2 5 8 7 4 1 output: 5\n\n" }, { "title": "", "content": "Problem Statement\n2 <= N <= 10^5\nN is an even number.\n1 <= d_i <= 10^5\nAll values in input are integers.", "constraint": "", "input": "Input is given from Standard Input in the following format:\nN\nd_1 d_2 . . . d_N", "output": "Print the number of choices of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same.", "content_img": false, "lang": "nl", "error": false, "samples": ["input: 6\n9 1 4 4 6 7 output: 2\n\nIf we choose K=5 or 6, Problem 1,5, and 6 will be for ARCs, Problem 2,3, and 4 will be for ABCs, and the objective is achieved.\nThus, the answer is 2.", "input: 8\n9 1 14 5 5 4 4 14 output: 0\n\nThere may be no choice of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same.", "input: 14\n99592 10342 29105 78532 83018 11639 92015 77204 30914 21912 34519 80835 100000 1 output: 42685"], "Pid": "p02989", "ProblemText": "Task Description: Problem Statement\n2 <= N <= 10^5\nN is an even number.\n1 <= d_i <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nd_1 d_2 . . . d_N\nTask Output: Print the number of choices of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same.\nTask Samples: input: 6\n9 1 4 4 6 7 output: 2\n\nIf we choose K=5 or 6, Problem 1,5, and 6 will be for ARCs, Problem 2,3, and 4 will be for ABCs, and the objective is achieved.\nThus, the answer is 2.\ninput: 8\n9 1 14 5 5 4 4 14 output: 0\n\nThere may be no choice of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same.\ninput: 14\n99592 10342 29105 78532 83018 11639 92015 77204 30914 21912 34519 80835 100000 1 output: 42685\n\n" }, { "title": "", "content": "Problem Statement There are K blue balls and N-K red balls. The balls of the same color cannot be distinguished. Snuke and Takahashi are playing with these balls.\nFirst, Snuke will arrange the N balls in a row from left to right.\nThen, Takahashi will collect only the K blue balls. In one move, he can collect any number of consecutive blue balls. He will collect all the blue balls in the fewest moves possible.\nHow many ways are there for Snuke to arrange the N balls in a row so that Takahashi will need exactly i moves to collect all the blue balls? Compute this number modulo 10^9+7 for each i such that 1 <= i <= K.", "constraint": "1 <= K <= N <= 2000", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print K lines. The i-th line (1 <= i <= K) should contain the number of ways to arrange the N balls so that Takahashi will need exactly i moves to collect all the blue balls, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 output: 3\n6\n1\n\nThere are three ways to arrange the balls so that Takahashi will need exactly one move: (B, B, B, R, R), (R, B, B, B, R), and (R, R, B, B, B). (R and B stands for red and blue, respectively).\nThere are six ways to arrange the balls so that Takahashi will need exactly two moves: (B, B, R, B, R), (B, B, R, R, B), (R, B, B, R, B), (R, B, R, B, B), (B, R, B, B, R), and (B, R, R, B, B).\nThere is one way to arrange the balls so that Takahashi will need exactly three moves: (B, R, B, R, B).", "input: 2000 3 output: 1998\n3990006\n327341989\n\nBe sure to print the numbers of arrangements modulo 10^9+7."], "Pid": "p02990", "ProblemText": "Task Description: Problem Statement There are K blue balls and N-K red balls. The balls of the same color cannot be distinguished. Snuke and Takahashi are playing with these balls.\nFirst, Snuke will arrange the N balls in a row from left to right.\nThen, Takahashi will collect only the K blue balls. In one move, he can collect any number of consecutive blue balls. He will collect all the blue balls in the fewest moves possible.\nHow many ways are there for Snuke to arrange the N balls in a row so that Takahashi will need exactly i moves to collect all the blue balls? Compute this number modulo 10^9+7 for each i such that 1 <= i <= K.\nTask Constraint: 1 <= K <= N <= 2000\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print K lines. The i-th line (1 <= i <= K) should contain the number of ways to arrange the N balls so that Takahashi will need exactly i moves to collect all the blue balls, modulo 10^9+7.\nTask Samples: input: 5 3 output: 3\n6\n1\n\nThere are three ways to arrange the balls so that Takahashi will need exactly one move: (B, B, B, R, R), (R, B, B, B, R), and (R, R, B, B, B). (R and B stands for red and blue, respectively).\nThere are six ways to arrange the balls so that Takahashi will need exactly two moves: (B, B, R, B, R), (B, B, R, R, B), (R, B, B, R, B), (R, B, R, B, B), (B, R, B, B, R), and (B, R, R, B, B).\nThere is one way to arrange the balls so that Takahashi will need exactly three moves: (B, R, B, R, B).\ninput: 2000 3 output: 1998\n3990006\n327341989\n\nBe sure to print the numbers of arrangements modulo 10^9+7.\n\n" }, { "title": "", "content": "Problem Statement Ken loves ken-ken-pa (Japanese version of hopscotch). Today, he will play it on a directed graph G.\nG consists of N vertices numbered 1 to N, and M edges. The i-th edge points from Vertex u_i to Vertex v_i.\nFirst, Ken stands on Vertex S. He wants to reach Vertex T by repeating ken-ken-pa. In one ken-ken-pa, he does the following exactly three times: follow an edge pointing from the vertex on which he is standing.\nDetermine if he can reach Vertex T by repeating ken-ken-pa. If the answer is yes, find the minimum number of ken-ken-pa needed to reach Vertex T. Note that visiting Vertex T in the middle of a ken-ken-pa does not count as reaching Vertex T by repeating ken-ken-pa.", "constraint": "2 <= N <= 10^5\n0 <= M <= \\min(10^5, N (N-1))\n1 <= u_i, v_i <= N(1 <= i <= M)\nu_i \\neq v_i (1 <= i <= M)\nIf i \\neq j, (u_i, v_i) \\neq (u_j, v_j).\n1 <= S, T <= N\nS \\neq T", "input": "Input is given from Standard Input in the following format:\nN M\nu_1 v_1\n:\nu_M v_M\nS T", "output": "If Ken cannot reach Vertex T from Vertex S by repeating ken-ken-pa, print -1.\nIf he can, print the minimum number of ken-ken-pa needed to reach vertex T.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n1 2\n2 3\n3 4\n4 1\n1 3 output: 2\n\nKen can reach Vertex 3 from Vertex 1 in two ken-ken-pa, as follows: 1 \\rightarrow 2 \\rightarrow 3 \\rightarrow 4 in the first ken-ken-pa, then 4 \\rightarrow 1 \\rightarrow 2 \\rightarrow 3 in the second ken-ken-pa. This is the minimum number of ken-ken-pa needed.", "input: 3 3\n1 2\n2 3\n3 1\n1 2 output: -1\n\nAny number of ken-ken-pa will bring Ken back to Vertex 1, so he cannot reach Vertex 2, though he can pass through it in the middle of a ken-ken-pa.", "input: 2 0\n1 2 output: -1\n\nVertex S and Vertex T may be disconnected.", "input: 6 8\n1 2\n2 3\n3 4\n4 5\n5 1\n1 4\n1 5\n4 6\n1 6 output: 2"], "Pid": "p02991", "ProblemText": "Task Description: Problem Statement Ken loves ken-ken-pa (Japanese version of hopscotch). Today, he will play it on a directed graph G.\nG consists of N vertices numbered 1 to N, and M edges. The i-th edge points from Vertex u_i to Vertex v_i.\nFirst, Ken stands on Vertex S. He wants to reach Vertex T by repeating ken-ken-pa. In one ken-ken-pa, he does the following exactly three times: follow an edge pointing from the vertex on which he is standing.\nDetermine if he can reach Vertex T by repeating ken-ken-pa. If the answer is yes, find the minimum number of ken-ken-pa needed to reach Vertex T. Note that visiting Vertex T in the middle of a ken-ken-pa does not count as reaching Vertex T by repeating ken-ken-pa.\nTask Constraint: 2 <= N <= 10^5\n0 <= M <= \\min(10^5, N (N-1))\n1 <= u_i, v_i <= N(1 <= i <= M)\nu_i \\neq v_i (1 <= i <= M)\nIf i \\neq j, (u_i, v_i) \\neq (u_j, v_j).\n1 <= S, T <= N\nS \\neq T\nTask Input: Input is given from Standard Input in the following format:\nN M\nu_1 v_1\n:\nu_M v_M\nS T\nTask Output: If Ken cannot reach Vertex T from Vertex S by repeating ken-ken-pa, print -1.\nIf he can, print the minimum number of ken-ken-pa needed to reach vertex T.\nTask Samples: input: 4 4\n1 2\n2 3\n3 4\n4 1\n1 3 output: 2\n\nKen can reach Vertex 3 from Vertex 1 in two ken-ken-pa, as follows: 1 \\rightarrow 2 \\rightarrow 3 \\rightarrow 4 in the first ken-ken-pa, then 4 \\rightarrow 1 \\rightarrow 2 \\rightarrow 3 in the second ken-ken-pa. This is the minimum number of ken-ken-pa needed.\ninput: 3 3\n1 2\n2 3\n3 1\n1 2 output: -1\n\nAny number of ken-ken-pa will bring Ken back to Vertex 1, so he cannot reach Vertex 2, though he can pass through it in the middle of a ken-ken-pa.\ninput: 2 0\n1 2 output: -1\n\nVertex S and Vertex T may be disconnected.\ninput: 6 8\n1 2\n2 3\n3 4\n4 5\n5 1\n1 4\n1 5\n4 6\n1 6 output: 2\n\n" }, { "title": "", "content": "Problem Statement Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.", "constraint": "1<= N<= 10^9\n1 2<= K<= 100 (fixed at 21:33 JST)\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the number of sequences, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 5\n\n(1,1), (1,2), (1,3), (2,1), and (3,1) satisfy the condition.", "input: 10 3 output: 147", "input: 314159265 35 output: 457397712"], "Pid": "p02992", "ProblemText": "Task Description: Problem Statement Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.\nTask Constraint: 1<= N<= 10^9\n1 2<= K<= 100 (fixed at 21:33 JST)\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of sequences, modulo 10^9+7.\nTask Samples: input: 3 2 output: 5\n\n(1,1), (1,2), (1,3), (2,1), and (3,1) satisfy the condition.\ninput: 10 3 output: 147\ninput: 314159265 35 output: 457397712\n\n" }, { "title": "", "content": "Problem Statement\nThe door of Snuke's laboratory is locked with a security code.\nThe security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.\nYou are given the current security code S. If S is hard to enter, print Bad; otherwise, print Good.", "constraint": "S is a 4-character string consisting of digits.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S is hard to enter, print Bad; otherwise, print Good.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3776 output: Bad\n\nThe second and third digits are the same, so 3776 is hard to enter.", "input: 8080 output: Good\n\nThere are no two consecutive digits that are the same, so 8080 is not hard to enter.", "input: 1333 output: Bad", "input: 0024 output: Bad"], "Pid": "p02993", "ProblemText": "Task Description: Problem Statement\nThe door of Snuke's laboratory is locked with a security code.\nThe security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.\nYou are given the current security code S. If S is hard to enter, print Bad; otherwise, print Good.\nTask Constraint: S is a 4-character string consisting of digits.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S is hard to enter, print Bad; otherwise, print Good.\nTask Samples: input: 3776 output: Bad\n\nThe second and third digits are the same, so 3776 is hard to enter.\ninput: 8080 output: Good\n\nThere are no two consecutive digits that are the same, so 8080 is not hard to enter.\ninput: 1333 output: Bad\ninput: 0024 output: Bad\n\n" }, { "title": "", "content": "Problem Statement You have N apples, called Apple 1, Apple 2, Apple 3, . . . , Apple N. The flavor of Apple i is L+i-1, which can be negative.\nYou can make an apple pie using one or more of the apples. The flavor of the apple pie will be the sum of the flavors of the apples used.\nYou planned to make an apple pie using all of the apples, but being hungry tempts you to eat one of them, which can no longer be used to make the apple pie.\nYou want to make an apple pie that is as similar as possible to the one that you planned to make. Thus, you will choose the apple to eat so that the flavor of the apple pie made of the remaining N-1 apples will have the smallest possible absolute difference from the flavor of the apple pie made of all the N apples.\nFind the flavor of the apple pie made of the remaining N-1 apples when you choose the apple to eat as above.\nWe can prove that this value is uniquely determined.", "constraint": "2 <= N <= 200\n-100 <= L <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN L", "output": "Find the flavor of the apple pie made of the remaining N-1 apples when you optimally choose the apple to eat.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 output: 18\n\nThe flavors of Apple 1,2,3,4, and 5 are 2,3,4,5, and 6, respectively. The optimal choice is to eat Apple 1, so the answer is 3+4+5+6=18.", "input: 3 -1 output: 0\n\nThe flavors of Apple 1,2, and 3 are -1,0, and 1, respectively. The optimal choice is to eat Apple 2, so the answer is (-1)+1=0.", "input: 30 -50 output: -1044"], "Pid": "p02994", "ProblemText": "Task Description: Problem Statement You have N apples, called Apple 1, Apple 2, Apple 3, . . . , Apple N. The flavor of Apple i is L+i-1, which can be negative.\nYou can make an apple pie using one or more of the apples. The flavor of the apple pie will be the sum of the flavors of the apples used.\nYou planned to make an apple pie using all of the apples, but being hungry tempts you to eat one of them, which can no longer be used to make the apple pie.\nYou want to make an apple pie that is as similar as possible to the one that you planned to make. Thus, you will choose the apple to eat so that the flavor of the apple pie made of the remaining N-1 apples will have the smallest possible absolute difference from the flavor of the apple pie made of all the N apples.\nFind the flavor of the apple pie made of the remaining N-1 apples when you choose the apple to eat as above.\nWe can prove that this value is uniquely determined.\nTask Constraint: 2 <= N <= 200\n-100 <= L <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN L\nTask Output: Find the flavor of the apple pie made of the remaining N-1 apples when you optimally choose the apple to eat.\nTask Samples: input: 5 2 output: 18\n\nThe flavors of Apple 1,2,3,4, and 5 are 2,3,4,5, and 6, respectively. The optimal choice is to eat Apple 1, so the answer is 3+4+5+6=18.\ninput: 3 -1 output: 0\n\nThe flavors of Apple 1,2, and 3 are -1,0, and 1, respectively. The optimal choice is to eat Apple 2, so the answer is (-1)+1=0.\ninput: 30 -50 output: -1044\n\n" }, { "title": "", "content": "Problem Statement You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.", "constraint": "1<= A<= B<= 10^{18}\n1<= C,D<= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C D", "output": "Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 9 2 3 output: 2\n\n5 and 7 satisfy the condition.", "input: 10 40 6 8 output: 23", "input: 314159265358979323 846264338327950288 419716939 937510582 output: 532105071133627368"], "Pid": "p02995", "ProblemText": "Task Description: Problem Statement You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.\nTask Constraint: 1<= A<= B<= 10^{18}\n1<= C,D<= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C D\nTask Output: Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.\nTask Samples: input: 4 9 2 3 output: 2\n\n5 and 7 satisfy the condition.\ninput: 10 40 6 8 output: 23\ninput: 314159265358979323 846264338327950288 419716939 937510582 output: 532105071133627368\n\n" }, { "title": "", "content": "Problem Statement\nKizahashi, who was appointed as the administrator of ABC at National Problem Workshop in the Kingdom of At Coder, got too excited and took on too many jobs.\nLet the current time be time 0. Kizahashi has N jobs numbered 1 to N.\nIt takes A_i units of time for Kizahashi to complete Job i. The deadline for Job i is time B_i, and he must complete the job before or at this time.\nKizahashi cannot work on two or more jobs simultaneously, but when he completes a job, he can start working on another immediately.\nCan Kizahashi complete all the jobs in time? If he can, print Yes; if he cannot, print No.", "constraint": "All values in input are integers.\n1 <= N <= 2 * 10^5\n1 <= A_i, B_i <= 10^9 (1 <= i <= N)", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\n.\n.\n.\nA_N B_N", "output": "If Kizahashi can complete all the jobs in time, print Yes; if he cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 4\n1 9\n1 8\n4 9\n3 12 output: Yes\n\nHe can complete all the jobs in time by, for example, doing them in the following order:\n\nDo Job 2 from time 0 to 1.\nDo Job 1 from time 1 to 3.\nDo Job 4 from time 3 to 7.\nDo Job 3 from time 7 to 8.\nDo Job 5 from time 8 to 11.\n\nNote that it is fine to complete Job 3 exactly at the deadline, time 8.", "input: 3\n334 1000\n334 1000\n334 1000 output: No\n\nHe cannot complete all the jobs in time, no matter what order he does them in.", "input: 30\n384 8895\n1725 9791\n170 1024\n4 11105\n2 6\n578 1815\n702 3352\n143 5141\n1420 6980\n24 1602\n849 999\n76 7586\n85 5570\n444 4991\n719 11090\n470 10708\n1137 4547\n455 9003\n110 9901\n15 8578\n368 3692\n104 1286\n3 4\n366 12143\n7 6649\n610 2374\n152 7324\n4 7042\n292 11386\n334 5720 output: Yes"], "Pid": "p02996", "ProblemText": "Task Description: Problem Statement\nKizahashi, who was appointed as the administrator of ABC at National Problem Workshop in the Kingdom of At Coder, got too excited and took on too many jobs.\nLet the current time be time 0. Kizahashi has N jobs numbered 1 to N.\nIt takes A_i units of time for Kizahashi to complete Job i. The deadline for Job i is time B_i, and he must complete the job before or at this time.\nKizahashi cannot work on two or more jobs simultaneously, but when he completes a job, he can start working on another immediately.\nCan Kizahashi complete all the jobs in time? If he can, print Yes; if he cannot, print No.\nTask Constraint: All values in input are integers.\n1 <= N <= 2 * 10^5\n1 <= A_i, B_i <= 10^9 (1 <= i <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\n.\n.\n.\nA_N B_N\nTask Output: If Kizahashi can complete all the jobs in time, print Yes; if he cannot, print No.\nTask Samples: input: 5\n2 4\n1 9\n1 8\n4 9\n3 12 output: Yes\n\nHe can complete all the jobs in time by, for example, doing them in the following order:\n\nDo Job 2 from time 0 to 1.\nDo Job 1 from time 1 to 3.\nDo Job 4 from time 3 to 7.\nDo Job 3 from time 7 to 8.\nDo Job 5 from time 8 to 11.\n\nNote that it is fine to complete Job 3 exactly at the deadline, time 8.\ninput: 3\n334 1000\n334 1000\n334 1000 output: No\n\nHe cannot complete all the jobs in time, no matter what order he does them in.\ninput: 30\n384 8895\n1725 9791\n170 1024\n4 11105\n2 6\n578 1815\n702 3352\n143 5141\n1420 6980\n24 1602\n849 999\n76 7586\n85 5570\n444 4991\n719 11090\n470 10708\n1137 4547\n455 9003\n110 9901\n15 8578\n368 3692\n104 1286\n3 4\n366 12143\n7 6649\n610 2374\n152 7324\n4 7042\n292 11386\n334 5720 output: Yes\n\n" }, { "title": "", "content": "Problem Statement\nDoes there exist an undirected graph with N vertices satisfying the following conditions?\n\nThe graph is simple and connected.\nThe vertices are numbered 1,2, . . . , N.\nLet M be the number of edges in the graph. The edges are numbered 1,2, . . . , M, the length of each edge is 1, and Edge i connects Vertex u_i and Vertex v_i.\nThere are exactly K pairs of vertices (i, \\ j)\\ (i < j) such that the shortest distance between them is 2.\n\nIf there exists such a graph, construct an example.", "constraint": "All values in input are integers.\n2 <= N <= 100\n0 <= K <= \\frac{N(N - 1)}{2}", "input": "Input is given from Standard Input in the following format:\nN K", "output": "If there does not exist an undirected graph with N vertices satisfying the conditions, print -1.\nIf there exists such a graph, print an example in the following format (refer to Problem Statement for what the symbols stand for):\nM\nu_1 v_1\n:\nu_M v_M\n\nIf there exist multiple graphs satisfying the conditions, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 output: 5\n4 3\n1 2\n3 1\n4 5\n2 3\n\nThis graph has three pairs of vertices such that the shortest distance between them is 2: (1,\\ 4), (2,\\ 4), and (3,\\ 5). Thus, the condition is satisfied.", "input: 5 8 output: -1\n\nThere is no graph satisfying the conditions."], "Pid": "p02997", "ProblemText": "Task Description: Problem Statement\nDoes there exist an undirected graph with N vertices satisfying the following conditions?\n\nThe graph is simple and connected.\nThe vertices are numbered 1,2, . . . , N.\nLet M be the number of edges in the graph. The edges are numbered 1,2, . . . , M, the length of each edge is 1, and Edge i connects Vertex u_i and Vertex v_i.\nThere are exactly K pairs of vertices (i, \\ j)\\ (i < j) such that the shortest distance between them is 2.\n\nIf there exists such a graph, construct an example.\nTask Constraint: All values in input are integers.\n2 <= N <= 100\n0 <= K <= \\frac{N(N - 1)}{2}\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: If there does not exist an undirected graph with N vertices satisfying the conditions, print -1.\nIf there exists such a graph, print an example in the following format (refer to Problem Statement for what the symbols stand for):\nM\nu_1 v_1\n:\nu_M v_M\n\nIf there exist multiple graphs satisfying the conditions, any of them will be accepted.\nTask Samples: input: 5 3 output: 5\n4 3\n1 2\n3 1\n4 5\n2 3\n\nThis graph has three pairs of vertices such that the shortest distance between them is 2: (1,\\ 4), (2,\\ 4), and (3,\\ 5). Thus, the condition is satisfied.\ninput: 5 8 output: -1\n\nThere is no graph satisfying the conditions.\n\n" }, { "title": "", "content": "Problem Statement There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).\nWe will repeat the following operation as long as possible:\n\nChoose four integers a, b, c, d (a \\neq c, b \\neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.\n\nWe can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.", "constraint": "1 <= N <= 10^5\n1 <= x_i, y_i <= 10^5\nIf i \\neq j, x_i \\neq x_j or y_i \\neq y_j.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print the maximum number of times we can do the operation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1\n5 1\n5 5 output: 1\n\nBy choosing a = 1, b = 1, c = 5, d = 5, we can add a dot at (1,5). We cannot do the operation any more, so the maximum number of operations is 1.", "input: 2\n10 10\n20 20 output: 0\n\nThere are only two dots, so we cannot do the operation at all.", "input: 9\n1 1\n2 1\n3 1\n4 1\n5 1\n1 2\n1 3\n1 4\n1 5 output: 16\n\nWe can do the operation for all choices of the form a = 1, b = 1, c = i, d = j (2 <= i,j <= 5), and no more. Thus, the maximum number of operations is 16."], "Pid": "p02998", "ProblemText": "Task Description: Problem Statement There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).\nWe will repeat the following operation as long as possible:\n\nChoose four integers a, b, c, d (a \\neq c, b \\neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.\n\nWe can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.\nTask Constraint: 1 <= N <= 10^5\n1 <= x_i, y_i <= 10^5\nIf i \\neq j, x_i \\neq x_j or y_i \\neq y_j.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print the maximum number of times we can do the operation.\nTask Samples: input: 3\n1 1\n5 1\n5 5 output: 1\n\nBy choosing a = 1, b = 1, c = 5, d = 5, we can add a dot at (1,5). We cannot do the operation any more, so the maximum number of operations is 1.\ninput: 2\n10 10\n20 20 output: 0\n\nThere are only two dots, so we cannot do the operation at all.\ninput: 9\n1 1\n2 1\n3 1\n4 1\n5 1\n1 2\n1 3\n1 4\n1 5 output: 16\n\nWe can do the operation for all choices of the form a = 1, b = 1, c = i, d = j (2 <= i,j <= 5), and no more. Thus, the maximum number of operations is 16.\n\n" }, { "title": "", "content": "Problem Statement X and A are integers between 0 and 9 (inclusive).\nIf X is less than A, print 0; if X is not less than A, print 10.", "constraint": "0 <= X, A <= 9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX A", "output": "If X is less than A, print 0; if X is not less than A, print 10.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 output: 0\n\n3 is less than 5, so we should print 0.", "input: 7 5 output: 10\n\n7 is not less than 5, so we should print 10.", "input: 6 6 output: 10\n\n6 is not less than 6, so we should print 10."], "Pid": "p02999", "ProblemText": "Task Description: Problem Statement X and A are integers between 0 and 9 (inclusive).\nIf X is less than A, print 0; if X is not less than A, print 10.\nTask Constraint: 0 <= X, A <= 9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX A\nTask Output: If X is less than A, print 0; if X is not less than A, print 10.\nTask Samples: input: 3 5 output: 0\n\n3 is less than 5, so we should print 0.\ninput: 7 5 output: 10\n\n7 is not less than 5, so we should print 10.\ninput: 6 6 output: 10\n\n6 is not less than 6, so we should print 10.\n\n" }, { "title": "", "content": "Problem Statement A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 <= i <= N+1) at coordinate D_i = D_{i-1} + L_{i-1}.\nHow many times will the ball make a bounce where the coordinate is at most X?", "constraint": "1 <= N <= 100\n1 <= L_i <= 100\n1 <= X <= 10000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X\nL_1 L_2 . . . L_{N-1} L_N", "output": "Print the number of times the ball will make a bounce where the coordinate is at most X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 6\n3 4 5 output: 2\n\nThe ball will make a bounce at the coordinates 0,3,7 and 12, among which two are less than or equal to 6.", "input: 4 9\n3 3 3 3 output: 4\n\nThe ball will make a bounce at the coordinates 0,3,6,9 and 12, among which four are less than or equal to 9."], "Pid": "p03000", "ProblemText": "Task Description: Problem Statement A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 <= i <= N+1) at coordinate D_i = D_{i-1} + L_{i-1}.\nHow many times will the ball make a bounce where the coordinate is at most X?\nTask Constraint: 1 <= N <= 100\n1 <= L_i <= 100\n1 <= X <= 10000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X\nL_1 L_2 . . . L_{N-1} L_N\nTask Output: Print the number of times the ball will make a bounce where the coordinate is at most X.\nTask Samples: input: 3 6\n3 4 5 output: 2\n\nThe ball will make a bounce at the coordinates 0,3,7 and 12, among which two are less than or equal to 6.\ninput: 4 9\n3 3 3 3 output: 4\n\nThe ball will make a bounce at the coordinates 0,3,6,9 and 12, among which four are less than or equal to 9.\n\n" }, { "title": "", "content": "Problem Statement There is a rectangle in a coordinate plane. The coordinates of the four vertices are (0,0), (W, 0), (W, H), and (0, H).\nYou are given a point (x, y) which is within the rectangle or on its border. We will draw a straight line passing through (x, y) to cut the rectangle into two parts. Find the maximum possible area of the part whose area is not larger than that of the other. Additionally, determine if there are multiple ways to cut the rectangle and achieve that maximum.", "constraint": "1 <= W,H <= 10^9\n0<= x<= W\n0<= y<= H\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nW H x y", "output": "Print the maximum possible area of the part whose area is not larger than that of the other, followed by 1 if there are multiple ways to cut the rectangle and achieve that maximum, and 0 otherwise.\nThe area printed will be judged correct when its absolute or relative error is at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 1 2 output: 3.000000 0\n\nThe line x=1 gives the optimal cut, and no other line does.", "input: 2 2 1 1 output: 2.000000 1"], "Pid": "p03001", "ProblemText": "Task Description: Problem Statement There is a rectangle in a coordinate plane. The coordinates of the four vertices are (0,0), (W, 0), (W, H), and (0, H).\nYou are given a point (x, y) which is within the rectangle or on its border. We will draw a straight line passing through (x, y) to cut the rectangle into two parts. Find the maximum possible area of the part whose area is not larger than that of the other. Additionally, determine if there are multiple ways to cut the rectangle and achieve that maximum.\nTask Constraint: 1 <= W,H <= 10^9\n0<= x<= W\n0<= y<= H\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nW H x y\nTask Output: Print the maximum possible area of the part whose area is not larger than that of the other, followed by 1 if there are multiple ways to cut the rectangle and achieve that maximum, and 0 otherwise.\nThe area printed will be judged correct when its absolute or relative error is at most 10^{-9}.\nTask Samples: input: 2 3 1 2 output: 3.000000 0\n\nThe line x=1 gives the optimal cut, and no other line does.\ninput: 2 2 1 1 output: 2.000000 1\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence of positive integers of length N, A=a_1, a_2, …, a_{N}, and an integer K.\nHow many contiguous subsequences of A satisfy the following condition?\n\n(Condition) The sum of the elements in the contiguous subsequence is at least K.\n\nWe consider two contiguous subsequences different if they derive from different positions in A, even if they are the same in content.\nNote that the answer may not fit into a 32-bit integer type.", "constraint": "1 <= a_i <= 10^5\n1 <= N <= 10^5\n1 <= K <= 10^{10}", "input": "Input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N", "output": "Print the number of contiguous subsequences of A that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 10\n6 1 2 7 output: 2\n\nThe following two contiguous subsequences satisfy the condition:\n\nA[1..4]=a_1,a_2,a_3,a_4, with the sum of 16\nA[2..4]=a_2,a_3,a_4, with the sum of 10", "input: 3 5\n3 3 3 output: 3\n\nNote again that we consider two contiguous subsequences different if they derive from different positions, even if they are the same in content.", "input: 10 53462\n103 35322 232 342 21099 90000 18843 9010 35221 19352 output: 36"], "Pid": "p03002", "ProblemText": "Task Description: Problem Statement You are given a sequence of positive integers of length N, A=a_1, a_2, …, a_{N}, and an integer K.\nHow many contiguous subsequences of A satisfy the following condition?\n\n(Condition) The sum of the elements in the contiguous subsequence is at least K.\n\nWe consider two contiguous subsequences different if they derive from different positions in A, even if they are the same in content.\nNote that the answer may not fit into a 32-bit integer type.\nTask Constraint: 1 <= a_i <= 10^5\n1 <= N <= 10^5\n1 <= K <= 10^{10}\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N\nTask Output: Print the number of contiguous subsequences of A that satisfy the condition.\nTask Samples: input: 4 10\n6 1 2 7 output: 2\n\nThe following two contiguous subsequences satisfy the condition:\n\nA[1..4]=a_1,a_2,a_3,a_4, with the sum of 16\nA[2..4]=a_2,a_3,a_4, with the sum of 10\ninput: 3 5\n3 3 3 output: 3\n\nNote again that we consider two contiguous subsequences different if they derive from different positions, even if they are the same in content.\ninput: 10 53462\n103 35322 232 342 21099 90000 18843 9010 35221 19352 output: 36\n\n" }, { "title": "", "content": "Problem Statement You are given two integer sequences S and T of length N and M, respectively, both consisting of integers between 1 and 10^5 (inclusive).\nIn how many pairs of a subsequence of S and a subsequence of T do the two subsequences are the same in content?\nHere the subsequence of A is a sequence obtained by removing zero or more elements from A and concatenating the remaining elements without changing the order.\nFor both S and T, we distinguish two subsequences if the sets of the indices of the removed elements are different, even if the subsequences are the same in content.\nSince the answer can be tremendous, print the number modulo 10^9+7.", "constraint": "1 <= N, M <= 2 * 10^3\nThe length of S is N.\nThe length of T is M. \n1 <= S_i, T_i <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nS_1 S_2 . . . S_{N-1} S_{N}\nT_1 T_2 . . . T_{M-1} T_{M}", "output": "Print the number of pairs of a subsequence of S and a subsequence of T such that the subsequences are the same in content, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n1 3\n3 1 output: 3\n\nS has four subsequences: (), (1), (3), (1,3).\nT has four subsequences: (), (3), (1), (3,1).\nThere are 1 * 1 pair of subsequences in which the subsequences are both (), 1 * 1 pair of subsequences in which the subsequences are both (1), and 1 * 1 pair of subsequences in which the subsequences are both (3), for a total of three pairs.", "input: 2 2\n1 1\n1 1 output: 6\n\nS has four subsequences: (), (1), (1), (1,1).\nT has four subsequences: (), (1), (1), (1,1).\nThere are 1 * 1 pair of subsequences in which the subsequences are both (), 2 * 2 pairs of subsequences in which the subsequences are both (1), and 1 * 1 pair of subsequences in which the subsequences are both (1,1), for a total of six pairs.\nNote again that we distinguish two subsequences if the sets of the indices of the removed elements are different, even if the subsequences are the same in content.", "input: 4 4\n3 4 5 6\n3 4 5 6 output: 16", "input: 10 9\n9 6 5 7 5 9 8 5 6 7\n8 6 8 5 5 7 9 9 7 output: 191", "input: 20 20\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 output: 846527861\n\nBe sure to print the number modulo 10^9+7."], "Pid": "p03003", "ProblemText": "Task Description: Problem Statement You are given two integer sequences S and T of length N and M, respectively, both consisting of integers between 1 and 10^5 (inclusive).\nIn how many pairs of a subsequence of S and a subsequence of T do the two subsequences are the same in content?\nHere the subsequence of A is a sequence obtained by removing zero or more elements from A and concatenating the remaining elements without changing the order.\nFor both S and T, we distinguish two subsequences if the sets of the indices of the removed elements are different, even if the subsequences are the same in content.\nSince the answer can be tremendous, print the number modulo 10^9+7.\nTask Constraint: 1 <= N, M <= 2 * 10^3\nThe length of S is N.\nThe length of T is M. \n1 <= S_i, T_i <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nS_1 S_2 . . . S_{N-1} S_{N}\nT_1 T_2 . . . T_{M-1} T_{M}\nTask Output: Print the number of pairs of a subsequence of S and a subsequence of T such that the subsequences are the same in content, modulo 10^9+7.\nTask Samples: input: 2 2\n1 3\n3 1 output: 3\n\nS has four subsequences: (), (1), (3), (1,3).\nT has four subsequences: (), (3), (1), (3,1).\nThere are 1 * 1 pair of subsequences in which the subsequences are both (), 1 * 1 pair of subsequences in which the subsequences are both (1), and 1 * 1 pair of subsequences in which the subsequences are both (3), for a total of three pairs.\ninput: 2 2\n1 1\n1 1 output: 6\n\nS has four subsequences: (), (1), (1), (1,1).\nT has four subsequences: (), (1), (1), (1,1).\nThere are 1 * 1 pair of subsequences in which the subsequences are both (), 2 * 2 pairs of subsequences in which the subsequences are both (1), and 1 * 1 pair of subsequences in which the subsequences are both (1,1), for a total of six pairs.\nNote again that we distinguish two subsequences if the sets of the indices of the removed elements are different, even if the subsequences are the same in content.\ninput: 4 4\n3 4 5 6\n3 4 5 6 output: 16\ninput: 10 9\n9 6 5 7 5 9 8 5 6 7\n8 6 8 5 5 7 9 9 7 output: 191\ninput: 20 20\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 output: 846527861\n\nBe sure to print the number modulo 10^9+7.\n\n" }, { "title": "", "content": "Problem Statement There are N points in a two-dimensional plane. The initial coordinates of the i-th point are (x_i, y_i). Now, each point starts moving at a speed of 1 per second, in a direction parallel to the x- or y- axis. You are given a character d_i that represents the specific direction in which the i-th point moves, as follows:\n\nIf d_i = R, the i-th point moves in the positive x direction;\nIf d_i = L, the i-th point moves in the negative x direction;\nIf d_i = U, the i-th point moves in the positive y direction;\nIf d_i = D, the i-th point moves in the negative y direction.\n\nYou can stop all the points at some moment of your choice after they start moving (including the moment they start moving).\nThen, let x_{max} and x_{min} be the maximum and minimum among the x-coordinates of the N points, respectively. Similarly, let y_{max} and y_{min} be the maximum and minimum among the y-coordinates of the N points, respectively.\nFind the minimum possible value of (x_{max} - x_{min}) * (y_{max} - y_{min}) and print it.", "constraint": "1 <= N <= 10^5\n-10^8 <= x_i,\\ y_i <= 10^8\nx_i and y_i are integers.\nd_i is R, L, U, or D.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1 d_1\nx_2 y_2 d_2\n.\n.\n.\nx_N y_N d_N", "output": "Print the minimum possible value of (x_{max} - x_{min}) * (y_{max} - y_{min}).\nThe output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 3 D\n3 0 L output: 0\n\nAfter three seconds, the two points will meet at the origin. The value in question will be 0 at that moment.", "input: 5\n-7 -10 U\n7 -6 U\n-8 7 D\n-3 3 D\n0 -6 R output: 97.5\n\nThe answer may not be an integer.", "input: 20\n6 -10 R\n-4 -9 U\n9 6 D\n-3 -2 R\n0 7 D\n4 5 D\n10 -10 U\n-1 -8 U\n10 -6 D\n8 -5 U\n6 4 D\n0 3 D\n7 9 R\n9 -4 R\n3 10 D\n1 9 U\n1 -6 U\n9 -8 R\n6 7 D\n7 -3 D output: 273"], "Pid": "p03004", "ProblemText": "Task Description: Problem Statement There are N points in a two-dimensional plane. The initial coordinates of the i-th point are (x_i, y_i). Now, each point starts moving at a speed of 1 per second, in a direction parallel to the x- or y- axis. You are given a character d_i that represents the specific direction in which the i-th point moves, as follows:\n\nIf d_i = R, the i-th point moves in the positive x direction;\nIf d_i = L, the i-th point moves in the negative x direction;\nIf d_i = U, the i-th point moves in the positive y direction;\nIf d_i = D, the i-th point moves in the negative y direction.\n\nYou can stop all the points at some moment of your choice after they start moving (including the moment they start moving).\nThen, let x_{max} and x_{min} be the maximum and minimum among the x-coordinates of the N points, respectively. Similarly, let y_{max} and y_{min} be the maximum and minimum among the y-coordinates of the N points, respectively.\nFind the minimum possible value of (x_{max} - x_{min}) * (y_{max} - y_{min}) and print it.\nTask Constraint: 1 <= N <= 10^5\n-10^8 <= x_i,\\ y_i <= 10^8\nx_i and y_i are integers.\nd_i is R, L, U, or D.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1 d_1\nx_2 y_2 d_2\n.\n.\n.\nx_N y_N d_N\nTask Output: Print the minimum possible value of (x_{max} - x_{min}) * (y_{max} - y_{min}).\nThe output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-9}.\nTask Samples: input: 2\n0 3 D\n3 0 L output: 0\n\nAfter three seconds, the two points will meet at the origin. The value in question will be 0 at that moment.\ninput: 5\n-7 -10 U\n7 -6 U\n-8 7 D\n-3 3 D\n0 -6 R output: 97.5\n\nThe answer may not be an integer.\ninput: 20\n6 -10 R\n-4 -9 U\n9 6 D\n-3 -2 R\n0 7 D\n4 5 D\n10 -10 U\n-1 -8 U\n10 -6 D\n8 -5 U\n6 4 D\n0 3 D\n7 9 R\n9 -4 R\n3 10 D\n1 9 U\n1 -6 U\n9 -8 R\n6 7 D\n7 -3 D output: 273\n\n" }, { "title": "", "content": "Problem Statement Takahashi is distributing N balls to K persons.\nIf each person has to receive at least one ball, what is the maximum possible difference in the number of balls received between the person with the most balls and the person with the fewest balls?", "constraint": "1 <= K <= N <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the maximum possible difference in the number of balls received.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 1\n\nThe only way to distribute three balls to two persons so that each of them receives at least one ball is to give one ball to one person and give two balls to the other person.\nThus, the maximum possible difference in the number of balls received is 1.", "input: 3 1 output: 0\n\nWe have no choice but to give three balls to the only person, in which case the difference in the number of balls received is 0.", "input: 8 5 output: 3\n\nFor example, if we give 1,4,1,1,1 balls to the five persons, the number of balls received between the person with the most balls and the person with the fewest balls would be 3, which is the maximum result."], "Pid": "p03005", "ProblemText": "Task Description: Problem Statement Takahashi is distributing N balls to K persons.\nIf each person has to receive at least one ball, what is the maximum possible difference in the number of balls received between the person with the most balls and the person with the fewest balls?\nTask Constraint: 1 <= K <= N <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the maximum possible difference in the number of balls received.\nTask Samples: input: 3 2 output: 1\n\nThe only way to distribute three balls to two persons so that each of them receives at least one ball is to give one ball to one person and give two balls to the other person.\nThus, the maximum possible difference in the number of balls received is 1.\ninput: 3 1 output: 0\n\nWe have no choice but to give three balls to the only person, in which case the difference in the number of balls received is 0.\ninput: 8 5 output: 3\n\nFor example, if we give 1,4,1,1,1 balls to the five persons, the number of balls received between the person with the most balls and the person with the fewest balls would be 3, which is the maximum result.\n\n" }, { "title": "", "content": "Problem Statement There are N balls in a two-dimensional plane. The i-th ball is at coordinates (x_i, y_i).\nWe will collect all of these balls, by choosing two integers p and q such that p \\neq 0 or q \\neq 0 and then repeating the following operation:\n\nChoose a ball remaining in the plane and collect it. Let (a, b) be the coordinates of this ball. If we collected a ball at coordinates (a - p, b - q) in the previous operation, the cost of this operation is 0. Otherwise, including when this is the first time to do this operation, the cost of this operation is 1.\n\nFind the minimum total cost required to collect all the balls when we optimally choose p and q.", "constraint": "1 <= N <= 50\n|x_i|, |y_i| <= 10^9\nIf i \\neq j, x_i \\neq x_j or y_i \\neq y_j.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print the minimum total cost required to collect all the balls.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 1\n2 2 output: 1\n\nIf we choose p = 1, q = 1, we can collect all the balls at a cost of 1 by collecting them in the order (1,1), (2,2).", "input: 3\n1 4\n4 6\n7 8 output: 1\n\nIf we choose p = -3, q = -2, we can collect all the balls at a cost of 1 by collecting them in the order (7,8), (4,6), (1,4).", "input: 4\n1 1\n1 2\n2 1\n2 2 output: 2"], "Pid": "p03006", "ProblemText": "Task Description: Problem Statement There are N balls in a two-dimensional plane. The i-th ball is at coordinates (x_i, y_i).\nWe will collect all of these balls, by choosing two integers p and q such that p \\neq 0 or q \\neq 0 and then repeating the following operation:\n\nChoose a ball remaining in the plane and collect it. Let (a, b) be the coordinates of this ball. If we collected a ball at coordinates (a - p, b - q) in the previous operation, the cost of this operation is 0. Otherwise, including when this is the first time to do this operation, the cost of this operation is 1.\n\nFind the minimum total cost required to collect all the balls when we optimally choose p and q.\nTask Constraint: 1 <= N <= 50\n|x_i|, |y_i| <= 10^9\nIf i \\neq j, x_i \\neq x_j or y_i \\neq y_j.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print the minimum total cost required to collect all the balls.\nTask Samples: input: 2\n1 1\n2 2 output: 1\n\nIf we choose p = 1, q = 1, we can collect all the balls at a cost of 1 by collecting them in the order (1,1), (2,2).\ninput: 3\n1 4\n4 6\n7 8 output: 1\n\nIf we choose p = -3, q = -2, we can collect all the balls at a cost of 1 by collecting them in the order (7,8), (4,6), (1,4).\ninput: 4\n1 1\n1 2\n2 1\n2 2 output: 2\n\n" }, { "title": "", "content": "Problem Statement There are N integers, A_1, A_2, . . . , A_N, written on a blackboard.\nWe will repeat the following operation N-1 times so that we have only one integer on the blackboard.\n\nChoose two integers x and y on the blackboard and erase these two integers. Then, write a new integer x-y.\n\nFind the maximum possible value of the final integer on the blackboard and a sequence of operations that maximizes the final integer.", "constraint": "2 <= N <= 10^5\n-10^4 <= A_i <= 10^4\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum possible value M of the final integer on the blackboard, and a sequence of operations x_i, y_i that maximizes the final integer, in the format below.\nHere x_i and y_i represent the integers x and y chosen in the i-th operation, respectively.\nIf there are multiple sequences of operations that maximize the final integer, any of them will be accepted.\nM\nx_1 y_1\n:\nx_{N-1} y_{N-1}", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 -1 2 output: 4\n-1 1\n2 -2\n\nIf we choose x = -1 and y = 1 in the first operation, the set of integers written on the blackboard becomes (-2,2).\nThen, if we choose x = 2 and y = -2 in the second operation, the set of integers written on the blackboard becomes (4).\nIn this case, we have 4 as the final integer. We cannot end with a greater integer, so the answer is 4.", "input: 3\n1 1 1 output: 1\n1 1\n1 0"], "Pid": "p03007", "ProblemText": "Task Description: Problem Statement There are N integers, A_1, A_2, . . . , A_N, written on a blackboard.\nWe will repeat the following operation N-1 times so that we have only one integer on the blackboard.\n\nChoose two integers x and y on the blackboard and erase these two integers. Then, write a new integer x-y.\n\nFind the maximum possible value of the final integer on the blackboard and a sequence of operations that maximizes the final integer.\nTask Constraint: 2 <= N <= 10^5\n-10^4 <= A_i <= 10^4\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum possible value M of the final integer on the blackboard, and a sequence of operations x_i, y_i that maximizes the final integer, in the format below.\nHere x_i and y_i represent the integers x and y chosen in the i-th operation, respectively.\nIf there are multiple sequences of operations that maximize the final integer, any of them will be accepted.\nM\nx_1 y_1\n:\nx_{N-1} y_{N-1}\nTask Samples: input: 3\n1 -1 2 output: 4\n-1 1\n2 -2\n\nIf we choose x = -1 and y = 1 in the first operation, the set of integers written on the blackboard becomes (-2,2).\nThen, if we choose x = 2 and y = -2 in the second operation, the set of integers written on the blackboard becomes (4).\nIn this case, we have 4 as the final integer. We cannot end with a greater integer, so the answer is 4.\ninput: 3\n1 1 1 output: 1\n1 1\n1 0\n\n" }, { "title": "", "content": "Problem Statement The squirrel Chokudai has N acorns.\nOne day, he decides to do some trades in multiple precious metal exchanges to make more acorns.\nHis plan is as follows:\n\nGet out of the nest with N acorns in his hands.\nGo to Exchange A and do some trades.\nGo to Exchange B and do some trades.\nGo to Exchange A and do some trades.\nGo back to the nest.\n\nIn Exchange X (X = A, B), he can perform the following operations any integer number of times (possibly zero) in any order:\n\nLose g_{X} acorns and gain 1 gram of gold.\nGain g_{X} acorns and lose 1 gram of gold.\nLose s_{X} acorns and gain 1 gram of silver.\nGain s_{X} acorns and lose 1 gram of silver.\nLose b_{X} acorns and gain 1 gram of bronze.\nGain b_{X} acorns and lose 1 gram of bronze.\n\nNaturally, he cannot perform an operation that would leave him with a negative amount of acorns, gold, silver, or bronze.\nWhat is the maximum number of acorns that he can bring to the nest?\nNote that gold, silver, or bronze brought to the nest would be worthless because he is just a squirrel.", "constraint": "1 <= N <= 5000\n1 <= g_{X} <= 5000\n1 <= s_{X} <= 5000\n1 <= b_{X} <= 5000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\ng_A s_A b_A\ng_B s_B b_B", "output": "Print the maximum number of acorns that Chokudai can bring to the nest.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 23\n1 1 1\n2 1 1 output: 46\n\nHe can bring 46 acorns to the nest, as follows:\n\nIn Exchange A, trade 23 acorns for 23 grams of gold. {acorns, gold, silver, bronze}={ 0,23,0,0 }\nIn Exchange B, trade 23 grams of gold for 46 acorns. {acorns, gold, silver, bronze}={ 46,0,0,0 }\nIn Exchange A, trade nothing. {acorns, gold, silver, bronze}={ 46,0,0,0 }\n\nHe cannot have 47 or more acorns, so the answer is 46."], "Pid": "p03008", "ProblemText": "Task Description: Problem Statement The squirrel Chokudai has N acorns.\nOne day, he decides to do some trades in multiple precious metal exchanges to make more acorns.\nHis plan is as follows:\n\nGet out of the nest with N acorns in his hands.\nGo to Exchange A and do some trades.\nGo to Exchange B and do some trades.\nGo to Exchange A and do some trades.\nGo back to the nest.\n\nIn Exchange X (X = A, B), he can perform the following operations any integer number of times (possibly zero) in any order:\n\nLose g_{X} acorns and gain 1 gram of gold.\nGain g_{X} acorns and lose 1 gram of gold.\nLose s_{X} acorns and gain 1 gram of silver.\nGain s_{X} acorns and lose 1 gram of silver.\nLose b_{X} acorns and gain 1 gram of bronze.\nGain b_{X} acorns and lose 1 gram of bronze.\n\nNaturally, he cannot perform an operation that would leave him with a negative amount of acorns, gold, silver, or bronze.\nWhat is the maximum number of acorns that he can bring to the nest?\nNote that gold, silver, or bronze brought to the nest would be worthless because he is just a squirrel.\nTask Constraint: 1 <= N <= 5000\n1 <= g_{X} <= 5000\n1 <= s_{X} <= 5000\n1 <= b_{X} <= 5000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\ng_A s_A b_A\ng_B s_B b_B\nTask Output: Print the maximum number of acorns that Chokudai can bring to the nest.\nTask Samples: input: 23\n1 1 1\n2 1 1 output: 46\n\nHe can bring 46 acorns to the nest, as follows:\n\nIn Exchange A, trade 23 acorns for 23 grams of gold. {acorns, gold, silver, bronze}={ 0,23,0,0 }\nIn Exchange B, trade 23 grams of gold for 46 acorns. {acorns, gold, silver, bronze}={ 46,0,0,0 }\nIn Exchange A, trade nothing. {acorns, gold, silver, bronze}={ 46,0,0,0 }\n\nHe cannot have 47 or more acorns, so the answer is 46.\n\n" }, { "title": "", "content": "Problem Statement There are N squares arranged in a row, numbered 1 to N from left to right. Takahashi will stack building blocks on these squares, on which there are no blocks yet.\nHe wants to stack blocks on the squares evenly, so he will repeat the following operation until there are H blocks on every square:\n\nLet M and m be the maximum and minimum numbers of blocks currently stacked on a square, respectively. Choose a square on which m blocks are stacked (if there are multiple such squares, choose any one of them), and add a positive number of blocks on that square so that there will be at least M and at most M + D blocks on that square.\n\nTell him how many ways there are to have H blocks on every square by repeating this operation. Since there can be extremely many ways, print the number modulo 10^9+7.", "constraint": "2 <= N <= 10^6\n1 <= D <= H <= 10^6\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN H D", "output": "Print the number of ways to have H blocks on every square, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 1 output: 6\n\nThe possible transitions of (the number of blocks on Square 1, the number of blocks on Square 2) are as follows:\n(0,0) -> (0,1) -> (1,1) -> (1,2) -> (2,2)\n(0,0) -> (0,1) -> (1,1) -> (2,1) -> (2,2)\n(0,0) -> (0,1) -> (2,1) -> (2,2)\n(0,0) -> (1,0) -> (1,1) -> (1,2) -> (2,2)\n(0,0) -> (1,0) -> (1,1) -> (2,1) -> (2,2)\n(0,0) -> (1,0) -> (1,2) -> (2,2)\nThus, there are six ways to have two blocks on every square.", "input: 2 30 15 output: 94182806", "input: 31415 9265 3589 output: 312069529\n\nBe sure to print the number modulo 10^9+7."], "Pid": "p03009", "ProblemText": "Task Description: Problem Statement There are N squares arranged in a row, numbered 1 to N from left to right. Takahashi will stack building blocks on these squares, on which there are no blocks yet.\nHe wants to stack blocks on the squares evenly, so he will repeat the following operation until there are H blocks on every square:\n\nLet M and m be the maximum and minimum numbers of blocks currently stacked on a square, respectively. Choose a square on which m blocks are stacked (if there are multiple such squares, choose any one of them), and add a positive number of blocks on that square so that there will be at least M and at most M + D blocks on that square.\n\nTell him how many ways there are to have H blocks on every square by repeating this operation. Since there can be extremely many ways, print the number modulo 10^9+7.\nTask Constraint: 2 <= N <= 10^6\n1 <= D <= H <= 10^6\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN H D\nTask Output: Print the number of ways to have H blocks on every square, modulo 10^9+7.\nTask Samples: input: 2 2 1 output: 6\n\nThe possible transitions of (the number of blocks on Square 1, the number of blocks on Square 2) are as follows:\n(0,0) -> (0,1) -> (1,1) -> (1,2) -> (2,2)\n(0,0) -> (0,1) -> (1,1) -> (2,1) -> (2,2)\n(0,0) -> (0,1) -> (2,1) -> (2,2)\n(0,0) -> (1,0) -> (1,1) -> (1,2) -> (2,2)\n(0,0) -> (1,0) -> (1,1) -> (2,1) -> (2,2)\n(0,0) -> (1,0) -> (1,2) -> (2,2)\nThus, there are six ways to have two blocks on every square.\ninput: 2 30 15 output: 94182806\ninput: 31415 9265 3589 output: 312069529\n\nBe sure to print the number modulo 10^9+7.\n\n" }, { "title": "", "content": "Problem Statement\nDiverta City is a new city consisting of N towns numbered 1,2, . . . , N.\nThe mayor Ringo is planning to connect every pair of two different towns with a bidirectional road. The length of each road is undecided.\nA Hamiltonian path is a path that starts at one of the towns and visits each of the other towns exactly once.\nThe reversal of a Hamiltonian path is considered the same as the original Hamiltonian path.\nThere are N! / 2 Hamiltonian paths. Ringo wants all these paths to have distinct total lengths (the sum of the lengths of the roads on a path), to make the city diverse.\nFind one such set of the lengths of the roads, under the following conditions:\n\nThe length of each road must be a positive integer.\nThe maximum total length of a Hamiltonian path must be at most 10^{11}.", "constraint": "N is a integer between 2 and 10 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print a set of the lengths of the roads that meets the objective, in the following format:\nw_{1,1} \\ w_{1,2} \\ w_{1,3} \\ . . . \\ w_{1, N}\nw_{2,1} \\ w_{2,2} \\ w_{2,3} \\ . . . \\ w_{2, N}\n : : :\nw_{N, 1} \\ w_{N, 2} \\ w_{N, 3} \\ . . . \\ w_{N, N}\n\nwhere w_{i, j} is the length of the road connecting Town i and Town j, which must satisfy the following conditions:\n\nw_{i, i} = 0\nw_{i, j} = w_{j, i} \\ (i \\neq j)\n1 <= w_{i, j} <= 10^{11} \\ (i \\neq j)\n\nIf there are multiple sets of lengths of the roads that meet the objective, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 0 6 15\n6 0 21\n15 21 0\n\nThere are three Hamiltonian paths. The total lengths of these paths are as follows: \n\n1 → 2 → 3: The total length is 6 + 21 = 27.\n1 → 3 → 2: The total length is 15 + 21 = 36.\n2 → 1 → 3: The total length is 6 + 15 = 21.\n\nThey are distinct, so the objective is met.", "input: 4 output: 0 111 157 193\n111 0 224 239\n157 224 0 258\n193 239 258 0\n\nThere are 12 Hamiltonian paths, with distinct total lengths."], "Pid": "p03010", "ProblemText": "Task Description: Problem Statement\nDiverta City is a new city consisting of N towns numbered 1,2, . . . , N.\nThe mayor Ringo is planning to connect every pair of two different towns with a bidirectional road. The length of each road is undecided.\nA Hamiltonian path is a path that starts at one of the towns and visits each of the other towns exactly once.\nThe reversal of a Hamiltonian path is considered the same as the original Hamiltonian path.\nThere are N! / 2 Hamiltonian paths. Ringo wants all these paths to have distinct total lengths (the sum of the lengths of the roads on a path), to make the city diverse.\nFind one such set of the lengths of the roads, under the following conditions:\n\nThe length of each road must be a positive integer.\nThe maximum total length of a Hamiltonian path must be at most 10^{11}.\nTask Constraint: N is a integer between 2 and 10 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print a set of the lengths of the roads that meets the objective, in the following format:\nw_{1,1} \\ w_{1,2} \\ w_{1,3} \\ . . . \\ w_{1, N}\nw_{2,1} \\ w_{2,2} \\ w_{2,3} \\ . . . \\ w_{2, N}\n : : :\nw_{N, 1} \\ w_{N, 2} \\ w_{N, 3} \\ . . . \\ w_{N, N}\n\nwhere w_{i, j} is the length of the road connecting Town i and Town j, which must satisfy the following conditions:\n\nw_{i, i} = 0\nw_{i, j} = w_{j, i} \\ (i \\neq j)\n1 <= w_{i, j} <= 10^{11} \\ (i \\neq j)\n\nIf there are multiple sets of lengths of the roads that meet the objective, any of them will be accepted.\nTask Samples: input: 3 output: 0 6 15\n6 0 21\n15 21 0\n\nThere are three Hamiltonian paths. The total lengths of these paths are as follows: \n\n1 → 2 → 3: The total length is 6 + 21 = 27.\n1 → 3 → 2: The total length is 15 + 21 = 36.\n2 → 1 → 3: The total length is 6 + 15 = 21.\n\nThey are distinct, so the objective is met.\ninput: 4 output: 0 111 157 193\n111 0 224 239\n157 224 0 258\n193 239 258 0\n\nThere are 12 Hamiltonian paths, with distinct total lengths.\n\n" }, { "title": "", "content": "Problem Statement There are three airports A, B and C, and flights between each pair of airports in both directions.\nA one-way flight between airports A and B takes P hours, a one-way flight between airports B and C takes Q hours, and a one-way flight between airports C and A takes R hours.\nConsider a route where we start at one of the airports, fly to another airport and then fly to the other airport.\nWhat is the minimum possible sum of the flight times?", "constraint": "1 <= P,Q,R <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nP Q R", "output": "Print the minimum possible sum of the flight times.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 4 output: 4\nThe sum of the flight times in the route A \\rightarrow B \\rightarrow C: 1 + 3 = 4 hours\nThe sum of the flight times in the route A \\rightarrow C \\rightarrow C: 4 + 3 = 7 hours\nThe sum of the flight times in the route B \\rightarrow A \\rightarrow C: 1 + 4 = 5 hours\nThe sum of the flight times in the route B \\rightarrow C \\rightarrow A: 3 + 4 = 7 hours\nThe sum of the flight times in the route C \\rightarrow A \\rightarrow B: 4 + 1 = 5 hours\nThe sum of the flight times in the route C \\rightarrow B \\rightarrow A: 3 + 1 = 4 hours\n\nThe minimum of these is 4 hours.", "input: 3 2 3 output: 5"], "Pid": "p03011", "ProblemText": "Task Description: Problem Statement There are three airports A, B and C, and flights between each pair of airports in both directions.\nA one-way flight between airports A and B takes P hours, a one-way flight between airports B and C takes Q hours, and a one-way flight between airports C and A takes R hours.\nConsider a route where we start at one of the airports, fly to another airport and then fly to the other airport.\nWhat is the minimum possible sum of the flight times?\nTask Constraint: 1 <= P,Q,R <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nP Q R\nTask Output: Print the minimum possible sum of the flight times.\nTask Samples: input: 1 3 4 output: 4\nThe sum of the flight times in the route A \\rightarrow B \\rightarrow C: 1 + 3 = 4 hours\nThe sum of the flight times in the route A \\rightarrow C \\rightarrow C: 4 + 3 = 7 hours\nThe sum of the flight times in the route B \\rightarrow A \\rightarrow C: 1 + 4 = 5 hours\nThe sum of the flight times in the route B \\rightarrow C \\rightarrow A: 3 + 4 = 7 hours\nThe sum of the flight times in the route C \\rightarrow A \\rightarrow B: 4 + 1 = 5 hours\nThe sum of the flight times in the route C \\rightarrow B \\rightarrow A: 3 + 1 = 4 hours\n\nThe minimum of these is 4 hours.\ninput: 3 2 3 output: 5\n\n" }, { "title": "", "content": "Problem Statement We have N weights indexed 1 to N. The \bmass of the weight indexed i is W_i.\nWe will divide these weights into two groups: the weights with indices not greater than T, and those with indices greater than T, for some integer 1 <= T < N. Let S_1 be the sum of the masses of the weights in the former group, and S_2 be the sum of the masses of the weights in the latter group.\nConsider all possible such divisions and find the minimum possible absolute difference of S_1 and S_2.", "constraint": "2 <= N <= 100\n1 <= W_i <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nW_1 W_2 . . . W_{N-1} W_N", "output": "Print the minimum possible absolute difference of S_1 and S_2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 0\n\nIf T = 2, S_1 = 1 + 2 = 3 and S_2 = 3, with the absolute difference of 0.", "input: 4\n1 3 1 1 output: 2\n\nIf T = 2, S_1 = 1 + 3 = 4 and S_2 = 1 + 1 = 2, with the absolute difference of 2. We cannot have a smaller absolute difference.", "input: 8\n27 23 76 2 3 5 62 52 output: 2"], "Pid": "p03012", "ProblemText": "Task Description: Problem Statement We have N weights indexed 1 to N. The \bmass of the weight indexed i is W_i.\nWe will divide these weights into two groups: the weights with indices not greater than T, and those with indices greater than T, for some integer 1 <= T < N. Let S_1 be the sum of the masses of the weights in the former group, and S_2 be the sum of the masses of the weights in the latter group.\nConsider all possible such divisions and find the minimum possible absolute difference of S_1 and S_2.\nTask Constraint: 2 <= N <= 100\n1 <= W_i <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nW_1 W_2 . . . W_{N-1} W_N\nTask Output: Print the minimum possible absolute difference of S_1 and S_2.\nTask Samples: input: 3\n1 2 3 output: 0\n\nIf T = 2, S_1 = 1 + 2 = 3 and S_2 = 3, with the absolute difference of 0.\ninput: 4\n1 3 1 1 output: 2\n\nIf T = 2, S_1 = 1 + 3 = 4 and S_2 = 1 + 1 = 2, with the absolute difference of 2. We cannot have a smaller absolute difference.\ninput: 8\n27 23 76 2 3 5 62 52 output: 2\n\n" }, { "title": "", "content": "Problem Statement There is a staircase with N steps. Takahashi is now standing at the foot of the stairs, that is, on the 0-th step.\nHe can climb up one or two steps at a time.\nHowever, the treads of the a_1-th, a_2-th, a_3-th, \\ldots, a_M-th steps are broken, so it is dangerous to set foot on those steps.\nHow many are there to climb up to the top step, that is, the N-th step, without setting foot on the broken steps?\nFind the count modulo 1\\ 000\\ 000\\ 007.", "constraint": "1 <= N <= 10^5\n0 <= M <= N-1\n1 <= a_1 < a_2 < ... < a_M <= N-1", "input": "Input is given from Standard Input in the following format:\nN M\na_1\na_2\n .\n .\n .\na_M", "output": "Print the number of ways to climb up the stairs under the condition, modulo 1\\ 000\\ 000\\ 007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 1\n3 output: 4\n\nThere are four ways to climb up the stairs, as follows:\n\n0 \\to 1 \\to 2 \\to 4 \\to 5 \\to 6\n0 \\to 1 \\to 2 \\to 4 \\to 6\n0 \\to 2 \\to 4 \\to 5 \\to 6\n0 \\to 2 \\to 4 \\to 6", "input: 10 2\n4\n5 output: 0\n\nThere may be no way to climb up the stairs without setting foot on the broken steps.", "input: 100 5\n1\n23\n45\n67\n89 output: 608200469\n\nBe sure to print the count modulo 1\\ 000\\ 000\\ 007."], "Pid": "p03013", "ProblemText": "Task Description: Problem Statement There is a staircase with N steps. Takahashi is now standing at the foot of the stairs, that is, on the 0-th step.\nHe can climb up one or two steps at a time.\nHowever, the treads of the a_1-th, a_2-th, a_3-th, \\ldots, a_M-th steps are broken, so it is dangerous to set foot on those steps.\nHow many are there to climb up to the top step, that is, the N-th step, without setting foot on the broken steps?\nFind the count modulo 1\\ 000\\ 000\\ 007.\nTask Constraint: 1 <= N <= 10^5\n0 <= M <= N-1\n1 <= a_1 < a_2 < ... < a_M <= N-1\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1\na_2\n .\n .\n .\na_M\nTask Output: Print the number of ways to climb up the stairs under the condition, modulo 1\\ 000\\ 000\\ 007.\nTask Samples: input: 6 1\n3 output: 4\n\nThere are four ways to climb up the stairs, as follows:\n\n0 \\to 1 \\to 2 \\to 4 \\to 5 \\to 6\n0 \\to 1 \\to 2 \\to 4 \\to 6\n0 \\to 2 \\to 4 \\to 5 \\to 6\n0 \\to 2 \\to 4 \\to 6\ninput: 10 2\n4\n5 output: 0\n\nThere may be no way to climb up the stairs without setting foot on the broken steps.\ninput: 100 5\n1\n23\n45\n67\n89 output: 608200469\n\nBe sure to print the count modulo 1\\ 000\\ 000\\ 007.\n\n" }, { "title": "", "content": "Problem Statement There is a grid with H horizontal rows and W vertical columns, and there are obstacles on some of the squares.\nSnuke is going to choose one of the squares not occupied by an obstacle and place a lamp on it.\nThe lamp placed on the square will emit straight beams of light in four cardinal directions: up, down, left, and right.\nIn each direction, the beam will continue traveling until it hits a square occupied by an obstacle or it hits the border of the grid. It will light all the squares on the way, including the square on which the lamp is placed, but not the square occupied by an obstacle.\nSnuke wants to maximize the number of squares lighted by the lamp.\nYou are given H strings S_i (1 <= i <= H), each of length W. If the j-th character (1 <= j <= W) of S_i is #, there is an obstacle on the square at the i-th row from the top and the j-th column from the left; if that character is . , there is no obstacle on that square.\nFind the maximum possible number of squares lighted by the lamp.", "constraint": "1 <= H <= 2,000\n1 <= W <= 2,000\nS_i is a string of length W consisting of # and ..\n. occurs at least once in one of the strings S_i (1 <= i <= H).", "input": "Input is given from Standard Input in the following format:\nH W\nS_1\n:\nS_H", "output": "Print the maximum possible number of squares lighted by the lamp.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n#..#..\n.....#\n....#.\n#.#... output: 8\n\nIf Snuke places the lamp on the square at the second row from the top and the second column from the left, it will light the following squares: the first through fifth squares from the left in the second row, and the first through fourth squares from the top in the second column, for a total of eight squares.", "input: 8 8\n..#...#.\n....#...\n##......\n..###..#\n...#..#.\n##....#.\n#...#...\n###.#..# output: 13"], "Pid": "p03014", "ProblemText": "Task Description: Problem Statement There is a grid with H horizontal rows and W vertical columns, and there are obstacles on some of the squares.\nSnuke is going to choose one of the squares not occupied by an obstacle and place a lamp on it.\nThe lamp placed on the square will emit straight beams of light in four cardinal directions: up, down, left, and right.\nIn each direction, the beam will continue traveling until it hits a square occupied by an obstacle or it hits the border of the grid. It will light all the squares on the way, including the square on which the lamp is placed, but not the square occupied by an obstacle.\nSnuke wants to maximize the number of squares lighted by the lamp.\nYou are given H strings S_i (1 <= i <= H), each of length W. If the j-th character (1 <= j <= W) of S_i is #, there is an obstacle on the square at the i-th row from the top and the j-th column from the left; if that character is . , there is no obstacle on that square.\nFind the maximum possible number of squares lighted by the lamp.\nTask Constraint: 1 <= H <= 2,000\n1 <= W <= 2,000\nS_i is a string of length W consisting of # and ..\n. occurs at least once in one of the strings S_i (1 <= i <= H).\nTask Input: Input is given from Standard Input in the following format:\nH W\nS_1\n:\nS_H\nTask Output: Print the maximum possible number of squares lighted by the lamp.\nTask Samples: input: 4 6\n#..#..\n.....#\n....#.\n#.#... output: 8\n\nIf Snuke places the lamp on the square at the second row from the top and the second column from the left, it will light the following squares: the first through fifth squares from the left in the second row, and the first through fourth squares from the top in the second column, for a total of eight squares.\ninput: 8 8\n..#...#.\n....#...\n##......\n..###..#\n...#..#.\n##....#.\n#...#...\n###.#..# output: 13\n\n" }, { "title": "", "content": "Problem Statement You are given a positive integer L in base two.\nHow many pairs of non-negative integers (a, b) satisfy the following conditions?\n\na + b <= L\na + b = a \\mbox{ XOR } b\n\nSince there can be extremely many such pairs, print the count modulo 10^9 + 7.\n What is XOR?\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03015", "ProblemText": "Task Description: Problem Statement You are given a positive integer L in base two.\nHow many pairs of non-negative integers (a, b) satisfy the following conditions?\n\na + b <= L\na + b = a \\mbox{ XOR } b\n\nSince there can be extremely many such pairs, print the count modulo 10^9 + 7.\n What is XOR?\nThe XOR of integers A and B, A \\mbox{ XOR } B, is defined as follows:\n\nWhen A \\mbox{ XOR } B is written in base two, the digit in the 2^k's place (k >= 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 \\mbox{ XOR } 5 = 6. (In base two: 011 \\mbox{ XOR } 101 = 110. )\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement\nThere is an arithmetic progression with L terms: s_0, s_1, s_2, . . . , s_{L-1}.\nThe initial term is A, and the common difference is B. That is, s_i = A + B * i holds.\nConsider the integer obtained by concatenating the terms written in base ten without leading zeros. For example, the sequence 3,7,11,15,19 would be concatenated into 37111519. What is the remainder when that integer is divided by M?", "constraint": "All values in input are integers.\n1 <= L, A, B < 10^{18}\n2 <= M <= 10^9\nAll terms in the arithmetic progression are less than 10^{18}.", "input": "Input is given from Standard Input in the following format:\nL A B M", "output": "Print the remainder when the integer obtained by concatenating the terms is divided by M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 4 10007 output: 5563\n\nOur arithmetic progression is 3,7,11,15,19, so the answer is 37111519 mod 10007, that is, 5563.", "input: 4 8 1 1000000 output: 891011", "input: 107 10000000000007 1000000000000007 998244353 output: 39122908"], "Pid": "p03016", "ProblemText": "Task Description: Problem Statement\nThere is an arithmetic progression with L terms: s_0, s_1, s_2, . . . , s_{L-1}.\nThe initial term is A, and the common difference is B. That is, s_i = A + B * i holds.\nConsider the integer obtained by concatenating the terms written in base ten without leading zeros. For example, the sequence 3,7,11,15,19 would be concatenated into 37111519. What is the remainder when that integer is divided by M?\nTask Constraint: All values in input are integers.\n1 <= L, A, B < 10^{18}\n2 <= M <= 10^9\nAll terms in the arithmetic progression are less than 10^{18}.\nTask Input: Input is given from Standard Input in the following format:\nL A B M\nTask Output: Print the remainder when the integer obtained by concatenating the terms is divided by M.\nTask Samples: input: 5 3 4 10007 output: 5563\n\nOur arithmetic progression is 3,7,11,15,19, so the answer is 37111519 mod 10007, that is, 5563.\ninput: 4 8 1 1000000 output: 891011\ninput: 107 10000000000007 1000000000000007 998244353 output: 39122908\n\n" }, { "title": "", "content": "Problem Statement There are N squares arranged in a row, numbered 1,2, . . . , N from left to right.\nYou are given a string S of length N consisting of . and #. If the i-th character of S is #, Square i contains a rock; if the i-th character of S is . , Square i is empty.\nIn the beginning, Snuke stands on Square A, and Fnuke stands on Square B.\nYou can repeat the following operation any number of times:\n\nChoose Snuke or Fnuke, and make him jump one or two squares to the right. The destination must be one of the squares, and it must not contain a rock or the other person.\n\nYou want to repeat this operation so that Snuke will stand on Square C and Fnuke will stand on Square D.\nDetermine whether this is possible.", "constraint": "4 <= N <= 200\\ 000\nS is a string of length N consisting of . and #.\n1 <= A, B, C, D <= N\nSquare A, B, C and D do not contain a rock.\nA, B, C and D are all different.\nA < B\nA < C\nB < D", "input": "Input is given from Standard Input in the following format:\nN A B C D\nS", "output": "Print Yes if the objective is achievable, and No if it is not.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 1 3 6 7\n.#..#.. output: Yes\n\nThe objective is achievable by, for example, moving the two persons as follows. (A and B represent Snuke and Fnuke, respectively.)\nA#B.#..\n\nA#.B#..\n\n.#AB#..\n\n.#A.#B.\n\n.#.A#B.\n\n.#.A#.B\n\n.#..#AB", "input: 7 1 3 7 6\n.#..#.. output: No", "input: 15 1 3 15 13\n...#.#...#.#... output: Yes"], "Pid": "p03017", "ProblemText": "Task Description: Problem Statement There are N squares arranged in a row, numbered 1,2, . . . , N from left to right.\nYou are given a string S of length N consisting of . and #. If the i-th character of S is #, Square i contains a rock; if the i-th character of S is . , Square i is empty.\nIn the beginning, Snuke stands on Square A, and Fnuke stands on Square B.\nYou can repeat the following operation any number of times:\n\nChoose Snuke or Fnuke, and make him jump one or two squares to the right. The destination must be one of the squares, and it must not contain a rock or the other person.\n\nYou want to repeat this operation so that Snuke will stand on Square C and Fnuke will stand on Square D.\nDetermine whether this is possible.\nTask Constraint: 4 <= N <= 200\\ 000\nS is a string of length N consisting of . and #.\n1 <= A, B, C, D <= N\nSquare A, B, C and D do not contain a rock.\nA, B, C and D are all different.\nA < B\nA < C\nB < D\nTask Input: Input is given from Standard Input in the following format:\nN A B C D\nS\nTask Output: Print Yes if the objective is achievable, and No if it is not.\nTask Samples: input: 7 1 3 6 7\n.#..#.. output: Yes\n\nThe objective is achievable by, for example, moving the two persons as follows. (A and B represent Snuke and Fnuke, respectively.)\nA#B.#..\n\nA#.B#..\n\n.#AB#..\n\n.#A.#B.\n\n.#.A#B.\n\n.#.A#.B\n\n.#..#AB\ninput: 7 1 3 7 6\n.#..#.. output: No\ninput: 15 1 3 15 13\n...#.#...#.#... output: Yes\n\n" }, { "title": "", "content": "Problem Statement You are given a string s consisting of A, B and C.\nSnuke wants to perform the following operation on s as many times as possible:\n\nChoose a contiguous substring of s that reads ABC and replace it with BCA.\n\nFind the maximum possible number of operations.", "constraint": "1 <= |s| <= 200000\nEach character of s is A, B and C.", "input": "Input is given from Standard Input in the following format:\ns", "output": "Find the maximum possible number of operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ABCABC output: 3\n\nYou can perform the operations three times as follows: ABCABC → BCAABC → BCABCA → BCBCAA. This is the maximum result.", "input: C output: 0", "input: ABCACCBABCBCAABCB output: 6"], "Pid": "p03018", "ProblemText": "Task Description: Problem Statement You are given a string s consisting of A, B and C.\nSnuke wants to perform the following operation on s as many times as possible:\n\nChoose a contiguous substring of s that reads ABC and replace it with BCA.\n\nFind the maximum possible number of operations.\nTask Constraint: 1 <= |s| <= 200000\nEach character of s is A, B and C.\nTask Input: Input is given from Standard Input in the following format:\ns\nTask Output: Find the maximum possible number of operations.\nTask Samples: input: ABCABC output: 3\n\nYou can perform the operations three times as follows: ABCABC → BCAABC → BCABCA → BCBCAA. This is the maximum result.\ninput: C output: 0\ninput: ABCACCBABCBCAABCB output: 6\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki will take N exams numbered 1 to N.\nThey have decided to compete in these exams.\nThe winner will be determined as follows:\nFor each exam i, Takahashi decides its importance c_i, which must be an integer between l_i and u_i (inclusive).\nLet A be \\sum_{i=1}^{N} c_i * (Takahashi's score on Exam i), and B be \\sum_{i=1}^{N} c_i * (Aoki's score on Exam i). Takahashi wins if A >= B, and Aoki wins if A < B.\nTakahashi knows that Aoki will score b_i on Exam i, with his supernatural power.\nTakahashi himself, on the other hand, will score 0 on all the exams without studying more. For each hour of study, he can increase his score on some exam by 1. (He can only study for an integer number of hours. )\nHowever, he cannot score more than X on an exam, since the perfect score for all the exams is X.\nPrint the minimum number of study hours required for Takahashi to win.", "constraint": "1 <= N <= 10^5\n1 <= X <= 10^5\n0 <= b_i <= X (1 <= i <= N)\n1 <= l_i <= u_i <= 10^5 (1 <= i <= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X\nb_1 l_1 u_1\nb_2 l_2 u_2\n:\nb_N l_N u_N", "output": "Print the minimum number of study hours required for Takahashi to win.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 100\n85 2 3\n60 1 1 output: 115\n\nOne optimal strategy is as follows:\nChoose c_1 = 3, c_2 = 1.\nStudy to score 100 on Exam 1 and 15 on Exam 2.\nThen, A = 3 * 100 + 1 * 15 = 315, B = 3 * 85 + 1 * 60 = 315 and Takahashi will win.", "input: 2 100\n85 2 3\n60 10 10 output: 77", "input: 1 100000\n31415 2718 2818 output: 31415", "input: 10 1000\n451 4593 6263\n324 310 6991\n378 1431 7068\n71 1757 9218\n204 3676 4328\n840 6221 9080\n684 1545 8511\n709 5467 8674\n862 6504 9835\n283 4965 9980 output: 2540"], "Pid": "p03019", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki will take N exams numbered 1 to N.\nThey have decided to compete in these exams.\nThe winner will be determined as follows:\nFor each exam i, Takahashi decides its importance c_i, which must be an integer between l_i and u_i (inclusive).\nLet A be \\sum_{i=1}^{N} c_i * (Takahashi's score on Exam i), and B be \\sum_{i=1}^{N} c_i * (Aoki's score on Exam i). Takahashi wins if A >= B, and Aoki wins if A < B.\nTakahashi knows that Aoki will score b_i on Exam i, with his supernatural power.\nTakahashi himself, on the other hand, will score 0 on all the exams without studying more. For each hour of study, he can increase his score on some exam by 1. (He can only study for an integer number of hours. )\nHowever, he cannot score more than X on an exam, since the perfect score for all the exams is X.\nPrint the minimum number of study hours required for Takahashi to win.\nTask Constraint: 1 <= N <= 10^5\n1 <= X <= 10^5\n0 <= b_i <= X (1 <= i <= N)\n1 <= l_i <= u_i <= 10^5 (1 <= i <= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X\nb_1 l_1 u_1\nb_2 l_2 u_2\n:\nb_N l_N u_N\nTask Output: Print the minimum number of study hours required for Takahashi to win.\nTask Samples: input: 2 100\n85 2 3\n60 1 1 output: 115\n\nOne optimal strategy is as follows:\nChoose c_1 = 3, c_2 = 1.\nStudy to score 100 on Exam 1 and 15 on Exam 2.\nThen, A = 3 * 100 + 1 * 15 = 315, B = 3 * 85 + 1 * 60 = 315 and Takahashi will win.\ninput: 2 100\n85 2 3\n60 10 10 output: 77\ninput: 1 100000\n31415 2718 2818 output: 31415\ninput: 10 1000\n451 4593 6263\n324 310 6991\n378 1431 7068\n71 1757 9218\n204 3676 4328\n840 6221 9080\n684 1545 8511\n709 5467 8674\n862 6504 9835\n283 4965 9980 output: 2540\n\n" }, { "title": "", "content": "Problem Statement Snuke is playing with red and blue balls, placing them on a two-dimensional plane.\nFirst, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i, RY_i).\nThen, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i, BY_i).\nThe total number of red balls placed and the total number of blue balls placed are equal, that is, \\sum_{i=1}^{N} RC_i = \\sum_{i=1}^{N} BC_i. Let this value be S.\nSnuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair.\nLet us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.\nSnuke wants to maximize the sum of the scores of the pairs.\nHelp him by finding the maximum possible sum of the scores of the pairs.", "constraint": "1 <= N <= 1000\n0 <= RX_i,RY_i,BX_i,BY_i <= 10^9\n1 <= RC_i,BC_i <= 10\n\\sum_{i=1}^{N} RC_i = \\sum_{i=1}^{N} BC_i\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nRX_1 RY_1 RC_1\nRX_2 RY_2 RC_2\n\\vdots\nRX_N RY_N RC_N\nBX_1 BY_1 BC_1\nBX_2 BY_2 BC_2\n\\vdots\nBX_N BY_N BC_N", "output": "Print the maximum possible sum of the scores of the pairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0 1\n3 2 1\n2 2 1\n5 0 1 output: 8\n\nIf we pair the red ball at coordinates (0,0) and the blue ball at coordinates (2,2), the score of this pair is |0-2| + |0-2|=4.\nThen, if we pair the red ball at coordinates (3,2) and the blue ball at coordinates (5,0), the score of this pair is |3-5| + |2-0|=4.\nMaking these two pairs results in the total score of 8, which is the maximum result.", "input: 3\n0 0 1\n2 2 1\n0 0 2\n1 1 1\n1 1 1\n3 3 2 output: 16\n\nSnuke may have performed multiple operations at the same coordinates.", "input: 10\n582463373 690528069 8\n621230322 318051944 4\n356524296 974059503 6\n372751381 111542460 9\n392867214 581476334 6\n606955458 513028121 5\n882201596 791660614 9\n250465517 91918758 3\n618624774 406956634 6\n426294747 736401096 5\n974896051 888765942 5\n726682138 336960821 3\n715144179 82444709 6\n599055841 501257806 6\n390484433 962747856 4\n912334580 219343832 8\n570458984 648862300 6\n638017635 572157978 10\n435958984 585073520 7\n445612658 234265014 6 output: 45152033546"], "Pid": "p03020", "ProblemText": "Task Description: Problem Statement Snuke is playing with red and blue balls, placing them on a two-dimensional plane.\nFirst, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i, RY_i).\nThen, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i, BY_i).\nThe total number of red balls placed and the total number of blue balls placed are equal, that is, \\sum_{i=1}^{N} RC_i = \\sum_{i=1}^{N} BC_i. Let this value be S.\nSnuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair.\nLet us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.\nSnuke wants to maximize the sum of the scores of the pairs.\nHelp him by finding the maximum possible sum of the scores of the pairs.\nTask Constraint: 1 <= N <= 1000\n0 <= RX_i,RY_i,BX_i,BY_i <= 10^9\n1 <= RC_i,BC_i <= 10\n\\sum_{i=1}^{N} RC_i = \\sum_{i=1}^{N} BC_i\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nRX_1 RY_1 RC_1\nRX_2 RY_2 RC_2\n\\vdots\nRX_N RY_N RC_N\nBX_1 BY_1 BC_1\nBX_2 BY_2 BC_2\n\\vdots\nBX_N BY_N BC_N\nTask Output: Print the maximum possible sum of the scores of the pairs.\nTask Samples: input: 2\n0 0 1\n3 2 1\n2 2 1\n5 0 1 output: 8\n\nIf we pair the red ball at coordinates (0,0) and the blue ball at coordinates (2,2), the score of this pair is |0-2| + |0-2|=4.\nThen, if we pair the red ball at coordinates (3,2) and the blue ball at coordinates (5,0), the score of this pair is |3-5| + |2-0|=4.\nMaking these two pairs results in the total score of 8, which is the maximum result.\ninput: 3\n0 0 1\n2 2 1\n0 0 2\n1 1 1\n1 1 1\n3 3 2 output: 16\n\nSnuke may have performed multiple operations at the same coordinates.\ninput: 10\n582463373 690528069 8\n621230322 318051944 4\n356524296 974059503 6\n372751381 111542460 9\n392867214 581476334 6\n606955458 513028121 5\n882201596 791660614 9\n250465517 91918758 3\n618624774 406956634 6\n426294747 736401096 5\n974896051 888765942 5\n726682138 336960821 3\n715144179 82444709 6\n599055841 501257806 6\n390484433 962747856 4\n912334580 219343832 8\n570458984 648862300 6\n638017635 572157978 10\n435958984 585073520 7\n445612658 234265014 6 output: 45152033546\n\n" }, { "title": "", "content": "Problem Statement You are given a tree with N vertices numbered 1,2, . . . , N. The i-th edge connects Vertex a_i and Vertex b_i.\nYou are also given a string S of length N consisting of 0 and 1. The i-th character of S represents the number of pieces placed on Vertex i.\nSnuke will perform the following operation some number of times:\n\nChoose two pieces the distance between which is at least 2, and bring these pieces closer to each other by 1. More formally, choose two vertices u and v, each with one or more pieces, and consider the shortest path between them. Here the path must contain at least two edges. Then, move one piece from u to its adjacent vertex on the path, and move one piece from v to its adjacent vertex on the path.\n\nBy repeating this operation, Snuke wants to have all the pieces on the same vertex. Is this possible?\nIf the answer is yes, also find the minimum number of operations required to achieve it.", "constraint": "2 <= N <= 2000\n|S| = N\nS consists of 0 and 1, and contains at least one 1.\n1 <= a_i, b_i <= N(a_i \\neq b_i)\nThe edges (a_1, b_1), (a_2, b_2), ..., (a_{N - 1}, b_{N - 1}) forms a tree.", "input": "Input is given from Standard Input in the following format:\nN\nS\na_1 b_1\na_2 b_2\n:\na_{N - 1} b_{N - 1}", "output": "If it is impossible to have all the pieces on the same vertex, print -1. If it is possible, print the minimum number of operations required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n0010101\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7 output: 3\n\nWe can gather all the pieces in three operations as follows:\n\nChoose the pieces on Vertex 3 and 5.\nChoose the pieces on Vertex 2 and 7.\nChoose the pieces on Vertex 4 and 6.", "input: 7\n0010110\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7 output: -1", "input: 2\n01\n1 2 output: 0"], "Pid": "p03021", "ProblemText": "Task Description: Problem Statement You are given a tree with N vertices numbered 1,2, . . . , N. The i-th edge connects Vertex a_i and Vertex b_i.\nYou are also given a string S of length N consisting of 0 and 1. The i-th character of S represents the number of pieces placed on Vertex i.\nSnuke will perform the following operation some number of times:\n\nChoose two pieces the distance between which is at least 2, and bring these pieces closer to each other by 1. More formally, choose two vertices u and v, each with one or more pieces, and consider the shortest path between them. Here the path must contain at least two edges. Then, move one piece from u to its adjacent vertex on the path, and move one piece from v to its adjacent vertex on the path.\n\nBy repeating this operation, Snuke wants to have all the pieces on the same vertex. Is this possible?\nIf the answer is yes, also find the minimum number of operations required to achieve it.\nTask Constraint: 2 <= N <= 2000\n|S| = N\nS consists of 0 and 1, and contains at least one 1.\n1 <= a_i, b_i <= N(a_i \\neq b_i)\nThe edges (a_1, b_1), (a_2, b_2), ..., (a_{N - 1}, b_{N - 1}) forms a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\na_1 b_1\na_2 b_2\n:\na_{N - 1} b_{N - 1}\nTask Output: If it is impossible to have all the pieces on the same vertex, print -1. If it is possible, print the minimum number of operations required.\nTask Samples: input: 7\n0010101\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7 output: 3\n\nWe can gather all the pieces in three operations as follows:\n\nChoose the pieces on Vertex 3 and 5.\nChoose the pieces on Vertex 2 and 7.\nChoose the pieces on Vertex 4 and 6.\ninput: 7\n0010110\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7 output: -1\ninput: 2\n01\n1 2 output: 0\n\n" }, { "title": "", "content": "Problem Statement Snuke found a random number generator.\nIt generates an integer between 0 and 2^N-1 (inclusive).\nAn integer sequence A_0, A_1, \\cdots, A_{2^N-1} represents the probability that each of these integers is generated. The integer i (0 <= i <= 2^N-1) is generated with probability A_i / S, where S = \\sum_{i=0}^{2^N-1} A_i. The process of generating an integer is done independently each time the generator is executed.\nSnuke has an integer X, which is now 0.\nHe can perform the following operation any number of times:\n\nGenerate an integer v with the generator and replace X with X \\oplus v, where \\oplus denotes the bitwise XOR.\n\nFor each integer i (0 <= i <= 2^N-1), find the expected number of operations until X becomes i, and print it modulo 998244353.\nMore formally, represent the expected number of operations as an irreducible fraction P/Q. Then, there exists a unique integer R such that R * Q \\equiv P \\mod 998244353, \\ 0 <= R < 998244353, so print this R.\nWe can prove that, for every i, the expected number of operations until X becomes i is a finite rational number, and its integer representation modulo 998244353 can be defined.", "constraint": "1 <= N <= 18\n1 <= A_i <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_0 A_1 \\cdots A_{2^N-1}", "output": "Print 2^N lines.\nThe (i+1)-th line (0 <= i <= 2^N-1) should contain the expected number of operations until X becomes i, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 1 1 1 output: 0\n4\n4\n4\n\nX=0 after zero operations, so the expected number of operations until X becomes 0 is 0.\nAlso, from any state, the value of X after one operation is 0,1,2 or 3 with equal probability.\nThus, the expected numbers of operations until X becomes 1,2 and 3 are all 4.", "input: 2\n1 2 1 2 output: 0\n499122180\n4\n499122180\n\nThe expected numbers of operations until X becomes 0,1,2 and 3 are 0,7/2,4 and 7/2, respectively.", "input: 4\n337 780 799 10 796 875 331 223 941 67 148 483 390 565 116 355 output: 0\n468683018\n635850749\n96019779\n657074071\n24757563\n745107950\n665159588\n551278361\n143136064\n557841197\n185790407\n988018173\n247117461\n129098626\n789682908"], "Pid": "p03022", "ProblemText": "Task Description: Problem Statement Snuke found a random number generator.\nIt generates an integer between 0 and 2^N-1 (inclusive).\nAn integer sequence A_0, A_1, \\cdots, A_{2^N-1} represents the probability that each of these integers is generated. The integer i (0 <= i <= 2^N-1) is generated with probability A_i / S, where S = \\sum_{i=0}^{2^N-1} A_i. The process of generating an integer is done independently each time the generator is executed.\nSnuke has an integer X, which is now 0.\nHe can perform the following operation any number of times:\n\nGenerate an integer v with the generator and replace X with X \\oplus v, where \\oplus denotes the bitwise XOR.\n\nFor each integer i (0 <= i <= 2^N-1), find the expected number of operations until X becomes i, and print it modulo 998244353.\nMore formally, represent the expected number of operations as an irreducible fraction P/Q. Then, there exists a unique integer R such that R * Q \\equiv P \\mod 998244353, \\ 0 <= R < 998244353, so print this R.\nWe can prove that, for every i, the expected number of operations until X becomes i is a finite rational number, and its integer representation modulo 998244353 can be defined.\nTask Constraint: 1 <= N <= 18\n1 <= A_i <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_0 A_1 \\cdots A_{2^N-1}\nTask Output: Print 2^N lines.\nThe (i+1)-th line (0 <= i <= 2^N-1) should contain the expected number of operations until X becomes i, modulo 998244353.\nTask Samples: input: 2\n1 1 1 1 output: 0\n4\n4\n4\n\nX=0 after zero operations, so the expected number of operations until X becomes 0 is 0.\nAlso, from any state, the value of X after one operation is 0,1,2 or 3 with equal probability.\nThus, the expected numbers of operations until X becomes 1,2 and 3 are all 4.\ninput: 2\n1 2 1 2 output: 0\n499122180\n4\n499122180\n\nThe expected numbers of operations until X becomes 0,1,2 and 3 are 0,7/2,4 and 7/2, respectively.\ninput: 4\n337 780 799 10 796 875 331 223 941 67 148 483 390 565 116 355 output: 0\n468683018\n635850749\n96019779\n657074071\n24757563\n745107950\n665159588\n551278361\n143136064\n557841197\n185790407\n988018173\n247117461\n129098626\n789682908\n\n" }, { "title": "", "content": "Problem Statement Given an integer N not less than 3, find the sum of the interior angles of a regular polygon with N sides.\nPrint the answer in degrees, but do not print units.", "constraint": "3 <= N <= 100", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print an integer representing the sum of the interior angles of a regular polygon with N sides.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 180\n\nThe sum of the interior angles of a regular triangle is 180 degrees.", "input: 100 output: 17640"], "Pid": "p03023", "ProblemText": "Task Description: Problem Statement Given an integer N not less than 3, find the sum of the interior angles of a regular polygon with N sides.\nPrint the answer in degrees, but do not print units.\nTask Constraint: 3 <= N <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print an integer representing the sum of the interior angles of a regular polygon with N sides.\nTask Samples: input: 3 output: 180\n\nThe sum of the interior angles of a regular triangle is 180 degrees.\ninput: 100 output: 17640\n\n" }, { "title": "", "content": "Problem Statement Takahashi is competing in a sumo tournament.\nThe tournament lasts for 15 days, during which he performs in one match per day.\nIf he wins 8 or more matches, he can also participate in the next tournament.\nThe matches for the first k days have finished.\nYou are given the results of Takahashi's matches as a string S consisting of o and x.\nIf the i-th character in S is o, it means that Takahashi won the match on the i-th day; if that character is x, it means that Takahashi lost the match on the i-th day.\nPrint YES if there is a possibility that Takahashi can participate in the next tournament, and print NO if there is no such possibility.", "constraint": "1 <= k <= 15\nS is a string of length k consisting of o and x.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print YES if there is a possibility that Takahashi can participate in the next tournament, and print NO otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: oxoxoxoxoxoxox output: YES\n\nTakahashi has 7 wins and 7 losses before the last match. If he wins that match, he will have 8 wins.", "input: xxxxxxxx output: NO"], "Pid": "p03024", "ProblemText": "Task Description: Problem Statement Takahashi is competing in a sumo tournament.\nThe tournament lasts for 15 days, during which he performs in one match per day.\nIf he wins 8 or more matches, he can also participate in the next tournament.\nThe matches for the first k days have finished.\nYou are given the results of Takahashi's matches as a string S consisting of o and x.\nIf the i-th character in S is o, it means that Takahashi won the match on the i-th day; if that character is x, it means that Takahashi lost the match on the i-th day.\nPrint YES if there is a possibility that Takahashi can participate in the next tournament, and print NO if there is no such possibility.\nTask Constraint: 1 <= k <= 15\nS is a string of length k consisting of o and x.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print YES if there is a possibility that Takahashi can participate in the next tournament, and print NO otherwise.\nTask Samples: input: oxoxoxoxoxoxox output: YES\n\nTakahashi has 7 wins and 7 losses before the last match. If he wins that match, he will have 8 wins.\ninput: xxxxxxxx output: NO\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total.\nWhen they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %.\nFind the expected number of games that will be played, and print it as follows.\nWe can represent the expected value as P/Q with coprime integers P and Q.\nPrint the integer R between 0 and 10^9+6 (inclusive) such that R * Q \\equiv P\\pmod {10^9+7}.\n(Such an integer R always uniquely exists under the constraints of this problem. )", "constraint": "1 <= N <= 100000\n0 <= A,B,C <= 100\n1 <= A+B\nA+B+C=100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B C", "output": "Print the expected number of games that will be played, in the manner specified in the statement.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 25 25 50 output: 2\n\nSince N=1, they will repeat the game until one of them wins.\nThe expected number of games played is 2.", "input: 4 50 50 0 output: 312500008\n\nC may be 0.", "input: 1 100 0 0 output: 1\n\nB may also be 0.", "input: 100000 31 41 28 output: 104136146"], "Pid": "p03025", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total.\nWhen they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %.\nFind the expected number of games that will be played, and print it as follows.\nWe can represent the expected value as P/Q with coprime integers P and Q.\nPrint the integer R between 0 and 10^9+6 (inclusive) such that R * Q \\equiv P\\pmod {10^9+7}.\n(Such an integer R always uniquely exists under the constraints of this problem. )\nTask Constraint: 1 <= N <= 100000\n0 <= A,B,C <= 100\n1 <= A+B\nA+B+C=100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B C\nTask Output: Print the expected number of games that will be played, in the manner specified in the statement.\nTask Samples: input: 1 25 25 50 output: 2\n\nSince N=1, they will repeat the game until one of them wins.\nThe expected number of games played is 2.\ninput: 4 50 50 0 output: 312500008\n\nC may be 0.\ninput: 1 100 0 0 output: 1\n\nB may also be 0.\ninput: 100000 31 41 28 output: 104136146\n\n" }, { "title": "", "content": "Problem Statement You are given a tree with N vertices 1,2, \\ldots, N, and positive integers c_1, c_2, \\ldots, c_N.\nThe i-th edge in the tree (1 <= i <= N-1) connects Vertex a_i and Vertex b_i.\nWe will write a positive integer on each vertex in T and calculate our score as follows:\n\nOn each edge, write the smaller of the integers written on the two endpoints.\nLet our score be the sum of the integers written on all the edges.\n\nFind the maximum possible score when we write each of c_1, c_2, \\ldots, c_N on one vertex in T, and show one way to achieve it. If an integer occurs multiple times in c_1, c_2, \\ldots, c_N, we must use it that number of times.", "constraint": "1 <= N <= 10000\n1 <= a_i,b_i <= N\n1 <= c_i <= 10^5\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 \\ldots c_N", "output": "Output Use the following format:\nM\nd_1 \\ldots d_N\n\nwhere M is the maximum possible score, and d_i is the integer to write on Vertex i.\nd_1, d_2, \\ldots, d_N must be a permutation of c_1, c_2, \\ldots, c_N.\nIf there are multiple ways to achieve the maximum score, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n2 3\n3 4\n4 5\n1 2 3 4 5 output: 10\n1 2 3 4 5\n\nIf we write 1,2,3,4,5 on Vertex 1,2,3,4,5, respectively, the integers written on the four edges will be 1,2,3,4, for the score of 10. This is the maximum possible score.", "input: 5\n1 2\n1 3\n1 4\n1 5\n3141 59 26 53 59 output: 197\n59 26 3141 59 53\n\nc_1,c_2,\\ldots,c_N may not be pairwise distinct."], "Pid": "p03026", "ProblemText": "Task Description: Problem Statement You are given a tree with N vertices 1,2, \\ldots, N, and positive integers c_1, c_2, \\ldots, c_N.\nThe i-th edge in the tree (1 <= i <= N-1) connects Vertex a_i and Vertex b_i.\nWe will write a positive integer on each vertex in T and calculate our score as follows:\n\nOn each edge, write the smaller of the integers written on the two endpoints.\nLet our score be the sum of the integers written on all the edges.\n\nFind the maximum possible score when we write each of c_1, c_2, \\ldots, c_N on one vertex in T, and show one way to achieve it. If an integer occurs multiple times in c_1, c_2, \\ldots, c_N, we must use it that number of times.\nTask Constraint: 1 <= N <= 10000\n1 <= a_i,b_i <= N\n1 <= c_i <= 10^5\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 \\ldots c_N\nTask Output: Output Use the following format:\nM\nd_1 \\ldots d_N\n\nwhere M is the maximum possible score, and d_i is the integer to write on Vertex i.\nd_1, d_2, \\ldots, d_N must be a permutation of c_1, c_2, \\ldots, c_N.\nIf there are multiple ways to achieve the maximum score, any of them will be accepted.\nTask Samples: input: 5\n1 2\n2 3\n3 4\n4 5\n1 2 3 4 5 output: 10\n1 2 3 4 5\n\nIf we write 1,2,3,4,5 on Vertex 1,2,3,4,5, respectively, the integers written on the four edges will be 1,2,3,4, for the score of 10. This is the maximum possible score.\ninput: 5\n1 2\n1 3\n1 4\n1 5\n3141 59 26 53 59 output: 197\n59 26 3141 59 53\n\nc_1,c_2,\\ldots,c_N may not be pairwise distinct.\n\n" }, { "title": "", "content": "Problem Statement Consider the following arithmetic progression with n terms:\n\nx, x + d, x + 2d, \\ldots, x + (n-1)d\n\nWhat is the product of all terms in this sequence?\nCompute the answer modulo 1\\ 000\\ 003.\nYou are given Q queries of this form.\nIn the i-th query, compute the answer in case x = x_i, d = d_i, n = n_i.", "constraint": "1 <= Q <= 10^5\n0 <= x_i, d_i <= 1\\ 000\\ 002\n1 <= n_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nQ\nx_1 d_1 n_1\n:\nx_Q d_Q n_Q", "output": "Print Q lines.\nIn the i-th line, print the answer for the i-th query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n7 2 4\n12345 67890 2019 output: 9009\n916936\n\nFor the first query, the answer is 7 * 9 * 11 * 13 = 9009.\nDon't forget to compute the answer modulo 1\\ 000\\ 003."], "Pid": "p03027", "ProblemText": "Task Description: Problem Statement Consider the following arithmetic progression with n terms:\n\nx, x + d, x + 2d, \\ldots, x + (n-1)d\n\nWhat is the product of all terms in this sequence?\nCompute the answer modulo 1\\ 000\\ 003.\nYou are given Q queries of this form.\nIn the i-th query, compute the answer in case x = x_i, d = d_i, n = n_i.\nTask Constraint: 1 <= Q <= 10^5\n0 <= x_i, d_i <= 1\\ 000\\ 002\n1 <= n_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nQ\nx_1 d_1 n_1\n:\nx_Q d_Q n_Q\nTask Output: Print Q lines.\nIn the i-th line, print the answer for the i-th query.\nTask Samples: input: 2\n7 2 4\n12345 67890 2019 output: 9009\n916936\n\nFor the first query, the answer is 7 * 9 * 11 * 13 = 9009.\nDon't forget to compute the answer modulo 1\\ 000\\ 003.\n\n" }, { "title": "", "content": "Problem Statement We will host a rock-paper-scissors tournament with N people. The participants are called Person 1, Person 2, \\ldots, Person N.\nFor any two participants, the result of the match between them is determined in advance.\nThis information is represented by positive integers A_{i, j} ( 1 <= j < i <= N ) as follows:\n\nIf A_{i, j} = 0, Person j defeats Person i.\nIf A_{i, j} = 1, Person i defeats Person j.\n\nThe tournament proceeds as follows:\n\nWe will arrange the N participants in a row, in the order Person 1, Person 2, \\ldots, Person N from left to right.\nWe will randomly choose two consecutive persons in the row. They will play a match against each other, and we will remove the loser from the row.\nWe will repeat this process N-1 times, and the last person remaining will be declared the champion.\n\nFind the number of persons with the possibility of becoming the champion.", "constraint": "1 <= N <= 2000\nA_{i,j} is 0 or 1.", "input": "Input is given from Standard Input in the following format:\nN\nA_{2,1}\nA_{3,1}A_{3,2}\n:\nA_{N, 1}\\ldots A_{N, N-1}", "output": "Print the number of persons with the possibility of becoming the champion.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0\n10 output: 2\n\nPerson 1 defeats Person 2, Person 2 defeats Person 3 and Person 3 defeats Person 1.\nIf Person 1 and Person 2 play the first match, Person 3 will become the champion.\nIf Person 2 and Person 3 play the first match, Person 1 will become the champion.", "input: 6\n0\n11\n111\n1111\n11001 output: 3"], "Pid": "p03028", "ProblemText": "Task Description: Problem Statement We will host a rock-paper-scissors tournament with N people. The participants are called Person 1, Person 2, \\ldots, Person N.\nFor any two participants, the result of the match between them is determined in advance.\nThis information is represented by positive integers A_{i, j} ( 1 <= j < i <= N ) as follows:\n\nIf A_{i, j} = 0, Person j defeats Person i.\nIf A_{i, j} = 1, Person i defeats Person j.\n\nThe tournament proceeds as follows:\n\nWe will arrange the N participants in a row, in the order Person 1, Person 2, \\ldots, Person N from left to right.\nWe will randomly choose two consecutive persons in the row. They will play a match against each other, and we will remove the loser from the row.\nWe will repeat this process N-1 times, and the last person remaining will be declared the champion.\n\nFind the number of persons with the possibility of becoming the champion.\nTask Constraint: 1 <= N <= 2000\nA_{i,j} is 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{2,1}\nA_{3,1}A_{3,2}\n:\nA_{N, 1}\\ldots A_{N, N-1}\nTask Output: Print the number of persons with the possibility of becoming the champion.\nTask Samples: input: 3\n0\n10 output: 2\n\nPerson 1 defeats Person 2, Person 2 defeats Person 3 and Person 3 defeats Person 1.\nIf Person 1 and Person 2 play the first match, Person 3 will become the champion.\nIf Person 2 and Person 3 play the first match, Person 1 will become the champion.\ninput: 6\n0\n11\n111\n1111\n11001 output: 3\n\n" }, { "title": "", "content": "Problem Statement We have A apples and P pieces of apple.\nWe can cut an apple into three pieces of apple, and make one apple pie by simmering two pieces of apple in a pan.\nFind the maximum number of apple pies we can make with what we have now.", "constraint": "All values in input are integers.\n0 <= A, P <= 100", "input": "Input is given from Standard Input in the following format:\nA P", "output": "Print the maximum number of apple pies we can make with what we have.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 output: 3\n\nWe can first make one apple pie by simmering two of the three pieces of apple. Then, we can make two more by simmering the remaining piece and three more pieces obtained by cutting the whole apple.", "input: 0 1 output: 0\n\nWe cannot make an apple pie in this case, unfortunately.", "input: 32 21 output: 58"], "Pid": "p03029", "ProblemText": "Task Description: Problem Statement We have A apples and P pieces of apple.\nWe can cut an apple into three pieces of apple, and make one apple pie by simmering two pieces of apple in a pan.\nFind the maximum number of apple pies we can make with what we have now.\nTask Constraint: All values in input are integers.\n0 <= A, P <= 100\nTask Input: Input is given from Standard Input in the following format:\nA P\nTask Output: Print the maximum number of apple pies we can make with what we have.\nTask Samples: input: 1 3 output: 3\n\nWe can first make one apple pie by simmering two of the three pieces of apple. Then, we can make two more by simmering the remaining piece and three more pieces obtained by cutting the whole apple.\ninput: 0 1 output: 0\n\nWe cannot make an apple pie in this case, unfortunately.\ninput: 32 21 output: 58\n\n" }, { "title": "", "content": "Problem Statement You have decided to write a book introducing good restaurants.\nThere are N restaurants that you want to introduce: Restaurant 1, Restaurant 2, . . . , Restaurant N. Restaurant i is in city S_i, and your assessment score of that restaurant on a 100-point scale is P_i.\nNo two restaurants have the same score.\nYou want to introduce the restaurants in the following order:\n\nThe restaurants are arranged in lexicographical order of the names of their cities.\nIf there are multiple restaurants in the same city, they are arranged in descending order of score.\n\nPrint the identification numbers of the restaurants in the order they are introduced in the book.", "constraint": "1 <= N <= 100\nS is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.\n0 <= P_i <= 100\nP_i is an integer.\nP_i != P_j (1 <= i < j <= N)", "input": "Input is given from Standard Input in the following format:\nN\nS_1 P_1\n:\nS_N P_N", "output": "Print N lines. The i-th line (1 <= i <= N) should contain the identification number of the restaurant that is introduced i-th in the book.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\nkhabarovsk 20\nmoscow 10\nkazan 50\nkazan 35\nmoscow 60\nkhabarovsk 40 output: 3\n4\n6\n1\n5\n2\n\nThe lexicographical order of the names of the three cities is kazan < khabarovsk < moscow. For each of these cities, the restaurants in it are introduced in descending order of score. Thus, the restaurants are introduced in the order 3,4,6,1,5,2.", "input: 10\nyakutsk 10\nyakutsk 20\nyakutsk 30\nyakutsk 40\nyakutsk 50\nyakutsk 60\nyakutsk 70\nyakutsk 80\nyakutsk 90\nyakutsk 100 output: 10\n9\n8\n7\n6\n5\n4\n3\n2\n1"], "Pid": "p03030", "ProblemText": "Task Description: Problem Statement You have decided to write a book introducing good restaurants.\nThere are N restaurants that you want to introduce: Restaurant 1, Restaurant 2, . . . , Restaurant N. Restaurant i is in city S_i, and your assessment score of that restaurant on a 100-point scale is P_i.\nNo two restaurants have the same score.\nYou want to introduce the restaurants in the following order:\n\nThe restaurants are arranged in lexicographical order of the names of their cities.\nIf there are multiple restaurants in the same city, they are arranged in descending order of score.\n\nPrint the identification numbers of the restaurants in the order they are introduced in the book.\nTask Constraint: 1 <= N <= 100\nS is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.\n0 <= P_i <= 100\nP_i is an integer.\nP_i != P_j (1 <= i < j <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1 P_1\n:\nS_N P_N\nTask Output: Print N lines. The i-th line (1 <= i <= N) should contain the identification number of the restaurant that is introduced i-th in the book.\nTask Samples: input: 6\nkhabarovsk 20\nmoscow 10\nkazan 50\nkazan 35\nmoscow 60\nkhabarovsk 40 output: 3\n4\n6\n1\n5\n2\n\nThe lexicographical order of the names of the three cities is kazan < khabarovsk < moscow. For each of these cities, the restaurants in it are introduced in descending order of score. Thus, the restaurants are introduced in the order 3,4,6,1,5,2.\ninput: 10\nyakutsk 10\nyakutsk 20\nyakutsk 30\nyakutsk 40\nyakutsk 50\nyakutsk 60\nyakutsk 70\nyakutsk 80\nyakutsk 90\nyakutsk 100 output: 10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n\n" }, { "title": "", "content": "Problem Statement We have N switches with \"on\" and \"off\" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.\nBulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, . . . , and s_{ik_i}. It is lighted when the number of switches that are \"on\" among these switches is congruent to p_i modulo 2.\nHow many combinations of \"on\" and \"off\" states of the switches light all the bulbs?", "constraint": "1 <= N, M <= 10\n1 <= k_i <= N\n1 <= s_{ij} <= N\ns_{ia} \\neq s_{ib} (a \\neq b)\np_i is 0 or 1.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nk_1 s_{11} s_{12} . . . s_{1k_1}\n:\nk_M s_{M1} s_{M2} . . . s_{Mk_M}\np_1 p_2 . . . p_M", "output": "Print the number of combinations of \"on\" and \"off\" states of the switches that light all the bulbs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n2 1 2\n1 2\n0 1 output: 1\nBulb 1 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1 and 2.\nBulb 2 is lighted when there is an odd number of switches that are \"on\" among the following: Switch 2.\n\nThere are four possible combinations of states of (Switch 1, Switch 2): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print 1.", "input: 2 3\n2 1 2\n1 1\n1 2\n0 0 1 output: 0\nBulb 1 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1 and 2.\nBulb 2 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1.\nBulb 3 is lighted when there is an odd number of switches that are \"on\" among the following: Switch 2.\n\nSwitch 1 has to be \"off\" to light Bulb 2 and Switch 2 has to be \"on\" to light Bulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print 0.", "input: 5 2\n3 1 2 5\n2 2 3\n1 0 output: 8"], "Pid": "p03031", "ProblemText": "Task Description: Problem Statement We have N switches with \"on\" and \"off\" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.\nBulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, . . . , and s_{ik_i}. It is lighted when the number of switches that are \"on\" among these switches is congruent to p_i modulo 2.\nHow many combinations of \"on\" and \"off\" states of the switches light all the bulbs?\nTask Constraint: 1 <= N, M <= 10\n1 <= k_i <= N\n1 <= s_{ij} <= N\ns_{ia} \\neq s_{ib} (a \\neq b)\np_i is 0 or 1.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nk_1 s_{11} s_{12} . . . s_{1k_1}\n:\nk_M s_{M1} s_{M2} . . . s_{Mk_M}\np_1 p_2 . . . p_M\nTask Output: Print the number of combinations of \"on\" and \"off\" states of the switches that light all the bulbs.\nTask Samples: input: 2 2\n2 1 2\n1 2\n0 1 output: 1\nBulb 1 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1 and 2.\nBulb 2 is lighted when there is an odd number of switches that are \"on\" among the following: Switch 2.\n\nThere are four possible combinations of states of (Switch 1, Switch 2): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print 1.\ninput: 2 3\n2 1 2\n1 1\n1 2\n0 0 1 output: 0\nBulb 1 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1 and 2.\nBulb 2 is lighted when there is an even number of switches that are \"on\" among the following: Switch 1.\nBulb 3 is lighted when there is an odd number of switches that are \"on\" among the following: Switch 2.\n\nSwitch 1 has to be \"off\" to light Bulb 2 and Switch 2 has to be \"on\" to light Bulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print 0.\ninput: 5 2\n3 1 2 5\n2 2 3\n1 0 output: 8\n\n" }, { "title": "", "content": "Problem Statement Your friend gave you a dequeue D as a birthday present.\nD is a horizontal cylinder that contains a row of N jewels.\nThe values of the jewels are V_1, V_2, . . . , V_N from left to right. There may be jewels with negative values.\nIn the beginning, you have no jewel in your hands.\nYou can perform at most K operations on D, chosen from the following, at most K times (possibly zero):\nOperation A: Take out the leftmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.\nOperation B: Take out the rightmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.\nOperation C: Choose a jewel in your hands and insert it to the left end of D. You cannot do this operation when you have no jewel in your hand.\nOperation D: Choose a jewel in your hands and insert it to the right end of D. You cannot do this operation when you have no jewel in your hand.\nFind the maximum possible sum of the values of jewels in your hands after the operations.", "constraint": "All values in input are integers.\n1 <= N <= 50\n1 <= K <= 100\n-10^7 <= V_i <= 10^7", "input": "Input is given from Standard Input in the following format:\nN K\nV_1 V_2 . . . V_N", "output": "Print the maximum possible sum of the values of jewels in your hands after the operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 4\n-10 8 2 1 2 6 output: 14\n\nAfter the following sequence of operations, you have two jewels of values 8 and 6 in your hands for a total of 14, which is the maximum result.\n\nDo operation A. You take out the jewel of value -10 from the left end of D.\nDo operation B. You take out the jewel of value 6 from the right end of D.\nDo operation A. You take out the jewel of value 8 from the left end of D.\nDo operation D. You insert the jewel of value -10 to the right end of D.", "input: 6 4\n-6 -100 50 -2 -5 -3 output: 44", "input: 6 3\n-6 -100 50 -2 -5 -3 output: 0\n\nIt is optimal to do no operation."], "Pid": "p03032", "ProblemText": "Task Description: Problem Statement Your friend gave you a dequeue D as a birthday present.\nD is a horizontal cylinder that contains a row of N jewels.\nThe values of the jewels are V_1, V_2, . . . , V_N from left to right. There may be jewels with negative values.\nIn the beginning, you have no jewel in your hands.\nYou can perform at most K operations on D, chosen from the following, at most K times (possibly zero):\nOperation A: Take out the leftmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.\nOperation B: Take out the rightmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.\nOperation C: Choose a jewel in your hands and insert it to the left end of D. You cannot do this operation when you have no jewel in your hand.\nOperation D: Choose a jewel in your hands and insert it to the right end of D. You cannot do this operation when you have no jewel in your hand.\nFind the maximum possible sum of the values of jewels in your hands after the operations.\nTask Constraint: All values in input are integers.\n1 <= N <= 50\n1 <= K <= 100\n-10^7 <= V_i <= 10^7\nTask Input: Input is given from Standard Input in the following format:\nN K\nV_1 V_2 . . . V_N\nTask Output: Print the maximum possible sum of the values of jewels in your hands after the operations.\nTask Samples: input: 6 4\n-10 8 2 1 2 6 output: 14\n\nAfter the following sequence of operations, you have two jewels of values 8 and 6 in your hands for a total of 14, which is the maximum result.\n\nDo operation A. You take out the jewel of value -10 from the left end of D.\nDo operation B. You take out the jewel of value 6 from the right end of D.\nDo operation A. You take out the jewel of value 8 from the left end of D.\nDo operation D. You insert the jewel of value -10 to the right end of D.\ninput: 6 4\n-6 -100 50 -2 -5 -3 output: 44\ninput: 6 3\n-6 -100 50 -2 -5 -3 output: 0\n\nIt is optimal to do no operation.\n\n" }, { "title": "", "content": "Problem Statement There is an infinitely long street that runs west to east, which we consider as a number line.\nThere are N roadworks scheduled on this street.\nThe i-th roadwork blocks the point at coordinate X_i from time S_i - 0.5 to time T_i - 0.5.\nQ people are standing at coordinate 0. The i-th person will start the coordinate 0 at time D_i, continue to walk with speed 1 in the positive direction and stop walking when reaching a blocked point.\nFind the distance each of the Q people will walk.", "constraint": "All values in input are integers.\n1 <= N, Q <= 2 * 10^5\n0 <= S_i < T_i <= 10^9\n1 <= X_i <= 10^9\n0 <= D_1 < D_2 < ... < D_Q <= 10^9\nIf i \\neq j and X_i = X_j, the intervals [S_i, T_i) and [S_j, T_j) do not overlap.", "input": "Input is given from Standard Input in the following format:\nN Q\nS_1 T_1 X_1\n:\nS_N T_N X_N\nD_1\n:\nD_Q", "output": "Print Q lines. The i-th line should contain the distance the i-th person will walk or -1 if that person walks forever.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n1 3 2\n7 13 10\n18 20 13\n3 4 2\n0\n1\n2\n3\n5\n8 output: 2\n2\n10\n-1\n13\n-1\n\nThe first person starts coordinate 0 at time 0 and stops walking at coordinate 2 when reaching a point blocked by the first roadwork at time 2.\nThe second person starts coordinate 0 at time 1 and reaches coordinate 2 at time 3. The first roadwork has ended, but the fourth roadwork has begun, so this person also stops walking at coordinate 2.\nThe fourth and sixth persons encounter no roadworks while walking, so they walk forever. The output for these cases is -1."], "Pid": "p03033", "ProblemText": "Task Description: Problem Statement There is an infinitely long street that runs west to east, which we consider as a number line.\nThere are N roadworks scheduled on this street.\nThe i-th roadwork blocks the point at coordinate X_i from time S_i - 0.5 to time T_i - 0.5.\nQ people are standing at coordinate 0. The i-th person will start the coordinate 0 at time D_i, continue to walk with speed 1 in the positive direction and stop walking when reaching a blocked point.\nFind the distance each of the Q people will walk.\nTask Constraint: All values in input are integers.\n1 <= N, Q <= 2 * 10^5\n0 <= S_i < T_i <= 10^9\n1 <= X_i <= 10^9\n0 <= D_1 < D_2 < ... < D_Q <= 10^9\nIf i \\neq j and X_i = X_j, the intervals [S_i, T_i) and [S_j, T_j) do not overlap.\nTask Input: Input is given from Standard Input in the following format:\nN Q\nS_1 T_1 X_1\n:\nS_N T_N X_N\nD_1\n:\nD_Q\nTask Output: Print Q lines. The i-th line should contain the distance the i-th person will walk or -1 if that person walks forever.\nTask Samples: input: 4 6\n1 3 2\n7 13 10\n18 20 13\n3 4 2\n0\n1\n2\n3\n5\n8 output: 2\n2\n10\n-1\n13\n-1\n\nThe first person starts coordinate 0 at time 0 and stops walking at coordinate 2 when reaching a point blocked by the first roadwork at time 2.\nThe second person starts coordinate 0 at time 1 and reaches coordinate 2 at time 3. The first roadwork has ended, but the fourth roadwork has begun, so this person also stops walking at coordinate 2.\nThe fourth and sixth persons encounter no roadworks while walking, so they walk forever. The output for these cases is -1.\n\n" }, { "title": "", "content": "Problem Statement There is an infinitely large pond, which we consider as a number line.\nIn this pond, there are N lotuses floating at coordinates 0,1,2, . . . , N-2 and N-1.\nOn the lotus at coordinate i, an integer s_i is written.\nYou are standing on the lotus at coordinate 0. You will play a game that proceeds as follows:\n\n1. Choose positive integers A and B. Your score is initially 0.\n2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y.\nIf y = N-1, the game ends.\nIf y \\neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y.\nIf y \\neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends.\n3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y.\nIf y = N-1, the game ends.\nIf y \\neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y.\nIf y \\neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends.\n4. Go back to step 2.\n\nYou want to end the game with as high a score as possible.\nWhat is the score obtained by the optimal choice of A and B?", "constraint": "3 <= N <= 10^5\n-10^9 <= s_i <= 10^9\ns_0=s_{N-1}=0\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\ns_0 s_1 . . . . . . s_{N-1}", "output": "Print the score obtained by the optimal choice of A and B.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 2 5 1 0 output: 3\n\nIf you choose A = 3 and B = 2, the game proceeds as follows:\n\nMove to coordinate 0 + 3 = 3. Your score increases by s_3 = 1.\nMove to coordinate 3 - 2 = 1. Your score increases by s_1 = 2.\nMove to coordinate 1 + 3 = 4. The game ends with a score of 3.\n\nThere is no way to end the game with a score of 4 or higher, so the answer is 3. Note that you cannot land the lotus at coordinate 2 without drowning later.", "input: 6\n0 10 -7 -4 -13 0 output: 0\n\nThe optimal strategy here is to land the final lotus immediately by choosing A = 5 (the value of B does not matter).", "input: 11\n0 -4 0 -99 31 14 -15 -39 43 18 0 output: 59"], "Pid": "p03034", "ProblemText": "Task Description: Problem Statement There is an infinitely large pond, which we consider as a number line.\nIn this pond, there are N lotuses floating at coordinates 0,1,2, . . . , N-2 and N-1.\nOn the lotus at coordinate i, an integer s_i is written.\nYou are standing on the lotus at coordinate 0. You will play a game that proceeds as follows:\n\n1. Choose positive integers A and B. Your score is initially 0.\n2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y.\nIf y = N-1, the game ends.\nIf y \\neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y.\nIf y \\neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends.\n3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y.\nIf y = N-1, the game ends.\nIf y \\neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y.\nIf y \\neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends.\n4. Go back to step 2.\n\nYou want to end the game with as high a score as possible.\nWhat is the score obtained by the optimal choice of A and B?\nTask Constraint: 3 <= N <= 10^5\n-10^9 <= s_i <= 10^9\ns_0=s_{N-1}=0\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\ns_0 s_1 . . . . . . s_{N-1}\nTask Output: Print the score obtained by the optimal choice of A and B.\nTask Samples: input: 5\n0 2 5 1 0 output: 3\n\nIf you choose A = 3 and B = 2, the game proceeds as follows:\n\nMove to coordinate 0 + 3 = 3. Your score increases by s_3 = 1.\nMove to coordinate 3 - 2 = 1. Your score increases by s_1 = 2.\nMove to coordinate 1 + 3 = 4. The game ends with a score of 3.\n\nThere is no way to end the game with a score of 4 or higher, so the answer is 3. Note that you cannot land the lotus at coordinate 2 without drowning later.\ninput: 6\n0 10 -7 -4 -13 0 output: 0\n\nThe optimal strategy here is to land the final lotus immediately by choosing A = 5 (the value of B does not matter).\ninput: 11\n0 -4 0 -99 31 14 -15 -39 43 18 0 output: 59\n\n" }, { "title": "", "content": "Problem Statement Takahashi, who is A years old, is riding a Ferris wheel.\nIt costs B yen (B is an even number) to ride the Ferris wheel if you are 13 years old or older, but children between 6 and 12 years old (inclusive) can ride it for half the cost, and children who are 5 years old or younger are free of charge. (Yen is the currency of Japan. )\nFind the cost of the Ferris wheel for Takahashi.", "constraint": "0 <= A <= 100\n2 <= B <= 1000\nB is an even number.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the cost of the Ferris wheel for Takahashi.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 30 100 output: 100\n\nTakahashi is 30 years old now, and the cost of the Ferris wheel is 100 yen.", "input: 12 100 output: 50\n\nTakahashi is 12 years old, and the cost of the Ferris wheel is the half of 100 yen, that is, 50 yen.", "input: 0 100 output: 0\n\nTakahashi is 0 years old, and he can ride the Ferris wheel for free."], "Pid": "p03035", "ProblemText": "Task Description: Problem Statement Takahashi, who is A years old, is riding a Ferris wheel.\nIt costs B yen (B is an even number) to ride the Ferris wheel if you are 13 years old or older, but children between 6 and 12 years old (inclusive) can ride it for half the cost, and children who are 5 years old or younger are free of charge. (Yen is the currency of Japan. )\nFind the cost of the Ferris wheel for Takahashi.\nTask Constraint: 0 <= A <= 100\n2 <= B <= 1000\nB is an even number.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the cost of the Ferris wheel for Takahashi.\nTask Samples: input: 30 100 output: 100\n\nTakahashi is 30 years old now, and the cost of the Ferris wheel is 100 yen.\ninput: 12 100 output: 50\n\nTakahashi is 12 years old, and the cost of the Ferris wheel is the half of 100 yen, that is, 50 yen.\ninput: 0 100 output: 0\n\nTakahashi is 0 years old, and he can ride the Ferris wheel for free.\n\n" }, { "title": "", "content": "Problem Statement The development of algae in a pond is as follows.\nLet the total weight of the algae at the beginning of the year i be x_i gram. For i>=2000, the following formula holds:\n\nx_{i+1} = rx_i - D\n\nYou are given r, D and x_{2000}. Calculate x_{2001}, . . . , x_{2010} and print them in order.", "constraint": "2 <= r <= 5\n1 <= D <= 100\nD < x_{2000} <= 200\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nr D x_{2000}", "output": "Print 10 lines. The i-th line (1 <= i <= 10) should contain x_{2000+i} as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 10 20 output: 30\n50\n90\n170\n330\n650\n1290\n2570\n5130\n10250\n\nFor example, x_{2001} = rx_{2000} - D = 2 * 20 - 10 = 30 and x_{2002} = rx_{2001} - D = 2 * 30 - 10 = 50.", "input: 4 40 60 output: 200\n760\n3000\n11960\n47800\n191160\n764600\n3058360\n12233400\n48933560"], "Pid": "p03036", "ProblemText": "Task Description: Problem Statement The development of algae in a pond is as follows.\nLet the total weight of the algae at the beginning of the year i be x_i gram. For i>=2000, the following formula holds:\n\nx_{i+1} = rx_i - D\n\nYou are given r, D and x_{2000}. Calculate x_{2001}, . . . , x_{2010} and print them in order.\nTask Constraint: 2 <= r <= 5\n1 <= D <= 100\nD < x_{2000} <= 200\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nr D x_{2000}\nTask Output: Print 10 lines. The i-th line (1 <= i <= 10) should contain x_{2000+i} as an integer.\nTask Samples: input: 2 10 20 output: 30\n50\n90\n170\n330\n650\n1290\n2570\n5130\n10250\n\nFor example, x_{2001} = rx_{2000} - D = 2 * 20 - 10 = 30 and x_{2002} = rx_{2001} - D = 2 * 30 - 10 = 50.\ninput: 4 40 60 output: 200\n760\n3000\n11960\n47800\n191160\n764600\n3058360\n12233400\n48933560\n\n" }, { "title": "", "content": "Problem Statement We have N ID cards, and there are M gates.\nWe can pass the i-th gate if we have one of the following ID cards: the L_i-th, (L_i+1)-th, . . . , and R_i-th ID cards.\nHow many of the ID cards allow us to pass all the gates alone?", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= L_i <= R_i <= N", "input": "Input is given from Standard Input in the following format:\nN M\nL_1 R_1\nL_2 R_2\n\\vdots\nL_M R_M", "output": "Print the number of ID cards that allow us to pass all the gates alone.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n1 3\n2 4 output: 2\n\nTwo ID cards allow us to pass all the gates alone, as follows:\n\nThe first ID card does not allow us to pass the second gate.\nThe second ID card allows us to pass all the gates.\nThe third ID card allows us to pass all the gates.\nThe fourth ID card does not allow us to pass the first gate.", "input: 10 3\n3 6\n5 7\n6 9 output: 1", "input: 100000 1\n1 100000 output: 100000"], "Pid": "p03037", "ProblemText": "Task Description: Problem Statement We have N ID cards, and there are M gates.\nWe can pass the i-th gate if we have one of the following ID cards: the L_i-th, (L_i+1)-th, . . . , and R_i-th ID cards.\nHow many of the ID cards allow us to pass all the gates alone?\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= L_i <= R_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN M\nL_1 R_1\nL_2 R_2\n\\vdots\nL_M R_M\nTask Output: Print the number of ID cards that allow us to pass all the gates alone.\nTask Samples: input: 4 2\n1 3\n2 4 output: 2\n\nTwo ID cards allow us to pass all the gates alone, as follows:\n\nThe first ID card does not allow us to pass the second gate.\nThe second ID card allows us to pass all the gates.\nThe third ID card allows us to pass all the gates.\nThe fourth ID card does not allow us to pass the first gate.\ninput: 10 3\n3 6\n5 7\n6 9 output: 1\ninput: 100000 1\n1 100000 output: 100000\n\n" }, { "title": "", "content": "Problem Statement You have N cards. On the i-th card, an integer A_i is written.\nFor each j = 1,2, . . . , M in this order, you will perform the following operation once:\nOperation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.\nFind the maximum possible sum of the integers written on the N cards after the M operations.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i, C_i <= 10^9\n1 <= B_i <= N", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N\nB_1 C_1\nB_2 C_2\n\\vdots\nB_M C_M", "output": "Print the maximum possible sum of the integers written on the N cards after the M operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n5 1 4\n2 3\n1 5 output: 14\n\nBy replacing the integer on the second card with 5, the sum of the integers written on the three cards becomes 5 + 5 + 4 = 14, which is the maximum result.", "input: 10 3\n1 8 5 7 100 4 52 33 13 5\n3 10\n4 30\n1 4 output: 338", "input: 3 2\n100 100 100\n3 99\n3 99 output: 300", "input: 11 3\n1 1 1 1 1 1 1 1 1 1 1\n3 1000000000\n4 1000000000\n3 1000000000 output: 10000000001\n\nThe output may not fit into a 32-bit integer type."], "Pid": "p03038", "ProblemText": "Task Description: Problem Statement You have N cards. On the i-th card, an integer A_i is written.\nFor each j = 1,2, . . . , M in this order, you will perform the following operation once:\nOperation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.\nFind the maximum possible sum of the integers written on the N cards after the M operations.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i, C_i <= 10^9\n1 <= B_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N\nB_1 C_1\nB_2 C_2\n\\vdots\nB_M C_M\nTask Output: Print the maximum possible sum of the integers written on the N cards after the M operations.\nTask Samples: input: 3 2\n5 1 4\n2 3\n1 5 output: 14\n\nBy replacing the integer on the second card with 5, the sum of the integers written on the three cards becomes 5 + 5 + 4 = 14, which is the maximum result.\ninput: 10 3\n1 8 5 7 100 4 52 33 13 5\n3 10\n4 30\n1 4 output: 338\ninput: 3 2\n100 100 100\n3 99\n3 99 output: 300\ninput: 11 3\n1 1 1 1 1 1 1 1 1 1 1\n3 1000000000\n4 1000000000\n3 1000000000 output: 10000000001\n\nThe output may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement We have a grid of squares with N rows and M columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. We will choose K of the squares and put a piece on each of them.\nIf we place the K pieces on squares (x_1, y_1), (x_2, y_2), . . . , and (x_K, y_K), the cost of this arrangement is computed as:\n\\sum_{i=1}^{K-1} \\sum_{j=i+1}^K (|x_i - x_j| + |y_i - y_j|)\nFind the sum of the costs of all possible arrangements of the pieces. Since this value can be tremendous, print it modulo 10^9+7.\nWe consider two arrangements of the pieces different if and only if there is a square that contains a piece in one of the arrangements but not in the other.", "constraint": "2 <= N * M <= 2 * 10^5\n2 <= K <= N * M\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M K", "output": "Print the sum of the costs of all possible arrangements of the pieces, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 2 output: 8\n\nThere are six possible arrangements of the pieces, as follows:\n\n((1,1),(1,2)), with the cost |1-1|+|1-2| = 1\n((1,1),(2,1)), with the cost |1-2|+|1-1| = 1\n((1,1),(2,2)), with the cost |1-2|+|1-2| = 2\n((1,2),(2,1)), with the cost |1-2|+|2-1| = 2\n((1,2),(2,2)), with the cost |1-2|+|2-2| = 1\n((2,1),(2,2)), with the cost |2-2|+|1-2| = 1\n\nThe sum of these costs is 8.", "input: 4 5 4 output: 87210", "input: 100 100 5000 output: 817260251\n\nBe sure to print the sum modulo 10^9+7."], "Pid": "p03039", "ProblemText": "Task Description: Problem Statement We have a grid of squares with N rows and M columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. We will choose K of the squares and put a piece on each of them.\nIf we place the K pieces on squares (x_1, y_1), (x_2, y_2), . . . , and (x_K, y_K), the cost of this arrangement is computed as:\n\\sum_{i=1}^{K-1} \\sum_{j=i+1}^K (|x_i - x_j| + |y_i - y_j|)\nFind the sum of the costs of all possible arrangements of the pieces. Since this value can be tremendous, print it modulo 10^9+7.\nWe consider two arrangements of the pieces different if and only if there is a square that contains a piece in one of the arrangements but not in the other.\nTask Constraint: 2 <= N * M <= 2 * 10^5\n2 <= K <= N * M\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M K\nTask Output: Print the sum of the costs of all possible arrangements of the pieces, modulo 10^9+7.\nTask Samples: input: 2 2 2 output: 8\n\nThere are six possible arrangements of the pieces, as follows:\n\n((1,1),(1,2)), with the cost |1-1|+|1-2| = 1\n((1,1),(2,1)), with the cost |1-2|+|1-1| = 1\n((1,1),(2,2)), with the cost |1-2|+|1-2| = 2\n((1,2),(2,1)), with the cost |1-2|+|2-1| = 2\n((1,2),(2,2)), with the cost |1-2|+|2-2| = 1\n((2,1),(2,2)), with the cost |2-2|+|1-2| = 1\n\nThe sum of these costs is 8.\ninput: 4 5 4 output: 87210\ninput: 100 100 5000 output: 817260251\n\nBe sure to print the sum modulo 10^9+7.\n\n" }, { "title": "", "content": "Problem Statement There is a function f(x), which is initially a constant function f(x) = 0.\nWe will ask you to process Q queries in order. There are two kinds of queries, update queries and evaluation queries, as follows:\n\nAn update query 1 a b: Given two integers a and b, let g(x) = f(x) + |x - a| + b and replace f(x) with g(x).\nAn evaluation query 2: Print x that minimizes f(x), and the minimum value of f(x). If there are multiple such values of x, choose the minimum such value.\n\nWe can show that the values to be output in an evaluation query are always integers, so we ask you to print those values as integers without decimal points.", "constraint": "All values in input are integers.\n1 <= Q <= 2 * 10^5\n-10^9 <= a, b <= 10^9\nThe first query is an update query.", "input": "Input is given from Standard Input in the following format:\nQ\nQuery_1\n:\nQuery_Q\n\nSee Sample Input 1 for an example.", "output": "For each evaluation query, print a line containing the response, in the order in which the queries are given.\nThe response to each evaluation query should be the minimum value of x that minimizes f(x), and the minimum value of f(x), in this order, with space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 4 2\n2\n1 1 -8\n2 output: 4 2\n1 -3\n\nIn the first evaluation query, f(x) = |x - 4| + 2, which attains the minimum value of 2 at x = 4.\nIn the second evaluation query, f(x) = |x - 1| + |x - 4| - 6, which attains the minimum value of -3 when 1 <= x <= 4. Among the multiple values of x that minimize f(x), we ask you to print the minimum, that is, 1.", "input: 4\n1 -1000000000 1000000000\n1 -1000000000 1000000000\n1 -1000000000 1000000000\n2 output: -1000000000 3000000000"], "Pid": "p03040", "ProblemText": "Task Description: Problem Statement There is a function f(x), which is initially a constant function f(x) = 0.\nWe will ask you to process Q queries in order. There are two kinds of queries, update queries and evaluation queries, as follows:\n\nAn update query 1 a b: Given two integers a and b, let g(x) = f(x) + |x - a| + b and replace f(x) with g(x).\nAn evaluation query 2: Print x that minimizes f(x), and the minimum value of f(x). If there are multiple such values of x, choose the minimum such value.\n\nWe can show that the values to be output in an evaluation query are always integers, so we ask you to print those values as integers without decimal points.\nTask Constraint: All values in input are integers.\n1 <= Q <= 2 * 10^5\n-10^9 <= a, b <= 10^9\nThe first query is an update query.\nTask Input: Input is given from Standard Input in the following format:\nQ\nQuery_1\n:\nQuery_Q\n\nSee Sample Input 1 for an example.\nTask Output: For each evaluation query, print a line containing the response, in the order in which the queries are given.\nThe response to each evaluation query should be the minimum value of x that minimizes f(x), and the minimum value of f(x), in this order, with space in between.\nTask Samples: input: 4\n1 4 2\n2\n1 1 -8\n2 output: 4 2\n1 -3\n\nIn the first evaluation query, f(x) = |x - 4| + 2, which attains the minimum value of 2 at x = 4.\nIn the second evaluation query, f(x) = |x - 1| + |x - 4| - 6, which attains the minimum value of -3 when 1 <= x <= 4. Among the multiple values of x that minimize f(x), we ask you to print the minimum, that is, 1.\ninput: 4\n1 -1000000000 1000000000\n1 -1000000000 1000000000\n1 -1000000000 1000000000\n2 output: -1000000000 3000000000\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N consisting of A, B and C, and an integer K which is between 1 and N (inclusive).\nPrint the string S after lowercasing the K-th character in it.", "constraint": "1 <= N <= 50\n1 <= K <= N\nS is a string of length N consisting of A, B and C.", "input": "Input is given from Standard Input in the following format:\nN K\nS", "output": "Print the string S after lowercasing the K-th character in it.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\nABC output: aBC", "input: 4 3\nCABA output: CAbA"], "Pid": "p03041", "ProblemText": "Task Description: Problem Statement You are given a string S of length N consisting of A, B and C, and an integer K which is between 1 and N (inclusive).\nPrint the string S after lowercasing the K-th character in it.\nTask Constraint: 1 <= N <= 50\n1 <= K <= N\nS is a string of length N consisting of A, B and C.\nTask Input: Input is given from Standard Input in the following format:\nN K\nS\nTask Output: Print the string S after lowercasing the K-th character in it.\nTask Samples: input: 3 1\nABC output: aBC\ninput: 4 3\nCABA output: CAbA\n\n" }, { "title": "", "content": "Problem Statement You have a digit sequence S of length 4. You are wondering which of the following formats S is in:\n\nYYMM format: the last two digits of the year and the two-digit representation of the month (example: 01 for January), concatenated in this order\nMMYY format: the two-digit representation of the month and the last two digits of the year, concatenated in this order\n\nIf S is valid in only YYMM format, print YYMM; if S is valid in only MMYY format, print MMYY; if S is valid in both formats, print AMBIGUOUS; if S is valid in neither format, print NA.", "constraint": "S is a digit sequence of length 4.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the specified string: YYMM, MMYY, AMBIGUOUS or NA.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1905 output: YYMM\n\nMay XX19 is a valid date, but 19 is not valid as a month. Thus, this string is only valid in YYMM format.", "input: 0112 output: AMBIGUOUS\n\nBoth December XX01 and January XX12 are valid dates. Thus, this string is valid in both formats.", "input: 1700 output: NA\n\nNeither 0 nor 17 is valid as a month. Thus, this string is valid in neither format."], "Pid": "p03042", "ProblemText": "Task Description: Problem Statement You have a digit sequence S of length 4. You are wondering which of the following formats S is in:\n\nYYMM format: the last two digits of the year and the two-digit representation of the month (example: 01 for January), concatenated in this order\nMMYY format: the two-digit representation of the month and the last two digits of the year, concatenated in this order\n\nIf S is valid in only YYMM format, print YYMM; if S is valid in only MMYY format, print MMYY; if S is valid in both formats, print AMBIGUOUS; if S is valid in neither format, print NA.\nTask Constraint: S is a digit sequence of length 4.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the specified string: YYMM, MMYY, AMBIGUOUS or NA.\nTask Samples: input: 1905 output: YYMM\n\nMay XX19 is a valid date, but 19 is not valid as a month. Thus, this string is only valid in YYMM format.\ninput: 0112 output: AMBIGUOUS\n\nBoth December XX01 and January XX12 are valid dates. Thus, this string is valid in both formats.\ninput: 1700 output: NA\n\nNeither 0 nor 17 is valid as a month. Thus, this string is valid in neither format.\n\n" }, { "title": "", "content": "Problem Statement Snuke has a fair N-sided die that shows the integers from 1 to N with equal probability and a fair coin. He will play the following game with them:\n\nThrow the die. The current score is the result of the die.\nAs long as the score is between 1 and K-1 (inclusive), keep flipping the coin. The score is doubled each time the coin lands heads up, and the score becomes 0 if the coin lands tails up.\nThe game ends when the score becomes 0 or becomes K or above. Snuke wins if the score is K or above, and loses if the score is 0.\n\nYou are given N and K. Find the probability that Snuke wins the game.", "constraint": "1 <= N <= 10^5\n1 <= K <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the probability that Snuke wins the game. The output is considered correct when the absolute or relative error is at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 10 output: 0.145833333333\nIf the die shows 1, Snuke needs to get four consecutive heads from four coin flips to obtain a score of 10 or above. The probability of this happening is \\frac{1}{3} * (\\frac{1}{2})^4 = \\frac{1}{48}.\nIf the die shows 2, Snuke needs to get three consecutive heads from three coin flips to obtain a score of 10 or above. The probability of this happening is \\frac{1}{3} * (\\frac{1}{2})^3 = \\frac{1}{24}.\nIf the die shows 3, Snuke needs to get two consecutive heads from two coin flips to obtain a score of 10 or above. The probability of this happening is \\frac{1}{3} * (\\frac{1}{2})^2 = \\frac{1}{12}.\n\nThus, the probability that Snuke wins is \\frac{1}{48} + \\frac{1}{24} + \\frac{1}{12} = \\frac{7}{48} \\simeq 0.1458333333.", "input: 100000 5 output: 0.999973749998"], "Pid": "p03043", "ProblemText": "Task Description: Problem Statement Snuke has a fair N-sided die that shows the integers from 1 to N with equal probability and a fair coin. He will play the following game with them:\n\nThrow the die. The current score is the result of the die.\nAs long as the score is between 1 and K-1 (inclusive), keep flipping the coin. The score is doubled each time the coin lands heads up, and the score becomes 0 if the coin lands tails up.\nThe game ends when the score becomes 0 or becomes K or above. Snuke wins if the score is K or above, and loses if the score is 0.\n\nYou are given N and K. Find the probability that Snuke wins the game.\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the probability that Snuke wins the game. The output is considered correct when the absolute or relative error is at most 10^{-9}.\nTask Samples: input: 3 10 output: 0.145833333333\nIf the die shows 1, Snuke needs to get four consecutive heads from four coin flips to obtain a score of 10 or above. The probability of this happening is \\frac{1}{3} * (\\frac{1}{2})^4 = \\frac{1}{48}.\nIf the die shows 2, Snuke needs to get three consecutive heads from three coin flips to obtain a score of 10 or above. The probability of this happening is \\frac{1}{3} * (\\frac{1}{2})^3 = \\frac{1}{24}.\nIf the die shows 3, Snuke needs to get two consecutive heads from two coin flips to obtain a score of 10 or above. The probability of this happening is \\frac{1}{3} * (\\frac{1}{2})^2 = \\frac{1}{12}.\n\nThus, the probability that Snuke wins is \\frac{1}{48} + \\frac{1}{24} + \\frac{1}{12} = \\frac{7}{48} \\simeq 0.1458333333.\ninput: 100000 5 output: 0.999973749998\n\n" }, { "title": "", "content": "Problem Statement We have a tree with N vertices numbered 1 to N.\nThe i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i.\nYour objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:\n\nFor any two vertices painted in the same color, the distance between them is an even number.\n\nFind a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= u_i < v_i <= N\n1 <= w_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nu_1 v_1 w_1\nu_2 v_2 w_2\n.\n.\n.\nu_{N - 1} v_{N - 1} w_{N - 1}", "output": "Print a coloring of the vertices that satisfies the condition, in N lines.\nThe i-th line should contain 0 if Vertex i is painted white and 1 if it is painted black.\nIf there are multiple colorings that satisfy the condition, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 2\n2 3 1 output: 0\n0\n1", "input: 5\n2 5 2\n2 3 10\n1 3 8\n3 4 2 output: 1\n0\n1\n0\n1"], "Pid": "p03044", "ProblemText": "Task Description: Problem Statement We have a tree with N vertices numbered 1 to N.\nThe i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i.\nYour objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:\n\nFor any two vertices painted in the same color, the distance between them is an even number.\n\nFind a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= u_i < v_i <= N\n1 <= w_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nu_1 v_1 w_1\nu_2 v_2 w_2\n.\n.\n.\nu_{N - 1} v_{N - 1} w_{N - 1}\nTask Output: Print a coloring of the vertices that satisfies the condition, in N lines.\nThe i-th line should contain 0 if Vertex i is painted white and 1 if it is painted black.\nIf there are multiple colorings that satisfy the condition, any of them will be accepted.\nTask Samples: input: 3\n1 2 2\n2 3 1 output: 0\n0\n1\ninput: 5\n2 5 2\n2 3 10\n1 3 8\n3 4 2 output: 1\n0\n1\n0\n1\n\n" }, { "title": "", "content": "Problem Statement There are N cards placed face down in a row. On each card, an integer 1 or 2 is written.\nLet A_i be the integer written on the i-th card.\nYour objective is to guess A_1, A_2, . . . , A_N correctly.\nYou know the following facts:\n\nFor each i = 1,2, . . . , M, the value A_{X_i} + A_{Y_i} + Z_i is an even number.\n\nYou are a magician and can use the following magic any number of times:\nMagic: Choose one card and know the integer A_i written on it. The cost of using this magic is 1.\nWhat is the minimum cost required to determine all of A_1, A_2, . . . , A_N?\nIt is guaranteed that there is no contradiction in given input.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= X_i < Y_i <= N\n1 <= Z_i <= 100\nThe pairs (X_i, Y_i) are distinct.\nThere is no contradiction in input. (That is, there exist integers A_1, A_2, ..., A_N that satisfy the conditions.)", "input": "Input is given from Standard Input in the following format:\nN M\nX_1 Y_1 Z_1\nX_2 Y_2 Z_2\n\\vdots\nX_M Y_M Z_M", "output": "Print the minimum total cost required to determine all of A_1, A_2, . . . , A_N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1 2 1 output: 2\n\nYou can determine all of A_1, A_2, A_3 by using the magic for the first and third cards.", "input: 6 5\n1 2 1\n2 3 2\n1 3 3\n4 5 4\n5 6 5 output: 2", "input: 100000 1\n1 100000 100 output: 99999"], "Pid": "p03045", "ProblemText": "Task Description: Problem Statement There are N cards placed face down in a row. On each card, an integer 1 or 2 is written.\nLet A_i be the integer written on the i-th card.\nYour objective is to guess A_1, A_2, . . . , A_N correctly.\nYou know the following facts:\n\nFor each i = 1,2, . . . , M, the value A_{X_i} + A_{Y_i} + Z_i is an even number.\n\nYou are a magician and can use the following magic any number of times:\nMagic: Choose one card and know the integer A_i written on it. The cost of using this magic is 1.\nWhat is the minimum cost required to determine all of A_1, A_2, . . . , A_N?\nIt is guaranteed that there is no contradiction in given input.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= X_i < Y_i <= N\n1 <= Z_i <= 100\nThe pairs (X_i, Y_i) are distinct.\nThere is no contradiction in input. (That is, there exist integers A_1, A_2, ..., A_N that satisfy the conditions.)\nTask Input: Input is given from Standard Input in the following format:\nN M\nX_1 Y_1 Z_1\nX_2 Y_2 Z_2\n\\vdots\nX_M Y_M Z_M\nTask Output: Print the minimum total cost required to determine all of A_1, A_2, . . . , A_N.\nTask Samples: input: 3 1\n1 2 1 output: 2\n\nYou can determine all of A_1, A_2, A_3 by using the magic for the first and third cards.\ninput: 6 5\n1 2 1\n2 3 2\n1 3 3\n4 5 4\n5 6 5 output: 2\ninput: 100000 1\n1 100000 100 output: 99999\n\n" }, { "title": "", "content": "Problem Statement Construct a sequence a = {a_1, \\ a_2, \\ . . . , \\ a_{2^{M + 1}}} of length 2^{M + 1} that satisfies the following conditions, if such a sequence exists.\n\nEach integer between 0 and 2^M - 1 (inclusive) occurs twice in a.\nFor any i and j (i < j) such that a_i = a_j, the formula a_i \\ xor \\ a_{i + 1} \\ xor \\ . . . \\ xor \\ a_j = K holds.\nWhat is xor (bitwise exclusive or)?\nThe xor of integers c_1, c_2, . . . , c_n is defined as follows:\n\nWhen c_1 \\ xor \\ c_2 \\ xor \\ . . . \\ xor \\ c_n is written in base two, the digit in the 2^k's place (k >= 0) is 1 if the number of integers among c_1, c_2, . . . c_m whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even.\n\nFor example, 3 \\ xor \\ 5 = 6. (If we write it in base two: 011 xor 101 = 110. )", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03046", "ProblemText": "Task Description: Problem Statement Construct a sequence a = {a_1, \\ a_2, \\ . . . , \\ a_{2^{M + 1}}} of length 2^{M + 1} that satisfies the following conditions, if such a sequence exists.\n\nEach integer between 0 and 2^M - 1 (inclusive) occurs twice in a.\nFor any i and j (i < j) such that a_i = a_j, the formula a_i \\ xor \\ a_{i + 1} \\ xor \\ . . . \\ xor \\ a_j = K holds.\nWhat is xor (bitwise exclusive or)?\nThe xor of integers c_1, c_2, . . . , c_n is defined as follows:\n\nWhen c_1 \\ xor \\ c_2 \\ xor \\ . . . \\ xor \\ c_n is written in base two, the digit in the 2^k's place (k >= 0) is 1 if the number of integers among c_1, c_2, . . . c_m whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even.\n\nFor example, 3 \\ xor \\ 5 = 6. (If we write it in base two: 011 xor 101 = 110. )\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement Snuke has N integers: 1,2, \\ldots, N.\nHe will choose K of them and give those to Takahashi.\nHow many ways are there to choose K consecutive integers?", "constraint": "All values in input are integers.\n1 <= K <= N <= 50", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 2\n\nThere are two ways to choose two consecutive integers: (1,2) and (2,3).", "input: 13 3 output: 11"], "Pid": "p03047", "ProblemText": "Task Description: Problem Statement Snuke has N integers: 1,2, \\ldots, N.\nHe will choose K of them and give those to Takahashi.\nHow many ways are there to choose K consecutive integers?\nTask Constraint: All values in input are integers.\n1 <= K <= N <= 50\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the answer.\nTask Samples: input: 3 2 output: 2\n\nThere are two ways to choose two consecutive integers: (1,2) and (2,3).\ninput: 13 3 output: 11\n\n" }, { "title": "", "content": "Problem Statement Snuke has come to a store that sells boxes containing balls. The store sells the following three kinds of boxes:\n\nRed boxes, each containing R red balls\nGreen boxes, each containing G green balls\nBlue boxes, each containing B blue balls\n\nSnuke wants to get a total of exactly N balls by buying r red boxes, g green boxes and b blue boxes.\nHow many triples of non-negative integers (r, g, b) achieve this?", "constraint": "All values in input are integers.\n1 <= R,G,B,N <= 3000", "input": "Input is given from Standard Input in the following format:\nR G B N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 3 4 output: 4\n\nFour triples achieve the objective, as follows:\n\n(4,0,0)\n(2,1,0)\n(1,0,1)\n(0,2,0)", "input: 13 1 4 3000 output: 87058"], "Pid": "p03048", "ProblemText": "Task Description: Problem Statement Snuke has come to a store that sells boxes containing balls. The store sells the following three kinds of boxes:\n\nRed boxes, each containing R red balls\nGreen boxes, each containing G green balls\nBlue boxes, each containing B blue balls\n\nSnuke wants to get a total of exactly N balls by buying r red boxes, g green boxes and b blue boxes.\nHow many triples of non-negative integers (r, g, b) achieve this?\nTask Constraint: All values in input are integers.\n1 <= R,G,B,N <= 3000\nTask Input: Input is given from Standard Input in the following format:\nR G B N\nTask Output: Print the answer.\nTask Samples: input: 1 2 3 4 output: 4\n\nFour triples achieve the objective, as follows:\n\n(4,0,0)\n(2,1,0)\n(1,0,1)\n(0,2,0)\ninput: 13 1 4 3000 output: 87058\n\n" }, { "title": "", "content": "Problem Statement Snuke has N strings. The i-th string is s_i.\nLet us concatenate these strings into one string after arranging them in some order.\nFind the maximum possible number of occurrences of AB in the resulting string.", "constraint": "1 <= N <= 10^{4}\n2 <= |s_i| <= 10\ns_i consists of uppercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\ns_1\n\\vdots\ns_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nABCA\nXBAZ\nBAD output: 2\n\nFor example, if we concatenate ABCA, BAD and XBAZ in this order, the resulting string ABCABADXBAZ has two occurrences of AB.", "input: 9\nBEWPVCRWH\nZZNQYIJX\nBAVREA\nPA\nHJMYITEOX\nBCJHMRMNK\nBP\nQVFABZ\nPRGKSPUNA output: 4", "input: 7\nRABYBBE\nJOZ\nBMHQUVA\nBPA\nISU\nMCMABAOBHZ\nSZMEHMA output: 4"], "Pid": "p03049", "ProblemText": "Task Description: Problem Statement Snuke has N strings. The i-th string is s_i.\nLet us concatenate these strings into one string after arranging them in some order.\nFind the maximum possible number of occurrences of AB in the resulting string.\nTask Constraint: 1 <= N <= 10^{4}\n2 <= |s_i| <= 10\ns_i consists of uppercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\ns_1\n\\vdots\ns_N\nTask Output: Print the answer.\nTask Samples: input: 3\nABCA\nXBAZ\nBAD output: 2\n\nFor example, if we concatenate ABCA, BAD and XBAZ in this order, the resulting string ABCABADXBAZ has two occurrences of AB.\ninput: 9\nBEWPVCRWH\nZZNQYIJX\nBAVREA\nPA\nHJMYITEOX\nBCJHMRMNK\nBP\nQVFABZ\nPRGKSPUNA output: 4\ninput: 7\nRABYBBE\nJOZ\nBMHQUVA\nBPA\nISU\nMCMABAOBHZ\nSZMEHMA output: 4\n\n" }, { "title": "", "content": "Problem Statement Snuke received a positive integer N from Takahashi.\nA positive integer m is called a favorite number when the following condition is satisfied:\n\nThe quotient and remainder of N divided by m are equal, that is, \\lfloor \\frac{N}{m} \\rfloor = N \\bmod m holds.\n\nFind all favorite numbers and print the sum of those.", "constraint": "All values in input are integers.\n1 <= N <= 10^{12}", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 output: 10\n\nThere are two favorite numbers: 3 and 7. Print the sum of these, 10.", "input: 1000000000000 output: 2499686339916\n\nWatch out for overflow."], "Pid": "p03050", "ProblemText": "Task Description: Problem Statement Snuke received a positive integer N from Takahashi.\nA positive integer m is called a favorite number when the following condition is satisfied:\n\nThe quotient and remainder of N divided by m are equal, that is, \\lfloor \\frac{N}{m} \\rfloor = N \\bmod m holds.\n\nFind all favorite numbers and print the sum of those.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^{12}\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 8 output: 10\n\nThere are two favorite numbers: 3 and 7. Print the sum of these, 10.\ninput: 1000000000000 output: 2499686339916\n\nWatch out for overflow.\n\n" }, { "title": "", "content": "Problem Statement The beauty of a sequence a of length n is defined as a_1 \\oplus \\cdots \\oplus a_n, where \\oplus denotes the bitwise exclusive or (XOR).\nYou are given a sequence A of length N.\nSnuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.\nThere are 2^{N-1} possible ways to insert partitions.\nHow many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.", "constraint": "All values in input are integers.\n1 <= N <= 5 * 10^5\n0 <= A_i < 2^{20}", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\ldots A_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 3\n\nFour ways of dividing A shown below satisfy the condition. The condition is not satisfied only if A is divided into (1),(2),(3).\n\n(1,2,3)\n(1),(2,3)\n(1,2),(3)", "input: 3\n1 2 2 output: 1", "input: 32\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 output: 147483634\n\nFind the count modulo 10^{9}+7.", "input: 24\n1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2 output: 292"], "Pid": "p03051", "ProblemText": "Task Description: Problem Statement The beauty of a sequence a of length n is defined as a_1 \\oplus \\cdots \\oplus a_n, where \\oplus denotes the bitwise exclusive or (XOR).\nYou are given a sequence A of length N.\nSnuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.\nThere are 2^{N-1} possible ways to insert partitions.\nHow many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.\nTask Constraint: All values in input are integers.\n1 <= N <= 5 * 10^5\n0 <= A_i < 2^{20}\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 \\ldots A_{N}\nTask Output: Print the answer.\nTask Samples: input: 3\n1 2 3 output: 3\n\nFour ways of dividing A shown below satisfy the condition. The condition is not satisfied only if A is divided into (1),(2),(3).\n\n(1,2,3)\n(1),(2,3)\n(1,2),(3)\ninput: 3\n1 2 2 output: 1\ninput: 32\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 output: 147483634\n\nFind the count modulo 10^{9}+7.\ninput: 24\n1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2 output: 292\n\n" }, { "title": "", "content": "Problem Statement You are given a simple connected undirected graph G consisting of N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nEdge i connects Vertex a_i and b_i bidirectionally.\nIt is guaranteed that the subgraph consisting of Vertex 1,2, \\ldots, N and Edge 1,2, \\ldots, N-1 is a spanning tree of G.\nAn allocation of weights to the edges is called a good allocation when the tree consisting of Vertex 1,2, \\ldots, N and Edge 1,2, \\ldots, N-1 is a minimum spanning tree of G.\nThere are M! ways to allocate the edges distinct integer weights between 1 and M.\nFor each good allocation among those, find the total weight of the edges in the minimum spanning tree, and print the sum of those total weights modulo 10^{9}+7.", "constraint": "All values in input are integers.\n2 <= N <= 20\nN-1 <= M <= N(N-1)/2\n1 <= a_i, b_i <= N\nG does not have self-loops or multiple edges.\nThe subgraph consisting of Vertex 1,2,\\ldots,N and Edge 1,2,\\ldots,N-1 is a spanning tree of G.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\n\\vdots\na_M b_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2\n2 3\n1 3 output: 6\n\nAn allocation is good only if Edge 3 has the weight 3. For these good allocations, the total weight of the edges in the minimum spanning tree is 3, and there are two good allocations, so the answer is 6.", "input: 4 4\n1 2\n3 2\n3 4\n1 3 output: 50", "input: 15 28\n10 7\n5 9\n2 13\n2 14\n6 1\n5 12\n2 10\n3 9\n10 15\n11 12\n12 6\n2 12\n12 8\n4 10\n15 3\n13 14\n1 15\n15 12\n4 14\n1 7\n5 11\n7 13\n9 10\n2 7\n1 9\n5 6\n12 14\n5 2 output: 657573092\n\nPrint the sum of those total weights modulo 10^{9}+7."], "Pid": "p03052", "ProblemText": "Task Description: Problem Statement You are given a simple connected undirected graph G consisting of N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nEdge i connects Vertex a_i and b_i bidirectionally.\nIt is guaranteed that the subgraph consisting of Vertex 1,2, \\ldots, N and Edge 1,2, \\ldots, N-1 is a spanning tree of G.\nAn allocation of weights to the edges is called a good allocation when the tree consisting of Vertex 1,2, \\ldots, N and Edge 1,2, \\ldots, N-1 is a minimum spanning tree of G.\nThere are M! ways to allocate the edges distinct integer weights between 1 and M.\nFor each good allocation among those, find the total weight of the edges in the minimum spanning tree, and print the sum of those total weights modulo 10^{9}+7.\nTask Constraint: All values in input are integers.\n2 <= N <= 20\nN-1 <= M <= N(N-1)/2\n1 <= a_i, b_i <= N\nG does not have self-loops or multiple edges.\nThe subgraph consisting of Vertex 1,2,\\ldots,N and Edge 1,2,\\ldots,N-1 is a spanning tree of G.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\n\\vdots\na_M b_M\nTask Output: Print the answer.\nTask Samples: input: 3 3\n1 2\n2 3\n1 3 output: 6\n\nAn allocation is good only if Edge 3 has the weight 3. For these good allocations, the total weight of the edges in the minimum spanning tree is 3, and there are two good allocations, so the answer is 6.\ninput: 4 4\n1 2\n3 2\n3 4\n1 3 output: 50\ninput: 15 28\n10 7\n5 9\n2 13\n2 14\n6 1\n5 12\n2 10\n3 9\n10 15\n11 12\n12 6\n2 12\n12 8\n4 10\n15 3\n13 14\n1 15\n15 12\n4 14\n1 7\n5 11\n7 13\n9 10\n2 7\n1 9\n5 6\n12 14\n5 2 output: 657573092\n\nPrint the sum of those total weights modulo 10^{9}+7.\n\n" }, { "title": "", "content": "Problem Statement You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.\nHW characters from A_{11} to A_{HW} represent the colors of the squares.\nA_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.\nWe will repeatedly perform the following operation until all the squares are black:\n\nEvery white square that shares a side with a black square, becomes black.\n\nFind the number of operations that will be performed.\nThe initial grid has at least one black square.", "constraint": "1 <= H,W <= 1000\nA_{ij} is # or ..\nThe given grid has at least one black square.", "input": "Input is given from Standard Input in the following format:\nH W\nA_{11}A_{12}. . . A_{1W}\n:\nA_{H1}A_{H2}. . . A_{HW}", "output": "Print the number of operations that will be performed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n...\n.#.\n... output: 2\n\nAfter one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.", "input: 6 6\n..#..#\n......\n#..#..\n......\n.#....\n....#. output: 3"], "Pid": "p03053", "ProblemText": "Task Description: Problem Statement You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.\nHW characters from A_{11} to A_{HW} represent the colors of the squares.\nA_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.\nWe will repeatedly perform the following operation until all the squares are black:\n\nEvery white square that shares a side with a black square, becomes black.\n\nFind the number of operations that will be performed.\nThe initial grid has at least one black square.\nTask Constraint: 1 <= H,W <= 1000\nA_{ij} is # or ..\nThe given grid has at least one black square.\nTask Input: Input is given from Standard Input in the following format:\nH W\nA_{11}A_{12}. . . A_{1W}\n:\nA_{H1}A_{H2}. . . A_{HW}\nTask Output: Print the number of operations that will be performed.\nTask Samples: input: 3 3\n...\n.#.\n... output: 2\n\nAfter one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.\ninput: 6 6\n..#..#\n......\n#..#..\n......\n.#....\n....#. output: 3\n\n" }, { "title": "", "content": "Problem Statement We have a rectangular grid of squares with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nOn this grid, there is a piece, which is initially placed at square (s_r, s_c).\nTakahashi and Aoki will play a game, where each player has a string of length N.\nTakahashi's string is S, and Aoki's string is T. S and T both consist of four kinds of letters: L, R, U and D.\nThe game consists of N steps. The i-th step proceeds as follows:\n\nFirst, Takahashi performs a move. He either moves the piece in the direction of S_i, or does not move the piece.\nSecond, Aoki performs a move. He either moves the piece in the direction of T_i, or does not move the piece.\n\nHere, to move the piece in the direction of L, R, U and D, is to move the piece from square (r, c) to square (r, c-1), (r, c+1), (r-1, c) and (r+1, c), respectively. If the destination square does not exist, the piece is removed from the grid, and the game ends, even if less than N steps are done.\nTakahashi wants to remove the piece from the grid in one of the N steps.\nAoki, on the other hand, wants to finish the N steps with the piece remaining on the grid.\nDetermine if the piece will remain on the grid at the end of the game when both players play optimally.", "constraint": "2 <= H,W <= 2 * 10^5\n2 <= N <= 2 * 10^5\n1 <= s_r <= H\n1 <= s_c <= W\n|S|=|T|=N\nS and T consists of the four kinds of letters L, R, U and D.", "input": "Input is given from Standard Input in the following format:\nH W N\ns_r s_c\nS\nT", "output": "If the piece will remain on the grid at the end of the game, print YES; otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 3\n2 2\nRRL\nLUD output: YES\n\nHere is one possible progress of the game:\n\nTakahashi moves the piece right. The piece is now at (2,3).\nAoki moves the piece left. The piece is now at (2,2).\nTakahashi does not move the piece. The piece remains at (2,2).\nAoki moves the piece up. The piece is now at (1,2).\nTakahashi moves the piece left. The piece is now at (1,1).\nAoki does not move the piece. The piece remains at (1,1).", "input: 4 3 5\n2 2\nUDRRR\nLLDUD output: NO", "input: 5 6 11\n2 1\nRLDRRUDDLRL\nURRDRLLDLRD output: NO"], "Pid": "p03054", "ProblemText": "Task Description: Problem Statement We have a rectangular grid of squares with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nOn this grid, there is a piece, which is initially placed at square (s_r, s_c).\nTakahashi and Aoki will play a game, where each player has a string of length N.\nTakahashi's string is S, and Aoki's string is T. S and T both consist of four kinds of letters: L, R, U and D.\nThe game consists of N steps. The i-th step proceeds as follows:\n\nFirst, Takahashi performs a move. He either moves the piece in the direction of S_i, or does not move the piece.\nSecond, Aoki performs a move. He either moves the piece in the direction of T_i, or does not move the piece.\n\nHere, to move the piece in the direction of L, R, U and D, is to move the piece from square (r, c) to square (r, c-1), (r, c+1), (r-1, c) and (r+1, c), respectively. If the destination square does not exist, the piece is removed from the grid, and the game ends, even if less than N steps are done.\nTakahashi wants to remove the piece from the grid in one of the N steps.\nAoki, on the other hand, wants to finish the N steps with the piece remaining on the grid.\nDetermine if the piece will remain on the grid at the end of the game when both players play optimally.\nTask Constraint: 2 <= H,W <= 2 * 10^5\n2 <= N <= 2 * 10^5\n1 <= s_r <= H\n1 <= s_c <= W\n|S|=|T|=N\nS and T consists of the four kinds of letters L, R, U and D.\nTask Input: Input is given from Standard Input in the following format:\nH W N\ns_r s_c\nS\nT\nTask Output: If the piece will remain on the grid at the end of the game, print YES; otherwise, print NO.\nTask Samples: input: 2 3 3\n2 2\nRRL\nLUD output: YES\n\nHere is one possible progress of the game:\n\nTakahashi moves the piece right. The piece is now at (2,3).\nAoki moves the piece left. The piece is now at (2,2).\nTakahashi does not move the piece. The piece remains at (2,2).\nAoki moves the piece up. The piece is now at (1,2).\nTakahashi moves the piece left. The piece is now at (1,1).\nAoki does not move the piece. The piece remains at (1,1).\ninput: 4 3 5\n2 2\nUDRRR\nLLDUD output: NO\ninput: 5 6 11\n2 1\nRLDRRUDDLRL\nURRDRLLDLRD output: NO\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki will play a game on a tree.\nThe tree has N vertices numbered 1 to N, and the i-th of the N-1 edges connects Vertex a_i and Vertex b_i.\nAt the beginning of the game, each vertex contains a coin.\nStarting from Takahashi, he and Aoki will alternately perform the following operation:\n\nChoose a vertex v that contains one or more coins, and remove all the coins from v.\nThen, move each coin remaining on the tree to the vertex that is nearest to v among the adjacent vertices of the coin's current vertex.\n\nThe player who becomes unable to play, loses the game.\nThat is, the player who takes his turn when there is no coin remaining on the tree, loses the game.\nDetermine the winner of the game when both players play optimally.", "constraint": "1 <= N <= 2 * 10^5\n1 <= a_i, b_i <= N\na_i \\neq b_i\nThe graph given as input is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_{N-1} b_{N-1}", "output": "Print First if Takahashi will win, and print Second if Aoki will win.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3 output: First\n\nHere is one possible progress of the game:\n\nTakahashi removes the coin from Vertex 1. Now, Vertex 1 and Vertex 2 contain one coin each.\nAoki removes the coin from Vertex 2. Now, Vertex 2 contains one coin.\nTakahashi removes the coin from Vertex 2. Now, there is no coin remaining on the tree.\nAoki takes his turn when there is no coin on the tree and loses.", "input: 6\n1 2\n2 3\n2 4\n4 6\n5 6 output: Second", "input: 7\n1 7\n7 4\n3 4\n7 5\n6 3\n2 1 output: First"], "Pid": "p03055", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki will play a game on a tree.\nThe tree has N vertices numbered 1 to N, and the i-th of the N-1 edges connects Vertex a_i and Vertex b_i.\nAt the beginning of the game, each vertex contains a coin.\nStarting from Takahashi, he and Aoki will alternately perform the following operation:\n\nChoose a vertex v that contains one or more coins, and remove all the coins from v.\nThen, move each coin remaining on the tree to the vertex that is nearest to v among the adjacent vertices of the coin's current vertex.\n\nThe player who becomes unable to play, loses the game.\nThat is, the player who takes his turn when there is no coin remaining on the tree, loses the game.\nDetermine the winner of the game when both players play optimally.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= a_i, b_i <= N\na_i \\neq b_i\nThe graph given as input is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_{N-1} b_{N-1}\nTask Output: Print First if Takahashi will win, and print Second if Aoki will win.\nTask Samples: input: 3\n1 2\n2 3 output: First\n\nHere is one possible progress of the game:\n\nTakahashi removes the coin from Vertex 1. Now, Vertex 1 and Vertex 2 contain one coin each.\nAoki removes the coin from Vertex 2. Now, Vertex 2 contains one coin.\nTakahashi removes the coin from Vertex 2. Now, there is no coin remaining on the tree.\nAoki takes his turn when there is no coin on the tree and loses.\ninput: 6\n1 2\n2 3\n2 4\n4 6\n5 6 output: Second\ninput: 7\n1 7\n7 4\n3 4\n7 5\n6 3\n2 1 output: First\n\n" }, { "title": "", "content": "Problem Statement Note the unusual memory limit.\nFor a rectangular grid where each square is painted white or black, we define its complexity as follows:\n\nIf all the squares are black or all the squares are white, the complexity is 0.\nOtherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \\max(c_1, c_2) in those divisions. The complexity of the grid is m+1.\n\nYou are given a grid with H horizontal rows and W vertical columns where each square is painted white or black.\nHW characters from A_{11} to A_{HW} represent the colors of the squares.\nA_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.\nFind the complexity of the given grid.", "constraint": "1 <= H,W <= 185\nA_{ij} is # or ..", "input": "Input is given from Standard Input in the following format:\nH W\nA_{11}A_{12}. . . A_{1W}\n:\nA_{H1}A_{H2}. . . A_{HW}", "output": "Print the complexity of the given grid.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n...\n.##\n.## output: 2\n\nLet us divide the grid by the boundary line between the first and second columns.\nThe subgrid consisting of the first column has the complexity of 0, and the subgrid consisting of the second and third columns has the complexity of 1, so the whole grid has the complexity of at most 2.", "input: 6 7\n.####.#\n#....#.\n#....#.\n#....#.\n.####.#\n#....## output: 4"], "Pid": "p03056", "ProblemText": "Task Description: Problem Statement Note the unusual memory limit.\nFor a rectangular grid where each square is painted white or black, we define its complexity as follows:\n\nIf all the squares are black or all the squares are white, the complexity is 0.\nOtherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \\max(c_1, c_2) in those divisions. The complexity of the grid is m+1.\n\nYou are given a grid with H horizontal rows and W vertical columns where each square is painted white or black.\nHW characters from A_{11} to A_{HW} represent the colors of the squares.\nA_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.\nFind the complexity of the given grid.\nTask Constraint: 1 <= H,W <= 185\nA_{ij} is # or ..\nTask Input: Input is given from Standard Input in the following format:\nH W\nA_{11}A_{12}. . . A_{1W}\n:\nA_{H1}A_{H2}. . . A_{HW}\nTask Output: Print the complexity of the given grid.\nTask Samples: input: 3 3\n...\n.##\n.## output: 2\n\nLet us divide the grid by the boundary line between the first and second columns.\nThe subgrid consisting of the first column has the complexity of 0, and the subgrid consisting of the second and third columns has the complexity of 1, so the whole grid has the complexity of at most 2.\ninput: 6 7\n.####.#\n#....#.\n#....#.\n#....#.\n.####.#\n#....## output: 4\n\n" }, { "title": "", "content": "Problem Statement Consider a circle whose perimeter is divided by N points into N arcs of equal length, and each of the arcs is painted red or blue. Such a circle is said to generate a string S from every point when the following condition is satisfied:\n\nWe will arbitrarily choose one of the N points on the perimeter and place a piece on it.\nThen, we will perform the following move M times: move the piece clockwise or counter-clockwise to an adjacent point.\nHere, whatever point we choose initially, it is always possible to move the piece so that the color of the i-th arc the piece goes along is S_i, by properly deciding the directions of the moves.\n\nAssume that, if S_i is R, it represents red; if S_i is B, it represents blue.\nNote that the directions of the moves can be decided separately for each choice of the initial point.\nYou are given a string S of length M consisting of R and B.\nOut of the 2^N ways to paint each of the arcs red or blue in a circle whose perimeter is divided into N arcs of equal length, find the number of ways resulting in a circle that generates S from every point, modulo 10^9+7.\nNote that the rotations of the same coloring are also distinguished.", "constraint": "2 <= N <= 2 * 10^5\n1 <= M <= 2 * 10^5\n|S|=M\nS_i is R or B.", "input": "Input is given from Standard Input in the following format:\nN M\nS", "output": "Print the number of ways to paint each of the arcs that satisfy the condition, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 7\nRBRRBRR output: 2\n\nThe condition is satisfied only if the arcs are alternately painted red and blue, so the answer here is 2.", "input: 3 3\nBBB output: 4", "input: 12 10\nRRRRBRRRRB output: 78"], "Pid": "p03057", "ProblemText": "Task Description: Problem Statement Consider a circle whose perimeter is divided by N points into N arcs of equal length, and each of the arcs is painted red or blue. Such a circle is said to generate a string S from every point when the following condition is satisfied:\n\nWe will arbitrarily choose one of the N points on the perimeter and place a piece on it.\nThen, we will perform the following move M times: move the piece clockwise or counter-clockwise to an adjacent point.\nHere, whatever point we choose initially, it is always possible to move the piece so that the color of the i-th arc the piece goes along is S_i, by properly deciding the directions of the moves.\n\nAssume that, if S_i is R, it represents red; if S_i is B, it represents blue.\nNote that the directions of the moves can be decided separately for each choice of the initial point.\nYou are given a string S of length M consisting of R and B.\nOut of the 2^N ways to paint each of the arcs red or blue in a circle whose perimeter is divided into N arcs of equal length, find the number of ways resulting in a circle that generates S from every point, modulo 10^9+7.\nNote that the rotations of the same coloring are also distinguished.\nTask Constraint: 2 <= N <= 2 * 10^5\n1 <= M <= 2 * 10^5\n|S|=M\nS_i is R or B.\nTask Input: Input is given from Standard Input in the following format:\nN M\nS\nTask Output: Print the number of ways to paint each of the arcs that satisfy the condition, modulo 10^9+7.\nTask Samples: input: 4 7\nRBRRBRR output: 2\n\nThe condition is satisfied only if the arcs are alternately painted red and blue, so the answer here is 2.\ninput: 3 3\nBBB output: 4\ninput: 12 10\nRRRRBRRRRB output: 78\n\n" }, { "title": "", "content": "Problem Statement You are given a tree T with N vertices and an undirected graph G with N vertices and M edges.\nThe vertices of each graph are numbered 1 to N.\nThe i-th of the N-1 edges in T connects Vertex a_i and Vertex b_i, and the j-th of the M edges in G connects Vertex c_j and Vertex d_j.\nConsider adding edges to G by repeatedly performing the following operation:\n\nChoose three integers a, b and c such that G has an edge connecting Vertex a and b and an edge connecting Vertex b and c but not an edge connecting Vertex a and c. If there is a simple path in T that contains all three of Vertex a, b and c in some order, add an edge in G connecting Vertex a and c.\n\nPrint the number of edges in G when no more edge can be added.\nIt can be shown that this number does not depend on the choices made in the operation.", "constraint": "2 <= N <= 2000\n1 <= M <= 2000\n1 <= a_i, b_i <= N\na_i \\neq b_i\n1 <= c_j, d_j <= N\nc_j \\neq d_j\nG does not contain multiple edges.\nT is a tree.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 d_1\n:\nc_M d_M", "output": "Print the final number of edges in G.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 2\n1 3\n3 4\n1 5\n5 4\n2 5\n1 5 output: 6\n\nWe can have at most six edges in G by adding edges as follows:\n\nLet (a,b,c)=(1,5,4) and add an edge connecting Vertex 1 and 4.\nLet (a,b,c)=(1,5,2) and add an edge connecting Vertex 1 and 2.\nLet (a,b,c)=(2,1,4) and add an edge connecting Vertex 2 and 4.", "input: 7 5\n1 5\n1 4\n1 7\n1 2\n2 6\n6 3\n2 5\n1 3\n1 6\n4 6\n4 7 output: 11", "input: 13 11\n6 13\n1 2\n5 1\n8 4\n9 7\n12 2\n10 11\n1 9\n13 7\n13 11\n8 10\n3 8\n4 13\n8 12\n4 7\n2 3\n5 11\n1 4\n2 11\n8 10\n3 5\n6 9\n4 10 output: 27"], "Pid": "p03058", "ProblemText": "Task Description: Problem Statement You are given a tree T with N vertices and an undirected graph G with N vertices and M edges.\nThe vertices of each graph are numbered 1 to N.\nThe i-th of the N-1 edges in T connects Vertex a_i and Vertex b_i, and the j-th of the M edges in G connects Vertex c_j and Vertex d_j.\nConsider adding edges to G by repeatedly performing the following operation:\n\nChoose three integers a, b and c such that G has an edge connecting Vertex a and b and an edge connecting Vertex b and c but not an edge connecting Vertex a and c. If there is a simple path in T that contains all three of Vertex a, b and c in some order, add an edge in G connecting Vertex a and c.\n\nPrint the number of edges in G when no more edge can be added.\nIt can be shown that this number does not depend on the choices made in the operation.\nTask Constraint: 2 <= N <= 2000\n1 <= M <= 2000\n1 <= a_i, b_i <= N\na_i \\neq b_i\n1 <= c_j, d_j <= N\nc_j \\neq d_j\nG does not contain multiple edges.\nT is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 d_1\n:\nc_M d_M\nTask Output: Print the final number of edges in G.\nTask Samples: input: 5 3\n1 2\n1 3\n3 4\n1 5\n5 4\n2 5\n1 5 output: 6\n\nWe can have at most six edges in G by adding edges as follows:\n\nLet (a,b,c)=(1,5,4) and add an edge connecting Vertex 1 and 4.\nLet (a,b,c)=(1,5,2) and add an edge connecting Vertex 1 and 2.\nLet (a,b,c)=(2,1,4) and add an edge connecting Vertex 2 and 4.\ninput: 7 5\n1 5\n1 4\n1 7\n1 2\n2 6\n6 3\n2 5\n1 3\n1 6\n4 6\n4 7 output: 11\ninput: 13 11\n6 13\n1 2\n5 1\n8 4\n9 7\n12 2\n10 11\n1 9\n13 7\n13 11\n8 10\n3 8\n4 13\n8 12\n4 7\n2 3\n5 11\n1 4\n2 11\n8 10\n3 5\n6 9\n4 10 output: 27\n\n" }, { "title": "", "content": "Problem Statement A biscuit making machine produces B biscuits at the following moments: A seconds, 2A seconds, 3A seconds and each subsequent multiple of A seconds after activation.\nFind the total number of biscuits produced within T + 0.5 seconds after activation.", "constraint": "All values in input are integers.\n1 <= A, B, T <= 20", "input": "Input is given from Standard Input in the following format:\nA B T", "output": "Print the total number of biscuits produced within T + 0.5 seconds after activation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 7 output: 10\nFive biscuits will be produced three seconds after activation.\nAnother five biscuits will be produced six seconds after activation.\nThus, a total of ten biscuits will be produced within 7.5 seconds after activation.", "input: 3 2 9 output: 6", "input: 20 20 19 output: 0"], "Pid": "p03059", "ProblemText": "Task Description: Problem Statement A biscuit making machine produces B biscuits at the following moments: A seconds, 2A seconds, 3A seconds and each subsequent multiple of A seconds after activation.\nFind the total number of biscuits produced within T + 0.5 seconds after activation.\nTask Constraint: All values in input are integers.\n1 <= A, B, T <= 20\nTask Input: Input is given from Standard Input in the following format:\nA B T\nTask Output: Print the total number of biscuits produced within T + 0.5 seconds after activation.\nTask Samples: input: 3 5 7 output: 10\nFive biscuits will be produced three seconds after activation.\nAnother five biscuits will be produced six seconds after activation.\nThus, a total of ten biscuits will be produced within 7.5 seconds after activation.\ninput: 3 2 9 output: 6\ninput: 20 20 19 output: 0\n\n" }, { "title": "", "content": "Problem Statement There are N gems. The value of the i-th gem is V_i.\nYou will choose some of these gems, possibly all or none, and get them.\nHowever, you need to pay a cost of C_i to get the i-th gem.\nLet X be the sum of the values of the gems obtained, and Y be the sum of the costs paid.\nFind the maximum possible value of X-Y.", "constraint": "All values in input are integers.\n1 <= N <= 20\n1 <= C_i, V_i <= 50", "input": "Input is given from Standard Input in the following format:\nN\nV_1 V_2 . . . V_N\nC_1 C_2 . . . C_N", "output": "Print the maximum possible value of X-Y.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10 2 5\n6 3 4 output: 5\n\nIf we choose the first and third gems, X = 10 + 5 = 15 and Y = 6 + 4 = 10.\nWe have X-Y = 5 here, which is the maximum possible value.", "input: 4\n13 21 6 19\n11 30 6 15 output: 6", "input: 1\n1\n50 output: 0"], "Pid": "p03060", "ProblemText": "Task Description: Problem Statement There are N gems. The value of the i-th gem is V_i.\nYou will choose some of these gems, possibly all or none, and get them.\nHowever, you need to pay a cost of C_i to get the i-th gem.\nLet X be the sum of the values of the gems obtained, and Y be the sum of the costs paid.\nFind the maximum possible value of X-Y.\nTask Constraint: All values in input are integers.\n1 <= N <= 20\n1 <= C_i, V_i <= 50\nTask Input: Input is given from Standard Input in the following format:\nN\nV_1 V_2 . . . V_N\nC_1 C_2 . . . C_N\nTask Output: Print the maximum possible value of X-Y.\nTask Samples: input: 3\n10 2 5\n6 3 4 output: 5\n\nIf we choose the first and third gems, X = 10 + 5 = 15 and Y = 6 + 4 = 10.\nWe have X-Y = 5 here, which is the maximum possible value.\ninput: 4\n13 21 6 19\n11 30 6 15 output: 6\ninput: 1\n1\n50 output: 0\n\n" }, { "title": "", "content": "Problem Statement There are N integers, A_1, A_2, . . . , A_N, written on the blackboard.\nYou will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.\nFind the maximum possible greatest common divisor of the N integers on the blackboard after your move.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n7 6 8 output: 2\n\nIf we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.", "input: 3\n12 15 18 output: 6", "input: 2\n1000000000 1000000000 output: 1000000000\n\nWe can replace an integer with itself."], "Pid": "p03061", "ProblemText": "Task Description: Problem Statement There are N integers, A_1, A_2, . . . , A_N, written on the blackboard.\nYou will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.\nFind the maximum possible greatest common divisor of the N integers on the blackboard after your move.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.\nTask Samples: input: 3\n7 6 8 output: 2\n\nIf we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.\ninput: 3\n12 15 18 output: 6\ninput: 2\n1000000000 1000000000 output: 1000000000\n\nWe can replace an integer with itself.\n\n" }, { "title": "", "content": "Problem Statement There are N integers, A_1, A_2, . . . , A_N, arranged in a row in this order.\nYou can perform the following operation on this integer sequence any number of times:\nOperation: Choose an integer i satisfying 1 <= i <= N-1. Multiply both A_i and A_{i+1} by -1.\nLet B_1, B_2, . . . , B_N be the integer sequence after your operations.\nFind the maximum possible value of B_1 + B_2 + . . . + B_N.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n-10^9 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum possible value of B_1 + B_2 + . . . + B_N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-10 5 -4 output: 19\n\nIf we perform the operation as follows:\n\nChoose 1 as i, which changes the sequence to 10, -5, -4.\nChoose 2 as i, which changes the sequence to 10,5,4.\n\nwe have B_1 = 10, B_2 = 5, B_3 = 4. The sum here, B_1 + B_2 + B_3 = 10 + 5 + 4 = 19, is the maximum possible result.", "input: 5\n10 -4 -8 -11 3 output: 30", "input: 11\n-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000 output: 10000000000\n\nThe output may not fit into a 32-bit integer type."], "Pid": "p03062", "ProblemText": "Task Description: Problem Statement There are N integers, A_1, A_2, . . . , A_N, arranged in a row in this order.\nYou can perform the following operation on this integer sequence any number of times:\nOperation: Choose an integer i satisfying 1 <= i <= N-1. Multiply both A_i and A_{i+1} by -1.\nLet B_1, B_2, . . . , B_N be the integer sequence after your operations.\nFind the maximum possible value of B_1 + B_2 + . . . + B_N.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n-10^9 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum possible value of B_1 + B_2 + . . . + B_N.\nTask Samples: input: 3\n-10 5 -4 output: 19\n\nIf we perform the operation as follows:\n\nChoose 1 as i, which changes the sequence to 10, -5, -4.\nChoose 2 as i, which changes the sequence to 10,5,4.\n\nwe have B_1 = 10, B_2 = 5, B_3 = 4. The sum here, B_1 + B_2 + B_3 = 10 + 5 + 4 = 19, is the maximum possible result.\ninput: 5\n10 -4 -8 -11 3 output: 30\ninput: 11\n-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000 output: 10000000000\n\nThe output may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement There are N stones arranged in a row. Every stone is painted white or black.\nA string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is . , and the stone is black if the character is #.\nTakahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone.\nFind the minimum number of stones that needs to be recolored.", "constraint": "1 <= N <= 2* 10^5\nS is a string of length N consisting of . and #.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the minimum number of stones that needs to be recolored.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n#.# output: 1\n\nIt is enough to change the color of the first stone to white.", "input: 5\n#.##. output: 2", "input: 9\n......... output: 0"], "Pid": "p03063", "ProblemText": "Task Description: Problem Statement There are N stones arranged in a row. Every stone is painted white or black.\nA string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is . , and the stone is black if the character is #.\nTakahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone.\nFind the minimum number of stones that needs to be recolored.\nTask Constraint: 1 <= N <= 2* 10^5\nS is a string of length N consisting of . and #.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the minimum number of stones that needs to be recolored.\nTask Samples: input: 3\n#.# output: 1\n\nIt is enough to change the color of the first stone to white.\ninput: 5\n#.##. output: 2\ninput: 9\n......... output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given N integers. The i-th integer is a_i.\nFind the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the following condition is satisfied:\n\nLet R, G and B be the sums of the integers painted red, green and blue, respectively. There exists a triangle with positive area whose sides have lengths R, G and B.", "constraint": "3 <= N <= 300\n1 <= a_i <= 300(1<= i<= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1\n:\na_N", "output": "Print the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the condition is satisfied.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1\n1\n1\n2 output: 18\n\nWe can only paint the integers so that the lengths of the sides of the triangle will be 1,2 and 2, and there are 18 such ways.", "input: 6\n1\n3\n2\n3\n5\n2 output: 150", "input: 20\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3\n5\n8\n9\n7\n9\n3\n2\n3\n8\n4 output: 563038556"], "Pid": "p03064", "ProblemText": "Task Description: Problem Statement You are given N integers. The i-th integer is a_i.\nFind the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the following condition is satisfied:\n\nLet R, G and B be the sums of the integers painted red, green and blue, respectively. There exists a triangle with positive area whose sides have lengths R, G and B.\nTask Constraint: 3 <= N <= 300\n1 <= a_i <= 300(1<= i<= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nTask Output: Print the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the condition is satisfied.\nTask Samples: input: 4\n1\n1\n1\n2 output: 18\n\nWe can only paint the integers so that the lengths of the sides of the triangle will be 1,2 and 2, and there are 18 such ways.\ninput: 6\n1\n3\n2\n3\n5\n2 output: 150\ninput: 20\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3\n5\n8\n9\n7\n9\n3\n2\n3\n8\n4 output: 563038556\n\n" }, { "title": "", "content": "Problem Statement You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+. . . +a_0. Find all prime numbers p that divide f(x) for every integer x.", "constraint": "0 <= N <= 10^4\n|a_i| <= 10^9(0<= i<= N)\na_N \\neq 0\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_N\n:\na_0", "output": "Print all prime numbers p that divide f(x) for every integer x, in ascending order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n7\n-7\n14 output: 2\n7\n\n2 and 7 divide, for example, f(1)=14 and f(2)=28.", "input: 3\n1\n4\n1\n5 output: There may be no integers that satisfy the condition.", "input: 0\n998244353 output: 998244353"], "Pid": "p03065", "ProblemText": "Task Description: Problem Statement You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+. . . +a_0. Find all prime numbers p that divide f(x) for every integer x.\nTask Constraint: 0 <= N <= 10^4\n|a_i| <= 10^9(0<= i<= N)\na_N \\neq 0\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_N\n:\na_0\nTask Output: Print all prime numbers p that divide f(x) for every integer x, in ascending order.\nTask Samples: input: 2\n7\n-7\n14 output: 2\n7\n\n2 and 7 divide, for example, f(1)=14 and f(2)=28.\ninput: 3\n1\n4\n1\n5 output: There may be no integers that satisfy the condition.\ninput: 0\n998244353 output: 998244353\n\n" }, { "title": "", "content": "Problem Statement Find the number, modulo 998244353, of sequences of length N consisting of 0,1 and 2 such that none of their contiguous subsequences totals to X.", "constraint": "1 <= N <= 3000\n1 <= X <= 2N\nN and X are integers.", "input": "Input is given from Standard Input in the following format:\nN X", "output": "Print the number, modulo 998244353, of sequences that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 output: 14\n\n14 sequences satisfy the condition: (0,0,0),(0,0,1),(0,0,2),(0,1,0),(0,1,1),(0,2,0),(0,2,2),(1,0,0),(1,0,1),(1,1,0),(2,0,0),(2,0,2),(2,2,0) and (2,2,2).", "input: 8 6 output: 1179", "input: 10 1 output: 1024", "input: 9 13 output: 18402", "input: 314 159 output: 459765451"], "Pid": "p03066", "ProblemText": "Task Description: Problem Statement Find the number, modulo 998244353, of sequences of length N consisting of 0,1 and 2 such that none of their contiguous subsequences totals to X.\nTask Constraint: 1 <= N <= 3000\n1 <= X <= 2N\nN and X are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X\nTask Output: Print the number, modulo 998244353, of sequences that satisfy the condition.\nTask Samples: input: 3 3 output: 14\n\n14 sequences satisfy the condition: (0,0,0),(0,0,1),(0,0,2),(0,1,0),(0,1,1),(0,2,0),(0,2,2),(1,0,0),(1,0,1),(1,1,0),(2,0,0),(2,0,2),(2,2,0) and (2,2,2).\ninput: 8 6 output: 1179\ninput: 10 1 output: 1024\ninput: 9 13 output: 18402\ninput: 314 159 output: 459765451\n\n" }, { "title": "", "content": "Problem Statement There are three houses on a number line: House 1,2 and 3, with coordinates A, B and C, respectively.\nPrint Yes if we pass the coordinate of House 3 on the straight way from House 1 to House 2 without making a detour, and print No otherwise.", "constraint": "0<= A,B,C<= 100\nA, B and C are distinct integers.", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "Print Yes if we pass the coordinate of House 3 on the straight way from House 1 to House 2 without making a detour, and print No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 8 5 output: Yes\n\nWe pass the coordinate 5 on the straight way from the house at coordinate 3 to the house at coordinate 8.", "input: 7 3 1 output: No", "input: 10 2 4 output: Yes", "input: 31 41 59 output: No"], "Pid": "p03067", "ProblemText": "Task Description: Problem Statement There are three houses on a number line: House 1,2 and 3, with coordinates A, B and C, respectively.\nPrint Yes if we pass the coordinate of House 3 on the straight way from House 1 to House 2 without making a detour, and print No otherwise.\nTask Constraint: 0<= A,B,C<= 100\nA, B and C are distinct integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: Print Yes if we pass the coordinate of House 3 on the straight way from House 1 to House 2 without making a detour, and print No otherwise.\nTask Samples: input: 3 8 5 output: Yes\n\nWe pass the coordinate 5 on the straight way from the house at coordinate 3 to the house at coordinate 8.\ninput: 7 3 1 output: No\ninput: 10 2 4 output: Yes\ninput: 31 41 59 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N consisting of lowercase English letters, and an integer K.\nPrint the string obtained by replacing every character in S that differs from the K-th character of S, with *.", "constraint": "1 <= K <= N<= 10\nS is a string of length N consisting of lowercase English letters.\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nN\nS\nK", "output": "Print the string obtained by replacing every character in S that differs from the K-th character of S, with *.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nerror\n2 output: *rr*r\n\nThe second character of S is r. When we replace every character in error that differs from r with *, we get the string *rr*r.", "input: 6\neleven\n5 output: e*e*e*", "input: 9\neducation\n7 output: ******i**"], "Pid": "p03068", "ProblemText": "Task Description: Problem Statement You are given a string S of length N consisting of lowercase English letters, and an integer K.\nPrint the string obtained by replacing every character in S that differs from the K-th character of S, with *.\nTask Constraint: 1 <= K <= N<= 10\nS is a string of length N consisting of lowercase English letters.\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nK\nTask Output: Print the string obtained by replacing every character in S that differs from the K-th character of S, with *.\nTask Samples: input: 5\nerror\n2 output: *rr*r\n\nThe second character of S is r. When we replace every character in error that differs from r with *, we get the string *rr*r.\ninput: 6\neleven\n5 output: e*e*e*\ninput: 9\neducation\n7 output: ******i**\n\n" }, { "title": "", "content": "Problem Statement There are N stones arranged in a row. Every stone is painted white or black.\nA string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is . , and the stone is black if the character is #.\nTakahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone.\nFind the minimum number of stones that needs to be recolored.", "constraint": "1 <= N <= 2* 10^5\nS is a string of length N consisting of . and #.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the minimum number of stones that needs to be recolored.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n#.# output: 1\n\nIt is enough to change the color of the first stone to white.", "input: 5\n#.##. output: 2", "input: 9\n......... output: 0"], "Pid": "p03069", "ProblemText": "Task Description: Problem Statement There are N stones arranged in a row. Every stone is painted white or black.\nA string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is . , and the stone is black if the character is #.\nTakahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone.\nFind the minimum number of stones that needs to be recolored.\nTask Constraint: 1 <= N <= 2* 10^5\nS is a string of length N consisting of . and #.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the minimum number of stones that needs to be recolored.\nTask Samples: input: 3\n#.# output: 1\n\nIt is enough to change the color of the first stone to white.\ninput: 5\n#.##. output: 2\ninput: 9\n......... output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given N integers. The i-th integer is a_i.\nFind the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the following condition is satisfied:\n\nLet R, G and B be the sums of the integers painted red, green and blue, respectively. There exists a triangle with positive area whose sides have lengths R, G and B.", "constraint": "3 <= N <= 300\n1 <= a_i <= 300(1<= i<= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1\n:\na_N", "output": "Print the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the condition is satisfied.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1\n1\n1\n2 output: 18\n\nWe can only paint the integers so that the lengths of the sides of the triangle will be 1,2 and 2, and there are 18 such ways.", "input: 6\n1\n3\n2\n3\n5\n2 output: 150", "input: 20\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3\n5\n8\n9\n7\n9\n3\n2\n3\n8\n4 output: 563038556"], "Pid": "p03070", "ProblemText": "Task Description: Problem Statement You are given N integers. The i-th integer is a_i.\nFind the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the following condition is satisfied:\n\nLet R, G and B be the sums of the integers painted red, green and blue, respectively. There exists a triangle with positive area whose sides have lengths R, G and B.\nTask Constraint: 3 <= N <= 300\n1 <= a_i <= 300(1<= i<= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nTask Output: Print the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the condition is satisfied.\nTask Samples: input: 4\n1\n1\n1\n2 output: 18\n\nWe can only paint the integers so that the lengths of the sides of the triangle will be 1,2 and 2, and there are 18 such ways.\ninput: 6\n1\n3\n2\n3\n5\n2 output: 150\ninput: 20\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3\n5\n8\n9\n7\n9\n3\n2\n3\n8\n4 output: 563038556\n\n" }, { "title": "", "content": "Problem Statement There are two buttons, one of size A and one of size B.\nWhen you press a button of size X, you get X coins and the size of that button decreases by 1.\nYou will press a button twice. Here, you can press the same button twice, or press both buttons once.\nAt most how many coins can you get?", "constraint": "All values in input are integers.\n3 <= A, B <= 20", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the maximum number of coins you can get.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 output: 9\n\nYou can get 5 + 4 = 9 coins by pressing the button of size 5 twice, and this is the maximum result.", "input: 3 4 output: 7", "input: 6 6 output: 12"], "Pid": "p03071", "ProblemText": "Task Description: Problem Statement There are two buttons, one of size A and one of size B.\nWhen you press a button of size X, you get X coins and the size of that button decreases by 1.\nYou will press a button twice. Here, you can press the same button twice, or press both buttons once.\nAt most how many coins can you get?\nTask Constraint: All values in input are integers.\n3 <= A, B <= 20\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the maximum number of coins you can get.\nTask Samples: input: 5 3 output: 9\n\nYou can get 5 + 4 = 9 coins by pressing the button of size 5 twice, and this is the maximum result.\ninput: 3 4 output: 7\ninput: 6 6 output: 12\n\n" }, { "title": "", "content": "Problem Statement There are N mountains ranging from east to west, and an ocean to the west.\nAt the top of each mountain, there is an inn. You have decided to choose where to stay from these inns.\nThe height of the i-th mountain from the west is H_i.\nYou can certainly see the ocean from the inn at the top of the westmost mountain.\nFor the inn at the top of the i-th mountain from the west (i = 2,3, . . . , N), you can see the ocean if and only if H_1 <= H_i, H_2 <= H_i, . . . , and H_{i-1} <= H_i.\nFrom how many of these N inns can you see the ocean?", "constraint": "All values in input are integers.\n1 <= N <= 20\n1 <= H_i <= 100", "input": "Input is given from Standard Input in the following format:\nN\nH_1 H_2 . . . H_N", "output": "Print the number of inns from which you can see the ocean.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n6 5 6 8 output: 3\n\nYou can see the ocean from the first, third and fourth inns from the west.", "input: 5\n4 5 3 5 4 output: 3", "input: 5\n9 5 6 8 4 output: 1"], "Pid": "p03072", "ProblemText": "Task Description: Problem Statement There are N mountains ranging from east to west, and an ocean to the west.\nAt the top of each mountain, there is an inn. You have decided to choose where to stay from these inns.\nThe height of the i-th mountain from the west is H_i.\nYou can certainly see the ocean from the inn at the top of the westmost mountain.\nFor the inn at the top of the i-th mountain from the west (i = 2,3, . . . , N), you can see the ocean if and only if H_1 <= H_i, H_2 <= H_i, . . . , and H_{i-1} <= H_i.\nFrom how many of these N inns can you see the ocean?\nTask Constraint: All values in input are integers.\n1 <= N <= 20\n1 <= H_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nH_1 H_2 . . . H_N\nTask Output: Print the number of inns from which you can see the ocean.\nTask Samples: input: 4\n6 5 6 8 output: 3\n\nYou can see the ocean from the first, third and fourth inns from the west.\ninput: 5\n4 5 3 5 4 output: 3\ninput: 5\n9 5 6 8 4 output: 1\n\n" }, { "title": "", "content": "Problem Statement N tiles are arranged in a row from left to right. The initial color of each tile is represented by a string S of length N.\nThe i-th tile from the left is painted black if the i-th character of S is 0, and painted white if that character is 1.\nYou want to repaint some of the tiles black or white, so that any two adjacent tiles have different colors.\nAt least how many tiles need to be repainted to satisfy the condition?", "constraint": "1 <= |S| <= 10^5\nS_i is 0 or 1.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the minimum number of tiles that need to be repainted to satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 000 output: 1\n\nThe condition can be satisfied by repainting the middle tile white.", "input: 10010010 output: 3", "input: 0 output: 0"], "Pid": "p03073", "ProblemText": "Task Description: Problem Statement N tiles are arranged in a row from left to right. The initial color of each tile is represented by a string S of length N.\nThe i-th tile from the left is painted black if the i-th character of S is 0, and painted white if that character is 1.\nYou want to repaint some of the tiles black or white, so that any two adjacent tiles have different colors.\nAt least how many tiles need to be repainted to satisfy the condition?\nTask Constraint: 1 <= |S| <= 10^5\nS_i is 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the minimum number of tiles that need to be repainted to satisfy the condition.\nTask Samples: input: 000 output: 1\n\nThe condition can be satisfied by repainting the middle tile white.\ninput: 10010010 output: 3\ninput: 0 output: 0\n\n" }, { "title": "", "content": "Problem Statement N people are arranged in a row from left to right.\nYou are given a string S of length N consisting of 0 and 1, and a positive integer K.\nThe i-th person from the left is standing on feet if the i-th character of S is 0, and standing on hands if that character is 1.\nYou will give the following direction at most K times (possibly zero):\nDirection: Choose integers l and r satisfying 1 <= l <= r <= N, and flip the l-th, (l+1)-th, . . . , and r-th persons. That is, for each i = l, l+1, . . . , r, the i-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.\nFind the maximum possible number of consecutive people standing on hands after at most K directions.", "constraint": "N is an integer satisfying 1 <= N <= 10^5.\nK is an integer satisfying 1 <= K <= 10^5.\nThe length of the string S is N.\nEach character of the string S is 0 or 1.", "input": "Input is given from Standard Input in the following format:\nN K\nS", "output": "Print the maximum possible number of consecutive people standing on hands after at most K directions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1\n00010 output: 4\n\nWe can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:\n\nGive the direction with l = 1, r = 3, which flips the first, second and third persons from the left.", "input: 14 2\n11101010110011 output: 8", "input: 1 1\n1 output: 1\n\nNo directions are necessary."], "Pid": "p03074", "ProblemText": "Task Description: Problem Statement N people are arranged in a row from left to right.\nYou are given a string S of length N consisting of 0 and 1, and a positive integer K.\nThe i-th person from the left is standing on feet if the i-th character of S is 0, and standing on hands if that character is 1.\nYou will give the following direction at most K times (possibly zero):\nDirection: Choose integers l and r satisfying 1 <= l <= r <= N, and flip the l-th, (l+1)-th, . . . , and r-th persons. That is, for each i = l, l+1, . . . , r, the i-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.\nFind the maximum possible number of consecutive people standing on hands after at most K directions.\nTask Constraint: N is an integer satisfying 1 <= N <= 10^5.\nK is an integer satisfying 1 <= K <= 10^5.\nThe length of the string S is N.\nEach character of the string S is 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nN K\nS\nTask Output: Print the maximum possible number of consecutive people standing on hands after at most K directions.\nTask Samples: input: 5 1\n00010 output: 4\n\nWe can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:\n\nGive the direction with l = 1, r = 3, which flips the first, second and third persons from the left.\ninput: 14 2\n11101010110011 output: 8\ninput: 1 1\n1 output: 1\n\nNo directions are necessary.\n\n" }, { "title": "", "content": "Problem Statement\nIn At Coder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.\nTwo antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.\nDetermine if there exists a pair of antennas that cannot communicate directly.\nHere, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.", "constraint": "a, b, c, d, e and k are integers between 0 and 123 (inclusive).\na < b < c < d < e", "input": "Input is given from Standard Input in the following format:\na\nb\nc\nd\ne\nk", "output": "Print : ( if there exists a pair of antennas that cannot communicate directly, and print Yay! if there is no such pair.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n2\n4\n8\n9\n15 output: Yay!\n\nIn this case, there is no pair of antennas that cannot communicate directly, because:\n\nthe distance between A and B is 2 - 1 = 1\nthe distance between A and C is 4 - 1 = 3\nthe distance between A and D is 8 - 1 = 7\nthe distance between A and E is 9 - 1 = 8\nthe distance between B and C is 4 - 2 = 2\nthe distance between B and D is 8 - 2 = 6\nthe distance between B and E is 9 - 2 = 7\nthe distance between C and D is 8 - 4 = 4\nthe distance between C and E is 9 - 4 = 5\nthe distance between D and E is 9 - 8 = 1\n\nand none of them is greater than 15. Thus, the correct output is Yay!.", "input: 15\n18\n26\n35\n36\n18 output: :(\n\nIn this case, the distance between antennas A and D is 35 - 15 = 20 and exceeds 18, so they cannot communicate directly.\nThus, the correct output is :(."], "Pid": "p03075", "ProblemText": "Task Description: Problem Statement\nIn At Coder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.\nTwo antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.\nDetermine if there exists a pair of antennas that cannot communicate directly.\nHere, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.\nTask Constraint: a, b, c, d, e and k are integers between 0 and 123 (inclusive).\na < b < c < d < e\nTask Input: Input is given from Standard Input in the following format:\na\nb\nc\nd\ne\nk\nTask Output: Print : ( if there exists a pair of antennas that cannot communicate directly, and print Yay! if there is no such pair.\nTask Samples: input: 1\n2\n4\n8\n9\n15 output: Yay!\n\nIn this case, there is no pair of antennas that cannot communicate directly, because:\n\nthe distance between A and B is 2 - 1 = 1\nthe distance between A and C is 4 - 1 = 3\nthe distance between A and D is 8 - 1 = 7\nthe distance between A and E is 9 - 1 = 8\nthe distance between B and C is 4 - 2 = 2\nthe distance between B and D is 8 - 2 = 6\nthe distance between B and E is 9 - 2 = 7\nthe distance between C and D is 8 - 4 = 4\nthe distance between C and E is 9 - 4 = 5\nthe distance between D and E is 9 - 8 = 1\n\nand none of them is greater than 15. Thus, the correct output is Yay!.\ninput: 15\n18\n26\n35\n36\n18 output: :(\n\nIn this case, the distance between antennas A and D is 35 - 15 = 20 and exceeds 18, so they cannot communicate directly.\nThus, the correct output is :(.\n\n" }, { "title": "", "content": "Problem Statement\nThe restaurant At Coder serves the following five dishes:\n\nABC Don (rice bowl): takes A minutes to serve.\nARC Curry: takes B minutes to serve.\nAGC Pasta: takes C minutes to serve.\nAPC Ramen: takes D minutes to serve.\nATC Hanbagu (hamburger patty): takes E minutes to serve.\n\nHere, the time to serve a dish is the time between when an order is placed and when the dish is delivered.\nThis restaurant has the following rules on orders:\n\nAn order can only be placed at a time that is a multiple of 10 (time 0,10,20, . . . ).\nOnly one dish can be ordered at a time.\nNo new order can be placed when an order is already placed and the dish is still not delivered, but a new order can be placed at the exact time when the dish is delivered.\n\nE869120 arrives at this restaurant at time 0. He will order all five dishes. Find the earliest possible time for the last dish to be delivered.\nHere, he can order the dishes in any order he likes, and he can place an order already at time 0.", "constraint": "A, B, C, D and E are integers between 1 and 123 (inclusive).", "input": "Input is given from Standard Input in the following format:\nA\nB\nC\nD\nE", "output": "Print the earliest possible time for the last dish to be delivered, as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 29\n20\n7\n35\n120 output: 215\n\nIf we decide to order the dishes in the order ABC Don, ARC Curry, AGC Pasta, ATC Hanbagu, APC Ramen, the earliest possible time for each order is as follows:\n\nOrder ABC Don at time 0, which will be delivered at time 29.\nOrder ARC Curry at time 30, which will be delivered at time 50.\nOrder AGC Pasta at time 50, which will be delivered at time 57.\nOrder ATC Hanbagu at time 60, which will be delivered at time 180.\nOrder APC Ramen at time 180, which will be delivered at time 215.\n\nThere is no way to order the dishes in which the last dish will be delivered earlier than this.", "input: 101\n86\n119\n108\n57 output: 481\n\nIf we decide to order the dishes in the order AGC Pasta, ARC Curry, ATC Hanbagu, APC Ramen, ABC Don, the earliest possible time for each order is as follows:\n\nOrder AGC Pasta at time 0, which will be delivered at time 119.\nOrder ARC Curry at time 120, which will be delivered at time 206.\nOrder ATC Hanbagu at time 210, which will be delivered at time 267.\nOrder APC Ramen at time 270, which will be delivered at time 378.\nOrder ABC Don at time 380, which will be delivered at time 481.\n\nThere is no way to order the dishes in which the last dish will be delivered earlier than this.", "input: 123\n123\n123\n123\n123 output: 643\n\nThis is the largest valid case."], "Pid": "p03076", "ProblemText": "Task Description: Problem Statement\nThe restaurant At Coder serves the following five dishes:\n\nABC Don (rice bowl): takes A minutes to serve.\nARC Curry: takes B minutes to serve.\nAGC Pasta: takes C minutes to serve.\nAPC Ramen: takes D minutes to serve.\nATC Hanbagu (hamburger patty): takes E minutes to serve.\n\nHere, the time to serve a dish is the time between when an order is placed and when the dish is delivered.\nThis restaurant has the following rules on orders:\n\nAn order can only be placed at a time that is a multiple of 10 (time 0,10,20, . . . ).\nOnly one dish can be ordered at a time.\nNo new order can be placed when an order is already placed and the dish is still not delivered, but a new order can be placed at the exact time when the dish is delivered.\n\nE869120 arrives at this restaurant at time 0. He will order all five dishes. Find the earliest possible time for the last dish to be delivered.\nHere, he can order the dishes in any order he likes, and he can place an order already at time 0.\nTask Constraint: A, B, C, D and E are integers between 1 and 123 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nA\nB\nC\nD\nE\nTask Output: Print the earliest possible time for the last dish to be delivered, as an integer.\nTask Samples: input: 29\n20\n7\n35\n120 output: 215\n\nIf we decide to order the dishes in the order ABC Don, ARC Curry, AGC Pasta, ATC Hanbagu, APC Ramen, the earliest possible time for each order is as follows:\n\nOrder ABC Don at time 0, which will be delivered at time 29.\nOrder ARC Curry at time 30, which will be delivered at time 50.\nOrder AGC Pasta at time 50, which will be delivered at time 57.\nOrder ATC Hanbagu at time 60, which will be delivered at time 180.\nOrder APC Ramen at time 180, which will be delivered at time 215.\n\nThere is no way to order the dishes in which the last dish will be delivered earlier than this.\ninput: 101\n86\n119\n108\n57 output: 481\n\nIf we decide to order the dishes in the order AGC Pasta, ARC Curry, ATC Hanbagu, APC Ramen, ABC Don, the earliest possible time for each order is as follows:\n\nOrder AGC Pasta at time 0, which will be delivered at time 119.\nOrder ARC Curry at time 120, which will be delivered at time 206.\nOrder ATC Hanbagu at time 210, which will be delivered at time 267.\nOrder APC Ramen at time 270, which will be delivered at time 378.\nOrder ABC Don at time 380, which will be delivered at time 481.\n\nThere is no way to order the dishes in which the last dish will be delivered earlier than this.\ninput: 123\n123\n123\n123\n123 output: 643\n\nThis is the largest valid case.\n\n" }, { "title": "", "content": "Problem Statement\nIn 2028 and after a continuous growth, At Coder Inc. finally built an empire with six cities (City 1,2,3,4,5,6)!\nThere are five means of transport in this empire:\n\nTrain: travels from City 1 to 2 in one minute. A train can occupy at most A people.\nBus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.\nTaxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.\nAirplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.\nShip: travels from City 5 to 6 in one minute. A ship can occupy at most E people.\n\nFor each of them, one vehicle leaves the city at each integer time (time 0,1,2, . . . ).\nThere is a group of N people at City 1, and they all want to go to City 6.\nAt least how long does it take for all of them to reach there? \nYou can ignore the time needed to transfer.", "constraint": "1 <= N, A, B, C, D, E <= 10^{15}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA\nB\nC\nD\nE", "output": "Print the minimum time required for all of the people to reach City 6, in minutes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3\n2\n4\n3\n5 output: 7\n\nOne possible way to travel is as follows.\nFirst, there are N = 5 people at City 1, as shown in the following image:\n\nIn the first minute, three people travels from City 1 to City 2 by train. Note that a train can only occupy at most three people.\n\nIn the second minute, the remaining two people travels from City 1 to City 2 by train, and two of the three people who were already at City 2 travels to City 3 by bus. Note that a bus can only occupy at most two people.\n\nIn the third minute, two people travels from City 2 to City 3 by train, and another two people travels from City 3 to City 4 by taxi.\n\nFrom then on, if they continue traveling without stopping until they reach City 6, all of them can reach there in seven minutes.\nThere is no way for them to reach City 6 in 6 minutes or less.", "input: 10\n123\n123\n123\n123\n123 output: 5\n\nAll kinds of vehicles can occupy N = 10 people at a time.\nThus, if they continue traveling without stopping until they reach City 6, all of them can reach there in five minutes.", "input: 10000000007\n2\n3\n5\n7\n11 output: 5000000008\n\nNote that the input or output may not fit into a 32-bit integer type."], "Pid": "p03077", "ProblemText": "Task Description: Problem Statement\nIn 2028 and after a continuous growth, At Coder Inc. finally built an empire with six cities (City 1,2,3,4,5,6)!\nThere are five means of transport in this empire:\n\nTrain: travels from City 1 to 2 in one minute. A train can occupy at most A people.\nBus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.\nTaxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.\nAirplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.\nShip: travels from City 5 to 6 in one minute. A ship can occupy at most E people.\n\nFor each of them, one vehicle leaves the city at each integer time (time 0,1,2, . . . ).\nThere is a group of N people at City 1, and they all want to go to City 6.\nAt least how long does it take for all of them to reach there? \nYou can ignore the time needed to transfer.\nTask Constraint: 1 <= N, A, B, C, D, E <= 10^{15}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA\nB\nC\nD\nE\nTask Output: Print the minimum time required for all of the people to reach City 6, in minutes.\nTask Samples: input: 5\n3\n2\n4\n3\n5 output: 7\n\nOne possible way to travel is as follows.\nFirst, there are N = 5 people at City 1, as shown in the following image:\n\nIn the first minute, three people travels from City 1 to City 2 by train. Note that a train can only occupy at most three people.\n\nIn the second minute, the remaining two people travels from City 1 to City 2 by train, and two of the three people who were already at City 2 travels to City 3 by bus. Note that a bus can only occupy at most two people.\n\nIn the third minute, two people travels from City 2 to City 3 by train, and another two people travels from City 3 to City 4 by taxi.\n\nFrom then on, if they continue traveling without stopping until they reach City 6, all of them can reach there in seven minutes.\nThere is no way for them to reach City 6 in 6 minutes or less.\ninput: 10\n123\n123\n123\n123\n123 output: 5\n\nAll kinds of vehicles can occupy N = 10 people at a time.\nThus, if they continue traveling without stopping until they reach City 6, all of them can reach there in five minutes.\ninput: 10000000007\n2\n3\n5\n7\n11 output: 5000000008\n\nNote that the input or output may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement\nThe Patisserie At Coder sells cakes with number-shaped candles.\nThere are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively.\nEach cake has an integer value called deliciousness, as follows:\n\nThe deliciousness of the cakes with 1-shaped candles are A_1, A_2, . . . , A_X.\nThe deliciousness of the cakes with 2-shaped candles are B_1, B_2, . . . , B_Y.\nThe deliciousness of the cakes with 3-shaped candles are C_1, C_2, . . . , C_Z.\n\nTakahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.\nThere are X * Y * Z such ways to choose three cakes.\nWe will arrange these X * Y * Z ways in descending order of the sum of the deliciousness of the cakes.\nPrint the sums of the deliciousness of the cakes for the first, second, . . . , K-th ways in this list.", "constraint": "1 <= X <= 1 \\ 000\n1 <= Y <= 1 \\ 000\n1 <= Z <= 1 \\ 000\n1 <= K <= \\min(3 \\ 000, X * Y * Z)\n1 <= A_i <= 10 \\ 000 \\ 000 \\ 000\n1 <= B_i <= 10 \\ 000 \\ 000 \\ 000\n1 <= C_i <= 10 \\ 000 \\ 000 \\ 000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX Y Z K\nA_1 \\ A_2 \\ A_3 \\ . . . \\ A_X\nB_1 \\ B_2 \\ B_3 \\ . . . \\ B_Y\nC_1 \\ C_2 \\ C_3 \\ . . . \\ C_Z", "output": "Print K lines. The i-th line should contain the i-th value stated in the problem statement.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 2 8\n4 6\n1 5\n3 8 output: 19\n17\n15\n14\n13\n12\n10\n8\n\nThere are 2 * 2 * 2 = 8 ways to choose three cakes, as shown below in descending order of the sum of the deliciousness of the cakes:\n\n(A_2, B_2, C_2): 6 + 5 + 8 = 19\n(A_1, B_2, C_2): 4 + 5 + 8 = 17\n(A_2, B_1, C_2): 6 + 1 + 8 = 15\n(A_2, B_2, C_1): 6 + 5 + 3 = 14\n(A_1, B_1, C_2): 4 + 1 + 8 = 13\n(A_1, B_2, C_1): 4 + 5 + 3 = 12\n(A_2, B_1, C_1): 6 + 1 + 3 = 10\n(A_1, B_1, C_1): 4 + 1 + 3 = 8", "input: 3 3 3 5\n1 10 100\n2 20 200\n1 10 100 output: 400\n310\n310\n301\n301\n\nThere may be multiple combinations of cakes with the same sum of the deliciousness. For example, in this test case, the sum of A_1, B_3, C_3 and the sum of A_3, B_3, C_1 are both 301.\nHowever, they are different ways of choosing cakes, so 301 occurs twice in the output.", "input: 10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736 output: 23379871545\n22444657051\n22302177772\n22095691512\n21667941469\n21366963278\n21287912315\n21279176669\n21160477018\n21085311041\n21059876163\n21017997739\n20703329561\n20702387965\n20590247696\n20383761436\n20343962175\n20254073196\n20210218542\n20150096547\n\nNote that the input or output may not fit into a 32-bit integer type."], "Pid": "p03078", "ProblemText": "Task Description: Problem Statement\nThe Patisserie At Coder sells cakes with number-shaped candles.\nThere are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively.\nEach cake has an integer value called deliciousness, as follows:\n\nThe deliciousness of the cakes with 1-shaped candles are A_1, A_2, . . . , A_X.\nThe deliciousness of the cakes with 2-shaped candles are B_1, B_2, . . . , B_Y.\nThe deliciousness of the cakes with 3-shaped candles are C_1, C_2, . . . , C_Z.\n\nTakahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.\nThere are X * Y * Z such ways to choose three cakes.\nWe will arrange these X * Y * Z ways in descending order of the sum of the deliciousness of the cakes.\nPrint the sums of the deliciousness of the cakes for the first, second, . . . , K-th ways in this list.\nTask Constraint: 1 <= X <= 1 \\ 000\n1 <= Y <= 1 \\ 000\n1 <= Z <= 1 \\ 000\n1 <= K <= \\min(3 \\ 000, X * Y * Z)\n1 <= A_i <= 10 \\ 000 \\ 000 \\ 000\n1 <= B_i <= 10 \\ 000 \\ 000 \\ 000\n1 <= C_i <= 10 \\ 000 \\ 000 \\ 000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y Z K\nA_1 \\ A_2 \\ A_3 \\ . . . \\ A_X\nB_1 \\ B_2 \\ B_3 \\ . . . \\ B_Y\nC_1 \\ C_2 \\ C_3 \\ . . . \\ C_Z\nTask Output: Print K lines. The i-th line should contain the i-th value stated in the problem statement.\nTask Samples: input: 2 2 2 8\n4 6\n1 5\n3 8 output: 19\n17\n15\n14\n13\n12\n10\n8\n\nThere are 2 * 2 * 2 = 8 ways to choose three cakes, as shown below in descending order of the sum of the deliciousness of the cakes:\n\n(A_2, B_2, C_2): 6 + 5 + 8 = 19\n(A_1, B_2, C_2): 4 + 5 + 8 = 17\n(A_2, B_1, C_2): 6 + 1 + 8 = 15\n(A_2, B_2, C_1): 6 + 5 + 3 = 14\n(A_1, B_1, C_2): 4 + 1 + 8 = 13\n(A_1, B_2, C_1): 4 + 5 + 3 = 12\n(A_2, B_1, C_1): 6 + 1 + 3 = 10\n(A_1, B_1, C_1): 4 + 1 + 3 = 8\ninput: 3 3 3 5\n1 10 100\n2 20 200\n1 10 100 output: 400\n310\n310\n301\n301\n\nThere may be multiple combinations of cakes with the same sum of the deliciousness. For example, in this test case, the sum of A_1, B_3, C_3 and the sum of A_3, B_3, C_1 are both 301.\nHowever, they are different ways of choosing cakes, so 301 occurs twice in the output.\ninput: 10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736 output: 23379871545\n22444657051\n22302177772\n22095691512\n21667941469\n21366963278\n21287912315\n21279176669\n21160477018\n21085311041\n21059876163\n21017997739\n20703329561\n20702387965\n20590247696\n20383761436\n20343962175\n20254073196\n20210218542\n20150096547\n\nNote that the input or output may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement\nYou are given three integers A, B and C.\nDetermine if there exists an equilateral triangle whose sides have lengths A, B and C.", "constraint": "All values in input are integers.\n1 <= A,B,C <= 100", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "If there exists an equilateral triangle whose sides have lengths A, B and C, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 2 output: Yes\nThere exists an equilateral triangle whose sides have lengths 2,2 and 2.", "input: 3 4 5 output: No\nThere is no equilateral triangle whose sides have lengths 3,4 and 5."], "Pid": "p03079", "ProblemText": "Task Description: Problem Statement\nYou are given three integers A, B and C.\nDetermine if there exists an equilateral triangle whose sides have lengths A, B and C.\nTask Constraint: All values in input are integers.\n1 <= A,B,C <= 100\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: If there exists an equilateral triangle whose sides have lengths A, B and C, print Yes; otherwise, print No.\nTask Samples: input: 2 2 2 output: Yes\nThere exists an equilateral triangle whose sides have lengths 2,2 and 2.\ninput: 3 4 5 output: No\nThere is no equilateral triangle whose sides have lengths 3,4 and 5.\n\n" }, { "title": "", "content": "Problem Statement\nThere are N people numbered 1 to N. Each person wears a red hat or a blue hat.\nYou are given a string s representing the colors of the people. Person i wears a red hat if s_i is R, and a blue hat if s_i is B.\nDetermine if there are more people wearing a red hat than people wearing a blue hat.", "constraint": "1 <= N <= 100\n|s| = N\ns_i is R or B.", "input": "Input is given from Standard Input in the following format:\nN\ns", "output": "If there are more people wearing a red hat than there are people wearing a blue hat, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nRRBR output: Yes\nThere are three people wearing a red hat, and one person wearing a blue hat.\nSince there are more people wearing a red hat than people wearing a blue hat, the answer is Yes.", "input: 4\nBRBR output: No\nThere are two people wearing a red hat, and two people wearing a blue hat.\nSince there are as many people wearing a red hat as people wearing a blue hat, the answer is No."], "Pid": "p03080", "ProblemText": "Task Description: Problem Statement\nThere are N people numbered 1 to N. Each person wears a red hat or a blue hat.\nYou are given a string s representing the colors of the people. Person i wears a red hat if s_i is R, and a blue hat if s_i is B.\nDetermine if there are more people wearing a red hat than people wearing a blue hat.\nTask Constraint: 1 <= N <= 100\n|s| = N\ns_i is R or B.\nTask Input: Input is given from Standard Input in the following format:\nN\ns\nTask Output: If there are more people wearing a red hat than there are people wearing a blue hat, print Yes; otherwise, print No.\nTask Samples: input: 4\nRRBR output: Yes\nThere are three people wearing a red hat, and one person wearing a blue hat.\nSince there are more people wearing a red hat than people wearing a blue hat, the answer is Yes.\ninput: 4\nBRBR output: No\nThere are two people wearing a red hat, and two people wearing a blue hat.\nSince there are as many people wearing a red hat as people wearing a blue hat, the answer is No.\n\n" }, { "title": "", "content": "Problem Statement\nThere are N squares numbered 1 to N from left to right.\nEach square has a character written on it, and Square i has a letter s_i. Besides, there is initially one golem on each square.\nSnuke cast Q spells to move the golems.\nThe i-th spell consisted of two characters t_i and d_i, where d_i is L or R.\nWhen Snuke cast this spell, for each square with the character t_i, all golems on that square moved to the square adjacent to the left if d_i is L, and moved to the square adjacent to the right if d_i is R.\nHowever, when a golem tried to move left from Square 1 or move right from Square N, it disappeared.\nFind the number of golems remaining after Snuke cast the Q spells.", "constraint": "1 <= N,Q <= 2 * 10^{5}\n|s| = N\ns_i and t_i are uppercase English letters.\nd_i is L or R.", "input": "Input is given from Standard Input in the following format:\nN Q\ns\nt_1 d_1\n\\vdots\nt_{Q} d_Q", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\nABC\nA L\nB L\nB R\nA R output: 2\nInitially, there is one golem on each square.\nIn the first spell, the golem on Square 1 tries to move left and disappears.\nIn the second spell, the golem on Square 2 moves left.\nIn the third spell, no golem moves.\nIn the fourth spell, the golem on Square 1 moves right.\nAfter the four spells are cast, there is one golem on Square 2 and one golem on Square 3, for a total of two golems remaining.", "input: 8 3\nAABCBDBA\nA L\nB R\nA R output: 5\nAfter the three spells are cast, there is one golem on Square 2, two golems on Square 4 and two golems on Square 6, for a total of five golems remaining.\nNote that a single spell may move multiple golems.", "input: 10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nS L output: 3"], "Pid": "p03081", "ProblemText": "Task Description: Problem Statement\nThere are N squares numbered 1 to N from left to right.\nEach square has a character written on it, and Square i has a letter s_i. Besides, there is initially one golem on each square.\nSnuke cast Q spells to move the golems.\nThe i-th spell consisted of two characters t_i and d_i, where d_i is L or R.\nWhen Snuke cast this spell, for each square with the character t_i, all golems on that square moved to the square adjacent to the left if d_i is L, and moved to the square adjacent to the right if d_i is R.\nHowever, when a golem tried to move left from Square 1 or move right from Square N, it disappeared.\nFind the number of golems remaining after Snuke cast the Q spells.\nTask Constraint: 1 <= N,Q <= 2 * 10^{5}\n|s| = N\ns_i and t_i are uppercase English letters.\nd_i is L or R.\nTask Input: Input is given from Standard Input in the following format:\nN Q\ns\nt_1 d_1\n\\vdots\nt_{Q} d_Q\nTask Output: Print the answer.\nTask Samples: input: 3 4\nABC\nA L\nB L\nB R\nA R output: 2\nInitially, there is one golem on each square.\nIn the first spell, the golem on Square 1 tries to move left and disappears.\nIn the second spell, the golem on Square 2 moves left.\nIn the third spell, no golem moves.\nIn the fourth spell, the golem on Square 1 moves right.\nAfter the four spells are cast, there is one golem on Square 2 and one golem on Square 3, for a total of two golems remaining.\ninput: 8 3\nAABCBDBA\nA L\nB R\nA R output: 5\nAfter the three spells are cast, there is one golem on Square 2, two golems on Square 4 and two golems on Square 6, for a total of five golems remaining.\nNote that a single spell may move multiple golems.\ninput: 10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nS L output: 3\n\n" }, { "title": "", "content": "Problem Statement\nSnuke has a blackboard and a set S consisting of N integers.\nThe i-th element in S is S_i.\nHe wrote an integer X on the blackboard, then performed the following operation N times:\n\nChoose one element from S and remove it.\nLet x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \\bmod {y}.\n\nThere are N! possible orders in which the elements are removed from S.\nFor each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.", "constraint": "All values in input are integers.\n1 <= N <= 200\n1 <= S_i, X <= 10^{5}\nS_i are pairwise distinct.", "input": "Input is given from Standard Input in the following format:\nN X\nS_1 S_2 \\ldots S_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 19\n3 7 output: 3\nThere are two possible orders in which we remove the numbers from S.\nIf we remove 3 and 7 in this order, the number on the blackboard changes as follows: 19 \\rightarrow 1 \\rightarrow 1.\nIf we remove 7 and 3 in this order, the number on the blackboard changes as follows: 19 \\rightarrow 5 \\rightarrow 2.\nThe output should be the sum of these: 3.", "input: 5 82\n22 11 6 5 13 output: 288", "input: 10 100000\n50000 50001 50002 50003 50004 50005 50006 50007 50008 50009 output: 279669259\nBe sure to compute the sum modulo 10^{9}+7."], "Pid": "p03082", "ProblemText": "Task Description: Problem Statement\nSnuke has a blackboard and a set S consisting of N integers.\nThe i-th element in S is S_i.\nHe wrote an integer X on the blackboard, then performed the following operation N times:\n\nChoose one element from S and remove it.\nLet x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \\bmod {y}.\n\nThere are N! possible orders in which the elements are removed from S.\nFor each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.\nTask Constraint: All values in input are integers.\n1 <= N <= 200\n1 <= S_i, X <= 10^{5}\nS_i are pairwise distinct.\nTask Input: Input is given from Standard Input in the following format:\nN X\nS_1 S_2 \\ldots S_{N}\nTask Output: Print the answer.\nTask Samples: input: 2 19\n3 7 output: 3\nThere are two possible orders in which we remove the numbers from S.\nIf we remove 3 and 7 in this order, the number on the blackboard changes as follows: 19 \\rightarrow 1 \\rightarrow 1.\nIf we remove 7 and 3 in this order, the number on the blackboard changes as follows: 19 \\rightarrow 5 \\rightarrow 2.\nThe output should be the sum of these: 3.\ninput: 5 82\n22 11 6 5 13 output: 288\ninput: 10 100000\n50000 50001 50002 50003 50004 50005 50006 50007 50008 50009 output: 279669259\nBe sure to compute the sum modulo 10^{9}+7.\n\n" }, { "title": "", "content": "Problem Statement Today, Snuke will eat B pieces of black chocolate and W pieces of white chocolate for an afternoon snack.\nHe will repeat the following procedure until there is no piece left:\n\nChoose black or white with equal probability, and eat a piece of that color if it exists.\n\nFor each integer i from 1 to B+W (inclusive), find the probability that the color of the i-th piece to be eaten is black.\nIt can be shown that these probabilities are rational, and we ask you to print them modulo 10^9 + 7, as described in Notes. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.", "constraint": "All values in input are integers.\n1 <= B,W <= 10^{5}", "input": "Input is given from Standard Input in the following format:\nB W", "output": "Print the answers in B+W lines. In the i-th line, print the probability that the color of the i-th piece to be eaten is black, modulo 10^{9}+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 output: 500000004\n750000006\n750000006\nThere are three possible orders in which Snuke eats the pieces:\nwhite, black, black\nblack, white, black\nblack, black, white\nwith probabilities \\frac{1}{2}, \\frac{1}{4}, \\frac{1}{4}, respectively. Thus, the probabilities of eating a black piece first, second and third are \\frac{1}{2},\\frac{3}{4} and \\frac{3}{4}, respectively.", "input: 3 2 output: 500000004\n500000004\n625000005\n187500002\n187500002\nThey are \\frac{1}{2},\\frac{1}{2},\\frac{5}{8},\\frac{11}{16} and \\frac{11}{16}, respectively.", "input: 6 9 output: 500000004\n500000004\n500000004\n500000004\n500000004\n500000004\n929687507\n218750002\n224609377\n303710940\n633300786\n694091802\n172485353\n411682132\n411682132"], "Pid": "p03083", "ProblemText": "Task Description: Problem Statement Today, Snuke will eat B pieces of black chocolate and W pieces of white chocolate for an afternoon snack.\nHe will repeat the following procedure until there is no piece left:\n\nChoose black or white with equal probability, and eat a piece of that color if it exists.\n\nFor each integer i from 1 to B+W (inclusive), find the probability that the color of the i-th piece to be eaten is black.\nIt can be shown that these probabilities are rational, and we ask you to print them modulo 10^9 + 7, as described in Notes. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.\nTask Constraint: All values in input are integers.\n1 <= B,W <= 10^{5}\nTask Input: Input is given from Standard Input in the following format:\nB W\nTask Output: Print the answers in B+W lines. In the i-th line, print the probability that the color of the i-th piece to be eaten is black, modulo 10^{9}+7.\nTask Samples: input: 2 1 output: 500000004\n750000006\n750000006\nThere are three possible orders in which Snuke eats the pieces:\nwhite, black, black\nblack, white, black\nblack, black, white\nwith probabilities \\frac{1}{2}, \\frac{1}{4}, \\frac{1}{4}, respectively. Thus, the probabilities of eating a black piece first, second and third are \\frac{1}{2},\\frac{3}{4} and \\frac{3}{4}, respectively.\ninput: 3 2 output: 500000004\n500000004\n625000005\n187500002\n187500002\nThey are \\frac{1}{2},\\frac{1}{2},\\frac{5}{8},\\frac{11}{16} and \\frac{11}{16}, respectively.\ninput: 6 9 output: 500000004\n500000004\n500000004\n500000004\n500000004\n500000004\n929687507\n218750002\n224609377\n303710940\n633300786\n694091802\n172485353\n411682132\n411682132\n\n" }, { "title": "", "content": "Problem Statement In Takaha-shi, the capital of Republic of At Coder, there are N roads extending east and west, and M roads extending north and south. There are no other roads.\nThe i-th east-west road from the north and the j-th north-south road from the west cross at the intersection (i, j).\nTwo east-west roads do not cross, nor do two north-south roads.\nThe distance between two adjacent roads in the same direction is 1.\nEach road is one-way; one can only walk in one direction. The permitted direction for each road is described by a string S of length N and a string T of length M, as follows:\n\nIf the i-th character in S is W, one can only walk westward along the i-th east-west road from the north;\nIf the i-th character in S is E, one can only walk eastward along the i-th east-west road from the north;\nIf the i-th character in T is N, one can only walk northward along the i-th north-south road from the west;\nIf the i-th character in T is S, one can only walk southward along the i-th south-west road from the west.\n\nProcess the following Q queries:\n\nIn the i-th query, a_i, b_i, c_i and d_i are given. What is the minimum distance to travel to reach the intersection (c_i, d_i) from the intersection (a_i, b_i) by walking along the roads?", "constraint": "2 <= N <= 100000\n2 <= M <= 100000\n2 <= Q <= 200000\n|S| = N\nS consists of W and E.\n|T| = M\nT consists of N and S.\n1 <= a_i <= N\n1 <= b_i <= M\n1 <= c_i <= N\n1 <= d_i <= M\n(a_i, b_i) \\neq (c_i, d_i)", "input": "Input is given from Standard Input in the following format:\nN M Q\nS\nT\na_1 b_1 c_1 d_1\na_2 b_2 c_2 d_2\n:\na_Q b_Q c_Q d_Q", "output": "In the i-th line, print the response to the i-th query. If the intersection (c_i, d_i) cannot be reached from the intersection (a_i, b_i) by walking along the roads, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 4\nEEWW\nNSNNS\n4 1 1 4\n1 3 1 2\n4 2 3 2\n3 3 3 5 output: 6\n11\n5\n4\n\nThe permitted direction for each road is shown in the following figure (north upward):\n\nFor each of the four queries, a route that achieves the minimum travel distance is as follows:", "input: 3 3 2\nEEE\nSSS\n1 1 3 3\n3 3 1 1 output: 4\n-1\n\nThe travel may be impossible.", "input: 9 7 10\nEEEEEWEWW\nNSSSNSN\n4 6 9 2\n3 7 6 7\n7 5 3 5\n1 1 8 1\n4 3 5 4\n7 4 6 4\n2 5 8 6\n6 6 2 7\n2 4 7 5\n7 2 9 7 output: 9\n-1\n4\n9\n2\n3\n7\n7\n6\n-1"], "Pid": "p03084", "ProblemText": "Task Description: Problem Statement In Takaha-shi, the capital of Republic of At Coder, there are N roads extending east and west, and M roads extending north and south. There are no other roads.\nThe i-th east-west road from the north and the j-th north-south road from the west cross at the intersection (i, j).\nTwo east-west roads do not cross, nor do two north-south roads.\nThe distance between two adjacent roads in the same direction is 1.\nEach road is one-way; one can only walk in one direction. The permitted direction for each road is described by a string S of length N and a string T of length M, as follows:\n\nIf the i-th character in S is W, one can only walk westward along the i-th east-west road from the north;\nIf the i-th character in S is E, one can only walk eastward along the i-th east-west road from the north;\nIf the i-th character in T is N, one can only walk northward along the i-th north-south road from the west;\nIf the i-th character in T is S, one can only walk southward along the i-th south-west road from the west.\n\nProcess the following Q queries:\n\nIn the i-th query, a_i, b_i, c_i and d_i are given. What is the minimum distance to travel to reach the intersection (c_i, d_i) from the intersection (a_i, b_i) by walking along the roads?\nTask Constraint: 2 <= N <= 100000\n2 <= M <= 100000\n2 <= Q <= 200000\n|S| = N\nS consists of W and E.\n|T| = M\nT consists of N and S.\n1 <= a_i <= N\n1 <= b_i <= M\n1 <= c_i <= N\n1 <= d_i <= M\n(a_i, b_i) \\neq (c_i, d_i)\nTask Input: Input is given from Standard Input in the following format:\nN M Q\nS\nT\na_1 b_1 c_1 d_1\na_2 b_2 c_2 d_2\n:\na_Q b_Q c_Q d_Q\nTask Output: In the i-th line, print the response to the i-th query. If the intersection (c_i, d_i) cannot be reached from the intersection (a_i, b_i) by walking along the roads, print -1 instead.\nTask Samples: input: 4 5 4\nEEWW\nNSNNS\n4 1 1 4\n1 3 1 2\n4 2 3 2\n3 3 3 5 output: 6\n11\n5\n4\n\nThe permitted direction for each road is shown in the following figure (north upward):\n\nFor each of the four queries, a route that achieves the minimum travel distance is as follows:\ninput: 3 3 2\nEEE\nSSS\n1 1 3 3\n3 3 1 1 output: 4\n-1\n\nThe travel may be impossible.\ninput: 9 7 10\nEEEEEWEWW\nNSSSNSN\n4 6 9 2\n3 7 6 7\n7 5 3 5\n1 1 8 1\n4 3 5 4\n7 4 6 4\n2 5 8 6\n6 6 2 7\n2 4 7 5\n7 2 9 7 output: 9\n-1\n4\n9\n2\n3\n7\n7\n6\n-1\n\n" }, { "title": "", "content": "Problem Statement On the Planet At Coder, there are four types of bases: A, C, G and T. A bonds with T, and C bonds with G.\nYou are given a letter b as input, which is A, C, G or T. Write a program that prints the letter representing the base that bonds with the base b.", "constraint": "b is one of the letters A, C, G and T.", "input": "Input is given from Standard Input in the following format:\nb", "output": "Print the letter representing the base that bonds with the base b.", "content_img": false, "lang": "en", "error": false, "samples": ["input: A output: T", "input: G output: C"], "Pid": "p03085", "ProblemText": "Task Description: Problem Statement On the Planet At Coder, there are four types of bases: A, C, G and T. A bonds with T, and C bonds with G.\nYou are given a letter b as input, which is A, C, G or T. Write a program that prints the letter representing the base that bonds with the base b.\nTask Constraint: b is one of the letters A, C, G and T.\nTask Input: Input is given from Standard Input in the following format:\nb\nTask Output: Print the letter representing the base that bonds with the base b.\nTask Samples: input: A output: T\ninput: G output: C\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of uppercase English letters. Find the length of the longest ACGT string that is a substring (see Notes) of S.\nHere, a ACGT string is a string that contains no characters other than A, C, G and T. note: Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.\nFor example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.", "constraint": "S is a string of length between 1 and 10 (inclusive).\nEach character in S is an uppercase English letter.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the length of the longest ACGT string that is a substring of S.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ATCODER output: 3\n\nAmong the ACGT strings that are substrings of ATCODER, the longest one is ATC.", "input: HATAGAYA output: 5\n\nAmong the ACGT strings that are substrings of HATAGAYA, the longest one is ATAGA.", "input: SHINJUKU output: 0\n\nAmong the ACGT strings that are substrings of SHINJUKU, the longest one is (the empty string)."], "Pid": "p03086", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of uppercase English letters. Find the length of the longest ACGT string that is a substring (see Notes) of S.\nHere, a ACGT string is a string that contains no characters other than A, C, G and T. note: Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.\nFor example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.\nTask Constraint: S is a string of length between 1 and 10 (inclusive).\nEach character in S is an uppercase English letter.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the length of the longest ACGT string that is a substring of S.\nTask Samples: input: ATCODER output: 3\n\nAmong the ACGT strings that are substrings of ATCODER, the longest one is ATC.\ninput: HATAGAYA output: 5\n\nAmong the ACGT strings that are substrings of HATAGAYA, the longest one is ATAGA.\ninput: SHINJUKU output: 0\n\nAmong the ACGT strings that are substrings of SHINJUKU, the longest one is (the empty string).\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N consisting of A, C, G and T. Answer the following Q queries:\n\nQuery i (1 <= i <= Q): You will be given integers l_i and r_i (1 <= l_i < r_i <= N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does AC occurs as a substring? note: Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.\nFor example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.", "constraint": "2 <= N <= 10^5\n1 <= Q <= 10^5\nS is a string of length N.\nEach character in S is A, C, G or T.\n1 <= l_i < r_i <= N", "input": "Input is given from Standard Input in the following format:\nN Q\nS\nl_1 r_1\n:\nl_Q r_Q", "output": "Print Q lines. The i-th line should contain the answer to the i-th query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 3\nACACTACG\n3 7\n2 3\n1 8 output: 2\n0\n3\nQuery 1: the substring of S starting at index 3 and ending at index 7 is ACTAC. In this string, AC occurs twice as a substring.\nQuery 2: the substring of S starting at index 2 and ending at index 3 is CA. In this string, AC occurs zero times as a substring.\nQuery 3: the substring of S starting at index 1 and ending at index 8 is ACACTACG. In this string, AC occurs three times as a substring."], "Pid": "p03087", "ProblemText": "Task Description: Problem Statement You are given a string S of length N consisting of A, C, G and T. Answer the following Q queries:\n\nQuery i (1 <= i <= Q): You will be given integers l_i and r_i (1 <= l_i < r_i <= N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does AC occurs as a substring? note: Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.\nFor example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.\nTask Constraint: 2 <= N <= 10^5\n1 <= Q <= 10^5\nS is a string of length N.\nEach character in S is A, C, G or T.\n1 <= l_i < r_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN Q\nS\nl_1 r_1\n:\nl_Q r_Q\nTask Output: Print Q lines. The i-th line should contain the answer to the i-th query.\nTask Samples: input: 8 3\nACACTACG\n3 7\n2 3\n1 8 output: 2\n0\n3\nQuery 1: the substring of S starting at index 3 and ending at index 7 is ACTAC. In this string, AC occurs twice as a substring.\nQuery 2: the substring of S starting at index 2 and ending at index 3 is CA. In this string, AC occurs zero times as a substring.\nQuery 3: the substring of S starting at index 1 and ending at index 8 is ACACTACG. In this string, AC occurs three times as a substring.\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N. Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7:\n\nThe string does not contain characters other than A, C, G and T.\nThe string does not contain AGC as a substring.\nThe condition above cannot be violated by swapping two adjacent characters once. note: Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.\nFor example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.", "constraint": "3 <= N <= 100", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 61\n\nThere are 4^3 = 64 strings of length 3 that do not contain characters other than A, C, G and T. Among them, only AGC, ACG and GAC violate the condition, so the answer is 64 - 3 = 61.", "input: 4 output: 230", "input: 100 output: 388130742\n\nBe sure to print the number of strings modulo 10^9+7."], "Pid": "p03088", "ProblemText": "Task Description: Problem Statement You are given an integer N. Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7:\n\nThe string does not contain characters other than A, C, G and T.\nThe string does not contain AGC as a substring.\nThe condition above cannot be violated by swapping two adjacent characters once. note: Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.\nFor example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.\nTask Constraint: 3 <= N <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7.\nTask Samples: input: 3 output: 61\n\nThere are 4^3 = 64 strings of length 3 that do not contain characters other than A, C, G and T. Among them, only AGC, ACG and GAC violate the condition, so the answer is 64 - 3 = 61.\ninput: 4 output: 230\ninput: 100 output: 388130742\n\nBe sure to print the number of strings modulo 10^9+7.\n\n" }, { "title": "", "content": "Problem Statement Snuke has an empty sequence a.\nHe will perform N operations on this sequence.\nIn the i-th operation, he chooses an integer j satisfying 1 <= j <= i, and insert j at position j in a (the beginning is position 1).\nYou are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= b_i <= N", "input": "Input is given from Standard Input in the following format:\nN\nb_1 \\dots b_N", "output": "If there is no sequence of N operations after which a would be equal to b, print -1.\nIf there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 1 output: 1\n1\n2\n\nIn this sequence of operations, the sequence a changes as follows:\n\nAfter the first operation: (1)\nAfter the second operation: (1,1)\nAfter the third operation: (1,2,1)", "input: 2\n2 2 output: -1\n\n2 cannot be inserted at the beginning of the sequence, so this is impossible.", "input: 9\n1 1 1 2 2 1 2 3 2 output: 1\n2\n2\n3\n1\n2\n2\n1\n1"], "Pid": "p03089", "ProblemText": "Task Description: Problem Statement Snuke has an empty sequence a.\nHe will perform N operations on this sequence.\nIn the i-th operation, he chooses an integer j satisfying 1 <= j <= i, and insert j at position j in a (the beginning is position 1).\nYou are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= b_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN\nb_1 \\dots b_N\nTask Output: If there is no sequence of N operations after which a would be equal to b, print -1.\nIf there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.\nTask Samples: input: 3\n1 2 1 output: 1\n1\n2\n\nIn this sequence of operations, the sequence a changes as follows:\n\nAfter the first operation: (1)\nAfter the second operation: (1,1)\nAfter the third operation: (1,2,1)\ninput: 2\n2 2 output: -1\n\n2 cannot be inserted at the beginning of the sequence, so this is impossible.\ninput: 9\n1 1 1 2 2 1 2 3 2 output: 1\n2\n2\n3\n1\n2\n2\n1\n1\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N.\nBuild an undirected graph with N vertices with indices 1 to N that satisfies the following two conditions:\n\nThe graph is simple and connected.\nThere exists an integer S such that, for every vertex, the sum of the indices of the vertices adjacent to that vertex is S.\n\nIt can be proved that at least one such graph exists under the constraints of this problem.", "constraint": "All values in input are integers.\n3 <= N <= 100", "input": "Input is given from Standard Input in the following format:\nN", "output": "In the first line, print the number of edges, M, in the graph you made. In the i-th of the following M lines, print two integers a_i and b_i, representing the endpoints of the i-th edge.\nThe output will be judged correct if the graph satisfies the conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 2\n1 3\n2 3\nFor every vertex, the sum of the indices of the vertices adjacent to that vertex is 3."], "Pid": "p03090", "ProblemText": "Task Description: Problem Statement You are given an integer N.\nBuild an undirected graph with N vertices with indices 1 to N that satisfies the following two conditions:\n\nThe graph is simple and connected.\nThere exists an integer S such that, for every vertex, the sum of the indices of the vertices adjacent to that vertex is S.\n\nIt can be proved that at least one such graph exists under the constraints of this problem.\nTask Constraint: All values in input are integers.\n3 <= N <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: In the first line, print the number of edges, M, in the graph you made. In the i-th of the following M lines, print two integers a_i and b_i, representing the endpoints of the i-th edge.\nThe output will be judged correct if the graph satisfies the conditions.\nTask Samples: input: 3 output: 2\n1 3\n2 3\nFor every vertex, the sum of the indices of the vertices adjacent to that vertex is 3.\n\n" }, { "title": "", "content": "Problem Statement You are given a simple connected undirected graph consisting of N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nEdge i connects Vertex a_i and b_i bidirectionally.\nDetermine if three circuits (see Notes) can be formed using each of the edges exactly once. note: Notes A circuit is a cycle allowing repetitions of vertices but not edges.", "constraint": "All values in input are integers.\n1 <= N,M <= 10^{5}\n1 <= a_i, b_i <= N\nThe given graph is simple and connected.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_M b_M", "output": "If three circuits can be formed using each of the edges exactly once, print Yes; if they cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 9\n1 2\n1 3\n2 3\n1 4\n1 5\n4 5\n1 6\n1 7\n6 7 output: Yes\nThree circuits can be formed using each of the edges exactly once, as follows:", "input: 3 3\n1 2\n2 3\n3 1 output: No\nThree circuits are needed.", "input: 18 27\n17 7\n12 15\n18 17\n13 18\n13 6\n5 7\n7 1\n14 5\n15 11\n7 6\n1 9\n5 4\n18 16\n4 6\n7 2\n7 11\n6 3\n12 14\n5 2\n10 5\n7 8\n10 15\n3 15\n9 8\n7 15\n5 16\n18 15 output: Yes"], "Pid": "p03091", "ProblemText": "Task Description: Problem Statement You are given a simple connected undirected graph consisting of N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nEdge i connects Vertex a_i and b_i bidirectionally.\nDetermine if three circuits (see Notes) can be formed using each of the edges exactly once. note: Notes A circuit is a cycle allowing repetitions of vertices but not edges.\nTask Constraint: All values in input are integers.\n1 <= N,M <= 10^{5}\n1 <= a_i, b_i <= N\nThe given graph is simple and connected.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_M b_M\nTask Output: If three circuits can be formed using each of the edges exactly once, print Yes; if they cannot, print No.\nTask Samples: input: 7 9\n1 2\n1 3\n2 3\n1 4\n1 5\n4 5\n1 6\n1 7\n6 7 output: Yes\nThree circuits can be formed using each of the edges exactly once, as follows:\ninput: 3 3\n1 2\n2 3\n3 1 output: No\nThree circuits are needed.\ninput: 18 27\n17 7\n12 15\n18 17\n13 18\n13 6\n5 7\n7 1\n14 5\n15 11\n7 6\n1 9\n5 4\n18 16\n4 6\n7 2\n7 11\n6 3\n12 14\n5 2\n10 5\n7 8\n10 15\n3 15\n9 8\n7 15\n5 16\n18 15 output: Yes\n\n" }, { "title": "", "content": "Problem Statement You are given a permutation p = (p_1, \\ldots, p_N) of \\{ 1, \\ldots, N \\}.\nYou can perform the following two kinds of operations repeatedly in any order:\n\nPay a cost A. Choose integers l and r (1 <= l < r <= N), and shift (p_l, \\ldots, p_r) to the left by one. That is, replace p_l, p_{l + 1}, \\ldots, p_{r - 1}, p_r with p_{l + 1}, p_{l + 2}, \\ldots, p_r, p_l, respectively.\nPay a cost B. Choose integers l and r (1 <= l < r <= N), and shift (p_l, \\ldots, p_r) to the right by one. That is, replace p_l, p_{l + 1}, \\ldots, p_{r - 1}, p_r with p_r, p_l, \\ldots, p_{r - 2}, p_{r - 1}, respectively.\n\nFind the minimum total cost required to sort p in ascending order.", "constraint": "All values in input are integers.\n1 <= N <= 5000\n1 <= A, B <= 10^9\n(p_1 \\ldots, p_N) is a permutation of \\{ 1, \\ldots, N \\}.", "input": "Input is given from Standard Input in the following format:\nN A B\np_1 \\cdots p_N", "output": "Print the minimum total cost required to sort p in ascending order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 20 30\n3 1 2 output: 20\n\nShifting (p_1, p_2, p_3) to the left by one results in p = (1,2,3).", "input: 4 20 30\n4 2 3 1 output: 50\n\nOne possible sequence of operations is as follows:\n\nShift (p_1, p_2, p_3, p_4) to the left by one. Now we have p = (2,3,1,4).\nShift (p_1, p_2, p_3) to the right by one. Now we have p = (1,2,3,4).\n\nHere, the total cost is 20 + 30 = 50.", "input: 1 10 10\n1 output: 0", "input: 4 1000000000 1000000000\n4 3 2 1 output: 3000000000", "input: 9 40 50\n5 3 4 7 6 1 2 9 8 output: 220"], "Pid": "p03092", "ProblemText": "Task Description: Problem Statement You are given a permutation p = (p_1, \\ldots, p_N) of \\{ 1, \\ldots, N \\}.\nYou can perform the following two kinds of operations repeatedly in any order:\n\nPay a cost A. Choose integers l and r (1 <= l < r <= N), and shift (p_l, \\ldots, p_r) to the left by one. That is, replace p_l, p_{l + 1}, \\ldots, p_{r - 1}, p_r with p_{l + 1}, p_{l + 2}, \\ldots, p_r, p_l, respectively.\nPay a cost B. Choose integers l and r (1 <= l < r <= N), and shift (p_l, \\ldots, p_r) to the right by one. That is, replace p_l, p_{l + 1}, \\ldots, p_{r - 1}, p_r with p_r, p_l, \\ldots, p_{r - 2}, p_{r - 1}, respectively.\n\nFind the minimum total cost required to sort p in ascending order.\nTask Constraint: All values in input are integers.\n1 <= N <= 5000\n1 <= A, B <= 10^9\n(p_1 \\ldots, p_N) is a permutation of \\{ 1, \\ldots, N \\}.\nTask Input: Input is given from Standard Input in the following format:\nN A B\np_1 \\cdots p_N\nTask Output: Print the minimum total cost required to sort p in ascending order.\nTask Samples: input: 3 20 30\n3 1 2 output: 20\n\nShifting (p_1, p_2, p_3) to the left by one results in p = (1,2,3).\ninput: 4 20 30\n4 2 3 1 output: 50\n\nOne possible sequence of operations is as follows:\n\nShift (p_1, p_2, p_3, p_4) to the left by one. Now we have p = (2,3,1,4).\nShift (p_1, p_2, p_3) to the right by one. Now we have p = (1,2,3,4).\n\nHere, the total cost is 20 + 30 = 50.\ninput: 1 10 10\n1 output: 0\ninput: 4 1000000000 1000000000\n4 3 2 1 output: 3000000000\ninput: 9 40 50\n5 3 4 7 6 1 2 9 8 output: 220\n\n" }, { "title": "", "content": "Problem Statement Let M be a positive integer.\nYou are given 2 N integers a_1, a_2, \\ldots, a_{2 N}, where 0 <= a_i < M for each i.\nConsider dividing the 2 N integers into N pairs.\nHere, each integer must belong to exactly one pair.\nWe define the ugliness of a pair (x, y) as (x + y) \\mod M.\nLet Z be the largest ugliness of the N pairs. Find the minimum possible value of Z.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^9\n0 <= a_i < M", "input": "Input is given from Standard Input in the following format:\nN M\na_1 a_2 \\cdots a_{2N}", "output": "Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 10\n0 2 3 4 5 9 output: 5\n\nOne solution is to form pairs (0,5), (2,3) and (4,9), with ugliness 5,5 and 3, respectively.", "input: 2 10\n1 9 1 9 output: 0\n\nPairs (1,9) and (1,9) should be formed, with ugliness both 0."], "Pid": "p03093", "ProblemText": "Task Description: Problem Statement Let M be a positive integer.\nYou are given 2 N integers a_1, a_2, \\ldots, a_{2 N}, where 0 <= a_i < M for each i.\nConsider dividing the 2 N integers into N pairs.\nHere, each integer must belong to exactly one pair.\nWe define the ugliness of a pair (x, y) as (x + y) \\mod M.\nLet Z be the largest ugliness of the N pairs. Find the minimum possible value of Z.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^9\n0 <= a_i < M\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 a_2 \\cdots a_{2N}\nTask Output: Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs.\nTask Samples: input: 3 10\n0 2 3 4 5 9 output: 5\n\nOne solution is to form pairs (0,5), (2,3) and (4,9), with ugliness 5,5 and 3, respectively.\ninput: 2 10\n1 9 1 9 output: 0\n\nPairs (1,9) and (1,9) should be formed, with ugliness both 0.\n\n" }, { "title": "", "content": "Problem Statement We have a round pizza. Snuke wants to eat one third of it, or something as close as possible to that.\nHe decides to cut this pizza as follows.\nFirst, he divides the pizza into N pieces by making N cuts with a knife. The knife can make a cut along the segment connecting the center of the pizza and some point on the circumference of the pizza. However, he is very poor at handling knives, so the cuts are made at uniformly random angles, independent from each other.\nThen, he chooses one or more consecutive pieces so that the total is as close as possible to one third of the pizza, and eat them. (Let the total be x of the pizza. He chooses consecutive pieces so that |x - 1/3| is minimized. )\nFind the expected value of |x - 1/3|. It can be shown that this value is rational, and we ask you to print it modulo 10^9 + 7, as described in Notes. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.", "constraint": "2 <= N <= 10^6", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the expected value of |x - 1/3| modulo 10^9 + 7, as described in Notes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 138888890\n\nThe expected value is \\frac{5}{36}.", "input: 3 output: 179012347\n\nThe expected value is \\frac{11}{162}.", "input: 10 output: 954859137", "input: 1000000 output: 44679646"], "Pid": "p03094", "ProblemText": "Task Description: Problem Statement We have a round pizza. Snuke wants to eat one third of it, or something as close as possible to that.\nHe decides to cut this pizza as follows.\nFirst, he divides the pizza into N pieces by making N cuts with a knife. The knife can make a cut along the segment connecting the center of the pizza and some point on the circumference of the pizza. However, he is very poor at handling knives, so the cuts are made at uniformly random angles, independent from each other.\nThen, he chooses one or more consecutive pieces so that the total is as close as possible to one third of the pizza, and eat them. (Let the total be x of the pizza. He chooses consecutive pieces so that |x - 1/3| is minimized. )\nFind the expected value of |x - 1/3|. It can be shown that this value is rational, and we ask you to print it modulo 10^9 + 7, as described in Notes. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.\nTask Constraint: 2 <= N <= 10^6\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the expected value of |x - 1/3| modulo 10^9 + 7, as described in Notes.\nTask Samples: input: 2 output: 138888890\n\nThe expected value is \\frac{5}{36}.\ninput: 3 output: 179012347\n\nThe expected value is \\frac{11}{162}.\ninput: 10 output: 954859137\ninput: 1000000 output: 44679646\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N.\nAmong its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.\nHere, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.", "constraint": "1 <= N <= 100000\nS consists of lowercase English letters.\n|S|=N", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the number of the subsequences such that all characters are different, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nabcd output: 15\n\nSince all characters in S itself are different, all its subsequences satisfy the condition.", "input: 3\nbaa output: 5\n\nThe answer is five: b, two occurrences of a, two occurrences of ba. Note that we do not count baa, since it contains two as.", "input: 5\nabcab output: 17"], "Pid": "p03095", "ProblemText": "Task Description: Problem Statement You are given a string S of length N.\nAmong its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.\nHere, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.\nTask Constraint: 1 <= N <= 100000\nS consists of lowercase English letters.\n|S|=N\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the number of the subsequences such that all characters are different, modulo 10^9+7.\nTask Samples: input: 4\nabcd output: 15\n\nSince all characters in S itself are different, all its subsequences satisfy the condition.\ninput: 3\nbaa output: 5\n\nThe answer is five: b, two occurrences of a, two occurrences of ba. Note that we do not count baa, since it contains two as.\ninput: 5\nabcab output: 17\n\n" }, { "title": "", "content": "Problem Statement There are N stones arranged in a row. The i-th stone from the left is painted in the color C_i.\nSnuke will perform the following operation zero or more times:\n\nChoose two stones painted in the same color. Repaint all the stones between them, with the color of the chosen stones.\n\nFind the number of possible final sequences of colors of the stones, modulo 10^9+7.", "constraint": "1 <= N <= 2* 10^5\n1 <= C_i <= 2* 10^5(1<= i<= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nC_1\n:\nC_N", "output": "Print the number of possible final sequences of colors of the stones, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1\n2\n1\n2\n2 output: 3\n\nWe can make three sequences of colors of stones, as follows:\n\n(1,2,1,2,2), by doing nothing.\n(1,1,1,2,2), by choosing the first and third stones to perform the operation.\n(1,2,2,2,2), by choosing the second and fourth stones to perform the operation.", "input: 6\n4\n2\n5\n4\n2\n4 output: 5", "input: 7\n1\n3\n1\n2\n3\n3\n2 output: 5"], "Pid": "p03096", "ProblemText": "Task Description: Problem Statement There are N stones arranged in a row. The i-th stone from the left is painted in the color C_i.\nSnuke will perform the following operation zero or more times:\n\nChoose two stones painted in the same color. Repaint all the stones between them, with the color of the chosen stones.\n\nFind the number of possible final sequences of colors of the stones, modulo 10^9+7.\nTask Constraint: 1 <= N <= 2* 10^5\n1 <= C_i <= 2* 10^5(1<= i<= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nC_1\n:\nC_N\nTask Output: Print the number of possible final sequences of colors of the stones, modulo 10^9+7.\nTask Samples: input: 5\n1\n2\n1\n2\n2 output: 3\n\nWe can make three sequences of colors of stones, as follows:\n\n(1,2,1,2,2), by doing nothing.\n(1,1,1,2,2), by choosing the first and third stones to perform the operation.\n(1,2,2,2,2), by choosing the second and fourth stones to perform the operation.\ninput: 6\n4\n2\n5\n4\n2\n4 output: 5\ninput: 7\n1\n3\n1\n2\n3\n3\n2 output: 5\n\n" }, { "title": "", "content": "Problem Statement You are given integers N, \\ A and B.\nDetermine if there exists a permutation (P_0, \\ P_1, \\ . . . \\ P_{2^N-1}) of (0, \\ 1, \\ . . . \\ 2^N-1) that satisfies all of the following conditions, and create one such permutation if it exists.\n\nP_0=A\nP_{2^N-1}=B\nFor all 0 <= i < 2^N-1, the binary representations of P_i and P_{i+1} differ by exactly one bit.", "constraint": "1 <= N <= 17\n0 <= A <= 2^N-1\n0 <= B <= 2^N-1\nA \\neq B\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "If there is no permutation that satisfies the conditions, print NO.\nIf there is such a permutation, print YES in the first line.\nThen, print (P_0, \\ P_1, \\ . . . \\ P_{2^N-1}) in the second line, with spaces in between.\nIf there are multiple solutions, any of them is accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 3 output: YES\n1 0 2 3\n\nThe binary representation of P=(1,0,2,3) is (01,00,10,11), where any two adjacent elements differ by exactly one bit.", "input: 3 2 1 output: NO"], "Pid": "p03097", "ProblemText": "Task Description: Problem Statement You are given integers N, \\ A and B.\nDetermine if there exists a permutation (P_0, \\ P_1, \\ . . . \\ P_{2^N-1}) of (0, \\ 1, \\ . . . \\ 2^N-1) that satisfies all of the following conditions, and create one such permutation if it exists.\n\nP_0=A\nP_{2^N-1}=B\nFor all 0 <= i < 2^N-1, the binary representations of P_i and P_{i+1} differ by exactly one bit.\nTask Constraint: 1 <= N <= 17\n0 <= A <= 2^N-1\n0 <= B <= 2^N-1\nA \\neq B\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: If there is no permutation that satisfies the conditions, print NO.\nIf there is such a permutation, print YES in the first line.\nThen, print (P_0, \\ P_1, \\ . . . \\ P_{2^N-1}) in the second line, with spaces in between.\nIf there are multiple solutions, any of them is accepted.\nTask Samples: input: 2 1 3 output: YES\n1 0 2 3\n\nThe binary representation of P=(1,0,2,3) is (01,00,10,11), where any two adjacent elements differ by exactly one bit.\ninput: 3 2 1 output: NO\n\n" }, { "title": "", "content": "Problem Statement For two permutations p and q of the integers from 1 through N, let f(p, q) be the permutation that satisfies the following:\n\nThe p_i-th element (1 <= i <= N) in f(p, q) is q_i.\nHere, p_i and q_i respectively denote the i-th element in p and q.\n\nYou are given two permutations p and q of the integers from 1 through N.\nWe will now define a sequence {a_n} of permutations of the integers from 1 through N, as follows:\n\na_1=p, a_2=q\na_{n+2}=f(a_n, a_{n+1}) ( n >= 1 )\n\nGiven a positive integer K, find a_K.", "constraint": "1 <= N <= 10^5\n1 <= K <= 10^9\np and q are permutations of the integers from 1 through N.", "input": "Input is given from Standard Input in the following format:\nN K\np_1 . . . p_N\nq_1 . . . q_N", "output": "Print N integers, with spaces in between.\nThe i-th integer (1 <= i <= N) should be the i-th element in a_K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 3\n3 2 1 output: 3 2 1\n\nSince a_3=f(p,q), we just need to find f(p,q).\nWe have p_i=i here, so f(p,q)=q.", "input: 5 5\n4 5 1 2 3\n3 2 1 5 4 output: 4 3 2 1 5", "input: 10 1000000000\n7 10 6 5 4 2 9 1 3 8\n4 1 9 2 3 7 8 10 6 5 output: 7 9 4 8 2 5 1 6 10 3"], "Pid": "p03098", "ProblemText": "Task Description: Problem Statement For two permutations p and q of the integers from 1 through N, let f(p, q) be the permutation that satisfies the following:\n\nThe p_i-th element (1 <= i <= N) in f(p, q) is q_i.\nHere, p_i and q_i respectively denote the i-th element in p and q.\n\nYou are given two permutations p and q of the integers from 1 through N.\nWe will now define a sequence {a_n} of permutations of the integers from 1 through N, as follows:\n\na_1=p, a_2=q\na_{n+2}=f(a_n, a_{n+1}) ( n >= 1 )\n\nGiven a positive integer K, find a_K.\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= 10^9\np and q are permutations of the integers from 1 through N.\nTask Input: Input is given from Standard Input in the following format:\nN K\np_1 . . . p_N\nq_1 . . . q_N\nTask Output: Print N integers, with spaces in between.\nThe i-th integer (1 <= i <= N) should be the i-th element in a_K.\nTask Samples: input: 3 3\n1 2 3\n3 2 1 output: 3 2 1\n\nSince a_3=f(p,q), we just need to find f(p,q).\nWe have p_i=i here, so f(p,q)=q.\ninput: 5 5\n4 5 1 2 3\n3 2 1 5 4 output: 4 3 2 1 5\ninput: 10 1000000000\n7 10 6 5 4 2 9 1 3 8\n4 1 9 2 3 7 8 10 6 5 output: 7 9 4 8 2 5 1 6 10 3\n\n" }, { "title": "", "content": "Problem Statement A museum exhibits N jewels, Jewel 1,2, . . . , N.\nThe coordinates of Jewel i are (x_i, y_i) (the museum can be regarded as a two-dimensional plane), and the value of that jewel is v_i.\nSnuke the thief will steal some of these jewels.\nThere are M conditions, Condition 1,2, . . . , M, that must be met when stealing jewels, or he will be caught by the detective.\nEach condition has one of the following four forms:\n\n(t_i =L, a_i, b_i) : Snuke can only steal at most b_i jewels whose x coordinates are a_i or smaller.\n(t_i =R, a_i, b_i) : Snuke can only steal at most b_i jewels whose x coordinates are a_i or larger.\n(t_i =D, a_i, b_i) : Snuke can only steal at most b_i jewels whose y coordinates are a_i or smaller.\n(t_i =U, a_i, b_i) : Snuke can only steal at most b_i jewels whose y coordinates are a_i or larger.\n\nFind the maximum sum of values of jewels that Snuke the thief can steal.", "constraint": "1 <= N <= 80\n1 <= x_i, y_i <= 100\n1 <= v_i <= 10^{15}\n1 <= M <= 320\nt_i is L, R, U or D.\n1 <= a_i <= 100\n0 <= b_i <= N - 1\n(x_i, y_i) are pairwise distinct.\n(t_i, a_i) are pairwise distinct.\n(t_i, b_i) are pairwise distinct.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1 v_1\nx_2 y_2 v_2\n:\nx_N y_N v_N\nM\nt_1 a_1 b_1\nt_2 a_2 b_2\n:\nt_M a_M b_M", "output": "Print the maximum sum of values of jewels that Snuke the thief can steal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n1 3 6\n1 5 9\n3 1 8\n4 3 8\n6 2 9\n5 4 11\n5 7 10\n4\nL 3 1\nR 2 3\nD 5 3\nU 4 2 output: 36\nStealing Jewel 1,5,6 and 7 results in the total value of 36.", "input: 3\n1 2 3\n4 5 6\n7 8 9\n1\nL 100 0 output: 0", "input: 4\n1 1 10\n1 2 11\n2 1 12\n2 2 13\n3\nL 8 3\nL 9 2\nL 10 1 output: 13", "input: 10\n66 47 71040136000\n65 77 74799603000\n80 53 91192869000\n24 34 24931901000\n91 78 49867703000\n68 71 46108236000\n46 73 74799603000\n56 63 93122668000\n32 51 71030136000\n51 26 70912345000\n21\nL 51 1\nL 7 0\nU 47 4\nR 92 0\nR 91 1\nD 53 2\nR 65 3\nD 13 0\nU 63 3\nL 68 3\nD 47 1\nL 91 5\nR 32 4\nL 66 2\nL 80 4\nD 77 4\nU 73 1\nD 78 5\nU 26 5\nR 80 2\nR 24 5 output: 305223377000"], "Pid": "p03099", "ProblemText": "Task Description: Problem Statement A museum exhibits N jewels, Jewel 1,2, . . . , N.\nThe coordinates of Jewel i are (x_i, y_i) (the museum can be regarded as a two-dimensional plane), and the value of that jewel is v_i.\nSnuke the thief will steal some of these jewels.\nThere are M conditions, Condition 1,2, . . . , M, that must be met when stealing jewels, or he will be caught by the detective.\nEach condition has one of the following four forms:\n\n(t_i =L, a_i, b_i) : Snuke can only steal at most b_i jewels whose x coordinates are a_i or smaller.\n(t_i =R, a_i, b_i) : Snuke can only steal at most b_i jewels whose x coordinates are a_i or larger.\n(t_i =D, a_i, b_i) : Snuke can only steal at most b_i jewels whose y coordinates are a_i or smaller.\n(t_i =U, a_i, b_i) : Snuke can only steal at most b_i jewels whose y coordinates are a_i or larger.\n\nFind the maximum sum of values of jewels that Snuke the thief can steal.\nTask Constraint: 1 <= N <= 80\n1 <= x_i, y_i <= 100\n1 <= v_i <= 10^{15}\n1 <= M <= 320\nt_i is L, R, U or D.\n1 <= a_i <= 100\n0 <= b_i <= N - 1\n(x_i, y_i) are pairwise distinct.\n(t_i, a_i) are pairwise distinct.\n(t_i, b_i) are pairwise distinct.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1 v_1\nx_2 y_2 v_2\n:\nx_N y_N v_N\nM\nt_1 a_1 b_1\nt_2 a_2 b_2\n:\nt_M a_M b_M\nTask Output: Print the maximum sum of values of jewels that Snuke the thief can steal.\nTask Samples: input: 7\n1 3 6\n1 5 9\n3 1 8\n4 3 8\n6 2 9\n5 4 11\n5 7 10\n4\nL 3 1\nR 2 3\nD 5 3\nU 4 2 output: 36\nStealing Jewel 1,5,6 and 7 results in the total value of 36.\ninput: 3\n1 2 3\n4 5 6\n7 8 9\n1\nL 100 0 output: 0\ninput: 4\n1 1 10\n1 2 11\n2 1 12\n2 2 13\n3\nL 8 3\nL 9 2\nL 10 1 output: 13\ninput: 10\n66 47 71040136000\n65 77 74799603000\n80 53 91192869000\n24 34 24931901000\n91 78 49867703000\n68 71 46108236000\n46 73 74799603000\n56 63 93122668000\n32 51 71030136000\n51 26 70912345000\n21\nL 51 1\nL 7 0\nU 47 4\nR 92 0\nR 91 1\nD 53 2\nR 65 3\nD 13 0\nU 63 3\nL 68 3\nD 47 1\nL 91 5\nR 32 4\nL 66 2\nL 80 4\nD 77 4\nU 73 1\nD 78 5\nU 26 5\nR 80 2\nR 24 5 output: 305223377000\n\n" }, { "title": "", "content": "Problem Statement You are given a connected graph with N vertices and M edges. The vertices are numbered 1 to N. The i-th edge is an undirected edge of length C_i connecting Vertex A_i and Vertex B_i.\nAdditionally, an odd number MOD is given.\nYou will be given Q queries, which should be processed. The queries take the following form:\n\nGiven in the i-th query are S_i, T_i and R_i. Print YES if there exists a path from Vertex S_i to Vertex T_i whose length is R_i modulo MOD, and print NO otherwise. A path may traverse the same edge multiple times, or go back using the edge it just used.\n\nHere, in this problem, the length of a path is NOT the sum of the lengths of its edges themselves, but the length of the first edge used in the path gets multiplied by 1, the second edge gets multiplied by 2, the third edge gets multiplied by 4, and so on. (More formally, let L_1, . . . , L_k be the lengths of the edges used, in this order. The length of that path is the sum of L_i * 2^{i-1}. )", "constraint": "1 <= N,M,Q <= 50000\n3 <= MOD <= 10^{6}\nMOD is odd.\n1 <= A_i,B_i<= N\n0 <= C_i <= MOD-1\n1 <= S_i,T_i <= N\n0 <= R_i <= MOD-1\nThe given graph is connected. (It may contain self-loops or multiple edges.)", "input": "Input is given from Standard Input in the following format:\nN M Q MOD\nA_1 B_1 C_1\n\\vdots\nA_M B_M C_M\nS_1 T_1 R_1\n\\vdots\nS_Q T_Q R_Q", "output": "Print the answers to the i-th query in the i-th line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 2 2019\n1 2 1\n2 3 2\n1 3 5\n1 3 4 output: YES\nNO\n\nThe answer to each query is as follows:\n\nThe first query: If we take the path 1,2,3, its length is 1 * 2^0 + 2 * 2^1 = 5, so there exists a path whose length is 5 modulo 2019. The answer is YES.\nThe second query: No matter what path we take from Vertex 1 to Vertex 3, its length will never be 4 modulo 2019. The answer is NO.", "input: 6 6 3 2019\n1 2 4\n2 3 4\n3 4 4\n4 5 4\n5 6 4\n6 1 4\n2 6 1110\n3 1 1111\n4 5 1112 output: YES\nNO\nNO", "input: 1 2 3 25\n1 1 1\n1 1 2\n1 1 13\n1 1 6\n1 1 14 output: YES\nYES\nYES", "input: 10 15 10 15\n1 2 1\n2 3 6\n3 4 6\n2 5 1\n5 6 1\n4 7 6\n1 8 11\n2 9 6\n5 10 11\n9 10 11\n3 6 1\n2 5 1\n2 7 11\n9 10 11\n5 6 11\n1 3 5\n9 8 3\n7 7 7\n7 10 13\n4 1 10\n9 3 12\n10 10 14\n9 2 1\n6 6 5\n8 8 4 output: YES\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nYES\nNO"], "Pid": "p03100", "ProblemText": "Task Description: Problem Statement You are given a connected graph with N vertices and M edges. The vertices are numbered 1 to N. The i-th edge is an undirected edge of length C_i connecting Vertex A_i and Vertex B_i.\nAdditionally, an odd number MOD is given.\nYou will be given Q queries, which should be processed. The queries take the following form:\n\nGiven in the i-th query are S_i, T_i and R_i. Print YES if there exists a path from Vertex S_i to Vertex T_i whose length is R_i modulo MOD, and print NO otherwise. A path may traverse the same edge multiple times, or go back using the edge it just used.\n\nHere, in this problem, the length of a path is NOT the sum of the lengths of its edges themselves, but the length of the first edge used in the path gets multiplied by 1, the second edge gets multiplied by 2, the third edge gets multiplied by 4, and so on. (More formally, let L_1, . . . , L_k be the lengths of the edges used, in this order. The length of that path is the sum of L_i * 2^{i-1}. )\nTask Constraint: 1 <= N,M,Q <= 50000\n3 <= MOD <= 10^{6}\nMOD is odd.\n1 <= A_i,B_i<= N\n0 <= C_i <= MOD-1\n1 <= S_i,T_i <= N\n0 <= R_i <= MOD-1\nThe given graph is connected. (It may contain self-loops or multiple edges.)\nTask Input: Input is given from Standard Input in the following format:\nN M Q MOD\nA_1 B_1 C_1\n\\vdots\nA_M B_M C_M\nS_1 T_1 R_1\n\\vdots\nS_Q T_Q R_Q\nTask Output: Print the answers to the i-th query in the i-th line.\nTask Samples: input: 3 2 2 2019\n1 2 1\n2 3 2\n1 3 5\n1 3 4 output: YES\nNO\n\nThe answer to each query is as follows:\n\nThe first query: If we take the path 1,2,3, its length is 1 * 2^0 + 2 * 2^1 = 5, so there exists a path whose length is 5 modulo 2019. The answer is YES.\nThe second query: No matter what path we take from Vertex 1 to Vertex 3, its length will never be 4 modulo 2019. The answer is NO.\ninput: 6 6 3 2019\n1 2 4\n2 3 4\n3 4 4\n4 5 4\n5 6 4\n6 1 4\n2 6 1110\n3 1 1111\n4 5 1112 output: YES\nNO\nNO\ninput: 1 2 3 25\n1 1 1\n1 1 2\n1 1 13\n1 1 6\n1 1 14 output: YES\nYES\nYES\ninput: 10 15 10 15\n1 2 1\n2 3 6\n3 4 6\n2 5 1\n5 6 1\n4 7 6\n1 8 11\n2 9 6\n5 10 11\n9 10 11\n3 6 1\n2 5 1\n2 7 11\n9 10 11\n5 6 11\n1 3 5\n9 8 3\n7 7 7\n7 10 13\n4 1 10\n9 3 12\n10 10 14\n9 2 1\n6 6 5\n8 8 4 output: YES\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nYES\nNO\n\n" }, { "title": "", "content": "Problem Statement There are H rows and W columns of white square cells.\nYou will choose h of the rows and w of the columns, and paint all of the cells contained in those rows or columns.\nHow many white cells will remain?\nIt can be proved that this count does not depend on what rows and columns are chosen.", "constraint": "All values in input are integers.\n1 <= H, W <= 20\n1 <= h <= H\n1 <= w <= W", "input": "Input is given from Standard Input in the following format:\nH W\nh w", "output": "Print the number of white cells that will remain.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n2 1 output: 1\n\nThere are 3 rows and 2 columns of cells. When two rows and one column are chosen and painted in black, there is always one white cell that remains.", "input: 5 5\n2 3 output: 6", "input: 2 4\n2 4 output: 0"], "Pid": "p03101", "ProblemText": "Task Description: Problem Statement There are H rows and W columns of white square cells.\nYou will choose h of the rows and w of the columns, and paint all of the cells contained in those rows or columns.\nHow many white cells will remain?\nIt can be proved that this count does not depend on what rows and columns are chosen.\nTask Constraint: All values in input are integers.\n1 <= H, W <= 20\n1 <= h <= H\n1 <= w <= W\nTask Input: Input is given from Standard Input in the following format:\nH W\nh w\nTask Output: Print the number of white cells that will remain.\nTask Samples: input: 3 2\n2 1 output: 1\n\nThere are 3 rows and 2 columns of cells. When two rows and one column are chosen and painted in black, there is always one white cell that remains.\ninput: 5 5\n2 3 output: 6\ninput: 2 4\n2 4 output: 0\n\n" }, { "title": "", "content": "Problem Statement There are N pieces of source code. The characteristics of the i-th code is represented by M integers A_{i1}, A_{i2}, . . . , A_{i M}.\nAdditionally, you are given integers B_1, B_2, . . . , B_M and C.\nThe i-th code correctly solves this problem if and only if A_{i1} B_1 + A_{i2} B_2 + . . . + A_{i M} B_M + C > 0.\nAmong the N codes, find the number of codes that correctly solve this problem.", "constraint": "All values in input are integers.\n1 <= N, M <= 20\n-100 <= A_{ij} <= 100\n-100 <= B_i <= 100\n-100 <= C <= 100", "input": "Input is given from Standard Input in the following format:\nN M C\nB_1 B_2 . . . B_M\nA_{11} A_{12} . . . A_{1M}\nA_{21} A_{22} . . . A_{2M}\n\\vdots\nA_{N1} A_{N2} . . . A_{NM}", "output": "Print the number of codes among the given N codes that correctly solve this problem.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 -10\n1 2 3\n3 2 1\n1 2 2 output: 1\n\nOnly the second code correctly solves this problem, as follows:\n\nSince 3 * 1 + 2 * 2 + 1 * 3 + (-10) = 0 <= 0, the first code does not solve this problem.\n1 * 1 + 2 * 2 + 2 * 3 + (-10) = 1 > 0, the second code solves this problem.", "input: 5 2 -4\n-2 5\n100 41\n100 40\n-3 0\n-6 -2\n18 -13 output: 2", "input: 3 3 0\n100 -100 0\n0 100 100\n100 100 100\n-100 100 100 output: 0\n\nAll of them are Wrong Answer. Except yours."], "Pid": "p03102", "ProblemText": "Task Description: Problem Statement There are N pieces of source code. The characteristics of the i-th code is represented by M integers A_{i1}, A_{i2}, . . . , A_{i M}.\nAdditionally, you are given integers B_1, B_2, . . . , B_M and C.\nThe i-th code correctly solves this problem if and only if A_{i1} B_1 + A_{i2} B_2 + . . . + A_{i M} B_M + C > 0.\nAmong the N codes, find the number of codes that correctly solve this problem.\nTask Constraint: All values in input are integers.\n1 <= N, M <= 20\n-100 <= A_{ij} <= 100\n-100 <= B_i <= 100\n-100 <= C <= 100\nTask Input: Input is given from Standard Input in the following format:\nN M C\nB_1 B_2 . . . B_M\nA_{11} A_{12} . . . A_{1M}\nA_{21} A_{22} . . . A_{2M}\n\\vdots\nA_{N1} A_{N2} . . . A_{NM}\nTask Output: Print the number of codes among the given N codes that correctly solve this problem.\nTask Samples: input: 2 3 -10\n1 2 3\n3 2 1\n1 2 2 output: 1\n\nOnly the second code correctly solves this problem, as follows:\n\nSince 3 * 1 + 2 * 2 + 1 * 3 + (-10) = 0 <= 0, the first code does not solve this problem.\n1 * 1 + 2 * 2 + 2 * 3 + (-10) = 1 > 0, the second code solves this problem.\ninput: 5 2 -4\n-2 5\n100 41\n100 40\n-3 0\n-6 -2\n18 -13 output: 2\ninput: 3 3 0\n100 -100 0\n0 100 100\n100 100 100\n-100 100 100 output: 0\n\nAll of them are Wrong Answer. Except yours.\n\n" }, { "title": "", "content": "Problem Statement Hearing that energy drinks increase rating in those sites, Takahashi decides to buy up M cans of energy drinks.\nThere are N stores that sell energy drinks. In the i-th store, he can buy at most B_i cans of energy drinks for A_i yen (the currency of Japan) each.\nWhat is the minimum amount of money with which he can buy M cans of energy drinks?\nIt is guaranteed that, in the given inputs, a sufficient amount of money can always buy M cans of energy drinks.", "constraint": "All values in input are integers.\n1 <= N, M <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^5\nB_1 + ... + B_N >= M", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N", "output": "Print the minimum amount of money with which Takahashi can buy M cans of energy drinks.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5\n4 9\n2 4 output: 12\n\nWith 12 yen, we can buy one drink at the first store and four drinks at the second store, for the total of five drinks. However, we cannot buy 5 drinks with 11 yen or less.", "input: 4 30\n6 18\n2 5\n3 10\n7 9 output: 130", "input: 1 100000\n1000000000 100000 output: 100000000000000\n\nThe output may not fit into a 32-bit integer type."], "Pid": "p03103", "ProblemText": "Task Description: Problem Statement Hearing that energy drinks increase rating in those sites, Takahashi decides to buy up M cans of energy drinks.\nThere are N stores that sell energy drinks. In the i-th store, he can buy at most B_i cans of energy drinks for A_i yen (the currency of Japan) each.\nWhat is the minimum amount of money with which he can buy M cans of energy drinks?\nIt is guaranteed that, in the given inputs, a sufficient amount of money can always buy M cans of energy drinks.\nTask Constraint: All values in input are integers.\n1 <= N, M <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^5\nB_1 + ... + B_N >= M\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n\\vdots\nA_N B_N\nTask Output: Print the minimum amount of money with which Takahashi can buy M cans of energy drinks.\nTask Samples: input: 2 5\n4 9\n2 4 output: 12\n\nWith 12 yen, we can buy one drink at the first store and four drinks at the second store, for the total of five drinks. However, we cannot buy 5 drinks with 11 yen or less.\ninput: 4 30\n6 18\n2 5\n3 10\n7 9 output: 130\ninput: 1 100000\n1000000000 100000 output: 100000000000000\n\nThe output may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement Let f(A, B) be the exclusive OR of A, A+1, . . . , B. Find f(A, B).\n\nWhat is exclusive OR?\nThe bitwise exclusive OR of integers c_1, c_2, . . . , c_n (let us call it y) is defined as follows:\n\nWhen y is written in base two, the digit in the 2^k's place (k >= 0) is 1 if, the number of integers among c_1, c_2, . . . c_m whose binary representations have 1 in the 2^k's place, is odd, and 0 if that count is even.\n\nFor example, the exclusive OR of 3 and 5 is 6. (When written in base two: the exclusive OR of 011 and 101 is 110. )", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03104", "ProblemText": "Task Description: Problem Statement Let f(A, B) be the exclusive OR of A, A+1, . . . , B. Find f(A, B).\n\nWhat is exclusive OR?\nThe bitwise exclusive OR of integers c_1, c_2, . . . , c_n (let us call it y) is defined as follows:\n\nWhen y is written in base two, the digit in the 2^k's place (k >= 0) is 1 if, the number of integers among c_1, c_2, . . . c_m whose binary representations have 1 in the 2^k's place, is odd, and 0 if that count is even.\n\nFor example, the exclusive OR of 3 and 5 is 6. (When written in base two: the exclusive OR of 011 and 101 is 110. )\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement Takahashi likes the sound when he buys a drink from a vending machine.\nThat sound can be heard by spending A yen (the currency of Japan) each time.\nTakahashi has B yen. He will hear the sound as many times as he can with that money, but at most C times, as he would be satisfied at that time.\nHow many times will he hear the sound?", "constraint": "All values in input are integers.\n1 <= A, B, C <= 100", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "Print the number of times Takahashi will hear his favorite sound.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 11 4 output: 4\n\nSince he has not less than 8 yen, he will hear the sound four times and be satisfied.", "input: 3 9 5 output: 3\n\nHe may not be able to be satisfied.", "input: 100 1 10 output: 0"], "Pid": "p03105", "ProblemText": "Task Description: Problem Statement Takahashi likes the sound when he buys a drink from a vending machine.\nThat sound can be heard by spending A yen (the currency of Japan) each time.\nTakahashi has B yen. He will hear the sound as many times as he can with that money, but at most C times, as he would be satisfied at that time.\nHow many times will he hear the sound?\nTask Constraint: All values in input are integers.\n1 <= A, B, C <= 100\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: Print the number of times Takahashi will hear his favorite sound.\nTask Samples: input: 2 11 4 output: 4\n\nSince he has not less than 8 yen, he will hear the sound four times and be satisfied.\ninput: 3 9 5 output: 3\n\nHe may not be able to be satisfied.\ninput: 100 1 10 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given positive integers A and B.\nFind the K-th largest positive integer that divides both A and B.\nThe input guarantees that there exists such a number.", "constraint": "All values in input are integers.\n1 <= A, B <= 100\nThe K-th largest positive integer that divides both A and B exists.\nK >= 1", "input": "Input is given from Standard Input in the following format:\nA B K", "output": "Print the K-th largest positive integer that divides both A and B.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 12 2 output: 2\n\nThree positive integers divides both 8 and 12: 1,2 and 4.\nAmong them, the second largest is 2.", "input: 100 50 4 output: 5", "input: 1 1 1 output: 1"], "Pid": "p03106", "ProblemText": "Task Description: Problem Statement You are given positive integers A and B.\nFind the K-th largest positive integer that divides both A and B.\nThe input guarantees that there exists such a number.\nTask Constraint: All values in input are integers.\n1 <= A, B <= 100\nThe K-th largest positive integer that divides both A and B exists.\nK >= 1\nTask Input: Input is given from Standard Input in the following format:\nA B K\nTask Output: Print the K-th largest positive integer that divides both A and B.\nTask Samples: input: 8 12 2 output: 2\n\nThree positive integers divides both 8 and 12: 1,2 and 4.\nAmong them, the second largest is 2.\ninput: 100 50 4 output: 5\ninput: 1 1 1 output: 1\n\n" }, { "title": "", "content": "Problem Statement There are N cubes stacked vertically on a desk.\nYou are given a string S of length N. The color of the i-th cube from the bottom is red if the i-th character in S is 0, and blue if that character is 1.\nYou can perform the following operation any number of times: choose a red cube and a blue cube that are adjacent, and remove them. Here, the cubes that were stacked on the removed cubes will fall down onto the object below them.\nAt most how many cubes can be removed?", "constraint": "1 <= N <= 10^5\n|S| = N\nEach character in S is 0 or 1.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the maximum number of cubes that can be removed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0011 output: 4\n\nAll four cubes can be removed, by performing the operation as follows:\n\nRemove the second and third cubes from the bottom. Then, the fourth cube drops onto the first cube.\nRemove the first and second cubes from the bottom.", "input: 11011010001011 output: 12", "input: 0 output: 0"], "Pid": "p03107", "ProblemText": "Task Description: Problem Statement There are N cubes stacked vertically on a desk.\nYou are given a string S of length N. The color of the i-th cube from the bottom is red if the i-th character in S is 0, and blue if that character is 1.\nYou can perform the following operation any number of times: choose a red cube and a blue cube that are adjacent, and remove them. Here, the cubes that were stacked on the removed cubes will fall down onto the object below them.\nAt most how many cubes can be removed?\nTask Constraint: 1 <= N <= 10^5\n|S| = N\nEach character in S is 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the maximum number of cubes that can be removed.\nTask Samples: input: 0011 output: 4\n\nAll four cubes can be removed, by performing the operation as follows:\n\nRemove the second and third cubes from the bottom. Then, the fourth cube drops onto the first cube.\nRemove the first and second cubes from the bottom.\ninput: 11011010001011 output: 12\ninput: 0 output: 0\n\n" }, { "title": "", "content": "Problem Statement There are N islands and M bridges.\nThe i-th bridge connects the A_i-th and B_i-th islands bidirectionally.\nInitially, we can travel between any two islands using some of these bridges.\nHowever, the results of a survey show that these bridges will all collapse because of aging, in the order from the first bridge to the M-th bridge.\nLet the inconvenience be the number of pairs of islands (a, b) (a < b) such that we are no longer able to travel between the a-th and b-th islands using some of the bridges remaining.\nFor each i (1 <= i <= M), find the inconvenience just after the i-th bridge collapses.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i < B_i <= N\nAll pairs (A_i, B_i) are distinct.\nThe inconvenience is initially 0.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n\\vdots\nA_M B_M", "output": "In the order i = 1,2, . . . , M, print the inconvenience just after the i-th bridge collapses.\nNote that the answer may not fit into a 32-bit integer type.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n1 2\n3 4\n1 3\n2 3\n1 4 output: 0\n0\n4\n5\n6\n\nFor example, when the first to third bridges have collapsed, the inconvenience is 4 since we can no longer travel between the pairs (1,2), (1,3), (2,4) and (3,4).", "input: 6 5\n2 3\n1 2\n5 6\n3 4\n4 5 output: 8\n9\n12\n14\n15", "input: 2 1\n1 2 output: 1"], "Pid": "p03108", "ProblemText": "Task Description: Problem Statement There are N islands and M bridges.\nThe i-th bridge connects the A_i-th and B_i-th islands bidirectionally.\nInitially, we can travel between any two islands using some of these bridges.\nHowever, the results of a survey show that these bridges will all collapse because of aging, in the order from the first bridge to the M-th bridge.\nLet the inconvenience be the number of pairs of islands (a, b) (a < b) such that we are no longer able to travel between the a-th and b-th islands using some of the bridges remaining.\nFor each i (1 <= i <= M), find the inconvenience just after the i-th bridge collapses.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i < B_i <= N\nAll pairs (A_i, B_i) are distinct.\nThe inconvenience is initially 0.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n\\vdots\nA_M B_M\nTask Output: In the order i = 1,2, . . . , M, print the inconvenience just after the i-th bridge collapses.\nNote that the answer may not fit into a 32-bit integer type.\nTask Samples: input: 4 5\n1 2\n3 4\n1 3\n2 3\n1 4 output: 0\n0\n4\n5\n6\n\nFor example, when the first to third bridges have collapsed, the inconvenience is 4 since we can no longer travel between the pairs (1,2), (1,3), (2,4) and (3,4).\ninput: 6 5\n2 3\n1 2\n5 6\n3 4\n4 5 output: 8\n9\n12\n14\n15\ninput: 2 1\n1 2 output: 1\n\n" }, { "title": "", "content": "Problem Statement You are given a string S as input. This represents a valid date in the year 2019 in the yyyy/mm/dd format. (For example, April 30,2019 is represented as 2019/04/30. )\nWrite a program that prints Heisei if the date represented by S is not later than April 30,2019, and prints TBD otherwise.", "constraint": "S is a string that represents a valid date in the year 2019 in the yyyy/mm/dd format.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print Heisei if the date represented by S is not later than April 30,2019, and print TBD otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2019/04/30 output: Heisei", "input: 2019/11/01 output: TBD"], "Pid": "p03109", "ProblemText": "Task Description: Problem Statement You are given a string S as input. This represents a valid date in the year 2019 in the yyyy/mm/dd format. (For example, April 30,2019 is represented as 2019/04/30. )\nWrite a program that prints Heisei if the date represented by S is not later than April 30,2019, and prints TBD otherwise.\nTask Constraint: S is a string that represents a valid date in the year 2019 in the yyyy/mm/dd format.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print Heisei if the date represented by S is not later than April 30,2019, and print TBD otherwise.\nTask Samples: input: 2019/04/30 output: Heisei\ninput: 2019/11/01 output: TBD\n\n" }, { "title": "", "content": "Problem Statement Takahashi received otoshidama (New Year's money gifts) from N of his relatives.\nYou are given N values x_1, x_2, . . . , x_N and N strings u_1, u_2, . . . , u_N as input. Each string u_i is either JPY or BTC, and x_i and u_i represent the content of the otoshidama from the i-th relative.\nFor example, if x_1 = 10000 and u_1 = JPY, the otoshidama from the first relative is 10000 Japanese yen; if x_2 = 0.10000000 and u_2 = BTC, the otoshidama from the second relative is 0.1 bitcoins.\nIf we convert the bitcoins into yen at the rate of 380000.0 JPY per 1.0 BTC, how much are the gifts worth in total?", "constraint": "2 <= N <= 10\nu_i = JPY or BTC.\nIf u_i = JPY, x_i is an integer such that 1 <= x_i <= 10^8.\nIf u_i = BTC, x_i is a decimal with 8 decimal digits, such that 0.00000001 <= x_i <= 100.00000000.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 u_1\nx_2 u_2\n:\nx_N u_N", "output": "If the gifts are worth Y yen in total, print the value Y (not necessarily an integer).\nOutput will be judged correct when the absolute or relative error from the judge's output is at most 10^{-5}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n10000 JPY\n0.10000000 BTC output: 48000.0\n\nThe otoshidama from the first relative is 10000 yen. The otoshidama from the second relative is 0.1 bitcoins, which is worth 38000.0 yen if converted at the rate of 380000.0 JPY per 1.0 BTC. The sum of these is 48000.0 yen.\nOutputs such as 48000 and 48000.1 will also be judged correct.", "input: 3\n100000000 JPY\n100.00000000 BTC\n0.00000001 BTC output: 138000000.0038\n\nIn this case, outputs such as 138001000 and 1.38e8 will also be judged correct."], "Pid": "p03110", "ProblemText": "Task Description: Problem Statement Takahashi received otoshidama (New Year's money gifts) from N of his relatives.\nYou are given N values x_1, x_2, . . . , x_N and N strings u_1, u_2, . . . , u_N as input. Each string u_i is either JPY or BTC, and x_i and u_i represent the content of the otoshidama from the i-th relative.\nFor example, if x_1 = 10000 and u_1 = JPY, the otoshidama from the first relative is 10000 Japanese yen; if x_2 = 0.10000000 and u_2 = BTC, the otoshidama from the second relative is 0.1 bitcoins.\nIf we convert the bitcoins into yen at the rate of 380000.0 JPY per 1.0 BTC, how much are the gifts worth in total?\nTask Constraint: 2 <= N <= 10\nu_i = JPY or BTC.\nIf u_i = JPY, x_i is an integer such that 1 <= x_i <= 10^8.\nIf u_i = BTC, x_i is a decimal with 8 decimal digits, such that 0.00000001 <= x_i <= 100.00000000.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 u_1\nx_2 u_2\n:\nx_N u_N\nTask Output: If the gifts are worth Y yen in total, print the value Y (not necessarily an integer).\nOutput will be judged correct when the absolute or relative error from the judge's output is at most 10^{-5}.\nTask Samples: input: 2\n10000 JPY\n0.10000000 BTC output: 48000.0\n\nThe otoshidama from the first relative is 10000 yen. The otoshidama from the second relative is 0.1 bitcoins, which is worth 38000.0 yen if converted at the rate of 380000.0 JPY per 1.0 BTC. The sum of these is 48000.0 yen.\nOutputs such as 48000 and 48000.1 will also be judged correct.\ninput: 3\n100000000 JPY\n100.00000000 BTC\n0.00000001 BTC output: 138000000.0038\n\nIn this case, outputs such as 138001000 and 1.38e8 will also be judged correct.\n\n" }, { "title": "", "content": "Problem Statement You have N bamboos. The lengths (in centimeters) of these are l_1, l_2, . . . , l_N, respectively.\nYour objective is to use some of these bamboos (possibly all) to obtain three bamboos of length A, B, C. For that, you can use the following three kinds of magics any number:\n\nExtension Magic: Consumes 1 MP (magic point). Choose one bamboo and increase its length by 1.\nShortening Magic: Consumes 1 MP. Choose one bamboo of length at least 2 and decrease its length by 1.\nComposition Magic: Consumes 10 MP. Choose two bamboos and combine them into one bamboo. The length of this new bamboo is equal to the sum of the lengths of the two bamboos combined. (Afterwards, further magics can be used on this bamboo. )\n\nAt least how much MP is needed to achieve the objective?", "constraint": "3 <= N <= 8\n1 <= C < B < A <= 1000\n1 <= l_i <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B C\nl_1\nl_2\n:\nl_N", "output": "Print the minimum amount of MP needed to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 100 90 80\n98\n40\n30\n21\n80 output: 23\n\nWe are obtaining three bamboos of lengths 100,90,80 from five bamboos 98,40,30,21,80. We already have a bamboo of length 80, and we can obtain bamboos of lengths 100,90 by using the magics as follows at the total cost of 23 MP, which is optimal.\n\nUse Extension Magic twice on the bamboo of length 98 to obtain a bamboo of length 100. (MP consumed: 2)\nUse Composition Magic on the bamboos of lengths 40,30 to obtain a bamboo of length 70. (MP consumed: 10)\nUse Shortening Magic once on the bamboo of length 21 to obtain a bamboo of length 20. (MP consumed: 1)\nUse Composition Magic on the bamboo of length 70 obtained in step 2 and the bamboo of length 20 obtained in step 3 to obtain a bamboo of length 90. (MP consumed: 10)", "input: 8 100 90 80\n100\n100\n90\n90\n90\n80\n80\n80 output: 0\n\nIf we already have all bamboos of the desired lengths, the amount of MP needed is 0. As seen here, we do not necessarily need to use all the bamboos.", "input: 8 1000 800 100\n300\n333\n400\n444\n500\n555\n600\n666 output: 243"], "Pid": "p03111", "ProblemText": "Task Description: Problem Statement You have N bamboos. The lengths (in centimeters) of these are l_1, l_2, . . . , l_N, respectively.\nYour objective is to use some of these bamboos (possibly all) to obtain three bamboos of length A, B, C. For that, you can use the following three kinds of magics any number:\n\nExtension Magic: Consumes 1 MP (magic point). Choose one bamboo and increase its length by 1.\nShortening Magic: Consumes 1 MP. Choose one bamboo of length at least 2 and decrease its length by 1.\nComposition Magic: Consumes 10 MP. Choose two bamboos and combine them into one bamboo. The length of this new bamboo is equal to the sum of the lengths of the two bamboos combined. (Afterwards, further magics can be used on this bamboo. )\n\nAt least how much MP is needed to achieve the objective?\nTask Constraint: 3 <= N <= 8\n1 <= C < B < A <= 1000\n1 <= l_i <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B C\nl_1\nl_2\n:\nl_N\nTask Output: Print the minimum amount of MP needed to achieve the objective.\nTask Samples: input: 5 100 90 80\n98\n40\n30\n21\n80 output: 23\n\nWe are obtaining three bamboos of lengths 100,90,80 from five bamboos 98,40,30,21,80. We already have a bamboo of length 80, and we can obtain bamboos of lengths 100,90 by using the magics as follows at the total cost of 23 MP, which is optimal.\n\nUse Extension Magic twice on the bamboo of length 98 to obtain a bamboo of length 100. (MP consumed: 2)\nUse Composition Magic on the bamboos of lengths 40,30 to obtain a bamboo of length 70. (MP consumed: 10)\nUse Shortening Magic once on the bamboo of length 21 to obtain a bamboo of length 20. (MP consumed: 1)\nUse Composition Magic on the bamboo of length 70 obtained in step 2 and the bamboo of length 20 obtained in step 3 to obtain a bamboo of length 90. (MP consumed: 10)\ninput: 8 100 90 80\n100\n100\n90\n90\n90\n80\n80\n80 output: 0\n\nIf we already have all bamboos of the desired lengths, the amount of MP needed is 0. As seen here, we do not necessarily need to use all the bamboos.\ninput: 8 1000 800 100\n300\n333\n400\n444\n500\n555\n600\n666 output: 243\n\n" }, { "title": "", "content": "Problem Statement Along a road running in an east-west direction, there are A shrines and B temples.\nThe i-th shrine from the west is located at a distance of s_i meters from the west end of the road, and the i-th temple from the west is located at a distance of t_i meters from the west end of the road.\nAnswer the following Q queries:\n\nQuery i (1 <= i <= Q): If we start from a point at a distance of x_i meters from the west end of the road and freely travel along the road, what is the minimum distance that needs to be traveled in order to visit one shrine and one temple? (It is allowed to pass by more shrines and temples than required. )", "constraint": "1 <= A, B <= 10^5\n1 <= Q <= 10^5\n1 <= s_1 < s_2 < ... < s_A <= 10^{10}\n1 <= t_1 < t_2 < ... < t_B <= 10^{10}\n1 <= x_i <= 10^{10}\ns_1, ..., s_A, t_1, ..., t_B, x_1, ..., x_Q are all different.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B Q\ns_1\n:\ns_A\nt_1\n:\nt_B\nx_1\n:\nx_Q", "output": "Print Q lines. The i-th line should contain the answer to the i-th query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 4\n100\n600\n400\n900\n1000\n150\n2000\n899\n799 output: 350\n1400\n301\n399\n\nThere are two shrines and three temples. The shrines are located at distances of 100,600 meters from the west end of the road, and the temples are located at distances of 400,900,1000 meters from the west end of the road.\n\nQuery 1: If we start from a point at a distance of 150 meters from the west end of the road, the optimal move is first to walk 50 meters west to visit a shrine, then to walk 300 meters east to visit a temple.\nQuery 2: If we start from a point at a distance of 2000 meters from the west end of the road, the optimal move is first to walk 1000 meters west to visit a temple, then to walk 400 meters west to visit a shrine. We will pass by another temple on the way, but it is fine.\nQuery 3: If we start from a point at a distance of 899 meters from the west end of the road, the optimal move is first to walk 1 meter east to visit a temple, then to walk 300 meters west to visit a shrine.\nQuery 4: If we start from a point at a distance of 799 meters from the west end of the road, the optimal move is first to walk 199 meters west to visit a shrine, then to walk 200 meters west to visit a temple.", "input: 1 1 3\n1\n10000000000\n2\n9999999999\n5000000000 output: 10000000000\n10000000000\n14999999998\n\nThe road is quite long, and we may need to travel a distance that does not fit into a 32-bit integer."], "Pid": "p03112", "ProblemText": "Task Description: Problem Statement Along a road running in an east-west direction, there are A shrines and B temples.\nThe i-th shrine from the west is located at a distance of s_i meters from the west end of the road, and the i-th temple from the west is located at a distance of t_i meters from the west end of the road.\nAnswer the following Q queries:\n\nQuery i (1 <= i <= Q): If we start from a point at a distance of x_i meters from the west end of the road and freely travel along the road, what is the minimum distance that needs to be traveled in order to visit one shrine and one temple? (It is allowed to pass by more shrines and temples than required. )\nTask Constraint: 1 <= A, B <= 10^5\n1 <= Q <= 10^5\n1 <= s_1 < s_2 < ... < s_A <= 10^{10}\n1 <= t_1 < t_2 < ... < t_B <= 10^{10}\n1 <= x_i <= 10^{10}\ns_1, ..., s_A, t_1, ..., t_B, x_1, ..., x_Q are all different.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B Q\ns_1\n:\ns_A\nt_1\n:\nt_B\nx_1\n:\nx_Q\nTask Output: Print Q lines. The i-th line should contain the answer to the i-th query.\nTask Samples: input: 2 3 4\n100\n600\n400\n900\n1000\n150\n2000\n899\n799 output: 350\n1400\n301\n399\n\nThere are two shrines and three temples. The shrines are located at distances of 100,600 meters from the west end of the road, and the temples are located at distances of 400,900,1000 meters from the west end of the road.\n\nQuery 1: If we start from a point at a distance of 150 meters from the west end of the road, the optimal move is first to walk 50 meters west to visit a shrine, then to walk 300 meters east to visit a temple.\nQuery 2: If we start from a point at a distance of 2000 meters from the west end of the road, the optimal move is first to walk 1000 meters west to visit a temple, then to walk 400 meters west to visit a shrine. We will pass by another temple on the way, but it is fine.\nQuery 3: If we start from a point at a distance of 899 meters from the west end of the road, the optimal move is first to walk 1 meter east to visit a temple, then to walk 300 meters west to visit a shrine.\nQuery 4: If we start from a point at a distance of 799 meters from the west end of the road, the optimal move is first to walk 199 meters west to visit a shrine, then to walk 200 meters west to visit a temple.\ninput: 1 1 3\n1\n10000000000\n2\n9999999999\n5000000000 output: 10000000000\n10000000000\n14999999998\n\nThe road is quite long, and we may need to travel a distance that does not fit into a 32-bit integer.\n\n" }, { "title": "", "content": "Problem Statement Snuke participated in a magic show.\nA magician prepared N identical-looking boxes.\nHe put a treasure in one of the boxes, closed the boxes, shuffled them, and numbered them 1 through N.\nSince the boxes are shuffled, now Snuke has no idea which box contains the treasure.\nSnuke wins the game if he opens a box containing the treasure.\nYou may think that if Snuke opens all boxes at once, he can always win the game.\nHowever, there are some tricks:\n\nSnuke must open the boxes one by one. After he opens a box and checks the content of the box, he must close the box before opening the next box.\nHe is only allowed to open Box i at most a_i times.\nThe magician may secretly move the treasure from a closed box to another closed box, using some magic trick.\nFor simplicity, assume that the magician never moves the treasure while Snuke is opening some box.\nHowever, he can move it at any other time (before Snuke opens the first box, or between he closes some box and opens the next box).\nThe magician can perform the magic trick at most K times.\n\nCan Snuke always win the game, regardless of the initial position of the treasure and the movements of the magician?", "constraint": "2 <= N <= 50\n1 <= K <= 50\n1 <= a_i <= 100", "input": "Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\cdots a_N", "output": "If the answer is no, print a single -1.\nOtherwise, print one possible move of Snuke in the following format:\nQ\nx_1 x_2 \\cdots x_Q\n\nIt means that he opens boxes x_1, x_2, \\cdots, x_Q in this order.\nIn case there are multiple possible solutions, you can output any.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n5 5 output: 7\n1 1 2 1 2 2 1\n\nIf Snuke opens the boxes 7 times in the order 1 \\rightarrow 1 \\rightarrow 2 \\rightarrow 1 \\rightarrow 2 \\rightarrow 2 \\rightarrow 1, he can always find the treasure regardless of its initial position and the movements of the magician.", "input: 3 50\n5 10 15 output: -1"], "Pid": "p03113", "ProblemText": "Task Description: Problem Statement Snuke participated in a magic show.\nA magician prepared N identical-looking boxes.\nHe put a treasure in one of the boxes, closed the boxes, shuffled them, and numbered them 1 through N.\nSince the boxes are shuffled, now Snuke has no idea which box contains the treasure.\nSnuke wins the game if he opens a box containing the treasure.\nYou may think that if Snuke opens all boxes at once, he can always win the game.\nHowever, there are some tricks:\n\nSnuke must open the boxes one by one. After he opens a box and checks the content of the box, he must close the box before opening the next box.\nHe is only allowed to open Box i at most a_i times.\nThe magician may secretly move the treasure from a closed box to another closed box, using some magic trick.\nFor simplicity, assume that the magician never moves the treasure while Snuke is opening some box.\nHowever, he can move it at any other time (before Snuke opens the first box, or between he closes some box and opens the next box).\nThe magician can perform the magic trick at most K times.\n\nCan Snuke always win the game, regardless of the initial position of the treasure and the movements of the magician?\nTask Constraint: 2 <= N <= 50\n1 <= K <= 50\n1 <= a_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\cdots a_N\nTask Output: If the answer is no, print a single -1.\nOtherwise, print one possible move of Snuke in the following format:\nQ\nx_1 x_2 \\cdots x_Q\n\nIt means that he opens boxes x_1, x_2, \\cdots, x_Q in this order.\nIn case there are multiple possible solutions, you can output any.\nTask Samples: input: 2 1\n5 5 output: 7\n1 1 2 1 2 2 1\n\nIf Snuke opens the boxes 7 times in the order 1 \\rightarrow 1 \\rightarrow 2 \\rightarrow 1 \\rightarrow 2 \\rightarrow 2 \\rightarrow 1, he can always find the treasure regardless of its initial position and the movements of the magician.\ninput: 3 50\n5 10 15 output: -1\n\n" }, { "title": "", "content": "Problem Statement Count the number of strings S that satisfy the following constraints, modulo 10^9 + 7.\n\nThe length of S is exactly N.\nS consists of digits (0. . . 9).\nYou are given Q intervals.\nFor each i (1 <= i <= Q), the integer represented by S[l_i \\ldots r_i] (the substring of S between the l_i-th (1-based) character and the r_i-th character, inclusive) must be a multiple of 9.\n\nHere, the string S and its substrings may have leading zeroes.\nFor example, 002019 represents the integer 2019.", "constraint": "1 <= N <= 10^9\n1 <= Q <= 15\n1 <= l_i <= r_i <= N", "input": "Input is given from Standard Input in the following format:\nN\nQ\nl_1 r_1\n:\nl_Q r_Q", "output": "Print the number of strings that satisfy the conditions, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2\n1 2\n2 4 output: 136\n\nFor example, S = 9072 satisfies the conditions because both S[1 \\ldots 2] = 90 and S[2 \\ldots 4] = 072 represent multiples of 9.", "input: 6\n3\n2 5\n3 5\n1 3 output: 2720", "input: 20\n10\n2 15\n5 6\n1 12\n7 9\n2 17\n5 15\n2 4\n16 17\n2 12\n8 17 output: 862268030"], "Pid": "p03114", "ProblemText": "Task Description: Problem Statement Count the number of strings S that satisfy the following constraints, modulo 10^9 + 7.\n\nThe length of S is exactly N.\nS consists of digits (0. . . 9).\nYou are given Q intervals.\nFor each i (1 <= i <= Q), the integer represented by S[l_i \\ldots r_i] (the substring of S between the l_i-th (1-based) character and the r_i-th character, inclusive) must be a multiple of 9.\n\nHere, the string S and its substrings may have leading zeroes.\nFor example, 002019 represents the integer 2019.\nTask Constraint: 1 <= N <= 10^9\n1 <= Q <= 15\n1 <= l_i <= r_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN\nQ\nl_1 r_1\n:\nl_Q r_Q\nTask Output: Print the number of strings that satisfy the conditions, modulo 10^9 + 7.\nTask Samples: input: 4\n2\n1 2\n2 4 output: 136\n\nFor example, S = 9072 satisfies the conditions because both S[1 \\ldots 2] = 90 and S[2 \\ldots 4] = 072 represent multiples of 9.\ninput: 6\n3\n2 5\n3 5\n1 3 output: 2720\ninput: 20\n10\n2 15\n5 6\n1 12\n7 9\n2 17\n5 15\n2 4\n16 17\n2 12\n8 17 output: 862268030\n\n" }, { "title": "", "content": "Problem Statement There is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, 0) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X.", "constraint": "1 <= N <= 10^5\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1\n\nThe following picture shows one possible sequence of operations:"], "Pid": "p03115", "ProblemText": "Task Description: Problem Statement There is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, 0) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X.\nTask Constraint: 1 <= N <= 10^5\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print X.\nTask Samples: input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1\n\nThe following picture shows one possible sequence of operations:\n\n" }, { "title": "", "content": "Problem Statement Red bold fonts show the difference from C1.\nThere is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, Y) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X and Y.", "constraint": "1 <= N <= 10^4\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X and Y.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print X and Y, separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1 0\n\nThe following picture shows one possible sequence of operations:"], "Pid": "p03116", "ProblemText": "Task Description: Problem Statement Red bold fonts show the difference from C1.\nThere is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, Y) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X and Y.\nTask Constraint: 1 <= N <= 10^4\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X and Y.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print X and Y, separated by a space.\nTask Samples: input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1 0\n\nThe following picture shows one possible sequence of operations:\n\n" }, { "title": "", "content": "Problem Statement Snuke has R red balls and B blue balls.\nHe distributes them into K boxes, so that no box is empty and no two boxes are identical.\nCompute the maximum possible value of K.\nFormally speaking, let's number the boxes 1 through K.\nIf Box i contains r_i red balls and b_i blue balls, the following conditions must be satisfied:\n\nFor each i (1 <= i <= K), r_i > 0 or b_i > 0.\nFor each i, j (1 <= i < j <= K), r_i \\neq r_j or b_i \\neq b_j.\n\\sum r_i = R and \\sum b_i = B (no balls can be left outside the boxes).", "constraint": "1 <= R, B <= 10^{9}", "input": "Input is given from Standard Input in the following format:\nR B", "output": "Print the maximum possible value of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 3 output: 5\n\nThe following picture shows one possible way to achieve K = 5:"], "Pid": "p03117", "ProblemText": "Task Description: Problem Statement Snuke has R red balls and B blue balls.\nHe distributes them into K boxes, so that no box is empty and no two boxes are identical.\nCompute the maximum possible value of K.\nFormally speaking, let's number the boxes 1 through K.\nIf Box i contains r_i red balls and b_i blue balls, the following conditions must be satisfied:\n\nFor each i (1 <= i <= K), r_i > 0 or b_i > 0.\nFor each i, j (1 <= i < j <= K), r_i \\neq r_j or b_i \\neq b_j.\n\\sum r_i = R and \\sum b_i = B (no balls can be left outside the boxes).\nTask Constraint: 1 <= R, B <= 10^{9}\nTask Input: Input is given from Standard Input in the following format:\nR B\nTask Output: Print the maximum possible value of K.\nTask Samples: input: 8 3 output: 5\n\nThe following picture shows one possible way to achieve K = 5:\n\n" }, { "title": "", "content": "Problem Statement There is a very long bench.\nThe bench is divided into M sections, where M is a very large integer.\nInitially, the bench is vacant.\nThen, M people come to the bench one by one, and perform the following action:\n\nWe call a section comfortable if the section is currently unoccupied and is not adjacent to any occupied sections.\nIf there is no comfortable section, the person leaves the bench.\nOtherwise, the person chooses one of comfortable sections uniformly at random, and sits there.\n(The choices are independent from each other).\n\nAfter all M people perform actions, Snuke chooses an interval of N consecutive sections uniformly at random (from M-N+1 possible intervals), and takes a photo.\nHis photo can be described by a string of length N consisting of X and -: the i-th character of the string is X if the i-th section from the left in the interval is occupied, and - otherwise.\nNote that the photo is directed.\nFor example, -X--X and X--X- are different photos.\nWhat is the probability that the photo matches a given string s?\nThis probability depends on M.\nYou need to compute the limit of this probability when M goes infinity.\nHere, we can prove that the limit can be uniquely written in the following format using three rational numbers p, q, r and e = 2.718 \\ldots (the base of natural logarithm):\np + \\frac{q}{e} + \\frac{r}{e^2}\nYour task is to compute these three rational numbers, and print them modulo 10^9 + 7, as described in Notes section. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.", "constraint": "1 <= N <= 1000\n|s| = N\ns consists of X and -.", "input": "Input is given from Standard Input in the following format:\nN\ns", "output": "Print three rational numbers p, q, r, separated by spaces.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\nX output: 500000004 0 500000003\n\nThe probability that a randomly chosen section is occupied converge to \\frac{1}{2} - \\frac{1}{2e^2}.", "input: 3\n--- output: 0 0 0\n\nAfter the actions, no three consecutive unoccupied sections can be left.", "input: 5\nX--X- output: 0 0 1\n\nThe limit is \\frac{1}{e^2}.", "input: 5\nX-X-X output: 500000004 0 833333337\n\nThe limit is \\frac{1}{2} - \\frac{13}{6e^2}.", "input: 20\n-X--X--X-X--X--X-X-X output: 0 0 183703705\n\nThe limit is \\frac{7}{675e^2}.", "input: 100\nX-X-X-X-X-X-X-X-X-X--X-X-X-X-X-X-X-X-X-X-X-X-X-X-X--X--X-X-X-X--X--X-X-X--X-X-X--X-X--X--X-X--X-X-X- output: 0 0 435664291"], "Pid": "p03118", "ProblemText": "Task Description: Problem Statement There is a very long bench.\nThe bench is divided into M sections, where M is a very large integer.\nInitially, the bench is vacant.\nThen, M people come to the bench one by one, and perform the following action:\n\nWe call a section comfortable if the section is currently unoccupied and is not adjacent to any occupied sections.\nIf there is no comfortable section, the person leaves the bench.\nOtherwise, the person chooses one of comfortable sections uniformly at random, and sits there.\n(The choices are independent from each other).\n\nAfter all M people perform actions, Snuke chooses an interval of N consecutive sections uniformly at random (from M-N+1 possible intervals), and takes a photo.\nHis photo can be described by a string of length N consisting of X and -: the i-th character of the string is X if the i-th section from the left in the interval is occupied, and - otherwise.\nNote that the photo is directed.\nFor example, -X--X and X--X- are different photos.\nWhat is the probability that the photo matches a given string s?\nThis probability depends on M.\nYou need to compute the limit of this probability when M goes infinity.\nHere, we can prove that the limit can be uniquely written in the following format using three rational numbers p, q, r and e = 2.718 \\ldots (the base of natural logarithm):\np + \\frac{q}{e} + \\frac{r}{e^2}\nYour task is to compute these three rational numbers, and print them modulo 10^9 + 7, as described in Notes section. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.\nTask Constraint: 1 <= N <= 1000\n|s| = N\ns consists of X and -.\nTask Input: Input is given from Standard Input in the following format:\nN\ns\nTask Output: Print three rational numbers p, q, r, separated by spaces.\nTask Samples: input: 1\nX output: 500000004 0 500000003\n\nThe probability that a randomly chosen section is occupied converge to \\frac{1}{2} - \\frac{1}{2e^2}.\ninput: 3\n--- output: 0 0 0\n\nAfter the actions, no three consecutive unoccupied sections can be left.\ninput: 5\nX--X- output: 0 0 1\n\nThe limit is \\frac{1}{e^2}.\ninput: 5\nX-X-X output: 500000004 0 833333337\n\nThe limit is \\frac{1}{2} - \\frac{13}{6e^2}.\ninput: 20\n-X--X--X-X--X--X-X-X output: 0 0 183703705\n\nThe limit is \\frac{7}{675e^2}.\ninput: 100\nX-X-X-X-X-X-X-X-X-X--X-X-X-X-X-X-X-X-X-X-X-X-X-X-X--X--X-X-X-X--X--X-X-X--X-X-X--X-X--X--X-X--X-X-X- output: 0 0 435664291\n\n" }, { "title": "", "content": "Problem Statement Snuke participated in a magic show.\nA magician prepared N identical-looking boxes.\nHe put a treasure in one of the boxes, closed the boxes, shuffled them, and numbered them 1 through N.\nSince the boxes are shuffled, now Snuke has no idea which box contains the treasure.\nSnuke wins the game if he opens a box containing the treasure.\nYou may think that if Snuke opens all boxes at once, he can always win the game.\nHowever, there are some tricks:\n\nSnuke must open the boxes one by one. After he opens a box and checks the content of the box, he must close the box before opening the next box.\nHe is only allowed to open Box i at most a_i times.\nThe magician may secretly move the treasure from a closed box to another closed box, using some magic trick.\nFor simplicity, assume that the magician never moves the treasure while Snuke is opening some box.\nHowever, he can move it at any other time (before Snuke opens the first box, or between he closes some box and opens the next box).\nThe magician can perform the magic trick at most K times.\n\nCan Snuke always win the game, regardless of the initial position of the treasure and the movements of the magician?", "constraint": "2 <= N <= 50\n1 <= K <= 50\n1 <= a_i <= 100", "input": "Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\cdots a_N", "output": "If the answer is no, print a single -1.\nOtherwise, print one possible move of Snuke in the following format:\nQ\nx_1 x_2 \\cdots x_Q\n\nIt means that he opens boxes x_1, x_2, \\cdots, x_Q in this order.\nIn case there are multiple possible solutions, you can output any.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n5 5 output: 7\n1 1 2 1 2 2 1\n\nIf Snuke opens the boxes 7 times in the order 1 \\rightarrow 1 \\rightarrow 2 \\rightarrow 1 \\rightarrow 2 \\rightarrow 2 \\rightarrow 1, he can always find the treasure regardless of its initial position and the movements of the magician.", "input: 3 50\n5 10 15 output: -1"], "Pid": "p03119", "ProblemText": "Task Description: Problem Statement Snuke participated in a magic show.\nA magician prepared N identical-looking boxes.\nHe put a treasure in one of the boxes, closed the boxes, shuffled them, and numbered them 1 through N.\nSince the boxes are shuffled, now Snuke has no idea which box contains the treasure.\nSnuke wins the game if he opens a box containing the treasure.\nYou may think that if Snuke opens all boxes at once, he can always win the game.\nHowever, there are some tricks:\n\nSnuke must open the boxes one by one. After he opens a box and checks the content of the box, he must close the box before opening the next box.\nHe is only allowed to open Box i at most a_i times.\nThe magician may secretly move the treasure from a closed box to another closed box, using some magic trick.\nFor simplicity, assume that the magician never moves the treasure while Snuke is opening some box.\nHowever, he can move it at any other time (before Snuke opens the first box, or between he closes some box and opens the next box).\nThe magician can perform the magic trick at most K times.\n\nCan Snuke always win the game, regardless of the initial position of the treasure and the movements of the magician?\nTask Constraint: 2 <= N <= 50\n1 <= K <= 50\n1 <= a_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\cdots a_N\nTask Output: If the answer is no, print a single -1.\nOtherwise, print one possible move of Snuke in the following format:\nQ\nx_1 x_2 \\cdots x_Q\n\nIt means that he opens boxes x_1, x_2, \\cdots, x_Q in this order.\nIn case there are multiple possible solutions, you can output any.\nTask Samples: input: 2 1\n5 5 output: 7\n1 1 2 1 2 2 1\n\nIf Snuke opens the boxes 7 times in the order 1 \\rightarrow 1 \\rightarrow 2 \\rightarrow 1 \\rightarrow 2 \\rightarrow 2 \\rightarrow 1, he can always find the treasure regardless of its initial position and the movements of the magician.\ninput: 3 50\n5 10 15 output: -1\n\n" }, { "title": "", "content": "Problem Statement Count the number of strings S that satisfy the following constraints, modulo 10^9 + 7.\n\nThe length of S is exactly N.\nS consists of digits (0. . . 9).\nYou are given Q intervals.\nFor each i (1 <= i <= Q), the integer represented by S[l_i \\ldots r_i] (the substring of S between the l_i-th (1-based) character and the r_i-th character, inclusive) must be a multiple of 9.\n\nHere, the string S and its substrings may have leading zeroes.\nFor example, 002019 represents the integer 2019.", "constraint": "1 <= N <= 10^9\n1 <= Q <= 15\n1 <= l_i <= r_i <= N", "input": "Input is given from Standard Input in the following format:\nN\nQ\nl_1 r_1\n:\nl_Q r_Q", "output": "Print the number of strings that satisfy the conditions, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2\n1 2\n2 4 output: 136\n\nFor example, S = 9072 satisfies the conditions because both S[1 \\ldots 2] = 90 and S[2 \\ldots 4] = 072 represent multiples of 9.", "input: 6\n3\n2 5\n3 5\n1 3 output: 2720", "input: 20\n10\n2 15\n5 6\n1 12\n7 9\n2 17\n5 15\n2 4\n16 17\n2 12\n8 17 output: 862268030"], "Pid": "p03120", "ProblemText": "Task Description: Problem Statement Count the number of strings S that satisfy the following constraints, modulo 10^9 + 7.\n\nThe length of S is exactly N.\nS consists of digits (0. . . 9).\nYou are given Q intervals.\nFor each i (1 <= i <= Q), the integer represented by S[l_i \\ldots r_i] (the substring of S between the l_i-th (1-based) character and the r_i-th character, inclusive) must be a multiple of 9.\n\nHere, the string S and its substrings may have leading zeroes.\nFor example, 002019 represents the integer 2019.\nTask Constraint: 1 <= N <= 10^9\n1 <= Q <= 15\n1 <= l_i <= r_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN\nQ\nl_1 r_1\n:\nl_Q r_Q\nTask Output: Print the number of strings that satisfy the conditions, modulo 10^9 + 7.\nTask Samples: input: 4\n2\n1 2\n2 4 output: 136\n\nFor example, S = 9072 satisfies the conditions because both S[1 \\ldots 2] = 90 and S[2 \\ldots 4] = 072 represent multiples of 9.\ninput: 6\n3\n2 5\n3 5\n1 3 output: 2720\ninput: 20\n10\n2 15\n5 6\n1 12\n7 9\n2 17\n5 15\n2 4\n16 17\n2 12\n8 17 output: 862268030\n\n" }, { "title": "", "content": "Problem Statement There is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, 0) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X.", "constraint": "1 <= N <= 10^5\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1\n\nThe following picture shows one possible sequence of operations:"], "Pid": "p03121", "ProblemText": "Task Description: Problem Statement There is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, 0) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X.\nTask Constraint: 1 <= N <= 10^5\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print X.\nTask Samples: input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1\n\nThe following picture shows one possible sequence of operations:\n\n" }, { "title": "", "content": "Problem Statement Red bold fonts show the difference from C1.\nThere is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, Y) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X and Y.", "constraint": "1 <= N <= 10^4\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X and Y.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print X and Y, separated by a space.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1 0\n\nThe following picture shows one possible sequence of operations:"], "Pid": "p03122", "ProblemText": "Task Description: Problem Statement Red bold fonts show the difference from C1.\nThere is an infinitely large triangular grid, as shown below.\nEach point with integer coordinates contains a lamp.\n\nInitially, only the lamp at (X, Y) was on, and all other lamps were off.\nThen, Snuke performed the following operation zero or more times:\n\nChoose two integers x and y.\nToggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).\n\nAfter the operations, N lamps (x_1, y_1), \\cdots, (x_N, y_N) are on, and all other lamps are off.\nFind X and Y.\nTask Constraint: 1 <= N <= 10^4\n-10^{17} <= x_i, y_i <= 10^{17}\n(x_i, y_i) are pairwise distinct.\nThe input is consistent with the statement, and you can uniquely determine X and Y.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print X and Y, separated by a space.\nTask Samples: input: 4\n-2 1\n-2 2\n0 1\n1 0 output: -1 0\n\nThe following picture shows one possible sequence of operations:\n\n" }, { "title": "", "content": "Problem Statement Snuke has R red balls and B blue balls.\nHe distributes them into K boxes, so that no box is empty and no two boxes are identical.\nCompute the maximum possible value of K.\nFormally speaking, let's number the boxes 1 through K.\nIf Box i contains r_i red balls and b_i blue balls, the following conditions must be satisfied:\n\nFor each i (1 <= i <= K), r_i > 0 or b_i > 0.\nFor each i, j (1 <= i < j <= K), r_i \\neq r_j or b_i \\neq b_j.\n\\sum r_i = R and \\sum b_i = B (no balls can be left outside the boxes).", "constraint": "1 <= R, B <= 10^{9}", "input": "Input is given from Standard Input in the following format:\nR B", "output": "Print the maximum possible value of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 3 output: 5\n\nThe following picture shows one possible way to achieve K = 5:"], "Pid": "p03123", "ProblemText": "Task Description: Problem Statement Snuke has R red balls and B blue balls.\nHe distributes them into K boxes, so that no box is empty and no two boxes are identical.\nCompute the maximum possible value of K.\nFormally speaking, let's number the boxes 1 through K.\nIf Box i contains r_i red balls and b_i blue balls, the following conditions must be satisfied:\n\nFor each i (1 <= i <= K), r_i > 0 or b_i > 0.\nFor each i, j (1 <= i < j <= K), r_i \\neq r_j or b_i \\neq b_j.\n\\sum r_i = R and \\sum b_i = B (no balls can be left outside the boxes).\nTask Constraint: 1 <= R, B <= 10^{9}\nTask Input: Input is given from Standard Input in the following format:\nR B\nTask Output: Print the maximum possible value of K.\nTask Samples: input: 8 3 output: 5\n\nThe following picture shows one possible way to achieve K = 5:\n\n" }, { "title": "", "content": "Problem Statement There is a very long bench.\nThe bench is divided into M sections, where M is a very large integer.\nInitially, the bench is vacant.\nThen, M people come to the bench one by one, and perform the following action:\n\nWe call a section comfortable if the section is currently unoccupied and is not adjacent to any occupied sections.\nIf there is no comfortable section, the person leaves the bench.\nOtherwise, the person chooses one of comfortable sections uniformly at random, and sits there.\n(The choices are independent from each other).\n\nAfter all M people perform actions, Snuke chooses an interval of N consecutive sections uniformly at random (from M-N+1 possible intervals), and takes a photo.\nHis photo can be described by a string of length N consisting of X and -: the i-th character of the string is X if the i-th section from the left in the interval is occupied, and - otherwise.\nNote that the photo is directed.\nFor example, -X--X and X--X- are different photos.\nWhat is the probability that the photo matches a given string s?\nThis probability depends on M.\nYou need to compute the limit of this probability when M goes infinity.\nHere, we can prove that the limit can be uniquely written in the following format using three rational numbers p, q, r and e = 2.718 \\ldots (the base of natural logarithm):\np + \\frac{q}{e} + \\frac{r}{e^2}\nYour task is to compute these three rational numbers, and print them modulo 10^9 + 7, as described in Notes section. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.", "constraint": "1 <= N <= 1000\n|s| = N\ns consists of X and -.", "input": "Input is given from Standard Input in the following format:\nN\ns", "output": "Print three rational numbers p, q, r, separated by spaces.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\nX output: 500000004 0 500000003\n\nThe probability that a randomly chosen section is occupied converge to \\frac{1}{2} - \\frac{1}{2e^2}.", "input: 3\n--- output: 0 0 0\n\nAfter the actions, no three consecutive unoccupied sections can be left.", "input: 5\nX--X- output: 0 0 1\n\nThe limit is \\frac{1}{e^2}.", "input: 5\nX-X-X output: 500000004 0 833333337\n\nThe limit is \\frac{1}{2} - \\frac{13}{6e^2}.", "input: 20\n-X--X--X-X--X--X-X-X output: 0 0 183703705\n\nThe limit is \\frac{7}{675e^2}.", "input: 100\nX-X-X-X-X-X-X-X-X-X--X-X-X-X-X-X-X-X-X-X-X-X-X-X-X--X--X-X-X-X--X--X-X-X--X-X-X--X-X--X--X-X--X-X-X- output: 0 0 435664291"], "Pid": "p03124", "ProblemText": "Task Description: Problem Statement There is a very long bench.\nThe bench is divided into M sections, where M is a very large integer.\nInitially, the bench is vacant.\nThen, M people come to the bench one by one, and perform the following action:\n\nWe call a section comfortable if the section is currently unoccupied and is not adjacent to any occupied sections.\nIf there is no comfortable section, the person leaves the bench.\nOtherwise, the person chooses one of comfortable sections uniformly at random, and sits there.\n(The choices are independent from each other).\n\nAfter all M people perform actions, Snuke chooses an interval of N consecutive sections uniformly at random (from M-N+1 possible intervals), and takes a photo.\nHis photo can be described by a string of length N consisting of X and -: the i-th character of the string is X if the i-th section from the left in the interval is occupied, and - otherwise.\nNote that the photo is directed.\nFor example, -X--X and X--X- are different photos.\nWhat is the probability that the photo matches a given string s?\nThis probability depends on M.\nYou need to compute the limit of this probability when M goes infinity.\nHere, we can prove that the limit can be uniquely written in the following format using three rational numbers p, q, r and e = 2.718 \\ldots (the base of natural logarithm):\np + \\frac{q}{e} + \\frac{r}{e^2}\nYour task is to compute these three rational numbers, and print them modulo 10^9 + 7, as described in Notes section. note: Notes When you print a rational number, first write it as a fraction \\frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7\n(under the constraints of the problem, such representation is always possible).\nThen, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \\equiv y \\pmod{10^9 + 7}.\nTask Constraint: 1 <= N <= 1000\n|s| = N\ns consists of X and -.\nTask Input: Input is given from Standard Input in the following format:\nN\ns\nTask Output: Print three rational numbers p, q, r, separated by spaces.\nTask Samples: input: 1\nX output: 500000004 0 500000003\n\nThe probability that a randomly chosen section is occupied converge to \\frac{1}{2} - \\frac{1}{2e^2}.\ninput: 3\n--- output: 0 0 0\n\nAfter the actions, no three consecutive unoccupied sections can be left.\ninput: 5\nX--X- output: 0 0 1\n\nThe limit is \\frac{1}{e^2}.\ninput: 5\nX-X-X output: 500000004 0 833333337\n\nThe limit is \\frac{1}{2} - \\frac{13}{6e^2}.\ninput: 20\n-X--X--X-X--X--X-X-X output: 0 0 183703705\n\nThe limit is \\frac{7}{675e^2}.\ninput: 100\nX-X-X-X-X-X-X-X-X-X--X-X-X-X-X-X-X-X-X-X-X-X-X-X-X--X--X-X-X-X--X--X-X-X--X-X-X--X-X--X--X-X--X-X-X- output: 0 0 435664291\n\n" }, { "title": "", "content": "Problem Statement You are given positive integers A and B.\nIf A is a divisor of B, print A + B; otherwise, print B - A.", "constraint": "All values in input are integers.\n1 <= A <= B <= 20", "input": "Input is given from Standard Input in the following format:\nA B", "output": "If A is a divisor of B, print A + B; otherwise, print B - A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 12 output: 16\n\nAs 4 is a divisor of 12,4 + 12 = 16 should be printed.", "input: 8 20 output: 12", "input: 1 1 output: 2\n\n1 is a divisor of 1."], "Pid": "p03125", "ProblemText": "Task Description: Problem Statement You are given positive integers A and B.\nIf A is a divisor of B, print A + B; otherwise, print B - A.\nTask Constraint: All values in input are integers.\n1 <= A <= B <= 20\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: If A is a divisor of B, print A + B; otherwise, print B - A.\nTask Samples: input: 4 12 output: 16\n\nAs 4 is a divisor of 12,4 + 12 = 16 should be printed.\ninput: 8 20 output: 12\ninput: 1 1 output: 2\n\n1 is a divisor of 1.\n\n" }, { "title": "", "content": "Problem Statement Katsusando loves omelette rice.\nBesides, he loves crème brûlée, tenderloin steak and so on, and believes that these foods are all loved by everyone.\nTo prove that hypothesis, he conducted a survey on M kinds of foods and asked N people whether they like these foods or not.\nThe i-th person answered that he/she only likes the A_{i1}-th, A_{i2}-th, . . . , A_{i K_i}-th food.\nFind the number of the foods liked by all the N people.", "constraint": "", "input": "Input is given from Standard Input in the following format:\nN M\nK_1 A_{11} A_{12} ... A_{1K_1}\nK_2 A_{21} A_{22} ... A_{2K_2}\n:\nK_N A_{N1} A_{N2} ... A_{NK_N}", "output": "Print the number of the foods liked by all the N people.", "content_img": false, "lang": "en", "error": true, "samples": ["input: 3 4\n2 1 3\n3 1 2 3\n2 3 2 output: 1\n\nAs only the third food is liked by all the three people, 1 should be printed.", "input: 5 5\n4 2 3 4 5\n4 1 3 4 5\n4 1 2 4 5\n4 1 2 3 5\n4 1 2 3 4 output: 0\n\nKatsusando's hypothesis turned out to be wrong.", "input: 1 30\n3 5 10 30 output: 3"], "Pid": "p03126", "ProblemText": "Task Description: Problem Statement Katsusando loves omelette rice.\nBesides, he loves crème brûlée, tenderloin steak and so on, and believes that these foods are all loved by everyone.\nTo prove that hypothesis, he conducted a survey on M kinds of foods and asked N people whether they like these foods or not.\nThe i-th person answered that he/she only likes the A_{i1}-th, A_{i2}-th, . . . , A_{i K_i}-th food.\nFind the number of the foods liked by all the N people.\nTask Input: Input is given from Standard Input in the following format:\nN M\nK_1 A_{11} A_{12} ... A_{1K_1}\nK_2 A_{21} A_{22} ... A_{2K_2}\n:\nK_N A_{N1} A_{N2} ... A_{NK_N}\nTask Output: Print the number of the foods liked by all the N people.\nTask Samples: input: 3 4\n2 1 3\n3 1 2 3\n2 3 2 output: 1\n\nAs only the third food is liked by all the three people, 1 should be printed.\ninput: 5 5\n4 2 3 4 5\n4 1 3 4 5\n4 1 2 4 5\n4 1 2 3 5\n4 1 2 3 4 output: 0\n\nKatsusando's hypothesis turned out to be wrong.\ninput: 1 30\n3 5 10 30 output: 3\n\n" }, { "title": "", "content": "Problem Statement There are N monsters, numbered 1,2, . . . , N.\nInitially, the health of Monster i is A_i.\nBelow, a monster with at least 1 health is called alive.\nUntil there is only one alive monster, the following is repeated:\n\nA random alive monster attacks another random alive monster.\nAs a result, the health of the monster attacked is reduced by the amount equal to the current health of the monster attacking.\n\nFind the minimum possible final health of the last monster alive.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the minimum possible final health of the last monster alive.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 10 8 40 output: 2\n\nWhen only the first monster keeps on attacking, the final health of the last monster will be 2, which is minimum.", "input: 4\n5 13 8 1000000000 output: 1", "input: 3\n1000000000 1000000000 1000000000 output: 1000000000"], "Pid": "p03127", "ProblemText": "Task Description: Problem Statement There are N monsters, numbered 1,2, . . . , N.\nInitially, the health of Monster i is A_i.\nBelow, a monster with at least 1 health is called alive.\nUntil there is only one alive monster, the following is repeated:\n\nA random alive monster attacks another random alive monster.\nAs a result, the health of the monster attacked is reduced by the amount equal to the current health of the monster attacking.\n\nFind the minimum possible final health of the last monster alive.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the minimum possible final health of the last monster alive.\nTask Samples: input: 4\n2 10 8 40 output: 2\n\nWhen only the first monster keeps on attacking, the final health of the last monster will be 2, which is minimum.\ninput: 4\n5 13 8 1000000000 output: 1\ninput: 3\n1000000000 1000000000 1000000000 output: 1000000000\n\n" }, { "title": "", "content": "Problem Statement Find the largest integer that can be formed with exactly N matchsticks, under the following conditions:\n\nEvery digit in the integer must be one of the digits A_1, A_2, . . . , A_M (1 <= A_i <= 9).\nThe number of matchsticks used to form digits 1,2,3,4,5,6,7,8,9 should be 2,5,5,4,5,6,3,7,6, respectively.", "constraint": "All values in input are integers.\n2 <= N <= 10^4\n1 <= M <= 9\n1 <= A_i <= 9\nA_i are all different.\nThere exists an integer that can be formed by exactly N matchsticks under the conditions.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_M", "output": "Print the largest integer that can be formed with exactly N matchsticks under the conditions in the problem statement.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 20 4\n3 7 8 4 output: 777773\n\nThe integer 777773 can be formed with 3 + 3 + 3 + 3 + 3 + 5 = 20 matchsticks, and this is the largest integer that can be formed by 20 matchsticks under the conditions.", "input: 101 9\n9 8 7 6 5 4 3 2 1 output: 71111111111111111111111111111111111111111111111111\n\nThe output may not fit into a 64-bit integer type.", "input: 15 3\n5 4 6 output: 654"], "Pid": "p03128", "ProblemText": "Task Description: Problem Statement Find the largest integer that can be formed with exactly N matchsticks, under the following conditions:\n\nEvery digit in the integer must be one of the digits A_1, A_2, . . . , A_M (1 <= A_i <= 9).\nThe number of matchsticks used to form digits 1,2,3,4,5,6,7,8,9 should be 2,5,5,4,5,6,3,7,6, respectively.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^4\n1 <= M <= 9\n1 <= A_i <= 9\nA_i are all different.\nThere exists an integer that can be formed by exactly N matchsticks under the conditions.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_M\nTask Output: Print the largest integer that can be formed with exactly N matchsticks under the conditions in the problem statement.\nTask Samples: input: 20 4\n3 7 8 4 output: 777773\n\nThe integer 777773 can be formed with 3 + 3 + 3 + 3 + 3 + 5 = 20 matchsticks, and this is the largest integer that can be formed by 20 matchsticks under the conditions.\ninput: 101 9\n9 8 7 6 5 4 3 2 1 output: 71111111111111111111111111111111111111111111111111\n\nThe output may not fit into a 64-bit integer type.\ninput: 15 3\n5 4 6 output: 654\n\n" }, { "title": "", "content": "Problem Statement Determine if we can choose K different integers between 1 and N (inclusive) so that no two of them differ by 1.", "constraint": "1<= N,K<= 100\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "If we can choose K integers as above, print YES; otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: YES\n\nWe can choose 1 and 3.", "input: 5 5 output: NO", "input: 31 10 output: YES", "input: 10 90 output: NO"], "Pid": "p03129", "ProblemText": "Task Description: Problem Statement Determine if we can choose K different integers between 1 and N (inclusive) so that no two of them differ by 1.\nTask Constraint: 1<= N,K<= 100\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: If we can choose K integers as above, print YES; otherwise, print NO.\nTask Samples: input: 3 2 output: YES\n\nWe can choose 1 and 3.\ninput: 5 5 output: NO\ninput: 31 10 output: YES\ninput: 10 90 output: NO\n\n" }, { "title": "", "content": "Problem Statement There are four towns, numbered 1,2,3 and 4.\nAlso, there are three roads. The i-th road connects different towns a_i and b_i bidirectionally.\nNo two roads connect the same pair of towns. Other than these roads, there is no way to travel between these towns, but any town can be reached from any other town using these roads.\nDetermine if we can visit all the towns by traversing each of the roads exactly once.", "constraint": "1 <= a_i,b_i <= 4(1<= i<= 3)\na_i and b_i are different. (1<= i<= 3)\nNo two roads connect the same pair of towns.\nAny town can be reached from any other town using the roads.", "input": "Input is given from Standard Input in the following format:\na_1 b_1\na_2 b_2\na_3 b_3", "output": "If we can visit all the towns by traversing each of the roads exactly once, print YES; otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n1 3\n2 3 output: YES\n\nWe can visit all the towns in the order 1,3,2,4.", "input: 3 2\n2 4\n1 2 output: NO", "input: 2 1\n3 2\n4 3 output: YES"], "Pid": "p03130", "ProblemText": "Task Description: Problem Statement There are four towns, numbered 1,2,3 and 4.\nAlso, there are three roads. The i-th road connects different towns a_i and b_i bidirectionally.\nNo two roads connect the same pair of towns. Other than these roads, there is no way to travel between these towns, but any town can be reached from any other town using these roads.\nDetermine if we can visit all the towns by traversing each of the roads exactly once.\nTask Constraint: 1 <= a_i,b_i <= 4(1<= i<= 3)\na_i and b_i are different. (1<= i<= 3)\nNo two roads connect the same pair of towns.\nAny town can be reached from any other town using the roads.\nTask Input: Input is given from Standard Input in the following format:\na_1 b_1\na_2 b_2\na_3 b_3\nTask Output: If we can visit all the towns by traversing each of the roads exactly once, print YES; otherwise, print NO.\nTask Samples: input: 4 2\n1 3\n2 3 output: YES\n\nWe can visit all the towns in the order 1,3,2,4.\ninput: 3 2\n2 4\n1 2 output: NO\ninput: 2 1\n3 2\n4 3 output: YES\n\n" }, { "title": "", "content": "Problem Statement Snuke has one biscuit and zero Japanese yen (the currency) in his pocket.\nHe will perform the following operations exactly K times in total, in the order he likes:\n\nHit his pocket, which magically increases the number of biscuits by one.\nExchange A biscuits to 1 yen.\nExchange 1 yen to B biscuits.\n\nFind the maximum possible number of biscuits in Snuke's pocket after K operations.", "constraint": "1 <= K,A,B <= 10^9\nK,A and B are integers.", "input": "Input is given from Standard Input in the following format:\nK A B", "output": "Print the maximum possible number of biscuits in Snuke's pocket after K operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 6 output: 7\n\nThe number of biscuits in Snuke's pocket after K operations is maximized as follows:\n\nHit his pocket. Now he has 2 biscuits and 0 yen.\nExchange 2 biscuits to 1 yen. his pocket. Now he has 0 biscuits and 1 yen.\nHit his pocket. Now he has 1 biscuits and 1 yen.\nExchange 1 yen to 6 biscuits. his pocket. Now he has 7 biscuits and 0 yen.", "input: 7 3 4 output: 8", "input: 314159265 35897932 384626433 output: 48518828981938099"], "Pid": "p03131", "ProblemText": "Task Description: Problem Statement Snuke has one biscuit and zero Japanese yen (the currency) in his pocket.\nHe will perform the following operations exactly K times in total, in the order he likes:\n\nHit his pocket, which magically increases the number of biscuits by one.\nExchange A biscuits to 1 yen.\nExchange 1 yen to B biscuits.\n\nFind the maximum possible number of biscuits in Snuke's pocket after K operations.\nTask Constraint: 1 <= K,A,B <= 10^9\nK,A and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nK A B\nTask Output: Print the maximum possible number of biscuits in Snuke's pocket after K operations.\nTask Samples: input: 4 2 6 output: 7\n\nThe number of biscuits in Snuke's pocket after K operations is maximized as follows:\n\nHit his pocket. Now he has 2 biscuits and 0 yen.\nExchange 2 biscuits to 1 yen. his pocket. Now he has 0 biscuits and 1 yen.\nHit his pocket. Now he has 1 biscuits and 1 yen.\nExchange 1 yen to 6 biscuits. his pocket. Now he has 7 biscuits and 0 yen.\ninput: 7 3 4 output: 8\ninput: 314159265 35897932 384626433 output: 48518828981938099\n\n" }, { "title": "", "content": "Problem Statement Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions:\n\nHe never visits a point with coordinate less than 0, or a point with coordinate greater than L.\nHe starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate.\nHe only changes direction at a point with integer coordinate.\n\nEach time when Snuke passes a point with coordinate i-0.5, where i is an integer, he put a stone in his i-th ear.\nAfter Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i, Snuke's i-th ear contains A_i stones:\n\nPut a stone in one of Snuke's ears.\nRemove a stone from one of Snuke's ears.\n\nFind the minimum number of operations required when Ringo can freely decide how Snuke walks.", "constraint": "1 <= L <= 2* 10^5\n0 <= A_i <= 10^9(1<= i<= L)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nL\nA_1\n:\nA_L", "output": "Print the minimum number of operations required when Ringo can freely decide how Snuke walks.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1\n0\n2\n3 output: 1\n\nAssume that Snuke walks as follows:\n\nHe starts walking at coordinate 3 and finishes walking at coordinate 4, visiting coordinates 3,4,3,2,3,4 in this order.\n\nThen, Snuke's four ears will contain 0,0,2,3 stones, respectively.\nRingo can satisfy the requirement by putting one stone in the first ear.", "input: 8\n2\n0\n0\n2\n1\n3\n4\n1 output: 3", "input: 7\n314159265\n358979323\n846264338\n327950288\n419716939\n937510582\n0 output: 1"], "Pid": "p03132", "ProblemText": "Task Description: Problem Statement Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions:\n\nHe never visits a point with coordinate less than 0, or a point with coordinate greater than L.\nHe starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate.\nHe only changes direction at a point with integer coordinate.\n\nEach time when Snuke passes a point with coordinate i-0.5, where i is an integer, he put a stone in his i-th ear.\nAfter Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i, Snuke's i-th ear contains A_i stones:\n\nPut a stone in one of Snuke's ears.\nRemove a stone from one of Snuke's ears.\n\nFind the minimum number of operations required when Ringo can freely decide how Snuke walks.\nTask Constraint: 1 <= L <= 2* 10^5\n0 <= A_i <= 10^9(1<= i<= L)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nL\nA_1\n:\nA_L\nTask Output: Print the minimum number of operations required when Ringo can freely decide how Snuke walks.\nTask Samples: input: 4\n1\n0\n2\n3 output: 1\n\nAssume that Snuke walks as follows:\n\nHe starts walking at coordinate 3 and finishes walking at coordinate 4, visiting coordinates 3,4,3,2,3,4 in this order.\n\nThen, Snuke's four ears will contain 0,0,2,3 stones, respectively.\nRingo can satisfy the requirement by putting one stone in the first ear.\ninput: 8\n2\n0\n0\n2\n1\n3\n4\n1 output: 3\ninput: 7\n314159265\n358979323\n846264338\n327950288\n419716939\n937510582\n0 output: 1\n\n" }, { "title": "", "content": "Problem Statement There is a square grid with N rows and M columns.\nEach square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.\nAmong the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:\n\nThe sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.", "constraint": "1 <= N,M <= 300\n0 <= a_{i,j} <= 1(1<= i<= N,1<= j<= M)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\na_{11} . . . a_{1M}\n:\na_{N1} . . . a_{NM}", "output": "Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n0 1\n1 0 output: 6\n\nFor example, if A consists of the first row and B consists of both columns, the sum of the numbers contained in the intersection is 0+1=1.", "input: 2 3\n0 0 0\n0 1 0 output: 8"], "Pid": "p03133", "ProblemText": "Task Description: Problem Statement There is a square grid with N rows and M columns.\nEach square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.\nAmong the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:\n\nThe sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.\nTask Constraint: 1 <= N,M <= 300\n0 <= a_{i,j} <= 1(1<= i<= N,1<= j<= M)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_{11} . . . a_{1M}\n:\na_{N1} . . . a_{NM}\nTask Output: Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.\nTask Samples: input: 2 2\n0 1\n1 0 output: 6\n\nFor example, if A consists of the first row and B consists of both columns, the sum of the numbers contained in the intersection is 0+1=1.\ninput: 2 3\n0 0 0\n0 1 0 output: 8\n\n" }, { "title": "", "content": "Problem Statement There are N Snukes lining up in a row.\nYou are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is 0; one red ball and one blue ball if the i-th character in S is 1; two blue balls if the i-th character in S is 2.\nTakahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:\n\nEach Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.\nTakahashi receives the ball and put it to the end of his sequence.", "constraint": "1 <= |S| <= 2000\nS consists of 0,1 and 2.\n\nNote that the integer N is not directly given in input; it is given indirectly as the length of the string S.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 02 output: 3\n\nThere are three sequences that Takahashi may have: rrbb, rbrb and rbbr, where r and b stand for red and blue balls, respectively.", "input: 1210 output: 55", "input: 12001021211100201020 output: 543589959"], "Pid": "p03134", "ProblemText": "Task Description: Problem Statement There are N Snukes lining up in a row.\nYou are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is 0; one red ball and one blue ball if the i-th character in S is 1; two blue balls if the i-th character in S is 2.\nTakahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:\n\nEach Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.\nTakahashi receives the ball and put it to the end of his sequence.\nTask Constraint: 1 <= |S| <= 2000\nS consists of 0,1 and 2.\n\nNote that the integer N is not directly given in input; it is given indirectly as the length of the string S.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.\nTask Samples: input: 02 output: 3\n\nThere are three sequences that Takahashi may have: rrbb, rbrb and rbbr, where r and b stand for red and blue balls, respectively.\ninput: 1210 output: 55\ninput: 12001021211100201020 output: 543589959\n\n" }, { "title": "", "content": "Problem Statement In order to pass the entrance examination tomorrow, Taro has to study for T more hours.\nFortunately, he can leap to World B where time passes X times as fast as it does in our world (World A).\nWhile (X * t) hours pass in World B, t hours pass in World A.\nHow many hours will pass in World A while Taro studies for T hours in World B?", "constraint": "All values in input are integers.\n1 <= T <= 100\n1 <= X <= 100", "input": "Input is given from Standard Input in the following format:\nT X", "output": "Print the number of hours that will pass in World A.\nThe output will be regarded as correct when its absolute or relative error from the judge's output is at most 10^{-3}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 3 output: 2.6666666667\n\nWhile Taro studies for eight hours in World B where time passes three times as fast, 2.6666... hours will pass in World A.\nNote that an absolute or relative error of at most 10^{-3} is allowed.", "input: 99 1 output: 99.0000000000", "input: 1 100 output: 0.0100000000"], "Pid": "p03135", "ProblemText": "Task Description: Problem Statement In order to pass the entrance examination tomorrow, Taro has to study for T more hours.\nFortunately, he can leap to World B where time passes X times as fast as it does in our world (World A).\nWhile (X * t) hours pass in World B, t hours pass in World A.\nHow many hours will pass in World A while Taro studies for T hours in World B?\nTask Constraint: All values in input are integers.\n1 <= T <= 100\n1 <= X <= 100\nTask Input: Input is given from Standard Input in the following format:\nT X\nTask Output: Print the number of hours that will pass in World A.\nThe output will be regarded as correct when its absolute or relative error from the judge's output is at most 10^{-3}.\nTask Samples: input: 8 3 output: 2.6666666667\n\nWhile Taro studies for eight hours in World B where time passes three times as fast, 2.6666... hours will pass in World A.\nNote that an absolute or relative error of at most 10^{-3} is allowed.\ninput: 99 1 output: 99.0000000000\ninput: 1 100 output: 0.0100000000\n\n" }, { "title": "", "content": "Problem Statement Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, . . . , L_N can be drawn in a two-dimensional plane.\nYou can use the following theorem:\nTheorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.", "constraint": "All values in input are integers.\n3 <= N <= 10\n1 <= L_i <= 100", "input": "Input is given from Standard Input in the following format:\nN\nL_1 L_2 . . . L_N", "output": "If an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 8 5 1 output: Yes\n\nSince 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.", "input: 4\n3 8 4 1 output: No\n\nSince 8 >= 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.", "input: 10\n1 8 10 5 8 12 34 100 11 3 output: No"], "Pid": "p03136", "ProblemText": "Task Description: Problem Statement Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, . . . , L_N can be drawn in a two-dimensional plane.\nYou can use the following theorem:\nTheorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.\nTask Constraint: All values in input are integers.\n3 <= N <= 10\n1 <= L_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nL_1 L_2 . . . L_N\nTask Output: If an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.\nTask Samples: input: 4\n3 8 5 1 output: Yes\n\nSince 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.\ninput: 4\n3 8 4 1 output: No\n\nSince 8 >= 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.\ninput: 10\n1 8 10 5 8 12 34 100 11 3 output: No\n\n" }, { "title": "", "content": "Problem Statement We will play a one-player game using a number line and N pieces.\nFirst, we place each of these pieces at some integer coordinate.\nHere, multiple pieces can be placed at the same coordinate.\nOur objective is to visit all of the M coordinates X_1, X_2, . . . , X_M with these pieces, by repeating the following move:\nMove: Choose a piece and let x be its coordinate. Put that piece at coordinate x+1 or x-1.\nNote that the coordinates where we initially place the pieces are already regarded as visited.\nFind the minimum number of moves required to achieve the objective.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n-10^5 <= X_i <= 10^5\nX_1, X_2, ..., X_M are all different.", "input": "Input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_M", "output": "Find the minimum number of moves required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5\n10 12 1 2 14 output: 5\n\nThe objective can be achieved in five moves as follows, and this is the minimum number of moves required.\n\nInitially, put the two pieces at coordinates 1 and 10.\nMove the piece at coordinate 1 to 2.\nMove the piece at coordinate 10 to 11.\nMove the piece at coordinate 11 to 12.\nMove the piece at coordinate 12 to 13.\nMove the piece at coordinate 13 to 14.", "input: 3 7\n-10 -3 0 9 -100 2 17 output: 19", "input: 100 1\n-100000 output: 0"], "Pid": "p03137", "ProblemText": "Task Description: Problem Statement We will play a one-player game using a number line and N pieces.\nFirst, we place each of these pieces at some integer coordinate.\nHere, multiple pieces can be placed at the same coordinate.\nOur objective is to visit all of the M coordinates X_1, X_2, . . . , X_M with these pieces, by repeating the following move:\nMove: Choose a piece and let x be its coordinate. Put that piece at coordinate x+1 or x-1.\nNote that the coordinates where we initially place the pieces are already regarded as visited.\nFind the minimum number of moves required to achieve the objective.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^5\n-10^5 <= X_i <= 10^5\nX_1, X_2, ..., X_M are all different.\nTask Input: Input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_M\nTask Output: Find the minimum number of moves required to achieve the objective.\nTask Samples: input: 2 5\n10 12 1 2 14 output: 5\n\nThe objective can be achieved in five moves as follows, and this is the minimum number of moves required.\n\nInitially, put the two pieces at coordinates 1 and 10.\nMove the piece at coordinate 1 to 2.\nMove the piece at coordinate 10 to 11.\nMove the piece at coordinate 11 to 12.\nMove the piece at coordinate 12 to 13.\nMove the piece at coordinate 13 to 14.\ninput: 3 7\n-10 -3 0 9 -100 2 17 output: 19\ninput: 100 1\n-100000 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given N non-negative integers A_1, A_2, . . . , A_N and another non-negative integer K.\nFor a integer X between 0 and K (inclusive), let f(X) = (X XOR A_1) + (X XOR A_2) + . . . + (X XOR A_N).\nHere, for non-negative integers a and b, a XOR b denotes the bitwise exclusive OR of a and b.\nFind the maximum value of f.\n\nWhat is XOR?\nThe bitwise exclusive OR of a and b, X, is defined as follows:\n\nWhen X is written in base two, the digit in the 2^k's place (k >= 0) is 1 if, when written in base two, exactly one of A and B has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 XOR 5 = 6. (When written in base two: 011 XOR 101 = 110. )", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03138", "ProblemText": "Task Description: Problem Statement You are given N non-negative integers A_1, A_2, . . . , A_N and another non-negative integer K.\nFor a integer X between 0 and K (inclusive), let f(X) = (X XOR A_1) + (X XOR A_2) + . . . + (X XOR A_N).\nHere, for non-negative integers a and b, a XOR b denotes the bitwise exclusive OR of a and b.\nFind the maximum value of f.\n\nWhat is XOR?\nThe bitwise exclusive OR of a and b, X, is defined as follows:\n\nWhen X is written in base two, the digit in the 2^k's place (k >= 0) is 1 if, when written in base two, exactly one of A and B has 1 in the 2^k's place, and 0 otherwise.\n\nFor example, 3 XOR 5 = 6. (When written in base two: 011 XOR 101 = 110. )\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement We conducted a survey on newspaper subscriptions.\nMore specifically, we asked each of the N respondents the following two questions:\n\nQuestion 1: Are you subscribing to Newspaper X?\nQuestion 2: Are you subscribing to Newspaper Y?\n\nAs the result, A respondents answered \"yes\" to Question 1, and B respondents answered \"yes\" to Question 2.\nWhat are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?\nWrite a program to answer this question.", "constraint": "1 <= N <= 100\n0 <= A <= N\n0 <= B <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 3 5 output: 3 0\n\nIn this sample, out of the 10 respondents, 3 answered they are subscribing to Newspaper X, and 5 answered they are subscribing to Newspaper Y.\nHere, the number of respondents subscribing to both newspapers is at most 3 and at least 0.", "input: 10 7 5 output: 5 2\n\nIn this sample, out of the 10 respondents, 7 answered they are subscribing to Newspaper X, and 5 answered they are subscribing to Newspaper Y.\nHere, the number of respondents subscribing to both newspapers is at most 5 and at least 2.", "input: 100 100 100 output: 100 100"], "Pid": "p03139", "ProblemText": "Task Description: Problem Statement We conducted a survey on newspaper subscriptions.\nMore specifically, we asked each of the N respondents the following two questions:\n\nQuestion 1: Are you subscribing to Newspaper X?\nQuestion 2: Are you subscribing to Newspaper Y?\n\nAs the result, A respondents answered \"yes\" to Question 1, and B respondents answered \"yes\" to Question 2.\nWhat are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?\nWrite a program to answer this question.\nTask Constraint: 1 <= N <= 100\n0 <= A <= N\n0 <= B <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.\nTask Samples: input: 10 3 5 output: 3 0\n\nIn this sample, out of the 10 respondents, 3 answered they are subscribing to Newspaper X, and 5 answered they are subscribing to Newspaper Y.\nHere, the number of respondents subscribing to both newspapers is at most 3 and at least 0.\ninput: 10 7 5 output: 5 2\n\nIn this sample, out of the 10 respondents, 7 answered they are subscribing to Newspaper X, and 5 answered they are subscribing to Newspaper Y.\nHere, the number of respondents subscribing to both newspapers is at most 5 and at least 2.\ninput: 100 100 100 output: 100 100\n\n" }, { "title": "", "content": "Problem Statement You are given three strings A, B and C. Each of these is a string of length N consisting of lowercase English letters.\nOur objective is to make all these three strings equal. For that, you can repeatedly perform the following operation:\n\nOperation: Choose one of the strings A, B and C, and specify an integer i between 1 and N (inclusive). Change the i-th character from the beginning of the chosen string to some other lowercase English letter.\n\nWhat is the minimum number of operations required to achieve the objective?", "constraint": "1 <= N <= 100\nEach of the strings A, B and C is a string of length N.\nEach character in each of the strings A, B and C is a lowercase English letter.", "input": "Input is given from Standard Input in the following format:\nN\nA\nB\nC", "output": "Print the minimum number of operations required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nwest\neast\nwait output: 3\n\nIn this sample, initially A = west、B = east、C = wait. We can achieve the objective in the minimum number of operations by performing three operations as follows:\n\nChange the second character in A to a. A is now wast.\nChange the first character in B to w. B is now wast.\nChange the third character in C to s. C is now wast.", "input: 9\ndifferent\ndifferent\ndifferent output: 0\n\nIf A, B and C are already equal in the beginning, the number of operations required is 0.", "input: 7\nzenkoku\ntouitsu\nprogram output: 13"], "Pid": "p03140", "ProblemText": "Task Description: Problem Statement You are given three strings A, B and C. Each of these is a string of length N consisting of lowercase English letters.\nOur objective is to make all these three strings equal. For that, you can repeatedly perform the following operation:\n\nOperation: Choose one of the strings A, B and C, and specify an integer i between 1 and N (inclusive). Change the i-th character from the beginning of the chosen string to some other lowercase English letter.\n\nWhat is the minimum number of operations required to achieve the objective?\nTask Constraint: 1 <= N <= 100\nEach of the strings A, B and C is a string of length N.\nEach character in each of the strings A, B and C is a lowercase English letter.\nTask Input: Input is given from Standard Input in the following format:\nN\nA\nB\nC\nTask Output: Print the minimum number of operations required.\nTask Samples: input: 4\nwest\neast\nwait output: 3\n\nIn this sample, initially A = west、B = east、C = wait. We can achieve the objective in the minimum number of operations by performing three operations as follows:\n\nChange the second character in A to a. A is now wast.\nChange the first character in B to w. B is now wast.\nChange the third character in C to s. C is now wast.\ninput: 9\ndifferent\ndifferent\ndifferent output: 0\n\nIf A, B and C are already equal in the beginning, the number of operations required is 0.\ninput: 7\nzenkoku\ntouitsu\nprogram output: 13\n\n" }, { "title": "", "content": "Problem Statement There are N dishes of cuisine placed in front of Takahashi and Aoki.\nFor convenience, we call these dishes Dish 1, Dish 2, . . . , Dish N.\nWhen Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.\nStarting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat.\nHere, both of them choose dishes so that the following value is maximized: \"the sum of the happiness he/she will earn in the end\" minus \"the sum of the happiness the other person will earn in the end\".\nFind the value: \"the sum of the happiness Takahashi earns in the end\" minus \"the sum of the happiness Aoki earns in the end\".", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_N B_N", "output": "Print the value: \"the sum of the happiness Takahashi earns in the end\" minus \"the sum of the happiness Aoki earns in the end\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10 10\n20 20\n30 30 output: 20\n\nIn this sample, both of them earns 10 points of happiness by eating Dish 1,20 points by eating Dish 2, and 30 points by eating Dish 3.\nIn this case, since Takahashi and Aoki have the same \"taste\", each time they will choose the dish with which they can earn the greatest happiness. Thus, first Takahashi will choose Dish 3, then Aoki will choose Dish 2, and finally Takahashi will choose Dish 1, so the answer is (30 + 10) - 20 = 20.", "input: 3\n20 10\n20 20\n20 30 output: 20\n\nIn this sample, Takahashi earns 20 points of happiness by eating any one of the dishes 1,2 and 3, but Aoki earns 10 points of happiness by eating Dish 1,20 points by eating Dish 2, and 30 points by eating Dish 3.\nIn this case, since only Aoki has likes and dislikes, each time they will choose the dish with which Aoki can earn the greatest happiness. Thus, first Takahashi will choose Dish 3, then Aoki will choose Dish 2, and finally Takahashi will choose Dish 1, so the answer is (20 + 20) - 20 = 20.", "input: 6\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000 output: -2999999997\n\nNote that the answer may not fit into a 32-bit integer."], "Pid": "p03141", "ProblemText": "Task Description: Problem Statement There are N dishes of cuisine placed in front of Takahashi and Aoki.\nFor convenience, we call these dishes Dish 1, Dish 2, . . . , Dish N.\nWhen Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.\nStarting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat.\nHere, both of them choose dishes so that the following value is maximized: \"the sum of the happiness he/she will earn in the end\" minus \"the sum of the happiness the other person will earn in the end\".\nFind the value: \"the sum of the happiness Takahashi earns in the end\" minus \"the sum of the happiness Aoki earns in the end\".\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_N B_N\nTask Output: Print the value: \"the sum of the happiness Takahashi earns in the end\" minus \"the sum of the happiness Aoki earns in the end\".\nTask Samples: input: 3\n10 10\n20 20\n30 30 output: 20\n\nIn this sample, both of them earns 10 points of happiness by eating Dish 1,20 points by eating Dish 2, and 30 points by eating Dish 3.\nIn this case, since Takahashi and Aoki have the same \"taste\", each time they will choose the dish with which they can earn the greatest happiness. Thus, first Takahashi will choose Dish 3, then Aoki will choose Dish 2, and finally Takahashi will choose Dish 1, so the answer is (30 + 10) - 20 = 20.\ninput: 3\n20 10\n20 20\n20 30 output: 20\n\nIn this sample, Takahashi earns 20 points of happiness by eating any one of the dishes 1,2 and 3, but Aoki earns 10 points of happiness by eating Dish 1,20 points by eating Dish 2, and 30 points by eating Dish 3.\nIn this case, since only Aoki has likes and dislikes, each time they will choose the dish with which Aoki can earn the greatest happiness. Thus, first Takahashi will choose Dish 3, then Aoki will choose Dish 2, and finally Takahashi will choose Dish 1, so the answer is (20 + 20) - 20 = 20.\ninput: 6\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000 output: -2999999997\n\nNote that the answer may not fit into a 32-bit integer.\n\n" }, { "title": "", "content": "Problem Statement There is a rooted tree (see Notes) with N vertices numbered 1 to N.\nEach of the vertices, except the root, has a directed edge coming from its parent.\nNote that the root may not be Vertex 1.\nTakahashi has added M new directed edges to this graph.\nEach of these M edges, u \\rightarrow v, extends from some vertex u to its descendant v.\nYou are given the directed graph with N vertices and N-1+M edges after Takahashi added edges.\nMore specifically, you are given N-1+M pairs of integers, (A_1, B_1), . . . , (A_{N-1+M}, B_{N-1+M}), which represent that the i-th edge extends from Vertex A_i to Vertex B_i.\nRestore the original rooted tree. note: Notes For \"tree\" and other related terms in graph theory, see the article in Wikipedia, for example.", "constraint": "3 <= N\n1 <= M\nN + M <= 10^5\n1 <= A_i, B_i <= N\nA_i \\neq B_i\nIf i \\neq j, (A_i, B_i) \\neq (A_j, B_j).\nThe graph in input can be obtained by adding M edges satisfying the condition in the problem statement to a rooted tree with N vertices.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_{N-1+M} B_{N-1+M}", "output": "Print N lines.\nIn the i-th line, print 0 if Vertex i is the root of the original tree, and otherwise print the integer representing the parent of Vertex i in the original tree.\nNote that it can be shown that the original tree is uniquely determined.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1 2\n1 3\n2 3 output: 0\n1\n2\n\nThe graph in this input is shown below:\n\nIt can be seen that this graph is obtained by adding the edge 1 \\rightarrow 3 to the rooted tree 1 \\rightarrow 2 \\rightarrow 3.", "input: 6 3\n2 1\n2 3\n4 1\n4 2\n6 1\n2 6\n4 6\n6 5 output: 6\n4\n2\n0\n6\n2"], "Pid": "p03142", "ProblemText": "Task Description: Problem Statement There is a rooted tree (see Notes) with N vertices numbered 1 to N.\nEach of the vertices, except the root, has a directed edge coming from its parent.\nNote that the root may not be Vertex 1.\nTakahashi has added M new directed edges to this graph.\nEach of these M edges, u \\rightarrow v, extends from some vertex u to its descendant v.\nYou are given the directed graph with N vertices and N-1+M edges after Takahashi added edges.\nMore specifically, you are given N-1+M pairs of integers, (A_1, B_1), . . . , (A_{N-1+M}, B_{N-1+M}), which represent that the i-th edge extends from Vertex A_i to Vertex B_i.\nRestore the original rooted tree. note: Notes For \"tree\" and other related terms in graph theory, see the article in Wikipedia, for example.\nTask Constraint: 3 <= N\n1 <= M\nN + M <= 10^5\n1 <= A_i, B_i <= N\nA_i \\neq B_i\nIf i \\neq j, (A_i, B_i) \\neq (A_j, B_j).\nThe graph in input can be obtained by adding M edges satisfying the condition in the problem statement to a rooted tree with N vertices.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\n:\nA_{N-1+M} B_{N-1+M}\nTask Output: Print N lines.\nIn the i-th line, print 0 if Vertex i is the root of the original tree, and otherwise print the integer representing the parent of Vertex i in the original tree.\nNote that it can be shown that the original tree is uniquely determined.\nTask Samples: input: 3 1\n1 2\n1 3\n2 3 output: 0\n1\n2\n\nThe graph in this input is shown below:\n\nIt can be seen that this graph is obtained by adding the edge 1 \\rightarrow 3 to the rooted tree 1 \\rightarrow 2 \\rightarrow 3.\ninput: 6 3\n2 1\n2 3\n4 1\n4 2\n6 1\n2 6\n4 6\n6 5 output: 6\n4\n2\n0\n6\n2\n\n" }, { "title": "", "content": "Problem Statement There is a connected undirected graph with N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nAlso, each of these vertices and edges has a specified weight.\nVertex i has a weight of X_i; Edge i has a weight of Y_i and connects Vertex A_i and B_i.\nWe would like to remove zero or more edges so that the following condition is satisfied:\n\nFor each edge that is not removed, the sum of the weights of the vertices in the connected component containing that edge, is greater than or equal to the weight of that edge.\n\nFind the minimum number of edges that need to be removed.", "constraint": "1 <= N <= 10^5\nN-1 <= M <= 10^5\n1 <= X_i <= 10^9\n1 <= A_i < B_i <= N\n1 <= Y_i <= 10^9\n(A_i,B_i) \\neq (A_j,B_j) (i \\neq j)\nThe given graph is connected.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_N\nA_1 B_1 Y_1\nA_2 B_2 Y_2\n:\nA_M B_M Y_M", "output": "Find the minimum number of edges that need to be removed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n2 3 5 7\n1 2 7\n1 3 9\n2 3 12\n3 4 18 output: 2\n\nAssume that we removed Edge 3 and 4.\nIn this case, the connected component containing Edge 1 contains Vertex 1,2 and 3, and the sum of the weights of these vertices is 2+3+5=10.\nThe weight of Edge 1 is 7, so the condition is satisfied for Edge 1.\nSimilarly, it can be seen that the condition is also satisfied for Edge 2.\nThus, a graph satisfying the condition can be obtained by removing two edges.\nThe condition cannot be satisfied by removing one or less edges, so the answer is 2.", "input: 6 10\n4 4 1 1 1 7\n3 5 19\n2 5 20\n4 5 8\n1 6 16\n2 3 9\n3 6 16\n3 4 1\n2 6 20\n2 4 19\n1 2 9 output: 4", "input: 10 9\n81 16 73 7 2 61 86 38 90 28\n6 8 725\n3 10 12\n1 4 558\n4 9 615\n5 6 942\n8 9 918\n2 7 720\n4 7 292\n7 10 414 output: 8"], "Pid": "p03143", "ProblemText": "Task Description: Problem Statement There is a connected undirected graph with N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nAlso, each of these vertices and edges has a specified weight.\nVertex i has a weight of X_i; Edge i has a weight of Y_i and connects Vertex A_i and B_i.\nWe would like to remove zero or more edges so that the following condition is satisfied:\n\nFor each edge that is not removed, the sum of the weights of the vertices in the connected component containing that edge, is greater than or equal to the weight of that edge.\n\nFind the minimum number of edges that need to be removed.\nTask Constraint: 1 <= N <= 10^5\nN-1 <= M <= 10^5\n1 <= X_i <= 10^9\n1 <= A_i < B_i <= N\n1 <= Y_i <= 10^9\n(A_i,B_i) \\neq (A_j,B_j) (i \\neq j)\nThe given graph is connected.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_N\nA_1 B_1 Y_1\nA_2 B_2 Y_2\n:\nA_M B_M Y_M\nTask Output: Find the minimum number of edges that need to be removed.\nTask Samples: input: 4 4\n2 3 5 7\n1 2 7\n1 3 9\n2 3 12\n3 4 18 output: 2\n\nAssume that we removed Edge 3 and 4.\nIn this case, the connected component containing Edge 1 contains Vertex 1,2 and 3, and the sum of the weights of these vertices is 2+3+5=10.\nThe weight of Edge 1 is 7, so the condition is satisfied for Edge 1.\nSimilarly, it can be seen that the condition is also satisfied for Edge 2.\nThus, a graph satisfying the condition can be obtained by removing two edges.\nThe condition cannot be satisfied by removing one or less edges, so the answer is 2.\ninput: 6 10\n4 4 1 1 1 7\n3 5 19\n2 5 20\n4 5 8\n1 6 16\n2 3 9\n3 6 16\n3 4 1\n2 6 20\n2 4 19\n1 2 9 output: 4\ninput: 10 9\n81 16 73 7 2 61 86 38 90 28\n6 8 725\n3 10 12\n1 4 558\n4 9 615\n5 6 942\n8 9 918\n2 7 720\n4 7 292\n7 10 414 output: 8\n\n" }, { "title": "", "content": "Problem Statement There are N jewels, numbered 1 to N.\nThe color of these jewels are represented by integers between 1 and K (inclusive), and the color of Jewel i is C_i.\nAlso, these jewels have specified values, and the value of Jewel i is V_i.\nSnuke would like to choose some of these jewels to exhibit.\nHere, the set of the chosen jewels must satisfy the following condition:\n\nFor each chosen jewel, there is at least one more jewel of the same color that is chosen.\n\nFor each integer x such that 1 <= x <= N, determine if it is possible to choose exactly x jewels, and if it is possible, find the maximum possible sum of the values of chosen jewels in that case.", "constraint": "1 <= N <= 2 * 10^5\n1 <= K <= \\lfloor N/2 \\rfloor\n1 <= C_i <= K\n1 <= V_i <= 10^9\nFor each of the colors, there are at least two jewels of that color.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nC_1 V_1\nC_2 V_2\n:\nC_N V_N", "output": "Print N lines.\nIn the i-th line, if it is possible to choose exactly i jewels, print the maximum possible sum of the values of chosen jewels in that case, and print -1 otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n1 1\n1 2\n1 3\n2 4\n2 5 output: -1\n9\n6\n14\n15\n\nWe cannot choose exactly one jewel.\nWhen choosing exactly two jewels, the total value is maximized when Jewel 4 and 5 are chosen.\nWhen choosing exactly three jewels, the total value is maximized when Jewel 1,2 and 3 are chosen.\nWhen choosing exactly four jewels, the total value is maximized when Jewel 2,3,4 and 5 are chosen.\nWhen choosing exactly five jewels, the total value is maximized when Jewel 1,2,3,4 and 5 are chosen.", "input: 5 2\n1 1\n1 2\n2 3\n2 4\n2 5 output: -1\n9\n12\n12\n15", "input: 8 4\n3 2\n2 3\n4 5\n1 7\n3 11\n4 13\n1 17\n2 19 output: -1\n24\n-1\n46\n-1\n64\n-1\n77", "input: 15 5\n3 87\n1 25\n1 27\n3 58\n2 85\n5 19\n5 39\n1 58\n3 12\n4 13\n5 54\n4 100\n2 33\n5 13\n2 55 output: -1\n145\n173\n285\n318\n398\n431\n491\n524\n576\n609\n634\n653\n666\n678"], "Pid": "p03144", "ProblemText": "Task Description: Problem Statement There are N jewels, numbered 1 to N.\nThe color of these jewels are represented by integers between 1 and K (inclusive), and the color of Jewel i is C_i.\nAlso, these jewels have specified values, and the value of Jewel i is V_i.\nSnuke would like to choose some of these jewels to exhibit.\nHere, the set of the chosen jewels must satisfy the following condition:\n\nFor each chosen jewel, there is at least one more jewel of the same color that is chosen.\n\nFor each integer x such that 1 <= x <= N, determine if it is possible to choose exactly x jewels, and if it is possible, find the maximum possible sum of the values of chosen jewels in that case.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= K <= \\lfloor N/2 \\rfloor\n1 <= C_i <= K\n1 <= V_i <= 10^9\nFor each of the colors, there are at least two jewels of that color.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nC_1 V_1\nC_2 V_2\n:\nC_N V_N\nTask Output: Print N lines.\nIn the i-th line, if it is possible to choose exactly i jewels, print the maximum possible sum of the values of chosen jewels in that case, and print -1 otherwise.\nTask Samples: input: 5 2\n1 1\n1 2\n1 3\n2 4\n2 5 output: -1\n9\n6\n14\n15\n\nWe cannot choose exactly one jewel.\nWhen choosing exactly two jewels, the total value is maximized when Jewel 4 and 5 are chosen.\nWhen choosing exactly three jewels, the total value is maximized when Jewel 1,2 and 3 are chosen.\nWhen choosing exactly four jewels, the total value is maximized when Jewel 2,3,4 and 5 are chosen.\nWhen choosing exactly five jewels, the total value is maximized when Jewel 1,2,3,4 and 5 are chosen.\ninput: 5 2\n1 1\n1 2\n2 3\n2 4\n2 5 output: -1\n9\n12\n12\n15\ninput: 8 4\n3 2\n2 3\n4 5\n1 7\n3 11\n4 13\n1 17\n2 19 output: -1\n24\n-1\n46\n-1\n64\n-1\n77\ninput: 15 5\n3 87\n1 25\n1 27\n3 58\n2 85\n5 19\n5 39\n1 58\n3 12\n4 13\n5 54\n4 100\n2 33\n5 13\n2 55 output: -1\n145\n173\n285\n318\n398\n431\n491\n524\n576\n609\n634\n653\n666\n678\n\n" }, { "title": "", "content": "Problem Statement There is a right triangle ABC with ∠ABC=90°.\nGiven the lengths of the three sides, |AB|, |BC| and |CA|, find the area of the right triangle ABC.\nIt is guaranteed that the area of the triangle ABC is an integer.", "constraint": "1 <= |AB|,|BC|,|CA| <= 100\nAll values in input are integers.\nThe area of the triangle ABC is an integer.", "input": "Input is given from Standard Input in the following format:\n|AB| |BC| |CA|", "output": "Print the area of the triangle ABC.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 5 output: 6\nThis triangle has an area of 6.", "input: 5 12 13 output: 30\n\nThis triangle has an area of 30.", "input: 45 28 53 output: 630\n\nThis triangle has an area of 630."], "Pid": "p03145", "ProblemText": "Task Description: Problem Statement There is a right triangle ABC with ∠ABC=90°.\nGiven the lengths of the three sides, |AB|, |BC| and |CA|, find the area of the right triangle ABC.\nIt is guaranteed that the area of the triangle ABC is an integer.\nTask Constraint: 1 <= |AB|,|BC|,|CA| <= 100\nAll values in input are integers.\nThe area of the triangle ABC is an integer.\nTask Input: Input is given from Standard Input in the following format:\n|AB| |BC| |CA|\nTask Output: Print the area of the triangle ABC.\nTask Samples: input: 3 4 5 output: 6\nThis triangle has an area of 6.\ninput: 5 12 13 output: 30\n\nThis triangle has an area of 30.\ninput: 45 28 53 output: 630\n\nThis triangle has an area of 630.\n\n" }, { "title": "", "content": "Problem Statement A sequence a=\\{a_1, a_2, a_3, . . . . . . \\} is determined as follows:\nThe first term s is given as input.\nLet f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\na_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n\nThere exists an integer n such that a_m = a_n (m > n).", "constraint": "1 <= s <= 100\nAll values in input are integers.\nIt is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.", "input": "Input is given from Standard Input in the following format:\ns", "output": "Print the minimum integer m that satisfies the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 output: 5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.", "input: 7 output: 18\n\na=\\{7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,......\\}.", "input: 54 output: 114"], "Pid": "p03146", "ProblemText": "Task Description: Problem Statement A sequence a=\\{a_1, a_2, a_3, . . . . . . \\} is determined as follows:\nThe first term s is given as input.\nLet f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\na_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n\nThere exists an integer n such that a_m = a_n (m > n).\nTask Constraint: 1 <= s <= 100\nAll values in input are integers.\nIt is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\nTask Input: Input is given from Standard Input in the following format:\ns\nTask Output: Print the minimum integer m that satisfies the condition.\nTask Samples: input: 8 output: 5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.\ninput: 7 output: 18\n\na=\\{7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,......\\}.\ninput: 54 output: 114\n\n" }, { "title": "", "content": "Problem Statement In a flower bed, there are N flowers, numbered 1,2, . . . . . . , N. Initially, the heights of all flowers are 0.\nYou are given a sequence h=\\{h_1, h_2, h_3, . . . . . . \\} as input. You would like to change the height of Flower k to h_k for all k (1 <= k <= N), by repeating the following \"watering\" operation:\n\nSpecify integers l and r. Increase the height of Flower x by 1 for all x such that l <= x <= r.\n\nFind the minimum number of watering operations required to satisfy the condition.", "constraint": "1 <= N <= 100\n0 <= h_i <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nh_1 h_2 h_3 . . . . . . h_N", "output": "Print the minimum number of watering operations required to satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 2 1 output: 2\n\nThe minimum number of watering operations required is 2.\nOne way to achieve it is:\n\nPerform the operation with (l,r)=(1,3).\nPerform the operation with (l,r)=(2,4).", "input: 5\n3 1 2 3 1 output: 5", "input: 8\n4 23 75 0 23 96 50 100 output: 221"], "Pid": "p03147", "ProblemText": "Task Description: Problem Statement In a flower bed, there are N flowers, numbered 1,2, . . . . . . , N. Initially, the heights of all flowers are 0.\nYou are given a sequence h=\\{h_1, h_2, h_3, . . . . . . \\} as input. You would like to change the height of Flower k to h_k for all k (1 <= k <= N), by repeating the following \"watering\" operation:\n\nSpecify integers l and r. Increase the height of Flower x by 1 for all x such that l <= x <= r.\n\nFind the minimum number of watering operations required to satisfy the condition.\nTask Constraint: 1 <= N <= 100\n0 <= h_i <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nh_1 h_2 h_3 . . . . . . h_N\nTask Output: Print the minimum number of watering operations required to satisfy the condition.\nTask Samples: input: 4\n1 2 2 1 output: 2\n\nThe minimum number of watering operations required is 2.\nOne way to achieve it is:\n\nPerform the operation with (l,r)=(1,3).\nPerform the operation with (l,r)=(2,4).\ninput: 5\n3 1 2 3 1 output: 5\ninput: 8\n4 23 75 0 23 96 50 100 output: 221\n\n" }, { "title": "", "content": "Problem Statement There are N pieces of sushi. Each piece has two parameters: \"kind of topping\" t_i and \"deliciousness\" d_i.\nYou are choosing K among these N pieces to eat.\nYour \"satisfaction\" here will be calculated as follows:\n\nThe satisfaction is the sum of the \"base total deliciousness\" and the \"variety bonus\".\nThe base total deliciousness is the sum of the deliciousness of the pieces you eat.\nThe variety bonus is x*x, where x is the number of different kinds of toppings of the pieces you eat.\n\nYou want to have as much satisfaction as possible.\nFind this maximum satisfaction.", "constraint": "1 <= K <= N <= 10^5\n1 <= t_i <= N\n1 <= d_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nt_1 d_1\nt_2 d_2\n.\n.\n.\nt_N d_N", "output": "Print the maximum satisfaction that you can obtain.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 9\n1 7\n2 6\n2 5\n3 1 output: 26\n\nIf you eat Sushi 1,2 and 3:\n\nThe base total deliciousness is 9+7+6=22.\nThe variety bonus is 2*2=4.\n\nThus, your satisfaction will be 26, which is optimal.", "input: 7 4\n1 1\n2 1\n3 1\n4 6\n4 5\n4 5\n4 5 output: 25\n\nIt is optimal to eat Sushi 1,2,3 and 4.", "input: 6 5\n5 1000000000\n2 990000000\n3 980000000\n6 970000000\n6 960000000\n4 950000000 output: 4900000016\n\nNote that the output may not fit into a 32-bit integer type."], "Pid": "p03148", "ProblemText": "Task Description: Problem Statement There are N pieces of sushi. Each piece has two parameters: \"kind of topping\" t_i and \"deliciousness\" d_i.\nYou are choosing K among these N pieces to eat.\nYour \"satisfaction\" here will be calculated as follows:\n\nThe satisfaction is the sum of the \"base total deliciousness\" and the \"variety bonus\".\nThe base total deliciousness is the sum of the deliciousness of the pieces you eat.\nThe variety bonus is x*x, where x is the number of different kinds of toppings of the pieces you eat.\n\nYou want to have as much satisfaction as possible.\nFind this maximum satisfaction.\nTask Constraint: 1 <= K <= N <= 10^5\n1 <= t_i <= N\n1 <= d_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nt_1 d_1\nt_2 d_2\n.\n.\n.\nt_N d_N\nTask Output: Print the maximum satisfaction that you can obtain.\nTask Samples: input: 5 3\n1 9\n1 7\n2 6\n2 5\n3 1 output: 26\n\nIf you eat Sushi 1,2 and 3:\n\nThe base total deliciousness is 9+7+6=22.\nThe variety bonus is 2*2=4.\n\nThus, your satisfaction will be 26, which is optimal.\ninput: 7 4\n1 1\n2 1\n3 1\n4 6\n4 5\n4 5\n4 5 output: 25\n\nIt is optimal to eat Sushi 1,2,3 and 4.\ninput: 6 5\n5 1000000000\n2 990000000\n3 980000000\n6 970000000\n6 960000000\n4 950000000 output: 4900000016\n\nNote that the output may not fit into a 32-bit integer type.\n\n" }, { "title": "", "content": "Problem Statement You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits \"1974\".", "constraint": "0 <= N_1, N_2, N_3, N_4 <= 9\nN_1, N_2, N_3 and N_4 are integers.", "input": "Input is given from Standard Input in the following format:\nN_1 N_2 N_3 N_4", "output": "If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits \"1974\", print YES; if they cannot, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 7 9 4 output: YES\n\nWe can get 1974 by swapping N_2 and N_3.", "input: 1 9 7 4 output: YES\n\nWe already have 1974 before doing anything.", "input: 1 2 9 1 output: NO", "input: 4 9 0 8 output: NO"], "Pid": "p03149", "ProblemText": "Task Description: Problem Statement You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits \"1974\".\nTask Constraint: 0 <= N_1, N_2, N_3, N_4 <= 9\nN_1, N_2, N_3 and N_4 are integers.\nTask Input: Input is given from Standard Input in the following format:\nN_1 N_2 N_3 N_4\nTask Output: If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits \"1974\", print YES; if they cannot, print NO.\nTask Samples: input: 1 7 9 4 output: YES\n\nWe can get 1974 by swapping N_2 and N_3.\ninput: 1 9 7 4 output: YES\n\nWe already have 1974 before doing anything.\ninput: 1 2 9 1 output: NO\ninput: 4 9 0 8 output: NO\n\n" }, { "title": "", "content": "Problem Statement A string is called a KEYENCE string when it can be changed to keyence by removing its contiguous substring (possibly empty) only once.\nGiven a string S consisting of lowercase English letters, determine if S is a KEYENCE string.", "constraint": "The length of S is between 7 and 100 (inclusive).\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S is a KEYENCE string, print YES; otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: keyofscience output: YES\n\nkeyence is an abbreviation of key of science.", "input: mpyszsbznf output: NO", "input: ashlfyha output: NO", "input: keyence output: YES"], "Pid": "p03150", "ProblemText": "Task Description: Problem Statement A string is called a KEYENCE string when it can be changed to keyence by removing its contiguous substring (possibly empty) only once.\nGiven a string S consisting of lowercase English letters, determine if S is a KEYENCE string.\nTask Constraint: The length of S is between 7 and 100 (inclusive).\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S is a KEYENCE string, print YES; otherwise, print NO.\nTask Samples: input: keyofscience output: YES\n\nkeyence is an abbreviation of key of science.\ninput: mpyszsbznf output: NO\ninput: ashlfyha output: NO\ninput: keyence output: YES\n\n" }, { "title": "", "content": "Problem Statement A university student, Takahashi, has to take N examinations and pass all of them.\nCurrently, his readiness for the i-th examination is A_{i}, and according to his investigation, it is known that he needs readiness of at least B_{i} in order to pass the i-th examination.\nTakahashi thinks that he may not be able to pass all the examinations, and he has decided to ask a magician, Aoki, to change the readiness for as few examinations as possible so that he can pass all of them, while not changing the total readiness.\nFor Takahashi, find the minimum possible number of indices i such that A_i and C_i are different, for a sequence C_1, C_2, . . . , C_{N} that satisfies the following conditions:\n\nThe sum of the sequence A_1, A_2, . . . , A_{N} and the sum of the sequence C_1, C_2, . . . , C_{N} are equal.\nFor every i, B_i <= C_i holds.\n\nIf such a sequence C_1, C_2, . . . , C_{N} cannot be constructed, print -1.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nA_i and B_i are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N}\nB_1 B_2 . . . B_{N}", "output": "Print the minimum possible number of indices i such that A_i and C_i are different, for a sequence C_1, C_2, . . . , C_{N} that satisfies the conditions.\nIf such a sequence C_1, C_2, . . . , C_{N} cannot be constructed, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3 5\n3 4 1 output: 3\n\n(A_1, A_2, A_3) = (2,3,5) and (B_1, B_2, B_3) = (3,4,1). If nothing is done, he cannot pass the first and second exams.\nThe minimum possible number of indices i such that A_i and C_i are different, 3, is achieved when:\n\n(C_1, C_2, C_3) = (3,5,2)", "input: 3\n2 3 3\n2 2 1 output: 0\n\nIn this case, he has to do nothing in order to pass all the exams.", "input: 3\n17 7 1\n25 6 14 output: -1\n\nIn this case, no matter what is done, he cannot pass all the exams.", "input: 12\n757232153 372327760 440075441 195848680 354974235 458054863 463477172 740174259 615762794 632963102 529866931 64991604\n74164189 98239366 465611891 362739947 147060907 118867039 63189252 78303147 501410831 110823640 122948912 572905212 output: 5"], "Pid": "p03151", "ProblemText": "Task Description: Problem Statement A university student, Takahashi, has to take N examinations and pass all of them.\nCurrently, his readiness for the i-th examination is A_{i}, and according to his investigation, it is known that he needs readiness of at least B_{i} in order to pass the i-th examination.\nTakahashi thinks that he may not be able to pass all the examinations, and he has decided to ask a magician, Aoki, to change the readiness for as few examinations as possible so that he can pass all of them, while not changing the total readiness.\nFor Takahashi, find the minimum possible number of indices i such that A_i and C_i are different, for a sequence C_1, C_2, . . . , C_{N} that satisfies the following conditions:\n\nThe sum of the sequence A_1, A_2, . . . , A_{N} and the sum of the sequence C_1, C_2, . . . , C_{N} are equal.\nFor every i, B_i <= C_i holds.\n\nIf such a sequence C_1, C_2, . . . , C_{N} cannot be constructed, print -1.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nA_i and B_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N}\nB_1 B_2 . . . B_{N}\nTask Output: Print the minimum possible number of indices i such that A_i and C_i are different, for a sequence C_1, C_2, . . . , C_{N} that satisfies the conditions.\nIf such a sequence C_1, C_2, . . . , C_{N} cannot be constructed, print -1.\nTask Samples: input: 3\n2 3 5\n3 4 1 output: 3\n\n(A_1, A_2, A_3) = (2,3,5) and (B_1, B_2, B_3) = (3,4,1). If nothing is done, he cannot pass the first and second exams.\nThe minimum possible number of indices i such that A_i and C_i are different, 3, is achieved when:\n\n(C_1, C_2, C_3) = (3,5,2)\ninput: 3\n2 3 3\n2 2 1 output: 0\n\nIn this case, he has to do nothing in order to pass all the exams.\ninput: 3\n17 7 1\n25 6 14 output: -1\n\nIn this case, no matter what is done, he cannot pass all the exams.\ninput: 12\n757232153 372327760 440075441 195848680 354974235 458054863 463477172 740174259 615762794 632963102 529866931 64991604\n74164189 98239366 465611891 362739947 147060907 118867039 63189252 78303147 501410831 110823640 122948912 572905212 output: 5\n\n" }, { "title": "", "content": "Problem Statement Consider writing each of the integers from 1 to N * M in a grid with N rows and M columns, without duplicates.\nTakahashi thinks it is not fun enough, and he will write the numbers under the following conditions:\n\nThe largest among the values in the i-th row (1 <= i <= N) is A_i.\nThe largest among the values in the j-th column (1 <= j <= M) is B_j.\n\nFor him, find the number of ways to write the numbers under these conditions, modulo 10^9 + 7.", "constraint": "1 <= N <= 1000\n1 <= M <= 1000\n1 <= A_i <= N * M\n1 <= B_j <= N * M\nA_i and B_j are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_{N}\nB_1 B_2 . . . B_{M}", "output": "Print the number of ways to write the numbers under the conditions, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n4 3\n3 4 output: 2\n\n(A_1, A_2) = (4,3) and (B_1, B_2) = (3,4). In this case, there are two ways to write the numbers, as follows:\n\n1 in (1,1), 4 in (1,2), 3 in (2,1) and 2 in (2,2).\n2 in (1,1), 4 in (1,2), 3 in (2,1) and 1 in (2,2).\n\nHere, (i, j) denotes the square at the i-th row and the j-th column.", "input: 3 3\n5 9 7\n3 6 9 output: 0\n\nSince there is no way to write the numbers under the condition, 0 should be printed.", "input: 2 2\n4 4\n4 4 output: 0", "input: 14 13\n158 167 181 147 178 151 179 182 176 169 180 129 175 168\n181 150 178 179 167 180 176 169 182 177 175 159 173 output: 343772227"], "Pid": "p03152", "ProblemText": "Task Description: Problem Statement Consider writing each of the integers from 1 to N * M in a grid with N rows and M columns, without duplicates.\nTakahashi thinks it is not fun enough, and he will write the numbers under the following conditions:\n\nThe largest among the values in the i-th row (1 <= i <= N) is A_i.\nThe largest among the values in the j-th column (1 <= j <= M) is B_j.\n\nFor him, find the number of ways to write the numbers under these conditions, modulo 10^9 + 7.\nTask Constraint: 1 <= N <= 1000\n1 <= M <= 1000\n1 <= A_i <= N * M\n1 <= B_j <= N * M\nA_i and B_j are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_{N}\nB_1 B_2 . . . B_{M}\nTask Output: Print the number of ways to write the numbers under the conditions, modulo 10^9 + 7.\nTask Samples: input: 2 2\n4 3\n3 4 output: 2\n\n(A_1, A_2) = (4,3) and (B_1, B_2) = (3,4). In this case, there are two ways to write the numbers, as follows:\n\n1 in (1,1), 4 in (1,2), 3 in (2,1) and 2 in (2,2).\n2 in (1,1), 4 in (1,2), 3 in (2,1) and 1 in (2,2).\n\nHere, (i, j) denotes the square at the i-th row and the j-th column.\ninput: 3 3\n5 9 7\n3 6 9 output: 0\n\nSince there is no way to write the numbers under the condition, 0 should be printed.\ninput: 2 2\n4 4\n4 4 output: 0\ninput: 14 13\n158 167 181 147 178 151 179 182 176 169 180 129 175 168\n181 150 178 179 167 180 176 169 182 177 175 159 173 output: 343772227\n\n" }, { "title": "", "content": "Problem Statement There are N cities in Republic of At Coder. The size of the i-th city is A_{i}.\nTakahashi would like to build N-1 bidirectional roads connecting two cities so that any city can be reached from any other city by using these roads.\nAssume that the cost of building a road connecting the i-th city and the j-th city is |i-j| * D + A_{i} + A_{j}.\nFor Takahashi, find the minimum possible total cost to achieve the objective.", "constraint": "1 <= N <= 2 * 10^5\n1 <= D <= 10^9\n1 <= A_{i} <= 10^9\nA_{i} and D are integers.", "input": "Input is given from Standard Input in the following format:\nN D\nA_1 A_2 . . . A_N", "output": "Print the minimum possible total cost.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1 100 1 output: 106\n\nThis cost can be achieved by, for example, building roads connecting City 1,2 and City 1,3.", "input: 3 1000\n1 100 1 output: 2202", "input: 6 14\n25 171 7 1 17 162 output: 497", "input: 12 5\n43 94 27 3 69 99 56 25 8 15 46 8 output: 658"], "Pid": "p03153", "ProblemText": "Task Description: Problem Statement There are N cities in Republic of At Coder. The size of the i-th city is A_{i}.\nTakahashi would like to build N-1 bidirectional roads connecting two cities so that any city can be reached from any other city by using these roads.\nAssume that the cost of building a road connecting the i-th city and the j-th city is |i-j| * D + A_{i} + A_{j}.\nFor Takahashi, find the minimum possible total cost to achieve the objective.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= D <= 10^9\n1 <= A_{i} <= 10^9\nA_{i} and D are integers.\nTask Input: Input is given from Standard Input in the following format:\nN D\nA_1 A_2 . . . A_N\nTask Output: Print the minimum possible total cost.\nTask Samples: input: 3 1\n1 100 1 output: 106\n\nThis cost can be achieved by, for example, building roads connecting City 1,2 and City 1,3.\ninput: 3 1000\n1 100 1 output: 2202\ninput: 6 14\n25 171 7 1 17 162 output: 497\ninput: 12 5\n43 94 27 3 69 99 56 25 8 15 46 8 output: 658\n\n" }, { "title": "", "content": "Problem Statement There is a rectangular sheet of paper with height H+1 and width W+1. We introduce an xy-coordinate system so that the four corners of the sheet are (0,0), (W + 1,0), (0, H + 1) and (W + 1, H + 1).\nThis sheet can be cut along the lines x = 1,2, . . . , W and the lines y = 1,2, . . . , H. Consider a sequence of operations of length K where we choose K of these H + W lines and cut the sheet along those lines one by one in some order.\nLet the score of a cut be the number of pieces of paper that exist just after the cut. The score of a sequence of operations is the sum of the scores of all of the K cuts.\nFind the sum of the scores of all possible sequences of operations of length K. Since this value can be extremely large, print the number modulo 10^9 + 7.", "constraint": "1 <= H,W <= 10^7\n1 <= K <= H + W\nH, W and K are integers.", "input": "Input is given from Standard Input in the following format:\nH W K", "output": "Print the sum of the scores, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 2 output: 34\n\nLet x_1, y_1 and y_2 denote the cuts along the lines x = 1, y = 1 and y = 2, respectively. The six possible sequences of operations and the score of each of them are as follows:\n\ny_1, y_2: 2 + 3 = 5\ny_2, y_1: 2 + 3 = 5\ny_1, x_1: 2 + 4 = 6\ny_2, x_1: 2 + 4 = 6\nx_1, y_1: 2 + 4 = 6\nx_1, y_2: 2 + 4 = 6\n\nThe sum of these is 34.", "input: 30 40 50 output: 616365902\n\nBe sure to print the sum modulo 10^9 + 7."], "Pid": "p03154", "ProblemText": "Task Description: Problem Statement There is a rectangular sheet of paper with height H+1 and width W+1. We introduce an xy-coordinate system so that the four corners of the sheet are (0,0), (W + 1,0), (0, H + 1) and (W + 1, H + 1).\nThis sheet can be cut along the lines x = 1,2, . . . , W and the lines y = 1,2, . . . , H. Consider a sequence of operations of length K where we choose K of these H + W lines and cut the sheet along those lines one by one in some order.\nLet the score of a cut be the number of pieces of paper that exist just after the cut. The score of a sequence of operations is the sum of the scores of all of the K cuts.\nFind the sum of the scores of all possible sequences of operations of length K. Since this value can be extremely large, print the number modulo 10^9 + 7.\nTask Constraint: 1 <= H,W <= 10^7\n1 <= K <= H + W\nH, W and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nH W K\nTask Output: Print the sum of the scores, modulo 10^9 + 7.\nTask Samples: input: 2 1 2 output: 34\n\nLet x_1, y_1 and y_2 denote the cuts along the lines x = 1, y = 1 and y = 2, respectively. The six possible sequences of operations and the score of each of them are as follows:\n\ny_1, y_2: 2 + 3 = 5\ny_2, y_1: 2 + 3 = 5\ny_1, x_1: 2 + 4 = 6\ny_2, x_1: 2 + 4 = 6\nx_1, y_1: 2 + 4 = 6\nx_1, y_2: 2 + 4 = 6\n\nThe sum of these is 34.\ninput: 30 40 50 output: 616365902\n\nBe sure to print the sum modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement It has been decided that a programming contest sponsored by company A will be held, so we will post the notice on a bulletin board.\nThe bulletin board is in the form of a grid with N rows and N columns, and the notice will occupy a rectangular region with H rows and W columns.\nHow many ways are there to choose where to put the notice so that it completely covers exactly HW squares?", "constraint": "1 <= H, W <= N <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nH\nW", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2\n3 output: 2\n\nThere are two ways to put the notice, as follows:\n### ...\n### ###\n... ###\n\nHere, # represents a square covered by the notice, and . represents a square not covered.", "input: 100\n1\n1 output: 10000", "input: 5\n4\n2 output: 8"], "Pid": "p03155", "ProblemText": "Task Description: Problem Statement It has been decided that a programming contest sponsored by company A will be held, so we will post the notice on a bulletin board.\nThe bulletin board is in the form of a grid with N rows and N columns, and the notice will occupy a rectangular region with H rows and W columns.\nHow many ways are there to choose where to put the notice so that it completely covers exactly HW squares?\nTask Constraint: 1 <= H, W <= N <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nH\nW\nTask Output: Print the answer.\nTask Samples: input: 3\n2\n3 output: 2\n\nThere are two ways to put the notice, as follows:\n### ...\n### ###\n... ###\n\nHere, # represents a square covered by the notice, and . represents a square not covered.\ninput: 100\n1\n1 output: 10000\ninput: 5\n4\n2 output: 8\n\n" }, { "title": "", "content": "Problem Statement You have written N problems to hold programming contests.\nThe i-th problem will have a score of P_i points if used in a contest.\nWith these problems, you would like to hold as many contests as possible under the following condition:\n\nA contest has three problems. The first problem has a score not greater than A points, the second has a score between A + 1 and B points (inclusive), and the third has a score not less than B + 1 points.\n\nThe same problem should not be used in multiple contests.\nAt most how many contests can be held?", "constraint": "3 <= N <= 100\n1 <= P_i <= 20 (1 <= i <= N)\n1 <= A < B < 20\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA B\nP_1 P_2 . . . P_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n5 15\n1 10 16 2 7 20 12 output: 2\n\nTwo contests can be held by putting the first, second, third problems and the fourth, fifth, sixth problems together.", "input: 8\n3 8\n5 5 5 10 10 10 15 20 output: 0\n\nNo contest can be held, because there is no problem with a score of A = 3 or less.", "input: 3\n5 6\n5 6 10 output: 1"], "Pid": "p03156", "ProblemText": "Task Description: Problem Statement You have written N problems to hold programming contests.\nThe i-th problem will have a score of P_i points if used in a contest.\nWith these problems, you would like to hold as many contests as possible under the following condition:\n\nA contest has three problems. The first problem has a score not greater than A points, the second has a score between A + 1 and B points (inclusive), and the third has a score not less than B + 1 points.\n\nThe same problem should not be used in multiple contests.\nAt most how many contests can be held?\nTask Constraint: 3 <= N <= 100\n1 <= P_i <= 20 (1 <= i <= N)\n1 <= A < B < 20\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA B\nP_1 P_2 . . . P_N\nTask Output: Print the answer.\nTask Samples: input: 7\n5 15\n1 10 16 2 7 20 12 output: 2\n\nTwo contests can be held by putting the first, second, third problems and the fourth, fifth, sixth problems together.\ninput: 8\n3 8\n5 5 5 10 10 10 15 20 output: 0\n\nNo contest can be held, because there is no problem with a score of A = 3 or less.\ninput: 3\n5 6\n5 6 10 output: 1\n\n" }, { "title": "", "content": "Problem Statement There is a grid with H rows and W columns, where each square is painted black or white.\nYou are given H strings S_1, S_2, . . . , S_H, each of length W.\nIf the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is #; if that square is painted white, the j-th character in the string S_i is . .\nFind the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:\n\nThere is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white. . .", "constraint": "1 <= H, W <= 400\n|S_i| = W (1 <= i <= H)\nFor each i (1 <= i <= H), the string S_i consists of characters # and ..", "input": "Input is given from Standard Input in the following format:\nH W\nS_1\nS_2\n:\nS_H", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n.#.\n..#\n#.. output: 10\n\nSome of the pairs satisfying the condition are ((1,2), (3,3)) and ((3,1), (3,2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.", "input: 2 4\n....\n.... output: 0", "input: 4 3\n###\n###\n...\n### output: 6"], "Pid": "p03157", "ProblemText": "Task Description: Problem Statement There is a grid with H rows and W columns, where each square is painted black or white.\nYou are given H strings S_1, S_2, . . . , S_H, each of length W.\nIf the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is #; if that square is painted white, the j-th character in the string S_i is . .\nFind the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:\n\nThere is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white. . .\nTask Constraint: 1 <= H, W <= 400\n|S_i| = W (1 <= i <= H)\nFor each i (1 <= i <= H), the string S_i consists of characters # and ..\nTask Input: Input is given from Standard Input in the following format:\nH W\nS_1\nS_2\n:\nS_H\nTask Output: Print the answer.\nTask Samples: input: 3 3\n.#.\n..#\n#.. output: 10\n\nSome of the pairs satisfying the condition are ((1,2), (3,3)) and ((3,1), (3,2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.\ninput: 2 4\n....\n.... output: 0\ninput: 4 3\n###\n###\n...\n### output: 6\n\n" }, { "title": "", "content": "Problem Statement There are N cards. The i-th card has an integer A_i written on it.\nFor any two cards, the integers on those cards are different.\nUsing these cards, Takahashi and Aoki will play the following game:\n\nAoki chooses an integer x.\nStarting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner:\nTakahashi should take the card with the largest integer among the remaining card.\nAoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards.\nThe game ends when there is no card remaining.\n\nYou are given Q candidates for the value of x: X_1, X_2, . . . , X_Q.\nFor each i (1 <= i <= Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i.", "constraint": "2 <= N <= 100 000\n1 <= Q <= 100 000\n1 <= A_1 < A_2 < ... < A_N <= 10^9\n1 <= X_i <= 10^9 (1 <= i <= Q)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN Q\nA_1 A_2 . . . A_N\nX_1\nX_2\n:\nX_Q", "output": "Print Q lines. The i-th line (1 <= i <= Q) should contain the answer for x = X_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n3 5 7 11 13\n1\n4\n9\n10\n13 output: 31\n31\n27\n23\n23\n\nFor example, when x = X_3(= 9), the game proceeds as follows:\n\nTakahashi takes the card with 13.\nAoki takes the card with 7.\nTakahashi takes the card with 11.\nAoki takes the card with 5.\nTakahashi takes the card with 3.\n\nThus, 13 + 11 + 3 = 27 should be printed on the third line.", "input: 4 3\n10 20 30 40\n2\n34\n34 output: 70\n60\n60"], "Pid": "p03158", "ProblemText": "Task Description: Problem Statement There are N cards. The i-th card has an integer A_i written on it.\nFor any two cards, the integers on those cards are different.\nUsing these cards, Takahashi and Aoki will play the following game:\n\nAoki chooses an integer x.\nStarting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner:\nTakahashi should take the card with the largest integer among the remaining card.\nAoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards.\nThe game ends when there is no card remaining.\n\nYou are given Q candidates for the value of x: X_1, X_2, . . . , X_Q.\nFor each i (1 <= i <= Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i.\nTask Constraint: 2 <= N <= 100 000\n1 <= Q <= 100 000\n1 <= A_1 < A_2 < ... < A_N <= 10^9\n1 <= X_i <= 10^9 (1 <= i <= Q)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN Q\nA_1 A_2 . . . A_N\nX_1\nX_2\n:\nX_Q\nTask Output: Print Q lines. The i-th line (1 <= i <= Q) should contain the answer for x = X_i.\nTask Samples: input: 5 5\n3 5 7 11 13\n1\n4\n9\n10\n13 output: 31\n31\n27\n23\n23\n\nFor example, when x = X_3(= 9), the game proceeds as follows:\n\nTakahashi takes the card with 13.\nAoki takes the card with 7.\nTakahashi takes the card with 11.\nAoki takes the card with 5.\nTakahashi takes the card with 3.\n\nThus, 13 + 11 + 3 = 27 should be printed on the third line.\ninput: 4 3\n10 20 30 40\n2\n34\n34 output: 70\n60\n60\n\n" }, { "title": "", "content": "Problem Statement The server in company A has a structure where N devices numbered 1,2, . . . , N are connected with N - 1 cables.\nThe i-th cable connects Device U_i and Device V_i.\nAny two different devices are connected through some number of cables.\nEach device v (1 <= v <= N) has a non-zero integer A_v, which represents the following:\n\nIf A_v < 0, Device v is a computer that consumes an electric power of -A_v.\nIf A_v > 0, Device v is a battery that supplies an electric power of A_v.\n\nYou have decided to disconnect some number of cables (possibly zero) to disable the server.\nWhen some cables are disconnected, the devices will be divided into some number of connected components.\nThe server will be disabled if all of these connected components satisfy one of the following conditions:\n\nThere is no computer in the connected component. That is, A_v is positive for every device v that belongs to the connected component.\nThere is not enough supply of electric power in the connected component. That is, the sum of A_v over all devices v that belong to the connected component is negative.\n\nAt least how many cables do you need to disconnect in order to disable the server?", "constraint": "1 <= N <= 5 000\n1 <= |A_i| <= 10^9 (1 <= i <= N)\n1 <= U_i, V_i <= N (1 <= i <= N - 1)\nU_i \\neq V_i (1 <= i <= N - 1)\nAny two different devices are connected through some number of cables.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nU_1 V_1\nU_2 V_2\n:\nU_{N - 1} V_{N - 1}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n-2 7 5 6 -8 3 4\n1 2\n2 3\n2 4\n1 5\n5 6\n5 7 output: 1\n\nWe should disconnect the cable connecting Device 1 and Device 2.", "input: 4\n1 2 3 4\n1 2\n1 3\n1 4 output: 0", "input: 6\n10 -1 10 -1 10 -1\n1 2\n2 3\n3 4\n4 5\n5 6 output: 5", "input: 8\n-2 3 6 -2 -2 -5 3 2\n3 4\n7 6\n6 2\n8 2\n5 3\n1 8\n3 7 output: 3", "input: 10\n3 4 9 6 1 5 -1 10 -10 -10\n7 4\n5 6\n8 1\n9 5\n7 1\n10 3\n2 8\n4 10\n9 2 output: 3"], "Pid": "p03159", "ProblemText": "Task Description: Problem Statement The server in company A has a structure where N devices numbered 1,2, . . . , N are connected with N - 1 cables.\nThe i-th cable connects Device U_i and Device V_i.\nAny two different devices are connected through some number of cables.\nEach device v (1 <= v <= N) has a non-zero integer A_v, which represents the following:\n\nIf A_v < 0, Device v is a computer that consumes an electric power of -A_v.\nIf A_v > 0, Device v is a battery that supplies an electric power of A_v.\n\nYou have decided to disconnect some number of cables (possibly zero) to disable the server.\nWhen some cables are disconnected, the devices will be divided into some number of connected components.\nThe server will be disabled if all of these connected components satisfy one of the following conditions:\n\nThere is no computer in the connected component. That is, A_v is positive for every device v that belongs to the connected component.\nThere is not enough supply of electric power in the connected component. That is, the sum of A_v over all devices v that belong to the connected component is negative.\n\nAt least how many cables do you need to disconnect in order to disable the server?\nTask Constraint: 1 <= N <= 5 000\n1 <= |A_i| <= 10^9 (1 <= i <= N)\n1 <= U_i, V_i <= N (1 <= i <= N - 1)\nU_i \\neq V_i (1 <= i <= N - 1)\nAny two different devices are connected through some number of cables.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nU_1 V_1\nU_2 V_2\n:\nU_{N - 1} V_{N - 1}\nTask Output: Print the answer.\nTask Samples: input: 7\n-2 7 5 6 -8 3 4\n1 2\n2 3\n2 4\n1 5\n5 6\n5 7 output: 1\n\nWe should disconnect the cable connecting Device 1 and Device 2.\ninput: 4\n1 2 3 4\n1 2\n1 3\n1 4 output: 0\ninput: 6\n10 -1 10 -1 10 -1\n1 2\n2 3\n3 4\n4 5\n5 6 output: 5\ninput: 8\n-2 3 6 -2 -2 -5 3 2\n3 4\n7 6\n6 2\n8 2\n5 3\n1 8\n3 7 output: 3\ninput: 10\n3 4 9 6 1 5 -1 10 -10 -10\n7 4\n5 6\n8 1\n9 5\n7 1\n10 3\n2 8\n4 10\n9 2 output: 3\n\n" }, { "title": "", "content": "Problem Statement There are N stones, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), the height of Stone i is h_i.\nThere is a frog who is initially on Stone 1.\nHe will repeat the following action some number of times to reach Stone N:\n\nIf the frog is currently on Stone i, jump to Stone i + 1 or Stone i + 2. Here, a cost of |h_i - h_j| is incurred, where j is the stone to land on.\n\nFind the minimum possible total cost incurred before the frog reaches Stone N.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= h_i <= 10^4", "input": "Input is given from Standard Input in the following format:\nN\nh_1 h_2 \\ldots h_N", "output": "Print the minimum possible total cost incurred.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n10 30 40 20 output: 30\n\nIf we follow the path 1 → 2 → 4, the total cost incurred would be |10 - 30| + |30 - 20| = 30.", "input: 2\n10 10 output: 0\n\nIf we follow the path 1 → 2, the total cost incurred would be |10 - 10| = 0.", "input: 6\n30 10 60 10 60 50 output: 40\n\nIf we follow the path 1 → 3 → 5 → 6, the total cost incurred would be |30 - 60| + |60 - 60| + |60 - 50| = 40."], "Pid": "p03160", "ProblemText": "Task Description: Problem Statement There are N stones, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), the height of Stone i is h_i.\nThere is a frog who is initially on Stone 1.\nHe will repeat the following action some number of times to reach Stone N:\n\nIf the frog is currently on Stone i, jump to Stone i + 1 or Stone i + 2. Here, a cost of |h_i - h_j| is incurred, where j is the stone to land on.\n\nFind the minimum possible total cost incurred before the frog reaches Stone N.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= h_i <= 10^4\nTask Input: Input is given from Standard Input in the following format:\nN\nh_1 h_2 \\ldots h_N\nTask Output: Print the minimum possible total cost incurred.\nTask Samples: input: 4\n10 30 40 20 output: 30\n\nIf we follow the path 1 → 2 → 4, the total cost incurred would be |10 - 30| + |30 - 20| = 30.\ninput: 2\n10 10 output: 0\n\nIf we follow the path 1 → 2, the total cost incurred would be |10 - 10| = 0.\ninput: 6\n30 10 60 10 60 50 output: 40\n\nIf we follow the path 1 → 3 → 5 → 6, the total cost incurred would be |30 - 60| + |60 - 60| + |60 - 50| = 40.\n\n" }, { "title": "", "content": "Problem Statement There are N stones, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), the height of Stone i is h_i.\nThere is a frog who is initially on Stone 1.\nHe will repeat the following action some number of times to reach Stone N:\n\nIf the frog is currently on Stone i, jump to one of the following: Stone i + 1, i + 2, \\ldots, i + K. Here, a cost of |h_i - h_j| is incurred, where j is the stone to land on.\n\nFind the minimum possible total cost incurred before the frog reaches Stone N.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= K <= 100\n1 <= h_i <= 10^4", "input": "Input is given from Standard Input in the following format:\nN K\nh_1 h_2 \\ldots h_N", "output": "Print the minimum possible total cost incurred.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n10 30 40 50 20 output: 30\n\nIf we follow the path 1 → 2 → 5, the total cost incurred would be |10 - 30| + |30 - 20| = 30.", "input: 3 1\n10 20 10 output: 20\n\nIf we follow the path 1 → 2 → 3, the total cost incurred would be |10 - 20| + |20 - 10| = 20.", "input: 2 100\n10 10 output: 0\n\nIf we follow the path 1 → 2, the total cost incurred would be |10 - 10| = 0.", "input: 10 4\n40 10 20 70 80 10 20 70 80 60 output: 40\n\nIf we follow the path 1 → 4 → 8 → 10, the total cost incurred would be |40 - 70| + |70 - 70| + |70 - 60| = 40."], "Pid": "p03161", "ProblemText": "Task Description: Problem Statement There are N stones, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), the height of Stone i is h_i.\nThere is a frog who is initially on Stone 1.\nHe will repeat the following action some number of times to reach Stone N:\n\nIf the frog is currently on Stone i, jump to one of the following: Stone i + 1, i + 2, \\ldots, i + K. Here, a cost of |h_i - h_j| is incurred, where j is the stone to land on.\n\nFind the minimum possible total cost incurred before the frog reaches Stone N.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= K <= 100\n1 <= h_i <= 10^4\nTask Input: Input is given from Standard Input in the following format:\nN K\nh_1 h_2 \\ldots h_N\nTask Output: Print the minimum possible total cost incurred.\nTask Samples: input: 5 3\n10 30 40 50 20 output: 30\n\nIf we follow the path 1 → 2 → 5, the total cost incurred would be |10 - 30| + |30 - 20| = 30.\ninput: 3 1\n10 20 10 output: 20\n\nIf we follow the path 1 → 2 → 3, the total cost incurred would be |10 - 20| + |20 - 10| = 20.\ninput: 2 100\n10 10 output: 0\n\nIf we follow the path 1 → 2, the total cost incurred would be |10 - 10| = 0.\ninput: 10 4\n40 10 20 70 80 10 20 70 80 60 output: 40\n\nIf we follow the path 1 → 4 → 8 → 10, the total cost incurred would be |40 - 70| + |70 - 70| + |70 - 60| = 40.\n\n" }, { "title": "", "content": "Problem Statement Taro's summer vacation starts tomorrow, and he has decided to make plans for it now.\nThe vacation consists of N days.\nFor each i (1 <= i <= N), Taro will choose one of the following activities and do it on the i-th day:\n\nA: Swim in the sea. Gain a_i points of happiness.\nB: Catch bugs in the mountains. Gain b_i points of happiness.\nC: Do homework at home. Gain c_i points of happiness.\n\nAs Taro gets bored easily, he cannot do the same activities for two or more consecutive days.\nFind the maximum possible total points of happiness that Taro gains.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= a_i, b_i, c_i <= 10^4", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1 c_1\na_2 b_2 c_2\n:\na_N b_N c_N", "output": "Print the maximum possible total points of happiness that Taro gains.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10 40 70\n20 50 80\n30 60 90 output: 210\n\nIf Taro does activities in the order C, B, C, he will gain 70 + 50 + 90 = 210 points of happiness.", "input: 1\n100 10 1 output: 100", "input: 7\n6 7 8\n8 8 3\n2 5 2\n7 8 6\n4 6 8\n2 3 4\n7 5 1 output: 46\n\nTaro should do activities in the order C, A, B, A, C, B, A."], "Pid": "p03162", "ProblemText": "Task Description: Problem Statement Taro's summer vacation starts tomorrow, and he has decided to make plans for it now.\nThe vacation consists of N days.\nFor each i (1 <= i <= N), Taro will choose one of the following activities and do it on the i-th day:\n\nA: Swim in the sea. Gain a_i points of happiness.\nB: Catch bugs in the mountains. Gain b_i points of happiness.\nC: Do homework at home. Gain c_i points of happiness.\n\nAs Taro gets bored easily, he cannot do the same activities for two or more consecutive days.\nFind the maximum possible total points of happiness that Taro gains.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= a_i, b_i, c_i <= 10^4\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1 c_1\na_2 b_2 c_2\n:\na_N b_N c_N\nTask Output: Print the maximum possible total points of happiness that Taro gains.\nTask Samples: input: 3\n10 40 70\n20 50 80\n30 60 90 output: 210\n\nIf Taro does activities in the order C, B, C, he will gain 70 + 50 + 90 = 210 points of happiness.\ninput: 1\n100 10 1 output: 100\ninput: 7\n6 7 8\n8 8 3\n2 5 2\n7 8 6\n4 6 8\n2 3 4\n7 5 1 output: 46\n\nTaro should do activities in the order C, A, B, A, C, B, A.\n\n" }, { "title": "", "content": "Problem Statement There are N items, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), Item i has a weight of w_i and a value of v_i.\nTaro has decided to choose some of the N items and carry them home in a knapsack.\nThe capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.\nFind the maximum possible sum of the values of items that Taro takes home.", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= W <= 10^5\n1 <= w_i <= W\n1 <= v_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN W\nw_1 v_1\nw_2 v_2\n:\nw_N v_N", "output": "Print the maximum possible sum of the values of items that Taro takes home.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 8\n3 30\n4 50\n5 60 output: 90\n\nItems 1 and 3 should be taken.\nThen, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.", "input: 5 5\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.", "input: 6 15\n6 5\n5 6\n6 4\n6 6\n3 5\n7 2 output: 17\n\nItems 2,4 and 5 should be taken.\nThen, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17."], "Pid": "p03163", "ProblemText": "Task Description: Problem Statement There are N items, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), Item i has a weight of w_i and a value of v_i.\nTaro has decided to choose some of the N items and carry them home in a knapsack.\nThe capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.\nFind the maximum possible sum of the values of items that Taro takes home.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= W <= 10^5\n1 <= w_i <= W\n1 <= v_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN W\nw_1 v_1\nw_2 v_2\n:\nw_N v_N\nTask Output: Print the maximum possible sum of the values of items that Taro takes home.\nTask Samples: input: 3 8\n3 30\n4 50\n5 60 output: 90\n\nItems 1 and 3 should be taken.\nThen, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.\ninput: 5 5\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.\ninput: 6 15\n6 5\n5 6\n6 4\n6 6\n3 5\n7 2 output: 17\n\nItems 2,4 and 5 should be taken.\nThen, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.\n\n" }, { "title": "", "content": "Problem Statement There are N items, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), Item i has a weight of w_i and a value of v_i.\nTaro has decided to choose some of the N items and carry them home in a knapsack.\nThe capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.\nFind the maximum possible sum of the values of items that Taro takes home.", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= W <= 10^9\n1 <= w_i <= W\n1 <= v_i <= 10^3", "input": "Input is given from Standard Input in the following format:\nN W\nw_1 v_1\nw_2 v_2\n:\nw_N v_N", "output": "Print the maximum possible sum of the values of items that Taro takes home.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 8\n3 30\n4 50\n5 60 output: 90\n\nItems 1 and 3 should be taken.\nThen, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.", "input: 1 1000000000\n1000000000 10 output: 10", "input: 6 15\n6 5\n5 6\n6 4\n6 6\n3 5\n7 2 output: 17\n\nItems 2,4 and 5 should be taken.\nThen, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17."], "Pid": "p03164", "ProblemText": "Task Description: Problem Statement There are N items, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), Item i has a weight of w_i and a value of v_i.\nTaro has decided to choose some of the N items and carry them home in a knapsack.\nThe capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.\nFind the maximum possible sum of the values of items that Taro takes home.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= W <= 10^9\n1 <= w_i <= W\n1 <= v_i <= 10^3\nTask Input: Input is given from Standard Input in the following format:\nN W\nw_1 v_1\nw_2 v_2\n:\nw_N v_N\nTask Output: Print the maximum possible sum of the values of items that Taro takes home.\nTask Samples: input: 3 8\n3 30\n4 50\n5 60 output: 90\n\nItems 1 and 3 should be taken.\nThen, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.\ninput: 1 1000000000\n1000000000 10 output: 10\ninput: 6 15\n6 5\n5 6\n6 4\n6 6\n3 5\n7 2 output: 17\n\nItems 2,4 and 5 should be taken.\nThen, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.\n\n" }, { "title": "", "content": "Problem Statement You are given strings s and t.\nFind one longest string that is a subsequence of both s and t. note: Notes A subsequence of a string x is the string obtained by removing zero or more characters from x and concatenating the remaining characters without changing the order.", "constraint": "s and t are strings consisting of lowercase English letters.\n1 <= |s|, |t| <= 3000", "input": "Input is given from Standard Input in the following format:\ns\nt", "output": "Print one longest string that is a subsequence of both s and t.\nIf there are multiple such strings, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: axyb\nabyxb output: axb\n\nThe answer is axb or ayb; either will be accepted.", "input: aa\nxayaz output: aa", "input: a\nz output: \nThe answer is (an empty string).", "input: abracadabra\navadakedavra output: aaadara"], "Pid": "p03165", "ProblemText": "Task Description: Problem Statement You are given strings s and t.\nFind one longest string that is a subsequence of both s and t. note: Notes A subsequence of a string x is the string obtained by removing zero or more characters from x and concatenating the remaining characters without changing the order.\nTask Constraint: s and t are strings consisting of lowercase English letters.\n1 <= |s|, |t| <= 3000\nTask Input: Input is given from Standard Input in the following format:\ns\nt\nTask Output: Print one longest string that is a subsequence of both s and t.\nIf there are multiple such strings, any of them will be accepted.\nTask Samples: input: axyb\nabyxb output: axb\n\nThe answer is axb or ayb; either will be accepted.\ninput: aa\nxayaz output: aa\ninput: a\nz output: \nThe answer is (an empty string).\ninput: abracadabra\navadakedavra output: aaadara\n\n" }, { "title": "", "content": "Problem Statement There is a directed graph G with N vertices and M edges.\nThe vertices are numbered 1,2, \\ldots, N, and for each i (1 <= i <= M), the i-th directed edge goes from Vertex x_i to y_i.\nG does not contain directed cycles.\nFind the length of the longest directed path in G.\nHere, the length of a directed path is the number of edges in it.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= x_i, y_i <= N\nAll pairs (x_i, y_i) are distinct.\nG does not contain directed cycles.", "input": "Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_M y_M", "output": "Print the length of the longest directed path in G.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n1 2\n1 3\n3 2\n2 4\n3 4 output: 3\n\nThe red directed path in the following figure is the longest:", "input: 6 3\n2 3\n4 5\n5 6 output: 2\n\nThe red directed path in the following figure is the longest:", "input: 5 8\n5 3\n2 3\n2 4\n5 2\n5 1\n1 4\n4 3\n1 3 output: 3\n\nThe red directed path in the following figure is one of the longest:"], "Pid": "p03166", "ProblemText": "Task Description: Problem Statement There is a directed graph G with N vertices and M edges.\nThe vertices are numbered 1,2, \\ldots, N, and for each i (1 <= i <= M), the i-th directed edge goes from Vertex x_i to y_i.\nG does not contain directed cycles.\nFind the length of the longest directed path in G.\nHere, the length of a directed path is the number of edges in it.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= x_i, y_i <= N\nAll pairs (x_i, y_i) are distinct.\nG does not contain directed cycles.\nTask Input: Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_M y_M\nTask Output: Print the length of the longest directed path in G.\nTask Samples: input: 4 5\n1 2\n1 3\n3 2\n2 4\n3 4 output: 3\n\nThe red directed path in the following figure is the longest:\ninput: 6 3\n2 3\n4 5\n5 6 output: 2\n\nThe red directed path in the following figure is the longest:\ninput: 5 8\n5 3\n2 3\n2 4\n5 2\n5 1\n1 4\n4 3\n1 3 output: 3\n\nThe red directed path in the following figure is one of the longest:\n\n" }, { "title": "", "content": "Problem Statement There is a grid with H horizontal rows and W vertical columns.\nLet (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nFor each i and j (1 <= i <= H, 1 <= j <= W), Square (i, j) is described by a character a_{i, j}.\nIf a_{i, j} is . , Square (i, j) is an empty square; if a_{i, j} is #, Square (i, j) is a wall square.\nIt is guaranteed that Squares (1,1) and (H, W) are empty squares.\nTaro will start from Square (1,1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.\nFind the number of Taro's paths from Square (1,1) to (H, W).\nAs the answer can be extremely large, find the count modulo 10^9 + 7.", "constraint": "H and W are integers.\n2 <= H, W <= 1000\na_{i, j} is . or #.\nSquares (1,1) and (H, W) are empty squares.", "input": "Input is given from Standard Input in the following format:\nH W\na_{1,1}\\ldotsa_{1, W}\n:\na_{H, 1}\\ldotsa_{H, W}", "output": "Print the number of Taro's paths from Square (1,1) to (H, W), modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n...#\n.#..\n.... output: 3\n\nThere are three paths as follows:", "input: 5 2\n..\n#.\n..\n.#\n.. output: 0\n\nThere may be no paths.", "input: 5 5\n..#..\n.....\n#...#\n.....\n..#.. output: 24", "input: 20 20\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n.................... output: 345263555\n\nBe sure to print the count modulo 10^9 + 7."], "Pid": "p03167", "ProblemText": "Task Description: Problem Statement There is a grid with H horizontal rows and W vertical columns.\nLet (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nFor each i and j (1 <= i <= H, 1 <= j <= W), Square (i, j) is described by a character a_{i, j}.\nIf a_{i, j} is . , Square (i, j) is an empty square; if a_{i, j} is #, Square (i, j) is a wall square.\nIt is guaranteed that Squares (1,1) and (H, W) are empty squares.\nTaro will start from Square (1,1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.\nFind the number of Taro's paths from Square (1,1) to (H, W).\nAs the answer can be extremely large, find the count modulo 10^9 + 7.\nTask Constraint: H and W are integers.\n2 <= H, W <= 1000\na_{i, j} is . or #.\nSquares (1,1) and (H, W) are empty squares.\nTask Input: Input is given from Standard Input in the following format:\nH W\na_{1,1}\\ldotsa_{1, W}\n:\na_{H, 1}\\ldotsa_{H, W}\nTask Output: Print the number of Taro's paths from Square (1,1) to (H, W), modulo 10^9 + 7.\nTask Samples: input: 3 4\n...#\n.#..\n.... output: 3\n\nThere are three paths as follows:\ninput: 5 2\n..\n#.\n..\n.#\n.. output: 0\n\nThere may be no paths.\ninput: 5 5\n..#..\n.....\n#...#\n.....\n..#.. output: 24\ninput: 20 20\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n....................\n.................... output: 345263555\n\nBe sure to print the count modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement Let N be a positive odd number.\nThere are N coins, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), when Coin i is tossed, it comes up heads with probability p_i and tails with probability 1 - p_i.\nTaro has tossed all the N coins.\nFind the probability of having more heads than tails.", "constraint": "N is an odd number.\n1 <= N <= 2999\np_i is a real number and has two decimal places.\n0 < p_i < 1", "input": "Input is given from Standard Input in the following format:\nN\np_1 p_2 \\ldots p_N", "output": "Print the probability of having more heads than tails.\nThe output is considered correct when the absolute error is not greater than 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0.30 0.60 0.80 output: 0.612\n\nThe probability of each case where we have more heads than tails is as follows:\n\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Head, Head, Head) is 0.3 * 0.6 * 0.8 = 0.144;\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Tail, Head, Head) is 0.7 * 0.6 * 0.8 = 0.336;\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Head, Tail, Head) is 0.3 * 0.4 * 0.8 = 0.096;\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Head, Head, Tail) is 0.3 * 0.6 * 0.2 = 0.036.\n\nThus, the probability of having more heads than tails is 0.144 + 0.336 + 0.096 + 0.036 = 0.612.", "input: 1\n0.50 output: 0.5\n\nOutputs such as 0.500,0.500000001 and 0.499999999 are also considered correct.", "input: 5\n0.42 0.01 0.42 0.99 0.42 output: 0.3821815872"], "Pid": "p03168", "ProblemText": "Task Description: Problem Statement Let N be a positive odd number.\nThere are N coins, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), when Coin i is tossed, it comes up heads with probability p_i and tails with probability 1 - p_i.\nTaro has tossed all the N coins.\nFind the probability of having more heads than tails.\nTask Constraint: N is an odd number.\n1 <= N <= 2999\np_i is a real number and has two decimal places.\n0 < p_i < 1\nTask Input: Input is given from Standard Input in the following format:\nN\np_1 p_2 \\ldots p_N\nTask Output: Print the probability of having more heads than tails.\nThe output is considered correct when the absolute error is not greater than 10^{-9}.\nTask Samples: input: 3\n0.30 0.60 0.80 output: 0.612\n\nThe probability of each case where we have more heads than tails is as follows:\n\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Head, Head, Head) is 0.3 * 0.6 * 0.8 = 0.144;\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Tail, Head, Head) is 0.7 * 0.6 * 0.8 = 0.336;\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Head, Tail, Head) is 0.3 * 0.4 * 0.8 = 0.096;\nThe probability of having (Coin 1, Coin 2, Coin 3) = (Head, Head, Tail) is 0.3 * 0.6 * 0.2 = 0.036.\n\nThus, the probability of having more heads than tails is 0.144 + 0.336 + 0.096 + 0.036 = 0.612.\ninput: 1\n0.50 output: 0.5\n\nOutputs such as 0.500,0.500000001 and 0.499999999 are also considered correct.\ninput: 5\n0.42 0.01 0.42 0.99 0.42 output: 0.3821815872\n\n" }, { "title": "", "content": "Problem Statement There are N dishes, numbered 1,2, \\ldots, N.\nInitially, for each i (1 <= i <= N), Dish i has a_i (1 <= a_i <= 3) pieces of sushi on it.\nTaro will perform the following operation repeatedly until all the pieces of sushi are eaten:\n\nRoll a die that shows the numbers 1,2, \\ldots, N with equal probabilities, and let i be the outcome. If there are some pieces of sushi on Dish i, eat one of them; if there is none, do nothing.\n\nFind the expected number of times the operation is performed before all the pieces of sushi are eaten.", "constraint": "All values in input are integers.\n1 <= N <= 300\n1 <= a_i <= 3", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N", "output": "Print the expected number of times the operation is performed before all the pieces of sushi are eaten.\nThe output is considered correct when the relative difference is not greater than 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1 1 output: 5.5\n\nThe expected number of operations before the first piece of sushi is eaten, is 1.\nAfter that, the expected number of operations before the second sushi is eaten, is 1.5.\nAfter that, the expected number of operations before the third sushi is eaten, is 3.\nThus, the expected total number of operations is 1 + 1.5 + 3 = 5.5.", "input: 1\n3 output: 3\n\nOutputs such as 3.00,3.000000003 and 2.999999997 will also be accepted.", "input: 2\n1 2 output: 4.5", "input: 10\n1 3 2 3 3 2 3 2 1 3 output: 54.48064457488221"], "Pid": "p03169", "ProblemText": "Task Description: Problem Statement There are N dishes, numbered 1,2, \\ldots, N.\nInitially, for each i (1 <= i <= N), Dish i has a_i (1 <= a_i <= 3) pieces of sushi on it.\nTaro will perform the following operation repeatedly until all the pieces of sushi are eaten:\n\nRoll a die that shows the numbers 1,2, \\ldots, N with equal probabilities, and let i be the outcome. If there are some pieces of sushi on Dish i, eat one of them; if there is none, do nothing.\n\nFind the expected number of times the operation is performed before all the pieces of sushi are eaten.\nTask Constraint: All values in input are integers.\n1 <= N <= 300\n1 <= a_i <= 3\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N\nTask Output: Print the expected number of times the operation is performed before all the pieces of sushi are eaten.\nThe output is considered correct when the relative difference is not greater than 10^{-9}.\nTask Samples: input: 3\n1 1 1 output: 5.5\n\nThe expected number of operations before the first piece of sushi is eaten, is 1.\nAfter that, the expected number of operations before the second sushi is eaten, is 1.5.\nAfter that, the expected number of operations before the third sushi is eaten, is 3.\nThus, the expected total number of operations is 1 + 1.5 + 3 = 5.5.\ninput: 1\n3 output: 3\n\nOutputs such as 3.00,3.000000003 and 2.999999997 will also be accepted.\ninput: 2\n1 2 output: 4.5\ninput: 10\n1 3 2 3 3 2 3 2 1 3 output: 54.48064457488221\n\n" }, { "title": "", "content": "Problem Statement There is a set A = \\{ a_1, a_2, \\ldots, a_N \\} consisting of N positive integers.\nTaro and Jiro will play the following game against each other.\nInitially, we have a pile consisting of K stones.\nThe two players perform the following operation alternately, starting from Taro:\n\nChoose an element x in A, and remove exactly x stones from the pile.\n\nA player loses when he becomes unable to play.\nAssuming that both players play optimally, determine the winner.", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= K <= 10^5\n1 <= a_1 < a_2 < \\cdots < a_N <= K", "input": "Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\ldots a_N", "output": "If Taro will win, print First; if Jiro will win, print Second.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 4\n2 3 output: First\n\nIf Taro removes three stones, Jiro cannot make a move.\nThus, Taro wins.", "input: 2 5\n2 3 output: Second\n\nWhatever Taro does in his operation, Jiro wins, as follows:\n\nIf Taro removes two stones, Jiro can remove three stones to make Taro unable to make a move.\nIf Taro removes three stones, Jiro can remove two stones to make Taro unable to make a move.", "input: 2 7\n2 3 output: First\n\nTaro should remove two stones. Then, whatever Jiro does in his operation, Taro wins, as follows:\n\nIf Jiro removes two stones, Taro can remove three stones to make Jiro unable to make a move.\nIf Jiro removes three stones, Taro can remove two stones to make Jiro unable to make a move.", "input: 3 20\n1 2 3 output: Second", "input: 3 21\n1 2 3 output: First", "input: 1 100000\n1 output: Second"], "Pid": "p03170", "ProblemText": "Task Description: Problem Statement There is a set A = \\{ a_1, a_2, \\ldots, a_N \\} consisting of N positive integers.\nTaro and Jiro will play the following game against each other.\nInitially, we have a pile consisting of K stones.\nThe two players perform the following operation alternately, starting from Taro:\n\nChoose an element x in A, and remove exactly x stones from the pile.\n\nA player loses when he becomes unable to play.\nAssuming that both players play optimally, determine the winner.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= K <= 10^5\n1 <= a_1 < a_2 < \\cdots < a_N <= K\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\ldots a_N\nTask Output: If Taro will win, print First; if Jiro will win, print Second.\nTask Samples: input: 2 4\n2 3 output: First\n\nIf Taro removes three stones, Jiro cannot make a move.\nThus, Taro wins.\ninput: 2 5\n2 3 output: Second\n\nWhatever Taro does in his operation, Jiro wins, as follows:\n\nIf Taro removes two stones, Jiro can remove three stones to make Taro unable to make a move.\nIf Taro removes three stones, Jiro can remove two stones to make Taro unable to make a move.\ninput: 2 7\n2 3 output: First\n\nTaro should remove two stones. Then, whatever Jiro does in his operation, Taro wins, as follows:\n\nIf Jiro removes two stones, Taro can remove three stones to make Jiro unable to make a move.\nIf Jiro removes three stones, Taro can remove two stones to make Jiro unable to make a move.\ninput: 3 20\n1 2 3 output: Second\ninput: 3 21\n1 2 3 output: First\ninput: 1 100000\n1 output: Second\n\n" }, { "title": "", "content": "Problem Statement Taro and Jiro will play the following game against each other.\nInitially, they are given a sequence a = (a_1, a_2, \\ldots, a_N).\nUntil a becomes empty, the two players perform the following operation alternately, starting from Taro:\n\nRemove the element at the beginning or the end of a. The player earns x points, where x is the removed element.\n\nLet X and Y be Taro's and Jiro's total score at the end of the game, respectively.\nTaro tries to maximize X - Y, while Jiro tries to minimize X - Y.\nAssuming that the two players play optimally, find the resulting value of X - Y.", "constraint": "All values in input are integers.\n1 <= N <= 3000\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N", "output": "Print the resulting value of X - Y, assuming that the two players play optimally.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n10 80 90 30 output: 10\n\nThe game proceeds as follows when the two players play optimally (the element being removed is written bold):\n\nTaro: (10,80,90,30) → (10,80,90)\nJiro: (10,80,90) → (10,80)\nTaro: (10,80) → (10)\nJiro: (10) → ()\n\nHere, X = 30 + 80 = 110 and Y = 90 + 10 = 100.", "input: 3\n10 100 10 output: -80\n\nThe game proceeds, for example, as follows when the two players play optimally:\n\nTaro: (10,100,10) → (100,10)\nJiro: (100,10) → (10)\nTaro: (10) → ()\n\nHere, X = 10 + 10 = 20 and Y = 100.", "input: 1\n10 output: 10", "input: 10\n1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 output: 4999999995\n\nThe answer may not fit into a 32-bit integer type.", "input: 6\n4 2 9 7 1 5 output: 2\n\nThe game proceeds, for example, as follows when the two players play optimally:\n\nTaro: (4,2,9,7,1,5) → (4,2,9,7,1)\nJiro: (4,2,9,7,1) → (2,9,7,1)\nTaro: (2,9,7,1) → (2,9,7)\nJiro: (2,9,7) → (2,9)\nTaro: (2,9) → (2)\nJiro: (2) → ()\n\nHere, X = 5 + 1 + 9 = 15 and Y = 4 + 7 + 2 = 13."], "Pid": "p03171", "ProblemText": "Task Description: Problem Statement Taro and Jiro will play the following game against each other.\nInitially, they are given a sequence a = (a_1, a_2, \\ldots, a_N).\nUntil a becomes empty, the two players perform the following operation alternately, starting from Taro:\n\nRemove the element at the beginning or the end of a. The player earns x points, where x is the removed element.\n\nLet X and Y be Taro's and Jiro's total score at the end of the game, respectively.\nTaro tries to maximize X - Y, while Jiro tries to minimize X - Y.\nAssuming that the two players play optimally, find the resulting value of X - Y.\nTask Constraint: All values in input are integers.\n1 <= N <= 3000\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N\nTask Output: Print the resulting value of X - Y, assuming that the two players play optimally.\nTask Samples: input: 4\n10 80 90 30 output: 10\n\nThe game proceeds as follows when the two players play optimally (the element being removed is written bold):\n\nTaro: (10,80,90,30) → (10,80,90)\nJiro: (10,80,90) → (10,80)\nTaro: (10,80) → (10)\nJiro: (10) → ()\n\nHere, X = 30 + 80 = 110 and Y = 90 + 10 = 100.\ninput: 3\n10 100 10 output: -80\n\nThe game proceeds, for example, as follows when the two players play optimally:\n\nTaro: (10,100,10) → (100,10)\nJiro: (100,10) → (10)\nTaro: (10) → ()\n\nHere, X = 10 + 10 = 20 and Y = 100.\ninput: 1\n10 output: 10\ninput: 10\n1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 output: 4999999995\n\nThe answer may not fit into a 32-bit integer type.\ninput: 6\n4 2 9 7 1 5 output: 2\n\nThe game proceeds, for example, as follows when the two players play optimally:\n\nTaro: (4,2,9,7,1,5) → (4,2,9,7,1)\nJiro: (4,2,9,7,1) → (2,9,7,1)\nTaro: (2,9,7,1) → (2,9,7)\nJiro: (2,9,7) → (2,9)\nTaro: (2,9) → (2)\nJiro: (2) → ()\n\nHere, X = 5 + 1 + 9 = 15 and Y = 4 + 7 + 2 = 13.\n\n" }, { "title": "", "content": "Problem Statement There are N children, numbered 1,2, \\ldots, N.\nThey have decided to share K candies among themselves.\nHere, for each i (1 <= i <= N), Child i must receive between 0 and a_i candies (inclusive).\nAlso, no candies should be left over.\nFind the number of ways for them to share candies, modulo 10^9 + 7.\nHere, two ways are said to be different when there exists a child who receives a different number of candies.", "constraint": "All values in input are integers.\n1 <= N <= 100\n0 <= K <= 10^5\n0 <= a_i <= K", "input": "Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\ldots a_N", "output": "Print the number of ways for the children to share candies, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n1 2 3 output: 5\n\nThere are five ways for the children to share candies, as follows:\n\n(0,1,3)\n(0,2,2)\n(1,0,3)\n(1,1,2)\n(1,2,1)\n\nHere, in each sequence, the i-th element represents the number of candies that Child i receives.", "input: 1 10\n9 output: 0\n\nThere may be no ways for the children to share candies.", "input: 2 0\n0 0 output: 1\n\nThere is one way for the children to share candies, as follows:\n\n(0,0)", "input: 4 100000\n100000 100000 100000 100000 output: 665683269\n\nBe sure to print the answer modulo 10^9 + 7."], "Pid": "p03172", "ProblemText": "Task Description: Problem Statement There are N children, numbered 1,2, \\ldots, N.\nThey have decided to share K candies among themselves.\nHere, for each i (1 <= i <= N), Child i must receive between 0 and a_i candies (inclusive).\nAlso, no candies should be left over.\nFind the number of ways for them to share candies, modulo 10^9 + 7.\nHere, two ways are said to be different when there exists a child who receives a different number of candies.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n0 <= K <= 10^5\n0 <= a_i <= K\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1 a_2 \\ldots a_N\nTask Output: Print the number of ways for the children to share candies, modulo 10^9 + 7.\nTask Samples: input: 3 4\n1 2 3 output: 5\n\nThere are five ways for the children to share candies, as follows:\n\n(0,1,3)\n(0,2,2)\n(1,0,3)\n(1,1,2)\n(1,2,1)\n\nHere, in each sequence, the i-th element represents the number of candies that Child i receives.\ninput: 1 10\n9 output: 0\n\nThere may be no ways for the children to share candies.\ninput: 2 0\n0 0 output: 1\n\nThere is one way for the children to share candies, as follows:\n\n(0,0)\ninput: 4 100000\n100000 100000 100000 100000 output: 665683269\n\nBe sure to print the answer modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement There are N slimes lining up in a row.\nInitially, the i-th slime from the left has a size of a_i.\nTaro is trying to combine all the slimes into a larger slime.\nHe will perform the following operation repeatedly until there is only one slime:\n\nChoose two adjacent slimes, and combine them into a new slime. The new slime has a size of x + y, where x and y are the sizes of the slimes before combining them. Here, a cost of x + y is incurred. The positional relationship of the slimes does not change while combining slimes.\n\nFind the minimum possible total cost incurred.", "constraint": "All values in input are integers.\n2 <= N <= 400\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N", "output": "Print the minimum possible total cost incurred.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n10 20 30 40 output: 190\n\nTaro should do as follows (slimes being combined are shown in bold):\n\n(10,20,30,40) → (30,30,40)\n(30,30,40) → (60,40)\n(60,40) → (100)", "input: 5\n10 10 10 10 10 output: 120\n\nTaro should do, for example, as follows:\n\n(10,10,10,10,10) → (20,10,10,10)\n(20,10,10,10) → (20,20,10)\n(20,20,10) → (20,30)\n(20,30) → (50)", "input: 3\n1000000000 1000000000 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.", "input: 6\n7 6 8 6 1 1 output: 68\n\nTaro should do, for example, as follows:\n\n(7,6,8,6,1,1) → (7,6,8,6,2)\n(7,6,8,6,2) → (7,6,8,8)\n(7,6,8,8) → (13,8,8)\n(13,8,8) → (13,16)\n(13,16) → (29)"], "Pid": "p03173", "ProblemText": "Task Description: Problem Statement There are N slimes lining up in a row.\nInitially, the i-th slime from the left has a size of a_i.\nTaro is trying to combine all the slimes into a larger slime.\nHe will perform the following operation repeatedly until there is only one slime:\n\nChoose two adjacent slimes, and combine them into a new slime. The new slime has a size of x + y, where x and y are the sizes of the slimes before combining them. Here, a cost of x + y is incurred. The positional relationship of the slimes does not change while combining slimes.\n\nFind the minimum possible total cost incurred.\nTask Constraint: All values in input are integers.\n2 <= N <= 400\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 \\ldots a_N\nTask Output: Print the minimum possible total cost incurred.\nTask Samples: input: 4\n10 20 30 40 output: 190\n\nTaro should do as follows (slimes being combined are shown in bold):\n\n(10,20,30,40) → (30,30,40)\n(30,30,40) → (60,40)\n(60,40) → (100)\ninput: 5\n10 10 10 10 10 output: 120\n\nTaro should do, for example, as follows:\n\n(10,10,10,10,10) → (20,10,10,10)\n(20,10,10,10) → (20,20,10)\n(20,20,10) → (20,30)\n(20,30) → (50)\ninput: 3\n1000000000 1000000000 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.\ninput: 6\n7 6 8 6 1 1 output: 68\n\nTaro should do, for example, as follows:\n\n(7,6,8,6,1,1) → (7,6,8,6,2)\n(7,6,8,6,2) → (7,6,8,8)\n(7,6,8,8) → (13,8,8)\n(13,8,8) → (13,16)\n(13,16) → (29)\n\n" }, { "title": "", "content": "Problem Statement There are N men and N women, both numbered 1,2, \\ldots, N.\nFor each i, j (1 <= i, j <= N), the compatibility of Man i and Woman j is given as an integer a_{i, j}.\nIf a_{i, j} = 1, Man i and Woman j are compatible; if a_{i, j} = 0, they are not.\nTaro is trying to make N pairs, each consisting of a man and a woman who are compatible.\nHere, each man and each woman must belong to exactly one pair.\nFind the number of ways in which Taro can make N pairs, modulo 10^9 + 7.", "constraint": "All values in input are integers.\n1 <= N <= 21\na_{i, j} is 0 or 1.", "input": "Input is given from Standard Input in the following format:\nN\na_{1,1} \\ldots a_{1, N}\n:\na_{N, 1} \\ldots a_{N, N}", "output": "Print the number of ways in which Taro can make N pairs, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 1 1\n1 0 1\n1 1 1 output: 3\n\nThere are three ways to make pairs, as follows ((i, j) denotes a pair of Man i and Woman j):\n\n(1,2), (2,1), (3,3)\n(1,2), (2,3), (3,1)\n(1,3), (2,1), (3,2)", "input: 4\n0 1 0 0\n0 0 0 1\n1 0 0 0\n0 0 1 0 output: 1\n\nThere is one way to make pairs, as follows:\n\n(1,2), (2,4), (3,1), (4,3)", "input: 1\n0 output: 0", "input: 21\n0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1\n1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0\n0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1\n0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0\n1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0\n0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1\n0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0\n0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1\n0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1\n0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1\n0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0\n0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1\n0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1\n1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1\n0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1\n1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0\n0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1\n0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1\n0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0\n1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0\n1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 output: 102515160\n\nBe sure to print the number modulo 10^9 + 7."], "Pid": "p03174", "ProblemText": "Task Description: Problem Statement There are N men and N women, both numbered 1,2, \\ldots, N.\nFor each i, j (1 <= i, j <= N), the compatibility of Man i and Woman j is given as an integer a_{i, j}.\nIf a_{i, j} = 1, Man i and Woman j are compatible; if a_{i, j} = 0, they are not.\nTaro is trying to make N pairs, each consisting of a man and a woman who are compatible.\nHere, each man and each woman must belong to exactly one pair.\nFind the number of ways in which Taro can make N pairs, modulo 10^9 + 7.\nTask Constraint: All values in input are integers.\n1 <= N <= 21\na_{i, j} is 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nN\na_{1,1} \\ldots a_{1, N}\n:\na_{N, 1} \\ldots a_{N, N}\nTask Output: Print the number of ways in which Taro can make N pairs, modulo 10^9 + 7.\nTask Samples: input: 3\n0 1 1\n1 0 1\n1 1 1 output: 3\n\nThere are three ways to make pairs, as follows ((i, j) denotes a pair of Man i and Woman j):\n\n(1,2), (2,1), (3,3)\n(1,2), (2,3), (3,1)\n(1,3), (2,1), (3,2)\ninput: 4\n0 1 0 0\n0 0 0 1\n1 0 0 0\n0 0 1 0 output: 1\n\nThere is one way to make pairs, as follows:\n\n(1,2), (2,4), (3,1), (4,3)\ninput: 1\n0 output: 0\ninput: 21\n0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1\n1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0\n0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1\n0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0\n1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0\n0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1\n0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0\n0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1\n0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1\n0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1\n0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0\n0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1\n0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1\n1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1\n0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1\n1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0\n0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1\n0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1\n0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0\n1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0\n1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 output: 102515160\n\nBe sure to print the number modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N - 1), the i-th edge connects Vertex x_i and y_i.\nTaro has decided to paint each vertex in white or black.\nHere, it is not allowed to paint two adjacent vertices both in black.\nFind the number of ways in which the vertices can be painted, modulo 10^9 + 7.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= x_i, y_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}", "output": "Print the number of ways in which the vertices can be painted, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3 output: 5\n\nThere are five ways to paint the vertices, as follows:", "input: 4\n1 2\n1 3\n1 4 output: 9\n\nThere are nine ways to paint the vertices, as follows:", "input: 1 output: 2", "input: 10\n8 5\n10 8\n6 5\n1 5\n4 8\n2 10\n3 6\n9 2\n1 7 output: 157"], "Pid": "p03175", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N - 1), the i-th edge connects Vertex x_i and y_i.\nTaro has decided to paint each vertex in white or black.\nHere, it is not allowed to paint two adjacent vertices both in black.\nFind the number of ways in which the vertices can be painted, modulo 10^9 + 7.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= x_i, y_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}\nTask Output: Print the number of ways in which the vertices can be painted, modulo 10^9 + 7.\nTask Samples: input: 3\n1 2\n2 3 output: 5\n\nThere are five ways to paint the vertices, as follows:\ninput: 4\n1 2\n1 3\n1 4 output: 9\n\nThere are nine ways to paint the vertices, as follows:\ninput: 1 output: 2\ninput: 10\n8 5\n10 8\n6 5\n1 5\n4 8\n2 10\n3 6\n9 2\n1 7 output: 157\n\n" }, { "title": "", "content": "Problem Statement There are N flowers arranged in a row.\nFor each i (1 <= i <= N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively.\nHere, h_1, h_2, \\ldots, h_N are all distinct.\nTaro is pulling out some flowers so that the following condition is met:\n\nThe heights of the remaining flowers are monotonically increasing from left to right.\n\nFind the maximum possible sum of the beauties of the remaining flowers.", "constraint": "All values in input are integers.\n1 <= N <= 2 * 10^5\n1 <= h_i <= N\nh_1, h_2, \\ldots, h_N are all distinct.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nh_1 h_2 \\ldots h_N\na_1 a_2 \\ldots a_N", "output": "Print the maximum possible sum of the beauties of the remaining flowers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 1 4 2\n10 20 30 40 output: 60\n\nWe should keep the second and fourth flowers from the left.\nThen, the heights would be 1,2 from left to right, which is monotonically increasing, and the sum of the beauties would be 20 + 40 = 60.", "input: 1\n1\n10 output: 10\n\nThe condition is met already at the beginning.", "input: 5\n1 2 3 4 5\n1000000000 1000000000 1000000000 1000000000 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.", "input: 9\n4 2 5 8 3 6 1 7 9\n6 8 8 4 6 3 5 7 5 output: 31\n\nWe should keep the second, third, sixth, eighth and ninth flowers from the left."], "Pid": "p03176", "ProblemText": "Task Description: Problem Statement There are N flowers arranged in a row.\nFor each i (1 <= i <= N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively.\nHere, h_1, h_2, \\ldots, h_N are all distinct.\nTaro is pulling out some flowers so that the following condition is met:\n\nThe heights of the remaining flowers are monotonically increasing from left to right.\n\nFind the maximum possible sum of the beauties of the remaining flowers.\nTask Constraint: All values in input are integers.\n1 <= N <= 2 * 10^5\n1 <= h_i <= N\nh_1, h_2, \\ldots, h_N are all distinct.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nh_1 h_2 \\ldots h_N\na_1 a_2 \\ldots a_N\nTask Output: Print the maximum possible sum of the beauties of the remaining flowers.\nTask Samples: input: 4\n3 1 4 2\n10 20 30 40 output: 60\n\nWe should keep the second and fourth flowers from the left.\nThen, the heights would be 1,2 from left to right, which is monotonically increasing, and the sum of the beauties would be 20 + 40 = 60.\ninput: 1\n1\n10 output: 10\n\nThe condition is met already at the beginning.\ninput: 5\n1 2 3 4 5\n1000000000 1000000000 1000000000 1000000000 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.\ninput: 9\n4 2 5 8 3 6 1 7 9\n6 8 8 4 6 3 5 7 5 output: 31\n\nWe should keep the second, third, sixth, eighth and ninth flowers from the left.\n\n" }, { "title": "", "content": "Problem Statement There is a simple directed graph G with N vertices, numbered 1,2, \\ldots, N.\nFor each i and j (1 <= i, j <= N), you are given an integer a_{i, j} that represents whether there is a directed edge from Vertex i to j.\nIf a_{i, j} = 1, there is a directed edge from Vertex i to j; if a_{i, j} = 0, there is not.\nFind the number of different directed paths of length K in G, modulo 10^9 + 7.\nWe will also count a path that traverses the same edge multiple times.", "constraint": "All values in input are integers.\n1 <= N <= 50\n1 <= K <= 10^{18}\na_{i, j} is 0 or 1.\na_{i, i} = 0", "input": "Input is given from Standard Input in the following format:\nN K\na_{1,1} \\ldots a_{1, N}\n:\na_{N, 1} \\ldots a_{N, N}", "output": "Print the number of different directed paths of length K in G, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n0 1 0 0\n0 0 1 1\n0 0 0 1\n1 0 0 0 output: 6\n\nG is drawn in the figure below:\n\nThere are six directed paths of length 2:\n\n1 → 2 → 3\n1 → 2 → 4\n2 → 3 → 4\n2 → 4 → 1\n3 → 4 → 1\n4 → 1 → 2", "input: 3 3\n0 1 0\n1 0 1\n0 0 0 output: 3\n\nG is drawn in the figure below:\n\nThere are three directed paths of length 3:\n\n1 → 2 → 1 → 2\n2 → 1 → 2 → 1\n2 → 1 → 2 → 3", "input: 6 2\n0 0 0 0 0 0\n0 0 1 0 0 0\n0 0 0 0 0 0\n0 0 0 0 1 0\n0 0 0 0 0 1\n0 0 0 0 0 0 output: 1\n\nG is drawn in the figure below:\n\nThere is one directed path of length 2:\n\n4 → 5 → 6", "input: 1 1\n0 output: 0", "input: 10 1000000000000000000\n0 0 1 1 0 0 0 1 1 0\n0 0 0 0 0 1 1 1 0 0\n0 1 0 0 0 1 0 1 0 1\n1 1 1 0 1 1 0 1 1 0\n0 1 1 1 0 1 0 1 1 1\n0 0 0 1 0 0 1 0 1 0\n0 0 0 1 1 0 0 1 0 1\n1 0 0 0 1 0 1 0 0 0\n0 0 0 0 0 1 0 0 0 0\n1 0 1 1 1 0 1 1 1 0 output: 957538352\n\nBe sure to print the count modulo 10^9 + 7."], "Pid": "p03177", "ProblemText": "Task Description: Problem Statement There is a simple directed graph G with N vertices, numbered 1,2, \\ldots, N.\nFor each i and j (1 <= i, j <= N), you are given an integer a_{i, j} that represents whether there is a directed edge from Vertex i to j.\nIf a_{i, j} = 1, there is a directed edge from Vertex i to j; if a_{i, j} = 0, there is not.\nFind the number of different directed paths of length K in G, modulo 10^9 + 7.\nWe will also count a path that traverses the same edge multiple times.\nTask Constraint: All values in input are integers.\n1 <= N <= 50\n1 <= K <= 10^{18}\na_{i, j} is 0 or 1.\na_{i, i} = 0\nTask Input: Input is given from Standard Input in the following format:\nN K\na_{1,1} \\ldots a_{1, N}\n:\na_{N, 1} \\ldots a_{N, N}\nTask Output: Print the number of different directed paths of length K in G, modulo 10^9 + 7.\nTask Samples: input: 4 2\n0 1 0 0\n0 0 1 1\n0 0 0 1\n1 0 0 0 output: 6\n\nG is drawn in the figure below:\n\nThere are six directed paths of length 2:\n\n1 → 2 → 3\n1 → 2 → 4\n2 → 3 → 4\n2 → 4 → 1\n3 → 4 → 1\n4 → 1 → 2\ninput: 3 3\n0 1 0\n1 0 1\n0 0 0 output: 3\n\nG is drawn in the figure below:\n\nThere are three directed paths of length 3:\n\n1 → 2 → 1 → 2\n2 → 1 → 2 → 1\n2 → 1 → 2 → 3\ninput: 6 2\n0 0 0 0 0 0\n0 0 1 0 0 0\n0 0 0 0 0 0\n0 0 0 0 1 0\n0 0 0 0 0 1\n0 0 0 0 0 0 output: 1\n\nG is drawn in the figure below:\n\nThere is one directed path of length 2:\n\n4 → 5 → 6\ninput: 1 1\n0 output: 0\ninput: 10 1000000000000000000\n0 0 1 1 0 0 0 1 1 0\n0 0 0 0 0 1 1 1 0 0\n0 1 0 0 0 1 0 1 0 1\n1 1 1 0 1 1 0 1 1 0\n0 1 1 1 0 1 0 1 1 1\n0 0 0 1 0 0 1 0 1 0\n0 0 0 1 1 0 0 1 0 1\n1 0 0 0 1 0 1 0 0 0\n0 0 0 0 0 1 0 0 0 0\n1 0 1 1 1 0 1 1 1 0 output: 957538352\n\nBe sure to print the count modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:\n\nThe sum of the digits in base ten is a multiple of D.", "constraint": "All values in input are integers.\n1 <= K < 10^{10000}\n1 <= D <= 100", "input": "Input is given from Standard Input in the following format:\nK\nD", "output": "Print the number of integers satisfying the condition, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 30\n4 output: 6\n\nThose six integers are: 4,8,13,17,22 and 26.", "input: 1000000009\n1 output: 2\n\nBe sure to print the number modulo 10^9 + 7.", "input: 98765432109876543210\n58 output: 635270834"], "Pid": "p03178", "ProblemText": "Task Description: Problem Statement Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:\n\nThe sum of the digits in base ten is a multiple of D.\nTask Constraint: All values in input are integers.\n1 <= K < 10^{10000}\n1 <= D <= 100\nTask Input: Input is given from Standard Input in the following format:\nK\nD\nTask Output: Print the number of integers satisfying the condition, modulo 10^9 + 7.\nTask Samples: input: 30\n4 output: 6\n\nThose six integers are: 4,8,13,17,22 and 26.\ninput: 1000000009\n1 output: 2\n\nBe sure to print the number modulo 10^9 + 7.\ninput: 98765432109876543210\n58 output: 635270834\n\n" }, { "title": "", "content": "Problem Statement Let N be a positive integer.\nYou are given a string s of length N - 1, consisting of < and >.\nFind the number of permutations (p_1, p_2, \\ldots, p_N) of (1,2, \\ldots, N) that satisfy the following condition, modulo 10^9 + 7:\n\nFor each i (1 <= i <= N - 1), p_i < p_{i + 1} if the i-th character in s is <, and p_i > p_{i + 1} if the i-th character in s is >.", "constraint": "N is an integer.\n2 <= N <= 3000\ns is a string of length N - 1.\ns consists of < and >.", "input": "Input is given from Standard Input in the following format:\nN\ns", "output": "Print the number of permutations that satisfy the condition, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n<>< output: 5\n\nThere are five permutations that satisfy the condition, as follows:\n\n(1,3,2,4)\n(1,4,2,3)\n(2,3,1,4)\n(2,4,1,3)\n(3,4,1,2)", "input: 5\n<<<< output: 1\n\nThere is one permutation that satisfies the condition, as follows:\n\n(1,2,3,4,5)", "input: 20\n>>>><>>><>><>>><<>> output: 217136290\n\nBe sure to print the number modulo 10^9 + 7."], "Pid": "p03179", "ProblemText": "Task Description: Problem Statement Let N be a positive integer.\nYou are given a string s of length N - 1, consisting of < and >.\nFind the number of permutations (p_1, p_2, \\ldots, p_N) of (1,2, \\ldots, N) that satisfy the following condition, modulo 10^9 + 7:\n\nFor each i (1 <= i <= N - 1), p_i < p_{i + 1} if the i-th character in s is <, and p_i > p_{i + 1} if the i-th character in s is >.\nTask Constraint: N is an integer.\n2 <= N <= 3000\ns is a string of length N - 1.\ns consists of < and >.\nTask Input: Input is given from Standard Input in the following format:\nN\ns\nTask Output: Print the number of permutations that satisfy the condition, modulo 10^9 + 7.\nTask Samples: input: 4\n<>< output: 5\n\nThere are five permutations that satisfy the condition, as follows:\n\n(1,3,2,4)\n(1,4,2,3)\n(2,3,1,4)\n(2,4,1,3)\n(3,4,1,2)\ninput: 5\n<<<< output: 1\n\nThere is one permutation that satisfies the condition, as follows:\n\n(1,2,3,4,5)\ninput: 20\n>>>><>>><>><>>><<>> output: 217136290\n\nBe sure to print the number modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement There are N rabbits, numbered 1,2, \\ldots, N.\nFor each i, j (1 <= i, j <= N), the compatibility of Rabbit i and j is described by an integer a_{i, j}.\nHere, a_{i, i} = 0 for each i (1 <= i <= N), and a_{i, j} = a_{j, i} for each i and j (1 <= i, j <= N).\nTaro is dividing the N rabbits into some number of groups.\nHere, each rabbit must belong to exactly one group.\nAfter grouping, for each i and j (1 <= i < j <= N), Taro earns a_{i, j} points if Rabbit i and j belong to the same group.\nFind Taro's maximum possible total score.", "constraint": "All values in input are integers.\n1 <= N <= 16\n|a_{i, j}| <= 10^9\na_{i, i} = 0\na_{i, j} = a_{j, i}", "input": "Input is given from Standard Input in the following format:\nN\na_{1,1} \\ldots a_{1, N}\n:\na_{N, 1} \\ldots a_{N, N}", "output": "Print Taro's maximum possible total score.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 10 20\n10 0 -100\n20 -100 0 output: 20\n\nThe rabbits should be divided as \\{1,3\\}, \\{2\\}.", "input: 2\n0 -10\n-10 0 output: 0\n\nThe rabbits should be divided as \\{1\\}, \\{2\\}.", "input: 4\n0 1000000000 1000000000 1000000000\n1000000000 0 1000000000 1000000000\n1000000000 1000000000 0 -1\n1000000000 1000000000 -1 0 output: 4999999999\n\nThe rabbits should be divided as \\{1,2,3,4\\}.\nNote that the answer may not fit into a 32-bit integer type.", "input: 16\n0 5 -4 -5 -8 -4 7 2 -4 0 7 0 2 -3 7 7\n5 0 8 -9 3 5 2 -7 2 -7 0 -1 -4 1 -1 9\n-4 8 0 -9 8 9 3 1 4 9 6 6 -6 1 8 9\n-5 -9 -9 0 -7 6 4 -1 9 -3 -5 0 1 2 -4 1\n-8 3 8 -7 0 -5 -9 9 1 -9 -6 -3 -8 3 4 3\n-4 5 9 6 -5 0 -6 1 -2 2 0 -5 -2 3 1 2\n7 2 3 4 -9 -6 0 -2 -2 -9 -3 9 -2 9 2 -5\n2 -7 1 -1 9 1 -2 0 -6 0 -6 6 4 -1 -7 8\n-4 2 4 9 1 -2 -2 -6 0 8 -6 -2 -4 8 7 7\n0 -7 9 -3 -9 2 -9 0 8 0 0 1 -3 3 -6 -6\n7 0 6 -5 -6 0 -3 -6 -6 0 0 5 7 -1 -5 3\n0 -1 6 0 -3 -5 9 6 -2 1 5 0 -2 7 -8 0\n2 -4 -6 1 -8 -2 -2 4 -4 -3 7 -2 0 -9 7 1\n-3 1 1 2 3 3 9 -1 8 3 -1 7 -9 0 -6 -8\n7 -1 8 -4 4 1 2 -7 7 -6 -5 -8 7 -6 0 -9\n7 9 9 1 3 2 -5 8 7 -6 3 0 1 -8 -9 0 output: 132"], "Pid": "p03180", "ProblemText": "Task Description: Problem Statement There are N rabbits, numbered 1,2, \\ldots, N.\nFor each i, j (1 <= i, j <= N), the compatibility of Rabbit i and j is described by an integer a_{i, j}.\nHere, a_{i, i} = 0 for each i (1 <= i <= N), and a_{i, j} = a_{j, i} for each i and j (1 <= i, j <= N).\nTaro is dividing the N rabbits into some number of groups.\nHere, each rabbit must belong to exactly one group.\nAfter grouping, for each i and j (1 <= i < j <= N), Taro earns a_{i, j} points if Rabbit i and j belong to the same group.\nFind Taro's maximum possible total score.\nTask Constraint: All values in input are integers.\n1 <= N <= 16\n|a_{i, j}| <= 10^9\na_{i, i} = 0\na_{i, j} = a_{j, i}\nTask Input: Input is given from Standard Input in the following format:\nN\na_{1,1} \\ldots a_{1, N}\n:\na_{N, 1} \\ldots a_{N, N}\nTask Output: Print Taro's maximum possible total score.\nTask Samples: input: 3\n0 10 20\n10 0 -100\n20 -100 0 output: 20\n\nThe rabbits should be divided as \\{1,3\\}, \\{2\\}.\ninput: 2\n0 -10\n-10 0 output: 0\n\nThe rabbits should be divided as \\{1\\}, \\{2\\}.\ninput: 4\n0 1000000000 1000000000 1000000000\n1000000000 0 1000000000 1000000000\n1000000000 1000000000 0 -1\n1000000000 1000000000 -1 0 output: 4999999999\n\nThe rabbits should be divided as \\{1,2,3,4\\}.\nNote that the answer may not fit into a 32-bit integer type.\ninput: 16\n0 5 -4 -5 -8 -4 7 2 -4 0 7 0 2 -3 7 7\n5 0 8 -9 3 5 2 -7 2 -7 0 -1 -4 1 -1 9\n-4 8 0 -9 8 9 3 1 4 9 6 6 -6 1 8 9\n-5 -9 -9 0 -7 6 4 -1 9 -3 -5 0 1 2 -4 1\n-8 3 8 -7 0 -5 -9 9 1 -9 -6 -3 -8 3 4 3\n-4 5 9 6 -5 0 -6 1 -2 2 0 -5 -2 3 1 2\n7 2 3 4 -9 -6 0 -2 -2 -9 -3 9 -2 9 2 -5\n2 -7 1 -1 9 1 -2 0 -6 0 -6 6 4 -1 -7 8\n-4 2 4 9 1 -2 -2 -6 0 8 -6 -2 -4 8 7 7\n0 -7 9 -3 -9 2 -9 0 8 0 0 1 -3 3 -6 -6\n7 0 6 -5 -6 0 -3 -6 -6 0 0 5 7 -1 -5 3\n0 -1 6 0 -3 -5 9 6 -2 1 5 0 -2 7 -8 0\n2 -4 -6 1 -8 -2 -2 4 -4 -3 7 -2 0 -9 7 1\n-3 1 1 2 3 3 9 -1 8 3 -1 7 -9 0 -6 -8\n7 -1 8 -4 4 1 2 -7 7 -6 -5 -8 7 -6 0 -9\n7 9 9 1 3 2 -5 8 7 -6 3 0 1 -8 -9 0 output: 132\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N - 1), the i-th edge connects Vertex x_i and y_i.\nTaro has decided to paint each vertex in white or black, so that any black vertex can be reached from any other black vertex by passing through only black vertices.\nYou are given a positive integer M.\nFor each v (1 <= v <= N), answer the following question:\n\nAssuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n2 <= M <= 10^9\n1 <= x_i, y_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}", "output": "Print N lines.\nThe v-th (1 <= v <= N) line should contain the answer to the following question:\n\nAssuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 100\n1 2\n2 3 output: 3\n4\n3\n\nThere are seven ways to paint the vertices, as shown in the figure below.\nAmong them, there are three ways such that Vertex 1 is black, four ways such that Vertex 2 is black and three ways such that Vertex 3 is black.", "input: 4 100\n1 2\n1 3\n1 4 output: 8\n5\n5\n5", "input: 1 100 output: 1", "input: 10 2\n8 5\n10 8\n6 5\n1 5\n4 8\n2 10\n3 6\n9 2\n1 7 output: 0\n0\n1\n1\n1\n0\n1\n0\n1\n1\n\nBe sure to print the answers modulo M."], "Pid": "p03181", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N - 1), the i-th edge connects Vertex x_i and y_i.\nTaro has decided to paint each vertex in white or black, so that any black vertex can be reached from any other black vertex by passing through only black vertices.\nYou are given a positive integer M.\nFor each v (1 <= v <= N), answer the following question:\n\nAssuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n2 <= M <= 10^9\n1 <= x_i, y_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}\nTask Output: Print N lines.\nThe v-th (1 <= v <= N) line should contain the answer to the following question:\n\nAssuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.\nTask Samples: input: 3 100\n1 2\n2 3 output: 3\n4\n3\n\nThere are seven ways to paint the vertices, as shown in the figure below.\nAmong them, there are three ways such that Vertex 1 is black, four ways such that Vertex 2 is black and three ways such that Vertex 3 is black.\ninput: 4 100\n1 2\n1 3\n1 4 output: 8\n5\n5\n5\ninput: 1 100 output: 1\ninput: 10 2\n8 5\n10 8\n6 5\n1 5\n4 8\n2 10\n3 6\n9 2\n1 7 output: 0\n0\n1\n1\n1\n0\n1\n0\n1\n1\n\nBe sure to print the answers modulo M.\n\n" }, { "title": "", "content": "Problem Statement Consider a string of length N consisting of 0 and 1.\nThe score for the string is calculated as follows:\n\nFor each i (1 <= i <= M), a_i is added to the score if the string contains 1 at least once between the l_i-th and r_i-th characters (inclusive).\n\nFind the maximum possible score of a string.", "constraint": "All values in input are integers.\n1 <= N <= 2 * 10^5\n1 <= M <= 2 * 10^5\n1 <= l_i <= r_i <= N\n|a_i| <= 10^9", "input": "Input is given from Standard Input in the following format:\nN M\nl_1 r_1 a_1\nl_2 r_2 a_2\n:\nl_M r_M a_M", "output": "Print the maximum possible score of a string.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 3 10\n2 4 -10\n3 5 10 output: 20\n\nThe score for 10001 is a_1 + a_3 = 10 + 10 = 20.", "input: 3 4\n1 3 100\n1 1 -10\n2 2 -20\n3 3 -30 output: 90\n\nThe score for 100 is a_1 + a_2 = 100 + (-10) = 90.", "input: 1 1\n1 1 -10 output: 0\n\nThe score for 0 is 0.", "input: 1 5\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.", "input: 6 8\n5 5 3\n1 1 10\n1 6 -8\n3 6 5\n3 4 9\n5 5 -2\n1 3 -6\n4 6 -7 output: 10\n\nFor example, the score for 101000 is a_2 + a_3 + a_4 + a_5 + a_7 = 10 + (-8) + 5 + 9 + (-6) = 10."], "Pid": "p03182", "ProblemText": "Task Description: Problem Statement Consider a string of length N consisting of 0 and 1.\nThe score for the string is calculated as follows:\n\nFor each i (1 <= i <= M), a_i is added to the score if the string contains 1 at least once between the l_i-th and r_i-th characters (inclusive).\n\nFind the maximum possible score of a string.\nTask Constraint: All values in input are integers.\n1 <= N <= 2 * 10^5\n1 <= M <= 2 * 10^5\n1 <= l_i <= r_i <= N\n|a_i| <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN M\nl_1 r_1 a_1\nl_2 r_2 a_2\n:\nl_M r_M a_M\nTask Output: Print the maximum possible score of a string.\nTask Samples: input: 5 3\n1 3 10\n2 4 -10\n3 5 10 output: 20\n\nThe score for 10001 is a_1 + a_3 = 10 + 10 = 20.\ninput: 3 4\n1 3 100\n1 1 -10\n2 2 -20\n3 3 -30 output: 90\n\nThe score for 100 is a_1 + a_2 = 100 + (-10) = 90.\ninput: 1 1\n1 1 -10 output: 0\n\nThe score for 0 is 0.\ninput: 1 5\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000\n1 1 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.\ninput: 6 8\n5 5 3\n1 1 10\n1 6 -8\n3 6 5\n3 4 9\n5 5 -2\n1 3 -6\n4 6 -7 output: 10\n\nFor example, the score for 101000 is a_2 + a_3 + a_4 + a_5 + a_7 = 10 + (-8) + 5 + 9 + (-6) = 10.\n\n" }, { "title": "", "content": "Problem Statement There are N blocks, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), Block i has a weight of w_i, a solidness of s_i and a value of v_i.\nTaro has decided to build a tower by choosing some of the N blocks and stacking them vertically in some order.\nHere, the tower must satisfy the following condition:\n\nFor each Block i contained in the tower, the sum of the weights of the blocks stacked above it is not greater than s_i.\n\nFind the maximum possible sum of the values of the blocks contained in the tower.", "constraint": "All values in input are integers.\n1 <= N <= 10^3\n1 <= w_i, s_i <= 10^4\n1 <= v_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nw_1 s_1 v_1\nw_2 s_2 v_2\n:\nw_N s_N v_N", "output": "Print the maximum possible sum of the values of the blocks contained in the tower.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 2 20\n2 1 30\n3 1 40 output: 50\n\nIf Blocks 2,1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.", "input: 4\n1 2 10\n3 1 10\n2 4 10\n1 6 10 output: 40\n\nBlocks 1,2,3,4 should be stacked in this order from top to bottom.", "input: 5\n1 10000 1000000000\n1 10000 1000000000\n1 10000 1000000000\n1 10000 1000000000\n1 10000 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.", "input: 8\n9 5 7\n6 2 7\n5 7 3\n7 8 8\n1 9 6\n3 3 3\n4 1 7\n4 5 5 output: 22\n\nWe should, for example, stack Blocks 5,6,8,4 in this order from top to bottom."], "Pid": "p03183", "ProblemText": "Task Description: Problem Statement There are N blocks, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), Block i has a weight of w_i, a solidness of s_i and a value of v_i.\nTaro has decided to build a tower by choosing some of the N blocks and stacking them vertically in some order.\nHere, the tower must satisfy the following condition:\n\nFor each Block i contained in the tower, the sum of the weights of the blocks stacked above it is not greater than s_i.\n\nFind the maximum possible sum of the values of the blocks contained in the tower.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^3\n1 <= w_i, s_i <= 10^4\n1 <= v_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nw_1 s_1 v_1\nw_2 s_2 v_2\n:\nw_N s_N v_N\nTask Output: Print the maximum possible sum of the values of the blocks contained in the tower.\nTask Samples: input: 3\n2 2 20\n2 1 30\n3 1 40 output: 50\n\nIf Blocks 2,1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.\ninput: 4\n1 2 10\n3 1 10\n2 4 10\n1 6 10 output: 40\n\nBlocks 1,2,3,4 should be stacked in this order from top to bottom.\ninput: 5\n1 10000 1000000000\n1 10000 1000000000\n1 10000 1000000000\n1 10000 1000000000\n1 10000 1000000000 output: 5000000000\n\nThe answer may not fit into a 32-bit integer type.\ninput: 8\n9 5 7\n6 2 7\n5 7 3\n7 8 8\n1 9 6\n3 3 3\n4 1 7\n4 5 5 output: 22\n\nWe should, for example, stack Blocks 5,6,8,4 in this order from top to bottom.\n\n" }, { "title": "", "content": "Problem Statement There is a grid with H horizontal rows and W vertical columns.\nLet (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nIn the grid, N Squares (r_1, c_1), (r_2, c_2), \\ldots, (r_N, c_N) are wall squares, and the others are all empty squares.\nIt is guaranteed that Squares (1,1) and (H, W) are empty squares.\nTaro will start from Square (1,1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.\nFind the number of Taro's paths from Square (1,1) to (H, W), modulo 10^9 + 7.", "constraint": "All values in input are integers.\n2 <= H, W <= 10^5\n1 <= N <= 3000\n1 <= r_i <= H\n1 <= c_i <= W\nSquares (r_i, c_i) are all distinct.\nSquares (1,1) and (H, W) are empty squares.", "input": "Input is given from Standard Input in the following format:\nH W N\nr_1 c_1\nr_2 c_2\n:\nr_N c_N", "output": "Print the number of Taro's paths from Square (1,1) to (H, W), modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 2\n2 2\n1 4 output: 3\n\nThere are three paths as follows:", "input: 5 2 2\n2 1\n4 2 output: 0\n\nThere may be no paths.", "input: 5 5 4\n3 1\n3 5\n1 3\n5 3 output: 24", "input: 100000 100000 1\n50000 50000 output: 123445622\n\nBe sure to print the count modulo 10^9 + 7."], "Pid": "p03184", "ProblemText": "Task Description: Problem Statement There is a grid with H horizontal rows and W vertical columns.\nLet (i, j) denote the square at the i-th row from the top and the j-th column from the left.\nIn the grid, N Squares (r_1, c_1), (r_2, c_2), \\ldots, (r_N, c_N) are wall squares, and the others are all empty squares.\nIt is guaranteed that Squares (1,1) and (H, W) are empty squares.\nTaro will start from Square (1,1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.\nFind the number of Taro's paths from Square (1,1) to (H, W), modulo 10^9 + 7.\nTask Constraint: All values in input are integers.\n2 <= H, W <= 10^5\n1 <= N <= 3000\n1 <= r_i <= H\n1 <= c_i <= W\nSquares (r_i, c_i) are all distinct.\nSquares (1,1) and (H, W) are empty squares.\nTask Input: Input is given from Standard Input in the following format:\nH W N\nr_1 c_1\nr_2 c_2\n:\nr_N c_N\nTask Output: Print the number of Taro's paths from Square (1,1) to (H, W), modulo 10^9 + 7.\nTask Samples: input: 3 4 2\n2 2\n1 4 output: 3\n\nThere are three paths as follows:\ninput: 5 2 2\n2 1\n4 2 output: 0\n\nThere may be no paths.\ninput: 5 5 4\n3 1\n3 5\n1 3\n5 3 output: 24\ninput: 100000 100000 1\n50000 50000 output: 123445622\n\nBe sure to print the count modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement There are N stones, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), the height of Stone i is h_i.\nHere, h_1 < h_2 < \\cdots < h_N holds.\nThere is a frog who is initially on Stone 1.\nHe will repeat the following action some number of times to reach Stone N:\n\nIf the frog is currently on Stone i, jump to one of the following: Stone i + 1, i + 2, \\ldots, N. Here, a cost of (h_j - h_i)^2 + C is incurred, where j is the stone to land on.\n\nFind the minimum possible total cost incurred before the frog reaches Stone N.", "constraint": "All values in input are integers.\n2 <= N <= 2 * 10^5\n1 <= C <= 10^{12}\n1 <= h_1 < h_2 < \\cdots < h_N <= 10^6", "input": "Input is given from Standard Input in the following format:\nN C\nh_1 h_2 \\ldots h_N", "output": "Print the minimum possible total cost incurred.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 6\n1 2 3 4 5 output: 20\n\nIf we follow the path 1 → 3 → 5, the total cost incurred would be ((3 - 1)^2 + 6) + ((5 - 3)^2 + 6) = 20.", "input: 2 1000000000000\n500000 1000000 output: 1250000000000\n\nThe answer may not fit into a 32-bit integer type.", "input: 8 5\n1 3 4 5 10 11 12 13 output: 62\n\nIf we follow the path 1 → 2 → 4 → 5 → 8, the total cost incurred would be ((3 - 1)^2 + 5) + ((5 - 3)^2 + 5) + ((10 - 5)^2 + 5) + ((13 - 10)^2 + 5) = 62."], "Pid": "p03185", "ProblemText": "Task Description: Problem Statement There are N stones, numbered 1,2, \\ldots, N.\nFor each i (1 <= i <= N), the height of Stone i is h_i.\nHere, h_1 < h_2 < \\cdots < h_N holds.\nThere is a frog who is initially on Stone 1.\nHe will repeat the following action some number of times to reach Stone N:\n\nIf the frog is currently on Stone i, jump to one of the following: Stone i + 1, i + 2, \\ldots, N. Here, a cost of (h_j - h_i)^2 + C is incurred, where j is the stone to land on.\n\nFind the minimum possible total cost incurred before the frog reaches Stone N.\nTask Constraint: All values in input are integers.\n2 <= N <= 2 * 10^5\n1 <= C <= 10^{12}\n1 <= h_1 < h_2 < \\cdots < h_N <= 10^6\nTask Input: Input is given from Standard Input in the following format:\nN C\nh_1 h_2 \\ldots h_N\nTask Output: Print the minimum possible total cost incurred.\nTask Samples: input: 5 6\n1 2 3 4 5 output: 20\n\nIf we follow the path 1 → 3 → 5, the total cost incurred would be ((3 - 1)^2 + 6) + ((5 - 3)^2 + 6) = 20.\ninput: 2 1000000000000\n500000 1000000 output: 1250000000000\n\nThe answer may not fit into a 32-bit integer type.\ninput: 8 5\n1 3 4 5 10 11 12 13 output: 62\n\nIf we follow the path 1 → 2 → 4 → 5 → 8, the total cost incurred would be ((3 - 1)^2 + 5) + ((5 - 3)^2 + 5) + ((10 - 5)^2 + 5) + ((13 - 10)^2 + 5) = 62.\n\n" }, { "title": "", "content": "Problem Statement Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.\nEating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death.\nAs he wants to live, he cannot eat one in such a situation.\nEating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.\nFind the maximum number of tasty cookies that Takahashi can eat.", "constraint": "0 <= A,B,C <= 10^9\nA,B and C are integers.", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "Print the maximum number of tasty cookies that Takahashi can eat.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 4 output: 5\n\nWe can eat all tasty cookies, in the following order:\n\nA tasty cookie containing poison\nAn untasty cookie containing antidotes\nA tasty cookie containing poison\nA tasty cookie containing antidotes\nA tasty cookie containing poison\nAn untasty cookie containing antidotes\nA tasty cookie containing poison", "input: 5 2 9 output: 10", "input: 8 8 1 output: 9"], "Pid": "p03186", "ProblemText": "Task Description: Problem Statement Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.\nEating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death.\nAs he wants to live, he cannot eat one in such a situation.\nEating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.\nFind the maximum number of tasty cookies that Takahashi can eat.\nTask Constraint: 0 <= A,B,C <= 10^9\nA,B and C are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: Print the maximum number of tasty cookies that Takahashi can eat.\nTask Samples: input: 3 1 4 output: 5\n\nWe can eat all tasty cookies, in the following order:\n\nA tasty cookie containing poison\nAn untasty cookie containing antidotes\nA tasty cookie containing poison\nA tasty cookie containing antidotes\nA tasty cookie containing poison\nAn untasty cookie containing antidotes\nA tasty cookie containing poison\ninput: 5 2 9 output: 10\ninput: 8 8 1 output: 9\n\n" }, { "title": "", "content": "Problem Statement Takahashi Lake has a perimeter of L. On the circumference of the lake, there is a residence of the lake's owner, Takahashi.\nEach point on the circumference of the lake has a coordinate between 0 and L (including 0 but not L), which is the distance from the Takahashi's residence, measured counter-clockwise.\nThere are N trees around the lake; the coordinate of the i-th tree is X_i. There is no tree at coordinate 0, the location of Takahashi's residence.\nStarting at his residence, Takahashi will repeat the following action:\n\nIf all trees are burnt, terminate the process.\nSpecify a direction: clockwise or counter-clockwise.\nWalk around the lake in the specified direction, until the coordinate of a tree that is not yet burnt is reached for the first time.\nWhen the coordinate with the tree is reached, burn that tree, stay at the position and go back to the first step.\n\nFind the longest possible total distance Takahashi walks during the process. partial score: Partial Score A partial score can be obtained in this problem:\n\n300 points will be awarded for passing the input satisfying N <= 2000.", "constraint": "2 <= L <= 10^9\n1 <= N <= 2* 10^5\n1 <= X_1 < ... < X_N <= L-1\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nL N\nX_1\n:\nX_N", "output": "Print the longest possible total distance Takahashi walks during the process.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 3\n2\n7\n9 output: 15\n\nTakahashi walks the distance of 15 if the process goes as follows:\n\nWalk a distance of 2 counter-clockwise, burn the tree at the coordinate 2 and stay there.\nWalk a distance of 5 counter-clockwise, burn the tree at the coordinate 7 and stay there.\nWalk a distance of 8 clockwise, burn the tree at the coordinate 9 and stay there.", "input: 10 6\n1\n2\n3\n6\n7\n9 output: 27", "input: 314159265 7\n21662711\n77271666\n89022761\n156626166\n160332356\n166902656\n298992265 output: 1204124749"], "Pid": "p03187", "ProblemText": "Task Description: Problem Statement Takahashi Lake has a perimeter of L. On the circumference of the lake, there is a residence of the lake's owner, Takahashi.\nEach point on the circumference of the lake has a coordinate between 0 and L (including 0 but not L), which is the distance from the Takahashi's residence, measured counter-clockwise.\nThere are N trees around the lake; the coordinate of the i-th tree is X_i. There is no tree at coordinate 0, the location of Takahashi's residence.\nStarting at his residence, Takahashi will repeat the following action:\n\nIf all trees are burnt, terminate the process.\nSpecify a direction: clockwise or counter-clockwise.\nWalk around the lake in the specified direction, until the coordinate of a tree that is not yet burnt is reached for the first time.\nWhen the coordinate with the tree is reached, burn that tree, stay at the position and go back to the first step.\n\nFind the longest possible total distance Takahashi walks during the process. partial score: Partial Score A partial score can be obtained in this problem:\n\n300 points will be awarded for passing the input satisfying N <= 2000.\nTask Constraint: 2 <= L <= 10^9\n1 <= N <= 2* 10^5\n1 <= X_1 < ... < X_N <= L-1\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nL N\nX_1\n:\nX_N\nTask Output: Print the longest possible total distance Takahashi walks during the process.\nTask Samples: input: 10 3\n2\n7\n9 output: 15\n\nTakahashi walks the distance of 15 if the process goes as follows:\n\nWalk a distance of 2 counter-clockwise, burn the tree at the coordinate 2 and stay there.\nWalk a distance of 5 counter-clockwise, burn the tree at the coordinate 7 and stay there.\nWalk a distance of 8 clockwise, burn the tree at the coordinate 9 and stay there.\ninput: 10 6\n1\n2\n3\n6\n7\n9 output: 27\ninput: 314159265 7\n21662711\n77271666\n89022761\n156626166\n160332356\n166902656\n298992265 output: 1204124749\n\n" }, { "title": "", "content": "Problem Statement For an n * n grid, let (r, c) denote the square at the (r+1)-th row from the top and the (c+1)-th column from the left.\nA good coloring of this grid using K colors is a coloring that satisfies the following:\n\nEach square is painted in one of the K colors.\nEach of the K colors is used for some squares.\nLet us number the K colors 1,2, . . . , K. For any colors i and j (1 <= i <= K, 1 <= j <= K), every square in Color i has the same number of adjacent squares in Color j. Here, the squares adjacent to square (r, c) are ((r-1)\\; mod\\; n, c), ((r+1)\\; mod\\; n, c), (r, (c-1)\\; mod\\; n) and (r, (c+1)\\; mod\\; n) (if the same square appears multiple times among these four, the square is counted that number of times).\n\nGiven K, choose n between 1 and 500 (inclusive) freely and construct a good coloring of an n * n grid using K colors.\nIt can be proved that this is always possible under the constraints of this problem,", "constraint": "1 <= K <= 1000", "input": "Input is given from Standard Input in the following format:\nK", "output": "Output should be in the following format:\nn\nc_{0,0} c_{0,1} . . . c_{0, n-1}\nc_{1,0} c_{1,1} . . . c_{1, n-1}\n:\nc_{n-1,0} c_{n-1,1} . . . c_{n-1, n-1}\n\nn should represent the size of the grid, and 1 <= n <= 500 must hold.\nc_{r, c} should be an integer such that 1 <= c_{r, c} <= K and represent the color for the square (r, c).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 3\n1 1 1\n1 1 1\n2 2 2\nEvery square in Color 1 has three adjacent squares in Color 1 and one adjacent square in Color 2.\nEvery square in Color 2 has two adjacent squares in Color 1 and two adjacent squares in Color 2.\n\nOutput such as the following will be judged incorrect:\n2\n1 2\n2 2\n\n3\n1 1 1\n1 1 1\n1 1 1", "input: 9 output: 3\n1 2 3\n4 5 6\n7 8 9"], "Pid": "p03188", "ProblemText": "Task Description: Problem Statement For an n * n grid, let (r, c) denote the square at the (r+1)-th row from the top and the (c+1)-th column from the left.\nA good coloring of this grid using K colors is a coloring that satisfies the following:\n\nEach square is painted in one of the K colors.\nEach of the K colors is used for some squares.\nLet us number the K colors 1,2, . . . , K. For any colors i and j (1 <= i <= K, 1 <= j <= K), every square in Color i has the same number of adjacent squares in Color j. Here, the squares adjacent to square (r, c) are ((r-1)\\; mod\\; n, c), ((r+1)\\; mod\\; n, c), (r, (c-1)\\; mod\\; n) and (r, (c+1)\\; mod\\; n) (if the same square appears multiple times among these four, the square is counted that number of times).\n\nGiven K, choose n between 1 and 500 (inclusive) freely and construct a good coloring of an n * n grid using K colors.\nIt can be proved that this is always possible under the constraints of this problem,\nTask Constraint: 1 <= K <= 1000\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Output should be in the following format:\nn\nc_{0,0} c_{0,1} . . . c_{0, n-1}\nc_{1,0} c_{1,1} . . . c_{1, n-1}\n:\nc_{n-1,0} c_{n-1,1} . . . c_{n-1, n-1}\n\nn should represent the size of the grid, and 1 <= n <= 500 must hold.\nc_{r, c} should be an integer such that 1 <= c_{r, c} <= K and represent the color for the square (r, c).\nTask Samples: input: 2 output: 3\n1 1 1\n1 1 1\n2 2 2\nEvery square in Color 1 has three adjacent squares in Color 1 and one adjacent square in Color 2.\nEvery square in Color 2 has two adjacent squares in Color 1 and two adjacent squares in Color 2.\n\nOutput such as the following will be judged incorrect:\n2\n1 2\n2 2\n\n3\n1 1 1\n1 1 1\n1 1 1\ninput: 9 output: 3\n1 2 3\n4 5 6\n7 8 9\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length N: A_1, A_2, . . . , A_N. Let us perform Q operations in order.\nThe i-th operation is described by two integers X_i and Y_i. In this operation, we will choose one of the following two actions and perform it:\n\nSwap the values of A_{X_i} and A_{Y_i}\nDo nothing\n\nThere are 2^Q ways to perform these operations. Find the sum of the inversion numbers of the final sequences for all of these ways to perform operations, modulo 10^9+7.\nHere, the inversion number of a sequence P_1, P_2, . . . , P_M is the number of pairs of integers (i, j) such that 1<= i < j<= M and P_i > P_j.", "constraint": "1 <= N <= 3000\n0 <= Q <= 3000\n0 <= A_i <= 10^9(1<= i<= N)\n1 <= X_i,Y_i <= N(1<= i<= Q)\nX_i\\neq Y_i(1<= i<= Q)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN Q\nA_1\n:\nA_N\nX_1 Y_1\n:\nX_Q Y_Q", "output": "Print the sum of the inversion numbers of the final sequences, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1\n2\n3\n1 2\n1 3 output: 6\n\nThere are four ways to perform operations, as follows:\n\nDo nothing, both in the first and second operations. The final sequence would be 1,2,3, with the inversion number of 0.\nDo nothing in the first operation, then perform the swap in the second. The final sequence would be 3,2,1, with the inversion number of 3.\nPerform the swap in the first operation, then do nothing in the second. The final sequence would be 2,1,3, with the inversion number of 1.\nPerform the swap, both in the first and second operations. The final sequence would be 3,1,2, with the inversion number of 2.\n\nThe sum of these inversion numbers, 0+3+1+2=6, should be printed.", "input: 5 3\n3\n2\n3\n1\n4\n1 5\n2 3\n4 2 output: 36", "input: 9 5\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3 5\n8 9\n7 9\n3 2\n3 8 output: 425"], "Pid": "p03189", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length N: A_1, A_2, . . . , A_N. Let us perform Q operations in order.\nThe i-th operation is described by two integers X_i and Y_i. In this operation, we will choose one of the following two actions and perform it:\n\nSwap the values of A_{X_i} and A_{Y_i}\nDo nothing\n\nThere are 2^Q ways to perform these operations. Find the sum of the inversion numbers of the final sequences for all of these ways to perform operations, modulo 10^9+7.\nHere, the inversion number of a sequence P_1, P_2, . . . , P_M is the number of pairs of integers (i, j) such that 1<= i < j<= M and P_i > P_j.\nTask Constraint: 1 <= N <= 3000\n0 <= Q <= 3000\n0 <= A_i <= 10^9(1<= i<= N)\n1 <= X_i,Y_i <= N(1<= i<= Q)\nX_i\\neq Y_i(1<= i<= Q)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN Q\nA_1\n:\nA_N\nX_1 Y_1\n:\nX_Q Y_Q\nTask Output: Print the sum of the inversion numbers of the final sequences, modulo 10^9+7.\nTask Samples: input: 3 2\n1\n2\n3\n1 2\n1 3 output: 6\n\nThere are four ways to perform operations, as follows:\n\nDo nothing, both in the first and second operations. The final sequence would be 1,2,3, with the inversion number of 0.\nDo nothing in the first operation, then perform the swap in the second. The final sequence would be 3,2,1, with the inversion number of 3.\nPerform the swap in the first operation, then do nothing in the second. The final sequence would be 2,1,3, with the inversion number of 1.\nPerform the swap, both in the first and second operations. The final sequence would be 3,1,2, with the inversion number of 2.\n\nThe sum of these inversion numbers, 0+3+1+2=6, should be printed.\ninput: 5 3\n3\n2\n3\n1\n4\n1 5\n2 3\n4 2 output: 36\ninput: 9 5\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3 5\n8 9\n7 9\n3 2\n3 8 output: 425\n\n" }, { "title": "", "content": "Problem Statement You are given strings s and t, both of length N.\ns and t consist of 0 and 1. Additionally, in these strings, the same character never occurs three or more times in a row.\nYou can modify s by repeatedly performing the following operation:\n\nChoose an index i (1 <= i <= N) freely and invert the i-th character in s (that is, replace 0 with 1, and 1 with 0), under the condition that the same character would not occur three or more times in a row in s after the operation.\n\nYour objective is to make s equal to t.\nFind the minimum number of operations required.", "constraint": "1 <= N <= 5000\nThe lengths of s and t are both N.\ns and t consists of 0 and 1.\nIn s and t, the same character never occurs three or more times in a row.", "input": "Input is given from Standard Input in the following format:\nN\ns\nt", "output": "Find the minimum number of operations required to make s equal to t. It can be proved that the objective is always achievable in a finite number of operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0011\n0101 output: 4\n\nOne possible solution is 0011 → 1011 → 1001 → 1101 → 0101.", "input: 1\n0\n0 output: 0", "input: 8\n00110011\n10101010 output: 10"], "Pid": "p03190", "ProblemText": "Task Description: Problem Statement You are given strings s and t, both of length N.\ns and t consist of 0 and 1. Additionally, in these strings, the same character never occurs three or more times in a row.\nYou can modify s by repeatedly performing the following operation:\n\nChoose an index i (1 <= i <= N) freely and invert the i-th character in s (that is, replace 0 with 1, and 1 with 0), under the condition that the same character would not occur three or more times in a row in s after the operation.\n\nYour objective is to make s equal to t.\nFind the minimum number of operations required.\nTask Constraint: 1 <= N <= 5000\nThe lengths of s and t are both N.\ns and t consists of 0 and 1.\nIn s and t, the same character never occurs three or more times in a row.\nTask Input: Input is given from Standard Input in the following format:\nN\ns\nt\nTask Output: Find the minimum number of operations required to make s equal to t. It can be proved that the objective is always achievable in a finite number of operations.\nTask Samples: input: 4\n0011\n0101 output: 4\n\nOne possible solution is 0011 → 1011 → 1001 → 1101 → 0101.\ninput: 1\n0\n0 output: 0\ninput: 8\n00110011\n10101010 output: 10\n\n" }, { "title": "", "content": "Problem Statement There is a sequence of length 2N: A_1, A_2, . . . , A_{2N}.\nEach A_i is either -1 or an integer between 1 and 2N (inclusive). Any integer other than -1 appears at most once in {A_i}.\nFor each i such that A_i = -1, Snuke replaces A_i with an integer between 1 and 2N (inclusive), so that {A_i} will be a permutation of 1,2, . . . , 2N.\nThen, he finds a sequence of length N, B_1, B_2, . . . , B_N, as B_i = min(A_{2i-1}, A_{2i}).\nFind the number of different sequences that B_1, B_2, . . . , B_N can be, modulo 10^9 + 7.", "constraint": "1 <= N <= 300\nA_i = -1 or 1 <= A_i <= 2N.\nIf A_i \\neq -1, A_j \\neq -1, then A_i \\neq A_j. (i \\neq j)", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{2N}", "output": "Print the number of different sequences that B_1, B_2, . . . , B_N can be, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 -1 -1 3 6 -1 output: 5\n\nThere are six ways to make {A_i} a permutation of 1,2, ..., 2N; for each of them, {B_i} would be as follows:\n\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,2,4,3,6,5): (B_1, B_2, B_3) = (1,3,5)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,2,5,3,6,4): (B_1, B_2, B_3) = (1,3,4)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,4,2,3,6,5): (B_1, B_2, B_3) = (1,2,5)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,4,5,3,6,2): (B_1, B_2, B_3) = (1,3,2)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,5,2,3,6,4): (B_1, B_2, B_3) = (1,2,4)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,5,4,3,6,2): (B_1, B_2, B_3) = (1,3,2)\n\nThus, there are five different sequences that B_1, B_2, B_3 can be.", "input: 4\n7 1 8 3 5 2 6 4 output: 1", "input: 10\n7 -1 -1 -1 -1 -1 -1 6 14 12 13 -1 15 -1 -1 -1 -1 20 -1 -1 output: 9540576", "input: 20\n-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 6 -1 -1 -1 -1 -1 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 34 -1 -1 -1 -1 31 -1 -1 -1 -1 -1 -1 -1 -1 output: 374984201"], "Pid": "p03191", "ProblemText": "Task Description: Problem Statement There is a sequence of length 2N: A_1, A_2, . . . , A_{2N}.\nEach A_i is either -1 or an integer between 1 and 2N (inclusive). Any integer other than -1 appears at most once in {A_i}.\nFor each i such that A_i = -1, Snuke replaces A_i with an integer between 1 and 2N (inclusive), so that {A_i} will be a permutation of 1,2, . . . , 2N.\nThen, he finds a sequence of length N, B_1, B_2, . . . , B_N, as B_i = min(A_{2i-1}, A_{2i}).\nFind the number of different sequences that B_1, B_2, . . . , B_N can be, modulo 10^9 + 7.\nTask Constraint: 1 <= N <= 300\nA_i = -1 or 1 <= A_i <= 2N.\nIf A_i \\neq -1, A_j \\neq -1, then A_i \\neq A_j. (i \\neq j)\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{2N}\nTask Output: Print the number of different sequences that B_1, B_2, . . . , B_N can be, modulo 10^9 + 7.\nTask Samples: input: 3\n1 -1 -1 3 6 -1 output: 5\n\nThere are six ways to make {A_i} a permutation of 1,2, ..., 2N; for each of them, {B_i} would be as follows:\n\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,2,4,3,6,5): (B_1, B_2, B_3) = (1,3,5)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,2,5,3,6,4): (B_1, B_2, B_3) = (1,3,4)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,4,2,3,6,5): (B_1, B_2, B_3) = (1,2,5)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,4,5,3,6,2): (B_1, B_2, B_3) = (1,3,2)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,5,2,3,6,4): (B_1, B_2, B_3) = (1,2,4)\n(A_1, A_2, A_3, A_4, A_5, A_6) = (1,5,4,3,6,2): (B_1, B_2, B_3) = (1,3,2)\n\nThus, there are five different sequences that B_1, B_2, B_3 can be.\ninput: 4\n7 1 8 3 5 2 6 4 output: 1\ninput: 10\n7 -1 -1 -1 -1 -1 -1 6 14 12 13 -1 15 -1 -1 -1 -1 20 -1 -1 output: 9540576\ninput: 20\n-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 6 -1 -1 -1 -1 -1 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 34 -1 -1 -1 -1 31 -1 -1 -1 -1 -1 -1 -1 -1 output: 374984201\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N that has exactly four digits in base ten.\nHow many times does 2 occur in the base-ten representation of N?", "constraint": "1000 <= N <= 9999", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1222 output: 3\n\n2 occurs three times in 1222. By the way, this contest is held on December 22 (JST).", "input: 3456 output: 0", "input: 9592 output: 1"], "Pid": "p03192", "ProblemText": "Task Description: Problem Statement You are given an integer N that has exactly four digits in base ten.\nHow many times does 2 occur in the base-ten representation of N?\nTask Constraint: 1000 <= N <= 9999\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 1222 output: 3\n\n2 occurs three times in 1222. By the way, this contest is held on December 22 (JST).\ninput: 3456 output: 0\ninput: 9592 output: 1\n\n" }, { "title": "", "content": "Problem Statement There are N rectangular plate materials made of special metal called At Coder Alloy.\nThe dimensions of the i-th material are A_i * B_i (A_i vertically and B_i horizontally).\nTakahashi wants a rectangular plate made of At Coder Alloy whose dimensions are exactly H * W.\nHe is trying to obtain such a plate by choosing one of the N materials and cutting it if necessary.\nWhen cutting a material, the cuts must be parallel to one of the sides of the material.\nAlso, the materials have fixed directions and cannot be rotated.\nFor example, a 5 * 3 material cannot be used as a 3 * 5 plate.\nOut of the N materials, how many can produce an H * W plate if properly cut?", "constraint": "1 <= N <= 1000\n1 <= H <= 10^9\n1 <= W <= 10^9\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN H W\nA_1 B_1\nA_2 B_2\n:\nA_N B_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 2\n10 3\n5 2\n2 5 output: 2\n\nTakahashi wants a 5 * 2 plate.\n\nThe dimensions of the first material are 10 * 3. We can obtain a 5 * 2 plate by properly cutting it.\nThe dimensions of the second material are 5 * 2. We can obtain a 5 * 2 plate without cutting it.\nThe dimensions of the third material are 2 * 5. We cannot obtain a 5 * 2 plate, whatever cuts are made. Note that the material cannot be rotated and used as a 5 * 2 plate.", "input: 10 587586158 185430194\n894597290 708587790\n680395892 306946994\n590262034 785368612\n922328576 106880540\n847058850 326169610\n936315062 193149191\n702035777 223363392\n11672949 146832978\n779291680 334178158\n615808191 701464268 output: 8"], "Pid": "p03193", "ProblemText": "Task Description: Problem Statement There are N rectangular plate materials made of special metal called At Coder Alloy.\nThe dimensions of the i-th material are A_i * B_i (A_i vertically and B_i horizontally).\nTakahashi wants a rectangular plate made of At Coder Alloy whose dimensions are exactly H * W.\nHe is trying to obtain such a plate by choosing one of the N materials and cutting it if necessary.\nWhen cutting a material, the cuts must be parallel to one of the sides of the material.\nAlso, the materials have fixed directions and cannot be rotated.\nFor example, a 5 * 3 material cannot be used as a 3 * 5 plate.\nOut of the N materials, how many can produce an H * W plate if properly cut?\nTask Constraint: 1 <= N <= 1000\n1 <= H <= 10^9\n1 <= W <= 10^9\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN H W\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nTask Output: Print the answer.\nTask Samples: input: 3 5 2\n10 3\n5 2\n2 5 output: 2\n\nTakahashi wants a 5 * 2 plate.\n\nThe dimensions of the first material are 10 * 3. We can obtain a 5 * 2 plate by properly cutting it.\nThe dimensions of the second material are 5 * 2. We can obtain a 5 * 2 plate without cutting it.\nThe dimensions of the third material are 2 * 5. We cannot obtain a 5 * 2 plate, whatever cuts are made. Note that the material cannot be rotated and used as a 5 * 2 plate.\ninput: 10 587586158 185430194\n894597290 708587790\n680395892 306946994\n590262034 785368612\n922328576 106880540\n847058850 326169610\n936315062 193149191\n702035777 223363392\n11672949 146832978\n779291680 334178158\n615808191 701464268 output: 8\n\n" }, { "title": "", "content": "Problem Statement There are N integers a_1, a_2, . . . , a_N not less than 1.\nThe values of a_1, a_2, . . . , a_N are not known, but it is known that a_1 * a_2 * . . . * a_N = P.\nFind the maximum possible greatest common divisor of a_1, a_2, . . . , a_N.", "constraint": "1 <= N <= 10^{12}\n1 <= P <= 10^{12}", "input": "Input is given from Standard Input in the following format:\nN P", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 24 output: 2\n\nThe greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.", "input: 5 1 output: 1\n\nAs a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.", "input: 1 111 output: 111", "input: 4 972439611840 output: 206"], "Pid": "p03194", "ProblemText": "Task Description: Problem Statement There are N integers a_1, a_2, . . . , a_N not less than 1.\nThe values of a_1, a_2, . . . , a_N are not known, but it is known that a_1 * a_2 * . . . * a_N = P.\nFind the maximum possible greatest common divisor of a_1, a_2, . . . , a_N.\nTask Constraint: 1 <= N <= 10^{12}\n1 <= P <= 10^{12}\nTask Input: Input is given from Standard Input in the following format:\nN P\nTask Output: Print the answer.\nTask Samples: input: 3 24 output: 2\n\nThe greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.\ninput: 5 1 output: 1\n\nAs a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.\ninput: 1 111 output: 111\ninput: 4 972439611840 output: 206\n\n" }, { "title": "", "content": "Problem Statement There is an apple tree that bears apples of N colors. The N colors of these apples are numbered 1 to N, and there are a_i apples of Color i.\nYou and Lunlun the dachshund alternately perform the following operation (starting from you):\n\nChoose one or more apples from the tree and eat them. Here, the apples chosen at the same time must all have different colors.\n\nThe one who eats the last apple from the tree will be declared winner. If both you and Lunlun play optimally, which will win?", "constraint": "1 <= N <= 10^5\n1 <= a_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1\na_2\n:\na_N", "output": "If you will win, print first; if Lunlun will win, print second.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1\n2 output: first\n\nLet Color 1 be red, and Color 2 be blue. In this case, the tree bears one red apple and two blue apples.\nYou should eat the red apple in your first turn. Lunlun is then forced to eat one of the blue apples, and you can win by eating the other in your next turn.\nNote that you are also allowed to eat two apples in your first turn, one red and one blue (not a winning move, though).", "input: 3\n100000\n30000\n20000 output: second"], "Pid": "p03195", "ProblemText": "Task Description: Problem Statement There is an apple tree that bears apples of N colors. The N colors of these apples are numbered 1 to N, and there are a_i apples of Color i.\nYou and Lunlun the dachshund alternately perform the following operation (starting from you):\n\nChoose one or more apples from the tree and eat them. Here, the apples chosen at the same time must all have different colors.\n\nThe one who eats the last apple from the tree will be declared winner. If both you and Lunlun play optimally, which will win?\nTask Constraint: 1 <= N <= 10^5\n1 <= a_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1\na_2\n:\na_N\nTask Output: If you will win, print first; if Lunlun will win, print second.\nTask Samples: input: 2\n1\n2 output: first\n\nLet Color 1 be red, and Color 2 be blue. In this case, the tree bears one red apple and two blue apples.\nYou should eat the red apple in your first turn. Lunlun is then forced to eat one of the blue apples, and you can win by eating the other in your next turn.\nNote that you are also allowed to eat two apples in your first turn, one red and one blue (not a winning move, though).\ninput: 3\n100000\n30000\n20000 output: second\n\n" }, { "title": "", "content": "Problem Statement There are N integers a_1, a_2, . . . , a_N not less than 1.\nThe values of a_1, a_2, . . . , a_N are not known, but it is known that a_1 * a_2 * . . . * a_N = P.\nFind the maximum possible greatest common divisor of a_1, a_2, . . . , a_N.", "constraint": "1 <= N <= 10^{12}\n1 <= P <= 10^{12}", "input": "Input is given from Standard Input in the following format:\nN P", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 24 output: 2\n\nThe greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.", "input: 5 1 output: 1\n\nAs a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.", "input: 1 111 output: 111", "input: 4 972439611840 output: 206"], "Pid": "p03196", "ProblemText": "Task Description: Problem Statement There are N integers a_1, a_2, . . . , a_N not less than 1.\nThe values of a_1, a_2, . . . , a_N are not known, but it is known that a_1 * a_2 * . . . * a_N = P.\nFind the maximum possible greatest common divisor of a_1, a_2, . . . , a_N.\nTask Constraint: 1 <= N <= 10^{12}\n1 <= P <= 10^{12}\nTask Input: Input is given from Standard Input in the following format:\nN P\nTask Output: Print the answer.\nTask Samples: input: 3 24 output: 2\n\nThe greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.\ninput: 5 1 output: 1\n\nAs a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.\ninput: 1 111 output: 111\ninput: 4 972439611840 output: 206\n\n" }, { "title": "", "content": "Problem Statement There is an apple tree that bears apples of N colors. The N colors of these apples are numbered 1 to N, and there are a_i apples of Color i.\nYou and Lunlun the dachshund alternately perform the following operation (starting from you):\n\nChoose one or more apples from the tree and eat them. Here, the apples chosen at the same time must all have different colors.\n\nThe one who eats the last apple from the tree will be declared winner. If both you and Lunlun play optimally, which will win?", "constraint": "1 <= N <= 10^5\n1 <= a_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1\na_2\n:\na_N", "output": "If you will win, print first; if Lunlun will win, print second.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1\n2 output: first\n\nLet Color 1 be red, and Color 2 be blue. In this case, the tree bears one red apple and two blue apples.\nYou should eat the red apple in your first turn. Lunlun is then forced to eat one of the blue apples, and you can win by eating the other in your next turn.\nNote that you are also allowed to eat two apples in your first turn, one red and one blue (not a winning move, though).", "input: 3\n100000\n30000\n20000 output: second"], "Pid": "p03197", "ProblemText": "Task Description: Problem Statement There is an apple tree that bears apples of N colors. The N colors of these apples are numbered 1 to N, and there are a_i apples of Color i.\nYou and Lunlun the dachshund alternately perform the following operation (starting from you):\n\nChoose one or more apples from the tree and eat them. Here, the apples chosen at the same time must all have different colors.\n\nThe one who eats the last apple from the tree will be declared winner. If both you and Lunlun play optimally, which will win?\nTask Constraint: 1 <= N <= 10^5\n1 <= a_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1\na_2\n:\na_N\nTask Output: If you will win, print first; if Lunlun will win, print second.\nTask Samples: input: 2\n1\n2 output: first\n\nLet Color 1 be red, and Color 2 be blue. In this case, the tree bears one red apple and two blue apples.\nYou should eat the red apple in your first turn. Lunlun is then forced to eat one of the blue apples, and you can win by eating the other in your next turn.\nNote that you are also allowed to eat two apples in your first turn, one red and one blue (not a winning move, though).\ninput: 3\n100000\n30000\n20000 output: second\n\n" }, { "title": "", "content": "Problem Statement There are N positive integers A_1, A_2, . . . , A_N.\nTakahashi can perform the following operation on these integers any number of times:\n\nChoose 1 <= i <= N and multiply the value of A_i by -2.\n\nNotice that he multiplies it by minus two.\nHe would like to make A_1 <= A_2 <= . . . <= A_N holds.\nFind the minimum number of operations required. If it is impossible, print -1.", "constraint": "1 <= N <= 200000\n1 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 1 4 1 output: 3\n\nOne possible solution is:\n\nChoose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now 3,1,4, -2.\nChoose i=1 and multiply the value of A_1 by -2. A_1, A_2, A_3, A_4 are now -6,1,4, -2.\nChoose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now -6,1,4,4.", "input: 5\n1 2 3 4 5 output: 0\n\nA_1 <= A_2 <= ... <= A_N holds before any operation is performed.", "input: 8\n657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097 output: 7"], "Pid": "p03198", "ProblemText": "Task Description: Problem Statement There are N positive integers A_1, A_2, . . . , A_N.\nTakahashi can perform the following operation on these integers any number of times:\n\nChoose 1 <= i <= N and multiply the value of A_i by -2.\n\nNotice that he multiplies it by minus two.\nHe would like to make A_1 <= A_2 <= . . . <= A_N holds.\nFind the minimum number of operations required. If it is impossible, print -1.\nTask Constraint: 1 <= N <= 200000\n1 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the answer.\nTask Samples: input: 4\n3 1 4 1 output: 3\n\nOne possible solution is:\n\nChoose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now 3,1,4, -2.\nChoose i=1 and multiply the value of A_1 by -2. A_1, A_2, A_3, A_4 are now -6,1,4, -2.\nChoose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now -6,1,4,4.\ninput: 5\n1 2 3 4 5 output: 0\n\nA_1 <= A_2 <= ... <= A_N holds before any operation is performed.\ninput: 8\n657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097 output: 7\n\n" }, { "title": "", "content": "Problem Statement Takahashi has an N * N grid. The square at the i-th row and the j-th column of the grid is denoted by (i, j).\nParticularly, the top-left square of the grid is (1,1), and the bottom-right square is (N, N).\nAn integer, 0 or 1, is written on M of the squares in the Takahashi's grid.\nThree integers a_i, b_i and c_i describe the i-th of those squares with integers written on them: the integer c_i is written on the square (a_i, b_i).\nTakahashi decides to write an integer, 0 or 1, on each of the remaining squares so that the condition below is satisfied.\nFind the number of such ways to write integers, modulo 998244353.\n\nFor all 1<= i < j<= N, there are even number of 1s in the square region whose top-left square is (i, i) and whose bottom-right square is (j, j).", "constraint": "2 <= N <= 10^5\n0 <= M <= min(5 * 10^4,N^2)\n1 <= a_i,b_i <= N(1<= i<= M)\n0 <= c_i <= 1(1<= i<= M)\nIf i \\neq j, then (a_i,b_i) \\neq (a_j,b_j).\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1 c_1\n:\na_M b_M c_M", "output": "Print the number of possible ways to write integers, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 1 1\n3 1 0\n2 3 1 output: 8\n\nFor example, the following ways to write integers satisfy the condition:\n101 111\n011 111\n000 011", "input: 4 5\n1 3 1\n2 4 0\n2 3 1\n4 2 1\n4 4 1 output: 32", "input: 3 5\n1 3 1\n3 3 0\n3 1 0\n2 3 1\n3 2 1 output: 0", "input: 4 8\n1 1 1\n1 2 0\n3 2 1\n1 4 0\n2 1 1\n1 3 0\n3 4 1\n4 4 1 output: 4", "input: 100000 0 output: 342016343"], "Pid": "p03199", "ProblemText": "Task Description: Problem Statement Takahashi has an N * N grid. The square at the i-th row and the j-th column of the grid is denoted by (i, j).\nParticularly, the top-left square of the grid is (1,1), and the bottom-right square is (N, N).\nAn integer, 0 or 1, is written on M of the squares in the Takahashi's grid.\nThree integers a_i, b_i and c_i describe the i-th of those squares with integers written on them: the integer c_i is written on the square (a_i, b_i).\nTakahashi decides to write an integer, 0 or 1, on each of the remaining squares so that the condition below is satisfied.\nFind the number of such ways to write integers, modulo 998244353.\n\nFor all 1<= i < j<= N, there are even number of 1s in the square region whose top-left square is (i, i) and whose bottom-right square is (j, j).\nTask Constraint: 2 <= N <= 10^5\n0 <= M <= min(5 * 10^4,N^2)\n1 <= a_i,b_i <= N(1<= i<= M)\n0 <= c_i <= 1(1<= i<= M)\nIf i \\neq j, then (a_i,b_i) \\neq (a_j,b_j).\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1 c_1\n:\na_M b_M c_M\nTask Output: Print the number of possible ways to write integers, modulo 998244353.\nTask Samples: input: 3 3\n1 1 1\n3 1 0\n2 3 1 output: 8\n\nFor example, the following ways to write integers satisfy the condition:\n101 111\n011 111\n000 011\ninput: 4 5\n1 3 1\n2 4 0\n2 3 1\n4 2 1\n4 4 1 output: 32\ninput: 3 5\n1 3 1\n3 3 0\n3 1 0\n2 3 1\n3 2 1 output: 0\ninput: 4 8\n1 1 1\n1 2 0\n3 2 1\n1 4 0\n2 1 1\n1 3 0\n3 4 1\n4 4 1 output: 4\ninput: 100000 0 output: 342016343\n\n" }, { "title": "", "content": "Problem Statement There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side. )\nThe state of each piece is represented by a string S of length N.\nIf S_i=B, the i-th piece from the left is showing black;\nIf S_i=W, the i-th piece from the left is showing white.\nConsider performing the following operation:\n\nChoose i (1 <= i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.\n\nFind the maximum possible number of times this operation can be performed.", "constraint": "1 <= |S| <= 2* 10^5\nS_i=B or W", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the maximum possible number of times the operation can be performed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: BBW output: 2\n\nThe operation can be performed twice, as follows:\n\nFlip the second and third pieces from the left.\nFlip the first and second pieces from the left.", "input: BWBWBW output: 6"], "Pid": "p03200", "ProblemText": "Task Description: Problem Statement There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side. )\nThe state of each piece is represented by a string S of length N.\nIf S_i=B, the i-th piece from the left is showing black;\nIf S_i=W, the i-th piece from the left is showing white.\nConsider performing the following operation:\n\nChoose i (1 <= i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.\n\nFind the maximum possible number of times this operation can be performed.\nTask Constraint: 1 <= |S| <= 2* 10^5\nS_i=B or W\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the maximum possible number of times the operation can be performed.\nTask Samples: input: BBW output: 2\n\nThe operation can be performed twice, as follows:\n\nFlip the second and third pieces from the left.\nFlip the first and second pieces from the left.\ninput: BWBWBW output: 6\n\n" }, { "title": "", "content": "Problem Statement Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i.\nHe would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2.\nNote that a ball cannot belong to multiple pairs.\nFind the maximum possible number of pairs that can be formed.\nHere, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.", "constraint": "1 <= N <= 2* 10^5\n1 <= A_i <= 10^9\nA_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 1\n\nWe can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.\nNote that we cannot pair the second ball with itself.", "input: 5\n3 11 14 5 13 output: 2"], "Pid": "p03201", "ProblemText": "Task Description: Problem Statement Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i.\nHe would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2.\nNote that a ball cannot belong to multiple pairs.\nFind the maximum possible number of pairs that can be formed.\nHere, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.\nTask Constraint: 1 <= N <= 2* 10^5\n1 <= A_i <= 10^9\nA_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.\nTask Samples: input: 3\n1 2 3 output: 1\n\nWe can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.\nNote that we cannot pair the second ball with itself.\ninput: 5\n3 11 14 5 13 output: 2\n\n" }, { "title": "", "content": "Problem Statement There are N strings arranged in a row.\nIt is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right.\nThat is, S_1= 2\nThe sum of |E_i| is at most 2 * 10^5.", "input": "Input is given from Standard Input in the following format:\nN\nc_1 w_{1,1} w_{1,2} . . . w_{1, c_1}\n:\nc_{N-1} w_{N-1,1} w_{N-1,2} . . . w_{N-1, c_{N-1}}\n\nHere, c_i stands for the number of elements in E_i, and w_{i, 1}, . . . , w_{i, c_i} are the c_i elements in c_i.\nHere, 2 <= c_i <= N, 1 <= w_{i, j} <= N, and w_{i, j} \\neq w_{i, k} (1 <= j < k <= c_i) hold.", "output": "If T cannot be a tree, print -1; otherwise, print the choices of (u_i, v_i) that satisfy the condition, in the following format:\nu_1 v_1\n:\nu_{N-1} v_{N-1}", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 1 2\n3 1 2 3\n3 3 4 5\n2 4 5 output: 1 2\n1 3\n3 4\n4 5", "input: 6\n3 1 2 3\n3 2 3 4\n3 1 3 4\n3 1 2 4\n3 4 5 6 output: -1", "input: 10\n5 1 2 3 4 5\n5 2 3 4 5 6\n5 3 4 5 6 7\n5 4 5 6 7 8\n5 5 6 7 8 9\n5 6 7 8 9 10\n5 7 8 9 10 1\n5 8 9 10 1 2\n5 9 10 1 2 3 output: 1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n8 9\n9 10"], "Pid": "p03205", "ProblemText": "Task Description: Problem Statement You are given N-1 subsets of \\{1,2, . . . , N\\}. Let the i-th set be E_i.\nLet us choose two distinct elements u_i and v_i from each set E_i, and consider a graph T with N vertices and N-1 edges, whose vertex set is \\{1,2, . . , N\\} and whose edge set is (u_1, v_1), (u_2, v_2), . . . , (u_{N-1}, v_{N-1}).\nDetermine if T can be a tree by properly deciding u_i and v_i.\nIf it can, additionally find one instance of (u_1, v_1), (u_2, v_2), . . . , (u_{N-1}, v_{N-1}) such that T is actually a tree.\nTask Constraint: 2 <= N <= 10^5\nE_i is a subset of \\{1,2,..,N\\}.\n|E_i| >= 2\nThe sum of |E_i| is at most 2 * 10^5.\nTask Input: Input is given from Standard Input in the following format:\nN\nc_1 w_{1,1} w_{1,2} . . . w_{1, c_1}\n:\nc_{N-1} w_{N-1,1} w_{N-1,2} . . . w_{N-1, c_{N-1}}\n\nHere, c_i stands for the number of elements in E_i, and w_{i, 1}, . . . , w_{i, c_i} are the c_i elements in c_i.\nHere, 2 <= c_i <= N, 1 <= w_{i, j} <= N, and w_{i, j} \\neq w_{i, k} (1 <= j < k <= c_i) hold.\nTask Output: If T cannot be a tree, print -1; otherwise, print the choices of (u_i, v_i) that satisfy the condition, in the following format:\nu_1 v_1\n:\nu_{N-1} v_{N-1}\nTask Samples: input: 5\n2 1 2\n3 1 2 3\n3 3 4 5\n2 4 5 output: 1 2\n1 3\n3 4\n4 5\ninput: 6\n3 1 2 3\n3 2 3 4\n3 1 3 4\n3 1 2 4\n3 4 5 6 output: -1\ninput: 10\n5 1 2 3 4 5\n5 2 3 4 5 6\n5 3 4 5 6 7\n5 4 5 6 7 8\n5 5 6 7 8 9\n5 6 7 8 9 10\n5 7 8 9 10 1\n5 8 9 10 1 2\n5 9 10 1 2 3 output: 1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n8 9\n9 10\n\n" }, { "title": "", "content": "Problem Statement In some other world, today is December D-th.\nWrite a program that prints Christmas if D = 25, Christmas Eve if D = 24, Christmas Eve Eve if D = 23 and Christmas Eve Eve Eve if D = 22.", "constraint": "22 <= D <= 25\nD is an integer.", "input": "Input is given from Standard Input in the following format:\nD", "output": "Print the specified string (case-sensitive).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 25 output: Christmas", "input: 22 output: Christmas Eve Eve Eve\n\nBe sure to print spaces between the words."], "Pid": "p03206", "ProblemText": "Task Description: Problem Statement In some other world, today is December D-th.\nWrite a program that prints Christmas if D = 25, Christmas Eve if D = 24, Christmas Eve Eve if D = 23 and Christmas Eve Eve Eve if D = 22.\nTask Constraint: 22 <= D <= 25\nD is an integer.\nTask Input: Input is given from Standard Input in the following format:\nD\nTask Output: Print the specified string (case-sensitive).\nTask Samples: input: 25 output: Christmas\ninput: 22 output: Christmas Eve Eve Eve\n\nBe sure to print spaces between the words.\n\n" }, { "title": "", "content": "Problem Statement In some other world, today is the day before Christmas Eve.\nMr. Takaha is buying N items at a department store. The regular price of the i-th item (1 <= i <= N) is p_i yen (the currency of Japan).\nHe has a discount coupon, and can buy one item with the highest price for half the regular price. The remaining N-1 items cost their regular prices. What is the total amount he will pay?", "constraint": "2 <= N <= 10\n100 <= p_i <= 10000\np_i is an even number.", "input": "Input is given from Standard Input in the following format:\nN\np_1\np_2\n:\np_N", "output": "Print the total amount Mr. Takaha will pay.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n4980\n7980\n6980 output: 15950\n\nThe 7980-yen item gets the discount and the total is 4980 + 7980 / 2 + 6980 = 15950 yen.\nNote that outputs such as 15950.0 will be judged as Wrong Answer.", "input: 4\n4320\n4320\n4320\n4320 output: 15120\n\nOnly one of the four items gets the discount and the total is 4320 / 2 + 4320 + 4320 + 4320 = 15120 yen."], "Pid": "p03207", "ProblemText": "Task Description: Problem Statement In some other world, today is the day before Christmas Eve.\nMr. Takaha is buying N items at a department store. The regular price of the i-th item (1 <= i <= N) is p_i yen (the currency of Japan).\nHe has a discount coupon, and can buy one item with the highest price for half the regular price. The remaining N-1 items cost their regular prices. What is the total amount he will pay?\nTask Constraint: 2 <= N <= 10\n100 <= p_i <= 10000\np_i is an even number.\nTask Input: Input is given from Standard Input in the following format:\nN\np_1\np_2\n:\np_N\nTask Output: Print the total amount Mr. Takaha will pay.\nTask Samples: input: 3\n4980\n7980\n6980 output: 15950\n\nThe 7980-yen item gets the discount and the total is 4980 + 7980 / 2 + 6980 = 15950 yen.\nNote that outputs such as 15950.0 will be judged as Wrong Answer.\ninput: 4\n4320\n4320\n4320\n4320 output: 15120\n\nOnly one of the four items gets the discount and the total is 4320 / 2 + 4320 + 4320 + 4320 = 15120 yen.\n\n" }, { "title": "", "content": "Problem Statement In some other world, today is Christmas Eve.\nThere are N trees planted in Mr. Takaha's garden. The height of the i-th tree (1 <= i <= N) is h_i meters.\nHe decides to choose K trees from these trees and decorate them with electric lights. To make the scenery more beautiful, the heights of the decorated trees should be as close to each other as possible.\nMore specifically, let the height of the tallest decorated tree be h_{max} meters, and the height of the shortest decorated tree be h_{min} meters. The smaller the value h_{max} - h_{min} is, the better. What is the minimum possible value of h_{max} - h_{min}?", "constraint": "2 <= K < N <= 10^5\n1 <= h_i <= 10^9\nh_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN K\nh_1\nh_2\n:\nh_N", "output": "Print the minimum possible value of h_{max} - h_{min}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n10\n15\n11\n14\n12 output: 2\n\nIf we decorate the first, third and fifth trees, h_{max} = 12, h_{min} = 10 so h_{max} - h_{min} = 2. This is optimal.", "input: 5 3\n5\n7\n5\n7\n7 output: 0\n\nIf we decorate the second, fourth and fifth trees, h_{max} = 7, h_{min} = 7 so h_{max} - h_{min} = 0. This is optimal.\nThere are not too many trees in these sample inputs, but note that there can be at most one hundred thousand trees (we just can't put a sample with a hundred thousand lines here)."], "Pid": "p03208", "ProblemText": "Task Description: Problem Statement In some other world, today is Christmas Eve.\nThere are N trees planted in Mr. Takaha's garden. The height of the i-th tree (1 <= i <= N) is h_i meters.\nHe decides to choose K trees from these trees and decorate them with electric lights. To make the scenery more beautiful, the heights of the decorated trees should be as close to each other as possible.\nMore specifically, let the height of the tallest decorated tree be h_{max} meters, and the height of the shortest decorated tree be h_{min} meters. The smaller the value h_{max} - h_{min} is, the better. What is the minimum possible value of h_{max} - h_{min}?\nTask Constraint: 2 <= K < N <= 10^5\n1 <= h_i <= 10^9\nh_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN K\nh_1\nh_2\n:\nh_N\nTask Output: Print the minimum possible value of h_{max} - h_{min}.\nTask Samples: input: 5 3\n10\n15\n11\n14\n12 output: 2\n\nIf we decorate the first, third and fifth trees, h_{max} = 12, h_{min} = 10 so h_{max} - h_{min} = 2. This is optimal.\ninput: 5 3\n5\n7\n5\n7\n7 output: 0\n\nIf we decorate the second, fourth and fifth trees, h_{max} = 7, h_{min} = 7 so h_{max} - h_{min} = 0. This is optimal.\nThere are not too many trees in these sample inputs, but note that there can be at most one hundred thousand trees (we just can't put a sample with a hundred thousand lines here).\n\n" }, { "title": "", "content": "Problem Statement In some other world, today is Christmas.\nMr. Takaha decides to make a multi-dimensional burger in his party. A level-L burger (L is an integer greater than or equal to 0) is the following thing:\n\nA level-0 burger is a patty.\nA level-L burger (L >= 1) is a bun, a level-(L-1) burger, a patty, another level-(L-1) burger and another bun, stacked vertically in this order from the bottom.\n\nFor example, a level-1 burger and a level-2 burger look like BPPPB and BBPPPBPBPPPBB (rotated 90 degrees), where B and P stands for a bun and a patty.\nThe burger Mr. Takaha will make is a level-N burger. Lunlun the Dachshund will eat X layers from the bottom of this burger (a layer is a patty or a bun). How many patties will she eat?", "constraint": "1 <= N <= 50\n1 <= X <= ( the total number of layers in a level-N burger )\nN and X are integers.", "input": "Input is given from Standard Input in the following format:\nN X", "output": "Print the number of patties in the bottom-most X layers from the bottom of a level-N burger.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 7 output: 4\n\nThere are 4 patties in the bottom-most 7 layers of a level-2 burger (BBPPPBPBPPPBB).", "input: 1 1 output: 0\n\nThe bottom-most layer of a level-1 burger is a bun.", "input: 50 4321098765432109 output: 2160549382716056\n\nA level-50 burger is rather thick, to the extent that the number of its layers does not fit into a 32-bit integer."], "Pid": "p03209", "ProblemText": "Task Description: Problem Statement In some other world, today is Christmas.\nMr. Takaha decides to make a multi-dimensional burger in his party. A level-L burger (L is an integer greater than or equal to 0) is the following thing:\n\nA level-0 burger is a patty.\nA level-L burger (L >= 1) is a bun, a level-(L-1) burger, a patty, another level-(L-1) burger and another bun, stacked vertically in this order from the bottom.\n\nFor example, a level-1 burger and a level-2 burger look like BPPPB and BBPPPBPBPPPBB (rotated 90 degrees), where B and P stands for a bun and a patty.\nThe burger Mr. Takaha will make is a level-N burger. Lunlun the Dachshund will eat X layers from the bottom of this burger (a layer is a patty or a bun). How many patties will she eat?\nTask Constraint: 1 <= N <= 50\n1 <= X <= ( the total number of layers in a level-N burger )\nN and X are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X\nTask Output: Print the number of patties in the bottom-most X layers from the bottom of a level-N burger.\nTask Samples: input: 2 7 output: 4\n\nThere are 4 patties in the bottom-most 7 layers of a level-2 burger (BBPPPBPBPPPBB).\ninput: 1 1 output: 0\n\nThe bottom-most layer of a level-1 burger is a bun.\ninput: 50 4321098765432109 output: 2160549382716056\n\nA level-50 burger is rather thick, to the extent that the number of its layers does not fit into a 32-bit integer.\n\n" }, { "title": "", "content": "Problem Statement Shichi-Go-San (literally \"Seven-Five-Three\") is a traditional event in a certain country to celebrate the growth of seven-, five- and three-year-old children.\nTakahashi is now X years old. Will his growth be celebrated in Shichi-Go-San this time?", "constraint": "1 <= X <= 9\nX is an integer.", "input": "Input is given from Standard Input in the following format:\nX", "output": "If Takahashi's growth will be celebrated, print YES; if it will not, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 output: YES\n\nThe growth of a five-year-old child will be celebrated.", "input: 6 output: NO\n\nSee you next year."], "Pid": "p03210", "ProblemText": "Task Description: Problem Statement Shichi-Go-San (literally \"Seven-Five-Three\") is a traditional event in a certain country to celebrate the growth of seven-, five- and three-year-old children.\nTakahashi is now X years old. Will his growth be celebrated in Shichi-Go-San this time?\nTask Constraint: 1 <= X <= 9\nX is an integer.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: If Takahashi's growth will be celebrated, print YES; if it will not, print NO.\nTask Samples: input: 5 output: YES\n\nThe growth of a five-year-old child will be celebrated.\ninput: 6 output: NO\n\nSee you next year.\n\n" }, { "title": "", "content": "Problem Statement There is a string S consisting of digits 1,2, . . . , 9.\nLunlun, the Dachshund, will take out three consecutive digits from S, treat them as a single integer X and bring it to her master. (She cannot rearrange the digits. )\nThe master's favorite number is 753. The closer to this number, the better.\nWhat is the minimum possible (absolute) difference between X and 753?", "constraint": "S is a string of length between 4 and 10 (inclusive).\nEach character in S is 1,2, ..., or 9.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the minimum possible difference between X and 753.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1234567876 output: 34\n\nTaking out the seventh to ninth characters results in X = 787, and the difference between this and 753 is 787 - 753 = 34. The difference cannot be made smaller, no matter where X is taken from.\nNote that the digits cannot be rearranged. For example, taking out 567 and rearranging it to 765 is not allowed.\nWe cannot take out three digits that are not consecutive from S, either. For example, taking out the seventh digit 7, the ninth digit 7 and the tenth digit 6 to obtain 776 is not allowed.", "input: 35753 output: 0\n\nIf 753 itself can be taken out, the answer is 0.", "input: 1111111111 output: 642\n\nNo matter where X is taken from, X = 111, with the difference 753 - 111 = 642."], "Pid": "p03211", "ProblemText": "Task Description: Problem Statement There is a string S consisting of digits 1,2, . . . , 9.\nLunlun, the Dachshund, will take out three consecutive digits from S, treat them as a single integer X and bring it to her master. (She cannot rearrange the digits. )\nThe master's favorite number is 753. The closer to this number, the better.\nWhat is the minimum possible (absolute) difference between X and 753?\nTask Constraint: S is a string of length between 4 and 10 (inclusive).\nEach character in S is 1,2, ..., or 9.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the minimum possible difference between X and 753.\nTask Samples: input: 1234567876 output: 34\n\nTaking out the seventh to ninth characters results in X = 787, and the difference between this and 753 is 787 - 753 = 34. The difference cannot be made smaller, no matter where X is taken from.\nNote that the digits cannot be rearranged. For example, taking out 567 and rearranging it to 765 is not allowed.\nWe cannot take out three digits that are not consecutive from S, either. For example, taking out the seventh digit 7, the ninth digit 7 and the tenth digit 6 to obtain 776 is not allowed.\ninput: 35753 output: 0\n\nIf 753 itself can be taken out, the answer is 0.\ninput: 1111111111 output: 642\n\nNo matter where X is taken from, X = 111, with the difference 753 - 111 = 642.\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N. Among the integers between 1 and N (inclusive), how many Shichi-Go-San numbers (literally \"Seven-Five-Three numbers\") are there?\nHere, a Shichi-Go-San number is a positive integer that satisfies the following condition:\n\nWhen the number is written in base ten, each of the digits 7,5 and 3 appears at least once, and the other digits never appear.", "constraint": "1 <= N < 10^9\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of the Shichi-Go-San numbers between 1 and N (inclusive).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 575 output: 4\n\nThere are four Shichi-Go-San numbers not greater than 575: 357,375,537 and 573.", "input: 3600 output: 13\n\nThere are 13 Shichi-Go-San numbers not greater than 3600: the above four numbers, 735,753,3357,3375,3537,3557,3573,3575 and 3577.", "input: 999999999 output: 26484"], "Pid": "p03212", "ProblemText": "Task Description: Problem Statement You are given an integer N. Among the integers between 1 and N (inclusive), how many Shichi-Go-San numbers (literally \"Seven-Five-Three numbers\") are there?\nHere, a Shichi-Go-San number is a positive integer that satisfies the following condition:\n\nWhen the number is written in base ten, each of the digits 7,5 and 3 appears at least once, and the other digits never appear.\nTask Constraint: 1 <= N < 10^9\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of the Shichi-Go-San numbers between 1 and N (inclusive).\nTask Samples: input: 575 output: 4\n\nThere are four Shichi-Go-San numbers not greater than 575: 357,375,537 and 573.\ninput: 3600 output: 13\n\nThere are 13 Shichi-Go-San numbers not greater than 3600: the above four numbers, 735,753,3357,3375,3537,3557,3573,3575 and 3577.\ninput: 999999999 output: 26484\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N. Among the divisors of N! (= 1 * 2 * . . . * N), how many Shichi-Go numbers (literally \"Seven-Five numbers\") are there?\nHere, a Shichi-Go number is a positive integer that has exactly 75 divisors. note: Note When a positive integer A divides a positive integer B, A is said to a divisor of B.\nFor example, 6 has four divisors: 1,2,3 and 6.", "constraint": "1 <= N <= 100\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of the Shichi-Go numbers that are divisors of N! .", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 output: 0\n\nThere are no Shichi-Go numbers among the divisors of 9! = 1 * 2 * ... * 9 = 362880.", "input: 10 output: 1\n\nThere is one Shichi-Go number among the divisors of 10! = 3628800: 32400.", "input: 100 output: 543"], "Pid": "p03213", "ProblemText": "Task Description: Problem Statement You are given an integer N. Among the divisors of N! (= 1 * 2 * . . . * N), how many Shichi-Go numbers (literally \"Seven-Five numbers\") are there?\nHere, a Shichi-Go number is a positive integer that has exactly 75 divisors. note: Note When a positive integer A divides a positive integer B, A is said to a divisor of B.\nFor example, 6 has four divisors: 1,2,3 and 6.\nTask Constraint: 1 <= N <= 100\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of the Shichi-Go numbers that are divisors of N! .\nTask Samples: input: 9 output: 0\n\nThere are no Shichi-Go numbers among the divisors of 9! = 1 * 2 * ... * 9 = 362880.\ninput: 10 output: 1\n\nThere is one Shichi-Go number among the divisors of 10! = 3628800: 32400.\ninput: 100 output: 543\n\n" }, { "title": "", "content": "Problem Statement\nNiwango-kun is an employee of Dwango Co. , Ltd.\nOne day, he is asked to generate a thumbnail from a video a user submitted.\nTo generate a thumbnail, he needs to select a frame of the video according to the following procedure:\n\nGet an integer N and N integers a_0, a_1, . . . , a_{N-1} as inputs. N denotes the number of the frames of the video, and each a_i denotes the representation of the i-th frame of the video.\nSelect t-th frame whose representation a_t is nearest to the average of all frame representations.\nIf there are multiple such frames, select the frame with the smallest index.\n\nFind the index t of the frame he should select to generate a thumbnail.", "constraint": "1 <= N <= 100\n1 <= a_i <= 100\nAll numbers given in input are integers", "input": "Input is given from Standard Input in the following format:\nN\na_{0} a_{1} . . . a_{N-1}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 1\n\nSince the average of frame representations is 2, Niwango-kun needs to select the index 1, whose representation is 2, that is, the nearest value to the average.", "input: 4\n2 5 2 5 output: 0\n\nThe average of frame representations is 3.5.\nIn this case, every frame has the same distance from its representation to the average.\nTherefore, Niwango-kun should select index 0, the smallest index among them."], "Pid": "p03214", "ProblemText": "Task Description: Problem Statement\nNiwango-kun is an employee of Dwango Co. , Ltd.\nOne day, he is asked to generate a thumbnail from a video a user submitted.\nTo generate a thumbnail, he needs to select a frame of the video according to the following procedure:\n\nGet an integer N and N integers a_0, a_1, . . . , a_{N-1} as inputs. N denotes the number of the frames of the video, and each a_i denotes the representation of the i-th frame of the video.\nSelect t-th frame whose representation a_t is nearest to the average of all frame representations.\nIf there are multiple such frames, select the frame with the smallest index.\n\nFind the index t of the frame he should select to generate a thumbnail.\nTask Constraint: 1 <= N <= 100\n1 <= a_i <= 100\nAll numbers given in input are integers\nTask Input: Input is given from Standard Input in the following format:\nN\na_{0} a_{1} . . . a_{N-1}\nTask Output: Print the answer.\nTask Samples: input: 3\n1 2 3 output: 1\n\nSince the average of frame representations is 2, Niwango-kun needs to select the index 1, whose representation is 2, that is, the nearest value to the average.\ninput: 4\n2 5 2 5 output: 0\n\nThe average of frame representations is 3.5.\nIn this case, every frame has the same distance from its representation to the average.\nTherefore, Niwango-kun should select index 0, the smallest index among them.\n\n" }, { "title": "", "content": "Problem Statement\nOne day, Niwango-kun, an employee of Dwango Co. , Ltd. , found an integer sequence (a_1, . . . , a_N) of length N.\nHe is interested in properties of the sequence a.\nFor a nonempty contiguous subsequence a_l, . . . , a_r (1 <= l <= r <= N) of the sequence a, its beauty is defined as a_l + . . . + a_r. Niwango-kun wants to know the maximum possible value of the bitwise AND of the beauties of K nonempty contiguous subsequences among all N(N+1)/2 nonempty contiguous subsequences. (Subsequences may share elements. )\nFind the maximum possible value for him.", "constraint": "2 <= N <= 1000\n1 <= a_i <= 10^9\n1 <= K <= N(N+1)/2\nAll numbers given in input are integers", "input": "Input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n2 5 2 5 output: 12\n\nThere are 10 nonempty contiguous subsequences of a. Let us enumerate them:\n\ncontiguous subsequences starting from the first element: \\{2\\}, \\{2,5\\}, \\{2,5,2\\}, \\{2,5,2,5\\}\ncontiguous subsequences starting from the second element: \\{5\\}, \\{5,2\\}, \\{5,2,5\\}\ncontiguous subsequences starting from the third element: \\{2\\}, \\{2,5\\}\ncontiguous subsequences starting from the fourth element: \\{5\\}\n\n(Note that even if the elements of subsequences are equal, subsequences that have different starting indices are considered to be different.)\nThe maximum possible bitwise AND of the beauties of two different contiguous subsequences is 12.\nThis can be achieved by choosing \\{5,2,5\\} (with beauty 12) and \\{2,5,2,5\\} (with beauty 14).", "input: 8 4\n9 1 8 2 7 5 6 4 output: 32"], "Pid": "p03215", "ProblemText": "Task Description: Problem Statement\nOne day, Niwango-kun, an employee of Dwango Co. , Ltd. , found an integer sequence (a_1, . . . , a_N) of length N.\nHe is interested in properties of the sequence a.\nFor a nonempty contiguous subsequence a_l, . . . , a_r (1 <= l <= r <= N) of the sequence a, its beauty is defined as a_l + . . . + a_r. Niwango-kun wants to know the maximum possible value of the bitwise AND of the beauties of K nonempty contiguous subsequences among all N(N+1)/2 nonempty contiguous subsequences. (Subsequences may share elements. )\nFind the maximum possible value for him.\nTask Constraint: 2 <= N <= 1000\n1 <= a_i <= 10^9\n1 <= K <= N(N+1)/2\nAll numbers given in input are integers\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N\nTask Output: Print the answer.\nTask Samples: input: 4 2\n2 5 2 5 output: 12\n\nThere are 10 nonempty contiguous subsequences of a. Let us enumerate them:\n\ncontiguous subsequences starting from the first element: \\{2\\}, \\{2,5\\}, \\{2,5,2\\}, \\{2,5,2,5\\}\ncontiguous subsequences starting from the second element: \\{5\\}, \\{5,2\\}, \\{5,2,5\\}\ncontiguous subsequences starting from the third element: \\{2\\}, \\{2,5\\}\ncontiguous subsequences starting from the fourth element: \\{5\\}\n\n(Note that even if the elements of subsequences are equal, subsequences that have different starting indices are considered to be different.)\nThe maximum possible bitwise AND of the beauties of two different contiguous subsequences is 12.\nThis can be achieved by choosing \\{5,2,5\\} (with beauty 12) and \\{2,5,2,5\\} (with beauty 14).\ninput: 8 4\n9 1 8 2 7 5 6 4 output: 32\n\n" }, { "title": "", "content": "Problem Statement\nIn Dwango Co. , Ltd. , there is a content distribution system named 'Dwango Media Cluster', and it is called 'DMC' for short.\nThe name 'DMC' sounds cool for Niwango-kun, so he starts to define DMC-ness of a string.\nGiven a string S of length N and an integer k (k >= 3),\nhe defines the k-DMC number of S as the number of triples (a, b, c) of integers that satisfy the following conditions:\n\n0 <= a < b < c <= N - 1\nS[a] = D\nS[b] = M\nS[c] = C\nc-a < k\n\nHere S[a] is the a-th character of the string S. Indexing is zero-based, that is, 0 <= a <= N - 1 holds.\nFor a string S and Q integers k_0, k_1, . . . , k_{Q-1}, calculate the k_i-DMC number of S for each i (0 <= i <= Q-1).", "constraint": "3 <= N <= 10^6\nS consists of uppercase English letters\n1 <= Q <= 75\n3 <= k_i <= N\nAll numbers given in input are integers", "input": "Input is given from Standard Input in the following format:\nN\nS\nQ\nk_{0} k_{1} . . . k_{Q-1}", "output": "Print Q lines.\nThe i-th line should contain the k_i-DMC number of the string S.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 18\nDWANGOMEDIACLUSTER\n1\n18 output: 1\n\n(a,b,c) = (0,6,11) satisfies the conditions.\nStrangely, Dwango Media Cluster does not have so much DMC-ness by his definition.", "input: 18\nDDDDDDMMMMMCCCCCCC\n1\n18 output: 210\n\nThe number of triples can be calculated as 6* 5* 7.", "input: 54\nDIALUPWIDEAREANETWORKGAMINGOPERATIONCORPORATIONLIMITED\n3\n20 30 40 output: 0\n1\n2\n\n(a, b, c) = (0,23,36), (8,23,36) satisfy the conditions except the last one, namely, c-a < k_i.\nBy the way, DWANGO is an acronym for \"Dial-up Wide Area Network Gaming Operation\".", "input: 30\nDMCDMCDMCDMCDMCDMCDMCDMCDMCDMC\n4\n5 10 15 20\n output: 4\n10\n52\n110\n140"], "Pid": "p03216", "ProblemText": "Task Description: Problem Statement\nIn Dwango Co. , Ltd. , there is a content distribution system named 'Dwango Media Cluster', and it is called 'DMC' for short.\nThe name 'DMC' sounds cool for Niwango-kun, so he starts to define DMC-ness of a string.\nGiven a string S of length N and an integer k (k >= 3),\nhe defines the k-DMC number of S as the number of triples (a, b, c) of integers that satisfy the following conditions:\n\n0 <= a < b < c <= N - 1\nS[a] = D\nS[b] = M\nS[c] = C\nc-a < k\n\nHere S[a] is the a-th character of the string S. Indexing is zero-based, that is, 0 <= a <= N - 1 holds.\nFor a string S and Q integers k_0, k_1, . . . , k_{Q-1}, calculate the k_i-DMC number of S for each i (0 <= i <= Q-1).\nTask Constraint: 3 <= N <= 10^6\nS consists of uppercase English letters\n1 <= Q <= 75\n3 <= k_i <= N\nAll numbers given in input are integers\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nQ\nk_{0} k_{1} . . . k_{Q-1}\nTask Output: Print Q lines.\nThe i-th line should contain the k_i-DMC number of the string S.\nTask Samples: input: 18\nDWANGOMEDIACLUSTER\n1\n18 output: 1\n\n(a,b,c) = (0,6,11) satisfies the conditions.\nStrangely, Dwango Media Cluster does not have so much DMC-ness by his definition.\ninput: 18\nDDDDDDMMMMMCCCCCCC\n1\n18 output: 210\n\nThe number of triples can be calculated as 6* 5* 7.\ninput: 54\nDIALUPWIDEAREANETWORKGAMINGOPERATIONCORPORATIONLIMITED\n3\n20 30 40 output: 0\n1\n2\n\n(a, b, c) = (0,23,36), (8,23,36) satisfy the conditions except the last one, namely, c-a < k_i.\nBy the way, DWANGO is an acronym for \"Dial-up Wide Area Network Gaming Operation\".\ninput: 30\nDMCDMCDMCDMCDMCDMCDMCDMCDMCDMC\n4\n5 10 15 20\n output: 4\n10\n52\n110\n140\n\n" }, { "title": "", "content": "Problem Statement\nNiwango-kun, an employee of Dwango Co. , Ltd. , likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.\nNiwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.\nIn an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i, y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).\nHe may perform the following operation arbitrarily many times:\n\nPut an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x, y) \\rightarrow (x+D, y) \\rightarrow (x+D, y+D) \\rightarrow (x, y+D) \\rightarrow (x, y) in this order. Each of the four corners of the square must be on a lattice point.\n\nLet's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.\nFind the minimum scatteredness after he performs arbitrarily many operations. partial scores: Partial Scores\n\n500 points will be awarded for passing the test set satisfying 1 <= D <= 30.", "constraint": "2 <= N <= 10^5\n1 <= D <= 1000\n0 <= x_i, y_i <= 10^9\nGiven coordinates are pairwise distinct\nAll numbers given in input are integers", "input": "Input is given from Standard Input in the following format:\nN D\nx_1 y_1\n:\nx_N y_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n0 0\n1 0\n2 0 output: 1", "input: 19 2\n1 3\n2 3\n0 1\n1 1\n2 1\n3 1\n4 4\n5 4\n6 4\n7 4\n8 4\n8 3\n8 2\n8 1\n8 0\n7 0\n6 0\n5 0\n4 0 output: 4", "input: 8 3\n0 0\n0 3\n3 0\n3 3\n2 2\n2 5\n5 2\n5 5 output: 4"], "Pid": "p03217", "ProblemText": "Task Description: Problem Statement\nNiwango-kun, an employee of Dwango Co. , Ltd. , likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.\nNiwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.\nIn an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i, y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).\nHe may perform the following operation arbitrarily many times:\n\nPut an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x, y) \\rightarrow (x+D, y) \\rightarrow (x+D, y+D) \\rightarrow (x, y+D) \\rightarrow (x, y) in this order. Each of the four corners of the square must be on a lattice point.\n\nLet's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.\nFind the minimum scatteredness after he performs arbitrarily many operations. partial scores: Partial Scores\n\n500 points will be awarded for passing the test set satisfying 1 <= D <= 30.\nTask Constraint: 2 <= N <= 10^5\n1 <= D <= 1000\n0 <= x_i, y_i <= 10^9\nGiven coordinates are pairwise distinct\nAll numbers given in input are integers\nTask Input: Input is given from Standard Input in the following format:\nN D\nx_1 y_1\n:\nx_N y_N\nTask Output: Print the answer.\nTask Samples: input: 3 1\n0 0\n1 0\n2 0 output: 1\ninput: 19 2\n1 3\n2 3\n0 1\n1 1\n2 1\n3 1\n4 4\n5 4\n6 4\n7 4\n8 4\n8 3\n8 2\n8 1\n8 0\n7 0\n6 0\n5 0\n4 0 output: 4\ninput: 8 3\n0 0\n0 3\n3 0\n3 3\n2 2\n2 5\n5 2\n5 5 output: 4\n\n" }, { "title": "", "content": "Problem Statement\nNiwango-kun has \\(N\\) chickens as his pets. The chickens are identified by numbers \\(1\\) to \\(N\\), and the size of the \\(i\\)-th chicken is a positive integer \\(a_i\\).\n\\(N\\) chickens decided to take each other's hand (wing) and form some cycles. The way to make cycles is represented by a permutation \\(p\\) of \\(1, \\ldots , N\\). Chicken \\(i\\) takes chicken \\(p_i\\)'s left hand by its right hand. Chickens may take their own hand.\nLet us define the cycle containing chicken \\(i\\) as the set consisting of chickens \\(p_i, p_{p_i}, \\ldots, p_{\\ddots_i} = i\\). It can be proven that after each chicken takes some chicken's hand, the \\(N\\) chickens can be decomposed into cycles.\nThe beauty \\(f(p)\\) of a way of forming cycles is defined as the product of the size of the smallest chicken in each cycle.\nLet \\(b_i \\ (1 <= i <= N)\\) be the sum of \\(f(p)\\) among all possible permutations \\(p\\) for which \\(i\\) cycles are formed in the procedure above.\nFind the greatest common divisor of \\(b_1, b_2, \\ldots, b_N\\) and print it \\({\\rm mod} \\ 998244353\\).", "constraint": "\\(1 <= N <= 10^5\\)\n\\(1 <= a_i <= 10^9\\)\nAll numbers given in input are integers", "input": "Input is given from Standard Input in the following format:\n\\(N\\)\n\\(a_1\\) \\(a_2\\) \\(\\ldots\\) \\(a_N\\)", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4 3 output: 3\n\nIn this case, \\(N = 2, a = [ 4,3 ]\\).\nFor the permutation \\(p = [ 1,2 ]\\), a cycle of an only chicken \\(1\\) and a cycle of an only chicken \\(2\\) are made, thus \\(f([1,2]) = a_1 * a_2 = 12\\).\nFor the permutation \\(p = [ 2,1 ]\\), a cycle of two chickens \\(1\\) and \\(2\\) is made, and the size of the smallest chicken is \\(a_2 = 3\\), thus \\(f([2,1]) = a_2 = 3\\).\nNow we know \\(b_1 = f([2,1]) = 3, b_2 = f([1,2]) = 12\\), and the greatest common divisor of \\(b_1\\) and \\(b_2\\) is \\(3\\).", "input: 4\n2 5 2 5 output: 2\n\nThere are always \\(N!\\) permutations because chickens of the same size can be distinguished from each other.\nThe following picture illustrates the cycles formed and their beauties when \\(p = (2,1,4,3)\\) and \\(p = (3,4,1,2)\\), respectively."], "Pid": "p03218", "ProblemText": "Task Description: Problem Statement\nNiwango-kun has \\(N\\) chickens as his pets. The chickens are identified by numbers \\(1\\) to \\(N\\), and the size of the \\(i\\)-th chicken is a positive integer \\(a_i\\).\n\\(N\\) chickens decided to take each other's hand (wing) and form some cycles. The way to make cycles is represented by a permutation \\(p\\) of \\(1, \\ldots , N\\). Chicken \\(i\\) takes chicken \\(p_i\\)'s left hand by its right hand. Chickens may take their own hand.\nLet us define the cycle containing chicken \\(i\\) as the set consisting of chickens \\(p_i, p_{p_i}, \\ldots, p_{\\ddots_i} = i\\). It can be proven that after each chicken takes some chicken's hand, the \\(N\\) chickens can be decomposed into cycles.\nThe beauty \\(f(p)\\) of a way of forming cycles is defined as the product of the size of the smallest chicken in each cycle.\nLet \\(b_i \\ (1 <= i <= N)\\) be the sum of \\(f(p)\\) among all possible permutations \\(p\\) for which \\(i\\) cycles are formed in the procedure above.\nFind the greatest common divisor of \\(b_1, b_2, \\ldots, b_N\\) and print it \\({\\rm mod} \\ 998244353\\).\nTask Constraint: \\(1 <= N <= 10^5\\)\n\\(1 <= a_i <= 10^9\\)\nAll numbers given in input are integers\nTask Input: Input is given from Standard Input in the following format:\n\\(N\\)\n\\(a_1\\) \\(a_2\\) \\(\\ldots\\) \\(a_N\\)\nTask Output: Print the answer.\nTask Samples: input: 2\n4 3 output: 3\n\nIn this case, \\(N = 2, a = [ 4,3 ]\\).\nFor the permutation \\(p = [ 1,2 ]\\), a cycle of an only chicken \\(1\\) and a cycle of an only chicken \\(2\\) are made, thus \\(f([1,2]) = a_1 * a_2 = 12\\).\nFor the permutation \\(p = [ 2,1 ]\\), a cycle of two chickens \\(1\\) and \\(2\\) is made, and the size of the smallest chicken is \\(a_2 = 3\\), thus \\(f([2,1]) = a_2 = 3\\).\nNow we know \\(b_1 = f([2,1]) = 3, b_2 = f([1,2]) = 12\\), and the greatest common divisor of \\(b_1\\) and \\(b_2\\) is \\(3\\).\ninput: 4\n2 5 2 5 output: 2\n\nThere are always \\(N!\\) permutations because chickens of the same size can be distinguished from each other.\nThe following picture illustrates the cycles formed and their beauties when \\(p = (2,1,4,3)\\) and \\(p = (3,4,1,2)\\), respectively.\n\n" }, { "title": "", "content": "Problem Statement There is a train going from Station A to Station B that costs X yen (the currency of Japan).\nAlso, there is a bus going from Station B to Station C that costs Y yen.\nJoisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.\nHow much does it cost to travel from Station A to Station C if she uses this ticket?", "constraint": "1 <= X,Y <= 100\nY is an even number.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "If it costs x yen to travel from Station A to Station C, print x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 81 58 output: 110\nThe train fare is 81 yen.\nThe train fare is 58 ⁄ 2=29 yen with the 50% discount.\n\nThus, it costs 110 yen to travel from Station A to Station C.", "input: 4 54 output: 31"], "Pid": "p03219", "ProblemText": "Task Description: Problem Statement There is a train going from Station A to Station B that costs X yen (the currency of Japan).\nAlso, there is a bus going from Station B to Station C that costs Y yen.\nJoisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.\nHow much does it cost to travel from Station A to Station C if she uses this ticket?\nTask Constraint: 1 <= X,Y <= 100\nY is an even number.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: If it costs x yen to travel from Station A to Station C, print x.\nTask Samples: input: 81 58 output: 110\nThe train fare is 81 yen.\nThe train fare is 58 ⁄ 2=29 yen with the 50% discount.\n\nThus, it costs 110 yen to travel from Station A to Station C.\ninput: 4 54 output: 31\n\n" }, { "title": "", "content": "Problem Statement A country decides to build a palace.\nIn this country, the average temperature of a point at an elevation of x meters is T-x * 0.006 degrees Celsius.\nThere are N places proposed for the place. The elevation of Place i is H_i meters.\nAmong them, Princess Joisino orders you to select the place whose average temperature is the closest to A degrees Celsius, and build the palace there.\nPrint the index of the place where the palace should be built.\nIt is guaranteed that the solution is unique.", "constraint": "1 <= N <= 1000\n0 <= T <= 50\n-60 <= A <= T\n0 <= H_i <= 10^5\nAll values in input are integers.\nThe solution is unique.", "input": "Input is given from Standard Input in the following format:\nN\nT A\nH_1 H_2 . . . H_N", "output": "Print the index of the place where the palace should be built.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n12 5\n1000 2000 output: 1\nThe average temperature of Place 1 is 12-1000 * 0.006=6 degrees Celsius.\nThe average temperature of Place 2 is 12-2000 * 0.006=0 degrees Celsius.\n\nThus, the palace should be built at Place 1.", "input: 3\n21 -11\n81234 94124 52141 output: 3"], "Pid": "p03220", "ProblemText": "Task Description: Problem Statement A country decides to build a palace.\nIn this country, the average temperature of a point at an elevation of x meters is T-x * 0.006 degrees Celsius.\nThere are N places proposed for the place. The elevation of Place i is H_i meters.\nAmong them, Princess Joisino orders you to select the place whose average temperature is the closest to A degrees Celsius, and build the palace there.\nPrint the index of the place where the palace should be built.\nIt is guaranteed that the solution is unique.\nTask Constraint: 1 <= N <= 1000\n0 <= T <= 50\n-60 <= A <= T\n0 <= H_i <= 10^5\nAll values in input are integers.\nThe solution is unique.\nTask Input: Input is given from Standard Input in the following format:\nN\nT A\nH_1 H_2 . . . H_N\nTask Output: Print the index of the place where the palace should be built.\nTask Samples: input: 2\n12 5\n1000 2000 output: 1\nThe average temperature of Place 1 is 12-1000 * 0.006=6 degrees Celsius.\nThe average temperature of Place 2 is 12-2000 * 0.006=0 degrees Celsius.\n\nThus, the palace should be built at Place 1.\ninput: 3\n21 -11\n81234 94124 52141 output: 3\n\n" }, { "title": "", "content": "Problem Statement In Republic of Atcoder, there are N prefectures, and a total of M cities that belong to those prefectures.\nCity i is established in year Y_i and belongs to Prefecture P_i.\nYou can assume that there are no multiple cities that are established in the same year.\nIt is decided to allocate a 12-digit ID number to each city.\nIf City i is the x-th established city among the cities that belong to Prefecture i, the first six digits of the ID number of City i is P_i, and the last six digits of the ID number is x.\nHere, if P_i or x (or both) has less than six digits, zeros are added to the left until it has six digits.\nFind the ID numbers for all the cities.\nNote that there can be a prefecture with no cities.", "constraint": "1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= P_i <= N\n1 <= Y_i <= 10^9\nY_i are all different.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nP_1 Y_1\n:\nP_M Y_M", "output": "Print the ID numbers for all the cities, in ascending order of indices (City 1, City 2, . . . ).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n1 32\n2 63\n1 12 output: 000001000002\n000002000001\n000001000001\nAs City 1 is the second established city among the cities that belong to Prefecture 1, its ID number is 000001000002.\nAs City 2 is the first established city among the cities that belong to Prefecture 2, its ID number is 000002000001.\nAs City 3 is the first established city among the cities that belong to Prefecture 1, its ID number is 000001000001.", "input: 2 3\n2 55\n2 77\n2 99 output: 000002000001\n000002000002\n000002000003"], "Pid": "p03221", "ProblemText": "Task Description: Problem Statement In Republic of Atcoder, there are N prefectures, and a total of M cities that belong to those prefectures.\nCity i is established in year Y_i and belongs to Prefecture P_i.\nYou can assume that there are no multiple cities that are established in the same year.\nIt is decided to allocate a 12-digit ID number to each city.\nIf City i is the x-th established city among the cities that belong to Prefecture i, the first six digits of the ID number of City i is P_i, and the last six digits of the ID number is x.\nHere, if P_i or x (or both) has less than six digits, zeros are added to the left until it has six digits.\nFind the ID numbers for all the cities.\nNote that there can be a prefecture with no cities.\nTask Constraint: 1 <= N <= 10^5\n1 <= M <= 10^5\n1 <= P_i <= N\n1 <= Y_i <= 10^9\nY_i are all different.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nP_1 Y_1\n:\nP_M Y_M\nTask Output: Print the ID numbers for all the cities, in ascending order of indices (City 1, City 2, . . . ).\nTask Samples: input: 2 3\n1 32\n2 63\n1 12 output: 000001000002\n000002000001\n000001000001\nAs City 1 is the second established city among the cities that belong to Prefecture 1, its ID number is 000001000002.\nAs City 2 is the first established city among the cities that belong to Prefecture 2, its ID number is 000002000001.\nAs City 3 is the first established city among the cities that belong to Prefecture 1, its ID number is 000001000001.\ninput: 2 3\n2 55\n2 77\n2 99 output: 000002000001\n000002000002\n000002000003\n\n" }, { "title": "", "content": "Problem Statement Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1,2,3, . . . , or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n\nNo two horizontal lines share an endpoint.\nThe two endpoints of each horizontal lines must be at the same height.\nA horizontal line must connect adjacent vertical lines.\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.", "constraint": "H is an integer between 1 and 100 (inclusive).\nW is an integer between 1 and 8 (inclusive).\nK is an integer between 1 and W (inclusive).", "input": "Input is given from Standard Input in the following format:\nH W K", "output": "Print the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 2 output: 1\n\nOnly the following one amidakuji satisfies the condition:", "input: 1 3 1 output: 2\n\nOnly the following two amidakuji satisfy the condition:", "input: 2 3 3 output: 1\n\nOnly the following one amidakuji satisfies the condition:", "input: 2 3 1 output: 5\n\nOnly the following five amidakuji satisfy the condition:", "input: 7 1 1 output: 1\n\nAs there is only one vertical line, we cannot draw any horizontal lines. Thus, there is only one amidakuji that satisfies the condition: the amidakuji with no horizontal lines.", "input: 15 8 5 output: 437760187\n\nBe sure to print the answer modulo 1\\ 000\\ 000\\ 007."], "Pid": "p03222", "ProblemText": "Task Description: Problem Statement Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1,2,3, . . . , or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n\nNo two horizontal lines share an endpoint.\nThe two endpoints of each horizontal lines must be at the same height.\nA horizontal line must connect adjacent vertical lines.\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\nTask Constraint: H is an integer between 1 and 100 (inclusive).\nW is an integer between 1 and 8 (inclusive).\nK is an integer between 1 and W (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nH W K\nTask Output: Print the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\nTask Samples: input: 1 3 2 output: 1\n\nOnly the following one amidakuji satisfies the condition:\ninput: 1 3 1 output: 2\n\nOnly the following two amidakuji satisfy the condition:\ninput: 2 3 3 output: 1\n\nOnly the following one amidakuji satisfies the condition:\ninput: 2 3 1 output: 5\n\nOnly the following five amidakuji satisfy the condition:\ninput: 7 1 1 output: 1\n\nAs there is only one vertical line, we cannot draw any horizontal lines. Thus, there is only one amidakuji that satisfies the condition: the amidakuji with no horizontal lines.\ninput: 15 8 5 output: 437760187\n\nBe sure to print the answer modulo 1\\ 000\\ 000\\ 007.\n\n" }, { "title": "", "content": "Problem Statement You are given N integers; the i-th of them is A_i.\nFind the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.", "constraint": "2 <= N <= 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n6\n8\n1\n2\n3 output: 21\n\nWhen the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.", "input: 6\n3\n1\n4\n1\n5\n9 output: 25", "input: 3\n5\n5\n1 output: 8"], "Pid": "p03223", "ProblemText": "Task Description: Problem Statement You are given N integers; the i-th of them is A_i.\nFind the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.\nTask Constraint: 2 <= N <= 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.\nTask Samples: input: 5\n6\n8\n1\n2\n3 output: 21\n\nWhen the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.\ninput: 6\n3\n1\n4\n1\n5\n9 output: 25\ninput: 3\n5\n5\n1 output: 8\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2, . . . N\\}, (S_1, S_2, . . . , S_k), that satisfies the following conditions:\n\nEach of the integers 1,2, . . . , N is contained in exactly two of the sets S_1, S_2, . . . , S_k.\nAny two of the sets S_1, S_2, . . . , S_k have exactly one element in common.\n\nIf such a tuple exists, construct one such tuple.", "constraint": "1 <= N <= 10^5\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If a tuple of subsets of \\{1,2, . . . N\\} that satisfies the conditions does not exist, print No.\nIf such a tuple exists, print Yes first, then print such subsets in the following format:\nk\n|S_1| S_{1,1} S_{1,2} . . . S_{1, |S_1|}\n:\n|S_k| S_{k, 1} S_{k, 2} . . . S_{k, |S_k|}\n\nwhere S_i={S_{i, 1}, S_{i, 2}, . . . , S_{i, |S_i|}}.\nIf there are multiple such tuples, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: Yes\n3\n2 1 2\n2 3 1\n2 2 3\n\nIt can be seen that (S_1,S_2,S_3)=(\\{1,2\\},\\{3,1\\},\\{2,3\\}) satisfies the conditions.", "input: 4 output: No"], "Pid": "p03224", "ProblemText": "Task Description: Problem Statement You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2, . . . N\\}, (S_1, S_2, . . . , S_k), that satisfies the following conditions:\n\nEach of the integers 1,2, . . . , N is contained in exactly two of the sets S_1, S_2, . . . , S_k.\nAny two of the sets S_1, S_2, . . . , S_k have exactly one element in common.\n\nIf such a tuple exists, construct one such tuple.\nTask Constraint: 1 <= N <= 10^5\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If a tuple of subsets of \\{1,2, . . . N\\} that satisfies the conditions does not exist, print No.\nIf such a tuple exists, print Yes first, then print such subsets in the following format:\nk\n|S_1| S_{1,1} S_{1,2} . . . S_{1, |S_1|}\n:\n|S_k| S_{k, 1} S_{k, 2} . . . S_{k, |S_k|}\n\nwhere S_i={S_{i, 1}, S_{i, 2}, . . . , S_{i, |S_i|}}.\nIf there are multiple such tuples, any of them will be accepted.\nTask Samples: input: 3 output: Yes\n3\n2 1 2\n2 3 1\n2 2 3\n\nIt can be seen that (S_1,S_2,S_3)=(\\{1,2\\},\\{3,1\\},\\{2,3\\}) satisfies the conditions.\ninput: 4 output: No\n\n" }, { "title": "", "content": "Problem Statement There are some coins in the xy-plane.\nThe positions of the coins are represented by a grid of characters with H rows and W columns.\nIf the character at the i-th row and j-th column, s_{ij}, is #, there is one coin at point (i, j); if that character is . , there is no coin at point (i, j). There are no other coins in the xy-plane.\nThere is no coin at point (x, y) where 1<= i<= H, 1<= j<= W does not hold.\nThere is also no coin at point (x, y) where x or y (or both) is not an integer.\nAdditionally, two or more coins never exist at the same point.\nFind the number of triples of different coins that satisfy the following condition:\n\nChoosing any two of the three coins would result in the same Manhattan distance between the points where they exist.\n\nHere, the Manhattan distance between points (x, y) and (x', y') is |x-x'|+|y-y'|.\nTwo triples are considered the same if the only difference between them is the order of the coins.", "constraint": "1 <= H,W <= 300\ns_{ij} is # or ..", "input": "Input is given from Standard Input in the following format:\nH W\ns_{11}. . . s_{1W}\n:\ns_{H1}. . . s_{HW}", "output": "Print the number of triples that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4\n#.##\n.##.\n#...\n..##\n...# output: 3\n\n((1,1),(1,3),(2,2)),((1,1),(2,2),(3,1)) and ((1,3),(3,1),(4,4)) satisfy the condition.", "input: 13 27\n......#.........#.......#..\n#############...#.....###..\n..............#####...##...\n...#######......#...#######\n...#.....#.....###...#...#.\n...#######....#.#.#.#.###.#\n..............#.#.#...#.#..\n#############.#.#.#...###..\n#...........#...#...#######\n#..#######..#...#...#.....#\n#..#.....#..#...#...#.###.#\n#..#######..#...#...#.#.#.#\n#..........##...#...#.##### output: 870"], "Pid": "p03225", "ProblemText": "Task Description: Problem Statement There are some coins in the xy-plane.\nThe positions of the coins are represented by a grid of characters with H rows and W columns.\nIf the character at the i-th row and j-th column, s_{ij}, is #, there is one coin at point (i, j); if that character is . , there is no coin at point (i, j). There are no other coins in the xy-plane.\nThere is no coin at point (x, y) where 1<= i<= H, 1<= j<= W does not hold.\nThere is also no coin at point (x, y) where x or y (or both) is not an integer.\nAdditionally, two or more coins never exist at the same point.\nFind the number of triples of different coins that satisfy the following condition:\n\nChoosing any two of the three coins would result in the same Manhattan distance between the points where they exist.\n\nHere, the Manhattan distance between points (x, y) and (x', y') is |x-x'|+|y-y'|.\nTwo triples are considered the same if the only difference between them is the order of the coins.\nTask Constraint: 1 <= H,W <= 300\ns_{ij} is # or ..\nTask Input: Input is given from Standard Input in the following format:\nH W\ns_{11}. . . s_{1W}\n:\ns_{H1}. . . s_{HW}\nTask Output: Print the number of triples that satisfy the condition.\nTask Samples: input: 5 4\n#.##\n.##.\n#...\n..##\n...# output: 3\n\n((1,1),(1,3),(2,2)),((1,1),(2,2),(3,1)) and ((1,3),(3,1),(4,4)) satisfy the condition.\ninput: 13 27\n......#.........#.......#..\n#############...#.....###..\n..............#####...##...\n...#######......#...#######\n...#.....#.....###...#...#.\n...#######....#.#.#.#.###.#\n..............#.#.#...#.#..\n#############.#.#.#...###..\n#...........#...#...#######\n#..#######..#...#...#.....#\n#..#.....#..#...#...#.###.#\n#..#######..#...#...#.#.#.#\n#..........##...#...#.##### output: 870\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence of N integers: A_1, A_2, . . . , A_N.\nFind the number of permutations p_1, p_2, . . . , p_N of 1,2, . . . , N that can be changed to A_1, A_2, . . . , A_N by performing the following operation some number of times (possibly zero), modulo 998244353:\n\nFor each 1<= i<= N, let q_i=min(p_{i-1}, p_{i}), where p_0=p_N. Replace the sequence p with the sequence q.", "constraint": "1 <= N <= 3 * 10^5\n1 <= A_i <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print the number of the sequences that satisfy the condition, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1\n2\n1 output: 2\n\n(2,3,1) and (3,2,1) satisfy the condition.", "input: 5\n3\n1\n4\n1\n5 output: 0", "input: 8\n4\n4\n4\n1\n1\n1\n2\n2 output: 24", "input: 6\n1\n1\n6\n2\n2\n2 output: 0"], "Pid": "p03226", "ProblemText": "Task Description: Problem Statement You are given a sequence of N integers: A_1, A_2, . . . , A_N.\nFind the number of permutations p_1, p_2, . . . , p_N of 1,2, . . . , N that can be changed to A_1, A_2, . . . , A_N by performing the following operation some number of times (possibly zero), modulo 998244353:\n\nFor each 1<= i<= N, let q_i=min(p_{i-1}, p_{i}), where p_0=p_N. Replace the sequence p with the sequence q.\nTask Constraint: 1 <= N <= 3 * 10^5\n1 <= A_i <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print the number of the sequences that satisfy the condition, modulo 998244353.\nTask Samples: input: 3\n1\n2\n1 output: 2\n\n(2,3,1) and (3,2,1) satisfy the condition.\ninput: 5\n3\n1\n4\n1\n5 output: 0\ninput: 8\n4\n4\n4\n1\n1\n1\n2\n2 output: 24\ninput: 6\n1\n1\n6\n2\n2\n2 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.", "constraint": "The length of S is 2 or 3.\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If the length of S is 2, print S as is; if the length is 3, print S after reversing it.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abc output: cba\n\nAs the length of S is 3, we print it after reversing it.", "input: ac output: ac\n\nAs the length of S is 2, we print it as is."], "Pid": "p03227", "ProblemText": "Task Description: Problem Statement You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.\nTask Constraint: The length of S is 2 or 3.\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If the length of S is 2, print S as is; if the length is 3, print S after reversing it.\nTask Samples: input: abc output: cba\n\nAs the length of S is 3, we print it after reversing it.\ninput: ac output: ac\n\nAs the length of S is 2, we print it as is.\n\n" }, { "title": "", "content": "Problem Statement In the beginning, Takahashi has A cookies, and Aoki has B cookies.\nThey will perform the following operation alternately, starting from Takahashi:\n\nIf the number of cookies in his hand is odd, eat one of those cookies; if the number is even, do nothing. Then, give one-half of the cookies in his hand to the other person.\n\nFind the numbers of cookies Takahashi and Aoki respectively have after performing K operations in total.", "constraint": "1 <= A,B <= 10^9\n1 <= K <= 100\nA,B and K are integers.", "input": "Input is given from Standard Input in the following format:\nA B K", "output": "Print the number of cookies Takahashi has, and the number of cookies Aoki has, in this order, after performing K operations in total.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 2 output: 5 3\n\nThe process will go as follows:\n\nIn the beginning, Takahashi and Aoki have 5 and 4 cookies, respectively.\nTakahashi eats one cookie and gives two cookies to Aoki. They now have 2 and 6 cookies, respectively.\nAoki gives three cookies to Takahashi. They now have 5 and 3 cookies, respectively.", "input: 3 3 3 output: 1 3", "input: 314159265 358979323 84 output: 448759046 224379523"], "Pid": "p03228", "ProblemText": "Task Description: Problem Statement In the beginning, Takahashi has A cookies, and Aoki has B cookies.\nThey will perform the following operation alternately, starting from Takahashi:\n\nIf the number of cookies in his hand is odd, eat one of those cookies; if the number is even, do nothing. Then, give one-half of the cookies in his hand to the other person.\n\nFind the numbers of cookies Takahashi and Aoki respectively have after performing K operations in total.\nTask Constraint: 1 <= A,B <= 10^9\n1 <= K <= 100\nA,B and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B K\nTask Output: Print the number of cookies Takahashi has, and the number of cookies Aoki has, in this order, after performing K operations in total.\nTask Samples: input: 5 4 2 output: 5 3\n\nThe process will go as follows:\n\nIn the beginning, Takahashi and Aoki have 5 and 4 cookies, respectively.\nTakahashi eats one cookie and gives two cookies to Aoki. They now have 2 and 6 cookies, respectively.\nAoki gives three cookies to Takahashi. They now have 5 and 3 cookies, respectively.\ninput: 3 3 3 output: 1 3\ninput: 314159265 358979323 84 output: 448759046 224379523\n\n" }, { "title": "", "content": "Problem Statement You are given N integers; the i-th of them is A_i.\nFind the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.", "constraint": "2 <= N <= 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n6\n8\n1\n2\n3 output: 21\n\nWhen the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.", "input: 6\n3\n1\n4\n1\n5\n9 output: 25", "input: 3\n5\n5\n1 output: 8"], "Pid": "p03229", "ProblemText": "Task Description: Problem Statement You are given N integers; the i-th of them is A_i.\nFind the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.\nTask Constraint: 2 <= N <= 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.\nTask Samples: input: 5\n6\n8\n1\n2\n3 output: 21\n\nWhen the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.\ninput: 6\n3\n1\n4\n1\n5\n9 output: 25\ninput: 3\n5\n5\n1 output: 8\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2, . . . N\\}, (S_1, S_2, . . . , S_k), that satisfies the following conditions:\n\nEach of the integers 1,2, . . . , N is contained in exactly two of the sets S_1, S_2, . . . , S_k.\nAny two of the sets S_1, S_2, . . . , S_k have exactly one element in common.\n\nIf such a tuple exists, construct one such tuple.", "constraint": "1 <= N <= 10^5\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If a tuple of subsets of \\{1,2, . . . N\\} that satisfies the conditions does not exist, print No.\nIf such a tuple exists, print Yes first, then print such subsets in the following format:\nk\n|S_1| S_{1,1} S_{1,2} . . . S_{1, |S_1|}\n:\n|S_k| S_{k, 1} S_{k, 2} . . . S_{k, |S_k|}\n\nwhere S_i={S_{i, 1}, S_{i, 2}, . . . , S_{i, |S_i|}}.\nIf there are multiple such tuples, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: Yes\n3\n2 1 2\n2 3 1\n2 2 3\n\nIt can be seen that (S_1,S_2,S_3)=(\\{1,2\\},\\{3,1\\},\\{2,3\\}) satisfies the conditions.", "input: 4 output: No"], "Pid": "p03230", "ProblemText": "Task Description: Problem Statement You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2, . . . N\\}, (S_1, S_2, . . . , S_k), that satisfies the following conditions:\n\nEach of the integers 1,2, . . . , N is contained in exactly two of the sets S_1, S_2, . . . , S_k.\nAny two of the sets S_1, S_2, . . . , S_k have exactly one element in common.\n\nIf such a tuple exists, construct one such tuple.\nTask Constraint: 1 <= N <= 10^5\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If a tuple of subsets of \\{1,2, . . . N\\} that satisfies the conditions does not exist, print No.\nIf such a tuple exists, print Yes first, then print such subsets in the following format:\nk\n|S_1| S_{1,1} S_{1,2} . . . S_{1, |S_1|}\n:\n|S_k| S_{k, 1} S_{k, 2} . . . S_{k, |S_k|}\n\nwhere S_i={S_{i, 1}, S_{i, 2}, . . . , S_{i, |S_i|}}.\nIf there are multiple such tuples, any of them will be accepted.\nTask Samples: input: 3 output: Yes\n3\n2 1 2\n2 3 1\n2 2 3\n\nIt can be seen that (S_1,S_2,S_3)=(\\{1,2\\},\\{3,1\\},\\{2,3\\}) satisfies the conditions.\ninput: 4 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N and another string T of length M.\nThese strings consist of lowercase English letters.\nA string X is called a good string when the following conditions are all met:\n\nLet L be the length of X. L is divisible by both N and M.\nConcatenating the 1-st, (\\frac{L}{N}+1)-th, (2 * \\frac{L}{N}+1)-th, . . . , ((N-1)*\\frac{L}{N}+1)-th characters of X, without changing the order, results in S.\nConcatenating the 1-st, (\\frac{L}{M}+1)-th, (2 * \\frac{L}{M}+1)-th, . . . , ((M-1)*\\frac{L}{M}+1)-th characters of X, without changing the order, results in T.\n\nDetermine if there exists a good string. If it exists, find the length of the shortest such string.", "constraint": "1 <= N,M <= 10^5\nS and T consist of lowercase English letters.\n|S|=N\n|T|=M", "input": "Input is given from Standard Input in the following format:\nN M\nS\nT", "output": "If a good string does not exist, print -1; if it exists, print the length of the shortest such string.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\nacp\nae output: 6\n\nFor example, the string accept is a good string.\nThere is no good string shorter than this, so the answer is 6.", "input: 6 3\nabcdef\nabc output: -1", "input: 15 9\ndnsusrayukuaiia\ndujrunuma output: 45"], "Pid": "p03231", "ProblemText": "Task Description: Problem Statement You are given a string S of length N and another string T of length M.\nThese strings consist of lowercase English letters.\nA string X is called a good string when the following conditions are all met:\n\nLet L be the length of X. L is divisible by both N and M.\nConcatenating the 1-st, (\\frac{L}{N}+1)-th, (2 * \\frac{L}{N}+1)-th, . . . , ((N-1)*\\frac{L}{N}+1)-th characters of X, without changing the order, results in S.\nConcatenating the 1-st, (\\frac{L}{M}+1)-th, (2 * \\frac{L}{M}+1)-th, . . . , ((M-1)*\\frac{L}{M}+1)-th characters of X, without changing the order, results in T.\n\nDetermine if there exists a good string. If it exists, find the length of the shortest such string.\nTask Constraint: 1 <= N,M <= 10^5\nS and T consist of lowercase English letters.\n|S|=N\n|T|=M\nTask Input: Input is given from Standard Input in the following format:\nN M\nS\nT\nTask Output: If a good string does not exist, print -1; if it exists, print the length of the shortest such string.\nTask Samples: input: 3 2\nacp\nae output: 6\n\nFor example, the string accept is a good string.\nThere is no good string shorter than this, so the answer is 6.\ninput: 6 3\nabcdef\nabc output: -1\ninput: 15 9\ndnsusrayukuaiia\ndujrunuma output: 45\n\n" }, { "title": "", "content": "Problem Statement There are N blocks arranged in a row, numbered 1 to N from left to right.\nEach block has a weight, and the weight of Block i is A_i.\nSnuke will perform the following operation on these blocks N times:\n\nChoose one block that is still not removed, and remove it.\nThe cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself).\nHere, two blocks x and y ( x <= y ) are connected when, for all z ( x <= z <= y ), Block z is still not removed.\n\nThere are N! possible orders in which Snuke removes the blocks.\nFor all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs.\nAs the answer can be extremely large, compute the sum modulo 10^9+7.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2 output: 9\n\nFirst, we will consider the order \"Block 1 -> Block 2\".\nIn the first operation, the cost of the operation is 1+2=3, as Block 1 and 2 are connected.\nIn the second operation, the cost of the operation is 2, as only Block 2 remains.\nThus, the total cost of the two operations for this order is 3+2=5.\nThen, we will consider the order \"Block 2 -> Block 1\".\nIn the first operation, the cost of the operation is 1+2=3, as Block 1 and 2 are connected.\nIn the second operation, the cost of the operation is 1, as only Block 1 remains.\nThus, the total cost of the two operations for this order is 3+1=4.\nTherefore, the answer is 5+4=9.", "input: 4\n1 1 1 1 output: 212", "input: 10\n1 2 4 8 16 32 64 128 256 512 output: 880971923"], "Pid": "p03232", "ProblemText": "Task Description: Problem Statement There are N blocks arranged in a row, numbered 1 to N from left to right.\nEach block has a weight, and the weight of Block i is A_i.\nSnuke will perform the following operation on these blocks N times:\n\nChoose one block that is still not removed, and remove it.\nThe cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself).\nHere, two blocks x and y ( x <= y ) are connected when, for all z ( x <= z <= y ), Block z is still not removed.\n\nThere are N! possible orders in which Snuke removes the blocks.\nFor all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs.\nAs the answer can be extremely large, compute the sum modulo 10^9+7.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.\nTask Samples: input: 2\n1 2 output: 9\n\nFirst, we will consider the order \"Block 1 -> Block 2\".\nIn the first operation, the cost of the operation is 1+2=3, as Block 1 and 2 are connected.\nIn the second operation, the cost of the operation is 2, as only Block 2 remains.\nThus, the total cost of the two operations for this order is 3+2=5.\nThen, we will consider the order \"Block 2 -> Block 1\".\nIn the first operation, the cost of the operation is 1+2=3, as Block 1 and 2 are connected.\nIn the second operation, the cost of the operation is 1, as only Block 1 remains.\nThus, the total cost of the two operations for this order is 3+1=4.\nTherefore, the answer is 5+4=9.\ninput: 4\n1 1 1 1 output: 212\ninput: 10\n1 2 4 8 16 32 64 128 256 512 output: 880971923\n\n" }, { "title": "", "content": "Problem Statement We have a directed weighted graph with N vertices.\nEach vertex has two integers written on it, and the integers written on Vertex i are A_i and B_i.\nIn this graph, there is an edge from Vertex x to Vertex y for all pairs 1 <= x, y <= N, and its weight is {\\rm min}(A_x, B_y).\nWe will consider a directed cycle in this graph that visits every vertex exactly once.\nFind the minimum total weight of the edges in such a cycle.", "constraint": "2 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N", "output": "Print the minimum total weight of the edges in such a cycle.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 5\n4 2\n6 3 output: 7\n\nConsider the cycle 1→3→2→1. The weights of those edges are {\\rm min}(A_1,B_3)=1, {\\rm min}(A_3,B_2)=2 and {\\rm min}(A_2,B_1)=4, for a total of 7.\nAs there is no cycle with a total weight of less than 7, the answer is 7.", "input: 4\n1 5\n2 6\n3 7\n4 8 output: 10", "input: 6\n19 92\n64 64\n78 48\n57 33\n73 6\n95 73 output: 227"], "Pid": "p03233", "ProblemText": "Task Description: Problem Statement We have a directed weighted graph with N vertices.\nEach vertex has two integers written on it, and the integers written on Vertex i are A_i and B_i.\nIn this graph, there is an edge from Vertex x to Vertex y for all pairs 1 <= x, y <= N, and its weight is {\\rm min}(A_x, B_y).\nWe will consider a directed cycle in this graph that visits every vertex exactly once.\nFind the minimum total weight of the edges in such a cycle.\nTask Constraint: 2 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nTask Output: Print the minimum total weight of the edges in such a cycle.\nTask Samples: input: 3\n1 5\n4 2\n6 3 output: 7\n\nConsider the cycle 1→3→2→1. The weights of those edges are {\\rm min}(A_1,B_3)=1, {\\rm min}(A_3,B_2)=2 and {\\rm min}(A_2,B_1)=4, for a total of 7.\nAs there is no cycle with a total weight of less than 7, the answer is 7.\ninput: 4\n1 5\n2 6\n3 7\n4 8 output: 10\ninput: 6\n19 92\n64 64\n78 48\n57 33\n73 6\n95 73 output: 227\n\n" }, { "title": "", "content": "Problem Statement There are 2N points evenly spaced on the circumference of a circle.\nThese points are numbered 1 to 2N in clockwise order, starting from some of them.\nSnuke will divide these points into N pairs, then for each pair, he will draw a line segment connecting the two points.\nAfter the line segments are drawn, two points are connected when one can reach from one of those points to the other by traveling only on the line segments.\nThe number of the connected parts here is the number of the connected components in the graph with 2N vertices, corresponding to the 2N points, where every pair of vertices corresponding to two connected points is connected with an edge.\nSnuke has already decided K of the pairs, and the i-th of them is a pair of Point A_i and Point B_i.\nHe is thinking of trying all possible ways to make the remaining N-K pairs and counting the number of the connected parts for each of those ways.\nFind the sum of those numbers of the connected parts.\nAs the answer can be extremely large, compute the sum modulo 10^9+7.", "constraint": "1 <= N <= 300\n0 <= K <= N\n1 <= A_i,B_i <= 2N\nA_1,\\ A_2,\\ ...\\ A_K,\\ B_1,\\ B_2,\\ ...\\ B_K are all distinct.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 B_1\nA_2 B_2\n:\nA_K B_K", "output": "Print the sum of the numbers of the connected parts for all possible ways to make the remaining N-K pairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 0 output: 5\n\nThere are three ways to draw line segments, as shown below, and the number of the connected parts for these ways are 2,2 and 1, respectively.\nThus, the answer is 2+2+1=5.", "input: 4 2\n5 2\n6 1 output: 6", "input: 20 10\n10 18\n11 17\n14 7\n4 6\n30 28\n19 24\n29 22\n25 32\n38 34\n36 39 output: 27087418"], "Pid": "p03234", "ProblemText": "Task Description: Problem Statement There are 2N points evenly spaced on the circumference of a circle.\nThese points are numbered 1 to 2N in clockwise order, starting from some of them.\nSnuke will divide these points into N pairs, then for each pair, he will draw a line segment connecting the two points.\nAfter the line segments are drawn, two points are connected when one can reach from one of those points to the other by traveling only on the line segments.\nThe number of the connected parts here is the number of the connected components in the graph with 2N vertices, corresponding to the 2N points, where every pair of vertices corresponding to two connected points is connected with an edge.\nSnuke has already decided K of the pairs, and the i-th of them is a pair of Point A_i and Point B_i.\nHe is thinking of trying all possible ways to make the remaining N-K pairs and counting the number of the connected parts for each of those ways.\nFind the sum of those numbers of the connected parts.\nAs the answer can be extremely large, compute the sum modulo 10^9+7.\nTask Constraint: 1 <= N <= 300\n0 <= K <= N\n1 <= A_i,B_i <= 2N\nA_1,\\ A_2,\\ ...\\ A_K,\\ B_1,\\ B_2,\\ ...\\ B_K are all distinct.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 B_1\nA_2 B_2\n:\nA_K B_K\nTask Output: Print the sum of the numbers of the connected parts for all possible ways to make the remaining N-K pairs.\nTask Samples: input: 2 0 output: 5\n\nThere are three ways to draw line segments, as shown below, and the number of the connected parts for these ways are 2,2 and 1, respectively.\nThus, the answer is 2+2+1=5.\ninput: 4 2\n5 2\n6 1 output: 6\ninput: 20 10\n10 18\n11 17\n14 7\n4 6\n30 28\n19 24\n29 22\n25 32\n38 34\n36 39 output: 27087418\n\n" }, { "title": "", "content": "Problem Statement You are given P, a permutation of (1, \\ 2, \\ . . . \\ N).\nA string S of length N consisting of 0 and 1 is a good string when it meets the following criterion:\n\nThe sequences X and Y are constructed as follows:\nFirst, let X and Y be empty sequences.\nFor each i=1, \\ 2, \\ . . . \\ N, in this order, append P_i to the end of X if S_i= 0, and append it to the end of Y if S_i= 1.\nIf X and Y have the same number of high elements, S is a good string.\nHere, the i-th element of a sequence is called high when that element is the largest among the elements from the 1-st to i-th element in the sequence.\n\nDetermine if there exists a good string. If it exists, find the lexicographically smallest such string.", "constraint": "1 <= N <= 2 * 10^5\n1 <= P_i <= N\nP_1,\\ P_2,\\ ...\\ P_N are all distinct.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nP_1 P_2 . . . P_N", "output": "If a good string does not exist, print -1.\nIf it exists, print the lexicographically smallest such string.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n3 1 4 6 2 5 output: 001001\n\nLet S= 001001. Then, X=(3,\\ 1,\\ 6,\\ 2) and Y=(4,\\ 5).\nThe high elements in X is the first and third elements, and the high elements in Y is the first and second elements.\nAs they have the same number of high elements, 001001 is a good string.\nThere is no good string that is lexicographically smaller than this, so the answer is 001001.", "input: 5\n1 2 3 4 5 output: -1", "input: 7\n1 3 2 5 6 4 7 output: 0001101", "input: 30\n1 2 6 3 5 7 9 8 11 12 10 13 16 23 15 18 14 24 22 26 19 21 28 17 4 27 29 25 20 30 output: 000000000001100101010010011101"], "Pid": "p03235", "ProblemText": "Task Description: Problem Statement You are given P, a permutation of (1, \\ 2, \\ . . . \\ N).\nA string S of length N consisting of 0 and 1 is a good string when it meets the following criterion:\n\nThe sequences X and Y are constructed as follows:\nFirst, let X and Y be empty sequences.\nFor each i=1, \\ 2, \\ . . . \\ N, in this order, append P_i to the end of X if S_i= 0, and append it to the end of Y if S_i= 1.\nIf X and Y have the same number of high elements, S is a good string.\nHere, the i-th element of a sequence is called high when that element is the largest among the elements from the 1-st to i-th element in the sequence.\n\nDetermine if there exists a good string. If it exists, find the lexicographically smallest such string.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= P_i <= N\nP_1,\\ P_2,\\ ...\\ P_N are all distinct.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nP_1 P_2 . . . P_N\nTask Output: If a good string does not exist, print -1.\nIf it exists, print the lexicographically smallest such string.\nTask Samples: input: 6\n3 1 4 6 2 5 output: 001001\n\nLet S= 001001. Then, X=(3,\\ 1,\\ 6,\\ 2) and Y=(4,\\ 5).\nThe high elements in X is the first and third elements, and the high elements in Y is the first and second elements.\nAs they have the same number of high elements, 001001 is a good string.\nThere is no good string that is lexicographically smaller than this, so the answer is 001001.\ninput: 5\n1 2 3 4 5 output: -1\ninput: 7\n1 3 2 5 6 4 7 output: 0001101\ninput: 30\n1 2 6 3 5 7 9 8 11 12 10 13 16 23 15 18 14 24 22 26 19 21 28 17 4 27 29 25 20 30 output: 000000000001100101010010011101\n\n" }, { "title": "", "content": "Problem Statement Problem F and F2 are the same problem, but with different constraints and time limits.\nWe have a board divided into N horizontal rows and N vertical columns of square cells.\nThe cell at the i-th row from the top and the j-th column from the left is called Cell (i, j).\nEach cell is either empty or occupied by an obstacle.\nAlso, each empty cell has a digit written on it.\nIf A_{i, j}= 1,2, . . . , or 9, Cell (i, j) is empty and the digit A_{i, j} is written on it.\nIf A_{i, j}= #, Cell (i, j) is occupied by an obstacle.\nCell Y is reachable from cell X when the following conditions are all met:\n\nCells X and Y are different.\nCells X and Y are both empty.\nOne can reach from Cell X to Cell Y by repeatedly moving right or down to an adjacent empty cell.\n\nConsider all pairs of cells (X, Y) such that cell Y is reachable from cell X.\nFind the sum of the products of the digits written on cell X and cell Y for all of those pairs.", "constraint": "1 <= N <= 500\nA_{i,j} is one of the following characters: 1,2, ... 9 and #.", "input": "Input is given from Standard Input in the following format:\nN\nA_{1,1}A_{1,2}. . . A_{1, N}\nA_{2,1}A_{2,2}. . . A_{2, N}\n:\nA_{N, 1}A_{N, 2}. . . A_{N, N}", "output": "Print the sum of the products of the digits written on cell X and cell Y for all pairs (X, Y) such that cell Y is reachable from cell X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n11\n11 output: 5\n\nThere are five pairs of cells (X,Y) such that cell Y is reachable from cell X, as follows:\n\nX=(1,1), Y=(1,2)\nX=(1,1), Y=(2,1)\nX=(1,1), Y=(2,2)\nX=(1,2), Y=(2,2)\nX=(2,1), Y=(2,2)\n\nThe product of the digits written on cell X and cell Y is 1 for all of those pairs, so the answer is 5.", "input: 4\n1111\n11#1\n1#11\n1111 output: 47", "input: 10\n76##63##3#\n8445669721\n75#9542133\n3#285##445\n749632##89\n2458##9515\n5952578#77\n1#3#44196#\n4355#99#1#\n#298#63587 output: 36065", "input: 10\n4177143673\n7#########\n5#1716155#\n6#4#####5#\n2#3#597#6#\n6#9#8#3#5#\n5#2#899#9#\n1#6#####6#\n6#5359657#\n5######### output: 6525"], "Pid": "p03236", "ProblemText": "Task Description: Problem Statement Problem F and F2 are the same problem, but with different constraints and time limits.\nWe have a board divided into N horizontal rows and N vertical columns of square cells.\nThe cell at the i-th row from the top and the j-th column from the left is called Cell (i, j).\nEach cell is either empty or occupied by an obstacle.\nAlso, each empty cell has a digit written on it.\nIf A_{i, j}= 1,2, . . . , or 9, Cell (i, j) is empty and the digit A_{i, j} is written on it.\nIf A_{i, j}= #, Cell (i, j) is occupied by an obstacle.\nCell Y is reachable from cell X when the following conditions are all met:\n\nCells X and Y are different.\nCells X and Y are both empty.\nOne can reach from Cell X to Cell Y by repeatedly moving right or down to an adjacent empty cell.\n\nConsider all pairs of cells (X, Y) such that cell Y is reachable from cell X.\nFind the sum of the products of the digits written on cell X and cell Y for all of those pairs.\nTask Constraint: 1 <= N <= 500\nA_{i,j} is one of the following characters: 1,2, ... 9 and #.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{1,1}A_{1,2}. . . A_{1, N}\nA_{2,1}A_{2,2}. . . A_{2, N}\n:\nA_{N, 1}A_{N, 2}. . . A_{N, N}\nTask Output: Print the sum of the products of the digits written on cell X and cell Y for all pairs (X, Y) such that cell Y is reachable from cell X.\nTask Samples: input: 2\n11\n11 output: 5\n\nThere are five pairs of cells (X,Y) such that cell Y is reachable from cell X, as follows:\n\nX=(1,1), Y=(1,2)\nX=(1,1), Y=(2,1)\nX=(1,1), Y=(2,2)\nX=(1,2), Y=(2,2)\nX=(2,1), Y=(2,2)\n\nThe product of the digits written on cell X and cell Y is 1 for all of those pairs, so the answer is 5.\ninput: 4\n1111\n11#1\n1#11\n1111 output: 47\ninput: 10\n76##63##3#\n8445669721\n75#9542133\n3#285##445\n749632##89\n2458##9515\n5952578#77\n1#3#44196#\n4355#99#1#\n#298#63587 output: 36065\ninput: 10\n4177143673\n7#########\n5#1716155#\n6#4#####5#\n2#3#597#6#\n6#9#8#3#5#\n5#2#899#9#\n1#6#####6#\n6#5359657#\n5######### output: 6525\n\n" }, { "title": "", "content": "Problem Statement Problem F and F2 are the same problem, but with different constraints and time limits.\nWe have a board divided into N horizontal rows and N vertical columns of square cells.\nThe cell at the i-th row from the top and the j-th column from the left is called Cell (i, j).\nEach cell is either empty or occupied by an obstacle.\nAlso, each empty cell has a digit written on it.\nIf A_{i, j}= 1,2, . . . , or 9, Cell (i, j) is empty and the digit A_{i, j} is written on it.\nIf A_{i, j}= #, Cell (i, j) is occupied by an obstacle.\nCell Y is reachable from cell X when the following conditions are all met:\n\nCells X and Y are different.\nCells X and Y are both empty.\nOne can reach from Cell X to Cell Y by repeatedly moving right or down to an adjacent empty cell.\n\nConsider all pairs of cells (X, Y) such that cell Y is reachable from cell X.\nFind the sum of the products of the digits written on cell X and cell Y for all of those pairs.", "constraint": "1 <= N <= 1500\nA_{i,j} is one of the following characters: 1,2, ... 9 and #.", "input": "Input is given from Standard Input in the following format:\nN\nA_{1,1}A_{1,2}. . . A_{1, N}\nA_{2,1}A_{2,2}. . . A_{2, N}\n:\nA_{N, 1}A_{N, 2}. . . A_{N, N}", "output": "Print the sum of the products of the digits written on cell X and cell Y for all pairs (X, Y) such that cell Y is reachable from cell X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n11\n11 output: 5\n\nThere are five pairs of cells (X,Y) such that cell Y is reachable from cell X, as follows:\n\nX=(1,1), Y=(1,2)\nX=(1,1), Y=(2,1)\nX=(1,1), Y=(2,2)\nX=(1,2), Y=(2,2)\nX=(2,1), Y=(2,2)\n\nThe product of the digits written on cell X and cell Y is 1 for all of those pairs, so the answer is 5.", "input: 4\n1111\n11#1\n1#11\n1111 output: 47", "input: 10\n76##63##3#\n8445669721\n75#9542133\n3#285##445\n749632##89\n2458##9515\n5952578#77\n1#3#44196#\n4355#99#1#\n#298#63587 output: 36065", "input: 10\n4177143673\n7#########\n5#1716155#\n6#4#####5#\n2#3#597#6#\n6#9#8#3#5#\n5#2#899#9#\n1#6#####6#\n6#5359657#\n5######### output: 6525"], "Pid": "p03237", "ProblemText": "Task Description: Problem Statement Problem F and F2 are the same problem, but with different constraints and time limits.\nWe have a board divided into N horizontal rows and N vertical columns of square cells.\nThe cell at the i-th row from the top and the j-th column from the left is called Cell (i, j).\nEach cell is either empty or occupied by an obstacle.\nAlso, each empty cell has a digit written on it.\nIf A_{i, j}= 1,2, . . . , or 9, Cell (i, j) is empty and the digit A_{i, j} is written on it.\nIf A_{i, j}= #, Cell (i, j) is occupied by an obstacle.\nCell Y is reachable from cell X when the following conditions are all met:\n\nCells X and Y are different.\nCells X and Y are both empty.\nOne can reach from Cell X to Cell Y by repeatedly moving right or down to an adjacent empty cell.\n\nConsider all pairs of cells (X, Y) such that cell Y is reachable from cell X.\nFind the sum of the products of the digits written on cell X and cell Y for all of those pairs.\nTask Constraint: 1 <= N <= 1500\nA_{i,j} is one of the following characters: 1,2, ... 9 and #.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{1,1}A_{1,2}. . . A_{1, N}\nA_{2,1}A_{2,2}. . . A_{2, N}\n:\nA_{N, 1}A_{N, 2}. . . A_{N, N}\nTask Output: Print the sum of the products of the digits written on cell X and cell Y for all pairs (X, Y) such that cell Y is reachable from cell X.\nTask Samples: input: 2\n11\n11 output: 5\n\nThere are five pairs of cells (X,Y) such that cell Y is reachable from cell X, as follows:\n\nX=(1,1), Y=(1,2)\nX=(1,1), Y=(2,1)\nX=(1,1), Y=(2,2)\nX=(1,2), Y=(2,2)\nX=(2,1), Y=(2,2)\n\nThe product of the digits written on cell X and cell Y is 1 for all of those pairs, so the answer is 5.\ninput: 4\n1111\n11#1\n1#11\n1111 output: 47\ninput: 10\n76##63##3#\n8445669721\n75#9542133\n3#285##445\n749632##89\n2458##9515\n5952578#77\n1#3#44196#\n4355#99#1#\n#298#63587 output: 36065\ninput: 10\n4177143673\n7#########\n5#1716155#\n6#4#####5#\n2#3#597#6#\n6#9#8#3#5#\n5#2#899#9#\n1#6#####6#\n6#5359657#\n5######### output: 6525\n\n" }, { "title": "", "content": "Problem Statement\nIn 2020, At Coder Inc. with an annual sales of more than one billion yen (the currency of Japan) has started a business in programming education.\nOne day, there was an exam where a one-year-old child must write a program that prints Hello World, and a two-year-old child must write a program that receives integers A, B and prints A+B.\nTakahashi, who is taking this exam, suddenly forgets his age.\nHe decides to write a program that first receives his age N (1 or 2) as input, then prints Hello World if N=1, and additionally receives integers A, B and prints A+B if N=2.\nWrite this program for him.", "constraint": "N is 1 or 2.\nA is an integer between 1 and 9 (inclusive).\nB is an integer between 1 and 9 (inclusive).", "input": "Input is given from Standard Input in one of the following formats: \n1\n\n2\nA\nB", "output": "If N=1, print Hello World; if N=2, print A+B.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 output: Hello World\n\nAs N=1, Takahashi is one year old. Thus, we should print Hello World.", "input: 2\n3\n5 output: 8\n\nAs N=2, Takahashi is two years old. Thus, we should print A+B, which is 8 since A=3 and B=5."], "Pid": "p03238", "ProblemText": "Task Description: Problem Statement\nIn 2020, At Coder Inc. with an annual sales of more than one billion yen (the currency of Japan) has started a business in programming education.\nOne day, there was an exam where a one-year-old child must write a program that prints Hello World, and a two-year-old child must write a program that receives integers A, B and prints A+B.\nTakahashi, who is taking this exam, suddenly forgets his age.\nHe decides to write a program that first receives his age N (1 or 2) as input, then prints Hello World if N=1, and additionally receives integers A, B and prints A+B if N=2.\nWrite this program for him.\nTask Constraint: N is 1 or 2.\nA is an integer between 1 and 9 (inclusive).\nB is an integer between 1 and 9 (inclusive).\nTask Input: Input is given from Standard Input in one of the following formats: \n1\n\n2\nA\nB\nTask Output: If N=1, print Hello World; if N=2, print A+B.\nTask Samples: input: 1 output: Hello World\n\nAs N=1, Takahashi is one year old. Thus, we should print Hello World.\ninput: 2\n3\n5 output: 8\n\nAs N=2, Takahashi is two years old. Thus, we should print A+B, which is 8 since A=3 and B=5.\n\n" }, { "title": "", "content": "Problem Statement When Mr. X is away from home, he has decided to use his smartwatch to search the best route to go back home, to participate in ABC.\nYou, the smartwatch, has found N routes to his home.\nIf Mr. X uses the i-th of these routes, he will get home in time t_i at cost c_i.\nFind the smallest cost of a route that takes not longer than time T.", "constraint": "All values in input are integers.\n1 <= N <= 100\n1 <= T <= 1000\n1 <= c_i <= 1000\n1 <= t_i <= 1000\nThe pairs (c_i, t_i) are distinct.", "input": "Input is given from Standard Input in the following format:\nN T\nc_1 t_1\nc_2 t_2\n:\nc_N t_N", "output": "Print the smallest cost of a route that takes not longer than time T.\nIf there is no route that takes not longer than time T, print TLE instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 70\n7 60\n1 80\n4 50 output: 4\nThe first route gets him home at cost 7.\nThe second route takes longer than time T = 70.\nThe third route gets him home at cost 4.\n\nThus, the cost 4 of the third route is the minimum.", "input: 4 3\n1 1000\n2 4\n3 1000\n4 500 output: TLE\n\nThere is no route that takes not longer than time T = 3.", "input: 5 9\n25 8\n5 9\n4 10\n1000 1000\n6 1 output: 5"], "Pid": "p03239", "ProblemText": "Task Description: Problem Statement When Mr. X is away from home, he has decided to use his smartwatch to search the best route to go back home, to participate in ABC.\nYou, the smartwatch, has found N routes to his home.\nIf Mr. X uses the i-th of these routes, he will get home in time t_i at cost c_i.\nFind the smallest cost of a route that takes not longer than time T.\nTask Constraint: All values in input are integers.\n1 <= N <= 100\n1 <= T <= 1000\n1 <= c_i <= 1000\n1 <= t_i <= 1000\nThe pairs (c_i, t_i) are distinct.\nTask Input: Input is given from Standard Input in the following format:\nN T\nc_1 t_1\nc_2 t_2\n:\nc_N t_N\nTask Output: Print the smallest cost of a route that takes not longer than time T.\nIf there is no route that takes not longer than time T, print TLE instead.\nTask Samples: input: 3 70\n7 60\n1 80\n4 50 output: 4\nThe first route gets him home at cost 7.\nThe second route takes longer than time T = 70.\nThe third route gets him home at cost 4.\n\nThus, the cost 4 of the third route is the minimum.\ninput: 4 3\n1 1000\n2 4\n3 1000\n4 500 output: TLE\n\nThere is no route that takes not longer than time T = 3.\ninput: 5 9\n25 8\n5 9\n4 10\n1000 1000\n6 1 output: 5\n\n" }, { "title": "", "content": "Problem Statement\nIn the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of At Coder Inc.\nThe pyramid had center coordinates (C_X, C_Y) and height H. The altitude of coordinates (X, Y) is max(H - |X - C_X| - |Y - C_Y|, 0). \nAoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information: \n\nC_X, C_Y was integers between 0 and 100 (inclusive), and H was an integer not less than 1. \nAdditionally, he obtained N pieces of information. The i-th of them is: \"the altitude of point (x_i, y_i) is h_i. \" \n\nThis was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above.", "constraint": "N is an integer between 1 and 100 (inclusive).\nx_i and y_i are integers between 0 and 100 (inclusive).\nh_i is an integer between 0 and 10^9 (inclusive).\nThe N coordinates (x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N) are all different.\nThe center coordinates and the height of the pyramid can be uniquely identified.", "input": "Input is given from Standard Input in the following format: \nN\nx_1 y_1 h_1\nx_2 y_2 h_2\nx_3 y_3 h_3\n:\nx_N y_N h_N", "output": "Print values C_X, C_Y and H representing the center coordinates and the height of the pyramid in one line, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 3 5\n2 1 5\n1 2 5\n3 2 5 output: 2 2 6\n\nIn this case, the center coordinates and the height can be identified as (2,2) and 6.", "input: 2\n0 0 100\n1 1 98 output: 0 0 100\n\nIn this case, the center coordinates and the height can be identified as (0,0) and 100.\nNote that C_X and C_Y are known to be integers between 0 and 100.", "input: 3\n99 1 191\n100 1 192\n99 0 192 output: 100 0 193\n\nIn this case, the center coordinates and the height can be identified as (100,0) and 193."], "Pid": "p03240", "ProblemText": "Task Description: Problem Statement\nIn the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of At Coder Inc.\nThe pyramid had center coordinates (C_X, C_Y) and height H. The altitude of coordinates (X, Y) is max(H - |X - C_X| - |Y - C_Y|, 0). \nAoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information: \n\nC_X, C_Y was integers between 0 and 100 (inclusive), and H was an integer not less than 1. \nAdditionally, he obtained N pieces of information. The i-th of them is: \"the altitude of point (x_i, y_i) is h_i. \" \n\nThis was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above.\nTask Constraint: N is an integer between 1 and 100 (inclusive).\nx_i and y_i are integers between 0 and 100 (inclusive).\nh_i is an integer between 0 and 10^9 (inclusive).\nThe N coordinates (x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N) are all different.\nThe center coordinates and the height of the pyramid can be uniquely identified.\nTask Input: Input is given from Standard Input in the following format: \nN\nx_1 y_1 h_1\nx_2 y_2 h_2\nx_3 y_3 h_3\n:\nx_N y_N h_N\nTask Output: Print values C_X, C_Y and H representing the center coordinates and the height of the pyramid in one line, with spaces in between.\nTask Samples: input: 4\n2 3 5\n2 1 5\n1 2 5\n3 2 5 output: 2 2 6\n\nIn this case, the center coordinates and the height can be identified as (2,2) and 6.\ninput: 2\n0 0 100\n1 1 98 output: 0 0 100\n\nIn this case, the center coordinates and the height can be identified as (0,0) and 100.\nNote that C_X and C_Y are known to be integers between 0 and 100.\ninput: 3\n99 1 191\n100 1 192\n99 0 192 output: 100 0 193\n\nIn this case, the center coordinates and the height can be identified as (100,0) and 193.\n\n" }, { "title": "", "content": "Problem Statement You are given integers N and M.\nConsider a sequence a of length N consisting of positive integers such that a_1 + a_2 + . . . + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, . . . , a_N.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\nN <= M <= 10^9", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, . . . , a_N that satisfies the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 14 output: 2\n\nConsider the sequence (a_1, a_2, a_3) = (2,4,8). Their greatest common divisor is 2, and this is the maximum value.", "input: 10 123 output: 3", "input: 100000 1000000000 output: 10000"], "Pid": "p03241", "ProblemText": "Task Description: Problem Statement You are given integers N and M.\nConsider a sequence a of length N consisting of positive integers such that a_1 + a_2 + . . . + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, . . . , a_N.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\nN <= M <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, . . . , a_N that satisfies the condition.\nTask Samples: input: 3 14 output: 2\n\nConsider the sequence (a_1, a_2, a_3) = (2,4,8). Their greatest common divisor is 2, and this is the maximum value.\ninput: 10 123 output: 3\ninput: 100000 1000000000 output: 10000\n\n" }, { "title": "", "content": "Problem Statement Cat Snuke is learning to write characters.\nToday, he practiced writing digits 1 and 9, but he did it the other way around.\nYou are given a three-digit integer n written by Snuke.\nPrint the integer obtained by replacing each digit 1 with 9 and each digit 9 with 1 in n.", "constraint": "111 <= n <= 999\nn is an integer consisting of digits 1 and 9.", "input": "Input is given from Standard Input in the following format:\nn", "output": "Print the integer obtained by replacing each occurrence of 1 with 9 and each occurrence of 9 with 1 in n.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 119 output: 991\n\nReplace the 9 in the ones place with 1, the 1 in the tens place with 9 and the 1 in the hundreds place with 9. The answer is 991.", "input: 999 output: 111"], "Pid": "p03242", "ProblemText": "Task Description: Problem Statement Cat Snuke is learning to write characters.\nToday, he practiced writing digits 1 and 9, but he did it the other way around.\nYou are given a three-digit integer n written by Snuke.\nPrint the integer obtained by replacing each digit 1 with 9 and each digit 9 with 1 in n.\nTask Constraint: 111 <= n <= 999\nn is an integer consisting of digits 1 and 9.\nTask Input: Input is given from Standard Input in the following format:\nn\nTask Output: Print the integer obtained by replacing each occurrence of 1 with 9 and each occurrence of 9 with 1 in n.\nTask Samples: input: 119 output: 991\n\nReplace the 9 in the ones place with 1, the 1 in the tens place with 9 and the 1 in the hundreds place with 9. The answer is 991.\ninput: 999 output: 111\n\n" }, { "title": "", "content": "Problem Statement Kurohashi has never participated in At Coder Beginner Contest (ABC).\nThe next ABC to be held is ABC N (the N-th ABC ever held).\nKurohashi wants to make his debut in some ABC x such that all the digits of x in base ten are the same.\nWhat is the earliest ABC where Kurohashi can make his debut?", "constraint": "100 <= N <= 999\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If the earliest ABC where Kurohashi can make his debut is ABC n, print n.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 111 output: 111\n\nThe next ABC to be held is ABC 111, where Kurohashi can make his debut.", "input: 112 output: 222\n\nThe next ABC to be held is ABC 112, which means Kurohashi can no longer participate in ABC 111.\nAmong the ABCs where Kurohashi can make his debut, the earliest one is ABC 222.", "input: 750 output: 777"], "Pid": "p03243", "ProblemText": "Task Description: Problem Statement Kurohashi has never participated in At Coder Beginner Contest (ABC).\nThe next ABC to be held is ABC N (the N-th ABC ever held).\nKurohashi wants to make his debut in some ABC x such that all the digits of x in base ten are the same.\nWhat is the earliest ABC where Kurohashi can make his debut?\nTask Constraint: 100 <= N <= 999\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If the earliest ABC where Kurohashi can make his debut is ABC n, print n.\nTask Samples: input: 111 output: 111\n\nThe next ABC to be held is ABC 111, where Kurohashi can make his debut.\ninput: 112 output: 222\n\nThe next ABC to be held is ABC 112, which means Kurohashi can no longer participate in ABC 111.\nAmong the ABCs where Kurohashi can make his debut, the earliest one is ABC 222.\ninput: 750 output: 777\n\n" }, { "title": "", "content": "Problem Statement A sequence a_1, a_2, . . . , a_n is said to be /\\/\\/\\/ when the following conditions are satisfied:\n\nFor each i = 1,2, . . . , n-2, a_i = a_{i+2}.\nExactly two different numbers appear in the sequence.\n\nYou are given a sequence v_1, v_2, . . . , v_n whose length is even.\nWe would like to make this sequence /\\/\\/\\/ by replacing some of its elements.\nFind the minimum number of elements that needs to be replaced.", "constraint": "2 <= n <= 10^5\nn is even.\n1 <= v_i <= 10^5\nv_i is an integer.", "input": "Input is given from Standard Input in the following format:\nn\nv_1 v_2 . . . v_n", "output": "Print the minimum number of elements that needs to be replaced.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 1 3 2 output: 1\n\nThe sequence 3,1,3,2 is not /\\/\\/\\/, but we can make it /\\/\\/\\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.", "input: 6\n105 119 105 119 105 119 output: 0\n\nThe sequence 105,119,105,119,105,119 is /\\/\\/\\/.", "input: 4\n1 1 1 1 output: 2\n\nThe elements of the sequence 1,1,1,1 are all the same, so it is not /\\/\\/\\/."], "Pid": "p03244", "ProblemText": "Task Description: Problem Statement A sequence a_1, a_2, . . . , a_n is said to be /\\/\\/\\/ when the following conditions are satisfied:\n\nFor each i = 1,2, . . . , n-2, a_i = a_{i+2}.\nExactly two different numbers appear in the sequence.\n\nYou are given a sequence v_1, v_2, . . . , v_n whose length is even.\nWe would like to make this sequence /\\/\\/\\/ by replacing some of its elements.\nFind the minimum number of elements that needs to be replaced.\nTask Constraint: 2 <= n <= 10^5\nn is even.\n1 <= v_i <= 10^5\nv_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nn\nv_1 v_2 . . . v_n\nTask Output: Print the minimum number of elements that needs to be replaced.\nTask Samples: input: 4\n3 1 3 2 output: 1\n\nThe sequence 3,1,3,2 is not /\\/\\/\\/, but we can make it /\\/\\/\\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.\ninput: 6\n105 119 105 119 105 119 output: 0\n\nThe sequence 105,119,105,119,105,119 is /\\/\\/\\/.\ninput: 4\n1 1 1 1 output: 2\n\nThe elements of the sequence 1,1,1,1 are all the same, so it is not /\\/\\/\\/.\n\n" }, { "title": "", "content": "Problem Statement Snuke is introducing a robot arm with the following properties to his factory:\n\nThe robot arm consists of m sections and m+1 joints. The sections are numbered 1,2, . . . , m, and the joints are numbered 0,1, . . . , m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.\nFor each section, its mode can be specified individually. There are four modes: L, R, D and U. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):\n(x_0, y_0) = (0,0).\nIf the mode of Section i is L, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).\nIf the mode of Section i is R, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).\nIf the mode of Section i is D, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).\nIf the mode of Section i is U, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).\n\nSnuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), . . . , (X_N, Y_N) by properly specifying the modes of the sections.\nIs this possible?\nIf so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j). partial score: Partial Score\nIn the test cases worth 300 points, -10 <= X_i <= 10 and -10 <= Y_i <= 10 hold.", "constraint": "All values in input are integers.\n1 <= N <= 1000\n-10^9 <= X_i <= 10^9\n-10^9 <= Y_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nX_1 Y_1\nX_2 Y_2\n:\nX_N Y_N", "output": "If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print -1.\nm\nd_1 d_2 . . . d_m\nw_1\nw_2\n:\nw_N\n\nm and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means.\nHere, 1 <= m <= 40 and 1 <= d_i <= 10^{12} must hold. Also, m and d_i must all be integers.\nw_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j).\nThe i-th character of w_j should be one of the letters L, R, D and U, representing the mode of Section i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-1 0\n0 3\n2 -1 output: 2\n1 2\nRL\nUU\nDR\n\nIn the given way to bring Joint m of the robot arm to each (X_j, Y_j), the positions of the joints will be as follows:\n\nTo (X_1, Y_1) = (-1,0): First, the position of Joint 0 is (x_0, y_0) = (0,0). As the mode of Section 1 is R, the position of Joint 1 is (x_1, y_1) = (1,0). Then, as the mode of Section 2 is L, the position of Joint 2 is (x_2, y_2) = (-1,0).\nTo (X_2, Y_2) = (0,3): (x_0, y_0) = (0,0), (x_1, y_1) = (0,1), (x_2, y_2) = (0,3).\nTo (X_3, Y_3) = (2, -1): (x_0, y_0) = (0,0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1).", "input: 5\n0 0\n1 0\n2 0\n3 0\n4 0 output: -1", "input: 2\n1 1\n1 1 output: 2\n1 1\nRU\nUR\n\nThere may be duplicated points among (X_j, Y_j).", "input: 3\n-7 -3\n7 3\n-3 -7 output: 5\n3 1 4 1 5\nLRDUL\nRDULR\nDULRD"], "Pid": "p03245", "ProblemText": "Task Description: Problem Statement Snuke is introducing a robot arm with the following properties to his factory:\n\nThe robot arm consists of m sections and m+1 joints. The sections are numbered 1,2, . . . , m, and the joints are numbered 0,1, . . . , m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.\nFor each section, its mode can be specified individually. There are four modes: L, R, D and U. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):\n(x_0, y_0) = (0,0).\nIf the mode of Section i is L, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).\nIf the mode of Section i is R, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).\nIf the mode of Section i is D, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).\nIf the mode of Section i is U, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).\n\nSnuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), . . . , (X_N, Y_N) by properly specifying the modes of the sections.\nIs this possible?\nIf so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j). partial score: Partial Score\nIn the test cases worth 300 points, -10 <= X_i <= 10 and -10 <= Y_i <= 10 hold.\nTask Constraint: All values in input are integers.\n1 <= N <= 1000\n-10^9 <= X_i <= 10^9\n-10^9 <= Y_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 Y_1\nX_2 Y_2\n:\nX_N Y_N\nTask Output: If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print -1.\nm\nd_1 d_2 . . . d_m\nw_1\nw_2\n:\nw_N\n\nm and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means.\nHere, 1 <= m <= 40 and 1 <= d_i <= 10^{12} must hold. Also, m and d_i must all be integers.\nw_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j).\nThe i-th character of w_j should be one of the letters L, R, D and U, representing the mode of Section i.\nTask Samples: input: 3\n-1 0\n0 3\n2 -1 output: 2\n1 2\nRL\nUU\nDR\n\nIn the given way to bring Joint m of the robot arm to each (X_j, Y_j), the positions of the joints will be as follows:\n\nTo (X_1, Y_1) = (-1,0): First, the position of Joint 0 is (x_0, y_0) = (0,0). As the mode of Section 1 is R, the position of Joint 1 is (x_1, y_1) = (1,0). Then, as the mode of Section 2 is L, the position of Joint 2 is (x_2, y_2) = (-1,0).\nTo (X_2, Y_2) = (0,3): (x_0, y_0) = (0,0), (x_1, y_1) = (0,1), (x_2, y_2) = (0,3).\nTo (X_3, Y_3) = (2, -1): (x_0, y_0) = (0,0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1).\ninput: 5\n0 0\n1 0\n2 0\n3 0\n4 0 output: -1\ninput: 2\n1 1\n1 1 output: 2\n1 1\nRU\nUR\n\nThere may be duplicated points among (X_j, Y_j).\ninput: 3\n-7 -3\n7 3\n-3 -7 output: 5\n3 1 4 1 5\nLRDUL\nRDULR\nDULRD\n\n" }, { "title": "", "content": "Problem Statement A sequence a_1, a_2, . . . , a_n is said to be /\\/\\/\\/ when the following conditions are satisfied:\n\nFor each i = 1,2, . . . , n-2, a_i = a_{i+2}.\nExactly two different numbers appear in the sequence.\n\nYou are given a sequence v_1, v_2, . . . , v_n whose length is even.\nWe would like to make this sequence /\\/\\/\\/ by replacing some of its elements.\nFind the minimum number of elements that needs to be replaced.", "constraint": "2 <= n <= 10^5\nn is even.\n1 <= v_i <= 10^5\nv_i is an integer.", "input": "Input is given from Standard Input in the following format:\nn\nv_1 v_2 . . . v_n", "output": "Print the minimum number of elements that needs to be replaced.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 1 3 2 output: 1\n\nThe sequence 3,1,3,2 is not /\\/\\/\\/, but we can make it /\\/\\/\\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.", "input: 6\n105 119 105 119 105 119 output: 0\n\nThe sequence 105,119,105,119,105,119 is /\\/\\/\\/.", "input: 4\n1 1 1 1 output: 2\n\nThe elements of the sequence 1,1,1,1 are all the same, so it is not /\\/\\/\\/."], "Pid": "p03246", "ProblemText": "Task Description: Problem Statement A sequence a_1, a_2, . . . , a_n is said to be /\\/\\/\\/ when the following conditions are satisfied:\n\nFor each i = 1,2, . . . , n-2, a_i = a_{i+2}.\nExactly two different numbers appear in the sequence.\n\nYou are given a sequence v_1, v_2, . . . , v_n whose length is even.\nWe would like to make this sequence /\\/\\/\\/ by replacing some of its elements.\nFind the minimum number of elements that needs to be replaced.\nTask Constraint: 2 <= n <= 10^5\nn is even.\n1 <= v_i <= 10^5\nv_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nn\nv_1 v_2 . . . v_n\nTask Output: Print the minimum number of elements that needs to be replaced.\nTask Samples: input: 4\n3 1 3 2 output: 1\n\nThe sequence 3,1,3,2 is not /\\/\\/\\/, but we can make it /\\/\\/\\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.\ninput: 6\n105 119 105 119 105 119 output: 0\n\nThe sequence 105,119,105,119,105,119 is /\\/\\/\\/.\ninput: 4\n1 1 1 1 output: 2\n\nThe elements of the sequence 1,1,1,1 are all the same, so it is not /\\/\\/\\/.\n\n" }, { "title": "", "content": "Problem Statement Snuke is introducing a robot arm with the following properties to his factory:\n\nThe robot arm consists of m sections and m+1 joints. The sections are numbered 1,2, . . . , m, and the joints are numbered 0,1, . . . , m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.\nFor each section, its mode can be specified individually. There are four modes: L, R, D and U. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):\n(x_0, y_0) = (0,0).\nIf the mode of Section i is L, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).\nIf the mode of Section i is R, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).\nIf the mode of Section i is D, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).\nIf the mode of Section i is U, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).\n\nSnuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), . . . , (X_N, Y_N) by properly specifying the modes of the sections.\nIs this possible?\nIf so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j). partial score: Partial Score\nIn the test cases worth 300 points, -10 <= X_i <= 10 and -10 <= Y_i <= 10 hold.", "constraint": "All values in input are integers.\n1 <= N <= 1000\n-10^9 <= X_i <= 10^9\n-10^9 <= Y_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nX_1 Y_1\nX_2 Y_2\n:\nX_N Y_N", "output": "If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print -1.\nm\nd_1 d_2 . . . d_m\nw_1\nw_2\n:\nw_N\n\nm and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means.\nHere, 1 <= m <= 40 and 1 <= d_i <= 10^{12} must hold. Also, m and d_i must all be integers.\nw_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j).\nThe i-th character of w_j should be one of the letters L, R, D and U, representing the mode of Section i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-1 0\n0 3\n2 -1 output: 2\n1 2\nRL\nUU\nDR\n\nIn the given way to bring Joint m of the robot arm to each (X_j, Y_j), the positions of the joints will be as follows:\n\nTo (X_1, Y_1) = (-1,0): First, the position of Joint 0 is (x_0, y_0) = (0,0). As the mode of Section 1 is R, the position of Joint 1 is (x_1, y_1) = (1,0). Then, as the mode of Section 2 is L, the position of Joint 2 is (x_2, y_2) = (-1,0).\nTo (X_2, Y_2) = (0,3): (x_0, y_0) = (0,0), (x_1, y_1) = (0,1), (x_2, y_2) = (0,3).\nTo (X_3, Y_3) = (2, -1): (x_0, y_0) = (0,0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1).", "input: 5\n0 0\n1 0\n2 0\n3 0\n4 0 output: -1", "input: 2\n1 1\n1 1 output: 2\n1 1\nRU\nUR\n\nThere may be duplicated points among (X_j, Y_j).", "input: 3\n-7 -3\n7 3\n-3 -7 output: 5\n3 1 4 1 5\nLRDUL\nRDULR\nDULRD"], "Pid": "p03247", "ProblemText": "Task Description: Problem Statement Snuke is introducing a robot arm with the following properties to his factory:\n\nThe robot arm consists of m sections and m+1 joints. The sections are numbered 1,2, . . . , m, and the joints are numbered 0,1, . . . , m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.\nFor each section, its mode can be specified individually. There are four modes: L, R, D and U. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):\n(x_0, y_0) = (0,0).\nIf the mode of Section i is L, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).\nIf the mode of Section i is R, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).\nIf the mode of Section i is D, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).\nIf the mode of Section i is U, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).\n\nSnuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), . . . , (X_N, Y_N) by properly specifying the modes of the sections.\nIs this possible?\nIf so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j). partial score: Partial Score\nIn the test cases worth 300 points, -10 <= X_i <= 10 and -10 <= Y_i <= 10 hold.\nTask Constraint: All values in input are integers.\n1 <= N <= 1000\n-10^9 <= X_i <= 10^9\n-10^9 <= Y_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 Y_1\nX_2 Y_2\n:\nX_N Y_N\nTask Output: If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print -1.\nm\nd_1 d_2 . . . d_m\nw_1\nw_2\n:\nw_N\n\nm and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means.\nHere, 1 <= m <= 40 and 1 <= d_i <= 10^{12} must hold. Also, m and d_i must all be integers.\nw_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j).\nThe i-th character of w_j should be one of the letters L, R, D and U, representing the mode of Section i.\nTask Samples: input: 3\n-1 0\n0 3\n2 -1 output: 2\n1 2\nRL\nUU\nDR\n\nIn the given way to bring Joint m of the robot arm to each (X_j, Y_j), the positions of the joints will be as follows:\n\nTo (X_1, Y_1) = (-1,0): First, the position of Joint 0 is (x_0, y_0) = (0,0). As the mode of Section 1 is R, the position of Joint 1 is (x_1, y_1) = (1,0). Then, as the mode of Section 2 is L, the position of Joint 2 is (x_2, y_2) = (-1,0).\nTo (X_2, Y_2) = (0,3): (x_0, y_0) = (0,0), (x_1, y_1) = (0,1), (x_2, y_2) = (0,3).\nTo (X_3, Y_3) = (2, -1): (x_0, y_0) = (0,0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1).\ninput: 5\n0 0\n1 0\n2 0\n3 0\n4 0 output: -1\ninput: 2\n1 1\n1 1 output: 2\n1 1\nRU\nUR\n\nThere may be duplicated points among (X_j, Y_j).\ninput: 3\n-7 -3\n7 3\n-3 -7 output: 5\n3 1 4 1 5\nLRDUL\nRDULR\nDULRD\n\n" }, { "title": "", "content": "Problem Statement You are given a string s of length n.\nDoes a tree with n vertices that satisfies the following conditions exist?\n\nThe vertices are numbered 1,2, . . . , n.\nThe edges are numbered 1,2, . . . , n-1, and Edge i connects Vertex u_i and v_i.\nIf the i-th character in s is 1, we can have a connected component of size i by removing one edge from the tree.\nIf the i-th character in s is 0, we cannot have a connected component of size i by removing any one edge from the tree.\n\nIf such a tree exists, construct one such tree.", "constraint": "2 <= n <= 10^5\ns is a string of length n consisting of 0 and 1.", "input": "Input is given from Standard Input in the following format:\ns", "output": "If a tree with n vertices that satisfies the conditions does not exist, print -1.\nIf a tree with n vertices that satisfies the conditions exist, print n-1 lines.\nThe i-th line should contain u_i and v_i with a space in between.\nIf there are multiple trees that satisfy the conditions, any such tree will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1111 output: -1\n\nIt is impossible to have a connected component of size n after removing one edge from a tree with n vertices.", "input: 1110 output: 1 2\n2 3\n3 4\n\nIf Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.", "input: 1010 output: 1 2\n1 3\n1 4\n\nRemoving any edge will result in a connected component of size 1 and another of size 3."], "Pid": "p03248", "ProblemText": "Task Description: Problem Statement You are given a string s of length n.\nDoes a tree with n vertices that satisfies the following conditions exist?\n\nThe vertices are numbered 1,2, . . . , n.\nThe edges are numbered 1,2, . . . , n-1, and Edge i connects Vertex u_i and v_i.\nIf the i-th character in s is 1, we can have a connected component of size i by removing one edge from the tree.\nIf the i-th character in s is 0, we cannot have a connected component of size i by removing any one edge from the tree.\n\nIf such a tree exists, construct one such tree.\nTask Constraint: 2 <= n <= 10^5\ns is a string of length n consisting of 0 and 1.\nTask Input: Input is given from Standard Input in the following format:\ns\nTask Output: If a tree with n vertices that satisfies the conditions does not exist, print -1.\nIf a tree with n vertices that satisfies the conditions exist, print n-1 lines.\nThe i-th line should contain u_i and v_i with a space in between.\nIf there are multiple trees that satisfy the conditions, any such tree will be accepted.\nTask Samples: input: 1111 output: -1\n\nIt is impossible to have a connected component of size n after removing one edge from a tree with n vertices.\ninput: 1110 output: 1 2\n2 3\n3 4\n\nIf Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.\ninput: 1010 output: 1 2\n1 3\n1 4\n\nRemoving any edge will result in a connected component of size 1 and another of size 3.\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence D_1, D_2, . . . , D_N of length N.\nThe values of D_i are all distinct.\nDoes a tree with N vertices that satisfies the following conditions exist?\n\nThe vertices are numbered 1,2, . . . , N.\nThe edges are numbered 1,2, . . . , N-1, and Edge i connects Vertex u_i and v_i.\nFor each vertex i, the sum of the distances from i to the other vertices is D_i, assuming that the length of each edge is 1.\n\nIf such a tree exists, construct one such tree.", "constraint": "2 <= N <= 100000\n1 <= D_i <= 10^{12}\nD_i are all distinct.", "input": "Input is given from Standard Input in the following format:\nN\nD_1\nD_2\n:\nD_N", "output": "If a tree with n vertices that satisfies the conditions does not exist, print -1.\nIf a tree with n vertices that satisfies the conditions exist, print n-1 lines.\nThe i-th line should contain u_i and v_i with a space in between.\nIf there are multiple trees that satisfy the conditions, any such tree will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n10\n15\n13\n18\n11\n14\n19 output: 1 2\n1 3\n1 5\n3 4\n5 6\n6 7\n\nThe tree shown below satisfies the conditions.", "input: 2\n1\n2 output: -1", "input: 15\n57\n62\n47\n45\n42\n74\n90\n75\n54\n50\n66\n63\n77\n87\n51 output: 1 10\n1 11\n2 8\n2 15\n3 5\n3 9\n4 5\n4 10\n5 15\n6 12\n6 14\n7 13\n9 12\n11 13"], "Pid": "p03249", "ProblemText": "Task Description: Problem Statement You are given a sequence D_1, D_2, . . . , D_N of length N.\nThe values of D_i are all distinct.\nDoes a tree with N vertices that satisfies the following conditions exist?\n\nThe vertices are numbered 1,2, . . . , N.\nThe edges are numbered 1,2, . . . , N-1, and Edge i connects Vertex u_i and v_i.\nFor each vertex i, the sum of the distances from i to the other vertices is D_i, assuming that the length of each edge is 1.\n\nIf such a tree exists, construct one such tree.\nTask Constraint: 2 <= N <= 100000\n1 <= D_i <= 10^{12}\nD_i are all distinct.\nTask Input: Input is given from Standard Input in the following format:\nN\nD_1\nD_2\n:\nD_N\nTask Output: If a tree with n vertices that satisfies the conditions does not exist, print -1.\nIf a tree with n vertices that satisfies the conditions exist, print n-1 lines.\nThe i-th line should contain u_i and v_i with a space in between.\nIf there are multiple trees that satisfy the conditions, any such tree will be accepted.\nTask Samples: input: 7\n10\n15\n13\n18\n11\n14\n19 output: 1 2\n1 3\n1 5\n3 4\n5 6\n6 7\n\nThe tree shown below satisfies the conditions.\ninput: 2\n1\n2 output: -1\ninput: 15\n57\n62\n47\n45\n42\n74\n90\n75\n54\n50\n66\n63\n77\n87\n51 output: 1 10\n1 11\n2 8\n2 15\n3 5\n3 9\n4 5\n4 10\n5 15\n6 12\n6 14\n7 13\n9 12\n11 13\n\n" }, { "title": "", "content": "Problem Statement You have decided to give an allowance to your child depending on the outcome of the game that he will play now.\nThe game is played as follows:\n\nThere are three \"integer panels\", each with a digit between 1 and 9 (inclusive) printed on it, and one \"operator panel\" with a + printed on it.\nThe player should construct a formula of the form X + Y, by arranging the four panels from left to right. (The operator panel should not be placed at either end of the formula. )\nThen, the amount of the allowance will be equal to the resulting value of the formula.\n\nGiven the values A, B and C printed on the integer panels used in the game, find the maximum possible amount of the allowance.", "constraint": "All values in input are integers.\n1 <= A, B, C <= 9", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "Print the maximum possible amount of the allowance.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 5 2 output: 53\n\nThe amount of the allowance will be 53 when the panels are arranged as 52+1, and this is the maximum possible amount.", "input: 9 9 9 output: 108", "input: 6 6 7 output: 82"], "Pid": "p03250", "ProblemText": "Task Description: Problem Statement You have decided to give an allowance to your child depending on the outcome of the game that he will play now.\nThe game is played as follows:\n\nThere are three \"integer panels\", each with a digit between 1 and 9 (inclusive) printed on it, and one \"operator panel\" with a + printed on it.\nThe player should construct a formula of the form X + Y, by arranging the four panels from left to right. (The operator panel should not be placed at either end of the formula. )\nThen, the amount of the allowance will be equal to the resulting value of the formula.\n\nGiven the values A, B and C printed on the integer panels used in the game, find the maximum possible amount of the allowance.\nTask Constraint: All values in input are integers.\n1 <= A, B, C <= 9\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: Print the maximum possible amount of the allowance.\nTask Samples: input: 1 5 2 output: 53\n\nThe amount of the allowance will be 53 when the panels are arranged as 52+1, and this is the maximum possible amount.\ninput: 9 9 9 output: 108\ninput: 6 6 7 output: 82\n\n" }, { "title": "", "content": "Problem Statement Our world is one-dimensional, and ruled by two empires called Empire A and Empire B.\nThe capital of Empire A is located at coordinate X, and that of Empire B is located at coordinate Y.\nOne day, Empire A becomes inclined to put the cities at coordinates x_1, x_2, . . . , x_N under its control, and Empire B becomes inclined to put the cities at coordinates y_1, y_2, . . . , y_M under its control.\nIf there exists an integer Z that satisfies all of the following three conditions, they will come to an agreement, but otherwise war will break out.\n\nX < Z <= Y\nx_1, x_2, . . . , x_N < Z\ny_1, y_2, . . . , y_M >= Z\n\nDetermine if war will break out.", "constraint": "All values in input are integers.\n1 <= N, M <= 100\n-100 <= X < Y <= 100\n-100 <= x_i, y_i <= 100\nx_1, x_2, ..., x_N \\neq X\nx_i are all different.\ny_1, y_2, ..., y_M \\neq Y\ny_i are all different.", "input": "Input is given from Standard Input in the following format:\nN M X Y\nx_1 x_2 . . . x_N\ny_1 y_2 . . . y_M", "output": "If war will break out, print War; otherwise, print No War.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 10 20\n8 15 13\n16 22 output: No War\n\nThe choice Z = 16 satisfies all of the three conditions as follows, thus they will come to an agreement.\n\nX = 10 < 16 <= 20 = Y\n8,15,13 < 16\n16,22 >= 16", "input: 4 2 -48 -1\n-20 -35 -91 -23\n-22 66 output: War", "input: 5 3 6 8\n-10 3 1 5 -100\n100 6 14 output: War"], "Pid": "p03251", "ProblemText": "Task Description: Problem Statement Our world is one-dimensional, and ruled by two empires called Empire A and Empire B.\nThe capital of Empire A is located at coordinate X, and that of Empire B is located at coordinate Y.\nOne day, Empire A becomes inclined to put the cities at coordinates x_1, x_2, . . . , x_N under its control, and Empire B becomes inclined to put the cities at coordinates y_1, y_2, . . . , y_M under its control.\nIf there exists an integer Z that satisfies all of the following three conditions, they will come to an agreement, but otherwise war will break out.\n\nX < Z <= Y\nx_1, x_2, . . . , x_N < Z\ny_1, y_2, . . . , y_M >= Z\n\nDetermine if war will break out.\nTask Constraint: All values in input are integers.\n1 <= N, M <= 100\n-100 <= X < Y <= 100\n-100 <= x_i, y_i <= 100\nx_1, x_2, ..., x_N \\neq X\nx_i are all different.\ny_1, y_2, ..., y_M \\neq Y\ny_i are all different.\nTask Input: Input is given from Standard Input in the following format:\nN M X Y\nx_1 x_2 . . . x_N\ny_1 y_2 . . . y_M\nTask Output: If war will break out, print War; otherwise, print No War.\nTask Samples: input: 3 2 10 20\n8 15 13\n16 22 output: No War\n\nThe choice Z = 16 satisfies all of the three conditions as follows, thus they will come to an agreement.\n\nX = 10 < 16 <= 20 = Y\n8,15,13 < 16\n16,22 >= 16\ninput: 4 2 -48 -1\n-20 -35 -91 -23\n-22 66 output: War\ninput: 5 3 6 8\n-10 3 1 5 -100\n100 6 14 output: War\n\n" }, { "title": "", "content": "Problem Statement You are given strings S and T consisting of lowercase English letters.\nYou can perform the following operation on S any number of times:\nOperation: Choose two distinct lowercase English letters c_1 and c_2, then replace every occurrence of c_1 with c_2, and every occurrence of c_2 with c_1.\nDetermine if S and T can be made equal by performing the operation zero or more times.", "constraint": "1 <= |S| <= 2 * 10^5\n|S| = |T|\nS and T consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS\nT", "output": "If S and T can be made equal, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: azzel\napple output: Yes\n\nazzel can be changed to apple, as follows:\n\nChoose e as c_1 and l as c_2. azzel becomes azzle.\nChoose z as c_1 and p as c_2. azzle becomes apple.", "input: chokudai\nredcoder output: No\n\nNo sequences of operation can change chokudai to redcoder.", "input: abcdefghijklmnopqrstuvwxyz\nibyhqfrekavclxjstdwgpzmonu output: Yes"], "Pid": "p03252", "ProblemText": "Task Description: Problem Statement You are given strings S and T consisting of lowercase English letters.\nYou can perform the following operation on S any number of times:\nOperation: Choose two distinct lowercase English letters c_1 and c_2, then replace every occurrence of c_1 with c_2, and every occurrence of c_2 with c_1.\nDetermine if S and T can be made equal by performing the operation zero or more times.\nTask Constraint: 1 <= |S| <= 2 * 10^5\n|S| = |T|\nS and T consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nT\nTask Output: If S and T can be made equal, print Yes; otherwise, print No.\nTask Samples: input: azzel\napple output: Yes\n\nazzel can be changed to apple, as follows:\n\nChoose e as c_1 and l as c_2. azzel becomes azzle.\nChoose z as c_1 and p as c_2. azzle becomes apple.\ninput: chokudai\nredcoder output: No\n\nNo sequences of operation can change chokudai to redcoder.\ninput: abcdefghijklmnopqrstuvwxyz\nibyhqfrekavclxjstdwgpzmonu output: Yes\n\n" }, { "title": "", "content": "Problem Statement You are given positive integers N and M.\nHow many sequences a of length N consisting of positive integers satisfy a_1 * a_2 * . . . * a_N = M? Find the count modulo 10^9+7.\nHere, two sequences a' and a'' are considered different when there exists some i such that a_i' \\neq a_i''.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^9", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 6 output: 4\n\nFour sequences satisfy the condition: \\{a_1, a_2\\} = \\{1,6\\}, \\{2,3\\}, \\{3,2\\} and \\{6,1\\}.", "input: 3 12 output: 18", "input: 100000 1000000000 output: 957870001"], "Pid": "p03253", "ProblemText": "Task Description: Problem Statement You are given positive integers N and M.\nHow many sequences a of length N consisting of positive integers satisfy a_1 * a_2 * . . . * a_N = M? Find the count modulo 10^9+7.\nHere, two sequences a' and a'' are considered different when there exists some i such that a_i' \\neq a_i''.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= M <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.\nTask Samples: input: 2 6 output: 4\n\nFour sequences satisfy the condition: \\{a_1, a_2\\} = \\{1,6\\}, \\{2,3\\}, \\{3,2\\} and \\{6,1\\}.\ninput: 3 12 output: 18\ninput: 100000 1000000000 output: 957870001\n\n" }, { "title": "", "content": "Problem Statement There are N children, numbered 1,2, . . . , N.\nSnuke has decided to distribute x sweets among them.\nHe needs to give out all the x sweets, but some of the children may get zero sweets.\nFor each i (1 <= i <= N), Child i will be happy if he/she gets exactly a_i sweets.\nSnuke is trying to maximize the number of happy children by optimally distributing the sweets.\nFind the maximum possible number of happy children.", "constraint": "All values in input are integers.\n2 <= N <= 100\n1 <= x <= 10^9\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N", "output": "Print the maximum possible number of happy children.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 70\n20 30 10 output: 2\n\nOne optimal way to distribute sweets is (20,30,20).", "input: 3 10\n20 30 10 output: 1\n\nThe optimal way to distribute sweets is (0,0,10).", "input: 4 1111\n1 10 100 1000 output: 4\n\nThe optimal way to distribute sweets is (1,10,100,1000).", "input: 2 10\n20 20 output: 0\n\nNo children will be happy, no matter how the sweets are distributed."], "Pid": "p03254", "ProblemText": "Task Description: Problem Statement There are N children, numbered 1,2, . . . , N.\nSnuke has decided to distribute x sweets among them.\nHe needs to give out all the x sweets, but some of the children may get zero sweets.\nFor each i (1 <= i <= N), Child i will be happy if he/she gets exactly a_i sweets.\nSnuke is trying to maximize the number of happy children by optimally distributing the sweets.\nFind the maximum possible number of happy children.\nTask Constraint: All values in input are integers.\n2 <= N <= 100\n1 <= x <= 10^9\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N\nTask Output: Print the maximum possible number of happy children.\nTask Samples: input: 3 70\n20 30 10 output: 2\n\nOne optimal way to distribute sweets is (20,30,20).\ninput: 3 10\n20 30 10 output: 1\n\nThe optimal way to distribute sweets is (0,0,10).\ninput: 4 1111\n1 10 100 1000 output: 4\n\nThe optimal way to distribute sweets is (1,10,100,1000).\ninput: 2 10\n20 20 output: 0\n\nNo children will be happy, no matter how the sweets are distributed.\n\n" }, { "title": "", "content": "Problem Statement Snuke has decided to use a robot to clean his room.\nThere are N pieces of trash on a number line.\nThe i-th piece from the left is at position x_i.\nWe would like to put all of them in a trash bin at position 0.\nFor the positions of the pieces of trash, 0 < x_1 < x_2 < . . . < x_{N} <= 10^{9} holds.\nThe robot is initially at position 0.\nIt can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.\nThe robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy. )\nAlso, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.\nFind the minimum amount of energy required to put all the N pieces of trash in the trash bin. partial scores: Partial Scores\n400 points will be awarded for passing the test set satisfying N <= 2000.", "constraint": "1 <= N <= 2 * 10^{5}\n0 < x_1 < ... < x_N <= 10^9\n1 <= X <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X\nx_1 x_2 . . . x_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 100\n1 10 output: 355\nTravel to position 10 by consuming 10 points of energy.\nPick up the piece of trash by consuming 100 points of energy.\nTravel to position 1 by consuming 36 points of energy.\nPick up the piece of trash by consuming 100 points of energy.\nTravel to position 0 by consuming 9 points of energy.\nPut the two pieces of trash in the trash bin by consuming 100 points of energy.\n\nThis strategy consumes a total of 10+100+36+100+9+100=355 points of energy.", "input: 5 1\n1 999999997 999999998 999999999 1000000000 output: 19999999983", "input: 10 8851025\n38 87 668 3175 22601 65499 90236 790604 4290609 4894746 output: 150710136", "input: 16 10\n1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408 output: 3256017715"], "Pid": "p03255", "ProblemText": "Task Description: Problem Statement Snuke has decided to use a robot to clean his room.\nThere are N pieces of trash on a number line.\nThe i-th piece from the left is at position x_i.\nWe would like to put all of them in a trash bin at position 0.\nFor the positions of the pieces of trash, 0 < x_1 < x_2 < . . . < x_{N} <= 10^{9} holds.\nThe robot is initially at position 0.\nIt can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.\nThe robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy. )\nAlso, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.\nFind the minimum amount of energy required to put all the N pieces of trash in the trash bin. partial scores: Partial Scores\n400 points will be awarded for passing the test set satisfying N <= 2000.\nTask Constraint: 1 <= N <= 2 * 10^{5}\n0 < x_1 < ... < x_N <= 10^9\n1 <= X <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X\nx_1 x_2 . . . x_{N}\nTask Output: Print the answer.\nTask Samples: input: 2 100\n1 10 output: 355\nTravel to position 10 by consuming 10 points of energy.\nPick up the piece of trash by consuming 100 points of energy.\nTravel to position 1 by consuming 36 points of energy.\nPick up the piece of trash by consuming 100 points of energy.\nTravel to position 0 by consuming 9 points of energy.\nPut the two pieces of trash in the trash bin by consuming 100 points of energy.\n\nThis strategy consumes a total of 10+100+36+100+9+100=355 points of energy.\ninput: 5 1\n1 999999997 999999998 999999999 1000000000 output: 19999999983\ninput: 10 8851025\n38 87 668 3175 22601 65499 90236 790604 4290609 4894746 output: 150710136\ninput: 16 10\n1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408 output: 3256017715\n\n" }, { "title": "", "content": "Problem Statement You are given an undirected graph consisting of N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nIn addition, each vertex has a label, A or B. The label of Vertex i is s_i.\nEdge i bidirectionally connects vertex a_i and b_i.\nThe phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times.\nToday, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint.\nFor example, in a graph where Vertex 1 has the label A and Vertex 2 has the label B, if Nusook travels along the path 1 \\rightarrow 2 \\rightarrow 1 \\rightarrow 2 \\rightarrow 2, the resulting string is ABABB.\nDetermine if Nusook can make all strings consisting of A and B.", "constraint": "2 <= N <= 2 * 10^{5}\n1 <= M <= 2 * 10^{5}\n|s| = N\ns_i is A or B.\n1 <= a_i, b_i <= N\nThe given graph may NOT be simple or connected.", "input": "Input is given from Standard Input in the following format:\nN M\ns\na_1 b_1\n:\na_{M} b_{M}", "output": "If Nusook can make all strings consisting of A and B, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\nAB\n1 1\n1 2\n2 2 output: Yes\nSince Nusook can visit Vertex 1 and Vertex 2 in any way he likes, he can make all strings consisting of A and B.", "input: 4 3\nABAB\n1 2\n2 3\n3 1 output: No\nFor example, Nusook cannot make BB.\nThe given graph may not be connected.", "input: 13 23\nABAAAABBBBAAB\n7 1\n10 6\n1 11\n2 10\n2 8\n2 11\n11 12\n8 3\n7 12\n11 2\n13 13\n11 9\n4 1\n9 7\n9 6\n8 13\n8 6\n4 10\n8 7\n4 3\n2 1\n8 12\n6 9 output: Yes", "input: 13 17\nBBABBBAABABBA\n7 1\n7 9\n11 12\n3 9\n11 9\n2 1\n11 5\n12 11\n10 8\n1 11\n1 8\n7 7\n9 10\n8 8\n8 12\n6 2\n13 11 output: No"], "Pid": "p03256", "ProblemText": "Task Description: Problem Statement You are given an undirected graph consisting of N vertices and M edges.\nThe vertices are numbered 1 to N, and the edges are numbered 1 to M.\nIn addition, each vertex has a label, A or B. The label of Vertex i is s_i.\nEdge i bidirectionally connects vertex a_i and b_i.\nThe phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times.\nToday, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint.\nFor example, in a graph where Vertex 1 has the label A and Vertex 2 has the label B, if Nusook travels along the path 1 \\rightarrow 2 \\rightarrow 1 \\rightarrow 2 \\rightarrow 2, the resulting string is ABABB.\nDetermine if Nusook can make all strings consisting of A and B.\nTask Constraint: 2 <= N <= 2 * 10^{5}\n1 <= M <= 2 * 10^{5}\n|s| = N\ns_i is A or B.\n1 <= a_i, b_i <= N\nThe given graph may NOT be simple or connected.\nTask Input: Input is given from Standard Input in the following format:\nN M\ns\na_1 b_1\n:\na_{M} b_{M}\nTask Output: If Nusook can make all strings consisting of A and B, print Yes; otherwise, print No.\nTask Samples: input: 2 3\nAB\n1 1\n1 2\n2 2 output: Yes\nSince Nusook can visit Vertex 1 and Vertex 2 in any way he likes, he can make all strings consisting of A and B.\ninput: 4 3\nABAB\n1 2\n2 3\n3 1 output: No\nFor example, Nusook cannot make BB.\nThe given graph may not be connected.\ninput: 13 23\nABAAAABBBBAAB\n7 1\n10 6\n1 11\n2 10\n2 8\n2 11\n11 12\n8 3\n7 12\n11 2\n13 13\n11 9\n4 1\n9 7\n9 6\n8 13\n8 6\n4 10\n8 7\n4 3\n2 1\n8 12\n6 9 output: Yes\ninput: 13 17\nBBABBBAABABBA\n7 1\n7 9\n11 12\n3 9\n11 9\n2 1\n11 5\n12 11\n10 8\n1 11\n1 8\n7 7\n9 10\n8 8\n8 12\n6 2\n13 11 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N.\nConstruct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.\n\n1 <= a_{i, j} <= 10^{15}\na_{i, j} are pairwise distinct integers.\nThere exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\\rm max}(x, y) {\\rm mod} {\\rm min}(x, y) is always m.", "constraint": "2 <= N <= 500", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print your solution in the following format:\na_{1,1} . . . a_{1, N}\n:\na_{N, 1} . . . a_{N, N}", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 4 7\n23 10\nFor any two elements x and y that are vertically or horizontally adjacent, {\\rm max}(x,y) {\\rm mod} {\\rm min}(x,y) is always 3."], "Pid": "p03257", "ProblemText": "Task Description: Problem Statement You are given an integer N.\nConstruct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.\n\n1 <= a_{i, j} <= 10^{15}\na_{i, j} are pairwise distinct integers.\nThere exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\\rm max}(x, y) {\\rm mod} {\\rm min}(x, y) is always m.\nTask Constraint: 2 <= N <= 500\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print your solution in the following format:\na_{1,1} . . . a_{1, N}\n:\na_{N, 1} . . . a_{N, N}\nTask Samples: input: 2 output: 4 7\n23 10\nFor any two elements x and y that are vertically or horizontally adjacent, {\\rm max}(x,y) {\\rm mod} {\\rm min}(x,y) is always 3.\n\n" }, { "title": "", "content": "Problem Statement There is a string s consisting of a and b.\nSnuke can perform the following two kinds of operation any number of times in any order:\n\nChoose an occurrence of aa as a substring, and replace it with b.\nChoose an occurrence of bb as a substring, and replace it with a.\n\nHow many strings s can be obtained by this sequence of operations?\nFind the count modulo 10^9 + 7.", "constraint": "1 <= |s| <= 10^5\ns consists of a and b.", "input": "Input is given from Standard Input in the following format:\ns", "output": "Print the number of strings s that can be obtained, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aaaa output: 6\n\nSix strings can be obtained:\n\naaaa\naab\naba\nbaa\nbb\na", "input: aabb output: 5\n\nFive strings can be obtained:\n\naabb\naaa\nbbb\nab\nba", "input: ababababa output: 1\n\nSnuke cannot perform any operation.", "input: babbabaaba output: 35"], "Pid": "p03258", "ProblemText": "Task Description: Problem Statement There is a string s consisting of a and b.\nSnuke can perform the following two kinds of operation any number of times in any order:\n\nChoose an occurrence of aa as a substring, and replace it with b.\nChoose an occurrence of bb as a substring, and replace it with a.\n\nHow many strings s can be obtained by this sequence of operations?\nFind the count modulo 10^9 + 7.\nTask Constraint: 1 <= |s| <= 10^5\ns consists of a and b.\nTask Input: Input is given from Standard Input in the following format:\ns\nTask Output: Print the number of strings s that can be obtained, modulo 10^9 + 7.\nTask Samples: input: aaaa output: 6\n\nSix strings can be obtained:\n\naaaa\naab\naba\nbaa\nbb\na\ninput: aabb output: 5\n\nFive strings can be obtained:\n\naabb\naaa\nbbb\nab\nba\ninput: ababababa output: 1\n\nSnuke cannot perform any operation.\ninput: babbabaaba output: 35\n\n" }, { "title": "", "content": "Problem Statement Snuke has found two trees A and B, each with N vertices numbered 1 to N.\nThe i-th edge of A connects Vertex a_i and b_i, and the j-th edge of B connects Vertex c_j and d_j.\nAlso, all vertices of A are initially painted white.\nSnuke would like to perform the following operation on A zero or more times so that A coincides with B:\n\nChoose a leaf vertex that is painted white. (Let this vertex be v. )\nRemove the edge incident to v, and add a new edge that connects v to another vertex.\nPaint v black.\n\nDetermine if A can be made to coincide with B, ignoring color. If the answer is yes, find the minimum number of operations required.\nYou are given T cases of this kind. Find the answer for each of them.", "constraint": "1 <= T <= 20\n3 <= N <= 50\n1 <= a_i,b_i,c_i,d_i <= N\nAll given graphs are trees.", "input": "Input is given from Standard Input in the following format:\nT\ncase_1\n:\ncase_{T}\n\nEach case is given in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 d_1\n:\nc_{N-1} d_{N-1}", "output": "For each case, if A can be made to coincide with B ignoring color, print the minimum number of operations required, and print -1 if it cannot.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3\n1 2\n2 3\n1 3\n3 2\n6\n1 2\n2 3\n3 4\n4 5\n5 6\n1 2\n2 4\n4 3\n3 5\n5 6 output: 1\n-1\nThe graph in each case is shown below.\nIn case 1, A can be made to coincide with B by choosing Vertex 1, removing the edge connecting 1 and 2, and adding an edge connecting 1 and 3. Note that Vertex 2 is not a leaf vertex and thus cannot be chosen.", "input: 3\n8\n2 7\n4 8\n8 6\n7 1\n7 3\n5 7\n7 8\n4 2\n5 2\n1 2\n8 1\n3 2\n2 6\n2 7\n4\n1 2\n2 3\n3 4\n3 4\n2 1\n3 2\n9\n5 3\n4 3\n9 3\n6 8\n2 3\n1 3\n3 8\n1 7\n4 1\n2 8\n9 6\n3 6\n3 5\n1 8\n9 7\n1 6 output: 6\n0\n7\nA may coincide with B from the beginning."], "Pid": "p03259", "ProblemText": "Task Description: Problem Statement Snuke has found two trees A and B, each with N vertices numbered 1 to N.\nThe i-th edge of A connects Vertex a_i and b_i, and the j-th edge of B connects Vertex c_j and d_j.\nAlso, all vertices of A are initially painted white.\nSnuke would like to perform the following operation on A zero or more times so that A coincides with B:\n\nChoose a leaf vertex that is painted white. (Let this vertex be v. )\nRemove the edge incident to v, and add a new edge that connects v to another vertex.\nPaint v black.\n\nDetermine if A can be made to coincide with B, ignoring color. If the answer is yes, find the minimum number of operations required.\nYou are given T cases of this kind. Find the answer for each of them.\nTask Constraint: 1 <= T <= 20\n3 <= N <= 50\n1 <= a_i,b_i,c_i,d_i <= N\nAll given graphs are trees.\nTask Input: Input is given from Standard Input in the following format:\nT\ncase_1\n:\ncase_{T}\n\nEach case is given in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nc_1 d_1\n:\nc_{N-1} d_{N-1}\nTask Output: For each case, if A can be made to coincide with B ignoring color, print the minimum number of operations required, and print -1 if it cannot.\nTask Samples: input: 2\n3\n1 2\n2 3\n1 3\n3 2\n6\n1 2\n2 3\n3 4\n4 5\n5 6\n1 2\n2 4\n4 3\n3 5\n5 6 output: 1\n-1\nThe graph in each case is shown below.\nIn case 1, A can be made to coincide with B by choosing Vertex 1, removing the edge connecting 1 and 2, and adding an edge connecting 1 and 3. Note that Vertex 2 is not a leaf vertex and thus cannot be chosen.\ninput: 3\n8\n2 7\n4 8\n8 6\n7 1\n7 3\n5 7\n7 8\n4 2\n5 2\n1 2\n8 1\n3 2\n2 6\n2 7\n4\n1 2\n2 3\n3 4\n3 4\n2 1\n3 2\n9\n5 3\n4 3\n9 3\n6 8\n2 3\n1 3\n3 8\n1 7\n4 1\n2 8\n9 6\n3 6\n3 5\n1 8\n9 7\n1 6 output: 6\n0\n7\nA may coincide with B from the beginning.\n\n" }, { "title": "", "content": "Problem Statement You are given integers A and B, each between 1 and 3 (inclusive).\nDetermine if there is an integer C between 1 and 3 (inclusive) such that A * B * C is an odd number.", "constraint": "All values in input are integers.\n1 <= A, B <= 3", "input": "Input is given from Standard Input in the following format:\nA B", "output": "If there is an integer C between 1 and 3 that satisfies the condition, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 output: Yes\n\nLet C = 3. Then, A * B * C = 3 * 1 * 3 = 9, which is an odd number.", "input: 1 2 output: No", "input: 2 2 output: No"], "Pid": "p03260", "ProblemText": "Task Description: Problem Statement You are given integers A and B, each between 1 and 3 (inclusive).\nDetermine if there is an integer C between 1 and 3 (inclusive) such that A * B * C is an odd number.\nTask Constraint: All values in input are integers.\n1 <= A, B <= 3\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: If there is an integer C between 1 and 3 that satisfies the condition, print Yes; otherwise, print No.\nTask Samples: input: 3 1 output: Yes\n\nLet C = 3. Then, A * B * C = 3 * 1 * 3 = 9, which is an odd number.\ninput: 1 2 output: No\ninput: 2 2 output: No\n\n" }, { "title": "", "content": "Problem Statement Takahashi is practicing shiritori alone again today.\nShiritori is a game as follows:\n\nIn the first turn, a player announces any one word.\nIn the subsequent turns, a player announces a word that satisfies the following conditions:\nThat word is not announced before.\nThe first character of that word is the same as the last character of the last word announced.\n\nIn this game, he is practicing to announce as many words as possible in ten seconds.\nYou are given the number of words Takahashi announced, N, and the i-th word he announced, W_i, for each i. Determine if the rules of shiritori was observed, that is, every word announced by him satisfied the conditions.", "constraint": "N is an integer satisfying 2 <= N <= 100.\nW_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\nW_1\nW_2\n:\nW_N", "output": "If every word announced by Takahashi satisfied the conditions, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\nhoge\nenglish\nhoge\nenigma output: No\n\nAs hoge is announced multiple times, the rules of shiritori was not observed.", "input: 9\nbasic\nc\ncpp\nphp\npython\nnadesico\nocaml\nlua\nassembly output: Yes", "input: 8\na\naa\naaa\naaaa\naaaaa\naaaaaa\naaa\naaaaaaa output: No", "input: 3\nabc\narc\nagc output: No"], "Pid": "p03261", "ProblemText": "Task Description: Problem Statement Takahashi is practicing shiritori alone again today.\nShiritori is a game as follows:\n\nIn the first turn, a player announces any one word.\nIn the subsequent turns, a player announces a word that satisfies the following conditions:\nThat word is not announced before.\nThe first character of that word is the same as the last character of the last word announced.\n\nIn this game, he is practicing to announce as many words as possible in ten seconds.\nYou are given the number of words Takahashi announced, N, and the i-th word he announced, W_i, for each i. Determine if the rules of shiritori was observed, that is, every word announced by him satisfied the conditions.\nTask Constraint: N is an integer satisfying 2 <= N <= 100.\nW_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\nW_1\nW_2\n:\nW_N\nTask Output: If every word announced by Takahashi satisfied the conditions, print Yes; otherwise, print No.\nTask Samples: input: 4\nhoge\nenglish\nhoge\nenigma output: No\n\nAs hoge is announced multiple times, the rules of shiritori was not observed.\ninput: 9\nbasic\nc\ncpp\nphp\npython\nnadesico\nocaml\nlua\nassembly output: Yes\ninput: 8\na\naa\naaa\naaaa\naaaaa\naaaaaa\naaa\naaaaaaa output: No\ninput: 3\nabc\narc\nagc output: No\n\n" }, { "title": "", "content": "Problem Statement There are N cities on a number line. The i-th city is located at coordinate x_i.\nYour objective is to visit all these cities at least once.\nIn order to do so, you will first set a positive integer D.\nThen, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:\n\nMove 1: travel from coordinate y to coordinate y + D.\nMove 2: travel from coordinate y to coordinate y - D.\n\nFind the maximum value of D that enables you to visit all the cities.\nHere, to visit a city is to travel to the coordinate where that city is located.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n1 <= X <= 10^9\n1 <= x_i <= 10^9\nx_i are all different.\nx_1, x_2, ..., x_N \\neq X", "input": "Input is given from Standard Input in the following format:\nN X\nx_1 x_2 . . . x_N", "output": "Print the maximum value of D that enables you to visit all the cities.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 7 11 output: 2\n\nSetting D = 2 enables you to visit all the cities as follows, and this is the maximum value of such D.\n\nPerform Move 2 to travel to coordinate 1.\nPerform Move 1 to travel to coordinate 3.\nPerform Move 1 to travel to coordinate 5.\nPerform Move 1 to travel to coordinate 7.\nPerform Move 1 to travel to coordinate 9.\nPerform Move 1 to travel to coordinate 11.", "input: 3 81\n33 105 57 output: 24", "input: 1 1\n1000000000 output: 999999999"], "Pid": "p03262", "ProblemText": "Task Description: Problem Statement There are N cities on a number line. The i-th city is located at coordinate x_i.\nYour objective is to visit all these cities at least once.\nIn order to do so, you will first set a positive integer D.\nThen, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:\n\nMove 1: travel from coordinate y to coordinate y + D.\nMove 2: travel from coordinate y to coordinate y - D.\n\nFind the maximum value of D that enables you to visit all the cities.\nHere, to visit a city is to travel to the coordinate where that city is located.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n1 <= X <= 10^9\n1 <= x_i <= 10^9\nx_i are all different.\nx_1, x_2, ..., x_N \\neq X\nTask Input: Input is given from Standard Input in the following format:\nN X\nx_1 x_2 . . . x_N\nTask Output: Print the maximum value of D that enables you to visit all the cities.\nTask Samples: input: 3 3\n1 7 11 output: 2\n\nSetting D = 2 enables you to visit all the cities as follows, and this is the maximum value of such D.\n\nPerform Move 2 to travel to coordinate 1.\nPerform Move 1 to travel to coordinate 3.\nPerform Move 1 to travel to coordinate 5.\nPerform Move 1 to travel to coordinate 7.\nPerform Move 1 to travel to coordinate 9.\nPerform Move 1 to travel to coordinate 11.\ninput: 3 81\n33 105 57 output: 24\ninput: 1 1\n1000000000 output: 999999999\n\n" }, { "title": "", "content": "Problem Statement There is a grid of square cells with H horizontal rows and W vertical columns. The cell at the i-th row and the j-th column will be denoted as Cell (i, j).\nIn Cell (i, j), a_{ij} coins are placed.\nYou can perform the following operation any number of times:\nOperation: Choose a cell that was not chosen before and contains one or more coins, then move one of those coins to a vertically or horizontally adjacent cell.\nMaximize the number of cells containing an even number of coins.", "constraint": "All values in input are integers.\n1 <= H, W <= 500\n0 <= a_{ij} <= 9", "input": "Input is given from Standard Input in the following format:\nH W\na_{11} a_{12} . . . a_{1W}\na_{21} a_{22} . . . a_{2W}\n:\na_{H1} a_{H2} . . . a_{HW}", "output": "Print a sequence of operations that maximizes the number of cells containing an even number of coins, in the following format:\nN\ny_1 x_1 y_1' x_1'\ny_2 x_2 y_2' x_2'\n:\ny_N x_N y_N' x_N'\n\nThat is, in the first line, print an integer N between 0 and H * W (inclusive), representing the number of operations.\nIn the (i+1)-th line (1 <= i <= N), print four integers y_i, x_i, y_i' and x_i' (1 <= y_i, y_i' <= H and 1 <= x_i, x_i' <= W), representing the i-th operation. These four integers represents the operation of moving one of the coins placed in Cell (y_i, x_i) to a vertically or horizontally adjacent cell, (y_i', x_i').\nNote that if the specified operation violates the specification in the problem statement or the output format is invalid, it will result in Wrong Answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n1 2 3\n0 1 1 output: 3\n2 2 2 3\n1 1 1 2\n1 3 1 2\n\nEvery cell contains an even number of coins after the following sequence of operations:\n\nMove the coin in Cell (2,2) to Cell (2,3).\nMove the coin in Cell (1,1) to Cell (1,2).\nMove one of the coins in Cell (1,3) to Cell (1,2).", "input: 3 2\n1 0\n2 1\n1 0 output: 3\n1 1 1 2\n1 2 2 2\n3 1 3 2", "input: 1 5\n9 9 9 9 9 output: 2\n1 1 1 2\n1 3 1 4"], "Pid": "p03263", "ProblemText": "Task Description: Problem Statement There is a grid of square cells with H horizontal rows and W vertical columns. The cell at the i-th row and the j-th column will be denoted as Cell (i, j).\nIn Cell (i, j), a_{ij} coins are placed.\nYou can perform the following operation any number of times:\nOperation: Choose a cell that was not chosen before and contains one or more coins, then move one of those coins to a vertically or horizontally adjacent cell.\nMaximize the number of cells containing an even number of coins.\nTask Constraint: All values in input are integers.\n1 <= H, W <= 500\n0 <= a_{ij} <= 9\nTask Input: Input is given from Standard Input in the following format:\nH W\na_{11} a_{12} . . . a_{1W}\na_{21} a_{22} . . . a_{2W}\n:\na_{H1} a_{H2} . . . a_{HW}\nTask Output: Print a sequence of operations that maximizes the number of cells containing an even number of coins, in the following format:\nN\ny_1 x_1 y_1' x_1'\ny_2 x_2 y_2' x_2'\n:\ny_N x_N y_N' x_N'\n\nThat is, in the first line, print an integer N between 0 and H * W (inclusive), representing the number of operations.\nIn the (i+1)-th line (1 <= i <= N), print four integers y_i, x_i, y_i' and x_i' (1 <= y_i, y_i' <= H and 1 <= x_i, x_i' <= W), representing the i-th operation. These four integers represents the operation of moving one of the coins placed in Cell (y_i, x_i) to a vertically or horizontally adjacent cell, (y_i', x_i').\nNote that if the specified operation violates the specification in the problem statement or the output format is invalid, it will result in Wrong Answer.\nTask Samples: input: 2 3\n1 2 3\n0 1 1 output: 3\n2 2 2 3\n1 1 1 2\n1 3 1 2\n\nEvery cell contains an even number of coins after the following sequence of operations:\n\nMove the coin in Cell (2,2) to Cell (2,3).\nMove the coin in Cell (1,1) to Cell (1,2).\nMove one of the coins in Cell (1,3) to Cell (1,2).\ninput: 3 2\n1 0\n2 1\n1 0 output: 3\n1 1 1 2\n1 2 2 2\n3 1 3 2\ninput: 1 5\n9 9 9 9 9 output: 2\n1 1 1 2\n1 3 1 4\n\n" }, { "title": "", "content": "Problem Statement Find the number of ways to choose a pair of an even number and an odd number from the positive integers between 1 and K (inclusive). The order does not matter.", "constraint": "2<= K<= 100\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print the number of ways to choose a pair of an even number and an odd number from the positive integers between 1 and K (inclusive).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 2\n\nTwo pairs can be chosen: (2,1) and (2,3).", "input: 6 output: 9", "input: 11 output: 30", "input: 50 output: 625"], "Pid": "p03264", "ProblemText": "Task Description: Problem Statement Find the number of ways to choose a pair of an even number and an odd number from the positive integers between 1 and K (inclusive). The order does not matter.\nTask Constraint: 2<= K<= 100\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print the number of ways to choose a pair of an even number and an odd number from the positive integers between 1 and K (inclusive).\nTask Samples: input: 3 output: 2\n\nTwo pairs can be chosen: (2,1) and (2,3).\ninput: 6 output: 9\ninput: 11 output: 30\ninput: 50 output: 625\n\n" }, { "title": "", "content": "Problem Statement There is a square in the xy-plane. The coordinates of its four vertices are (x_1, y_1), (x_2, y_2), (x_3, y_3) and (x_4, y_4) in counter-clockwise order.\n(Assume that the positive x-axis points right, and the positive y-axis points up. )\nTakahashi remembers (x_1, y_1) and (x_2, y_2), but he has forgot (x_3, y_3) and (x_4, y_4).\nGiven x_1, x_2, y_1, y_2, restore x_3, y_3, x_4, y_4. It can be shown that x_3, y_3, x_4 and y_4 uniquely exist and have integer values.", "constraint": "|x_1|,|y_1|,|x_2|,|y_2| <= 100\n(x_1,y_1) != (x_2,y_2)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nx_1 y_1 x_2 y_2", "output": "Print x_3, y_3, x_4 and y_4 as integers, in this order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0 0 1 output: -1 1 -1 0\n\n(0,0),(0,1),(-1,1),(-1,0) is the four vertices of a square in counter-clockwise order.\nNote that (x_3,y_3)=(1,1),(x_4,y_4)=(1,0) is not accepted, as the vertices are in clockwise order.", "input: 2 3 6 6 output: 3 10 -1 7", "input: 31 -41 -59 26 output: -126 -64 -36 -131"], "Pid": "p03265", "ProblemText": "Task Description: Problem Statement There is a square in the xy-plane. The coordinates of its four vertices are (x_1, y_1), (x_2, y_2), (x_3, y_3) and (x_4, y_4) in counter-clockwise order.\n(Assume that the positive x-axis points right, and the positive y-axis points up. )\nTakahashi remembers (x_1, y_1) and (x_2, y_2), but he has forgot (x_3, y_3) and (x_4, y_4).\nGiven x_1, x_2, y_1, y_2, restore x_3, y_3, x_4, y_4. It can be shown that x_3, y_3, x_4 and y_4 uniquely exist and have integer values.\nTask Constraint: |x_1|,|y_1|,|x_2|,|y_2| <= 100\n(x_1,y_1) != (x_2,y_2)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nx_1 y_1 x_2 y_2\nTask Output: Print x_3, y_3, x_4 and y_4 as integers, in this order.\nTask Samples: input: 0 0 0 1 output: -1 1 -1 0\n\n(0,0),(0,1),(-1,1),(-1,0) is the four vertices of a square in counter-clockwise order.\nNote that (x_3,y_3)=(1,1),(x_4,y_4)=(1,0) is not accepted, as the vertices are in clockwise order.\ninput: 2 3 6 6 output: 3 10 -1 7\ninput: 31 -41 -59 26 output: -126 -64 -36 -131\n\n" }, { "title": "", "content": "Problem Statement You are given integers N and K. Find the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.\nThe order of a, b, c does matter, and some of them can be the same.", "constraint": "1 <= N,K <= 2* 10^5\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 9\n\n(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.", "input: 5 3 output: 1", "input: 31415 9265 output: 27", "input: 35897 932 output: 114191"], "Pid": "p03266", "ProblemText": "Task Description: Problem Statement You are given integers N and K. Find the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.\nThe order of a, b, c does matter, and some of them can be the same.\nTask Constraint: 1 <= N,K <= 2* 10^5\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.\nTask Samples: input: 3 2 output: 9\n\n(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.\ninput: 5 3 output: 1\ninput: 31415 9265 output: 27\ninput: 35897 932 output: 114191\n\n" }, { "title": "", "content": "Problem Statement You are given an integer L. Construct a directed graph that satisfies the conditions below. The graph may contain multiple edges between the same pair of vertices. It can be proved that such a graph always exists.\n\nThe number of vertices, N, is at most 20. The vertices are given ID numbers from 1 to N.\nThe number of edges, M, is at most 60. Each edge has an integer length between 0 and 10^6 (inclusive).\nEvery edge is directed from the vertex with the smaller ID to the vertex with the larger ID. That is, 1,2, . . . , N is one possible topological order of the vertices.\nThere are exactly L different paths from Vertex 1 to Vertex N. The lengths of these paths are all different, and they are integers between 0 and L-1.\n\nHere, the length of a path is the sum of the lengths of the edges contained in that path, and two paths are considered different when the sets of the edges contained in those paths are different.", "constraint": "2 <= L <= 10^6\nL is an integer.", "input": "Input is given from Standard Input in the following format:\nL", "output": "In the first line, print N and M, the number of the vertices and edges in your graph.\nIn the i-th of the following M lines, print three integers u_i, v_i and w_i, representing the starting vertex, the ending vertex and the length of the i-th edge.\nIf there are multiple solutions, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 8 10\n1 2 0\n2 3 0\n3 4 0\n1 5 0\n2 6 0\n3 7 0\n4 8 0\n5 6 1\n6 7 1\n7 8 1\n\nIn the graph represented by the sample output, there are four paths from Vertex 1 to N=8:\n\n1 → 2 → 3 → 4 → 8 with length 0\n1 → 2 → 3 → 7 → 8 with length 1\n1 → 2 → 6 → 7 → 8 with length 2\n1 → 5 → 6 → 7 → 8 with length 3\n\nThere are other possible solutions.", "input: 5 output: 5 7\n1 2 0\n2 3 1\n3 4 0\n4 5 0\n2 4 0\n1 3 3\n3 5 1"], "Pid": "p03267", "ProblemText": "Task Description: Problem Statement You are given an integer L. Construct a directed graph that satisfies the conditions below. The graph may contain multiple edges between the same pair of vertices. It can be proved that such a graph always exists.\n\nThe number of vertices, N, is at most 20. The vertices are given ID numbers from 1 to N.\nThe number of edges, M, is at most 60. Each edge has an integer length between 0 and 10^6 (inclusive).\nEvery edge is directed from the vertex with the smaller ID to the vertex with the larger ID. That is, 1,2, . . . , N is one possible topological order of the vertices.\nThere are exactly L different paths from Vertex 1 to Vertex N. The lengths of these paths are all different, and they are integers between 0 and L-1.\n\nHere, the length of a path is the sum of the lengths of the edges contained in that path, and two paths are considered different when the sets of the edges contained in those paths are different.\nTask Constraint: 2 <= L <= 10^6\nL is an integer.\nTask Input: Input is given from Standard Input in the following format:\nL\nTask Output: In the first line, print N and M, the number of the vertices and edges in your graph.\nIn the i-th of the following M lines, print three integers u_i, v_i and w_i, representing the starting vertex, the ending vertex and the length of the i-th edge.\nIf there are multiple solutions, any of them will be accepted.\nTask Samples: input: 4 output: 8 10\n1 2 0\n2 3 0\n3 4 0\n1 5 0\n2 6 0\n3 7 0\n4 8 0\n5 6 1\n6 7 1\n7 8 1\n\nIn the graph represented by the sample output, there are four paths from Vertex 1 to N=8:\n\n1 → 2 → 3 → 4 → 8 with length 0\n1 → 2 → 3 → 7 → 8 with length 1\n1 → 2 → 6 → 7 → 8 with length 2\n1 → 5 → 6 → 7 → 8 with length 3\n\nThere are other possible solutions.\ninput: 5 output: 5 7\n1 2 0\n2 3 1\n3 4 0\n4 5 0\n2 4 0\n1 3 3\n3 5 1\n\n" }, { "title": "", "content": "Problem Statement You are given integers N and K. Find the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.\nThe order of a, b, c does matter, and some of them can be the same.", "constraint": "1 <= N,K <= 2* 10^5\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 9\n\n(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.", "input: 5 3 output: 1", "input: 31415 9265 output: 27", "input: 35897 932 output: 114191"], "Pid": "p03268", "ProblemText": "Task Description: Problem Statement You are given integers N and K. Find the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.\nThe order of a, b, c does matter, and some of them can be the same.\nTask Constraint: 1 <= N,K <= 2* 10^5\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of triples (a, b, c) of positive integers not greater than N such that a+b, b+c and c+a are all multiples of K.\nTask Samples: input: 3 2 output: 9\n\n(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.\ninput: 5 3 output: 1\ninput: 31415 9265 output: 27\ninput: 35897 932 output: 114191\n\n" }, { "title": "", "content": "Problem Statement You are given an integer L. Construct a directed graph that satisfies the conditions below. The graph may contain multiple edges between the same pair of vertices. It can be proved that such a graph always exists.\n\nThe number of vertices, N, is at most 20. The vertices are given ID numbers from 1 to N.\nThe number of edges, M, is at most 60. Each edge has an integer length between 0 and 10^6 (inclusive).\nEvery edge is directed from the vertex with the smaller ID to the vertex with the larger ID. That is, 1,2, . . . , N is one possible topological order of the vertices.\nThere are exactly L different paths from Vertex 1 to Vertex N. The lengths of these paths are all different, and they are integers between 0 and L-1.\n\nHere, the length of a path is the sum of the lengths of the edges contained in that path, and two paths are considered different when the sets of the edges contained in those paths are different.", "constraint": "2 <= L <= 10^6\nL is an integer.", "input": "Input is given from Standard Input in the following format:\nL", "output": "In the first line, print N and M, the number of the vertices and edges in your graph.\nIn the i-th of the following M lines, print three integers u_i, v_i and w_i, representing the starting vertex, the ending vertex and the length of the i-th edge.\nIf there are multiple solutions, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 8 10\n1 2 0\n2 3 0\n3 4 0\n1 5 0\n2 6 0\n3 7 0\n4 8 0\n5 6 1\n6 7 1\n7 8 1\n\nIn the graph represented by the sample output, there are four paths from Vertex 1 to N=8:\n\n1 → 2 → 3 → 4 → 8 with length 0\n1 → 2 → 3 → 7 → 8 with length 1\n1 → 2 → 6 → 7 → 8 with length 2\n1 → 5 → 6 → 7 → 8 with length 3\n\nThere are other possible solutions.", "input: 5 output: 5 7\n1 2 0\n2 3 1\n3 4 0\n4 5 0\n2 4 0\n1 3 3\n3 5 1"], "Pid": "p03269", "ProblemText": "Task Description: Problem Statement You are given an integer L. Construct a directed graph that satisfies the conditions below. The graph may contain multiple edges between the same pair of vertices. It can be proved that such a graph always exists.\n\nThe number of vertices, N, is at most 20. The vertices are given ID numbers from 1 to N.\nThe number of edges, M, is at most 60. Each edge has an integer length between 0 and 10^6 (inclusive).\nEvery edge is directed from the vertex with the smaller ID to the vertex with the larger ID. That is, 1,2, . . . , N is one possible topological order of the vertices.\nThere are exactly L different paths from Vertex 1 to Vertex N. The lengths of these paths are all different, and they are integers between 0 and L-1.\n\nHere, the length of a path is the sum of the lengths of the edges contained in that path, and two paths are considered different when the sets of the edges contained in those paths are different.\nTask Constraint: 2 <= L <= 10^6\nL is an integer.\nTask Input: Input is given from Standard Input in the following format:\nL\nTask Output: In the first line, print N and M, the number of the vertices and edges in your graph.\nIn the i-th of the following M lines, print three integers u_i, v_i and w_i, representing the starting vertex, the ending vertex and the length of the i-th edge.\nIf there are multiple solutions, any of them will be accepted.\nTask Samples: input: 4 output: 8 10\n1 2 0\n2 3 0\n3 4 0\n1 5 0\n2 6 0\n3 7 0\n4 8 0\n5 6 1\n6 7 1\n7 8 1\n\nIn the graph represented by the sample output, there are four paths from Vertex 1 to N=8:\n\n1 → 2 → 3 → 4 → 8 with length 0\n1 → 2 → 3 → 7 → 8 with length 1\n1 → 2 → 6 → 7 → 8 with length 2\n1 → 5 → 6 → 7 → 8 with length 3\n\nThere are other possible solutions.\ninput: 5 output: 5 7\n1 2 0\n2 3 1\n3 4 0\n4 5 0\n2 4 0\n1 3 3\n3 5 1\n\n" }, { "title": "", "content": "Problem Statement Takahashi throws N dice, each having K sides with all integers from 1 to K. The dice are NOT pairwise distinguishable.\nFor each i=2,3, . . . , 2K, find the following value modulo 998244353:\n\nThe number of combinations of N sides shown by the dice such that the sum of no two different sides is i.\n\nNote that the dice are NOT distinguishable, that is, two combinations are considered different when there exists an integer k such that the number of dice showing k is different in those two.", "constraint": "1 <= K <= 2000\n2 <= N <= 2000\nK and N are integers.", "input": "Input is given from Standard Input in the following format:\nK N", "output": "Print 2K-1 integers. The t-th of them (1<= t<= 2K-1) should be the answer for i=t+1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 output: 7\n7\n4\n7\n7\nFor i=2, the combinations (1,2,2),(1,2,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3) satisfy the condition, so the answer is 7.\nFor i=3, the combinations (1,1,1),(1,1,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3) satisfy the condition, so the answer is 7.\nFor i=4, the combinations (1,1,1),(1,1,2),(2,3,3),(3,3,3) satisfy the condition, so the answer is 4.", "input: 4 5 output: 36\n36\n20\n20\n20\n36\n36", "input: 6 1000 output: 149393349\n149393349\n668669001\n668669001\n4000002\n4000002\n4000002\n668669001\n668669001\n149393349\n149393349"], "Pid": "p03270", "ProblemText": "Task Description: Problem Statement Takahashi throws N dice, each having K sides with all integers from 1 to K. The dice are NOT pairwise distinguishable.\nFor each i=2,3, . . . , 2K, find the following value modulo 998244353:\n\nThe number of combinations of N sides shown by the dice such that the sum of no two different sides is i.\n\nNote that the dice are NOT distinguishable, that is, two combinations are considered different when there exists an integer k such that the number of dice showing k is different in those two.\nTask Constraint: 1 <= K <= 2000\n2 <= N <= 2000\nK and N are integers.\nTask Input: Input is given from Standard Input in the following format:\nK N\nTask Output: Print 2K-1 integers. The t-th of them (1<= t<= 2K-1) should be the answer for i=t+1.\nTask Samples: input: 3 3 output: 7\n7\n4\n7\n7\nFor i=2, the combinations (1,2,2),(1,2,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3) satisfy the condition, so the answer is 7.\nFor i=3, the combinations (1,1,1),(1,1,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3) satisfy the condition, so the answer is 7.\nFor i=4, the combinations (1,1,1),(1,1,2),(2,3,3),(3,3,3) satisfy the condition, so the answer is 4.\ninput: 4 5 output: 36\n36\n20\n20\n20\n36\n36\ninput: 6 1000 output: 149393349\n149393349\n668669001\n668669001\n4000002\n4000002\n4000002\n668669001\n668669001\n149393349\n149393349\n\n" }, { "title": "", "content": "Problem Statement You are given a permutation of 1,2, . . . , N: p_1, p_2, . . . , p_N. Determine if the state where p_i=i for every i can be reached by performing the following operation any number of times:\n\nChoose three elements p_{i-1}, p_{i}, p_{i+1} (2<= i<= N-1) such that p_{i-1}>p_{i}>p_{i+1} and reverse the order of these three.", "constraint": "3 <= N <= 3 * 10^5\np_1,p_2,...,p_N is a permutation of 1,2,...,N.", "input": "Input is given from Standard Input in the following format:\nN\np_1\n:\np_N", "output": "If the state where p_i=i for every i can be reached by performing the operation, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n5\n2\n1\n4\n3 output: Yes\n\nThe state where p_i=i for every i can be reached as follows:\n\nReverse the order of p_1,p_2,p_3. The sequence p becomes 1,2,5,4,3.\nReverse the order of p_3,p_4,p_5. The sequence p becomes 1,2,3,4,5.", "input: 4\n3\n2\n4\n1 output: No", "input: 7\n3\n2\n1\n6\n5\n4\n7 output: Yes", "input: 6\n5\n3\n4\n1\n2\n6 output: No"], "Pid": "p03271", "ProblemText": "Task Description: Problem Statement You are given a permutation of 1,2, . . . , N: p_1, p_2, . . . , p_N. Determine if the state where p_i=i for every i can be reached by performing the following operation any number of times:\n\nChoose three elements p_{i-1}, p_{i}, p_{i+1} (2<= i<= N-1) such that p_{i-1}>p_{i}>p_{i+1} and reverse the order of these three.\nTask Constraint: 3 <= N <= 3 * 10^5\np_1,p_2,...,p_N is a permutation of 1,2,...,N.\nTask Input: Input is given from Standard Input in the following format:\nN\np_1\n:\np_N\nTask Output: If the state where p_i=i for every i can be reached by performing the operation, print Yes; otherwise, print No.\nTask Samples: input: 5\n5\n2\n1\n4\n3 output: Yes\n\nThe state where p_i=i for every i can be reached as follows:\n\nReverse the order of p_1,p_2,p_3. The sequence p becomes 1,2,5,4,3.\nReverse the order of p_3,p_4,p_5. The sequence p becomes 1,2,3,4,5.\ninput: 4\n3\n2\n4\n1 output: No\ninput: 7\n3\n2\n1\n6\n5\n4\n7 output: Yes\ninput: 6\n5\n3\n4\n1\n2\n6 output: No\n\n" }, { "title": "", "content": "Problem Statement There is an N-car train.\nYou are given an integer i. Find the value of j such that the following statement is true: \"the i-th car from the front of the train is the j-th car from the back. \"", "constraint": "1 <= N <= 100\n1 <= i <= N", "input": "Input is given from Standard Input in the following format:\nN i", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 output: 3\n\nThe second car from the front of a 4-car train is the third car from the back.", "input: 1 1 output: 1", "input: 15 11 output: 5"], "Pid": "p03272", "ProblemText": "Task Description: Problem Statement There is an N-car train.\nYou are given an integer i. Find the value of j such that the following statement is true: \"the i-th car from the front of the train is the j-th car from the back. \"\nTask Constraint: 1 <= N <= 100\n1 <= i <= N\nTask Input: Input is given from Standard Input in the following format:\nN i\nTask Output: Print the answer.\nTask Samples: input: 4 2 output: 3\n\nThe second car from the front of a 4-car train is the third car from the back.\ninput: 1 1 output: 1\ninput: 15 11 output: 5\n\n" }, { "title": "", "content": "Problem Statement There is a grid of squares with H horizontal rows and W vertical columns.\nThe square at the i-th row from the top and the j-th column from the left is represented as (i, j).\nEach square is black or white.\nThe color of the square is given as an H-by-W matrix (a_{i, j}).\nIf a_{i, j} is . , the square (i, j) is white; if a_{i, j} is #, the square (i, j) is black.\nSnuke is compressing this grid.\nHe will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:\n\nOperation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.\n\nIt can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation.\nFind the final state of the grid.", "constraint": "1 <= H, W <= 100\na_{i, j} is . or #.\nThere is at least one black square in the whole grid.", "input": "Input is given from Standard Input in the following format:\nH W\na_{1,1}. . . a_{1, W}\n:\na_{H, 1}. . . a_{H, W}", "output": "Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n##.#\n....\n##.#\n.#.# output: ###\n###\n.##\n\nThe second row and the third column in the original grid will be removed.", "input: 3 3\n#..\n.#.\n..# output: #..\n.#.\n..#\n\nAs there is no row or column that consists only of white squares, no operation will be performed.", "input: 4 5\n.....\n.....\n..#..\n..... output: #", "input: 7 6\n......\n....#.\n.#....\n..#...\n..#...\n......\n.#..#. output: ..#\n#..\n.#.\n.#.\n#.#"], "Pid": "p03273", "ProblemText": "Task Description: Problem Statement There is a grid of squares with H horizontal rows and W vertical columns.\nThe square at the i-th row from the top and the j-th column from the left is represented as (i, j).\nEach square is black or white.\nThe color of the square is given as an H-by-W matrix (a_{i, j}).\nIf a_{i, j} is . , the square (i, j) is white; if a_{i, j} is #, the square (i, j) is black.\nSnuke is compressing this grid.\nHe will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:\n\nOperation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.\n\nIt can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation.\nFind the final state of the grid.\nTask Constraint: 1 <= H, W <= 100\na_{i, j} is . or #.\nThere is at least one black square in the whole grid.\nTask Input: Input is given from Standard Input in the following format:\nH W\na_{1,1}. . . a_{1, W}\n:\na_{H, 1}. . . a_{H, W}\nTask Output: Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.\nTask Samples: input: 4 4\n##.#\n....\n##.#\n.#.# output: ###\n###\n.##\n\nThe second row and the third column in the original grid will be removed.\ninput: 3 3\n#..\n.#.\n..# output: #..\n.#.\n..#\n\nAs there is no row or column that consists only of white squares, no operation will be performed.\ninput: 4 5\n.....\n.....\n..#..\n..... output: #\ninput: 7 6\n......\n....#.\n.#....\n..#...\n..#...\n......\n.#..#. output: ..#\n#..\n.#.\n.#.\n#.#\n\n" }, { "title": "", "content": "Problem Statement There are N candles placed on a number line.\nThe i-th candle from the left is placed on coordinate x_i.\nHere, x_1 < x_2 < . . . < x_N holds.\nInitially, no candles are burning.\nSnuke decides to light K of the N candles.\nNow, he is at coordinate 0.\nHe can move left and right along the line with speed 1.\nHe can also light a candle when he is at the same position as the candle, in negligible time.\nFind the minimum time required to light K candles.", "constraint": "1 <= N <= 10^5\n1 <= K <= N\nx_i is an integer.\n|x_i| <= 10^8\nx_1 < x_2 < ... < x_N", "input": "Input is given from Standard Input in the following format:\nN K\nx_1 x_2 . . . x_N", "output": "Print the minimum time required to light K candles.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n-30 -10 10 20 50 output: 40\n\nHe should move and light candles as follows:\n\nMove from coordinate 0 to -10.\nLight the second candle from the left.\nMove from coordinate -10 to 10.\nLight the third candle from the left.\nMove from coordinate 10 to 20.\nLight the fourth candle from the left.", "input: 3 2\n10 20 30 output: 20", "input: 1 1\n0 output: 0\nThere may be a candle placed at coordinate 0.", "input: 8 5\n-9 -7 -4 -3 1 2 3 4 output: 10"], "Pid": "p03274", "ProblemText": "Task Description: Problem Statement There are N candles placed on a number line.\nThe i-th candle from the left is placed on coordinate x_i.\nHere, x_1 < x_2 < . . . < x_N holds.\nInitially, no candles are burning.\nSnuke decides to light K of the N candles.\nNow, he is at coordinate 0.\nHe can move left and right along the line with speed 1.\nHe can also light a candle when he is at the same position as the candle, in negligible time.\nFind the minimum time required to light K candles.\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= N\nx_i is an integer.\n|x_i| <= 10^8\nx_1 < x_2 < ... < x_N\nTask Input: Input is given from Standard Input in the following format:\nN K\nx_1 x_2 . . . x_N\nTask Output: Print the minimum time required to light K candles.\nTask Samples: input: 5 3\n-30 -10 10 20 50 output: 40\n\nHe should move and light candles as follows:\n\nMove from coordinate 0 to -10.\nLight the second candle from the left.\nMove from coordinate -10 to 10.\nLight the third candle from the left.\nMove from coordinate 10 to 20.\nLight the fourth candle from the left.\ninput: 3 2\n10 20 30 output: 20\ninput: 1 1\n0 output: 0\nThere may be a candle placed at coordinate 0.\ninput: 8 5\n-9 -7 -4 -3 1 2 3 4 output: 10\n\n" }, { "title": "", "content": "Problem Statement We will define the median of a sequence b of length M, as follows:\n\nLet b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.\n\nFor example, the median of (10,30,20) is 20; the median of (10,30,20,40) is 30; the median of (10,10,10,20,30) is 10.\nSnuke comes up with the following problem.\nYou are given a sequence a of length N.\nFor each pair (l, r) (1 <= l <= r <= N), let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, . . . , a_r) of a.\nWe will list m_{l, r} for all pairs (l, r) to create a new sequence m.\nFind the median of m.", "constraint": "1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the median of m.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10 30 20 output: 30\n\nThe median of each contiguous subsequence of a is as follows:\n\nThe median of (10) is 10.\nThe median of (30) is 30.\nThe median of (20) is 20.\nThe median of (10,30) is 30.\nThe median of (30,20) is 30.\nThe median of (10,30,20) is 20.\n\nThus, m = (10,30,20,30,30,20) and the median of m is 30.", "input: 1\n10 output: 10", "input: 10\n5 9 5 9 8 9 3 5 4 3 output: 8"], "Pid": "p03275", "ProblemText": "Task Description: Problem Statement We will define the median of a sequence b of length M, as follows:\n\nLet b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.\n\nFor example, the median of (10,30,20) is 20; the median of (10,30,20,40) is 30; the median of (10,10,10,20,30) is 10.\nSnuke comes up with the following problem.\nYou are given a sequence a of length N.\nFor each pair (l, r) (1 <= l <= r <= N), let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, . . . , a_r) of a.\nWe will list m_{l, r} for all pairs (l, r) to create a new sequence m.\nFind the median of m.\nTask Constraint: 1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the median of m.\nTask Samples: input: 3\n10 30 20 output: 30\n\nThe median of each contiguous subsequence of a is as follows:\n\nThe median of (10) is 10.\nThe median of (30) is 30.\nThe median of (20) is 20.\nThe median of (10,30) is 30.\nThe median of (30,20) is 30.\nThe median of (10,30,20) is 20.\n\nThus, m = (10,30,20,30,30,20) and the median of m is 30.\ninput: 1\n10 output: 10\ninput: 10\n5 9 5 9 8 9 3 5 4 3 output: 8\n\n" }, { "title": "", "content": "Problem Statement There are N candles placed on a number line.\nThe i-th candle from the left is placed on coordinate x_i.\nHere, x_1 < x_2 < . . . < x_N holds.\nInitially, no candles are burning.\nSnuke decides to light K of the N candles.\nNow, he is at coordinate 0.\nHe can move left and right along the line with speed 1.\nHe can also light a candle when he is at the same position as the candle, in negligible time.\nFind the minimum time required to light K candles.", "constraint": "1 <= N <= 10^5\n1 <= K <= N\nx_i is an integer.\n|x_i| <= 10^8\nx_1 < x_2 < ... < x_N", "input": "Input is given from Standard Input in the following format:\nN K\nx_1 x_2 . . . x_N", "output": "Print the minimum time required to light K candles.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n-30 -10 10 20 50 output: 40\n\nHe should move and light candles as follows:\n\nMove from coordinate 0 to -10.\nLight the second candle from the left.\nMove from coordinate -10 to 10.\nLight the third candle from the left.\nMove from coordinate 10 to 20.\nLight the fourth candle from the left.", "input: 3 2\n10 20 30 output: 20", "input: 1 1\n0 output: 0\nThere may be a candle placed at coordinate 0.", "input: 8 5\n-9 -7 -4 -3 1 2 3 4 output: 10"], "Pid": "p03276", "ProblemText": "Task Description: Problem Statement There are N candles placed on a number line.\nThe i-th candle from the left is placed on coordinate x_i.\nHere, x_1 < x_2 < . . . < x_N holds.\nInitially, no candles are burning.\nSnuke decides to light K of the N candles.\nNow, he is at coordinate 0.\nHe can move left and right along the line with speed 1.\nHe can also light a candle when he is at the same position as the candle, in negligible time.\nFind the minimum time required to light K candles.\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= N\nx_i is an integer.\n|x_i| <= 10^8\nx_1 < x_2 < ... < x_N\nTask Input: Input is given from Standard Input in the following format:\nN K\nx_1 x_2 . . . x_N\nTask Output: Print the minimum time required to light K candles.\nTask Samples: input: 5 3\n-30 -10 10 20 50 output: 40\n\nHe should move and light candles as follows:\n\nMove from coordinate 0 to -10.\nLight the second candle from the left.\nMove from coordinate -10 to 10.\nLight the third candle from the left.\nMove from coordinate 10 to 20.\nLight the fourth candle from the left.\ninput: 3 2\n10 20 30 output: 20\ninput: 1 1\n0 output: 0\nThere may be a candle placed at coordinate 0.\ninput: 8 5\n-9 -7 -4 -3 1 2 3 4 output: 10\n\n" }, { "title": "", "content": "Problem Statement We will define the median of a sequence b of length M, as follows:\n\nLet b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.\n\nFor example, the median of (10,30,20) is 20; the median of (10,30,20,40) is 30; the median of (10,10,10,20,30) is 10.\nSnuke comes up with the following problem.\nYou are given a sequence a of length N.\nFor each pair (l, r) (1 <= l <= r <= N), let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, . . . , a_r) of a.\nWe will list m_{l, r} for all pairs (l, r) to create a new sequence m.\nFind the median of m.", "constraint": "1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the median of m.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n10 30 20 output: 30\n\nThe median of each contiguous subsequence of a is as follows:\n\nThe median of (10) is 10.\nThe median of (30) is 30.\nThe median of (20) is 20.\nThe median of (10,30) is 30.\nThe median of (30,20) is 30.\nThe median of (10,30,20) is 20.\n\nThus, m = (10,30,20,30,30,20) and the median of m is 30.", "input: 1\n10 output: 10", "input: 10\n5 9 5 9 8 9 3 5 4 3 output: 8"], "Pid": "p03277", "ProblemText": "Task Description: Problem Statement We will define the median of a sequence b of length M, as follows:\n\nLet b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.\n\nFor example, the median of (10,30,20) is 20; the median of (10,30,20,40) is 30; the median of (10,10,10,20,30) is 10.\nSnuke comes up with the following problem.\nYou are given a sequence a of length N.\nFor each pair (l, r) (1 <= l <= r <= N), let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, . . . , a_r) of a.\nWe will list m_{l, r} for all pairs (l, r) to create a new sequence m.\nFind the median of m.\nTask Constraint: 1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the median of m.\nTask Samples: input: 3\n10 30 20 output: 30\n\nThe median of each contiguous subsequence of a is as follows:\n\nThe median of (10) is 10.\nThe median of (30) is 30.\nThe median of (20) is 20.\nThe median of (10,30) is 30.\nThe median of (30,20) is 30.\nThe median of (10,30,20) is 20.\n\nThus, m = (10,30,20,30,30,20) and the median of m is 30.\ninput: 1\n10 output: 10\ninput: 10\n5 9 5 9 8 9 3 5 4 3 output: 8\n\n" }, { "title": "", "content": "Problem Statement Let N be an even number.\nThere is a tree with N vertices.\nThe vertices are numbered 1,2, . . . , N.\nFor each i (1 <= i <= N - 1), the i-th edge connects Vertex x_i and y_i.\nSnuke would like to decorate the tree with ribbons, as follows.\nFirst, he will divide the N vertices into N / 2 pairs.\nHere, each vertex must belong to exactly one pair.\nThen, for each pair (u, v), put a ribbon through all the edges contained in the shortest path between u and v.\nSnuke is trying to divide the vertices into pairs so that the following condition is satisfied: \"for every edge, there is at least one ribbon going through it. \"\nHow many ways are there to divide the vertices into pairs, satisfying this condition?\nFind the count modulo 10^9 + 7.\nHere, two ways to divide the vertices into pairs are considered different when there is a pair that is contained in one of the two ways but not in the other.", "constraint": "N is an even number.\n2 <= N <= 5000\n1 <= x_i, y_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}", "output": "Print the number of the ways to divide the vertices into pairs, satisfying the condition, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2\n2 3\n3 4 output: 2\n\nThere are three possible ways to divide the vertices into pairs, as shown below, and two satisfy the condition: the middle one and the right one.", "input: 4\n1 2\n1 3\n1 4 output: 3\n\nThere are three possible ways to divide the vertices into pairs, as shown below, and all of them satisfy the condition.", "input: 6\n1 2\n1 3\n3 4\n1 5\n5 6 output: 10", "input: 10\n8 5\n10 8\n6 5\n1 5\n4 8\n2 10\n3 6\n9 2\n1 7 output: 672"], "Pid": "p03278", "ProblemText": "Task Description: Problem Statement Let N be an even number.\nThere is a tree with N vertices.\nThe vertices are numbered 1,2, . . . , N.\nFor each i (1 <= i <= N - 1), the i-th edge connects Vertex x_i and y_i.\nSnuke would like to decorate the tree with ribbons, as follows.\nFirst, he will divide the N vertices into N / 2 pairs.\nHere, each vertex must belong to exactly one pair.\nThen, for each pair (u, v), put a ribbon through all the edges contained in the shortest path between u and v.\nSnuke is trying to divide the vertices into pairs so that the following condition is satisfied: \"for every edge, there is at least one ribbon going through it. \"\nHow many ways are there to divide the vertices into pairs, satisfying this condition?\nFind the count modulo 10^9 + 7.\nHere, two ways to divide the vertices into pairs are considered different when there is a pair that is contained in one of the two ways but not in the other.\nTask Constraint: N is an even number.\n2 <= N <= 5000\n1 <= x_i, y_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}\nTask Output: Print the number of the ways to divide the vertices into pairs, satisfying the condition, modulo 10^9 + 7.\nTask Samples: input: 4\n1 2\n2 3\n3 4 output: 2\n\nThere are three possible ways to divide the vertices into pairs, as shown below, and two satisfy the condition: the middle one and the right one.\ninput: 4\n1 2\n1 3\n1 4 output: 3\n\nThere are three possible ways to divide the vertices into pairs, as shown below, and all of them satisfy the condition.\ninput: 6\n1 2\n1 3\n3 4\n1 5\n5 6 output: 10\ninput: 10\n8 5\n10 8\n6 5\n1 5\n4 8\n2 10\n3 6\n9 2\n1 7 output: 672\n\n" }, { "title": "", "content": "Problem Statement There are N robots and M exits on a number line.\nThe N + M coordinates of these are all integers and all distinct.\nFor each i (1 <= i <= N), the coordinate of the i-th robot from the left is x_i.\nAlso, for each j (1 <= j <= M), the coordinate of the j-th exit from the left is y_j.\nSnuke can repeatedly perform the following two kinds of operations in any order to move all the robots simultaneously:\n\nIncrement the coordinates of all the robots on the number line by 1.\nDecrement the coordinates of all the robots on the number line by 1.\n\nEach robot will disappear from the number line when its position coincides with that of an exit, going through that exit.\nSnuke will continue performing operations until all the robots disappear.\nWhen all the robots disappear, how many combinations of exits can be used by the robots?\nFind the count modulo 10^9 + 7.\nHere, two combinations of exits are considered different when there is a robot that used different exits in those two combinations.", "constraint": "1 <= N, M <= 10^5\n1 <= x_1 < x_2 < ... < x_N <= 10^9\n1 <= y_1 < y_2 < ... < y_M <= 10^9\nAll given coordinates are integers.\nAll given coordinates are distinct.", "input": "Input is given from Standard Input in the following format:\nN M\nx_1 x_2 . . . x_N\ny_1 y_2 . . . y_M", "output": "Print the number of the combinations of exits that can be used by the robots when all the robots disappear, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n2 3\n1 4 output: 3\n\nThe i-th robot from the left will be called Robot i, and the j-th exit from the left will be called Exit j.\nThere are three possible combinations of exits (the exit used by Robot 1, the exit used by Robot 2) as follows:\n\n(Exit 1, Exit 1)\n(Exit 1, Exit 2)\n(Exit 2, Exit 2)", "input: 3 4\n2 5 10\n1 3 7 13 output: 8\n\nThe exit for each robot can be chosen independently, so there are 2^3 = 8 possible combinations of exits.", "input: 4 1\n1 2 4 5\n3 output: 1\n\nEvery robot uses Exit 1.", "input: 4 5\n2 5 7 11\n1 3 6 9 13 output: 6", "input: 10 10\n4 13 15 18 19 20 21 22 25 27\n1 5 11 12 14 16 23 26 29 30 output: 22"], "Pid": "p03279", "ProblemText": "Task Description: Problem Statement There are N robots and M exits on a number line.\nThe N + M coordinates of these are all integers and all distinct.\nFor each i (1 <= i <= N), the coordinate of the i-th robot from the left is x_i.\nAlso, for each j (1 <= j <= M), the coordinate of the j-th exit from the left is y_j.\nSnuke can repeatedly perform the following two kinds of operations in any order to move all the robots simultaneously:\n\nIncrement the coordinates of all the robots on the number line by 1.\nDecrement the coordinates of all the robots on the number line by 1.\n\nEach robot will disappear from the number line when its position coincides with that of an exit, going through that exit.\nSnuke will continue performing operations until all the robots disappear.\nWhen all the robots disappear, how many combinations of exits can be used by the robots?\nFind the count modulo 10^9 + 7.\nHere, two combinations of exits are considered different when there is a robot that used different exits in those two combinations.\nTask Constraint: 1 <= N, M <= 10^5\n1 <= x_1 < x_2 < ... < x_N <= 10^9\n1 <= y_1 < y_2 < ... < y_M <= 10^9\nAll given coordinates are integers.\nAll given coordinates are distinct.\nTask Input: Input is given from Standard Input in the following format:\nN M\nx_1 x_2 . . . x_N\ny_1 y_2 . . . y_M\nTask Output: Print the number of the combinations of exits that can be used by the robots when all the robots disappear, modulo 10^9 + 7.\nTask Samples: input: 2 2\n2 3\n1 4 output: 3\n\nThe i-th robot from the left will be called Robot i, and the j-th exit from the left will be called Exit j.\nThere are three possible combinations of exits (the exit used by Robot 1, the exit used by Robot 2) as follows:\n\n(Exit 1, Exit 1)\n(Exit 1, Exit 2)\n(Exit 2, Exit 2)\ninput: 3 4\n2 5 10\n1 3 7 13 output: 8\n\nThe exit for each robot can be chosen independently, so there are 2^3 = 8 possible combinations of exits.\ninput: 4 1\n1 2 4 5\n3 output: 1\n\nEvery robot uses Exit 1.\ninput: 4 5\n2 5 7 11\n1 3 6 9 13 output: 6\ninput: 10 10\n4 13 15 18 19 20 21 22 25 27\n1 5 11 12 14 16 23 26 29 30 output: 22\n\n" }, { "title": "", "content": "Problem Statement\nThere is a farm whose length and width are A yard and B yard, respectively. A farmer, John, made a vertical road and a horizontal road inside the farm from one border to another, as shown below: (The gray part represents the roads. )\n\nWhat is the area of this yard excluding the roads? Find it. note: Note\nIt can be proved that the positions of the roads do not affect the area.", "constraint": "A is an integer between 2 and 100 (inclusive).\nB is an integer between 2 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the area of this yard excluding the roads (in square yards).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 1\n\nIn this case, the area is 1 square yard.", "input: 5 7 output: 24\n\nIn this case, the area is 24 square yards."], "Pid": "p03280", "ProblemText": "Task Description: Problem Statement\nThere is a farm whose length and width are A yard and B yard, respectively. A farmer, John, made a vertical road and a horizontal road inside the farm from one border to another, as shown below: (The gray part represents the roads. )\n\nWhat is the area of this yard excluding the roads? Find it. note: Note\nIt can be proved that the positions of the roads do not affect the area.\nTask Constraint: A is an integer between 2 and 100 (inclusive).\nB is an integer between 2 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the area of this yard excluding the roads (in square yards).\nTask Samples: input: 2 2 output: 1\n\nIn this case, the area is 1 square yard.\ninput: 5 7 output: 24\n\nIn this case, the area is 24 square yards.\n\n" }, { "title": "", "content": "Problem Statement\nThe number 105 is quite special - it is odd but still it has eight divisors.\nNow, your task is this: how many odd numbers with exactly eight positive divisors are there between 1 and N (inclusive)?", "constraint": "N is an integer between 1 and 200 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the count.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 105 output: 1\n\nAmong the numbers between 1 and 105, the only number that is odd and has exactly eight divisors is 105.", "input: 7 output: 0\n\n1 has one divisor. 3,5 and 7 are all prime and have two divisors. Thus, there is no number that satisfies the condition."], "Pid": "p03281", "ProblemText": "Task Description: Problem Statement\nThe number 105 is quite special - it is odd but still it has eight divisors.\nNow, your task is this: how many odd numbers with exactly eight positive divisors are there between 1 and N (inclusive)?\nTask Constraint: N is an integer between 1 and 200 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the count.\nTask Samples: input: 105 output: 1\n\nAmong the numbers between 1 and 105, the only number that is odd and has exactly eight divisors is 105.\ninput: 7 output: 0\n\n1 has one divisor. 3,5 and 7 are all prime and have two divisors. Thus, there is no number that satisfies the condition.\n\n" }, { "title": "", "content": "Problem Statement\nMr. Infinity has a string S consisting of digits from 1 to 9. Each time the date changes, this string changes as follows:\n\nEach occurrence of 2 in S is replaced with 22. Similarly, each 3 becomes 333,4 becomes 4444,5 becomes 55555,6 becomes 666666,7 becomes 7777777,8 becomes 88888888 and 9 becomes 999999999.1 remains as 1.\n\nFor example, if S is 1324, it becomes 1333224444 the next day, and it becomes 133333333322224444444444444444 the day after next.\nYou are interested in what the string looks like after 5 * 10^{15} days. What is the K-th character from the left in the string after 5 * 10^{15} days?", "constraint": "S is a string of length between 1 and 100 (inclusive).\nK is an integer between 1 and 10^{18} (inclusive).\nThe length of the string after 5 * 10^{15} days is at least K.", "input": "Input is given from Standard Input in the following format:\nS\nK", "output": "Print the K-th character from the left in Mr. Infinity's string after 5 * 10^{15} days.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1214\n4 output: 2\n\nThe string S changes as follows: \n\nNow: 1214\nAfter one day: 12214444\nAfter two days: 1222214444444444444444\nAfter three days: 12222222214444444444444444444444444444444444444444444444444444444444444444\n\nThe first five characters in the string after 5 * 10^{15} days is 12222. As K=4, we should print the fourth character, 2.", "input: 3\n157 output: 3\n\nThe initial string is 3. The string after 5 * 10^{15} days consists only of 3.", "input: 299792458\n9460730472580800 output: 2"], "Pid": "p03282", "ProblemText": "Task Description: Problem Statement\nMr. Infinity has a string S consisting of digits from 1 to 9. Each time the date changes, this string changes as follows:\n\nEach occurrence of 2 in S is replaced with 22. Similarly, each 3 becomes 333,4 becomes 4444,5 becomes 55555,6 becomes 666666,7 becomes 7777777,8 becomes 88888888 and 9 becomes 999999999.1 remains as 1.\n\nFor example, if S is 1324, it becomes 1333224444 the next day, and it becomes 133333333322224444444444444444 the day after next.\nYou are interested in what the string looks like after 5 * 10^{15} days. What is the K-th character from the left in the string after 5 * 10^{15} days?\nTask Constraint: S is a string of length between 1 and 100 (inclusive).\nK is an integer between 1 and 10^{18} (inclusive).\nThe length of the string after 5 * 10^{15} days is at least K.\nTask Input: Input is given from Standard Input in the following format:\nS\nK\nTask Output: Print the K-th character from the left in Mr. Infinity's string after 5 * 10^{15} days.\nTask Samples: input: 1214\n4 output: 2\n\nThe string S changes as follows: \n\nNow: 1214\nAfter one day: 12214444\nAfter two days: 1222214444444444444444\nAfter three days: 12222222214444444444444444444444444444444444444444444444444444444444444444\n\nThe first five characters in the string after 5 * 10^{15} days is 12222. As K=4, we should print the fourth character, 2.\ninput: 3\n157 output: 3\n\nThe initial string is 3. The string after 5 * 10^{15} days consists only of 3.\ninput: 299792458\n9460730472580800 output: 2\n\n" }, { "title": "", "content": "Problem Statement\nIn Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1,2,3, . . . , N from west to east.\nA company called At Coder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i).\nTakahashi the king is interested in the following Q matters:\n\nThe number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i <= L_j and R_j <= q_i.\n\nAlthough he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.", "constraint": "N is an integer between 1 and 500 (inclusive).\nM is an integer between 1 and 200 \\ 000 (inclusive).\nQ is an integer between 1 and 100 \\ 000 (inclusive).\n1 <= L_i <= R_i <= N (1 <= i <= M)\n1 <= p_i <= q_i <= N (1 <= i <= Q)", "input": "Input is given from Standard Input in the following format:\nN M Q\nL_1 R_1\nL_2 R_2\n:\nL_M R_M\np_1 q_1\np_2 q_2\n:\np_Q q_Q", "output": "Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 1\n1 1\n1 2\n2 2\n1 2 output: 3\n\nAs all the trains runs within the section from City 1 to City 2, the answer to the only query is 3.", "input: 10 3 2\n1 5\n2 8\n7 10\n1 7\n3 10 output: 1\n1\n\nThe first query is on the section from City 1 to 7. There is only one train that runs strictly within that section: Train 1.\nThe second query is on the section from City 3 to 10. There is only one train that runs strictly within that section: Train 3.", "input: 10 10 10\n1 6\n2 9\n4 5\n4 7\n4 7\n5 8\n6 6\n6 7\n7 9\n10 10\n1 8\n1 9\n1 10\n2 8\n2 9\n2 10\n3 8\n3 9\n3 10\n1 10 output: 7\n9\n10\n6\n8\n9\n6\n7\n8\n10"], "Pid": "p03283", "ProblemText": "Task Description: Problem Statement\nIn Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1,2,3, . . . , N from west to east.\nA company called At Coder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i).\nTakahashi the king is interested in the following Q matters:\n\nThe number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i <= L_j and R_j <= q_i.\n\nAlthough he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.\nTask Constraint: N is an integer between 1 and 500 (inclusive).\nM is an integer between 1 and 200 \\ 000 (inclusive).\nQ is an integer between 1 and 100 \\ 000 (inclusive).\n1 <= L_i <= R_i <= N (1 <= i <= M)\n1 <= p_i <= q_i <= N (1 <= i <= Q)\nTask Input: Input is given from Standard Input in the following format:\nN M Q\nL_1 R_1\nL_2 R_2\n:\nL_M R_M\np_1 q_1\np_2 q_2\n:\np_Q q_Q\nTask Output: Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.\nTask Samples: input: 2 3 1\n1 1\n1 2\n2 2\n1 2 output: 3\n\nAs all the trains runs within the section from City 1 to City 2, the answer to the only query is 3.\ninput: 10 3 2\n1 5\n2 8\n7 10\n1 7\n3 10 output: 1\n1\n\nThe first query is on the section from City 1 to 7. There is only one train that runs strictly within that section: Train 1.\nThe second query is on the section from City 3 to 10. There is only one train that runs strictly within that section: Train 3.\ninput: 10 10 10\n1 6\n2 9\n4 5\n4 7\n4 7\n5 8\n6 6\n6 7\n7 9\n10 10\n1 8\n1 9\n1 10\n2 8\n2 9\n2 10\n3 8\n3 9\n3 10\n1 10 output: 7\n9\n10\n6\n8\n9\n6\n7\n8\n10\n\n" }, { "title": "", "content": "Problem Statement Takahashi has decided to distribute N At Coder Crackers to K users of as evenly as possible.\nWhen all the crackers are distributed, find the minimum possible (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user.", "constraint": "1 <= N,K <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the minimum possible (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 3 output: 1\n\nWhen the users receive two, two and three crackers, respectively, the (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user, is 1.", "input: 100 10 output: 0\n\nThe crackers can be distributed evenly.", "input: 1 1 output: 0"], "Pid": "p03284", "ProblemText": "Task Description: Problem Statement Takahashi has decided to distribute N At Coder Crackers to K users of as evenly as possible.\nWhen all the crackers are distributed, find the minimum possible (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user.\nTask Constraint: 1 <= N,K <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the minimum possible (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user.\nTask Samples: input: 7 3 output: 1\n\nWhen the users receive two, two and three crackers, respectively, the (absolute) difference between the largest number of crackers received by a user and the smallest number received by a user, is 1.\ninput: 100 10 output: 0\n\nThe crackers can be distributed evenly.\ninput: 1 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each.\nDetermine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.", "constraint": "N is an integer between 1 and 100, inclusive.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If there is a way to buy some cakes and some doughnuts for exactly N dollars, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11 output: Yes\n\nIf you buy one cake and one doughnut, the total will be 4 + 7 = 11 dollars.", "input: 40 output: Yes\n\nIf you buy ten cakes, the total will be 4 * 10 = 40 dollars.", "input: 3 output: No\n\nThe prices of cakes (4 dollars) and doughnuts (7 dollars) are both higher than 3 dollars, so there is no such way."], "Pid": "p03285", "ProblemText": "Task Description: Problem Statement La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each.\nDetermine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.\nTask Constraint: N is an integer between 1 and 100, inclusive.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If there is a way to buy some cakes and some doughnuts for exactly N dollars, print Yes; otherwise, print No.\nTask Samples: input: 11 output: Yes\n\nIf you buy one cake and one doughnut, the total will be 4 + 7 = 11 dollars.\ninput: 40 output: Yes\n\nIf you buy ten cakes, the total will be 4 * 10 = 40 dollars.\ninput: 3 output: No\n\nThe prices of cakes (4 dollars) and doughnuts (7 dollars) are both higher than 3 dollars, so there is no such way.\n\n" }, { "title": "", "content": "Problem Statement Given an integer N, find the base -2 representation of N.\nHere, S is the base -2 representation of N when the following are all satisfied:\n\nS is a string consisting of 0 and 1.\nUnless S = 0, the initial character of S is 1.\nLet S = S_k S_{k-1} . . . S_0, then S_0 * (-2)^0 + S_1 * (-2)^1 + . . . + S_k * (-2)^k = N.\n\nIt can be proved that, for any integer M, the base -2 representation of M is uniquely determined.", "constraint": "Every value in input is integer.\n-10^9 <= N <= 10^9", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the base -2 representation of N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: -9 output: 1011\n\nAs (-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9,1011 is the base -2 representation of -9.", "input: 123456789 output: 11000101011001101110100010101", "input: 0 output: 0"], "Pid": "p03286", "ProblemText": "Task Description: Problem Statement Given an integer N, find the base -2 representation of N.\nHere, S is the base -2 representation of N when the following are all satisfied:\n\nS is a string consisting of 0 and 1.\nUnless S = 0, the initial character of S is 1.\nLet S = S_k S_{k-1} . . . S_0, then S_0 * (-2)^0 + S_1 * (-2)^1 + . . . + S_k * (-2)^k = N.\n\nIt can be proved that, for any integer M, the base -2 representation of M is uniquely determined.\nTask Constraint: Every value in input is integer.\n-10^9 <= N <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the base -2 representation of N.\nTask Samples: input: -9 output: 1011\n\nAs (-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9,1011 is the base -2 representation of -9.\ninput: 123456789 output: 11000101011001101110100010101\ninput: 0 output: 0\n\n" }, { "title": "", "content": "Problem Statement There are N boxes arranged in a row from left to right. The i-th box from the left contains A_i candies.\nYou will take out the candies from some consecutive boxes and distribute them evenly to M children.\nSuch being the case, find the number of the pairs (l, r) that satisfy the following:\n\nl and r are both integers and satisfy 1 <= l <= r <= N.\nA_l + A_{l+1} + . . . + A_r is a multiple of M.", "constraint": "All values in input are integers.\n1 <= N <= 10^5\n2 <= M <= 10^9\n1 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N", "output": "Print the number of the pairs (l, r) that satisfy the conditions.\nNote that the number may not fit into a 32-bit integer type.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n4 1 5 output: 3\n\nThe sum A_l + A_{l+1} + ... + A_r for each pair (l, r) is as follows:\n\nSum for (1,1): 4\nSum for (1,2): 5\nSum for (1,3): 10\nSum for (2,2): 1\nSum for (2,3): 6\nSum for (3,3): 5\n\nAmong these, three are multiples of 2.", "input: 13 17\n29 7 5 7 9 51 7 13 8 55 42 9 81 output: 6", "input: 10 400000000\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 25"], "Pid": "p03287", "ProblemText": "Task Description: Problem Statement There are N boxes arranged in a row from left to right. The i-th box from the left contains A_i candies.\nYou will take out the candies from some consecutive boxes and distribute them evenly to M children.\nSuch being the case, find the number of the pairs (l, r) that satisfy the following:\n\nl and r are both integers and satisfy 1 <= l <= r <= N.\nA_l + A_{l+1} + . . . + A_r is a multiple of M.\nTask Constraint: All values in input are integers.\n1 <= N <= 10^5\n2 <= M <= 10^9\n1 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N\nTask Output: Print the number of the pairs (l, r) that satisfy the conditions.\nNote that the number may not fit into a 32-bit integer type.\nTask Samples: input: 3 2\n4 1 5 output: 3\n\nThe sum A_l + A_{l+1} + ... + A_r for each pair (l, r) is as follows:\n\nSum for (1,1): 4\nSum for (1,2): 5\nSum for (1,3): 10\nSum for (2,2): 1\nSum for (2,3): 6\nSum for (3,3): 5\n\nAmong these, three are multiples of 2.\ninput: 13 17\n29 7 5 7 9 51 7 13 8 55 42 9 81 output: 6\ninput: 10 400000000\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 25\n\n" }, { "title": "", "content": "Problem Statement A programming competition site At Code regularly holds programming contests.\nThe next contest on At Code is called ABC, which is rated for contestants with ratings less than 1200.\nThe contest after the ABC is called ARC, which is rated for contestants with ratings less than 2800.\nThe contest after the ARC is called AGC, which is rated for all contestants.\nTakahashi's rating on At Code is R. What is the next contest rated for him?", "constraint": "0 <= R <= 4208\nR is an integer.", "input": "Input is given from Standard Input in the following format:\nR", "output": "Print the name of the next contest rated for Takahashi (ABC, ARC or AGC).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1199 output: ABC\n\n1199 is less than 1200, so ABC will be rated.", "input: 1200 output: ARC\n\n1200 is not less than 1200 and ABC will be unrated, but it is less than 2800 and ARC will be rated.", "input: 4208 output: AGC"], "Pid": "p03288", "ProblemText": "Task Description: Problem Statement A programming competition site At Code regularly holds programming contests.\nThe next contest on At Code is called ABC, which is rated for contestants with ratings less than 1200.\nThe contest after the ABC is called ARC, which is rated for contestants with ratings less than 2800.\nThe contest after the ARC is called AGC, which is rated for all contestants.\nTakahashi's rating on At Code is R. What is the next contest rated for him?\nTask Constraint: 0 <= R <= 4208\nR is an integer.\nTask Input: Input is given from Standard Input in the following format:\nR\nTask Output: Print the name of the next contest rated for Takahashi (ABC, ARC or AGC).\nTask Samples: input: 1199 output: ABC\n\n1199 is less than 1200, so ABC will be rated.\ninput: 1200 output: ARC\n\n1200 is not less than 1200 and ABC will be unrated, but it is less than 2800 and ARC will be rated.\ninput: 4208 output: AGC\n\n" }, { "title": "", "content": "Problem Statement You are given a string S. Each character of S is uppercase or lowercase English letter.\nDetermine if S satisfies all of the following conditions:\n\nThe initial character of S is an uppercase A.\nThere is exactly one occurrence of C between the third character from the beginning and the second to last character (inclusive).\nAll letters except the A and C mentioned above are lowercase.", "constraint": "4 <= |S| <= 10 (|S| is the length of the string S.)\nEach character of S is uppercase or lowercase English letter.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S satisfies all of the conditions in the problem statement, print AC; otherwise, print WA.", "content_img": false, "lang": "en", "error": false, "samples": ["input: AtCoder output: AC\n\nThe first letter is A, the third letter is C and the remaining letters are all lowercase, so all the conditions are satisfied.", "input: ACoder output: WA\n\nThe second letter should not be C.", "input: AcycliC output: WA\n\nThe last letter should not be C, either.", "input: AtCoCo output: WA\n\nThere should not be two or more occurrences of C.", "input: Atcoder output: WA\n\nThe number of C should not be zero, either."], "Pid": "p03289", "ProblemText": "Task Description: Problem Statement You are given a string S. Each character of S is uppercase or lowercase English letter.\nDetermine if S satisfies all of the following conditions:\n\nThe initial character of S is an uppercase A.\nThere is exactly one occurrence of C between the third character from the beginning and the second to last character (inclusive).\nAll letters except the A and C mentioned above are lowercase.\nTask Constraint: 4 <= |S| <= 10 (|S| is the length of the string S.)\nEach character of S is uppercase or lowercase English letter.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S satisfies all of the conditions in the problem statement, print AC; otherwise, print WA.\nTask Samples: input: AtCoder output: AC\n\nThe first letter is A, the third letter is C and the remaining letters are all lowercase, so all the conditions are satisfied.\ninput: ACoder output: WA\n\nThe second letter should not be C.\ninput: AcycliC output: WA\n\nThe last letter should not be C, either.\ninput: AtCoCo output: WA\n\nThere should not be two or more occurrences of C.\ninput: Atcoder output: WA\n\nThe number of C should not be zero, either.\n\n" }, { "title": "", "content": "Problem Statement A programming competition site At Code provides algorithmic problems.\nEach problem is allocated a score based on its difficulty.\nCurrently, for each integer i between 1 and D (inclusive), there are p_i problems with a score of 100i points.\nThese p_1 + … + p_D problems are all of the problems available on At Code.\nA user of At Code has a value called total score.\nThe total score of a user is the sum of the following two elements:\n\nBase score: the sum of the scores of all problems solved by the user.\nPerfect bonuses: when a user solves all problems with a score of 100i points, he/she earns the perfect bonus of c_i points, aside from the base score (1 <= i <= D).\n\nTakahashi, who is the new user of At Code, has not solved any problem.\nHis objective is to have a total score of G or more points.\nAt least how many problems does he need to solve for this objective?", "constraint": "1 <= D <= 10\n1 <= p_i <= 100\n100 <= c_i <= 10^6\n100 <= G\nAll values in input are integers.\nc_i and G are all multiples of 100.\nIt is possible to have a total score of G or more points.", "input": "Input is given from Standard Input in the following format:\nD G\np_1 c_1\n:\np_D c_D", "output": "Print the minimum number of problems that needs to be solved in order to have a total score of G or more points. Note that this objective is always achievable (see Constraints).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 700\n3 500\n5 800 output: 3\n\nIn this case, there are three problems each with 100 points and five problems each with 200 points. The perfect bonus for solving all the 100-point problems is 500 points, and the perfect bonus for solving all the 200-point problems is 800 points. Takahashi's objective is to have a total score of 700 points or more.\nOne way to achieve this objective is to solve four 200-point problems and earn a base score of 800 points. However, if we solve three 100-point problems, we can earn the perfect bonus of 500 points in addition to the base score of 300 points, for a total score of 800 points, and we can achieve the objective with fewer problems.", "input: 2 2000\n3 500\n5 800 output: 7\n\nThis case is similar to Sample Input 1, but the Takahashi's objective this time is 2000 points or more. In this case, we inevitably need to solve all five 200-point problems, and by solving two 100-point problems additionally we have the total score of 2000 points.", "input: 2 400\n3 500\n5 800 output: 2\n\nThis case is again similar to Sample Input 1, but the Takahashi's objective this time is 400 points or more. In this case, we only need to solve two 200-point problems to achieve the objective.", "input: 5 25000\n20 1000\n40 1000\n50 1000\n30 1000\n1 1000 output: 66\n\nThere is only one 500-point problem, but the perfect bonus can be earned even in such a case."], "Pid": "p03290", "ProblemText": "Task Description: Problem Statement A programming competition site At Code provides algorithmic problems.\nEach problem is allocated a score based on its difficulty.\nCurrently, for each integer i between 1 and D (inclusive), there are p_i problems with a score of 100i points.\nThese p_1 + … + p_D problems are all of the problems available on At Code.\nA user of At Code has a value called total score.\nThe total score of a user is the sum of the following two elements:\n\nBase score: the sum of the scores of all problems solved by the user.\nPerfect bonuses: when a user solves all problems with a score of 100i points, he/she earns the perfect bonus of c_i points, aside from the base score (1 <= i <= D).\n\nTakahashi, who is the new user of At Code, has not solved any problem.\nHis objective is to have a total score of G or more points.\nAt least how many problems does he need to solve for this objective?\nTask Constraint: 1 <= D <= 10\n1 <= p_i <= 100\n100 <= c_i <= 10^6\n100 <= G\nAll values in input are integers.\nc_i and G are all multiples of 100.\nIt is possible to have a total score of G or more points.\nTask Input: Input is given from Standard Input in the following format:\nD G\np_1 c_1\n:\np_D c_D\nTask Output: Print the minimum number of problems that needs to be solved in order to have a total score of G or more points. Note that this objective is always achievable (see Constraints).\nTask Samples: input: 2 700\n3 500\n5 800 output: 3\n\nIn this case, there are three problems each with 100 points and five problems each with 200 points. The perfect bonus for solving all the 100-point problems is 500 points, and the perfect bonus for solving all the 200-point problems is 800 points. Takahashi's objective is to have a total score of 700 points or more.\nOne way to achieve this objective is to solve four 200-point problems and earn a base score of 800 points. However, if we solve three 100-point problems, we can earn the perfect bonus of 500 points in addition to the base score of 300 points, for a total score of 800 points, and we can achieve the objective with fewer problems.\ninput: 2 2000\n3 500\n5 800 output: 7\n\nThis case is similar to Sample Input 1, but the Takahashi's objective this time is 2000 points or more. In this case, we inevitably need to solve all five 200-point problems, and by solving two 100-point problems additionally we have the total score of 2000 points.\ninput: 2 400\n3 500\n5 800 output: 2\n\nThis case is again similar to Sample Input 1, but the Takahashi's objective this time is 400 points or more. In this case, we only need to solve two 200-point problems to achieve the objective.\ninput: 5 25000\n20 1000\n40 1000\n50 1000\n30 1000\n1 1000 output: 66\n\nThere is only one 500-point problem, but the perfect bonus can be earned even in such a case.\n\n" }, { "title": "", "content": "Problem Statement The ABC number of a string T is the number of triples of integers (i, j, k) that satisfy all of the following conditions:\n\n1 <= i < j < k <= |T| (|T| is the length of T. )\nT_i = A (T_i is the i-th character of T from the beginning. )\nT_j = B\nT_k = C\n\nFor example, when T = ABCBC, there are three triples of integers (i, j, k) that satisfy the conditions: (1,2,3), (1,2,5), (1,4,5). Thus, the ABC number of T is 3.\nYou are given a string S. Each character of S is A, B, C or ? .\nLet Q be the number of occurrences of ? in S. We can make 3^Q strings by replacing each occurrence of ? in S with A, B or C. Find the sum of the ABC numbers of all these strings.\nThis sum can be extremely large, so print the sum modulo 10^9 + 7.", "constraint": "3 <= |S| <= 10^5\nEach character of S is A, B, C or ?.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the sum of the ABC numbers of all the 3^Q strings, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: A??C output: 8\n\nIn this case, Q = 2, and we can make 3^Q = 9 strings by by replacing each occurrence of ? with A, B or C. The ABC number of each of these strings is as follows:\n\nAAAC: 0\nAABC: 2\nAACC: 0\nABAC: 1\nABBC: 2\nABCC: 2\nACAC: 0\nACBC: 1\nACCC: 0\n\nThe sum of these is 0 + 2 + 0 + 1 + 2 + 2 + 0 + 1 + 0 = 8, so we print 8 modulo 10^9 + 7, that is, 8.", "input: ABCBC output: 3\n\nWhen Q = 0, we print the ABC number of S itself, modulo 10^9 + 7. This string is the same as the one given as an example in the problem statement, and its ABC number is 3.", "input: ????C?????B??????A??????? output: 979596887\n\nIn this case, the sum of the ABC numbers of all the 3^Q strings is 2291979612924, and we should print this number modulo 10^9 + 7, that is, 979596887."], "Pid": "p03291", "ProblemText": "Task Description: Problem Statement The ABC number of a string T is the number of triples of integers (i, j, k) that satisfy all of the following conditions:\n\n1 <= i < j < k <= |T| (|T| is the length of T. )\nT_i = A (T_i is the i-th character of T from the beginning. )\nT_j = B\nT_k = C\n\nFor example, when T = ABCBC, there are three triples of integers (i, j, k) that satisfy the conditions: (1,2,3), (1,2,5), (1,4,5). Thus, the ABC number of T is 3.\nYou are given a string S. Each character of S is A, B, C or ? .\nLet Q be the number of occurrences of ? in S. We can make 3^Q strings by replacing each occurrence of ? in S with A, B or C. Find the sum of the ABC numbers of all these strings.\nThis sum can be extremely large, so print the sum modulo 10^9 + 7.\nTask Constraint: 3 <= |S| <= 10^5\nEach character of S is A, B, C or ?.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the sum of the ABC numbers of all the 3^Q strings, modulo 10^9 + 7.\nTask Samples: input: A??C output: 8\n\nIn this case, Q = 2, and we can make 3^Q = 9 strings by by replacing each occurrence of ? with A, B or C. The ABC number of each of these strings is as follows:\n\nAAAC: 0\nAABC: 2\nAACC: 0\nABAC: 1\nABBC: 2\nABCC: 2\nACAC: 0\nACBC: 1\nACCC: 0\n\nThe sum of these is 0 + 2 + 0 + 1 + 2 + 2 + 0 + 1 + 0 = 8, so we print 8 modulo 10^9 + 7, that is, 8.\ninput: ABCBC output: 3\n\nWhen Q = 0, we print the ABC number of S itself, modulo 10^9 + 7. This string is the same as the one given as an example in the problem statement, and its ABC number is 3.\ninput: ????C?????B??????A??????? output: 979596887\n\nIn this case, the sum of the ABC numbers of all the 3^Q strings is 2291979612924, and we should print this number modulo 10^9 + 7, that is, 979596887.\n\n" }, { "title": "", "content": "Problem Statement You have three tasks, all of which need to be completed.\nFirst, you can complete any one task at cost 0.\nThen, just after completing the i-th task, you can complete the j-th task at cost |A_j - A_i|.\nHere, |x| denotes the absolute value of x.\nFind the minimum total cost required to complete all the task.", "constraint": "All values in input are integers.\n1 <= A_1, A_2, A_3 <= 100", "input": "Input is given from Standard Input in the following format:\nA_1 A_2 A_3", "output": "Print the minimum total cost required to complete all the task.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 6 3 output: 5\n\nWhen the tasks are completed in the following order, the total cost will be 5, which is the minimum:\n\nComplete the first task at cost 0.\nComplete the third task at cost 2.\nComplete the second task at cost 3.", "input: 11 5 5 output: 6", "input: 100 100 100 output: 0"], "Pid": "p03292", "ProblemText": "Task Description: Problem Statement You have three tasks, all of which need to be completed.\nFirst, you can complete any one task at cost 0.\nThen, just after completing the i-th task, you can complete the j-th task at cost |A_j - A_i|.\nHere, |x| denotes the absolute value of x.\nFind the minimum total cost required to complete all the task.\nTask Constraint: All values in input are integers.\n1 <= A_1, A_2, A_3 <= 100\nTask Input: Input is given from Standard Input in the following format:\nA_1 A_2 A_3\nTask Output: Print the minimum total cost required to complete all the task.\nTask Samples: input: 1 6 3 output: 5\n\nWhen the tasks are completed in the following order, the total cost will be 5, which is the minimum:\n\nComplete the first task at cost 0.\nComplete the third task at cost 2.\nComplete the second task at cost 3.\ninput: 11 5 5 output: 6\ninput: 100 100 100 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given string S and T consisting of lowercase English letters.\nDetermine if S equals T after rotation.\nThat is, determine if S equals T after the following operation is performed some number of times:\nOperation: Let S = S_1 S_2 . . . S_{|S|}. Change S to S_{|S|} S_1 S_2 . . . S_{|S|-1}.\nHere, |X| denotes the length of the string X.", "constraint": "2 <= |S| <= 100\n|S| = |T|\nS and T consist of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS\nT", "output": "If S equals T after rotation, print Yes; if it does not, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: kyoto\ntokyo output: Yes\nIn the first operation, kyoto becomes okyot.\nIn the second operation, okyot becomes tokyo.", "input: abc\narc output: No\n\nabc does not equal arc after any number of operations.", "input: aaaaaaaaaaaaaaab\naaaaaaaaaaaaaaab output: Yes"], "Pid": "p03293", "ProblemText": "Task Description: Problem Statement You are given string S and T consisting of lowercase English letters.\nDetermine if S equals T after rotation.\nThat is, determine if S equals T after the following operation is performed some number of times:\nOperation: Let S = S_1 S_2 . . . S_{|S|}. Change S to S_{|S|} S_1 S_2 . . . S_{|S|-1}.\nHere, |X| denotes the length of the string X.\nTask Constraint: 2 <= |S| <= 100\n|S| = |T|\nS and T consist of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nT\nTask Output: If S equals T after rotation, print Yes; if it does not, print No.\nTask Samples: input: kyoto\ntokyo output: Yes\nIn the first operation, kyoto becomes okyot.\nIn the second operation, okyot becomes tokyo.\ninput: abc\narc output: No\n\nabc does not equal arc after any number of operations.\ninput: aaaaaaaaaaaaaaab\naaaaaaaaaaaaaaab output: Yes\n\n" }, { "title": "", "content": "Problem Statement You are given N positive integers a_1, a_2, . . . , a_N.\nFor a non-negative integer m, let f(m) = (m\\ mod\\ a_1) + (m\\ mod\\ a_2) + . . . + (m\\ mod\\ a_N).\nHere, X\\ mod\\ Y denotes the remainder of the division of X by Y.\nFind the maximum value of f.", "constraint": "All values in input are integers.\n2 <= N <= 3000\n2 <= a_i <= 10^5", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the maximum value of f.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 4 6 output: 10\n\nf(11) = (11\\ mod\\ 3) + (11\\ mod\\ 4) + (11\\ mod\\ 6) = 10 is the maximum value of f.", "input: 5\n7 46 11 20 11 output: 90", "input: 7\n994 518 941 851 647 2 581 output: 4527"], "Pid": "p03294", "ProblemText": "Task Description: Problem Statement You are given N positive integers a_1, a_2, . . . , a_N.\nFor a non-negative integer m, let f(m) = (m\\ mod\\ a_1) + (m\\ mod\\ a_2) + . . . + (m\\ mod\\ a_N).\nHere, X\\ mod\\ Y denotes the remainder of the division of X by Y.\nFind the maximum value of f.\nTask Constraint: All values in input are integers.\n2 <= N <= 3000\n2 <= a_i <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the maximum value of f.\nTask Samples: input: 3\n3 4 6 output: 10\n\nf(11) = (11\\ mod\\ 3) + (11\\ mod\\ 4) + (11\\ mod\\ 6) = 10 is the maximum value of f.\ninput: 5\n7 46 11 20 11 output: 90\ninput: 7\n994 518 941 851 647 2 581 output: 4527\n\n" }, { "title": "", "content": "Problem Statement There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.", "constraint": "All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= a_i < b_i <= N\nAll pairs (a_i, b_i) are distinct.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M", "output": "Print the minimum number of bridges that must be removed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n1 4\n2 5 output: 1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.", "input: 9 5\n1 8\n2 7\n3 5\n4 6\n7 9 output: 2", "input: 5 10\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5 output: 4"], "Pid": "p03295", "ProblemText": "Task Description: Problem Statement There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\nTask Constraint: All values in input are integers.\n2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= a_i < b_i <= N\nAll pairs (a_i, b_i) are distinct.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Output: Print the minimum number of bridges that must be removed.\nTask Samples: input: 5 2\n1 4\n2 5 output: 1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.\ninput: 9 5\n1 8\n2 7\n3 5\n4 6\n7 9 output: 2\ninput: 5 10\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5 output: 4\n\n" }, { "title": "", "content": "Problem Statement Takahashi lives in another world. There are slimes (creatures) of 10000 colors in this world. Let us call these colors Color 1,2, . . . , 10000.\nTakahashi has N slimes, and they are standing in a row from left to right. The color of the i-th slime from the left is a_i.\nIf two slimes of the same color are adjacent, they will start to combine themselves. Because Takahashi likes smaller slimes, he has decided to change the colors of some of the slimes with his magic.\nTakahashi can change the color of one slime to any of the 10000 colors by one spell.\nHow many spells are required so that no slimes will start to combine themselves?", "constraint": "2 <= N <= 100\n1 <= a_i <= N\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum number of spells required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 1 2 2 2 output: 2\n\nFor example, if we change the color of the second slime from the left to 4, and the color of the fourth slime to 5, the colors of the slimes will be 1,4,2,5,2, which satisfy the condition.", "input: 3\n1 2 1 output: 0\n\nAlthough the colors of the first and third slimes are the same, they are not adjacent, so no spell is required.", "input: 5\n1 1 1 1 1 output: 2\n\nFor example, if we change the colors of the second and fourth slimes from the left to 2, the colors of the slimes will be 1,2,1,2,1, which satisfy the condition.", "input: 14\n1 2 2 3 3 3 4 4 4 4 1 2 3 4 output: 4"], "Pid": "p03296", "ProblemText": "Task Description: Problem Statement Takahashi lives in another world. There are slimes (creatures) of 10000 colors in this world. Let us call these colors Color 1,2, . . . , 10000.\nTakahashi has N slimes, and they are standing in a row from left to right. The color of the i-th slime from the left is a_i.\nIf two slimes of the same color are adjacent, they will start to combine themselves. Because Takahashi likes smaller slimes, he has decided to change the colors of some of the slimes with his magic.\nTakahashi can change the color of one slime to any of the 10000 colors by one spell.\nHow many spells are required so that no slimes will start to combine themselves?\nTask Constraint: 2 <= N <= 100\n1 <= a_i <= N\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum number of spells required.\nTask Samples: input: 5\n1 1 2 2 2 output: 2\n\nFor example, if we change the color of the second slime from the left to 4, and the color of the fourth slime to 5, the colors of the slimes will be 1,4,2,5,2, which satisfy the condition.\ninput: 3\n1 2 1 output: 0\n\nAlthough the colors of the first and third slimes are the same, they are not adjacent, so no spell is required.\ninput: 5\n1 1 1 1 1 output: 2\n\nFor example, if we change the colors of the second and fourth slimes from the left to 2, the colors of the slimes will be 1,2,1,2,1, which satisfy the condition.\ninput: 14\n1 2 2 3 3 3 4 4 4 4 1 2 3 4 output: 4\n\n" }, { "title": "", "content": "Problem Statement Ringo Mart, a convenience store, sells apple juice.\nOn the opening day of Ringo Mart, there were A cans of juice in stock in the morning.\nSnuke buys B cans of juice here every day in the daytime.\nThen, the manager checks the number of cans of juice remaining in stock every night.\nIf there are C or less cans, D new cans will be added to the stock by the next morning.\nDetermine if Snuke can buy juice indefinitely, that is, there is always B or more cans of juice in stock when he attempts to buy them.\nNobody besides Snuke buy juice at this store.\nNote that each test case in this problem consists of T queries.", "constraint": "1 <= T <= 300\n1 <= A, B, C, D <= 10^{18}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nT\nA_1 B_1 C_1 D_1\nA_2 B_2 C_2 D_2\n:\nA_T B_T C_T D_T\n\nIn the i-th query, A = A_i, B = B_i, C = C_i, D = D_i.", "output": "Print T lines. The i-th line should contain Yes if Snuke can buy apple juice indefinitely in the i-th query; No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 14\n9 7 5 9\n9 7 6 9\n14 10 7 12\n14 10 8 12\n14 10 9 12\n14 10 7 11\n14 10 8 11\n14 10 9 11\n9 10 5 10\n10 10 5 10\n11 10 5 10\n16 10 5 10\n1000000000000000000 17 14 999999999999999985\n1000000000000000000 17 15 999999999999999985 output: No\nYes\nNo\nYes\nYes\nNo\nNo\nYes\nNo\nYes\nYes\nNo\nNo\nYes\n\nIn the first query, the number of cans of juice in stock changes as follows: (D represents daytime and N represents night.)\n9\n→D 2\n→N 11\n→D 4\n→N 13\n→D 6\n→N 6\n→D x\nIn the second query, the number of cans of juice in stock changes as follows:\n9\n→D 2\n→N 11\n→D 4\n→N 13\n→D 6\n→N 15\n→D 8\n→N 8\n→D 1\n→N 10\n→D 3\n→N 12\n→D 5\n→N 14\n→D 7\n→N 7\n→D 0\n→N 9\n→D 2\n→N 11\n→D …\nand so on, thus Snuke can buy juice indefinitely.", "input: 24\n1 2 3 4\n1 2 4 3\n1 3 2 4\n1 3 4 2\n1 4 2 3\n1 4 3 2\n2 1 3 4\n2 1 4 3\n2 3 1 4\n2 3 4 1\n2 4 1 3\n2 4 3 1\n3 1 2 4\n3 1 4 2\n3 2 1 4\n3 2 4 1\n3 4 1 2\n3 4 2 1\n4 1 2 3\n4 1 3 2\n4 2 1 3\n4 2 3 1\n4 3 1 2\n4 3 2 1 output: No\nNo\nNo\nNo\nNo\nNo\nYes\nYes\nNo\nNo\nNo\nNo\nYes\nYes\nYes\nNo\nNo\nNo\nYes\nYes\nYes\nNo\nNo\nNo"], "Pid": "p03297", "ProblemText": "Task Description: Problem Statement Ringo Mart, a convenience store, sells apple juice.\nOn the opening day of Ringo Mart, there were A cans of juice in stock in the morning.\nSnuke buys B cans of juice here every day in the daytime.\nThen, the manager checks the number of cans of juice remaining in stock every night.\nIf there are C or less cans, D new cans will be added to the stock by the next morning.\nDetermine if Snuke can buy juice indefinitely, that is, there is always B or more cans of juice in stock when he attempts to buy them.\nNobody besides Snuke buy juice at this store.\nNote that each test case in this problem consists of T queries.\nTask Constraint: 1 <= T <= 300\n1 <= A, B, C, D <= 10^{18}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nT\nA_1 B_1 C_1 D_1\nA_2 B_2 C_2 D_2\n:\nA_T B_T C_T D_T\n\nIn the i-th query, A = A_i, B = B_i, C = C_i, D = D_i.\nTask Output: Print T lines. The i-th line should contain Yes if Snuke can buy apple juice indefinitely in the i-th query; No otherwise.\nTask Samples: input: 14\n9 7 5 9\n9 7 6 9\n14 10 7 12\n14 10 8 12\n14 10 9 12\n14 10 7 11\n14 10 8 11\n14 10 9 11\n9 10 5 10\n10 10 5 10\n11 10 5 10\n16 10 5 10\n1000000000000000000 17 14 999999999999999985\n1000000000000000000 17 15 999999999999999985 output: No\nYes\nNo\nYes\nYes\nNo\nNo\nYes\nNo\nYes\nYes\nNo\nNo\nYes\n\nIn the first query, the number of cans of juice in stock changes as follows: (D represents daytime and N represents night.)\n9\n→D 2\n→N 11\n→D 4\n→N 13\n→D 6\n→N 6\n→D x\nIn the second query, the number of cans of juice in stock changes as follows:\n9\n→D 2\n→N 11\n→D 4\n→N 13\n→D 6\n→N 15\n→D 8\n→N 8\n→D 1\n→N 10\n→D 3\n→N 12\n→D 5\n→N 14\n→D 7\n→N 7\n→D 0\n→N 9\n→D 2\n→N 11\n→D …\nand so on, thus Snuke can buy juice indefinitely.\ninput: 24\n1 2 3 4\n1 2 4 3\n1 3 2 4\n1 3 4 2\n1 4 2 3\n1 4 3 2\n2 1 3 4\n2 1 4 3\n2 3 1 4\n2 3 4 1\n2 4 1 3\n2 4 3 1\n3 1 2 4\n3 1 4 2\n3 2 1 4\n3 2 4 1\n3 4 1 2\n3 4 2 1\n4 1 2 3\n4 1 3 2\n4 2 1 3\n4 2 3 1\n4 3 1 2\n4 3 2 1 output: No\nNo\nNo\nNo\nNo\nNo\nYes\nYes\nNo\nNo\nNo\nNo\nYes\nYes\nYes\nNo\nNo\nNo\nYes\nYes\nYes\nNo\nNo\nNo\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length 2N consisting of lowercase English letters.\nThere are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?\n\nThe string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.", "constraint": "1 <= N <= 18\nThe length of S is 2N.\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the number of ways to paint the string that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\ncabaacba output: 4\n\nThere are four ways to paint the string, as follows:\n\ncabaacba\ncabaacba\ncabaacba\ncabaacba", "input: 11\nmippiisssisssiipsspiim output: 504", "input: 4\nabcdefgh output: 0", "input: 18\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa output: 9075135300\n\nThe answer may not be representable as a 32-bit integer."], "Pid": "p03298", "ProblemText": "Task Description: Problem Statement You are given a string S of length 2N consisting of lowercase English letters.\nThere are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?\n\nThe string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.\nTask Constraint: 1 <= N <= 18\nThe length of S is 2N.\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the number of ways to paint the string that satisfy the condition.\nTask Samples: input: 4\ncabaacba output: 4\n\nThere are four ways to paint the string, as follows:\n\ncabaacba\ncabaacba\ncabaacba\ncabaacba\ninput: 11\nmippiisssisssiipsspiim output: 504\ninput: 4\nabcdefgh output: 0\ninput: 18\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa output: 9075135300\n\nThe answer may not be representable as a 32-bit integer.\n\n" }, { "title": "", "content": "Problem Statement Let us consider a grid of squares with 10^9 rows and N columns. Let (i, j) be the square at the i-th column (1 <= i <= N) from the left and j-th row (1 <= j <= 10^9) from the bottom.\nSnuke has cut out some part of the grid so that, for each i = 1,2, . . . , N, the bottom-most h_i squares are remaining in the i-th column from the left.\nNow, he will paint the remaining squares in red and blue.\nFind the number of the ways to paint the squares so that the following condition is satisfied:\n\nEvery remaining square is painted either red or blue.\nFor all 1 <= i <= N-1 and 1 <= j <= min(h_i, h_{i+1})-1, there are exactly two squares painted red and two squares painted blue among the following four squares: (i, j), (i, j+1), (i+1, j) and (i+1, j+1).\n\nSince the number of ways can be extremely large, print the count modulo 10^9+7.", "constraint": "1 <= N <= 100\n1 <= h_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nh_1 h_2 . . . h_N", "output": "Print the number of the ways to paint the squares, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\n2 3 5 4 1 2 4 2 1 output: 12800\n\nOne of the ways to paint the squares is shown below:\n\n #\n ## #\n ### #\n#### ###\n#########", "input: 2\n2 2 output: 6\n\nThere are six ways to paint the squares, as follows:\n\n## ## ## ## ## ##\n## ## ## ## ## ##", "input: 5\n2 1 2 1 2 output: 256\n\nEvery way to paint the squares satisfies the condition.", "input: 9\n27 18 28 18 28 45 90 45 23 output: 844733013\n\nRemember to print the number of ways modulo 10^9 + 7."], "Pid": "p03299", "ProblemText": "Task Description: Problem Statement Let us consider a grid of squares with 10^9 rows and N columns. Let (i, j) be the square at the i-th column (1 <= i <= N) from the left and j-th row (1 <= j <= 10^9) from the bottom.\nSnuke has cut out some part of the grid so that, for each i = 1,2, . . . , N, the bottom-most h_i squares are remaining in the i-th column from the left.\nNow, he will paint the remaining squares in red and blue.\nFind the number of the ways to paint the squares so that the following condition is satisfied:\n\nEvery remaining square is painted either red or blue.\nFor all 1 <= i <= N-1 and 1 <= j <= min(h_i, h_{i+1})-1, there are exactly two squares painted red and two squares painted blue among the following four squares: (i, j), (i, j+1), (i+1, j) and (i+1, j+1).\n\nSince the number of ways can be extremely large, print the count modulo 10^9+7.\nTask Constraint: 1 <= N <= 100\n1 <= h_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nh_1 h_2 . . . h_N\nTask Output: Print the number of the ways to paint the squares, modulo 10^9+7.\nTask Samples: input: 9\n2 3 5 4 1 2 4 2 1 output: 12800\n\nOne of the ways to paint the squares is shown below:\n\n #\n ## #\n ### #\n#### ###\n#########\ninput: 2\n2 2 output: 6\n\nThere are six ways to paint the squares, as follows:\n\n## ## ## ## ## ##\n## ## ## ## ## ##\ninput: 5\n2 1 2 1 2 output: 256\n\nEvery way to paint the squares satisfies the condition.\ninput: 9\n27 18 28 18 28 45 90 45 23 output: 844733013\n\nRemember to print the number of ways modulo 10^9 + 7.\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length 2N, containing N occurrences of a and N occurrences of b.\nYou will choose some of the characters in S. Here, for each i = 1,2, . . . , N, it is not allowed to choose exactly one of the following two: the i-th occurrence of a and the i-th occurrence of b. (That is, you can only choose both or neither. ) Then, you will concatenate the chosen characters (without changing the order).\nFind the lexicographically largest string that can be obtained in this way.", "constraint": "1 <= N <= 3000\nS is a string of length 2N containing N occurrences of a and N occurrences of b.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the lexicographically largest string that satisfies the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\naababb output: abab\n\nA subsequence of T obtained from taking the first, third, fourth and sixth characters in S, satisfies the condition.", "input: 3\nbbabaa output: bbabaa\n\nYou can choose all the characters.", "input: 6\nbbbaabbabaaa output: bbbabaaa", "input: 9\nabbbaababaababbaba output: bbaababababa"], "Pid": "p03300", "ProblemText": "Task Description: Problem Statement You are given a string S of length 2N, containing N occurrences of a and N occurrences of b.\nYou will choose some of the characters in S. Here, for each i = 1,2, . . . , N, it is not allowed to choose exactly one of the following two: the i-th occurrence of a and the i-th occurrence of b. (That is, you can only choose both or neither. ) Then, you will concatenate the chosen characters (without changing the order).\nFind the lexicographically largest string that can be obtained in this way.\nTask Constraint: 1 <= N <= 3000\nS is a string of length 2N containing N occurrences of a and N occurrences of b.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the lexicographically largest string that satisfies the condition.\nTask Samples: input: 3\naababb output: abab\n\nA subsequence of T obtained from taking the first, third, fourth and sixth characters in S, satisfies the condition.\ninput: 3\nbbabaa output: bbabaa\n\nYou can choose all the characters.\ninput: 6\nbbbaabbabaaa output: bbbabaaa\ninput: 9\nabbbaababaababbaba output: bbaababababa\n\n" }, { "title": "", "content": "Problem Statement There are N boxes arranged in a row from left to right. The i-th box from the left contains a_i manju (buns stuffed with bean paste).\nSugim and Sigma play a game using these boxes.\nThey alternately perform the following operation. Sugim goes first, and the game ends when a total of N operations are performed.\n\nChoose a box that still does not contain a piece and is adjacent to the box chosen in the other player's last operation, then put a piece in that box. If there are multiple such boxes, any of them can be chosen.\nIf there is no box that satisfies the condition above, or this is Sugim's first operation, choose any one box that still does not contain a piece, then put a piece in that box.\n\nAt the end of the game, each player can have the manju in the boxes in which he put his pieces.\nThey love manju, and each of them is wise enough to perform the optimal moves in order to have the maximum number of manju at the end of the game.\nFind the number of manju that each player will have at the end of the game.", "constraint": "2 <= N <= 300 000\n1 <= a_i <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the numbers of Sugim's manju and Sigma's manju at the end of the game, in this order, with a space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n20 100 10 1 10 output: 120 21\n\nIf the two performs the optimal moves, the game proceeds as follows:\n\nFirst, Sugim has to put his piece in the second box from the left.\nThen, Sigma has to put his piece in the leftmost box.\nThen, Sugim puts his piece in the third or fifth box.\nThen, Sigma puts his piece in the fourth box.\nFinally, Sugim puts his piece in the remaining box.", "input: 6\n4 5 1 1 4 5 output: 11 9", "input: 5\n1 10 100 10 1 output: 102 20"], "Pid": "p03301", "ProblemText": "Task Description: Problem Statement There are N boxes arranged in a row from left to right. The i-th box from the left contains a_i manju (buns stuffed with bean paste).\nSugim and Sigma play a game using these boxes.\nThey alternately perform the following operation. Sugim goes first, and the game ends when a total of N operations are performed.\n\nChoose a box that still does not contain a piece and is adjacent to the box chosen in the other player's last operation, then put a piece in that box. If there are multiple such boxes, any of them can be chosen.\nIf there is no box that satisfies the condition above, or this is Sugim's first operation, choose any one box that still does not contain a piece, then put a piece in that box.\n\nAt the end of the game, each player can have the manju in the boxes in which he put his pieces.\nThey love manju, and each of them is wise enough to perform the optimal moves in order to have the maximum number of manju at the end of the game.\nFind the number of manju that each player will have at the end of the game.\nTask Constraint: 2 <= N <= 300 000\n1 <= a_i <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the numbers of Sugim's manju and Sigma's manju at the end of the game, in this order, with a space in between.\nTask Samples: input: 5\n20 100 10 1 10 output: 120 21\n\nIf the two performs the optimal moves, the game proceeds as follows:\n\nFirst, Sugim has to put his piece in the second box from the left.\nThen, Sigma has to put his piece in the leftmost box.\nThen, Sugim puts his piece in the third or fifth box.\nThen, Sigma puts his piece in the fourth box.\nFinally, Sugim puts his piece in the remaining box.\ninput: 6\n4 5 1 1 4 5 output: 11 9\ninput: 5\n1 10 100 10 1 output: 102 20\n\n" }, { "title": "", "content": "Problem Statement You are given two integers a and b.\nDetermine if a+b=15 or a* b=15 or neither holds.\nNote that a+b=15 and a* b=15 do not hold at the same time.", "constraint": "1 <= a,b <= 15\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\na b", "output": "If a+b=15, print +;\nif a* b=15, print *;\nif neither holds, print x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 11 output: +\n\n4+11=15.", "input: 3 5 output: *\n\n3* 5=15.", "input: 1 1 output: x\n\n1+1=2 and 1* 1=1, neither of which is 15."], "Pid": "p03302", "ProblemText": "Task Description: Problem Statement You are given two integers a and b.\nDetermine if a+b=15 or a* b=15 or neither holds.\nNote that a+b=15 and a* b=15 do not hold at the same time.\nTask Constraint: 1 <= a,b <= 15\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\na b\nTask Output: If a+b=15, print +;\nif a* b=15, print *;\nif neither holds, print x.\nTask Samples: input: 4 11 output: +\n\n4+11=15.\ninput: 3 5 output: *\n\n3* 5=15.\ninput: 1 1 output: x\n\n1+1=2 and 1* 1=1, neither of which is 15.\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of lowercase English letters.\nWe will write down this string, starting a new line after every w letters. Print the string obtained by concatenating the letters at the beginnings of these lines from top to bottom.", "constraint": "1 <= w <= |S| <= 1000\nS consists of lowercase English letters.\nw is an integer.", "input": "Input is given from Standard Input in the following format:\nS\nw", "output": "Print the desired string in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abcdefgh\n3 output: adg\n\nWhen we write down abcdefgh, starting a new line after every three letters, we get the following:\nabc\ndef\ngh\nConcatenating the letters at the beginnings of these lines, we obtain adg.", "input: lllll\n1 output: lllll", "input: souuundhound\n2 output: suudon"], "Pid": "p03303", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of lowercase English letters.\nWe will write down this string, starting a new line after every w letters. Print the string obtained by concatenating the letters at the beginnings of these lines from top to bottom.\nTask Constraint: 1 <= w <= |S| <= 1000\nS consists of lowercase English letters.\nw is an integer.\nTask Input: Input is given from Standard Input in the following format:\nS\nw\nTask Output: Print the desired string in one line.\nTask Samples: input: abcdefgh\n3 output: adg\n\nWhen we write down abcdefgh, starting a new line after every three letters, we get the following:\nabc\ndef\ngh\nConcatenating the letters at the beginnings of these lines, we obtain adg.\ninput: lllll\n1 output: lllll\ninput: souuundhound\n2 output: suudon\n\n" }, { "title": "", "content": "Problem Statement Let us define the beauty of a sequence (a_1, . . . , a_n) as the number of pairs of two adjacent elements in it whose absolute differences are d.\nFor example, when d=1, the beauty of the sequence (3,2,3,10,9) is 3.\nThere are a total of n^m sequences of length m where each element is an integer between 1 and n (inclusive).\nFind the beauty of each of these n^m sequences, and print the average of those values.", "constraint": "0 <= d < n <= 10^9\n2 <= m <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nn m d", "output": "Print the average of the beauties of the sequences of length m where each element is an integer between 1 and n.\nThe output will be judged correct if the absolute or relative error is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 1 output: 1.0000000000\n\nThe beauty of (1,1,1) is 0.\nThe beauty of (1,1,2) is 1.\nThe beauty of (1,2,1) is 2.\nThe beauty of (1,2,2) is 1.\nThe beauty of (2,1,1) is 1.\nThe beauty of (2,1,2) is 2.\nThe beauty of (2,2,1) is 1.\nThe beauty of (2,2,2) is 0.\nThe answer is the average of these values: (0+1+2+1+1+2+1+0)/8=1.", "input: 1000000000 180707 0 output: 0.0001807060"], "Pid": "p03304", "ProblemText": "Task Description: Problem Statement Let us define the beauty of a sequence (a_1, . . . , a_n) as the number of pairs of two adjacent elements in it whose absolute differences are d.\nFor example, when d=1, the beauty of the sequence (3,2,3,10,9) is 3.\nThere are a total of n^m sequences of length m where each element is an integer between 1 and n (inclusive).\nFind the beauty of each of these n^m sequences, and print the average of those values.\nTask Constraint: 0 <= d < n <= 10^9\n2 <= m <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nn m d\nTask Output: Print the average of the beauties of the sequences of length m where each element is an integer between 1 and n.\nThe output will be judged correct if the absolute or relative error is at most 10^{-6}.\nTask Samples: input: 2 3 1 output: 1.0000000000\n\nThe beauty of (1,1,1) is 0.\nThe beauty of (1,1,2) is 1.\nThe beauty of (1,2,1) is 2.\nThe beauty of (1,2,2) is 1.\nThe beauty of (2,1,1) is 1.\nThe beauty of (2,1,2) is 2.\nThe beauty of (2,2,1) is 1.\nThe beauty of (2,2,2) is 0.\nThe answer is the average of these values: (0+1+2+1+1+2+1+0)/8=1.\ninput: 1000000000 180707 0 output: 0.0001807060\n\n" }, { "title": "", "content": "Problem Statement Kenkoooo is planning a trip in Republic of Snuke.\nIn this country, there are n cities and m trains running.\nThe cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally.\nAny city can be reached from any city by changing trains.\nTwo currencies are used in the country: yen and snuuk.\nAny train fare can be paid by both yen and snuuk.\nThe fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.\nIn a city with a money exchange office, you can change 1 yen into 1 snuuk.\nHowever, when you do a money exchange, you have to change all your yen into snuuk.\nThat is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk.\nCurrently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.\nKenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling.\nIt is acceptable to do the exchange in City s or City t.\nKenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange.\nFor each i=0, . . . , n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years.\nYou can assume that the trip finishes within the year.", "constraint": "2 <= n <= 10^5\n1 <= m <= 10^5\n1 <= s,t <= n\ns \\neq t\n1 <= u_i < v_i <= n\n1 <= a_i,b_i <= 10^9\nIf i\\neq j, then u_i \\neq u_j or v_i \\neq v_j.\nAny city can be reached from any city by changing trains.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nn m s t\nu_1 v_1 a_1 b_1\n:\nu_m v_m a_m b_m", "output": "Print n lines.\nIn the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 2 3\n1 4 1 100\n1 2 1 10\n1 3 20 1 output: 999999999999998\n999999999999989\n999999999999979\n999999999999897\n\nAfter 0 years, it is optimal to do the exchange in City 1.\nAfter 1 years, it is optimal to do the exchange in City 2.\nNote that City 1 can still be visited even after the exchange office is closed.\nAlso note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.\nAfter 2 years, it is optimal to do the exchange in City 3.\nAfter 3 years, it is optimal to do the exchange in City 4.\nNote that the same train can be used multiple times.", "input: 8 12 3 8\n2 8 685087149 857180777\n6 7 298270585 209942236\n2 4 346080035 234079976\n2 5 131857300 22507157\n4 8 30723332 173476334\n2 6 480845267 448565596\n1 4 181424400 548830121\n4 5 57429995 195056405\n7 8 160277628 479932440\n1 6 475692952 203530153\n3 5 336869679 160714712\n2 7 389775999 199123879 output: 999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994"], "Pid": "p03305", "ProblemText": "Task Description: Problem Statement Kenkoooo is planning a trip in Republic of Snuke.\nIn this country, there are n cities and m trains running.\nThe cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally.\nAny city can be reached from any city by changing trains.\nTwo currencies are used in the country: yen and snuuk.\nAny train fare can be paid by both yen and snuuk.\nThe fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.\nIn a city with a money exchange office, you can change 1 yen into 1 snuuk.\nHowever, when you do a money exchange, you have to change all your yen into snuuk.\nThat is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk.\nCurrently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.\nKenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling.\nIt is acceptable to do the exchange in City s or City t.\nKenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange.\nFor each i=0, . . . , n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years.\nYou can assume that the trip finishes within the year.\nTask Constraint: 2 <= n <= 10^5\n1 <= m <= 10^5\n1 <= s,t <= n\ns \\neq t\n1 <= u_i < v_i <= n\n1 <= a_i,b_i <= 10^9\nIf i\\neq j, then u_i \\neq u_j or v_i \\neq v_j.\nAny city can be reached from any city by changing trains.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nn m s t\nu_1 v_1 a_1 b_1\n:\nu_m v_m a_m b_m\nTask Output: Print n lines.\nIn the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.\nTask Samples: input: 4 3 2 3\n1 4 1 100\n1 2 1 10\n1 3 20 1 output: 999999999999998\n999999999999989\n999999999999979\n999999999999897\n\nAfter 0 years, it is optimal to do the exchange in City 1.\nAfter 1 years, it is optimal to do the exchange in City 2.\nNote that City 1 can still be visited even after the exchange office is closed.\nAlso note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.\nAfter 2 years, it is optimal to do the exchange in City 3.\nAfter 3 years, it is optimal to do the exchange in City 4.\nNote that the same train can be used multiple times.\ninput: 8 12 3 8\n2 8 685087149 857180777\n6 7 298270585 209942236\n2 4 346080035 234079976\n2 5 131857300 22507157\n4 8 30723332 173476334\n2 6 480845267 448565596\n1 4 181424400 548830121\n4 5 57429995 195056405\n7 8 160277628 479932440\n1 6 475692952 203530153\n3 5 336869679 160714712\n2 7 389775999 199123879 output: 999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n999999574976994\n\n" }, { "title": "", "content": "Problem Statement Kenkoooo found a simple connected graph.\nThe vertices are numbered 1 through n.\nThe i-th edge connects Vertex u_i and v_i, and has a fixed integer s_i.\nKenkoooo is trying to write a positive integer in each vertex so that the following condition is satisfied:\n\nFor every edge i, the sum of the positive integers written in Vertex u_i and v_i is equal to s_i.\n\nFind the number of such ways to write positive integers in the vertices.", "constraint": "2 <= n <= 10^5\n1 <= m <= 10^5\n1 <= u_i < v_i <= n\n2 <= s_i <= 10^9\nIf i\\neq j, then u_i \\neq u_j or v_i \\neq v_j.\nThe graph is connected.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nn m\nu_1 v_1 s_1\n:\nu_m v_m s_m", "output": "Print the number of ways to write positive integers in the vertices so that the condition is satisfied.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 3\n2 3 5\n1 3 4 output: 1\n\nThe condition will be satisfied if we write 1,2 and 3 in vertices 1,2 and 3, respectively.\nThere is no other way to satisfy the condition, so the answer is 1.", "input: 4 3\n1 2 6\n2 3 7\n3 4 5 output: 3\n\nLet a,b,c and d be the numbers to write in vertices 1,2,3 and 4, respectively.\nThere are three quadruples (a,b,c,d) that satisfy the condition:\n\n(a,b,c,d)=(1,5,2,3)\n(a,b,c,d)=(2,4,3,2)\n(a,b,c,d)=(3,3,4,1)", "input: 8 7\n1 2 1000000000\n2 3 2\n3 4 1000000000\n4 5 2\n5 6 1000000000\n6 7 2\n7 8 1000000000 output: 0"], "Pid": "p03306", "ProblemText": "Task Description: Problem Statement Kenkoooo found a simple connected graph.\nThe vertices are numbered 1 through n.\nThe i-th edge connects Vertex u_i and v_i, and has a fixed integer s_i.\nKenkoooo is trying to write a positive integer in each vertex so that the following condition is satisfied:\n\nFor every edge i, the sum of the positive integers written in Vertex u_i and v_i is equal to s_i.\n\nFind the number of such ways to write positive integers in the vertices.\nTask Constraint: 2 <= n <= 10^5\n1 <= m <= 10^5\n1 <= u_i < v_i <= n\n2 <= s_i <= 10^9\nIf i\\neq j, then u_i \\neq u_j or v_i \\neq v_j.\nThe graph is connected.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nn m\nu_1 v_1 s_1\n:\nu_m v_m s_m\nTask Output: Print the number of ways to write positive integers in the vertices so that the condition is satisfied.\nTask Samples: input: 3 3\n1 2 3\n2 3 5\n1 3 4 output: 1\n\nThe condition will be satisfied if we write 1,2 and 3 in vertices 1,2 and 3, respectively.\nThere is no other way to satisfy the condition, so the answer is 1.\ninput: 4 3\n1 2 6\n2 3 7\n3 4 5 output: 3\n\nLet a,b,c and d be the numbers to write in vertices 1,2,3 and 4, respectively.\nThere are three quadruples (a,b,c,d) that satisfy the condition:\n\n(a,b,c,d)=(1,5,2,3)\n(a,b,c,d)=(2,4,3,2)\n(a,b,c,d)=(3,3,4,1)\ninput: 8 7\n1 2 1000000000\n2 3 2\n3 4 1000000000\n4 5 2\n5 6 1000000000\n6 7 2\n7 8 1000000000 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.", "constraint": "1 <= N <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the minimum positive integer divisible by both 2 and N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.", "input: 10 output: 10", "input: 999999999 output: 1999999998"], "Pid": "p03307", "ProblemText": "Task Description: Problem Statement You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\nTask Constraint: 1 <= N <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the minimum positive integer divisible by both 2 and N.\nTask Samples: input: 3 output: 6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.\ninput: 10 output: 10\ninput: 999999999 output: 1999999998\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence A of length N.\nFind the maximum absolute difference of two elements (with different indices) in A.", "constraint": "2 <= N <= 100\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum absolute difference of two elements (with different indices) in A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 4 6 3 output: 5\n\nThe maximum absolute difference of two elements is A_3-A_1=6-1=5.", "input: 2\n1000000000 1 output: 999999999", "input: 5\n1 1 1 1 1 output: 0"], "Pid": "p03308", "ProblemText": "Task Description: Problem Statement You are given an integer sequence A of length N.\nFind the maximum absolute difference of two elements (with different indices) in A.\nTask Constraint: 2 <= N <= 100\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum absolute difference of two elements (with different indices) in A.\nTask Samples: input: 4\n1 4 6 3 output: 5\n\nThe maximum absolute difference of two elements is A_3-A_1=6-1=5.\ninput: 2\n1000000000 1 output: 999999999\ninput: 5\n1 1 1 1 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement Snuke has an integer sequence A of length N.\nHe will freely choose an integer b.\nHere, he will get sad if A_i and b+i are far from each other.\nMore specifically, the sadness of Snuke is calculated as follows:\n\nabs(A_1 - (b+1)) + abs(A_2 - (b+2)) + . . . + abs(A_N - (b+N))\n\nHere, abs(x) is a function that returns the absolute value of x.\nFind the minimum possible sadness of Snuke.", "constraint": "1 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the minimum possible sadness of Snuke.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 2 3 5 5 output: 2\n\nIf we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.\nAny choice of b does not make the sadness of Snuke less than 2, so the answer is 2.", "input: 9\n1 2 3 4 5 6 7 8 9 output: 0", "input: 6\n6 5 4 3 2 1 output: 18", "input: 7\n1 1 1 1 2 3 4 output: 6"], "Pid": "p03309", "ProblemText": "Task Description: Problem Statement Snuke has an integer sequence A of length N.\nHe will freely choose an integer b.\nHere, he will get sad if A_i and b+i are far from each other.\nMore specifically, the sadness of Snuke is calculated as follows:\n\nabs(A_1 - (b+1)) + abs(A_2 - (b+2)) + . . . + abs(A_N - (b+N))\n\nHere, abs(x) is a function that returns the absolute value of x.\nFind the minimum possible sadness of Snuke.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the minimum possible sadness of Snuke.\nTask Samples: input: 5\n2 2 3 5 5 output: 2\n\nIf we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.\nAny choice of b does not make the sadness of Snuke less than 2, so the answer is 2.\ninput: 9\n1 2 3 4 5 6 7 8 9 output: 0\ninput: 6\n6 5 4 3 2 1 output: 18\ninput: 7\n1 1 1 1 2 3 4 output: 6\n\n" }, { "title": "", "content": "Problem Statement Snuke has an integer sequence A of length N.\nHe will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E.\nThe positions of the cuts can be freely chosen.\nLet P, Q, R, S be the sums of the elements in B, C, D, E, respectively.\nSnuke is happier when the absolute difference of the maximum and the minimum among P, Q, R, S is smaller.\nFind the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.", "constraint": "4 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Find the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3 2 4 1 2 output: 2\n\nIf we divide A as B,C,D,E=(3),(2),(4),(1,2), then P=3,Q=2,R=4,S=1+2=3.\nHere, the maximum and the minimum among P,Q,R,S are 4 and 2, with the absolute difference of 2.\nWe cannot make the absolute difference of the maximum and the minimum less than 2, so the answer is 2.", "input: 10\n10 71 84 33 6 47 23 25 52 64 output: 36", "input: 7\n1 2 3 1000000000 4 5 6 output: 999999994"], "Pid": "p03310", "ProblemText": "Task Description: Problem Statement Snuke has an integer sequence A of length N.\nHe will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E.\nThe positions of the cuts can be freely chosen.\nLet P, Q, R, S be the sums of the elements in B, C, D, E, respectively.\nSnuke is happier when the absolute difference of the maximum and the minimum among P, Q, R, S is smaller.\nFind the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.\nTask Constraint: 4 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Find the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.\nTask Samples: input: 5\n3 2 4 1 2 output: 2\n\nIf we divide A as B,C,D,E=(3),(2),(4),(1,2), then P=3,Q=2,R=4,S=1+2=3.\nHere, the maximum and the minimum among P,Q,R,S are 4 and 2, with the absolute difference of 2.\nWe cannot make the absolute difference of the maximum and the minimum less than 2, so the answer is 2.\ninput: 10\n10 71 84 33 6 47 23 25 52 64 output: 36\ninput: 7\n1 2 3 1000000000 4 5 6 output: 999999994\n\n" }, { "title": "", "content": "Problem Statement Snuke has an integer sequence A of length N.\nHe will freely choose an integer b.\nHere, he will get sad if A_i and b+i are far from each other.\nMore specifically, the sadness of Snuke is calculated as follows:\n\nabs(A_1 - (b+1)) + abs(A_2 - (b+2)) + . . . + abs(A_N - (b+N))\n\nHere, abs(x) is a function that returns the absolute value of x.\nFind the minimum possible sadness of Snuke.", "constraint": "1 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the minimum possible sadness of Snuke.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 2 3 5 5 output: 2\n\nIf we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.\nAny choice of b does not make the sadness of Snuke less than 2, so the answer is 2.", "input: 9\n1 2 3 4 5 6 7 8 9 output: 0", "input: 6\n6 5 4 3 2 1 output: 18", "input: 7\n1 1 1 1 2 3 4 output: 6"], "Pid": "p03311", "ProblemText": "Task Description: Problem Statement Snuke has an integer sequence A of length N.\nHe will freely choose an integer b.\nHere, he will get sad if A_i and b+i are far from each other.\nMore specifically, the sadness of Snuke is calculated as follows:\n\nabs(A_1 - (b+1)) + abs(A_2 - (b+2)) + . . . + abs(A_N - (b+N))\n\nHere, abs(x) is a function that returns the absolute value of x.\nFind the minimum possible sadness of Snuke.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the minimum possible sadness of Snuke.\nTask Samples: input: 5\n2 2 3 5 5 output: 2\n\nIf we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.\nAny choice of b does not make the sadness of Snuke less than 2, so the answer is 2.\ninput: 9\n1 2 3 4 5 6 7 8 9 output: 0\ninput: 6\n6 5 4 3 2 1 output: 18\ninput: 7\n1 1 1 1 2 3 4 output: 6\n\n" }, { "title": "", "content": "Problem Statement Snuke has an integer sequence A of length N.\nHe will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E.\nThe positions of the cuts can be freely chosen.\nLet P, Q, R, S be the sums of the elements in B, C, D, E, respectively.\nSnuke is happier when the absolute difference of the maximum and the minimum among P, Q, R, S is smaller.\nFind the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.", "constraint": "4 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Find the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3 2 4 1 2 output: 2\n\nIf we divide A as B,C,D,E=(3),(2),(4),(1,2), then P=3,Q=2,R=4,S=1+2=3.\nHere, the maximum and the minimum among P,Q,R,S are 4 and 2, with the absolute difference of 2.\nWe cannot make the absolute difference of the maximum and the minimum less than 2, so the answer is 2.", "input: 10\n10 71 84 33 6 47 23 25 52 64 output: 36", "input: 7\n1 2 3 1000000000 4 5 6 output: 999999994"], "Pid": "p03312", "ProblemText": "Task Description: Problem Statement Snuke has an integer sequence A of length N.\nHe will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E.\nThe positions of the cuts can be freely chosen.\nLet P, Q, R, S be the sums of the elements in B, C, D, E, respectively.\nSnuke is happier when the absolute difference of the maximum and the minimum among P, Q, R, S is smaller.\nFind the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.\nTask Constraint: 4 <= N <= 2 * 10^5\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Find the minimum possible absolute difference of the maximum and the minimum among P, Q, R, S.\nTask Samples: input: 5\n3 2 4 1 2 output: 2\n\nIf we divide A as B,C,D,E=(3),(2),(4),(1,2), then P=3,Q=2,R=4,S=1+2=3.\nHere, the maximum and the minimum among P,Q,R,S are 4 and 2, with the absolute difference of 2.\nWe cannot make the absolute difference of the maximum and the minimum less than 2, so the answer is 2.\ninput: 10\n10 71 84 33 6 47 23 25 52 64 output: 36\ninput: 7\n1 2 3 1000000000 4 5 6 output: 999999994\n\n" }, { "title": "", "content": "Problem Statement There is an integer sequence of length 2^N: A_0, A_1, . . . , A_{2^N-1}. (Note that the sequence is 0-indexed. )\nFor every integer K satisfying 1 <= K <= 2^N-1, solve the following problem:\n\nLet i and j be integers. Find the maximum value of A_i + A_j where 0 <= i < j <= 2^N-1 and (i or j) <= K.\nHere, or denotes the bitwise OR.", "constraint": "1 <= N <= 18\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_0 A_1 . . . A_{2^N-1}", "output": "Print 2^N-1 lines.\nIn the i-th line, print the answer of the problem above for K=i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2 3 1 output: 3\n4\n5\n\nFor K=1, the only possible pair of i and j is (i,j)=(0,1), so the answer is A_0+A_1=1+2=3.\nFor K=2, the possible pairs of i and j are (i,j)=(0,1),(0,2).\nWhen (i,j)=(0,2), A_i+A_j=1+3=4. This is the maximum value, so the answer is 4.\nFor K=3, the possible pairs of i and j are (i,j)=(0,1),(0,2),(0,3),(1,2),(1,3),(2,3) .\nWhen (i,j)=(1,2), A_i+A_j=2+3=5. This is the maximum value, so the answer is 5.", "input: 3\n10 71 84 33 6 47 23 25 output: 81\n94\n155\n155\n155\n155\n155", "input: 4\n75 26 45 72 81 47 97 97 2 2 25 82 84 17 56 32 output: 101\n120\n147\n156\n156\n178\n194\n194\n194\n194\n194\n194\n194\n194\n194"], "Pid": "p03313", "ProblemText": "Task Description: Problem Statement There is an integer sequence of length 2^N: A_0, A_1, . . . , A_{2^N-1}. (Note that the sequence is 0-indexed. )\nFor every integer K satisfying 1 <= K <= 2^N-1, solve the following problem:\n\nLet i and j be integers. Find the maximum value of A_i + A_j where 0 <= i < j <= 2^N-1 and (i or j) <= K.\nHere, or denotes the bitwise OR.\nTask Constraint: 1 <= N <= 18\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_0 A_1 . . . A_{2^N-1}\nTask Output: Print 2^N-1 lines.\nIn the i-th line, print the answer of the problem above for K=i.\nTask Samples: input: 2\n1 2 3 1 output: 3\n4\n5\n\nFor K=1, the only possible pair of i and j is (i,j)=(0,1), so the answer is A_0+A_1=1+2=3.\nFor K=2, the possible pairs of i and j are (i,j)=(0,1),(0,2).\nWhen (i,j)=(0,2), A_i+A_j=1+3=4. This is the maximum value, so the answer is 4.\nFor K=3, the possible pairs of i and j are (i,j)=(0,1),(0,2),(0,3),(1,2),(1,3),(2,3) .\nWhen (i,j)=(1,2), A_i+A_j=2+3=5. This is the maximum value, so the answer is 5.\ninput: 3\n10 71 84 33 6 47 23 25 output: 81\n94\n155\n155\n155\n155\n155\ninput: 4\n75 26 45 72 81 47 97 97 2 2 25 82 84 17 56 32 output: 101\n120\n147\n156\n156\n178\n194\n194\n194\n194\n194\n194\n194\n194\n194\n\n" }, { "title": "", "content": "Problem Statement You are given integers N, K, and an integer sequence A of length M.\nAn integer sequence where each element is between 1 and K (inclusive) is said to be colorful when there exists a contiguous subsequence of length K of the sequence that contains one occurrence of each integer between 1 and K (inclusive).\nFor every colorful integer sequence of length N, count the number of the contiguous subsequences of that sequence which coincide with A, then find the sum of all the counts.\nHere, the answer can be extremely large, so find the sum modulo 10^9+7.", "constraint": "1 <= N <= 25000\n1 <= K <= 400\n1 <= M <= N\n1 <= A_i <= K\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K M\nA_1 A_2 . . . A_M", "output": "For every colorful integer sequence of length N, count the number of the contiguous subsequences of that sequence which coincide with A, then print the sum of all the counts modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 1\n1 output: 9\n\nThere are six colorful sequences of length 3: (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2) and (2,2,1).\nThe numbers of the contiguous subsequences of these sequences that coincide with A=(1) are 2,2,1,2,1 and 1, respectively.\nThus, the answer is their sum, 9.", "input: 4 2 2\n1 2 output: 12", "input: 7 4 5\n1 2 3 1 2 output: 17", "input: 5 4 3\n1 1 1 output: 0", "input: 10 3 5\n1 1 2 3 3 output: 1458", "input: 25000 400 4\n3 7 31 127 output: 923966268", "input: 9954 310 12\n267 193 278 294 6 63 86 166 157 193 168 43 output: 979180369"], "Pid": "p03314", "ProblemText": "Task Description: Problem Statement You are given integers N, K, and an integer sequence A of length M.\nAn integer sequence where each element is between 1 and K (inclusive) is said to be colorful when there exists a contiguous subsequence of length K of the sequence that contains one occurrence of each integer between 1 and K (inclusive).\nFor every colorful integer sequence of length N, count the number of the contiguous subsequences of that sequence which coincide with A, then find the sum of all the counts.\nHere, the answer can be extremely large, so find the sum modulo 10^9+7.\nTask Constraint: 1 <= N <= 25000\n1 <= K <= 400\n1 <= M <= N\n1 <= A_i <= K\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K M\nA_1 A_2 . . . A_M\nTask Output: For every colorful integer sequence of length N, count the number of the contiguous subsequences of that sequence which coincide with A, then print the sum of all the counts modulo 10^9+7.\nTask Samples: input: 3 2 1\n1 output: 9\n\nThere are six colorful sequences of length 3: (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2) and (2,2,1).\nThe numbers of the contiguous subsequences of these sequences that coincide with A=(1) are 2,2,1,2,1 and 1, respectively.\nThus, the answer is their sum, 9.\ninput: 4 2 2\n1 2 output: 12\ninput: 7 4 5\n1 2 3 1 2 output: 17\ninput: 5 4 3\n1 1 1 output: 0\ninput: 10 3 5\n1 1 2 3 3 output: 1458\ninput: 25000 400 4\n3 7 31 127 output: 923966268\ninput: 9954 310 12\n267 193 278 294 6 63 86 166 157 193 168 43 output: 979180369\n\n" }, { "title": "", "content": "Problem Statement There is always an integer in Takahashi's mind.\nInitially, the integer in Takahashi's mind is 0. Takahashi is now going to eat four symbols, each of which is + or -. When he eats +, the integer in his mind increases by 1; when he eats -, the integer in his mind decreases by 1.\nThe symbols Takahashi is going to eat are given to you as a string S. The i-th character in S is the i-th symbol for him to eat.\nFind the integer in Takahashi's mind after he eats all the symbols.", "constraint": "The length of S is 4.\nEach character in S is + or -.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the integer in Takahashi's mind after he eats all the symbols.", "content_img": false, "lang": "en", "error": false, "samples": ["input: +-++ output: 2\nInitially, the integer in Takahashi's mind is 0.\nThe first integer for him to eat is +. After eating it, the integer in his mind becomes 1.\nThe second integer to eat is -. After eating it, the integer in his mind becomes 0.\nThe third integer to eat is +. After eating it, the integer in his mind becomes 1.\nThe fourth integer to eat is +. After eating it, the integer in his mind becomes 2.\n\nThus, the integer in Takahashi's mind after he eats all the symbols is 2.", "input: -+-- output: -2", "input: ---- output: -4"], "Pid": "p03315", "ProblemText": "Task Description: Problem Statement There is always an integer in Takahashi's mind.\nInitially, the integer in Takahashi's mind is 0. Takahashi is now going to eat four symbols, each of which is + or -. When he eats +, the integer in his mind increases by 1; when he eats -, the integer in his mind decreases by 1.\nThe symbols Takahashi is going to eat are given to you as a string S. The i-th character in S is the i-th symbol for him to eat.\nFind the integer in Takahashi's mind after he eats all the symbols.\nTask Constraint: The length of S is 4.\nEach character in S is + or -.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the integer in Takahashi's mind after he eats all the symbols.\nTask Samples: input: +-++ output: 2\nInitially, the integer in Takahashi's mind is 0.\nThe first integer for him to eat is +. After eating it, the integer in his mind becomes 1.\nThe second integer to eat is -. After eating it, the integer in his mind becomes 0.\nThe third integer to eat is +. After eating it, the integer in his mind becomes 1.\nThe fourth integer to eat is +. After eating it, the integer in his mind becomes 2.\n\nThus, the integer in Takahashi's mind after he eats all the symbols is 2.\ninput: -+-- output: -2\ninput: ---- output: -4\n\n" }, { "title": "", "content": "Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n.\nFor example, S(101) = 1 + 0 + 1 = 2.\nGiven an integer N, determine if S(N) divides N.", "constraint": "1 <= N <= 10^9", "input": "Input is given from Standard Input in the following format:\nN", "output": "If S(N) divides N, print Yes; if it does not, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12 output: Yes\n\nIn this input, N=12.\nAs S(12) = 1 + 2 = 3, S(N) divides N.", "input: 101 output: No\n\nAs S(101) = 1 + 0 + 1 = 2, S(N) does not divide N.", "input: 999999999 output: Yes"], "Pid": "p03316", "ProblemText": "Task Description: Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n.\nFor example, S(101) = 1 + 0 + 1 = 2.\nGiven an integer N, determine if S(N) divides N.\nTask Constraint: 1 <= N <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If S(N) divides N, print Yes; if it does not, print No.\nTask Samples: input: 12 output: Yes\n\nIn this input, N=12.\nAs S(12) = 1 + 2 = 3, S(N) divides N.\ninput: 101 output: No\n\nAs S(101) = 1 + 0 + 1 = 2, S(N) does not divide N.\ninput: 999999999 output: Yes\n\n" }, { "title": "", "content": "Problem Statement There is a sequence of length N: A_1, A_2, . . . , A_N. Initially, this sequence is a permutation of 1,2, . . . , N.\nOn this sequence, Snuke can perform the following operation:\n\nChoose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.\n\nSnuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.\nFind the minimum number of operations required.\nIt can be proved that, Under the constraints of this problem, this objective is always achievable.", "constraint": "2 <= K <= N <= 100000\nA_1, A_2, ..., A_N is a permutation of 1,2, ..., N.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N", "output": "Print the minimum number of operations required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n2 3 1 4 output: 2\n\nOne optimal strategy is as follows:\nIn the first operation, choose the first, second and third elements. The sequence A becomes 1,1,1,4.\nIn the second operation, choose the second, third and fourth elements. The sequence A becomes 1,1,1,1.", "input: 3 3\n1 2 3 output: 1", "input: 8 3\n7 3 1 8 4 6 2 5 output: 4"], "Pid": "p03317", "ProblemText": "Task Description: Problem Statement There is a sequence of length N: A_1, A_2, . . . , A_N. Initially, this sequence is a permutation of 1,2, . . . , N.\nOn this sequence, Snuke can perform the following operation:\n\nChoose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.\n\nSnuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.\nFind the minimum number of operations required.\nIt can be proved that, Under the constraints of this problem, this objective is always achievable.\nTask Constraint: 2 <= K <= N <= 100000\nA_1, A_2, ..., A_N is a permutation of 1,2, ..., N.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nTask Output: Print the minimum number of operations required.\nTask Samples: input: 4 3\n2 3 1 4 output: 2\n\nOne optimal strategy is as follows:\nIn the first operation, choose the first, second and third elements. The sequence A becomes 1,1,1,4.\nIn the second operation, choose the second, third and fourth elements. The sequence A becomes 1,1,1,1.\ninput: 3 3\n1 2 3 output: 1\ninput: 8 3\n7 3 1 8 4 6 2 5 output: 4\n\n" }, { "title": "", "content": "Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n.\nFor example, S(123) = 1 + 2 + 3 = 6.\nWe will call an integer n a Snuke number when, for all positive integers m such that m > n, \\frac{n}{S(n)} <= \\frac{m}{S(m)} holds.\nGiven an integer K, list the K smallest Snuke numbers.", "constraint": "1 <= K\nThe K-th smallest Snuke number is not greater than 10^{15}.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print K lines. The i-th line should contain the i-th smallest Snuke number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 output: 1\n2\n3\n4\n5\n6\n7\n8\n9\n19"], "Pid": "p03318", "ProblemText": "Task Description: Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n.\nFor example, S(123) = 1 + 2 + 3 = 6.\nWe will call an integer n a Snuke number when, for all positive integers m such that m > n, \\frac{n}{S(n)} <= \\frac{m}{S(m)} holds.\nGiven an integer K, list the K smallest Snuke numbers.\nTask Constraint: 1 <= K\nThe K-th smallest Snuke number is not greater than 10^{15}.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print K lines. The i-th line should contain the i-th smallest Snuke number.\nTask Samples: input: 10 output: 1\n2\n3\n4\n5\n6\n7\n8\n9\n19\n\n" }, { "title": "", "content": "Problem Statement There is a sequence of length N: A_1, A_2, . . . , A_N. Initially, this sequence is a permutation of 1,2, . . . , N.\nOn this sequence, Snuke can perform the following operation:\n\nChoose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.\n\nSnuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.\nFind the minimum number of operations required.\nIt can be proved that, Under the constraints of this problem, this objective is always achievable.", "constraint": "2 <= K <= N <= 100000\nA_1, A_2, ..., A_N is a permutation of 1,2, ..., N.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N", "output": "Print the minimum number of operations required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n2 3 1 4 output: 2\n\nOne optimal strategy is as follows:\nIn the first operation, choose the first, second and third elements. The sequence A becomes 1,1,1,4.\nIn the second operation, choose the second, third and fourth elements. The sequence A becomes 1,1,1,1.", "input: 3 3\n1 2 3 output: 1", "input: 8 3\n7 3 1 8 4 6 2 5 output: 4"], "Pid": "p03319", "ProblemText": "Task Description: Problem Statement There is a sequence of length N: A_1, A_2, . . . , A_N. Initially, this sequence is a permutation of 1,2, . . . , N.\nOn this sequence, Snuke can perform the following operation:\n\nChoose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.\n\nSnuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.\nFind the minimum number of operations required.\nIt can be proved that, Under the constraints of this problem, this objective is always achievable.\nTask Constraint: 2 <= K <= N <= 100000\nA_1, A_2, ..., A_N is a permutation of 1,2, ..., N.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nTask Output: Print the minimum number of operations required.\nTask Samples: input: 4 3\n2 3 1 4 output: 2\n\nOne optimal strategy is as follows:\nIn the first operation, choose the first, second and third elements. The sequence A becomes 1,1,1,4.\nIn the second operation, choose the second, third and fourth elements. The sequence A becomes 1,1,1,1.\ninput: 3 3\n1 2 3 output: 1\ninput: 8 3\n7 3 1 8 4 6 2 5 output: 4\n\n" }, { "title": "", "content": "Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n.\nFor example, S(123) = 1 + 2 + 3 = 6.\nWe will call an integer n a Snuke number when, for all positive integers m such that m > n, \\frac{n}{S(n)} <= \\frac{m}{S(m)} holds.\nGiven an integer K, list the K smallest Snuke numbers.", "constraint": "1 <= K\nThe K-th smallest Snuke number is not greater than 10^{15}.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print K lines. The i-th line should contain the i-th smallest Snuke number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 output: 1\n2\n3\n4\n5\n6\n7\n8\n9\n19"], "Pid": "p03320", "ProblemText": "Task Description: Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n.\nFor example, S(123) = 1 + 2 + 3 = 6.\nWe will call an integer n a Snuke number when, for all positive integers m such that m > n, \\frac{n}{S(n)} <= \\frac{m}{S(m)} holds.\nGiven an integer K, list the K smallest Snuke numbers.\nTask Constraint: 1 <= K\nThe K-th smallest Snuke number is not greater than 10^{15}.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print K lines. The i-th line should contain the i-th smallest Snuke number.\nTask Samples: input: 10 output: 1\n2\n3\n4\n5\n6\n7\n8\n9\n19\n\n" }, { "title": "", "content": "Problem Statement In the State of Takahashi in At Coderian Federation, there are N cities, numbered 1,2, . . . , N.\nM bidirectional roads connect these cities.\nThe i-th road connects City A_i and City B_i.\nEvery road connects two distinct cities.\nAlso, for any two cities, there is at most one road that directly connects them.\nOne day, it was decided that the State of Takahashi would be divided into two states, Taka and Hashi.\nAfter the division, each city in Takahashi would belong to either Taka or Hashi.\nIt is acceptable for all the cities to belong Taka, or for all the cities to belong Hashi.\nHere, the following condition should be satisfied:\n\nAny two cities in the same state, Taka or Hashi, are directly connected by a road.\n\nFind the minimum possible number of roads whose endpoint cities belong to the same state.\nIf it is impossible to divide the cities into Taka and Hashi so that the condition is satisfied, print -1.", "constraint": "2 <= N <= 700\n0 <= M <= N(N-1)/2\n1 <= A_i <= N\n1 <= B_i <= N\nA_i \\neq B_i\nIf i \\neq j, at least one of the following holds: A_i \\neq A_j and B_i \\neq B_j.\nIf i \\neq j, at least one of the following holds: A_i \\neq B_j and B_i \\neq A_j.", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n:\nA_M B_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n1 2\n1 3\n3 4\n3 5\n4 5 output: 4\n\nFor example, if the cities 1,2 belong to Taka and the cities 3,4,5 belong to Hashi, the condition is satisfied.\nHere, the number of roads whose endpoint cities belong to the same state, is 4.", "input: 5 1\n1 2 output: -1\n\nIn this sample, the condition cannot be satisfied regardless of which cities belong to each state.", "input: 4 3\n1 2\n1 3\n2 3 output: 3", "input: 10 39\n7 2\n7 1\n5 6\n5 8\n9 10\n2 8\n8 7\n3 10\n10 1\n8 10\n2 3\n7 4\n3 9\n4 10\n3 4\n6 1\n6 7\n9 5\n9 7\n6 9\n9 4\n4 6\n7 5\n8 3\n2 5\n9 2\n10 7\n8 6\n8 9\n7 3\n5 3\n4 5\n6 3\n2 10\n5 10\n4 2\n6 2\n8 4\n10 6 output: 21"], "Pid": "p03321", "ProblemText": "Task Description: Problem Statement In the State of Takahashi in At Coderian Federation, there are N cities, numbered 1,2, . . . , N.\nM bidirectional roads connect these cities.\nThe i-th road connects City A_i and City B_i.\nEvery road connects two distinct cities.\nAlso, for any two cities, there is at most one road that directly connects them.\nOne day, it was decided that the State of Takahashi would be divided into two states, Taka and Hashi.\nAfter the division, each city in Takahashi would belong to either Taka or Hashi.\nIt is acceptable for all the cities to belong Taka, or for all the cities to belong Hashi.\nHere, the following condition should be satisfied:\n\nAny two cities in the same state, Taka or Hashi, are directly connected by a road.\n\nFind the minimum possible number of roads whose endpoint cities belong to the same state.\nIf it is impossible to divide the cities into Taka and Hashi so that the condition is satisfied, print -1.\nTask Constraint: 2 <= N <= 700\n0 <= M <= N(N-1)/2\n1 <= A_i <= N\n1 <= B_i <= N\nA_i \\neq B_i\nIf i \\neq j, at least one of the following holds: A_i \\neq A_j and B_i \\neq B_j.\nIf i \\neq j, at least one of the following holds: A_i \\neq B_j and B_i \\neq A_j.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n:\nA_M B_M\nTask Output: Print the answer.\nTask Samples: input: 5 5\n1 2\n1 3\n3 4\n3 5\n4 5 output: 4\n\nFor example, if the cities 1,2 belong to Taka and the cities 3,4,5 belong to Hashi, the condition is satisfied.\nHere, the number of roads whose endpoint cities belong to the same state, is 4.\ninput: 5 1\n1 2 output: -1\n\nIn this sample, the condition cannot be satisfied regardless of which cities belong to each state.\ninput: 4 3\n1 2\n1 3\n2 3 output: 3\ninput: 10 39\n7 2\n7 1\n5 6\n5 8\n9 10\n2 8\n8 7\n3 10\n10 1\n8 10\n2 3\n7 4\n3 9\n4 10\n3 4\n6 1\n6 7\n9 5\n9 7\n6 9\n9 4\n4 6\n7 5\n8 3\n2 5\n9 2\n10 7\n8 6\n8 9\n7 3\n5 3\n4 5\n6 3\n2 10\n5 10\n4 2\n6 2\n8 4\n10 6 output: 21\n\n" }, { "title": "", "content": "Problem Statement In Takahashi's mind, there is always an integer sequence of length 2 * 10^9 + 1: A = (A_{-10^9}, A_{-10^9 + 1}, . . . , A_{10^9 - 1}, A_{10^9}) and an integer P.\nInitially, all the elements in the sequence A in Takahashi's mind are 0, and the value of the integer P is 0.\nWhen Takahashi eats symbols +, -, > and <, the sequence A and the integer P will change as follows:\n\nWhen he eats +, the value of A_P increases by 1;\nWhen he eats -, the value of A_P decreases by 1;\nWhen he eats >, the value of P increases by 1;\nWhen he eats <, the value of P decreases by 1.\n\nTakahashi has a string S of length N. Each character in S is one of the symbols +, -, > and <.\nHe chose a pair of integers (i, j) such that 1 <= i <= j <= N and ate the symbols that are the i-th, (i+1)-th, . . . , j-th characters in S, in this order.\nWe heard that, after he finished eating, the sequence A became the same as if he had eaten all the symbols in S from first to last.\nHow many such possible pairs (i, j) are there?", "constraint": "1 <= N <= 250000\n|S| = N\nEach character in S is +, -, > or <.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n+>+<- output: 3\n\nIf Takahashi eats all the symbols in S, A_1 = 1 and all other elements would be 0.\nThe pairs (i, j) that leads to the same sequence A are as follows:\n\n(1,5)\n(2,3)\n(2,4)", "input: 5\n+>+-< output: 5\n\nNote that the value of P may be different from the value when Takahashi eats all the symbols in S.", "input: 48\n-+><<><><><>>>+-<<>->>><<><<-+<>><+<<>+><-+->><< output: 475"], "Pid": "p03322", "ProblemText": "Task Description: Problem Statement In Takahashi's mind, there is always an integer sequence of length 2 * 10^9 + 1: A = (A_{-10^9}, A_{-10^9 + 1}, . . . , A_{10^9 - 1}, A_{10^9}) and an integer P.\nInitially, all the elements in the sequence A in Takahashi's mind are 0, and the value of the integer P is 0.\nWhen Takahashi eats symbols +, -, > and <, the sequence A and the integer P will change as follows:\n\nWhen he eats +, the value of A_P increases by 1;\nWhen he eats -, the value of A_P decreases by 1;\nWhen he eats >, the value of P increases by 1;\nWhen he eats <, the value of P decreases by 1.\n\nTakahashi has a string S of length N. Each character in S is one of the symbols +, -, > and <.\nHe chose a pair of integers (i, j) such that 1 <= i <= j <= N and ate the symbols that are the i-th, (i+1)-th, . . . , j-th characters in S, in this order.\nWe heard that, after he finished eating, the sequence A became the same as if he had eaten all the symbols in S from first to last.\nHow many such possible pairs (i, j) are there?\nTask Constraint: 1 <= N <= 250000\n|S| = N\nEach character in S is +, -, > or <.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the answer.\nTask Samples: input: 5\n+>+<- output: 3\n\nIf Takahashi eats all the symbols in S, A_1 = 1 and all other elements would be 0.\nThe pairs (i, j) that leads to the same sequence A are as follows:\n\n(1,5)\n(2,3)\n(2,4)\ninput: 5\n+>+-< output: 5\n\nNote that the value of P may be different from the value when Takahashi eats all the symbols in S.\ninput: 48\n-+><<><><><>>>+-<<>->>><<><<-+<>><+<<>+><-+->><< output: 475\n\n" }, { "title": "", "content": "Problem Statement\nE869120's and square1001's 16-th birthday is coming soon.\nTakahashi from At Coder Kingdom gave them a round cake cut into 16 equal fan-shaped pieces.\nE869120 and square1001 were just about to eat A and B of those pieces, respectively,\nwhen they found a note attached to the cake saying that \"the same person should not take two adjacent pieces of cake\".\nCan both of them obey the instruction in the note and take desired numbers of pieces of cake?", "constraint": "A and B are integers between 1 and 16 (inclusive).\nA+B is at most 16.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "If both E869120 and square1001 can obey the instruction in the note and take desired numbers of pieces of cake, print Yay! ; otherwise, print : (.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 output: Yay!\n\nBoth of them can take desired number of pieces as follows:", "input: 8 8 output: Yay!\n\nBoth of them can take desired number of pieces as follows:", "input: 11 4 output: :(\n\nIn this case, there is no way for them to take desired number of pieces, unfortunately."], "Pid": "p03323", "ProblemText": "Task Description: Problem Statement\nE869120's and square1001's 16-th birthday is coming soon.\nTakahashi from At Coder Kingdom gave them a round cake cut into 16 equal fan-shaped pieces.\nE869120 and square1001 were just about to eat A and B of those pieces, respectively,\nwhen they found a note attached to the cake saying that \"the same person should not take two adjacent pieces of cake\".\nCan both of them obey the instruction in the note and take desired numbers of pieces of cake?\nTask Constraint: A and B are integers between 1 and 16 (inclusive).\nA+B is at most 16.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: If both E869120 and square1001 can obey the instruction in the note and take desired numbers of pieces of cake, print Yay! ; otherwise, print : (.\nTask Samples: input: 5 4 output: Yay!\n\nBoth of them can take desired number of pieces as follows:\ninput: 8 8 output: Yay!\n\nBoth of them can take desired number of pieces as follows:\ninput: 11 4 output: :(\n\nIn this case, there is no way for them to take desired number of pieces, unfortunately.\n\n" }, { "title": "", "content": "Problem Statement\nToday, the memorable At Coder Beginner Contest 100 takes place. On this occasion, Takahashi would like to give an integer to Ringo.\nAs the name of the contest is At Coder Beginner Contest 100, Ringo would be happy if he is given a positive integer that can be divided by 100 exactly D times.\nFind the N-th smallest integer that would make Ringo happy.", "constraint": "D is 0,1 or 2.\nN is an integer between 1 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format:\nD N", "output": "Print the N-th smallest integer that can be divided by 100 exactly D times.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 5 output: 5\n\nThe integers that can be divided by 100 exactly 0 times (that is, not divisible by 100) are as follows: 1,2,3,4,5,6,7, ...\nThus, the 5-th smallest integer that would make Ringo happy is 5.", "input: 1 11 output: 1100\n\nThe integers that can be divided by 100 exactly once are as follows: 100,200,300,400,500,600,700,800,900,1 \\ 000,1 \\ 100, ...\nThus, the integer we are seeking is 1 \\ 100.", "input: 2 85 output: 850000\n\nThe integers that can be divided by 100 exactly twice are as follows: 10 \\ 000,20 \\ 000,30 \\ 000, ...\nThus, the integer we are seeking is 850 \\ 000."], "Pid": "p03324", "ProblemText": "Task Description: Problem Statement\nToday, the memorable At Coder Beginner Contest 100 takes place. On this occasion, Takahashi would like to give an integer to Ringo.\nAs the name of the contest is At Coder Beginner Contest 100, Ringo would be happy if he is given a positive integer that can be divided by 100 exactly D times.\nFind the N-th smallest integer that would make Ringo happy.\nTask Constraint: D is 0,1 or 2.\nN is an integer between 1 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nD N\nTask Output: Print the N-th smallest integer that can be divided by 100 exactly D times.\nTask Samples: input: 0 5 output: 5\n\nThe integers that can be divided by 100 exactly 0 times (that is, not divisible by 100) are as follows: 1,2,3,4,5,6,7, ...\nThus, the 5-th smallest integer that would make Ringo happy is 5.\ninput: 1 11 output: 1100\n\nThe integers that can be divided by 100 exactly once are as follows: 100,200,300,400,500,600,700,800,900,1 \\ 000,1 \\ 100, ...\nThus, the integer we are seeking is 1 \\ 100.\ninput: 2 85 output: 850000\n\nThe integers that can be divided by 100 exactly twice are as follows: 10 \\ 000,20 \\ 000,30 \\ 000, ...\nThus, the integer we are seeking is 850 \\ 000.\n\n" }, { "title": "", "content": "Problem Statement\nAs At Coder Beginner Contest 100 is taking place, the office of At Coder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, . . . , a_N}.\nSnuke, an employee, would like to play with this sequence.\nSpecifically, he would like to repeat the following operation as many times as possible:\nFor every i satisfying 1 <= i <= N, perform one of the following: \"divide a_i by 2\" and \"multiply a_i by 3\". \nHere, choosing \"multiply a_i by 3\" for every i is not allowed, and the value of a_i after the operation must be an integer.\n\nAt most how many operations can be performed?", "constraint": "N is an integer between 1 and 10 \\ 000 (inclusive).\na_i is an integer between 1 and 1 \\ 000 \\ 000 \\ 000 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 a_3 . . . a_N", "output": "Print the maximum number of operations that Snuke can perform.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n5 2 4 output: 3\n\nThe sequence is initially {5,2,4}. Three operations can be performed as follows:\n\nFirst, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {15,6,2}.\nNext, multiply a_1 by 3, divide a_2 by 2 and multiply a_3 by 3. The sequence is now {45,3,6}.\nFinally, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {135,9,3}.", "input: 4\n631 577 243 199 output: 0\n\nNo operation can be performed since all the elements are odd. Thus, the answer is 0.", "input: 10\n2184 2126 1721 1800 1024 2528 3360 1945 1280 1776 output: 39"], "Pid": "p03325", "ProblemText": "Task Description: Problem Statement\nAs At Coder Beginner Contest 100 is taking place, the office of At Coder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, . . . , a_N}.\nSnuke, an employee, would like to play with this sequence.\nSpecifically, he would like to repeat the following operation as many times as possible:\nFor every i satisfying 1 <= i <= N, perform one of the following: \"divide a_i by 2\" and \"multiply a_i by 3\". \nHere, choosing \"multiply a_i by 3\" for every i is not allowed, and the value of a_i after the operation must be an integer.\n\nAt most how many operations can be performed?\nTask Constraint: N is an integer between 1 and 10 \\ 000 (inclusive).\na_i is an integer between 1 and 1 \\ 000 \\ 000 \\ 000 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 a_3 . . . a_N\nTask Output: Print the maximum number of operations that Snuke can perform.\nTask Samples: input: 3\n5 2 4 output: 3\n\nThe sequence is initially {5,2,4}. Three operations can be performed as follows:\n\nFirst, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {15,6,2}.\nNext, multiply a_1 by 3, divide a_2 by 2 and multiply a_3 by 3. The sequence is now {45,3,6}.\nFinally, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {135,9,3}.\ninput: 4\n631 577 243 199 output: 0\n\nNo operation can be performed since all the elements are odd. Thus, the answer is 0.\ninput: 10\n2184 2126 1721 1800 1024 2528 3360 1945 1280 1776 output: 39\n\n" }, { "title": "", "content": "Problem Statement\nTakahashi became a pastry chef and opened a shop La Confiserie d'ABC to celebrate At Coder Beginner Contest 100.\nThe shop sells N kinds of cakes.\nEach kind of cake has three parameters \"beauty\", \"tastiness\" and \"popularity\". The i-th kind of cake has the beauty of x_i, the tastiness of y_i and the popularity of z_i.\nThese values may be zero or negative.\nRingo has decided to have M pieces of cakes here. He will choose the set of cakes as follows:\n\nDo not have two or more pieces of the same kind of cake.\nUnder the condition above, choose the set of cakes to maximize (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity).\n\nFind the maximum possible value of (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) for the set of cakes that Ringo chooses.", "constraint": "N is an integer between 1 and 1 \\ 000 (inclusive).\nM is an integer between 0 and N (inclusive).\nx_i, y_i, z_i \\ (1 <= i <= N) are integers between -10 \\ 000 \\ 000 \\ 000 and 10 \\ 000 \\ 000 \\ 000 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN M\nx_1 y_1 z_1\nx_2 y_2 z_2\n : :\nx_N y_N z_N", "output": "Print the maximum possible value of (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) for the set of cakes that Ringo chooses.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n3 1 4\n1 5 9\n2 6 5\n3 5 8\n9 7 9 output: 56\n\nConsider having the 2-nd, 4-th and 5-th kinds of cakes. The total beauty, tastiness and popularity will be as follows:\n\nBeauty: 1 + 3 + 9 = 13\nTastiness: 5 + 5 + 7 = 17\nPopularity: 9 + 8 + 9 = 26\n\nThe value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 13 + 17 + 26 = 56. This is the maximum value.", "input: 5 3\n1 -2 3\n-4 5 -6\n7 -8 -9\n-10 11 -12\n13 -14 15 output: 54\n\nConsider having the 1-st, 3-rd and 5-th kinds of cakes. The total beauty, tastiness and popularity will be as follows:\n\nBeauty: 1 + 7 + 13 = 21\nTastiness: (-2) + (-8) + (-14) = -24\nPopularity: 3 + (-9) + 15 = 9\n\nThe value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 21 + 24 + 9 = 54. This is the maximum value.", "input: 10 5\n10 -80 21\n23 8 38\n-94 28 11\n-26 -2 18\n-69 72 79\n-26 -86 -54\n-72 -50 59\n21 65 -32\n40 -94 87\n-62 18 82 output: 638\n\nIf we have the 3-rd, 4-th, 5-th, 7-th and 10-th kinds of cakes, the total beauty, tastiness and popularity will be -323,66 and 249, respectively.\nThe value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 323 + 66 + 249 = 638. This is the maximum value.", "input: 3 2\n2000000000 -9000000000 4000000000\n7000000000 -5000000000 3000000000\n6000000000 -1000000000 8000000000 output: 30000000000\n\nThe values of the beauty, tastiness and popularity of the cakes and the value to be printed may not fit into 32-bit integers."], "Pid": "p03326", "ProblemText": "Task Description: Problem Statement\nTakahashi became a pastry chef and opened a shop La Confiserie d'ABC to celebrate At Coder Beginner Contest 100.\nThe shop sells N kinds of cakes.\nEach kind of cake has three parameters \"beauty\", \"tastiness\" and \"popularity\". The i-th kind of cake has the beauty of x_i, the tastiness of y_i and the popularity of z_i.\nThese values may be zero or negative.\nRingo has decided to have M pieces of cakes here. He will choose the set of cakes as follows:\n\nDo not have two or more pieces of the same kind of cake.\nUnder the condition above, choose the set of cakes to maximize (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity).\n\nFind the maximum possible value of (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) for the set of cakes that Ringo chooses.\nTask Constraint: N is an integer between 1 and 1 \\ 000 (inclusive).\nM is an integer between 0 and N (inclusive).\nx_i, y_i, z_i \\ (1 <= i <= N) are integers between -10 \\ 000 \\ 000 \\ 000 and 10 \\ 000 \\ 000 \\ 000 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN M\nx_1 y_1 z_1\nx_2 y_2 z_2\n : :\nx_N y_N z_N\nTask Output: Print the maximum possible value of (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) for the set of cakes that Ringo chooses.\nTask Samples: input: 5 3\n3 1 4\n1 5 9\n2 6 5\n3 5 8\n9 7 9 output: 56\n\nConsider having the 2-nd, 4-th and 5-th kinds of cakes. The total beauty, tastiness and popularity will be as follows:\n\nBeauty: 1 + 3 + 9 = 13\nTastiness: 5 + 5 + 7 = 17\nPopularity: 9 + 8 + 9 = 26\n\nThe value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 13 + 17 + 26 = 56. This is the maximum value.\ninput: 5 3\n1 -2 3\n-4 5 -6\n7 -8 -9\n-10 11 -12\n13 -14 15 output: 54\n\nConsider having the 1-st, 3-rd and 5-th kinds of cakes. The total beauty, tastiness and popularity will be as follows:\n\nBeauty: 1 + 7 + 13 = 21\nTastiness: (-2) + (-8) + (-14) = -24\nPopularity: 3 + (-9) + 15 = 9\n\nThe value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 21 + 24 + 9 = 54. This is the maximum value.\ninput: 10 5\n10 -80 21\n23 8 38\n-94 28 11\n-26 -2 18\n-69 72 79\n-26 -86 -54\n-72 -50 59\n21 65 -32\n40 -94 87\n-62 18 82 output: 638\n\nIf we have the 3-rd, 4-th, 5-th, 7-th and 10-th kinds of cakes, the total beauty, tastiness and popularity will be -323,66 and 249, respectively.\nThe value (the absolute value of the total beauty) + (the absolute value of the total tastiness) + (the absolute value of the total popularity) here is 323 + 66 + 249 = 638. This is the maximum value.\ninput: 3 2\n2000000000 -9000000000 4000000000\n7000000000 -5000000000 3000000000\n6000000000 -1000000000 8000000000 output: 30000000000\n\nThe values of the beauty, tastiness and popularity of the cakes and the value to be printed may not fit into 32-bit integers.\n\n" }, { "title": "", "content": "Problem Statement Decades have passed since the beginning of At Coder Beginner Contest.\nThe contests are labeled as ABC001, ABC002, . . . from the first round, but after the 999-th round ABC999, a problem occurred: how the future rounds should be labeled?\nIn the end, the labels for the rounds from the 1000-th to the 1998-th are decided: ABD001, ABD002, . . . , ABD999.\nYou are given an integer N between 1 and 1998 (inclusive). Print the first three characters of the label of the N-th round of At Coder Beginner Contest.", "constraint": "1 <= N <= 1998\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the first three characters of the label of the N-th round of At Coder Beginner Contest.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 999 output: ABC\n\nThe 999-th round of AtCoder Beginner Contest is labeled as ABC999.", "input: 1000 output: ABD\n\nThe 1000-th round of AtCoder Beginner Contest is labeled as ABD001.", "input: 1481 output: ABD\n\nThe 1481-th round of AtCoder Beginner Contest is labeled as ABD482."], "Pid": "p03327", "ProblemText": "Task Description: Problem Statement Decades have passed since the beginning of At Coder Beginner Contest.\nThe contests are labeled as ABC001, ABC002, . . . from the first round, but after the 999-th round ABC999, a problem occurred: how the future rounds should be labeled?\nIn the end, the labels for the rounds from the 1000-th to the 1998-th are decided: ABD001, ABD002, . . . , ABD999.\nYou are given an integer N between 1 and 1998 (inclusive). Print the first three characters of the label of the N-th round of At Coder Beginner Contest.\nTask Constraint: 1 <= N <= 1998\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the first three characters of the label of the N-th round of At Coder Beginner Contest.\nTask Samples: input: 999 output: ABC\n\nThe 999-th round of AtCoder Beginner Contest is labeled as ABC999.\ninput: 1000 output: ABD\n\nThe 1000-th round of AtCoder Beginner Contest is labeled as ABD001.\ninput: 1481 output: ABD\n\nThe 1481-th round of AtCoder Beginner Contest is labeled as ABD482.\n\n" }, { "title": "", "content": "Problem Statement In some village, there are 999 towers that are 1, (1+2), (1+2+3), . . . , (1+2+3+. . . +999) meters high from west to east, at intervals of 1 meter.\nIt had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.\nAssuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.\nAssume also that the depth of the snow cover is always at least 1 meter.", "constraint": "1 <= a < b < 499500(=1+2+3+...+999)\nAll values in input are integers.\nThere is no input that contradicts the assumption.", "input": "Input is given from Standard Input in the following format:\na b", "output": "If the depth of the snow cover is x meters, print x as an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 13 output: 2\n\nThe heights of the two towers are 10 meters and 15 meters, respectively.\nThus, we can see that the depth of the snow cover is 2 meters.", "input: 54 65 output: 1"], "Pid": "p03328", "ProblemText": "Task Description: Problem Statement In some village, there are 999 towers that are 1, (1+2), (1+2+3), . . . , (1+2+3+. . . +999) meters high from west to east, at intervals of 1 meter.\nIt had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.\nAssuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.\nAssume also that the depth of the snow cover is always at least 1 meter.\nTask Constraint: 1 <= a < b < 499500(=1+2+3+...+999)\nAll values in input are integers.\nThere is no input that contradicts the assumption.\nTask Input: Input is given from Standard Input in the following format:\na b\nTask Output: If the depth of the snow cover is x meters, print x as an integer.\nTask Samples: input: 8 13 output: 2\n\nThe heights of the two towers are 10 meters and 15 meters, respectively.\nThus, we can see that the depth of the snow cover is 2 meters.\ninput: 54 65 output: 1\n\n" }, { "title": "", "content": "Problem Statement To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:\n1 yen (the currency of Japan)\n6 yen, 6^2(=36) yen, 6^3(=216) yen, . . .\n9 yen, 9^2(=81) yen, 9^3(=729) yen, . . .\nAt least how many operations are required to withdraw exactly N yen in total?\nIt is not allowed to re-deposit the money you withdrew.", "constraint": "1 <= N <= 100000\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If at least x operations are required to withdraw exactly N yen in total, print x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 127 output: 4\n\nBy withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.", "input: 3 output: 3\n\nBy withdrawing 1 yen three times, we can withdraw 3 yen in three operations.", "input: 44852 output: 16"], "Pid": "p03329", "ProblemText": "Task Description: Problem Statement To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:\n1 yen (the currency of Japan)\n6 yen, 6^2(=36) yen, 6^3(=216) yen, . . .\n9 yen, 9^2(=81) yen, 9^3(=729) yen, . . .\nAt least how many operations are required to withdraw exactly N yen in total?\nIt is not allowed to re-deposit the money you withdrew.\nTask Constraint: 1 <= N <= 100000\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If at least x operations are required to withdraw exactly N yen in total, print x.\nTask Samples: input: 127 output: 4\n\nBy withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.\ninput: 3 output: 3\n\nBy withdrawing 1 yen three times, we can withdraw 3 yen in three operations.\ninput: 44852 output: 16\n\n" }, { "title": "", "content": "Problem Statement There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.\nThese squares have to be painted in one of the C colors from Color 1 to Color C. Initially, (i, j) is painted in Color c_{i, j}.\nWe say the grid is a good grid when the following condition is met for all i, j, x, y satisfying 1 <= i, j, x, y <= N:\n\nIf (i+j) \\% 3=(x+y) \\% 3, the color of (i, j) and the color of (x, y) are the same.\nIf (i+j) \\% 3 \\neq (x+y) \\% 3, the color of (i, j) and the color of (x, y) are different.\n\nHere, X \\% Y represents X modulo Y.\nWe will repaint zero or more squares so that the grid will be a good grid.\nFor a square, the wrongness when the color of the square is X before repainting and Y after repainting, is D_{X, Y}.\nFind the minimum possible sum of the wrongness of all the squares.", "constraint": "1 <= N <= 500\n3 <= C <= 30\n1 <= D_{i,j} <= 1000 (i \\neq j),D_{i,j}=0 (i=j)\n1 <= c_{i,j} <= C\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN C\nD_{1,1} . . . D_{1, C}\n:\nD_{C, 1} . . . D_{C, C}\nc_{1,1} . . . c_{1, N}\n:\nc_{N, 1} . . . c_{N, N}", "output": "If the minimum possible sum of the wrongness of all the squares is x, print x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n0 1 1\n1 0 1\n1 4 0\n1 2\n3 3 output: 3\nRepaint (1,1) to Color 2. The wrongness of (1,1) becomes D_{1,2}=1.\nRepaint (1,2) to Color 3. The wrongness of (1,2) becomes D_{2,3}=1.\nRepaint (2,2) to Color 1. The wrongness of (2,2) becomes D_{3,1}=1.\n\nIn this case, the sum of the wrongness of all the squares is 3.\nNote that D_{i,j} \\neq D_{j,i} is possible.", "input: 4 3\n0 12 71\n81 0 53\n14 92 0\n1 1 2 1\n2 1 1 2\n2 2 1 3\n1 1 2 2 output: 428"], "Pid": "p03330", "ProblemText": "Task Description: Problem Statement There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.\nThese squares have to be painted in one of the C colors from Color 1 to Color C. Initially, (i, j) is painted in Color c_{i, j}.\nWe say the grid is a good grid when the following condition is met for all i, j, x, y satisfying 1 <= i, j, x, y <= N:\n\nIf (i+j) \\% 3=(x+y) \\% 3, the color of (i, j) and the color of (x, y) are the same.\nIf (i+j) \\% 3 \\neq (x+y) \\% 3, the color of (i, j) and the color of (x, y) are different.\n\nHere, X \\% Y represents X modulo Y.\nWe will repaint zero or more squares so that the grid will be a good grid.\nFor a square, the wrongness when the color of the square is X before repainting and Y after repainting, is D_{X, Y}.\nFind the minimum possible sum of the wrongness of all the squares.\nTask Constraint: 1 <= N <= 500\n3 <= C <= 30\n1 <= D_{i,j} <= 1000 (i \\neq j),D_{i,j}=0 (i=j)\n1 <= c_{i,j} <= C\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN C\nD_{1,1} . . . D_{1, C}\n:\nD_{C, 1} . . . D_{C, C}\nc_{1,1} . . . c_{1, N}\n:\nc_{N, 1} . . . c_{N, N}\nTask Output: If the minimum possible sum of the wrongness of all the squares is x, print x.\nTask Samples: input: 2 3\n0 1 1\n1 0 1\n1 4 0\n1 2\n3 3 output: 3\nRepaint (1,1) to Color 2. The wrongness of (1,1) becomes D_{1,2}=1.\nRepaint (1,2) to Color 3. The wrongness of (1,2) becomes D_{2,3}=1.\nRepaint (2,2) to Color 1. The wrongness of (2,2) becomes D_{3,1}=1.\n\nIn this case, the sum of the wrongness of all the squares is 3.\nNote that D_{i,j} \\neq D_{j,i} is possible.\ninput: 4 3\n0 12 71\n81 0 53\n14 92 0\n1 1 2 1\n2 1 1 2\n2 2 1 3\n1 1 2 2 output: 428\n\n" }, { "title": "", "content": "Problem Statement Takahashi has two positive integers A and B.\nIt is known that A plus B equals N.\nFind the minimum possible value of \"the sum of the digits of A\" plus \"the sum of the digits of B\" (in base 10).", "constraint": "2 <= N <= 10^5\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the minimum possible value of \"the sum of the digits of A\" plus \"the sum of the digits of B\".", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15 output: 6\n\nWhen A=2 and B=13, the sums of their digits are 2 and 4, which minimizes the value in question.", "input: 100000 output: 10"], "Pid": "p03331", "ProblemText": "Task Description: Problem Statement Takahashi has two positive integers A and B.\nIt is known that A plus B equals N.\nFind the minimum possible value of \"the sum of the digits of A\" plus \"the sum of the digits of B\" (in base 10).\nTask Constraint: 2 <= N <= 10^5\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the minimum possible value of \"the sum of the digits of A\" plus \"the sum of the digits of B\".\nTask Samples: input: 15 output: 6\n\nWhen A=2 and B=13, the sums of their digits are 2 and 4, which minimizes the value in question.\ninput: 100000 output: 10\n\n" }, { "title": "", "content": "Problem Statement Takahashi has a tower which is divided into N layers.\nInitially, all the layers are uncolored. Takahashi is going to paint some of the layers in red, green or blue to make a beautiful tower.\nHe defines the beauty of the tower as follows:\n\nThe beauty of the tower is the sum of the scores of the N layers, where the score of a layer is A if the layer is painted red, A+B if the layer is painted green, B if the layer is painted blue, and 0 if the layer is uncolored.\n\nHere, A and B are positive integer constants given beforehand. Also note that a layer may not be painted in two or more colors.\nTakahashi is planning to paint the tower so that the beauty of the tower becomes exactly K.\nHow many such ways are there to paint the tower? Find the count modulo 998244353.\nTwo ways to paint the tower are considered different when there exists a layer that is painted in different colors, or a layer that is painted in some color in one of the ways and not in the other.", "constraint": "1 <= N <= 3*10^5\n1 <= A,B <= 3*10^5\n0 <= K <= 18*10^{10}\nAll values in the input are integers.", "input": "Input is given from Standard Input in the following format:\nN A B K", "output": "Print the number of the ways to paint tiles, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1 2 5 output: 40\n\nIn this case, a red layer worth 1 points, a green layer worth 3 points and the blue layer worth 2 points. The beauty of the tower is 5 when we have one of the following sets of painted layers:\n\n1 green, 1 blue\n1 red, 2 blues\n2 reds, 1 green\n3 reds, 1 blue\n\nThe total number of the ways to produce them is 40.", "input: 2 5 6 0 output: 1\n\nThe beauty of the tower is 0 only when all the layers are uncolored. Thus, the answer is 1.", "input: 90081 33447 90629 6391049189 output: 577742975"], "Pid": "p03332", "ProblemText": "Task Description: Problem Statement Takahashi has a tower which is divided into N layers.\nInitially, all the layers are uncolored. Takahashi is going to paint some of the layers in red, green or blue to make a beautiful tower.\nHe defines the beauty of the tower as follows:\n\nThe beauty of the tower is the sum of the scores of the N layers, where the score of a layer is A if the layer is painted red, A+B if the layer is painted green, B if the layer is painted blue, and 0 if the layer is uncolored.\n\nHere, A and B are positive integer constants given beforehand. Also note that a layer may not be painted in two or more colors.\nTakahashi is planning to paint the tower so that the beauty of the tower becomes exactly K.\nHow many such ways are there to paint the tower? Find the count modulo 998244353.\nTwo ways to paint the tower are considered different when there exists a layer that is painted in different colors, or a layer that is painted in some color in one of the ways and not in the other.\nTask Constraint: 1 <= N <= 3*10^5\n1 <= A,B <= 3*10^5\n0 <= K <= 18*10^{10}\nAll values in the input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B K\nTask Output: Print the number of the ways to paint tiles, modulo 998244353.\nTask Samples: input: 4 1 2 5 output: 40\n\nIn this case, a red layer worth 1 points, a green layer worth 3 points and the blue layer worth 2 points. The beauty of the tower is 5 when we have one of the following sets of painted layers:\n\n1 green, 1 blue\n1 red, 2 blues\n2 reds, 1 green\n3 reds, 1 blue\n\nThe total number of the ways to produce them is 40.\ninput: 2 5 6 0 output: 1\n\nThe beauty of the tower is 0 only when all the layers are uncolored. Thus, the answer is 1.\ninput: 90081 33447 90629 6391049189 output: 577742975\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki will play a game with a number line and some segments.\nTakahashi is standing on the number line and he is initially at coordinate 0.\nAoki has N segments. The i-th segment is [L_i, R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).\nThe game has N steps. The i-th step proceeds as follows:\n\nFirst, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.\nThen, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.\n\nAfter N steps are performed, Takahashi will return to coordinate 0 and the game ends.\nLet K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?", "constraint": "1 <= N <= 10^5\n-10^5 <= L_i < R_i <= 10^5\nL_i and R_i are integers.", "input": "Input is given from Standard Input in the following format:\nN\nL_1 R_1\n:\nL_N R_N", "output": "Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above.\nIt is guaranteed that K is always an integer when L_i, R_i are integers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-5 1\n3 7\n-4 -2 output: 10\n\nOne possible sequence of actions of Takahashi and Aoki is as follows:\n\nAoki chooses the first segment. Takahashi moves from coordinate 0 to -4, covering a distance of 4.\nAoki chooses the third segment. Takahashi stays at coordinate -4.\nAoki chooses the second segment. Takahashi moves from coordinate -4 to 3, covering a distance of 7.\nTakahashi moves from coordinate 3 to 0, covering a distance of 3.\n\nThe distance covered by Takahashi here is 14 (because Takahashi didn't move optimally).\nIt turns out that if both players move optimally, the distance covered by Takahashi will be 10.", "input: 3\n1 2\n3 4\n5 6 output: 12", "input: 5\n-2 0\n-2 0\n7 8\n9 10\n-2 -1 output: 34"], "Pid": "p03333", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki will play a game with a number line and some segments.\nTakahashi is standing on the number line and he is initially at coordinate 0.\nAoki has N segments. The i-th segment is [L_i, R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).\nThe game has N steps. The i-th step proceeds as follows:\n\nFirst, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.\nThen, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.\n\nAfter N steps are performed, Takahashi will return to coordinate 0 and the game ends.\nLet K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?\nTask Constraint: 1 <= N <= 10^5\n-10^5 <= L_i < R_i <= 10^5\nL_i and R_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nL_1 R_1\n:\nL_N R_N\nTask Output: Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above.\nIt is guaranteed that K is always an integer when L_i, R_i are integers.\nTask Samples: input: 3\n-5 1\n3 7\n-4 -2 output: 10\n\nOne possible sequence of actions of Takahashi and Aoki is as follows:\n\nAoki chooses the first segment. Takahashi moves from coordinate 0 to -4, covering a distance of 4.\nAoki chooses the third segment. Takahashi stays at coordinate -4.\nAoki chooses the second segment. Takahashi moves from coordinate -4 to 3, covering a distance of 7.\nTakahashi moves from coordinate 3 to 0, covering a distance of 3.\n\nThe distance covered by Takahashi here is 14 (because Takahashi didn't move optimally).\nIt turns out that if both players move optimally, the distance covered by Takahashi will be 10.\ninput: 3\n1 2\n3 4\n5 6 output: 12\ninput: 5\n-2 0\n-2 0\n7 8\n9 10\n-2 -1 output: 34\n\n" }, { "title": "", "content": "Problem Statement Takahashi is doing a research on sets of points in a plane.\nTakahashi thinks a set S of points in a coordinate plane is a good set when S satisfies both of the following conditions:\n\nThe distance between any two points in S is not \\sqrt{D_1}.\nThe distance between any two points in S is not \\sqrt{D_2}.\n\nHere, D_1 and D_2 are positive integer constants that Takahashi specified.\nLet X be a set of points (i, j) on a coordinate plane where i and j are integers and satisfy 0 <= i, j < 2N.\nTakahashi has proved that, for any choice of D_1 and D_2, there exists a way to choose N^2 points from X so that the chosen points form a good set.\nHowever, he does not know the specific way to choose such points to form a good set.\nFind a subset of X whose size is N^2 that forms a good set.", "constraint": "1 <= N <= 300\n1 <= D_1 <= 2*10^5\n1 <= D_2 <= 2*10^5\nAll values in the input are integers.", "input": "Input is given from Standard Input in the following format:\nN D_1 D_2", "output": "Print N^2 distinct points that satisfy the condition in the following format:\nx_1 y_1\nx_2 y_2\n:\nx_{N^2} y_{N^2}\n\nHere, (x_i, y_i) represents the i-th chosen point.\n0 <= x_i, y_i < 2N must hold, and they must be integers.\nThe chosen points may be printed in any order.\nIn case there are multiple possible solutions, you can output any.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 2 output: 0 0\n0 2\n2 0\n2 2\n\nAmong these points, the distance between 2 points is either 2 or 2\\sqrt{2}, thus it satisfies the condition.", "input: 3 1 5 output: 0 0\n0 2\n0 4\n1 1\n1 3\n1 5\n2 0\n2 2\n2 4"], "Pid": "p03334", "ProblemText": "Task Description: Problem Statement Takahashi is doing a research on sets of points in a plane.\nTakahashi thinks a set S of points in a coordinate plane is a good set when S satisfies both of the following conditions:\n\nThe distance between any two points in S is not \\sqrt{D_1}.\nThe distance between any two points in S is not \\sqrt{D_2}.\n\nHere, D_1 and D_2 are positive integer constants that Takahashi specified.\nLet X be a set of points (i, j) on a coordinate plane where i and j are integers and satisfy 0 <= i, j < 2N.\nTakahashi has proved that, for any choice of D_1 and D_2, there exists a way to choose N^2 points from X so that the chosen points form a good set.\nHowever, he does not know the specific way to choose such points to form a good set.\nFind a subset of X whose size is N^2 that forms a good set.\nTask Constraint: 1 <= N <= 300\n1 <= D_1 <= 2*10^5\n1 <= D_2 <= 2*10^5\nAll values in the input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN D_1 D_2\nTask Output: Print N^2 distinct points that satisfy the condition in the following format:\nx_1 y_1\nx_2 y_2\n:\nx_{N^2} y_{N^2}\n\nHere, (x_i, y_i) represents the i-th chosen point.\n0 <= x_i, y_i < 2N must hold, and they must be integers.\nThe chosen points may be printed in any order.\nIn case there are multiple possible solutions, you can output any.\nTask Samples: input: 2 1 2 output: 0 0\n0 2\n2 0\n2 2\n\nAmong these points, the distance between 2 points is either 2 or 2\\sqrt{2}, thus it satisfies the condition.\ninput: 3 1 5 output: 0 0\n0 2\n0 4\n1 1\n1 3\n1 5\n2 0\n2 2\n2 4\n\n" }, { "title": "", "content": "Problem Statement Takahashi loves walking on a tree.\nThe tree where Takahashi walks has N vertices numbered 1 through N.\nThe i-th of the N-1 edges connects Vertex a_i and Vertex b_i.\nTakahashi has scheduled M walks. The i-th walk is done as follows:\n\nThe walk involves two vertices u_i and v_i that are fixed beforehand.\nTakahashi will walk from u_i to v_i or from v_i to u_i along the shortest path.\n\nThe happiness gained from the i-th walk is defined as follows:\n\nThe happiness gained is the number of the edges traversed during the i-th walk that satisfies one of the following conditions:\nIn the previous walks, the edge has never been traversed.\nIn the previous walks, the edge has only been traversed in the direction opposite to the direction taken in the i-th walk.\n\nTakahashi would like to decide the direction of each walk so that the total happiness gained from the M walks is maximized.\nFind the maximum total happiness that can be gained, and one specific way to choose the directions of the walks that maximizes the total happiness.", "constraint": "1 <= N,M <= 2000\n1 <= a_i , b_i <= N\n1 <= u_i , v_i <= N\na_i \\neq b_i\nu_i \\neq v_i\nThe graph given as input is a tree.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_{N-1} b_{N-1}\nu_1 v_1\n:\nu_M v_M", "output": "Print the maximum total happiness T that can be gained, and one specific way to choose the directions of the walks that maximizes the total happiness, in the following format:\nT\nu^'_1 v^'_1\n:\nu^'_M v^'_M\n\nwhere (u^'_i, v^'_i) is either (u_i, v_i) or (v_i, u_i), which means that the i-th walk is from vertex u^'_i to v^'_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n2 1\n3 1\n4 1\n2 3\n3 4\n4 2 output: 6\n2 3\n3 4\n4 2\n\nIf we decide the directions of the walks as above, he gains the happiness of 2 in each walk, and the total happiness will be 6.", "input: 5 3\n1 2\n1 3\n3 4\n3 5\n2 4\n3 5\n1 5 output: 6\n2 4\n3 5\n5 1", "input: 6 4\n1 2\n2 3\n1 4\n4 5\n4 6\n2 4\n3 6\n5 6\n4 5 output: 9\n2 4\n6 3\n5 6\n4 5"], "Pid": "p03335", "ProblemText": "Task Description: Problem Statement Takahashi loves walking on a tree.\nThe tree where Takahashi walks has N vertices numbered 1 through N.\nThe i-th of the N-1 edges connects Vertex a_i and Vertex b_i.\nTakahashi has scheduled M walks. The i-th walk is done as follows:\n\nThe walk involves two vertices u_i and v_i that are fixed beforehand.\nTakahashi will walk from u_i to v_i or from v_i to u_i along the shortest path.\n\nThe happiness gained from the i-th walk is defined as follows:\n\nThe happiness gained is the number of the edges traversed during the i-th walk that satisfies one of the following conditions:\nIn the previous walks, the edge has never been traversed.\nIn the previous walks, the edge has only been traversed in the direction opposite to the direction taken in the i-th walk.\n\nTakahashi would like to decide the direction of each walk so that the total happiness gained from the M walks is maximized.\nFind the maximum total happiness that can be gained, and one specific way to choose the directions of the walks that maximizes the total happiness.\nTask Constraint: 1 <= N,M <= 2000\n1 <= a_i , b_i <= N\n1 <= u_i , v_i <= N\na_i \\neq b_i\nu_i \\neq v_i\nThe graph given as input is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_{N-1} b_{N-1}\nu_1 v_1\n:\nu_M v_M\nTask Output: Print the maximum total happiness T that can be gained, and one specific way to choose the directions of the walks that maximizes the total happiness, in the following format:\nT\nu^'_1 v^'_1\n:\nu^'_M v^'_M\n\nwhere (u^'_i, v^'_i) is either (u_i, v_i) or (v_i, u_i), which means that the i-th walk is from vertex u^'_i to v^'_i.\nTask Samples: input: 4 3\n2 1\n3 1\n4 1\n2 3\n3 4\n4 2 output: 6\n2 3\n3 4\n4 2\n\nIf we decide the directions of the walks as above, he gains the happiness of 2 in each walk, and the total happiness will be 6.\ninput: 5 3\n1 2\n1 3\n3 4\n3 5\n2 4\n3 5\n1 5 output: 6\n2 4\n3 5\n5 1\ninput: 6 4\n1 2\n2 3\n1 4\n4 5\n4 6\n2 4\n3 6\n5 6\n4 5 output: 9\n2 4\n6 3\n5 6\n4 5\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki love calculating things, so they will play with numbers now.\nFirst, they came up with one positive integer each. Takahashi came up with X, and Aoki came up with Y.\nThen, they will enjoy themselves by repeating the following operation K times:\n\nCompute the bitwise AND of the number currently kept by Takahashi and the number currently kept by Aoki. Let Z be the result.\nThen, add Z to both of the numbers kept by Takahashi and Aoki.\n\nHowever, it turns out that even for the two math maniacs this is just too much work.\nCould you find the number that would be kept by Takahashi and the one that would be kept by Aoki eventually?\nNote that input and output are done in binary.\nEspecially, X and Y are given as strings S and T of length N and M consisting of 0 and 1, respectively, whose initial characters are guaranteed to be 1.", "constraint": "1 <= K <= 10^6\n1 <= N,M <= 10^6\nThe initial characters of S and T are 1.", "input": "Input is given from Standard Input in the following format:\nN M K\nS\nT", "output": "In the first line, print the number that would be kept by Takahashi eventually; in the second line, print the number that would be kept by Aoki eventually.\nThose numbers should be represented in binary and printed as strings consisting of 0 and 1 that begin with 1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 3\n11\n101 output: 10000\n10010\n\nThe values of X and Y after each operation are as follows:\n\nAfter the first operation: (X,Y)=(4,6).\nAfter the second operation: (X,Y)=(8,10).\nAfter the third operation: (X,Y)=(16,18).", "input: 5 8 3\n10101\n10101001 output: 100000\n10110100", "input: 10 10 10\n1100110011\n1011001101 output: 10000100000010001000\n10000100000000100010"], "Pid": "p03336", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki love calculating things, so they will play with numbers now.\nFirst, they came up with one positive integer each. Takahashi came up with X, and Aoki came up with Y.\nThen, they will enjoy themselves by repeating the following operation K times:\n\nCompute the bitwise AND of the number currently kept by Takahashi and the number currently kept by Aoki. Let Z be the result.\nThen, add Z to both of the numbers kept by Takahashi and Aoki.\n\nHowever, it turns out that even for the two math maniacs this is just too much work.\nCould you find the number that would be kept by Takahashi and the one that would be kept by Aoki eventually?\nNote that input and output are done in binary.\nEspecially, X and Y are given as strings S and T of length N and M consisting of 0 and 1, respectively, whose initial characters are guaranteed to be 1.\nTask Constraint: 1 <= K <= 10^6\n1 <= N,M <= 10^6\nThe initial characters of S and T are 1.\nTask Input: Input is given from Standard Input in the following format:\nN M K\nS\nT\nTask Output: In the first line, print the number that would be kept by Takahashi eventually; in the second line, print the number that would be kept by Aoki eventually.\nThose numbers should be represented in binary and printed as strings consisting of 0 and 1 that begin with 1.\nTask Samples: input: 2 3 3\n11\n101 output: 10000\n10010\n\nThe values of X and Y after each operation are as follows:\n\nAfter the first operation: (X,Y)=(4,6).\nAfter the second operation: (X,Y)=(8,10).\nAfter the third operation: (X,Y)=(16,18).\ninput: 5 8 3\n10101\n10101001 output: 100000\n10110100\ninput: 10 10 10\n1100110011\n1011001101 output: 10000100000010001000\n10000100000000100010\n\n" }, { "title": "", "content": "Problem Statement You are given two integers A and B.\nFind the largest value among A+B, A-B and A * B.", "constraint": "-1000 <= A,B <= 1000\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the largest value among A+B, A-B and A * B.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 output: 4\n\n3+1=4,3-1=2 and 3 * 1=3. The largest among them is 4.", "input: 4 -2 output: 6\n\nThe largest is 4 - (-2) = 6.", "input: 0 0 output: 0"], "Pid": "p03337", "ProblemText": "Task Description: Problem Statement You are given two integers A and B.\nFind the largest value among A+B, A-B and A * B.\nTask Constraint: -1000 <= A,B <= 1000\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the largest value among A+B, A-B and A * B.\nTask Samples: input: 3 1 output: 4\n\n3+1=4,3-1=2 and 3 * 1=3. The largest among them is 4.\ninput: 4 -2 output: 6\n\nThe largest is 4 - (-2) = 6.\ninput: 0 0 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N consisting of lowercase English letters.\nWe will cut this string at one position into two strings X and Y.\nHere, we would like to maximize the number of different letters contained in both X and Y.\nFind the largest possible number of different letters contained in both X and Y when we cut the string at the optimal position.", "constraint": "2 <= N <= 100\n|S| = N\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the largest possible number of different letters contained in both X and Y.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\naabbca output: 2\n\nIf we cut the string between the third and fourth letters into X = aab and Y = bca, the letters contained in both X and Y are a and b.\nThere will never be three or more different letters contained in both X and Y, so the answer is 2.", "input: 10\naaaaaaaaaa output: 1\n\nHowever we divide S, only a will be contained in both X and Y.", "input: 45\ntgxgdqkyjzhyputjjtllptdfxocrylqfqjynmfbfucbir output: 9"], "Pid": "p03338", "ProblemText": "Task Description: Problem Statement You are given a string S of length N consisting of lowercase English letters.\nWe will cut this string at one position into two strings X and Y.\nHere, we would like to maximize the number of different letters contained in both X and Y.\nFind the largest possible number of different letters contained in both X and Y when we cut the string at the optimal position.\nTask Constraint: 2 <= N <= 100\n|S| = N\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the largest possible number of different letters contained in both X and Y.\nTask Samples: input: 6\naabbca output: 2\n\nIf we cut the string between the third and fourth letters into X = aab and Y = bca, the letters contained in both X and Y are a and b.\nThere will never be three or more different letters contained in both X and Y, so the answer is 2.\ninput: 10\naaaaaaaaaa output: 1\n\nHowever we divide S, only a will be contained in both X and Y.\ninput: 45\ntgxgdqkyjzhyputjjtllptdfxocrylqfqjynmfbfucbir output: 9\n\n" }, { "title": "", "content": "Problem Statement There are N people standing in a row from west to east.\nEach person is facing east or west.\nThe directions of the people is given as a string S of length N.\nThe i-th person from the west is facing east if S_i = E, and west if S_i = W.\nYou will appoint one of the N people as the leader, then command the rest of them to face in the direction of the leader.\nHere, we do not care which direction the leader is facing.\nThe people in the row hate to change their directions, so you would like to select the leader so that the number of people who have to change their directions is minimized.\nFind the minimum number of people who have to change their directions.", "constraint": "2 <= N <= 3 * 10^5\n|S| = N\nS_i is E or W.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the minimum number of people who have to change their directions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nWEEWW output: 1\n\nAssume that we appoint the third person from the west as the leader.\nThen, the first person from the west needs to face east and has to turn around.\nThe other people do not need to change their directions, so the number of people who have to change their directions is 1 in this case.\nIt is not possible to have 0 people who have to change their directions, so the answer is 1.", "input: 12\nWEWEWEEEWWWE output: 4", "input: 8\nWWWWWEEE output: 3"], "Pid": "p03339", "ProblemText": "Task Description: Problem Statement There are N people standing in a row from west to east.\nEach person is facing east or west.\nThe directions of the people is given as a string S of length N.\nThe i-th person from the west is facing east if S_i = E, and west if S_i = W.\nYou will appoint one of the N people as the leader, then command the rest of them to face in the direction of the leader.\nHere, we do not care which direction the leader is facing.\nThe people in the row hate to change their directions, so you would like to select the leader so that the number of people who have to change their directions is minimized.\nFind the minimum number of people who have to change their directions.\nTask Constraint: 2 <= N <= 3 * 10^5\n|S| = N\nS_i is E or W.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the minimum number of people who have to change their directions.\nTask Samples: input: 5\nWEEWW output: 1\n\nAssume that we appoint the third person from the west as the leader.\nThen, the first person from the west needs to face east and has to turn around.\nThe other people do not need to change their directions, so the number of people who have to change their directions is 1 in this case.\nIt is not possible to have 0 people who have to change their directions, so the answer is 1.\ninput: 12\nWEWEWEEEWWWE output: 4\ninput: 8\nWWWWWEEE output: 3\n\n" }, { "title": "", "content": "Problem Statement There is an integer sequence A of length N.\nFind the number of the pairs of integers l and r (1 <= l <= r <= N) that satisfy the following condition:\n\nA_l\\ xor\\ A_{l+1}\\ xor\\ . . . \\ xor\\ A_r = A_l\\ +\\ A_{l+1}\\ +\\ . . . \\ +\\ A_r\n\nHere, xor denotes the bitwise exclusive OR.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03340", "ProblemText": "Task Description: Problem Statement There is an integer sequence A of length N.\nFind the number of the pairs of integers l and r (1 <= l <= r <= N) that satisfy the following condition:\n\nA_l\\ xor\\ A_{l+1}\\ xor\\ . . . \\ xor\\ A_r = A_l\\ +\\ A_{l+1}\\ +\\ . . . \\ +\\ A_r\n\nHere, xor denotes the bitwise exclusive OR.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement There are N people standing in a row from west to east.\nEach person is facing east or west.\nThe directions of the people is given as a string S of length N.\nThe i-th person from the west is facing east if S_i = E, and west if S_i = W.\nYou will appoint one of the N people as the leader, then command the rest of them to face in the direction of the leader.\nHere, we do not care which direction the leader is facing.\nThe people in the row hate to change their directions, so you would like to select the leader so that the number of people who have to change their directions is minimized.\nFind the minimum number of people who have to change their directions.", "constraint": "2 <= N <= 3 * 10^5\n|S| = N\nS_i is E or W.", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the minimum number of people who have to change their directions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nWEEWW output: 1\n\nAssume that we appoint the third person from the west as the leader.\nThen, the first person from the west needs to face east and has to turn around.\nThe other people do not need to change their directions, so the number of people who have to change their directions is 1 in this case.\nIt is not possible to have 0 people who have to change their directions, so the answer is 1.", "input: 12\nWEWEWEEEWWWE output: 4", "input: 8\nWWWWWEEE output: 3"], "Pid": "p03341", "ProblemText": "Task Description: Problem Statement There are N people standing in a row from west to east.\nEach person is facing east or west.\nThe directions of the people is given as a string S of length N.\nThe i-th person from the west is facing east if S_i = E, and west if S_i = W.\nYou will appoint one of the N people as the leader, then command the rest of them to face in the direction of the leader.\nHere, we do not care which direction the leader is facing.\nThe people in the row hate to change their directions, so you would like to select the leader so that the number of people who have to change their directions is minimized.\nFind the minimum number of people who have to change their directions.\nTask Constraint: 2 <= N <= 3 * 10^5\n|S| = N\nS_i is E or W.\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the minimum number of people who have to change their directions.\nTask Samples: input: 5\nWEEWW output: 1\n\nAssume that we appoint the third person from the west as the leader.\nThen, the first person from the west needs to face east and has to turn around.\nThe other people do not need to change their directions, so the number of people who have to change their directions is 1 in this case.\nIt is not possible to have 0 people who have to change their directions, so the answer is 1.\ninput: 12\nWEWEWEEEWWWE output: 4\ninput: 8\nWWWWWEEE output: 3\n\n" }, { "title": "", "content": "Problem Statement There is an integer sequence A of length N.\nFind the number of the pairs of integers l and r (1 <= l <= r <= N) that satisfy the following condition:\n\nA_l\\ xor\\ A_{l+1}\\ xor\\ . . . \\ xor\\ A_r = A_l\\ +\\ A_{l+1}\\ +\\ . . . \\ +\\ A_r\n\nHere, xor denotes the bitwise exclusive OR.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03342", "ProblemText": "Task Description: Problem Statement There is an integer sequence A of length N.\nFind the number of the pairs of integers l and r (1 <= l <= r <= N) that satisfy the following condition:\n\nA_l\\ xor\\ A_{l+1}\\ xor\\ . . . \\ xor\\ A_r = A_l\\ +\\ A_{l+1}\\ +\\ . . . \\ +\\ A_r\n\nHere, xor denotes the bitwise exclusive OR.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence A of length N and an integer K.\nYou will perform the following operation on this sequence Q times:\n\nChoose a contiguous subsequence of length K, then remove the smallest element among the K elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like).\n\nLet X and Y be the values of the largest and smallest element removed in the Q operations. You would like X-Y to be as small as possible.\nFind the smallest possible value of X-Y when the Q operations are performed optimally.", "constraint": "1 <= N <= 2000\n1 <= K <= N\n1 <= Q <= N-K+1\n1 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN K Q\nA_1 A_2 . . . A_N", "output": "Print the smallest possible value of X-Y.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 2\n4 3 1 5 2 output: 1\n\nIn the first operation, whichever contiguous subsequence of length 3 we choose, the minimum element in it is 1.\nThus, the first operation removes A_3=1 and now we have A=(4,3,5,2).\nIn the second operation, it is optimal to choose (A_2,A_3,A_4)=(3,5,2) as the contiguous subsequence of length 3 and remove A_4=2.\nIn this case, the largest element removed is 2, and the smallest is 1, so their difference is 2-1=1.", "input: 10 1 6\n1 1 2 3 5 8 13 21 34 55 output: 7", "input: 11 7 5\n24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784 output: 451211184"], "Pid": "p03343", "ProblemText": "Task Description: Problem Statement You are given an integer sequence A of length N and an integer K.\nYou will perform the following operation on this sequence Q times:\n\nChoose a contiguous subsequence of length K, then remove the smallest element among the K elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like).\n\nLet X and Y be the values of the largest and smallest element removed in the Q operations. You would like X-Y to be as small as possible.\nFind the smallest possible value of X-Y when the Q operations are performed optimally.\nTask Constraint: 1 <= N <= 2000\n1 <= K <= N\n1 <= Q <= N-K+1\n1 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K Q\nA_1 A_2 . . . A_N\nTask Output: Print the smallest possible value of X-Y.\nTask Samples: input: 5 3 2\n4 3 1 5 2 output: 1\n\nIn the first operation, whichever contiguous subsequence of length 3 we choose, the minimum element in it is 1.\nThus, the first operation removes A_3=1 and now we have A=(4,3,5,2).\nIn the second operation, it is optimal to choose (A_2,A_3,A_4)=(3,5,2) as the contiguous subsequence of length 3 and remove A_4=2.\nIn this case, the largest element removed is 2, and the smallest is 1, so their difference is 2-1=1.\ninput: 10 1 6\n1 1 2 3 5 8 13 21 34 55 output: 7\ninput: 11 7 5\n24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784 output: 451211184\n\n" }, { "title": "", "content": "Problem Statement There is a simple undirected graph with N vertices and M edges.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i connects Vertex U_i and V_i.\nAlso, Vertex i has two predetermined integers A_i and B_i.\nYou will play the following game on this graph.\nFirst, choose one vertex and stand on it, with W yen (the currency of Japan) in your pocket.\nHere, A_s <= W must hold, where s is the vertex you choose.\nThen, perform the following two kinds of operations any number of times in any order:\n\nChoose one vertex v that is directly connected by an edge to the vertex you are standing on, and move to vertex v. Here, you need to have at least A_v yen in your pocket when you perform this move.\nDonate B_v yen to the vertex v you are standing on. Here, the amount of money in your pocket must not become less than 0 yen.\n\nYou win the game when you donate once to every vertex.\nFind the smallest initial amount of money W that enables you to win the game.", "constraint": "1 <= N <= 10^5\nN-1 <= M <= 10^5\n1 <= A_i,B_i <= 10^9\n1 <= U_i < V_i <= N\nThe given graph is connected and simple (there is at most one edge between any pair of vertices).", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nU_1 V_1\nU_2 V_2\n:\nU_M V_M", "output": "Print the smallest initial amount of money W that enables you to win the game.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n3 1\n1 2\n4 1\n6 2\n1 2\n2 3\n2 4\n1 4\n3 4 output: 6\n\nIf you have 6 yen initially, you can win the game as follows:\n\nStand on Vertex 4. This is possible since you have not less than 6 yen.\nDonate 2 yen to Vertex 4. Now you have 4 yen.\nMove to Vertex 3. This is possible since you have not less than 4 yen.\nDonate 1 yen to Vertex 3. Now you have 3 yen.\nMove to Vertex 2. This is possible since you have not less than 1 yen.\nMove to Vertex 1. This is possible since you have not less than 3 yen.\nDonate 1 yen to Vertex 1. Now you have 2 yen.\nMove to Vertex 2. This is possible since you have not less than 1 yen.\nDonate 2 yen to Vertex 2. Now you have 0 yen.\n\nIf you have less than 6 yen initially, you cannot win the game. Thus, the answer is 6.", "input: 5 8\n6 4\n15 13\n15 19\n15 1\n20 7\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 5\n4 5 output: 44", "input: 9 10\n131 2\n98 79\n242 32\n231 38\n382 82\n224 22\n140 88\n209 70\n164 64\n6 8\n1 6\n1 4\n1 3\n4 7\n4 9\n3 7\n3 9\n5 9\n2 5 output: 582"], "Pid": "p03344", "ProblemText": "Task Description: Problem Statement There is a simple undirected graph with N vertices and M edges.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i connects Vertex U_i and V_i.\nAlso, Vertex i has two predetermined integers A_i and B_i.\nYou will play the following game on this graph.\nFirst, choose one vertex and stand on it, with W yen (the currency of Japan) in your pocket.\nHere, A_s <= W must hold, where s is the vertex you choose.\nThen, perform the following two kinds of operations any number of times in any order:\n\nChoose one vertex v that is directly connected by an edge to the vertex you are standing on, and move to vertex v. Here, you need to have at least A_v yen in your pocket when you perform this move.\nDonate B_v yen to the vertex v you are standing on. Here, the amount of money in your pocket must not become less than 0 yen.\n\nYou win the game when you donate once to every vertex.\nFind the smallest initial amount of money W that enables you to win the game.\nTask Constraint: 1 <= N <= 10^5\nN-1 <= M <= 10^5\n1 <= A_i,B_i <= 10^9\n1 <= U_i < V_i <= N\nThe given graph is connected and simple (there is at most one edge between any pair of vertices).\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nU_1 V_1\nU_2 V_2\n:\nU_M V_M\nTask Output: Print the smallest initial amount of money W that enables you to win the game.\nTask Samples: input: 4 5\n3 1\n1 2\n4 1\n6 2\n1 2\n2 3\n2 4\n1 4\n3 4 output: 6\n\nIf you have 6 yen initially, you can win the game as follows:\n\nStand on Vertex 4. This is possible since you have not less than 6 yen.\nDonate 2 yen to Vertex 4. Now you have 4 yen.\nMove to Vertex 3. This is possible since you have not less than 4 yen.\nDonate 1 yen to Vertex 3. Now you have 3 yen.\nMove to Vertex 2. This is possible since you have not less than 1 yen.\nMove to Vertex 1. This is possible since you have not less than 3 yen.\nDonate 1 yen to Vertex 1. Now you have 2 yen.\nMove to Vertex 2. This is possible since you have not less than 1 yen.\nDonate 2 yen to Vertex 2. Now you have 0 yen.\n\nIf you have less than 6 yen initially, you cannot win the game. Thus, the answer is 6.\ninput: 5 8\n6 4\n15 13\n15 19\n15 1\n20 7\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 5\n4 5 output: 44\ninput: 9 10\n131 2\n98 79\n242 32\n231 38\n382 82\n224 22\n140 88\n209 70\n164 64\n6 8\n1 6\n1 4\n1 3\n4 7\n4 9\n3 7\n3 9\n5 9\n2 5 output: 582\n\n" }, { "title": "", "content": "Problem Statement Takahashi, Nakahashi and Hikuhashi have integers A, B and C, respectively.\nAfter repeating the following operation K times, find the integer Takahashi will get minus the integer Nakahashi will get:\n\nEach of them simultaneously calculate the sum of the integers that the other two people have, then replace his own integer with the result.\n\nHowever, if the absolute value of the answer exceeds 10^{18}, print Unfair instead.", "constraint": "1 <= A,B,C <= 10^9\n0 <= K <= 10^{18}\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C K", "output": "Print the integer Takahashi will get minus the integer Nakahashi will get, after repeating the following operation K times.\nIf the absolute value of the answer exceeds 10^{18}, print Unfair instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 3 1 output: 1\n\nAfter one operation, Takahashi, Nakahashi and Hikuhashi have 5,4 and 3, respectively. We should print 5-4=1.", "input: 2 3 2 0 output: -1", "input: 1000000000 1000000000 1000000000 1000000000000000000 output: 0"], "Pid": "p03345", "ProblemText": "Task Description: Problem Statement Takahashi, Nakahashi and Hikuhashi have integers A, B and C, respectively.\nAfter repeating the following operation K times, find the integer Takahashi will get minus the integer Nakahashi will get:\n\nEach of them simultaneously calculate the sum of the integers that the other two people have, then replace his own integer with the result.\n\nHowever, if the absolute value of the answer exceeds 10^{18}, print Unfair instead.\nTask Constraint: 1 <= A,B,C <= 10^9\n0 <= K <= 10^{18}\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C K\nTask Output: Print the integer Takahashi will get minus the integer Nakahashi will get, after repeating the following operation K times.\nIf the absolute value of the answer exceeds 10^{18}, print Unfair instead.\nTask Samples: input: 1 2 3 1 output: 1\n\nAfter one operation, Takahashi, Nakahashi and Hikuhashi have 5,4 and 3, respectively. We should print 5-4=1.\ninput: 2 3 2 0 output: -1\ninput: 1000000000 1000000000 1000000000 1000000000000000000 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence (P_1, P_2, . . . , P_N) which is a permutation of the integers from 1 through N.\nYou would like to sort this sequence in ascending order by repeating the following operation:\n\nChoose an element in the sequence and move it to the beginning or the end of the sequence.\n\nFind the minimum number of operations required.\nIt can be proved that it is actually possible to sort the sequence using this operation.", "constraint": "1 <= N <= 2* 10^5\n(P_1,P_2,...,P_N) is a permutation of (1,2,...,N).\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nP_1\n:\nP_N", "output": "Print the minimum number of operations required.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1\n3\n2\n4 output: 2\n\nFor example, the sequence can be sorted in ascending order as follows:\n\nMove 2 to the beginning. The sequence is now (2,1,3,4).\nMove 1 to the beginning. The sequence is now (1,2,3,4).", "input: 6\n3\n2\n5\n1\n4\n6 output: 4", "input: 8\n6\n3\n1\n2\n7\n4\n8\n5 output: 5"], "Pid": "p03346", "ProblemText": "Task Description: Problem Statement You are given a sequence (P_1, P_2, . . . , P_N) which is a permutation of the integers from 1 through N.\nYou would like to sort this sequence in ascending order by repeating the following operation:\n\nChoose an element in the sequence and move it to the beginning or the end of the sequence.\n\nFind the minimum number of operations required.\nIt can be proved that it is actually possible to sort the sequence using this operation.\nTask Constraint: 1 <= N <= 2* 10^5\n(P_1,P_2,...,P_N) is a permutation of (1,2,...,N).\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nP_1\n:\nP_N\nTask Output: Print the minimum number of operations required.\nTask Samples: input: 4\n1\n3\n2\n4 output: 2\n\nFor example, the sequence can be sorted in ascending order as follows:\n\nMove 2 to the beginning. The sequence is now (2,1,3,4).\nMove 1 to the beginning. The sequence is now (1,2,3,4).\ninput: 6\n3\n2\n5\n1\n4\n6 output: 4\ninput: 8\n6\n3\n1\n2\n7\n4\n8\n5 output: 5\n\n" }, { "title": "", "content": "Problem Statement There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.\nYou are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.\n\nChoose an integer i such that 1<= i<= N-1. Replace the value of X_{i+1} with the value of X_i plus 1.", "constraint": "1 <= N <= 2 * 10^5\n0 <= A_i <= 10^9(1<= i<= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0\n1\n1\n2 output: 3\n\nWe can make X equal to A as follows:\n\nChoose i=2. X becomes (0,0,1,0).\nChoose i=1. X becomes (0,1,1,0).\nChoose i=3. X becomes (0,1,1,2).", "input: 3\n1\n2\n1 output: -1", "input: 9\n0\n1\n1\n0\n1\n2\n2\n1\n2 output: 8"], "Pid": "p03347", "ProblemText": "Task Description: Problem Statement There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.\nYou are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.\n\nChoose an integer i such that 1<= i<= N-1. Replace the value of X_{i+1} with the value of X_i plus 1.\nTask Constraint: 1 <= N <= 2 * 10^5\n0 <= A_i <= 10^9(1<= i<= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.\nTask Samples: input: 4\n0\n1\n1\n2 output: 3\n\nWe can make X equal to A as follows:\n\nChoose i=2. X becomes (0,0,1,0).\nChoose i=1. X becomes (0,1,1,0).\nChoose i=3. X becomes (0,1,1,2).\ninput: 3\n1\n2\n1 output: -1\ninput: 9\n0\n1\n1\n0\n1\n2\n2\n1\n2 output: 8\n\n" }, { "title": "", "content": "Problem Statement Coloring of the vertices of a tree G is called a good coloring when, for every pair of two vertices u and v painted in the same color, picking u as the root and picking v as the root would result in isomorphic rooted trees.\nAlso, the colorfulness of G is defined as the minimum possible number of different colors used in a good coloring of G.\nYou are given a tree with N vertices. The vertices are numbered 1 through N, and the i-th edge connects Vertex a_i and Vertex b_i. We will construct a new tree T by repeating the following operation on this tree some number of times:\n\nAdd a new vertex to the tree by connecting it to one of the vertices in the current tree with an edge.\n\nFind the minimum possible colorfulness of T.\nAdditionally, print the minimum number of leaves (vertices with degree 1) in a tree T that achieves the minimum colorfulness. note: Notes The phrase \"picking u as the root and picking v as the root would result in isomorphic rooted trees\" for a tree G means that there exists a bijective function f_{uv} from the vertex set of G to itself such that both of the following conditions are met:\n\nf_{uv}(u)=v\nFor every pair of two vertices (a, b), edge (a, b) exists if and only if edge (f_{uv}(a), f_{uv}(b)) exists.", "constraint": "2 <= N <= 100\n1 <= a_i,b_i <= N(1<= i<= N-1)\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}", "output": "Print two integers with a space in between.\nFirst, print the minimum possible colorfulness of a tree T that can be constructed.\nSecond, print the minimum number of leaves in a tree that achieves it.\nIt can be shown that, under the constraints of this problem, the values that should be printed fit into 64-bit signed integers.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n2 3\n3 4\n3 5 output: 2 4\n\nIf we connect a new vertex 6 to vertex 2, painting the vertices (1,4,5,6) red and painting the vertices (2,3) blue is a good coloring.\nSince painting all the vertices in a single color is not a good coloring, we can see that the colorfulness of this tree is 2.\nThis is actually the optimal solution. There are four leaves, so we should print 2 and 4.", "input: 8\n1 2\n2 3\n4 3\n5 4\n6 7\n6 8\n3 6 output: 3 4", "input: 10\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n3 8\n5 9\n3 10 output: 4 6", "input: 13\n5 6\n6 4\n2 8\n4 7\n8 9\n3 2\n10 4\n11 10\n2 4\n13 10\n1 8\n12 1 output: 4 12"], "Pid": "p03348", "ProblemText": "Task Description: Problem Statement Coloring of the vertices of a tree G is called a good coloring when, for every pair of two vertices u and v painted in the same color, picking u as the root and picking v as the root would result in isomorphic rooted trees.\nAlso, the colorfulness of G is defined as the minimum possible number of different colors used in a good coloring of G.\nYou are given a tree with N vertices. The vertices are numbered 1 through N, and the i-th edge connects Vertex a_i and Vertex b_i. We will construct a new tree T by repeating the following operation on this tree some number of times:\n\nAdd a new vertex to the tree by connecting it to one of the vertices in the current tree with an edge.\n\nFind the minimum possible colorfulness of T.\nAdditionally, print the minimum number of leaves (vertices with degree 1) in a tree T that achieves the minimum colorfulness. note: Notes The phrase \"picking u as the root and picking v as the root would result in isomorphic rooted trees\" for a tree G means that there exists a bijective function f_{uv} from the vertex set of G to itself such that both of the following conditions are met:\n\nf_{uv}(u)=v\nFor every pair of two vertices (a, b), edge (a, b) exists if and only if edge (f_{uv}(a), f_{uv}(b)) exists.\nTask Constraint: 2 <= N <= 100\n1 <= a_i,b_i <= N(1<= i<= N-1)\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nTask Output: Print two integers with a space in between.\nFirst, print the minimum possible colorfulness of a tree T that can be constructed.\nSecond, print the minimum number of leaves in a tree that achieves it.\nIt can be shown that, under the constraints of this problem, the values that should be printed fit into 64-bit signed integers.\nTask Samples: input: 5\n1 2\n2 3\n3 4\n3 5 output: 2 4\n\nIf we connect a new vertex 6 to vertex 2, painting the vertices (1,4,5,6) red and painting the vertices (2,3) blue is a good coloring.\nSince painting all the vertices in a single color is not a good coloring, we can see that the colorfulness of this tree is 2.\nThis is actually the optimal solution. There are four leaves, so we should print 2 and 4.\ninput: 8\n1 2\n2 3\n4 3\n5 4\n6 7\n6 8\n3 6 output: 3 4\ninput: 10\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n3 8\n5 9\n3 10 output: 4 6\ninput: 13\n5 6\n6 4\n2 8\n4 7\n8 9\n3 2\n10 4\n11 10\n2 4\n13 10\n1 8\n12 1 output: 4 12\n\n" }, { "title": "", "content": "Problem Statement Find the number of the possible tuples of sequences (A_0, A_1, . . . , A_N) that satisfy all of the following conditions, modulo M:\n\nFor every i (0<= i<= N), A_i is a sequence of length i consisting of integers between 1 and K (inclusive);\nFor every i (1<= i<= N), A_{i-1} is a subsequence of A_i, that is, there exists 1<= x_i<= i such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};\nFor every i (1<= i<= N), A_i is lexicographically larger than A_{i-1}.", "constraint": "1 <= N,K <= 300\n2 <= M <= 10^9\nN, K and M are integers.", "input": "Input is given from Standard Input in the following format:\nN K M", "output": "Print the number of the possible tuples of sequences (A_0, A_1, . . . , A_N), modulo M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 100 output: 5\n\nFive tuples below satisfy the conditions:\n\n(),(1),(1,1)\n(),(1),(1,2)\n(),(1),(2,1)\n(),(2),(2,1)\n(),(2),(2,2)", "input: 4 3 999999999 output: 358", "input: 150 150 998244353 output: 186248260"], "Pid": "p03349", "ProblemText": "Task Description: Problem Statement Find the number of the possible tuples of sequences (A_0, A_1, . . . , A_N) that satisfy all of the following conditions, modulo M:\n\nFor every i (0<= i<= N), A_i is a sequence of length i consisting of integers between 1 and K (inclusive);\nFor every i (1<= i<= N), A_{i-1} is a subsequence of A_i, that is, there exists 1<= x_i<= i such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};\nFor every i (1<= i<= N), A_i is lexicographically larger than A_{i-1}.\nTask Constraint: 1 <= N,K <= 300\n2 <= M <= 10^9\nN, K and M are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K M\nTask Output: Print the number of the possible tuples of sequences (A_0, A_1, . . . , A_N), modulo M.\nTask Samples: input: 2 2 100 output: 5\n\nFive tuples below satisfy the conditions:\n\n(),(1),(1,1)\n(),(1),(1,2)\n(),(1),(2,1)\n(),(2),(2,1)\n(),(2),(2,2)\ninput: 4 3 999999999 output: 358\ninput: 150 150 998244353 output: 186248260\n\n" }, { "title": "", "content": "Problem Statement You are given a set S of strings consisting of 0 and 1, and an integer K.\nFind the longest string that is a subsequence of K or more different strings in S.\nIf there are multiple strings that satisfy this condition, find the lexicographically smallest such string.\nHere, S is given in the format below:\n\nThe data directly given to you is an integer N, and N+1 strings X_0, X_1, . . . , X_N. For every i (0<= i<= N), the length of X_i is 2^i.\nFor every pair of two integers (i, j) (0<= i<= N, 0<= j<= 2^i-1), the j-th character of X_i is 1 if and only if the binary representation of j with i digits (possibly with leading zeros) belongs to S. Here, the first and last characters in X_i are called the 0-th and (2^i-1)-th characters, respectively.\nS does not contain a string with length N+1 or more.\n\nHere, a string A is a subsequence of another string B when there exists a sequence of integers t_1 < . . . < t_{|A|} such that, for every i (1<= i<= |A|), the i-th character of A and the t_i-th character of B is equal.", "constraint": "0 <= N <= 20\nX_i(0<= i<= N) is a string of length 2^i consisting of 0 and 1.\n1 <= K <= |S|\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nN K\nX_0\n:\nX_N", "output": "Print the lexicographically smallest string among the longest strings that are subsequences of K or more different strings in S.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n1\n01\n1011\n01001110 output: 10\n\nThe following strings belong to S: the empty string, 1,00,10,11,001,100,101 and 110.\nThe lexicographically smallest string among the longest strings that are subsequences of four or more of them is 10.", "input: 4 6\n1\n01\n1011\n10111010\n1101110011111101 output: 100", "input: 2 5\n0\n11\n1111 output: \nThe answer is the empty string."], "Pid": "p03350", "ProblemText": "Task Description: Problem Statement You are given a set S of strings consisting of 0 and 1, and an integer K.\nFind the longest string that is a subsequence of K or more different strings in S.\nIf there are multiple strings that satisfy this condition, find the lexicographically smallest such string.\nHere, S is given in the format below:\n\nThe data directly given to you is an integer N, and N+1 strings X_0, X_1, . . . , X_N. For every i (0<= i<= N), the length of X_i is 2^i.\nFor every pair of two integers (i, j) (0<= i<= N, 0<= j<= 2^i-1), the j-th character of X_i is 1 if and only if the binary representation of j with i digits (possibly with leading zeros) belongs to S. Here, the first and last characters in X_i are called the 0-th and (2^i-1)-th characters, respectively.\nS does not contain a string with length N+1 or more.\n\nHere, a string A is a subsequence of another string B when there exists a sequence of integers t_1 < . . . < t_{|A|} such that, for every i (1<= i<= |A|), the i-th character of A and the t_i-th character of B is equal.\nTask Constraint: 0 <= N <= 20\nX_i(0<= i<= N) is a string of length 2^i consisting of 0 and 1.\n1 <= K <= |S|\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN K\nX_0\n:\nX_N\nTask Output: Print the lexicographically smallest string among the longest strings that are subsequences of K or more different strings in S.\nTask Samples: input: 3 4\n1\n01\n1011\n01001110 output: 10\n\nThe following strings belong to S: the empty string, 1,00,10,11,001,100,101 and 110.\nThe lexicographically smallest string among the longest strings that are subsequences of four or more of them is 10.\ninput: 4 6\n1\n01\n1011\n10111010\n1101110011111101 output: 100\ninput: 2 5\n0\n11\n1111 output: \nThe answer is the empty string.\n\n" }, { "title": "", "content": "Problem Statement Three people, A, B and C, are trying to communicate using transceivers.\nThey are standing along a number line, and the coordinates of A, B and C are a, b and c (in meters), respectively.\nTwo people can directly communicate when the distance between them is at most d meters.\nDetermine if A and C can communicate, either directly or indirectly.\nHere, A and C can indirectly communicate when A and B can directly communicate and also B and C can directly communicate.", "constraint": "1 <= a,b,c <= 100\n1 <= d <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\na b c d", "output": "If A and C can communicate, print Yes; if they cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 7 9 3 output: Yes\n\nA and B can directly communicate, and also B and C can directly communicate, so we should print Yes.", "input: 100 10 1 2 output: No\n\nThey cannot communicate in this case.", "input: 10 10 10 1 output: Yes\n\nThere can be multiple people at the same position.", "input: 1 100 2 10 output: Yes"], "Pid": "p03351", "ProblemText": "Task Description: Problem Statement Three people, A, B and C, are trying to communicate using transceivers.\nThey are standing along a number line, and the coordinates of A, B and C are a, b and c (in meters), respectively.\nTwo people can directly communicate when the distance between them is at most d meters.\nDetermine if A and C can communicate, either directly or indirectly.\nHere, A and C can indirectly communicate when A and B can directly communicate and also B and C can directly communicate.\nTask Constraint: 1 <= a,b,c <= 100\n1 <= d <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\na b c d\nTask Output: If A and C can communicate, print Yes; if they cannot, print No.\nTask Samples: input: 4 7 9 3 output: Yes\n\nA and B can directly communicate, and also B and C can directly communicate, so we should print Yes.\ninput: 100 10 1 2 output: No\n\nThey cannot communicate in this case.\ninput: 10 10 10 1 output: Yes\n\nThere can be multiple people at the same position.\ninput: 1 100 2 10 output: Yes\n\n" }, { "title": "", "content": "Problem Statement You are given a positive integer X.\nFind the largest perfect power that is at most X.\nHere, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.", "constraint": "1 <= X <= 1000\nX is an integer.", "input": "Input is given from Standard Input in the following format:\nX", "output": "Print the largest perfect power that is at most X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 output: 9\n\nThere are four perfect powers that are at most 10: 1,4,8 and 9.\nWe should print the largest among them, 9.", "input: 1 output: 1", "input: 999 output: 961"], "Pid": "p03352", "ProblemText": "Task Description: Problem Statement You are given a positive integer X.\nFind the largest perfect power that is at most X.\nHere, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.\nTask Constraint: 1 <= X <= 1000\nX is an integer.\nTask Input: Input is given from Standard Input in the following format:\nX\nTask Output: Print the largest perfect power that is at most X.\nTask Samples: input: 10 output: 9\n\nThere are four perfect powers that are at most 10: 1,4,8 and 9.\nWe should print the largest among them, 9.\ninput: 1 output: 1\ninput: 999 output: 961\n\n" }, { "title": "", "content": "Problem Statement You are given a string s.\nAmong the different substrings of s, print the K-th lexicographically smallest one.\nA substring of s is a string obtained by taking out a non-empty contiguous part in s.\nFor example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.\nAlso, we say that substrings are different when they are different as strings.\nLet X = x_{1}x_{2}. . . x_{n} and Y = y_{1}y_{2}. . . y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \\neq y_{j}. partial score: Partial Score\n200 points will be awarded as a partial score for passing the test set satisfying |s| <= 50.", "constraint": "1 <= |s| <= 5000\ns consists of lowercase English letters.\n1 <= K <= 5\ns has at least K different substrings.", "input": "Input is given from Standard Input in the following format:\ns\nK", "output": "Print the K-th lexicographically smallest substring of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aba\n4 output: b\n\ns has five substrings: a, b, ab, ba and aba.\nAmong them, we should print the fourth smallest one, b.\nNote that we do not count a twice.", "input: atcoderandatcodeer\n5 output: andat", "input: z\n1 output: z"], "Pid": "p03353", "ProblemText": "Task Description: Problem Statement You are given a string s.\nAmong the different substrings of s, print the K-th lexicographically smallest one.\nA substring of s is a string obtained by taking out a non-empty contiguous part in s.\nFor example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.\nAlso, we say that substrings are different when they are different as strings.\nLet X = x_{1}x_{2}. . . x_{n} and Y = y_{1}y_{2}. . . y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \\neq y_{j}. partial score: Partial Score\n200 points will be awarded as a partial score for passing the test set satisfying |s| <= 50.\nTask Constraint: 1 <= |s| <= 5000\ns consists of lowercase English letters.\n1 <= K <= 5\ns has at least K different substrings.\nTask Input: Input is given from Standard Input in the following format:\ns\nK\nTask Output: Print the K-th lexicographically smallest substring of K.\nTask Samples: input: aba\n4 output: b\n\ns has five substrings: a, b, ab, ba and aba.\nAmong them, we should print the fourth smallest one, b.\nNote that we do not count a twice.\ninput: atcoderandatcodeer\n5 output: andat\ninput: z\n1 output: z\n\n" }, { "title": "", "content": "Problem Statement We have a permutation of the integers from 1 through N, p_1, p_2, . . , p_N.\nWe also have M pairs of two integers between 1 and N (inclusive), represented as (x_1, y_1), (x_2, y_2), . . , (x_M, y_M).\nAt Co Deer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 <= i <= N) such that p_i = i is maximized:\n\nChoose j such that 1 <= j <= M, and swap p_{x_j} and p_{y_j}.\n\nFind the maximum possible number of i such that p_i = i after operations.", "constraint": "2 <= N <= 10^5\n1 <= M <= 10^5\np is a permutation of integers from 1 through N.\n1 <= x_j,y_j <= N\nx_j != y_j\nIf i != j, \\{x_i,y_i\\} != \\{x_j,y_j\\}.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\np_1 p_2 . . p_N\nx_1 y_1\nx_2 y_2\n:\nx_M y_M", "output": "Print the maximum possible number of i such that p_i = i after operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n5 3 1 4 2\n1 3\n5 4 output: 2\n\nIf we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.", "input: 3 2\n3 2 1\n1 2\n2 3 output: 3\n\nIf we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.\nNote that we may choose the same j any number of times.", "input: 10 8\n5 3 6 8 7 10 9 1 2 4\n3 1\n4 1\n5 9\n2 5\n6 5\n3 5\n8 9\n7 9 output: 8", "input: 5 1\n1 2 3 4 5\n1 5 output: 5\n\nWe do not have to perform the operation."], "Pid": "p03354", "ProblemText": "Task Description: Problem Statement We have a permutation of the integers from 1 through N, p_1, p_2, . . , p_N.\nWe also have M pairs of two integers between 1 and N (inclusive), represented as (x_1, y_1), (x_2, y_2), . . , (x_M, y_M).\nAt Co Deer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 <= i <= N) such that p_i = i is maximized:\n\nChoose j such that 1 <= j <= M, and swap p_{x_j} and p_{y_j}.\n\nFind the maximum possible number of i such that p_i = i after operations.\nTask Constraint: 2 <= N <= 10^5\n1 <= M <= 10^5\np is a permutation of integers from 1 through N.\n1 <= x_j,y_j <= N\nx_j != y_j\nIf i != j, \\{x_i,y_i\\} != \\{x_j,y_j\\}.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\np_1 p_2 . . p_N\nx_1 y_1\nx_2 y_2\n:\nx_M y_M\nTask Output: Print the maximum possible number of i such that p_i = i after operations.\nTask Samples: input: 5 2\n5 3 1 4 2\n1 3\n5 4 output: 2\n\nIf we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.\ninput: 3 2\n3 2 1\n1 2\n2 3 output: 3\n\nIf we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.\nNote that we may choose the same j any number of times.\ninput: 10 8\n5 3 6 8 7 10 9 1 2 4\n3 1\n4 1\n5 9\n2 5\n6 5\n3 5\n8 9\n7 9 output: 8\ninput: 5 1\n1 2 3 4 5\n1 5 output: 5\n\nWe do not have to perform the operation.\n\n" }, { "title": "", "content": "Problem Statement You are given a string s.\nAmong the different substrings of s, print the K-th lexicographically smallest one.\nA substring of s is a string obtained by taking out a non-empty contiguous part in s.\nFor example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.\nAlso, we say that substrings are different when they are different as strings.\nLet X = x_{1}x_{2}. . . x_{n} and Y = y_{1}y_{2}. . . y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \\neq y_{j}. partial score: Partial Score\n200 points will be awarded as a partial score for passing the test set satisfying |s| <= 50.", "constraint": "1 <= |s| <= 5000\ns consists of lowercase English letters.\n1 <= K <= 5\ns has at least K different substrings.", "input": "Input is given from Standard Input in the following format:\ns\nK", "output": "Print the K-th lexicographically smallest substring of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aba\n4 output: b\n\ns has five substrings: a, b, ab, ba and aba.\nAmong them, we should print the fourth smallest one, b.\nNote that we do not count a twice.", "input: atcoderandatcodeer\n5 output: andat", "input: z\n1 output: z"], "Pid": "p03355", "ProblemText": "Task Description: Problem Statement You are given a string s.\nAmong the different substrings of s, print the K-th lexicographically smallest one.\nA substring of s is a string obtained by taking out a non-empty contiguous part in s.\nFor example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.\nAlso, we say that substrings are different when they are different as strings.\nLet X = x_{1}x_{2}. . . x_{n} and Y = y_{1}y_{2}. . . y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \\neq y_{j}. partial score: Partial Score\n200 points will be awarded as a partial score for passing the test set satisfying |s| <= 50.\nTask Constraint: 1 <= |s| <= 5000\ns consists of lowercase English letters.\n1 <= K <= 5\ns has at least K different substrings.\nTask Input: Input is given from Standard Input in the following format:\ns\nK\nTask Output: Print the K-th lexicographically smallest substring of K.\nTask Samples: input: aba\n4 output: b\n\ns has five substrings: a, b, ab, ba and aba.\nAmong them, we should print the fourth smallest one, b.\nNote that we do not count a twice.\ninput: atcoderandatcodeer\n5 output: andat\ninput: z\n1 output: z\n\n" }, { "title": "", "content": "Problem Statement We have a permutation of the integers from 1 through N, p_1, p_2, . . , p_N.\nWe also have M pairs of two integers between 1 and N (inclusive), represented as (x_1, y_1), (x_2, y_2), . . , (x_M, y_M).\nAt Co Deer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 <= i <= N) such that p_i = i is maximized:\n\nChoose j such that 1 <= j <= M, and swap p_{x_j} and p_{y_j}.\n\nFind the maximum possible number of i such that p_i = i after operations.", "constraint": "2 <= N <= 10^5\n1 <= M <= 10^5\np is a permutation of integers from 1 through N.\n1 <= x_j,y_j <= N\nx_j != y_j\nIf i != j, \\{x_i,y_i\\} != \\{x_j,y_j\\}.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M\np_1 p_2 . . p_N\nx_1 y_1\nx_2 y_2\n:\nx_M y_M", "output": "Print the maximum possible number of i such that p_i = i after operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n5 3 1 4 2\n1 3\n5 4 output: 2\n\nIf we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.", "input: 3 2\n3 2 1\n1 2\n2 3 output: 3\n\nIf we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.\nNote that we may choose the same j any number of times.", "input: 10 8\n5 3 6 8 7 10 9 1 2 4\n3 1\n4 1\n5 9\n2 5\n6 5\n3 5\n8 9\n7 9 output: 8", "input: 5 1\n1 2 3 4 5\n1 5 output: 5\n\nWe do not have to perform the operation."], "Pid": "p03356", "ProblemText": "Task Description: Problem Statement We have a permutation of the integers from 1 through N, p_1, p_2, . . , p_N.\nWe also have M pairs of two integers between 1 and N (inclusive), represented as (x_1, y_1), (x_2, y_2), . . , (x_M, y_M).\nAt Co Deer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 <= i <= N) such that p_i = i is maximized:\n\nChoose j such that 1 <= j <= M, and swap p_{x_j} and p_{y_j}.\n\nFind the maximum possible number of i such that p_i = i after operations.\nTask Constraint: 2 <= N <= 10^5\n1 <= M <= 10^5\np is a permutation of integers from 1 through N.\n1 <= x_j,y_j <= N\nx_j != y_j\nIf i != j, \\{x_i,y_i\\} != \\{x_j,y_j\\}.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\np_1 p_2 . . p_N\nx_1 y_1\nx_2 y_2\n:\nx_M y_M\nTask Output: Print the maximum possible number of i such that p_i = i after operations.\nTask Samples: input: 5 2\n5 3 1 4 2\n1 3\n5 4 output: 2\n\nIf we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.\ninput: 3 2\n3 2 1\n1 2\n2 3 output: 3\n\nIf we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.\nNote that we may choose the same j any number of times.\ninput: 10 8\n5 3 6 8 7 10 9 1 2 4\n3 1\n4 1\n5 9\n2 5\n6 5\n3 5\n8 9\n7 9 output: 8\ninput: 5 1\n1 2 3 4 5\n1 5 output: 5\n\nWe do not have to perform the operation.\n\n" }, { "title": "", "content": "Problem Statement There are 2N balls, N white and N black, arranged in a row. The integers from 1 through N are written on the white balls, one on each ball, and they are also written on the black balls, one on each ball.\nThe integer written on the i-th ball from the left (1 <= i <= 2N) is a_i, and the color of this ball is represented by a letter c_i.\nc_i = W represents the ball is white; c_i = B represents the ball is black.\nTakahashi the human wants to achieve the following objective:\n\nFor every pair of integers (i, j) such that 1 <= i < j <= N, the white ball with i written on it is to the left of the white ball with j written on it.\nFor every pair of integers (i, j) such that 1 <= i < j <= N, the black ball with i written on it is to the left of the black ball with j written on it.\n\nIn order to achieve this, he can perform the following operation:\n\nSwap two adjacent balls.\n\nFind the minimum number of operations required to achieve the objective.", "constraint": "1 <= N <= 2000\n1 <= a_i <= N\nc_i = W or c_i = B.\nIf i != j, (a_i,c_i) != (a_j,c_j).", "input": "Input is given from Standard Input in the following format:\nN\nc_1 a_1\nc_2 a_2\n:\nc_{2N} a_{2N}", "output": "Print the minimum number of operations required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nB 1\nW 2\nB 3\nW 1\nW 3\nB 2 output: 4\n\nThe objective can be achieved in four operations, for example, as follows:\n\nSwap the black 3 and white 1.\nSwap the white 1 and white 2.\nSwap the black 3 and white 3.\nSwap the black 3 and black 2.", "input: 4\nB 4\nW 4\nB 3\nW 3\nB 2\nW 2\nB 1\nW 1 output: 18", "input: 9\nW 3\nB 1\nB 4\nW 1\nB 5\nW 9\nW 2\nB 6\nW 5\nB 3\nW 8\nB 9\nW 7\nB 2\nB 8\nW 4\nW 6\nB 7 output: 41"], "Pid": "p03357", "ProblemText": "Task Description: Problem Statement There are 2N balls, N white and N black, arranged in a row. The integers from 1 through N are written on the white balls, one on each ball, and they are also written on the black balls, one on each ball.\nThe integer written on the i-th ball from the left (1 <= i <= 2N) is a_i, and the color of this ball is represented by a letter c_i.\nc_i = W represents the ball is white; c_i = B represents the ball is black.\nTakahashi the human wants to achieve the following objective:\n\nFor every pair of integers (i, j) such that 1 <= i < j <= N, the white ball with i written on it is to the left of the white ball with j written on it.\nFor every pair of integers (i, j) such that 1 <= i < j <= N, the black ball with i written on it is to the left of the black ball with j written on it.\n\nIn order to achieve this, he can perform the following operation:\n\nSwap two adjacent balls.\n\nFind the minimum number of operations required to achieve the objective.\nTask Constraint: 1 <= N <= 2000\n1 <= a_i <= N\nc_i = W or c_i = B.\nIf i != j, (a_i,c_i) != (a_j,c_j).\nTask Input: Input is given from Standard Input in the following format:\nN\nc_1 a_1\nc_2 a_2\n:\nc_{2N} a_{2N}\nTask Output: Print the minimum number of operations required to achieve the objective.\nTask Samples: input: 3\nB 1\nW 2\nB 3\nW 1\nW 3\nB 2 output: 4\n\nThe objective can be achieved in four operations, for example, as follows:\n\nSwap the black 3 and white 1.\nSwap the white 1 and white 2.\nSwap the black 3 and white 3.\nSwap the black 3 and black 2.\ninput: 4\nB 4\nW 4\nB 3\nW 3\nB 2\nW 2\nB 1\nW 1 output: 18\ninput: 9\nW 3\nB 1\nB 4\nW 1\nB 5\nW 9\nW 2\nB 6\nW 5\nB 3\nW 8\nB 9\nW 7\nB 2\nB 8\nW 4\nW 6\nB 7 output: 41\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices numbered 1 through N.\nThe i-th edge connects Vertex x_i and y_i.\nEach vertex is painted white or black.\nThe initial color of Vertex i is represented by a letter c_i.\nc_i = W represents the vertex is white; c_i = B represents the vertex is black.\nA cat will walk along this tree.\nMore specifically, she performs one of the following in one second repeatedly:\n\nChoose a vertex that is adjacent to the vertex where she is currently, and move to that vertex. Then, invert the color of the destination vertex.\nInvert the color of the vertex where she is currently.\n\nThe cat's objective is to paint all the vertices black. She may start and end performing actions at any vertex.\nAt least how many seconds does it takes for the cat to achieve her objective?", "constraint": "1 <= N <= 10^5\n1 <= x_i,y_i <= N (1 <= i <= N-1)\nThe given graph is a tree.\nc_i = W or c_i = B.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N-1} y_{N-1}\nc_1c_2. . c_N", "output": "Print the minimum number of seconds required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n2 3\n2 4\n4 5\nWBBWW output: 5\n\nThe objective can be achieved in five seconds, for example, as follows:\n\nStart at Vertex 1. Change the color of Vertex 1 to black.\nMove to Vertex 2, then change the color of Vertex 2 to white.\nChange the color of Vertex 2 to black.\nMove to Vertex 4, then change the color of Vertex 4 to black.\nMove to Vertex 5, then change the color of Vertex 5 to black.", "input: 6\n3 1\n4 5\n2 6\n6 1\n3 4\nWWBWBB output: 7", "input: 1\nB output: 0", "input: 20\n2 19\n5 13\n6 4\n15 6\n12 19\n13 19\n3 11\n8 3\n3 20\n16 13\n7 14\n3 17\n7 8\n10 20\n11 9\n8 18\n8 2\n10 1\n6 13\nWBWBWBBWWWBBWWBBBBBW output: 21"], "Pid": "p03358", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices numbered 1 through N.\nThe i-th edge connects Vertex x_i and y_i.\nEach vertex is painted white or black.\nThe initial color of Vertex i is represented by a letter c_i.\nc_i = W represents the vertex is white; c_i = B represents the vertex is black.\nA cat will walk along this tree.\nMore specifically, she performs one of the following in one second repeatedly:\n\nChoose a vertex that is adjacent to the vertex where she is currently, and move to that vertex. Then, invert the color of the destination vertex.\nInvert the color of the vertex where she is currently.\n\nThe cat's objective is to paint all the vertices black. She may start and end performing actions at any vertex.\nAt least how many seconds does it takes for the cat to achieve her objective?\nTask Constraint: 1 <= N <= 10^5\n1 <= x_i,y_i <= N (1 <= i <= N-1)\nThe given graph is a tree.\nc_i = W or c_i = B.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N-1} y_{N-1}\nc_1c_2. . c_N\nTask Output: Print the minimum number of seconds required to achieve the objective.\nTask Samples: input: 5\n1 2\n2 3\n2 4\n4 5\nWBBWW output: 5\n\nThe objective can be achieved in five seconds, for example, as follows:\n\nStart at Vertex 1. Change the color of Vertex 1 to black.\nMove to Vertex 2, then change the color of Vertex 2 to white.\nChange the color of Vertex 2 to black.\nMove to Vertex 4, then change the color of Vertex 4 to black.\nMove to Vertex 5, then change the color of Vertex 5 to black.\ninput: 6\n3 1\n4 5\n2 6\n6 1\n3 4\nWWBWBB output: 7\ninput: 1\nB output: 0\ninput: 20\n2 19\n5 13\n6 4\n15 6\n12 19\n13 19\n3 11\n8 3\n3 20\n16 13\n7 14\n3 17\n7 8\n10 20\n11 9\n8 18\n8 2\n10 1\n6 13\nWBWBWBBWWWBBWWBBBBBW output: 21\n\n" }, { "title": "", "content": "Problem Statement\nIn At Coder Kingdom, Gregorian calendar is used, and dates are written in the \"year-month-day\" order, or the \"month-day\" order without the year.\nFor example, May 3,2018 is written as 2018-5-3, or 5-3 without the year. \nIn this country, a date is called Takahashi when the month and the day are equal as numbers. For example, 5-5 is Takahashi.\nHow many days from 2018-1-1 through 2018-a-b are Takahashi?", "constraint": "a is an integer between 1 and 12 (inclusive).\nb is an integer between 1 and 31 (inclusive).\n2018-a-b is a valid date in Gregorian calendar.", "input": "Input is given from Standard Input in the following format:\na b", "output": "Print the number of days from 2018-1-1 through 2018-a-b that are Takahashi.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5 output: 5\n\nThere are five days that are Takahashi: 1-1,2-2,3-3,4-4 and 5-5.", "input: 2 1 output: 1\n\nThere is only one day that is Takahashi: 1-1.", "input: 11 30 output: 11\n\nThere are eleven days that are Takahashi: 1-1,2-2,3-3,4-4,5-5,6-6,7-7,8-8,9-9,10-10 and 11-11."], "Pid": "p03359", "ProblemText": "Task Description: Problem Statement\nIn At Coder Kingdom, Gregorian calendar is used, and dates are written in the \"year-month-day\" order, or the \"month-day\" order without the year.\nFor example, May 3,2018 is written as 2018-5-3, or 5-3 without the year. \nIn this country, a date is called Takahashi when the month and the day are equal as numbers. For example, 5-5 is Takahashi.\nHow many days from 2018-1-1 through 2018-a-b are Takahashi?\nTask Constraint: a is an integer between 1 and 12 (inclusive).\nb is an integer between 1 and 31 (inclusive).\n2018-a-b is a valid date in Gregorian calendar.\nTask Input: Input is given from Standard Input in the following format:\na b\nTask Output: Print the number of days from 2018-1-1 through 2018-a-b that are Takahashi.\nTask Samples: input: 5 5 output: 5\n\nThere are five days that are Takahashi: 1-1,2-2,3-3,4-4 and 5-5.\ninput: 2 1 output: 1\n\nThere is only one day that is Takahashi: 1-1.\ninput: 11 30 output: 11\n\nThere are eleven days that are Takahashi: 1-1,2-2,3-3,4-4,5-5,6-6,7-7,8-8,9-9,10-10 and 11-11.\n\n" }, { "title": "", "content": "Problem Statement\nThere are three positive integers A, B and C written on a blackboard. E869120 performs the following operation K times:\n\nChoose one integer written on the blackboard and let the chosen integer be n. Replace the chosen integer with 2n.\n\nWhat is the largest possible sum of the integers written on the blackboard after K operations?", "constraint": "A, B and C are integers between 1 and 50 (inclusive).\nK is an integer between 1 and 10 (inclusive).", "input": "Input is given from Standard Input in the following format:\nA B C\nK", "output": "Print the largest possible sum of the integers written on the blackboard after K operations by E869220.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 11\n1 output: 30\n\nIn this sample, 5,3,11 are initially written on the blackboard, and E869120 can perform the operation once.\nThere are three choices: \n\nDouble 5: The integers written on the board after the operation are 10,3,11.\nDouble 3: The integers written on the board after the operation are 5,6,11.\nDouble 11: The integers written on the board after the operation are 5,3,22.\n\nIf he chooses 3., the sum of the integers written on the board afterwards is 5 + 3 + 22 = 30, which is the largest among 1. through 3.", "input: 3 3 4\n2 output: 22\n\nE869120 can perform the operation twice. The sum of the integers eventually written on the blackboard is maximized as follows: \n\nFirst, double 4. The integers written on the board are now 3,3,8. \nNext, double 8. The integers written on the board are now 3,3,16. \n\nThen, the sum of the integers eventually written on the blackboard is 3 + 3 + 16 = 22."], "Pid": "p03360", "ProblemText": "Task Description: Problem Statement\nThere are three positive integers A, B and C written on a blackboard. E869120 performs the following operation K times:\n\nChoose one integer written on the blackboard and let the chosen integer be n. Replace the chosen integer with 2n.\n\nWhat is the largest possible sum of the integers written on the blackboard after K operations?\nTask Constraint: A, B and C are integers between 1 and 50 (inclusive).\nK is an integer between 1 and 10 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nA B C\nK\nTask Output: Print the largest possible sum of the integers written on the blackboard after K operations by E869220.\nTask Samples: input: 5 3 11\n1 output: 30\n\nIn this sample, 5,3,11 are initially written on the blackboard, and E869120 can perform the operation once.\nThere are three choices: \n\nDouble 5: The integers written on the board after the operation are 10,3,11.\nDouble 3: The integers written on the board after the operation are 5,6,11.\nDouble 11: The integers written on the board after the operation are 5,3,22.\n\nIf he chooses 3., the sum of the integers written on the board afterwards is 5 + 3 + 22 = 30, which is the largest among 1. through 3.\ninput: 3 3 4\n2 output: 22\n\nE869120 can perform the operation twice. The sum of the integers eventually written on the blackboard is maximized as follows: \n\nFirst, double 4. The integers written on the board are now 3,3,8. \nNext, double 8. The integers written on the board are now 3,3,16. \n\nThen, the sum of the integers eventually written on the blackboard is 3 + 3 + 16 = 22.\n\n" }, { "title": "", "content": "Problem Statement\nWe have a canvas divided into a grid with H rows and W columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j).\nInitially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= #, and to make Square (i, j) white when s_{i, j}= . .\nHowever, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black.\nDetermine if square1001 can achieve his objective.", "constraint": "H is an integer between 1 and 50 (inclusive).\nW is an integer between 1 and 50 (inclusive).\nFor every (i, j) (1 <= i <= H, 1 <= j <= W), s_{i, j} is # or ..", "input": "Input is given from Standard Input in the following format:\nH W\ns_{1,1} s_{1,2} s_{1,3} . . . s_{1, W}\ns_{2,1} s_{2,2} s_{2,3} . . . s_{2, W}\n : :\ns_{H, 1} s_{H, 2} s_{H, 3} . . . s_{H, W}", "output": "If square1001 can achieve his objective, print Yes; if he cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n.#.\n###\n.#. output: Yes\n\nOne possible way to achieve the objective is shown in the figure below. Here, the squares being painted are marked by stars.", "input: 5 5\n#.#.#\n.#.#.\n#.#.#\n.#.#.\n#.#.# output: No\n\nsquare1001 cannot achieve his objective here.", "input: 11 11\n...#####...\n.##.....##.\n#..##.##..#\n#..##.##..#\n#.........#\n#...###...#\n.#########.\n.#.#.#.#.#.\n##.#.#.#.##\n..##.#.##..\n.##..#..##. output: Yes"], "Pid": "p03361", "ProblemText": "Task Description: Problem Statement\nWe have a canvas divided into a grid with H rows and W columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j).\nInitially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= #, and to make Square (i, j) white when s_{i, j}= . .\nHowever, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black.\nDetermine if square1001 can achieve his objective.\nTask Constraint: H is an integer between 1 and 50 (inclusive).\nW is an integer between 1 and 50 (inclusive).\nFor every (i, j) (1 <= i <= H, 1 <= j <= W), s_{i, j} is # or ..\nTask Input: Input is given from Standard Input in the following format:\nH W\ns_{1,1} s_{1,2} s_{1,3} . . . s_{1, W}\ns_{2,1} s_{2,2} s_{2,3} . . . s_{2, W}\n : :\ns_{H, 1} s_{H, 2} s_{H, 3} . . . s_{H, W}\nTask Output: If square1001 can achieve his objective, print Yes; if he cannot, print No.\nTask Samples: input: 3 3\n.#.\n###\n.#. output: Yes\n\nOne possible way to achieve the objective is shown in the figure below. Here, the squares being painted are marked by stars.\ninput: 5 5\n#.#.#\n.#.#.\n#.#.#\n.#.#.\n#.#.# output: No\n\nsquare1001 cannot achieve his objective here.\ninput: 11 11\n...#####...\n.##.....##.\n#..##.##..#\n#..##.##..#\n#.........#\n#...###...#\n.#########.\n.#.#.#.#.#.\n##.#.#.#.##\n..##.#.##..\n.##..#..##. output: Yes\n\n" }, { "title": "", "content": "Problem Statement\nPrint a sequence a_1, a_2, . . . , a_N whose length is N that satisfies the following conditions:\n\na_i (1 <= i <= N) is a prime number at most 55 555.\nThe values of a_1, a_2, . . . , a_N are all different.\nIn every choice of five different integers from a_1, a_2, . . . , a_N, the sum of those integers is a composite number.\n\nIf there are multiple such sequences, printing any of them is accepted. note: Notes\nAn integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.", "constraint": "N is an integer between 5 and 55 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print N numbers a_1, a_2, a_3, . . . , a_N in a line, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 output: 3 5 7 11 31\n\nLet us see if this output actually satisfies the conditions.\nFirst, 3,5,7,11 and 31 are all different, and all of them are prime numbers.\nThe only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.\nThere are also other possible outputs, such as 2 3 5 7 13,11 13 17 19 31 and 7 11 5 31 3.", "input: 6 output: 2 3 5 7 11 13\n2,3,5,7,11,13 are all different prime numbers.\n2+3+5+7+11=28 is a composite number.\n2+3+5+7+13=30 is a composite number.\n2+3+5+11+13=34 is a composite number.\n2+3+7+11+13=36 is a composite number.\n2+5+7+11+13=38 is a composite number.\n3+5+7+11+13=39 is a composite number.\n\nThus, the sequence 2 3 5 7 11 13 satisfies the conditions.", "input: 8 output: 2 5 7 13 19 37 67 79"], "Pid": "p03362", "ProblemText": "Task Description: Problem Statement\nPrint a sequence a_1, a_2, . . . , a_N whose length is N that satisfies the following conditions:\n\na_i (1 <= i <= N) is a prime number at most 55 555.\nThe values of a_1, a_2, . . . , a_N are all different.\nIn every choice of five different integers from a_1, a_2, . . . , a_N, the sum of those integers is a composite number.\n\nIf there are multiple such sequences, printing any of them is accepted. note: Notes\nAn integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.\nTask Constraint: N is an integer between 5 and 55 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print N numbers a_1, a_2, a_3, . . . , a_N in a line, with spaces in between.\nTask Samples: input: 5 output: 3 5 7 11 31\n\nLet us see if this output actually satisfies the conditions.\nFirst, 3,5,7,11 and 31 are all different, and all of them are prime numbers.\nThe only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.\nThere are also other possible outputs, such as 2 3 5 7 13,11 13 17 19 31 and 7 11 5 31 3.\ninput: 6 output: 2 3 5 7 11 13\n2,3,5,7,11,13 are all different prime numbers.\n2+3+5+7+11=28 is a composite number.\n2+3+5+7+13=30 is a composite number.\n2+3+5+11+13=34 is a composite number.\n2+3+7+11+13=36 is a composite number.\n2+5+7+11+13=38 is a composite number.\n3+5+7+11+13=39 is a composite number.\n\nThus, the sequence 2 3 5 7 11 13 satisfies the conditions.\ninput: 8 output: 2 5 7 13 19 37 67 79\n\n" }, { "title": "", "content": "Problem Statement We have an integer sequence A, whose length is N.\nFind the number of the non-empty contiguous subsequences of A whose sums are 0.\nNote that we are counting the ways to take out subsequences.\nThat is, even if the contents of some two subsequences are the same, they are counted individually if they are taken from different positions.", "constraint": "1 <= N <= 2 * 10^5\n-10^9 <= A_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Find the number of the non-empty contiguous subsequences of A whose sum is 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 3 -4 2 2 -2 output: 3\n\nThere are three contiguous subsequences whose sums are 0: (1,3,-4), (-4,2,2) and (2,-2).", "input: 7\n1 -1 1 -1 1 -1 1 output: 12\n\nIn this case, some subsequences that have the same contents but are taken from different positions are counted individually.\nFor example, three occurrences of (1, -1) are counted.", "input: 5\n1 -2 3 -4 5 output: 0\n\nThere are no contiguous subsequences whose sums are 0."], "Pid": "p03363", "ProblemText": "Task Description: Problem Statement We have an integer sequence A, whose length is N.\nFind the number of the non-empty contiguous subsequences of A whose sums are 0.\nNote that we are counting the ways to take out subsequences.\nThat is, even if the contents of some two subsequences are the same, they are counted individually if they are taken from different positions.\nTask Constraint: 1 <= N <= 2 * 10^5\n-10^9 <= A_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Find the number of the non-empty contiguous subsequences of A whose sum is 0.\nTask Samples: input: 6\n1 3 -4 2 2 -2 output: 3\n\nThere are three contiguous subsequences whose sums are 0: (1,3,-4), (-4,2,2) and (2,-2).\ninput: 7\n1 -1 1 -1 1 -1 1 output: 12\n\nIn this case, some subsequences that have the same contents but are taken from different positions are counted individually.\nFor example, three occurrences of (1, -1) are counted.\ninput: 5\n1 -2 3 -4 5 output: 0\n\nThere are no contiguous subsequences whose sums are 0.\n\n" }, { "title": "", "content": "Problem Statement Snuke has two boards, each divided into a grid with N rows and N columns.\nFor both of these boards, the square at the i-th row from the top and the j-th column from the left is called Square (i, j).\nThere is a lowercase English letter written in each square on the first board. The letter written in Square (i, j) is S_{i, j}. On the second board, nothing is written yet.\nSnuke will write letters on the second board, as follows:\n\nFirst, choose two integers A and B ( 0 <= A, B < N ).\nWrite one letter in each square on the second board.\nSpecifically, write the letter written in Square ( i+A, j+B ) on the first board into Square (i, j) on the second board.\nHere, the k-th row is also represented as the (N+k)-th row, and the k-th column is also represented as the (N+k)-th column.\n\nAfter this operation, the second board is called a good board when, for every i and j ( 1 <= i, j <= N ), the letter in Square (i, j) and the letter in Square (j, i) are equal.\nFind the number of the ways to choose integers A and B ( 0 <= A, B < N ) such that the second board is a good board.", "constraint": "1 <= N <= 300\nS_{i,j} ( 1 <= i, j <= N ) is a lowercase English letter.", "input": "Input is given from Standard Input in the following format:\nN\nS_{1,1}S_{1,2}. . S_{1, N}\nS_{2,1}S_{2,2}. . S_{2, N}\n:\nS_{N, 1}S_{N, 2}. . S_{N, N}", "output": "Print the number of the ways to choose integers A and B ( 0 <= A, B < N ) such that the second board is a good board.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\nab\nca output: 2\n\nFor each pair of A and B, the second board will look as shown below:\n\nThe second board is a good board when (A,B) = (0,1) or (A,B) = (1,0), thus the answer is 2.", "input: 4\naaaa\naaaa\naaaa\naaaa output: 16\n\nEvery possible choice of A and B makes the second board good.", "input: 5\nabcde\nfghij\nklmno\npqrst\nuvwxy output: 0\n\nNo possible choice of A and B makes the second board good."], "Pid": "p03364", "ProblemText": "Task Description: Problem Statement Snuke has two boards, each divided into a grid with N rows and N columns.\nFor both of these boards, the square at the i-th row from the top and the j-th column from the left is called Square (i, j).\nThere is a lowercase English letter written in each square on the first board. The letter written in Square (i, j) is S_{i, j}. On the second board, nothing is written yet.\nSnuke will write letters on the second board, as follows:\n\nFirst, choose two integers A and B ( 0 <= A, B < N ).\nWrite one letter in each square on the second board.\nSpecifically, write the letter written in Square ( i+A, j+B ) on the first board into Square (i, j) on the second board.\nHere, the k-th row is also represented as the (N+k)-th row, and the k-th column is also represented as the (N+k)-th column.\n\nAfter this operation, the second board is called a good board when, for every i and j ( 1 <= i, j <= N ), the letter in Square (i, j) and the letter in Square (j, i) are equal.\nFind the number of the ways to choose integers A and B ( 0 <= A, B < N ) such that the second board is a good board.\nTask Constraint: 1 <= N <= 300\nS_{i,j} ( 1 <= i, j <= N ) is a lowercase English letter.\nTask Input: Input is given from Standard Input in the following format:\nN\nS_{1,1}S_{1,2}. . S_{1, N}\nS_{2,1}S_{2,2}. . S_{2, N}\n:\nS_{N, 1}S_{N, 2}. . S_{N, N}\nTask Output: Print the number of the ways to choose integers A and B ( 0 <= A, B < N ) such that the second board is a good board.\nTask Samples: input: 2\nab\nca output: 2\n\nFor each pair of A and B, the second board will look as shown below:\n\nThe second board is a good board when (A,B) = (0,1) or (A,B) = (1,0), thus the answer is 2.\ninput: 4\naaaa\naaaa\naaaa\naaaa output: 16\n\nEvery possible choice of A and B makes the second board good.\ninput: 5\nabcde\nfghij\nklmno\npqrst\nuvwxy output: 0\n\nNo possible choice of A and B makes the second board good.\n\n" }, { "title": "", "content": "Problem Statement There are N squares lining up in a row, numbered 1 through N from left to right.\nInitially, all squares are white.\nWe also have N-1 painting machines, numbered 1 through N-1.\nWhen operated, Machine i paints Square i and i+1 black.\nSnuke will operate these machines one by one.\nThe order in which he operates them is represented by a permutation of (1,2, . . . , N-1), P, which means that the i-th operated machine is Machine P_i.\nHere, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P.\nSnuke has not decided what permutation P to use, but he is interested in the scores of possible permutations.\nFind the sum of the scores over all possible permutations for him.\nSince this can be extremely large, compute the sum modulo 10^9+7.", "constraint": "2 <= N <= 10^6", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the sum of the scores over all possible permutations, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 16\n\nThere are six possible permutations as P.\nAmong them, P = (1,3,2) and P = (3,1,2) have a score of 2, and the others have a score of 3.\nThus, the answer is 2 * 2 + 3 * 4 = 16.", "input: 2 output: 1\n\nThere is only one possible permutation: P = (1), which has a score of 1.", "input: 5 output: 84", "input: 100000 output: 341429644"], "Pid": "p03365", "ProblemText": "Task Description: Problem Statement There are N squares lining up in a row, numbered 1 through N from left to right.\nInitially, all squares are white.\nWe also have N-1 painting machines, numbered 1 through N-1.\nWhen operated, Machine i paints Square i and i+1 black.\nSnuke will operate these machines one by one.\nThe order in which he operates them is represented by a permutation of (1,2, . . . , N-1), P, which means that the i-th operated machine is Machine P_i.\nHere, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P.\nSnuke has not decided what permutation P to use, but he is interested in the scores of possible permutations.\nFind the sum of the scores over all possible permutations for him.\nSince this can be extremely large, compute the sum modulo 10^9+7.\nTask Constraint: 2 <= N <= 10^6\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the sum of the scores over all possible permutations, modulo 10^9+7.\nTask Samples: input: 4 output: 16\n\nThere are six possible permutations as P.\nAmong them, P = (1,3,2) and P = (3,1,2) have a score of 2, and the others have a score of 3.\nThus, the answer is 2 * 2 + 3 * 4 = 16.\ninput: 2 output: 1\n\nThere is only one possible permutation: P = (1), which has a score of 1.\ninput: 5 output: 84\ninput: 100000 output: 341429644\n\n" }, { "title": "", "content": "Problem Statement There are N apartments along a number line, numbered 1 through N.\nApartment i is located at coordinate X_i.\nAlso, the office of At Coder Inc. is located at coordinate S.\nEvery employee of At Coder lives in one of the N apartments.\nThere are P_i employees who are living in Apartment i.\nAll employees of At Coder are now leaving the office all together.\nSince they are tired from work, they would like to get home by the company's bus.\nAt Coder owns only one bus, but it can accommodate all the employees.\nThis bus will leave coordinate S with all the employees and move according to the following rule:\nEveryone on the bus casts a vote on which direction the bus should proceed, positive or negative. (The bus is autonomous and has no driver. ) Each person has one vote, and abstaining from voting is not allowed. Then, the bus moves a distance of 1 in the direction with the greater number of votes. If a tie occurs, the bus moves in the negative direction. If there is an apartment at the coordinate of the bus after the move, all the employees who live there get off.\nRepeat the operation above as long as there is one or more employees on the bus.\nFor a specific example, see Sample Input 1.\nThe bus takes one seconds to travel a distance of 1.\nThe time required to vote and get off the bus is ignorable.\nEvery employee will vote so that he himself/she herself can get off the bus at the earliest possible time.\nStrictly speaking, when a vote is taking place, each employee see which direction results in the earlier arrival at his/her apartment, assuming that all the employees follow the same strategy in the future.\nBased on this information, each employee makes the optimal choice, but if either direction results in the arrival at the same time, he/she casts a vote to the negative direction.\nFind the time the bus will take from departure to arrival at the last employees' apartment.\nIt can be proved that, given the positions of the apartments, the numbers of employees living in each apartment and the initial position of the bus, the future movement of the bus is uniquely determined, and the process will end in a finite time.", "constraint": "1 <= N <= 10^5\n1 <= S <= 10^9\n1 <= X_1 < X_2 < ... < X_N <= 10^9\nX_i \\neq S ( 1 <= i <= N )\n1 <= P_i <= 10^9 ( 1 <= i <= N )\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN S\nX_1 P_1\nX_2 P_2\n:\nX_N P_N", "output": "Print the number of seconds the bus will take from departure to arrival at the last employees' apartment.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 3\n3 4\n4 2 output: 4\n\nAssume that the bus moves in the negative direction first.\nThen, the coordinate of the bus changes from 2 to 1, and the employees living in Apartment 1 get off.\nThe movement of the bus after that is obvious: it just continues moving in the positive direction.\nThus, if the bus moves in the negative direction first, the coordinate of the bus changes as 2 → 1 → 2 → 3 → 4 from departure.\nThe time it takes to get home for the employees living in Apartment 1,2,3 are 1,3,4 seconds, respectively.\nNext, assume that the bus moves in the positive direction first.\nThen, the coordinate of the bus changes from 2 to 3, and the employees living in Apartment 2 get off.\nAfterwards, the bus starts heading to Apartment 1, because there are more employees living in Apartment 1 than in Apartment 3.\nThen, after arriving at Apartment 1, the bus heads to Apartment 3.\nThus, if the bus moves in the positive direction first, the coordinate of the bus changes as 2 → 3 → 2 → 1 → 2 → 3 → 4 from departure.\nThe time it takes to get home for the employees living in Apartment 1,2,3 are 3,1,6 seconds, respectively.\nTherefore, in the beginning, the employees living in Apartment 1 or 3 will try to move the bus in the negative direction.\nOn the other hand, the employees living in Apartment 2 will try to move the bus in the positive direction in the beginning.\nThere are a total of 3 + 2 = 5 employees living in Apartment 1 and 3 combined, which is more than those living in Apartment 2, which is 4.\nThus, the bus will move in the negative direction first, and the coordinate of the bus will change as 2 → 1 → 2 → 3 → 4 from departure.", "input: 6 4\n1 10\n2 1000\n3 100000\n5 1000000\n6 10000\n7 100 output: 21\n\nSince the numbers of employees living in different apartments are literally off by a digit, the bus consistently head to the apartment where the most number of employees on the bus lives.", "input: 15 409904902\n94198000 15017\n117995501 7656764\n275583856 313263626\n284496300 356635175\n324233841 607\n360631781 148\n472103717 5224\n497641071 34695\n522945827 816241\n554305668 32\n623788284 22832\n667409501 124410641\n876731548 12078\n904557302 291749534\n918215789 5 output: 2397671583"], "Pid": "p03366", "ProblemText": "Task Description: Problem Statement There are N apartments along a number line, numbered 1 through N.\nApartment i is located at coordinate X_i.\nAlso, the office of At Coder Inc. is located at coordinate S.\nEvery employee of At Coder lives in one of the N apartments.\nThere are P_i employees who are living in Apartment i.\nAll employees of At Coder are now leaving the office all together.\nSince they are tired from work, they would like to get home by the company's bus.\nAt Coder owns only one bus, but it can accommodate all the employees.\nThis bus will leave coordinate S with all the employees and move according to the following rule:\nEveryone on the bus casts a vote on which direction the bus should proceed, positive or negative. (The bus is autonomous and has no driver. ) Each person has one vote, and abstaining from voting is not allowed. Then, the bus moves a distance of 1 in the direction with the greater number of votes. If a tie occurs, the bus moves in the negative direction. If there is an apartment at the coordinate of the bus after the move, all the employees who live there get off.\nRepeat the operation above as long as there is one or more employees on the bus.\nFor a specific example, see Sample Input 1.\nThe bus takes one seconds to travel a distance of 1.\nThe time required to vote and get off the bus is ignorable.\nEvery employee will vote so that he himself/she herself can get off the bus at the earliest possible time.\nStrictly speaking, when a vote is taking place, each employee see which direction results in the earlier arrival at his/her apartment, assuming that all the employees follow the same strategy in the future.\nBased on this information, each employee makes the optimal choice, but if either direction results in the arrival at the same time, he/she casts a vote to the negative direction.\nFind the time the bus will take from departure to arrival at the last employees' apartment.\nIt can be proved that, given the positions of the apartments, the numbers of employees living in each apartment and the initial position of the bus, the future movement of the bus is uniquely determined, and the process will end in a finite time.\nTask Constraint: 1 <= N <= 10^5\n1 <= S <= 10^9\n1 <= X_1 < X_2 < ... < X_N <= 10^9\nX_i \\neq S ( 1 <= i <= N )\n1 <= P_i <= 10^9 ( 1 <= i <= N )\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN S\nX_1 P_1\nX_2 P_2\n:\nX_N P_N\nTask Output: Print the number of seconds the bus will take from departure to arrival at the last employees' apartment.\nTask Samples: input: 3 2\n1 3\n3 4\n4 2 output: 4\n\nAssume that the bus moves in the negative direction first.\nThen, the coordinate of the bus changes from 2 to 1, and the employees living in Apartment 1 get off.\nThe movement of the bus after that is obvious: it just continues moving in the positive direction.\nThus, if the bus moves in the negative direction first, the coordinate of the bus changes as 2 → 1 → 2 → 3 → 4 from departure.\nThe time it takes to get home for the employees living in Apartment 1,2,3 are 1,3,4 seconds, respectively.\nNext, assume that the bus moves in the positive direction first.\nThen, the coordinate of the bus changes from 2 to 3, and the employees living in Apartment 2 get off.\nAfterwards, the bus starts heading to Apartment 1, because there are more employees living in Apartment 1 than in Apartment 3.\nThen, after arriving at Apartment 1, the bus heads to Apartment 3.\nThus, if the bus moves in the positive direction first, the coordinate of the bus changes as 2 → 3 → 2 → 1 → 2 → 3 → 4 from departure.\nThe time it takes to get home for the employees living in Apartment 1,2,3 are 3,1,6 seconds, respectively.\nTherefore, in the beginning, the employees living in Apartment 1 or 3 will try to move the bus in the negative direction.\nOn the other hand, the employees living in Apartment 2 will try to move the bus in the positive direction in the beginning.\nThere are a total of 3 + 2 = 5 employees living in Apartment 1 and 3 combined, which is more than those living in Apartment 2, which is 4.\nThus, the bus will move in the negative direction first, and the coordinate of the bus will change as 2 → 1 → 2 → 3 → 4 from departure.\ninput: 6 4\n1 10\n2 1000\n3 100000\n5 1000000\n6 10000\n7 100 output: 21\n\nSince the numbers of employees living in different apartments are literally off by a digit, the bus consistently head to the apartment where the most number of employees on the bus lives.\ninput: 15 409904902\n94198000 15017\n117995501 7656764\n275583856 313263626\n284496300 356635175\n324233841 607\n360631781 148\n472103717 5224\n497641071 34695\n522945827 816241\n554305668 32\n623788284 22832\n667409501 124410641\n876731548 12078\n904557302 291749534\n918215789 5 output: 2397671583\n\n" }, { "title": "", "content": "Problem Statement Snuke has an integer sequence A whose length is N.\nHe likes permutations of (1,2, . . . , N), P, that satisfy the following condition:\n\nP_i <= A_i for all i ( 1 <= i <= N ).\n\nSnuke is interested in the inversion numbers of such permutations.\nFind the sum of the inversion numbers over all permutations that satisfy the condition.\nSince this can be extremely large, compute the sum modulo 10^9+7. note: Notes The inversion number of a sequence Z whose length N is the number of pairs of integers i and j ( 1 <= i < j <= N ) such that Z_i > Z_j.", "constraint": "1 <= N <= 2 * 10^5\n1 <= A_i <= N ( 1 <= i <= N )\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the sum of the inversion numbers over all permutations that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3 3 output: 4\n\nThere are four permutations that satisfy the condition: (1,2,3), (1,3,2), (2,1,3) and (2,3,1).\nThe inversion numbers of these permutations are 0,1,1 and 2, respectively, for a total of 4.", "input: 6\n4 2 5 1 6 3 output: 7\n\nOnly one permutation (4,2,5,1,6,3) satisfies the condition.\nThe inversion number of this permutation is 7, so the answer is 7.", "input: 5\n4 4 4 4 4 output: 0\n\nNo permutation satisfies the condition.", "input: 30\n22 30 15 20 10 29 11 29 28 11 26 10 18 28 22 5 29 16 24 24 27 10 21 30 29 19 28 27 18 23 output: 848414012"], "Pid": "p03367", "ProblemText": "Task Description: Problem Statement Snuke has an integer sequence A whose length is N.\nHe likes permutations of (1,2, . . . , N), P, that satisfy the following condition:\n\nP_i <= A_i for all i ( 1 <= i <= N ).\n\nSnuke is interested in the inversion numbers of such permutations.\nFind the sum of the inversion numbers over all permutations that satisfy the condition.\nSince this can be extremely large, compute the sum modulo 10^9+7. note: Notes The inversion number of a sequence Z whose length N is the number of pairs of integers i and j ( 1 <= i < j <= N ) such that Z_i > Z_j.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= A_i <= N ( 1 <= i <= N )\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the sum of the inversion numbers over all permutations that satisfy the condition.\nTask Samples: input: 3\n2 3 3 output: 4\n\nThere are four permutations that satisfy the condition: (1,2,3), (1,3,2), (2,1,3) and (2,3,1).\nThe inversion numbers of these permutations are 0,1,1 and 2, respectively, for a total of 4.\ninput: 6\n4 2 5 1 6 3 output: 7\n\nOnly one permutation (4,2,5,1,6,3) satisfies the condition.\nThe inversion number of this permutation is 7, so the answer is 7.\ninput: 5\n4 4 4 4 4 output: 0\n\nNo permutation satisfies the condition.\ninput: 30\n22 30 15 20 10 29 11 29 28 11 26 10 18 28 22 5 29 16 24 24 27 10 21 30 29 19 28 27 18 23 output: 848414012\n\n" }, { "title": "", "content": "Problem Statement Snuke has a rooted tree with N vertices, numbered 1 through N.\nVertex 1 is the root of the tree, and the parent of Vertex i ( 2<= i <= N ) is Vertex P_i ( P_i < i ).\nThere is a number, 0 or 1, written on each vertex. The number written on Vertex i is V_i.\nSnuke would like to arrange the vertices of this tree in a horizontal row.\nHere, for every vertex, there should be no ancestor of that vertex to the right of that vertex.\nAfter arranging the vertices, let X be the sequence obtained by reading the numbers written on the vertices from left to right in the arrangement.\nSnuke would like to minimize the inversion number of X.\nFind the minimum possible inversion number of X. note: Notes The inversion number of a sequence Z whose length N is the number of pairs of integers i and j ( 1 <= i < j <= N ) such that Z_i > Z_j.", "constraint": "1 <= N <= 2 * 10^5\n1 <= P_i < i ( 2 <= i <= N )\n0 <= V_i <= 1 ( 1 <= i <= N )\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nP_2 P_3 . . . P_N\nV_1 V_2 . . . V_N", "output": "Print the minimum possible inversion number of X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 1 2 3 3\n0 1 1 0 0 0 output: 4\n\nWhen the vertices are arranged in the order 1,3,5,6,2,4, X will be (0,1,0,0,1,0), whose inversion number is 4.\nIt is impossible to have fewer inversions, so the answer is 4.", "input: 1\n\n0 output: 0\n\nX = (0), whose inversion number is 0.", "input: 15\n1 2 3 2 5 6 2 2 9 10 1 12 13 12\n1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 output: 31"], "Pid": "p03368", "ProblemText": "Task Description: Problem Statement Snuke has a rooted tree with N vertices, numbered 1 through N.\nVertex 1 is the root of the tree, and the parent of Vertex i ( 2<= i <= N ) is Vertex P_i ( P_i < i ).\nThere is a number, 0 or 1, written on each vertex. The number written on Vertex i is V_i.\nSnuke would like to arrange the vertices of this tree in a horizontal row.\nHere, for every vertex, there should be no ancestor of that vertex to the right of that vertex.\nAfter arranging the vertices, let X be the sequence obtained by reading the numbers written on the vertices from left to right in the arrangement.\nSnuke would like to minimize the inversion number of X.\nFind the minimum possible inversion number of X. note: Notes The inversion number of a sequence Z whose length N is the number of pairs of integers i and j ( 1 <= i < j <= N ) such that Z_i > Z_j.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= P_i < i ( 2 <= i <= N )\n0 <= V_i <= 1 ( 1 <= i <= N )\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nP_2 P_3 . . . P_N\nV_1 V_2 . . . V_N\nTask Output: Print the minimum possible inversion number of X.\nTask Samples: input: 6\n1 1 2 3 3\n0 1 1 0 0 0 output: 4\n\nWhen the vertices are arranged in the order 1,3,5,6,2,4, X will be (0,1,0,0,1,0), whose inversion number is 4.\nIt is impossible to have fewer inversions, so the answer is 4.\ninput: 1\n\n0 output: 0\n\nX = (0), whose inversion number is 0.\ninput: 15\n1 2 3 2 5 6 2 2 9 10 1 12 13 12\n1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 output: 31\n\n" }, { "title": "", "content": "Problem Statement In \"Takahashi-ya\", a ramen restaurant, a bowl of ramen costs 700 yen (the currency of Japan), plus 100 yen for each kind of topping (boiled egg, sliced pork, green onions).\nA customer ordered a bowl of ramen and told which toppings to put on his ramen to a clerk. The clerk took a memo of the order as a string S. S is three characters long, and if the first character in S is o, it means the ramen should be topped with boiled egg; if that character is x, it means the ramen should not be topped with boiled egg. Similarly, the second and third characters in S mean the presence or absence of sliced pork and green onions on top of the ramen.\nWrite a program that, when S is given, prints the price of the corresponding bowl of ramen.", "constraint": "S is a string of length 3.\nEach character in S is o or x.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the price of the bowl of ramen corresponding to S.", "content_img": false, "lang": "en", "error": false, "samples": ["input: oxo output: 900\n\nThe price of a ramen topped with two kinds of toppings, boiled egg and green onions, is 700 + 100 * 2 = 900 yen.", "input: ooo output: 1000\n\nThe price of a ramen topped with all three kinds of toppings is 700 + 100 * 3 = 1000 yen.", "input: xxx output: 700\n\nThe price of a ramen without any toppings is 700 yen."], "Pid": "p03369", "ProblemText": "Task Description: Problem Statement In \"Takahashi-ya\", a ramen restaurant, a bowl of ramen costs 700 yen (the currency of Japan), plus 100 yen for each kind of topping (boiled egg, sliced pork, green onions).\nA customer ordered a bowl of ramen and told which toppings to put on his ramen to a clerk. The clerk took a memo of the order as a string S. S is three characters long, and if the first character in S is o, it means the ramen should be topped with boiled egg; if that character is x, it means the ramen should not be topped with boiled egg. Similarly, the second and third characters in S mean the presence or absence of sliced pork and green onions on top of the ramen.\nWrite a program that, when S is given, prints the price of the corresponding bowl of ramen.\nTask Constraint: S is a string of length 3.\nEach character in S is o or x.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the price of the bowl of ramen corresponding to S.\nTask Samples: input: oxo output: 900\n\nThe price of a ramen topped with two kinds of toppings, boiled egg and green onions, is 700 + 100 * 2 = 900 yen.\ninput: ooo output: 1000\n\nThe price of a ramen topped with all three kinds of toppings is 700 + 100 * 3 = 1000 yen.\ninput: xxx output: 700\n\nThe price of a ramen without any toppings is 700 yen.\n\n" }, { "title": "", "content": "Problem Statement Akaki, a patissier, can make N kinds of doughnut using only a certain powder called \"Okashi no Moto\" (literally \"material of pastry\", simply called Moto below) as ingredient. These doughnuts are called Doughnut 1, Doughnut 2, . . . , Doughnut N. In order to make one Doughnut i (1 <= i <= N), she needs to consume m_i grams of Moto. She cannot make a non-integer number of doughnuts, such as 0.5 doughnuts.\nNow, she has X grams of Moto. She decides to make as many doughnuts as possible for a party tonight. However, since the tastes of the guests differ, she will obey the following condition:\n\nFor each of the N kinds of doughnuts, make at least one doughnut of that kind.\n\nAt most how many doughnuts can be made here? She does not necessarily need to consume all of her Moto. Also, under the constraints of this problem, it is always possible to obey the condition.", "constraint": "2 <= N <= 100\n1 <= m_i <= 1000\nm_1 + m_2 + ... + m_N <= X <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X\nm_1\nm_2\n:\nm_N", "output": "Print the maximum number of doughnuts that can be made under the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1000\n120\n100\n140 output: 9\n\nShe has 1000 grams of Moto and can make three kinds of doughnuts. If she makes one doughnut for each of the three kinds, she consumes 120 + 100 + 140 = 360 grams of Moto. From the 640 grams of Moto that remains here, she can make additional six Doughnuts 2. This is how she can made a total of nine doughnuts, which is the maximum.", "input: 4 360\n90\n90\n90\n90 output: 4\n\nMaking one doughnut for each of the four kinds consumes all of her Moto.", "input: 5 3000\n150\n130\n150\n130\n110 output: 26"], "Pid": "p03370", "ProblemText": "Task Description: Problem Statement Akaki, a patissier, can make N kinds of doughnut using only a certain powder called \"Okashi no Moto\" (literally \"material of pastry\", simply called Moto below) as ingredient. These doughnuts are called Doughnut 1, Doughnut 2, . . . , Doughnut N. In order to make one Doughnut i (1 <= i <= N), she needs to consume m_i grams of Moto. She cannot make a non-integer number of doughnuts, such as 0.5 doughnuts.\nNow, she has X grams of Moto. She decides to make as many doughnuts as possible for a party tonight. However, since the tastes of the guests differ, she will obey the following condition:\n\nFor each of the N kinds of doughnuts, make at least one doughnut of that kind.\n\nAt most how many doughnuts can be made here? She does not necessarily need to consume all of her Moto. Also, under the constraints of this problem, it is always possible to obey the condition.\nTask Constraint: 2 <= N <= 100\n1 <= m_i <= 1000\nm_1 + m_2 + ... + m_N <= X <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X\nm_1\nm_2\n:\nm_N\nTask Output: Print the maximum number of doughnuts that can be made under the condition.\nTask Samples: input: 3 1000\n120\n100\n140 output: 9\n\nShe has 1000 grams of Moto and can make three kinds of doughnuts. If she makes one doughnut for each of the three kinds, she consumes 120 + 100 + 140 = 360 grams of Moto. From the 640 grams of Moto that remains here, she can make additional six Doughnuts 2. This is how she can made a total of nine doughnuts, which is the maximum.\ninput: 4 360\n90\n90\n90\n90 output: 4\n\nMaking one doughnut for each of the four kinds consumes all of her Moto.\ninput: 5 3000\n150\n130\n150\n130\n110 output: 26\n\n" }, { "title": "", "content": "Problem Statement\"Pizza At\", a fast food chain, offers three kinds of pizza: \"A-pizza\", \"B-pizza\" and \"AB-pizza\". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.\nNakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.", "constraint": "1 <= A, B, C <= 5000\n1 <= X, Y <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C X Y", "output": "Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1500 2000 1600 3 2 output: 7900\n\nIt is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.", "input: 1500 2000 1900 3 2 output: 8500\n\nIt is optimal to directly buy three A-pizzas and two B-pizzas.", "input: 1500 2000 500 90000 100000 output: 100000000\n\nIt is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine."], "Pid": "p03371", "ProblemText": "Task Description: Problem Statement\"Pizza At\", a fast food chain, offers three kinds of pizza: \"A-pizza\", \"B-pizza\" and \"AB-pizza\". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.\nNakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.\nTask Constraint: 1 <= A, B, C <= 5000\n1 <= X, Y <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C X Y\nTask Output: Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.\nTask Samples: input: 1500 2000 1600 3 2 output: 7900\n\nIt is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.\ninput: 1500 2000 1900 3 2 output: 8500\n\nIt is optimal to directly buy three A-pizzas and two B-pizzas.\ninput: 1500 2000 500 90000 100000 output: 100000000\n\nIt is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine.\n\n" }, { "title": "", "content": "Problem Statement\"Teishi-zushi\", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.\nNakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.\nNakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.\nWhenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger. score: Subscores\n300 points will be awarded for passing the test set satisfying N <= 100.", "constraint": "1 <= N <= 10^5\n2 <= C <= 10^{14}\n1 <= x_1 < x_2 < ... < x_N < C\n1 <= v_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN C\nx_1 v_1\nx_2 v_2\n:\nx_N v_N", "output": "If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 20\n2 80\n9 120\n16 1 output: 191\n\nThere are three sushi on the counter with a circumference of 20 meters. If he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks seven more meters clockwise, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 9 kilocalories, thus he can take in 191 kilocalories on balance, which is the largest possible value.", "input: 3 20\n2 80\n9 1\n16 120 output: 192\n\nThe second and third sushi have been swapped. Again, if he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks six more meters counterclockwise this time, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 8 kilocalories, thus he can take in 192 kilocalories on balance, which is the largest possible value.", "input: 1 100000000000000\n50000000000000 1 output: 0\n\nEven though the only sushi is so far that it does not fit into a 32-bit integer, its nutritive value is low, thus he should immediately leave without doing anything.", "input: 15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000 output: 6500000000\n\nAll these sample inputs above are included in the test set for the partial score."], "Pid": "p03372", "ProblemText": "Task Description: Problem Statement\"Teishi-zushi\", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.\nNakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.\nNakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.\nWhenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger. score: Subscores\n300 points will be awarded for passing the test set satisfying N <= 100.\nTask Constraint: 1 <= N <= 10^5\n2 <= C <= 10^{14}\n1 <= x_1 < x_2 < ... < x_N < C\n1 <= v_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN C\nx_1 v_1\nx_2 v_2\n:\nx_N v_N\nTask Output: If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.\nTask Samples: input: 3 20\n2 80\n9 120\n16 1 output: 191\n\nThere are three sushi on the counter with a circumference of 20 meters. If he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks seven more meters clockwise, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 9 kilocalories, thus he can take in 191 kilocalories on balance, which is the largest possible value.\ninput: 3 20\n2 80\n9 1\n16 120 output: 192\n\nThe second and third sushi have been swapped. Again, if he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks six more meters counterclockwise this time, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 8 kilocalories, thus he can take in 192 kilocalories on balance, which is the largest possible value.\ninput: 1 100000000000000\n50000000000000 1 output: 0\n\nEven though the only sushi is so far that it does not fit into a 32-bit integer, its nutritive value is low, thus he should immediately leave without doing anything.\ninput: 15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000 output: 6500000000\n\nAll these sample inputs above are included in the test set for the partial score.\n\n" }, { "title": "", "content": "Problem Statement\"Pizza At\", a fast food chain, offers three kinds of pizza: \"A-pizza\", \"B-pizza\" and \"AB-pizza\". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.\nNakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.", "constraint": "1 <= A, B, C <= 5000\n1 <= X, Y <= 10^5\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C X Y", "output": "Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1500 2000 1600 3 2 output: 7900\n\nIt is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.", "input: 1500 2000 1900 3 2 output: 8500\n\nIt is optimal to directly buy three A-pizzas and two B-pizzas.", "input: 1500 2000 500 90000 100000 output: 100000000\n\nIt is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine."], "Pid": "p03373", "ProblemText": "Task Description: Problem Statement\"Pizza At\", a fast food chain, offers three kinds of pizza: \"A-pizza\", \"B-pizza\" and \"AB-pizza\". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.\nNakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.\nTask Constraint: 1 <= A, B, C <= 5000\n1 <= X, Y <= 10^5\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C X Y\nTask Output: Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.\nTask Samples: input: 1500 2000 1600 3 2 output: 7900\n\nIt is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.\ninput: 1500 2000 1900 3 2 output: 8500\n\nIt is optimal to directly buy three A-pizzas and two B-pizzas.\ninput: 1500 2000 500 90000 100000 output: 100000000\n\nIt is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine.\n\n" }, { "title": "", "content": "Problem Statement\"Teishi-zushi\", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.\nNakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.\nNakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.\nWhenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger. score: Subscores\n300 points will be awarded for passing the test set satisfying N <= 100.", "constraint": "1 <= N <= 10^5\n2 <= C <= 10^{14}\n1 <= x_1 < x_2 < ... < x_N < C\n1 <= v_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN C\nx_1 v_1\nx_2 v_2\n:\nx_N v_N", "output": "If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 20\n2 80\n9 120\n16 1 output: 191\n\nThere are three sushi on the counter with a circumference of 20 meters. If he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks seven more meters clockwise, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 9 kilocalories, thus he can take in 191 kilocalories on balance, which is the largest possible value.", "input: 3 20\n2 80\n9 1\n16 120 output: 192\n\nThe second and third sushi have been swapped. Again, if he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks six more meters counterclockwise this time, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 8 kilocalories, thus he can take in 192 kilocalories on balance, which is the largest possible value.", "input: 1 100000000000000\n50000000000000 1 output: 0\n\nEven though the only sushi is so far that it does not fit into a 32-bit integer, its nutritive value is low, thus he should immediately leave without doing anything.", "input: 15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000 output: 6500000000\n\nAll these sample inputs above are included in the test set for the partial score."], "Pid": "p03374", "ProblemText": "Task Description: Problem Statement\"Teishi-zushi\", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.\nNakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.\nNakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.\nWhenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger. score: Subscores\n300 points will be awarded for passing the test set satisfying N <= 100.\nTask Constraint: 1 <= N <= 10^5\n2 <= C <= 10^{14}\n1 <= x_1 < x_2 < ... < x_N < C\n1 <= v_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN C\nx_1 v_1\nx_2 v_2\n:\nx_N v_N\nTask Output: If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.\nTask Samples: input: 3 20\n2 80\n9 120\n16 1 output: 191\n\nThere are three sushi on the counter with a circumference of 20 meters. If he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks seven more meters clockwise, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 9 kilocalories, thus he can take in 191 kilocalories on balance, which is the largest possible value.\ninput: 3 20\n2 80\n9 1\n16 120 output: 192\n\nThe second and third sushi have been swapped. Again, if he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks six more meters counterclockwise this time, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 8 kilocalories, thus he can take in 192 kilocalories on balance, which is the largest possible value.\ninput: 1 100000000000000\n50000000000000 1 output: 0\n\nEven though the only sushi is so far that it does not fit into a 32-bit integer, its nutritive value is low, thus he should immediately leave without doing anything.\ninput: 15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000 output: 6500000000\n\nAll these sample inputs above are included in the test set for the partial score.\n\n" }, { "title": "", "content": "Problem Statement In \"Takahashi-ya\", a ramen restaurant, basically they have one menu: \"ramen\", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.\nAkaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:\n\nDo not order multiple bowls of ramen with the exactly same set of toppings.\nEach of the N kinds of toppings is on two or more bowls of ramen ordered.\n\nYou are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine. score: Subscores\n600 points will be awarded for passing the test set satisfying N <= 50.", "constraint": "2 <= N <= 3000\n10^8 <= M <= 10^9 + 9\nN is an integer.\nM is a prime number.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1000000007 output: 2\n\nLet the two kinds of toppings be A and B. Four types of ramen can be ordered: \"no toppings\", \"with A\", \"with B\" and \"with A, B\". There are two sets of ramen that satisfy the conditions:\n\nThe following three ramen: \"with A\", \"with B\", \"with A, B\".\nFour ramen, one for each type.", "input: 3 1000000009 output: 118\n\nLet the three kinds of toppings be A, B and C. In addition to the four types of ramen above, four more types of ramen can be ordered, where C is added to the above four. There are 118 sets of ramen that satisfy the conditions, and here are some of them:\n\nThe following three ramen: \"with A, B\", \"with A, C\", \"with B, C\".\nThe following five ramen: \"no toppings\", \"with A\", \"with A, B\", \"with B, C\", \"with A, B, C\".\nEight ramen, one for each type.\n\nNote that the set of the following three does not satisfy the condition: \"'with A', 'with B', 'with A, B'\", because C is not on any of them.", "input: 50 111111113 output: 1456748\n\nRemember to print the number of the sets modulo M. Note that these three sample inputs above are included in the test set for the partial score.", "input: 3000 123456791 output: 16369789\n\nThis sample input is not included in the test set for the partial score."], "Pid": "p03375", "ProblemText": "Task Description: Problem Statement In \"Takahashi-ya\", a ramen restaurant, basically they have one menu: \"ramen\", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.\nAkaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:\n\nDo not order multiple bowls of ramen with the exactly same set of toppings.\nEach of the N kinds of toppings is on two or more bowls of ramen ordered.\n\nYou are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine. score: Subscores\n600 points will be awarded for passing the test set satisfying N <= 50.\nTask Constraint: 2 <= N <= 3000\n10^8 <= M <= 10^9 + 9\nN is an integer.\nM is a prime number.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.\nTask Samples: input: 2 1000000007 output: 2\n\nLet the two kinds of toppings be A and B. Four types of ramen can be ordered: \"no toppings\", \"with A\", \"with B\" and \"with A, B\". There are two sets of ramen that satisfy the conditions:\n\nThe following three ramen: \"with A\", \"with B\", \"with A, B\".\nFour ramen, one for each type.\ninput: 3 1000000009 output: 118\n\nLet the three kinds of toppings be A, B and C. In addition to the four types of ramen above, four more types of ramen can be ordered, where C is added to the above four. There are 118 sets of ramen that satisfy the conditions, and here are some of them:\n\nThe following three ramen: \"with A, B\", \"with A, C\", \"with B, C\".\nThe following five ramen: \"no toppings\", \"with A\", \"with A, B\", \"with B, C\", \"with A, B, C\".\nEight ramen, one for each type.\n\nNote that the set of the following three does not satisfy the condition: \"'with A', 'with B', 'with A, B'\", because C is not on any of them.\ninput: 50 111111113 output: 1456748\n\nRemember to print the number of the sets modulo M. Note that these three sample inputs above are included in the test set for the partial score.\ninput: 3000 123456791 output: 16369789\n\nThis sample input is not included in the test set for the partial score.\n\n" }, { "title": "", "content": "Problem Statement Akaki, a patissier, can make N kinds of doughnut using only a certain powder called \"Okashi no Moto\" (literally \"material of pastry\", simply called Moto below) as ingredient. These doughnuts are called Doughnut 1, Doughnut 2, . . . , Doughnut N. In order to make one Doughnut i (1 <= i <= N), she needs to consume m_i grams of Moto. She cannot make a non-integer number of doughnuts, such as 0.5 doughnuts.\nThe recipes of these doughnuts are developed by repeated modifications from the recipe of Doughnut 1. Specifically, the recipe of Doughnut i (2 <= i <= N) is a direct modification of the recipe of Doughnut p_i (1 <= p_i < i).\nNow, she has X grams of Moto. She decides to make as many doughnuts as possible for a party tonight. However, since the tastes of the guests differ, she will obey the following condition:\n\nLet c_i be the number of Doughnut i (1 <= i <= N) that she makes. For each integer i such that 2 <= i <= N, c_{p_i} <= c_i <= c_{p_i} + D must hold. Here, D is a predetermined value.\n\nAt most how many doughnuts can be made here? She does not necessarily need to consume all of her Moto.", "constraint": "2 <= N <= 50\n1 <= X <= 10^9\n0 <= D <= 10^9\n1 <= m_i <= 10^9 (1 <= i <= N)\n1 <= p_i < i (2 <= i <= N)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN X D\nm_1\nm_2 p_2\n:\nm_N p_N", "output": "Print the maximum number of doughnuts that can be made under the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 100 1\n15\n10 1\n20 1 output: 7\n\nShe has 100 grams of Moto, can make three kinds of doughnuts, and the conditions that must hold are c_1 <= c_2 <= c_1 + 1 and c_1 <= c_3 <= c_1 + 1. It is optimal to make two Doughnuts 1, three Doughnuts 2 and two Doughnuts 3.", "input: 3 100 10\n15\n10 1\n20 1 output: 10\n\nThe amount of Moto and the recipes of the doughnuts are not changed from Sample Input 1, but the last conditions are relaxed. In this case, it is optimal to make just ten Doughnuts 2. As seen here, she does not necessarily need to make all kinds of doughnuts.", "input: 5 1000000000 1000000\n123\n159 1\n111 1\n135 3\n147 3 output: 7496296"], "Pid": "p03376", "ProblemText": "Task Description: Problem Statement Akaki, a patissier, can make N kinds of doughnut using only a certain powder called \"Okashi no Moto\" (literally \"material of pastry\", simply called Moto below) as ingredient. These doughnuts are called Doughnut 1, Doughnut 2, . . . , Doughnut N. In order to make one Doughnut i (1 <= i <= N), she needs to consume m_i grams of Moto. She cannot make a non-integer number of doughnuts, such as 0.5 doughnuts.\nThe recipes of these doughnuts are developed by repeated modifications from the recipe of Doughnut 1. Specifically, the recipe of Doughnut i (2 <= i <= N) is a direct modification of the recipe of Doughnut p_i (1 <= p_i < i).\nNow, she has X grams of Moto. She decides to make as many doughnuts as possible for a party tonight. However, since the tastes of the guests differ, she will obey the following condition:\n\nLet c_i be the number of Doughnut i (1 <= i <= N) that she makes. For each integer i such that 2 <= i <= N, c_{p_i} <= c_i <= c_{p_i} + D must hold. Here, D is a predetermined value.\n\nAt most how many doughnuts can be made here? She does not necessarily need to consume all of her Moto.\nTask Constraint: 2 <= N <= 50\n1 <= X <= 10^9\n0 <= D <= 10^9\n1 <= m_i <= 10^9 (1 <= i <= N)\n1 <= p_i < i (2 <= i <= N)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN X D\nm_1\nm_2 p_2\n:\nm_N p_N\nTask Output: Print the maximum number of doughnuts that can be made under the condition.\nTask Samples: input: 3 100 1\n15\n10 1\n20 1 output: 7\n\nShe has 100 grams of Moto, can make three kinds of doughnuts, and the conditions that must hold are c_1 <= c_2 <= c_1 + 1 and c_1 <= c_3 <= c_1 + 1. It is optimal to make two Doughnuts 1, three Doughnuts 2 and two Doughnuts 3.\ninput: 3 100 10\n15\n10 1\n20 1 output: 10\n\nThe amount of Moto and the recipes of the doughnuts are not changed from Sample Input 1, but the last conditions are relaxed. In this case, it is optimal to make just ten Doughnuts 2. As seen here, she does not necessarily need to make all kinds of doughnuts.\ninput: 5 1000000000 1000000\n123\n159 1\n111 1\n135 3\n147 3 output: 7496296\n\n" }, { "title": "", "content": "Problem Statement There are a total of A + B cats and dogs.\nAmong them, A are known to be cats, but the remaining B are not known to be either cats or dogs.\nDetermine if it is possible that there are exactly X cats among these A + B animals.", "constraint": "1 <= A <= 100\n1 <= B <= 100\n1 <= X <= 200\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B X", "output": "If it is possible that there are exactly X cats, print YES; if it is impossible, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 4 output: YES\n\nIf there are one cat and four dogs among the B = 5 animals, there are X = 4 cats in total.", "input: 2 2 6 output: NO\n\nEven if all of the B = 2 animals are cats, there are less than X = 6 cats in total.", "input: 5 3 2 output: NO\n\nEven if all of the B = 3 animals are dogs, there are more than X = 2 cats in total."], "Pid": "p03377", "ProblemText": "Task Description: Problem Statement There are a total of A + B cats and dogs.\nAmong them, A are known to be cats, but the remaining B are not known to be either cats or dogs.\nDetermine if it is possible that there are exactly X cats among these A + B animals.\nTask Constraint: 1 <= A <= 100\n1 <= B <= 100\n1 <= X <= 200\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B X\nTask Output: If it is possible that there are exactly X cats, print YES; if it is impossible, print NO.\nTask Samples: input: 3 5 4 output: YES\n\nIf there are one cat and four dogs among the B = 5 animals, there are X = 4 cats in total.\ninput: 2 2 6 output: NO\n\nEven if all of the B = 2 animals are cats, there are less than X = 6 cats in total.\ninput: 5 3 2 output: NO\n\nEven if all of the B = 3 animals are dogs, there are more than X = 2 cats in total.\n\n" }, { "title": "", "content": "Problem Statement There are N + 1 squares arranged in a row, numbered 0,1, . . . , N from left to right.\nInitially, you are in Square X.\nYou can freely travel between adjacent squares. Your goal is to reach Square 0 or Square N.\nHowever, for each i = 1,2, . . . , M, there is a toll gate in Square A_i, and traveling to Square A_i incurs a cost of 1.\nIt is guaranteed that there is no toll gate in Square 0, Square X and Square N.\nFind the minimum cost incurred before reaching the goal.", "constraint": "1 <= N <= 100\n1 <= M <= 100\n1 <= X <= N - 1\n1 <= A_1 < A_2 < ... < A_M <= N\nA_i \\neq X\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN M X\nA_1 A_2 . . . A_M", "output": "Print the minimum cost incurred before reaching the goal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 3\n1 2 4 output: 1\n\nThe optimal solution is as follows:\n\nFirst, travel from Square 3 to Square 4. Here, there is a toll gate in Square 4, so the cost of 1 is incurred.\nThen, travel from Square 4 to Square 5. This time, no cost is incurred.\nNow, we are in Square 5 and we have reached the goal.\n\nIn this case, the total cost incurred is 1.", "input: 7 3 2\n4 5 6 output: 0\n\nWe may be able to reach the goal at no cost.", "input: 10 7 5\n1 2 3 4 6 8 9 output: 3"], "Pid": "p03378", "ProblemText": "Task Description: Problem Statement There are N + 1 squares arranged in a row, numbered 0,1, . . . , N from left to right.\nInitially, you are in Square X.\nYou can freely travel between adjacent squares. Your goal is to reach Square 0 or Square N.\nHowever, for each i = 1,2, . . . , M, there is a toll gate in Square A_i, and traveling to Square A_i incurs a cost of 1.\nIt is guaranteed that there is no toll gate in Square 0, Square X and Square N.\nFind the minimum cost incurred before reaching the goal.\nTask Constraint: 1 <= N <= 100\n1 <= M <= 100\n1 <= X <= N - 1\n1 <= A_1 < A_2 < ... < A_M <= N\nA_i \\neq X\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M X\nA_1 A_2 . . . A_M\nTask Output: Print the minimum cost incurred before reaching the goal.\nTask Samples: input: 5 3 3\n1 2 4 output: 1\n\nThe optimal solution is as follows:\n\nFirst, travel from Square 3 to Square 4. Here, there is a toll gate in Square 4, so the cost of 1 is incurred.\nThen, travel from Square 4 to Square 5. This time, no cost is incurred.\nNow, we are in Square 5 and we have reached the goal.\n\nIn this case, the total cost incurred is 1.\ninput: 7 3 2\n4 5 6 output: 0\n\nWe may be able to reach the goal at no cost.\ninput: 10 7 5\n1 2 3 4 6 8 9 output: 3\n\n" }, { "title": "", "content": "Problem Statement When l is an odd number, the median of l numbers a_1, a_2, . . . , a_l is the (\\frac{l+1}{2})-th largest value among a_1, a_2, . . . , a_l.\nYou are given N numbers X_1, X_2, . . . , X_N, where N is an even number.\nFor each i = 1,2, . . . , N, let the median of X_1, X_2, . . . , X_N excluding X_i, that is, the median of X_1, X_2, . . . , X_{i-1}, X_{i+1}, . . . , X_N be B_i.\nFind B_i for each i = 1,2, . . . , N.", "constraint": "2 <= N <= 200000\nN is even.\n1 <= X_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N", "output": "Print N lines.\nThe i-th line should contain B_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 4 4 3 output: 4\n3\n3\n4\nSince the median of X_2, X_3, X_4 is 4, B_1 = 4.\nSince the median of X_1, X_3, X_4 is 3, B_2 = 3.\nSince the median of X_1, X_2, X_4 is 3, B_3 = 3.\nSince the median of X_1, X_2, X_3 is 4, B_4 = 4.", "input: 2\n1 2 output: 2\n1", "input: 6\n5 5 4 4 3 3 output: 4\n4\n4\n4\n4\n4"], "Pid": "p03379", "ProblemText": "Task Description: Problem Statement When l is an odd number, the median of l numbers a_1, a_2, . . . , a_l is the (\\frac{l+1}{2})-th largest value among a_1, a_2, . . . , a_l.\nYou are given N numbers X_1, X_2, . . . , X_N, where N is an even number.\nFor each i = 1,2, . . . , N, let the median of X_1, X_2, . . . , X_N excluding X_i, that is, the median of X_1, X_2, . . . , X_{i-1}, X_{i+1}, . . . , X_N be B_i.\nFind B_i for each i = 1,2, . . . , N.\nTask Constraint: 2 <= N <= 200000\nN is even.\n1 <= X_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N\nTask Output: Print N lines.\nThe i-th line should contain B_i.\nTask Samples: input: 4\n2 4 4 3 output: 4\n3\n3\n4\nSince the median of X_2, X_3, X_4 is 4, B_1 = 4.\nSince the median of X_1, X_3, X_4 is 3, B_2 = 3.\nSince the median of X_1, X_2, X_4 is 3, B_3 = 3.\nSince the median of X_1, X_2, X_3 is 4, B_4 = 4.\ninput: 2\n1 2 output: 2\n1\ninput: 6\n5 5 4 4 3 3 output: 4\n4\n4\n4\n4\n4\n\n" }, { "title": "", "content": "Problem Statement Let {\\rm comb}(n, r) be the number of ways to choose r objects from among n objects, disregarding order.\nFrom n non-negative integers a_1, a_2, . . . , a_n, select two numbers a_i > a_j so that {\\rm comb}(a_i, a_j) is maximized.\nIf there are multiple pairs that maximize the value, any of them is accepted.", "constraint": "2 <= n <= 10^5\n0 <= a_i <= 10^9\na_1,a_2,...,a_n are pairwise distinct.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n", "output": "Print a_i and a_j that you selected, with a space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n6 9 4 2 11 output: 11 6\n\n\\rm{comb}(a_i,a_j) for each possible selection is as follows:\n\n\\rm{comb}(4,2)=6 \n\\rm{comb}(6,2)=15 \n\\rm{comb}(6,4)=15 \n\\rm{comb}(9,2)=36 \n\\rm{comb}(9,4)=126 \n\\rm{comb}(9,6)=84 \n\\rm{comb}(11,2)=55 \n\\rm{comb}(11,4)=330 \n\\rm{comb}(11,6)=462 \n\\rm{comb}(11,9)=55\n\nThus, we should print 11 and 6.", "input: 2\n100 0 output: 100 0"], "Pid": "p03380", "ProblemText": "Task Description: Problem Statement Let {\\rm comb}(n, r) be the number of ways to choose r objects from among n objects, disregarding order.\nFrom n non-negative integers a_1, a_2, . . . , a_n, select two numbers a_i > a_j so that {\\rm comb}(a_i, a_j) is maximized.\nIf there are multiple pairs that maximize the value, any of them is accepted.\nTask Constraint: 2 <= n <= 10^5\n0 <= a_i <= 10^9\na_1,a_2,...,a_n are pairwise distinct.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n\nTask Output: Print a_i and a_j that you selected, with a space in between.\nTask Samples: input: 5\n6 9 4 2 11 output: 11 6\n\n\\rm{comb}(a_i,a_j) for each possible selection is as follows:\n\n\\rm{comb}(4,2)=6 \n\\rm{comb}(6,2)=15 \n\\rm{comb}(6,4)=15 \n\\rm{comb}(9,2)=36 \n\\rm{comb}(9,4)=126 \n\\rm{comb}(9,6)=84 \n\\rm{comb}(11,2)=55 \n\\rm{comb}(11,4)=330 \n\\rm{comb}(11,6)=462 \n\\rm{comb}(11,9)=55\n\nThus, we should print 11 and 6.\ninput: 2\n100 0 output: 100 0\n\n" }, { "title": "", "content": "Problem Statement When l is an odd number, the median of l numbers a_1, a_2, . . . , a_l is the (\\frac{l+1}{2})-th largest value among a_1, a_2, . . . , a_l.\nYou are given N numbers X_1, X_2, . . . , X_N, where N is an even number.\nFor each i = 1,2, . . . , N, let the median of X_1, X_2, . . . , X_N excluding X_i, that is, the median of X_1, X_2, . . . , X_{i-1}, X_{i+1}, . . . , X_N be B_i.\nFind B_i for each i = 1,2, . . . , N.", "constraint": "2 <= N <= 200000\nN is even.\n1 <= X_i <= 10^9\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N", "output": "Print N lines.\nThe i-th line should contain B_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 4 4 3 output: 4\n3\n3\n4\nSince the median of X_2, X_3, X_4 is 4, B_1 = 4.\nSince the median of X_1, X_3, X_4 is 3, B_2 = 3.\nSince the median of X_1, X_2, X_4 is 3, B_3 = 3.\nSince the median of X_1, X_2, X_3 is 4, B_4 = 4.", "input: 2\n1 2 output: 2\n1", "input: 6\n5 5 4 4 3 3 output: 4\n4\n4\n4\n4\n4"], "Pid": "p03381", "ProblemText": "Task Description: Problem Statement When l is an odd number, the median of l numbers a_1, a_2, . . . , a_l is the (\\frac{l+1}{2})-th largest value among a_1, a_2, . . . , a_l.\nYou are given N numbers X_1, X_2, . . . , X_N, where N is an even number.\nFor each i = 1,2, . . . , N, let the median of X_1, X_2, . . . , X_N excluding X_i, that is, the median of X_1, X_2, . . . , X_{i-1}, X_{i+1}, . . . , X_N be B_i.\nFind B_i for each i = 1,2, . . . , N.\nTask Constraint: 2 <= N <= 200000\nN is even.\n1 <= X_i <= 10^9\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N\nTask Output: Print N lines.\nThe i-th line should contain B_i.\nTask Samples: input: 4\n2 4 4 3 output: 4\n3\n3\n4\nSince the median of X_2, X_3, X_4 is 4, B_1 = 4.\nSince the median of X_1, X_3, X_4 is 3, B_2 = 3.\nSince the median of X_1, X_2, X_4 is 3, B_3 = 3.\nSince the median of X_1, X_2, X_3 is 4, B_4 = 4.\ninput: 2\n1 2 output: 2\n1\ninput: 6\n5 5 4 4 3 3 output: 4\n4\n4\n4\n4\n4\n\n" }, { "title": "", "content": "Problem Statement Let {\\rm comb}(n, r) be the number of ways to choose r objects from among n objects, disregarding order.\nFrom n non-negative integers a_1, a_2, . . . , a_n, select two numbers a_i > a_j so that {\\rm comb}(a_i, a_j) is maximized.\nIf there are multiple pairs that maximize the value, any of them is accepted.", "constraint": "2 <= n <= 10^5\n0 <= a_i <= 10^9\na_1,a_2,...,a_n are pairwise distinct.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n", "output": "Print a_i and a_j that you selected, with a space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n6 9 4 2 11 output: 11 6\n\n\\rm{comb}(a_i,a_j) for each possible selection is as follows:\n\n\\rm{comb}(4,2)=6 \n\\rm{comb}(6,2)=15 \n\\rm{comb}(6,4)=15 \n\\rm{comb}(9,2)=36 \n\\rm{comb}(9,4)=126 \n\\rm{comb}(9,6)=84 \n\\rm{comb}(11,2)=55 \n\\rm{comb}(11,4)=330 \n\\rm{comb}(11,6)=462 \n\\rm{comb}(11,9)=55\n\nThus, we should print 11 and 6.", "input: 2\n100 0 output: 100 0"], "Pid": "p03382", "ProblemText": "Task Description: Problem Statement Let {\\rm comb}(n, r) be the number of ways to choose r objects from among n objects, disregarding order.\nFrom n non-negative integers a_1, a_2, . . . , a_n, select two numbers a_i > a_j so that {\\rm comb}(a_i, a_j) is maximized.\nIf there are multiple pairs that maximize the value, any of them is accepted.\nTask Constraint: 2 <= n <= 10^5\n0 <= a_i <= 10^9\na_1,a_2,...,a_n are pairwise distinct.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n\nTask Output: Print a_i and a_j that you selected, with a space in between.\nTask Samples: input: 5\n6 9 4 2 11 output: 11 6\n\n\\rm{comb}(a_i,a_j) for each possible selection is as follows:\n\n\\rm{comb}(4,2)=6 \n\\rm{comb}(6,2)=15 \n\\rm{comb}(6,4)=15 \n\\rm{comb}(9,2)=36 \n\\rm{comb}(9,4)=126 \n\\rm{comb}(9,6)=84 \n\\rm{comb}(11,2)=55 \n\\rm{comb}(11,4)=330 \n\\rm{comb}(11,6)=462 \n\\rm{comb}(11,9)=55\n\nThus, we should print 11 and 6.\ninput: 2\n100 0 output: 100 0\n\n" }, { "title": "", "content": "Problem Statement There is an H * W grid (H vertical, W horizontal), where each square contains a lowercase English letter.\nSpecifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.\nSnuke can apply the following operation to this grid any number of times:\n\nChoose two different rows and swap them. Or, choose two different columns and swap them.\n\nSnuke wants this grid to be symmetric.\nThat is, for any 1 <= i <= H and 1 <= j <= W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.\nDetermine if Snuke can achieve this objective.", "constraint": "1 <= H <= 12\n1 <= W <= 12\n|S_i| = W\nS_i consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nH W\nS_1\nS_2\n:\nS_H", "output": "If Snuke can make the grid symmetric, print YES; if he cannot, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\narc\nrac output: YES\n\nIf the second and third columns from the left are swapped, the grid becomes symmetric, as shown in the image below:", "input: 3 7\natcoder\nregular\ncontest output: NO", "input: 12 12\nbimonigaloaf\nfaurwlkbleht\ndexwimqxzxbb\nlxdgyoifcxid\nydxiliocfdgx\nnfoabgilamoi\nibxbdqmzxxwe\npqirylfrcrnf\nwtehfkllbura\nyfrnpflcrirq\nwvcclwgiubrk\nlkbrwgwuiccv output: YES"], "Pid": "p03383", "ProblemText": "Task Description: Problem Statement There is an H * W grid (H vertical, W horizontal), where each square contains a lowercase English letter.\nSpecifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.\nSnuke can apply the following operation to this grid any number of times:\n\nChoose two different rows and swap them. Or, choose two different columns and swap them.\n\nSnuke wants this grid to be symmetric.\nThat is, for any 1 <= i <= H and 1 <= j <= W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.\nDetermine if Snuke can achieve this objective.\nTask Constraint: 1 <= H <= 12\n1 <= W <= 12\n|S_i| = W\nS_i consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nH W\nS_1\nS_2\n:\nS_H\nTask Output: If Snuke can make the grid symmetric, print YES; if he cannot, print NO.\nTask Samples: input: 2 3\narc\nrac output: YES\n\nIf the second and third columns from the left are swapped, the grid becomes symmetric, as shown in the image below:\ninput: 3 7\natcoder\nregular\ncontest output: NO\ninput: 12 12\nbimonigaloaf\nfaurwlkbleht\ndexwimqxzxbb\nlxdgyoifcxid\nydxiliocfdgx\nnfoabgilamoi\nibxbdqmzxxwe\npqirylfrcrnf\nwtehfkllbura\nyfrnpflcrirq\nwvcclwgiubrk\nlkbrwgwuiccv output: YES\n\n" }, { "title": "", "content": "Problem Statement Takahashi has an ability to generate a tree using a permutation (p_1, p_2, . . . , p_n) of (1,2, . . . , n), in the following process:\nFirst, prepare Vertex 1, Vertex 2, . . . , Vertex N.\nFor each i=1,2, . . . , n, perform the following operation:\n\nIf p_i = 1, do nothing.\nIf p_i \\neq 1, let j' be the largest j such that p_j < p_i. Span an edge between Vertex i and Vertex j'.\n\nTakahashi is trying to make his favorite tree with this ability.\nHis favorite tree has n vertices from Vertex 1 through Vertex n, and its i-th edge connects Vertex v_i and w_i.\nDetermine if he can make a tree isomorphic to his favorite tree by using a proper permutation.\nIf he can do so, find the lexicographically smallest such permutation. note: Notes For the definition of isomorphism of trees, see wikipedia. Intuitively, two trees are isomorphic when they are the \"same\" if we disregard the indices of their vertices.", "constraint": "2 <= n <= 10^5\n1 <= v_i, w_i <= n\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nn\nv_1 w_1\nv_2 w_2\n:\nv_{n-1} w_{n-1}", "output": "If there is no permutation that can generate a tree isomorphic to Takahashi's favorite tree, print -1.\nIf it exists, print the lexicographically smallest such permutation, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 2\n1 3\n1 4\n1 5\n5 6 output: 1 2 4 5 3 6\n\nIf the permutation (1,2,4,5,3,6) is used to generate a tree, it looks as follows:\n\nThis is isomorphic to the given graph.", "input: 6\n1 2\n2 3\n3 4\n1 5\n5 6 output: 1 2 3 4 5 6", "input: 15\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7\n4 8\n4 9\n5 10\n5 11\n6 12\n6 13\n7 14\n7 15 output: -1"], "Pid": "p03384", "ProblemText": "Task Description: Problem Statement Takahashi has an ability to generate a tree using a permutation (p_1, p_2, . . . , p_n) of (1,2, . . . , n), in the following process:\nFirst, prepare Vertex 1, Vertex 2, . . . , Vertex N.\nFor each i=1,2, . . . , n, perform the following operation:\n\nIf p_i = 1, do nothing.\nIf p_i \\neq 1, let j' be the largest j such that p_j < p_i. Span an edge between Vertex i and Vertex j'.\n\nTakahashi is trying to make his favorite tree with this ability.\nHis favorite tree has n vertices from Vertex 1 through Vertex n, and its i-th edge connects Vertex v_i and w_i.\nDetermine if he can make a tree isomorphic to his favorite tree by using a proper permutation.\nIf he can do so, find the lexicographically smallest such permutation. note: Notes For the definition of isomorphism of trees, see wikipedia. Intuitively, two trees are isomorphic when they are the \"same\" if we disregard the indices of their vertices.\nTask Constraint: 2 <= n <= 10^5\n1 <= v_i, w_i <= n\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nn\nv_1 w_1\nv_2 w_2\n:\nv_{n-1} w_{n-1}\nTask Output: If there is no permutation that can generate a tree isomorphic to Takahashi's favorite tree, print -1.\nIf it exists, print the lexicographically smallest such permutation, with spaces in between.\nTask Samples: input: 6\n1 2\n1 3\n1 4\n1 5\n5 6 output: 1 2 4 5 3 6\n\nIf the permutation (1,2,4,5,3,6) is used to generate a tree, it looks as follows:\n\nThis is isomorphic to the given graph.\ninput: 6\n1 2\n2 3\n3 4\n1 5\n5 6 output: 1 2 3 4 5 6\ninput: 15\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7\n4 8\n4 9\n5 10\n5 11\n6 12\n6 13\n7 14\n7 15 output: -1\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length 3 consisting of a, b and c. Determine if S can be obtained by permuting abc.", "constraint": "|S|=3\nS consists of a, b and c.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If S can be obtained by permuting abc, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: bac output: Yes\n\nSwapping the first and second characters in bac results in abc.", "input: bab output: No", "input: abc output: Yes", "input: aaa output: No"], "Pid": "p03385", "ProblemText": "Task Description: Problem Statement You are given a string S of length 3 consisting of a, b and c. Determine if S can be obtained by permuting abc.\nTask Constraint: |S|=3\nS consists of a, b and c.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If S can be obtained by permuting abc, print Yes; otherwise, print No.\nTask Samples: input: bac output: Yes\n\nSwapping the first and second characters in bac results in abc.\ninput: bab output: No\ninput: abc output: Yes\ninput: aaa output: No\n\n" }, { "title": "", "content": "Problem Statement Print all the integers that satisfies the following in ascending order:\n\nAmong the integers between A and B (inclusive), it is either within the K smallest integers or within the K largest integers.", "constraint": "1 <= A <= B <= 10^9\n1 <= K <= 100\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B K", "output": "Print all the integers that satisfies the condition above in ascending order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 8 2 output: 3\n4\n7\n8\n3 is the first smallest integer among the integers between 3 and 8.\n4 is the second smallest integer among the integers between 3 and 8.\n7 is the second largest integer among the integers between 3 and 8.\n8 is the first largest integer among the integers between 3 and 8.", "input: 4 8 3 output: 4\n5\n6\n7\n8", "input: 2 9 100 output: 2\n3\n4\n5\n6\n7\n8\n9"], "Pid": "p03386", "ProblemText": "Task Description: Problem Statement Print all the integers that satisfies the following in ascending order:\n\nAmong the integers between A and B (inclusive), it is either within the K smallest integers or within the K largest integers.\nTask Constraint: 1 <= A <= B <= 10^9\n1 <= K <= 100\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B K\nTask Output: Print all the integers that satisfies the condition above in ascending order.\nTask Samples: input: 3 8 2 output: 3\n4\n7\n8\n3 is the first smallest integer among the integers between 3 and 8.\n4 is the second smallest integer among the integers between 3 and 8.\n7 is the second largest integer among the integers between 3 and 8.\n8 is the first largest integer among the integers between 3 and 8.\ninput: 4 8 3 output: 4\n5\n6\n7\n8\ninput: 2 9 100 output: 2\n3\n4\n5\n6\n7\n8\n9\n\n" }, { "title": "", "content": "Problem Statement You are given three integers A, B and C. Find the minimum number of operations required to make A, B and C all equal by repeatedly performing the following two kinds of operations in any order:\n\nChoose two among A, B and C, then increase both by 1.\nChoose one among A, B and C, then increase it by 2.\n\nIt can be proved that we can always make A, B and C all equal by repeatedly performing these operations.", "constraint": "0 <= A,B,C <= 50\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "Print the minimum number of operations required to make A, B and C all equal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5 4 output: 2\n\nWe can make A, B and C all equal by the following operations:\n\nIncrease A and C by 1. Now, A, B, C are 3,5,5, respectively.\nIncrease A by 2. Now, A, B, C are 5,5,5, respectively.", "input: 2 6 3 output: 5", "input: 31 41 5 output: 23"], "Pid": "p03387", "ProblemText": "Task Description: Problem Statement You are given three integers A, B and C. Find the minimum number of operations required to make A, B and C all equal by repeatedly performing the following two kinds of operations in any order:\n\nChoose two among A, B and C, then increase both by 1.\nChoose one among A, B and C, then increase it by 2.\n\nIt can be proved that we can always make A, B and C all equal by repeatedly performing these operations.\nTask Constraint: 0 <= A,B,C <= 50\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: Print the minimum number of operations required to make A, B and C all equal.\nTask Samples: input: 2 5 4 output: 2\n\nWe can make A, B and C all equal by the following operations:\n\nIncrease A and C by 1. Now, A, B, C are 3,5,5, respectively.\nIncrease A by 2. Now, A, B, C are 5,5,5, respectively.\ninput: 2 6 3 output: 5\ninput: 31 41 5 output: 23\n\n" }, { "title": "", "content": "Problem Statement10^{10^{10}} participants, including Takahashi, competed in two programming contests.\nIn each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.\nThe score of a participant is the product of his/her ranks in the two contests.\nProcess the following Q queries:\n\nIn the i-th query, you are given two positive integers A_i and B_i. Assuming that Takahashi was ranked A_i-th in the first contest and B_i-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's.", "constraint": "1 <= Q <= 100\n1<= A_i,B_i<= 10^9(1<= i<= Q)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nQ\nA_1 B_1\n:\nA_Q B_Q", "output": "For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n1 4\n10 5\n3 3\n4 11\n8 9\n22 40\n8 36\n314159265 358979323 output: 1\n12\n4\n11\n14\n57\n31\n671644785\n\nLet us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).\nIn the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 1."], "Pid": "p03388", "ProblemText": "Task Description: Problem Statement10^{10^{10}} participants, including Takahashi, competed in two programming contests.\nIn each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.\nThe score of a participant is the product of his/her ranks in the two contests.\nProcess the following Q queries:\n\nIn the i-th query, you are given two positive integers A_i and B_i. Assuming that Takahashi was ranked A_i-th in the first contest and B_i-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's.\nTask Constraint: 1 <= Q <= 100\n1<= A_i,B_i<= 10^9(1<= i<= Q)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nQ\nA_1 B_1\n:\nA_Q B_Q\nTask Output: For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.\nTask Samples: input: 8\n1 4\n10 5\n3 3\n4 11\n8 9\n22 40\n8 36\n314159265 358979323 output: 1\n12\n4\n11\n14\n57\n31\n671644785\n\nLet us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).\nIn the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 1.\n\n" }, { "title": "", "content": "Problem Statement You are given three integers A, B and C. Find the minimum number of operations required to make A, B and C all equal by repeatedly performing the following two kinds of operations in any order:\n\nChoose two among A, B and C, then increase both by 1.\nChoose one among A, B and C, then increase it by 2.\n\nIt can be proved that we can always make A, B and C all equal by repeatedly performing these operations.", "constraint": "0 <= A,B,C <= 50\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "Print the minimum number of operations required to make A, B and C all equal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 5 4 output: 2\n\nWe can make A, B and C all equal by the following operations:\n\nIncrease A and C by 1. Now, A, B, C are 3,5,5, respectively.\nIncrease A by 2. Now, A, B, C are 5,5,5, respectively.", "input: 2 6 3 output: 5", "input: 31 41 5 output: 23"], "Pid": "p03389", "ProblemText": "Task Description: Problem Statement You are given three integers A, B and C. Find the minimum number of operations required to make A, B and C all equal by repeatedly performing the following two kinds of operations in any order:\n\nChoose two among A, B and C, then increase both by 1.\nChoose one among A, B and C, then increase it by 2.\n\nIt can be proved that we can always make A, B and C all equal by repeatedly performing these operations.\nTask Constraint: 0 <= A,B,C <= 50\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: Print the minimum number of operations required to make A, B and C all equal.\nTask Samples: input: 2 5 4 output: 2\n\nWe can make A, B and C all equal by the following operations:\n\nIncrease A and C by 1. Now, A, B, C are 3,5,5, respectively.\nIncrease A by 2. Now, A, B, C are 5,5,5, respectively.\ninput: 2 6 3 output: 5\ninput: 31 41 5 output: 23\n\n" }, { "title": "", "content": "Problem Statement10^{10^{10}} participants, including Takahashi, competed in two programming contests.\nIn each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.\nThe score of a participant is the product of his/her ranks in the two contests.\nProcess the following Q queries:\n\nIn the i-th query, you are given two positive integers A_i and B_i. Assuming that Takahashi was ranked A_i-th in the first contest and B_i-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's.", "constraint": "1 <= Q <= 100\n1<= A_i,B_i<= 10^9(1<= i<= Q)\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nQ\nA_1 B_1\n:\nA_Q B_Q", "output": "For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n1 4\n10 5\n3 3\n4 11\n8 9\n22 40\n8 36\n314159265 358979323 output: 1\n12\n4\n11\n14\n57\n31\n671644785\n\nLet us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).\nIn the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 1."], "Pid": "p03390", "ProblemText": "Task Description: Problem Statement10^{10^{10}} participants, including Takahashi, competed in two programming contests.\nIn each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.\nThe score of a participant is the product of his/her ranks in the two contests.\nProcess the following Q queries:\n\nIn the i-th query, you are given two positive integers A_i and B_i. Assuming that Takahashi was ranked A_i-th in the first contest and B_i-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's.\nTask Constraint: 1 <= Q <= 100\n1<= A_i,B_i<= 10^9(1<= i<= Q)\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nQ\nA_1 B_1\n:\nA_Q B_Q\nTask Output: For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.\nTask Samples: input: 8\n1 4\n10 5\n3 3\n4 11\n8 9\n22 40\n8 36\n314159265 358979323 output: 1\n12\n4\n11\n14\n57\n31\n671644785\n\nLet us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).\nIn the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 1.\n\n" }, { "title": "", "content": "Problem Statement You are given sequences A and B consisting of non-negative integers.\nThe lengths of both A and B are N, and the sums of the elements in A and B are equal.\nThe i-th element in A is A_i, and the i-th element in B is B_i.\nTozan and Gezan repeats the following sequence of operations:\n\nIf A and B are equal sequences, terminate the process.\nOtherwise, first Tozan chooses a positive element in A and decrease it by 1.\nThen, Gezan chooses a positive element in B and decrease it by 1.\nThen, give one candy to Takahashi, their pet.\n\nTozan wants the number of candies given to Takahashi until the process is terminated to be as large as possible, while Gezan wants it to be as small as possible.\nFind the number of candies given to Takahashi when both of them perform the operations optimally.", "constraint": "1 <= N <= 2 * 10^5\n0 <= A_i,B_i <= 10^9(1<= i<= N)\nThe sums of the elements in A and B are equal.\nAll values in input are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_N B_N", "output": "Print the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2\n3 2 output: 2\n\nWhen both Tozan and Gezan perform the operations optimally, the process will proceed as follows:\n\nTozan decreases A_1 by 1.\nGezan decreases B_1 by 1.\nOne candy is given to Takahashi.\nTozan decreases A_2 by 1.\nGezan decreases B_1 by 1.\nOne candy is given to Takahashi.\nAs A and B are equal, the process is terminated.", "input: 3\n8 3\n0 1\n4 8 output: 9", "input: 1\n1 1 output: 0"], "Pid": "p03391", "ProblemText": "Task Description: Problem Statement You are given sequences A and B consisting of non-negative integers.\nThe lengths of both A and B are N, and the sums of the elements in A and B are equal.\nThe i-th element in A is A_i, and the i-th element in B is B_i.\nTozan and Gezan repeats the following sequence of operations:\n\nIf A and B are equal sequences, terminate the process.\nOtherwise, first Tozan chooses a positive element in A and decrease it by 1.\nThen, Gezan chooses a positive element in B and decrease it by 1.\nThen, give one candy to Takahashi, their pet.\n\nTozan wants the number of candies given to Takahashi until the process is terminated to be as large as possible, while Gezan wants it to be as small as possible.\nFind the number of candies given to Takahashi when both of them perform the operations optimally.\nTask Constraint: 1 <= N <= 2 * 10^5\n0 <= A_i,B_i <= 10^9(1<= i<= N)\nThe sums of the elements in A and B are equal.\nAll values in input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\n:\nA_N B_N\nTask Output: Print the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.\nTask Samples: input: 2\n1 2\n3 2 output: 2\n\nWhen both Tozan and Gezan perform the operations optimally, the process will proceed as follows:\n\nTozan decreases A_1 by 1.\nGezan decreases B_1 by 1.\nOne candy is given to Takahashi.\nTozan decreases A_2 by 1.\nGezan decreases B_1 by 1.\nOne candy is given to Takahashi.\nAs A and B are equal, the process is terminated.\ninput: 3\n8 3\n0 1\n4 8 output: 9\ninput: 1\n1 1 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of a, b and c. Find the number of strings that can be possibly obtained by repeatedly performing the following operation zero or more times, modulo 998244353:\n\nChoose an integer i such that 1<= i<= |S|-1 and the i-th and (i+1)-th characters in S are different. Replace each of the i-th and (i+1)-th characters in S with the character that differs from both of them (among a, b and c).", "constraint": "2 <= |S| <= 2 * 10^5\nS consists of a, b and c.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of strings that can be possibly obtained by repeatedly performing the operation, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abc output: 3\n\nabc, aaa and ccc can be obtained.", "input: abbac output: 65", "input: babacabac output: 6310", "input: ababacbcacbacacbcbbcbbacbaccacbacbacba output: 148010497"], "Pid": "p03392", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of a, b and c. Find the number of strings that can be possibly obtained by repeatedly performing the following operation zero or more times, modulo 998244353:\n\nChoose an integer i such that 1<= i<= |S|-1 and the i-th and (i+1)-th characters in S are different. Replace each of the i-th and (i+1)-th characters in S with the character that differs from both of them (among a, b and c).\nTask Constraint: 2 <= |S| <= 2 * 10^5\nS consists of a, b and c.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of strings that can be possibly obtained by repeatedly performing the operation, modulo 998244353.\nTask Samples: input: abc output: 3\n\nabc, aaa and ccc can be obtained.\ninput: abbac output: 65\ninput: babacabac output: 6310\ninput: ababacbcacbacacbcbbcbbacbaccacbacbacba output: 148010497\n\n" }, { "title": "", "content": "Problem Statement Gotou just received a dictionary. However, he doesn't recognize the language used in the dictionary. He did some analysis on the dictionary and realizes that the dictionary contains all possible diverse words in lexicographical order.\nA word is called diverse if and only if it is a nonempty string of English lowercase letters and all letters in the word are distinct. For example, atcoder, zscoder and agc are diverse words while gotou and connect aren't diverse words.\nGiven a diverse word S, determine the next word that appears after S in the dictionary, i. e. the lexicographically smallest diverse word that is lexicographically larger than S, or determine that it doesn't exist.\nLet X = x_{1}x_{2}. . . x_{n} and Y = y_{1}y_{2}. . . y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \\neq y_{j}.", "constraint": "1 <= |S| <= 26\nS is a diverse word.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the next word that appears after S in the dictionary, or -1 if it doesn't exist.", "content_img": false, "lang": "en", "error": false, "samples": ["input: atcoder output: atcoderb\n\natcoderb is the lexicographically smallest diverse word that is lexicographically larger than atcoder. Note that atcoderb is lexicographically smaller than b.", "input: abc output: abcd", "input: zyxwvutsrqponmlkjihgfedcba output: -1\n\nThis is the lexicographically largest diverse word, so the answer is -1.", "input: abcdefghijklmnopqrstuvwzyx output: abcdefghijklmnopqrstuvx"], "Pid": "p03393", "ProblemText": "Task Description: Problem Statement Gotou just received a dictionary. However, he doesn't recognize the language used in the dictionary. He did some analysis on the dictionary and realizes that the dictionary contains all possible diverse words in lexicographical order.\nA word is called diverse if and only if it is a nonempty string of English lowercase letters and all letters in the word are distinct. For example, atcoder, zscoder and agc are diverse words while gotou and connect aren't diverse words.\nGiven a diverse word S, determine the next word that appears after S in the dictionary, i. e. the lexicographically smallest diverse word that is lexicographically larger than S, or determine that it doesn't exist.\nLet X = x_{1}x_{2}. . . x_{n} and Y = y_{1}y_{2}. . . y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \\neq y_{j}.\nTask Constraint: 1 <= |S| <= 26\nS is a diverse word.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the next word that appears after S in the dictionary, or -1 if it doesn't exist.\nTask Samples: input: atcoder output: atcoderb\n\natcoderb is the lexicographically smallest diverse word that is lexicographically larger than atcoder. Note that atcoderb is lexicographically smaller than b.\ninput: abc output: abcd\ninput: zyxwvutsrqponmlkjihgfedcba output: -1\n\nThis is the lexicographically largest diverse word, so the answer is -1.\ninput: abcdefghijklmnopqrstuvwzyx output: abcdefghijklmnopqrstuvx\n\n" }, { "title": "", "content": "Problem Statement Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers. \nShe thinks that a set S = \\{a_{1}, a_{2}, . . . , a_{N}\\} of distinct positive integers is called special if for all 1 <= i <= N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.\nNagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.", "constraint": "3 <= N <= 20000", "input": "Input is given from Standard Input in the following format:\nN", "output": "Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :\n\nThe elements must be distinct positive integers not exceeding 30000.\nThe gcd of all elements of S is 1, i. e. there does not exist an integer d > 1 that divides all elements of S.\nS is a special set.\n\nIf there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 2 5 63\n\n\\{2,5,63\\} is special because gcd(2,5 + 63) = 2, gcd(5,2 + 63) = 5, gcd(63,2 + 5) = 7. Also, gcd(2,5,63) = 1. Thus, this set satisfies all the criteria.\nNote that \\{2,4,6\\} is not a valid solution because gcd(2,4,6) = 2 > 1.", "input: 4 output: 2 5 20 63\n\n\\{2,5,20,63\\} is special because gcd(2,5 + 20 + 63) = 2, gcd(5,2 + 20 + 63) = 5, gcd(20,2 + 5 + 63) = 10, gcd(63,2 + 5 + 20) = 9. Also, gcd(2,5,20,63) = 1. Thus, this set satisfies all the criteria."], "Pid": "p03394", "ProblemText": "Task Description: Problem Statement Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers. \nShe thinks that a set S = \\{a_{1}, a_{2}, . . . , a_{N}\\} of distinct positive integers is called special if for all 1 <= i <= N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.\nNagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.\nTask Constraint: 3 <= N <= 20000\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :\n\nThe elements must be distinct positive integers not exceeding 30000.\nThe gcd of all elements of S is 1, i. e. there does not exist an integer d > 1 that divides all elements of S.\nS is a special set.\n\nIf there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.\nTask Samples: input: 3 output: 2 5 63\n\n\\{2,5,63\\} is special because gcd(2,5 + 63) = 2, gcd(5,2 + 63) = 5, gcd(63,2 + 5) = 7. Also, gcd(2,5,63) = 1. Thus, this set satisfies all the criteria.\nNote that \\{2,4,6\\} is not a valid solution because gcd(2,4,6) = 2 > 1.\ninput: 4 output: 2 5 20 63\n\n\\{2,5,20,63\\} is special because gcd(2,5 + 20 + 63) = 2, gcd(5,2 + 20 + 63) = 5, gcd(20,2 + 5 + 63) = 10, gcd(63,2 + 5 + 20) = 9. Also, gcd(2,5,20,63) = 1. Thus, this set satisfies all the criteria.\n\n" }, { "title": "", "content": "Problem Statement Aoki is playing with a sequence of numbers a_{1}, a_{2}, . . . , a_{N}. Every second, he performs the following operation :\n\nChoose a positive integer k. For each element of the sequence v, Aoki may choose to replace v with its remainder when divided by k, or do nothing with v. The cost of this operation is 2^{k} (regardless of how many elements he changes).\n\nAoki wants to turn the sequence into b_{1}, b_{2}, . . . , b_{N} (the order of the elements is important). Determine if it is possible for Aoki to perform this task and if yes, find the minimum cost required.", "constraint": "1 <= N <= 50\n0 <= a_{i}, b_{i} <= 50\nAll values in the input are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_{1} a_{2} . . . a_{N}\nb_{1} b_{2} . . . b_{N}", "output": "Print the minimum cost required to turn the original sequence into b_{1}, b_{2}, . . . , b_{N}. If the task is impossible, output -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n19 10 14\n0 3 4 output: 160\n\nHere's a possible sequence of operations :\nChoose k = 7. Replace 19 with 5,10 with 3 and do nothing to 14. The sequence is now 5,3,14.\nChoose k = 5. Replace 5 with 0, do nothing to 3 and replace 14 with 4. The sequence is now 0,3,4.\nThe total cost is 2^{7} + 2^{5} = 160.", "input: 3\n19 15 14\n0 0 0 output: 2\n\nAoki can just choose k = 1 and turn everything into 0. The cost is 2^{1} = 2.", "input: 2\n8 13\n5 13 output: -1\n\nThe task is impossible because we can never turn 8 into 5 using the given operation.", "input: 4\n2 0 1 8\n2 0 1 8 output: 0\n\nAoki doesn't need to do anything here. The cost is 0.", "input: 1\n50\n13 output: 137438953472\n\nBeware of overflow issues."], "Pid": "p03395", "ProblemText": "Task Description: Problem Statement Aoki is playing with a sequence of numbers a_{1}, a_{2}, . . . , a_{N}. Every second, he performs the following operation :\n\nChoose a positive integer k. For each element of the sequence v, Aoki may choose to replace v with its remainder when divided by k, or do nothing with v. The cost of this operation is 2^{k} (regardless of how many elements he changes).\n\nAoki wants to turn the sequence into b_{1}, b_{2}, . . . , b_{N} (the order of the elements is important). Determine if it is possible for Aoki to perform this task and if yes, find the minimum cost required.\nTask Constraint: 1 <= N <= 50\n0 <= a_{i}, b_{i} <= 50\nAll values in the input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_{1} a_{2} . . . a_{N}\nb_{1} b_{2} . . . b_{N}\nTask Output: Print the minimum cost required to turn the original sequence into b_{1}, b_{2}, . . . , b_{N}. If the task is impossible, output -1 instead.\nTask Samples: input: 3\n19 10 14\n0 3 4 output: 160\n\nHere's a possible sequence of operations :\nChoose k = 7. Replace 19 with 5,10 with 3 and do nothing to 14. The sequence is now 5,3,14.\nChoose k = 5. Replace 5 with 0, do nothing to 3 and replace 14 with 4. The sequence is now 0,3,4.\nThe total cost is 2^{7} + 2^{5} = 160.\ninput: 3\n19 15 14\n0 0 0 output: 2\n\nAoki can just choose k = 1 and turn everything into 0. The cost is 2^{1} = 2.\ninput: 2\n8 13\n5 13 output: -1\n\nThe task is impossible because we can never turn 8 into 5 using the given operation.\ninput: 4\n2 0 1 8\n2 0 1 8 output: 0\n\nAoki doesn't need to do anything here. The cost is 0.\ninput: 1\n50\n13 output: 137438953472\n\nBeware of overflow issues.\n\n" }, { "title": "", "content": "Problem Statement Yui loves shopping. She lives in Yamaboshi City and there is a train service in the city. The city can be modelled as a very long number line. Yui's house is at coordinate 0.\nThere are N shopping centres in the city, located at coordinates x_{1}, x_{2}, . . . , x_{N} respectively. There are N + 2 train stations, one located at coordinate 0, one located at coordinate L, and one located at each shopping centre.\nAt time 0, the train departs from position 0 to the positive direction. The train travels at a constant speed of 1 unit per second. At time L, the train will reach the last station, the station at coordinate L. The train immediately moves in the opposite direction at the same speed. At time 2L, the train will reach the station at coordinate 0 and it immediately moves in the opposite direction again. The process repeats indefinitely.\nWhen the train arrives at a station where Yui is located, Yui can board or leave the train immediately. At time 0, Yui is at the station at coordinate 0. \nYui wants to go shopping in all N shopping centres, in any order, and return home after she finishes her shopping. She needs to shop for t_{i} seconds in the shopping centre at coordinate x_{i}. She must finish her shopping in one shopping centre before moving to the next shopping centre. Yui can immediately start shopping when she reaches a station with a shopping centre and she can immediately board the train when she finishes shopping.\nYui wants to spend the minimum amount of time to finish her shopping. Can you help her determine the minimum number of seconds required to complete her shopping? partial score: Partial Score\n1000 points will be awarded for passing the testset satisfying 1 <= N <= 3000.", "constraint": "1 <= N <= 300000\n1 <= L <= 10^{9}\n0 < x_{1} < x_{2} < ... < x_{N} < L\n1 <= t_{i} <= 10^{9}\nAll values in the input are integers.", "input": "Input is given from Standard Input in the following format:\nN L\nx_{1} x_{2} . . . x_{N}\nt_{1} t_{2} . . . t_{N}", "output": "Print the minimum time (in seconds) required for Yui to finish shopping at all N shopping centres and return home.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 10\n5 8\n10 4 output: 40\n\nHere's one possible way for Yui to finish her shopping :\nTravel to the station at coordinate 8 with the train. She arrives at coordinate 8 at time 8.\nShop in the shopping centre at coordinate 8. She finishes her shopping at time 12.\nThe train arrives at coordinate 8 at time 12. She boards the train which is currently moving in the negative direction.\nShe arrives at coordinate 5 at time 15. She finishes her shopping at time 25.\nThe train arrives at coordinate 5 at time 25. She boards the train which is currently moving in the positive direction.\nShe arrives at coordinate L = 10 at time 30. The train starts moving in the negative direction immediately.\nShe arrives at coordinate 0 at time 40, ending the trip.", "input: 2 10\n5 8\n10 5 output: 60", "input: 5 100\n10 19 28 47 68\n200 200 200 200 200 output: 1200", "input: 8 1000000000\n2018 123456 1719128 1929183 9129198 10100101 77777777 120182018\n99999999 1000000000 1000000000 11291341 1 200 1 123812831 output: 14000000000\n\nBeware of overflow issues."], "Pid": "p03396", "ProblemText": "Task Description: Problem Statement Yui loves shopping. She lives in Yamaboshi City and there is a train service in the city. The city can be modelled as a very long number line. Yui's house is at coordinate 0.\nThere are N shopping centres in the city, located at coordinates x_{1}, x_{2}, . . . , x_{N} respectively. There are N + 2 train stations, one located at coordinate 0, one located at coordinate L, and one located at each shopping centre.\nAt time 0, the train departs from position 0 to the positive direction. The train travels at a constant speed of 1 unit per second. At time L, the train will reach the last station, the station at coordinate L. The train immediately moves in the opposite direction at the same speed. At time 2L, the train will reach the station at coordinate 0 and it immediately moves in the opposite direction again. The process repeats indefinitely.\nWhen the train arrives at a station where Yui is located, Yui can board or leave the train immediately. At time 0, Yui is at the station at coordinate 0. \nYui wants to go shopping in all N shopping centres, in any order, and return home after she finishes her shopping. She needs to shop for t_{i} seconds in the shopping centre at coordinate x_{i}. She must finish her shopping in one shopping centre before moving to the next shopping centre. Yui can immediately start shopping when she reaches a station with a shopping centre and she can immediately board the train when she finishes shopping.\nYui wants to spend the minimum amount of time to finish her shopping. Can you help her determine the minimum number of seconds required to complete her shopping? partial score: Partial Score\n1000 points will be awarded for passing the testset satisfying 1 <= N <= 3000.\nTask Constraint: 1 <= N <= 300000\n1 <= L <= 10^{9}\n0 < x_{1} < x_{2} < ... < x_{N} < L\n1 <= t_{i} <= 10^{9}\nAll values in the input are integers.\nTask Input: Input is given from Standard Input in the following format:\nN L\nx_{1} x_{2} . . . x_{N}\nt_{1} t_{2} . . . t_{N}\nTask Output: Print the minimum time (in seconds) required for Yui to finish shopping at all N shopping centres and return home.\nTask Samples: input: 2 10\n5 8\n10 4 output: 40\n\nHere's one possible way for Yui to finish her shopping :\nTravel to the station at coordinate 8 with the train. She arrives at coordinate 8 at time 8.\nShop in the shopping centre at coordinate 8. She finishes her shopping at time 12.\nThe train arrives at coordinate 8 at time 12. She boards the train which is currently moving in the negative direction.\nShe arrives at coordinate 5 at time 15. She finishes her shopping at time 25.\nThe train arrives at coordinate 5 at time 25. She boards the train which is currently moving in the positive direction.\nShe arrives at coordinate L = 10 at time 30. The train starts moving in the negative direction immediately.\nShe arrives at coordinate 0 at time 40, ending the trip.\ninput: 2 10\n5 8\n10 5 output: 60\ninput: 5 100\n10 19 28 47 68\n200 200 200 200 200 output: 1200\ninput: 8 1000000000\n2018 123456 1719128 1929183 9129198 10100101 77777777 120182018\n99999999 1000000000 1000000000 11291341 1 200 1 123812831 output: 14000000000\n\nBeware of overflow issues.\n\n" }, { "title": "", "content": "Problem Statement Taichi thinks a binary string X of odd length N is beautiful if it is possible to apply the following operation \\frac{N-1}{2} times so that the only character of the resulting string is 1 :\n\nChoose three consecutive bits of X and replace them by their median. For example, we can turn 00110 into 010 by applying the operation to the middle three bits.\n\nTaichi has a string S consisting of characters 0,1 and ? . Taichi wants to know the number of ways to replace the question marks with 1 or 0 so that the resulting string is beautiful, modulo 10^{9} + 7.", "constraint": "1 <= |S| <= 300000\n|S| is odd.\nAll characters of S are either 0,1 or ?.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the number of ways to replace the question marks so that the resulting string is beautiful, modulo 10^{9} + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1??00 output: 2\n\nThere are 4 ways to replace the question marks with 0 or 1 :\n11100 : This string is beautiful because we can first perform the operation on the last 3 bits to get 110 and then on the only 3 bits to get 1.\n11000 : This string is beautiful because we can first perform the operation on the last 3 bits to get 110 and then on the only 3 bits to get 1.\n10100 : This string is not beautiful because there is no sequence of operations such that the final string is 1.\n10000 : This string is not beautiful because there is no sequence of operations such that the final string is 1.\nThus, there are 2 ways to form a beautiful string.", "input: ? output: 1\n\nIn this case, 1 is the only beautiful string.", "input: ?0101???10???00?1???????????????0????????????1????0 output: 402589311\n\nRemember to output your answer modulo 10^{9} + 7."], "Pid": "p03397", "ProblemText": "Task Description: Problem Statement Taichi thinks a binary string X of odd length N is beautiful if it is possible to apply the following operation \\frac{N-1}{2} times so that the only character of the resulting string is 1 :\n\nChoose three consecutive bits of X and replace them by their median. For example, we can turn 00110 into 010 by applying the operation to the middle three bits.\n\nTaichi has a string S consisting of characters 0,1 and ? . Taichi wants to know the number of ways to replace the question marks with 1 or 0 so that the resulting string is beautiful, modulo 10^{9} + 7.\nTask Constraint: 1 <= |S| <= 300000\n|S| is odd.\nAll characters of S are either 0,1 or ?.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the number of ways to replace the question marks so that the resulting string is beautiful, modulo 10^{9} + 7.\nTask Samples: input: 1??00 output: 2\n\nThere are 4 ways to replace the question marks with 0 or 1 :\n11100 : This string is beautiful because we can first perform the operation on the last 3 bits to get 110 and then on the only 3 bits to get 1.\n11000 : This string is beautiful because we can first perform the operation on the last 3 bits to get 110 and then on the only 3 bits to get 1.\n10100 : This string is not beautiful because there is no sequence of operations such that the final string is 1.\n10000 : This string is not beautiful because there is no sequence of operations such that the final string is 1.\nThus, there are 2 ways to form a beautiful string.\ninput: ? output: 1\n\nIn this case, 1 is the only beautiful string.\ninput: ?0101???10???00?1???????????????0????????????1????0 output: 402589311\n\nRemember to output your answer modulo 10^{9} + 7.\n\n" }, { "title": "", "content": "Problem Statement Let X = 10^{100}. Inaba has N checker pieces on the number line, where the i-th checker piece is at coordinate X^{i} for all 1 <= i <= N.\nEvery second, Inaba chooses two checker pieces, A and B, and move A to the symmetric point of its current position with respect to B. After that, B is removed. (It is possible that A and B occupy the same position, and it is also possible for A to occupy the same position as another checker piece after the move).\nAfter N - 1 seconds, only one checker piece will remain. Find the number of distinct possible positions of that checker piece, modulo 10^{9} + 7.", "constraint": "1 <= N <= 50\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the number of distinct possible positions of the final checker piece, modulo 10^{9} + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 12\n\nThere are 3 checker pieces, positioned at 10^{100}, 10^{200}, 10^{300} respectively. Call them A, B, C respectively.\nHere are two (of the 12) possible sequence of moves :\nLet A jump over B in the first second, and let A jump over C in the second second. The final position of A is 2 * 10^{300} - 2 * 10^{200} + 10^{100}.\nLet C jump over A in the first second, and let B jump over C in the second second. The final position of B is -2 * 10^{300} - 10^{200} + 4 * 10^{100}.\nThere are a total of 3 * 2 * 2 = 12 possible sequence of moves, and the final piece are in different positions in all of them.", "input: 4 output: 84", "input: 22 output: 487772376\n\nRemember to output your answer modulo 10^{9} + 7."], "Pid": "p03398", "ProblemText": "Task Description: Problem Statement Let X = 10^{100}. Inaba has N checker pieces on the number line, where the i-th checker piece is at coordinate X^{i} for all 1 <= i <= N.\nEvery second, Inaba chooses two checker pieces, A and B, and move A to the symmetric point of its current position with respect to B. After that, B is removed. (It is possible that A and B occupy the same position, and it is also possible for A to occupy the same position as another checker piece after the move).\nAfter N - 1 seconds, only one checker piece will remain. Find the number of distinct possible positions of that checker piece, modulo 10^{9} + 7.\nTask Constraint: 1 <= N <= 50\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the number of distinct possible positions of the final checker piece, modulo 10^{9} + 7.\nTask Samples: input: 3 output: 12\n\nThere are 3 checker pieces, positioned at 10^{100}, 10^{200}, 10^{300} respectively. Call them A, B, C respectively.\nHere are two (of the 12) possible sequence of moves :\nLet A jump over B in the first second, and let A jump over C in the second second. The final position of A is 2 * 10^{300} - 2 * 10^{200} + 10^{100}.\nLet C jump over A in the first second, and let B jump over C in the second second. The final position of B is -2 * 10^{300} - 10^{200} + 4 * 10^{100}.\nThere are a total of 3 * 2 * 2 = 12 possible sequence of moves, and the final piece are in different positions in all of them.\ninput: 4 output: 84\ninput: 22 output: 487772376\n\nRemember to output your answer modulo 10^{9} + 7.\n\n" }, { "title": "", "content": "Problem Statement You planned a trip using trains and buses.\nThe train fare will be A yen (the currency of Japan) if you buy ordinary tickets along the way, and B yen if you buy an unlimited ticket.\nSimilarly, the bus fare will be C yen if you buy ordinary tickets along the way, and D yen if you buy an unlimited ticket.\nFind the minimum total fare when the optimal choices are made for trains and buses.", "constraint": "1 <= A <= 1 000\n1 <= B <= 1 000\n1 <= C <= 1 000\n1 <= D <= 1 000\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nA\nB\nC\nD", "output": "Print the minimum total fare.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 600\n300\n220\n420 output: 520\n\nThe train fare will be 600 yen if you buy ordinary tickets, and 300 yen if you buy an unlimited ticket.\nThus, the optimal choice for trains is to buy an unlimited ticket for 300 yen.\nOn the other hand, the optimal choice for buses is to buy ordinary tickets for 220 yen.\nTherefore, the minimum total fare is 300 + 220 = 520 yen.", "input: 555\n555\n400\n200 output: 755", "input: 549\n817\n715\n603 output: 1152"], "Pid": "p03399", "ProblemText": "Task Description: Problem Statement You planned a trip using trains and buses.\nThe train fare will be A yen (the currency of Japan) if you buy ordinary tickets along the way, and B yen if you buy an unlimited ticket.\nSimilarly, the bus fare will be C yen if you buy ordinary tickets along the way, and D yen if you buy an unlimited ticket.\nFind the minimum total fare when the optimal choices are made for trains and buses.\nTask Constraint: 1 <= A <= 1 000\n1 <= B <= 1 000\n1 <= C <= 1 000\n1 <= D <= 1 000\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nA\nB\nC\nD\nTask Output: Print the minimum total fare.\nTask Samples: input: 600\n300\n220\n420 output: 520\n\nThe train fare will be 600 yen if you buy ordinary tickets, and 300 yen if you buy an unlimited ticket.\nThus, the optimal choice for trains is to buy an unlimited ticket for 300 yen.\nOn the other hand, the optimal choice for buses is to buy ordinary tickets for 220 yen.\nTherefore, the minimum total fare is 300 + 220 = 520 yen.\ninput: 555\n555\n400\n200 output: 755\ninput: 549\n817\n715\n603 output: 1152\n\n" }, { "title": "", "content": "Problem Statement Some number of chocolate pieces were prepared for a training camp.\nThe camp had N participants and lasted for D days.\nThe i-th participant (1 <= i <= N) ate one chocolate piece on each of the following days in the camp: the 1-st day, the (A_i + 1)-th day, the (2A_i + 1)-th day, and so on.\nAs a result, there were X chocolate pieces remaining at the end of the camp. During the camp, nobody except the participants ate chocolate pieces.\nFind the number of chocolate pieces prepared at the beginning of the camp.", "constraint": "1 <= N <= 100\n1 <= D <= 100\n1 <= X <= 100\n1 <= A_i <= 100 (1 <= i <= N)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nD X\nA_1\nA_2\n:\nA_N", "output": "Find the number of chocolate pieces prepared at the beginning of the camp.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n7 1\n2\n5\n10 output: 8\n\nThe camp has 3 participants and lasts for 7 days.\nEach participant eats chocolate pieces as follows:\n\nThe first participant eats one chocolate piece on Day 1,3,5 and 7, for a total of four.\nThe second participant eats one chocolate piece on Day 1 and 6, for a total of two.\nThe third participant eats one chocolate piece only on Day 1, for a total of one.\n\nSince the number of pieces remaining at the end of the camp is one, the number of pieces prepared at the beginning of the camp is 1 + 4 + 2 + 1 = 8.", "input: 2\n8 20\n1\n10 output: 29", "input: 5\n30 44\n26\n18\n81\n18\n6 output: 56"], "Pid": "p03400", "ProblemText": "Task Description: Problem Statement Some number of chocolate pieces were prepared for a training camp.\nThe camp had N participants and lasted for D days.\nThe i-th participant (1 <= i <= N) ate one chocolate piece on each of the following days in the camp: the 1-st day, the (A_i + 1)-th day, the (2A_i + 1)-th day, and so on.\nAs a result, there were X chocolate pieces remaining at the end of the camp. During the camp, nobody except the participants ate chocolate pieces.\nFind the number of chocolate pieces prepared at the beginning of the camp.\nTask Constraint: 1 <= N <= 100\n1 <= D <= 100\n1 <= X <= 100\n1 <= A_i <= 100 (1 <= i <= N)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nD X\nA_1\nA_2\n:\nA_N\nTask Output: Find the number of chocolate pieces prepared at the beginning of the camp.\nTask Samples: input: 3\n7 1\n2\n5\n10 output: 8\n\nThe camp has 3 participants and lasts for 7 days.\nEach participant eats chocolate pieces as follows:\n\nThe first participant eats one chocolate piece on Day 1,3,5 and 7, for a total of four.\nThe second participant eats one chocolate piece on Day 1 and 6, for a total of two.\nThe third participant eats one chocolate piece only on Day 1, for a total of one.\n\nSince the number of pieces remaining at the end of the camp is one, the number of pieces prepared at the beginning of the camp is 1 + 4 + 2 + 1 = 8.\ninput: 2\n8 20\n1\n10 output: 29\ninput: 5\n30 44\n26\n18\n81\n18\n6 output: 56\n\n" }, { "title": "", "content": "Problem Statement There are N sightseeing spots on the x-axis, numbered 1,2, . . . , N.\nSpot i is at the point with coordinate A_i.\nIt costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.\nYou planned a trip along the axis.\nIn this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.\nHowever, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i.\nYou will visit the remaining spots as planned in the order they are numbered.\nYou will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.\nFor each i = 1,2, . . . , N, find the total cost of travel during the trip when the visit to Spot i is canceled.", "constraint": "2 <= N <= 10^5\n-5000 <= A_i <= 5000 (1 <= i <= N)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print N lines.\nIn the i-th line, print the total cost of travel during the trip when the visit to Spot i is canceled.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 5 -1 output: 12\n8\n10\n\nSpot 1,2 and 3 are at the points with coordinates 3,5 and -1, respectively.\nFor each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:\n\nFor i = 1, the course of the trip is 0 \\rightarrow 5 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.\nFor i = 2, the course of the trip is 0 \\rightarrow 3 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.\nFor i = 3, the course of the trip is 0 \\rightarrow 3 \\rightarrow 5 \\rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.", "input: 5\n1 1 1 2 0 output: 4\n4\n4\n2\n4", "input: 6\n-679 -2409 -3258 3095 -3291 -4462 output: 21630\n21630\n19932\n8924\n21630\n19288"], "Pid": "p03401", "ProblemText": "Task Description: Problem Statement There are N sightseeing spots on the x-axis, numbered 1,2, . . . , N.\nSpot i is at the point with coordinate A_i.\nIt costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.\nYou planned a trip along the axis.\nIn this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.\nHowever, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i.\nYou will visit the remaining spots as planned in the order they are numbered.\nYou will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.\nFor each i = 1,2, . . . , N, find the total cost of travel during the trip when the visit to Spot i is canceled.\nTask Constraint: 2 <= N <= 10^5\n-5000 <= A_i <= 5000 (1 <= i <= N)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print N lines.\nIn the i-th line, print the total cost of travel during the trip when the visit to Spot i is canceled.\nTask Samples: input: 3\n3 5 -1 output: 12\n8\n10\n\nSpot 1,2 and 3 are at the points with coordinates 3,5 and -1, respectively.\nFor each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:\n\nFor i = 1, the course of the trip is 0 \\rightarrow 5 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.\nFor i = 2, the course of the trip is 0 \\rightarrow 3 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.\nFor i = 3, the course of the trip is 0 \\rightarrow 3 \\rightarrow 5 \\rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.\ninput: 5\n1 1 1 2 0 output: 4\n4\n4\n2\n4\ninput: 6\n-679 -2409 -3258 3095 -3291 -4462 output: 21630\n21630\n19932\n8924\n21630\n19288\n\n" }, { "title": "", "content": "Problem Statement You are given two integers A and B.\nPrint a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:\n\nLet the size of the grid be h * w (h vertical, w horizontal). Both h and w are at most 100.\nThe set of the squares painted white is divided into exactly A connected components.\nThe set of the squares painted black is divided into exactly B connected components.\n\nIt can be proved that there always exist one or more solutions under the conditions specified in Constraints section.\nIf there are multiple solutions, any of them may be printed. note: Notes Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.\nA set of squares painted white, S, forms a connected component when the following conditions are met:\n\nAny two squares in S are connected.\nNo pair of a square painted white that is not included in S and a square included in S is connected.\n\nA connected component of squares painted black is defined similarly.", "constraint": "1 <= A <= 500\n1 <= B <= 500", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Output should be in the following format:\n\nIn the first line, print integers h and w representing the size of the grid you constructed, with a space in between.\nThen, print h more lines. The i-th (1 <= i <= h) of these lines should contain a string s_i as follows:\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted white, the j-th character in s_i should be . .\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted black, the j-th character in s_i should be #.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 output: 3 3\n##.\n..#\n#.#\n\nThis output corresponds to the grid below:", "input: 7 8 output: 3 5\n#.#.#\n.#.#.\n#.#.#", "input: 1 1 output: 4 2\n..\n#.\n##\n##", "input: 3 14 output: 8 18\n..................\n..................\n....##.......####.\n....#.#.....#.....\n...#...#....#.....\n..#.###.#...#.....\n.#.......#..#.....\n#.........#..####."], "Pid": "p03402", "ProblemText": "Task Description: Problem Statement You are given two integers A and B.\nPrint a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:\n\nLet the size of the grid be h * w (h vertical, w horizontal). Both h and w are at most 100.\nThe set of the squares painted white is divided into exactly A connected components.\nThe set of the squares painted black is divided into exactly B connected components.\n\nIt can be proved that there always exist one or more solutions under the conditions specified in Constraints section.\nIf there are multiple solutions, any of them may be printed. note: Notes Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.\nA set of squares painted white, S, forms a connected component when the following conditions are met:\n\nAny two squares in S are connected.\nNo pair of a square painted white that is not included in S and a square included in S is connected.\n\nA connected component of squares painted black is defined similarly.\nTask Constraint: 1 <= A <= 500\n1 <= B <= 500\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Output should be in the following format:\n\nIn the first line, print integers h and w representing the size of the grid you constructed, with a space in between.\nThen, print h more lines. The i-th (1 <= i <= h) of these lines should contain a string s_i as follows:\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted white, the j-th character in s_i should be . .\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted black, the j-th character in s_i should be #.\nTask Samples: input: 2 3 output: 3 3\n##.\n..#\n#.#\n\nThis output corresponds to the grid below:\ninput: 7 8 output: 3 5\n#.#.#\n.#.#.\n#.#.#\ninput: 1 1 output: 4 2\n..\n#.\n##\n##\ninput: 3 14 output: 8 18\n..................\n..................\n....##.......####.\n....#.#.....#.....\n...#...#....#.....\n..#.###.#...#.....\n.#.......#..#.....\n#.........#..####.\n\n" }, { "title": "", "content": "Problem Statement There are N sightseeing spots on the x-axis, numbered 1,2, . . . , N.\nSpot i is at the point with coordinate A_i.\nIt costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.\nYou planned a trip along the axis.\nIn this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.\nHowever, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i.\nYou will visit the remaining spots as planned in the order they are numbered.\nYou will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.\nFor each i = 1,2, . . . , N, find the total cost of travel during the trip when the visit to Spot i is canceled.", "constraint": "2 <= N <= 10^5\n-5000 <= A_i <= 5000 (1 <= i <= N)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print N lines.\nIn the i-th line, print the total cost of travel during the trip when the visit to Spot i is canceled.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3 5 -1 output: 12\n8\n10\n\nSpot 1,2 and 3 are at the points with coordinates 3,5 and -1, respectively.\nFor each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:\n\nFor i = 1, the course of the trip is 0 \\rightarrow 5 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.\nFor i = 2, the course of the trip is 0 \\rightarrow 3 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.\nFor i = 3, the course of the trip is 0 \\rightarrow 3 \\rightarrow 5 \\rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.", "input: 5\n1 1 1 2 0 output: 4\n4\n4\n2\n4", "input: 6\n-679 -2409 -3258 3095 -3291 -4462 output: 21630\n21630\n19932\n8924\n21630\n19288"], "Pid": "p03403", "ProblemText": "Task Description: Problem Statement There are N sightseeing spots on the x-axis, numbered 1,2, . . . , N.\nSpot i is at the point with coordinate A_i.\nIt costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.\nYou planned a trip along the axis.\nIn this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.\nHowever, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i.\nYou will visit the remaining spots as planned in the order they are numbered.\nYou will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.\nFor each i = 1,2, . . . , N, find the total cost of travel during the trip when the visit to Spot i is canceled.\nTask Constraint: 2 <= N <= 10^5\n-5000 <= A_i <= 5000 (1 <= i <= N)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print N lines.\nIn the i-th line, print the total cost of travel during the trip when the visit to Spot i is canceled.\nTask Samples: input: 3\n3 5 -1 output: 12\n8\n10\n\nSpot 1,2 and 3 are at the points with coordinates 3,5 and -1, respectively.\nFor each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:\n\nFor i = 1, the course of the trip is 0 \\rightarrow 5 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.\nFor i = 2, the course of the trip is 0 \\rightarrow 3 \\rightarrow -1 \\rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.\nFor i = 3, the course of the trip is 0 \\rightarrow 3 \\rightarrow 5 \\rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.\ninput: 5\n1 1 1 2 0 output: 4\n4\n4\n2\n4\ninput: 6\n-679 -2409 -3258 3095 -3291 -4462 output: 21630\n21630\n19932\n8924\n21630\n19288\n\n" }, { "title": "", "content": "Problem Statement You are given two integers A and B.\nPrint a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:\n\nLet the size of the grid be h * w (h vertical, w horizontal). Both h and w are at most 100.\nThe set of the squares painted white is divided into exactly A connected components.\nThe set of the squares painted black is divided into exactly B connected components.\n\nIt can be proved that there always exist one or more solutions under the conditions specified in Constraints section.\nIf there are multiple solutions, any of them may be printed. note: Notes Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.\nA set of squares painted white, S, forms a connected component when the following conditions are met:\n\nAny two squares in S are connected.\nNo pair of a square painted white that is not included in S and a square included in S is connected.\n\nA connected component of squares painted black is defined similarly.", "constraint": "1 <= A <= 500\n1 <= B <= 500", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Output should be in the following format:\n\nIn the first line, print integers h and w representing the size of the grid you constructed, with a space in between.\nThen, print h more lines. The i-th (1 <= i <= h) of these lines should contain a string s_i as follows:\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted white, the j-th character in s_i should be . .\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted black, the j-th character in s_i should be #.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 output: 3 3\n##.\n..#\n#.#\n\nThis output corresponds to the grid below:", "input: 7 8 output: 3 5\n#.#.#\n.#.#.\n#.#.#", "input: 1 1 output: 4 2\n..\n#.\n##\n##", "input: 3 14 output: 8 18\n..................\n..................\n....##.......####.\n....#.#.....#.....\n...#...#....#.....\n..#.###.#...#.....\n.#.......#..#.....\n#.........#..####."], "Pid": "p03404", "ProblemText": "Task Description: Problem Statement You are given two integers A and B.\nPrint a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:\n\nLet the size of the grid be h * w (h vertical, w horizontal). Both h and w are at most 100.\nThe set of the squares painted white is divided into exactly A connected components.\nThe set of the squares painted black is divided into exactly B connected components.\n\nIt can be proved that there always exist one or more solutions under the conditions specified in Constraints section.\nIf there are multiple solutions, any of them may be printed. note: Notes Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.\nA set of squares painted white, S, forms a connected component when the following conditions are met:\n\nAny two squares in S are connected.\nNo pair of a square painted white that is not included in S and a square included in S is connected.\n\nA connected component of squares painted black is defined similarly.\nTask Constraint: 1 <= A <= 500\n1 <= B <= 500\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Output should be in the following format:\n\nIn the first line, print integers h and w representing the size of the grid you constructed, with a space in between.\nThen, print h more lines. The i-th (1 <= i <= h) of these lines should contain a string s_i as follows:\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted white, the j-th character in s_i should be . .\nIf the square at the i-th row and j-th column (1 <= j <= w) in the grid is painted black, the j-th character in s_i should be #.\nTask Samples: input: 2 3 output: 3 3\n##.\n..#\n#.#\n\nThis output corresponds to the grid below:\ninput: 7 8 output: 3 5\n#.#.#\n.#.#.\n#.#.#\ninput: 1 1 output: 4 2\n..\n#.\n##\n##\ninput: 3 14 output: 8 18\n..................\n..................\n....##.......####.\n....#.#.....#.....\n...#...#....#.....\n..#.###.#...#.....\n.#.......#..#.....\n#.........#..####.\n\n" }, { "title": "", "content": "Problem Statement We have an undirected weighted graph with N vertices and M edges.\nThe i-th edge in the graph connects Vertex U_i and Vertex V_i, and has a weight of W_i.\nAdditionally, you are given an integer X.\nFind the number of ways to paint each edge in this graph either white or black such that the following condition is met, modulo 10^9 + 7:\n\nThe graph has a spanning tree that contains both an edge painted white and an edge painted black. Furthermore, among such spanning trees, the one with the smallest weight has a weight of X.\n\nHere, the weight of a spanning tree is the sum of the weights of the edges contained in the spanning tree.", "constraint": "1 <= N <= 1 000\n1 <= M <= 2 000\n1 <= U_i, V_i <= N (1 <= i <= M)\n1 <= W_i <= 10^9 (1 <= i <= M)\nIf i \\neq j, then (U_i, V_i) \\neq (U_j, V_j) and (U_i, V_i) \\neq (V_j, U_j).\nU_i \\neq V_i (1 <= i <= M)\nThe given graph is connected.\n1 <= X <= 10^{12}\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nX\nU_1 V_1 W_1\nU_2 V_2 W_2\n:\nU_M V_M W_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n2\n1 2 1\n2 3 1\n3 1 1 output: 6", "input: 3 3\n3\n1 2 1\n2 3 1\n3 1 2 output: 2", "input: 5 4\n1\n1 2 3\n1 3 3\n2 4 6\n2 5 8 output: 0", "input: 8 10\n49\n4 6 10\n8 4 11\n5 8 9\n1 8 10\n3 8 128773450\n7 8 10\n4 2 4\n3 4 1\n3 1 13\n5 2 2 output: 4"], "Pid": "p03405", "ProblemText": "Task Description: Problem Statement We have an undirected weighted graph with N vertices and M edges.\nThe i-th edge in the graph connects Vertex U_i and Vertex V_i, and has a weight of W_i.\nAdditionally, you are given an integer X.\nFind the number of ways to paint each edge in this graph either white or black such that the following condition is met, modulo 10^9 + 7:\n\nThe graph has a spanning tree that contains both an edge painted white and an edge painted black. Furthermore, among such spanning trees, the one with the smallest weight has a weight of X.\n\nHere, the weight of a spanning tree is the sum of the weights of the edges contained in the spanning tree.\nTask Constraint: 1 <= N <= 1 000\n1 <= M <= 2 000\n1 <= U_i, V_i <= N (1 <= i <= M)\n1 <= W_i <= 10^9 (1 <= i <= M)\nIf i \\neq j, then (U_i, V_i) \\neq (U_j, V_j) and (U_i, V_i) \\neq (V_j, U_j).\nU_i \\neq V_i (1 <= i <= M)\nThe given graph is connected.\n1 <= X <= 10^{12}\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nX\nU_1 V_1 W_1\nU_2 V_2 W_2\n:\nU_M V_M W_M\nTask Output: Print the answer.\nTask Samples: input: 3 3\n2\n1 2 1\n2 3 1\n3 1 1 output: 6\ninput: 3 3\n3\n1 2 1\n2 3 1\n3 1 2 output: 2\ninput: 5 4\n1\n1 2 3\n1 3 3\n2 4 6\n2 5 8 output: 0\ninput: 8 10\n49\n4 6 10\n8 4 11\n5 8 9\n1 8 10\n3 8 128773450\n7 8 10\n4 2 4\n3 4 1\n3 1 13\n5 2 2 output: 4\n\n" }, { "title": "", "content": "Problem Statement There are 2^N players, numbered 1,2, . . . , 2^N.\nThey decided to hold a tournament.\nThe tournament proceeds as follows:\n\nChoose a permutation of 1,2, . . . , 2^N: p_1, p_2, . . . , p_{2^N}.\nThe players stand in a row in the order of Player p_1, Player p_2, . . . , Player p_{2^N}.\nRepeat the following until there is only one player remaining in the row:\nPlay the following matches: the first player in the row versus the second player in the row, the third player versus the fourth player, and so on. The players who lose leave the row. The players who win stand in a row again, preserving the relative order of the players.\nThe last player who remains in the row is the champion.\n\nIt is known that, the result of the match between two players can be written as follows, using M integers A_1, A_2, . . . , A_M given as input:\n\nWhen y = A_i for some i, the winner of the match between Player 1 and Player y (2 <= y <= 2^N) will be Player y.\nWhen y \\neq A_i for every i, the winner of the match between Player 1 and Player y (2 <= y <= 2^N) will be Player 1.\nWhen 2 <= x < y <= 2^N, the winner of the match between Player x and Player y will be Player x.\n\nThe champion of this tournament depends only on the permutation p_1, p_2, . . . , p_{2^N} chosen at the beginning.\nFind the number of permutation p_1, p_2, . . . , p_{2^N} chosen at the beginning of the tournament that would result in Player 1 becoming the champion, modulo 10^9 + 7.", "constraint": "1 <= N <= 16\n0 <= M <= 16\n2 <= A_i <= 2^N (1 <= i <= M)\nA_i < A_{i + 1} (1 <= i < M)", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n3 output: 8\n\nExamples of p that satisfy the condition are: [1,4,2,3] and [3,2,1,4]. Examples of p that do not satisfy the condition are: [1,2,3,4] and [1,3,2,4].", "input: 4 3\n2 4 6 output: 0", "input: 3 0 output: 40320", "input: 3 3\n3 4 7 output: 2688", "input: 16 16\n5489 5490 5491 5492 5493 5494 5495 5497 18993 18995 18997 18999 19000 19001 19002 19003 output: 816646464"], "Pid": "p03406", "ProblemText": "Task Description: Problem Statement There are 2^N players, numbered 1,2, . . . , 2^N.\nThey decided to hold a tournament.\nThe tournament proceeds as follows:\n\nChoose a permutation of 1,2, . . . , 2^N: p_1, p_2, . . . , p_{2^N}.\nThe players stand in a row in the order of Player p_1, Player p_2, . . . , Player p_{2^N}.\nRepeat the following until there is only one player remaining in the row:\nPlay the following matches: the first player in the row versus the second player in the row, the third player versus the fourth player, and so on. The players who lose leave the row. The players who win stand in a row again, preserving the relative order of the players.\nThe last player who remains in the row is the champion.\n\nIt is known that, the result of the match between two players can be written as follows, using M integers A_1, A_2, . . . , A_M given as input:\n\nWhen y = A_i for some i, the winner of the match between Player 1 and Player y (2 <= y <= 2^N) will be Player y.\nWhen y \\neq A_i for every i, the winner of the match between Player 1 and Player y (2 <= y <= 2^N) will be Player 1.\nWhen 2 <= x < y <= 2^N, the winner of the match between Player x and Player y will be Player x.\n\nThe champion of this tournament depends only on the permutation p_1, p_2, . . . , p_{2^N} chosen at the beginning.\nFind the number of permutation p_1, p_2, . . . , p_{2^N} chosen at the beginning of the tournament that would result in Player 1 becoming the champion, modulo 10^9 + 7.\nTask Constraint: 1 <= N <= 16\n0 <= M <= 16\n2 <= A_i <= 2^N (1 <= i <= M)\nA_i < A_{i + 1} (1 <= i < M)\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_M\nTask Output: Print the answer.\nTask Samples: input: 2 1\n3 output: 8\n\nExamples of p that satisfy the condition are: [1,4,2,3] and [3,2,1,4]. Examples of p that do not satisfy the condition are: [1,2,3,4] and [1,3,2,4].\ninput: 4 3\n2 4 6 output: 0\ninput: 3 0 output: 40320\ninput: 3 3\n3 4 7 output: 2688\ninput: 16 16\n5489 5490 5491 5492 5493 5494 5495 5497 18993 18995 18997 18999 19000 19001 19002 19003 output: 816646464\n\n" }, { "title": "", "content": "Problem Statement An elementary school student Takahashi has come to a variety store.\nHe has two coins, A-yen and B-yen coins (yen is the currency of Japan), and wants to buy a toy that costs C yen. Can he buy it?\nNote that he lives in Takahashi Kingdom, and may have coins that do not exist in Japan.", "constraint": "All input values are integers.\n1 <= A, B <= 500\n1 <= C <= 1000", "input": "Input is given from Standard Input in the following format:\nA B C", "output": "If Takahashi can buy the toy, print Yes; if he cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 50 100 120 output: Yes\n\nHe has 50 + 100 = 150 yen, so he can buy the 120-yen toy.", "input: 500 100 1000 output: No\n\nHe has 500 + 100 = 600 yen, but he cannot buy the 1000-yen toy.", "input: 19 123 143 output: No\n\nThere are 19-yen and 123-yen coins in Takahashi Kingdom, which are rather hard to use.", "input: 19 123 142 output: Yes"], "Pid": "p03407", "ProblemText": "Task Description: Problem Statement An elementary school student Takahashi has come to a variety store.\nHe has two coins, A-yen and B-yen coins (yen is the currency of Japan), and wants to buy a toy that costs C yen. Can he buy it?\nNote that he lives in Takahashi Kingdom, and may have coins that do not exist in Japan.\nTask Constraint: All input values are integers.\n1 <= A, B <= 500\n1 <= C <= 1000\nTask Input: Input is given from Standard Input in the following format:\nA B C\nTask Output: If Takahashi can buy the toy, print Yes; if he cannot, print No.\nTask Samples: input: 50 100 120 output: Yes\n\nHe has 50 + 100 = 150 yen, so he can buy the 120-yen toy.\ninput: 500 100 1000 output: No\n\nHe has 500 + 100 = 600 yen, but he cannot buy the 1000-yen toy.\ninput: 19 123 143 output: No\n\nThere are 19-yen and 123-yen coins in Takahashi Kingdom, which are rather hard to use.\ninput: 19 123 142 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Takahashi has N blue cards and M red cards.\nA string is written on each card. The string written on the i-th blue card is s_i, and the string written on the i-th red card is t_i.\nTakahashi will now announce a string, and then check every card. Each time he finds a blue card with the string announced by him, he will earn 1 yen (the currency of Japan); each time he finds a red card with that string, he will lose 1 yen.\nHere, we only consider the case where the string announced by Takahashi and the string on the card are exactly the same. For example, if he announces atcoder, he will not earn money even if there are blue cards with atcoderr, atcode, btcoder, and so on. (On the other hand, he will not lose money even if there are red cards with such strings, either. )\nAt most how much can he earn on balance?\nNote that the same string may be written on multiple cards.", "constraint": "N and M are integers.\n1 <= N, M <= 100\ns_1, s_2, ..., s_N, t_1, t_2, ..., t_M are all strings of lengths between 1 and 10 (inclusive) consisting of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N\nM\nt_1\nt_2\n:\nt_M", "output": "If Takahashi can earn at most X yen on balance, print X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\napple\norange\napple\n1\ngrape output: 2\n\nHe can earn 2 yen by announcing apple.", "input: 3\napple\norange\napple\n5\napple\napple\napple\napple\napple output: 1\n\nIf he announces apple, he will lose 3 yen. If he announces orange, he can earn 1 yen.", "input: 1\nvoldemort\n10\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort output: 0\n\nIf he announces voldemort, he will lose 9 yen. If he announces orange, for example, he can avoid losing a yen.", "input: 6\nred\nred\nblue\nyellow\nyellow\nred\n5\nred\nred\nyellow\ngreen\nblue output: 1"], "Pid": "p03408", "ProblemText": "Task Description: Problem Statement Takahashi has N blue cards and M red cards.\nA string is written on each card. The string written on the i-th blue card is s_i, and the string written on the i-th red card is t_i.\nTakahashi will now announce a string, and then check every card. Each time he finds a blue card with the string announced by him, he will earn 1 yen (the currency of Japan); each time he finds a red card with that string, he will lose 1 yen.\nHere, we only consider the case where the string announced by Takahashi and the string on the card are exactly the same. For example, if he announces atcoder, he will not earn money even if there are blue cards with atcoderr, atcode, btcoder, and so on. (On the other hand, he will not lose money even if there are red cards with such strings, either. )\nAt most how much can he earn on balance?\nNote that the same string may be written on multiple cards.\nTask Constraint: N and M are integers.\n1 <= N, M <= 100\ns_1, s_2, ..., s_N, t_1, t_2, ..., t_M are all strings of lengths between 1 and 10 (inclusive) consisting of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N\nM\nt_1\nt_2\n:\nt_M\nTask Output: If Takahashi can earn at most X yen on balance, print X.\nTask Samples: input: 3\napple\norange\napple\n1\ngrape output: 2\n\nHe can earn 2 yen by announcing apple.\ninput: 3\napple\norange\napple\n5\napple\napple\napple\napple\napple output: 1\n\nIf he announces apple, he will lose 3 yen. If he announces orange, he can earn 1 yen.\ninput: 1\nvoldemort\n10\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort\nvoldemort output: 0\n\nIf he announces voldemort, he will lose 9 yen. If he announces orange, for example, he can avoid losing a yen.\ninput: 6\nred\nred\nblue\nyellow\nyellow\nred\n5\nred\nred\nyellow\ngreen\nblue output: 1\n\n" }, { "title": "", "content": "Problem Statement On a two-dimensional plane, there are N red points and N blue points.\nThe coordinates of the i-th red point are (a_i, b_i), and the coordinates of the i-th blue point are (c_i, d_i).\nA red point and a blue point can form a friendly pair when, the x-coordinate of the red point is smaller than that of the blue point, and the y-coordinate of the red point is also smaller than that of the blue point.\nAt most how many friendly pairs can you form? Note that a point cannot belong to multiple pairs.", "constraint": "All input values are integers.\n1 <= N <= 100\n0 <= a_i, b_i, c_i, d_i < 2N\na_1, a_2, ..., a_N, c_1, c_2, ..., c_N are all different.\nb_1, b_2, ..., b_N, d_1, d_2, ..., d_N are all different.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_N b_N\nc_1 d_1\nc_2 d_2\n:\nc_N d_N", "output": "Print the maximum number of friendly pairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 0\n3 1\n1 3\n4 2\n0 4\n5 5 output: 2\n\nFor example, you can pair (2,0) and (4,2), then (3,1) and (5,5).", "input: 3\n0 0\n1 1\n5 2\n2 3\n3 4\n4 5 output: 2\n\nFor example, you can pair (0,0) and (2,3), then (1,1) and (3,4).", "input: 2\n2 2\n3 3\n0 0\n1 1 output: 0\n\nIt is possible that no pair can be formed.", "input: 5\n0 0\n7 3\n2 2\n4 8\n1 6\n8 5\n6 9\n5 4\n9 1\n3 7 output: 5", "input: 5\n0 0\n1 1\n5 5\n6 6\n7 7\n2 2\n3 3\n4 4\n8 8\n9 9 output: 4"], "Pid": "p03409", "ProblemText": "Task Description: Problem Statement On a two-dimensional plane, there are N red points and N blue points.\nThe coordinates of the i-th red point are (a_i, b_i), and the coordinates of the i-th blue point are (c_i, d_i).\nA red point and a blue point can form a friendly pair when, the x-coordinate of the red point is smaller than that of the blue point, and the y-coordinate of the red point is also smaller than that of the blue point.\nAt most how many friendly pairs can you form? Note that a point cannot belong to multiple pairs.\nTask Constraint: All input values are integers.\n1 <= N <= 100\n0 <= a_i, b_i, c_i, d_i < 2N\na_1, a_2, ..., a_N, c_1, c_2, ..., c_N are all different.\nb_1, b_2, ..., b_N, d_1, d_2, ..., d_N are all different.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_N b_N\nc_1 d_1\nc_2 d_2\n:\nc_N d_N\nTask Output: Print the maximum number of friendly pairs.\nTask Samples: input: 3\n2 0\n3 1\n1 3\n4 2\n0 4\n5 5 output: 2\n\nFor example, you can pair (2,0) and (4,2), then (3,1) and (5,5).\ninput: 3\n0 0\n1 1\n5 2\n2 3\n3 4\n4 5 output: 2\n\nFor example, you can pair (0,0) and (2,3), then (1,1) and (3,4).\ninput: 2\n2 2\n3 3\n0 0\n1 1 output: 0\n\nIt is possible that no pair can be formed.\ninput: 5\n0 0\n7 3\n2 2\n4 8\n1 6\n8 5\n6 9\n5 4\n9 1\n3 7 output: 5\ninput: 5\n0 0\n1 1\n5 5\n6 6\n7 7\n2 2\n3 3\n4 4\n8 8\n9 9 output: 4\n\n" }, { "title": "", "content": "Problem Statement You are given two integer sequences, each of length N: a_1, . . . , a_N and b_1, . . . , b_N.\nThere are N^2 ways to choose two integers i and j such that 1 <= i, j <= N. For each of these N^2 pairs, we will compute a_i + b_j and write it on a sheet of paper.\nThat is, we will write N^2 integers in total.\nCompute the XOR of these N^2 integers.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03410", "ProblemText": "Task Description: Problem Statement You are given two integer sequences, each of length N: a_1, . . . , a_N and b_1, . . . , b_N.\nThere are N^2 ways to choose two integers i and j such that 1 <= i, j <= N. For each of these N^2 pairs, we will compute a_i + b_j and write it on a sheet of paper.\nThat is, we will write N^2 integers in total.\nCompute the XOR of these N^2 integers.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement On a two-dimensional plane, there are N red points and N blue points.\nThe coordinates of the i-th red point are (a_i, b_i), and the coordinates of the i-th blue point are (c_i, d_i).\nA red point and a blue point can form a friendly pair when, the x-coordinate of the red point is smaller than that of the blue point, and the y-coordinate of the red point is also smaller than that of the blue point.\nAt most how many friendly pairs can you form? Note that a point cannot belong to multiple pairs.", "constraint": "All input values are integers.\n1 <= N <= 100\n0 <= a_i, b_i, c_i, d_i < 2N\na_1, a_2, ..., a_N, c_1, c_2, ..., c_N are all different.\nb_1, b_2, ..., b_N, d_1, d_2, ..., d_N are all different.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_N b_N\nc_1 d_1\nc_2 d_2\n:\nc_N d_N", "output": "Print the maximum number of friendly pairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 0\n3 1\n1 3\n4 2\n0 4\n5 5 output: 2\n\nFor example, you can pair (2,0) and (4,2), then (3,1) and (5,5).", "input: 3\n0 0\n1 1\n5 2\n2 3\n3 4\n4 5 output: 2\n\nFor example, you can pair (0,0) and (2,3), then (1,1) and (3,4).", "input: 2\n2 2\n3 3\n0 0\n1 1 output: 0\n\nIt is possible that no pair can be formed.", "input: 5\n0 0\n7 3\n2 2\n4 8\n1 6\n8 5\n6 9\n5 4\n9 1\n3 7 output: 5", "input: 5\n0 0\n1 1\n5 5\n6 6\n7 7\n2 2\n3 3\n4 4\n8 8\n9 9 output: 4"], "Pid": "p03411", "ProblemText": "Task Description: Problem Statement On a two-dimensional plane, there are N red points and N blue points.\nThe coordinates of the i-th red point are (a_i, b_i), and the coordinates of the i-th blue point are (c_i, d_i).\nA red point and a blue point can form a friendly pair when, the x-coordinate of the red point is smaller than that of the blue point, and the y-coordinate of the red point is also smaller than that of the blue point.\nAt most how many friendly pairs can you form? Note that a point cannot belong to multiple pairs.\nTask Constraint: All input values are integers.\n1 <= N <= 100\n0 <= a_i, b_i, c_i, d_i < 2N\na_1, a_2, ..., a_N, c_1, c_2, ..., c_N are all different.\nb_1, b_2, ..., b_N, d_1, d_2, ..., d_N are all different.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_N b_N\nc_1 d_1\nc_2 d_2\n:\nc_N d_N\nTask Output: Print the maximum number of friendly pairs.\nTask Samples: input: 3\n2 0\n3 1\n1 3\n4 2\n0 4\n5 5 output: 2\n\nFor example, you can pair (2,0) and (4,2), then (3,1) and (5,5).\ninput: 3\n0 0\n1 1\n5 2\n2 3\n3 4\n4 5 output: 2\n\nFor example, you can pair (0,0) and (2,3), then (1,1) and (3,4).\ninput: 2\n2 2\n3 3\n0 0\n1 1 output: 0\n\nIt is possible that no pair can be formed.\ninput: 5\n0 0\n7 3\n2 2\n4 8\n1 6\n8 5\n6 9\n5 4\n9 1\n3 7 output: 5\ninput: 5\n0 0\n1 1\n5 5\n6 6\n7 7\n2 2\n3 3\n4 4\n8 8\n9 9 output: 4\n\n" }, { "title": "", "content": "Problem Statement You are given two integer sequences, each of length N: a_1, . . . , a_N and b_1, . . . , b_N.\nThere are N^2 ways to choose two integers i and j such that 1 <= i, j <= N. For each of these N^2 pairs, we will compute a_i + b_j and write it on a sheet of paper.\nThat is, we will write N^2 integers in total.\nCompute the XOR of these N^2 integers.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.", "constraint": "", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03412", "ProblemText": "Task Description: Problem Statement You are given two integer sequences, each of length N: a_1, . . . , a_N and b_1, . . . , b_N.\nThere are N^2 ways to choose two integers i and j such that 1 <= i, j <= N. For each of these N^2 pairs, we will compute a_i + b_j and write it on a sheet of paper.\nThat is, we will write N^2 integers in total.\nCompute the XOR of these N^2 integers.\n\nDefinition of XOR\nThe XOR of integers c_1, c_2, . . . , c_m is defined as follows:\n\nLet the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 <= k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, . . . c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.\n\nFor example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement You have an integer sequence of length N: a_1, a_2, . . . , a_N.\nYou repeatedly perform the following operation until the length of the sequence becomes 1:\n\nFirst, choose an element of the sequence.\nIf that element is at either end of the sequence, delete the element.\nIf that element is not at either end of the sequence, replace the element with the sum of the two elements that are adjacent to it. Then, delete those two elements.\n\nYou would like to maximize the final element that remains in the sequence.\nFind the maximum possible value of the final element, and the way to achieve it.", "constraint": "All input values are integers.\n2 <= N <= 1000\n|a_i| <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "In the first line, print the maximum possible value of the final element in the sequence.\nIn the second line, print the number of operations that you perform.\nIn the (2+i)-th line, if the element chosen in the i-th operation is the x-th element from the left in the sequence at that moment, print x.\nIf there are multiple ways to achieve the maximum value of the final element, any of them may be printed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 4 3 7 5 output: 11\n3\n1\n4\n2\n\nThe sequence would change as follows:\n\nAfter the first operation: 4,3,7,5\nAfter the second operation: 4,3,7\nAfter the third operation: 11(4+7)", "input: 4\n100 100 -1 100 output: 200\n2\n3\n1\nAfter the first operation: 100,200(100+100)\nAfter the second operation: 200", "input: 6\n-1 -2 -3 1 2 3 output: 4\n3\n2\n1\n2\nAfter the first operation: -4,1,2,3\nAfter the second operation: 1,2,3\nAfter the third operation: 4", "input: 9\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 5000000000\n4\n2\n2\n2\n2"], "Pid": "p03413", "ProblemText": "Task Description: Problem Statement You have an integer sequence of length N: a_1, a_2, . . . , a_N.\nYou repeatedly perform the following operation until the length of the sequence becomes 1:\n\nFirst, choose an element of the sequence.\nIf that element is at either end of the sequence, delete the element.\nIf that element is not at either end of the sequence, replace the element with the sum of the two elements that are adjacent to it. Then, delete those two elements.\n\nYou would like to maximize the final element that remains in the sequence.\nFind the maximum possible value of the final element, and the way to achieve it.\nTask Constraint: All input values are integers.\n2 <= N <= 1000\n|a_i| <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: In the first line, print the maximum possible value of the final element in the sequence.\nIn the second line, print the number of operations that you perform.\nIn the (2+i)-th line, if the element chosen in the i-th operation is the x-th element from the left in the sequence at that moment, print x.\nIf there are multiple ways to achieve the maximum value of the final element, any of them may be printed.\nTask Samples: input: 5\n1 4 3 7 5 output: 11\n3\n1\n4\n2\n\nThe sequence would change as follows:\n\nAfter the first operation: 4,3,7,5\nAfter the second operation: 4,3,7\nAfter the third operation: 11(4+7)\ninput: 4\n100 100 -1 100 output: 200\n2\n3\n1\nAfter the first operation: 100,200(100+100)\nAfter the second operation: 200\ninput: 6\n-1 -2 -3 1 2 3 output: 4\n3\n2\n1\n2\nAfter the first operation: -4,1,2,3\nAfter the second operation: 1,2,3\nAfter the third operation: 4\ninput: 9\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 5000000000\n4\n2\n2\n2\n2\n\n" }, { "title": "", "content": "Problem Statement You are given a directed graph with N vertices and M edges.\nThe vertices are numbered 1,2, . . . , N, and the edges are numbered 1,2, . . . , M.\nEdge i points from Vertex a_i to Vertex b_i.\nFor each edge, determine whether the reversion of that edge would change the number of the strongly connected components in the graph.\nHere, the reversion of Edge i means deleting Edge i and then adding a new edge that points from Vertex b_i to Vertex a_i.", "constraint": "2 <= N <= 1000\n1 <= M <= 200,000\n1 <= a_i, b_i <= N\na_i \\neq b_i\nIf i \\neq j, then a_i \\neq a_j or b_i \\neq b_j.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M", "output": "Print M lines. In the i-th line, if the reversion of Edge i would change the number of the strongly connected components in the graph, print diff; if it would not, print same.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2\n1 3\n2 3 output: same\ndiff\nsame\n\nThe number of the strongly connected components is 3 without reversion of edges, but it will become 1 if Edge 2 is reversed.", "input: 2 2\n1 2\n2 1 output: diff\ndiff\n\nReversion of an edge may result in multiple edges in the graph.", "input: 5 9\n3 2\n3 1\n4 1\n4 2\n3 5\n5 3\n3 4\n1 2\n2 5 output: same\nsame\nsame\nsame\nsame\ndiff\ndiff\ndiff\ndiff"], "Pid": "p03414", "ProblemText": "Task Description: Problem Statement You are given a directed graph with N vertices and M edges.\nThe vertices are numbered 1,2, . . . , N, and the edges are numbered 1,2, . . . , M.\nEdge i points from Vertex a_i to Vertex b_i.\nFor each edge, determine whether the reversion of that edge would change the number of the strongly connected components in the graph.\nHere, the reversion of Edge i means deleting Edge i and then adding a new edge that points from Vertex b_i to Vertex a_i.\nTask Constraint: 2 <= N <= 1000\n1 <= M <= 200,000\n1 <= a_i, b_i <= N\na_i \\neq b_i\nIf i \\neq j, then a_i \\neq a_j or b_i \\neq b_j.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Output: Print M lines. In the i-th line, if the reversion of Edge i would change the number of the strongly connected components in the graph, print diff; if it would not, print same.\nTask Samples: input: 3 3\n1 2\n1 3\n2 3 output: same\ndiff\nsame\n\nThe number of the strongly connected components is 3 without reversion of edges, but it will become 1 if Edge 2 is reversed.\ninput: 2 2\n1 2\n2 1 output: diff\ndiff\n\nReversion of an edge may result in multiple edges in the graph.\ninput: 5 9\n3 2\n3 1\n4 1\n4 2\n3 5\n5 3\n3 4\n1 2\n2 5 output: same\nsame\nsame\nsame\nsame\ndiff\ndiff\ndiff\ndiff\n\n" }, { "title": "", "content": "Problem Statement We have a 3*3 square grid, where each square contains a lowercase English letters.\nThe letter in the square at the i-th row from the top and j-th column from the left is c_{ij}.\nPrint the string of length 3 that can be obtained by concatenating the letters in the squares on the diagonal connecting the top-left and bottom-right corner of the grid, from the top-left to bottom-right.", "constraint": "Input consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nc_{11}c_{12}c_{13}\nc_{21}c_{22}c_{23}\nc_{31}c_{32}c_{33}", "output": "Print the string of length 3 that can be obtained by concatenating the letters on the diagonal connecting the top-left and bottom-right corner of the grid, from the top-left to bottom-right.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ant\nobe\nrec output: abc\n\nThe letters in the squares on the diagonal connecting the top-left and bottom-right corner of the grid are a, b and c from top-right to bottom-left. Concatenate these letters and print abc.", "input: edu\ncat\nion output: ean"], "Pid": "p03415", "ProblemText": "Task Description: Problem Statement We have a 3*3 square grid, where each square contains a lowercase English letters.\nThe letter in the square at the i-th row from the top and j-th column from the left is c_{ij}.\nPrint the string of length 3 that can be obtained by concatenating the letters in the squares on the diagonal connecting the top-left and bottom-right corner of the grid, from the top-left to bottom-right.\nTask Constraint: Input consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nc_{11}c_{12}c_{13}\nc_{21}c_{22}c_{23}\nc_{31}c_{32}c_{33}\nTask Output: Print the string of length 3 that can be obtained by concatenating the letters on the diagonal connecting the top-left and bottom-right corner of the grid, from the top-left to bottom-right.\nTask Samples: input: ant\nobe\nrec output: abc\n\nThe letters in the squares on the diagonal connecting the top-left and bottom-right corner of the grid are a, b and c from top-right to bottom-left. Concatenate these letters and print abc.\ninput: edu\ncat\nion output: ean\n\n" }, { "title": "", "content": "Problem Statement Find the number of palindromic numbers among the integers between A and B (inclusive).\nHere, a palindromic number is a positive integer whose string representation in base 10 (without leading zeros) reads the same forward and backward.", "constraint": "10000 <= A <= B <= 99999\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "Print the number of palindromic numbers among the integers between A and B (inclusive).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 11009 11332 output: 4\n\nThere are four integers that satisfy the conditions: 11011,11111,11211 and 11311.", "input: 31415 92653 output: 612"], "Pid": "p03416", "ProblemText": "Task Description: Problem Statement Find the number of palindromic numbers among the integers between A and B (inclusive).\nHere, a palindromic number is a positive integer whose string representation in base 10 (without leading zeros) reads the same forward and backward.\nTask Constraint: 10000 <= A <= B <= 99999\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: Print the number of palindromic numbers among the integers between A and B (inclusive).\nTask Samples: input: 11009 11332 output: 4\n\nThere are four integers that satisfy the conditions: 11011,11111,11211 and 11311.\ninput: 31415 92653 output: 612\n\n" }, { "title": "", "content": "Problem Statement There is a grid with infinitely many rows and columns. In this grid, there is a rectangular region with consecutive N rows and M columns, and a card is placed in each square in this region.\nThe front and back sides of these cards can be distinguished, and initially every card faces up.\nWe will perform the following operation once for each square contains a card:\n\nFor each of the following nine squares, flip the card in it if it exists: the target square itself and the eight squares that shares a corner or a side with the target square.\n\nIt can be proved that, whether each card faces up or down after all the operations does not depend on the order the operations are performed.\nFind the number of cards that face down after all the operations.", "constraint": "1 <= N,M <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of cards that face down after all the operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 0\n\nWe will flip every card in any of the four operations. Thus, after all the operations, all cards face up.", "input: 1 7 output: 5\n\nAfter all the operations, all cards except at both ends face down.", "input: 314 1592 output: 496080"], "Pid": "p03417", "ProblemText": "Task Description: Problem Statement There is a grid with infinitely many rows and columns. In this grid, there is a rectangular region with consecutive N rows and M columns, and a card is placed in each square in this region.\nThe front and back sides of these cards can be distinguished, and initially every card faces up.\nWe will perform the following operation once for each square contains a card:\n\nFor each of the following nine squares, flip the card in it if it exists: the target square itself and the eight squares that shares a corner or a side with the target square.\n\nIt can be proved that, whether each card faces up or down after all the operations does not depend on the order the operations are performed.\nFind the number of cards that face down after all the operations.\nTask Constraint: 1 <= N,M <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of cards that face down after all the operations.\nTask Samples: input: 2 2 output: 0\n\nWe will flip every card in any of the four operations. Thus, after all the operations, all cards face up.\ninput: 1 7 output: 5\n\nAfter all the operations, all cards except at both ends face down.\ninput: 314 1592 output: 496080\n\n" }, { "title": "", "content": "Problem Statement Takahashi had a pair of two positive integers not exceeding N, (a, b), which he has forgotten.\nHe remembers that the remainder of a divided by b was greater than or equal to K.\nFind the number of possible pairs that he may have had.", "constraint": "1 <= N <= 10^5\n0 <= K <= N-1\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the number of possible pairs that he may have had.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 output: 7\n\nThere are seven possible pairs: (2,3),(5,3),(2,4),(3,4),(2,5),(3,5) and (4,5).", "input: 10 0 output: 100", "input: 31415 9265 output: 287927211"], "Pid": "p03418", "ProblemText": "Task Description: Problem Statement Takahashi had a pair of two positive integers not exceeding N, (a, b), which he has forgotten.\nHe remembers that the remainder of a divided by b was greater than or equal to K.\nFind the number of possible pairs that he may have had.\nTask Constraint: 1 <= N <= 10^5\n0 <= K <= N-1\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of possible pairs that he may have had.\nTask Samples: input: 5 2 output: 7\n\nThere are seven possible pairs: (2,3),(5,3),(2,4),(3,4),(2,5),(3,5) and (4,5).\ninput: 10 0 output: 100\ninput: 31415 9265 output: 287927211\n\n" }, { "title": "", "content": "Problem Statement There is a grid with infinitely many rows and columns. In this grid, there is a rectangular region with consecutive N rows and M columns, and a card is placed in each square in this region.\nThe front and back sides of these cards can be distinguished, and initially every card faces up.\nWe will perform the following operation once for each square contains a card:\n\nFor each of the following nine squares, flip the card in it if it exists: the target square itself and the eight squares that shares a corner or a side with the target square.\n\nIt can be proved that, whether each card faces up or down after all the operations does not depend on the order the operations are performed.\nFind the number of cards that face down after all the operations.", "constraint": "1 <= N,M <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of cards that face down after all the operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 0\n\nWe will flip every card in any of the four operations. Thus, after all the operations, all cards face up.", "input: 1 7 output: 5\n\nAfter all the operations, all cards except at both ends face down.", "input: 314 1592 output: 496080"], "Pid": "p03419", "ProblemText": "Task Description: Problem Statement There is a grid with infinitely many rows and columns. In this grid, there is a rectangular region with consecutive N rows and M columns, and a card is placed in each square in this region.\nThe front and back sides of these cards can be distinguished, and initially every card faces up.\nWe will perform the following operation once for each square contains a card:\n\nFor each of the following nine squares, flip the card in it if it exists: the target square itself and the eight squares that shares a corner or a side with the target square.\n\nIt can be proved that, whether each card faces up or down after all the operations does not depend on the order the operations are performed.\nFind the number of cards that face down after all the operations.\nTask Constraint: 1 <= N,M <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of cards that face down after all the operations.\nTask Samples: input: 2 2 output: 0\n\nWe will flip every card in any of the four operations. Thus, after all the operations, all cards face up.\ninput: 1 7 output: 5\n\nAfter all the operations, all cards except at both ends face down.\ninput: 314 1592 output: 496080\n\n" }, { "title": "", "content": "Problem Statement Takahashi had a pair of two positive integers not exceeding N, (a, b), which he has forgotten.\nHe remembers that the remainder of a divided by b was greater than or equal to K.\nFind the number of possible pairs that he may have had.", "constraint": "1 <= N <= 10^5\n0 <= K <= N-1\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the number of possible pairs that he may have had.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 output: 7\n\nThere are seven possible pairs: (2,3),(5,3),(2,4),(3,4),(2,5),(3,5) and (4,5).", "input: 10 0 output: 100", "input: 31415 9265 output: 287927211"], "Pid": "p03420", "ProblemText": "Task Description: Problem Statement Takahashi had a pair of two positive integers not exceeding N, (a, b), which he has forgotten.\nHe remembers that the remainder of a divided by b was greater than or equal to K.\nFind the number of possible pairs that he may have had.\nTask Constraint: 1 <= N <= 10^5\n0 <= K <= N-1\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of possible pairs that he may have had.\nTask Samples: input: 5 2 output: 7\n\nThere are seven possible pairs: (2,3),(5,3),(2,4),(3,4),(2,5),(3,5) and (4,5).\ninput: 10 0 output: 100\ninput: 31415 9265 output: 287927211\n\n" }, { "title": "", "content": "Problem Statement Determine if there exists a sequence obtained by permuting 1,2, . . . , N that satisfies the following conditions:\n\nThe length of its longest increasing subsequence is A.\nThe length of its longest decreasing subsequence is B.\n\nIf it exists, construct one such sequence. note: Notes A subsequence of a sequence P is a sequence that can be obtained by extracting some of the elements in P without changing the order.\nA longest increasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically increasing.\nSimilarly, a longest decreasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically decreasing.", "constraint": "1 <= N,A,B <= 3* 10^5\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "If there are no sequences that satisfy the conditions, print -1.\nOtherwise, print N integers. The i-th integer should be the i-th element of the sequence that you constructed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3 2 output: 2 4 1 5 3\n\nOne longest increasing subsequence of this sequence is {2,4,5}, and one longest decreasing subsequence of it is {4,3}.", "input: 7 7 1 output: 1 2 3 4 5 6 7", "input: 300000 300000 300000 output: -1"], "Pid": "p03421", "ProblemText": "Task Description: Problem Statement Determine if there exists a sequence obtained by permuting 1,2, . . . , N that satisfies the following conditions:\n\nThe length of its longest increasing subsequence is A.\nThe length of its longest decreasing subsequence is B.\n\nIf it exists, construct one such sequence. note: Notes A subsequence of a sequence P is a sequence that can be obtained by extracting some of the elements in P without changing the order.\nA longest increasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically increasing.\nSimilarly, a longest decreasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically decreasing.\nTask Constraint: 1 <= N,A,B <= 3* 10^5\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: If there are no sequences that satisfy the conditions, print -1.\nOtherwise, print N integers. The i-th integer should be the i-th element of the sequence that you constructed.\nTask Samples: input: 5 3 2 output: 2 4 1 5 3\n\nOne longest increasing subsequence of this sequence is {2,4,5}, and one longest decreasing subsequence of it is {4,3}.\ninput: 7 7 1 output: 1 2 3 4 5 6 7\ninput: 300000 300000 300000 output: -1\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i.\nStarting from Takahashi, Takahashi and Aoki take alternate turns to perform the following operation:\n\nChoose a pile. If the i-th pile is selected and there are X stones left in the pile, remove some number of stones between 1 and floor(X/K_i) (inclusive) from the pile.\n\nThe player who first becomes unable to perform the operation loses the game. Assuming that both players play optimally, determine the winner of the game.\nHere, floor(x) represents the largest integer not greater than x.", "constraint": "1 <= N <= 200\n1 <= A_i,K_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 K_1\n:\nA_N K_N", "output": "If Takahashi will win, print Takahashi; if Aoki will win, print Aoki.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n5 2\n3 3 output: Aoki\n\nInitially, from the first pile at most floor(5/2)=2 stones can be removed at a time, and from the second pile at most floor(3/3)=1 stone can be removed at a time.\n\nIf Takahashi first takes two stones from the first pile, from the first pile at most floor(3/2)=1 stone can now be removed at a time, and from the second pile at most floor(3/3)=1 stone can be removed at a time.\nThen, if Aoki takes one stone from the second pile, from the first pile at most floor(3/2)=1 stone can be removed at a time, and from the second pile no more stones can be removed (since floor(2/3)=0).\nThen, if Takahashi takes one stone from the first pile, from the first pile at most floor(2/2)=1 stone can now be removed at a time, and from the second pile no more stones can be removed.\nThen, if Aoki takes one stone from the first pile, from the first pile at most floor(1/2)=0 stones can now be removed at a time, and from the second pile no more stones can be removed.\n\nNo more operation can be performed, thus Aoki wins. If Takahashi plays differently, Aoki can also win by play accordingly.", "input: 3\n3 2\n4 3\n5 1 output: Takahashi", "input: 3\n28 3\n16 4\n19 2 output: Aoki", "input: 4\n3141 59\n26535 897\n93 23\n8462 64 output: Takahashi"], "Pid": "p03422", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i.\nStarting from Takahashi, Takahashi and Aoki take alternate turns to perform the following operation:\n\nChoose a pile. If the i-th pile is selected and there are X stones left in the pile, remove some number of stones between 1 and floor(X/K_i) (inclusive) from the pile.\n\nThe player who first becomes unable to perform the operation loses the game. Assuming that both players play optimally, determine the winner of the game.\nHere, floor(x) represents the largest integer not greater than x.\nTask Constraint: 1 <= N <= 200\n1 <= A_i,K_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 K_1\n:\nA_N K_N\nTask Output: If Takahashi will win, print Takahashi; if Aoki will win, print Aoki.\nTask Samples: input: 2\n5 2\n3 3 output: Aoki\n\nInitially, from the first pile at most floor(5/2)=2 stones can be removed at a time, and from the second pile at most floor(3/3)=1 stone can be removed at a time.\n\nIf Takahashi first takes two stones from the first pile, from the first pile at most floor(3/2)=1 stone can now be removed at a time, and from the second pile at most floor(3/3)=1 stone can be removed at a time.\nThen, if Aoki takes one stone from the second pile, from the first pile at most floor(3/2)=1 stone can be removed at a time, and from the second pile no more stones can be removed (since floor(2/3)=0).\nThen, if Takahashi takes one stone from the first pile, from the first pile at most floor(2/2)=1 stone can now be removed at a time, and from the second pile no more stones can be removed.\nThen, if Aoki takes one stone from the first pile, from the first pile at most floor(1/2)=0 stones can now be removed at a time, and from the second pile no more stones can be removed.\n\nNo more operation can be performed, thus Aoki wins. If Takahashi plays differently, Aoki can also win by play accordingly.\ninput: 3\n3 2\n4 3\n5 1 output: Takahashi\ninput: 3\n28 3\n16 4\n19 2 output: Aoki\ninput: 4\n3141 59\n26535 897\n93 23\n8462 64 output: Takahashi\n\n" }, { "title": "", "content": "Problem Statement There are N students in a school.\nWe will divide these students into some groups, and in each group they will discuss some themes.\nYou think that groups consisting of two or less students cannot have an effective discussion, so you want to have as many groups consisting of three or more students as possible.\nDivide the students so that the number of groups consisting of three or more students is maximized.", "constraint": "1 <= N <= 1000\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If you can form at most x groups consisting of three or more students, print x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 output: 2\n\nFor example, you can form a group of three students and another of five students.", "input: 2 output: 0\n\nSometimes you cannot form any group consisting of three or more students, regardless of how you divide the students.", "input: 9 output: 3"], "Pid": "p03423", "ProblemText": "Task Description: Problem Statement There are N students in a school.\nWe will divide these students into some groups, and in each group they will discuss some themes.\nYou think that groups consisting of two or less students cannot have an effective discussion, so you want to have as many groups consisting of three or more students as possible.\nDivide the students so that the number of groups consisting of three or more students is maximized.\nTask Constraint: 1 <= N <= 1000\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If you can form at most x groups consisting of three or more students, print x.\nTask Samples: input: 8 output: 2\n\nFor example, you can form a group of three students and another of five students.\ninput: 2 output: 0\n\nSometimes you cannot form any group consisting of three or more students, regardless of how you divide the students.\ninput: 9 output: 3\n\n" }, { "title": "", "content": "Problem Statement In Japan, people make offerings called hina arare, colorful crackers, on March 3.\nWe have a bag that contains N hina arare. (From here, we call them arare. )\nIt is known that the bag either contains arare in three colors: pink, white and green, or contains arare in four colors: pink, white, green and yellow.\nWe have taken out the arare in the bag one by one, and the color of the i-th arare was S_i, where colors are represented as follows - pink: P, white: W, green: G, yellow: Y.\nIf the number of colors of the arare in the bag was three, print Three; if the number of colors was four, print Four.", "constraint": "1 <= N <= 100\nS_i is P, W, G or Y.\nThere always exist i, j and k such that S_i=P, S_j=W and S_k=G.", "input": "Input is given from Standard Input in the following format:\nN\nS_1 S_2 . . . S_N", "output": "If the number of colors of the arare in the bag was three, print Three; if the number of colors was four, print Four.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\nG W Y P Y W output: Four\n\nThe bag contained arare in four colors, so you should print Four.", "input: 9\nG W W G P W P G G output: Three\n\nThe bag contained arare in three colors, so you should print Three.", "input: 8\nP Y W G Y W Y Y output: Four"], "Pid": "p03424", "ProblemText": "Task Description: Problem Statement In Japan, people make offerings called hina arare, colorful crackers, on March 3.\nWe have a bag that contains N hina arare. (From here, we call them arare. )\nIt is known that the bag either contains arare in three colors: pink, white and green, or contains arare in four colors: pink, white, green and yellow.\nWe have taken out the arare in the bag one by one, and the color of the i-th arare was S_i, where colors are represented as follows - pink: P, white: W, green: G, yellow: Y.\nIf the number of colors of the arare in the bag was three, print Three; if the number of colors was four, print Four.\nTask Constraint: 1 <= N <= 100\nS_i is P, W, G or Y.\nThere always exist i, j and k such that S_i=P, S_j=W and S_k=G.\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1 S_2 . . . S_N\nTask Output: If the number of colors of the arare in the bag was three, print Three; if the number of colors was four, print Four.\nTask Samples: input: 6\nG W Y P Y W output: Four\n\nThe bag contained arare in four colors, so you should print Four.\ninput: 9\nG W W G P W P G G output: Three\n\nThe bag contained arare in three colors, so you should print Three.\ninput: 8\nP Y W G Y W Y Y output: Four\n\n" }, { "title": "", "content": "Problem Statement There are N people. The name of the i-th person is S_i.\nWe would like to choose three people so that the following conditions are met:\n\nThe name of every chosen person begins with M, A, R, C or H.\nThere are no multiple people whose names begin with the same letter.\n\nHow many such ways are there to choose three people, disregarding order?\nNote that the answer may not fit into a 32-bit integer type.", "constraint": "1 <= N <= 10^5\nS_i consists of uppercase English letters.\n1 <= |S_i| <= 10\nS_i \\neq S_j (i \\neq j)", "input": "Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N", "output": "If there are x ways to choose three people so that the given conditions are met, print x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nMASHIKE\nRUMOI\nOBIRA\nHABORO\nHOROKANAI output: 2\n\nWe can choose three people with the following names:\nMASHIKE, RUMOI, HABORO\nMASHIKE, RUMOI, HOROKANAI\nThus, we have two ways.", "input: 4\nZZ\nZZZ\nZ\nZZZZZZZZZZ output: 0\n\nNote that there may be no ways to choose three people so that the given conditions are met.", "input: 5\nCHOKUDAI\nRNG\nMAKOTO\nAOKI\nRINGO output: 7"], "Pid": "p03425", "ProblemText": "Task Description: Problem Statement There are N people. The name of the i-th person is S_i.\nWe would like to choose three people so that the following conditions are met:\n\nThe name of every chosen person begins with M, A, R, C or H.\nThere are no multiple people whose names begin with the same letter.\n\nHow many such ways are there to choose three people, disregarding order?\nNote that the answer may not fit into a 32-bit integer type.\nTask Constraint: 1 <= N <= 10^5\nS_i consists of uppercase English letters.\n1 <= |S_i| <= 10\nS_i \\neq S_j (i \\neq j)\nTask Input: Input is given from Standard Input in the following format:\nN\nS_1\n:\nS_N\nTask Output: If there are x ways to choose three people so that the given conditions are met, print x.\nTask Samples: input: 5\nMASHIKE\nRUMOI\nOBIRA\nHABORO\nHOROKANAI output: 2\n\nWe can choose three people with the following names:\nMASHIKE, RUMOI, HABORO\nMASHIKE, RUMOI, HOROKANAI\nThus, we have two ways.\ninput: 4\nZZ\nZZZ\nZ\nZZZZZZZZZZ output: 0\n\nNote that there may be no ways to choose three people so that the given conditions are met.\ninput: 5\nCHOKUDAI\nRNG\nMAKOTO\nAOKI\nRINGO output: 7\n\n" }, { "title": "", "content": "Problem Statement We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i, j).\nThe integers from 1 through H*W are written throughout the grid, and the integer written in Square (i, j) is A_{i, j}.\nYou, a magical girl, can teleport a piece placed on Square (i, j) to Square (x, y) by consuming |x-i|+|y-j| magic points.\nYou now have to take Q practical tests of your ability as a magical girl.\nThe i-th test will be conducted as follows:\nInitially, a piece is placed on the square where the integer L_i is written.\nLet x be the integer written in the square occupied by the piece. Repeatedly move the piece to the square where the integer x+D is written, as long as x is not R_i. The test ends when x=R_i.\nHere, it is guaranteed that R_i-L_i is a multiple of D.\nFor each test, find the sum of magic points consumed during that test.", "constraint": "1 <= H,W <= 300\n1 <= D <= H*W\n1 <= A_{i,j} <= H*W\nA_{i,j} \\neq A_{x,y} ((i,j) \\neq (x,y))\n1 <= Q <= 10^5\n1 <= L_i <= R_i <= H*W\n(R_i-L_i) is a multiple of D.", "input": "Input is given from Standard Input in the following format:\nH W D\nA_{1,1} A_{1,2} . . . A_{1, W}\n:\nA_{H, 1} A_{H, 2} . . . A_{H, W}\nQ\nL_1 R_1\n:\nL_Q R_Q", "output": "For each test, print the sum of magic points consumed during that test.\nOutput should be in the order the tests are conducted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 2\n1 4 3\n2 5 7\n8 9 6\n1\n4 8 output: 5\n\n4 is written in Square (1,2).\n6 is written in Square (3,3).\n8 is written in Square (3,1).\nThus, the sum of magic points consumed during the first test is (|3-1|+|3-2|)+(|3-3|+|1-3|)=5.", "input: 4 2 3\n3 7\n1 4\n5 2\n6 8\n2\n2 2\n2 2 output: 0\n0\n\nNote that there may be a test where the piece is not moved at all, and there may be multiple identical tests.", "input: 5 5 4\n13 25 7 15 17\n16 22 20 2 9\n14 11 12 1 19\n10 6 23 8 18\n3 21 5 24 4\n3\n13 13\n2 10\n13 13 output: 0\n5\n0"], "Pid": "p03426", "ProblemText": "Task Description: Problem Statement We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i, j).\nThe integers from 1 through H*W are written throughout the grid, and the integer written in Square (i, j) is A_{i, j}.\nYou, a magical girl, can teleport a piece placed on Square (i, j) to Square (x, y) by consuming |x-i|+|y-j| magic points.\nYou now have to take Q practical tests of your ability as a magical girl.\nThe i-th test will be conducted as follows:\nInitially, a piece is placed on the square where the integer L_i is written.\nLet x be the integer written in the square occupied by the piece. Repeatedly move the piece to the square where the integer x+D is written, as long as x is not R_i. The test ends when x=R_i.\nHere, it is guaranteed that R_i-L_i is a multiple of D.\nFor each test, find the sum of magic points consumed during that test.\nTask Constraint: 1 <= H,W <= 300\n1 <= D <= H*W\n1 <= A_{i,j} <= H*W\nA_{i,j} \\neq A_{x,y} ((i,j) \\neq (x,y))\n1 <= Q <= 10^5\n1 <= L_i <= R_i <= H*W\n(R_i-L_i) is a multiple of D.\nTask Input: Input is given from Standard Input in the following format:\nH W D\nA_{1,1} A_{1,2} . . . A_{1, W}\n:\nA_{H, 1} A_{H, 2} . . . A_{H, W}\nQ\nL_1 R_1\n:\nL_Q R_Q\nTask Output: For each test, print the sum of magic points consumed during that test.\nOutput should be in the order the tests are conducted.\nTask Samples: input: 3 3 2\n1 4 3\n2 5 7\n8 9 6\n1\n4 8 output: 5\n\n4 is written in Square (1,2).\n6 is written in Square (3,3).\n8 is written in Square (3,1).\nThus, the sum of magic points consumed during the first test is (|3-1|+|3-2|)+(|3-3|+|1-3|)=5.\ninput: 4 2 3\n3 7\n1 4\n5 2\n6 8\n2\n2 2\n2 2 output: 0\n0\n\nNote that there may be a test where the piece is not moved at all, and there may be multiple identical tests.\ninput: 5 5 4\n13 25 7 15 17\n16 22 20 2 9\n14 11 12 1 19\n10 6 23 8 18\n3 21 5 24 4\n3\n13 13\n2 10\n13 13 output: 0\n5\n0\n\n" }, { "title": "", "content": "Problem Statement Find the maximum possible sum of the digits (in base 10) of a positive integer not greater than N.", "constraint": "1<= N <= 10^{16}\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the maximum possible sum of the digits (in base 10) of a positive integer not greater than N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100 output: 18\n\nFor example, the sum of the digits in 99 is 18, which turns out to be the maximum value.", "input: 9995 output: 35\n\nFor example, the sum of the digits in 9989 is 35, which turns out to be the maximum value.", "input: 3141592653589793 output: 137"], "Pid": "p03427", "ProblemText": "Task Description: Problem Statement Find the maximum possible sum of the digits (in base 10) of a positive integer not greater than N.\nTask Constraint: 1<= N <= 10^{16}\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the maximum possible sum of the digits (in base 10) of a positive integer not greater than N.\nTask Samples: input: 100 output: 18\n\nFor example, the sum of the digits in 99 is 18, which turns out to be the maximum value.\ninput: 9995 output: 35\n\nFor example, the sum of the digits in 9989 is 35, which turns out to be the maximum value.\ninput: 3141592653589793 output: 137\n\n" }, { "title": "", "content": "Problem Statement There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i, y_i).\nLet R=10^{10^{10^{10}}}. Ringo performs the following operation:\n\nRandomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.\n\nFor every i (1 <= i <= N), find the probability that Snuke falls into the i-th hole.\nHere, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:\n\nPick two real numbers x and y independently according to uniform distribution on [-R, R].\nIf x^2+y^2<= R^2, the point (x, y) is chosen. Otherwise, repeat picking the real numbers x, y until the condition is met.", "constraint": "2 <= N <= 100\n|x_i|,|y_i| <= 10^6(1<= i<= N)\nAll given points are pairwise distinct.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N", "output": "Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.\nThe output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0\n1 1 output: 0.5\n0.5\n\nIf Ringo put Snuke in the region x+y<= 1, Snuke will fall into the first hole. The probability of this happening is very close to 0.5.\nOtherwise, Snuke will fall into the second hole, the probability of which happening is also very close to 0.5.", "input: 5\n0 0\n2 8\n4 5\n2 6\n3 10 output: 0.43160120892732328768\n0.03480224363653196956\n0.13880483535586193855\n0.00000000000000000000\n0.39479171208028279727"], "Pid": "p03428", "ProblemText": "Task Description: Problem Statement There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i, y_i).\nLet R=10^{10^{10^{10}}}. Ringo performs the following operation:\n\nRandomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.\n\nFor every i (1 <= i <= N), find the probability that Snuke falls into the i-th hole.\nHere, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:\n\nPick two real numbers x and y independently according to uniform distribution on [-R, R].\nIf x^2+y^2<= R^2, the point (x, y) is chosen. Otherwise, repeat picking the real numbers x, y until the condition is met.\nTask Constraint: 2 <= N <= 100\n|x_i|,|y_i| <= 10^6(1<= i<= N)\nAll given points are pairwise distinct.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\n:\nx_N y_N\nTask Output: Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.\nThe output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.\nTask Samples: input: 2\n0 0\n1 1 output: 0.5\n0.5\n\nIf Ringo put Snuke in the region x+y<= 1, Snuke will fall into the first hole. The probability of this happening is very close to 0.5.\nOtherwise, Snuke will fall into the second hole, the probability of which happening is also very close to 0.5.\ninput: 5\n0 0\n2 8\n4 5\n2 6\n3 10 output: 0.43160120892732328768\n0.03480224363653196956\n0.13880483535586193855\n0.00000000000000000000\n0.39479171208028279727\n\n" }, { "title": "", "content": "Problem Statement Takahashi has an N * M grid, with N horizontal rows and M vertical columns.\nDetermine if we can place A 1 * 2 tiles (1 vertical, 2 horizontal) and B 2 * 1 tiles (2 vertical, 1 horizontal) satisfying the following conditions, and construct one arrangement of the tiles if it is possible:\n\nAll the tiles must be placed on the grid.\nTiles must not stick out of the grid, and no two different tiles may intersect.\nNeither the grid nor the tiles may be rotated.\nEvery tile completely covers exactly two squares.", "constraint": "1 <= N,M <= 1000\n0 <= A,B <= 500000\nN, M, A and B are integers.", "input": "Input is given from Standard Input in the following format:\nN M A B", "output": "If it is impossible to place all the tiles, print NO.\nOtherwise, print the following:\nYES\nc_{11}. . . c_{1M}\n:\nc_{N1}. . . c_{NM}\n\nHere, c_{ij} must be one of the following characters: . , <, >, ^ and v. Represent an arrangement by using each of these characters as follows:\n\nWhen c_{ij} is . , it indicates that the square at the i-th row and j-th column is empty;\nWhen c_{ij} is <, it indicates that the square at the i-th row and j-th column is covered by the left half of a 1 * 2 tile;\nWhen c_{ij} is >, it indicates that the square at the i-th row and j-th column is covered by the right half of a 1 * 2 tile;\nWhen c_{ij} is ^, it indicates that the square at the i-th row and j-th column is covered by the top half of a 2 * 1 tile;\nWhen c_{ij} is v, it indicates that the square at the i-th row and j-th column is covered by the bottom half of a 2 * 1 tile.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 4 2 output: YES\n<><>\n^<>^\nv<>v\n\nThis is one example of a way to place four 1 * 2 tiles and three 2 * 1 tiles on a 3 * 4 grid.", "input: 4 5 5 3 output: YES\n<>..^\n^.<>v\nv<>.^\n<><>v", "input: 7 9 20 20 output: NO"], "Pid": "p03429", "ProblemText": "Task Description: Problem Statement Takahashi has an N * M grid, with N horizontal rows and M vertical columns.\nDetermine if we can place A 1 * 2 tiles (1 vertical, 2 horizontal) and B 2 * 1 tiles (2 vertical, 1 horizontal) satisfying the following conditions, and construct one arrangement of the tiles if it is possible:\n\nAll the tiles must be placed on the grid.\nTiles must not stick out of the grid, and no two different tiles may intersect.\nNeither the grid nor the tiles may be rotated.\nEvery tile completely covers exactly two squares.\nTask Constraint: 1 <= N,M <= 1000\n0 <= A,B <= 500000\nN, M, A and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M A B\nTask Output: If it is impossible to place all the tiles, print NO.\nOtherwise, print the following:\nYES\nc_{11}. . . c_{1M}\n:\nc_{N1}. . . c_{NM}\n\nHere, c_{ij} must be one of the following characters: . , <, >, ^ and v. Represent an arrangement by using each of these characters as follows:\n\nWhen c_{ij} is . , it indicates that the square at the i-th row and j-th column is empty;\nWhen c_{ij} is <, it indicates that the square at the i-th row and j-th column is covered by the left half of a 1 * 2 tile;\nWhen c_{ij} is >, it indicates that the square at the i-th row and j-th column is covered by the right half of a 1 * 2 tile;\nWhen c_{ij} is ^, it indicates that the square at the i-th row and j-th column is covered by the top half of a 2 * 1 tile;\nWhen c_{ij} is v, it indicates that the square at the i-th row and j-th column is covered by the bottom half of a 2 * 1 tile.\nTask Samples: input: 3 4 4 2 output: YES\n<><>\n^<>^\nv<>v\n\nThis is one example of a way to place four 1 * 2 tiles and three 2 * 1 tiles on a 3 * 4 grid.\ninput: 4 5 5 3 output: YES\n<>..^\n^.<>v\nv<>.^\n<><>v\ninput: 7 9 20 20 output: NO\n\n" }, { "title": "", "content": "Problem Statement Takahashi has decided to give a string to his mother.\nThe value of a string T is the length of the longest common subsequence of T and T', where T' is the string obtained by reversing T.\nThat is, the value is the longest length of the following two strings that are equal: a subsequence of T (possibly non-contiguous), and a subsequence of T' (possibly non-contiguous).\nTakahashi has a string S. He wants to give her mother a string of the highest possible value, so he would like to change at most K characters in S to any other characters in order to obtain a string of the highest possible value.\nFind the highest possible value achievable.", "constraint": "1 <= |S| <= 300\n0 <= K <= |S|\nS consists of lowercase English letters.\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nS\nK", "output": "Print the highest possible value achievable.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abcabcabc\n1 output: 7\n\nChanging the first character to c results in cbcabcabc.\nLet this tring be T, then one longest common subsequence of T and T' is cbabcbc, whose length is 7.", "input: atcodergrandcontest\n3 output: 15"], "Pid": "p03430", "ProblemText": "Task Description: Problem Statement Takahashi has decided to give a string to his mother.\nThe value of a string T is the length of the longest common subsequence of T and T', where T' is the string obtained by reversing T.\nThat is, the value is the longest length of the following two strings that are equal: a subsequence of T (possibly non-contiguous), and a subsequence of T' (possibly non-contiguous).\nTakahashi has a string S. He wants to give her mother a string of the highest possible value, so he would like to change at most K characters in S to any other characters in order to obtain a string of the highest possible value.\nFind the highest possible value achievable.\nTask Constraint: 1 <= |S| <= 300\n0 <= K <= |S|\nS consists of lowercase English letters.\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nS\nK\nTask Output: Print the highest possible value achievable.\nTask Samples: input: abcabcabc\n1 output: 7\n\nChanging the first character to c results in cbcabcabc.\nLet this tring be T, then one longest common subsequence of T and T' is cbabcbc, whose length is 7.\ninput: atcodergrandcontest\n3 output: 15\n\n" }, { "title": "", "content": "Problem Statement In Republic of At Coder, Snuke Chameleons (Family: Chamaeleonidae, Genus: Bartaberia) are very popular pets.\nRingo keeps N Snuke Chameleons in a cage.\nA Snuke Chameleon that has not eaten anything is blue. It changes its color according to the following rules:\n\nA Snuke Chameleon that is blue will change its color to red when the number of red balls it has eaten becomes strictly larger than the number of blue balls it has eaten.\nA Snuke Chameleon that is red will change its color to blue when the number of blue balls it has eaten becomes strictly larger than the number of red balls it has eaten.\n\nInitially, every Snuke Chameleon had not eaten anything. Ringo fed them by repeating the following process K times:\n\nGrab either a red ball or a blue ball.\nThrow that ball into the cage. Then, one of the chameleons eats it.\n\nAfter Ringo threw in K balls, all the chameleons were red. We are interested in the possible ways Ringo could have thrown in K balls. How many such ways are there? Find the count modulo 998244353. Here, two ways to throw in balls are considered different when there exists i such that the color of the ball that are thrown in the i-th throw is different.", "constraint": "1 <= N,K <= 5 * 10^5\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the possible ways Ringo could have thrown in K balls, modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 4 output: 7\n\nWe will use R to represent a red ball, and B to represent a blue ball. There are seven ways to throw in balls that satisfy the condition: BRRR, RBRB, RBRR, RRBB, RRBR, RRRB and RRRR.", "input: 3 7 output: 57", "input: 8 3 output: 0", "input: 8 10 output: 46", "input: 123456 234567 output: 857617983"], "Pid": "p03431", "ProblemText": "Task Description: Problem Statement In Republic of At Coder, Snuke Chameleons (Family: Chamaeleonidae, Genus: Bartaberia) are very popular pets.\nRingo keeps N Snuke Chameleons in a cage.\nA Snuke Chameleon that has not eaten anything is blue. It changes its color according to the following rules:\n\nA Snuke Chameleon that is blue will change its color to red when the number of red balls it has eaten becomes strictly larger than the number of blue balls it has eaten.\nA Snuke Chameleon that is red will change its color to blue when the number of blue balls it has eaten becomes strictly larger than the number of red balls it has eaten.\n\nInitially, every Snuke Chameleon had not eaten anything. Ringo fed them by repeating the following process K times:\n\nGrab either a red ball or a blue ball.\nThrow that ball into the cage. Then, one of the chameleons eats it.\n\nAfter Ringo threw in K balls, all the chameleons were red. We are interested in the possible ways Ringo could have thrown in K balls. How many such ways are there? Find the count modulo 998244353. Here, two ways to throw in balls are considered different when there exists i such that the color of the ball that are thrown in the i-th throw is different.\nTask Constraint: 1 <= N,K <= 5 * 10^5\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the possible ways Ringo could have thrown in K balls, modulo 998244353.\nTask Samples: input: 2 4 output: 7\n\nWe will use R to represent a red ball, and B to represent a blue ball. There are seven ways to throw in balls that satisfy the condition: BRRR, RBRB, RBRR, RRBB, RRBR, RRRB and RRRR.\ninput: 3 7 output: 57\ninput: 8 3 output: 0\ninput: 8 10 output: 46\ninput: 123456 234567 output: 857617983\n\n" }, { "title": "", "content": "Problem Statement We have an N * M grid. The square at the i-th row and j-th column will be denoted as (i, j).\nParticularly, the top-left square will be denoted as (1,1), and the bottom-right square will be denoted as (N, M).\nTakahashi painted some of the squares (possibly zero) black, and painted the other squares white.\nWe will define an integer sequence A of length N, and two integer sequences B and C of length M each, as follows:\n\nA_i(1<= i<= N) is the minimum j such that (i, j) is painted black, or M+1 if it does not exist.\nB_i(1<= i<= M) is the minimum k such that (k, i) is painted black, or N+1 if it does not exist.\nC_i(1<= i<= M) is the maximum k such that (k, i) is painted black, or 0 if it does not exist.\n\nHow many triples (A, B, C) can occur? Find the count modulo 998244353. note: Notice In this problem, the length of your source code must be at most 20000 B.\nNote that we will invalidate submissions that exceed the maximum length. partial score: Partial Score\n1500 points will be awarded for passing the test set satisfying N<= 300.", "constraint": "1 <= N <= 8000\n1 <= M <= 200\nN and M are integers.", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of triples (A, B, C), modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 output: 64\n\nSince N=2, given B_i and C_i, we can uniquely determine the arrangement of black squares in each column.\nFor each i, there are four possible pairs (B_i,C_i): (1,1), (1,2), (2,2) and (3,0). Thus, the answer is 4^M=64.", "input: 4 3 output: 2588", "input: 17 13 output: 229876268", "input: 5000 100 output: 57613837"], "Pid": "p03432", "ProblemText": "Task Description: Problem Statement We have an N * M grid. The square at the i-th row and j-th column will be denoted as (i, j).\nParticularly, the top-left square will be denoted as (1,1), and the bottom-right square will be denoted as (N, M).\nTakahashi painted some of the squares (possibly zero) black, and painted the other squares white.\nWe will define an integer sequence A of length N, and two integer sequences B and C of length M each, as follows:\n\nA_i(1<= i<= N) is the minimum j such that (i, j) is painted black, or M+1 if it does not exist.\nB_i(1<= i<= M) is the minimum k such that (k, i) is painted black, or N+1 if it does not exist.\nC_i(1<= i<= M) is the maximum k such that (k, i) is painted black, or 0 if it does not exist.\n\nHow many triples (A, B, C) can occur? Find the count modulo 998244353. note: Notice In this problem, the length of your source code must be at most 20000 B.\nNote that we will invalidate submissions that exceed the maximum length. partial score: Partial Score\n1500 points will be awarded for passing the test set satisfying N<= 300.\nTask Constraint: 1 <= N <= 8000\n1 <= M <= 200\nN and M are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of triples (A, B, C), modulo 998244353.\nTask Samples: input: 2 3 output: 64\n\nSince N=2, given B_i and C_i, we can uniquely determine the arrangement of black squares in each column.\nFor each i, there are four possible pairs (B_i,C_i): (1,1), (1,2), (2,2) and (3,0). Thus, the answer is 4^M=64.\ninput: 4 3 output: 2588\ninput: 17 13 output: 229876268\ninput: 5000 100 output: 57613837\n\n" }, { "title": "", "content": "Problem Statement\nE869120 has A 1-yen coins and infinitely many 500-yen coins.\nDetermine if he can pay exactly N yen using only these coins.", "constraint": "N is an integer between 1 and 10000 (inclusive).\nA is an integer between 0 and 1000 (inclusive).", "input": "Input is given from Standard Input in the following format:\nN\nA", "output": "If E869120 can pay exactly N yen using only his 1-yen and 500-yen coins, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2018\n218 output: Yes\n\nWe can pay 2018 yen with four 500-yen coins and 18 1-yen coins, so the answer is Yes.", "input: 2763\n0 output: No\n\nWhen we have no 1-yen coins, we can only pay a multiple of 500 yen using only 500-yen coins. Since 2763 is not a multiple of 500, we cannot pay this amount.", "input: 37\n514 output: Yes"], "Pid": "p03433", "ProblemText": "Task Description: Problem Statement\nE869120 has A 1-yen coins and infinitely many 500-yen coins.\nDetermine if he can pay exactly N yen using only these coins.\nTask Constraint: N is an integer between 1 and 10000 (inclusive).\nA is an integer between 0 and 1000 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\nA\nTask Output: If E869120 can pay exactly N yen using only his 1-yen and 500-yen coins, print Yes; otherwise, print No.\nTask Samples: input: 2018\n218 output: Yes\n\nWe can pay 2018 yen with four 500-yen coins and 18 1-yen coins, so the answer is Yes.\ninput: 2763\n0 output: No\n\nWhen we have no 1-yen coins, we can only pay a multiple of 500 yen using only 500-yen coins. Since 2763 is not a multiple of 500, we cannot pay this amount.\ninput: 37\n514 output: Yes\n\n" }, { "title": "", "content": "Problem Statement\nWe have N cards. A number a_i is written on the i-th card.\nAlice and Bob will play a game using these cards. In this game, Alice and Bob alternately take one card. Alice goes first.\nThe game ends when all the cards are taken by the two players, and the score of each player is the sum of the numbers written on the cards he/she has taken. When both players take the optimal strategy to maximize their scores, find Alice's score minus Bob's score.", "constraint": "N is an integer between 1 and 100 (inclusive).\na_i \\ (1 <= i <= N) is an integer between 1 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format: \nN\na_1 a_2 a_3 . . . a_N", "output": "Print Alice's score minus Bob's score when both players take the optimal strategy to maximize their scores.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 1 output: 2\n\nFirst, Alice will take the card with 3. Then, Bob will take the card with 1.\nThe difference of their scores will be 3 - 1 = 2.", "input: 3\n2 7 4 output: 5\n\nFirst, Alice will take the card with 7. Then, Bob will take the card with 4. Lastly, Alice will take the card with 2. The difference of their scores will be 7 - 4 + 2 = 5. The difference of their scores will be 3 - 1 = 2.", "input: 4\n20 18 2 18 output: 18"], "Pid": "p03434", "ProblemText": "Task Description: Problem Statement\nWe have N cards. A number a_i is written on the i-th card.\nAlice and Bob will play a game using these cards. In this game, Alice and Bob alternately take one card. Alice goes first.\nThe game ends when all the cards are taken by the two players, and the score of each player is the sum of the numbers written on the cards he/she has taken. When both players take the optimal strategy to maximize their scores, find Alice's score minus Bob's score.\nTask Constraint: N is an integer between 1 and 100 (inclusive).\na_i \\ (1 <= i <= N) is an integer between 1 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format: \nN\na_1 a_2 a_3 . . . a_N\nTask Output: Print Alice's score minus Bob's score when both players take the optimal strategy to maximize their scores.\nTask Samples: input: 2\n3 1 output: 2\n\nFirst, Alice will take the card with 3. Then, Bob will take the card with 1.\nThe difference of their scores will be 3 - 1 = 2.\ninput: 3\n2 7 4 output: 5\n\nFirst, Alice will take the card with 7. Then, Bob will take the card with 4. Lastly, Alice will take the card with 2. The difference of their scores will be 7 - 4 + 2 = 5. The difference of their scores will be 3 - 1 = 2.\ninput: 4\n20 18 2 18 output: 18\n\n" }, { "title": "", "content": "Problem Statement\nWe have a 3 * 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.\nAccording to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.\nDetermine if he is correct.", "constraint": "c_{i, j} \\ (1 <= i <= 3,1 <= j <= 3) is an integer between 0 and 100 (inclusive).", "input": "Input is given from Standard Input in the following format:\nc_{1,1} c_{1,2} c_{1,3}\nc_{2,1} c_{2,2} c_{2,3}\nc_{3,1} c_{3,2} c_{3,3}", "output": "If Takahashi's statement is correct, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 0 1\n2 1 2\n1 0 1 output: Yes\n\nTakahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.", "input: 2 2 2\n2 1 2\n2 2 2 output: No\n\nTakahashi is incorrect in this case.", "input: 0 8 8\n0 8 8\n0 8 8 output: Yes", "input: 1 8 6\n2 9 7\n0 7 7 output: No"], "Pid": "p03435", "ProblemText": "Task Description: Problem Statement\nWe have a 3 * 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.\nAccording to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.\nDetermine if he is correct.\nTask Constraint: c_{i, j} \\ (1 <= i <= 3,1 <= j <= 3) is an integer between 0 and 100 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nc_{1,1} c_{1,2} c_{1,3}\nc_{2,1} c_{2,2} c_{2,3}\nc_{3,1} c_{3,2} c_{3,3}\nTask Output: If Takahashi's statement is correct, print Yes; otherwise, print No.\nTask Samples: input: 1 0 1\n2 1 2\n1 0 1 output: Yes\n\nTakahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.\ninput: 2 2 2\n2 1 2\n2 2 2 output: No\n\nTakahashi is incorrect in this case.\ninput: 0 8 8\n0 8 8\n0 8 8 output: Yes\ninput: 1 8 6\n2 9 7\n0 7 7 output: No\n\n" }, { "title": "", "content": "Problem statement\nWe have an H * W grid whose squares are painted black or white. The square at the i-th row from the top and the j-th column from the left is denoted as (i, j).\nSnuke would like to play the following game on this grid. At the beginning of the game, there is a character called Kenus at square (1,1). The player repeatedly moves Kenus up, down, left or right by one square. The game is completed when Kenus reaches square (H, W) passing only white squares.\nBefore Snuke starts the game, he can change the color of some of the white squares to black. However, he cannot change the color of square (1,1) and (H, W). Also, changes of color must all be carried out before the beginning of the game.\nWhen the game is completed, Snuke's score will be the number of times he changed the color of a square before the beginning of the game. Find the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed, that is, Kenus can never reach square (H, W) regardless of how Snuke changes the color of the squares. \nThe color of the squares are given to you as characters s_{i, j}. If square (i, j) is initially painted by white, s_{i, j} is . ; if square (i, j) is initially painted by black, s_{i, j} is #.", "constraint": "H is an integer between 2 and 50 (inclusive).\nW is an integer between 2 and 50 (inclusive).\ns_{i, j} is . or # (1 <= i <= H, 1 <= j <= W).\ns_{1,1} and s_{H, W} are ..", "input": "Input is given from Standard Input in the following format:\nH W\ns_{1,1}s_{1,2}s_{1,3} . . . s_{1, W}\ns_{2,1}s_{2,2}s_{2,3} . . . s_{2, W}\n : :\ns_{H, 1}s_{H, 2}s_{H, 3} . . . s_{H, W}", "output": "Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.", "content_img": false, "lang": "", "error": false, "samples": ["input: 3 3\n..#\n#..\n... output: 2\n\nThe score 2 can be achieved by changing the color of squares as follows:", "input: 10 37\n.....................................\n...#...####...####..###...###...###..\n..#.#..#...#.##....#...#.#...#.#...#.\n..#.#..#...#.#.....#...#.#...#.#...#.\n.#...#.#..##.#.....#...#.#.###.#.###.\n.#####.####..#.....#...#..##....##...\n.#...#.#...#.#.....#...#.#...#.#...#.\n.#...#.#...#.##....#...#.#...#.#...#.\n.#...#.####...####..###...###...###..\n..................................... output: 209"], "Pid": "p03436", "ProblemText": "Task Description: Problem statement\nWe have an H * W grid whose squares are painted black or white. The square at the i-th row from the top and the j-th column from the left is denoted as (i, j).\nSnuke would like to play the following game on this grid. At the beginning of the game, there is a character called Kenus at square (1,1). The player repeatedly moves Kenus up, down, left or right by one square. The game is completed when Kenus reaches square (H, W) passing only white squares.\nBefore Snuke starts the game, he can change the color of some of the white squares to black. However, he cannot change the color of square (1,1) and (H, W). Also, changes of color must all be carried out before the beginning of the game.\nWhen the game is completed, Snuke's score will be the number of times he changed the color of a square before the beginning of the game. Find the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed, that is, Kenus can never reach square (H, W) regardless of how Snuke changes the color of the squares. \nThe color of the squares are given to you as characters s_{i, j}. If square (i, j) is initially painted by white, s_{i, j} is . ; if square (i, j) is initially painted by black, s_{i, j} is #.\nTask Constraint: H is an integer between 2 and 50 (inclusive).\nW is an integer between 2 and 50 (inclusive).\ns_{i, j} is . or # (1 <= i <= H, 1 <= j <= W).\ns_{1,1} and s_{H, W} are ..\nTask Input: Input is given from Standard Input in the following format:\nH W\ns_{1,1}s_{1,2}s_{1,3} . . . s_{1, W}\ns_{2,1}s_{2,2}s_{2,3} . . . s_{2, W}\n : :\ns_{H, 1}s_{H, 2}s_{H, 3} . . . s_{H, W}\nTask Output: Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.\nTask Samples: input: 3 3\n..#\n#..\n... output: 2\n\nThe score 2 can be achieved by changing the color of squares as follows:\ninput: 10 37\n.....................................\n...#...####...####..###...###...###..\n..#.#..#...#.##....#...#.#...#.#...#.\n..#.#..#...#.#.....#...#.#...#.#...#.\n.#...#.#..##.#.....#...#.#.###.#.###.\n.#####.####..#.....#...#..##....##...\n.#...#.#...#.#.....#...#.#...#.#...#.\n.#...#.#...#.##....#...#.#...#.#...#.\n.#...#.####...####..###...###...###..\n..................................... output: 209\n\n" }, { "title": "", "content": "Problem Statement You are given positive integers X and Y.\nIf there exists a positive integer not greater than 10^{18} that is a multiple of X but not a multiple of Y, choose one such integer and print it.\nIf it does not exist, print -1.", "constraint": "1 <= X,Y <= 10^9\nX and Y are integers.", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "Print a positive integer not greater than 10^{18} that is a multiple of X but not a multiple of Y, or print -1 if it does not exist.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 6 output: 16\n\nFor example, 16 is a multiple of 8 but not a multiple of 6.", "input: 3 3 output: -1\n\nA multiple of 3 is a multiple of 3."], "Pid": "p03437", "ProblemText": "Task Description: Problem Statement You are given positive integers X and Y.\nIf there exists a positive integer not greater than 10^{18} that is a multiple of X but not a multiple of Y, choose one such integer and print it.\nIf it does not exist, print -1.\nTask Constraint: 1 <= X,Y <= 10^9\nX and Y are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: Print a positive integer not greater than 10^{18} that is a multiple of X but not a multiple of Y, or print -1 if it does not exist.\nTask Samples: input: 8 6 output: 16\n\nFor example, 16 is a multiple of 8 but not a multiple of 6.\ninput: 3 3 output: -1\n\nA multiple of 3 is a multiple of 3.\n\n" }, { "title": "", "content": "Problem Statement You are given two integer sequences of length N: a_1, a_2, . . , a_N and b_1, b_2, . . , b_N.\nDetermine if we can repeat the following operation zero or more times so that the sequences a and b become equal.\nOperation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:\n\nAdd 2 to a_i.\nAdd 1 to b_j.", "constraint": "1 <= N <= 10 000\n0 <= a_i,b_i <= 10^9 (1 <= i <= N)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . a_N\nb_1 b_2 . . b_N", "output": "If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3\n5 2 2 output: Yes\n\nFor example, we can perform three operations as follows to do our job:\n\nFirst operation: i=1 and j=2. Now we have a = \\{3,2,3\\}, b = \\{5,3,2\\}.\nSecond operation: i=1 and j=2. Now we have a = \\{5,2,3\\}, b = \\{5,4,2\\}.\nThird operation: i=2 and j=3. Now we have a = \\{5,4,3\\}, b = \\{5,4,3\\}.", "input: 5\n3 1 4 1 5\n2 7 1 8 2 output: No", "input: 5\n2 7 1 8 2\n3 1 4 1 5 output: No"], "Pid": "p03438", "ProblemText": "Task Description: Problem Statement You are given two integer sequences of length N: a_1, a_2, . . , a_N and b_1, b_2, . . , b_N.\nDetermine if we can repeat the following operation zero or more times so that the sequences a and b become equal.\nOperation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:\n\nAdd 2 to a_i.\nAdd 1 to b_j.\nTask Constraint: 1 <= N <= 10 000\n0 <= a_i,b_i <= 10^9 (1 <= i <= N)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . a_N\nb_1 b_2 . . b_N\nTask Output: If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.\nTask Samples: input: 3\n1 2 3\n5 2 2 output: Yes\n\nFor example, we can perform three operations as follows to do our job:\n\nFirst operation: i=1 and j=2. Now we have a = \\{3,2,3\\}, b = \\{5,3,2\\}.\nSecond operation: i=1 and j=2. Now we have a = \\{5,2,3\\}, b = \\{5,4,2\\}.\nThird operation: i=2 and j=3. Now we have a = \\{5,4,3\\}, b = \\{5,4,3\\}.\ninput: 5\n3 1 4 1 5\n2 7 1 8 2 output: No\ninput: 5\n2 7 1 8 2\n3 1 4 1 5 output: No\n\n" }, { "title": "", "content": "Problem Statement This is an interactive task.\nLet N be an odd number at least 3.\nThere are N seats arranged in a circle.\nThe seats are numbered 0 through N-1.\nFor each i (0 <= i <= N - 2), Seat i and Seat i + 1 are adjacent.\nAlso, Seat N - 1 and Seat 0 are adjacent.\nEach seat is either vacant, or oppupied by a man or a woman.\nHowever, no two adjacent seats are occupied by two people of the same sex.\nIt can be shown that there is at least one empty seat where N is an odd number at least 3.\nYou are given N, but the states of the seats are not given.\nYour objective is to correctly guess the ID number of any one of the empty seats.\nTo do so, you can repeatedly send the following query:\n\nChoose an integer i (0 <= i <= N - 1). If Seat i is empty, the problem is solved. Otherwise, you are notified of the sex of the person in Seat i.\n\nGuess the ID number of an empty seat by sending at most 20 queries. note: Notice\nFlush Standard Output each time you print something. Failure to do so may result in TLE.\nImmediately terminate the program when s is Vacant. Otherwise, the verdict is indeterminate.\nThe verdict is indeterminate if more than 20 queries or ill-formatted queries are sent. Sample Input / Output 1\nIn this sample, N = 3, and Seat 0,1,2 are occupied by a man, occupied by a woman and vacant, respectively.\nInput Output\n3\\n0\\n Male\\n1\\n Female\\n2\\n Vacant", "constraint": "N is an odd number.\n3 <= N <= 99 999", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": ["In this sample, N = 3, and Seat 0,1,2 are occupied by a man, occupied by a woman and vacant, respectively. output: 3\n0\nMale\n1\nFemale\n2\nVacant"], "Pid": "p03439", "ProblemText": "Task Description: Problem Statement This is an interactive task.\nLet N be an odd number at least 3.\nThere are N seats arranged in a circle.\nThe seats are numbered 0 through N-1.\nFor each i (0 <= i <= N - 2), Seat i and Seat i + 1 are adjacent.\nAlso, Seat N - 1 and Seat 0 are adjacent.\nEach seat is either vacant, or oppupied by a man or a woman.\nHowever, no two adjacent seats are occupied by two people of the same sex.\nIt can be shown that there is at least one empty seat where N is an odd number at least 3.\nYou are given N, but the states of the seats are not given.\nYour objective is to correctly guess the ID number of any one of the empty seats.\nTo do so, you can repeatedly send the following query:\n\nChoose an integer i (0 <= i <= N - 1). If Seat i is empty, the problem is solved. Otherwise, you are notified of the sex of the person in Seat i.\n\nGuess the ID number of an empty seat by sending at most 20 queries. note: Notice\nFlush Standard Output each time you print something. Failure to do so may result in TLE.\nImmediately terminate the program when s is Vacant. Otherwise, the verdict is indeterminate.\nThe verdict is indeterminate if more than 20 queries or ill-formatted queries are sent. Sample Input / Output 1\nIn this sample, N = 3, and Seat 0,1,2 are occupied by a man, occupied by a woman and vacant, respectively.\nInput Output\n3\\n0\\n Male\\n1\\n Female\\n2\\n Vacant\nTask Constraint: N is an odd number.\n3 <= N <= 99 999\nTask Input: \nTask Output: \nTask Samples: In this sample, N = 3, and Seat 0,1,2 are occupied by a man, occupied by a woman and vacant, respectively. output: 3\n0\nMale\n1\nFemale\n2\nVacant\n\n" }, { "title": "", "content": "Problem Statement You are given a forest with N vertices and M edges. The vertices are numbered 0 through N-1.\nThe edges are given in the format (x_i, y_i), which means that Vertex x_i and y_i are connected by an edge.\nEach vertex i has a value a_i.\nYou want to add edges in the given forest so that the forest becomes connected.\nTo add an edge, you choose two different vertices i and j, then span an edge between i and j.\nThis operation costs a_i + a_j dollars, and afterward neither Vertex i nor j can be selected again.\nFind the minimum total cost required to make the forest connected, or print Impossible if it is impossible.", "constraint": "1 <= N <= 100,000\n0 <= M <= N-1\n1 <= a_i <= 10^9\n0 <= x_i,y_i <= N-1\nThe given graph is a forest.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M\na_0 a_1 . . a_{N-1}\nx_1 y_1\nx_2 y_2\n:\nx_M y_M", "output": "Print the minimum total cost required to make the forest connected, or print Impossible if it is impossible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 5\n1 2 3 4 5 6 7\n3 0\n4 0\n1 2\n1 3\n5 6 output: 7\n\nIf we connect vertices 0 and 5, the graph becomes connected, for the cost of 1 + 6 = 7 dollars.", "input: 5 0\n3 1 4 1 5 output: Impossible\n\nWe can't make the graph connected.", "input: 1 0\n5 output: 0\n\nThe graph is already connected, so we do not need to add any edges."], "Pid": "p03440", "ProblemText": "Task Description: Problem Statement You are given a forest with N vertices and M edges. The vertices are numbered 0 through N-1.\nThe edges are given in the format (x_i, y_i), which means that Vertex x_i and y_i are connected by an edge.\nEach vertex i has a value a_i.\nYou want to add edges in the given forest so that the forest becomes connected.\nTo add an edge, you choose two different vertices i and j, then span an edge between i and j.\nThis operation costs a_i + a_j dollars, and afterward neither Vertex i nor j can be selected again.\nFind the minimum total cost required to make the forest connected, or print Impossible if it is impossible.\nTask Constraint: 1 <= N <= 100,000\n0 <= M <= N-1\n1 <= a_i <= 10^9\n0 <= x_i,y_i <= N-1\nThe given graph is a forest.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_0 a_1 . . a_{N-1}\nx_1 y_1\nx_2 y_2\n:\nx_M y_M\nTask Output: Print the minimum total cost required to make the forest connected, or print Impossible if it is impossible.\nTask Samples: input: 7 5\n1 2 3 4 5 6 7\n3 0\n4 0\n1 2\n1 3\n5 6 output: 7\n\nIf we connect vertices 0 and 5, the graph becomes connected, for the cost of 1 + 6 = 7 dollars.\ninput: 5 0\n3 1 4 1 5 output: Impossible\n\nWe can't make the graph connected.\ninput: 1 0\n5 output: 0\n\nThe graph is already connected, so we do not need to add any edges.\n\n" }, { "title": "", "content": "Problem Statement We have a tree with N vertices.\nThe vertices are numbered 0 through N - 1, and the i-th edge (0 <= i < N - 1) comnnects Vertex a_i and b_i.\nFor each pair of vertices u and v (0 <= u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.\nIt is expected that one of the vertices will be invaded by aliens from outer space.\nSnuke wants to immediately identify that vertex when the invasion happens.\nTo do so, he has decided to install an antenna on some vertices.\nFirst, he decides the number of antennas, K (1 <= K <= N).\nThen, he chooses K different vertices, x_0, x_1, . . . , x_{K - 1}, on which he installs Antenna 0,1, . . . , K - 1, respectively.\nIf Vertex v is invaded by aliens, Antenna k (0 <= k < K) will output the distance d(x_k, v).\nBased on these K outputs, Snuke will identify the vertex that is invaded.\nThus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:\n\nFor each vertex u (0 <= u < N), consider the vector (d(x_0, u), . . . , d(x_{K - 1}, u)). These N vectors are distinct.\n\nFind the minumum value of K, the number of antennas, when the condition is satisfied.", "constraint": "2 <= N <= 10^5\n0 <= a_i, b_i < N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_0 b_0\na_1 b_1\n:\na_{N - 2} b_{N - 2}", "output": "Print the minumum value of K, the number of antennas, when the condition is satisfied.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 1\n0 2\n0 3\n3 4 output: 2\n\nFor example, install an antenna on Vertex 1 and 3.\nThen, the following five vectors are distinct:\n\n(d(1,0), d(3,0)) = (1,1)\n(d(1,1), d(3,1)) = (0,2)\n(d(1,2), d(3,2)) = (2,2)\n(d(1,3), d(3,3)) = (2,0)\n(d(1,4), d(3,4)) = (3,1)", "input: 2\n0 1 output: 1\n\nFor example, install an antenna on Vertex 0.", "input: 10\n2 8\n6 0\n4 1\n7 6\n2 3\n8 6\n6 9\n2 4\n5 8 output: 3\n\nFor example, install an antenna on Vertex 0,4,9."], "Pid": "p03441", "ProblemText": "Task Description: Problem Statement We have a tree with N vertices.\nThe vertices are numbered 0 through N - 1, and the i-th edge (0 <= i < N - 1) comnnects Vertex a_i and b_i.\nFor each pair of vertices u and v (0 <= u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.\nIt is expected that one of the vertices will be invaded by aliens from outer space.\nSnuke wants to immediately identify that vertex when the invasion happens.\nTo do so, he has decided to install an antenna on some vertices.\nFirst, he decides the number of antennas, K (1 <= K <= N).\nThen, he chooses K different vertices, x_0, x_1, . . . , x_{K - 1}, on which he installs Antenna 0,1, . . . , K - 1, respectively.\nIf Vertex v is invaded by aliens, Antenna k (0 <= k < K) will output the distance d(x_k, v).\nBased on these K outputs, Snuke will identify the vertex that is invaded.\nThus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:\n\nFor each vertex u (0 <= u < N), consider the vector (d(x_0, u), . . . , d(x_{K - 1}, u)). These N vectors are distinct.\n\nFind the minumum value of K, the number of antennas, when the condition is satisfied.\nTask Constraint: 2 <= N <= 10^5\n0 <= a_i, b_i < N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_0 b_0\na_1 b_1\n:\na_{N - 2} b_{N - 2}\nTask Output: Print the minumum value of K, the number of antennas, when the condition is satisfied.\nTask Samples: input: 5\n0 1\n0 2\n0 3\n3 4 output: 2\n\nFor example, install an antenna on Vertex 1 and 3.\nThen, the following five vectors are distinct:\n\n(d(1,0), d(3,0)) = (1,1)\n(d(1,1), d(3,1)) = (0,2)\n(d(1,2), d(3,2)) = (2,2)\n(d(1,3), d(3,3)) = (2,0)\n(d(1,4), d(3,4)) = (3,1)\ninput: 2\n0 1 output: 1\n\nFor example, install an antenna on Vertex 0.\ninput: 10\n2 8\n6 0\n4 1\n7 6\n2 3\n8 6\n6 9\n2 4\n5 8 output: 3\n\nFor example, install an antenna on Vertex 0,4,9.\n\n" }, { "title": "", "content": "Problem Statement You are given a tree with N vertices. The vertices are numbered 0 through N-1, and the edges are numbered 1 through N-1.\nEdge i connects Vertex x_i and y_i, and has a value a_i.\nYou can perform the following operation any number of times:\n\nChoose a simple path and a non-negative integer x, then for each edge e that belongs to the path, change a_e by executing a_e ← a_e ⊕ x (⊕ denotes XOR).\n\nYour objective is to have a_e = 0 for all edges e.\nFind the minimum number of operations required to achieve it.", "constraint": "2 <= N <= 10^5\n0 <= x_i,y_i <= N-1\n0 <= a_i <= 15\nThe given graph is a tree.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1 a_1\nx_2 y_2 a_2\n:\nx_{N-1} y_{N-1} a_{N-1}", "output": "Find the minimum number of operations required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 1 1\n0 2 3\n0 3 6\n3 4 4 output: 3\n\nThe objective can be achieved in three operations, as follows:\n\nFirst, choose the path connecting Vertex 1,2, and x = 1.\nThen, choose the path connecting Vertex 2,3, and x = 2.\nLastly, choose the path connecting Vertex 0,4, and x = 4.", "input: 2\n1 0 0 output: 0"], "Pid": "p03442", "ProblemText": "Task Description: Problem Statement You are given a tree with N vertices. The vertices are numbered 0 through N-1, and the edges are numbered 1 through N-1.\nEdge i connects Vertex x_i and y_i, and has a value a_i.\nYou can perform the following operation any number of times:\n\nChoose a simple path and a non-negative integer x, then for each edge e that belongs to the path, change a_e by executing a_e ← a_e ⊕ x (⊕ denotes XOR).\n\nYour objective is to have a_e = 0 for all edges e.\nFind the minimum number of operations required to achieve it.\nTask Constraint: 2 <= N <= 10^5\n0 <= x_i,y_i <= N-1\n0 <= a_i <= 15\nThe given graph is a tree.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1 a_1\nx_2 y_2 a_2\n:\nx_{N-1} y_{N-1} a_{N-1}\nTask Output: Find the minimum number of operations required to achieve the objective.\nTask Samples: input: 5\n0 1 1\n0 2 3\n0 3 6\n3 4 4 output: 3\n\nThe objective can be achieved in three operations, as follows:\n\nFirst, choose the path connecting Vertex 1,2, and x = 1.\nThen, choose the path connecting Vertex 2,3, and x = 2.\nLastly, choose the path connecting Vertex 0,4, and x = 4.\ninput: 2\n1 0 0 output: 0\n\n" }, { "title": "", "content": "Problem Statement There is a bridge that connects the left and right banks of a river.\nThere are 2 N doors placed at different positions on this bridge, painted in some colors.\nThe colors of the doors are represented by integers from 1 through N.\nFor each k (1 <= k <= N), there are exactly two doors painted in Color k.\nSnuke decides to cross the bridge from the left bank to the right bank.\nHe will keep on walking to the right, but the following event will happen while doing so:\n\nAt the moment Snuke touches a door painted in Color k (1 <= k <= N), he teleports to the right side of the other door painted in Color k.\n\nIt can be shown that he will eventually get to the right bank.\nFor each i (1 <= i <= 2 N - 1), the section between the i-th and (i + 1)-th doors from the left will be referred to as Section i.\nAfter crossing the bridge, Snuke recorded whether or not he walked through Section i, for each i (1 <= i <= 2 N - 1).\nThis record is given to you as a string s of length 2 N - 1.\nFor each i (1 <= i <= 2 N - 1), if Snuke walked through Section i, the i-th character in s is 1; otherwise, the i-th character is 0.\nFigure: A possible arrangement of doors for Sample Input 3\n\nDetermine if there exists an arrangement of doors that is consistent with the record. If it exists, construct one such arrangement.", "constraint": "1 <= N <= 10^5\n|s| = 2 N - 1\ns consists of 0 and 1.", "input": "Input is given from Standard Input in the following format:\nN\ns", "output": "If there is no arrangement of doors that is consistent with the record, print No.\nIf there exists such an arrangement, print Yes in the first line, then print one such arrangement in the second line, in the following format:\nc_1 c_2 . . . c_{2 N}\n\nHere, for each i (1 <= i <= 2 N), c_i is the color of the i-th door from the left.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n010 output: Yes\n1 1 2 2", "input: 2\n001 output: No", "input: 3\n10110 output: Yes\n1 3 2 1 2 3\n\nThe figure below is identical to the one in the statement.", "input: 3\n10101 output: No", "input: 6\n00111011100 output: Yes\n1 6 1 2 3 4 4 2 3 5 6 5"], "Pid": "p03443", "ProblemText": "Task Description: Problem Statement There is a bridge that connects the left and right banks of a river.\nThere are 2 N doors placed at different positions on this bridge, painted in some colors.\nThe colors of the doors are represented by integers from 1 through N.\nFor each k (1 <= k <= N), there are exactly two doors painted in Color k.\nSnuke decides to cross the bridge from the left bank to the right bank.\nHe will keep on walking to the right, but the following event will happen while doing so:\n\nAt the moment Snuke touches a door painted in Color k (1 <= k <= N), he teleports to the right side of the other door painted in Color k.\n\nIt can be shown that he will eventually get to the right bank.\nFor each i (1 <= i <= 2 N - 1), the section between the i-th and (i + 1)-th doors from the left will be referred to as Section i.\nAfter crossing the bridge, Snuke recorded whether or not he walked through Section i, for each i (1 <= i <= 2 N - 1).\nThis record is given to you as a string s of length 2 N - 1.\nFor each i (1 <= i <= 2 N - 1), if Snuke walked through Section i, the i-th character in s is 1; otherwise, the i-th character is 0.\nFigure: A possible arrangement of doors for Sample Input 3\n\nDetermine if there exists an arrangement of doors that is consistent with the record. If it exists, construct one such arrangement.\nTask Constraint: 1 <= N <= 10^5\n|s| = 2 N - 1\ns consists of 0 and 1.\nTask Input: Input is given from Standard Input in the following format:\nN\ns\nTask Output: If there is no arrangement of doors that is consistent with the record, print No.\nIf there exists such an arrangement, print Yes in the first line, then print one such arrangement in the second line, in the following format:\nc_1 c_2 . . . c_{2 N}\n\nHere, for each i (1 <= i <= 2 N), c_i is the color of the i-th door from the left.\nTask Samples: input: 2\n010 output: Yes\n1 1 2 2\ninput: 2\n001 output: No\ninput: 3\n10110 output: Yes\n1 3 2 1 2 3\n\nThe figure below is identical to the one in the statement.\ninput: 3\n10101 output: No\ninput: 6\n00111011100 output: Yes\n1 6 1 2 3 4 4 2 3 5 6 5\n\n" }, { "title": "", "content": "Problem Statement You are given a rooted tree with N vertices.\nThe vertices are numbered 0,1, . . . , N-1.\nThe root is Vertex 0, and the parent of Vertex i (i = 1,2, . . . , N-1) is Vertex p_i.\nInitially, an integer a_i is written in Vertex i.\nHere, (a_0, a_1, . . . , a_{N-1}) is a permutation of (0,1, . . . , N-1).\nYou can execute the following operation at most 25 000 times. Do it so that the value written in Vertex i becomes i.\n\nChoose a vertex and call it v. Consider the path connecting Vertex 0 and v.\nRotate the values written on the path. That is, For each edge (i, p_i) along the path, replace the value written in Vertex p_i with the value written in Vertex i (just before this operation), and replace the value of v with the value written in Vertex 0 (just before this operation).\nYou may choose Vertex 0, in which case the operation does nothing.", "constraint": "2 <= N <= 2000\n0 <= p_i <= i-1\n(a_0, a_1, ..., a_{N-1}) is a permutation of (0,1, ..., N-1).", "input": "Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_{N-1}\na_0 a_1 . . . a_{N-1}", "output": "In the first line, print the number of operations, Q.\nIn the second through (Q+1)-th lines, print the chosen vertices in order.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n0 1 2 3\n2 4 0 1 3 output: 2\n3\n4\nAfter the first operation, the values written in Vertex 0,1, .., 4 are 4,0,1,2,3.", "input: 5\n0 1 2 2\n4 3 1 2 0 output: 3\n4\n3\n1\nAfter the first operation, the values written in Vertex 0,1, .., 4 are 3,1,0,2,4.\nAfter the second operation, the values written in Vertex 0,1, .., 4 are 1,0,2,3,4."], "Pid": "p03444", "ProblemText": "Task Description: Problem Statement You are given a rooted tree with N vertices.\nThe vertices are numbered 0,1, . . . , N-1.\nThe root is Vertex 0, and the parent of Vertex i (i = 1,2, . . . , N-1) is Vertex p_i.\nInitially, an integer a_i is written in Vertex i.\nHere, (a_0, a_1, . . . , a_{N-1}) is a permutation of (0,1, . . . , N-1).\nYou can execute the following operation at most 25 000 times. Do it so that the value written in Vertex i becomes i.\n\nChoose a vertex and call it v. Consider the path connecting Vertex 0 and v.\nRotate the values written on the path. That is, For each edge (i, p_i) along the path, replace the value written in Vertex p_i with the value written in Vertex i (just before this operation), and replace the value of v with the value written in Vertex 0 (just before this operation).\nYou may choose Vertex 0, in which case the operation does nothing.\nTask Constraint: 2 <= N <= 2000\n0 <= p_i <= i-1\n(a_0, a_1, ..., a_{N-1}) is a permutation of (0,1, ..., N-1).\nTask Input: Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_{N-1}\na_0 a_1 . . . a_{N-1}\nTask Output: In the first line, print the number of operations, Q.\nIn the second through (Q+1)-th lines, print the chosen vertices in order.\nTask Samples: input: 5\n0 1 2 3\n2 4 0 1 3 output: 2\n3\n4\nAfter the first operation, the values written in Vertex 0,1, .., 4 are 4,0,1,2,3.\ninput: 5\n0 1 2 2\n4 3 1 2 0 output: 3\n4\n3\n1\nAfter the first operation, the values written in Vertex 0,1, .., 4 are 3,1,0,2,4.\nAfter the second operation, the values written in Vertex 0,1, .., 4 are 1,0,2,3,4.\n\n" }, { "title": "", "content": "Problem Statement You are given an H * W grid.\nThe square at the top-left corner will be represented by (0,0), and the square at the bottom-right corner will be represented by (H-1, W-1).\nOf those squares, N squares (x_1, y_1), (x_2, y_2), . . . , (x_N, y_N) are painted black, and the other squares are painted white.\nLet the shortest distance between white squares A and B be the minimum number of moves required to reach B from A visiting only white squares, where one can travel to an adjacent square sharing a side (up, down, left or right) in one move.\nSince there are H * W - N white squares in total, there are _{(H*W-N)}C_2 ways to choose two of the white squares.\nFor each of these _{(H*W-N)}C_2 ways, find the shortest distance between the chosen squares, then find the sum of all those distances, modulo 1 000 000 007=10^9+7.", "constraint": "1 <= H, W <= 10^6\n1 <= N <= 30\n0 <= x_i <= H-1\n0 <= y_i <= W-1\nIf i \\neq j, then either x_i \\neq x_j or y_i \\neq y_j.\nThere is at least one white square.\nFor every pair of white squares A and B, it is possible to reach B from A visiting only white squares.", "input": "Input is given from Standard Input in the following format:\nH W\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N", "output": "Print the sum of the shortest distances, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n1\n1 1 output: 20\n\nWe have the following grid (.: a white square, #: a black square).\n...\n.#.\n\nLet us assign a letter to each white square as follows:\nABC\nD#E\n\nThen, we have:\n\ndist(A, B) = 1\ndist(A, C) = 2\ndist(A, D) = 1\ndist(A, E) = 3\ndist(B, C) = 1\ndist(B, D) = 2\ndist(B, E) = 2\ndist(C, D) = 3\ndist(C, E) = 1\ndist(D, E) = 4\n\nwhere dist(A, B) is the shortest distance between A and B. The sum of these distances is 20.", "input: 2 3\n1\n1 2 output: 16\n\nLet us assign a letter to each white square as follows:\nABC\nDE#\n\nThen, we have:\n\ndist(A, B) = 1\ndist(A, C) = 2\ndist(A, D) = 1\ndist(A, E) = 2\ndist(B, C) = 1\ndist(B, D) = 2\ndist(B, E) = 1\ndist(C, D) = 3\ndist(C, E) = 2\ndist(D, E) = 1\n\nThe sum of these distances is 16.", "input: 3 3\n1\n1 1 output: 64", "input: 4 4\n4\n0 1\n1 1\n2 1\n2 2 output: 268", "input: 1000000 1000000\n1\n0 0 output: 333211937"], "Pid": "p03445", "ProblemText": "Task Description: Problem Statement You are given an H * W grid.\nThe square at the top-left corner will be represented by (0,0), and the square at the bottom-right corner will be represented by (H-1, W-1).\nOf those squares, N squares (x_1, y_1), (x_2, y_2), . . . , (x_N, y_N) are painted black, and the other squares are painted white.\nLet the shortest distance between white squares A and B be the minimum number of moves required to reach B from A visiting only white squares, where one can travel to an adjacent square sharing a side (up, down, left or right) in one move.\nSince there are H * W - N white squares in total, there are _{(H*W-N)}C_2 ways to choose two of the white squares.\nFor each of these _{(H*W-N)}C_2 ways, find the shortest distance between the chosen squares, then find the sum of all those distances, modulo 1 000 000 007=10^9+7.\nTask Constraint: 1 <= H, W <= 10^6\n1 <= N <= 30\n0 <= x_i <= H-1\n0 <= y_i <= W-1\nIf i \\neq j, then either x_i \\neq x_j or y_i \\neq y_j.\nThere is at least one white square.\nFor every pair of white squares A and B, it is possible to reach B from A visiting only white squares.\nTask Input: Input is given from Standard Input in the following format:\nH W\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\nTask Output: Print the sum of the shortest distances, modulo 10^9+7.\nTask Samples: input: 2 3\n1\n1 1 output: 20\n\nWe have the following grid (.: a white square, #: a black square).\n...\n.#.\n\nLet us assign a letter to each white square as follows:\nABC\nD#E\n\nThen, we have:\n\ndist(A, B) = 1\ndist(A, C) = 2\ndist(A, D) = 1\ndist(A, E) = 3\ndist(B, C) = 1\ndist(B, D) = 2\ndist(B, E) = 2\ndist(C, D) = 3\ndist(C, E) = 1\ndist(D, E) = 4\n\nwhere dist(A, B) is the shortest distance between A and B. The sum of these distances is 20.\ninput: 2 3\n1\n1 2 output: 16\n\nLet us assign a letter to each white square as follows:\nABC\nDE#\n\nThen, we have:\n\ndist(A, B) = 1\ndist(A, C) = 2\ndist(A, D) = 1\ndist(A, E) = 2\ndist(B, C) = 1\ndist(B, D) = 2\ndist(B, E) = 1\ndist(C, D) = 3\ndist(C, E) = 2\ndist(D, E) = 1\n\nThe sum of these distances is 16.\ninput: 3 3\n1\n1 1 output: 64\ninput: 4 4\n4\n0 1\n1 1\n2 1\n2 2 output: 268\ninput: 1000000 1000000\n1\n0 0 output: 333211937\n\n" }, { "title": "", "content": "Problem Statement We have a rectangular parallelepiped of dimensions A*B*C, divided into 1*1*1 small cubes.\nThe small cubes have coordinates from (0,0,0) through (A-1, B-1, C-1).\nLet p, q and r be integers. Consider the following set of abc small cubes:\n\\{(\\ (p + i) mod A, (q + j) mod B, (r + k) mod C\\ ) | i, j and k are integers satisfying 0 <= i < a, 0 <= j < b, 0 <= k < c \\}\nA set of small cubes that can be expressed in the above format using some integers p, q and r, is called a torus cuboid of size a*b*c.\nFind the number of the sets of torus cuboids of size a*b*c that satisfy the following condition, modulo 10^9+7:\n\nNo two torus cuboids in the set have intersection.\nThe union of all torus cuboids in the set is the whole rectangular parallelepiped of dimensions A*B*C.", "constraint": "1 <= a < A <= 100\n1 <= b < B <= 100\n1 <= c < C <= 100\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\na b c A B C", "output": "Print the number of the sets of torus cuboids of size a*b*c that satisfy the condition, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 1 2 2 2 output: 1", "input: 2 2 2 4 4 4 output: 744", "input: 2 3 4 6 7 8 output: 0", "input: 2 3 4 98 99 100 output: 471975164"], "Pid": "p03446", "ProblemText": "Task Description: Problem Statement We have a rectangular parallelepiped of dimensions A*B*C, divided into 1*1*1 small cubes.\nThe small cubes have coordinates from (0,0,0) through (A-1, B-1, C-1).\nLet p, q and r be integers. Consider the following set of abc small cubes:\n\\{(\\ (p + i) mod A, (q + j) mod B, (r + k) mod C\\ ) | i, j and k are integers satisfying 0 <= i < a, 0 <= j < b, 0 <= k < c \\}\nA set of small cubes that can be expressed in the above format using some integers p, q and r, is called a torus cuboid of size a*b*c.\nFind the number of the sets of torus cuboids of size a*b*c that satisfy the following condition, modulo 10^9+7:\n\nNo two torus cuboids in the set have intersection.\nThe union of all torus cuboids in the set is the whole rectangular parallelepiped of dimensions A*B*C.\nTask Constraint: 1 <= a < A <= 100\n1 <= b < B <= 100\n1 <= c < C <= 100\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\na b c A B C\nTask Output: Print the number of the sets of torus cuboids of size a*b*c that satisfy the condition, modulo 10^9+7.\nTask Samples: input: 1 1 1 2 2 2 output: 1\ninput: 2 2 2 4 4 4 output: 744\ninput: 2 3 4 6 7 8 output: 0\ninput: 2 3 4 98 99 100 output: 471975164\n\n" }, { "title": "", "content": "Problem Statement You went shopping to buy cakes and donuts with X yen (the currency of Japan).\nFirst, you bought one cake for A yen at a cake shop.\nThen, you bought as many donuts as possible for B yen each, at a donut shop.\nHow much do you have left after shopping?", "constraint": "1 <= A, B <= 1 000\nA + B <= X <= 10 000\nX, A and B are integers.", "input": "Input is given from Standard Input in the following format:\nX\nA\nB", "output": "Print the amount you have left after shopping.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1234\n150\n100 output: 84\n\nYou have 1234 - 150 = 1084 yen left after buying a cake.\nWith this amount, you can buy 10 donuts, after which you have 84 yen left.", "input: 1000\n108\n108 output: 28", "input: 579\n123\n456 output: 0", "input: 7477\n549\n593 output: 405"], "Pid": "p03447", "ProblemText": "Task Description: Problem Statement You went shopping to buy cakes and donuts with X yen (the currency of Japan).\nFirst, you bought one cake for A yen at a cake shop.\nThen, you bought as many donuts as possible for B yen each, at a donut shop.\nHow much do you have left after shopping?\nTask Constraint: 1 <= A, B <= 1 000\nA + B <= X <= 10 000\nX, A and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nX\nA\nB\nTask Output: Print the amount you have left after shopping.\nTask Samples: input: 1234\n150\n100 output: 84\n\nYou have 1234 - 150 = 1084 yen left after buying a cake.\nWith this amount, you can buy 10 donuts, after which you have 84 yen left.\ninput: 1000\n108\n108 output: 28\ninput: 579\n123\n456 output: 0\ninput: 7477\n549\n593 output: 405\n\n" }, { "title": "", "content": "Problem Statement You have A 500-yen coins, B 100-yen coins and C 50-yen coins (yen is the currency of Japan).\nIn how many ways can we select some of these coins so that they are X yen in total?\nCoins of the same kind cannot be distinguished. Two ways to select coins are distinguished when, for some kind of coin, the numbers of that coin are different.", "constraint": "0 <= A, B, C <= 50\nA + B + C >= 1\n50 <= X <= 20 000\nA, B and C are integers.\nX is a multiple of 50.", "input": "Input is given from Standard Input in the following format:\nA\nB\nC\nX", "output": "Print the number of ways to select coins.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n2\n2\n100 output: 2\n\nThere are two ways to satisfy the condition:\n\nSelect zero 500-yen coins, one 100-yen coin and zero 50-yen coins.\nSelect zero 500-yen coins, zero 100-yen coins and two 50-yen coins.", "input: 5\n1\n0\n150 output: 0\n\nNote that the total must be exactly X yen.", "input: 30\n40\n50\n6000 output: 213"], "Pid": "p03448", "ProblemText": "Task Description: Problem Statement You have A 500-yen coins, B 100-yen coins and C 50-yen coins (yen is the currency of Japan).\nIn how many ways can we select some of these coins so that they are X yen in total?\nCoins of the same kind cannot be distinguished. Two ways to select coins are distinguished when, for some kind of coin, the numbers of that coin are different.\nTask Constraint: 0 <= A, B, C <= 50\nA + B + C >= 1\n50 <= X <= 20 000\nA, B and C are integers.\nX is a multiple of 50.\nTask Input: Input is given from Standard Input in the following format:\nA\nB\nC\nX\nTask Output: Print the number of ways to select coins.\nTask Samples: input: 2\n2\n2\n100 output: 2\n\nThere are two ways to satisfy the condition:\n\nSelect zero 500-yen coins, one 100-yen coin and zero 50-yen coins.\nSelect zero 500-yen coins, zero 100-yen coins and two 50-yen coins.\ninput: 5\n1\n0\n150 output: 0\n\nNote that the total must be exactly X yen.\ninput: 30\n40\n50\n6000 output: 213\n\n" }, { "title": "", "content": "Problem Statement We have a 2 * N grid. We will denote the square at the i-th row and j-th column (1 <= i <= 2,1 <= j <= N) as (i, j).\nYou are initially in the top-left square, (1,1).\nYou will travel to the bottom-right square, (2, N), by repeatedly moving right or down.\nThe square (i, j) contains A_{i, j} candies.\nYou will collect all the candies you visit during the travel.\nThe top-left and bottom-right squares also contain candies, and you will also collect them.\nAt most how many candies can you collect when you choose the best way to travel?", "constraint": "1 <= N <= 100\n1 <= A_{i, j} <= 100 (1 <= i <= 2,1 <= j <= N)", "input": "Input is given from Standard Input in the following format:\nN\nA_{1,1} A_{1,2} . . . A_{1, N}\nA_{2,1} A_{2,2} . . . A_{2, N}", "output": "Print the maximum number of candies that can be collected.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3 2 2 4 1\n1 2 2 2 1 output: 14\n\nThe number of collected candies will be maximized when you:\n\nmove right three times, then move down once, then move right once.", "input: 4\n1 1 1 1\n1 1 1 1 output: 5\n\nYou will always collect the same number of candies, regardless of how you travel.", "input: 7\n3 3 4 5 4 5 3\n5 3 4 4 2 3 2 output: 29", "input: 1\n2\n3 output: 5"], "Pid": "p03449", "ProblemText": "Task Description: Problem Statement We have a 2 * N grid. We will denote the square at the i-th row and j-th column (1 <= i <= 2,1 <= j <= N) as (i, j).\nYou are initially in the top-left square, (1,1).\nYou will travel to the bottom-right square, (2, N), by repeatedly moving right or down.\nThe square (i, j) contains A_{i, j} candies.\nYou will collect all the candies you visit during the travel.\nThe top-left and bottom-right squares also contain candies, and you will also collect them.\nAt most how many candies can you collect when you choose the best way to travel?\nTask Constraint: 1 <= N <= 100\n1 <= A_{i, j} <= 100 (1 <= i <= 2,1 <= j <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{1,1} A_{1,2} . . . A_{1, N}\nA_{2,1} A_{2,2} . . . A_{2, N}\nTask Output: Print the maximum number of candies that can be collected.\nTask Samples: input: 5\n3 2 2 4 1\n1 2 2 2 1 output: 14\n\nThe number of collected candies will be maximized when you:\n\nmove right three times, then move down once, then move right once.\ninput: 4\n1 1 1 1\n1 1 1 1 output: 5\n\nYou will always collect the same number of candies, regardless of how you travel.\ninput: 7\n3 3 4 5 4 5 3\n5 3 4 4 2 3 2 output: 29\ninput: 1\n2\n3 output: 5\n\n" }, { "title": "", "content": "Problem Statement There are N people standing on the x-axis.\nLet the coordinate of Person i be x_i.\nFor every i, x_i is an integer between 0 and 10^9 (inclusive).\nIt is possible that more than one person is standing at the same coordinate.\nYou will given M pieces of information regarding the positions of these people.\nThe i-th piece of information has the form (L_i, R_i, D_i).\nThis means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.\nIt turns out that some of these M pieces of information may be incorrect.\nDetermine if there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with the given pieces of information.", "constraint": "1 <= N <= 100 000\n0 <= M <= 200 000\n1 <= L_i, R_i <= N (1 <= i <= M)\n0 <= D_i <= 10 000 (1 <= i <= M)\nL_i \\neq R_i (1 <= i <= M)\nIf i \\neq j, then (L_i, R_i) \\neq (L_j, R_j) and (L_i, R_i) \\neq (R_j, L_j).\nD_i are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nL_1 R_1 D_1\nL_2 R_2 D_2\n:\nL_M R_M D_M", "output": "If there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 1\n2 3 1\n1 3 2 output: Yes\n\nSome possible sets of values (x_1, x_2, x_3) are (0,1,2) and (101,102,103).", "input: 3 3\n1 2 1\n2 3 1\n1 3 5 output: No\n\nIf the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.", "input: 4 3\n2 1 1\n2 3 5\n3 4 2 output: Yes", "input: 10 3\n8 7 100\n7 9 100\n9 8 100 output: No", "input: 100 0 output: Yes"], "Pid": "p03450", "ProblemText": "Task Description: Problem Statement There are N people standing on the x-axis.\nLet the coordinate of Person i be x_i.\nFor every i, x_i is an integer between 0 and 10^9 (inclusive).\nIt is possible that more than one person is standing at the same coordinate.\nYou will given M pieces of information regarding the positions of these people.\nThe i-th piece of information has the form (L_i, R_i, D_i).\nThis means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.\nIt turns out that some of these M pieces of information may be incorrect.\nDetermine if there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with the given pieces of information.\nTask Constraint: 1 <= N <= 100 000\n0 <= M <= 200 000\n1 <= L_i, R_i <= N (1 <= i <= M)\n0 <= D_i <= 10 000 (1 <= i <= M)\nL_i \\neq R_i (1 <= i <= M)\nIf i \\neq j, then (L_i, R_i) \\neq (L_j, R_j) and (L_i, R_i) \\neq (R_j, L_j).\nD_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nL_1 R_1 D_1\nL_2 R_2 D_2\n:\nL_M R_M D_M\nTask Output: If there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.\nTask Samples: input: 3 3\n1 2 1\n2 3 1\n1 3 2 output: Yes\n\nSome possible sets of values (x_1, x_2, x_3) are (0,1,2) and (101,102,103).\ninput: 3 3\n1 2 1\n2 3 1\n1 3 5 output: No\n\nIf the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.\ninput: 4 3\n2 1 1\n2 3 5\n3 4 2 output: Yes\ninput: 10 3\n8 7 100\n7 9 100\n9 8 100 output: No\ninput: 100 0 output: Yes\n\n" }, { "title": "", "content": "Problem Statement We have a 2 * N grid. We will denote the square at the i-th row and j-th column (1 <= i <= 2,1 <= j <= N) as (i, j).\nYou are initially in the top-left square, (1,1).\nYou will travel to the bottom-right square, (2, N), by repeatedly moving right or down.\nThe square (i, j) contains A_{i, j} candies.\nYou will collect all the candies you visit during the travel.\nThe top-left and bottom-right squares also contain candies, and you will also collect them.\nAt most how many candies can you collect when you choose the best way to travel?", "constraint": "1 <= N <= 100\n1 <= A_{i, j} <= 100 (1 <= i <= 2,1 <= j <= N)", "input": "Input is given from Standard Input in the following format:\nN\nA_{1,1} A_{1,2} . . . A_{1, N}\nA_{2,1} A_{2,2} . . . A_{2, N}", "output": "Print the maximum number of candies that can be collected.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3 2 2 4 1\n1 2 2 2 1 output: 14\n\nThe number of collected candies will be maximized when you:\n\nmove right three times, then move down once, then move right once.", "input: 4\n1 1 1 1\n1 1 1 1 output: 5\n\nYou will always collect the same number of candies, regardless of how you travel.", "input: 7\n3 3 4 5 4 5 3\n5 3 4 4 2 3 2 output: 29", "input: 1\n2\n3 output: 5"], "Pid": "p03451", "ProblemText": "Task Description: Problem Statement We have a 2 * N grid. We will denote the square at the i-th row and j-th column (1 <= i <= 2,1 <= j <= N) as (i, j).\nYou are initially in the top-left square, (1,1).\nYou will travel to the bottom-right square, (2, N), by repeatedly moving right or down.\nThe square (i, j) contains A_{i, j} candies.\nYou will collect all the candies you visit during the travel.\nThe top-left and bottom-right squares also contain candies, and you will also collect them.\nAt most how many candies can you collect when you choose the best way to travel?\nTask Constraint: 1 <= N <= 100\n1 <= A_{i, j} <= 100 (1 <= i <= 2,1 <= j <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\nA_{1,1} A_{1,2} . . . A_{1, N}\nA_{2,1} A_{2,2} . . . A_{2, N}\nTask Output: Print the maximum number of candies that can be collected.\nTask Samples: input: 5\n3 2 2 4 1\n1 2 2 2 1 output: 14\n\nThe number of collected candies will be maximized when you:\n\nmove right three times, then move down once, then move right once.\ninput: 4\n1 1 1 1\n1 1 1 1 output: 5\n\nYou will always collect the same number of candies, regardless of how you travel.\ninput: 7\n3 3 4 5 4 5 3\n5 3 4 4 2 3 2 output: 29\ninput: 1\n2\n3 output: 5\n\n" }, { "title": "", "content": "Problem Statement There are N people standing on the x-axis.\nLet the coordinate of Person i be x_i.\nFor every i, x_i is an integer between 0 and 10^9 (inclusive).\nIt is possible that more than one person is standing at the same coordinate.\nYou will given M pieces of information regarding the positions of these people.\nThe i-th piece of information has the form (L_i, R_i, D_i).\nThis means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.\nIt turns out that some of these M pieces of information may be incorrect.\nDetermine if there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with the given pieces of information.", "constraint": "1 <= N <= 100 000\n0 <= M <= 200 000\n1 <= L_i, R_i <= N (1 <= i <= M)\n0 <= D_i <= 10 000 (1 <= i <= M)\nL_i \\neq R_i (1 <= i <= M)\nIf i \\neq j, then (L_i, R_i) \\neq (L_j, R_j) and (L_i, R_i) \\neq (R_j, L_j).\nD_i are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nL_1 R_1 D_1\nL_2 R_2 D_2\n:\nL_M R_M D_M", "output": "If there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 1\n2 3 1\n1 3 2 output: Yes\n\nSome possible sets of values (x_1, x_2, x_3) are (0,1,2) and (101,102,103).", "input: 3 3\n1 2 1\n2 3 1\n1 3 5 output: No\n\nIf the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.", "input: 4 3\n2 1 1\n2 3 5\n3 4 2 output: Yes", "input: 10 3\n8 7 100\n7 9 100\n9 8 100 output: No", "input: 100 0 output: Yes"], "Pid": "p03452", "ProblemText": "Task Description: Problem Statement There are N people standing on the x-axis.\nLet the coordinate of Person i be x_i.\nFor every i, x_i is an integer between 0 and 10^9 (inclusive).\nIt is possible that more than one person is standing at the same coordinate.\nYou will given M pieces of information regarding the positions of these people.\nThe i-th piece of information has the form (L_i, R_i, D_i).\nThis means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.\nIt turns out that some of these M pieces of information may be incorrect.\nDetermine if there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with the given pieces of information.\nTask Constraint: 1 <= N <= 100 000\n0 <= M <= 200 000\n1 <= L_i, R_i <= N (1 <= i <= M)\n0 <= D_i <= 10 000 (1 <= i <= M)\nL_i \\neq R_i (1 <= i <= M)\nIf i \\neq j, then (L_i, R_i) \\neq (L_j, R_j) and (L_i, R_i) \\neq (R_j, L_j).\nD_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nL_1 R_1 D_1\nL_2 R_2 D_2\n:\nL_M R_M D_M\nTask Output: If there exists a set of values (x_1, x_2, . . . , x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.\nTask Samples: input: 3 3\n1 2 1\n2 3 1\n1 3 2 output: Yes\n\nSome possible sets of values (x_1, x_2, x_3) are (0,1,2) and (101,102,103).\ninput: 3 3\n1 2 1\n2 3 1\n1 3 5 output: No\n\nIf the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.\ninput: 4 3\n2 1 1\n2 3 5\n3 4 2 output: Yes\ninput: 10 3\n8 7 100\n7 9 100\n9 8 100 output: No\ninput: 100 0 output: Yes\n\n" }, { "title": "", "content": "Problem Statement We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.\nThe i-th edge connects Vertex U_i and Vertex V_i.\nThe time it takes to traverse this edge is D_i minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).\nTakahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible.\nFind the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 10^9 + 7.", "constraint": "1 <= N <= 100 000\n1 <= M <= 200 000\n1 <= S, T <= N\nS \\neq T\n1 <= U_i, V_i <= N (1 <= i <= M)\n1 <= D_i <= 10^9 (1 <= i <= M)\nIf i \\neq j, then (U_i, V_i) \\neq (U_j, V_j) and (U_i, V_i) \\neq (V_j, U_j).\nU_i \\neq V_i (1 <= i <= M)\nD_i are integers.\nThe given graph is connected.", "input": "Input is given from Standard Input in the following format:\nN M\nS T\nU_1 V_1 D_1\nU_2 V_2 D_2\n:\nU_M V_M D_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n1 3\n1 2 1\n2 3 1\n3 4 1\n4 1 1 output: 2\n\nThere are two ways to choose shortest paths that satisfies the condition:\n\nTakahashi chooses the path 1 \\rightarrow 2 \\rightarrow 3, and Aoki chooses the path 3 \\rightarrow 4 \\rightarrow 1.\nTakahashi chooses the path 1 \\rightarrow 4 \\rightarrow 3, and Aoki chooses the path 3 \\rightarrow 2 \\rightarrow 1.", "input: 3 3\n1 3\n1 2 1\n2 3 1\n3 1 2 output: 2", "input: 3 3\n1 3\n1 2 1\n2 3 1\n3 1 2 output: 2", "input: 8 13\n4 2\n7 3 9\n6 2 3\n1 6 4\n7 6 9\n3 8 9\n1 2 2\n2 8 12\n8 6 9\n2 5 5\n4 2 18\n5 3 7\n5 1 515371567\n4 8 6 output: 6"], "Pid": "p03453", "ProblemText": "Task Description: Problem Statement We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.\nThe i-th edge connects Vertex U_i and Vertex V_i.\nThe time it takes to traverse this edge is D_i minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).\nTakahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible.\nFind the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 10^9 + 7.\nTask Constraint: 1 <= N <= 100 000\n1 <= M <= 200 000\n1 <= S, T <= N\nS \\neq T\n1 <= U_i, V_i <= N (1 <= i <= M)\n1 <= D_i <= 10^9 (1 <= i <= M)\nIf i \\neq j, then (U_i, V_i) \\neq (U_j, V_j) and (U_i, V_i) \\neq (V_j, U_j).\nU_i \\neq V_i (1 <= i <= M)\nD_i are integers.\nThe given graph is connected.\nTask Input: Input is given from Standard Input in the following format:\nN M\nS T\nU_1 V_1 D_1\nU_2 V_2 D_2\n:\nU_M V_M D_M\nTask Output: Print the answer.\nTask Samples: input: 4 4\n1 3\n1 2 1\n2 3 1\n3 4 1\n4 1 1 output: 2\n\nThere are two ways to choose shortest paths that satisfies the condition:\n\nTakahashi chooses the path 1 \\rightarrow 2 \\rightarrow 3, and Aoki chooses the path 3 \\rightarrow 4 \\rightarrow 1.\nTakahashi chooses the path 1 \\rightarrow 4 \\rightarrow 3, and Aoki chooses the path 3 \\rightarrow 2 \\rightarrow 1.\ninput: 3 3\n1 3\n1 2 1\n2 3 1\n3 1 2 output: 2\ninput: 3 3\n1 3\n1 2 1\n2 3 1\n3 1 2 output: 2\ninput: 8 13\n4 2\n7 3 9\n6 2 3\n1 6 4\n7 6 9\n3 8 9\n1 2 2\n2 8 12\n8 6 9\n2 5 5\n4 2 18\n5 3 7\n5 1 515371567\n4 8 6 output: 6\n\n" }, { "title": "", "content": "Problem Statement For a positive integer n, let us define f(n) as the number of digits in base 10.\nYou are given an integer S.\nCount the number of the pairs of positive integers (l, r) (l <= r) such that f(l) + f(l + 1) + . . . + f(r) = S, and find the count modulo 10^9 + 7.", "constraint": "1 <= S <= 10^8", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 output: 9\n\nThere are nine pairs (l, r) that satisfies the condition: (1,1), (2,2), ..., (9,9).", "input: 2 output: 98\n\nThere are 98 pairs (l, r) that satisfies the condition, such as (1,2) and (33,33).", "input: 123 output: 460191684", "input: 36018 output: 966522825", "input: 1000 output: 184984484"], "Pid": "p03454", "ProblemText": "Task Description: Problem Statement For a positive integer n, let us define f(n) as the number of digits in base 10.\nYou are given an integer S.\nCount the number of the pairs of positive integers (l, r) (l <= r) such that f(l) + f(l + 1) + . . . + f(r) = S, and find the count modulo 10^9 + 7.\nTask Constraint: 1 <= S <= 10^8\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the answer.\nTask Samples: input: 1 output: 9\n\nThere are nine pairs (l, r) that satisfies the condition: (1,1), (2,2), ..., (9,9).\ninput: 2 output: 98\n\nThere are 98 pairs (l, r) that satisfies the condition, such as (1,2) and (33,33).\ninput: 123 output: 460191684\ninput: 36018 output: 966522825\ninput: 1000 output: 184984484\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer found two positive integers, a and b.\nDetermine whether the product of a and b is even or odd.", "constraint": "1 <= a,b <= 10000\na and b are integers.", "input": "Input is given from Standard Input in the following format:\na b", "output": "If the product is odd, print Odd; if it is even, print Even.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 output: Even\n\nAs 3 * 4 = 12 is even, print Even.", "input: 1 21 output: Odd\n\nAs 1 * 21 = 21 is odd, print Odd."], "Pid": "p03455", "ProblemText": "Task Description: Problem Statement At Co Deer the deer found two positive integers, a and b.\nDetermine whether the product of a and b is even or odd.\nTask Constraint: 1 <= a,b <= 10000\na and b are integers.\nTask Input: Input is given from Standard Input in the following format:\na b\nTask Output: If the product is odd, print Odd; if it is even, print Even.\nTask Samples: input: 3 4 output: Even\n\nAs 3 * 4 = 12 is even, print Even.\ninput: 1 21 output: Odd\n\nAs 1 * 21 = 21 is odd, print Odd.\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer has found two positive integers, a and b.\nDetermine whether the concatenation of a and b in this order is a square number.", "constraint": "1 <= a,b <= 100\na and b are integers.", "input": "Input is given from Standard Input in the following format:\na b", "output": "If the concatenation of a and b in this order is a square number, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 21 output: Yes\n\nAs 121 = 11 * 11, it is a square number.", "input: 100 100 output: No\n\n100100 is not a square number.", "input: 12 10 output: No"], "Pid": "p03456", "ProblemText": "Task Description: Problem Statement At Co Deer the deer has found two positive integers, a and b.\nDetermine whether the concatenation of a and b in this order is a square number.\nTask Constraint: 1 <= a,b <= 100\na and b are integers.\nTask Input: Input is given from Standard Input in the following format:\na b\nTask Output: If the concatenation of a and b in this order is a square number, print Yes; otherwise, print No.\nTask Samples: input: 1 21 output: Yes\n\nAs 121 = 11 * 11, it is a square number.\ninput: 100 100 output: No\n\n100100 is not a square number.\ninput: 12 10 output: No\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer is going on a trip in a two-dimensional plane.\nIn his plan, he will depart from point (0,0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i, y_i) at time t_i.\nIf At Co Deer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1, y), (x-1, y), (x, y+1) and (x, y-1).\nNote that he cannot stay at his place.\nDetermine whether he can carry out his plan.", "constraint": "1 <= N <= 10^5\n0 <= x_i <= 10^5\n0 <= y_i <= 10^5\n1 <= t_i <= 10^5\nt_i < t_{i+1} (1 <= i <= N-1)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nt_1 x_1 y_1\nt_2 x_2 y_2\n:\nt_N x_N y_N", "output": "If At Co Deer can carry out his plan, print Yes; if he cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 1 2\n6 1 1 output: Yes\n\nFor example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).", "input: 1\n2 100 100 output: No\n\nIt is impossible to be at (100,100) two seconds after being at (0,0).", "input: 2\n5 1 1\n100 1 1 output: No"], "Pid": "p03457", "ProblemText": "Task Description: Problem Statement At Co Deer the deer is going on a trip in a two-dimensional plane.\nIn his plan, he will depart from point (0,0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i, y_i) at time t_i.\nIf At Co Deer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1, y), (x-1, y), (x, y+1) and (x, y-1).\nNote that he cannot stay at his place.\nDetermine whether he can carry out his plan.\nTask Constraint: 1 <= N <= 10^5\n0 <= x_i <= 10^5\n0 <= y_i <= 10^5\n1 <= t_i <= 10^5\nt_i < t_{i+1} (1 <= i <= N-1)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nt_1 x_1 y_1\nt_2 x_2 y_2\n:\nt_N x_N y_N\nTask Output: If At Co Deer can carry out his plan, print Yes; if he cannot, print No.\nTask Samples: input: 2\n3 1 2\n6 1 1 output: Yes\n\nFor example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).\ninput: 1\n2 100 100 output: No\n\nIt is impossible to be at (100,100) two seconds after being at (0,0).\ninput: 2\n5 1 1\n100 1 1 output: No\n\n" }, { "title": "", "content": "Problem Statement At Co Deer is thinking of painting an infinite two-dimensional grid in a checked pattern of side K.\nHere, a checked pattern of side K is a pattern where each square is painted black or white so that each connected component of each color is a K * K square.\nBelow is an example of a checked pattern of side 3:\n\nAt Co Deer has N desires.\nThe i-th desire is represented by x_i, y_i and c_i.\nIf c_i is B, it means that he wants to paint the square (x_i, y_i) black; if c_i is W, he wants to paint the square (x_i, y_i) white.\nAt most how many desires can he satisfy at the same time?", "constraint": "1 <= N <= 10^5\n1 <= K <= 1000\n0 <= x_i <= 10^9\n0 <= y_i <= 10^9\nIf i != j, then (x_i,y_i) != (x_j,y_j).\nc_i is B or W.\nN, K, x_i and y_i are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nx_1 y_1 c_1\nx_2 y_2 c_2\n:\nx_N y_N c_N", "output": "Print the maximum number of desires that can be satisfied at the same time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n0 1 W\n1 2 W\n5 3 B\n5 4 B output: 4\n\nHe can satisfy all his desires by painting as shown in the example above.", "input: 2 1000\n0 0 B\n0 1 W output: 2", "input: 6 2\n1 2 B\n2 1 W\n2 2 B\n1 0 B\n0 6 W\n4 5 W output: 4"], "Pid": "p03458", "ProblemText": "Task Description: Problem Statement At Co Deer is thinking of painting an infinite two-dimensional grid in a checked pattern of side K.\nHere, a checked pattern of side K is a pattern where each square is painted black or white so that each connected component of each color is a K * K square.\nBelow is an example of a checked pattern of side 3:\n\nAt Co Deer has N desires.\nThe i-th desire is represented by x_i, y_i and c_i.\nIf c_i is B, it means that he wants to paint the square (x_i, y_i) black; if c_i is W, he wants to paint the square (x_i, y_i) white.\nAt most how many desires can he satisfy at the same time?\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= 1000\n0 <= x_i <= 10^9\n0 <= y_i <= 10^9\nIf i != j, then (x_i,y_i) != (x_j,y_j).\nc_i is B or W.\nN, K, x_i and y_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nx_1 y_1 c_1\nx_2 y_2 c_2\n:\nx_N y_N c_N\nTask Output: Print the maximum number of desires that can be satisfied at the same time.\nTask Samples: input: 4 3\n0 1 W\n1 2 W\n5 3 B\n5 4 B output: 4\n\nHe can satisfy all his desires by painting as shown in the example above.\ninput: 2 1000\n0 0 B\n0 1 W output: 2\ninput: 6 2\n1 2 B\n2 1 W\n2 2 B\n1 0 B\n0 6 W\n4 5 W output: 4\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer is going on a trip in a two-dimensional plane.\nIn his plan, he will depart from point (0,0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i, y_i) at time t_i.\nIf At Co Deer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1, y), (x-1, y), (x, y+1) and (x, y-1).\nNote that he cannot stay at his place.\nDetermine whether he can carry out his plan.", "constraint": "1 <= N <= 10^5\n0 <= x_i <= 10^5\n0 <= y_i <= 10^5\n1 <= t_i <= 10^5\nt_i < t_{i+1} (1 <= i <= N-1)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nt_1 x_1 y_1\nt_2 x_2 y_2\n:\nt_N x_N y_N", "output": "If At Co Deer can carry out his plan, print Yes; if he cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 1 2\n6 1 1 output: Yes\n\nFor example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).", "input: 1\n2 100 100 output: No\n\nIt is impossible to be at (100,100) two seconds after being at (0,0).", "input: 2\n5 1 1\n100 1 1 output: No"], "Pid": "p03459", "ProblemText": "Task Description: Problem Statement At Co Deer the deer is going on a trip in a two-dimensional plane.\nIn his plan, he will depart from point (0,0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i, y_i) at time t_i.\nIf At Co Deer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1, y), (x-1, y), (x, y+1) and (x, y-1).\nNote that he cannot stay at his place.\nDetermine whether he can carry out his plan.\nTask Constraint: 1 <= N <= 10^5\n0 <= x_i <= 10^5\n0 <= y_i <= 10^5\n1 <= t_i <= 10^5\nt_i < t_{i+1} (1 <= i <= N-1)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nt_1 x_1 y_1\nt_2 x_2 y_2\n:\nt_N x_N y_N\nTask Output: If At Co Deer can carry out his plan, print Yes; if he cannot, print No.\nTask Samples: input: 2\n3 1 2\n6 1 1 output: Yes\n\nFor example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).\ninput: 1\n2 100 100 output: No\n\nIt is impossible to be at (100,100) two seconds after being at (0,0).\ninput: 2\n5 1 1\n100 1 1 output: No\n\n" }, { "title": "", "content": "Problem Statement At Co Deer is thinking of painting an infinite two-dimensional grid in a checked pattern of side K.\nHere, a checked pattern of side K is a pattern where each square is painted black or white so that each connected component of each color is a K * K square.\nBelow is an example of a checked pattern of side 3:\n\nAt Co Deer has N desires.\nThe i-th desire is represented by x_i, y_i and c_i.\nIf c_i is B, it means that he wants to paint the square (x_i, y_i) black; if c_i is W, he wants to paint the square (x_i, y_i) white.\nAt most how many desires can he satisfy at the same time?", "constraint": "1 <= N <= 10^5\n1 <= K <= 1000\n0 <= x_i <= 10^9\n0 <= y_i <= 10^9\nIf i != j, then (x_i,y_i) != (x_j,y_j).\nc_i is B or W.\nN, K, x_i and y_i are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nx_1 y_1 c_1\nx_2 y_2 c_2\n:\nx_N y_N c_N", "output": "Print the maximum number of desires that can be satisfied at the same time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n0 1 W\n1 2 W\n5 3 B\n5 4 B output: 4\n\nHe can satisfy all his desires by painting as shown in the example above.", "input: 2 1000\n0 0 B\n0 1 W output: 2", "input: 6 2\n1 2 B\n2 1 W\n2 2 B\n1 0 B\n0 6 W\n4 5 W output: 4"], "Pid": "p03460", "ProblemText": "Task Description: Problem Statement At Co Deer is thinking of painting an infinite two-dimensional grid in a checked pattern of side K.\nHere, a checked pattern of side K is a pattern where each square is painted black or white so that each connected component of each color is a K * K square.\nBelow is an example of a checked pattern of side 3:\n\nAt Co Deer has N desires.\nThe i-th desire is represented by x_i, y_i and c_i.\nIf c_i is B, it means that he wants to paint the square (x_i, y_i) black; if c_i is W, he wants to paint the square (x_i, y_i) white.\nAt most how many desires can he satisfy at the same time?\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= 1000\n0 <= x_i <= 10^9\n0 <= y_i <= 10^9\nIf i != j, then (x_i,y_i) != (x_j,y_j).\nc_i is B or W.\nN, K, x_i and y_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nx_1 y_1 c_1\nx_2 y_2 c_2\n:\nx_N y_N c_N\nTask Output: Print the maximum number of desires that can be satisfied at the same time.\nTask Samples: input: 4 3\n0 1 W\n1 2 W\n5 3 B\n5 4 B output: 4\n\nHe can satisfy all his desires by painting as shown in the example above.\ninput: 2 1000\n0 0 B\n0 1 W output: 2\ninput: 6 2\n1 2 B\n2 1 W\n2 2 B\n1 0 B\n0 6 W\n4 5 W output: 4\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer wants a directed graph that satisfies the following conditions:\n\nThe number of vertices, N, is at most 300.\nThere must not be self-loops or multiple edges.\nThe vertices are numbered from 1 through N.\nEach edge has either an integer weight between 0 and 100 (inclusive), or a label X or Y.\nFor every pair of two integers (x, y) such that 1 <= x <= A, 1 <= y <= B,\n the shortest distance from Vertex S to Vertex T in the graph where the edges labeled X have the weight x and the edges labeled Y have the weight y, is d_{x, y}.\n\nConstruct such a graph (and a pair of S and T) for him, or report that it does not exist.\nRefer to Output section for output format.", "constraint": "1 <= A,B <= 10\n1 <= d_{x,y} <= 100 (1 <= x <= A, 1 <= y <= B)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nA B\nd_{1,1} d_{1,2} . . d_{1, B}\nd_{2,1} d_{2,2} . . d_{2, B}\n:\nd_{A, 1} d_{A, 2} . . d_{A, B}", "output": "If no graph satisfies the condition, print Impossible.\nIf there exists a graph that satisfies the condition, print Possible in the first line.\nThen, in the subsequent lines, print the constructed graph in the following format:\nN M\nu_1 v_1 c_1\nu_2 v_2 c_2\n:\nu_M v_M c_M\nS T\n\nHere, M is the number of the edges, and u_i, v_i, c_i represent edges as follows: there is an edge from Vertex u_i to Vertex v_i whose weight or label is c_i.\nAlso refer to Sample Outputs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n1 2 2\n1 2 3 output: Possible\n3 4\n1 2 X\n2 3 1\n3 2 Y\n1 3 Y\n1 3", "input: 1 3\n100 50 1 output: Impossible"], "Pid": "p03461", "ProblemText": "Task Description: Problem Statement At Co Deer the deer wants a directed graph that satisfies the following conditions:\n\nThe number of vertices, N, is at most 300.\nThere must not be self-loops or multiple edges.\nThe vertices are numbered from 1 through N.\nEach edge has either an integer weight between 0 and 100 (inclusive), or a label X or Y.\nFor every pair of two integers (x, y) such that 1 <= x <= A, 1 <= y <= B,\n the shortest distance from Vertex S to Vertex T in the graph where the edges labeled X have the weight x and the edges labeled Y have the weight y, is d_{x, y}.\n\nConstruct such a graph (and a pair of S and T) for him, or report that it does not exist.\nRefer to Output section for output format.\nTask Constraint: 1 <= A,B <= 10\n1 <= d_{x,y} <= 100 (1 <= x <= A, 1 <= y <= B)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nd_{1,1} d_{1,2} . . d_{1, B}\nd_{2,1} d_{2,2} . . d_{2, B}\n:\nd_{A, 1} d_{A, 2} . . d_{A, B}\nTask Output: If no graph satisfies the condition, print Impossible.\nIf there exists a graph that satisfies the condition, print Possible in the first line.\nThen, in the subsequent lines, print the constructed graph in the following format:\nN M\nu_1 v_1 c_1\nu_2 v_2 c_2\n:\nu_M v_M c_M\nS T\n\nHere, M is the number of the edges, and u_i, v_i, c_i represent edges as follows: there is an edge from Vertex u_i to Vertex v_i whose weight or label is c_i.\nAlso refer to Sample Outputs.\nTask Samples: input: 2 3\n1 2 2\n1 2 3 output: Possible\n3 4\n1 2 X\n2 3 1\n3 2 Y\n1 3 Y\n1 3\ninput: 1 3\n100 50 1 output: Impossible\n\n" }, { "title": "", "content": "Problem Statement There are N white balls arranged in a row, numbered 1,2, . . , N from left to right.\nAt Co Deer the deer is thinking of painting some of these balls red and blue, while leaving some of them white.\nYou are given a string s of length K.\nAt Co Deer performs the following operation for each i from 1 through K in order:\n\nThe i-th operation: Choose a contiguous segment of balls (possibly empty), and paint these balls red if the i-th character in s is r; paint them blue if the character is b.\n\nHere, if a ball which is already painted is again painted, the color of the ball will be overwritten.\nHowever, due to the properties of dyes, it is not possible to paint a white, unpainted ball directly in blue.\nThat is, when the i-th character in s is b, the chosen segment must not contain a white ball.\nAfter all the operations, how many different sequences of colors of the balls are possible?\nSince the count can be large, find it modulo 10^9+7.", "constraint": "1 <= N <= 70\n1 <= K <= 70\n|s| = K\ns consists of r and b.\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nN K\ns", "output": "Print the number of the different possible sequences of colors of the balls after all the operations, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\nrb output: 9\n\nThere are nine possible sequences of colors of the balls, as follows:\nww, wr, rw, rr, wb, bw, bb, rb, br.\nHere, r represents red, b represents blue and wrepresents white.", "input: 5 2\nbr output: 16\n\nSince we cannot directly paint white balls in blue, we can only choose an empty segment in the first operation.", "input: 7 4\nrbrb output: 1569", "input: 70 70\nbbrbrrbbrrbbbbrbbrbrrbbrrbbrbrrbrbrbbbbrbbrbrrbbrrbbbbrbbrbrrbbrrbbbbr output: 841634130"], "Pid": "p03462", "ProblemText": "Task Description: Problem Statement There are N white balls arranged in a row, numbered 1,2, . . , N from left to right.\nAt Co Deer the deer is thinking of painting some of these balls red and blue, while leaving some of them white.\nYou are given a string s of length K.\nAt Co Deer performs the following operation for each i from 1 through K in order:\n\nThe i-th operation: Choose a contiguous segment of balls (possibly empty), and paint these balls red if the i-th character in s is r; paint them blue if the character is b.\n\nHere, if a ball which is already painted is again painted, the color of the ball will be overwritten.\nHowever, due to the properties of dyes, it is not possible to paint a white, unpainted ball directly in blue.\nThat is, when the i-th character in s is b, the chosen segment must not contain a white ball.\nAfter all the operations, how many different sequences of colors of the balls are possible?\nSince the count can be large, find it modulo 10^9+7.\nTask Constraint: 1 <= N <= 70\n1 <= K <= 70\n|s| = K\ns consists of r and b.\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\ns\nTask Output: Print the number of the different possible sequences of colors of the balls after all the operations, modulo 10^9+7.\nTask Samples: input: 2 2\nrb output: 9\n\nThere are nine possible sequences of colors of the balls, as follows:\nww, wr, rw, rr, wb, bw, bb, rb, br.\nHere, r represents red, b represents blue and wrepresents white.\ninput: 5 2\nbr output: 16\n\nSince we cannot directly paint white balls in blue, we can only choose an empty segment in the first operation.\ninput: 7 4\nrbrb output: 1569\ninput: 70 70\nbbrbrrbbrrbbbbrbbrbrrbbrrbbrbrrbrbrbbbbrbbrbrrbbrrbbbbrbbrbrrbbrrbbbbr output: 841634130\n\n" }, { "title": "", "content": "Problem Statement A game is played on a strip consisting of N cells consecutively numbered from 1 to N. \nAlice has her token on cell A. Borys has his token on a different cell B.\nPlayers take turns, Alice moves first.\nThe moving player must shift his or her token from its current cell X to the neighboring cell on the left, cell X-1, or on the right, cell X+1.\nNote that it's disallowed to move the token outside the strip or to the cell with the other player's token.\nIn one turn, the token of the moving player must be shifted exactly once.\nThe player who can't make a move loses, and the other player wins.\nBoth players want to win. Who wins if they play optimally?", "constraint": "2 <= N <= 100\n1 <= A < B <= N\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print Alice if Alice wins, Borys if Borys wins, and Draw if nobody wins.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 4 output: Alice\n\nAlice can move her token to cell 3. \nAfter that, Borys will be unable to move his token to cell 3, so he will have to move his token to cell 5. \nThen, Alice moves her token to cell 4. Borys can't make a move and loses.", "input: 2 1 2 output: Borys\n\nAlice can't make the very first move and loses.", "input: 58 23 42 output: Borys"], "Pid": "p03463", "ProblemText": "Task Description: Problem Statement A game is played on a strip consisting of N cells consecutively numbered from 1 to N. \nAlice has her token on cell A. Borys has his token on a different cell B.\nPlayers take turns, Alice moves first.\nThe moving player must shift his or her token from its current cell X to the neighboring cell on the left, cell X-1, or on the right, cell X+1.\nNote that it's disallowed to move the token outside the strip or to the cell with the other player's token.\nIn one turn, the token of the moving player must be shifted exactly once.\nThe player who can't make a move loses, and the other player wins.\nBoth players want to win. Who wins if they play optimally?\nTask Constraint: 2 <= N <= 100\n1 <= A < B <= N\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print Alice if Alice wins, Borys if Borys wins, and Draw if nobody wins.\nTask Samples: input: 5 2 4 output: Alice\n\nAlice can move her token to cell 3. \nAfter that, Borys will be unable to move his token to cell 3, so he will have to move his token to cell 5. \nThen, Alice moves her token to cell 4. Borys can't make a move and loses.\ninput: 2 1 2 output: Borys\n\nAlice can't make the very first move and loses.\ninput: 58 23 42 output: Borys\n\n" }, { "title": "", "content": "Problem Statement An adult game master and N children are playing a game on an ice rink.\nThe game consists of K rounds.\nIn the i-th round, the game master announces:\n\nForm groups consisting of A_i children each!\n\nThen the children who are still in the game form as many groups of A_i children as possible.\nOne child may belong to at most one group.\nThose who are left without a group leave the game. The others proceed to the next round.\nNote that it's possible that nobody leaves the game in some round.\nIn the end, after the K-th round, there are exactly two children left, and they are declared the winners.\nYou have heard the values of A_1, A_2, . . . , A_K. You don't know N, but you want to estimate it.\nFind the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.", "constraint": "1 <= K <= 10^5\n2 <= A_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nK\nA_1 A_2 . . . A_K", "output": "Print two integers representing the smallest and the largest possible value of N, respectively,\nor a single integer -1 if the described situation is impossible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 4 3 2 output: 6 8\n\nFor example, if the game starts with 6 children, then it proceeds as follows:\n\nIn the first round, 6 children form 2 groups of 3 children, and nobody leaves the game.\nIn the second round, 6 children form 1 group of 4 children, and 2 children leave the game.\nIn the third round, 4 children form 1 group of 3 children, and 1 child leaves the game.\nIn the fourth round, 3 children form 1 group of 2 children, and 1 child leaves the game.\n\nThe last 2 children are declared the winners.", "input: 5\n3 4 100 3 2 output: -1\n\nThis situation is impossible.\nIn particular, if the game starts with less than 100 children, everyone leaves after the third round.", "input: 10\n2 2 2 2 2 2 2 2 2 2 output: 2 3"], "Pid": "p03464", "ProblemText": "Task Description: Problem Statement An adult game master and N children are playing a game on an ice rink.\nThe game consists of K rounds.\nIn the i-th round, the game master announces:\n\nForm groups consisting of A_i children each!\n\nThen the children who are still in the game form as many groups of A_i children as possible.\nOne child may belong to at most one group.\nThose who are left without a group leave the game. The others proceed to the next round.\nNote that it's possible that nobody leaves the game in some round.\nIn the end, after the K-th round, there are exactly two children left, and they are declared the winners.\nYou have heard the values of A_1, A_2, . . . , A_K. You don't know N, but you want to estimate it.\nFind the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.\nTask Constraint: 1 <= K <= 10^5\n2 <= A_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nK\nA_1 A_2 . . . A_K\nTask Output: Print two integers representing the smallest and the largest possible value of N, respectively,\nor a single integer -1 if the described situation is impossible.\nTask Samples: input: 4\n3 4 3 2 output: 6 8\n\nFor example, if the game starts with 6 children, then it proceeds as follows:\n\nIn the first round, 6 children form 2 groups of 3 children, and nobody leaves the game.\nIn the second round, 6 children form 1 group of 4 children, and 2 children leave the game.\nIn the third round, 4 children form 1 group of 3 children, and 1 child leaves the game.\nIn the fourth round, 3 children form 1 group of 2 children, and 1 child leaves the game.\n\nThe last 2 children are declared the winners.\ninput: 5\n3 4 100 3 2 output: -1\n\nThis situation is impossible.\nIn particular, if the game starts with less than 100 children, everyone leaves after the third round.\ninput: 10\n2 2 2 2 2 2 2 2 2 2 output: 2 3\n\n" }, { "title": "", "content": "Problem Statement You are given N integers A_1, A_2, . . . , A_N.\nConsider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.\nLet the list of these sums in non-decreasing order be S_1, S_2, . . . , S_{2^N - 1}.\nFind the median of this list, S_{2^{N-1}}.", "constraint": "1 <= N <= 2000\n1 <= A_i <= 2000\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the median of the sorted list of the sums of all non-empty subsequences of A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 1 output: 2\n\nIn this case, S = (1,1,2,2,3,3,4). Its median is S_4 = 2.", "input: 1\n58 output: 58\n\nIn this case, S = (58)."], "Pid": "p03465", "ProblemText": "Task Description: Problem Statement You are given N integers A_1, A_2, . . . , A_N.\nConsider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.\nLet the list of these sums in non-decreasing order be S_1, S_2, . . . , S_{2^N - 1}.\nFind the median of this list, S_{2^{N-1}}.\nTask Constraint: 1 <= N <= 2000\n1 <= A_i <= 2000\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the median of the sorted list of the sums of all non-empty subsequences of A.\nTask Samples: input: 3\n1 2 1 output: 2\n\nIn this case, S = (1,1,2,2,3,3,4). Its median is S_4 = 2.\ninput: 1\n58 output: 58\n\nIn this case, S = (58).\n\n" }, { "title": "", "content": "Problem Statement Let f(A, B), where A and B are positive integers, be the string satisfying the following conditions:\n\nf(A, B) has length A + B;\nf(A, B) contains exactly A letters A and exactly B letters B;\nThe length of the longest substring of f(A, B) consisting of equal letters (ex. , AAAAA or BBBB) is as small as possible under the conditions above;\nf(A, B) is the lexicographically smallest string satisfying the conditions above.\n\nFor example, f(2,3) = BABAB, and f(6,4) = AABAABAABB.\nAnswer Q queries: find the substring of f(A_i, B_i) from position C_i to position D_i (1-based). partial score: Partial Score\n500 points will be awarded for passing the testset satisfying 1 <= A_i, B_i <= 10^3.", "constraint": "1 <= Q <= 10^3\n1 <= A_i, B_i <= 5 * 10^8\n1 <= C_i <= D_i <= A_i + B_i\nD_i - C_i + 1 <= 100\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nQ\nA_1 B_1 C_1 D_1\nA_2 B_2 C_2 D_2\n:\nA_Q B_Q C_Q D_Q", "output": "For each query i in order of input, print a line containing the substring of f(A_i, B_i) from position C_i to position D_i (1-based).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 3 1 5\n6 4 1 10\n2 3 4 4\n6 4 3 7\n8 10 5 8 output: BABAB\nAABAABAABB\nA\nBAABA\nABAB"], "Pid": "p03466", "ProblemText": "Task Description: Problem Statement Let f(A, B), where A and B are positive integers, be the string satisfying the following conditions:\n\nf(A, B) has length A + B;\nf(A, B) contains exactly A letters A and exactly B letters B;\nThe length of the longest substring of f(A, B) consisting of equal letters (ex. , AAAAA or BBBB) is as small as possible under the conditions above;\nf(A, B) is the lexicographically smallest string satisfying the conditions above.\n\nFor example, f(2,3) = BABAB, and f(6,4) = AABAABAABB.\nAnswer Q queries: find the substring of f(A_i, B_i) from position C_i to position D_i (1-based). partial score: Partial Score\n500 points will be awarded for passing the testset satisfying 1 <= A_i, B_i <= 10^3.\nTask Constraint: 1 <= Q <= 10^3\n1 <= A_i, B_i <= 5 * 10^8\n1 <= C_i <= D_i <= A_i + B_i\nD_i - C_i + 1 <= 100\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nQ\nA_1 B_1 C_1 D_1\nA_2 B_2 C_2 D_2\n:\nA_Q B_Q C_Q D_Q\nTask Output: For each query i in order of input, print a line containing the substring of f(A_i, B_i) from position C_i to position D_i (1-based).\nTask Samples: input: 5\n2 3 1 5\n6 4 1 10\n2 3 4 4\n6 4 3 7\n8 10 5 8 output: BABAB\nAABAABAABB\nA\nBAABA\nABAB\n\n" }, { "title": "", "content": "Problem Statement Consider the following set of rules for encoding strings consisting of 0 and 1:\n\nStrings 0 and 1 can be encoded as 0 and 1, respectively. \nIf strings A and B can be encoded as P and Q, respectively, then string AB can be encoded as PQ.\nIf string A can be encoded as P and K >= 2 is a positive integer, then string AA. . . A (A repeated K times) can be encoded as (Px K).\n\nFor example, string 001001001, among other possibilities, can be encoded as 001001001,00(1(0x2)x2)1 and (001x3).\nLet's call string A a subset of string B if:\n\nA and B are equal in length and consist of 0 and 1;\nfor all indices i such that A_i = 1, it's also true that B_i = 1.\n\nYou are given string S consisting of 0 and 1. Find the total number of distinct encodings of all subsets of S, modulo 998244353.", "constraint": "1 <= |S| <= 100\nS consists of 0 and 1.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the total number of distinct encodings of all subsets of S modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 011 output: 9\n\nThere are four subsets of S:\n\n011 can be encoded as 011 and 0(1x2);\n010 can be encoded as 010;\n001 can be encoded as 001 and (0x2)1;\n000 can be encoded as 000,0(0x2), (0x2)0 and (0x3).\n\nThus, the total number of encodings of all subsets of S is 2 + 1 + 2 + 4 = 9.", "input: 0000 output: 10\n\nThis time S has only one subset, but it can be encoded in 10 different ways.", "input: 101110 output: 156", "input: 001110111010110001100000100111 output: 363383189\n\nDon't forget to take the result modulo 998244353."], "Pid": "p03467", "ProblemText": "Task Description: Problem Statement Consider the following set of rules for encoding strings consisting of 0 and 1:\n\nStrings 0 and 1 can be encoded as 0 and 1, respectively. \nIf strings A and B can be encoded as P and Q, respectively, then string AB can be encoded as PQ.\nIf string A can be encoded as P and K >= 2 is a positive integer, then string AA. . . A (A repeated K times) can be encoded as (Px K).\n\nFor example, string 001001001, among other possibilities, can be encoded as 001001001,00(1(0x2)x2)1 and (001x3).\nLet's call string A a subset of string B if:\n\nA and B are equal in length and consist of 0 and 1;\nfor all indices i such that A_i = 1, it's also true that B_i = 1.\n\nYou are given string S consisting of 0 and 1. Find the total number of distinct encodings of all subsets of S, modulo 998244353.\nTask Constraint: 1 <= |S| <= 100\nS consists of 0 and 1.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the total number of distinct encodings of all subsets of S modulo 998244353.\nTask Samples: input: 011 output: 9\n\nThere are four subsets of S:\n\n011 can be encoded as 011 and 0(1x2);\n010 can be encoded as 010;\n001 can be encoded as 001 and (0x2)1;\n000 can be encoded as 000,0(0x2), (0x2)0 and (0x3).\n\nThus, the total number of encodings of all subsets of S is 2 + 1 + 2 + 4 = 9.\ninput: 0000 output: 10\n\nThis time S has only one subset, but it can be encoded in 10 different ways.\ninput: 101110 output: 156\ninput: 001110111010110001100000100111 output: 363383189\n\nDon't forget to take the result modulo 998244353.\n\n" }, { "title": "", "content": "Problem Statement You have a circle of length C, and you are placing N arcs on it. Arc i has length L_i.\nEvery arc i is placed on the circle uniformly at random:\na random real point on the circle is chosen, then an arc of length L_i centered at this point appears.\nNote that the arcs are placed independently. For example, they may intersect or contain each other.\nWhat is the probability that every real point of the circle will be covered by at least one arc?\nAssume that an arc covers its ends.", "constraint": "2 <= N <= 6\n2 <= C <= 50\n1 <= L_i < C\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN C\nL_1 L_2 . . . L_N", "output": "Print the probability that every real point of the circle will be covered by at least one arc.\nYour answer will be considered correct if its absolute error doesn't exceed 10^{-11}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n2 2 output: 0.3333333333333333\n\nThe centers of the two arcs must be at distance at least 1. The probability of this on a circle of length 3 is 1 / 3.", "input: 4 10\n1 2 3 4 output: 0.0000000000000000\n\nEven though the total length of the arcs is exactly C and it's possible that every real point of the circle is covered by at least one arc,\nthe probability of this event is 0.", "input: 4 2\n1 1 1 1 output: 0.5000000000000000", "input: 3 5\n2 2 4 output: 0.4000000000000000", "input: 4 6\n4 1 3 2 output: 0.3148148148148148", "input: 6 49\n22 13 27 8 2 19 output: 0.2832340720702695"], "Pid": "p03468", "ProblemText": "Task Description: Problem Statement You have a circle of length C, and you are placing N arcs on it. Arc i has length L_i.\nEvery arc i is placed on the circle uniformly at random:\na random real point on the circle is chosen, then an arc of length L_i centered at this point appears.\nNote that the arcs are placed independently. For example, they may intersect or contain each other.\nWhat is the probability that every real point of the circle will be covered by at least one arc?\nAssume that an arc covers its ends.\nTask Constraint: 2 <= N <= 6\n2 <= C <= 50\n1 <= L_i < C\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN C\nL_1 L_2 . . . L_N\nTask Output: Print the probability that every real point of the circle will be covered by at least one arc.\nYour answer will be considered correct if its absolute error doesn't exceed 10^{-11}.\nTask Samples: input: 2 3\n2 2 output: 0.3333333333333333\n\nThe centers of the two arcs must be at distance at least 1. The probability of this on a circle of length 3 is 1 / 3.\ninput: 4 10\n1 2 3 4 output: 0.0000000000000000\n\nEven though the total length of the arcs is exactly C and it's possible that every real point of the circle is covered by at least one arc,\nthe probability of this event is 0.\ninput: 4 2\n1 1 1 1 output: 0.5000000000000000\ninput: 3 5\n2 2 4 output: 0.4000000000000000\ninput: 4 6\n4 1 3 2 output: 0.3148148148148148\ninput: 6 49\n22 13 27 8 2 19 output: 0.2832340720702695\n\n" }, { "title": "", "content": "Problem Statement On some day in January 2018, Takaki is writing a document. The document has a column where the current date is written in yyyy/mm/dd format. For example, January 23,2018 should be written as 2018/01/23.\nAfter finishing the document, she noticed that she had mistakenly wrote 2017 at the beginning of the date column. Write a program that, when the string that Takaki wrote in the date column, S, is given as input, modifies the first four characters in S to 2018 and prints it.", "constraint": "S is a string of length 10.\nThe first eight characters in S are 2017/01/.\nThe last two characters in S are digits and represent an integer between 1 and 31 (inclusive).", "input": "Input is given from Standard Input in the following format:\nS", "output": "Output Replace the first four characters in S with 2018 and print it.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2017/01/07 output: 2018/01/07", "input: 2017/01/31 output: 2018/01/31"], "Pid": "p03469", "ProblemText": "Task Description: Problem Statement On some day in January 2018, Takaki is writing a document. The document has a column where the current date is written in yyyy/mm/dd format. For example, January 23,2018 should be written as 2018/01/23.\nAfter finishing the document, she noticed that she had mistakenly wrote 2017 at the beginning of the date column. Write a program that, when the string that Takaki wrote in the date column, S, is given as input, modifies the first four characters in S to 2018 and prints it.\nTask Constraint: S is a string of length 10.\nThe first eight characters in S are 2017/01/.\nThe last two characters in S are digits and represent an integer between 1 and 31 (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Output Replace the first four characters in S with 2018 and print it.\nTask Samples: input: 2017/01/07 output: 2018/01/07\ninput: 2017/01/31 output: 2018/01/31\n\n" }, { "title": "", "content": "Problem Statement An X-layered kagami mochi (X >= 1) is a pile of X round mochi (rice cake) stacked vertically where each mochi (except the bottom one) has a smaller diameter than that of the mochi directly below it. For example, if you stack three mochi with diameters of 10,8 and 6 centimeters from bottom to top in this order, you have a 3-layered kagami mochi; if you put just one mochi, you have a 1-layered kagami mochi.\nLunlun the dachshund has N round mochi, and the diameter of the i-th mochi is d_i centimeters. When we make a kagami mochi using some or all of them, at most how many layers can our kagami mochi have?", "constraint": "1 <= N <= 100\n1 <= d_i <= 100\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nd_1\n:\nd_N", "output": "Print the maximum number of layers in a kagami mochi that can be made.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n10\n8\n8\n6 output: 3\n\nIf we stack the mochi with diameters of 10,8 and 6 centimeters from bottom to top in this order, we have a 3-layered kagami mochi, which is the maximum number of layers.", "input: 3\n15\n15\n15 output: 1\n\nWhen all the mochi have the same diameter, we can only have a 1-layered kagami mochi.", "input: 7\n50\n30\n50\n100\n50\n80\n30 output: 4"], "Pid": "p03470", "ProblemText": "Task Description: Problem Statement An X-layered kagami mochi (X >= 1) is a pile of X round mochi (rice cake) stacked vertically where each mochi (except the bottom one) has a smaller diameter than that of the mochi directly below it. For example, if you stack three mochi with diameters of 10,8 and 6 centimeters from bottom to top in this order, you have a 3-layered kagami mochi; if you put just one mochi, you have a 1-layered kagami mochi.\nLunlun the dachshund has N round mochi, and the diameter of the i-th mochi is d_i centimeters. When we make a kagami mochi using some or all of them, at most how many layers can our kagami mochi have?\nTask Constraint: 1 <= N <= 100\n1 <= d_i <= 100\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nd_1\n:\nd_N\nTask Output: Print the maximum number of layers in a kagami mochi that can be made.\nTask Samples: input: 4\n10\n8\n8\n6 output: 3\n\nIf we stack the mochi with diameters of 10,8 and 6 centimeters from bottom to top in this order, we have a 3-layered kagami mochi, which is the maximum number of layers.\ninput: 3\n15\n15\n15 output: 1\n\nWhen all the mochi have the same diameter, we can only have a 1-layered kagami mochi.\ninput: 7\n50\n30\n50\n100\n50\n80\n30 output: 4\n\n" }, { "title": "", "content": "Problem Statement The commonly used bills in Japan are 10000-yen, 5000-yen and 1000-yen bills. Below, the word \"bill\" refers to only these.\nAccording to Aohashi, he received an otoshidama (New Year money gift) envelope from his grandfather that contained N bills for a total of Y yen, but he may be lying. Determine whether such a situation is possible, and if it is, find a possible set of bills contained in the envelope. Assume that his grandfather is rich enough, and the envelope was large enough.", "constraint": "1 <= N <= 2000\n1000 <= Y <= 2 * 10^7\nN is an integer.\nY is a multiple of 1000.", "input": "Input is given from Standard Input in the following format:\nN Y", "output": "If the total value of N bills cannot be Y yen, print -1 -1 -1.\nIf the total value of N bills can be Y yen, let one such set of bills be \"x 10000-yen bills, y 5000-yen bills and z 1000-yen bills\", and print x, y, z with spaces in between. If there are multiple possibilities, any of them may be printed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 45000 output: 4 0 5\n\nIf the envelope contained 4 10000-yen bills and 5 1000-yen bills, he had 9 bills and 45000 yen in total. It is also possible that the envelope contained 9 5000-yen bills, so the output 0 9 0 is also correct.", "input: 20 196000 output: -1 -1 -1\n\nWhen the envelope contained 20 bills in total, the total value would be 200000 yen if all the bills were 10000-yen bills, and would be at most 195000 yen otherwise, so it would never be 196000 yen.", "input: 1000 1234000 output: 14 27 959\n\nThere are also many other possibilities.", "input: 2000 20000000 output: 2000 0 0"], "Pid": "p03471", "ProblemText": "Task Description: Problem Statement The commonly used bills in Japan are 10000-yen, 5000-yen and 1000-yen bills. Below, the word \"bill\" refers to only these.\nAccording to Aohashi, he received an otoshidama (New Year money gift) envelope from his grandfather that contained N bills for a total of Y yen, but he may be lying. Determine whether such a situation is possible, and if it is, find a possible set of bills contained in the envelope. Assume that his grandfather is rich enough, and the envelope was large enough.\nTask Constraint: 1 <= N <= 2000\n1000 <= Y <= 2 * 10^7\nN is an integer.\nY is a multiple of 1000.\nTask Input: Input is given from Standard Input in the following format:\nN Y\nTask Output: If the total value of N bills cannot be Y yen, print -1 -1 -1.\nIf the total value of N bills can be Y yen, let one such set of bills be \"x 10000-yen bills, y 5000-yen bills and z 1000-yen bills\", and print x, y, z with spaces in between. If there are multiple possibilities, any of them may be printed.\nTask Samples: input: 9 45000 output: 4 0 5\n\nIf the envelope contained 4 10000-yen bills and 5 1000-yen bills, he had 9 bills and 45000 yen in total. It is also possible that the envelope contained 9 5000-yen bills, so the output 0 9 0 is also correct.\ninput: 20 196000 output: -1 -1 -1\n\nWhen the envelope contained 20 bills in total, the total value would be 200000 yen if all the bills were 10000-yen bills, and would be at most 195000 yen otherwise, so it would never be 196000 yen.\ninput: 1000 1234000 output: 14 27 959\n\nThere are also many other possibilities.\ninput: 2000 20000000 output: 2000 0 0\n\n" }, { "title": "", "content": "Problem Statement You are going out for a walk, when you suddenly encounter a monster. Fortunately, you have N katana (swords), Katana 1, Katana 2, …, Katana N, and can perform the following two kinds of attacks in any order:\n\nWield one of the katana you have. When you wield Katana i (1 <= i <= N), the monster receives a_i points of damage. The same katana can be wielded any number of times.\nThrow one of the katana you have. When you throw Katana i (1 <= i <= N) at the monster, it receives b_i points of damage, and you lose the katana. That is, you can no longer wield or throw that katana.\n\nThe monster will vanish when the total damage it has received is H points or more. At least how many attacks do you need in order to vanish it in total?", "constraint": "1 <= N <= 10^5\n1 <= H <= 10^9\n1 <= a_i <= b_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN H\na_1 b_1\n:\na_N b_N", "output": "Print the minimum total number of attacks required to vanish the monster.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 10\n3 5 output: 3\n\nYou have one katana. Wielding it deals 3 points of damage, and throwing it deals 5 points of damage. By wielding it twice and then throwing it, you will deal 3 + 3 + 5 = 11 points of damage in a total of three attacks, vanishing the monster.", "input: 2 10\n3 5\n2 6 output: 2\n\nIn addition to the katana above, you also have another katana. Wielding it deals 2 points of damage, and throwing it deals 6 points of damage. By throwing both katana, you will deal 5 + 6 = 11 points of damage in two attacks, vanishing the monster.", "input: 4 1000000000\n1 1\n1 10000000\n1 30000000\n1 99999999 output: 860000004", "input: 5 500\n35 44\n28 83\n46 62\n31 79\n40 43 output: 9"], "Pid": "p03472", "ProblemText": "Task Description: Problem Statement You are going out for a walk, when you suddenly encounter a monster. Fortunately, you have N katana (swords), Katana 1, Katana 2, …, Katana N, and can perform the following two kinds of attacks in any order:\n\nWield one of the katana you have. When you wield Katana i (1 <= i <= N), the monster receives a_i points of damage. The same katana can be wielded any number of times.\nThrow one of the katana you have. When you throw Katana i (1 <= i <= N) at the monster, it receives b_i points of damage, and you lose the katana. That is, you can no longer wield or throw that katana.\n\nThe monster will vanish when the total damage it has received is H points or more. At least how many attacks do you need in order to vanish it in total?\nTask Constraint: 1 <= N <= 10^5\n1 <= H <= 10^9\n1 <= a_i <= b_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN H\na_1 b_1\n:\na_N b_N\nTask Output: Print the minimum total number of attacks required to vanish the monster.\nTask Samples: input: 1 10\n3 5 output: 3\n\nYou have one katana. Wielding it deals 3 points of damage, and throwing it deals 5 points of damage. By wielding it twice and then throwing it, you will deal 3 + 3 + 5 = 11 points of damage in a total of three attacks, vanishing the monster.\ninput: 2 10\n3 5\n2 6 output: 2\n\nIn addition to the katana above, you also have another katana. Wielding it deals 2 points of damage, and throwing it deals 6 points of damage. By throwing both katana, you will deal 5 + 6 = 11 points of damage in two attacks, vanishing the monster.\ninput: 4 1000000000\n1 1\n1 10000000\n1 30000000\n1 99999999 output: 860000004\ninput: 5 500\n35 44\n28 83\n46 62\n31 79\n40 43 output: 9\n\n" }, { "title": "", "content": "Problem Statement How many hours do we have until New Year at M o'clock (24-hour notation) on 30th, December?", "constraint": "1<=M<=23\nM is an integer.", "input": "Input is given from Standard Input in the following format:\nM", "output": "If we have x hours until New Year at M o'clock on 30th, December, print x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 21 output: 27\n\nWe have 27 hours until New Year at 21 o'clock on 30th, December.", "input: 12 output: 36"], "Pid": "p03473", "ProblemText": "Task Description: Problem Statement How many hours do we have until New Year at M o'clock (24-hour notation) on 30th, December?\nTask Constraint: 1<=M<=23\nM is an integer.\nTask Input: Input is given from Standard Input in the following format:\nM\nTask Output: If we have x hours until New Year at M o'clock on 30th, December, print x.\nTask Samples: input: 21 output: 27\n\nWe have 27 hours until New Year at 21 o'clock on 30th, December.\ninput: 12 output: 36\n\n" }, { "title": "", "content": "Problem Statement The postal code in Atcoder Kingdom is A+B+1 characters long, its (A+1)-th character is a hyphen -, and the other characters are digits from 0 through 9.\nYou are given a string S. Determine whether it follows the postal code format in Atcoder Kingdom.", "constraint": "1<=A,B<=5\n|S|=A+B+1\nS consists of - and digits from 0 through 9.", "input": "Input is given from Standard Input in the following format:\nA B\nS", "output": "Print Yes if S follows the postal code format in At Coder Kingdom; print No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n269-6650 output: Yes\n\nThe (A+1)-th character of S is -, and the other characters are digits from 0 through 9, so it follows the format.", "input: 1 1\n--- output: No\n\nS contains unnecessary -s other than the (A+1)-th character, so it does not follow the format.", "input: 1 2\n7444 output: No"], "Pid": "p03474", "ProblemText": "Task Description: Problem Statement The postal code in Atcoder Kingdom is A+B+1 characters long, its (A+1)-th character is a hyphen -, and the other characters are digits from 0 through 9.\nYou are given a string S. Determine whether it follows the postal code format in Atcoder Kingdom.\nTask Constraint: 1<=A,B<=5\n|S|=A+B+1\nS consists of - and digits from 0 through 9.\nTask Input: Input is given from Standard Input in the following format:\nA B\nS\nTask Output: Print Yes if S follows the postal code format in At Coder Kingdom; print No otherwise.\nTask Samples: input: 3 4\n269-6650 output: Yes\n\nThe (A+1)-th character of S is -, and the other characters are digits from 0 through 9, so it follows the format.\ninput: 1 1\n--- output: No\n\nS contains unnecessary -s other than the (A+1)-th character, so it does not follow the format.\ninput: 1 2\n7444 output: No\n\n" }, { "title": "", "content": "Problem Statement A railroad running from west to east in Atcoder Kingdom is now complete.\nThere are N stations on the railroad, numbered 1 through N from west to east.\nTomorrow, the opening ceremony of the railroad will take place.\nOn this railroad, for each integer i such that 1<=i<=N-1, there will be trains that run from Station i to Station i+1 in C_i seconds. No other trains will be operated.\nThe first train from Station i to Station i+1 will depart Station i S_i seconds after the ceremony begins. Thereafter, there will be a train that departs Station i every F_i seconds.\nHere, it is guaranteed that F_i divides S_i.\nThat is, for each Time t satisfying S_i<=t and t％F_i=0, there will be a train that departs Station i t seconds after the ceremony begins and arrives at Station i+1 t+C_i seconds after the ceremony begins, where A％B denotes A modulo B, and there will be no other trains.\nFor each i, find the earliest possible time we can reach Station N if we are at Station i when the ceremony begins, ignoring the time needed to change trains.", "constraint": "1<=N<=500\n1<=C_i<=100\n1<=S_i<=10^5\n1<=F_i<=10\nS_i％F_i=0\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nC_1 S_1 F_1\n:\nC_{N-1} S_{N-1} F_{N-1}", "output": "Print N lines. Assuming that we are at Station i (1<=i<=N) when the ceremony begins, if the earliest possible time we can reach Station N is x seconds after the ceremony begins, the i-th line should contain x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n6 5 1\n1 10 1 output: 12\n11\n0\n\nWe will travel from Station 1 as follows:\n\n5 seconds after the beginning: take the train to Station 2.\n11 seconds: arrive at Station 2.\n11 seconds: take the train to Station 3.\n12 seconds: arrive at Station 3.\n\nWe will travel from Station 2 as follows:\n\n10 seconds: take the train to Station 3.\n11 seconds: arrive at Station 3.\n\nNote that we should print 0 for Station 3.", "input: 4\n12 24 6\n52 16 4\n99 2 2 output: 187\n167\n101\n0", "input: 4\n12 13 1\n44 17 17\n66 4096 64 output: 4162\n4162\n4162\n0"], "Pid": "p03475", "ProblemText": "Task Description: Problem Statement A railroad running from west to east in Atcoder Kingdom is now complete.\nThere are N stations on the railroad, numbered 1 through N from west to east.\nTomorrow, the opening ceremony of the railroad will take place.\nOn this railroad, for each integer i such that 1<=i<=N-1, there will be trains that run from Station i to Station i+1 in C_i seconds. No other trains will be operated.\nThe first train from Station i to Station i+1 will depart Station i S_i seconds after the ceremony begins. Thereafter, there will be a train that departs Station i every F_i seconds.\nHere, it is guaranteed that F_i divides S_i.\nThat is, for each Time t satisfying S_i<=t and t％F_i=0, there will be a train that departs Station i t seconds after the ceremony begins and arrives at Station i+1 t+C_i seconds after the ceremony begins, where A％B denotes A modulo B, and there will be no other trains.\nFor each i, find the earliest possible time we can reach Station N if we are at Station i when the ceremony begins, ignoring the time needed to change trains.\nTask Constraint: 1<=N<=500\n1<=C_i<=100\n1<=S_i<=10^5\n1<=F_i<=10\nS_i％F_i=0\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nC_1 S_1 F_1\n:\nC_{N-1} S_{N-1} F_{N-1}\nTask Output: Print N lines. Assuming that we are at Station i (1<=i<=N) when the ceremony begins, if the earliest possible time we can reach Station N is x seconds after the ceremony begins, the i-th line should contain x.\nTask Samples: input: 3\n6 5 1\n1 10 1 output: 12\n11\n0\n\nWe will travel from Station 1 as follows:\n\n5 seconds after the beginning: take the train to Station 2.\n11 seconds: arrive at Station 2.\n11 seconds: take the train to Station 3.\n12 seconds: arrive at Station 3.\n\nWe will travel from Station 2 as follows:\n\n10 seconds: take the train to Station 3.\n11 seconds: arrive at Station 3.\n\nNote that we should print 0 for Station 3.\ninput: 4\n12 24 6\n52 16 4\n99 2 2 output: 187\n167\n101\n0\ninput: 4\n12 13 1\n44 17 17\n66 4096 64 output: 4162\n4162\n4162\n0\n\n" }, { "title": "", "content": "Problem Statement We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.\nYou are given Q queries.\nIn the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i <= x <= r_i.", "constraint": "1<=Q<=10^5\n1<=l_i<=r_i<=10^5\nl_i and r_i are odd.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nQ\nl_1 r_1\n:\nl_Q r_Q", "output": "Print Q lines. The i-th line (1<=i<=Q) should contain the response to the i-th query.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n3 7 output: 2\n3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.\n5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.\n7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.\n\nThus, the response to the first query should be 2.", "input: 4\n13 13\n7 11\n7 11\n2017 2017 output: 1\n0\n0\n1\n\nNote that 2017 is also similar to 2017.", "input: 6\n1 53\n13 91\n37 55\n19 51\n73 91\n13 49 output: 4\n4\n1\n1\n1\n2"], "Pid": "p03476", "ProblemText": "Task Description: Problem Statement We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.\nYou are given Q queries.\nIn the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i <= x <= r_i.\nTask Constraint: 1<=Q<=10^5\n1<=l_i<=r_i<=10^5\nl_i and r_i are odd.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nQ\nl_1 r_1\n:\nl_Q r_Q\nTask Output: Print Q lines. The i-th line (1<=i<=Q) should contain the response to the i-th query.\nTask Samples: input: 1\n3 7 output: 2\n3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.\n5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.\n7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.\n\nThus, the response to the first query should be 2.\ninput: 4\n13 13\n7 11\n7 11\n2017 2017 output: 1\n0\n0\n1\n\nNote that 2017 is also similar to 2017.\ninput: 6\n1 53\n13 91\n37 55\n19 51\n73 91\n13 49 output: 4\n4\n1\n1\n1\n2\n\n" }, { "title": "", "content": "Problem Statement A balance scale tips to the left if L>R, where L is the total weight of the masses on the left pan and R is the total weight of the masses on the right pan. Similarly, it balances if L=R, and tips to the right if L8, we should print Left.", "input: 3 4 5 2 output: Balanced\n\nThe total weight of the masses on the left pan is 7, and the total weight of the masses on the right pan is 7. Since 7=7, we should print Balanced.", "input: 1 7 6 4 output: Right\n\nThe total weight of the masses on the left pan is 8, and the total weight of the masses on the right pan is 10. Since 8<10, we should print Right."], "Pid": "p03477", "ProblemText": "Task Description: Problem Statement A balance scale tips to the left if L>R, where L is the total weight of the masses on the left pan and R is the total weight of the masses on the right pan. Similarly, it balances if L=R, and tips to the right if L8, we should print Left.\ninput: 3 4 5 2 output: Balanced\n\nThe total weight of the masses on the left pan is 7, and the total weight of the masses on the right pan is 7. Since 7=7, we should print Balanced.\ninput: 1 7 6 4 output: Right\n\nThe total weight of the masses on the left pan is 8, and the total weight of the masses on the right pan is 10. Since 8<10, we should print Right.\n\n" }, { "title": "", "content": "Problem Statement Find the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).", "constraint": "1 <= N <= 10^4\n1 <= A <= B <= 36\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 20 2 5 output: 84\n\nAmong the integers not greater than 20, the ones whose sums of digits are between 2 and 5, are: 2,3,4,5,11,12,13,14 and 20. We should print the sum of these, 84.", "input: 10 1 2 output: 13", "input: 100 4 16 output: 4554"], "Pid": "p03478", "ProblemText": "Task Description: Problem Statement Find the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).\nTask Constraint: 1 <= N <= 10^4\n1 <= A <= B <= 36\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print the sum of the integers between 1 and N (inclusive), whose sum of digits written in base 10 is between A and B (inclusive).\nTask Samples: input: 20 2 5 output: 84\n\nAmong the integers not greater than 20, the ones whose sums of digits are between 2 and 5, are: 2,3,4,5,11,12,13,14 and 20. We should print the sum of these, 84.\ninput: 10 1 2 output: 13\ninput: 100 4 16 output: 4554\n\n" }, { "title": "", "content": "Problem Statement As a token of his gratitude, Takahashi has decided to give his mother an integer sequence.\nThe sequence A needs to satisfy the conditions below:\n\nA consists of integers between X and Y (inclusive).\nFor each 1<= i <= |A|-1, A_{i+1} is a multiple of A_i and strictly greater than A_i.\n\nFind the maximum possible length of the sequence.", "constraint": "1 <= X <= Y <= 10^{18}\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "Print the maximum possible length of the sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 20 output: 3\n\nThe sequence 3,6,18 satisfies the conditions.", "input: 25 100 output: 3", "input: 314159265 358979323846264338 output: 31"], "Pid": "p03479", "ProblemText": "Task Description: Problem Statement As a token of his gratitude, Takahashi has decided to give his mother an integer sequence.\nThe sequence A needs to satisfy the conditions below:\n\nA consists of integers between X and Y (inclusive).\nFor each 1<= i <= |A|-1, A_{i+1} is a multiple of A_i and strictly greater than A_i.\n\nFind the maximum possible length of the sequence.\nTask Constraint: 1 <= X <= Y <= 10^{18}\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: Print the maximum possible length of the sequence.\nTask Samples: input: 3 20 output: 3\n\nThe sequence 3,6,18 satisfies the conditions.\ninput: 25 100 output: 3\ninput: 314159265 358979323846264338 output: 31\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of 0 and 1.\nFind the maximum integer K not greater than |S| such that we can turn all the characters of S into 0 by repeating the following operation some number of times.\n\nChoose a contiguous segment [l, r] in S whose length is at least K (that is, r-l+1>= K must be satisfied). For each integer i such that l<= i<= r, do the following: if S_i is 0, replace it with 1; if S_i is 1, replace it with 0.", "constraint": "1<= |S|<= 10^5\nS_i(1<= i<= N) is either 0 or 1.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the maximum integer K such that we can turn all the characters of S into 0 by repeating the operation some number of times.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 010 output: 2\n\nWe can turn all the characters of S into 0 by the following operations:\n\nPerform the operation on the segment S[1,3] with length 3. S is now 101.\nPerform the operation on the segment S[1,2] with length 2. S is now 011.\nPerform the operation on the segment S[2,3] with length 2. S is now 000.", "input: 100000000 output: 8", "input: 00001111 output: 4"], "Pid": "p03480", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of 0 and 1.\nFind the maximum integer K not greater than |S| such that we can turn all the characters of S into 0 by repeating the following operation some number of times.\n\nChoose a contiguous segment [l, r] in S whose length is at least K (that is, r-l+1>= K must be satisfied). For each integer i such that l<= i<= r, do the following: if S_i is 0, replace it with 1; if S_i is 1, replace it with 0.\nTask Constraint: 1<= |S|<= 10^5\nS_i(1<= i<= N) is either 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the maximum integer K such that we can turn all the characters of S into 0 by repeating the operation some number of times.\nTask Samples: input: 010 output: 2\n\nWe can turn all the characters of S into 0 by the following operations:\n\nPerform the operation on the segment S[1,3] with length 3. S is now 101.\nPerform the operation on the segment S[1,2] with length 2. S is now 011.\nPerform the operation on the segment S[2,3] with length 2. S is now 000.\ninput: 100000000 output: 8\ninput: 00001111 output: 4\n\n" }, { "title": "", "content": "Problem Statement As a token of his gratitude, Takahashi has decided to give his mother an integer sequence.\nThe sequence A needs to satisfy the conditions below:\n\nA consists of integers between X and Y (inclusive).\nFor each 1<= i <= |A|-1, A_{i+1} is a multiple of A_i and strictly greater than A_i.\n\nFind the maximum possible length of the sequence.", "constraint": "1 <= X <= Y <= 10^{18}\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "Print the maximum possible length of the sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 20 output: 3\n\nThe sequence 3,6,18 satisfies the conditions.", "input: 25 100 output: 3", "input: 314159265 358979323846264338 output: 31"], "Pid": "p03481", "ProblemText": "Task Description: Problem Statement As a token of his gratitude, Takahashi has decided to give his mother an integer sequence.\nThe sequence A needs to satisfy the conditions below:\n\nA consists of integers between X and Y (inclusive).\nFor each 1<= i <= |A|-1, A_{i+1} is a multiple of A_i and strictly greater than A_i.\n\nFind the maximum possible length of the sequence.\nTask Constraint: 1 <= X <= Y <= 10^{18}\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: Print the maximum possible length of the sequence.\nTask Samples: input: 3 20 output: 3\n\nThe sequence 3,6,18 satisfies the conditions.\ninput: 25 100 output: 3\ninput: 314159265 358979323846264338 output: 31\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of 0 and 1.\nFind the maximum integer K not greater than |S| such that we can turn all the characters of S into 0 by repeating the following operation some number of times.\n\nChoose a contiguous segment [l, r] in S whose length is at least K (that is, r-l+1>= K must be satisfied). For each integer i such that l<= i<= r, do the following: if S_i is 0, replace it with 1; if S_i is 1, replace it with 0.", "constraint": "1<= |S|<= 10^5\nS_i(1<= i<= N) is either 0 or 1.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the maximum integer K such that we can turn all the characters of S into 0 by repeating the operation some number of times.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 010 output: 2\n\nWe can turn all the characters of S into 0 by the following operations:\n\nPerform the operation on the segment S[1,3] with length 3. S is now 101.\nPerform the operation on the segment S[1,2] with length 2. S is now 011.\nPerform the operation on the segment S[2,3] with length 2. S is now 000.", "input: 100000000 output: 8", "input: 00001111 output: 4"], "Pid": "p03482", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of 0 and 1.\nFind the maximum integer K not greater than |S| such that we can turn all the characters of S into 0 by repeating the following operation some number of times.\n\nChoose a contiguous segment [l, r] in S whose length is at least K (that is, r-l+1>= K must be satisfied). For each integer i such that l<= i<= r, do the following: if S_i is 0, replace it with 1; if S_i is 1, replace it with 0.\nTask Constraint: 1<= |S|<= 10^5\nS_i(1<= i<= N) is either 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the maximum integer K such that we can turn all the characters of S into 0 by repeating the operation some number of times.\nTask Samples: input: 010 output: 2\n\nWe can turn all the characters of S into 0 by the following operations:\n\nPerform the operation on the segment S[1,3] with length 3. S is now 101.\nPerform the operation on the segment S[1,2] with length 2. S is now 011.\nPerform the operation on the segment S[2,3] with length 2. S is now 000.\ninput: 100000000 output: 8\ninput: 00001111 output: 4\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of lowercase English letters.\nDetermine whether we can turn S into a palindrome by repeating the operation of swapping two adjacent characters. If it is possible, find the minimum required number of operations.", "constraint": "1 <= |S| <= 2 * 10^5\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If we cannot turn S into a palindrome, print -1. Otherwise, print the minimum required number of operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: eel output: 1\n\nWe can turn S into a palindrome by the following operation:\n\nSwap the 2-nd and 3-rd characters. S is now ele.", "input: ataatmma output: 4\n\nWe can turn S into a palindrome by the following operation:\n\nSwap the 5-th and 6-th characters. S is now ataamtma.\nSwap the 4-th and 5-th characters. S is now atamatma.\nSwap the 3-rd and 4-th characters. S is now atmaatma.\nSwap the 2-nd and 3-rd characters. S is now amtaatma.", "input: snuke output: -1\n\nWe cannot turn S into a palindrome."], "Pid": "p03483", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of lowercase English letters.\nDetermine whether we can turn S into a palindrome by repeating the operation of swapping two adjacent characters. If it is possible, find the minimum required number of operations.\nTask Constraint: 1 <= |S| <= 2 * 10^5\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If we cannot turn S into a palindrome, print -1. Otherwise, print the minimum required number of operations.\nTask Samples: input: eel output: 1\n\nWe can turn S into a palindrome by the following operation:\n\nSwap the 2-nd and 3-rd characters. S is now ele.\ninput: ataatmma output: 4\n\nWe can turn S into a palindrome by the following operation:\n\nSwap the 5-th and 6-th characters. S is now ataamtma.\nSwap the 4-th and 5-th characters. S is now atamatma.\nSwap the 3-rd and 4-th characters. S is now atmaatma.\nSwap the 2-nd and 3-rd characters. S is now amtaatma.\ninput: snuke output: -1\n\nWe cannot turn S into a palindrome.\n\n" }, { "title": "", "content": "Problem Statement Takahashi has decided to make a Christmas Tree for the Christmas party in At Coder, Inc.\nA Christmas Tree is a tree with N vertices numbered 1 through N and N-1 edges, whose i-th edge (1<= i<= N-1) connects Vertex a_i and b_i.\nHe would like to make one as follows:\n\nSpecify two non-negative integers A and B.\nPrepare A Christmas Paths whose lengths are at most B. Here, a Christmas Path of length X is a graph with X+1 vertices and X edges such that, if we properly number the vertices 1 through X+1, the i-th edge (1<= i<= X) will connect Vertex i and i+1.\nRepeat the following operation until he has one connected tree:\nSelect two vertices x and y that belong to different connected components. Combine x and y into one vertex. More precisely, for each edge (p, y) incident to the vertex y, add the edge (p, x). Then, delete the vertex y and all the edges incident to y.\nProperly number the vertices in the tree.\n\nTakahashi would like to find the lexicographically smallest pair (A, B) such that he can make a Christmas Tree, that is, find the smallest A, and find the smallest B under the condition that A is minimized.\nSolve this problem for him.", "constraint": "2 <= N <= 10^5\n1 <= a_i,b_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}", "output": "For the lexicographically smallest (A, B), print A and B with a space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n1 2\n2 3\n2 4\n4 5\n4 6\n6 7 output: 3 2\n\nWe can make a Christmas Tree as shown in the figure below:", "input: 8\n1 2\n2 3\n3 4\n4 5\n5 6\n5 7\n5 8 output: 2 5", "input: 10\n1 2\n2 3\n3 4\n2 5\n6 5\n6 7\n7 8\n5 9\n10 5 output: 3 4"], "Pid": "p03484", "ProblemText": "Task Description: Problem Statement Takahashi has decided to make a Christmas Tree for the Christmas party in At Coder, Inc.\nA Christmas Tree is a tree with N vertices numbered 1 through N and N-1 edges, whose i-th edge (1<= i<= N-1) connects Vertex a_i and b_i.\nHe would like to make one as follows:\n\nSpecify two non-negative integers A and B.\nPrepare A Christmas Paths whose lengths are at most B. Here, a Christmas Path of length X is a graph with X+1 vertices and X edges such that, if we properly number the vertices 1 through X+1, the i-th edge (1<= i<= X) will connect Vertex i and i+1.\nRepeat the following operation until he has one connected tree:\nSelect two vertices x and y that belong to different connected components. Combine x and y into one vertex. More precisely, for each edge (p, y) incident to the vertex y, add the edge (p, x). Then, delete the vertex y and all the edges incident to y.\nProperly number the vertices in the tree.\n\nTakahashi would like to find the lexicographically smallest pair (A, B) such that he can make a Christmas Tree, that is, find the smallest A, and find the smallest B under the condition that A is minimized.\nSolve this problem for him.\nTask Constraint: 2 <= N <= 10^5\n1 <= a_i,b_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nTask Output: For the lexicographically smallest (A, B), print A and B with a space in between.\nTask Samples: input: 7\n1 2\n2 3\n2 4\n4 5\n4 6\n6 7 output: 3 2\n\nWe can make a Christmas Tree as shown in the figure below:\ninput: 8\n1 2\n2 3\n3 4\n4 5\n5 6\n5 7\n5 8 output: 2 5\ninput: 10\n1 2\n2 3\n3 4\n2 5\n6 5\n6 7\n7 8\n5 9\n10 5 output: 3 4\n\n" }, { "title": "", "content": "Problem Statement You are given two positive integers a and b.\nLet x be the average of a and b.\nPrint x rounded up to the nearest integer.", "constraint": "a and b are integers.\n1 <= a, b <= 100", "input": "Input is given from Standard Input in the following format:\na b", "output": "Print x rounded up to the nearest integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 output: 2\n\nThe average of 1 and 3 is 2.0, and it will be rounded up to the nearest integer, 2.", "input: 7 4 output: 6\n\nThe average of 7 and 4 is 5.5, and it will be rounded up to the nearest integer, 6.", "input: 5 5 output: 5"], "Pid": "p03485", "ProblemText": "Task Description: Problem Statement You are given two positive integers a and b.\nLet x be the average of a and b.\nPrint x rounded up to the nearest integer.\nTask Constraint: a and b are integers.\n1 <= a, b <= 100\nTask Input: Input is given from Standard Input in the following format:\na b\nTask Output: Print x rounded up to the nearest integer.\nTask Samples: input: 1 3 output: 2\n\nThe average of 1 and 3 is 2.0, and it will be rounded up to the nearest integer, 2.\ninput: 7 4 output: 6\n\nThe average of 7 and 4 is 5.5, and it will be rounded up to the nearest integer, 6.\ninput: 5 5 output: 5\n\n" }, { "title": "", "content": "Problem Statement You are given strings s and t, consisting of lowercase English letters.\nYou will create a string s' by freely rearranging the characters in s.\nYou will also create a string t' by freely rearranging the characters in t.\nDetermine whether it is possible to satisfy s' < t' for the lexicographic order. note: Notes For a string a = a_1 a_2 . . . a_N of length N and a string b = b_1 b_2 . . . b_M of length M, we say a < b for the lexicographic order if either one of the following two conditions holds true:\n\nN < M and a_1 = b_1, a_2 = b_2, . . . , a_N = b_N.\nThere exists i (1 <= i <= N, M) such that a_1 = b_1, a_2 = b_2, . . . , a_{i - 1} = b_{i - 1} and a_i < b_i. Here, letters are compared using alphabetical order.\n\nFor example, xy < xya and atcoder < atlas.", "constraint": "The lengths of s and t are between 1 and 100 (inclusive).\ns and t consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\ns\nt", "output": "If it is possible to satisfy s' < t', print Yes; if it is not, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: yx\naxy output: Yes\n\nWe can, for example, rearrange yx into xy and axy into yxa. Then, xy < yxa.", "input: ratcode\natlas output: Yes\n\nWe can, for example, rearrange ratcode into acdeort and atlas into tslaa. Then, acdeort < tslaa.", "input: cd\nabc output: No\n\nNo matter how we rearrange cd and abc, we cannot achieve our objective.", "input: w\nww output: Yes", "input: zzz\nzzz output: No"], "Pid": "p03486", "ProblemText": "Task Description: Problem Statement You are given strings s and t, consisting of lowercase English letters.\nYou will create a string s' by freely rearranging the characters in s.\nYou will also create a string t' by freely rearranging the characters in t.\nDetermine whether it is possible to satisfy s' < t' for the lexicographic order. note: Notes For a string a = a_1 a_2 . . . a_N of length N and a string b = b_1 b_2 . . . b_M of length M, we say a < b for the lexicographic order if either one of the following two conditions holds true:\n\nN < M and a_1 = b_1, a_2 = b_2, . . . , a_N = b_N.\nThere exists i (1 <= i <= N, M) such that a_1 = b_1, a_2 = b_2, . . . , a_{i - 1} = b_{i - 1} and a_i < b_i. Here, letters are compared using alphabetical order.\n\nFor example, xy < xya and atcoder < atlas.\nTask Constraint: The lengths of s and t are between 1 and 100 (inclusive).\ns and t consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\ns\nt\nTask Output: If it is possible to satisfy s' < t', print Yes; if it is not, print No.\nTask Samples: input: yx\naxy output: Yes\n\nWe can, for example, rearrange yx into xy and axy into yxa. Then, xy < yxa.\ninput: ratcode\natlas output: Yes\n\nWe can, for example, rearrange ratcode into acdeort and atlas into tslaa. Then, acdeort < tslaa.\ninput: cd\nabc output: No\n\nNo matter how we rearrange cd and abc, we cannot achieve our objective.\ninput: w\nww output: Yes\ninput: zzz\nzzz output: No\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence of positive integers of length N, a = (a_1, a_2, . . . , a_N).\nYour objective is to remove some of the elements in a so that a will be a good sequence.\nHere, an sequence b is a good sequence when the following condition holds true:\n\nFor each element x in b, the value x occurs exactly x times in b.\n\nFor example, (3,3,3), (4,2,4,1,4,2,4) and () (an empty sequence) are good sequences, while (3,3,3,3) and (2,4,1,4,2) are not.\nFind the minimum number of elements that needs to be removed so that a will be a good sequence.", "constraint": "1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum number of elements that needs to be removed so that a will be a good sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 3 3 3 output: 1\n\nWe can, for example, remove one occurrence of 3. Then, (3,3,3) is a good sequence.", "input: 5\n2 4 1 4 2 output: 2\n\nWe can, for example, remove two occurrences of 4. Then, (2,1,2) is a good sequence.", "input: 6\n1 2 2 3 3 3 output: 0", "input: 1\n1000000000 output: 1\n\nRemove one occurrence of 10^9. Then, () is a good sequence.", "input: 8\n2 7 1 8 2 8 1 8 output: 5"], "Pid": "p03487", "ProblemText": "Task Description: Problem Statement You are given a sequence of positive integers of length N, a = (a_1, a_2, . . . , a_N).\nYour objective is to remove some of the elements in a so that a will be a good sequence.\nHere, an sequence b is a good sequence when the following condition holds true:\n\nFor each element x in b, the value x occurs exactly x times in b.\n\nFor example, (3,3,3), (4,2,4,1,4,2,4) and () (an empty sequence) are good sequences, while (3,3,3,3) and (2,4,1,4,2) are not.\nFind the minimum number of elements that needs to be removed so that a will be a good sequence.\nTask Constraint: 1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum number of elements that needs to be removed so that a will be a good sequence.\nTask Samples: input: 4\n3 3 3 3 output: 1\n\nWe can, for example, remove one occurrence of 3. Then, (3,3,3) is a good sequence.\ninput: 5\n2 4 1 4 2 output: 2\n\nWe can, for example, remove two occurrences of 4. Then, (2,1,2) is a good sequence.\ninput: 6\n1 2 2 3 3 3 output: 0\ninput: 1\n1000000000 output: 1\n\nRemove one occurrence of 10^9. Then, () is a good sequence.\ninput: 8\n2 7 1 8 2 8 1 8 output: 5\n\n" }, { "title": "", "content": "Problem Statement A robot is put at the origin in a two-dimensional plane.\nInitially, the robot is facing in the positive x-axis direction.\nThis robot will be given an instruction sequence s.\ns consists of the following two kinds of letters, and will be executed in order from front to back.\n\nF : Move in the current direction by distance 1.\nT : Turn 90 degrees, either clockwise or counterclockwise.\n\nThe objective of the robot is to be at coordinates (x, y) after all the instructions are executed.\nDetermine whether this objective is achievable.", "constraint": "s consists of F and T.\n1 <= |s| <= 8 000\nx and y are integers.\n|x|, |y| <= |s|", "input": "Input is given from Standard Input in the following format:\ns\nx y", "output": "If the objective is achievable, print Yes; if it is not, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: FTFFTFFF\n4 2 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.", "input: FTFFTFFF\n-2 -2 output: Yes\n\nThe objective can be achieved by, for example, turning clockwise in the first T and turning clockwise in the second T.", "input: FF\n1 0 output: No", "input: TF\n1 0 output: No", "input: FFTTFF\n0 0 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning counterclockwise in the second T.", "input: TTTT\n1 0 output: No"], "Pid": "p03488", "ProblemText": "Task Description: Problem Statement A robot is put at the origin in a two-dimensional plane.\nInitially, the robot is facing in the positive x-axis direction.\nThis robot will be given an instruction sequence s.\ns consists of the following two kinds of letters, and will be executed in order from front to back.\n\nF : Move in the current direction by distance 1.\nT : Turn 90 degrees, either clockwise or counterclockwise.\n\nThe objective of the robot is to be at coordinates (x, y) after all the instructions are executed.\nDetermine whether this objective is achievable.\nTask Constraint: s consists of F and T.\n1 <= |s| <= 8 000\nx and y are integers.\n|x|, |y| <= |s|\nTask Input: Input is given from Standard Input in the following format:\ns\nx y\nTask Output: If the objective is achievable, print Yes; if it is not, print No.\nTask Samples: input: FTFFTFFF\n4 2 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.\ninput: FTFFTFFF\n-2 -2 output: Yes\n\nThe objective can be achieved by, for example, turning clockwise in the first T and turning clockwise in the second T.\ninput: FF\n1 0 output: No\ninput: TF\n1 0 output: No\ninput: FFTTFF\n0 0 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning counterclockwise in the second T.\ninput: TTTT\n1 0 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence of positive integers of length N, a = (a_1, a_2, . . . , a_N).\nYour objective is to remove some of the elements in a so that a will be a good sequence.\nHere, an sequence b is a good sequence when the following condition holds true:\n\nFor each element x in b, the value x occurs exactly x times in b.\n\nFor example, (3,3,3), (4,2,4,1,4,2,4) and () (an empty sequence) are good sequences, while (3,3,3,3) and (2,4,1,4,2) are not.\nFind the minimum number of elements that needs to be removed so that a will be a good sequence.", "constraint": "1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum number of elements that needs to be removed so that a will be a good sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 3 3 3 output: 1\n\nWe can, for example, remove one occurrence of 3. Then, (3,3,3) is a good sequence.", "input: 5\n2 4 1 4 2 output: 2\n\nWe can, for example, remove two occurrences of 4. Then, (2,1,2) is a good sequence.", "input: 6\n1 2 2 3 3 3 output: 0", "input: 1\n1000000000 output: 1\n\nRemove one occurrence of 10^9. Then, () is a good sequence.", "input: 8\n2 7 1 8 2 8 1 8 output: 5"], "Pid": "p03489", "ProblemText": "Task Description: Problem Statement You are given a sequence of positive integers of length N, a = (a_1, a_2, . . . , a_N).\nYour objective is to remove some of the elements in a so that a will be a good sequence.\nHere, an sequence b is a good sequence when the following condition holds true:\n\nFor each element x in b, the value x occurs exactly x times in b.\n\nFor example, (3,3,3), (4,2,4,1,4,2,4) and () (an empty sequence) are good sequences, while (3,3,3,3) and (2,4,1,4,2) are not.\nFind the minimum number of elements that needs to be removed so that a will be a good sequence.\nTask Constraint: 1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum number of elements that needs to be removed so that a will be a good sequence.\nTask Samples: input: 4\n3 3 3 3 output: 1\n\nWe can, for example, remove one occurrence of 3. Then, (3,3,3) is a good sequence.\ninput: 5\n2 4 1 4 2 output: 2\n\nWe can, for example, remove two occurrences of 4. Then, (2,1,2) is a good sequence.\ninput: 6\n1 2 2 3 3 3 output: 0\ninput: 1\n1000000000 output: 1\n\nRemove one occurrence of 10^9. Then, () is a good sequence.\ninput: 8\n2 7 1 8 2 8 1 8 output: 5\n\n" }, { "title": "", "content": "Problem Statement A robot is put at the origin in a two-dimensional plane.\nInitially, the robot is facing in the positive x-axis direction.\nThis robot will be given an instruction sequence s.\ns consists of the following two kinds of letters, and will be executed in order from front to back.\n\nF : Move in the current direction by distance 1.\nT : Turn 90 degrees, either clockwise or counterclockwise.\n\nThe objective of the robot is to be at coordinates (x, y) after all the instructions are executed.\nDetermine whether this objective is achievable.", "constraint": "s consists of F and T.\n1 <= |s| <= 8 000\nx and y are integers.\n|x|, |y| <= |s|", "input": "Input is given from Standard Input in the following format:\ns\nx y", "output": "If the objective is achievable, print Yes; if it is not, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: FTFFTFFF\n4 2 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.", "input: FTFFTFFF\n-2 -2 output: Yes\n\nThe objective can be achieved by, for example, turning clockwise in the first T and turning clockwise in the second T.", "input: FF\n1 0 output: No", "input: TF\n1 0 output: No", "input: FFTTFF\n0 0 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning counterclockwise in the second T.", "input: TTTT\n1 0 output: No"], "Pid": "p03490", "ProblemText": "Task Description: Problem Statement A robot is put at the origin in a two-dimensional plane.\nInitially, the robot is facing in the positive x-axis direction.\nThis robot will be given an instruction sequence s.\ns consists of the following two kinds of letters, and will be executed in order from front to back.\n\nF : Move in the current direction by distance 1.\nT : Turn 90 degrees, either clockwise or counterclockwise.\n\nThe objective of the robot is to be at coordinates (x, y) after all the instructions are executed.\nDetermine whether this objective is achievable.\nTask Constraint: s consists of F and T.\n1 <= |s| <= 8 000\nx and y are integers.\n|x|, |y| <= |s|\nTask Input: Input is given from Standard Input in the following format:\ns\nx y\nTask Output: If the objective is achievable, print Yes; if it is not, print No.\nTask Samples: input: FTFFTFFF\n4 2 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.\ninput: FTFFTFFF\n-2 -2 output: Yes\n\nThe objective can be achieved by, for example, turning clockwise in the first T and turning clockwise in the second T.\ninput: FF\n1 0 output: No\ninput: TF\n1 0 output: No\ninput: FFTTFF\n0 0 output: Yes\n\nThe objective can be achieved by, for example, turning counterclockwise in the first T and turning counterclockwise in the second T.\ninput: TTTT\n1 0 output: No\n\n" }, { "title": "", "content": "Problem Statement For strings s and t, we will say that s and t are prefix-free when neither is a prefix of the other.\nLet L be a positive integer. A set of strings S is a good string set when the following conditions hold true:\n\nEach string in S has a length between 1 and L (inclusive) and consists of the characters 0 and 1.\nAny two distinct strings in S are prefix-free.\n\nWe have a good string set S = \\{ s_1, s_2, . . . , s_N \\}. Alice and Bob will play a game against each other. They will alternately perform the following operation, starting from Alice:\n\nAdd a new string to S. After addition, S must still be a good string set.\n\nThe first player who becomes unable to perform the operation loses the game. Determine the winner of the game when both players play optimally.", "constraint": "1 <= N <= 10^5\n1 <= L <= 10^{18}\ns_1, s_2, ..., s_N are all distinct.\n{ s_1, s_2, ..., s_N } is a good string set.\n|s_1| + |s_2| + ... + |s_N| <= 10^5", "input": "Input is given from Standard Input in the following format:\nN L\ns_1\ns_2\n:\ns_N", "output": "If Alice will win, print Alice; if Bob will win, print Bob.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n00\n01 output: Alice\n\nIf Alice adds 1, Bob will be unable to add a new string.", "input: 2 2\n00\n11 output: Bob\n\nThere are two strings that Alice can add on the first turn: 01 and 10.\nIn case she adds 01, if Bob add 10, she will be unable to add a new string.\nAlso, in case she adds 10, if Bob add 01, she will be unable to add a new string.", "input: 3 3\n0\n10\n110 output: Alice\n\nIf Alice adds 111, Bob will be unable to add a new string.", "input: 2 1\n0\n1 output: Bob\n\nAlice is unable to add a new string on the first turn.", "input: 1 2\n11 output: Alice", "input: 2 3\n101\n11 output: Bob"], "Pid": "p03491", "ProblemText": "Task Description: Problem Statement For strings s and t, we will say that s and t are prefix-free when neither is a prefix of the other.\nLet L be a positive integer. A set of strings S is a good string set when the following conditions hold true:\n\nEach string in S has a length between 1 and L (inclusive) and consists of the characters 0 and 1.\nAny two distinct strings in S are prefix-free.\n\nWe have a good string set S = \\{ s_1, s_2, . . . , s_N \\}. Alice and Bob will play a game against each other. They will alternately perform the following operation, starting from Alice:\n\nAdd a new string to S. After addition, S must still be a good string set.\n\nThe first player who becomes unable to perform the operation loses the game. Determine the winner of the game when both players play optimally.\nTask Constraint: 1 <= N <= 10^5\n1 <= L <= 10^{18}\ns_1, s_2, ..., s_N are all distinct.\n{ s_1, s_2, ..., s_N } is a good string set.\n|s_1| + |s_2| + ... + |s_N| <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nN L\ns_1\ns_2\n:\ns_N\nTask Output: If Alice will win, print Alice; if Bob will win, print Bob.\nTask Samples: input: 2 2\n00\n01 output: Alice\n\nIf Alice adds 1, Bob will be unable to add a new string.\ninput: 2 2\n00\n11 output: Bob\n\nThere are two strings that Alice can add on the first turn: 01 and 10.\nIn case she adds 01, if Bob add 10, she will be unable to add a new string.\nAlso, in case she adds 10, if Bob add 01, she will be unable to add a new string.\ninput: 3 3\n0\n10\n110 output: Alice\n\nIf Alice adds 111, Bob will be unable to add a new string.\ninput: 2 1\n0\n1 output: Bob\n\nAlice is unable to add a new string on the first turn.\ninput: 1 2\n11 output: Alice\ninput: 2 3\n101\n11 output: Bob\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices. The vertices are numbered 1 through N. The i-th edge (1 <= i <= N - 1) connects Vertex x_i and y_i. For vertices v and w (1 <= v, w <= N), we will define the distance between v and w d(v, w) as \"the number of edges contained in the path v-w\".\nA squirrel lives in each vertex of the tree. They are planning to move, as follows. First, they will freely choose a permutation of (1,2, . . . , N), p = (p_1, p_2, . . . , p_N). Then, for each 1 <= i <= N, the squirrel that lived in Vertex i will move to Vertex p_i.\nSince they like long travels, they have decided to maximize the total distance they traveled during the process. That is, they will choose p so that d(1, p_1) + d(2, p_2) + . . . + d(N, p_N) will be maximized. How many such ways are there to choose p, modulo 10^9 + 7?", "constraint": "2 <= N <= 5,000\n1 <= x_i, y_i <= N\nThe input graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}", "output": "Print the number of the ways to choose p so that the condition is satisfied, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3 output: 3\n\nThe maximum possible distance traveled by squirrels is 4.\nThere are three choices of p that achieve it, as follows:\n\n(2,3,1)\n(3,1,2)\n(3,2,1)", "input: 4\n1 2\n1 3\n1 4 output: 11\n\nThe maximum possible distance traveled by squirrels is 6.\nFor example, p = (2,1,4,3) achieves it.", "input: 6\n1 2\n1 3\n1 4\n2 5\n2 6 output: 36", "input: 7\n1 2\n6 3\n4 5\n1 7\n1 5\n2 3 output: 396"], "Pid": "p03492", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices. The vertices are numbered 1 through N. The i-th edge (1 <= i <= N - 1) connects Vertex x_i and y_i. For vertices v and w (1 <= v, w <= N), we will define the distance between v and w d(v, w) as \"the number of edges contained in the path v-w\".\nA squirrel lives in each vertex of the tree. They are planning to move, as follows. First, they will freely choose a permutation of (1,2, . . . , N), p = (p_1, p_2, . . . , p_N). Then, for each 1 <= i <= N, the squirrel that lived in Vertex i will move to Vertex p_i.\nSince they like long travels, they have decided to maximize the total distance they traveled during the process. That is, they will choose p so that d(1, p_1) + d(2, p_2) + . . . + d(N, p_N) will be maximized. How many such ways are there to choose p, modulo 10^9 + 7?\nTask Constraint: 2 <= N <= 5,000\n1 <= x_i, y_i <= N\nThe input graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N - 1} y_{N - 1}\nTask Output: Print the number of the ways to choose p so that the condition is satisfied, modulo 10^9 + 7.\nTask Samples: input: 3\n1 2\n2 3 output: 3\n\nThe maximum possible distance traveled by squirrels is 4.\nThere are three choices of p that achieve it, as follows:\n\n(2,3,1)\n(3,1,2)\n(3,2,1)\ninput: 4\n1 2\n1 3\n1 4 output: 11\n\nThe maximum possible distance traveled by squirrels is 6.\nFor example, p = (2,1,4,3) achieves it.\ninput: 6\n1 2\n1 3\n1 4\n2 5\n2 6 output: 36\ninput: 7\n1 2\n6 3\n4 5\n1 7\n1 5\n2 3 output: 396\n\n" }, { "title": "", "content": "Problem Statement Snuke has a grid consisting of three squares numbered 1,2 and 3.\nIn each square, either 0 or 1 is written. The number written in Square i is s_i.\nSnuke will place a marble on each square that says 1.\nFind the number of squares on which Snuke will place a marble.", "constraint": "Each of s_1, s_2 and s_3 is either 1 or 0.", "input": "Input is given from Standard Input in the following format:\ns_{1}s_{2}s_{3}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 101 output: 2\nA marble will be placed on Square 1 and 3.", "input: 000 output: 0\nNo marble will be placed on any square."], "Pid": "p03493", "ProblemText": "Task Description: Problem Statement Snuke has a grid consisting of three squares numbered 1,2 and 3.\nIn each square, either 0 or 1 is written. The number written in Square i is s_i.\nSnuke will place a marble on each square that says 1.\nFind the number of squares on which Snuke will place a marble.\nTask Constraint: Each of s_1, s_2 and s_3 is either 1 or 0.\nTask Input: Input is given from Standard Input in the following format:\ns_{1}s_{2}s_{3}\nTask Output: Print the answer.\nTask Samples: input: 101 output: 2\nA marble will be placed on Square 1 and 3.\ninput: 000 output: 0\nNo marble will be placed on any square.\n\n" }, { "title": "", "content": "Problem Statement There are N positive integers written on a blackboard: A_1, . . . , A_N.\nSnuke can perform the following operation when all integers on the blackboard are even:\n\nReplace each integer X on the blackboard by X divided by 2.\n\nFind the maximum possible number of operations that Snuke can perform.", "constraint": "1 <= N <= 200\n1 <= A_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the maximum possible number of operations that Snuke can perform.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n8 12 40 output: 2\n\nInitially, [8,12,40] are written on the blackboard.\nSince all those integers are even, Snuke can perform the operation.\nAfter the operation is performed once, [4,6,20] are written on the blackboard.\nSince all those integers are again even, he can perform the operation.\nAfter the operation is performed twice, [2,3,10] are written on the blackboard.\nNow, there is an odd number 3 on the blackboard, so he cannot perform the operation any more.\nThus, Snuke can perform the operation at most twice.", "input: 4\n5 6 8 10 output: 0\n\nSince there is an odd number 5 on the blackboard already in the beginning, Snuke cannot perform the operation at all.", "input: 6\n382253568 723152896 37802240 379425024 404894720 471526144 output: 8"], "Pid": "p03494", "ProblemText": "Task Description: Problem Statement There are N positive integers written on a blackboard: A_1, . . . , A_N.\nSnuke can perform the following operation when all integers on the blackboard are even:\n\nReplace each integer X on the blackboard by X divided by 2.\n\nFind the maximum possible number of operations that Snuke can perform.\nTask Constraint: 1 <= N <= 200\n1 <= A_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the maximum possible number of operations that Snuke can perform.\nTask Samples: input: 3\n8 12 40 output: 2\n\nInitially, [8,12,40] are written on the blackboard.\nSince all those integers are even, Snuke can perform the operation.\nAfter the operation is performed once, [4,6,20] are written on the blackboard.\nSince all those integers are again even, he can perform the operation.\nAfter the operation is performed twice, [2,3,10] are written on the blackboard.\nNow, there is an odd number 3 on the blackboard, so he cannot perform the operation any more.\nThus, Snuke can perform the operation at most twice.\ninput: 4\n5 6 8 10 output: 0\n\nSince there is an odd number 5 on the blackboard already in the beginning, Snuke cannot perform the operation at all.\ninput: 6\n382253568 723152896 37802240 379425024 404894720 471526144 output: 8\n\n" }, { "title": "", "content": "Problem Statement Takahashi has N balls. Initially, an integer A_i is written on the i-th ball.\nHe would like to rewrite the integer on some balls so that there are at most K different integers written on the N balls.\nFind the minimum number of balls that Takahashi needs to rewrite the integers on them.", "constraint": "1 <= K <= N <= 200000\n1 <= A_i <= N\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N", "output": "Print the minimum number of balls that Takahashi needs to rewrite the integers on them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n1 1 2 2 5 output: 1\n\nFor example, if we rewrite the integer on the fifth ball to 2, there are two different integers written on the balls: 1 and 2.\nOn the other hand, it is not possible to rewrite the integers on zero balls so that there are at most two different integers written on the balls, so we should print 1.", "input: 4 4\n1 1 2 2 output: 0\n\nAlready in the beginning, there are two different integers written on the balls, so we do not need to rewrite anything.", "input: 10 3\n5 1 3 2 4 1 1 2 3 4 output: 3"], "Pid": "p03495", "ProblemText": "Task Description: Problem Statement Takahashi has N balls. Initially, an integer A_i is written on the i-th ball.\nHe would like to rewrite the integer on some balls so that there are at most K different integers written on the N balls.\nFind the minimum number of balls that Takahashi needs to rewrite the integers on them.\nTask Constraint: 1 <= K <= N <= 200000\n1 <= A_i <= N\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nTask Output: Print the minimum number of balls that Takahashi needs to rewrite the integers on them.\nTask Samples: input: 5 2\n1 1 2 2 5 output: 1\n\nFor example, if we rewrite the integer on the fifth ball to 2, there are two different integers written on the balls: 1 and 2.\nOn the other hand, it is not possible to rewrite the integers on zero balls so that there are at most two different integers written on the balls, so we should print 1.\ninput: 4 4\n1 1 2 2 output: 0\n\nAlready in the beginning, there are two different integers written on the balls, so we do not need to rewrite anything.\ninput: 10 3\n5 1 3 2 4 1 1 2 3 4 output: 3\n\n" }, { "title": "", "content": "Problem Statement Snuke has an integer sequence, a, of length N. The i-th element of a (1-indexed) is a_{i}.\nHe can perform the following operation any number of times:\n\nOperation: Choose integers x and y between 1 and N (inclusive), and add a_x to a_y.\n\nHe would like to perform this operation between 0 and 2N times (inclusive) so that a satisfies the condition below. Show one such sequence of operations.\nIt can be proved that such a sequence of operations always exists under the constraints in this problem.\n\nCondition: a_1 <= a_2 <= . . . <= a_{N}", "constraint": "2 <= N <= 50\n-10^{6} <= a_i <= 10^{6}\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}", "output": "Let m be the number of operations in your solution. In the first line, print m.\nIn the i-th of the subsequent m lines, print the numbers x and y chosen in the i-th operation, with a space in between.\nThe output will be considered correct if m is between 0 and 2N (inclusive) and a satisfies the condition after the m operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-2 5 -1 output: 2\n2 3\n3 3\nAfter the first operation, a = (-2,5,4).\nAfter the second operation, a = (-2,5,8), and the condition is now satisfied.", "input: 2\n-1 -3 output: 1\n2 1\nAfter the first operation, a = (-4,-3) and the condition is now satisfied.", "input: 5\n0 0 0 0 0 output: 0\nThe condition is satisfied already in the beginning."], "Pid": "p03496", "ProblemText": "Task Description: Problem Statement Snuke has an integer sequence, a, of length N. The i-th element of a (1-indexed) is a_{i}.\nHe can perform the following operation any number of times:\n\nOperation: Choose integers x and y between 1 and N (inclusive), and add a_x to a_y.\n\nHe would like to perform this operation between 0 and 2N times (inclusive) so that a satisfies the condition below. Show one such sequence of operations.\nIt can be proved that such a sequence of operations always exists under the constraints in this problem.\n\nCondition: a_1 <= a_2 <= . . . <= a_{N}\nTask Constraint: 2 <= N <= 50\n-10^{6} <= a_i <= 10^{6}\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}\nTask Output: Let m be the number of operations in your solution. In the first line, print m.\nIn the i-th of the subsequent m lines, print the numbers x and y chosen in the i-th operation, with a space in between.\nThe output will be considered correct if m is between 0 and 2N (inclusive) and a satisfies the condition after the m operations.\nTask Samples: input: 3\n-2 5 -1 output: 2\n2 3\n3 3\nAfter the first operation, a = (-2,5,4).\nAfter the second operation, a = (-2,5,8), and the condition is now satisfied.\ninput: 2\n-1 -3 output: 1\n2 1\nAfter the first operation, a = (-4,-3) and the condition is now satisfied.\ninput: 5\n0 0 0 0 0 output: 0\nThe condition is satisfied already in the beginning.\n\n" }, { "title": "", "content": "Problem Statement Takahashi has N balls. Initially, an integer A_i is written on the i-th ball.\nHe would like to rewrite the integer on some balls so that there are at most K different integers written on the N balls.\nFind the minimum number of balls that Takahashi needs to rewrite the integers on them.", "constraint": "1 <= K <= N <= 200000\n1 <= A_i <= N\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N", "output": "Print the minimum number of balls that Takahashi needs to rewrite the integers on them.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n1 1 2 2 5 output: 1\n\nFor example, if we rewrite the integer on the fifth ball to 2, there are two different integers written on the balls: 1 and 2.\nOn the other hand, it is not possible to rewrite the integers on zero balls so that there are at most two different integers written on the balls, so we should print 1.", "input: 4 4\n1 1 2 2 output: 0\n\nAlready in the beginning, there are two different integers written on the balls, so we do not need to rewrite anything.", "input: 10 3\n5 1 3 2 4 1 1 2 3 4 output: 3"], "Pid": "p03497", "ProblemText": "Task Description: Problem Statement Takahashi has N balls. Initially, an integer A_i is written on the i-th ball.\nHe would like to rewrite the integer on some balls so that there are at most K different integers written on the N balls.\nFind the minimum number of balls that Takahashi needs to rewrite the integers on them.\nTask Constraint: 1 <= K <= N <= 200000\n1 <= A_i <= N\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nTask Output: Print the minimum number of balls that Takahashi needs to rewrite the integers on them.\nTask Samples: input: 5 2\n1 1 2 2 5 output: 1\n\nFor example, if we rewrite the integer on the fifth ball to 2, there are two different integers written on the balls: 1 and 2.\nOn the other hand, it is not possible to rewrite the integers on zero balls so that there are at most two different integers written on the balls, so we should print 1.\ninput: 4 4\n1 1 2 2 output: 0\n\nAlready in the beginning, there are two different integers written on the balls, so we do not need to rewrite anything.\ninput: 10 3\n5 1 3 2 4 1 1 2 3 4 output: 3\n\n" }, { "title": "", "content": "Problem Statement Snuke has an integer sequence, a, of length N. The i-th element of a (1-indexed) is a_{i}.\nHe can perform the following operation any number of times:\n\nOperation: Choose integers x and y between 1 and N (inclusive), and add a_x to a_y.\n\nHe would like to perform this operation between 0 and 2N times (inclusive) so that a satisfies the condition below. Show one such sequence of operations.\nIt can be proved that such a sequence of operations always exists under the constraints in this problem.\n\nCondition: a_1 <= a_2 <= . . . <= a_{N}", "constraint": "2 <= N <= 50\n-10^{6} <= a_i <= 10^{6}\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}", "output": "Let m be the number of operations in your solution. In the first line, print m.\nIn the i-th of the subsequent m lines, print the numbers x and y chosen in the i-th operation, with a space in between.\nThe output will be considered correct if m is between 0 and 2N (inclusive) and a satisfies the condition after the m operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-2 5 -1 output: 2\n2 3\n3 3\nAfter the first operation, a = (-2,5,4).\nAfter the second operation, a = (-2,5,8), and the condition is now satisfied.", "input: 2\n-1 -3 output: 1\n2 1\nAfter the first operation, a = (-4,-3) and the condition is now satisfied.", "input: 5\n0 0 0 0 0 output: 0\nThe condition is satisfied already in the beginning."], "Pid": "p03498", "ProblemText": "Task Description: Problem Statement Snuke has an integer sequence, a, of length N. The i-th element of a (1-indexed) is a_{i}.\nHe can perform the following operation any number of times:\n\nOperation: Choose integers x and y between 1 and N (inclusive), and add a_x to a_y.\n\nHe would like to perform this operation between 0 and 2N times (inclusive) so that a satisfies the condition below. Show one such sequence of operations.\nIt can be proved that such a sequence of operations always exists under the constraints in this problem.\n\nCondition: a_1 <= a_2 <= . . . <= a_{N}\nTask Constraint: 2 <= N <= 50\n-10^{6} <= a_i <= 10^{6}\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}\nTask Output: Let m be the number of operations in your solution. In the first line, print m.\nIn the i-th of the subsequent m lines, print the numbers x and y chosen in the i-th operation, with a space in between.\nThe output will be considered correct if m is between 0 and 2N (inclusive) and a satisfies the condition after the m operations.\nTask Samples: input: 3\n-2 5 -1 output: 2\n2 3\n3 3\nAfter the first operation, a = (-2,5,4).\nAfter the second operation, a = (-2,5,8), and the condition is now satisfied.\ninput: 2\n-1 -3 output: 1\n2 1\nAfter the first operation, a = (-4,-3) and the condition is now satisfied.\ninput: 5\n0 0 0 0 0 output: 0\nThe condition is satisfied already in the beginning.\n\n" }, { "title": "", "content": "Problem Statement Snuke has a rooted tree with N+1 vertices.\nThe vertices are numbered 0 through N, and Vertex 0 is the root of the tree.\nThe parent of Vertex i (1 <= i <= N) is Vertex p_i.\nBesides this tree, Snuke also has an box which is initially empty and many marbles, and playing with them.\nThe play begins with placing one marble on some of the vertices, then proceeds as follows:\n\nIf there is a marble on Vertex 0, move the marble into the box.\nMove each marble from the vertex to its parent (all at once).\nFor each vertex occupied by two or more marbles, remove all the marbles from the vertex.\nIf there exists a vertex with some marbles, go to Step 1. Otherwise, end the play.\n\nThere are 2^{N+1} ways to place marbles on some of the vertices.\nFor each of them, find the number of marbles that will be in the box at the end of the play, and compute the sum of all those numbers modulo 1,000,000,007. partial scores: Partial Scores\nIn the test set worth 400 points, N < 2{, }000.", "constraint": "1 <= N < 2 * 10^{5}\n0 <= p_i < i", "input": "Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 0 output: 8\n\nWhen we place a marble on both Vertex 1 and 2, there will be multiple marbles on Vertex 0 by step 2. In such a case, these marbles will be removed instead of being moved to the box.", "input: 5\n0 1 1 0 4 output: 96", "input: 31\n0 1 0 2 4 0 4 1 6 4 3 9 7 3 7 2 15 6 12 10 12 16 5 3 20 1 25 20 23 24 23 output: 730395550\n\nBe sure to compute the sum modulo 1,000,000,007."], "Pid": "p03499", "ProblemText": "Task Description: Problem Statement Snuke has a rooted tree with N+1 vertices.\nThe vertices are numbered 0 through N, and Vertex 0 is the root of the tree.\nThe parent of Vertex i (1 <= i <= N) is Vertex p_i.\nBesides this tree, Snuke also has an box which is initially empty and many marbles, and playing with them.\nThe play begins with placing one marble on some of the vertices, then proceeds as follows:\n\nIf there is a marble on Vertex 0, move the marble into the box.\nMove each marble from the vertex to its parent (all at once).\nFor each vertex occupied by two or more marbles, remove all the marbles from the vertex.\nIf there exists a vertex with some marbles, go to Step 1. Otherwise, end the play.\n\nThere are 2^{N+1} ways to place marbles on some of the vertices.\nFor each of them, find the number of marbles that will be in the box at the end of the play, and compute the sum of all those numbers modulo 1,000,000,007. partial scores: Partial Scores\nIn the test set worth 400 points, N < 2{, }000.\nTask Constraint: 1 <= N < 2 * 10^{5}\n0 <= p_i < i\nTask Input: Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_{N}\nTask Output: Print the answer.\nTask Samples: input: 2\n0 0 output: 8\n\nWhen we place a marble on both Vertex 1 and 2, there will be multiple marbles on Vertex 0 by step 2. In such a case, these marbles will be removed instead of being moved to the box.\ninput: 5\n0 1 1 0 4 output: 96\ninput: 31\n0 1 0 2 4 0 4 1 6 4 3 9 7 3 7 2 15 6 12 10 12 16 5 3 20 1 25 20 23 24 23 output: 730395550\n\nBe sure to compute the sum modulo 1,000,000,007.\n\n" }, { "title": "", "content": "Problem Statement There are N non-negative integers written on the blackboard: A_1, . . . , A_N.\nSnuke can perform the following two operations at most K times in total in any order:\n\nOperation A: Replace each integer X on the blackboard with X divided by 2, rounded down to the nearest integer.\nOperation B: Replace each integer X on the blackboard with X minus 1. This operation cannot be performed if one or more 0s are written on the blackboard.\n\nFind the number of the different possible combinations of integers written on the blackboard after Snuke performs the operations, modulo 1,000,000,007.", "constraint": "1 <= N <= 200\n1 <= A_i <= 10^{18}\n1 <= K <= 10^{18}\nA_i and K are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N", "output": "Print the number of the different possible combinations of integers written on the blackboard after Snuke performs the operations, modulo 1,000,000,007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n5 7 output: 6\n\nThere are six possible combinations of integers on the blackboard: (1,1), (1,2), (2,3), (3,5), (4,6) and (5,7).\nFor example, (1,2) can be obtained by performing Operation A and Operation B in this order.", "input: 3 4\n10 13 22 output: 20", "input: 1 100\n10 output: 11", "input: 10 123456789012345678\n228344079825412349 478465001534875275 398048921164061989 329102208281783917 779698519704384319 617456682030809556 561259383338846380 254083246422083141 458181156833851984 502254767369499613 output: 164286011"], "Pid": "p03500", "ProblemText": "Task Description: Problem Statement There are N non-negative integers written on the blackboard: A_1, . . . , A_N.\nSnuke can perform the following two operations at most K times in total in any order:\n\nOperation A: Replace each integer X on the blackboard with X divided by 2, rounded down to the nearest integer.\nOperation B: Replace each integer X on the blackboard with X minus 1. This operation cannot be performed if one or more 0s are written on the blackboard.\n\nFind the number of the different possible combinations of integers written on the blackboard after Snuke performs the operations, modulo 1,000,000,007.\nTask Constraint: 1 <= N <= 200\n1 <= A_i <= 10^{18}\n1 <= K <= 10^{18}\nA_i and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nTask Output: Print the number of the different possible combinations of integers written on the blackboard after Snuke performs the operations, modulo 1,000,000,007.\nTask Samples: input: 2 2\n5 7 output: 6\n\nThere are six possible combinations of integers on the blackboard: (1,1), (1,2), (2,3), (3,5), (4,6) and (5,7).\nFor example, (1,2) can be obtained by performing Operation A and Operation B in this order.\ninput: 3 4\n10 13 22 output: 20\ninput: 1 100\n10 output: 11\ninput: 10 123456789012345678\n228344079825412349 478465001534875275 398048921164061989 329102208281783917 779698519704384319 617456682030809556 561259383338846380 254083246422083141 458181156833851984 502254767369499613 output: 164286011\n\n" }, { "title": "", "content": "Problem Statement You are parking at a parking lot. You can choose from the following two fee plans:\n\nPlan 1: The fee will be A*T yen (the currency of Japan) when you park for T hours.\nPlan 2: The fee will be B yen, regardless of the duration.\n\nFind the minimum fee when you park for N hours.", "constraint": "1<=N<=20\n1<=A<=100\n1<=B<=2000\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Output When the minimum fee is x yen, print the value of x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 17 120 output: 119\nIf you choose Plan 1, the fee will be 7*17=119 yen.\nIf you choose Plan 2, the fee will be 120 yen.\n\nThus, the minimum fee is 119 yen.", "input: 5 20 100 output: 100\n\nThe fee might be the same in the two plans.", "input: 6 18 100 output: 100"], "Pid": "p03501", "ProblemText": "Task Description: Problem Statement You are parking at a parking lot. You can choose from the following two fee plans:\n\nPlan 1: The fee will be A*T yen (the currency of Japan) when you park for T hours.\nPlan 2: The fee will be B yen, regardless of the duration.\n\nFind the minimum fee when you park for N hours.\nTask Constraint: 1<=N<=20\n1<=A<=100\n1<=B<=2000\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Output When the minimum fee is x yen, print the value of x.\nTask Samples: input: 7 17 120 output: 119\nIf you choose Plan 1, the fee will be 7*17=119 yen.\nIf you choose Plan 2, the fee will be 120 yen.\n\nThus, the minimum fee is 119 yen.\ninput: 5 20 100 output: 100\n\nThe fee might be the same in the two plans.\ninput: 6 18 100 output: 100\n\n" }, { "title": "", "content": "Problem Statement An integer X is called a Harshad number if X is divisible by f(X), where f(X) is the sum of the digits in X when written in base 10.\nGiven an integer N, determine whether it is a Harshad number.", "constraint": "1?N?10^8\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print Yes if N is a Harshad number; print No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 12 output: Yes\n\nf(12)=1+2=3. Since 12 is divisible by 3,12 is a Harshad number.", "input: 57 output: No\n\nf(57)=5+7=12. Since 57 is not divisible by 12,12 is not a Harshad number.", "input: 148 output: No"], "Pid": "p03502", "ProblemText": "Task Description: Problem Statement An integer X is called a Harshad number if X is divisible by f(X), where f(X) is the sum of the digits in X when written in base 10.\nGiven an integer N, determine whether it is a Harshad number.\nTask Constraint: 1?N?10^8\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print Yes if N is a Harshad number; print No otherwise.\nTask Samples: input: 12 output: Yes\n\nf(12)=1+2=3. Since 12 is divisible by 3,12 is a Harshad number.\ninput: 57 output: No\n\nf(57)=5+7=12. Since 57 is not divisible by 12,12 is not a Harshad number.\ninput: 148 output: No\n\n" }, { "title": "", "content": "Problem Statement Joisino is planning to open a shop in a shopping street.\nEach of the five weekdays is divided into two periods, the morning and the evening. For each of those ten periods, a shop must be either open during the whole period, or closed during the whole period. Naturally, a shop must be open during at least one of those periods.\nThere are already N stores in the street, numbered 1 through N.\nYou are given information of the business hours of those shops, F_{i, j, k}. If F_{i, j, k}=1, Shop i is open during Period k on Day j (this notation is explained below); if F_{i, j, k}=0, Shop i is closed during that period. Here, the days of the week are denoted as follows. Monday: Day 1, Tuesday: Day 2, Wednesday: Day 3, Thursday: Day 4, Friday: Day 5. Also, the morning is denoted as Period 1, and the afternoon is denoted as Period 2.\nLet c_i be the number of periods during which both Shop i and Joisino's shop are open. Then, the profit of Joisino's shop will be P_{1, c_1}+P_{2, c_2}+. . . +P_{N, c_N}.\nFind the maximum possible profit of Joisino's shop when she decides whether her shop is open during each period, making sure that it is open during at least one period.", "constraint": "1<=N<=100\n0<=F_{i,j,k}<=1\nFor every integer i such that 1<=i<=N, there exists at least one pair (j,k) such that F_{i,j,k}=1.\n-10^7<=P_{i,j}<=10^7\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nF_{1,1,1} F_{1,1,2} . . . F_{1,5,1} F_{1,5,2}\n:\nF_{N, 1,1} F_{N, 1,2} . . . F_{N, 5,1} F_{N, 5,2}\nP_{1,0} . . . P_{1,10}\n:\nP_{N, 0} . . . P_{N, 10}", "output": "Print the maximum possible profit of Joisino's shop.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n1 1 0 1 0 0 0 1 0 1\n3 4 5 6 7 8 9 -2 -3 4 -2 output: 8\n\nIf her shop is open only during the periods when Shop 1 is opened, the profit will be 8, which is the maximum possible profit.", "input: 2\n1 1 1 1 1 0 0 0 0 0\n0 0 0 0 0 1 1 1 1 1\n0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1\n0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 output: -2\n\nNote that a shop must be open during at least one period, and the profit may be negative.", "input: 3\n1 1 1 1 1 1 0 0 1 1\n0 1 0 1 1 1 1 0 1 0\n1 0 1 1 0 1 0 1 0 1\n-8 6 -2 -8 -8 4 8 7 -6 2 2\n-9 2 0 1 7 -5 0 -2 -6 5 5\n6 -6 7 -9 6 -5 8 0 -9 -7 -7 output: 23"], "Pid": "p03503", "ProblemText": "Task Description: Problem Statement Joisino is planning to open a shop in a shopping street.\nEach of the five weekdays is divided into two periods, the morning and the evening. For each of those ten periods, a shop must be either open during the whole period, or closed during the whole period. Naturally, a shop must be open during at least one of those periods.\nThere are already N stores in the street, numbered 1 through N.\nYou are given information of the business hours of those shops, F_{i, j, k}. If F_{i, j, k}=1, Shop i is open during Period k on Day j (this notation is explained below); if F_{i, j, k}=0, Shop i is closed during that period. Here, the days of the week are denoted as follows. Monday: Day 1, Tuesday: Day 2, Wednesday: Day 3, Thursday: Day 4, Friday: Day 5. Also, the morning is denoted as Period 1, and the afternoon is denoted as Period 2.\nLet c_i be the number of periods during which both Shop i and Joisino's shop are open. Then, the profit of Joisino's shop will be P_{1, c_1}+P_{2, c_2}+. . . +P_{N, c_N}.\nFind the maximum possible profit of Joisino's shop when she decides whether her shop is open during each period, making sure that it is open during at least one period.\nTask Constraint: 1<=N<=100\n0<=F_{i,j,k}<=1\nFor every integer i such that 1<=i<=N, there exists at least one pair (j,k) such that F_{i,j,k}=1.\n-10^7<=P_{i,j}<=10^7\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nF_{1,1,1} F_{1,1,2} . . . F_{1,5,1} F_{1,5,2}\n:\nF_{N, 1,1} F_{N, 1,2} . . . F_{N, 5,1} F_{N, 5,2}\nP_{1,0} . . . P_{1,10}\n:\nP_{N, 0} . . . P_{N, 10}\nTask Output: Print the maximum possible profit of Joisino's shop.\nTask Samples: input: 1\n1 1 0 1 0 0 0 1 0 1\n3 4 5 6 7 8 9 -2 -3 4 -2 output: 8\n\nIf her shop is open only during the periods when Shop 1 is opened, the profit will be 8, which is the maximum possible profit.\ninput: 2\n1 1 1 1 1 0 0 0 0 0\n0 0 0 0 0 1 1 1 1 1\n0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1\n0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 output: -2\n\nNote that a shop must be open during at least one period, and the profit may be negative.\ninput: 3\n1 1 1 1 1 1 0 0 1 1\n0 1 0 1 1 1 1 0 1 0\n1 0 1 1 0 1 0 1 0 1\n-8 6 -2 -8 -8 4 8 7 -6 2 2\n-9 2 0 1 7 -5 0 -2 -6 5 5\n6 -6 7 -9 6 -5 8 0 -9 -7 -7 output: 23\n\n" }, { "title": "", "content": "Problem Statement Joisino is planning to record N TV programs with recorders.\nThe TV can receive C channels numbered 1 through C.\nThe i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.\nHere, there will never be more than one program that are broadcast on the same channel at the same time.\nWhen the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).\nFind the minimum number of recorders required to record the channels so that all the N programs are completely recorded.", "constraint": "1<=N<=10^5\n1<=C<=30\n1<=s_i=t_j.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN C\ns_1 t_1 c_1\n:\ns_N t_N c_N", "output": "Output When the minimum required number of recorders is x, print the value of x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 7 2\n7 8 1\n8 12 1 output: 2\n\nTwo recorders can record all the programs, for example, as follows:\n\nWith the first recorder, record Channel 2 from time 1 to time 7. The first program will be recorded. Note that this recorder will be unable to record other channels from time 0.5 to time 7.\nWith the second recorder, record Channel 1 from time 7 to time 12. The second and third programs will be recorded. Note that this recorder will be unable to record other channels from time 6.5 to time 12.", "input: 3 4\n1 3 2\n3 4 4\n1 4 3 output: 3\n\nThere may be a channel where there is no program to record.", "input: 9 4\n56 60 4\n33 37 2\n89 90 3\n32 43 1\n67 68 3\n49 51 3\n31 32 3\n70 71 1\n11 12 3 output: 2"], "Pid": "p03504", "ProblemText": "Task Description: Problem Statement Joisino is planning to record N TV programs with recorders.\nThe TV can receive C channels numbered 1 through C.\nThe i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.\nHere, there will never be more than one program that are broadcast on the same channel at the same time.\nWhen the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).\nFind the minimum number of recorders required to record the channels so that all the N programs are completely recorded.\nTask Constraint: 1<=N<=10^5\n1<=C<=30\n1<=s_i=t_j.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN C\ns_1 t_1 c_1\n:\ns_N t_N c_N\nTask Output: Output When the minimum required number of recorders is x, print the value of x.\nTask Samples: input: 3 2\n1 7 2\n7 8 1\n8 12 1 output: 2\n\nTwo recorders can record all the programs, for example, as follows:\n\nWith the first recorder, record Channel 2 from time 1 to time 7. The first program will be recorded. Note that this recorder will be unable to record other channels from time 0.5 to time 7.\nWith the second recorder, record Channel 1 from time 7 to time 12. The second and third programs will be recorded. Note that this recorder will be unable to record other channels from time 6.5 to time 12.\ninput: 3 4\n1 3 2\n3 4 4\n1 4 3 output: 3\n\nThere may be a channel where there is no program to record.\ninput: 9 4\n56 60 4\n33 37 2\n89 90 3\n32 43 1\n67 68 3\n49 51 3\n31 32 3\n70 71 1\n11 12 3 output: 2\n\n" }, { "title": "", "content": "Problem Statement But Coder Inc. runs a programming competition site called But Coder. In this site, a user is given an integer value called rating that represents his/her skill, which changes each time he/she participates in a contest. The initial value of a new user's rating is 0, and a user whose rating reaches K or higher is called Kaiden (\"total transmission\"). Note that a user's rating may become negative.\nHikuhashi is a new user in But Coder. It is estimated that, his rating increases by A in each of his odd-numbered contests (first, third, fifth, . . . ), and decreases by B in each of his even-numbered contests (second, fourth, sixth, . . . ).\nAccording to this estimate, after how many contests will he become Kaiden for the first time, or will he never become Kaiden?", "constraint": "1 <= K, A, B <= 10^{18}\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nK A B", "output": "If it is estimated that Hikuhashi will never become Kaiden, print -1. Otherwise, print the estimated number of contests before he become Kaiden for the first time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4000 2000 500 output: 5\n\nEach time Hikuhashi participates in a contest, his rating is estimated to change as 0 → 2000 → 1500 → 3500 → 3000 → 5000 → … After his fifth contest, his rating will reach 4000 or higher for the first time.", "input: 4000 500 2000 output: -1\n\nEach time Hikuhashi participates in a contest, his rating is estimated to change as 0 → 500 → -1500 → -1000 → -3000 → -2500 → … He will never become Kaiden.", "input: 1000000000000000000 2 1 output: 1999999999999999997\n\nThe input and output values may not fit into 32-bit integers."], "Pid": "p03505", "ProblemText": "Task Description: Problem Statement But Coder Inc. runs a programming competition site called But Coder. In this site, a user is given an integer value called rating that represents his/her skill, which changes each time he/she participates in a contest. The initial value of a new user's rating is 0, and a user whose rating reaches K or higher is called Kaiden (\"total transmission\"). Note that a user's rating may become negative.\nHikuhashi is a new user in But Coder. It is estimated that, his rating increases by A in each of his odd-numbered contests (first, third, fifth, . . . ), and decreases by B in each of his even-numbered contests (second, fourth, sixth, . . . ).\nAccording to this estimate, after how many contests will he become Kaiden for the first time, or will he never become Kaiden?\nTask Constraint: 1 <= K, A, B <= 10^{18}\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nK A B\nTask Output: If it is estimated that Hikuhashi will never become Kaiden, print -1. Otherwise, print the estimated number of contests before he become Kaiden for the first time.\nTask Samples: input: 4000 2000 500 output: 5\n\nEach time Hikuhashi participates in a contest, his rating is estimated to change as 0 → 2000 → 1500 → 3500 → 3000 → 5000 → … After his fifth contest, his rating will reach 4000 or higher for the first time.\ninput: 4000 500 2000 output: -1\n\nEach time Hikuhashi participates in a contest, his rating is estimated to change as 0 → 500 → -1500 → -1000 → -3000 → -2500 → … He will never become Kaiden.\ninput: 1000000000000000000 2 1 output: 1999999999999999997\n\nThe input and output values may not fit into 32-bit integers.\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N. Consider an infinite N-ary tree as shown below:\nFigure: an infinite N-ary tree for the case N = 3\n\nAs shown in the figure, each vertex is indexed with a unique positive integer, and for every positive integer there is a vertex indexed with it. The root of the tree has the index 1. For the remaining vertices, vertices in the upper row have smaller indices than those in the lower row. Among the vertices in the same row, a vertex that is more to the left has a smaller index.\nRegarding this tree, process Q queries. The i-th query is as follows:\n\nFind the index of the lowest common ancestor (see Notes) of Vertex v_i and w_i. note: Notes\nIn a rooted tree, the lowest common ancestor (LCA) of Vertex v and w is the farthest vertex from the root that is an ancestor of both Vertex v and w. Here, a vertex is considered to be an ancestor of itself. For example, in the tree shown in Problem Statement, the LCA of Vertex 5 and 7 is Vertex 2, the LCA of Vertex 8 and 11 is Vertex 1, and the LCA of Vertex 3 and 9 is Vertex 3.", "constraint": "1 <= N <= 10^9\n1 <= Q <= 10^5\n1 <= v_i < w_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN Q\nv_1 w_1\n:\nv_Q w_Q", "output": "Print Q lines. The i-th line (1 <= i <= Q) must contain the index of the lowest common ancestor of Vertex v_i and w_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n5 7\n8 11\n3 9 output: 2\n1\n3\n\nThe queries in this case correspond to the examples shown in Notes.", "input: 100000 2\n1 2\n3 4 output: 1\n1"], "Pid": "p03506", "ProblemText": "Task Description: Problem Statement You are given an integer N. Consider an infinite N-ary tree as shown below:\nFigure: an infinite N-ary tree for the case N = 3\n\nAs shown in the figure, each vertex is indexed with a unique positive integer, and for every positive integer there is a vertex indexed with it. The root of the tree has the index 1. For the remaining vertices, vertices in the upper row have smaller indices than those in the lower row. Among the vertices in the same row, a vertex that is more to the left has a smaller index.\nRegarding this tree, process Q queries. The i-th query is as follows:\n\nFind the index of the lowest common ancestor (see Notes) of Vertex v_i and w_i. note: Notes\nIn a rooted tree, the lowest common ancestor (LCA) of Vertex v and w is the farthest vertex from the root that is an ancestor of both Vertex v and w. Here, a vertex is considered to be an ancestor of itself. For example, in the tree shown in Problem Statement, the LCA of Vertex 5 and 7 is Vertex 2, the LCA of Vertex 8 and 11 is Vertex 1, and the LCA of Vertex 3 and 9 is Vertex 3.\nTask Constraint: 1 <= N <= 10^9\n1 <= Q <= 10^5\n1 <= v_i < w_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN Q\nv_1 w_1\n:\nv_Q w_Q\nTask Output: Print Q lines. The i-th line (1 <= i <= Q) must contain the index of the lowest common ancestor of Vertex v_i and w_i.\nTask Samples: input: 3 3\n5 7\n8 11\n3 9 output: 2\n1\n3\n\nThe queries in this case correspond to the examples shown in Notes.\ninput: 100000 2\n1 2\n3 4 output: 1\n1\n\n" }, { "title": "", "content": "Problem Statement In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1,2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.\nYou will plant Flower i (1 <= i <= N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.\nFind the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.", "constraint": "1 <= N <= 10^5\n1 <= K <= 10^9\n1 <= w_i <= 10^{18}\n1 <= d_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nw_1 d_1\n:\nw_N d_N", "output": "Output When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower. )", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 6\n20 10\n25 15 output: 50\n\nTwo kinds of flowers are planted at the following positions:\n\nFlower 1: Position 20,30,40,50,60, …\nFlower 2: Position 25,40,55,70,85, …\n\nThe sixth flower from the west is the Flower 1 planted at Position 50. Note that the two flowers planted at Position 40 are counted individually.", "input: 3 9\n10 10\n10 10\n10 10 output: 30\n\nThree flowers are planted at each of the positions 10,20,30, … Thus, the ninth flower from the west is planted at Position 30.", "input: 1 1000000000\n1000000000000000000 1000000000 output: 1999999999000000000"], "Pid": "p03507", "ProblemText": "Task Description: Problem Statement In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1,2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.\nYou will plant Flower i (1 <= i <= N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.\nFind the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= 10^9\n1 <= w_i <= 10^{18}\n1 <= d_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nw_1 d_1\n:\nw_N d_N\nTask Output: Output When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower. )\nTask Samples: input: 2 6\n20 10\n25 15 output: 50\n\nTwo kinds of flowers are planted at the following positions:\n\nFlower 1: Position 20,30,40,50,60, …\nFlower 2: Position 25,40,55,70,85, …\n\nThe sixth flower from the west is the Flower 1 planted at Position 50. Note that the two flowers planted at Position 40 are counted individually.\ninput: 3 9\n10 10\n10 10\n10 10 output: 30\n\nThree flowers are planted at each of the positions 10,20,30, … Thus, the ninth flower from the west is planted at Position 30.\ninput: 1 1000000000\n1000000000000000000 1000000000 output: 1999999999000000000\n\n" }, { "title": "", "content": "Problem Statement You are given an undirected graph G. G has N vertices and M edges. The vertices are numbered from 1 through N, and the i-th edge (1 <= i <= M) connects Vertex a_i and b_i. G does not have self-loops and multiple edges.\nYou can repeatedly perform the operation of adding an edge between two vertices. However, G must not have self-loops or multiple edges as the result. Also, if Vertex 1 and 2 are connected directly or indirectly by edges, your body will be exposed to a voltage of 1000000007 volts. This must also be avoided.\nUnder these conditions, at most how many edges can you add? Note that Vertex 1 and 2 are never connected directly or indirectly in the beginning.", "constraint": "2 <= N <= 10^5\n0 <= M <= 10^5\n1 <= a_i < b_i <= N\nAll pairs (a_i, b_i) are distinct.\nVertex 1 and 2 in G are not connected directly or indirectly by edges.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_M b_M", "output": "Print the maximum number of edges that can be added.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1\n1 3 output: 2\nAs shown above, two edges can be added. It is not possible to add three or more edges.", "input: 2 0 output: 0\nNo edge can be added.", "input: 9 6\n1 4\n1 8\n2 5\n3 6\n4 8\n5 7 output: 12"], "Pid": "p03508", "ProblemText": "Task Description: Problem Statement You are given an undirected graph G. G has N vertices and M edges. The vertices are numbered from 1 through N, and the i-th edge (1 <= i <= M) connects Vertex a_i and b_i. G does not have self-loops and multiple edges.\nYou can repeatedly perform the operation of adding an edge between two vertices. However, G must not have self-loops or multiple edges as the result. Also, if Vertex 1 and 2 are connected directly or indirectly by edges, your body will be exposed to a voltage of 1000000007 volts. This must also be avoided.\nUnder these conditions, at most how many edges can you add? Note that Vertex 1 and 2 are never connected directly or indirectly in the beginning.\nTask Constraint: 2 <= N <= 10^5\n0 <= M <= 10^5\n1 <= a_i < b_i <= N\nAll pairs (a_i, b_i) are distinct.\nVertex 1 and 2 in G are not connected directly or indirectly by edges.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_M b_M\nTask Output: Print the maximum number of edges that can be added.\nTask Samples: input: 4 1\n1 3 output: 2\nAs shown above, two edges can be added. It is not possible to add three or more edges.\ninput: 2 0 output: 0\nNo edge can be added.\ninput: 9 6\n1 4\n1 8\n2 5\n3 6\n4 8\n5 7 output: 12\n\n" }, { "title": "", "content": "Problem Statement Ringo Kingdom Congress is voting on a bill.\nN members are present, and the i-th member (1 <= i <= N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.\nAfter all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.\nIn order for the bill to pass, at least how many members must be in favor of it?", "constraint": "1 <= N <= 10^5\n1 <= P <= 100\n1 <= w_i <= 10^9\n1 <= b_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN P\nw_1 b_1\nw_2 b_2\n:\nw_N b_N", "output": "Print the minimum number of members in favor of the bill required for passage.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 75\n1 1\n1 1\n1 1\n1 1 output: 3\n\nThis is a \"normal\" vote, where each of the four members has one white ballot and one blue ballot. For the bill to pass, at least 75 percent of the four, that is, at least three must be in favor of it.", "input: 4 75\n1 1\n1 1\n1 1\n100 1 output: 1\n\nThe \"yes\" vote of the member with 100 white ballots alone is enough to pass the bill.", "input: 5 60\n6 3\n5 9\n3 4\n7 8\n4 7 output: 3"], "Pid": "p03509", "ProblemText": "Task Description: Problem Statement Ringo Kingdom Congress is voting on a bill.\nN members are present, and the i-th member (1 <= i <= N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.\nAfter all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.\nIn order for the bill to pass, at least how many members must be in favor of it?\nTask Constraint: 1 <= N <= 10^5\n1 <= P <= 100\n1 <= w_i <= 10^9\n1 <= b_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN P\nw_1 b_1\nw_2 b_2\n:\nw_N b_N\nTask Output: Print the minimum number of members in favor of the bill required for passage.\nTask Samples: input: 4 75\n1 1\n1 1\n1 1\n1 1 output: 3\n\nThis is a \"normal\" vote, where each of the four members has one white ballot and one blue ballot. For the bill to pass, at least 75 percent of the four, that is, at least three must be in favor of it.\ninput: 4 75\n1 1\n1 1\n1 1\n100 1 output: 1\n\nThe \"yes\" vote of the member with 100 white ballots alone is enough to pass the bill.\ninput: 5 60\n6 3\n5 9\n3 4\n7 8\n4 7 output: 3\n\n" }, { "title": "", "content": "Problem Statement In a long narrow forest stretching east-west, there are N beasts. Below, we will call the point that is p meters from the west end Point p. The i-th beast from the west (1 <= i <= N) is at Point x_i, and can be sold for s_i yen (the currency of Japan) if captured.\nYou will choose two integers L and R (L <= R), and throw a net to cover the range from Point L to Point R including both ends, [L, R]. Then, all the beasts in the range will be captured. However, the net costs R - L yen and your profit will be (the sum of s_i over all captured beasts i) - (R - L) yen.\nWhat is the maximum profit that can be earned by throwing a net only once?", "constraint": "1 <= N <= 2 * 10^5\n1 <= x_1 < x_2 < ... < x_N <= 10^{15}\n1 <= s_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 s_1\nx_2 s_2\n:\nx_N s_N", "output": "Output When the maximum profit is X yen, print the value of X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n10 20\n40 50\n60 30\n70 40\n90 10 output: 90\n\nIf you throw a net covering the range [L = 40, R = 70], the second, third and fourth beasts from the west will be captured, generating the profit of s_2 + s_3 + s_4 - (R - L) = 90 yen. It is not possible to earn 91 yen or more.", "input: 5\n10 2\n40 5\n60 3\n70 4\n90 1 output: 5\n\nThe positions of the beasts are the same as Sample 1, but the selling prices dropped significantly, so you should not aim for two or more beasts. By throwing a net covering the range [L = 40, R = 40], you can earn s_2 - (R - L) = 5 yen, and this is the maximum possible profit.", "input: 4\n1 100\n3 200\n999999999999999 150\n1000000000000000 150 output: 299"], "Pid": "p03510", "ProblemText": "Task Description: Problem Statement In a long narrow forest stretching east-west, there are N beasts. Below, we will call the point that is p meters from the west end Point p. The i-th beast from the west (1 <= i <= N) is at Point x_i, and can be sold for s_i yen (the currency of Japan) if captured.\nYou will choose two integers L and R (L <= R), and throw a net to cover the range from Point L to Point R including both ends, [L, R]. Then, all the beasts in the range will be captured. However, the net costs R - L yen and your profit will be (the sum of s_i over all captured beasts i) - (R - L) yen.\nWhat is the maximum profit that can be earned by throwing a net only once?\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= x_1 < x_2 < ... < x_N <= 10^{15}\n1 <= s_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 s_1\nx_2 s_2\n:\nx_N s_N\nTask Output: Output When the maximum profit is X yen, print the value of X.\nTask Samples: input: 5\n10 20\n40 50\n60 30\n70 40\n90 10 output: 90\n\nIf you throw a net covering the range [L = 40, R = 70], the second, third and fourth beasts from the west will be captured, generating the profit of s_2 + s_3 + s_4 - (R - L) = 90 yen. It is not possible to earn 91 yen or more.\ninput: 5\n10 2\n40 5\n60 3\n70 4\n90 1 output: 5\n\nThe positions of the beasts are the same as Sample 1, but the selling prices dropped significantly, so you should not aim for two or more beasts. By throwing a net covering the range [L = 40, R = 40], you can earn s_2 - (R - L) = 5 yen, and this is the maximum possible profit.\ninput: 4\n1 100\n3 200\n999999999999999 150\n1000000000000000 150 output: 299\n\n" }, { "title": "", "content": "Problem Statement You are given two strings s and t consisting of lowercase English letters and an integer L.\nWe will consider generating a string of length L by concatenating one or more copies of s and t. Here, it is allowed to use the same string more than once.\nFor example, when s = at, t = code and L = 6, the strings atatat, atcode and codeat can be generated.\nAmong the strings that can be generated in this way, find the lexicographically smallest one. In the cases given as input, it is always possible to generate a string of length L.", "constraint": "1 <= L <= 2 * 10^5\n1 <= |s|, |t| <= L\ns and t consist of lowercase English letters.\nIt is possible to generate a string of length L in the way described in Problem Statement.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 s_1\nx_2 s_2\n:\nx_N s_N", "output": "Print the lexicographically smallest string among the ones that can be generated in the way described in Problem Statement.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\nat\ncode output: atatat\n\nThis input corresponds to the example shown in Problem Statement.", "input: 8\ncoding\nfestival output: festival\n\nIt is possible that either s or t cannot be used at all in generating a string of length L.", "input: 8\nsame\nsame output: samesame\n\nIt is also possible that s = t.", "input: 10\ncoin\nage output: ageagecoin"], "Pid": "p03511", "ProblemText": "Task Description: Problem Statement You are given two strings s and t consisting of lowercase English letters and an integer L.\nWe will consider generating a string of length L by concatenating one or more copies of s and t. Here, it is allowed to use the same string more than once.\nFor example, when s = at, t = code and L = 6, the strings atatat, atcode and codeat can be generated.\nAmong the strings that can be generated in this way, find the lexicographically smallest one. In the cases given as input, it is always possible to generate a string of length L.\nTask Constraint: 1 <= L <= 2 * 10^5\n1 <= |s|, |t| <= L\ns and t consist of lowercase English letters.\nIt is possible to generate a string of length L in the way described in Problem Statement.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 s_1\nx_2 s_2\n:\nx_N s_N\nTask Output: Print the lexicographically smallest string among the ones that can be generated in the way described in Problem Statement.\nTask Samples: input: 6\nat\ncode output: atatat\n\nThis input corresponds to the example shown in Problem Statement.\ninput: 8\ncoding\nfestival output: festival\n\nIt is possible that either s or t cannot be used at all in generating a string of length L.\ninput: 8\nsame\nsame output: samesame\n\nIt is also possible that s = t.\ninput: 10\ncoin\nage output: ageagecoin\n\n" }, { "title": "", "content": "Problem Statement Consider an infinite sequence a_1, a_2, … Initially, the values of all the terms are 0, and from this state we will sequentially perform Q operations. The i-th operation (1 <= i <= Q) is as follows:\n\nFor every positive integer j, add x_i to the value of a_{j * m_i}.\n\nFind the value of the largest term after these Q operations.", "constraint": "1 <= Q <= 299\n2 <= m_i <= 300\n-10^6 <= x_i <= 10^6\nAll m_i are distinct.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nQ\nm_1 x_1\n:\nm_Q x_Q", "output": "Print the value of the largest term after the Q operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 10\n3 -20\n6 15 output: 10\n\nThe values of each terms in the sequence a_1, a_2, … change as follows:\n\nBefore the operations: 0,0,0,0,0,0, …\nAfter the 1-st operation: 0,10,0,10,0,10, …\nAfter the 2-nd operation: 0,10, -20,10,0, -10, …\nAfter the 3-rd operation: 0,10, -20,10,0,5, …\n\nThe value of the largest term after all the operations is 10.", "input: 3\n10 -3\n50 4\n100 -5 output: 1", "input: 5\n56 114834\n72 -149861\n100 190757\n192 -132693\n240 133108 output: 438699"], "Pid": "p03512", "ProblemText": "Task Description: Problem Statement Consider an infinite sequence a_1, a_2, … Initially, the values of all the terms are 0, and from this state we will sequentially perform Q operations. The i-th operation (1 <= i <= Q) is as follows:\n\nFor every positive integer j, add x_i to the value of a_{j * m_i}.\n\nFind the value of the largest term after these Q operations.\nTask Constraint: 1 <= Q <= 299\n2 <= m_i <= 300\n-10^6 <= x_i <= 10^6\nAll m_i are distinct.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nQ\nm_1 x_1\n:\nm_Q x_Q\nTask Output: Print the value of the largest term after the Q operations.\nTask Samples: input: 3\n2 10\n3 -20\n6 15 output: 10\n\nThe values of each terms in the sequence a_1, a_2, … change as follows:\n\nBefore the operations: 0,0,0,0,0,0, …\nAfter the 1-st operation: 0,10,0,10,0,10, …\nAfter the 2-nd operation: 0,10, -20,10,0, -10, …\nAfter the 3-rd operation: 0,10, -20,10,0,5, …\n\nThe value of the largest term after all the operations is 10.\ninput: 3\n10 -3\n50 4\n100 -5 output: 1\ninput: 5\n56 114834\n72 -149861\n100 190757\n192 -132693\n240 133108 output: 438699\n\n" }, { "title": "", "content": "Problem Statement There are N islands floating in Ringo Sea, and M travel agents operate ships between these islands. For convenience, we will call these islands Island 1,2, …, N, and call these agents Agent 1,2, …, M.\nThe sea currents in Ringo Sea change significantly each day. Depending on the state of the sea on the day, Agent i (1 <= i <= M) operates ships from Island a_i to b_i, or Island b_i to a_i, but not both at the same time. Assume that the direction of the ships of each agent is independently selected with equal probability.\nNow, Takahashi is on Island 1, and Hikuhashi is on Island 2. Let P be the probability that Takahashi and Hikuhashi can travel to the same island in the day by ships operated by the M agents, ignoring the factors such as the travel time for ships. Then, P * 2^M is an integer. Find P * 2^M modulo 10^9 + 7.", "constraint": "2 <= N <= 15\n1 <= M <= N(N-1)/2\n1 <= a_i < b_i <= N\nAll pairs (a_i, b_i) are distinct.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_M b_M", "output": "Print the value P * 2^M modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n1 3\n2 3\n3 4 output: 6\nThe 2^M = 8 scenarios shown above occur with equal probability, and Takahashi and Hikuhashi can meet on the same island in 6 of them. Thus, P = 6/2^M and P * 2^M = 6.", "input: 5 5\n1 3\n2 4\n3 4\n3 5\n4 5 output: 18", "input: 6 6\n1 2\n2 3\n3 4\n4 5\n5 6\n1 6 output: 64"], "Pid": "p03513", "ProblemText": "Task Description: Problem Statement There are N islands floating in Ringo Sea, and M travel agents operate ships between these islands. For convenience, we will call these islands Island 1,2, …, N, and call these agents Agent 1,2, …, M.\nThe sea currents in Ringo Sea change significantly each day. Depending on the state of the sea on the day, Agent i (1 <= i <= M) operates ships from Island a_i to b_i, or Island b_i to a_i, but not both at the same time. Assume that the direction of the ships of each agent is independently selected with equal probability.\nNow, Takahashi is on Island 1, and Hikuhashi is on Island 2. Let P be the probability that Takahashi and Hikuhashi can travel to the same island in the day by ships operated by the M agents, ignoring the factors such as the travel time for ships. Then, P * 2^M is an integer. Find P * 2^M modulo 10^9 + 7.\nTask Constraint: 2 <= N <= 15\n1 <= M <= N(N-1)/2\n1 <= a_i < b_i <= N\nAll pairs (a_i, b_i) are distinct.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_M b_M\nTask Output: Print the value P * 2^M modulo 10^9 + 7.\nTask Samples: input: 4 3\n1 3\n2 3\n3 4 output: 6\nThe 2^M = 8 scenarios shown above occur with equal probability, and Takahashi and Hikuhashi can meet on the same island in 6 of them. Thus, P = 6/2^M and P * 2^M = 6.\ninput: 5 5\n1 3\n2 4\n3 4\n3 5\n4 5 output: 18\ninput: 6 6\n1 2\n2 3\n3 4\n4 5\n5 6\n1 6 output: 64\n\n" }, { "title": "", "content": "Problem Statement We have 2N pots. The market price of the i-th pot (1 <= i <= 2N) is p_i yen (the currency of Japan).\nNow, you and Lunlun the dachshund will alternately take one pot. You will go first, and we will continue until all the pots are taken by you or Lunlun. Since Lunlun does not know the market prices of the pots, she will always choose a pot randomly from the remaining pots with equal probability. You know this behavior of Lunlun, and the market prices of the pots.\nLet the sum of the market prices of the pots you take be S yen. Your objective is to maximize the expected value of S. Find the expected value of S when the optimal strategy is adopted.", "constraint": "1 <= N <= 10^5\n1 <= p_i <= 2 * 10^5\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\np_1\n:\np_{2N}", "output": "Print the expected value of S when the strategy to maximize the expected value of S is adopted. The output is considered correct if its absolute or relative error from the judge's output is at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n150000\n108 output: 150000.0\n\nNaturally, you should choose the 150000 yen pot.", "input: 2\n50000\n50000\n100000\n100000 output: 183333.3333333333\n\nFirst, you will take one of the 100000 yen pots. The other 100000 yen pot will become yours if it is not taken in Lunlun's next turn, with probability 2/3. If it is taken, you will have to settle for a 50000 yen pot. Thus, the expected value of S when the optimal strategy is adopted is 2/3 * (100000 + 100000) + 1/3 * (100000 + 50000) = 183333.3333…"], "Pid": "p03514", "ProblemText": "Task Description: Problem Statement We have 2N pots. The market price of the i-th pot (1 <= i <= 2N) is p_i yen (the currency of Japan).\nNow, you and Lunlun the dachshund will alternately take one pot. You will go first, and we will continue until all the pots are taken by you or Lunlun. Since Lunlun does not know the market prices of the pots, she will always choose a pot randomly from the remaining pots with equal probability. You know this behavior of Lunlun, and the market prices of the pots.\nLet the sum of the market prices of the pots you take be S yen. Your objective is to maximize the expected value of S. Find the expected value of S when the optimal strategy is adopted.\nTask Constraint: 1 <= N <= 10^5\n1 <= p_i <= 2 * 10^5\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\np_1\n:\np_{2N}\nTask Output: Print the expected value of S when the strategy to maximize the expected value of S is adopted. The output is considered correct if its absolute or relative error from the judge's output is at most 10^{-9}.\nTask Samples: input: 1\n150000\n108 output: 150000.0\n\nNaturally, you should choose the 150000 yen pot.\ninput: 2\n50000\n50000\n100000\n100000 output: 183333.3333333333\n\nFirst, you will take one of the 100000 yen pots. The other 100000 yen pot will become yours if it is not taken in Lunlun's next turn, with probability 2/3. If it is taken, you will have to settle for a 50000 yen pot. Thus, the expected value of S when the optimal strategy is adopted is 2/3 * (100000 + 100000) + 1/3 * (100000 + 50000) = 183333.3333…\n\n" }, { "title": "", "content": "Problem Statement Snuke Festival 2017 will be held in a tree with N vertices numbered 1,2, . . . , N.\nThe i-th edge connects Vertex a_i and b_i, and has joyfulness c_i.\nThe staff is Snuke and N-1 black cats.\nSnuke will set up the headquarters in some vertex, and from there he will deploy a cat to each of the other N-1 vertices.\nFor each vertex, calculate the niceness when the headquarters are set up in that vertex.\nThe niceness when the headquarters are set up in Vertex i is calculated as follows:\n\nLet X=0.\nFor each integer j between 1 and N (inclusive) except i, do the following:\nAdd c to X, where c is the smallest joyfulness of an edge on the path from Vertex i to Vertex j.\nThe niceness is the final value of X. partial scores: Partial Scores\nIn the test set worth 200 points, N <= 1000.\nIn the test set worth 200 points, c_i <= 2.", "constraint": "1 <= N <= 10^{5}\n1 <= a_i,b_i <= N\n1 <= c_i <= 10^{9}\nThe given graph is a tree.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1 c_1\n:\na_{N-1} b_{N-1} c_{N-1}", "output": "Print N lines. The i-th line must contain the niceness when the headquarters are set up in Vertex i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 10\n2 3 20 output: 20\n30\n30\nThe figure below shows the case when headquarters are set up in each of the vertices 1,2 and 3.\nThe number on top of an edge denotes the joyfulness of the edge, and the number below an vertex denotes the smallest joyfulness of an edge on the path from the headquarters to that vertex.", "input: 15\n6 3 2\n13 3 1\n1 13 2\n7 1 2\n8 1 1\n2 8 2\n2 12 2\n5 2 2\n2 11 2\n10 2 2\n10 9 1\n9 14 2\n4 14 1\n11 15 2 output: 16\n20\n15\n14\n20\n15\n16\n20\n15\n20\n20\n20\n16\n15\n20", "input: 19\n19 14 48\n11 19 23\n17 14 30\n7 11 15\n2 19 15\n2 18 21\n19 10 43\n12 11 25\n3 11 4\n5 19 50\n4 11 19\n9 12 29\n14 13 3\n14 6 12\n14 15 14\n5 1 6\n8 18 13\n7 16 14 output: 103\n237\n71\n263\n370\n193\n231\n207\n299\n358\n295\n299\n54\n368\n220\n220\n319\n237\n370"], "Pid": "p03515", "ProblemText": "Task Description: Problem Statement Snuke Festival 2017 will be held in a tree with N vertices numbered 1,2, . . . , N.\nThe i-th edge connects Vertex a_i and b_i, and has joyfulness c_i.\nThe staff is Snuke and N-1 black cats.\nSnuke will set up the headquarters in some vertex, and from there he will deploy a cat to each of the other N-1 vertices.\nFor each vertex, calculate the niceness when the headquarters are set up in that vertex.\nThe niceness when the headquarters are set up in Vertex i is calculated as follows:\n\nLet X=0.\nFor each integer j between 1 and N (inclusive) except i, do the following:\nAdd c to X, where c is the smallest joyfulness of an edge on the path from Vertex i to Vertex j.\nThe niceness is the final value of X. partial scores: Partial Scores\nIn the test set worth 200 points, N <= 1000.\nIn the test set worth 200 points, c_i <= 2.\nTask Constraint: 1 <= N <= 10^{5}\n1 <= a_i,b_i <= N\n1 <= c_i <= 10^{9}\nThe given graph is a tree.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1 c_1\n:\na_{N-1} b_{N-1} c_{N-1}\nTask Output: Print N lines. The i-th line must contain the niceness when the headquarters are set up in Vertex i.\nTask Samples: input: 3\n1 2 10\n2 3 20 output: 20\n30\n30\nThe figure below shows the case when headquarters are set up in each of the vertices 1,2 and 3.\nThe number on top of an edge denotes the joyfulness of the edge, and the number below an vertex denotes the smallest joyfulness of an edge on the path from the headquarters to that vertex.\ninput: 15\n6 3 2\n13 3 1\n1 13 2\n7 1 2\n8 1 1\n2 8 2\n2 12 2\n5 2 2\n2 11 2\n10 2 2\n10 9 1\n9 14 2\n4 14 1\n11 15 2 output: 16\n20\n15\n14\n20\n15\n16\n20\n15\n20\n20\n20\n16\n15\n20\ninput: 19\n19 14 48\n11 19 23\n17 14 30\n7 11 15\n2 19 15\n2 18 21\n19 10 43\n12 11 25\n3 11 4\n5 19 50\n4 11 19\n9 12 29\n14 13 3\n14 6 12\n14 15 14\n5 1 6\n8 18 13\n7 16 14 output: 103\n237\n71\n263\n370\n193\n231\n207\n299\n358\n295\n299\n54\n368\n220\n220\n319\n237\n370\n\n" }, { "title": "", "content": "Problem Statement Snuke has come up with the following problem.\n\nYou are given a sequence d of length N.\nFind the number of the undirected graphs with N vertices labeled 1,2, . . . , N satisfying the following conditions, modulo 10^{9} + 7:\n\nThe graph is simple and connected.\nThe degree of Vertex i is d_i.\nWhen 2 <= N, 1 <= d_i <= N-1, {\\rm Σ} d_i = 2(N-1), it can be proved that the answer to the problem is \\frac{(N-2)! }{(d_{1} -1)! (d_{2} - 1)! . . . (d_{N}-1)! }.\nSnuke is wondering what the answer is when 3 <= N, 1 <= d_i <= N-1, { \\rm Σ} d_i = 2N.\nSolve the problem under this condition for him. partial scores: Partial Scores\nIn the test set worth 200 points, N <= 5.\nIn the test set worth another 200 points, N <= 18.\nIn the test set worth another 300 points, N <= 50.", "constraint": "3 <= N <= 300\n1 <= d_i <= N-1\n{ \\rm Σ} d_i = 2N", "input": "Input is given from Standard Input in the following format:\nN\nd_1 d_2 . . . d_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 2 3 2 output: 6\nThere are six graphs as shown below:", "input: 16\n2 1 3 1 2 1 4 1 1 2 1 1 3 2 4 3 output: 555275958\nBe sure to find the answer modulo 10^{9} + 7."], "Pid": "p03516", "ProblemText": "Task Description: Problem Statement Snuke has come up with the following problem.\n\nYou are given a sequence d of length N.\nFind the number of the undirected graphs with N vertices labeled 1,2, . . . , N satisfying the following conditions, modulo 10^{9} + 7:\n\nThe graph is simple and connected.\nThe degree of Vertex i is d_i.\nWhen 2 <= N, 1 <= d_i <= N-1, {\\rm Σ} d_i = 2(N-1), it can be proved that the answer to the problem is \\frac{(N-2)! }{(d_{1} -1)! (d_{2} - 1)! . . . (d_{N}-1)! }.\nSnuke is wondering what the answer is when 3 <= N, 1 <= d_i <= N-1, { \\rm Σ} d_i = 2N.\nSolve the problem under this condition for him. partial scores: Partial Scores\nIn the test set worth 200 points, N <= 5.\nIn the test set worth another 200 points, N <= 18.\nIn the test set worth another 300 points, N <= 50.\nTask Constraint: 3 <= N <= 300\n1 <= d_i <= N-1\n{ \\rm Σ} d_i = 2N\nTask Input: Input is given from Standard Input in the following format:\nN\nd_1 d_2 . . . d_{N}\nTask Output: Print the answer.\nTask Samples: input: 5\n1 2 2 3 2 output: 6\nThere are six graphs as shown below:\ninput: 16\n2 1 3 1 2 1 4 1 1 2 1 1 3 2 4 3 output: 555275958\nBe sure to find the answer modulo 10^{9} + 7.\n\n" }, { "title": "", "content": "Problem Statement Ringo has an undirected graph G with N vertices numbered 1,2, . . . , N and M edges numbered 1,2, . . . , M.\nEdge i connects Vertex a_{i} and b_{i} and has a length of w_i.\nNow, he is in the middle of painting these N vertices in K colors numbered 1,2, . . . , K. Vertex i is already painted in Color c_i, except when c_i = 0, in which case Vertex i is not yet painted.\nAfter he paints each vertex that is not yet painted in one of the K colors, he will give G to Snuke.\nBased on G, Snuke will make another undirected graph G' with K vertices numbered 1,2, . . . , K and M edges.\nInitially, there is no edge in G'. The i-th edge will be added as follows:\n\nLet x and y be the colors of the two vertices connected by Edge i in G.\nAdd an edge of length w_i connecting Vertex x and y in G'.\n\nWhat is the minimum possible sum of the lengths of the edges in the minimum spanning tree of G'? If G' will not be connected regardless of how Ringo paints the vertices, print -1. partial scores: Partial Scores\nIn the test set worth 100 points, N = K and c_i = i.\nIn the test set worth another 100 points, c_i \\neq 0.\nIn the test set worth another 200 points, c_i = 0.", "constraint": "1 <= N,M <= 10^{5}\n1 <= K <= N\n0 <= c_i <= K\n1 <= a_i,b_i <= N\n1 <= w_i <= 10^{9}\nThe given graph may NOT be simple or connected.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M K\nc_1 c_2 . . . c_{N}\na_1 b_1 w_1\n:\na_M b_M w_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 3\n1 0 1 2\n1 2 10\n2 3 20\n2 4 50 output: 60\n\nG' will only be connected when Vertex 2 is painted in Color 3.", "input: 5 2 4\n0 0 0 0 0\n1 2 10\n2 3 10 output: -1\n\nRegardless of how Ringo paints the vertices, two edges is not enough to connect four vertices as one.", "input: 9 12 9\n1 2 3 4 5 6 7 8 9\n6 9 9\n8 9 6\n6 7 85\n9 5 545631016\n2 1 321545\n1 6 33562944\n7 3 84946329\n9 7 15926167\n4 7 53386480\n5 8 70476\n4 6 4549\n4 8 8 output: 118901402", "input: 18 37 12\n5 0 4 10 8 7 2 10 6 0 9 12 12 11 11 11 0 1\n17 1 1\n11 16 7575\n11 15 9\n10 10 289938980\n5 10 17376\n18 4 1866625\n8 11 959154208\n18 13 200\n16 13 2\n2 7 982223\n12 12 9331\n13 12 8861390\n14 13 743\n2 10 162440\n2 4 981849\n7 9 1\n14 17 2800\n2 7 7225452\n3 7 85\n5 17 4\n2 13 1\n10 3 45\n1 15 973\n14 7 56553306\n16 17 70476\n7 18 9\n9 13 27911\n18 14 7788322\n11 11 8925\n9 13 654295\n2 10 9\n10 1 545631016\n3 4 5\n17 12 1929\n2 11 57\n1 5 4\n1 17 7807368 output: 171"], "Pid": "p03517", "ProblemText": "Task Description: Problem Statement Ringo has an undirected graph G with N vertices numbered 1,2, . . . , N and M edges numbered 1,2, . . . , M.\nEdge i connects Vertex a_{i} and b_{i} and has a length of w_i.\nNow, he is in the middle of painting these N vertices in K colors numbered 1,2, . . . , K. Vertex i is already painted in Color c_i, except when c_i = 0, in which case Vertex i is not yet painted.\nAfter he paints each vertex that is not yet painted in one of the K colors, he will give G to Snuke.\nBased on G, Snuke will make another undirected graph G' with K vertices numbered 1,2, . . . , K and M edges.\nInitially, there is no edge in G'. The i-th edge will be added as follows:\n\nLet x and y be the colors of the two vertices connected by Edge i in G.\nAdd an edge of length w_i connecting Vertex x and y in G'.\n\nWhat is the minimum possible sum of the lengths of the edges in the minimum spanning tree of G'? If G' will not be connected regardless of how Ringo paints the vertices, print -1. partial scores: Partial Scores\nIn the test set worth 100 points, N = K and c_i = i.\nIn the test set worth another 100 points, c_i \\neq 0.\nIn the test set worth another 200 points, c_i = 0.\nTask Constraint: 1 <= N,M <= 10^{5}\n1 <= K <= N\n0 <= c_i <= K\n1 <= a_i,b_i <= N\n1 <= w_i <= 10^{9}\nThe given graph may NOT be simple or connected.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M K\nc_1 c_2 . . . c_{N}\na_1 b_1 w_1\n:\na_M b_M w_M\nTask Output: Print the answer.\nTask Samples: input: 4 3 3\n1 0 1 2\n1 2 10\n2 3 20\n2 4 50 output: 60\n\nG' will only be connected when Vertex 2 is painted in Color 3.\ninput: 5 2 4\n0 0 0 0 0\n1 2 10\n2 3 10 output: -1\n\nRegardless of how Ringo paints the vertices, two edges is not enough to connect four vertices as one.\ninput: 9 12 9\n1 2 3 4 5 6 7 8 9\n6 9 9\n8 9 6\n6 7 85\n9 5 545631016\n2 1 321545\n1 6 33562944\n7 3 84946329\n9 7 15926167\n4 7 53386480\n5 8 70476\n4 6 4549\n4 8 8 output: 118901402\ninput: 18 37 12\n5 0 4 10 8 7 2 10 6 0 9 12 12 11 11 11 0 1\n17 1 1\n11 16 7575\n11 15 9\n10 10 289938980\n5 10 17376\n18 4 1866625\n8 11 959154208\n18 13 200\n16 13 2\n2 7 982223\n12 12 9331\n13 12 8861390\n14 13 743\n2 10 162440\n2 4 981849\n7 9 1\n14 17 2800\n2 7 7225452\n3 7 85\n5 17 4\n2 13 1\n10 3 45\n1 15 973\n14 7 56553306\n16 17 70476\n7 18 9\n9 13 27911\n18 14 7788322\n11 11 8925\n9 13 654295\n2 10 9\n10 1 545631016\n3 4 5\n17 12 1929\n2 11 57\n1 5 4\n1 17 7807368 output: 171\n\n" }, { "title": "", "content": "Problem Statement Snuke has a sequence p, which is a permutation of (0,1,2, . . . , N-1).\nThe i-th element (0-indexed) in p is p_i.\nHe can perform N-1 kinds of operations labeled 1,2, . . . , N-1 any number of times in any order.\nWhen the operation labeled k is executed, the procedure represented by the following code will be performed:\nfor(int i=k; i= 3, a_i = 1, b_i = i+1.", "constraint": "2 <= N <= 10^{5}\n1 <= a_i,b_i <= N\n1 <= s_i <= 10^{18}\nThe given graph is a tree.\nAll input values are integers.\nIt is possible to consistently restore the lengths of the edges.\nIn the restored graph, the length of each edge is an integer between 1 and 10^{18} (inclusive).", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\ns_1 s_2 . . . s_{N}", "output": "Print N-1 lines. The i-th line must contain the length of Edge i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2\n2 3\n3 4\n8 6 6 8 output: 1\n2\n1\nThe given record corresponds to the tree shown below:", "input: 5\n1 2\n1 3\n1 4\n1 5\n10 13 16 19 22 output: 1\n2\n3\n4\nThe given record corresponds to the tree shown below:", "input: 15\n9 10\n9 15\n15 4\n4 13\n13 2\n13 11\n2 14\n13 6\n11 1\n1 12\n12 3\n12 7\n2 5\n14 8\n1154 890 2240 883 2047 2076 1590 1104 1726 1791 1091 1226 841 1000 901 output: 5\n75\n2\n6\n7\n50\n10\n95\n9\n8\n78\n28\n89\n8"], "Pid": "p03520", "ProblemText": "Task Description: Problem Statement Snuke found a record of a tree with N vertices in ancient ruins.\nThe findings are as follows:\n\nThe vertices of the tree were numbered 1,2, . . . , N, and the edges were numbered 1,2, . . . , N-1.\nEdge i connected Vertex a_i and b_i.\nThe length of each edge was an integer between 1 and 10^{18} (inclusive).\nThe sum of the shortest distances from Vertex i to Vertex 1, . . . , N was s_i.\n\nFrom the information above, restore the length of each edge.\nThe input guarantees that it is possible to determine the lengths of the edges consistently with the record.\nFurthermore, it can be proved that the length of each edge is uniquely determined in such a case. partial scores: Partial Scores\nIn the test set worth 300 points, a_i = i, b_i = i+1.\nIn the test set worth 200 points, N >= 3, a_i = 1, b_i = i+1.\nTask Constraint: 2 <= N <= 10^{5}\n1 <= a_i,b_i <= N\n1 <= s_i <= 10^{18}\nThe given graph is a tree.\nAll input values are integers.\nIt is possible to consistently restore the lengths of the edges.\nIn the restored graph, the length of each edge is an integer between 1 and 10^{18} (inclusive).\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\ns_1 s_2 . . . s_{N}\nTask Output: Print N-1 lines. The i-th line must contain the length of Edge i.\nTask Samples: input: 4\n1 2\n2 3\n3 4\n8 6 6 8 output: 1\n2\n1\nThe given record corresponds to the tree shown below:\ninput: 5\n1 2\n1 3\n1 4\n1 5\n10 13 16 19 22 output: 1\n2\n3\n4\nThe given record corresponds to the tree shown below:\ninput: 15\n9 10\n9 15\n15 4\n4 13\n13 2\n13 11\n2 14\n13 6\n11 1\n1 12\n12 3\n12 7\n2 5\n14 8\n1154 890 2240 883 2047 2076 1590 1104 1726 1791 1091 1226 841 1000 901 output: 5\n75\n2\n6\n7\n50\n10\n95\n9\n8\n78\n28\n89\n8\n\n" }, { "title": "", "content": "Problem Statement But Coder Inc. is a startup company whose main business is the development and operation of the programming competition site \"But Coder\".\nThere are N members of the company including the president, and each member except the president has exactly one direct boss. Each member has a unique ID number from 1 to N, and the member with the ID i is called Member i. The president is Member 1, and the direct boss of Member i (2 <= i <= N) is Member b_i (1 <= b_i < i).\nAll the members in But Coder have gathered in the great hall in the main office to take a group photo. The hall is very large, and all N people can stand in one line. However, they have been unable to decide the order in which they stand. For some reason, all of them except the president want to avoid standing next to their direct bosses.\nHow many ways are there for them to stand in a line that satisfy their desires? Find the count modulo 10^9+7.", "constraint": "2 <= N <= 2000\n1 <= b_i < i (2 <= i <= N)", "input": "Input is given from Standard Input in the following format:\nN\nb_2\nb_3\n:\nb_N", "output": "Print the number of ways for the N members to stand in a line, such that no member except the president is next to his/her direct boss, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1\n2\n3 output: 2\n\nBelow, we will write A → B to denote the fact that Member A is the direct boss of Member B.\nIn this case, the hierarchy of the members is 1 → 2 → 3 → 4. There are two ways for them to stand in a line that satisfy their desires:\n\n2,4,1,3\n3,1,4,2\n\nNote that the latter is the reverse of the former, but we count them individually.", "input: 3\n1\n2 output: 0\n\nThe hierarchy of the members is 1 → 2 → 3. No matter what order they stand in, at least one of the desires of Member 2 and 3 is not satisfied, so the answer is 0.", "input: 5\n1\n1\n3\n3 output: 8\n\nThe hierarchy of the members is shown below:\n\nThere are eight ways for them to stand in a line that satisfy their desires:\n\n1,4,5,2,3\n1,5,4,2,3\n3,2,4,1,5\n3,2,4,5,1\n3,2,5,1,4\n3,2,5,4,1\n4,1,5,2,3\n5,1,4,2,3", "input: 15\n1\n2\n3\n1\n4\n2\n7\n1\n8\n2\n8\n1\n8\n2 output: 97193524"], "Pid": "p03521", "ProblemText": "Task Description: Problem Statement But Coder Inc. is a startup company whose main business is the development and operation of the programming competition site \"But Coder\".\nThere are N members of the company including the president, and each member except the president has exactly one direct boss. Each member has a unique ID number from 1 to N, and the member with the ID i is called Member i. The president is Member 1, and the direct boss of Member i (2 <= i <= N) is Member b_i (1 <= b_i < i).\nAll the members in But Coder have gathered in the great hall in the main office to take a group photo. The hall is very large, and all N people can stand in one line. However, they have been unable to decide the order in which they stand. For some reason, all of them except the president want to avoid standing next to their direct bosses.\nHow many ways are there for them to stand in a line that satisfy their desires? Find the count modulo 10^9+7.\nTask Constraint: 2 <= N <= 2000\n1 <= b_i < i (2 <= i <= N)\nTask Input: Input is given from Standard Input in the following format:\nN\nb_2\nb_3\n:\nb_N\nTask Output: Print the number of ways for the N members to stand in a line, such that no member except the president is next to his/her direct boss, modulo 10^9+7.\nTask Samples: input: 4\n1\n2\n3 output: 2\n\nBelow, we will write A → B to denote the fact that Member A is the direct boss of Member B.\nIn this case, the hierarchy of the members is 1 → 2 → 3 → 4. There are two ways for them to stand in a line that satisfy their desires:\n\n2,4,1,3\n3,1,4,2\n\nNote that the latter is the reverse of the former, but we count them individually.\ninput: 3\n1\n2 output: 0\n\nThe hierarchy of the members is 1 → 2 → 3. No matter what order they stand in, at least one of the desires of Member 2 and 3 is not satisfied, so the answer is 0.\ninput: 5\n1\n1\n3\n3 output: 8\n\nThe hierarchy of the members is shown below:\n\nThere are eight ways for them to stand in a line that satisfy their desires:\n\n1,4,5,2,3\n1,5,4,2,3\n3,2,4,1,5\n3,2,4,5,1\n3,2,5,1,4\n3,2,5,4,1\n4,1,5,2,3\n5,1,4,2,3\ninput: 15\n1\n2\n3\n1\n4\n2\n7\n1\n8\n2\n8\n1\n8\n2 output: 97193524\n\n" }, { "title": "", "content": "Problem Statement We have a sequence A of length N.\nOn this sequence, we can perform the following two kinds of operations:\nSwap two adjacent elements.\nSelect one element, and increment it by 1.\nWe will repeatedly perform these operations so that A will be a non-decreasing sequence. Find the minimum required number of operations.", "constraint": "1 <= N <= 200000\n1 <= A_i <= 10^9\nA_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\nA_1\nA_2\n:\nA_N", "output": "Print the minimum number of operations required to turn A into a non-decreasing sequence.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n4\n1\n8\n8\n7 output: 2\n\nWe can turn A into a non-decreasing sequence in two operations:\n\nInitially, A = \\{4,1,8,8,7\\}.\nSwap the first two elements. Now, A = \\{1,4,8,8,7\\}.\nIncrement the last element by 1. Now, A = \\{1,4,8,8,8\\}.", "input: 20\n8\n2\n9\n7\n4\n6\n7\n9\n7\n4\n7\n4\n4\n3\n6\n2\n3\n4\n4\n9 output: 62"], "Pid": "p03522", "ProblemText": "Task Description: Problem Statement We have a sequence A of length N.\nOn this sequence, we can perform the following two kinds of operations:\nSwap two adjacent elements.\nSelect one element, and increment it by 1.\nWe will repeatedly perform these operations so that A will be a non-decreasing sequence. Find the minimum required number of operations.\nTask Constraint: 1 <= N <= 200000\n1 <= A_i <= 10^9\nA_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\nA_2\n:\nA_N\nTask Output: Print the minimum number of operations required to turn A into a non-decreasing sequence.\nTask Samples: input: 5\n4\n1\n8\n8\n7 output: 2\n\nWe can turn A into a non-decreasing sequence in two operations:\n\nInitially, A = \\{4,1,8,8,7\\}.\nSwap the first two elements. Now, A = \\{1,4,8,8,7\\}.\nIncrement the last element by 1. Now, A = \\{1,4,8,8,8\\}.\ninput: 20\n8\n2\n9\n7\n4\n6\n7\n9\n7\n4\n7\n4\n4\n3\n6\n2\n3\n4\n4\n9 output: 62\n\n" }, { "title": "", "content": "Problem Statement You are given a string S.\nTakahashi can insert the character A at any position in this string any number of times.\nCan he change S into AKIHABARA?", "constraint": "1 <= |S| <= 50\nS consists of uppercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If it is possible to change S into AKIHABARA, print YES; otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: KIHBR output: YES\n\nInsert one A at each of the four positions: the beginning, immediately after H, immediately after B and the end.", "input: AKIBAHARA output: NO\n\nThe correct spell is AKIHABARA.", "input: AAKIAHBAARA output: NO"], "Pid": "p03523", "ProblemText": "Task Description: Problem Statement You are given a string S.\nTakahashi can insert the character A at any position in this string any number of times.\nCan he change S into AKIHABARA?\nTask Constraint: 1 <= |S| <= 50\nS consists of uppercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If it is possible to change S into AKIHABARA, print YES; otherwise, print NO.\nTask Samples: input: KIHBR output: YES\n\nInsert one A at each of the four positions: the beginning, immediately after H, immediately after B and the end.\ninput: AKIBAHARA output: NO\n\nThe correct spell is AKIHABARA.\ninput: AAKIAHBAARA output: NO\n\n" }, { "title": "", "content": "Problem Statement Snuke has a string S consisting of three kinds of letters: a, b and c.\nHe has a phobia for palindromes, and wants to permute the characters in S so that S will not contain a palindrome of length 2 or more as a substring. Determine whether this is possible.", "constraint": "1 <= |S| <= 10^5\nS consists of a, b and c.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If the objective is achievable, print YES; if it is unachievable, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abac output: YES\n\nAs it stands now, S contains a palindrome aba, but we can permute the characters to get acba, for example, that does not contain a palindrome of length 2 or more.", "input: aba output: NO", "input: babacccabab output: YES"], "Pid": "p03524", "ProblemText": "Task Description: Problem Statement Snuke has a string S consisting of three kinds of letters: a, b and c.\nHe has a phobia for palindromes, and wants to permute the characters in S so that S will not contain a palindrome of length 2 or more as a substring. Determine whether this is possible.\nTask Constraint: 1 <= |S| <= 10^5\nS consists of a, b and c.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If the objective is achievable, print YES; if it is unachievable, print NO.\nTask Samples: input: abac output: YES\n\nAs it stands now, S contains a palindrome aba, but we can permute the characters to get acba, for example, that does not contain a palindrome of length 2 or more.\ninput: aba output: NO\ninput: babacccabab output: YES\n\n" }, { "title": "", "content": "Problem Statement In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.\nTakahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.\nThe time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d, 24-d) hours.\nHere, we are using 24-hour notation.\nThat is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.\nThen, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.\nFind the maximum possible value of s.", "constraint": "1 <= N <= 50\n0 <= D_i <= 12\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nD_1 D_2 . . . D_N", "output": "Print the maximum possible value of s.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n7 12 8 output: 4\n\nFor example, consider the situation where it is 7,12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.", "input: 2\n11 11 output: 2", "input: 1\n0 output: 0\n\nNote that Takahashi himself is also a participant."], "Pid": "p03525", "ProblemText": "Task Description: Problem Statement In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.\nTakahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.\nThe time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d, 24-d) hours.\nHere, we are using 24-hour notation.\nThat is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.\nThen, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.\nFind the maximum possible value of s.\nTask Constraint: 1 <= N <= 50\n0 <= D_i <= 12\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nD_1 D_2 . . . D_N\nTask Output: Print the maximum possible value of s.\nTask Samples: input: 3\n7 12 8 output: 4\n\nFor example, consider the situation where it is 7,12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.\ninput: 2\n11 11 output: 2\ninput: 1\n0 output: 0\n\nNote that Takahashi himself is also a participant.\n\n" }, { "title": "", "content": "Problem Statement In the final of CODE FESTIVAL in some year, there are N participants.\nThe height and power of Participant i is H_i and P_i, respectively.\nRingo is hosting a game of stacking zabuton (cushions).\nThe participants will line up in a row in some order, and they will in turn try to add zabuton to the stack of zabuton.\nInitially, the stack is empty.\nWhen it is Participant i's turn, if there are H_i or less zabuton already stacked, he/she will add exactly P_i zabuton to the stack. Otherwise, he/she will give up and do nothing.\nRingo wants to maximize the number of participants who can add zabuton to the stack.\nHow many participants can add zabuton to the stack in the optimal order of participants?", "constraint": "1 <= N <= 5000\n0 <= H_i <= 10^9\n1 <= P_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nH_1 P_1\nH_2 P_2\n:\nH_N P_N", "output": "Print the maximum number of participants who can add zabuton to the stack.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 2\n1 3\n3 4 output: 2\n\nWhen the participants line up in the same order as the input, Participants 1 and 3 will be able to add zabuton.\nOn the other hand, there is no order such that all three participants can add zabuton. Thus, the answer is 2.", "input: 3\n2 4\n3 1\n4 1 output: 3\n\nWhen the participants line up in the order 2,3,1, all of them will be able to add zabuton.", "input: 10\n1 3\n8 4\n8 3\n9 1\n6 4\n2 3\n4 2\n9 2\n8 3\n0 1 output: 5"], "Pid": "p03526", "ProblemText": "Task Description: Problem Statement In the final of CODE FESTIVAL in some year, there are N participants.\nThe height and power of Participant i is H_i and P_i, respectively.\nRingo is hosting a game of stacking zabuton (cushions).\nThe participants will line up in a row in some order, and they will in turn try to add zabuton to the stack of zabuton.\nInitially, the stack is empty.\nWhen it is Participant i's turn, if there are H_i or less zabuton already stacked, he/she will add exactly P_i zabuton to the stack. Otherwise, he/she will give up and do nothing.\nRingo wants to maximize the number of participants who can add zabuton to the stack.\nHow many participants can add zabuton to the stack in the optimal order of participants?\nTask Constraint: 1 <= N <= 5000\n0 <= H_i <= 10^9\n1 <= P_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nH_1 P_1\nH_2 P_2\n:\nH_N P_N\nTask Output: Print the maximum number of participants who can add zabuton to the stack.\nTask Samples: input: 3\n0 2\n1 3\n3 4 output: 2\n\nWhen the participants line up in the same order as the input, Participants 1 and 3 will be able to add zabuton.\nOn the other hand, there is no order such that all three participants can add zabuton. Thus, the answer is 2.\ninput: 3\n2 4\n3 1\n4 1 output: 3\n\nWhen the participants line up in the order 2,3,1, all of them will be able to add zabuton.\ninput: 10\n1 3\n8 4\n8 3\n9 1\n6 4\n2 3\n4 2\n9 2\n8 3\n0 1 output: 5\n\n" }, { "title": "", "content": "Problem Statement Ringo has a string S.\nHe can perform the following N kinds of operations any number of times in any order.\n\nOperation i: For each of the characters from the L_i-th through the R_i-th characters in S, replace it with its succeeding letter in the English alphabet. (That is, replace a with b, replace b with c and so on. ) For z, we assume that its succeeding letter is a.\n\nRingo loves palindromes and wants to turn S into a palindrome.\nDetermine whether this is possible.", "constraint": "1 <= |S| <= 10^5\nS consists of lowercase English letters.\n1 <= N <= 10^5\n1 <= L_i <= R_i <= |S|", "input": "Input is given from Standard Input in the following format:\nS\nN\nL_1 R_1\nL_2 R_2\n:\nL_N R_N", "output": "Print YES if it is possible to turn S into a palindrome; print NO if it is impossible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: bixzja\n2\n2 3\n3 6 output: YES\n\nFor example, if we perform Operation 1,2 and 1 in this order, S changes as bixzja → bjyzja → bjzakb → bkaakb and becomes a palindrome.", "input: abc\n1\n2 2 output: NO", "input: cassert\n4\n1 2\n3 4\n1 1\n2 2 output: YES"], "Pid": "p03527", "ProblemText": "Task Description: Problem Statement Ringo has a string S.\nHe can perform the following N kinds of operations any number of times in any order.\n\nOperation i: For each of the characters from the L_i-th through the R_i-th characters in S, replace it with its succeeding letter in the English alphabet. (That is, replace a with b, replace b with c and so on. ) For z, we assume that its succeeding letter is a.\n\nRingo loves palindromes and wants to turn S into a palindrome.\nDetermine whether this is possible.\nTask Constraint: 1 <= |S| <= 10^5\nS consists of lowercase English letters.\n1 <= N <= 10^5\n1 <= L_i <= R_i <= |S|\nTask Input: Input is given from Standard Input in the following format:\nS\nN\nL_1 R_1\nL_2 R_2\n:\nL_N R_N\nTask Output: Print YES if it is possible to turn S into a palindrome; print NO if it is impossible.\nTask Samples: input: bixzja\n2\n2 3\n3 6 output: YES\n\nFor example, if we perform Operation 1,2 and 1 in this order, S changes as bixzja → bjyzja → bjzakb → bkaakb and becomes a palindrome.\ninput: abc\n1\n2 2 output: NO\ninput: cassert\n4\n1 2\n3 4\n1 1\n2 2 output: YES\n\n" }, { "title": "", "content": "Problem Statement Select any integer N between 1000 and 2000 (inclusive), and any integer K not less than 1, then solve the problem below.\nProblem\nWe have N sheets of paper.\nWrite K integers on each of them to satisfy the following conditions:\n\nEach integer written must be between 1 and N (inclusive).\nThe K integers written on the same sheet must be all different.\nEach of the integers between 1 and N must be written on exactly K sheets.\nFor any two sheet, there is exactly one integer that appears on both.", "constraint": "", "input": "Input There is no input in this problem.", "output": "In the first line, print N and K separated by a space.\nIn the subsequent N lines, print your solution.\nThe i-th of these lines must contain the K integers written on the i-th sheet, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p03528", "ProblemText": "Task Description: Problem Statement Select any integer N between 1000 and 2000 (inclusive), and any integer K not less than 1, then solve the problem below.\nProblem\nWe have N sheets of paper.\nWrite K integers on each of them to satisfy the following conditions:\n\nEach integer written must be between 1 and N (inclusive).\nThe K integers written on the same sheet must be all different.\nEach of the integers between 1 and N must be written on exactly K sheets.\nFor any two sheet, there is exactly one integer that appears on both.\nTask Input: Input There is no input in this problem.\nTask Output: In the first line, print N and K separated by a space.\nIn the subsequent N lines, print your solution.\nThe i-th of these lines must contain the K integers written on the i-th sheet, with spaces in between.\n\n" }, { "title": "", "content": "Problem Statement Consider the following game:\n\nThe game is played using a row of N squares and many stones.\nFirst, a_i stones are put in Square i\\ (1 <= i <= N).\nA player can perform the following operation as many time as desired: \"Select an integer i such that Square i contains exactly i stones. Remove all the stones from Square i, and add one stone to each of the i-1 squares from Square 1 to Square i-1. \"\nThe final score of the player is the total number of the stones remaining in the squares.\n\nFor a sequence a of length N, let f(a) be the minimum score that can be obtained when the game is played on a.\nFind the sum of f(a) over all sequences a of length N where each element is between 0 and K (inclusive).\nSince it can be extremely large, find the answer modulo 1000000007 (= 10^9+7).", "constraint": "1 <= N <= 100\n1 <= K <= N", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the sum of f(a) modulo 1000000007 (= 10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 10\n\nThere are nine sequences of length 2 where each element is between 0 and 2. For each of them, the value of f(a) and how to achieve it is as follows:\n\nf(\\{0,0\\}): 0 (Nothing can be done)\nf(\\{0,1\\}): 1 (Nothing can be done)\nf(\\{0,2\\}): 0 (Select Square 2, then Square 1)\nf(\\{1,0\\}): 0 (Select Square 1)\nf(\\{1,1\\}): 1 (Select Square 1)\nf(\\{1,2\\}): 0 (Select Square 1, Square 2, then Square 1)\nf(\\{2,0\\}): 2 (Nothing can be done)\nf(\\{2,1\\}): 3 (Nothing can be done)\nf(\\{2,2\\}): 3 (Select Square 2)", "input: 20 17 output: 983853488"], "Pid": "p03529", "ProblemText": "Task Description: Problem Statement Consider the following game:\n\nThe game is played using a row of N squares and many stones.\nFirst, a_i stones are put in Square i\\ (1 <= i <= N).\nA player can perform the following operation as many time as desired: \"Select an integer i such that Square i contains exactly i stones. Remove all the stones from Square i, and add one stone to each of the i-1 squares from Square 1 to Square i-1. \"\nThe final score of the player is the total number of the stones remaining in the squares.\n\nFor a sequence a of length N, let f(a) be the minimum score that can be obtained when the game is played on a.\nFind the sum of f(a) over all sequences a of length N where each element is between 0 and K (inclusive).\nSince it can be extremely large, find the answer modulo 1000000007 (= 10^9+7).\nTask Constraint: 1 <= N <= 100\n1 <= K <= N\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the sum of f(a) modulo 1000000007 (= 10^9+7).\nTask Samples: input: 2 2 output: 10\n\nThere are nine sequences of length 2 where each element is between 0 and 2. For each of them, the value of f(a) and how to achieve it is as follows:\n\nf(\\{0,0\\}): 0 (Nothing can be done)\nf(\\{0,1\\}): 1 (Nothing can be done)\nf(\\{0,2\\}): 0 (Select Square 2, then Square 1)\nf(\\{1,0\\}): 0 (Select Square 1)\nf(\\{1,1\\}): 1 (Select Square 1)\nf(\\{1,2\\}): 0 (Select Square 1, Square 2, then Square 1)\nf(\\{2,0\\}): 2 (Nothing can be done)\nf(\\{2,1\\}): 3 (Nothing can be done)\nf(\\{2,2\\}): 3 (Select Square 2)\ninput: 20 17 output: 983853488\n\n" }, { "title": "", "content": "Problem Statement In some place in the Arctic Ocean, there are H rows and W columns of ice pieces floating on the sea.\nWe regard this area as a grid, and denote the square at the i-th row and j-th column as Square (i, j).\nThe ice piece floating in each square is either thin ice or an iceberg, and a penguin lives in one of the squares that contain thin ice.\nThere are no ice pieces floating outside the grid.\nThe ice piece at Square (i, j) is represented by the character S_{i, j}.\nS_{i, j} is +, # or P, each of which means the following:\n\n+: Occupied by thin ice.\n#: Occupied by an iceberg.\nP: Occupied by thin ice. The penguin lives here.\n\nWhen summer comes, unstable thin ice that is not held between some pieces of ice collapses one after another.\nFormally, thin ice at Square (i, j) will collapse when it does NOT satisfy either of the following conditions:\n\nBoth Square (i-1, j) and Square (i+1, j) are occupied by an iceberg or uncollapsed thin ice.\nBoth Square (i, j-1) and Square (i, j+1) are occupied by an iceberg or uncollapsed thin ice.\n\nWhen a collapse happens, it may cause another. Note that icebergs do not collapse.\nNow, a mischievous tourist comes here. He will do a little work so that, when summer comes, the thin ice inhabited by the penguin will collapse.\nHe can smash an iceberg with a hammer to turn it to thin ice.\nAt least how many icebergs does he need to smash?", "constraint": "1 <= H,W <= 40\nS_{i,j} is +, # or P.\nS contains exactly one P.", "input": "Input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}", "output": "Print the minimum number of icebergs that needs to be changed to thin ice in order to cause the collapse of the thin ice inhabited by the penguin when summer comes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n+#+\n#P#\n+#+ output: 2\n\nFor example, when the right and bottom icebergs are changed to thin ice, collapses happen as follows:\n+#+ .#. .#. .#.\n#P+ -> #P+ -> #P. -> #..\n+++ .+. ... ...", "input: 6 6\n#+++++\n+++#++\n#+++++\n+++P+#\n+##+++\n++++#+ output: 1", "input: 40 40\n#++#+++++#+#+#+##+++++++##+#+++#++##++##\n+##++++++++++#+###+##++++#+++++++++#++##\n+++#+++++#++#++####+++#+#+###+++##+++#++\n+++#+######++##+#+##+#+++#+++++++++#++#+\n+++##+#+#++#+++#++++##+++++++++#++#+#+#+\n#++#+++#+#++++##+#+#+++##+#+##+#++++##++\n++#+##+++#++####+#++##++#+++#+#+#++++#++\n+#+###++++++##++++++#++##+#####++#++##++\n##+##+#+++#+#+##++#+###+######++++#+###+\n+++#+++##+#####+#+#++++#+#+++++#+##++##+\n#+++#+##+++++++#++#++++++++++###+#++#+#+\n##+++##++#+++++#++++#++#+##++#+#+#++##+#\n##+++#+###+++++##++#+#+++####+#+++++#+++\n+++#++#++#+++++++++#++###++++++++###+##+\n++#+++#++++++#####++##++#+++#+++++#++++#\n++#++#+##++++#####+###+++####+#+#+######\n++++++##+++++##+++++#++###++#++##+++++++\n+#++++##++++++#++++#+#++++#++++##+++##+#\n+++++++#+#++##+##+#+++++++###+###++##+++\n++++++#++###+#+#+++##+#++++++#++#+#++#+#\n##+##++++++#+++++#++#+#++##+++#+#+++##+#\n#+++#+#+##+#+##++#P#++#++++++##++#+#++##\n#+++#++##+##+#++++#++#++##++++++#+#+#+++\n++++####+#++#####+++#+###+#++###++++#++#\n#+#++####++##++#+#+#+##+#+#+##++++##++#+\n+###+###+#+##+++#++++++#+#++++###+#+++++\n+++#+++++#+++#+++++##++++++++###++#+#+++\n+#+#++#+#++++++###+#++##+#+##+##+#+#####\n#++++++++#+#+###+######++#++#+++++++++++\n##+++##+#+#++#++#++#++++++#++##+#+#++###\n+#+#+#+++++++#+++++++######+##++#++##+##\n++#+++#+###+#++###+++#+++#+#++++#+###+++\n#+#+###++#+#####+++++#+####++#++#+###+++\n+#+##+#++#++##+++++++######++#++++++++++\n+####+#+#+++++##+#+#++#+#++#+++##++++#+#\n#++##++#+#+++++##+#++++####+++++###+#+#+\n##+#++#++#+##+#+#++##++###+###+#+++++##+\n##++###+###+#+#++#++#########+++###+#+##\n+++#+++#++++++++++#+#+++#++#++###+####+#\n++##+###+++++++##+++++#++#++++++++++++++ output: 151", "input: 1 1\nP output: 0"], "Pid": "p03530", "ProblemText": "Task Description: Problem Statement In some place in the Arctic Ocean, there are H rows and W columns of ice pieces floating on the sea.\nWe regard this area as a grid, and denote the square at the i-th row and j-th column as Square (i, j).\nThe ice piece floating in each square is either thin ice or an iceberg, and a penguin lives in one of the squares that contain thin ice.\nThere are no ice pieces floating outside the grid.\nThe ice piece at Square (i, j) is represented by the character S_{i, j}.\nS_{i, j} is +, # or P, each of which means the following:\n\n+: Occupied by thin ice.\n#: Occupied by an iceberg.\nP: Occupied by thin ice. The penguin lives here.\n\nWhen summer comes, unstable thin ice that is not held between some pieces of ice collapses one after another.\nFormally, thin ice at Square (i, j) will collapse when it does NOT satisfy either of the following conditions:\n\nBoth Square (i-1, j) and Square (i+1, j) are occupied by an iceberg or uncollapsed thin ice.\nBoth Square (i, j-1) and Square (i, j+1) are occupied by an iceberg or uncollapsed thin ice.\n\nWhen a collapse happens, it may cause another. Note that icebergs do not collapse.\nNow, a mischievous tourist comes here. He will do a little work so that, when summer comes, the thin ice inhabited by the penguin will collapse.\nHe can smash an iceberg with a hammer to turn it to thin ice.\nAt least how many icebergs does he need to smash?\nTask Constraint: 1 <= H,W <= 40\nS_{i,j} is +, # or P.\nS contains exactly one P.\nTask Input: Input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}\nTask Output: Print the minimum number of icebergs that needs to be changed to thin ice in order to cause the collapse of the thin ice inhabited by the penguin when summer comes.\nTask Samples: input: 3 3\n+#+\n#P#\n+#+ output: 2\n\nFor example, when the right and bottom icebergs are changed to thin ice, collapses happen as follows:\n+#+ .#. .#. .#.\n#P+ -> #P+ -> #P. -> #..\n+++ .+. ... ...\ninput: 6 6\n#+++++\n+++#++\n#+++++\n+++P+#\n+##+++\n++++#+ output: 1\ninput: 40 40\n#++#+++++#+#+#+##+++++++##+#+++#++##++##\n+##++++++++++#+###+##++++#+++++++++#++##\n+++#+++++#++#++####+++#+#+###+++##+++#++\n+++#+######++##+#+##+#+++#+++++++++#++#+\n+++##+#+#++#+++#++++##+++++++++#++#+#+#+\n#++#+++#+#++++##+#+#+++##+#+##+#++++##++\n++#+##+++#++####+#++##++#+++#+#+#++++#++\n+#+###++++++##++++++#++##+#####++#++##++\n##+##+#+++#+#+##++#+###+######++++#+###+\n+++#+++##+#####+#+#++++#+#+++++#+##++##+\n#+++#+##+++++++#++#++++++++++###+#++#+#+\n##+++##++#+++++#++++#++#+##++#+#+#++##+#\n##+++#+###+++++##++#+#+++####+#+++++#+++\n+++#++#++#+++++++++#++###++++++++###+##+\n++#+++#++++++#####++##++#+++#+++++#++++#\n++#++#+##++++#####+###+++####+#+#+######\n++++++##+++++##+++++#++###++#++##+++++++\n+#++++##++++++#++++#+#++++#++++##+++##+#\n+++++++#+#++##+##+#+++++++###+###++##+++\n++++++#++###+#+#+++##+#++++++#++#+#++#+#\n##+##++++++#+++++#++#+#++##+++#+#+++##+#\n#+++#+#+##+#+##++#P#++#++++++##++#+#++##\n#+++#++##+##+#++++#++#++##++++++#+#+#+++\n++++####+#++#####+++#+###+#++###++++#++#\n#+#++####++##++#+#+#+##+#+#+##++++##++#+\n+###+###+#+##+++#++++++#+#++++###+#+++++\n+++#+++++#+++#+++++##++++++++###++#+#+++\n+#+#++#+#++++++###+#++##+#+##+##+#+#####\n#++++++++#+#+###+######++#++#+++++++++++\n##+++##+#+#++#++#++#++++++#++##+#+#++###\n+#+#+#+++++++#+++++++######+##++#++##+##\n++#+++#+###+#++###+++#+++#+#++++#+###+++\n#+#+###++#+#####+++++#+####++#++#+###+++\n+#+##+#++#++##+++++++######++#++++++++++\n+####+#+#+++++##+#+#++#+#++#+++##++++#+#\n#++##++#+#+++++##+#++++####+++++###+#+#+\n##+#++#++#+##+#+#++##++###+###+#+++++##+\n##++###+###+#+#++#++#########+++###+#+##\n+++#+++#++++++++++#+#+++#++#++###+####+#\n++##+###+++++++##+++++#++#++++++++++++++ output: 151\ninput: 1 1\nP output: 0\n\n" }, { "title": "", "content": "Problem Statement2^N players competed in a tournament.\nEach player has a unique ID number from 1 through 2^N. When two players play a match, the player with the smaller ID always wins.\nThis tournament was a little special, in which losers are not eliminated to fully rank all the players.\nWe will call such a tournament that involves 2^n players a full tournament of level n.\nIn a full tournament of level n, the players are ranked as follows:\n\nIn a full tournament of level 0, the only player is ranked first.\nIn a full tournament of level n\\ (1 <= n), initially all 2^n players are lined up in a row. Then:\nFirst, starting from the two leftmost players, the players are successively divided into 2^{n-1} pairs of two players.\nEach of the pairs plays a match. The winner enters the \"Won\" group, and the loser enters the \"Lost\" group.\nThe players in the \"Won\" group are lined up in a row, maintaining the relative order in the previous row. Then, a full tournament of level n-1 is held to fully rank these players.\nThe players in the \"Lost\" group are also ranked in the same manner, then the rank of each of these players increases by 2^{n-1}.\n\nFor example, the figure below shows how a full tournament of level 3 progresses when eight players are lined up in the order 3,4,8,6,2,1,7,5. The list of the players sorted by the final ranking will be 1,3,5,6,2,4,7,8.\n\nTakahashi has a sheet of paper with the list of the players sorted by the final ranking in the tournament, but some of it blurred and became unreadable.\nYou are given the information on the sheet as a sequence A of length N. When A_i is 1 or greater, it means that the i-th ranked player had the ID A_i. If A_i is 0, it means that the ID of the i-th ranked player is lost.\nDetermine whether there exists a valid order in the first phase of the tournament which is consistent with the sheet. If it exists, provide one such order.", "constraint": "1 <= N <= 18\n0 <= A_i <= 2^N\nNo integer, except 0, occurs more than once in A_i.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{2^N}", "output": "If there exists a valid order in the first phase of the tournament, print YES first, then in the subsequent line, print the IDs of the players sorted by the final ranking, with spaces in between.\nIf there is no such order, print NO instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 3 0 6 0 0 0 8 output: YES\n3 4 8 6 2 1 7 5\n\nThis is the same order as the one in the statement.", "input: 1\n2 1 output: NO"], "Pid": "p03531", "ProblemText": "Task Description: Problem Statement2^N players competed in a tournament.\nEach player has a unique ID number from 1 through 2^N. When two players play a match, the player with the smaller ID always wins.\nThis tournament was a little special, in which losers are not eliminated to fully rank all the players.\nWe will call such a tournament that involves 2^n players a full tournament of level n.\nIn a full tournament of level n, the players are ranked as follows:\n\nIn a full tournament of level 0, the only player is ranked first.\nIn a full tournament of level n\\ (1 <= n), initially all 2^n players are lined up in a row. Then:\nFirst, starting from the two leftmost players, the players are successively divided into 2^{n-1} pairs of two players.\nEach of the pairs plays a match. The winner enters the \"Won\" group, and the loser enters the \"Lost\" group.\nThe players in the \"Won\" group are lined up in a row, maintaining the relative order in the previous row. Then, a full tournament of level n-1 is held to fully rank these players.\nThe players in the \"Lost\" group are also ranked in the same manner, then the rank of each of these players increases by 2^{n-1}.\n\nFor example, the figure below shows how a full tournament of level 3 progresses when eight players are lined up in the order 3,4,8,6,2,1,7,5. The list of the players sorted by the final ranking will be 1,3,5,6,2,4,7,8.\n\nTakahashi has a sheet of paper with the list of the players sorted by the final ranking in the tournament, but some of it blurred and became unreadable.\nYou are given the information on the sheet as a sequence A of length N. When A_i is 1 or greater, it means that the i-th ranked player had the ID A_i. If A_i is 0, it means that the ID of the i-th ranked player is lost.\nDetermine whether there exists a valid order in the first phase of the tournament which is consistent with the sheet. If it exists, provide one such order.\nTask Constraint: 1 <= N <= 18\n0 <= A_i <= 2^N\nNo integer, except 0, occurs more than once in A_i.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{2^N}\nTask Output: If there exists a valid order in the first phase of the tournament, print YES first, then in the subsequent line, print the IDs of the players sorted by the final ranking, with spaces in between.\nIf there is no such order, print NO instead.\nTask Samples: input: 3\n0 3 0 6 0 0 0 8 output: YES\n3 4 8 6 2 1 7 5\n\nThis is the same order as the one in the statement.\ninput: 1\n2 1 output: NO\n\n" }, { "title": "", "content": "Problem Statement Ringo has a tree with N vertices.\nThe i-th of the N-1 edges in this tree connects Vertex A_i and Vertex B_i and has a weight of C_i.\nAdditionally, Vertex i has a weight of X_i.\nHere, we define f(u, v) as the distance between Vertex u and Vertex v, plus X_u + X_v.\nWe will consider a complete graph G with N vertices.\nThe cost of its edge that connects Vertex u and Vertex v is f(u, v).\nFind the minimum spanning tree of G.", "constraint": "2 <= N <= 200,000\n1 <= X_i <= 10^9\n1 <= A_i,B_i <= N\n1 <= C_i <= 10^9\nThe given graph is a tree.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{N-1} B_{N-1} C_{N-1}", "output": "Print the cost of the minimum spanning tree of G.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 3 5 1\n1 2 1\n2 3 2\n3 4 3 output: 22\n\nWe connect the following pairs: Vertex 1 and 2, Vertex 1 and 4, Vertex 3 and 4. The costs are 5,8 and 9, respectively, for a total of 22.", "input: 6\n44 23 31 29 32 15\n1 2 10\n1 3 12\n1 4 16\n4 5 8\n4 6 15 output: 359", "input: 2\n1000000000 1000000000\n2 1 1000000000 output: 3000000000"], "Pid": "p03532", "ProblemText": "Task Description: Problem Statement Ringo has a tree with N vertices.\nThe i-th of the N-1 edges in this tree connects Vertex A_i and Vertex B_i and has a weight of C_i.\nAdditionally, Vertex i has a weight of X_i.\nHere, we define f(u, v) as the distance between Vertex u and Vertex v, plus X_u + X_v.\nWe will consider a complete graph G with N vertices.\nThe cost of its edge that connects Vertex u and Vertex v is f(u, v).\nFind the minimum spanning tree of G.\nTask Constraint: 2 <= N <= 200,000\n1 <= X_i <= 10^9\n1 <= A_i,B_i <= N\n1 <= C_i <= 10^9\nThe given graph is a tree.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{N-1} B_{N-1} C_{N-1}\nTask Output: Print the cost of the minimum spanning tree of G.\nTask Samples: input: 4\n1 3 5 1\n1 2 1\n2 3 2\n3 4 3 output: 22\n\nWe connect the following pairs: Vertex 1 and 2, Vertex 1 and 4, Vertex 3 and 4. The costs are 5,8 and 9, respectively, for a total of 22.\ninput: 6\n44 23 31 29 32 15\n1 2 10\n1 3 12\n1 4 16\n4 5 8\n4 6 15 output: 359\ninput: 2\n1000000000 1000000000\n2 1 1000000000 output: 3000000000\n\n" }, { "title": "", "content": "Problem Statement You are given a string S.\nTakahashi can insert the character A at any position in this string any number of times.\nCan he change S into AKIHABARA?", "constraint": "1 <= |S| <= 50\nS consists of uppercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If it is possible to change S into AKIHABARA, print YES; otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: KIHBR output: YES\n\nInsert one A at each of the four positions: the beginning, immediately after H, immediately after B and the end.", "input: AKIBAHARA output: NO\n\nThe correct spell is AKIHABARA.", "input: AAKIAHBAARA output: NO"], "Pid": "p03533", "ProblemText": "Task Description: Problem Statement You are given a string S.\nTakahashi can insert the character A at any position in this string any number of times.\nCan he change S into AKIHABARA?\nTask Constraint: 1 <= |S| <= 50\nS consists of uppercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If it is possible to change S into AKIHABARA, print YES; otherwise, print NO.\nTask Samples: input: KIHBR output: YES\n\nInsert one A at each of the four positions: the beginning, immediately after H, immediately after B and the end.\ninput: AKIBAHARA output: NO\n\nThe correct spell is AKIHABARA.\ninput: AAKIAHBAARA output: NO\n\n" }, { "title": "", "content": "Problem Statement Snuke has a string S consisting of three kinds of letters: a, b and c.\nHe has a phobia for palindromes, and wants to permute the characters in S so that S will not contain a palindrome of length 2 or more as a substring. Determine whether this is possible.", "constraint": "1 <= |S| <= 10^5\nS consists of a, b and c.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If the objective is achievable, print YES; if it is unachievable, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abac output: YES\n\nAs it stands now, S contains a palindrome aba, but we can permute the characters to get acba, for example, that does not contain a palindrome of length 2 or more.", "input: aba output: NO", "input: babacccabab output: YES"], "Pid": "p03534", "ProblemText": "Task Description: Problem Statement Snuke has a string S consisting of three kinds of letters: a, b and c.\nHe has a phobia for palindromes, and wants to permute the characters in S so that S will not contain a palindrome of length 2 or more as a substring. Determine whether this is possible.\nTask Constraint: 1 <= |S| <= 10^5\nS consists of a, b and c.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If the objective is achievable, print YES; if it is unachievable, print NO.\nTask Samples: input: abac output: YES\n\nAs it stands now, S contains a palindrome aba, but we can permute the characters to get acba, for example, that does not contain a palindrome of length 2 or more.\ninput: aba output: NO\ninput: babacccabab output: YES\n\n" }, { "title": "", "content": "Problem Statement In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.\nTakahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.\nThe time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d, 24-d) hours.\nHere, we are using 24-hour notation.\nThat is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.\nThen, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.\nFind the maximum possible value of s.", "constraint": "1 <= N <= 50\n0 <= D_i <= 12\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nD_1 D_2 . . . D_N", "output": "Print the maximum possible value of s.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n7 12 8 output: 4\n\nFor example, consider the situation where it is 7,12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.", "input: 2\n11 11 output: 2", "input: 1\n0 output: 0\n\nNote that Takahashi himself is also a participant."], "Pid": "p03535", "ProblemText": "Task Description: Problem Statement In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.\nTakahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.\nThe time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d, 24-d) hours.\nHere, we are using 24-hour notation.\nThat is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.\nThen, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.\nFind the maximum possible value of s.\nTask Constraint: 1 <= N <= 50\n0 <= D_i <= 12\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nD_1 D_2 . . . D_N\nTask Output: Print the maximum possible value of s.\nTask Samples: input: 3\n7 12 8 output: 4\n\nFor example, consider the situation where it is 7,12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.\ninput: 2\n11 11 output: 2\ninput: 1\n0 output: 0\n\nNote that Takahashi himself is also a participant.\n\n" }, { "title": "", "content": "Problem Statement In the final of CODE FESTIVAL in some year, there are N participants.\nThe height and power of Participant i is H_i and P_i, respectively.\nRingo is hosting a game of stacking zabuton (cushions).\nThe participants will line up in a row in some order, and they will in turn try to add zabuton to the stack of zabuton.\nInitially, the stack is empty.\nWhen it is Participant i's turn, if there are H_i or less zabuton already stacked, he/she will add exactly P_i zabuton to the stack. Otherwise, he/she will give up and do nothing.\nRingo wants to maximize the number of participants who can add zabuton to the stack.\nHow many participants can add zabuton to the stack in the optimal order of participants?", "constraint": "1 <= N <= 5000\n0 <= H_i <= 10^9\n1 <= P_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nH_1 P_1\nH_2 P_2\n:\nH_N P_N", "output": "Print the maximum number of participants who can add zabuton to the stack.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 2\n1 3\n3 4 output: 2\n\nWhen the participants line up in the same order as the input, Participants 1 and 3 will be able to add zabuton.\nOn the other hand, there is no order such that all three participants can add zabuton. Thus, the answer is 2.", "input: 3\n2 4\n3 1\n4 1 output: 3\n\nWhen the participants line up in the order 2,3,1, all of them will be able to add zabuton.", "input: 10\n1 3\n8 4\n8 3\n9 1\n6 4\n2 3\n4 2\n9 2\n8 3\n0 1 output: 5"], "Pid": "p03536", "ProblemText": "Task Description: Problem Statement In the final of CODE FESTIVAL in some year, there are N participants.\nThe height and power of Participant i is H_i and P_i, respectively.\nRingo is hosting a game of stacking zabuton (cushions).\nThe participants will line up in a row in some order, and they will in turn try to add zabuton to the stack of zabuton.\nInitially, the stack is empty.\nWhen it is Participant i's turn, if there are H_i or less zabuton already stacked, he/she will add exactly P_i zabuton to the stack. Otherwise, he/she will give up and do nothing.\nRingo wants to maximize the number of participants who can add zabuton to the stack.\nHow many participants can add zabuton to the stack in the optimal order of participants?\nTask Constraint: 1 <= N <= 5000\n0 <= H_i <= 10^9\n1 <= P_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nH_1 P_1\nH_2 P_2\n:\nH_N P_N\nTask Output: Print the maximum number of participants who can add zabuton to the stack.\nTask Samples: input: 3\n0 2\n1 3\n3 4 output: 2\n\nWhen the participants line up in the same order as the input, Participants 1 and 3 will be able to add zabuton.\nOn the other hand, there is no order such that all three participants can add zabuton. Thus, the answer is 2.\ninput: 3\n2 4\n3 1\n4 1 output: 3\n\nWhen the participants line up in the order 2,3,1, all of them will be able to add zabuton.\ninput: 10\n1 3\n8 4\n8 3\n9 1\n6 4\n2 3\n4 2\n9 2\n8 3\n0 1 output: 5\n\n" }, { "title": "", "content": "Problem Statement Ringo has a string S.\nHe can perform the following N kinds of operations any number of times in any order.\n\nOperation i: For each of the characters from the L_i-th through the R_i-th characters in S, replace it with its succeeding letter in the English alphabet. (That is, replace a with b, replace b with c and so on. ) For z, we assume that its succeeding letter is a.\n\nRingo loves palindromes and wants to turn S into a palindrome.\nDetermine whether this is possible.", "constraint": "1 <= |S| <= 10^5\nS consists of lowercase English letters.\n1 <= N <= 10^5\n1 <= L_i <= R_i <= |S|", "input": "Input is given from Standard Input in the following format:\nS\nN\nL_1 R_1\nL_2 R_2\n:\nL_N R_N", "output": "Print YES if it is possible to turn S into a palindrome; print NO if it is impossible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: bixzja\n2\n2 3\n3 6 output: YES\n\nFor example, if we perform Operation 1,2 and 1 in this order, S changes as bixzja → bjyzja → bjzakb → bkaakb and becomes a palindrome.", "input: abc\n1\n2 2 output: NO", "input: cassert\n4\n1 2\n3 4\n1 1\n2 2 output: YES"], "Pid": "p03537", "ProblemText": "Task Description: Problem Statement Ringo has a string S.\nHe can perform the following N kinds of operations any number of times in any order.\n\nOperation i: For each of the characters from the L_i-th through the R_i-th characters in S, replace it with its succeeding letter in the English alphabet. (That is, replace a with b, replace b with c and so on. ) For z, we assume that its succeeding letter is a.\n\nRingo loves palindromes and wants to turn S into a palindrome.\nDetermine whether this is possible.\nTask Constraint: 1 <= |S| <= 10^5\nS consists of lowercase English letters.\n1 <= N <= 10^5\n1 <= L_i <= R_i <= |S|\nTask Input: Input is given from Standard Input in the following format:\nS\nN\nL_1 R_1\nL_2 R_2\n:\nL_N R_N\nTask Output: Print YES if it is possible to turn S into a palindrome; print NO if it is impossible.\nTask Samples: input: bixzja\n2\n2 3\n3 6 output: YES\n\nFor example, if we perform Operation 1,2 and 1 in this order, S changes as bixzja → bjyzja → bjzakb → bkaakb and becomes a palindrome.\ninput: abc\n1\n2 2 output: NO\ninput: cassert\n4\n1 2\n3 4\n1 1\n2 2 output: YES\n\n" }, { "title": "", "content": "Problem Statement Select any integer N between 1000 and 2000 (inclusive), and any integer K not less than 1, then solve the problem below.\nProblem\nWe have N sheets of paper.\nWrite K integers on each of them to satisfy the following conditions:\n\nEach integer written must be between 1 and N (inclusive).\nThe K integers written on the same sheet must be all different.\nEach of the integers between 1 and N must be written on exactly K sheets.\nFor any two sheet, there is exactly one integer that appears on both.", "constraint": "", "input": "Input There is no input in this problem.", "output": "In the first line, print N and K separated by a space.\nIn the subsequent N lines, print your solution.\nThe i-th of these lines must contain the K integers written on the i-th sheet, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": [], "Pid": "p03538", "ProblemText": "Task Description: Problem Statement Select any integer N between 1000 and 2000 (inclusive), and any integer K not less than 1, then solve the problem below.\nProblem\nWe have N sheets of paper.\nWrite K integers on each of them to satisfy the following conditions:\n\nEach integer written must be between 1 and N (inclusive).\nThe K integers written on the same sheet must be all different.\nEach of the integers between 1 and N must be written on exactly K sheets.\nFor any two sheet, there is exactly one integer that appears on both.\nTask Input: Input There is no input in this problem.\nTask Output: In the first line, print N and K separated by a space.\nIn the subsequent N lines, print your solution.\nThe i-th of these lines must contain the K integers written on the i-th sheet, with spaces in between.\n\n" }, { "title": "", "content": "Problem Statement Consider the following game:\n\nThe game is played using a row of N squares and many stones.\nFirst, a_i stones are put in Square i\\ (1 <= i <= N).\nA player can perform the following operation as many time as desired: \"Select an integer i such that Square i contains exactly i stones. Remove all the stones from Square i, and add one stone to each of the i-1 squares from Square 1 to Square i-1. \"\nThe final score of the player is the total number of the stones remaining in the squares.\n\nFor a sequence a of length N, let f(a) be the minimum score that can be obtained when the game is played on a.\nFind the sum of f(a) over all sequences a of length N where each element is between 0 and K (inclusive).\nSince it can be extremely large, find the answer modulo 1000000007 (= 10^9+7).", "constraint": "1 <= N <= 100\n1 <= K <= N", "input": "Input is given from Standard Input in the following format:\nN K", "output": "Print the sum of f(a) modulo 1000000007 (= 10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 10\n\nThere are nine sequences of length 2 where each element is between 0 and 2. For each of them, the value of f(a) and how to achieve it is as follows:\n\nf(\\{0,0\\}): 0 (Nothing can be done)\nf(\\{0,1\\}): 1 (Nothing can be done)\nf(\\{0,2\\}): 0 (Select Square 2, then Square 1)\nf(\\{1,0\\}): 0 (Select Square 1)\nf(\\{1,1\\}): 1 (Select Square 1)\nf(\\{1,2\\}): 0 (Select Square 1, Square 2, then Square 1)\nf(\\{2,0\\}): 2 (Nothing can be done)\nf(\\{2,1\\}): 3 (Nothing can be done)\nf(\\{2,2\\}): 3 (Select Square 2)", "input: 20 17 output: 983853488"], "Pid": "p03539", "ProblemText": "Task Description: Problem Statement Consider the following game:\n\nThe game is played using a row of N squares and many stones.\nFirst, a_i stones are put in Square i\\ (1 <= i <= N).\nA player can perform the following operation as many time as desired: \"Select an integer i such that Square i contains exactly i stones. Remove all the stones from Square i, and add one stone to each of the i-1 squares from Square 1 to Square i-1. \"\nThe final score of the player is the total number of the stones remaining in the squares.\n\nFor a sequence a of length N, let f(a) be the minimum score that can be obtained when the game is played on a.\nFind the sum of f(a) over all sequences a of length N where each element is between 0 and K (inclusive).\nSince it can be extremely large, find the answer modulo 1000000007 (= 10^9+7).\nTask Constraint: 1 <= N <= 100\n1 <= K <= N\nTask Input: Input is given from Standard Input in the following format:\nN K\nTask Output: Print the sum of f(a) modulo 1000000007 (= 10^9+7).\nTask Samples: input: 2 2 output: 10\n\nThere are nine sequences of length 2 where each element is between 0 and 2. For each of them, the value of f(a) and how to achieve it is as follows:\n\nf(\\{0,0\\}): 0 (Nothing can be done)\nf(\\{0,1\\}): 1 (Nothing can be done)\nf(\\{0,2\\}): 0 (Select Square 2, then Square 1)\nf(\\{1,0\\}): 0 (Select Square 1)\nf(\\{1,1\\}): 1 (Select Square 1)\nf(\\{1,2\\}): 0 (Select Square 1, Square 2, then Square 1)\nf(\\{2,0\\}): 2 (Nothing can be done)\nf(\\{2,1\\}): 3 (Nothing can be done)\nf(\\{2,2\\}): 3 (Select Square 2)\ninput: 20 17 output: 983853488\n\n" }, { "title": "", "content": "Problem Statement In some place in the Arctic Ocean, there are H rows and W columns of ice pieces floating on the sea.\nWe regard this area as a grid, and denote the square at the i-th row and j-th column as Square (i, j).\nThe ice piece floating in each square is either thin ice or an iceberg, and a penguin lives in one of the squares that contain thin ice.\nThere are no ice pieces floating outside the grid.\nThe ice piece at Square (i, j) is represented by the character S_{i, j}.\nS_{i, j} is +, # or P, each of which means the following:\n\n+: Occupied by thin ice.\n#: Occupied by an iceberg.\nP: Occupied by thin ice. The penguin lives here.\n\nWhen summer comes, unstable thin ice that is not held between some pieces of ice collapses one after another.\nFormally, thin ice at Square (i, j) will collapse when it does NOT satisfy either of the following conditions:\n\nBoth Square (i-1, j) and Square (i+1, j) are occupied by an iceberg or uncollapsed thin ice.\nBoth Square (i, j-1) and Square (i, j+1) are occupied by an iceberg or uncollapsed thin ice.\n\nWhen a collapse happens, it may cause another. Note that icebergs do not collapse.\nNow, a mischievous tourist comes here. He will do a little work so that, when summer comes, the thin ice inhabited by the penguin will collapse.\nHe can smash an iceberg with a hammer to turn it to thin ice.\nAt least how many icebergs does he need to smash?", "constraint": "1 <= H,W <= 40\nS_{i,j} is +, # or P.\nS contains exactly one P.", "input": "Input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}", "output": "Print the minimum number of icebergs that needs to be changed to thin ice in order to cause the collapse of the thin ice inhabited by the penguin when summer comes.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n+#+\n#P#\n+#+ output: 2\n\nFor example, when the right and bottom icebergs are changed to thin ice, collapses happen as follows:\n+#+ .#. .#. .#.\n#P+ -> #P+ -> #P. -> #..\n+++ .+. ... ...", "input: 6 6\n#+++++\n+++#++\n#+++++\n+++P+#\n+##+++\n++++#+ output: 1", "input: 40 40\n#++#+++++#+#+#+##+++++++##+#+++#++##++##\n+##++++++++++#+###+##++++#+++++++++#++##\n+++#+++++#++#++####+++#+#+###+++##+++#++\n+++#+######++##+#+##+#+++#+++++++++#++#+\n+++##+#+#++#+++#++++##+++++++++#++#+#+#+\n#++#+++#+#++++##+#+#+++##+#+##+#++++##++\n++#+##+++#++####+#++##++#+++#+#+#++++#++\n+#+###++++++##++++++#++##+#####++#++##++\n##+##+#+++#+#+##++#+###+######++++#+###+\n+++#+++##+#####+#+#++++#+#+++++#+##++##+\n#+++#+##+++++++#++#++++++++++###+#++#+#+\n##+++##++#+++++#++++#++#+##++#+#+#++##+#\n##+++#+###+++++##++#+#+++####+#+++++#+++\n+++#++#++#+++++++++#++###++++++++###+##+\n++#+++#++++++#####++##++#+++#+++++#++++#\n++#++#+##++++#####+###+++####+#+#+######\n++++++##+++++##+++++#++###++#++##+++++++\n+#++++##++++++#++++#+#++++#++++##+++##+#\n+++++++#+#++##+##+#+++++++###+###++##+++\n++++++#++###+#+#+++##+#++++++#++#+#++#+#\n##+##++++++#+++++#++#+#++##+++#+#+++##+#\n#+++#+#+##+#+##++#P#++#++++++##++#+#++##\n#+++#++##+##+#++++#++#++##++++++#+#+#+++\n++++####+#++#####+++#+###+#++###++++#++#\n#+#++####++##++#+#+#+##+#+#+##++++##++#+\n+###+###+#+##+++#++++++#+#++++###+#+++++\n+++#+++++#+++#+++++##++++++++###++#+#+++\n+#+#++#+#++++++###+#++##+#+##+##+#+#####\n#++++++++#+#+###+######++#++#+++++++++++\n##+++##+#+#++#++#++#++++++#++##+#+#++###\n+#+#+#+++++++#+++++++######+##++#++##+##\n++#+++#+###+#++###+++#+++#+#++++#+###+++\n#+#+###++#+#####+++++#+####++#++#+###+++\n+#+##+#++#++##+++++++######++#++++++++++\n+####+#+#+++++##+#+#++#+#++#+++##++++#+#\n#++##++#+#+++++##+#++++####+++++###+#+#+\n##+#++#++#+##+#+#++##++###+###+#+++++##+\n##++###+###+#+#++#++#########+++###+#+##\n+++#+++#++++++++++#+#+++#++#++###+####+#\n++##+###+++++++##+++++#++#++++++++++++++ output: 151", "input: 1 1\nP output: 0"], "Pid": "p03540", "ProblemText": "Task Description: Problem Statement In some place in the Arctic Ocean, there are H rows and W columns of ice pieces floating on the sea.\nWe regard this area as a grid, and denote the square at the i-th row and j-th column as Square (i, j).\nThe ice piece floating in each square is either thin ice or an iceberg, and a penguin lives in one of the squares that contain thin ice.\nThere are no ice pieces floating outside the grid.\nThe ice piece at Square (i, j) is represented by the character S_{i, j}.\nS_{i, j} is +, # or P, each of which means the following:\n\n+: Occupied by thin ice.\n#: Occupied by an iceberg.\nP: Occupied by thin ice. The penguin lives here.\n\nWhen summer comes, unstable thin ice that is not held between some pieces of ice collapses one after another.\nFormally, thin ice at Square (i, j) will collapse when it does NOT satisfy either of the following conditions:\n\nBoth Square (i-1, j) and Square (i+1, j) are occupied by an iceberg or uncollapsed thin ice.\nBoth Square (i, j-1) and Square (i, j+1) are occupied by an iceberg or uncollapsed thin ice.\n\nWhen a collapse happens, it may cause another. Note that icebergs do not collapse.\nNow, a mischievous tourist comes here. He will do a little work so that, when summer comes, the thin ice inhabited by the penguin will collapse.\nHe can smash an iceberg with a hammer to turn it to thin ice.\nAt least how many icebergs does he need to smash?\nTask Constraint: 1 <= H,W <= 40\nS_{i,j} is +, # or P.\nS contains exactly one P.\nTask Input: Input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}\nTask Output: Print the minimum number of icebergs that needs to be changed to thin ice in order to cause the collapse of the thin ice inhabited by the penguin when summer comes.\nTask Samples: input: 3 3\n+#+\n#P#\n+#+ output: 2\n\nFor example, when the right and bottom icebergs are changed to thin ice, collapses happen as follows:\n+#+ .#. .#. .#.\n#P+ -> #P+ -> #P. -> #..\n+++ .+. ... ...\ninput: 6 6\n#+++++\n+++#++\n#+++++\n+++P+#\n+##+++\n++++#+ output: 1\ninput: 40 40\n#++#+++++#+#+#+##+++++++##+#+++#++##++##\n+##++++++++++#+###+##++++#+++++++++#++##\n+++#+++++#++#++####+++#+#+###+++##+++#++\n+++#+######++##+#+##+#+++#+++++++++#++#+\n+++##+#+#++#+++#++++##+++++++++#++#+#+#+\n#++#+++#+#++++##+#+#+++##+#+##+#++++##++\n++#+##+++#++####+#++##++#+++#+#+#++++#++\n+#+###++++++##++++++#++##+#####++#++##++\n##+##+#+++#+#+##++#+###+######++++#+###+\n+++#+++##+#####+#+#++++#+#+++++#+##++##+\n#+++#+##+++++++#++#++++++++++###+#++#+#+\n##+++##++#+++++#++++#++#+##++#+#+#++##+#\n##+++#+###+++++##++#+#+++####+#+++++#+++\n+++#++#++#+++++++++#++###++++++++###+##+\n++#+++#++++++#####++##++#+++#+++++#++++#\n++#++#+##++++#####+###+++####+#+#+######\n++++++##+++++##+++++#++###++#++##+++++++\n+#++++##++++++#++++#+#++++#++++##+++##+#\n+++++++#+#++##+##+#+++++++###+###++##+++\n++++++#++###+#+#+++##+#++++++#++#+#++#+#\n##+##++++++#+++++#++#+#++##+++#+#+++##+#\n#+++#+#+##+#+##++#P#++#++++++##++#+#++##\n#+++#++##+##+#++++#++#++##++++++#+#+#+++\n++++####+#++#####+++#+###+#++###++++#++#\n#+#++####++##++#+#+#+##+#+#+##++++##++#+\n+###+###+#+##+++#++++++#+#++++###+#+++++\n+++#+++++#+++#+++++##++++++++###++#+#+++\n+#+#++#+#++++++###+#++##+#+##+##+#+#####\n#++++++++#+#+###+######++#++#+++++++++++\n##+++##+#+#++#++#++#++++++#++##+#+#++###\n+#+#+#+++++++#+++++++######+##++#++##+##\n++#+++#+###+#++###+++#+++#+#++++#+###+++\n#+#+###++#+#####+++++#+####++#++#+###+++\n+#+##+#++#++##+++++++######++#++++++++++\n+####+#+#+++++##+#+#++#+#++#+++##++++#+#\n#++##++#+#+++++##+#++++####+++++###+#+#+\n##+#++#++#+##+#+#++##++###+###+#+++++##+\n##++###+###+#+#++#++#########+++###+#+##\n+++#+++#++++++++++#+#+++#++#++###+####+#\n++##+###+++++++##+++++#++#++++++++++++++ output: 151\ninput: 1 1\nP output: 0\n\n" }, { "title": "", "content": "Problem Statement2^N players competed in a tournament.\nEach player has a unique ID number from 1 through 2^N. When two players play a match, the player with the smaller ID always wins.\nThis tournament was a little special, in which losers are not eliminated to fully rank all the players.\nWe will call such a tournament that involves 2^n players a full tournament of level n.\nIn a full tournament of level n, the players are ranked as follows:\n\nIn a full tournament of level 0, the only player is ranked first.\nIn a full tournament of level n\\ (1 <= n), initially all 2^n players are lined up in a row. Then:\nFirst, starting from the two leftmost players, the players are successively divided into 2^{n-1} pairs of two players.\nEach of the pairs plays a match. The winner enters the \"Won\" group, and the loser enters the \"Lost\" group.\nThe players in the \"Won\" group are lined up in a row, maintaining the relative order in the previous row. Then, a full tournament of level n-1 is held to fully rank these players.\nThe players in the \"Lost\" group are also ranked in the same manner, then the rank of each of these players increases by 2^{n-1}.\n\nFor example, the figure below shows how a full tournament of level 3 progresses when eight players are lined up in the order 3,4,8,6,2,1,7,5. The list of the players sorted by the final ranking will be 1,3,5,6,2,4,7,8.\n\nTakahashi has a sheet of paper with the list of the players sorted by the final ranking in the tournament, but some of it blurred and became unreadable.\nYou are given the information on the sheet as a sequence A of length N. When A_i is 1 or greater, it means that the i-th ranked player had the ID A_i. If A_i is 0, it means that the ID of the i-th ranked player is lost.\nDetermine whether there exists a valid order in the first phase of the tournament which is consistent with the sheet. If it exists, provide one such order.", "constraint": "1 <= N <= 18\n0 <= A_i <= 2^N\nNo integer, except 0, occurs more than once in A_i.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{2^N}", "output": "If there exists a valid order in the first phase of the tournament, print YES first, then in the subsequent line, print the IDs of the players sorted by the final ranking, with spaces in between.\nIf there is no such order, print NO instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 3 0 6 0 0 0 8 output: YES\n3 4 8 6 2 1 7 5\n\nThis is the same order as the one in the statement.", "input: 1\n2 1 output: NO"], "Pid": "p03541", "ProblemText": "Task Description: Problem Statement2^N players competed in a tournament.\nEach player has a unique ID number from 1 through 2^N. When two players play a match, the player with the smaller ID always wins.\nThis tournament was a little special, in which losers are not eliminated to fully rank all the players.\nWe will call such a tournament that involves 2^n players a full tournament of level n.\nIn a full tournament of level n, the players are ranked as follows:\n\nIn a full tournament of level 0, the only player is ranked first.\nIn a full tournament of level n\\ (1 <= n), initially all 2^n players are lined up in a row. Then:\nFirst, starting from the two leftmost players, the players are successively divided into 2^{n-1} pairs of two players.\nEach of the pairs plays a match. The winner enters the \"Won\" group, and the loser enters the \"Lost\" group.\nThe players in the \"Won\" group are lined up in a row, maintaining the relative order in the previous row. Then, a full tournament of level n-1 is held to fully rank these players.\nThe players in the \"Lost\" group are also ranked in the same manner, then the rank of each of these players increases by 2^{n-1}.\n\nFor example, the figure below shows how a full tournament of level 3 progresses when eight players are lined up in the order 3,4,8,6,2,1,7,5. The list of the players sorted by the final ranking will be 1,3,5,6,2,4,7,8.\n\nTakahashi has a sheet of paper with the list of the players sorted by the final ranking in the tournament, but some of it blurred and became unreadable.\nYou are given the information on the sheet as a sequence A of length N. When A_i is 1 or greater, it means that the i-th ranked player had the ID A_i. If A_i is 0, it means that the ID of the i-th ranked player is lost.\nDetermine whether there exists a valid order in the first phase of the tournament which is consistent with the sheet. If it exists, provide one such order.\nTask Constraint: 1 <= N <= 18\n0 <= A_i <= 2^N\nNo integer, except 0, occurs more than once in A_i.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{2^N}\nTask Output: If there exists a valid order in the first phase of the tournament, print YES first, then in the subsequent line, print the IDs of the players sorted by the final ranking, with spaces in between.\nIf there is no such order, print NO instead.\nTask Samples: input: 3\n0 3 0 6 0 0 0 8 output: YES\n3 4 8 6 2 1 7 5\n\nThis is the same order as the one in the statement.\ninput: 1\n2 1 output: NO\n\n" }, { "title": "", "content": "Problem Statement Ringo has a tree with N vertices.\nThe i-th of the N-1 edges in this tree connects Vertex A_i and Vertex B_i and has a weight of C_i.\nAdditionally, Vertex i has a weight of X_i.\nHere, we define f(u, v) as the distance between Vertex u and Vertex v, plus X_u + X_v.\nWe will consider a complete graph G with N vertices.\nThe cost of its edge that connects Vertex u and Vertex v is f(u, v).\nFind the minimum spanning tree of G.", "constraint": "2 <= N <= 200,000\n1 <= X_i <= 10^9\n1 <= A_i,B_i <= N\n1 <= C_i <= 10^9\nThe given graph is a tree.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{N-1} B_{N-1} C_{N-1}", "output": "Print the cost of the minimum spanning tree of G.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 3 5 1\n1 2 1\n2 3 2\n3 4 3 output: 22\n\nWe connect the following pairs: Vertex 1 and 2, Vertex 1 and 4, Vertex 3 and 4. The costs are 5,8 and 9, respectively, for a total of 22.", "input: 6\n44 23 31 29 32 15\n1 2 10\n1 3 12\n1 4 16\n4 5 8\n4 6 15 output: 359", "input: 2\n1000000000 1000000000\n2 1 1000000000 output: 3000000000"], "Pid": "p03542", "ProblemText": "Task Description: Problem Statement Ringo has a tree with N vertices.\nThe i-th of the N-1 edges in this tree connects Vertex A_i and Vertex B_i and has a weight of C_i.\nAdditionally, Vertex i has a weight of X_i.\nHere, we define f(u, v) as the distance between Vertex u and Vertex v, plus X_u + X_v.\nWe will consider a complete graph G with N vertices.\nThe cost of its edge that connects Vertex u and Vertex v is f(u, v).\nFind the minimum spanning tree of G.\nTask Constraint: 2 <= N <= 200,000\n1 <= X_i <= 10^9\n1 <= A_i,B_i <= N\n1 <= C_i <= 10^9\nThe given graph is a tree.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nX_1 X_2 . . . X_N\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{N-1} B_{N-1} C_{N-1}\nTask Output: Print the cost of the minimum spanning tree of G.\nTask Samples: input: 4\n1 3 5 1\n1 2 1\n2 3 2\n3 4 3 output: 22\n\nWe connect the following pairs: Vertex 1 and 2, Vertex 1 and 4, Vertex 3 and 4. The costs are 5,8 and 9, respectively, for a total of 22.\ninput: 6\n44 23 31 29 32 15\n1 2 10\n1 3 12\n1 4 16\n4 5 8\n4 6 15 output: 359\ninput: 2\n1000000000 1000000000\n2 1 1000000000 output: 3000000000\n\n" }, { "title": "", "content": "Problem Statement We call a 4-digit integer with three or more consecutive same digits, such as 1118, good.\nYou are given a 4-digit integer N. Answer the question: Is N good?", "constraint": "1000 <= N <= 9999\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "If N is good, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1118 output: Yes\n\nN is good, since it contains three consecutive 1.", "input: 7777 output: Yes\n\nAn integer is also good when all the digits are the same.", "input: 1234 output: No"], "Pid": "p03543", "ProblemText": "Task Description: Problem Statement We call a 4-digit integer with three or more consecutive same digits, such as 1118, good.\nYou are given a 4-digit integer N. Answer the question: Is N good?\nTask Constraint: 1000 <= N <= 9999\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If N is good, print Yes; otherwise, print No.\nTask Samples: input: 1118 output: Yes\n\nN is good, since it contains three consecutive 1.\ninput: 7777 output: Yes\n\nAn integer is also good when all the digits are the same.\ninput: 1234 output: No\n\n" }, { "title": "", "content": "Problem Statement It is November 18 now in Japan. By the way, 11 and 18 are adjacent Lucas numbers.\nYou are given an integer N. Find the N-th Lucas number.\nHere, the i-th Lucas number L_i is defined as follows:\n\nL_0=2\nL_1=1\nL_i=L_{i-1}+L_{i-2} (i>=2)", "constraint": "1<=N<=86\nIt is guaranteed that the answer is less than 10^{18}.\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the N-th Lucas number.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 output: 11\nL_0=2\nL_1=1\nL_2=L_0+L_1=3\nL_3=L_1+L_2=4\nL_4=L_2+L_3=7\nL_5=L_3+L_4=11\n\nThus, the 5-th Lucas number is 11.", "input: 86 output: 939587134549734843"], "Pid": "p03544", "ProblemText": "Task Description: Problem Statement It is November 18 now in Japan. By the way, 11 and 18 are adjacent Lucas numbers.\nYou are given an integer N. Find the N-th Lucas number.\nHere, the i-th Lucas number L_i is defined as follows:\n\nL_0=2\nL_1=1\nL_i=L_{i-1}+L_{i-2} (i>=2)\nTask Constraint: 1<=N<=86\nIt is guaranteed that the answer is less than 10^{18}.\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the N-th Lucas number.\nTask Samples: input: 5 output: 11\nL_0=2\nL_1=1\nL_2=L_0+L_1=3\nL_3=L_1+L_2=4\nL_4=L_2+L_3=7\nL_5=L_3+L_4=11\n\nThus, the 5-th Lucas number is 11.\ninput: 86 output: 939587134549734843\n\n" }, { "title": "", "content": "Problem Statement Sitting in a station waiting room, Joisino is gazing at her train ticket.\nThe ticket is numbered with four digits A, B, C and D in this order, each between 0 and 9 (inclusive).\nIn the formula A op1 B op2 C op3 D = 7, replace each of the symbols op1, op2 and op3 with + or - so that the formula holds.\nThe given input guarantees that there is a solution. If there are multiple solutions, any of them will be accepted.", "constraint": "0<=A,B,C,D<=9\nAll input values are integers.\nIt is guaranteed that there is a solution.", "input": "Input is given from Standard Input in the following format:\nABCD", "output": "Print the formula you made, including the part =7.\nUse the signs + and -.\nDo not print a space between a digit and a sign.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1222 output: 1+2+2+2=7\n\nThis is the only valid solution.", "input: 0290 output: 0-2+9+0=7\n\n0 - 2 + 9 - 0 = 7 is also a valid solution.", "input: 3242 output: 3+2+4-2=7"], "Pid": "p03545", "ProblemText": "Task Description: Problem Statement Sitting in a station waiting room, Joisino is gazing at her train ticket.\nThe ticket is numbered with four digits A, B, C and D in this order, each between 0 and 9 (inclusive).\nIn the formula A op1 B op2 C op3 D = 7, replace each of the symbols op1, op2 and op3 with + or - so that the formula holds.\nThe given input guarantees that there is a solution. If there are multiple solutions, any of them will be accepted.\nTask Constraint: 0<=A,B,C,D<=9\nAll input values are integers.\nIt is guaranteed that there is a solution.\nTask Input: Input is given from Standard Input in the following format:\nABCD\nTask Output: Print the formula you made, including the part =7.\nUse the signs + and -.\nDo not print a space between a digit and a sign.\nTask Samples: input: 1222 output: 1+2+2+2=7\n\nThis is the only valid solution.\ninput: 0290 output: 0-2+9+0=7\n\n0 - 2 + 9 - 0 = 7 is also a valid solution.\ninput: 3242 output: 3+2+4-2=7\n\n" }, { "title": "", "content": "Problem Statement Joisino the magical girl has decided to turn every single digit that exists on this world into 1.\nRewriting a digit i with j (0<=i, j<=9) costs c_{i, j} MP (Magic Points).\nShe is now standing before a wall. The wall is divided into HW squares in H rows and W columns, and at least one square contains a digit between 0 and 9 (inclusive).\nYou are given A_{i, j} that describes the square at the i-th row from the top and j-th column from the left, as follows:\n\nIf A_{i, j}! =-1, the square contains a digit A_{i, j}.\nIf A_{i, j}=-1, the square does not contain a digit.\n\nFind the minimum total amount of MP required to turn every digit on this wall into 1 in the end.", "constraint": "1<=H,W<=200\n1<=c_{i,j}<=10^3 (i!=j)\nc_{i,j}=0 (i=j)\n-1<=A_{i,j}<=9\nAll input values are integers.\nThere is at least one digit on the wall.", "input": "Input is given from Standard Input in the following format:\nH W\nc_{0,0} . . . c_{0,9}\n:\nc_{9,0} . . . c_{9,9}\nA_{1,1} . . . A_{1, W}\n:\nA_{H, 1} . . . A_{H, W}", "output": "Print the minimum total amount of MP required to turn every digit on the wall into 1 in the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 4\n0 9 9 9 9 9 9 9 9 9\n9 0 9 9 9 9 9 9 9 9\n9 9 0 9 9 9 9 9 9 9\n9 9 9 0 9 9 9 9 9 9\n9 9 9 9 0 9 9 9 9 2\n9 9 9 9 9 0 9 9 9 9\n9 9 9 9 9 9 0 9 9 9\n9 9 9 9 9 9 9 0 9 9\n9 9 9 9 2 9 9 9 0 9\n9 2 9 9 9 9 9 9 9 0\n-1 -1 -1 -1\n8 1 1 8 output: 12\n\nTo turn a single 8 into 1, it is optimal to first turn 8 into 4, then turn 4 into 9, and finally turn 9 into 1, costing 6 MP.\nThe wall contains two 8s, so the minimum total MP required is 6*2=12.", "input: 5 5\n0 999 999 999 999 999 999 999 999 999\n999 0 999 999 999 999 999 999 999 999\n999 999 0 999 999 999 999 999 999 999\n999 999 999 0 999 999 999 999 999 999\n999 999 999 999 0 999 999 999 999 999\n999 999 999 999 999 0 999 999 999 999\n999 999 999 999 999 999 0 999 999 999\n999 999 999 999 999 999 999 0 999 999\n999 999 999 999 999 999 999 999 0 999\n999 999 999 999 999 999 999 999 999 0\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1 output: 0\n\nNote that she may not need to change any digit.", "input: 3 5\n0 4 3 6 2 7 2 5 3 3\n4 0 5 3 7 5 3 7 2 7\n5 7 0 7 2 9 3 2 9 1\n3 6 2 0 2 4 6 4 2 3\n3 5 7 4 0 6 9 7 6 7\n9 8 5 2 2 0 4 7 6 5\n5 4 6 3 2 3 0 5 4 3\n3 6 2 3 4 2 4 0 8 9\n4 6 5 4 3 5 3 2 0 8\n2 1 3 4 5 7 8 6 4 0\n3 5 2 6 1\n2 5 3 2 1\n6 9 2 5 6 output: 47"], "Pid": "p03546", "ProblemText": "Task Description: Problem Statement Joisino the magical girl has decided to turn every single digit that exists on this world into 1.\nRewriting a digit i with j (0<=i, j<=9) costs c_{i, j} MP (Magic Points).\nShe is now standing before a wall. The wall is divided into HW squares in H rows and W columns, and at least one square contains a digit between 0 and 9 (inclusive).\nYou are given A_{i, j} that describes the square at the i-th row from the top and j-th column from the left, as follows:\n\nIf A_{i, j}! =-1, the square contains a digit A_{i, j}.\nIf A_{i, j}=-1, the square does not contain a digit.\n\nFind the minimum total amount of MP required to turn every digit on this wall into 1 in the end.\nTask Constraint: 1<=H,W<=200\n1<=c_{i,j}<=10^3 (i!=j)\nc_{i,j}=0 (i=j)\n-1<=A_{i,j}<=9\nAll input values are integers.\nThere is at least one digit on the wall.\nTask Input: Input is given from Standard Input in the following format:\nH W\nc_{0,0} . . . c_{0,9}\n:\nc_{9,0} . . . c_{9,9}\nA_{1,1} . . . A_{1, W}\n:\nA_{H, 1} . . . A_{H, W}\nTask Output: Print the minimum total amount of MP required to turn every digit on the wall into 1 in the end.\nTask Samples: input: 2 4\n0 9 9 9 9 9 9 9 9 9\n9 0 9 9 9 9 9 9 9 9\n9 9 0 9 9 9 9 9 9 9\n9 9 9 0 9 9 9 9 9 9\n9 9 9 9 0 9 9 9 9 2\n9 9 9 9 9 0 9 9 9 9\n9 9 9 9 9 9 0 9 9 9\n9 9 9 9 9 9 9 0 9 9\n9 9 9 9 2 9 9 9 0 9\n9 2 9 9 9 9 9 9 9 0\n-1 -1 -1 -1\n8 1 1 8 output: 12\n\nTo turn a single 8 into 1, it is optimal to first turn 8 into 4, then turn 4 into 9, and finally turn 9 into 1, costing 6 MP.\nThe wall contains two 8s, so the minimum total MP required is 6*2=12.\ninput: 5 5\n0 999 999 999 999 999 999 999 999 999\n999 0 999 999 999 999 999 999 999 999\n999 999 0 999 999 999 999 999 999 999\n999 999 999 0 999 999 999 999 999 999\n999 999 999 999 0 999 999 999 999 999\n999 999 999 999 999 0 999 999 999 999\n999 999 999 999 999 999 0 999 999 999\n999 999 999 999 999 999 999 0 999 999\n999 999 999 999 999 999 999 999 0 999\n999 999 999 999 999 999 999 999 999 0\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1 output: 0\n\nNote that she may not need to change any digit.\ninput: 3 5\n0 4 3 6 2 7 2 5 3 3\n4 0 5 3 7 5 3 7 2 7\n5 7 0 7 2 9 3 2 9 1\n3 6 2 0 2 4 6 4 2 3\n3 5 7 4 0 6 9 7 6 7\n9 8 5 2 2 0 4 7 6 5\n5 4 6 3 2 3 0 5 4 3\n3 6 2 3 4 2 4 0 8 9\n4 6 5 4 3 5 3 2 0 8\n2 1 3 4 5 7 8 6 4 0\n3 5 2 6 1\n2 5 3 2 1\n6 9 2 5 6 output: 47\n\n" }, { "title": "", "content": "Problem Statement In programming, hexadecimal notation is often used.\nIn hexadecimal notation, besides the ten digits 0,1, . . . , 9, the six letters A, B, C, D, E and F are used to represent the values 10,11,12,13,14 and 15, respectively.\nIn this problem, you are given two letters X and Y. Each X and Y is A, B, C, D, E or F.\nWhen X and Y are seen as hexadecimal numbers, which is larger?", "constraint": "Each X and Y is A, B, C, D, E or F.", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "If X is smaller, print <; if Y is smaller, print >; if they are equal, print =.", "content_img": false, "lang": "en", "error": false, "samples": ["input: A B output: <\n\n10 < 11.", "input: E C output: >\n\n14 > 12.", "input: F F output: =\n\n15 = 15."], "Pid": "p03547", "ProblemText": "Task Description: Problem Statement In programming, hexadecimal notation is often used.\nIn hexadecimal notation, besides the ten digits 0,1, . . . , 9, the six letters A, B, C, D, E and F are used to represent the values 10,11,12,13,14 and 15, respectively.\nIn this problem, you are given two letters X and Y. Each X and Y is A, B, C, D, E or F.\nWhen X and Y are seen as hexadecimal numbers, which is larger?\nTask Constraint: Each X and Y is A, B, C, D, E or F.\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: If X is smaller, print <; if Y is smaller, print >; if they are equal, print =.\nTask Samples: input: A B output: <\n\n10 < 11.\ninput: E C output: >\n\n14 > 12.\ninput: F F output: =\n\n15 = 15.\n\n" }, { "title": "", "content": "Problem Statement We have a long seat of width X centimeters.\nThere are many people who wants to sit here. A person sitting on the seat will always occupy an interval of length Y centimeters.\nWe would like to seat as many people as possible, but they are all very shy, and there must be a gap of length at least Z centimeters between two people, and between the end of the seat and a person.\nAt most how many people can sit on the seat?", "constraint": "All input values are integers.\n1 <= X, Y, Z <= 10^5\nY+2Z <= X", "input": "Input is given from Standard Input in the following format:\nX Y Z", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 13 3 1 output: 3\n\nThere is just enough room for three, as shown below:\nFigure", "input: 12 3 1 output: 2", "input: 100000 1 1 output: 49999", "input: 64146 123 456 output: 110", "input: 64145 123 456 output: 109"], "Pid": "p03548", "ProblemText": "Task Description: Problem Statement We have a long seat of width X centimeters.\nThere are many people who wants to sit here. A person sitting on the seat will always occupy an interval of length Y centimeters.\nWe would like to seat as many people as possible, but they are all very shy, and there must be a gap of length at least Z centimeters between two people, and between the end of the seat and a person.\nAt most how many people can sit on the seat?\nTask Constraint: All input values are integers.\n1 <= X, Y, Z <= 10^5\nY+2Z <= X\nTask Input: Input is given from Standard Input in the following format:\nX Y Z\nTask Output: Print the answer.\nTask Samples: input: 13 3 1 output: 3\n\nThere is just enough room for three, as shown below:\nFigure\ninput: 12 3 1 output: 2\ninput: 100000 1 1 output: 49999\ninput: 64146 123 456 output: 110\ninput: 64145 123 456 output: 109\n\n" }, { "title": "", "content": "Problem Statement Takahashi is now competing in a programming contest, but he received TLE in a problem where the answer is YES or NO.\nWhen he checked the detailed status of the submission, there were N test cases in the problem, and the code received TLE in M of those cases.\nThen, he rewrote the code to correctly solve each of those M cases with 1/2 probability in 1900 milliseconds, and correctly solve each of the other N-M cases without fail in 100 milliseconds.\nNow, he goes through the following process:\n\nSubmit the code.\nWait until the code finishes execution on all the cases.\nIf the code fails to correctly solve some of the M cases, submit it again.\nRepeat until the code correctly solve all the cases in one submission.\n\nLet the expected value of the total execution time of the code be X milliseconds. Print X (as an integer).", "constraint": "All input values are integers.\n1 <= N <= 100\n1 <= M <= {\\rm min}(N, 5)", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print X, the expected value of the total execution time of the code, as an integer. It can be proved that, under the constraints in this problem, X is an integer not exceeding 10^9.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 output: 3800\n\nIn this input, there is only one case. Takahashi will repeatedly submit the code that correctly solves this case with 1/2 probability in 1900 milliseconds.\nThe code will succeed in one attempt with 1/2 probability, in two attempts with 1/4 probability, and in three attempts with 1/8 probability, and so on.\nThus, the answer is 1900 * 1/2 + (2 * 1900) * 1/4 + (3 * 1900) * 1/8 + ... = 3800.", "input: 10 2 output: 18400\n\nThe code will take 1900 milliseconds in each of the 2 cases, and 100 milliseconds in each of the 10-2=8 cases. The probability of the code correctly solving all the cases is 1/2 * 1/2 = 1/4.", "input: 100 5 output: 608000"], "Pid": "p03549", "ProblemText": "Task Description: Problem Statement Takahashi is now competing in a programming contest, but he received TLE in a problem where the answer is YES or NO.\nWhen he checked the detailed status of the submission, there were N test cases in the problem, and the code received TLE in M of those cases.\nThen, he rewrote the code to correctly solve each of those M cases with 1/2 probability in 1900 milliseconds, and correctly solve each of the other N-M cases without fail in 100 milliseconds.\nNow, he goes through the following process:\n\nSubmit the code.\nWait until the code finishes execution on all the cases.\nIf the code fails to correctly solve some of the M cases, submit it again.\nRepeat until the code correctly solve all the cases in one submission.\n\nLet the expected value of the total execution time of the code be X milliseconds. Print X (as an integer).\nTask Constraint: All input values are integers.\n1 <= N <= 100\n1 <= M <= {\\rm min}(N, 5)\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print X, the expected value of the total execution time of the code, as an integer. It can be proved that, under the constraints in this problem, X is an integer not exceeding 10^9.\nTask Samples: input: 1 1 output: 3800\n\nIn this input, there is only one case. Takahashi will repeatedly submit the code that correctly solves this case with 1/2 probability in 1900 milliseconds.\nThe code will succeed in one attempt with 1/2 probability, in two attempts with 1/4 probability, and in three attempts with 1/8 probability, and so on.\nThus, the answer is 1900 * 1/2 + (2 * 1900) * 1/4 + (3 * 1900) * 1/8 + ... = 3800.\ninput: 10 2 output: 18400\n\nThe code will take 1900 milliseconds in each of the 2 cases, and 100 milliseconds in each of the 10-2=8 cases. The probability of the code correctly solving all the cases is 1/2 * 1/2 = 1/4.\ninput: 100 5 output: 608000\n\n" }, { "title": "", "content": "Problem Statement We have a deck consisting of N cards. Each card has an integer written on it. The integer on the i-th card from the top is a_i.\nTwo people X and Y will play a game using this deck. Initially, X has a card with Z written on it in his hand, and Y has a card with W written on it in his hand. Then, starting from X, they will alternately perform the following action:\n\nDraw some number of cards from the top of the deck. Then, discard the card in his hand and keep the last drawn card instead. Here, at least one card must be drawn.\n\nThe game ends when there is no more card in the deck. The score of the game is the absolute difference of the integers written on the cards in the two players' hand.\nX will play the game so that the score will be maximized, and Y will play the game so that the score will be minimized. What will be the score of the game?", "constraint": "All input values are integers.\n1 <= N <= 2000\n1 <= Z, W, a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN Z W\na_1 a_2 . . . a_N", "output": "Print the score.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 100 100\n10 1000 100 output: 900\n\nIf X draws two cards first, Y will draw the last card, and the score will be |1000 - 100| = 900.", "input: 3 100 1000\n10 100 100 output: 900\n\nIf X draws all the cards first, the score will be |1000 - 100| = 900.", "input: 5 1 1\n1 1 1 1 1 output: 0", "input: 1 1 1\n1000000000 output: 999999999"], "Pid": "p03550", "ProblemText": "Task Description: Problem Statement We have a deck consisting of N cards. Each card has an integer written on it. The integer on the i-th card from the top is a_i.\nTwo people X and Y will play a game using this deck. Initially, X has a card with Z written on it in his hand, and Y has a card with W written on it in his hand. Then, starting from X, they will alternately perform the following action:\n\nDraw some number of cards from the top of the deck. Then, discard the card in his hand and keep the last drawn card instead. Here, at least one card must be drawn.\n\nThe game ends when there is no more card in the deck. The score of the game is the absolute difference of the integers written on the cards in the two players' hand.\nX will play the game so that the score will be maximized, and Y will play the game so that the score will be minimized. What will be the score of the game?\nTask Constraint: All input values are integers.\n1 <= N <= 2000\n1 <= Z, W, a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN Z W\na_1 a_2 . . . a_N\nTask Output: Print the score.\nTask Samples: input: 3 100 100\n10 1000 100 output: 900\n\nIf X draws two cards first, Y will draw the last card, and the score will be |1000 - 100| = 900.\ninput: 3 100 1000\n10 100 100 output: 900\n\nIf X draws all the cards first, the score will be |1000 - 100| = 900.\ninput: 5 1 1\n1 1 1 1 1 output: 0\ninput: 1 1 1\n1000000000 output: 999999999\n\n" }, { "title": "", "content": "Problem Statement Takahashi is now competing in a programming contest, but he received TLE in a problem where the answer is YES or NO.\nWhen he checked the detailed status of the submission, there were N test cases in the problem, and the code received TLE in M of those cases.\nThen, he rewrote the code to correctly solve each of those M cases with 1/2 probability in 1900 milliseconds, and correctly solve each of the other N-M cases without fail in 100 milliseconds.\nNow, he goes through the following process:\n\nSubmit the code.\nWait until the code finishes execution on all the cases.\nIf the code fails to correctly solve some of the M cases, submit it again.\nRepeat until the code correctly solve all the cases in one submission.\n\nLet the expected value of the total execution time of the code be X milliseconds. Print X (as an integer).", "constraint": "All input values are integers.\n1 <= N <= 100\n1 <= M <= {\\rm min}(N, 5)", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print X, the expected value of the total execution time of the code, as an integer. It can be proved that, under the constraints in this problem, X is an integer not exceeding 10^9.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 output: 3800\n\nIn this input, there is only one case. Takahashi will repeatedly submit the code that correctly solves this case with 1/2 probability in 1900 milliseconds.\nThe code will succeed in one attempt with 1/2 probability, in two attempts with 1/4 probability, and in three attempts with 1/8 probability, and so on.\nThus, the answer is 1900 * 1/2 + (2 * 1900) * 1/4 + (3 * 1900) * 1/8 + ... = 3800.", "input: 10 2 output: 18400\n\nThe code will take 1900 milliseconds in each of the 2 cases, and 100 milliseconds in each of the 10-2=8 cases. The probability of the code correctly solving all the cases is 1/2 * 1/2 = 1/4.", "input: 100 5 output: 608000"], "Pid": "p03551", "ProblemText": "Task Description: Problem Statement Takahashi is now competing in a programming contest, but he received TLE in a problem where the answer is YES or NO.\nWhen he checked the detailed status of the submission, there were N test cases in the problem, and the code received TLE in M of those cases.\nThen, he rewrote the code to correctly solve each of those M cases with 1/2 probability in 1900 milliseconds, and correctly solve each of the other N-M cases without fail in 100 milliseconds.\nNow, he goes through the following process:\n\nSubmit the code.\nWait until the code finishes execution on all the cases.\nIf the code fails to correctly solve some of the M cases, submit it again.\nRepeat until the code correctly solve all the cases in one submission.\n\nLet the expected value of the total execution time of the code be X milliseconds. Print X (as an integer).\nTask Constraint: All input values are integers.\n1 <= N <= 100\n1 <= M <= {\\rm min}(N, 5)\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print X, the expected value of the total execution time of the code, as an integer. It can be proved that, under the constraints in this problem, X is an integer not exceeding 10^9.\nTask Samples: input: 1 1 output: 3800\n\nIn this input, there is only one case. Takahashi will repeatedly submit the code that correctly solves this case with 1/2 probability in 1900 milliseconds.\nThe code will succeed in one attempt with 1/2 probability, in two attempts with 1/4 probability, and in three attempts with 1/8 probability, and so on.\nThus, the answer is 1900 * 1/2 + (2 * 1900) * 1/4 + (3 * 1900) * 1/8 + ... = 3800.\ninput: 10 2 output: 18400\n\nThe code will take 1900 milliseconds in each of the 2 cases, and 100 milliseconds in each of the 10-2=8 cases. The probability of the code correctly solving all the cases is 1/2 * 1/2 = 1/4.\ninput: 100 5 output: 608000\n\n" }, { "title": "", "content": "Problem Statement We have a deck consisting of N cards. Each card has an integer written on it. The integer on the i-th card from the top is a_i.\nTwo people X and Y will play a game using this deck. Initially, X has a card with Z written on it in his hand, and Y has a card with W written on it in his hand. Then, starting from X, they will alternately perform the following action:\n\nDraw some number of cards from the top of the deck. Then, discard the card in his hand and keep the last drawn card instead. Here, at least one card must be drawn.\n\nThe game ends when there is no more card in the deck. The score of the game is the absolute difference of the integers written on the cards in the two players' hand.\nX will play the game so that the score will be maximized, and Y will play the game so that the score will be minimized. What will be the score of the game?", "constraint": "All input values are integers.\n1 <= N <= 2000\n1 <= Z, W, a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN Z W\na_1 a_2 . . . a_N", "output": "Print the score.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 100 100\n10 1000 100 output: 900\n\nIf X draws two cards first, Y will draw the last card, and the score will be |1000 - 100| = 900.", "input: 3 100 1000\n10 100 100 output: 900\n\nIf X draws all the cards first, the score will be |1000 - 100| = 900.", "input: 5 1 1\n1 1 1 1 1 output: 0", "input: 1 1 1\n1000000000 output: 999999999"], "Pid": "p03552", "ProblemText": "Task Description: Problem Statement We have a deck consisting of N cards. Each card has an integer written on it. The integer on the i-th card from the top is a_i.\nTwo people X and Y will play a game using this deck. Initially, X has a card with Z written on it in his hand, and Y has a card with W written on it in his hand. Then, starting from X, they will alternately perform the following action:\n\nDraw some number of cards from the top of the deck. Then, discard the card in his hand and keep the last drawn card instead. Here, at least one card must be drawn.\n\nThe game ends when there is no more card in the deck. The score of the game is the absolute difference of the integers written on the cards in the two players' hand.\nX will play the game so that the score will be maximized, and Y will play the game so that the score will be minimized. What will be the score of the game?\nTask Constraint: All input values are integers.\n1 <= N <= 2000\n1 <= Z, W, a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN Z W\na_1 a_2 . . . a_N\nTask Output: Print the score.\nTask Samples: input: 3 100 100\n10 1000 100 output: 900\n\nIf X draws two cards first, Y will draw the last card, and the score will be |1000 - 100| = 900.\ninput: 3 100 1000\n10 100 100 output: 900\n\nIf X draws all the cards first, the score will be |1000 - 100| = 900.\ninput: 5 1 1\n1 1 1 1 1 output: 0\ninput: 1 1 1\n1000000000 output: 999999999\n\n" }, { "title": "", "content": "Problem Statement We have N gemstones labeled 1 through N.\nYou can perform the following operation any number of times (possibly zero).\n\nSelect a positive integer x, and smash all the gems labeled with multiples of x.\n\nThen, for each i, if the gem labeled i remains without getting smashed, you will receive a_i yen (the currency of Japan).\nHowever, a_i may be negative, in which case you will be charged money.\nBy optimally performing the operation, how much yen can you earn?", "constraint": "All input values are integers.\n1 <= N <= 100\n|a_i| <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the maximum amount of money that can be earned.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 2 -6 4 5 3 output: 12\n\nIt is optimal to smash Gem 3 and 6.", "input: 6\n100 -100 -100 -100 100 -100 output: 200", "input: 5\n-1 -2 -3 -4 -5 output: 0\n\nIt is optimal to smash all the gems.", "input: 2\n-1000 100000 output: 99000"], "Pid": "p03553", "ProblemText": "Task Description: Problem Statement We have N gemstones labeled 1 through N.\nYou can perform the following operation any number of times (possibly zero).\n\nSelect a positive integer x, and smash all the gems labeled with multiples of x.\n\nThen, for each i, if the gem labeled i remains without getting smashed, you will receive a_i yen (the currency of Japan).\nHowever, a_i may be negative, in which case you will be charged money.\nBy optimally performing the operation, how much yen can you earn?\nTask Constraint: All input values are integers.\n1 <= N <= 100\n|a_i| <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the maximum amount of money that can be earned.\nTask Samples: input: 6\n1 2 -6 4 5 3 output: 12\n\nIt is optimal to smash Gem 3 and 6.\ninput: 6\n100 -100 -100 -100 100 -100 output: 200\ninput: 5\n-1 -2 -3 -4 -5 output: 0\n\nIt is optimal to smash all the gems.\ninput: 2\n-1000 100000 output: 99000\n\n" }, { "title": "", "content": "Problem Statement You are given a sequence a = \\{a_1, . . . , a_N\\} with all zeros, and a sequence b = \\{b_1, . . . , b_N\\} consisting of 0 and 1. The length of both is N.\nYou can perform Q kinds of operations. The i-th operation is as follows:\n\nReplace each of a_{l_i}, a_{l_i + 1}, . . . , a_{r_i} with 1.\n\nMinimize the hamming distance between a and b, that is, the number of i such that a_i \\neq b_i, by performing some of the Q operations.", "constraint": "1 <= N <= 200,000\nb consists of 0 and 1.\n1 <= Q <= 200,000\n1 <= l_i <= r_i <= N\nIf i \\neq j, either l_i \\neq l_j or r_i \\neq r_j.", "input": "Input is given from Standard Input in the following format:\nN\nb_1 b_2 . . . b_N\nQ\nl_1 r_1\nl_2 r_2\n:\nl_Q r_Q", "output": "Print the minimum possible hamming distance.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 0 1\n1\n1 3 output: 1\n\nIf you choose to perform the operation, a will become \\{1,1,1\\}, for a hamming distance of 1.", "input: 3\n1 0 1\n2\n1 1\n3 3 output: 0\n\nIf both operations are performed, a will become \\{1,0,1\\}, for a hamming distance of 0.", "input: 3\n1 0 1\n2\n1 1\n2 3 output: 1", "input: 5\n0 1 0 1 0\n1\n1 5 output: 2\n\nIt may be optimal to perform no operation.", "input: 9\n0 1 0 1 1 1 0 1 0\n3\n1 4\n5 8\n6 7 output: 3", "input: 15\n1 1 0 0 0 0 0 0 1 0 1 1 1 0 0\n9\n4 10\n13 14\n1 7\n4 14\n9 11\n2 6\n7 8\n3 12\n7 13 output: 5", "input: 10\n0 0 0 1 0 0 1 1 1 0\n7\n1 4\n2 5\n1 3\n6 7\n9 9\n1 5\n7 9 output: 1"], "Pid": "p03554", "ProblemText": "Task Description: Problem Statement You are given a sequence a = \\{a_1, . . . , a_N\\} with all zeros, and a sequence b = \\{b_1, . . . , b_N\\} consisting of 0 and 1. The length of both is N.\nYou can perform Q kinds of operations. The i-th operation is as follows:\n\nReplace each of a_{l_i}, a_{l_i + 1}, . . . , a_{r_i} with 1.\n\nMinimize the hamming distance between a and b, that is, the number of i such that a_i \\neq b_i, by performing some of the Q operations.\nTask Constraint: 1 <= N <= 200,000\nb consists of 0 and 1.\n1 <= Q <= 200,000\n1 <= l_i <= r_i <= N\nIf i \\neq j, either l_i \\neq l_j or r_i \\neq r_j.\nTask Input: Input is given from Standard Input in the following format:\nN\nb_1 b_2 . . . b_N\nQ\nl_1 r_1\nl_2 r_2\n:\nl_Q r_Q\nTask Output: Print the minimum possible hamming distance.\nTask Samples: input: 3\n1 0 1\n1\n1 3 output: 1\n\nIf you choose to perform the operation, a will become \\{1,1,1\\}, for a hamming distance of 1.\ninput: 3\n1 0 1\n2\n1 1\n3 3 output: 0\n\nIf both operations are performed, a will become \\{1,0,1\\}, for a hamming distance of 0.\ninput: 3\n1 0 1\n2\n1 1\n2 3 output: 1\ninput: 5\n0 1 0 1 0\n1\n1 5 output: 2\n\nIt may be optimal to perform no operation.\ninput: 9\n0 1 0 1 1 1 0 1 0\n3\n1 4\n5 8\n6 7 output: 3\ninput: 15\n1 1 0 0 0 0 0 0 1 0 1 1 1 0 0\n9\n4 10\n13 14\n1 7\n4 14\n9 11\n2 6\n7 8\n3 12\n7 13 output: 5\ninput: 10\n0 0 0 1 0 0 1 1 1 0\n7\n1 4\n2 5\n1 3\n6 7\n9 9\n1 5\n7 9 output: 1\n\n" }, { "title": "", "content": "Problem Statement You are given a grid with 2 rows and 3 columns of squares.\nThe color of the square at the i-th row and j-th column is represented by the character C_{ij}.\nWrite a program that prints YES if this grid remains the same when rotated 180 degrees, and prints NO otherwise.", "constraint": "C_{i,j}(1 <= i <= 2,1 <= j <= 3) is a lowercase English letter.", "input": "Input is given from Standard Input in the following format:\nC_{11}C_{12}C_{13}\nC_{21}C_{22}C_{23}", "output": "Print YES if this grid remains the same when rotated 180 degrees; print NO otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: pot\ntop output: YES\n\nThis grid remains the same when rotated 180 degrees.", "input: tab\nbet output: NO\n\nThis grid does not remain the same when rotated 180 degrees.", "input: eye\neel output: NO"], "Pid": "p03555", "ProblemText": "Task Description: Problem Statement You are given a grid with 2 rows and 3 columns of squares.\nThe color of the square at the i-th row and j-th column is represented by the character C_{ij}.\nWrite a program that prints YES if this grid remains the same when rotated 180 degrees, and prints NO otherwise.\nTask Constraint: C_{i,j}(1 <= i <= 2,1 <= j <= 3) is a lowercase English letter.\nTask Input: Input is given from Standard Input in the following format:\nC_{11}C_{12}C_{13}\nC_{21}C_{22}C_{23}\nTask Output: Print YES if this grid remains the same when rotated 180 degrees; print NO otherwise.\nTask Samples: input: pot\ntop output: YES\n\nThis grid remains the same when rotated 180 degrees.\ninput: tab\nbet output: NO\n\nThis grid does not remain the same when rotated 180 degrees.\ninput: eye\neel output: NO\n\n" }, { "title": "", "content": "Problem Statement Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.", "constraint": "1 <= N <= 10^9\nN is an integer.", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the largest square number not exceeding N.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 output: 9\n\n10 is not square, but 9 = 3 * 3 is. Thus, we print 9.", "input: 81 output: 81", "input: 271828182 output: 271821169"], "Pid": "p03556", "ProblemText": "Task Description: Problem Statement Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.\nTask Constraint: 1 <= N <= 10^9\nN is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the largest square number not exceeding N.\nTask Samples: input: 10 output: 9\n\n10 is not square, but 9 = 3 * 3 is. Thus, we print 9.\ninput: 81 output: 81\ninput: 271828182 output: 271821169\n\n" }, { "title": "", "content": "Problem Statement The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.\nHe has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.\nTo build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.\nHow many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9(1<= i<= N)\n1 <= B_i <= 10^9(1<= i<= N)\n1 <= C_i <= 10^9(1<= i<= N)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nB_1 . . . B_N\nC_1 . . . C_N", "output": "Print the number of different altars that Ringo can build.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 5\n2 4\n3 6 output: 3\n\nThe following three altars can be built:\n\nUpper: 1-st part, Middle: 1-st part, Lower: 1-st part\nUpper: 1-st part, Middle: 1-st part, Lower: 2-nd part\nUpper: 1-st part, Middle: 2-nd part, Lower: 2-nd part", "input: 3\n1 1 1\n2 2 2\n3 3 3 output: 27", "input: 6\n3 14 159 2 6 53\n58 9 79 323 84 6\n2643 383 2 79 50 288 output: 87"], "Pid": "p03557", "ProblemText": "Task Description: Problem Statement The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.\nHe has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.\nTo build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.\nHow many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9(1<= i<= N)\n1 <= B_i <= 10^9(1<= i<= N)\n1 <= C_i <= 10^9(1<= i<= N)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nB_1 . . . B_N\nC_1 . . . C_N\nTask Output: Print the number of different altars that Ringo can build.\nTask Samples: input: 2\n1 5\n2 4\n3 6 output: 3\n\nThe following three altars can be built:\n\nUpper: 1-st part, Middle: 1-st part, Lower: 1-st part\nUpper: 1-st part, Middle: 1-st part, Lower: 2-nd part\nUpper: 1-st part, Middle: 2-nd part, Lower: 2-nd part\ninput: 3\n1 1 1\n2 2 2\n3 3 3 output: 27\ninput: 6\n3 14 159 2 6 53\n58 9 79 323 84 6\n2643 383 2 79 50 288 output: 87\n\n" }, { "title": "", "content": "Problem Statement Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.", "constraint": "2 <= K <= 10^5\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 output: 3\n\n12=6*2 yields the smallest sum.", "input: 41 output: 5\n\n11111=41*271 yields the smallest sum.", "input: 79992 output: 36"], "Pid": "p03558", "ProblemText": "Task Description: Problem Statement Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.\nTask Constraint: 2 <= K <= 10^5\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.\nTask Samples: input: 6 output: 3\n\n12=6*2 yields the smallest sum.\ninput: 41 output: 5\n\n11111=41*271 yields the smallest sum.\ninput: 79992 output: 36\n\n" }, { "title": "", "content": "Problem Statement The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.\nHe has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.\nTo build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.\nHow many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9(1<= i<= N)\n1 <= B_i <= 10^9(1<= i<= N)\n1 <= C_i <= 10^9(1<= i<= N)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nB_1 . . . B_N\nC_1 . . . C_N", "output": "Print the number of different altars that Ringo can build.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 5\n2 4\n3 6 output: 3\n\nThe following three altars can be built:\n\nUpper: 1-st part, Middle: 1-st part, Lower: 1-st part\nUpper: 1-st part, Middle: 1-st part, Lower: 2-nd part\nUpper: 1-st part, Middle: 2-nd part, Lower: 2-nd part", "input: 3\n1 1 1\n2 2 2\n3 3 3 output: 27", "input: 6\n3 14 159 2 6 53\n58 9 79 323 84 6\n2643 383 2 79 50 288 output: 87"], "Pid": "p03559", "ProblemText": "Task Description: Problem Statement The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.\nHe has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.\nTo build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.\nHow many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9(1<= i<= N)\n1 <= B_i <= 10^9(1<= i<= N)\n1 <= C_i <= 10^9(1<= i<= N)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 . . . A_N\nB_1 . . . B_N\nC_1 . . . C_N\nTask Output: Print the number of different altars that Ringo can build.\nTask Samples: input: 2\n1 5\n2 4\n3 6 output: 3\n\nThe following three altars can be built:\n\nUpper: 1-st part, Middle: 1-st part, Lower: 1-st part\nUpper: 1-st part, Middle: 1-st part, Lower: 2-nd part\nUpper: 1-st part, Middle: 2-nd part, Lower: 2-nd part\ninput: 3\n1 1 1\n2 2 2\n3 3 3 output: 27\ninput: 6\n3 14 159 2 6 53\n58 9 79 323 84 6\n2643 383 2 79 50 288 output: 87\n\n" }, { "title": "", "content": "Problem Statement Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.", "constraint": "2 <= K <= 10^5\nK is an integer.", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 output: 3\n\n12=6*2 yields the smallest sum.", "input: 41 output: 5\n\n11111=41*271 yields the smallest sum.", "input: 79992 output: 36"], "Pid": "p03560", "ProblemText": "Task Description: Problem Statement Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.\nTask Constraint: 2 <= K <= 10^5\nK is an integer.\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.\nTask Samples: input: 6 output: 3\n\n12=6*2 yields the smallest sum.\ninput: 41 output: 5\n\n11111=41*271 yields the smallest sum.\ninput: 79992 output: 36\n\n" }, { "title": "", "content": "Problem Statement In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.\nLet the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.", "constraint": "1 <= N,K <= 3 * 10^5\nN and K are integers.", "input": "Input is given from Standard Input in the following format:\nK N", "output": "Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 output: 2 1 \n\nThere are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3).\nThe (12/2 = 6)-th lexicographically smallest one among them is (2,1).", "input: 2 4 output: 1 2 2 2", "input: 5 14 output: 3 3 3 3 3 3 3 3 3 3 3 3 2 2"], "Pid": "p03561", "ProblemText": "Task Description: Problem Statement In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.\nLet the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.\nTask Constraint: 1 <= N,K <= 3 * 10^5\nN and K are integers.\nTask Input: Input is given from Standard Input in the following format:\nK N\nTask Output: Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.\nTask Samples: input: 3 2 output: 2 1 \n\nThere are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3).\nThe (12/2 = 6)-th lexicographically smallest one among them is (2,1).\ninput: 2 4 output: 1 2 2 2\ninput: 5 14 output: 3 3 3 3 3 3 3 3 3 3 3 3 2 2\n\n" }, { "title": "", "content": "Problem Statement There are N non-negative integers written on a blackboard. The i-th integer is A_i.\nTakahashi can perform the following two kinds of operations any number of times in any order:\n\nSelect one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.\nSelect two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.\n\nHow many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board.\nSince the answer can be extremely large, find the count modulo 998244353.", "constraint": "1 <= N <= 6\n1 <= X < 2^{4000}\n1 <= A_i < 2^{4000}(1<= i<= N)\nAll input values are integers.\nX and A_i(1<= i<= N) are given in binary notation, with the most significant digit in each of them being 1.", "input": "Input is given from Standard Input in the following format:\nN X\nA_1\n:\nA_N", "output": "Print the number of different integers not exceeding X that can be written on the blackboard.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 111\n1111\n10111\n10010 output: 4\n\nInitially, 15,23 and 18 are written on the blackboard. Among the integers not exceeding 7, four integers, 0,3,5 and 6, can be written.\nFor example, 6 can be written as follows:\n\nDouble 15 to write 30.\nTake XOR of 30 and 18 to write 12.\nDouble 12 to write 24.\nTake XOR of 30 and 24 to write 6.", "input: 4 100100\n1011\n1110\n110101\n1010110 output: 37", "input: 4 111001100101001\n10111110\n1001000110\n100000101\n11110000011 output: 1843", "input: 1 111111111111111111111111111111111111111111111111111111111111111\n1 output: 466025955\n\nBe sure to find the count modulo 998244353."], "Pid": "p03562", "ProblemText": "Task Description: Problem Statement There are N non-negative integers written on a blackboard. The i-th integer is A_i.\nTakahashi can perform the following two kinds of operations any number of times in any order:\n\nSelect one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.\nSelect two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.\n\nHow many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board.\nSince the answer can be extremely large, find the count modulo 998244353.\nTask Constraint: 1 <= N <= 6\n1 <= X < 2^{4000}\n1 <= A_i < 2^{4000}(1<= i<= N)\nAll input values are integers.\nX and A_i(1<= i<= N) are given in binary notation, with the most significant digit in each of them being 1.\nTask Input: Input is given from Standard Input in the following format:\nN X\nA_1\n:\nA_N\nTask Output: Print the number of different integers not exceeding X that can be written on the blackboard.\nTask Samples: input: 3 111\n1111\n10111\n10010 output: 4\n\nInitially, 15,23 and 18 are written on the blackboard. Among the integers not exceeding 7, four integers, 0,3,5 and 6, can be written.\nFor example, 6 can be written as follows:\n\nDouble 15 to write 30.\nTake XOR of 30 and 18 to write 12.\nDouble 12 to write 24.\nTake XOR of 30 and 24 to write 6.\ninput: 4 100100\n1011\n1110\n110101\n1010110 output: 37\ninput: 4 111001100101001\n10111110\n1001000110\n100000101\n11110000011 output: 1843\ninput: 1 111111111111111111111111111111111111111111111111111111111111111\n1 output: 466025955\n\nBe sure to find the count modulo 998244353.\n\n" }, { "title": "", "content": "Problem Statement Takahashi is a user of a site that hosts programming contests.\nWhen a user competes in a contest, the rating of the user (not necessarily an integer) changes according to the performance of the user, as follows: \n\nLet the current rating of the user be a.\nSuppose that the performance of the user in the contest is b.\nThen, the new rating of the user will be the avarage of a and b.\n\nFor example, if a user with rating 1 competes in a contest and gives performance 1000, his/her new rating will be 500.5, the average of 1 and 1000.\nTakahashi's current rating is R, and he wants his rating to be exactly G after the next contest.\nFind the performance required to achieve it.", "constraint": "0 <= R, G <= 4500\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nR\nG", "output": "Print the performance required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2002\n2017 output: 2032\n\nTakahashi's current rating is 2002.\nIf his performance in the contest is 2032, his rating will be the average of 2002 and 2032, which is equal to the desired rating, 2017.", "input: 4500\n0 output: -4500\n\nAlthough the current and desired ratings are between 0 and 4500, the performance of a user can be below 0."], "Pid": "p03563", "ProblemText": "Task Description: Problem Statement Takahashi is a user of a site that hosts programming contests.\nWhen a user competes in a contest, the rating of the user (not necessarily an integer) changes according to the performance of the user, as follows: \n\nLet the current rating of the user be a.\nSuppose that the performance of the user in the contest is b.\nThen, the new rating of the user will be the avarage of a and b.\n\nFor example, if a user with rating 1 competes in a contest and gives performance 1000, his/her new rating will be 500.5, the average of 1 and 1000.\nTakahashi's current rating is R, and he wants his rating to be exactly G after the next contest.\nFind the performance required to achieve it.\nTask Constraint: 0 <= R, G <= 4500\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nR\nG\nTask Output: Print the performance required to achieve the objective.\nTask Samples: input: 2002\n2017 output: 2032\n\nTakahashi's current rating is 2002.\nIf his performance in the contest is 2032, his rating will be the average of 2002 and 2032, which is equal to the desired rating, 2017.\ninput: 4500\n0 output: -4500\n\nAlthough the current and desired ratings are between 0 and 4500, the performance of a user can be below 0.\n\n" }, { "title": "", "content": "Problem Statement Square1001 has seen an electric bulletin board displaying the integer 1.\nHe can perform the following operations A and B to change this value:\n\nOperation A: The displayed value is doubled.\nOperation B: The displayed value increases by K.\n\nSquare1001 needs to perform these operations N times in total.\nFind the minimum possible value displayed in the board after N operations.", "constraint": "1 <= N, K <= 10\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nK", "output": "Print the minimum possible value displayed in the board after N operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 output: 10\n\nThe value will be minimized when the operations are performed in the following order: A, A, B, B.\nIn this case, the value will change as follows: 1 → 2 → 4 → 7 → 10.", "input: 10\n10 output: 76\n\nThe value will be minimized when the operations are performed in the following order: A, A, A, A, B, B, B, B, B, B.\nIn this case, the value will change as follows: 1 → 2 → 4 → 8 → 16 → 26 → 36 → 46 → 56 → 66 → 76. \nBy the way, this contest is AtCoder Beginner Contest 076."], "Pid": "p03564", "ProblemText": "Task Description: Problem Statement Square1001 has seen an electric bulletin board displaying the integer 1.\nHe can perform the following operations A and B to change this value:\n\nOperation A: The displayed value is doubled.\nOperation B: The displayed value increases by K.\n\nSquare1001 needs to perform these operations N times in total.\nFind the minimum possible value displayed in the board after N operations.\nTask Constraint: 1 <= N, K <= 10\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nK\nTask Output: Print the minimum possible value displayed in the board after N operations.\nTask Samples: input: 4\n3 output: 10\n\nThe value will be minimized when the operations are performed in the following order: A, A, B, B.\nIn this case, the value will change as follows: 1 → 2 → 4 → 7 → 10.\ninput: 10\n10 output: 76\n\nThe value will be minimized when the operations are performed in the following order: A, A, A, A, B, B, B, B, B, B.\nIn this case, the value will change as follows: 1 → 2 → 4 → 8 → 16 → 26 → 36 → 46 → 56 → 66 → 76. \nBy the way, this contest is AtCoder Beginner Contest 076.\n\n" }, { "title": "", "content": "Problem Statement E869120 found a chest which is likely to contain treasure.\nHowever, the chest is locked. In order to open it, he needs to enter a string S consisting of lowercase English letters.\nHe also found a string S', which turns out to be the string S with some of its letters (possibly all or none) replaced with ? . \nOne more thing he found is a sheet of paper with the following facts written on it: \n\nCondition 1: The string S contains a string T as a contiguous substring.\nCondition 2: S is the lexicographically smallest string among the ones that satisfy Condition 1.\n\nPrint the string S.\nIf such a string does not exist, print UNRESTORABLE.", "constraint": "1 <= |S'|, |T| <= 50\nS' consists of lowercase English letters and ?.\nT consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS\nT'", "output": "Print the string S.\nIf such a string does not exist, print UNRESTORABLE instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: ?tc????\ncoder output: atcoder\n\nThere are 26 strings that satisfy Condition 1: atcoder, btcoder, ctcoder,..., ztcoder.\nAmong them, the lexicographically smallest is atcoder, so we can say S = atcoder.", "input: ??p??d??\nabc output: UNRESTORABLE\n\nThere is no string that satisfies Condition 1, so the string S does not exist."], "Pid": "p03565", "ProblemText": "Task Description: Problem Statement E869120 found a chest which is likely to contain treasure.\nHowever, the chest is locked. In order to open it, he needs to enter a string S consisting of lowercase English letters.\nHe also found a string S', which turns out to be the string S with some of its letters (possibly all or none) replaced with ? . \nOne more thing he found is a sheet of paper with the following facts written on it: \n\nCondition 1: The string S contains a string T as a contiguous substring.\nCondition 2: S is the lexicographically smallest string among the ones that satisfy Condition 1.\n\nPrint the string S.\nIf such a string does not exist, print UNRESTORABLE.\nTask Constraint: 1 <= |S'|, |T| <= 50\nS' consists of lowercase English letters and ?.\nT consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nT'\nTask Output: Print the string S.\nIf such a string does not exist, print UNRESTORABLE instead.\nTask Samples: input: ?tc????\ncoder output: atcoder\n\nThere are 26 strings that satisfy Condition 1: atcoder, btcoder, ctcoder,..., ztcoder.\nAmong them, the lexicographically smallest is atcoder, so we can say S = atcoder.\ninput: ??p??d??\nabc output: UNRESTORABLE\n\nThere is no string that satisfies Condition 1, so the string S does not exist.\n\n" }, { "title": "", "content": "Problem Statement In the year 2168, At Coder Inc. , which is much larger than now, is starting a limited express train service called At Coder Express.\nIn the plan developed by the president Takahashi, the trains will run as follows:\n\nA train will run for (t_1 + t_2 + t_3 + . . . + t_N) seconds.\nIn the first t_1 seconds, a train must run at a speed of at most v_1 m/s (meters per second). Similarly, in the subsequent t_2 seconds, a train must run at a speed of at most v_2 m/s, and so on.\n\nAccording to the specifications of the trains, the acceleration of a train must be always within ±1m/s^2. Additionally, a train must stop at the beginning and the end of the run.\nFind the maximum possible distance that a train can cover in the run.", "constraint": "1 <= N <= 100\n1 <= t_i <= 200\n1 <= v_i <= 100\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nt_1 t_2 t_3 … t_N\nv_1 v_2 v_3 … v_N", "output": "Print the maximum possible that a train can cover in the run.\nOutput is considered correct if its absolute difference from the judge's output is at most 10^{-3}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n100\n30 output: 2100.000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 30 seconds, it accelerates at a rate of 1m/s^2, covering 450 meters.\nIn the subsequent 40 seconds, it maintains the velocity of 30m/s, covering 1200 meters.\nIn the last 30 seconds, it decelerates at the acceleration of -1m/s^2, covering 450 meters.\n\nThe total distance covered is 450 + 1200 + 450 = 2100 meters.", "input: 2\n60 50\n34 38 output: 2632.000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 34 seconds, it accelerates at a rate of 1m/s^2, covering 578 meters.\nIn the subsequent 26 seconds, it maintains the velocity of 34m/s, covering 884 meters.\nIn the subsequent 4 seconds, it accelerates at a rate of 1m/s^2, covering 144 meters.\nIn the subsequent 8 seconds, it maintains the velocity of 38m/s, covering 304 meters.\nIn the last 38 seconds, it decelerates at the acceleration of -1m/s^2, covering 722 meters.\n\nThe total distance covered is 578 + 884 + 144 + 304 + 722 = 2632 meters.", "input: 3\n12 14 2\n6 2 7 output: 76.000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 6 seconds, it accelerates at a rate of 1m/s^2, covering 18 meters.\nIn the subsequent 2 seconds, it maintains the velocity of 6m/s, covering 12 meters.\nIn the subsequent 4 seconds, it decelerates at the acceleration of -1m/s^2, covering 16 meters.\nIn the subsequent 14 seconds, it maintains the velocity of 2m/s, covering 28 meters.\nIn the last 2 seconds, it decelerates at the acceleration of -1m/s^2, covering 2 meters.\n\nThe total distance covered is 18 + 12 + 16 + 28 + 2 = 76 meters.", "input: 1\n9\n10 output: 20.250000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 4.5 seconds, it accelerates at a rate of 1m/s^2, covering 10.125 meters.\nIn the last 4.5 seconds, it decelerates at the acceleration of -1m/s^2, covering 10.125 meters.\n\nThe total distance covered is 10.125 + 10.125 = 20.25 meters.", "input: 10\n64 55 27 35 76 119 7 18 49 100\n29 19 31 39 27 48 41 87 55 70 output: 20291.000000000000"], "Pid": "p03566", "ProblemText": "Task Description: Problem Statement In the year 2168, At Coder Inc. , which is much larger than now, is starting a limited express train service called At Coder Express.\nIn the plan developed by the president Takahashi, the trains will run as follows:\n\nA train will run for (t_1 + t_2 + t_3 + . . . + t_N) seconds.\nIn the first t_1 seconds, a train must run at a speed of at most v_1 m/s (meters per second). Similarly, in the subsequent t_2 seconds, a train must run at a speed of at most v_2 m/s, and so on.\n\nAccording to the specifications of the trains, the acceleration of a train must be always within ±1m/s^2. Additionally, a train must stop at the beginning and the end of the run.\nFind the maximum possible distance that a train can cover in the run.\nTask Constraint: 1 <= N <= 100\n1 <= t_i <= 200\n1 <= v_i <= 100\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nt_1 t_2 t_3 … t_N\nv_1 v_2 v_3 … v_N\nTask Output: Print the maximum possible that a train can cover in the run.\nOutput is considered correct if its absolute difference from the judge's output is at most 10^{-3}.\nTask Samples: input: 1\n100\n30 output: 2100.000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 30 seconds, it accelerates at a rate of 1m/s^2, covering 450 meters.\nIn the subsequent 40 seconds, it maintains the velocity of 30m/s, covering 1200 meters.\nIn the last 30 seconds, it decelerates at the acceleration of -1m/s^2, covering 450 meters.\n\nThe total distance covered is 450 + 1200 + 450 = 2100 meters.\ninput: 2\n60 50\n34 38 output: 2632.000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 34 seconds, it accelerates at a rate of 1m/s^2, covering 578 meters.\nIn the subsequent 26 seconds, it maintains the velocity of 34m/s, covering 884 meters.\nIn the subsequent 4 seconds, it accelerates at a rate of 1m/s^2, covering 144 meters.\nIn the subsequent 8 seconds, it maintains the velocity of 38m/s, covering 304 meters.\nIn the last 38 seconds, it decelerates at the acceleration of -1m/s^2, covering 722 meters.\n\nThe total distance covered is 578 + 884 + 144 + 304 + 722 = 2632 meters.\ninput: 3\n12 14 2\n6 2 7 output: 76.000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 6 seconds, it accelerates at a rate of 1m/s^2, covering 18 meters.\nIn the subsequent 2 seconds, it maintains the velocity of 6m/s, covering 12 meters.\nIn the subsequent 4 seconds, it decelerates at the acceleration of -1m/s^2, covering 16 meters.\nIn the subsequent 14 seconds, it maintains the velocity of 2m/s, covering 28 meters.\nIn the last 2 seconds, it decelerates at the acceleration of -1m/s^2, covering 2 meters.\n\nThe total distance covered is 18 + 12 + 16 + 28 + 2 = 76 meters.\ninput: 1\n9\n10 output: 20.250000000000000000\nThe maximum distance is achieved when a train runs as follows:\n\nIn the first 4.5 seconds, it accelerates at a rate of 1m/s^2, covering 10.125 meters.\nIn the last 4.5 seconds, it decelerates at the acceleration of -1m/s^2, covering 10.125 meters.\n\nThe total distance covered is 10.125 + 10.125 = 20.25 meters.\ninput: 10\n64 55 27 35 76 119 7 18 49 100\n29 19 31 39 27 48 41 87 55 70 output: 20291.000000000000\n\n" }, { "title": "", "content": "Problem Statement Snuke built an online judge to hold a programming contest.\nWhen a program is submitted to the judge, the judge returns a verdict, which is a two-character string that appears in the string S as a contiguous substring.\n(The judge can return any two-character substring of S. )\nDetermine whether the judge can return the string AC as the verdict to a program.", "constraint": "2 <= |S| <= 5\nS consists of uppercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If the judge can return the string AC as a verdict to a program, print Yes; if it cannot, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: BACD output: Yes\n\nThe string AC appears in BACD as a contiguous substring (the second and third characters).", "input: ABCD output: No\n\nAlthough the string ABCD contains both A and C (the first and third characters), the string AC does not appear in ABCD as a contiguous substring.", "input: CABD output: No", "input: ACACA output: Yes", "input: XX output: No"], "Pid": "p03567", "ProblemText": "Task Description: Problem Statement Snuke built an online judge to hold a programming contest.\nWhen a program is submitted to the judge, the judge returns a verdict, which is a two-character string that appears in the string S as a contiguous substring.\n(The judge can return any two-character substring of S. )\nDetermine whether the judge can return the string AC as the verdict to a program.\nTask Constraint: 2 <= |S| <= 5\nS consists of uppercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If the judge can return the string AC as a verdict to a program, print Yes; if it cannot, print No.\nTask Samples: input: BACD output: Yes\n\nThe string AC appears in BACD as a contiguous substring (the second and third characters).\ninput: ABCD output: No\n\nAlthough the string ABCD contains both A and C (the first and third characters), the string AC does not appear in ABCD as a contiguous substring.\ninput: CABD output: No\ninput: ACACA output: Yes\ninput: XX output: No\n\n" }, { "title": "", "content": "Problem Statement We will say that two integer sequences of length N, x_1, x_2, . . . , x_N and y_1, y_2, . . . , y_N, are similar when |x_i - y_i| <= 1 holds for all i (1 <= i <= N).\nIn particular, any integer sequence is similar to itself.\nYou are given an integer N and an integer sequence of length N, A_1, A_2, . . . , A_N.\nHow many integer sequences b_1, b_2, . . . , b_N are there such that b_1, b_2, . . . , b_N is similar to A and the product of all elements, b_1 b_2 . . . b_N, is even?", "constraint": "1 <= N <= 10\n1 <= A_i <= 100", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the number of integer sequences that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n2 3 output: 7\n\nThere are seven integer sequences that satisfy the condition:\n\n1,2\n1,4\n2,2\n2,3\n2,4\n3,2\n3,4", "input: 3\n3 3 3 output: 26", "input: 1\n100 output: 1", "input: 10\n90 52 56 71 44 8 13 30 57 84 output: 58921"], "Pid": "p03568", "ProblemText": "Task Description: Problem Statement We will say that two integer sequences of length N, x_1, x_2, . . . , x_N and y_1, y_2, . . . , y_N, are similar when |x_i - y_i| <= 1 holds for all i (1 <= i <= N).\nIn particular, any integer sequence is similar to itself.\nYou are given an integer N and an integer sequence of length N, A_1, A_2, . . . , A_N.\nHow many integer sequences b_1, b_2, . . . , b_N are there such that b_1, b_2, . . . , b_N is similar to A and the product of all elements, b_1 b_2 . . . b_N, is even?\nTask Constraint: 1 <= N <= 10\n1 <= A_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the number of integer sequences that satisfy the condition.\nTask Samples: input: 2\n2 3 output: 7\n\nThere are seven integer sequences that satisfy the condition:\n\n1,2\n1,4\n2,2\n2,3\n2,4\n3,2\n3,4\ninput: 3\n3 3 3 output: 26\ninput: 1\n100 output: 1\ninput: 10\n90 52 56 71 44 8 13 30 57 84 output: 58921\n\n" }, { "title": "", "content": "Problem Statement We have a string s consisting of lowercase English letters.\nSnuke can perform the following operation repeatedly:\n\nInsert a letter x to any position in s of his choice, including the beginning and end of s.\n\nSnuke's objective is to turn s into a palindrome.\nDetermine whether the objective is achievable. If it is achievable, find the minimum number of operations required. note: Notes A palindrome is a string that reads the same forward and backward.\nFor example, a, aa, abba and abcba are palindromes, while ab, abab and abcda are not.", "constraint": "1 <= |s| <= 10^5\ns consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\ns", "output": "If the objective is achievable, print the number of operations required.\nIf it is not, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: xabxa output: 2\n\nOne solution is as follows (newly inserted x are shown in bold):\nxabxa → xaxbxa → xaxbxax", "input: ab output: -1\n\nNo sequence of operations can turn s into a palindrome.", "input: a output: 0\n\ns is a palindrome already at the beginning.", "input: oxxx output: 3\n\nOne solution is as follows:\noxxx → xoxxx → xxoxxx → xxxoxxx"], "Pid": "p03569", "ProblemText": "Task Description: Problem Statement We have a string s consisting of lowercase English letters.\nSnuke can perform the following operation repeatedly:\n\nInsert a letter x to any position in s of his choice, including the beginning and end of s.\n\nSnuke's objective is to turn s into a palindrome.\nDetermine whether the objective is achievable. If it is achievable, find the minimum number of operations required. note: Notes A palindrome is a string that reads the same forward and backward.\nFor example, a, aa, abba and abcba are palindromes, while ab, abab and abcda are not.\nTask Constraint: 1 <= |s| <= 10^5\ns consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\ns\nTask Output: If the objective is achievable, print the number of operations required.\nIf it is not, print -1 instead.\nTask Samples: input: xabxa output: 2\n\nOne solution is as follows (newly inserted x are shown in bold):\nxabxa → xaxbxa → xaxbxax\ninput: ab output: -1\n\nNo sequence of operations can turn s into a palindrome.\ninput: a output: 0\n\ns is a palindrome already at the beginning.\ninput: oxxx output: 3\n\nOne solution is as follows:\noxxx → xoxxx → xxoxxx → xxxoxxx\n\n" }, { "title": "", "content": "Problem Statement We have a string s consisting of lowercase English letters.\nSnuke is partitioning s into some number of non-empty substrings.\nLet the subtrings obtained be s_1, s_2, . . . , s_N from left to right. (Here, s = s_1 + s_2 + . . . + s_N holds. )\nSnuke wants to satisfy the following condition:\n\nFor each i (1 <= i <= N), it is possible to permute the characters in s_i and obtain a palindrome.\n\nFind the minimum possible value of N when the partition satisfies the condition.", "constraint": "1 <= |s| <= 2 * 10^5\ns consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\ns", "output": "Print the minimum possible value of N when the partition satisfies the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aabxyyzz output: 2\n\nThe solution is to partition s as aabxyyzz = aab + xyyzz.\nHere, aab can be permuted to form a palindrome aba, and xyyzz can be permuted to form a palindrome zyxyz.", "input: byebye output: 1\n\nbyebye can be permuted to form a palindrome byeeyb.", "input: abcdefghijklmnopqrstuvwxyz output: 26", "input: abcabcxabcx output: 3\n\nThe solution is to partition s as abcabcxabcx = a + b + cabcxabcx."], "Pid": "p03570", "ProblemText": "Task Description: Problem Statement We have a string s consisting of lowercase English letters.\nSnuke is partitioning s into some number of non-empty substrings.\nLet the subtrings obtained be s_1, s_2, . . . , s_N from left to right. (Here, s = s_1 + s_2 + . . . + s_N holds. )\nSnuke wants to satisfy the following condition:\n\nFor each i (1 <= i <= N), it is possible to permute the characters in s_i and obtain a palindrome.\n\nFind the minimum possible value of N when the partition satisfies the condition.\nTask Constraint: 1 <= |s| <= 2 * 10^5\ns consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\ns\nTask Output: Print the minimum possible value of N when the partition satisfies the condition.\nTask Samples: input: aabxyyzz output: 2\n\nThe solution is to partition s as aabxyyzz = aab + xyyzz.\nHere, aab can be permuted to form a palindrome aba, and xyyzz can be permuted to form a palindrome zyxyz.\ninput: byebye output: 1\n\nbyebye can be permuted to form a palindrome byeeyb.\ninput: abcdefghijklmnopqrstuvwxyz output: 26\ninput: abcabcxabcx output: 3\n\nThe solution is to partition s as abcabcxabcx = a + b + cabcxabcx.\n\n" }, { "title": "", "content": "Problem Statement We constructed a rectangular parallelepiped of dimensions A * B * C built of ABC cubic blocks of side 1.\nThen, we placed the parallelepiped in xyz-space as follows:\n\nFor every triple i, j, k (0 <= i < A, 0 <= j < B, 0 <= k < C), there exists a block that has a diagonal connecting the points (i, j, k) and (i + 1, j + 1, k + 1). All sides of the block are parallel to a coordinate axis.\n\nFor each triple i, j, k, we will call the above block as block (i, j, k).\nFor two blocks (i_1, j_1, k_1) and (i_2, j_2, k_2), we will define the distance between them as max(|i_1 - i_2|, |j_1 - j_2|, |k_1 - k_2|).\nWe have passed a wire with a negligible thickness through a segment connecting the points (0,0,0) and (A, B, C).\nHow many blocks (x, y, z) satisfy the following condition? Find the count modulo 10^9 + 7.\n\nThere exists a block (x', y', z') such that the wire passes inside the block (x', y', z') (not just boundary) and the distance between the blocks (x, y, z) and (x', y', z') is at most D.", "constraint": "1 <= A < B < C <= 10^{9}\nAny two of the three integers A, B and C are coprime.\n0 <= D <= 50,000", "input": "Input is given from Standard Input in the following format:\nA B C D", "output": "Print the number of the blocks that satisfy the condition, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 5 1 output: 54\n\nThe figure below shows the parallelepiped, sliced into five layers by planes parallel to xy-plane.\nHere, the layer in the region i - 1 <= z <= i is called layer i.\nThe blocks painted black are penetrated by the wire, and satisfy the condition.\nThe other blocks that satisfy the condition are painted yellow.\n\nThere are 54 blocks that are painted black or yellow.", "input: 1 2 3 0 output: 4\n\nThere are four blocks that are penetrated by the wire, and only these blocks satisfy the condition.", "input: 3 5 7 100 output: 105\n\nAll blocks satisfy the condition.", "input: 3 123456781 1000000000 100 output: 444124403", "input: 1234 12345 1234567 5 output: 150673016", "input: 999999997 999999999 1000000000 50000 output: 8402143"], "Pid": "p03571", "ProblemText": "Task Description: Problem Statement We constructed a rectangular parallelepiped of dimensions A * B * C built of ABC cubic blocks of side 1.\nThen, we placed the parallelepiped in xyz-space as follows:\n\nFor every triple i, j, k (0 <= i < A, 0 <= j < B, 0 <= k < C), there exists a block that has a diagonal connecting the points (i, j, k) and (i + 1, j + 1, k + 1). All sides of the block are parallel to a coordinate axis.\n\nFor each triple i, j, k, we will call the above block as block (i, j, k).\nFor two blocks (i_1, j_1, k_1) and (i_2, j_2, k_2), we will define the distance between them as max(|i_1 - i_2|, |j_1 - j_2|, |k_1 - k_2|).\nWe have passed a wire with a negligible thickness through a segment connecting the points (0,0,0) and (A, B, C).\nHow many blocks (x, y, z) satisfy the following condition? Find the count modulo 10^9 + 7.\n\nThere exists a block (x', y', z') such that the wire passes inside the block (x', y', z') (not just boundary) and the distance between the blocks (x, y, z) and (x', y', z') is at most D.\nTask Constraint: 1 <= A < B < C <= 10^{9}\nAny two of the three integers A, B and C are coprime.\n0 <= D <= 50,000\nTask Input: Input is given from Standard Input in the following format:\nA B C D\nTask Output: Print the number of the blocks that satisfy the condition, modulo 10^9 + 7.\nTask Samples: input: 3 4 5 1 output: 54\n\nThe figure below shows the parallelepiped, sliced into five layers by planes parallel to xy-plane.\nHere, the layer in the region i - 1 <= z <= i is called layer i.\nThe blocks painted black are penetrated by the wire, and satisfy the condition.\nThe other blocks that satisfy the condition are painted yellow.\n\nThere are 54 blocks that are painted black or yellow.\ninput: 1 2 3 0 output: 4\n\nThere are four blocks that are penetrated by the wire, and only these blocks satisfy the condition.\ninput: 3 5 7 100 output: 105\n\nAll blocks satisfy the condition.\ninput: 3 123456781 1000000000 100 output: 444124403\ninput: 1234 12345 1234567 5 output: 150673016\ninput: 999999997 999999999 1000000000 50000 output: 8402143\n\n" }, { "title": "", "content": "Problem Statement Three men, A, B and C, are eating sushi together.\nInitially, there are N pieces of sushi, numbered 1 through N.\nHere, N is a multiple of 3.\nEach of the three has likes and dislikes in sushi.\nA's preference is represented by (a_1, \\ . . . , \\ a_N), a permutation of integers from 1 to N.\nFor each i (1 <= i <= N), A's i-th favorite sushi is Sushi a_i.\nSimilarly, B's and C's preferences are represented by (b_1, \\ . . . , \\ b_N) and (c_1, \\ . . . , \\ c_N), permutations of integers from 1 to N.\nThe three repeats the following action until all pieces of sushi are consumed or a fight brakes out (described later):\n\nEach of the three A, B and C finds his most favorite piece of sushi among the remaining pieces. Let these pieces be Sushi x, y and z, respectively. If x, y and z are all different, A, B and C eats Sushi x, y and z, respectively. Otherwise, a fight brakes out.\n\nYou are given A's and B's preferences, (a_1, \\ . . . , \\ a_N) and (b_1, \\ . . . , \\ b_N).\nHow many preferences of C, (c_1, \\ . . . , \\ c_N), leads to all the pieces of sushi being consumed without a fight?\nFind the count modulo 10^9+7.", "constraint": "3 <= N <= 399\nN is a multiple of 3.\n(a_1,\\ ...,\\ a_N) and (b_1,\\ ...,\\ b_N) are permutations of integers from 1 to N.", "input": "Input is given from Standard Input in the following format:\nN\na_1 . . . a_N\nb_1 . . . b_N", "output": "Print the number of the preferences of C that leads to all the pieces of sushi being consumed without a fight, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3\n2 3 1 output: 2\n\nThe answer is two, (c_1,\\ c_2,\\ c_3) = (3,\\ 1,\\ 2),\\ (3,\\ 2,\\ 1).\nIn both cases, A, B and C will eat Sushi 1,2 and 3, respectively, and there will be no more sushi.", "input: 3\n1 2 3\n1 2 3 output: 0\n\nRegardless of what permutation (c_1,\\ c_2,\\ c_3) is, A and B will try to eat Sushi 1, resulting in a fight.", "input: 6\n1 2 3 4 5 6\n2 1 4 3 6 5 output: 80\n\nFor example, if (c_1,\\ c_2,\\ c_3,\\ c_4,\\ c_5,\\ c_6) = (5,\\ 1,\\ 2,\\ 6,\\ 3,\\ 4), A, B and C will first eat Sushi 1,2 and 5, respectively, then they will eat Sushi 3,4 and 6, respectively, and there will be no more sushi.", "input: 6\n1 2 3 4 5 6\n6 5 4 3 2 1 output: 160", "input: 9\n4 5 6 7 8 9 1 2 3\n7 8 9 1 2 3 4 5 6 output: 33600"], "Pid": "p03572", "ProblemText": "Task Description: Problem Statement Three men, A, B and C, are eating sushi together.\nInitially, there are N pieces of sushi, numbered 1 through N.\nHere, N is a multiple of 3.\nEach of the three has likes and dislikes in sushi.\nA's preference is represented by (a_1, \\ . . . , \\ a_N), a permutation of integers from 1 to N.\nFor each i (1 <= i <= N), A's i-th favorite sushi is Sushi a_i.\nSimilarly, B's and C's preferences are represented by (b_1, \\ . . . , \\ b_N) and (c_1, \\ . . . , \\ c_N), permutations of integers from 1 to N.\nThe three repeats the following action until all pieces of sushi are consumed or a fight brakes out (described later):\n\nEach of the three A, B and C finds his most favorite piece of sushi among the remaining pieces. Let these pieces be Sushi x, y and z, respectively. If x, y and z are all different, A, B and C eats Sushi x, y and z, respectively. Otherwise, a fight brakes out.\n\nYou are given A's and B's preferences, (a_1, \\ . . . , \\ a_N) and (b_1, \\ . . . , \\ b_N).\nHow many preferences of C, (c_1, \\ . . . , \\ c_N), leads to all the pieces of sushi being consumed without a fight?\nFind the count modulo 10^9+7.\nTask Constraint: 3 <= N <= 399\nN is a multiple of 3.\n(a_1,\\ ...,\\ a_N) and (b_1,\\ ...,\\ b_N) are permutations of integers from 1 to N.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 . . . a_N\nb_1 . . . b_N\nTask Output: Print the number of the preferences of C that leads to all the pieces of sushi being consumed without a fight, modulo 10^9+7.\nTask Samples: input: 3\n1 2 3\n2 3 1 output: 2\n\nThe answer is two, (c_1,\\ c_2,\\ c_3) = (3,\\ 1,\\ 2),\\ (3,\\ 2,\\ 1).\nIn both cases, A, B and C will eat Sushi 1,2 and 3, respectively, and there will be no more sushi.\ninput: 3\n1 2 3\n1 2 3 output: 0\n\nRegardless of what permutation (c_1,\\ c_2,\\ c_3) is, A and B will try to eat Sushi 1, resulting in a fight.\ninput: 6\n1 2 3 4 5 6\n2 1 4 3 6 5 output: 80\n\nFor example, if (c_1,\\ c_2,\\ c_3,\\ c_4,\\ c_5,\\ c_6) = (5,\\ 1,\\ 2,\\ 6,\\ 3,\\ 4), A, B and C will first eat Sushi 1,2 and 5, respectively, then they will eat Sushi 3,4 and 6, respectively, and there will be no more sushi.\ninput: 6\n1 2 3 4 5 6\n6 5 4 3 2 1 output: 160\ninput: 9\n4 5 6 7 8 9 1 2 3\n7 8 9 1 2 3 4 5 6 output: 33600\n\n" }, { "title": "", "content": "Problem Statement You are given three integers, A, B and C.\nAmong them, two are the same, but the remaining one is different from the rest.\nFor example, when A=5, B=7, C=5, A and C are the same, but B is different.\nFind the one that is different from the rest among the given three integers.", "constraint": "-100 <= A,B,C <= 100 \nA, B and C are integers.\nThe input satisfies the condition in the statement.", "input": "Input is given from Standard Input in the following format: \nA B C", "output": "Output Among A, B and C, print the integer that is different from the rest.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 7 5 output: 7\n\nThis is the same case as the one in the statement.", "input: 1 1 7 output: 7\n\nIn this case, C is the one we seek.", "input: -100 100 100 output: -100"], "Pid": "p03573", "ProblemText": "Task Description: Problem Statement You are given three integers, A, B and C.\nAmong them, two are the same, but the remaining one is different from the rest.\nFor example, when A=5, B=7, C=5, A and C are the same, but B is different.\nFind the one that is different from the rest among the given three integers.\nTask Constraint: -100 <= A,B,C <= 100 \nA, B and C are integers.\nThe input satisfies the condition in the statement.\nTask Input: Input is given from Standard Input in the following format: \nA B C\nTask Output: Output Among A, B and C, print the integer that is different from the rest.\nTask Samples: input: 5 7 5 output: 7\n\nThis is the same case as the one in the statement.\ninput: 1 1 7 output: 7\n\nIn this case, C is the one we seek.\ninput: -100 100 100 output: -100\n\n" }, { "title": "", "content": "Problem Statement You are given an H * W grid.\nThe squares in the grid are described by H strings, S_1, . . . , S_H.\nThe j-th character in the string S_i corresponds to the square at the i-th row from the top and j-th column from the left (1 <= i <= H, 1 <= j <= W).\n. stands for an empty square, and # stands for a square containing a bomb. \nDolphin is interested in how many bomb squares are horizontally, vertically or diagonally adjacent to each empty square.\n(Below, we will simply say \"adjacent\" for this meaning. For each square, there are at most eight adjacent squares. )\nHe decides to replace each . in our H strings with a digit that represents the number of bomb squares adjacent to the corresponding empty square. \nPrint the strings after the process.", "constraint": "1 <= H,W <= 50\nS_i is a string of length W consisting of # and ..", "input": "Input is given from Standard Input in the following format: \nH W\nS_1\n:\nS_H", "output": "Print the H strings after the process.\nThe i-th line should contain a string T_i of length W, where the j-th character in T_i corresponds to the square at the i-th row from the top and j-th row from the left in the grid (1 <= i <= H, 1 <= j <= W).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5\n.....\n.#.#.\n..... output: 11211\n1#2#1\n11211\n\nFor example, let us observe the empty square at the first row from the top and first column from the left.\nThere is one bomb square adjacent to this empty square: the square at the second row and second column.\nThus, the . corresponding to this empty square is replaced with 1.", "input: 3 5\n#####\n#####\n##### output: #####\n#####\n#####\n\nIt is possible that there is no empty square.", "input: 6 6\n#####.\n#.#.##\n####.#\n.#..#.\n#.##..\n#.#... output: #####3\n#8#7##\n####5#\n4#65#2\n#5##21\n#4#310"], "Pid": "p03574", "ProblemText": "Task Description: Problem Statement You are given an H * W grid.\nThe squares in the grid are described by H strings, S_1, . . . , S_H.\nThe j-th character in the string S_i corresponds to the square at the i-th row from the top and j-th column from the left (1 <= i <= H, 1 <= j <= W).\n. stands for an empty square, and # stands for a square containing a bomb. \nDolphin is interested in how many bomb squares are horizontally, vertically or diagonally adjacent to each empty square.\n(Below, we will simply say \"adjacent\" for this meaning. For each square, there are at most eight adjacent squares. )\nHe decides to replace each . in our H strings with a digit that represents the number of bomb squares adjacent to the corresponding empty square. \nPrint the strings after the process.\nTask Constraint: 1 <= H,W <= 50\nS_i is a string of length W consisting of # and ..\nTask Input: Input is given from Standard Input in the following format: \nH W\nS_1\n:\nS_H\nTask Output: Print the H strings after the process.\nThe i-th line should contain a string T_i of length W, where the j-th character in T_i corresponds to the square at the i-th row from the top and j-th row from the left in the grid (1 <= i <= H, 1 <= j <= W).\nTask Samples: input: 3 5\n.....\n.#.#.\n..... output: 11211\n1#2#1\n11211\n\nFor example, let us observe the empty square at the first row from the top and first column from the left.\nThere is one bomb square adjacent to this empty square: the square at the second row and second column.\nThus, the . corresponding to this empty square is replaced with 1.\ninput: 3 5\n#####\n#####\n##### output: #####\n#####\n#####\n\nIt is possible that there is no empty square.\ninput: 6 6\n#####.\n#.#.##\n####.#\n.#..#.\n#.##..\n#.#... output: #####3\n#8#7##\n####5#\n4#65#2\n#5##21\n#4#310\n\n" }, { "title": "", "content": "Problem Statement You are given an undirected connected graph with N vertices and M edges that does not contain self-loops and double edges.\nThe i-th edge (1 <= i <= M) connects Vertex a_i and Vertex b_i. \nAn edge whose removal disconnects the graph is called a bridge.\nFind the number of the edges that are bridges among the M edges. note: Notes\nA self-loop is an edge i such that a_i=b_i (1 <= i <= M).\nDouble edges are a pair of edges i, j such that a_i=a_j and b_i=b_j (1 <= iN cities, and some pairs of cities are connected bidirectionally by roads.\nThe following are known about the road network:\n\nPeople traveled between cities only through roads. It was possible to reach any city from any other city, via intermediate cities if necessary.\nDifferent roads may have had different lengths, but all the lengths were positive integers.\n\nSnuke the archeologist found a table with >N rows and >N columns, >A, in the ruin of Takahashi Kingdom.\nHe thought that it represented the shortest distances between the cities along the roads in the kingdom.\nDetermine whether there exists a road network such that for each >u and >v, the integer >A_{u, v} at the >u-th row and >v-th column of >A is equal to the length of the shortest path from City >u to City >v.\nIf such a network exist, find the shortest possible total length of the roads.", "constraint": ">1 <= N <= 300\nIf >i != j, >1 <= A_{i, j} = A_{j, i} <= 10^9.\n>A_{i, i} = 0", "input": "Inputs Input is given from Standard Input in the following format: \\n>N\\n>A_{1,1} >A_{1,2} >. . . >A_{1, N}\\n>A_{2,1} >A_{2,2} >. . . >A_{2, N}\\n>. . . \\n>A_{N, 1} >A_{N, 2} >. . . >A_{N, N}", "output": "Outputs If there exists no network that satisfies the condition, print -1. If it exists, print the shortest possible total length of the roads.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 1 3\n1 0 2\n3 2 0 output: 3\n\nThe network below satisfies the condition:\n\nCity >1 and City >2 is connected by a road of length >1.\nCity >2 and City >3 is connected by a road of length >2.\nCity >3 and City >1 is not connected by a road.", "input: 3\n0 1 3\n1 0 1\n3 1 0 output: -1\n\nAs there is a path of length >1 from City >1 to City >2 and City >2 to City >3, there is a path of length >2 from City >1 to City >3.\nHowever, according to the table, the shortest distance between City >1 and City >3 must be >3.\nThus, we conclude that there exists no network that satisfies the condition.", "input: 5\n0 21 18 11 28\n21 0 13 10 26\n18 13 0 23 13\n11 10 23 0 17\n28 26 13 17 0 output: 82", "input: 3\n0 1000000000 1000000000\n1000000000 0 1000000000\n1000000000 1000000000 0 output: 3000000000"], "Pid": "p03602", "ProblemText": "Task Description: Problem Statement In Takahashi Kingdom, which once existed, there are >N cities, and some pairs of cities are connected bidirectionally by roads.\nThe following are known about the road network:\n\nPeople traveled between cities only through roads. It was possible to reach any city from any other city, via intermediate cities if necessary.\nDifferent roads may have had different lengths, but all the lengths were positive integers.\n\nSnuke the archeologist found a table with >N rows and >N columns, >A, in the ruin of Takahashi Kingdom.\nHe thought that it represented the shortest distances between the cities along the roads in the kingdom.\nDetermine whether there exists a road network such that for each >u and >v, the integer >A_{u, v} at the >u-th row and >v-th column of >A is equal to the length of the shortest path from City >u to City >v.\nIf such a network exist, find the shortest possible total length of the roads.\nTask Constraint: >1 <= N <= 300\nIf >i != j, >1 <= A_{i, j} = A_{j, i} <= 10^9.\n>A_{i, i} = 0\nTask Input: Inputs Input is given from Standard Input in the following format: \\n>N\\n>A_{1,1} >A_{1,2} >. . . >A_{1, N}\\n>A_{2,1} >A_{2,2} >. . . >A_{2, N}\\n>. . . \\n>A_{N, 1} >A_{N, 2} >. . . >A_{N, N}\nTask Output: Outputs If there exists no network that satisfies the condition, print -1. If it exists, print the shortest possible total length of the roads.\nTask Samples: input: 3\n0 1 3\n1 0 2\n3 2 0 output: 3\n\nThe network below satisfies the condition:\n\nCity >1 and City >2 is connected by a road of length >1.\nCity >2 and City >3 is connected by a road of length >2.\nCity >3 and City >1 is not connected by a road.\ninput: 3\n0 1 3\n1 0 1\n3 1 0 output: -1\n\nAs there is a path of length >1 from City >1 to City >2 and City >2 to City >3, there is a path of length >2 from City >1 to City >3.\nHowever, according to the table, the shortest distance between City >1 and City >3 must be >3.\nThus, we conclude that there exists no network that satisfies the condition.\ninput: 5\n0 21 18 11 28\n21 0 13 10 26\n18 13 0 23 13\n11 10 23 0 17\n28 26 13 17 0 output: 82\ninput: 3\n0 1000000000 1000000000\n1000000000 0 1000000000\n1000000000 1000000000 0 output: 3000000000\n\n" }, { "title": "", "content": "Problem Statement We have a tree with N vertices. Vertex 1 is the root of the tree, and the parent of Vertex i (2 <= i <= N) is Vertex P_i.\nTo each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight.\nSnuke has a favorite integer sequence, X_1, X_2, . . . , X_N, so he wants to allocate colors and weights so that the following condition is satisfied for all v.\n\nThe total weight of the vertices with the same color as v among the vertices contained in the subtree whose root is v, is X_v.\n\nHere, the subtree whose root is v is the tree consisting of Vertex v and all of its descendants.\nDetermine whether it is possible to allocate colors and weights in this way.", "constraint": "1 <= N <= 1 000\n1 <= P_i <= i - 1\n0 <= X_i <= 5 000", "input": "Inputs Input is given from Standard Input in the following format: \\n N\\n P_2 P_3 . . . P_N\\n X_1 X_2 . . . X_N", "output": "Outputs If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE; otherwise, print IMPOSSIBLE.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 1\n4 3 2 output: POSSIBLE\n\nFor example, the following allocation satisfies the condition:\n\nSet the color of Vertex 1 to white and its weight to 2.\nSet the color of Vertex 2 to black and its weight to 3.\nSet the color of Vertex 3 to white and its weight to 2.\n\nThere are also other possible allocations.", "input: 3\n1 2\n1 2 3 output: IMPOSSIBLE\n\nIf the same color is allocated to Vertex 2 and Vertex 3, Vertex 2 cannot be allocated a non-negative weight.\nIf different colors are allocated to Vertex 2 and 3, no matter which color is allocated to Vertex 1, it cannot be allocated a non-negative weight.\nThus, there exists no allocation of colors and weights that satisfies the condition.", "input: 8\n1 1 1 3 4 5 5\n4 1 6 2 2 1 3 3 output: POSSIBLE", "input: 1\n\n0 output: POSSIBLE"], "Pid": "p03603", "ProblemText": "Task Description: Problem Statement We have a tree with N vertices. Vertex 1 is the root of the tree, and the parent of Vertex i (2 <= i <= N) is Vertex P_i.\nTo each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight.\nSnuke has a favorite integer sequence, X_1, X_2, . . . , X_N, so he wants to allocate colors and weights so that the following condition is satisfied for all v.\n\nThe total weight of the vertices with the same color as v among the vertices contained in the subtree whose root is v, is X_v.\n\nHere, the subtree whose root is v is the tree consisting of Vertex v and all of its descendants.\nDetermine whether it is possible to allocate colors and weights in this way.\nTask Constraint: 1 <= N <= 1 000\n1 <= P_i <= i - 1\n0 <= X_i <= 5 000\nTask Input: Inputs Input is given from Standard Input in the following format: \\n N\\n P_2 P_3 . . . P_N\\n X_1 X_2 . . . X_N\nTask Output: Outputs If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE; otherwise, print IMPOSSIBLE.\nTask Samples: input: 3\n1 1\n4 3 2 output: POSSIBLE\n\nFor example, the following allocation satisfies the condition:\n\nSet the color of Vertex 1 to white and its weight to 2.\nSet the color of Vertex 2 to black and its weight to 3.\nSet the color of Vertex 3 to white and its weight to 2.\n\nThere are also other possible allocations.\ninput: 3\n1 2\n1 2 3 output: IMPOSSIBLE\n\nIf the same color is allocated to Vertex 2 and Vertex 3, Vertex 2 cannot be allocated a non-negative weight.\nIf different colors are allocated to Vertex 2 and 3, no matter which color is allocated to Vertex 1, it cannot be allocated a non-negative weight.\nThus, there exists no allocation of colors and weights that satisfies the condition.\ninput: 8\n1 1 1 3 4 5 5\n4 1 6 2 2 1 3 3 output: POSSIBLE\ninput: 1\n\n0 output: POSSIBLE\n\n" }, { "title": "", "content": "Problem Statement There are 2N balls in the xy-plane. The coordinates of the i-th of them is (x_i, y_i).\nHere, x_i and y_i are integers between 1 and N (inclusive) for all i, and no two balls occupy the same coordinates.\nIn order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B.\nThen, he placed the type-A robots at coordinates (1,0), (2,0), . . . , (N, 0), and the type-B robots at coordinates (0,1), (0,2), . . . , (0, N), one at each position.\nWhen activated, each type of robot will operate as follows.\nWhen a type-A robot is activated at coordinates (a, 0), it will move to the position of the ball with the lowest y-coordinate among the balls on the line x = a, collect the ball and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.\nWhen a type-B robot is activated at coordinates (0, b), it will move to the position of the ball with the lowest x-coordinate among the balls on the line y = b, collect the ball and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.\nOnce deactivated, a robot cannot be activated again. Also, while a robot is operating, no new robot can be activated until the operating robot is deactivated.\nWhen Snuke was about to activate a robot, he noticed that he may fail to collect all the balls, depending on the order of activating the robots.\nAmong the (2N)! possible orders of activating the robots, find the number of the ones such that all the balls can be collected, modulo 1 000 000 007.", "constraint": "2 <= N <= 10^5\n1 <= x_i <= N\n1 <= y_i <= N\nIf i != j, either x_i != x_j or y_i != y_j.", "input": "Inputs Input is given from Standard Input in the following format: \\n N\\nx_1 y_1\\n. . . \\nx_{2N} y_{2N}", "output": "Outputs Print the number of the orders of activating the robots such that all the balls can be collected, modulo 1 000 000 007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 1\n1 2\n2 1\n2 2 output: 8\n\nWe will refer to the robots placed at (1,0) and (2,0) as A1 and A2, respectively, and the robots placed at (0,1) and (0,2) as B1 and B2, respectively.\nThere are eight orders of activation that satisfy the condition, as follows:\n\nA1, B1, A2, B2\nA1, B1, B2, A2\nA1, B2, B1, A2\nA2, B1, A1, B2\nB1, A1, B2, A2\nB1, A1, A2, B2\nB1, A2, A1, B2\nB2, A1, B1, A2\n\nThus, the output should be 8.", "input: 4\n3 2\n1 2\n4 1\n4 2\n2 2\n4 4\n2 1\n1 3 output: 7392", "input: 4\n1 1\n2 2\n3 3\n4 4\n1 2\n2 1\n3 4\n4 3 output: 4480", "input: 8\n6 2\n5 1\n6 8\n7 8\n6 5\n5 7\n4 3\n1 4\n7 6\n8 3\n2 8\n3 6\n3 2\n8 5\n1 5\n5 8 output: 82060779", "input: 3\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3 output: 0\n\nWhen there is no order of activation that satisfies the condition, the output should be 0."], "Pid": "p03604", "ProblemText": "Task Description: Problem Statement There are 2N balls in the xy-plane. The coordinates of the i-th of them is (x_i, y_i).\nHere, x_i and y_i are integers between 1 and N (inclusive) for all i, and no two balls occupy the same coordinates.\nIn order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B.\nThen, he placed the type-A robots at coordinates (1,0), (2,0), . . . , (N, 0), and the type-B robots at coordinates (0,1), (0,2), . . . , (0, N), one at each position.\nWhen activated, each type of robot will operate as follows.\nWhen a type-A robot is activated at coordinates (a, 0), it will move to the position of the ball with the lowest y-coordinate among the balls on the line x = a, collect the ball and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.\nWhen a type-B robot is activated at coordinates (0, b), it will move to the position of the ball with the lowest x-coordinate among the balls on the line y = b, collect the ball and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.\nOnce deactivated, a robot cannot be activated again. Also, while a robot is operating, no new robot can be activated until the operating robot is deactivated.\nWhen Snuke was about to activate a robot, he noticed that he may fail to collect all the balls, depending on the order of activating the robots.\nAmong the (2N)! possible orders of activating the robots, find the number of the ones such that all the balls can be collected, modulo 1 000 000 007.\nTask Constraint: 2 <= N <= 10^5\n1 <= x_i <= N\n1 <= y_i <= N\nIf i != j, either x_i != x_j or y_i != y_j.\nTask Input: Inputs Input is given from Standard Input in the following format: \\n N\\nx_1 y_1\\n. . . \\nx_{2N} y_{2N}\nTask Output: Outputs Print the number of the orders of activating the robots such that all the balls can be collected, modulo 1 000 000 007.\nTask Samples: input: 2\n1 1\n1 2\n2 1\n2 2 output: 8\n\nWe will refer to the robots placed at (1,0) and (2,0) as A1 and A2, respectively, and the robots placed at (0,1) and (0,2) as B1 and B2, respectively.\nThere are eight orders of activation that satisfy the condition, as follows:\n\nA1, B1, A2, B2\nA1, B1, B2, A2\nA1, B2, B1, A2\nA2, B1, A1, B2\nB1, A1, B2, A2\nB1, A1, A2, B2\nB1, A2, A1, B2\nB2, A1, B1, A2\n\nThus, the output should be 8.\ninput: 4\n3 2\n1 2\n4 1\n4 2\n2 2\n4 4\n2 1\n1 3 output: 7392\ninput: 4\n1 1\n2 2\n3 3\n4 4\n1 2\n2 1\n3 4\n4 3 output: 4480\ninput: 8\n6 2\n5 1\n6 8\n7 8\n6 5\n5 7\n4 3\n1 4\n7 6\n8 3\n2 8\n3 6\n3 2\n8 5\n1 5\n5 8 output: 82060779\ninput: 3\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3 output: 0\n\nWhen there is no order of activation that satisfies the condition, the output should be 0.\n\n" }, { "title": "", "content": "Problem Statement It is September 9 in Japan now.\nYou are given a two-digit integer N. Answer the question: Is 9 contained in the decimal notation of N?", "constraint": "10<=N<=99", "input": "Input is given from Standard Input in the following format:\nN", "output": "If 9 is contained in the decimal notation of N, print Yes; if not, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 29 output: Yes\n\nThe one's digit of 29 is 9.", "input: 72 output: No\n\n72 does not contain 9.", "input: 91 output: Yes"], "Pid": "p03605", "ProblemText": "Task Description: Problem Statement It is September 9 in Japan now.\nYou are given a two-digit integer N. Answer the question: Is 9 contained in the decimal notation of N?\nTask Constraint: 10<=N<=99\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: If 9 is contained in the decimal notation of N, print Yes; if not, print No.\nTask Samples: input: 29 output: Yes\n\nThe one's digit of 29 is 9.\ninput: 72 output: No\n\n72 does not contain 9.\ninput: 91 output: Yes\n\n" }, { "title": "", "content": "Problem Statement Joisino is working as a receptionist at a theater.\nThe theater has 100000 seats, numbered from 1 to 100000.\nAccording to her memo, N groups of audiences have come so far, and the i-th group occupies the consecutive seats from Seat l_i to Seat r_i (inclusive).\nHow many people are sitting at the theater now?", "constraint": "1<=N<=1000\n1<=l_i<=r_i<=100000\nNo seat is occupied by more than one person.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nl_1 r_1\n:\nl_N r_N", "output": "Print the number of people sitting at the theater.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1\n24 30 output: 7\n\nThere are 7 people, sitting at Seat 24,25,26,27,28,29 and 30.", "input: 2\n6 8\n3 3 output: 4"], "Pid": "p03606", "ProblemText": "Task Description: Problem Statement Joisino is working as a receptionist at a theater.\nThe theater has 100000 seats, numbered from 1 to 100000.\nAccording to her memo, N groups of audiences have come so far, and the i-th group occupies the consecutive seats from Seat l_i to Seat r_i (inclusive).\nHow many people are sitting at the theater now?\nTask Constraint: 1<=N<=1000\n1<=l_i<=r_i<=100000\nNo seat is occupied by more than one person.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nl_1 r_1\n:\nl_N r_N\nTask Output: Print the number of people sitting at the theater.\nTask Samples: input: 1\n24 30 output: 7\n\nThere are 7 people, sitting at Seat 24,25,26,27,28,29 and 30.\ninput: 2\n6 8\n3 3 output: 4\n\n" }, { "title": "", "content": "Problem Statement You are playing the following game with Joisino.\n\nInitially, you have a blank sheet of paper.\nJoisino announces a number. If that number is written on the sheet, erase the number from the sheet; if not, write the number on the sheet. This process is repeated N times.\nThen, you are asked a question: How many numbers are written on the sheet now?\n\nThe numbers announced by Joisino are given as A_1, . . . , A_N in the order she announces them. How many numbers will be written on the sheet at the end of the game?", "constraint": "1<=N<=100000\n1<=A_i<=1000000000(=10^9)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print how many numbers will be written on the sheet at the end of the game.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n6\n2\n6 output: 1\n\nThe game proceeds as follows:\n6 is not written on the sheet, so write 6.\n2 is not written on the sheet, so write 2.\n6 is written on the sheet, so erase 6.\nThus, the sheet contains only 2 in the end. The answer is 1.", "input: 4\n2\n5\n5\n2 output: 0\n\nIt is possible that no number is written on the sheet in the end.", "input: 6\n12\n22\n16\n22\n18\n12 output: 2"], "Pid": "p03607", "ProblemText": "Task Description: Problem Statement You are playing the following game with Joisino.\n\nInitially, you have a blank sheet of paper.\nJoisino announces a number. If that number is written on the sheet, erase the number from the sheet; if not, write the number on the sheet. This process is repeated N times.\nThen, you are asked a question: How many numbers are written on the sheet now?\n\nThe numbers announced by Joisino are given as A_1, . . . , A_N in the order she announces them. How many numbers will be written on the sheet at the end of the game?\nTask Constraint: 1<=N<=100000\n1<=A_i<=1000000000(=10^9)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print how many numbers will be written on the sheet at the end of the game.\nTask Samples: input: 3\n6\n2\n6 output: 1\n\nThe game proceeds as follows:\n6 is not written on the sheet, so write 6.\n2 is not written on the sheet, so write 2.\n6 is written on the sheet, so erase 6.\nThus, the sheet contains only 2 in the end. The answer is 1.\ninput: 4\n2\n5\n5\n2 output: 0\n\nIt is possible that no number is written on the sheet in the end.\ninput: 6\n12\n22\n16\n22\n18\n12 output: 2\n\n" }, { "title": "", "content": "Problem Statement There are N towns in the State of Atcoder, connected by M bidirectional roads.\nThe i-th road connects Town A_i and B_i and has a length of C_i.\nJoisino is visiting R towns in the state, r_1, r_2, . . , r_R (not necessarily in this order).\nShe will fly to the first town she visits, and fly back from the last town she visits, but for the rest of the trip she will have to travel by road.\nIf she visits the towns in the order that minimizes the distance traveled by road, what will that distance be?", "constraint": "2<=N<=200\n1<=M<=N*(N-1)/2\n2<=R<=min(8,N) (min(8,N) is the smaller of 8 and N.)\nr_i!=r_j (i!=j)\n1<=A_i,B_i<=N, A_i!=B_i\n(A_i,B_i)!=(A_j,B_j),(A_i,B_i)!=(B_j,A_j) (i!=j)\n1<=C_i<=100000\nEvery town can be reached from every town by road.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M R\nr_1 . . . r_R\nA_1 B_1 C_1\n:\nA_M B_M C_M", "output": "Print the distance traveled by road if Joisino visits the towns in the order that minimizes it.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 3\n1 2 3\n1 2 1\n2 3 1\n3 1 4 output: 2\n\nFor example, if she visits the towns in the order of 1,2,3, the distance traveled will be 2, which is the minimum possible.", "input: 3 3 2\n1 3\n2 3 2\n1 3 6\n1 2 2 output: 4\n\nThe shortest distance between Towns 1 and 3 is 4. Thus, whether she visits Town 1 or 3 first, the distance traveled will be 4.", "input: 4 6 3\n2 3 4\n1 2 4\n2 3 3\n4 3 1\n1 4 1\n4 2 2\n3 1 6 output: 3"], "Pid": "p03608", "ProblemText": "Task Description: Problem Statement There are N towns in the State of Atcoder, connected by M bidirectional roads.\nThe i-th road connects Town A_i and B_i and has a length of C_i.\nJoisino is visiting R towns in the state, r_1, r_2, . . , r_R (not necessarily in this order).\nShe will fly to the first town she visits, and fly back from the last town she visits, but for the rest of the trip she will have to travel by road.\nIf she visits the towns in the order that minimizes the distance traveled by road, what will that distance be?\nTask Constraint: 2<=N<=200\n1<=M<=N*(N-1)/2\n2<=R<=min(8,N) (min(8,N) is the smaller of 8 and N.)\nr_i!=r_j (i!=j)\n1<=A_i,B_i<=N, A_i!=B_i\n(A_i,B_i)!=(A_j,B_j),(A_i,B_i)!=(B_j,A_j) (i!=j)\n1<=C_i<=100000\nEvery town can be reached from every town by road.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M R\nr_1 . . . r_R\nA_1 B_1 C_1\n:\nA_M B_M C_M\nTask Output: Print the distance traveled by road if Joisino visits the towns in the order that minimizes it.\nTask Samples: input: 3 3 3\n1 2 3\n1 2 1\n2 3 1\n3 1 4 output: 2\n\nFor example, if she visits the towns in the order of 1,2,3, the distance traveled will be 2, which is the minimum possible.\ninput: 3 3 2\n1 3\n2 3 2\n1 3 6\n1 2 2 output: 4\n\nThe shortest distance between Towns 1 and 3 is 4. Thus, whether she visits Town 1 or 3 first, the distance traveled will be 4.\ninput: 4 6 3\n2 3 4\n1 2 4\n2 3 3\n4 3 1\n1 4 1\n4 2 2\n3 1 6 output: 3\n\n" }, { "title": "", "content": "Problem Statement We have a sandglass that runs for X seconds. The sand drops from the upper bulb at a rate of 1 gram per second. That is, the upper bulb initially contains X grams of sand.\nHow many grams of sand will the upper bulb contains after t seconds?", "constraint": "1<=X<=10^9\n1<=t<=10^9\nX and t are integers.", "input": "Input The input is given from Standard Input in the following format:\nX t", "output": "Print the number of sand in the upper bulb after t second.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100 17 output: 83\n\n17 out of the initial 100 grams of sand will be consumed, resulting in 83 grams.", "input: 48 58 output: 0\n\nAll 48 grams of sand will be gone, resulting in 0 grams.", "input: 1000000000 1000000000 output: 0"], "Pid": "p03609", "ProblemText": "Task Description: Problem Statement We have a sandglass that runs for X seconds. The sand drops from the upper bulb at a rate of 1 gram per second. That is, the upper bulb initially contains X grams of sand.\nHow many grams of sand will the upper bulb contains after t seconds?\nTask Constraint: 1<=X<=10^9\n1<=t<=10^9\nX and t are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nX t\nTask Output: Print the number of sand in the upper bulb after t second.\nTask Samples: input: 100 17 output: 83\n\n17 out of the initial 100 grams of sand will be consumed, resulting in 83 grams.\ninput: 48 58 output: 0\n\nAll 48 grams of sand will be gone, resulting in 0 grams.\ninput: 1000000000 1000000000 output: 0\n\n" }, { "title": "", "content": "Problem Statement You are given a string s consisting of lowercase English letters. Extract all the characters in the odd-indexed positions and print the string obtained by concatenating them. Here, the leftmost character is assigned the index 1.", "constraint": "Each character in s is a lowercase English letter.\n1<=|s|<=10^5", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "Print the string obtained by concatenating all the characters in the odd-numbered positions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: atcoder output: acdr\n\nExtract the first character a, the third character c, the fifth character d and the seventh character r to obtain acdr.", "input: aaaa output: aa", "input: z output: z", "input: fukuokayamaguchi output: fkoaaauh"], "Pid": "p03610", "ProblemText": "Task Description: Problem Statement You are given a string s consisting of lowercase English letters. Extract all the characters in the odd-indexed positions and print the string obtained by concatenating them. Here, the leftmost character is assigned the index 1.\nTask Constraint: Each character in s is a lowercase English letter.\n1<=|s|<=10^5\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: Print the string obtained by concatenating all the characters in the odd-numbered positions.\nTask Samples: input: atcoder output: acdr\n\nExtract the first character a, the third character c, the fifth character d and the seventh character r to obtain acdr.\ninput: aaaa output: aa\ninput: z output: z\ninput: fukuokayamaguchi output: fkoaaauh\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length N, a_1, a_2, . . . , a_N.\nFor each 1<=i<=N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.\nAfter these operations, you select an integer X and count the number of i such that a_i=X.\nMaximize this count by making optimal choices.", "constraint": "1<=N<=10^5\n0<=a_i<10^5 (1<=i<=N)\na_i is an integer.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . a_N", "output": "Print the maximum possible number of i such that a_i=X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n3 1 4 1 5 9 2 output: 4\n\nFor example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.", "input: 10\n0 1 2 3 4 5 6 7 8 9 output: 3", "input: 1\n99999 output: 1"], "Pid": "p03611", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length N, a_1, a_2, . . . , a_N.\nFor each 1<=i<=N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.\nAfter these operations, you select an integer X and count the number of i such that a_i=X.\nMaximize this count by making optimal choices.\nTask Constraint: 1<=N<=10^5\n0<=a_i<10^5 (1<=i<=N)\na_i is an integer.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . a_N\nTask Output: Print the maximum possible number of i such that a_i=X.\nTask Samples: input: 7\n3 1 4 1 5 9 2 output: 4\n\nFor example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.\ninput: 10\n0 1 2 3 4 5 6 7 8 9 output: 3\ninput: 1\n99999 output: 1\n\n" }, { "title": "", "content": "Problem Statement You are given a permutation p_1, p_2, . . . , p_N consisting of 1,2, . . , N.\nYou can perform the following operation any number of times (possibly zero):\nOperation: Swap two adjacent elements in the permutation.\nYou want to have p_i ! = i for all 1<=i<=N.\nFind the minimum required number of operations to achieve this.", "constraint": "2<=N<=10^5\np_1,p_2,..,p_N is a permutation of 1,2,..,N.", "input": "Input The input is given from Standard Input in the following format:\nN\np_1 p_2 . . p_N", "output": "Print the minimum required number of operations", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 4 3 5 2 output: 2\n\nSwap 1 and 4, then swap 1 and 3. p is now 4,3,1,5,2 and satisfies the condition.\nThis is the minimum possible number, so the answer is 2.", "input: 2\n1 2 output: 1\n\nSwapping 1 and 2 satisfies the condition.", "input: 2\n2 1 output: 0\n\nThe condition is already satisfied initially.", "input: 9\n1 2 4 9 5 8 7 3 6 output: 3"], "Pid": "p03612", "ProblemText": "Task Description: Problem Statement You are given a permutation p_1, p_2, . . . , p_N consisting of 1,2, . . , N.\nYou can perform the following operation any number of times (possibly zero):\nOperation: Swap two adjacent elements in the permutation.\nYou want to have p_i ! = i for all 1<=i<=N.\nFind the minimum required number of operations to achieve this.\nTask Constraint: 2<=N<=10^5\np_1,p_2,..,p_N is a permutation of 1,2,..,N.\nTask Input: Input The input is given from Standard Input in the following format:\nN\np_1 p_2 . . p_N\nTask Output: Print the minimum required number of operations\nTask Samples: input: 5\n1 4 3 5 2 output: 2\n\nSwap 1 and 4, then swap 1 and 3. p is now 4,3,1,5,2 and satisfies the condition.\nThis is the minimum possible number, so the answer is 2.\ninput: 2\n1 2 output: 1\n\nSwapping 1 and 2 satisfies the condition.\ninput: 2\n2 1 output: 0\n\nThe condition is already satisfied initially.\ninput: 9\n1 2 4 9 5 8 7 3 6 output: 3\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length N, a_1, a_2, . . . , a_N.\nFor each 1<=i<=N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.\nAfter these operations, you select an integer X and count the number of i such that a_i=X.\nMaximize this count by making optimal choices.", "constraint": "1<=N<=10^5\n0<=a_i<10^5 (1<=i<=N)\na_i is an integer.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . a_N", "output": "Print the maximum possible number of i such that a_i=X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n3 1 4 1 5 9 2 output: 4\n\nFor example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.", "input: 10\n0 1 2 3 4 5 6 7 8 9 output: 3", "input: 1\n99999 output: 1"], "Pid": "p03613", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length N, a_1, a_2, . . . , a_N.\nFor each 1<=i<=N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.\nAfter these operations, you select an integer X and count the number of i such that a_i=X.\nMaximize this count by making optimal choices.\nTask Constraint: 1<=N<=10^5\n0<=a_i<10^5 (1<=i<=N)\na_i is an integer.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . a_N\nTask Output: Print the maximum possible number of i such that a_i=X.\nTask Samples: input: 7\n3 1 4 1 5 9 2 output: 4\n\nFor example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.\ninput: 10\n0 1 2 3 4 5 6 7 8 9 output: 3\ninput: 1\n99999 output: 1\n\n" }, { "title": "", "content": "Problem Statement You are given a permutation p_1, p_2, . . . , p_N consisting of 1,2, . . , N.\nYou can perform the following operation any number of times (possibly zero):\nOperation: Swap two adjacent elements in the permutation.\nYou want to have p_i ! = i for all 1<=i<=N.\nFind the minimum required number of operations to achieve this.", "constraint": "2<=N<=10^5\np_1,p_2,..,p_N is a permutation of 1,2,..,N.", "input": "Input The input is given from Standard Input in the following format:\nN\np_1 p_2 . . p_N", "output": "Print the minimum required number of operations", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 4 3 5 2 output: 2\n\nSwap 1 and 4, then swap 1 and 3. p is now 4,3,1,5,2 and satisfies the condition.\nThis is the minimum possible number, so the answer is 2.", "input: 2\n1 2 output: 1\n\nSwapping 1 and 2 satisfies the condition.", "input: 2\n2 1 output: 0\n\nThe condition is already satisfied initially.", "input: 9\n1 2 4 9 5 8 7 3 6 output: 3"], "Pid": "p03614", "ProblemText": "Task Description: Problem Statement You are given a permutation p_1, p_2, . . . , p_N consisting of 1,2, . . , N.\nYou can perform the following operation any number of times (possibly zero):\nOperation: Swap two adjacent elements in the permutation.\nYou want to have p_i ! = i for all 1<=i<=N.\nFind the minimum required number of operations to achieve this.\nTask Constraint: 2<=N<=10^5\np_1,p_2,..,p_N is a permutation of 1,2,..,N.\nTask Input: Input The input is given from Standard Input in the following format:\nN\np_1 p_2 . . p_N\nTask Output: Print the minimum required number of operations\nTask Samples: input: 5\n1 4 3 5 2 output: 2\n\nSwap 1 and 4, then swap 1 and 3. p is now 4,3,1,5,2 and satisfies the condition.\nThis is the minimum possible number, so the answer is 2.\ninput: 2\n1 2 output: 1\n\nSwapping 1 and 2 satisfies the condition.\ninput: 2\n2 1 output: 0\n\nThe condition is already satisfied initially.\ninput: 9\n1 2 4 9 5 8 7 3 6 output: 3\n\n" }, { "title": "", "content": "Problem Statement You are given N points (x_i, y_i) located on a two-dimensional plane.\nConsider a subset S of the N points that forms a convex polygon.\nHere, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.\n\nFor example, in the figure above, {A, C, E} and {B, D, E} form convex polygons; {A, C, D, E}, {A, B, C, E}, {A, B, C}, {D, E} and {} do not.\nFor a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.\nCompute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.\nHowever, since the sum can be extremely large, print the sum modulo 998244353.", "constraint": "1<=N<=200\n0<=x_i,y_i<10^4 (1<=i<=N)\nIf i!=j, x_i!=x_j or y_i!=y_j.\nx_i and y_i are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N", "output": "Print the sum of all the scores modulo 998244353.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 0\n0 1\n1 0\n1 1 output: 5\n\nWe have five possible sets as S, four sets that form triangles and one set that forms a square. Each of them has a score of 2^0=1, so the answer is 5.", "input: 5\n0 0\n0 1\n0 2\n0 3\n1 1 output: 11\n\nWe have three \"triangles\" with a score of 1 each, two \"triangles\" with a score of 2 each, and one \"triangle\" with a score of 4. Thus, the answer is 11.", "input: 1\n3141 2718 output: 0\n\nThere are no possible set as S, so the answer is 0."], "Pid": "p03615", "ProblemText": "Task Description: Problem Statement You are given N points (x_i, y_i) located on a two-dimensional plane.\nConsider a subset S of the N points that forms a convex polygon.\nHere, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.\n\nFor example, in the figure above, {A, C, E} and {B, D, E} form convex polygons; {A, C, D, E}, {A, B, C, E}, {A, B, C}, {D, E} and {} do not.\nFor a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.\nCompute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.\nHowever, since the sum can be extremely large, print the sum modulo 998244353.\nTask Constraint: 1<=N<=200\n0<=x_i,y_i<10^4 (1<=i<=N)\nIf i!=j, x_i!=x_j or y_i!=y_j.\nx_i and y_i are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\nTask Output: Print the sum of all the scores modulo 998244353.\nTask Samples: input: 4\n0 0\n0 1\n1 0\n1 1 output: 5\n\nWe have five possible sets as S, four sets that form triangles and one set that forms a square. Each of them has a score of 2^0=1, so the answer is 5.\ninput: 5\n0 0\n0 1\n0 2\n0 3\n1 1 output: 11\n\nWe have three \"triangles\" with a score of 1 each, two \"triangles\" with a score of 2 each, and one \"triangle\" with a score of 4. Thus, the answer is 11.\ninput: 1\n3141 2718 output: 0\n\nThere are no possible set as S, so the answer is 0.\n\n" }, { "title": "", "content": "Problem Statement We have a sandglass consisting of two bulbs, bulb A and bulb B. These bulbs contain some amount of sand.\nWhen we put the sandglass, either bulb A or B lies on top of the other and becomes the upper bulb. The other bulb becomes the lower bulb.\nThe sand drops from the upper bulb to the lower bulb at a rate of 1 gram per second.\nWhen the upper bulb no longer contains any sand, nothing happens.\nInitially at time 0, bulb A is the upper bulb and contains a grams of sand; bulb B contains X-a grams of sand (for a total of X grams).\nWe will turn over the sandglass at time r_1, r_2, . . , r_K. Assume that this is an instantaneous action and takes no time. Here, time t refer to the time t seconds after time 0.\nYou are given Q queries.\nEach query is in the form of (t_i, a_i).\nFor each query, assume that a=a_i and find the amount of sand that would be contained in bulb A at time t_i.", "constraint": "1<=X<=10^9\n1<=K<=10^5\n1<=r_1= 1\na_1 + a_2 + ... + a_N = H W", "input": "Input is given from Standard Input in the following format:\nH W\nN\na_1 a_2 . . . a_N", "output": "Print one way to paint the squares that satisfies the conditions.\nOutput in the following format:\nc_{1 1} . . . c_{1 W}\n:\nc_{H 1} . . . c_{H W}\n\nHere, c_{i j} is the color of the square at the i-th row from the top and j-th column from the left.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n3\n2 1 1 output: 1 1\n2 3\n\nBelow is an example of an invalid solution:\n1 2\n3 1\n\nThis is because the squares painted in Color 1 are not 4-connected.", "input: 3 5\n5\n1 2 3 4 5 output: 1 4 4 4 3\n2 5 4 5 3\n2 5 5 5 3", "input: 1 1\n1\n1 output: 1"], "Pid": "p03638", "ProblemText": "Task Description: Problem Statement We have a grid with H rows and W columns of squares.\nSnuke is painting these squares in colors 1,2, . . . , N.\nHere, the following conditions should be satisfied:\n\nFor each i (1 <= i <= N), there are exactly a_i squares painted in Color i. Here, a_1 + a_2 + . . . + a_N = H W.\nFor each i (1 <= i <= N), the squares painted in Color i are 4-connected. That is, every square painted in Color i can be reached from every square painted in Color i by repeatedly traveling to a horizontally or vertically adjacent square painted in Color i.\n\nFind a way to paint the squares so that the conditions are satisfied.\nIt can be shown that a solution always exists.\nTask Constraint: 1 <= H, W <= 100\n1 <= N <= H W\na_i >= 1\na_1 + a_2 + ... + a_N = H W\nTask Input: Input is given from Standard Input in the following format:\nH W\nN\na_1 a_2 . . . a_N\nTask Output: Print one way to paint the squares that satisfies the conditions.\nOutput in the following format:\nc_{1 1} . . . c_{1 W}\n:\nc_{H 1} . . . c_{H W}\n\nHere, c_{i j} is the color of the square at the i-th row from the top and j-th column from the left.\nTask Samples: input: 2 2\n3\n2 1 1 output: 1 1\n2 3\n\nBelow is an example of an invalid solution:\n1 2\n3 1\n\nThis is because the squares painted in Color 1 are not 4-connected.\ninput: 3 5\n5\n1 2 3 4 5 output: 1 4 4 4 3\n2 5 4 5 3\n2 5 5 5 3\ninput: 1 1\n1\n1 output: 1\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of length N, a = (a_1, a_2, . . . , a_N).\nEach a_i is a positive integer.\nSnuke's objective is to permute the element in a so that the following condition is satisfied:\n\nFor each 1 <= i <= N - 1, the product of a_i and a_{i + 1} is a multiple of 4.\n\nDetermine whether Snuke can achieve his objective.", "constraint": "2 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "If Snuke can achieve his objective, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 10 100 output: Yes\n\nOne solution is (1,100,10).", "input: 4\n1 2 3 4 output: No\n\nIt is impossible to permute a so that the condition is satisfied.", "input: 3\n1 4 1 output: Yes\n\nThe condition is already satisfied initially.", "input: 2\n1 1 output: No", "input: 6\n2 7 1 8 2 8 output: Yes"], "Pid": "p03639", "ProblemText": "Task Description: Problem Statement We have a sequence of length N, a = (a_1, a_2, . . . , a_N).\nEach a_i is a positive integer.\nSnuke's objective is to permute the element in a so that the following condition is satisfied:\n\nFor each 1 <= i <= N - 1, the product of a_i and a_{i + 1} is a multiple of 4.\n\nDetermine whether Snuke can achieve his objective.\nTask Constraint: 2 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: If Snuke can achieve his objective, print Yes; otherwise, print No.\nTask Samples: input: 3\n1 10 100 output: Yes\n\nOne solution is (1,100,10).\ninput: 4\n1 2 3 4 output: No\n\nIt is impossible to permute a so that the condition is satisfied.\ninput: 3\n1 4 1 output: Yes\n\nThe condition is already satisfied initially.\ninput: 2\n1 1 output: No\ninput: 6\n2 7 1 8 2 8 output: Yes\n\n" }, { "title": "", "content": "Problem Statement We have a grid with H rows and W columns of squares.\nSnuke is painting these squares in colors 1,2, . . . , N.\nHere, the following conditions should be satisfied:\n\nFor each i (1 <= i <= N), there are exactly a_i squares painted in Color i. Here, a_1 + a_2 + . . . + a_N = H W.\nFor each i (1 <= i <= N), the squares painted in Color i are 4-connected. That is, every square painted in Color i can be reached from every square painted in Color i by repeatedly traveling to a horizontally or vertically adjacent square painted in Color i.\n\nFind a way to paint the squares so that the conditions are satisfied.\nIt can be shown that a solution always exists.", "constraint": "1 <= H, W <= 100\n1 <= N <= H W\na_i >= 1\na_1 + a_2 + ... + a_N = H W", "input": "Input is given from Standard Input in the following format:\nH W\nN\na_1 a_2 . . . a_N", "output": "Print one way to paint the squares that satisfies the conditions.\nOutput in the following format:\nc_{1 1} . . . c_{1 W}\n:\nc_{H 1} . . . c_{H W}\n\nHere, c_{i j} is the color of the square at the i-th row from the top and j-th column from the left.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n3\n2 1 1 output: 1 1\n2 3\n\nBelow is an example of an invalid solution:\n1 2\n3 1\n\nThis is because the squares painted in Color 1 are not 4-connected.", "input: 3 5\n5\n1 2 3 4 5 output: 1 4 4 4 3\n2 5 4 5 3\n2 5 5 5 3", "input: 1 1\n1\n1 output: 1"], "Pid": "p03640", "ProblemText": "Task Description: Problem Statement We have a grid with H rows and W columns of squares.\nSnuke is painting these squares in colors 1,2, . . . , N.\nHere, the following conditions should be satisfied:\n\nFor each i (1 <= i <= N), there are exactly a_i squares painted in Color i. Here, a_1 + a_2 + . . . + a_N = H W.\nFor each i (1 <= i <= N), the squares painted in Color i are 4-connected. That is, every square painted in Color i can be reached from every square painted in Color i by repeatedly traveling to a horizontally or vertically adjacent square painted in Color i.\n\nFind a way to paint the squares so that the conditions are satisfied.\nIt can be shown that a solution always exists.\nTask Constraint: 1 <= H, W <= 100\n1 <= N <= H W\na_i >= 1\na_1 + a_2 + ... + a_N = H W\nTask Input: Input is given from Standard Input in the following format:\nH W\nN\na_1 a_2 . . . a_N\nTask Output: Print one way to paint the squares that satisfies the conditions.\nOutput in the following format:\nc_{1 1} . . . c_{1 W}\n:\nc_{H 1} . . . c_{H W}\n\nHere, c_{i j} is the color of the square at the i-th row from the top and j-th column from the left.\nTask Samples: input: 2 2\n3\n2 1 1 output: 1 1\n2 3\n\nBelow is an example of an invalid solution:\n1 2\n3 1\n\nThis is because the squares painted in Color 1 are not 4-connected.\ninput: 3 5\n5\n1 2 3 4 5 output: 1 4 4 4 3\n2 5 4 5 3\n2 5 5 5 3\ninput: 1 1\n1\n1 output: 1\n\n" }, { "title": "", "content": "Problem Statement Let N be a positive even number.\nWe have a permutation of (1,2, . . . , N), p = (p_1, p_2, . . . , p_N).\nSnuke is constructing another permutation of (1,2, . . . , N), q, following the procedure below.\nFirst, let q be an empty sequence.\nThen, perform the following operation until p becomes empty:\n\nSelect two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.\n\nWhen p becomes empty, q will be a permutation of (1,2, . . . , N).\nFind the lexicographically smallest permutation that can be obtained as q.", "constraint": "N is an even number.\n2 <= N <= 2 * 10^5\np is a permutation of (1,2, ..., N).", "input": "Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N", "output": "Print the lexicographically smallest permutation, with spaces in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 2 4 1 output: 3 1 2 4\n\nThe solution above is obtained as follows:\n\np\nq\n(3,2,4,1)\n()\n↓\n↓\n(3,1)\n(2,4)\n↓\n↓\n()\n(3,1,2,4)", "input: 2\n1 2 output: 1 2", "input: 8\n4 6 3 2 8 5 7 1 output: 3 1 2 7 4 6 8 5\n\nThe solution above is obtained as follows:\n\np\nq\n(4,6,3,2,8,5,7,1)\n()\n↓\n↓\n(4,6,3,2,7,1)\n(8,5)\n↓\n↓\n(3,2,7,1)\n(4,6,8,5)\n↓\n↓\n(3,1)\n(2,7,4,6,8,5)\n↓\n↓\n()\n(3,1,2,7,4,6,8,5)"], "Pid": "p03641", "ProblemText": "Task Description: Problem Statement Let N be a positive even number.\nWe have a permutation of (1,2, . . . , N), p = (p_1, p_2, . . . , p_N).\nSnuke is constructing another permutation of (1,2, . . . , N), q, following the procedure below.\nFirst, let q be an empty sequence.\nThen, perform the following operation until p becomes empty:\n\nSelect two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.\n\nWhen p becomes empty, q will be a permutation of (1,2, . . . , N).\nFind the lexicographically smallest permutation that can be obtained as q.\nTask Constraint: N is an even number.\n2 <= N <= 2 * 10^5\np is a permutation of (1,2, ..., N).\nTask Input: Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N\nTask Output: Print the lexicographically smallest permutation, with spaces in between.\nTask Samples: input: 4\n3 2 4 1 output: 3 1 2 4\n\nThe solution above is obtained as follows:\n\np\nq\n(3,2,4,1)\n()\n↓\n↓\n(3,1)\n(2,4)\n↓\n↓\n()\n(3,1,2,4)\ninput: 2\n1 2 output: 1 2\ninput: 8\n4 6 3 2 8 5 7 1 output: 3 1 2 7 4 6 8 5\n\nThe solution above is obtained as follows:\n\np\nq\n(4,6,3,2,8,5,7,1)\n()\n↓\n↓\n(4,6,3,2,7,1)\n(8,5)\n↓\n↓\n(3,2,7,1)\n(4,6,8,5)\n↓\n↓\n(3,1)\n(2,7,4,6,8,5)\n↓\n↓\n()\n(3,1,2,7,4,6,8,5)\n\n" }, { "title": "", "content": "Problem Statement There are infinitely many cards, numbered 1,2,3, . . .\nInitially, Cards x_1, x_2, . . . , x_N are face up, and the others are face down.\nSnuke can perform the following operation repeatedly:\n\nSelect a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.\n\nSnuke's objective is to have all the cards face down.\nFind the minimum number of operations required to achieve the objective.", "constraint": "1 <= N <= 100\n1 <= x_1 < x_2 < ... < x_N <= 10^7", "input": "Input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N", "output": "Print the minimum number of operations required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4 5 output: 2\n\nBelow is one way to achieve the objective in two operations:\n\nSelect p = 5 and flip Cards 1,2,3,4 and 5.\nSelect p = 3 and flip Cards 1,2 and 3.", "input: 9\n1 2 3 4 5 6 7 8 9 output: 3\n\nBelow is one way to achieve the objective in three operations:\n\nSelect p = 3 and flip Cards 1,2 and 3.\nSelect p = 3 and flip Cards 4,5 and 6.\nSelect p = 3 and flip Cards 7,8 and 9.", "input: 2\n1 10000000 output: 4"], "Pid": "p03642", "ProblemText": "Task Description: Problem Statement There are infinitely many cards, numbered 1,2,3, . . .\nInitially, Cards x_1, x_2, . . . , x_N are face up, and the others are face down.\nSnuke can perform the following operation repeatedly:\n\nSelect a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.\n\nSnuke's objective is to have all the cards face down.\nFind the minimum number of operations required to achieve the objective.\nTask Constraint: 1 <= N <= 100\n1 <= x_1 < x_2 < ... < x_N <= 10^7\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N\nTask Output: Print the minimum number of operations required to achieve the objective.\nTask Samples: input: 2\n4 5 output: 2\n\nBelow is one way to achieve the objective in two operations:\n\nSelect p = 5 and flip Cards 1,2,3,4 and 5.\nSelect p = 3 and flip Cards 1,2 and 3.\ninput: 9\n1 2 3 4 5 6 7 8 9 output: 3\n\nBelow is one way to achieve the objective in three operations:\n\nSelect p = 3 and flip Cards 1,2 and 3.\nSelect p = 3 and flip Cards 4,5 and 6.\nSelect p = 3 and flip Cards 7,8 and 9.\ninput: 2\n1 10000000 output: 4\n\n" }, { "title": "", "content": "Problem Statement This contest, At Coder Beginner Contest, is abbreviated as ABC.\nWhen we refer to a specific round of ABC, a three-digit number is appended after ABC. For example, ABC680 is the 680th round of ABC.\nWhat is the abbreviation for the N-th round of ABC? Write a program to output the answer.", "constraint": "100 <= N <= 999", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the abbreviation for the N-th round of ABC.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 100 output: ABC100\n\nThe 100th round of ABC is ABC100.", "input: 425 output: ABC425", "input: 999 output: ABC999"], "Pid": "p03643", "ProblemText": "Task Description: Problem Statement This contest, At Coder Beginner Contest, is abbreviated as ABC.\nWhen we refer to a specific round of ABC, a three-digit number is appended after ABC. For example, ABC680 is the 680th round of ABC.\nWhat is the abbreviation for the N-th round of ABC? Write a program to output the answer.\nTask Constraint: 100 <= N <= 999\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the abbreviation for the N-th round of ABC.\nTask Samples: input: 100 output: ABC100\n\nThe 100th round of ABC is ABC100.\ninput: 425 output: ABC425\ninput: 999 output: ABC999\n\n" }, { "title": "", "content": "Problem Statement Takahashi loves numbers divisible by 2.\nYou are given a positive integer N. Among the integers between 1 and N (inclusive), find the one that can be divisible by 2 for the most number of times. The solution is always unique.\nHere, the number of times an integer can be divisible by 2, is how many times the integer can be divided by 2 without remainder.\nFor example,\n\n6 can be divided by 2 once: 6 -> 3.\n8 can be divided by 2 three times: 8 -> 4 -> 2 -> 1.\n3 can be divided by 2 zero times.", "constraint": "1 <= N <= 100", "input": "Input is given from Standard Input in the following format:\nN", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 output: 4\n\n4 can be divided by 2 twice, which is the most number of times among 1,2, ..., 7.", "input: 32 output: 32", "input: 1 output: 1", "input: 100 output: 64"], "Pid": "p03644", "ProblemText": "Task Description: Problem Statement Takahashi loves numbers divisible by 2.\nYou are given a positive integer N. Among the integers between 1 and N (inclusive), find the one that can be divisible by 2 for the most number of times. The solution is always unique.\nHere, the number of times an integer can be divisible by 2, is how many times the integer can be divided by 2 without remainder.\nFor example,\n\n6 can be divided by 2 once: 6 -> 3.\n8 can be divided by 2 three times: 8 -> 4 -> 2 -> 1.\n3 can be divided by 2 zero times.\nTask Constraint: 1 <= N <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: Print the answer.\nTask Samples: input: 7 output: 4\n\n4 can be divided by 2 twice, which is the most number of times among 1,2, ..., 7.\ninput: 32 output: 32\ninput: 1 output: 1\ninput: 100 output: 64\n\n" }, { "title": "", "content": "Problem Statement In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.\nFor convenience, we will call them Island 1, Island 2, . . . , Island N.\nThere are M kinds of regular boat services between these islands.\nEach service connects two islands. The i-th service connects Island a_i and Island b_i.\nCat Snuke is on Island 1 now, and wants to go to Island N.\nHowever, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.\nHelp him.", "constraint": "3 <= N <= 200 000\n1 <= M <= 200 000\n1 <= a_i < b_i <= N\n(a_i, b_i) \\neq (1, N)\nIf i \\neq j, (a_i, b_i) \\neq (a_j, b_j).", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M", "output": "If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n2 3 output: POSSIBLE", "input: 4 3\n1 2\n2 3\n3 4 output: IMPOSSIBLE\n\nYou have to use three boat services to get to Island 4.", "input: 100000 1\n1 99999 output: IMPOSSIBLE", "input: 5 5\n1 3\n4 5\n2 3\n2 4\n1 4 output: POSSIBLE\n\nYou can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5."], "Pid": "p03645", "ProblemText": "Task Description: Problem Statement In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.\nFor convenience, we will call them Island 1, Island 2, . . . , Island N.\nThere are M kinds of regular boat services between these islands.\nEach service connects two islands. The i-th service connects Island a_i and Island b_i.\nCat Snuke is on Island 1 now, and wants to go to Island N.\nHowever, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.\nHelp him.\nTask Constraint: 3 <= N <= 200 000\n1 <= M <= 200 000\n1 <= a_i < b_i <= N\n(a_i, b_i) \\neq (1, N)\nIf i \\neq j, (a_i, b_i) \\neq (a_j, b_j).\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Output: If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.\nTask Samples: input: 3 2\n1 2\n2 3 output: POSSIBLE\ninput: 4 3\n1 2\n2 3\n3 4 output: IMPOSSIBLE\n\nYou have to use three boat services to get to Island 4.\ninput: 100000 1\n1 99999 output: IMPOSSIBLE\ninput: 5 5\n1 3\n4 5\n2 3\n2 4\n1 4 output: POSSIBLE\n\nYou can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.\n\nDetermine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.\n\nIt can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.\nYou are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.", "constraint": "0 <= K <= 50 * 10^{16}", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print a solution in the following format:\nN\na_1 a_2 . . . a_N\n\nHere, 2 <= N <= 50 and 0 <= a_i <= 10^{16} + 1000 must hold.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 output: 4\n3 3 3 3", "input: 1 output: 3\n1 0 3", "input: 2 output: 2\n2 2\n\nThe operation will be performed twice: [2,2] -> [0,3] -> [1,1].", "input: 3 output: 7\n27 0 0 0 0 0 0", "input: 1234567894848 output: 10\n1000 193 256 777 0 1 1192 1234567891011 48 425"], "Pid": "p03646", "ProblemText": "Task Description: Problem Statement We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.\n\nDetermine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.\n\nIt can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.\nYou are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.\nTask Constraint: 0 <= K <= 50 * 10^{16}\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print a solution in the following format:\nN\na_1 a_2 . . . a_N\n\nHere, 2 <= N <= 50 and 0 <= a_i <= 10^{16} + 1000 must hold.\nTask Samples: input: 0 output: 4\n3 3 3 3\ninput: 1 output: 3\n1 0 3\ninput: 2 output: 2\n2 2\n\nThe operation will be performed twice: [2,2] -> [0,3] -> [1,1].\ninput: 3 output: 7\n27 0 0 0 0 0 0\ninput: 1234567894848 output: 10\n1000 193 256 777 0 1 1192 1234567891011 48 425\n\n" }, { "title": "", "content": "Problem Statement In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.\nFor convenience, we will call them Island 1, Island 2, . . . , Island N.\nThere are M kinds of regular boat services between these islands.\nEach service connects two islands. The i-th service connects Island a_i and Island b_i.\nCat Snuke is on Island 1 now, and wants to go to Island N.\nHowever, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.\nHelp him.", "constraint": "3 <= N <= 200 000\n1 <= M <= 200 000\n1 <= a_i < b_i <= N\n(a_i, b_i) \\neq (1, N)\nIf i \\neq j, (a_i, b_i) \\neq (a_j, b_j).", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M", "output": "If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n2 3 output: POSSIBLE", "input: 4 3\n1 2\n2 3\n3 4 output: IMPOSSIBLE\n\nYou have to use three boat services to get to Island 4.", "input: 100000 1\n1 99999 output: IMPOSSIBLE", "input: 5 5\n1 3\n4 5\n2 3\n2 4\n1 4 output: POSSIBLE\n\nYou can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5."], "Pid": "p03647", "ProblemText": "Task Description: Problem Statement In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.\nFor convenience, we will call them Island 1, Island 2, . . . , Island N.\nThere are M kinds of regular boat services between these islands.\nEach service connects two islands. The i-th service connects Island a_i and Island b_i.\nCat Snuke is on Island 1 now, and wants to go to Island N.\nHowever, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.\nHelp him.\nTask Constraint: 3 <= N <= 200 000\n1 <= M <= 200 000\n1 <= a_i < b_i <= N\n(a_i, b_i) \\neq (1, N)\nIf i \\neq j, (a_i, b_i) \\neq (a_j, b_j).\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Output: If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.\nTask Samples: input: 3 2\n1 2\n2 3 output: POSSIBLE\ninput: 4 3\n1 2\n2 3\n3 4 output: IMPOSSIBLE\n\nYou have to use three boat services to get to Island 4.\ninput: 100000 1\n1 99999 output: IMPOSSIBLE\ninput: 5 5\n1 3\n4 5\n2 3\n2 4\n1 4 output: POSSIBLE\n\nYou can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.\n\nDetermine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.\n\nIt can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.\nYou are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.", "constraint": "0 <= K <= 50 * 10^{16}", "input": "Input is given from Standard Input in the following format:\nK", "output": "Print a solution in the following format:\nN\na_1 a_2 . . . a_N\n\nHere, 2 <= N <= 50 and 0 <= a_i <= 10^{16} + 1000 must hold.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 output: 4\n3 3 3 3", "input: 1 output: 3\n1 0 3", "input: 2 output: 2\n2 2\n\nThe operation will be performed twice: [2,2] -> [0,3] -> [1,1].", "input: 3 output: 7\n27 0 0 0 0 0 0", "input: 1234567894848 output: 10\n1000 193 256 777 0 1 1192 1234567891011 48 425"], "Pid": "p03648", "ProblemText": "Task Description: Problem Statement We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.\n\nDetermine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.\n\nIt can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.\nYou are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.\nTask Constraint: 0 <= K <= 50 * 10^{16}\nTask Input: Input is given from Standard Input in the following format:\nK\nTask Output: Print a solution in the following format:\nN\na_1 a_2 . . . a_N\n\nHere, 2 <= N <= 50 and 0 <= a_i <= 10^{16} + 1000 must hold.\nTask Samples: input: 0 output: 4\n3 3 3 3\ninput: 1 output: 3\n1 0 3\ninput: 2 output: 2\n2 2\n\nThe operation will be performed twice: [2,2] -> [0,3] -> [1,1].\ninput: 3 output: 7\n27 0 0 0 0 0 0\ninput: 1234567894848 output: 10\n1000 193 256 777 0 1 1192 1234567891011 48 425\n\n" }, { "title": "", "content": "Problem Statement We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller. (The operation is the same as the one in Problem D. )\n\nDetermine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.\n\nIt can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.\nYou are given the sequence a_i. Find the number of times we will perform the above operation.", "constraint": "2 <= N <= 50\n0 <= a_i <= 10^{16} + 1000", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the number of times the operation will be performed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n3 3 3 3 output: 0", "input: 3\n1 0 3 output: 1", "input: 2\n2 2 output: 2", "input: 7\n27 0 0 0 0 0 0 output: 3", "input: 10\n1000 193 256 777 0 1 1192 1234567891011 48 425 output: 1234567894848"], "Pid": "p03649", "ProblemText": "Task Description: Problem Statement We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller. (The operation is the same as the one in Problem D. )\n\nDetermine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.\n\nIt can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.\nYou are given the sequence a_i. Find the number of times we will perform the above operation.\nTask Constraint: 2 <= N <= 50\n0 <= a_i <= 10^{16} + 1000\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the number of times the operation will be performed.\nTask Samples: input: 4\n3 3 3 3 output: 0\ninput: 3\n1 0 3 output: 1\ninput: 2\n2 2 output: 2\ninput: 7\n27 0 0 0 0 0 0 output: 3\ninput: 10\n1000 193 256 777 0 1 1192 1234567891011 48 425 output: 1234567894848\n\n" }, { "title": "", "content": "Problem Statement There is a directed graph with N vertices and N edges. The vertices are numbered 1,2, . . . , N.\nThe graph has the following N edges: (p_1,1), (p_2,2), . . . , (p_N, N), and the graph is weakly connected. Here, an edge from Vertex u to Vertex v is denoted by (u, v), and a weakly connected graph is a graph which would be connected if each edge was bidirectional.\nWe would like to assign a value to each of the vertices in this graph so that the following conditions are satisfied. Here, a_i is the value assigned to Vertex i.\n\nEach a_i is a non-negative integer.\nFor each edge (i, j), a_i \\neq a_j holds.\nFor each i and each integer x(0 <= x < a_i), there exists a vertex j such that the edge (i, j) exists and x = a_j holds.\n\nDetermine whether there exists such an assignment.", "constraint": "2 <= N <= 200 000\n1 <= p_i <= N\np_i \\neq i\nThe graph is weakly connected.", "input": "Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N", "output": "If the assignment is possible, print POSSIBLE; otherwise, print IMPOSSIBLE.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 3 4 1 output: POSSIBLE\n\nThe assignment is possible: {a_i} = {0,1,0,1} or {a_i} = {1,0,1,0}.", "input: 3\n2 3 1 output: IMPOSSIBLE", "input: 4\n2 3 1 1 output: POSSIBLE\n\nThe assignment is possible: {a_i} = {2,0,1,0}.", "input: 6\n4 5 6 5 6 4 output: IMPOSSIBLE"], "Pid": "p03650", "ProblemText": "Task Description: Problem Statement There is a directed graph with N vertices and N edges. The vertices are numbered 1,2, . . . , N.\nThe graph has the following N edges: (p_1,1), (p_2,2), . . . , (p_N, N), and the graph is weakly connected. Here, an edge from Vertex u to Vertex v is denoted by (u, v), and a weakly connected graph is a graph which would be connected if each edge was bidirectional.\nWe would like to assign a value to each of the vertices in this graph so that the following conditions are satisfied. Here, a_i is the value assigned to Vertex i.\n\nEach a_i is a non-negative integer.\nFor each edge (i, j), a_i \\neq a_j holds.\nFor each i and each integer x(0 <= x < a_i), there exists a vertex j such that the edge (i, j) exists and x = a_j holds.\n\nDetermine whether there exists such an assignment.\nTask Constraint: 2 <= N <= 200 000\n1 <= p_i <= N\np_i \\neq i\nThe graph is weakly connected.\nTask Input: Input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N\nTask Output: If the assignment is possible, print POSSIBLE; otherwise, print IMPOSSIBLE.\nTask Samples: input: 4\n2 3 4 1 output: POSSIBLE\n\nThe assignment is possible: {a_i} = {0,1,0,1} or {a_i} = {1,0,1,0}.\ninput: 3\n2 3 1 output: IMPOSSIBLE\ninput: 4\n2 3 1 1 output: POSSIBLE\n\nThe assignment is possible: {a_i} = {2,0,1,0}.\ninput: 6\n4 5 6 5 6 4 output: IMPOSSIBLE\n\n" }, { "title": "", "content": "Problem Statement There is a box containing N balls. The i-th ball has the integer A_i written on it.\nSnuke can perform the following operation any number of times:\n\nTake out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.\n\nDetermine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= K <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N", "output": "If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 7\n9 3 4 output: POSSIBLE\n\nFirst, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.\nNext, take out 3 and 5, and return them back along with abs(3-5)=2.\nFinally, take out 9 and 2, and return them back along with abs(9-2)=7.\nNow we have 7 in the box, and the answer is therefore POSSIBLE.", "input: 3 5\n6 9 3 output: IMPOSSIBLE\n\nNo matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE.", "input: 4 11\n11 3 7 15 output: POSSIBLE\n\nThe box already contains 11 before we do anything. The answer is therefore POSSIBLE.", "input: 5 12\n10 2 8 6 4 output: IMPOSSIBLE"], "Pid": "p03651", "ProblemText": "Task Description: Problem Statement There is a box containing N balls. The i-th ball has the integer A_i written on it.\nSnuke can perform the following operation any number of times:\n\nTake out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.\n\nDetermine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9\n1 <= K <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN K\nA_1 A_2 . . . A_N\nTask Output: If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.\nTask Samples: input: 3 7\n9 3 4 output: POSSIBLE\n\nFirst, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.\nNext, take out 3 and 5, and return them back along with abs(3-5)=2.\nFinally, take out 9 and 2, and return them back along with abs(9-2)=7.\nNow we have 7 in the box, and the answer is therefore POSSIBLE.\ninput: 3 5\n6 9 3 output: IMPOSSIBLE\n\nNo matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE.\ninput: 4 11\n11 3 7 15 output: POSSIBLE\n\nThe box already contains 11 before we do anything. The answer is therefore POSSIBLE.\ninput: 5 12\n10 2 8 6 4 output: IMPOSSIBLE\n\n" }, { "title": "", "content": "Problem Statement Takahashi is hosting an sports meet.\nThere are N people who will participate. These people are conveniently numbered 1 through N.\nAlso, there are M options of sports for this event. These sports are numbered 1 through M.\nAmong these options, Takahashi will select one or more sports (possibly all) to be played in the event.\nTakahashi knows that Person i's j-th favorite sport is Sport A_{ij}.\nEach person will only participate in his/her most favorite sport among the ones that are actually played in the event, and will not participate in the other sports.\nTakahashi is worried that one of the sports will attract too many people.\nTherefore, he would like to carefully select sports to be played so that the number of the participants in the sport with the largest number of participants is minimized.\nFind the minimum possible number of the participants in the sport with the largest number of participants.", "constraint": "1 <= N <= 300\n1 <= M <= 300\nA_{i1} , A_{i2} , ... , A_{iM} is a permutation of the integers from 1 to M.", "input": "Input is given from Standard Input in the following format:\nN M\nA_{11} A_{12} . . . A_{1M}\nA_{21} A_{22} . . . A_{2M}\n:\nA_{N1} A_{N2} . . . A_{NM}", "output": "Print the minimum possible number of the participants in the sport with the largest number of participants.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n5 1 3 4 2\n2 5 3 1 4\n2 3 1 4 5\n2 5 4 3 1 output: 2\n\nAssume that Sports 1,3 and 4 are selected to be played. In this case, Person 1 will participate in Sport 1, Person 2 in Sport 3, Person 3 in Sport 3 and Person 4 in Sport 4.\nHere, the sport with the largest number of participants is Sport 3, with two participants.\nThere is no way to reduce the number of participants in the sport with the largest number of participants to 1. Therefore, the answer is 2.", "input: 3 3\n2 1 3\n2 1 3\n2 1 3 output: 3\n\nSince all the people have the same taste in sports, there will be a sport with three participants, no matter what sports are selected.\nTherefore, the answer is 3."], "Pid": "p03652", "ProblemText": "Task Description: Problem Statement Takahashi is hosting an sports meet.\nThere are N people who will participate. These people are conveniently numbered 1 through N.\nAlso, there are M options of sports for this event. These sports are numbered 1 through M.\nAmong these options, Takahashi will select one or more sports (possibly all) to be played in the event.\nTakahashi knows that Person i's j-th favorite sport is Sport A_{ij}.\nEach person will only participate in his/her most favorite sport among the ones that are actually played in the event, and will not participate in the other sports.\nTakahashi is worried that one of the sports will attract too many people.\nTherefore, he would like to carefully select sports to be played so that the number of the participants in the sport with the largest number of participants is minimized.\nFind the minimum possible number of the participants in the sport with the largest number of participants.\nTask Constraint: 1 <= N <= 300\n1 <= M <= 300\nA_{i1} , A_{i2} , ... , A_{iM} is a permutation of the integers from 1 to M.\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_{11} A_{12} . . . A_{1M}\nA_{21} A_{22} . . . A_{2M}\n:\nA_{N1} A_{N2} . . . A_{NM}\nTask Output: Print the minimum possible number of the participants in the sport with the largest number of participants.\nTask Samples: input: 4 5\n5 1 3 4 2\n2 5 3 1 4\n2 3 1 4 5\n2 5 4 3 1 output: 2\n\nAssume that Sports 1,3 and 4 are selected to be played. In this case, Person 1 will participate in Sport 1, Person 2 in Sport 3, Person 3 in Sport 3 and Person 4 in Sport 4.\nHere, the sport with the largest number of participants is Sport 3, with two participants.\nThere is no way to reduce the number of participants in the sport with the largest number of participants to 1. Therefore, the answer is 2.\ninput: 3 3\n2 1 3\n2 1 3\n2 1 3 output: 3\n\nSince all the people have the same taste in sports, there will be a sport with three participants, no matter what sports are selected.\nTherefore, the answer is 3.\n\n" }, { "title": "", "content": "Problem Statement There are X+Y+Z people, conveniently numbered 1 through X+Y+Z.\nPerson i has A_i gold coins, B_i silver coins and C_i bronze coins.\nSnuke is thinking of getting gold coins from X of those people, silver coins from Y of the people and bronze coins from Z of the people.\nIt is not possible to get two or more different colors of coins from a single person.\nOn the other hand, a person will give all of his/her coins of the color specified by Snuke.\nSnuke would like to maximize the total number of coins of all colors he gets.\nFind the maximum possible number of coins.", "constraint": "1 <= X\n1 <= Y\n1 <= Z\nX+Y+Z <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\n1 <= C_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nX Y Z\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{X+Y+Z} B_{X+Y+Z} C_{X+Y+Z}", "output": "Print the maximum possible total number of coins of all colors he gets.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 2 1\n2 4 4\n3 2 1\n7 6 7\n5 2 3 output: 18\n\nGet silver coins from Person 1, silver coins from Person 2, bronze coins from Person 3 and gold coins from Person 4.\nIn this case, the total number of coins will be 4+2+7+5=18.\nIt is not possible to get 19 or more coins, and the answer is therefore 18.", "input: 3 3 2\n16 17 1\n2 7 5\n2 16 12\n17 7 7\n13 2 10\n12 18 3\n16 15 19\n5 6 2 output: 110", "input: 6 2 4\n33189 87907 277349742\n71616 46764 575306520\n8801 53151 327161251\n58589 4337 796697686\n66854 17565 289910583\n50598 35195 478112689\n13919 88414 103962455\n7953 69657 699253752\n44255 98144 468443709\n2332 42580 752437097\n39752 19060 845062869\n60126 74101 382963164 output: 3093929975"], "Pid": "p03653", "ProblemText": "Task Description: Problem Statement There are X+Y+Z people, conveniently numbered 1 through X+Y+Z.\nPerson i has A_i gold coins, B_i silver coins and C_i bronze coins.\nSnuke is thinking of getting gold coins from X of those people, silver coins from Y of the people and bronze coins from Z of the people.\nIt is not possible to get two or more different colors of coins from a single person.\nOn the other hand, a person will give all of his/her coins of the color specified by Snuke.\nSnuke would like to maximize the total number of coins of all colors he gets.\nFind the maximum possible number of coins.\nTask Constraint: 1 <= X\n1 <= Y\n1 <= Z\nX+Y+Z <= 10^5\n1 <= A_i <= 10^9\n1 <= B_i <= 10^9\n1 <= C_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nX Y Z\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{X+Y+Z} B_{X+Y+Z} C_{X+Y+Z}\nTask Output: Print the maximum possible total number of coins of all colors he gets.\nTask Samples: input: 1 2 1\n2 4 4\n3 2 1\n7 6 7\n5 2 3 output: 18\n\nGet silver coins from Person 1, silver coins from Person 2, bronze coins from Person 3 and gold coins from Person 4.\nIn this case, the total number of coins will be 4+2+7+5=18.\nIt is not possible to get 19 or more coins, and the answer is therefore 18.\ninput: 3 3 2\n16 17 1\n2 7 5\n2 16 12\n17 7 7\n13 2 10\n12 18 3\n16 15 19\n5 6 2 output: 110\ninput: 6 2 4\n33189 87907 277349742\n71616 46764 575306520\n8801 53151 327161251\n58589 4337 796697686\n66854 17565 289910583\n50598 35195 478112689\n13919 88414 103962455\n7953 69657 699253752\n44255 98144 468443709\n2332 42580 752437097\n39752 19060 845062869\n60126 74101 382963164 output: 3093929975\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices, numbered 1 through N.\nThe i-th edge in this tree connects Vertices A_i and B_i and has a length of C_i.\nJoisino created a complete graph with N vertices.\nThe length of the edge connecting Vertices u and v in this graph, is equal to the shortest distance between Vertices u and v in the tree above.\nJoisino would like to know the length of the longest Hamiltonian path (see Notes) in this complete graph.\nFind the length of that path. note: Notes A Hamiltonian path in a graph is a path in the graph that visits each vertex exactly once.", "constraint": "2 <= N <= 10^5\n1 <= A_i < B_i <= N\nThe given graph is a tree.\n1 <= C_i <= 10^8\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{N-1} B_{N-1} C_{N-1}", "output": "Print the length of the longest Hamiltonian path in the complete graph created by Joisino.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2 5\n3 4 7\n2 3 3\n2 5 2 output: 38\n\nThe length of the Hamiltonian path 5 → 3 → 1 → 4 → 2 is 5+8+15+10=38. Since there is no Hamiltonian path with length 39 or greater in the graph, the answer is 38.", "input: 8\n2 8 8\n1 5 1\n4 8 2\n2 5 4\n3 8 6\n6 8 9\n2 7 12 output: 132"], "Pid": "p03654", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices, numbered 1 through N.\nThe i-th edge in this tree connects Vertices A_i and B_i and has a length of C_i.\nJoisino created a complete graph with N vertices.\nThe length of the edge connecting Vertices u and v in this graph, is equal to the shortest distance between Vertices u and v in the tree above.\nJoisino would like to know the length of the longest Hamiltonian path (see Notes) in this complete graph.\nFind the length of that path. note: Notes A Hamiltonian path in a graph is a path in the graph that visits each vertex exactly once.\nTask Constraint: 2 <= N <= 10^5\n1 <= A_i < B_i <= N\nThe given graph is a tree.\n1 <= C_i <= 10^8\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_{N-1} B_{N-1} C_{N-1}\nTask Output: Print the length of the longest Hamiltonian path in the complete graph created by Joisino.\nTask Samples: input: 5\n1 2 5\n3 4 7\n2 3 3\n2 5 2 output: 38\n\nThe length of the Hamiltonian path 5 → 3 → 1 → 4 → 2 is 5+8+15+10=38. Since there is no Hamiltonian path with length 39 or greater in the graph, the answer is 38.\ninput: 8\n2 8 8\n1 5 1\n4 8 2\n2 5 4\n3 8 6\n6 8 9\n2 7 12 output: 132\n\n" }, { "title": "", "content": "Problem Statement Joisino is planning on touring Takahashi Town.\nThe town is divided into square sections by north-south and east-west lines.\nWe will refer to the section that is the x-th from the west and the y-th from the north as (x, y).\nJoisino thinks that a touring plan is good if it satisfies the following conditions:\nLet (p, q) be the section where she starts the tour. Then, X_1 <= p <= X_2 and Y_1 <= q <= Y_2 hold.\nLet (s, t) be the section where she has lunch. Then, X_3 <= s <= X_4 and Y_3 <= t <= Y_4 hold.\nLet (u, v) be the section where she ends the tour. Then, X_5 <= u <= X_6 and Y_5 <= v <= Y_6 hold.\nBy repeatedly moving to the adjacent section (sharing a side), she travels from the starting section to the ending section in the shortest distance, passing the lunch section on the way.\nTwo touring plans are considered different if at least one of the following is different: the starting section, the lunch section, the ending section, and the sections that are visited on the way.\nJoisino would like to know how many different good touring plans there are.\nFind the number of the different good touring plans.\nSince it may be extremely large, find the count modulo 10^9+7.", "constraint": "1 <= X_1 <= X_2 < X_3 <= X_4 < X_5 <= X_6 <= 10^6\n1 <= Y_1 <= Y_2 < Y_3 <= Y_4 < Y_5 <= Y_6 <= 10^6", "input": "Input is given from Standard Input in the following format:\nX_1 X_2 X_3 X_4 X_5 X_6\nY_1 Y_2 Y_3 Y_4 Y_5 Y_6", "output": "Print the number of the different good touring plans, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 2 2 3 4\n1 1 2 2 3 3 output: 10\n\nThe starting section will always be (1,1), and the lunch section will always be (2,2).\nThere are four good touring plans where (3,3) is the ending section, and six good touring plans where (4,3) is the ending section.\nTherefore, the answer is 6+4=10.", "input: 1 2 3 4 5 6\n1 2 3 4 5 6 output: 2346", "input: 77523 89555 420588 604360 845669 973451\n2743 188053 544330 647651 709337 988194 output: 137477680"], "Pid": "p03655", "ProblemText": "Task Description: Problem Statement Joisino is planning on touring Takahashi Town.\nThe town is divided into square sections by north-south and east-west lines.\nWe will refer to the section that is the x-th from the west and the y-th from the north as (x, y).\nJoisino thinks that a touring plan is good if it satisfies the following conditions:\nLet (p, q) be the section where she starts the tour. Then, X_1 <= p <= X_2 and Y_1 <= q <= Y_2 hold.\nLet (s, t) be the section where she has lunch. Then, X_3 <= s <= X_4 and Y_3 <= t <= Y_4 hold.\nLet (u, v) be the section where she ends the tour. Then, X_5 <= u <= X_6 and Y_5 <= v <= Y_6 hold.\nBy repeatedly moving to the adjacent section (sharing a side), she travels from the starting section to the ending section in the shortest distance, passing the lunch section on the way.\nTwo touring plans are considered different if at least one of the following is different: the starting section, the lunch section, the ending section, and the sections that are visited on the way.\nJoisino would like to know how many different good touring plans there are.\nFind the number of the different good touring plans.\nSince it may be extremely large, find the count modulo 10^9+7.\nTask Constraint: 1 <= X_1 <= X_2 < X_3 <= X_4 < X_5 <= X_6 <= 10^6\n1 <= Y_1 <= Y_2 < Y_3 <= Y_4 < Y_5 <= Y_6 <= 10^6\nTask Input: Input is given from Standard Input in the following format:\nX_1 X_2 X_3 X_4 X_5 X_6\nY_1 Y_2 Y_3 Y_4 Y_5 Y_6\nTask Output: Print the number of the different good touring plans, modulo 10^9+7.\nTask Samples: input: 1 1 2 2 3 4\n1 1 2 2 3 3 output: 10\n\nThe starting section will always be (1,1), and the lunch section will always be (2,2).\nThere are four good touring plans where (3,3) is the ending section, and six good touring plans where (4,3) is the ending section.\nTherefore, the answer is 6+4=10.\ninput: 1 2 3 4 5 6\n1 2 3 4 5 6 output: 2346\ninput: 77523 89555 420588 604360 845669 973451\n2743 188053 544330 647651 709337 988194 output: 137477680\n\n" }, { "title": "", "content": "Problem Statement There are two rooted trees, each with N vertices.\nThe vertices of each tree are numbered 1 through N.\nIn the first tree, the parent of Vertex i is Vertex A_i.\nHere, A_i=-1 if Vertex i is the root of the first tree.\nIn the second tree, the parent of Vertex i is Vertex B_i.\nHere, B_i=-1 if Vertex i is the root of the second tree.\nSnuke would like to construct an integer sequence of length N, X_1 , X_2 , . . . , X_N, that satisfies the following condition:\n\nFor each vertex on each tree, let the indices of its descendants including itself be a_1 , a_2 , . . . , a_k. Then, abs(X_{a_1} + X_{a_2} + . . . + X_{a_k})=1 holds.\n\nDetermine whether it is possible to construct such a sequence. If the answer is possible, find one such sequence.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= N, if Vertex i is not the root in the first tree.\nA_i = -1, if Vertex i is the root in the first tree.\n1 <= B_i <= N, if Vertex i is not the root in the second tree.\nB_i = -1, if Vertex i is the root in the second tree.\nInput corresponds to valid rooted trees.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . A_N\nB_1 B_2 . . B_N", "output": "If it is not possible to construct an integer sequence that satisfies the condition, print IMPOSSIBLE.\nIf it is possible, print POSSIBLE in the first line.\nThen, in the second line, print X_1 , X_2 , . . . , X_N, an integer sequence that satisfies the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3 3 4 -1 4\n4 4 1 -1 1 output: POSSIBLE\n1 -1 -1 3 -1\n\nFor example, the indices of the descendants of Vertex 3 of the first tree including itself, is 3,1,2.\nIt can be seen that the sample output holds abs(X_3+X_1+X_2)=abs((-1)+(1)+(-1))=abs(-1)=1.\nSimilarly, the condition is also satisfied for other vertices.", "input: 6\n-1 5 1 5 1 3\n6 5 5 3 -1 3 output: IMPOSSIBLE\n\nIn this case, constructing a sequence that satisfies the condition is IMPOSSIBLE.", "input: 8\n2 7 1 2 2 1 -1 4\n4 -1 4 7 4 4 2 4 output: POSSIBLE\n1 2 -1 0 -1 1 0 -1"], "Pid": "p03656", "ProblemText": "Task Description: Problem Statement There are two rooted trees, each with N vertices.\nThe vertices of each tree are numbered 1 through N.\nIn the first tree, the parent of Vertex i is Vertex A_i.\nHere, A_i=-1 if Vertex i is the root of the first tree.\nIn the second tree, the parent of Vertex i is Vertex B_i.\nHere, B_i=-1 if Vertex i is the root of the second tree.\nSnuke would like to construct an integer sequence of length N, X_1 , X_2 , . . . , X_N, that satisfies the following condition:\n\nFor each vertex on each tree, let the indices of its descendants including itself be a_1 , a_2 , . . . , a_k. Then, abs(X_{a_1} + X_{a_2} + . . . + X_{a_k})=1 holds.\n\nDetermine whether it is possible to construct such a sequence. If the answer is possible, find one such sequence.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= N, if Vertex i is not the root in the first tree.\nA_i = -1, if Vertex i is the root in the first tree.\n1 <= B_i <= N, if Vertex i is not the root in the second tree.\nB_i = -1, if Vertex i is the root in the second tree.\nInput corresponds to valid rooted trees.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . A_N\nB_1 B_2 . . B_N\nTask Output: If it is not possible to construct an integer sequence that satisfies the condition, print IMPOSSIBLE.\nIf it is possible, print POSSIBLE in the first line.\nThen, in the second line, print X_1 , X_2 , . . . , X_N, an integer sequence that satisfies the condition.\nTask Samples: input: 5\n3 3 4 -1 4\n4 4 1 -1 1 output: POSSIBLE\n1 -1 -1 3 -1\n\nFor example, the indices of the descendants of Vertex 3 of the first tree including itself, is 3,1,2.\nIt can be seen that the sample output holds abs(X_3+X_1+X_2)=abs((-1)+(1)+(-1))=abs(-1)=1.\nSimilarly, the condition is also satisfied for other vertices.\ninput: 6\n-1 5 1 5 1 3\n6 5 5 3 -1 3 output: IMPOSSIBLE\n\nIn this case, constructing a sequence that satisfies the condition is IMPOSSIBLE.\ninput: 8\n2 7 1 2 2 1 -1 4\n4 -1 4 7 4 4 2 4 output: POSSIBLE\n1 2 -1 0 -1 1 0 -1\n\n" }, { "title": "", "content": "Problem Statement Snuke is giving cookies to his three goats.\nHe has two cookie tins. One contains A cookies, and the other contains B cookies. He can thus give A cookies, B cookies or A+B cookies to his goats (he cannot open the tins).\nYour task is to determine whether Snuke can give cookies to his three goats so that each of them can have the same number of cookies.", "constraint": "1 <= A,B <= 100\nBoth A and B are integers.", "input": "Input is given from Standard Input in the following format:\nA B", "output": "If it is possible to give cookies so that each of the three goats can have the same number of cookies, print Possible; otherwise, print Impossible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 output: Possible\n\nIf Snuke gives nine cookies, each of the three goats can have three cookies.", "input: 1 1 output: Impossible\n\nSince there are only two cookies, the three goats cannot have the same number of cookies no matter what Snuke gives to them."], "Pid": "p03657", "ProblemText": "Task Description: Problem Statement Snuke is giving cookies to his three goats.\nHe has two cookie tins. One contains A cookies, and the other contains B cookies. He can thus give A cookies, B cookies or A+B cookies to his goats (he cannot open the tins).\nYour task is to determine whether Snuke can give cookies to his three goats so that each of them can have the same number of cookies.\nTask Constraint: 1 <= A,B <= 100\nBoth A and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: If it is possible to give cookies so that each of the three goats can have the same number of cookies, print Possible; otherwise, print Impossible.\nTask Samples: input: 4 5 output: Possible\n\nIf Snuke gives nine cookies, each of the three goats can have three cookies.\ninput: 1 1 output: Impossible\n\nSince there are only two cookies, the three goats cannot have the same number of cookies no matter what Snuke gives to them.\n\n" }, { "title": "", "content": "Problem Statement Snuke has N sticks.\nThe length of the i-th stick is l_i.\nSnuke is making a snake toy by joining K of the sticks together.\nThe length of the toy is represented by the sum of the individual sticks that compose it.\nFind the maximum possible length of the toy.", "constraint": "1 <= K <= N <= 50\n1 <= l_i <= 50\nl_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN K\nl_1 l_2 l_3 . . . l_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 2 3 4 5 output: 12\n\nYou can make a toy of length 12 by joining the sticks of lengths 3,4 and 5, which is the maximum possible length.", "input: 15 14\n50 26 27 21 41 7 42 35 7 5 5 36 39 1 45 output: 386"], "Pid": "p03658", "ProblemText": "Task Description: Problem Statement Snuke has N sticks.\nThe length of the i-th stick is l_i.\nSnuke is making a snake toy by joining K of the sticks together.\nThe length of the toy is represented by the sum of the individual sticks that compose it.\nFind the maximum possible length of the toy.\nTask Constraint: 1 <= K <= N <= 50\n1 <= l_i <= 50\nl_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN K\nl_1 l_2 l_3 . . . l_{N}\nTask Output: Print the answer.\nTask Samples: input: 5 3\n1 2 3 4 5 output: 12\n\nYou can make a toy of length 12 by joining the sticks of lengths 3,4 and 5, which is the maximum possible length.\ninput: 15 14\n50 26 27 21 41 7 42 35 7 5 5 36 39 1 45 output: 386\n\n" }, { "title": "", "content": "Problem Statement Snuke and Raccoon have a heap of N cards. The i-th card from the top has the integer a_i written on it.\nThey will share these cards.\nFirst, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards.\nHere, both Snuke and Raccoon have to take at least one card.\nLet the sum of the integers on Snuke's cards and Raccoon's cards be x and y, respectively.\nThey would like to minimize |x-y|.\nFind the minimum possible value of |x-y|.", "constraint": "2 <= N <= 2 * 10^5\n-10^{9} <= a_i <= 10^{9}\na_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 2 3 4 5 6 output: 1\n\nIf Snuke takes four cards from the top, and Raccoon takes the remaining two cards, x=10, y=11, and thus |x-y|=1. This is the minimum possible value.", "input: 2\n10 -10 output: 20\n\nSnuke can only take one card from the top, and Raccoon can only take the remaining one card. In this case, x=10, y=-10, and thus |x-y|=20."], "Pid": "p03659", "ProblemText": "Task Description: Problem Statement Snuke and Raccoon have a heap of N cards. The i-th card from the top has the integer a_i written on it.\nThey will share these cards.\nFirst, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards.\nHere, both Snuke and Raccoon have to take at least one card.\nLet the sum of the integers on Snuke's cards and Raccoon's cards be x and y, respectively.\nThey would like to minimize |x-y|.\nFind the minimum possible value of |x-y|.\nTask Constraint: 2 <= N <= 2 * 10^5\n-10^{9} <= a_i <= 10^{9}\na_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}\nTask Output: Print the answer.\nTask Samples: input: 6\n1 2 3 4 5 6 output: 1\n\nIf Snuke takes four cards from the top, and Raccoon takes the remaining two cards, x=10, y=11, and thus |x-y|=1. This is the minimum possible value.\ninput: 2\n10 -10 output: 20\n\nSnuke can only take one card from the top, and Raccoon can only take the remaining one card. In this case, x=10, y=-10, and thus |x-y|=20.\n\n" }, { "title": "", "content": "Problem Statement Fennec and Snuke are playing a board game.\nOn the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree.\nInitially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored.\nFennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell.\nMore specifically, each player performs the following action in her/his turn:\n\nFennec: selects an uncolored cell that is adjacent to a black cell, and paints it black.\nSnuke: selects an uncolored cell that is adjacent to a white cell, and paints it white.\n\nA player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally.", "constraint": "2 <= N <= 10^5\n1 <= a_i, b_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}", "output": "If Fennec wins, print Fennec; if Snuke wins, print Snuke.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n3 6\n1 2\n3 1\n7 4\n5 7\n1 4 output: Fennec\n\nFor example, if Fennec first paints Cell 2 black, she will win regardless of Snuke's moves.", "input: 4\n1 4\n4 2\n2 3 output: Snuke"], "Pid": "p03660", "ProblemText": "Task Description: Problem Statement Fennec and Snuke are playing a board game.\nOn the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree.\nInitially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored.\nFennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell.\nMore specifically, each player performs the following action in her/his turn:\n\nFennec: selects an uncolored cell that is adjacent to a black cell, and paints it black.\nSnuke: selects an uncolored cell that is adjacent to a white cell, and paints it white.\n\nA player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally.\nTask Constraint: 2 <= N <= 10^5\n1 <= a_i, b_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nTask Output: If Fennec wins, print Fennec; if Snuke wins, print Snuke.\nTask Samples: input: 7\n3 6\n1 2\n3 1\n7 4\n5 7\n1 4 output: Fennec\n\nFor example, if Fennec first paints Cell 2 black, she will win regardless of Snuke's moves.\ninput: 4\n1 4\n4 2\n2 3 output: Snuke\n\n" }, { "title": "", "content": "Problem Statement Snuke and Raccoon have a heap of N cards. The i-th card from the top has the integer a_i written on it.\nThey will share these cards.\nFirst, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards.\nHere, both Snuke and Raccoon have to take at least one card.\nLet the sum of the integers on Snuke's cards and Raccoon's cards be x and y, respectively.\nThey would like to minimize |x-y|.\nFind the minimum possible value of |x-y|.", "constraint": "2 <= N <= 2 * 10^5\n-10^{9} <= a_i <= 10^{9}\na_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 2 3 4 5 6 output: 1\n\nIf Snuke takes four cards from the top, and Raccoon takes the remaining two cards, x=10, y=11, and thus |x-y|=1. This is the minimum possible value.", "input: 2\n10 -10 output: 20\n\nSnuke can only take one card from the top, and Raccoon can only take the remaining one card. In this case, x=10, y=-10, and thus |x-y|=20."], "Pid": "p03661", "ProblemText": "Task Description: Problem Statement Snuke and Raccoon have a heap of N cards. The i-th card from the top has the integer a_i written on it.\nThey will share these cards.\nFirst, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards.\nHere, both Snuke and Raccoon have to take at least one card.\nLet the sum of the integers on Snuke's cards and Raccoon's cards be x and y, respectively.\nThey would like to minimize |x-y|.\nFind the minimum possible value of |x-y|.\nTask Constraint: 2 <= N <= 2 * 10^5\n-10^{9} <= a_i <= 10^{9}\na_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{N}\nTask Output: Print the answer.\nTask Samples: input: 6\n1 2 3 4 5 6 output: 1\n\nIf Snuke takes four cards from the top, and Raccoon takes the remaining two cards, x=10, y=11, and thus |x-y|=1. This is the minimum possible value.\ninput: 2\n10 -10 output: 20\n\nSnuke can only take one card from the top, and Raccoon can only take the remaining one card. In this case, x=10, y=-10, and thus |x-y|=20.\n\n" }, { "title": "", "content": "Problem Statement Fennec and Snuke are playing a board game.\nOn the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree.\nInitially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored.\nFennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell.\nMore specifically, each player performs the following action in her/his turn:\n\nFennec: selects an uncolored cell that is adjacent to a black cell, and paints it black.\nSnuke: selects an uncolored cell that is adjacent to a white cell, and paints it white.\n\nA player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally.", "constraint": "2 <= N <= 10^5\n1 <= a_i, b_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}", "output": "If Fennec wins, print Fennec; if Snuke wins, print Snuke.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n3 6\n1 2\n3 1\n7 4\n5 7\n1 4 output: Fennec\n\nFor example, if Fennec first paints Cell 2 black, she will win regardless of Snuke's moves.", "input: 4\n1 4\n4 2\n2 3 output: Snuke"], "Pid": "p03662", "ProblemText": "Task Description: Problem Statement Fennec and Snuke are playing a board game.\nOn the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree.\nInitially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored.\nFennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell.\nMore specifically, each player performs the following action in her/his turn:\n\nFennec: selects an uncolored cell that is adjacent to a black cell, and paints it black.\nSnuke: selects an uncolored cell that is adjacent to a white cell, and paints it white.\n\nA player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally.\nTask Constraint: 2 <= N <= 10^5\n1 <= a_i, b_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 b_1\n:\na_{N-1} b_{N-1}\nTask Output: If Fennec wins, print Fennec; if Snuke wins, print Snuke.\nTask Samples: input: 7\n3 6\n1 2\n3 1\n7 4\n5 7\n1 4 output: Fennec\n\nFor example, if Fennec first paints Cell 2 black, she will win regardless of Snuke's moves.\ninput: 4\n1 4\n4 2\n2 3 output: Snuke\n\n" }, { "title": "", "content": "Problem Statement This is an interactive task.\nSnuke has a favorite positive integer, N. You can ask him the following type of question at most 64 times: \"Is n your favorite integer? \" Identify N.\nSnuke is twisted, and when asked \"Is n your favorite integer? \", he answers \"Yes\" if one of the two conditions below is satisfied, and answers \"No\" otherwise:\n\nBoth n <= N and str(n) <= str(N) hold.\nBoth n > N and str(n) > str(N) hold.\n\nHere, str(x) is the decimal representation of x (without leading zeros) as a string. For example, str(123) = 123 and str(2000) = 2000.\nStrings are compared lexicographically. For example, 11111 < 123 and 123456789 < 9. judging: Judging\nAfter each output, you must flush Standard Output. Otherwise you may get TLE.\nAfter you print the answer, the program must be terminated immediately. Otherwise, the behavior of the judge is undefined.\nWhen your output is invalid or incorrect, the behavior of the judge is undefined (it does not necessarily give WA). Input and Output Write your question to Standard Output in the following format:\n? n\n\nHere, n must be an integer between 1 and 10^{18} (inclusive).\nThen, the response to the question shall be given from Standard Input in the following format:\nans\n\nHere, ans is either Y or N. Y represents \"Yes\"; N represents \"No\".\nFinally, write your answer in the following format:\n! n\n\nHere, n=N must hold.", "constraint": "1 <= N <= 10^{9}", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03663", "ProblemText": "Task Description: Problem Statement This is an interactive task.\nSnuke has a favorite positive integer, N. You can ask him the following type of question at most 64 times: \"Is n your favorite integer? \" Identify N.\nSnuke is twisted, and when asked \"Is n your favorite integer? \", he answers \"Yes\" if one of the two conditions below is satisfied, and answers \"No\" otherwise:\n\nBoth n <= N and str(n) <= str(N) hold.\nBoth n > N and str(n) > str(N) hold.\n\nHere, str(x) is the decimal representation of x (without leading zeros) as a string. For example, str(123) = 123 and str(2000) = 2000.\nStrings are compared lexicographically. For example, 11111 < 123 and 123456789 < 9. judging: Judging\nAfter each output, you must flush Standard Output. Otherwise you may get TLE.\nAfter you print the answer, the program must be terminated immediately. Otherwise, the behavior of the judge is undefined.\nWhen your output is invalid or incorrect, the behavior of the judge is undefined (it does not necessarily give WA). Input and Output Write your question to Standard Output in the following format:\n? n\n\nHere, n must be an integer between 1 and 10^{18} (inclusive).\nThen, the response to the question shall be given from Standard Input in the following format:\nans\n\nHere, ans is either Y or N. Y represents \"Yes\"; N represents \"No\".\nFinally, write your answer in the following format:\n! n\n\nHere, n=N must hold.\nTask Constraint: 1 <= N <= 10^{9}\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement Mole decided to live in an abandoned mine. The structure of the mine is represented by a simple connected undirected graph which consists of N vertices numbered 1 through N and M edges.\nThe i-th edge connects Vertices a_i and b_i, and it costs c_i yen (the currency of Japan) to remove it.\nMole would like to remove some of the edges so that there is exactly one path from Vertex 1 to Vertex N that does not visit the same vertex more than once. Find the minimum budget needed to achieve this.", "constraint": "2 <= N <= 15\nN-1 <= M <= N(N-1)/2\n1 <= a_i, b_i <= N\n1 <= c_i <= 10^{6}\nThere are neither multiple edges nor self-loops in the given graph.\nThe given graph is connected.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1 c_1\n:\na_M b_M c_M", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n1 2 100\n3 1 100\n2 4 100\n4 3 100\n1 4 100\n3 2 100 output: 200\n\nBy removing the two edges represented by the red dotted lines in the figure below, the objective can be achieved for a cost of 200 yen.", "input: 2 1\n1 2 1 output: 0\n\nIt is possible that there is already only one path from Vertex 1 to Vertex N in the beginning.", "input: 15 22\n8 13 33418\n14 15 55849\n7 10 15207\n4 6 64328\n6 9 86902\n15 7 46978\n8 14 53526\n1 2 8720\n14 12 37748\n8 3 61543\n6 5 32425\n4 11 20932\n3 12 55123\n8 2 45333\n9 12 77796\n3 9 71922\n12 15 70793\n2 4 25485\n11 6 1436\n2 7 81563\n7 11 97843\n3 1 40491 output: 133677"], "Pid": "p03664", "ProblemText": "Task Description: Problem Statement Mole decided to live in an abandoned mine. The structure of the mine is represented by a simple connected undirected graph which consists of N vertices numbered 1 through N and M edges.\nThe i-th edge connects Vertices a_i and b_i, and it costs c_i yen (the currency of Japan) to remove it.\nMole would like to remove some of the edges so that there is exactly one path from Vertex 1 to Vertex N that does not visit the same vertex more than once. Find the minimum budget needed to achieve this.\nTask Constraint: 2 <= N <= 15\nN-1 <= M <= N(N-1)/2\n1 <= a_i, b_i <= N\n1 <= c_i <= 10^{6}\nThere are neither multiple edges nor self-loops in the given graph.\nThe given graph is connected.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1 c_1\n:\na_M b_M c_M\nTask Output: Print the answer.\nTask Samples: input: 4 6\n1 2 100\n3 1 100\n2 4 100\n4 3 100\n1 4 100\n3 2 100 output: 200\n\nBy removing the two edges represented by the red dotted lines in the figure below, the objective can be achieved for a cost of 200 yen.\ninput: 2 1\n1 2 1 output: 0\n\nIt is possible that there is already only one path from Vertex 1 to Vertex N in the beginning.\ninput: 15 22\n8 13 33418\n14 15 55849\n7 10 15207\n4 6 64328\n6 9 86902\n15 7 46978\n8 14 53526\n1 2 8720\n14 12 37748\n8 3 61543\n6 5 32425\n4 11 20932\n3 12 55123\n8 2 45333\n9 12 77796\n3 9 71922\n12 15 70793\n2 4 25485\n11 6 1436\n2 7 81563\n7 11 97843\n3 1 40491 output: 133677\n\n" }, { "title": "", "content": "Problem Statement There are N bags of biscuits. The i-th bag contains A_i biscuits.\nTakaki will select some of these bags and eat all of the biscuits inside.\nHere, it is also possible to select all or none of the bags.\nHe would like to select bags so that the total number of biscuits inside is congruent to P modulo 2.\nHow many such ways to select bags there are?", "constraint": "1 <= N <= 50\nP = 0 or 1\n1 <= A_i <= 100", "input": "Input is given from Standard Input in the following format:\nN P\nA_1 A_2 . . . A_N", "output": "Print the number of ways to select bags so that the total number of biscuits inside is congruent to P modulo 2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 0\n1 3 output: 2\n\nThere are two ways to select bags so that the total number of biscuits inside is congruent to 0 modulo 2:\n\nSelect neither bag. The total number of biscuits is 0.\nSelect both bags. The total number of biscuits is 4.", "input: 1 1\n50 output: 0", "input: 3 0\n1 1 1 output: 4\n\nTwo bags are distinguished even if they contain the same number of biscuits.", "input: 45 1\n17 55 85 55 74 20 90 67 40 70 39 89 91 50 16 24 14 43 24 66 25 9 89 71 41 16 53 13 61 15 85 72 62 67 42 26 36 66 4 87 59 91 4 25 26 output: 17592186044416"], "Pid": "p03665", "ProblemText": "Task Description: Problem Statement There are N bags of biscuits. The i-th bag contains A_i biscuits.\nTakaki will select some of these bags and eat all of the biscuits inside.\nHere, it is also possible to select all or none of the bags.\nHe would like to select bags so that the total number of biscuits inside is congruent to P modulo 2.\nHow many such ways to select bags there are?\nTask Constraint: 1 <= N <= 50\nP = 0 or 1\n1 <= A_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN P\nA_1 A_2 . . . A_N\nTask Output: Print the number of ways to select bags so that the total number of biscuits inside is congruent to P modulo 2.\nTask Samples: input: 2 0\n1 3 output: 2\n\nThere are two ways to select bags so that the total number of biscuits inside is congruent to 0 modulo 2:\n\nSelect neither bag. The total number of biscuits is 0.\nSelect both bags. The total number of biscuits is 4.\ninput: 1 1\n50 output: 0\ninput: 3 0\n1 1 1 output: 4\n\nTwo bags are distinguished even if they contain the same number of biscuits.\ninput: 45 1\n17 55 85 55 74 20 90 67 40 70 39 89 91 50 16 24 14 43 24 66 25 9 89 71 41 16 53 13 61 15 85 72 62 67 42 26 36 66 4 87 59 91 4 25 26 output: 17592186044416\n\n" }, { "title": "", "content": "Problem Statement There are N squares in a row.\nThe leftmost square contains the integer A, and the rightmost contains the integer B. The other squares are empty.\nAohashi would like to fill the empty squares with integers so that the following condition is satisfied:\n\nFor any two adjacent squares, the (absolute) difference of the two integers in those squares is between C and D (inclusive).\n\nAs long as the condition is satisfied, it is allowed to use arbitrarily large or small integers to fill the squares.\nDetermine whether it is possible to fill the squares under the condition.", "constraint": "3 <= N <= 500000\n0 <= A <= 10^9\n0 <= B <= 10^9\n0 <= C <= D <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN A B C D", "output": "Print YES if it is possible to fill the squares under the condition; print NO otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1 5 2 4 output: YES\n\nFor example, fill the squares with the following integers: 1, -1,3,7,5, from left to right.", "input: 4 7 6 4 5 output: NO", "input: 48792 105960835 681218449 90629745 90632170 output: NO", "input: 491995 412925347 825318103 59999126 59999339 output: YES"], "Pid": "p03666", "ProblemText": "Task Description: Problem Statement There are N squares in a row.\nThe leftmost square contains the integer A, and the rightmost contains the integer B. The other squares are empty.\nAohashi would like to fill the empty squares with integers so that the following condition is satisfied:\n\nFor any two adjacent squares, the (absolute) difference of the two integers in those squares is between C and D (inclusive).\n\nAs long as the condition is satisfied, it is allowed to use arbitrarily large or small integers to fill the squares.\nDetermine whether it is possible to fill the squares under the condition.\nTask Constraint: 3 <= N <= 500000\n0 <= A <= 10^9\n0 <= B <= 10^9\n0 <= C <= D <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B C D\nTask Output: Print YES if it is possible to fill the squares under the condition; print NO otherwise.\nTask Samples: input: 5 1 5 2 4 output: YES\n\nFor example, fill the squares with the following integers: 1, -1,3,7,5, from left to right.\ninput: 4 7 6 4 5 output: NO\ninput: 48792 105960835 681218449 90629745 90632170 output: NO\ninput: 491995 412925347 825318103 59999126 59999339 output: YES\n\n" }, { "title": "", "content": "Problem Statement There are N balls in a row.\nInitially, the i-th ball from the left has the integer A_i written on it.\nWhen Snuke cast a spell, the following happens:\n\nLet the current number of balls be k. All the balls with k written on them disappear at the same time.\n\nSnuke's objective is to vanish all the balls by casting the spell some number of times.\nThis may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.\nBy the way, the integers on these balls sometimes change by themselves.\nThere will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.\nAfter each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are. score: Subscore\nIn the test set worth 500 points, N <= 200 and M <= 200.", "constraint": "1 <= N <= 200000\n1 <= M <= 200000\n1 <= A_i <= N\n1 <= X_j <= N\n1 <= Y_j <= N", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N\nX_1 Y_1\nX_2 Y_2\n:\nX_M Y_M", "output": "Print M lines.\nThe j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n1 1 3 4 5\n1 2\n2 5\n5 4 output: 0\n1\n1\nAfter the first change, the integers on the balls become 2,1,3,4,5, from left to right. Here, all the balls can be vanished by casting the spell five times. Thus, no modification is necessary.\nAfter the second change, the integers on the balls become 2,5,3,4,5, from left to right. In this case, at least one modification must be made. One optimal solution is to modify the integer on the fifth ball from the left to 2, and cast the spell four times.\nAfter the third change, the integers on the balls become 2,5,3,4,4, from left to right. Also in this case, at least one modification must be made. One optimal solution is to modify the integer on the third ball from the left to 2, and cast the spell three times.", "input: 4 4\n4 4 4 4\n4 1\n3 1\n1 1\n2 1 output: 0\n1\n2\n3", "input: 10 10\n8 7 2 9 10 6 6 5 5 4\n8 1\n6 3\n6 2\n7 10\n9 7\n9 9\n2 4\n8 1\n1 8\n7 7 output: 1\n0\n1\n2\n2\n3\n3\n3\n3\n2"], "Pid": "p03667", "ProblemText": "Task Description: Problem Statement There are N balls in a row.\nInitially, the i-th ball from the left has the integer A_i written on it.\nWhen Snuke cast a spell, the following happens:\n\nLet the current number of balls be k. All the balls with k written on them disappear at the same time.\n\nSnuke's objective is to vanish all the balls by casting the spell some number of times.\nThis may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.\nBy the way, the integers on these balls sometimes change by themselves.\nThere will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.\nAfter each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are. score: Subscore\nIn the test set worth 500 points, N <= 200 and M <= 200.\nTask Constraint: 1 <= N <= 200000\n1 <= M <= 200000\n1 <= A_i <= N\n1 <= X_j <= N\n1 <= Y_j <= N\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 A_2 . . . A_N\nX_1 Y_1\nX_2 Y_2\n:\nX_M Y_M\nTask Output: Print M lines.\nThe j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.\nTask Samples: input: 5 3\n1 1 3 4 5\n1 2\n2 5\n5 4 output: 0\n1\n1\nAfter the first change, the integers on the balls become 2,1,3,4,5, from left to right. Here, all the balls can be vanished by casting the spell five times. Thus, no modification is necessary.\nAfter the second change, the integers on the balls become 2,5,3,4,5, from left to right. In this case, at least one modification must be made. One optimal solution is to modify the integer on the fifth ball from the left to 2, and cast the spell four times.\nAfter the third change, the integers on the balls become 2,5,3,4,4, from left to right. Also in this case, at least one modification must be made. One optimal solution is to modify the integer on the third ball from the left to 2, and cast the spell three times.\ninput: 4 4\n4 4 4 4\n4 1\n3 1\n1 1\n2 1 output: 0\n1\n2\n3\ninput: 10 10\n8 7 2 9 10 6 6 5 5 4\n8 1\n6 3\n6 2\n7 10\n9 7\n9 9\n2 4\n8 1\n1 8\n7 7 output: 1\n0\n1\n2\n2\n3\n3\n3\n3\n2\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices numbered 1,2, . . . , N.\nThe edges of the tree are denoted by (x_i, y_i).\nOn this tree, Alice and Bob play a game against each other.\nStarting from Alice, they alternately perform the following operation:\n\nSelect an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.\n\nA player loses the game when he/she is unable to perform the operation.\nDetermine the winner of the game assuming that both players play optimally.", "constraint": "2 <= N <= 100000\n1 <= x_i, y_i <= N\nThe given graph is a tree.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N-1} y_{N-1}", "output": "Print Alice if Alice wins; print Bob if Bob wins.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n2 3\n2 4\n4 5 output: Alice\n\nIf Alice first removes the edge connecting Vertices 1 and 2, the tree becomes a single vertex tree containing only Vertex 1.\nSince there is no edge anymore, Bob cannot perform the operation and Alice wins.", "input: 5\n1 2\n2 3\n1 4\n4 5 output: Bob", "input: 6\n1 2\n2 4\n5 1\n6 3\n3 2 output: Alice", "input: 7\n1 2\n3 7\n4 6\n2 3\n2 4\n1 5 output: Bob"], "Pid": "p03668", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices numbered 1,2, . . . , N.\nThe edges of the tree are denoted by (x_i, y_i).\nOn this tree, Alice and Bob play a game against each other.\nStarting from Alice, they alternately perform the following operation:\n\nSelect an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.\n\nA player loses the game when he/she is unable to perform the operation.\nDetermine the winner of the game assuming that both players play optimally.\nTask Constraint: 2 <= N <= 100000\n1 <= x_i, y_i <= N\nThe given graph is a tree.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_{N-1} y_{N-1}\nTask Output: Print Alice if Alice wins; print Bob if Bob wins.\nTask Samples: input: 5\n1 2\n2 3\n2 4\n4 5 output: Alice\n\nIf Alice first removes the edge connecting Vertices 1 and 2, the tree becomes a single vertex tree containing only Vertex 1.\nSince there is no edge anymore, Bob cannot perform the operation and Alice wins.\ninput: 5\n1 2\n2 3\n1 4\n4 5 output: Bob\ninput: 6\n1 2\n2 4\n5 1\n6 3\n3 2 output: Alice\ninput: 7\n1 2\n3 7\n4 6\n2 3\n2 4\n1 5 output: Bob\n\n" }, { "title": "", "content": "Problem Statement We have N irregular jigsaw pieces. Each piece is composed of three rectangular parts of width 1 and various heights joined together. More specifically:\n\nThe i-th piece is a part of height H, with another part of height A_i joined to the left, and yet another part of height B_i joined to the right, as shown below. Here, the bottom sides of the left and right parts are respectively at C_i and D_i units length above the bottom side of the center part.\nSnuke is arranging these pieces on a square table of side 10^{100}. Here, the following conditions must be held:\n\nAll pieces must be put on the table.\nThe entire bottom side of the center part of each piece must touch the front side of the table.\nThe entire bottom side of the non-center parts of each piece must either touch the front side of the table, or touch the top side of a part of some other piece.\nThe pieces must not be rotated or flipped.\n\nDetermine whether such an arrangement is possible.", "constraint": "1 <= N <= 100000\n1 <= H <= 200\n1 <= A_i <= H\n1 <= B_i <= H\n0 <= C_i <= H - A_i\n0 <= D_i <= H - B_i\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN H\nA_1 B_1 C_1 D_1\nA_2 B_2 C_2 D_2\n:\nA_N B_N C_N D_N", "output": "If it is possible to arrange the pieces under the conditions, print YES; if it is impossible, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n1 1 0 0\n2 2 0 1\n3 3 1 0 output: YES\n\nThe figure below shows a possible arrangement.", "input: 4 2\n1 1 0 1\n1 1 0 1\n1 1 0 1\n1 1 0 1 output: NO", "input: 10 4\n1 1 0 3\n2 3 2 0\n1 2 3 0\n2 1 0 0\n3 2 0 2\n1 1 3 0\n3 2 0 0\n1 3 2 0\n1 1 1 3\n2 3 0 0 output: YES"], "Pid": "p03669", "ProblemText": "Task Description: Problem Statement We have N irregular jigsaw pieces. Each piece is composed of three rectangular parts of width 1 and various heights joined together. More specifically:\n\nThe i-th piece is a part of height H, with another part of height A_i joined to the left, and yet another part of height B_i joined to the right, as shown below. Here, the bottom sides of the left and right parts are respectively at C_i and D_i units length above the bottom side of the center part.\nSnuke is arranging these pieces on a square table of side 10^{100}. Here, the following conditions must be held:\n\nAll pieces must be put on the table.\nThe entire bottom side of the center part of each piece must touch the front side of the table.\nThe entire bottom side of the non-center parts of each piece must either touch the front side of the table, or touch the top side of a part of some other piece.\nThe pieces must not be rotated or flipped.\n\nDetermine whether such an arrangement is possible.\nTask Constraint: 1 <= N <= 100000\n1 <= H <= 200\n1 <= A_i <= H\n1 <= B_i <= H\n0 <= C_i <= H - A_i\n0 <= D_i <= H - B_i\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN H\nA_1 B_1 C_1 D_1\nA_2 B_2 C_2 D_2\n:\nA_N B_N C_N D_N\nTask Output: If it is possible to arrange the pieces under the conditions, print YES; if it is impossible, print NO.\nTask Samples: input: 3 4\n1 1 0 0\n2 2 0 1\n3 3 1 0 output: YES\n\nThe figure below shows a possible arrangement.\ninput: 4 2\n1 1 0 1\n1 1 0 1\n1 1 0 1\n1 1 0 1 output: NO\ninput: 10 4\n1 1 0 3\n2 3 2 0\n1 2 3 0\n2 1 0 0\n3 2 0 2\n1 1 3 0\n3 2 0 0\n1 3 2 0\n1 1 1 3\n2 3 0 0 output: YES\n\n" }, { "title": "", "content": "Problem Statement There are N(N+1)/2 dots arranged to form an equilateral triangle whose sides consist of N dots, as shown below.\nThe j-th dot from the left in the i-th row from the top is denoted by (i, j) (1 <= i <= N, 1 <= j <= i).\nAlso, we will call (i+1, j) immediately lower-left to (i, j), and (i+1, j+1) immediately lower-right to (i, j).\n\nTakahashi is drawing M polygonal lines L_1, L_2, . . . , L_M by connecting these dots.\nEach L_i starts at (1,1), and visits the dot that is immediately lower-left or lower-right to the current dots N-1 times.\nMore formally, there exist X_{i, 1}, . . . , X_{i, N} such that:\n\nL_i connects the N points (1, X_{i, 1}), (2, X_{i, 2}), . . . , (N, X_{i, N}), in this order.\nFor each j=1,2, . . . , N-1, either X_{i, j+1} = X_{i, j} or X_{i, j+1} = X_{i, j}+1 holds.\n\nTakahashi would like to draw these lines so that no part of L_{i+1} is to the left of L_{i}.\nThat is, for each j=1,2, . . . , N, X_{1, j} <= X_{2, j} <= . . . <= X_{M, j} must hold.\nAdditionally, there are K conditions on the shape of the lines that must be followed.\nThe i-th condition is denoted by (A_i, B_i, C_i), which means:\n\nIf C_i=0, L_{A_i} must visit the immediately lower-left dot for the B_i-th move.\nIf C_i=1, L_{A_i} must visit the immediately lower-right dot for the B_i-th move.\n\nThat is, X_{A_i, {B_i}+1} = X_{A_i, B_i} + C_i must hold.\nIn how many ways can Takahashi draw M polygonal lines? Find the count modulo 1000000007. note: Notes Before submission, it is strongly recommended to measure the execution time of your code using \"Custom Test\".", "constraint": "1 <= N <= 20\n1 <= M <= 20\n0 <= K <= (N-1)M\n1 <= A_i <= M\n1 <= B_i <= N-1\nC_i = 0 or 1\nNo pair appears more than once as (A_i, B_i).", "input": "Input is given from Standard Input in the following format:\nN M K\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_K B_K C_K", "output": "Print the number of ways for Takahashi to draw M polygonal lines, modulo 1000000007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 1\n1 2 0 output: 6\n\nThere are six ways to draw lines, as shown below. Here, red lines represent L_1, and green lines represent L_2.", "input: 3 2 2\n1 1 1\n2 1 0 output: 0", "input: 5 4 2\n1 3 1\n4 2 0 output: 172", "input: 20 20 0 output: 881396682"], "Pid": "p03670", "ProblemText": "Task Description: Problem Statement There are N(N+1)/2 dots arranged to form an equilateral triangle whose sides consist of N dots, as shown below.\nThe j-th dot from the left in the i-th row from the top is denoted by (i, j) (1 <= i <= N, 1 <= j <= i).\nAlso, we will call (i+1, j) immediately lower-left to (i, j), and (i+1, j+1) immediately lower-right to (i, j).\n\nTakahashi is drawing M polygonal lines L_1, L_2, . . . , L_M by connecting these dots.\nEach L_i starts at (1,1), and visits the dot that is immediately lower-left or lower-right to the current dots N-1 times.\nMore formally, there exist X_{i, 1}, . . . , X_{i, N} such that:\n\nL_i connects the N points (1, X_{i, 1}), (2, X_{i, 2}), . . . , (N, X_{i, N}), in this order.\nFor each j=1,2, . . . , N-1, either X_{i, j+1} = X_{i, j} or X_{i, j+1} = X_{i, j}+1 holds.\n\nTakahashi would like to draw these lines so that no part of L_{i+1} is to the left of L_{i}.\nThat is, for each j=1,2, . . . , N, X_{1, j} <= X_{2, j} <= . . . <= X_{M, j} must hold.\nAdditionally, there are K conditions on the shape of the lines that must be followed.\nThe i-th condition is denoted by (A_i, B_i, C_i), which means:\n\nIf C_i=0, L_{A_i} must visit the immediately lower-left dot for the B_i-th move.\nIf C_i=1, L_{A_i} must visit the immediately lower-right dot for the B_i-th move.\n\nThat is, X_{A_i, {B_i}+1} = X_{A_i, B_i} + C_i must hold.\nIn how many ways can Takahashi draw M polygonal lines? Find the count modulo 1000000007. note: Notes Before submission, it is strongly recommended to measure the execution time of your code using \"Custom Test\".\nTask Constraint: 1 <= N <= 20\n1 <= M <= 20\n0 <= K <= (N-1)M\n1 <= A_i <= M\n1 <= B_i <= N-1\nC_i = 0 or 1\nNo pair appears more than once as (A_i, B_i).\nTask Input: Input is given from Standard Input in the following format:\nN M K\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_K B_K C_K\nTask Output: Print the number of ways for Takahashi to draw M polygonal lines, modulo 1000000007.\nTask Samples: input: 3 2 1\n1 2 0 output: 6\n\nThere are six ways to draw lines, as shown below. Here, red lines represent L_1, and green lines represent L_2.\ninput: 3 2 2\n1 1 1\n2 1 0 output: 0\ninput: 5 4 2\n1 3 1\n4 2 0 output: 172\ninput: 20 20 0 output: 881396682\n\n" }, { "title": "", "content": "Problem Statement Snuke is buying a bicycle.\nThe bicycle of his choice does not come with a bell, so he has to buy one separately.\nHe has very high awareness of safety, and decides to buy two bells, one for each hand.\nThe store sells three kinds of bells for the price of a, b and c yen (the currency of Japan), respectively.\nFind the minimum total price of two different bells.", "constraint": "1 <= a,b,c <= 10000\na, b and c are integers.", "input": "Input is given from Standard Input in the following format:\na b c", "output": "Print the minimum total price of two different bells.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 700 600 780 output: 1300\nBuying a 700-yen bell and a 600-yen bell costs 1300 yen.\nBuying a 700-yen bell and a 780-yen bell costs 1480 yen.\nBuying a 600-yen bell and a 780-yen bell costs 1380 yen.\n\nThe minimum among these is 1300 yen.", "input: 10000 10000 10000 output: 20000\n\nBuying any two bells costs 20000 yen."], "Pid": "p03671", "ProblemText": "Task Description: Problem Statement Snuke is buying a bicycle.\nThe bicycle of his choice does not come with a bell, so he has to buy one separately.\nHe has very high awareness of safety, and decides to buy two bells, one for each hand.\nThe store sells three kinds of bells for the price of a, b and c yen (the currency of Japan), respectively.\nFind the minimum total price of two different bells.\nTask Constraint: 1 <= a,b,c <= 10000\na, b and c are integers.\nTask Input: Input is given from Standard Input in the following format:\na b c\nTask Output: Print the minimum total price of two different bells.\nTask Samples: input: 700 600 780 output: 1300\nBuying a 700-yen bell and a 600-yen bell costs 1300 yen.\nBuying a 700-yen bell and a 780-yen bell costs 1480 yen.\nBuying a 600-yen bell and a 780-yen bell costs 1380 yen.\n\nThe minimum among these is 1300 yen.\ninput: 10000 10000 10000 output: 20000\n\nBuying any two bells costs 20000 yen.\n\n" }, { "title": "", "content": "Problem Statement We will call a string that can be obtained by concatenating two equal strings an even string.\nFor example, xyzxyz and aaaaaa are even, while ababab and xyzxy are not.\nYou are given an even string S consisting of lowercase English letters.\nFind the length of the longest even string that can be obtained by deleting one or more characters from the end of S.\nIt is guaranteed that such a non-empty string exists for a given input.", "constraint": "2 <= |S| <= 200\nS is an even string consisting of lowercase English letters.\nThere exists a non-empty even string that can be obtained by deleting one or more characters from the end of S.", "input": "Input is given from Standard Input in the following format:\nS", "output": "Print the length of the longest even string that can be obtained.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abaababaab output: 6\nabaababaab itself is even, but we need to delete at least one character.\nabaababaa is not even.\nabaababa is not even.\nabaabab is not even.\nabaaba is even. Thus, we should print its length, 6.", "input: xxxx output: 2\nxxx is not even.\nxx is even.", "input: abcabcabcabc output: 6\n\nThe longest even string that can be obtained is abcabc, whose length is 6.", "input: akasakaakasakasakaakas output: 14\n\nThe longest even string that can be obtained is akasakaakasaka, whose length is 14."], "Pid": "p03672", "ProblemText": "Task Description: Problem Statement We will call a string that can be obtained by concatenating two equal strings an even string.\nFor example, xyzxyz and aaaaaa are even, while ababab and xyzxy are not.\nYou are given an even string S consisting of lowercase English letters.\nFind the length of the longest even string that can be obtained by deleting one or more characters from the end of S.\nIt is guaranteed that such a non-empty string exists for a given input.\nTask Constraint: 2 <= |S| <= 200\nS is an even string consisting of lowercase English letters.\nThere exists a non-empty even string that can be obtained by deleting one or more characters from the end of S.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: Print the length of the longest even string that can be obtained.\nTask Samples: input: abaababaab output: 6\nabaababaab itself is even, but we need to delete at least one character.\nabaababaa is not even.\nabaababa is not even.\nabaabab is not even.\nabaaba is even. Thus, we should print its length, 6.\ninput: xxxx output: 2\nxxx is not even.\nxx is even.\ninput: abcabcabcabc output: 6\n\nThe longest even string that can be obtained is abcabc, whose length is 6.\ninput: akasakaakasakasakaakas output: 14\n\nThe longest even string that can be obtained is akasakaakasaka, whose length is 14.\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length n, a_1, . . . , a_n.\nLet us consider performing the following n operations on an empty sequence b.\nThe i-th operation is as follows:\n\nAppend a_i to the end of b.\nReverse the order of the elements in b.\n\nFind the sequence b obtained after these n operations.", "constraint": "1 <= n <= 2* 10^5\n0 <= a_i <= 10^9\nn and a_i are integers.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n", "output": "Print n integers in a line with spaces in between.\nThe i-th integer should be b_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 3 4 output: 4 2 1 3\nAfter step 1 of the first operation, b becomes: 1.\nAfter step 2 of the first operation, b becomes: 1.\nAfter step 1 of the second operation, b becomes: 1,2.\nAfter step 2 of the second operation, b becomes: 2,1.\nAfter step 1 of the third operation, b becomes: 2,1,3.\nAfter step 2 of the third operation, b becomes: 3,1,2.\nAfter step 1 of the fourth operation, b becomes: 3,1,2,4.\nAfter step 2 of the fourth operation, b becomes: 4,2,1,3.\n\nThus, the answer is 4 2 1 3.", "input: 3\n1 2 3 output: 3 1 2\n\nAs shown above in Sample Output 1, b becomes 3,1,2 after step 2 of the third operation. Thus, the answer is 3 1 2.", "input: 1\n1000000000 output: 1000000000", "input: 6\n0 6 7 6 7 0 output: 0 6 6 0 7 7"], "Pid": "p03673", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length n, a_1, . . . , a_n.\nLet us consider performing the following n operations on an empty sequence b.\nThe i-th operation is as follows:\n\nAppend a_i to the end of b.\nReverse the order of the elements in b.\n\nFind the sequence b obtained after these n operations.\nTask Constraint: 1 <= n <= 2* 10^5\n0 <= a_i <= 10^9\nn and a_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n\nTask Output: Print n integers in a line with spaces in between.\nThe i-th integer should be b_i.\nTask Samples: input: 4\n1 2 3 4 output: 4 2 1 3\nAfter step 1 of the first operation, b becomes: 1.\nAfter step 2 of the first operation, b becomes: 1.\nAfter step 1 of the second operation, b becomes: 1,2.\nAfter step 2 of the second operation, b becomes: 2,1.\nAfter step 1 of the third operation, b becomes: 2,1,3.\nAfter step 2 of the third operation, b becomes: 3,1,2.\nAfter step 1 of the fourth operation, b becomes: 3,1,2,4.\nAfter step 2 of the fourth operation, b becomes: 4,2,1,3.\n\nThus, the answer is 4 2 1 3.\ninput: 3\n1 2 3 output: 3 1 2\n\nAs shown above in Sample Output 1, b becomes 3,1,2 after step 2 of the third operation. Thus, the answer is 3 1 2.\ninput: 1\n1000000000 output: 1000000000\ninput: 6\n0 6 7 6 7 0 output: 0 6 6 0 7 7\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length n+1, a_1, a_2, . . . , a_{n+1}, which consists of the n integers 1, . . . , n.\nIt is known that each of the n integers 1, . . . , n appears at least once in this sequence.\nFor each integer k=1, . . . , n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7. note: Notes\n\nIf the contents of two subsequences are the same, they are not separately counted even if they originate from different positions in the original sequence.\nA subsequence of a sequence a with length k is a sequence obtained by selecting k of the elements of a and arranging them without changing their relative order. For example, the sequences 1,3,5 and 1,2,3 are subsequences of 1,2,3,4,5, while 3,1,2 and 1,10,100 are not.", "constraint": "1 <= n <= 10^5\n1 <= a_i <= n\nEach of the integers 1,...,n appears in the sequence.\nn and a_i are integers.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_{n+1}", "output": "Print n+1 lines.\nThe k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 1 3 output: 3\n5\n4\n1\n\nThere are three subsequences with length 1: 1 and 2 and 3.\nThere are five subsequences with length 2: 1,1 and 1,2 and 1,3 and 2,1 and 2,3.\nThere are four subsequences with length 3: 1,1,3 and 1,2,1 and 1,2,3 and 2,1,3.\nThere is one subsequence with length 4: 1,2,1,3.", "input: 1\n1 1 output: 1\n1\n\nThere is one subsequence with length 1: 1.\nThere is one subsequence with length 2: 1,1.", "input: 32\n29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9 output: 32\n525\n5453\n40919\n237336\n1107568\n4272048\n13884156\n38567100\n92561040\n193536720\n354817320\n573166440\n818809200\n37158313\n166803103\n166803103\n37158313\n818809200\n573166440\n354817320\n193536720\n92561040\n38567100\n13884156\n4272048\n1107568\n237336\n40920\n5456\n528\n33\n1\n\nBe sure to print the numbers modulo 10^9+7."], "Pid": "p03674", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length n+1, a_1, a_2, . . . , a_{n+1}, which consists of the n integers 1, . . . , n.\nIt is known that each of the n integers 1, . . . , n appears at least once in this sequence.\nFor each integer k=1, . . . , n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7. note: Notes\n\nIf the contents of two subsequences are the same, they are not separately counted even if they originate from different positions in the original sequence.\nA subsequence of a sequence a with length k is a sequence obtained by selecting k of the elements of a and arranging them without changing their relative order. For example, the sequences 1,3,5 and 1,2,3 are subsequences of 1,2,3,4,5, while 3,1,2 and 1,10,100 are not.\nTask Constraint: 1 <= n <= 10^5\n1 <= a_i <= n\nEach of the integers 1,...,n appears in the sequence.\nn and a_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_{n+1}\nTask Output: Print n+1 lines.\nThe k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.\nTask Samples: input: 3\n1 2 1 3 output: 3\n5\n4\n1\n\nThere are three subsequences with length 1: 1 and 2 and 3.\nThere are five subsequences with length 2: 1,1 and 1,2 and 1,3 and 2,1 and 2,3.\nThere are four subsequences with length 3: 1,1,3 and 1,2,1 and 1,2,3 and 2,1,3.\nThere is one subsequence with length 4: 1,2,1,3.\ninput: 1\n1 1 output: 1\n1\n\nThere is one subsequence with length 1: 1.\nThere is one subsequence with length 2: 1,1.\ninput: 32\n29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9 output: 32\n525\n5453\n40919\n237336\n1107568\n4272048\n13884156\n38567100\n92561040\n193536720\n354817320\n573166440\n818809200\n37158313\n166803103\n166803103\n37158313\n818809200\n573166440\n354817320\n193536720\n92561040\n38567100\n13884156\n4272048\n1107568\n237336\n40920\n5456\n528\n33\n1\n\nBe sure to print the numbers modulo 10^9+7.\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length n, a_1, . . . , a_n.\nLet us consider performing the following n operations on an empty sequence b.\nThe i-th operation is as follows:\n\nAppend a_i to the end of b.\nReverse the order of the elements in b.\n\nFind the sequence b obtained after these n operations.", "constraint": "1 <= n <= 2* 10^5\n0 <= a_i <= 10^9\nn and a_i are integers.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n", "output": "Print n integers in a line with spaces in between.\nThe i-th integer should be b_i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 3 4 output: 4 2 1 3\nAfter step 1 of the first operation, b becomes: 1.\nAfter step 2 of the first operation, b becomes: 1.\nAfter step 1 of the second operation, b becomes: 1,2.\nAfter step 2 of the second operation, b becomes: 2,1.\nAfter step 1 of the third operation, b becomes: 2,1,3.\nAfter step 2 of the third operation, b becomes: 3,1,2.\nAfter step 1 of the fourth operation, b becomes: 3,1,2,4.\nAfter step 2 of the fourth operation, b becomes: 4,2,1,3.\n\nThus, the answer is 4 2 1 3.", "input: 3\n1 2 3 output: 3 1 2\n\nAs shown above in Sample Output 1, b becomes 3,1,2 after step 2 of the third operation. Thus, the answer is 3 1 2.", "input: 1\n1000000000 output: 1000000000", "input: 6\n0 6 7 6 7 0 output: 0 6 6 0 7 7"], "Pid": "p03675", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length n, a_1, . . . , a_n.\nLet us consider performing the following n operations on an empty sequence b.\nThe i-th operation is as follows:\n\nAppend a_i to the end of b.\nReverse the order of the elements in b.\n\nFind the sequence b obtained after these n operations.\nTask Constraint: 1 <= n <= 2* 10^5\n0 <= a_i <= 10^9\nn and a_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n\nTask Output: Print n integers in a line with spaces in between.\nThe i-th integer should be b_i.\nTask Samples: input: 4\n1 2 3 4 output: 4 2 1 3\nAfter step 1 of the first operation, b becomes: 1.\nAfter step 2 of the first operation, b becomes: 1.\nAfter step 1 of the second operation, b becomes: 1,2.\nAfter step 2 of the second operation, b becomes: 2,1.\nAfter step 1 of the third operation, b becomes: 2,1,3.\nAfter step 2 of the third operation, b becomes: 3,1,2.\nAfter step 1 of the fourth operation, b becomes: 3,1,2,4.\nAfter step 2 of the fourth operation, b becomes: 4,2,1,3.\n\nThus, the answer is 4 2 1 3.\ninput: 3\n1 2 3 output: 3 1 2\n\nAs shown above in Sample Output 1, b becomes 3,1,2 after step 2 of the third operation. Thus, the answer is 3 1 2.\ninput: 1\n1000000000 output: 1000000000\ninput: 6\n0 6 7 6 7 0 output: 0 6 6 0 7 7\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length n+1, a_1, a_2, . . . , a_{n+1}, which consists of the n integers 1, . . . , n.\nIt is known that each of the n integers 1, . . . , n appears at least once in this sequence.\nFor each integer k=1, . . . , n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7. note: Notes\n\nIf the contents of two subsequences are the same, they are not separately counted even if they originate from different positions in the original sequence.\nA subsequence of a sequence a with length k is a sequence obtained by selecting k of the elements of a and arranging them without changing their relative order. For example, the sequences 1,3,5 and 1,2,3 are subsequences of 1,2,3,4,5, while 3,1,2 and 1,10,100 are not.", "constraint": "1 <= n <= 10^5\n1 <= a_i <= n\nEach of the integers 1,...,n appears in the sequence.\nn and a_i are integers.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_{n+1}", "output": "Print n+1 lines.\nThe k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 1 3 output: 3\n5\n4\n1\n\nThere are three subsequences with length 1: 1 and 2 and 3.\nThere are five subsequences with length 2: 1,1 and 1,2 and 1,3 and 2,1 and 2,3.\nThere are four subsequences with length 3: 1,1,3 and 1,2,1 and 1,2,3 and 2,1,3.\nThere is one subsequence with length 4: 1,2,1,3.", "input: 1\n1 1 output: 1\n1\n\nThere is one subsequence with length 1: 1.\nThere is one subsequence with length 2: 1,1.", "input: 32\n29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9 output: 32\n525\n5453\n40919\n237336\n1107568\n4272048\n13884156\n38567100\n92561040\n193536720\n354817320\n573166440\n818809200\n37158313\n166803103\n166803103\n37158313\n818809200\n573166440\n354817320\n193536720\n92561040\n38567100\n13884156\n4272048\n1107568\n237336\n40920\n5456\n528\n33\n1\n\nBe sure to print the numbers modulo 10^9+7."], "Pid": "p03676", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length n+1, a_1, a_2, . . . , a_{n+1}, which consists of the n integers 1, . . . , n.\nIt is known that each of the n integers 1, . . . , n appears at least once in this sequence.\nFor each integer k=1, . . . , n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7. note: Notes\n\nIf the contents of two subsequences are the same, they are not separately counted even if they originate from different positions in the original sequence.\nA subsequence of a sequence a with length k is a sequence obtained by selecting k of the elements of a and arranging them without changing their relative order. For example, the sequences 1,3,5 and 1,2,3 are subsequences of 1,2,3,4,5, while 3,1,2 and 1,10,100 are not.\nTask Constraint: 1 <= n <= 10^5\n1 <= a_i <= n\nEach of the integers 1,...,n appears in the sequence.\nn and a_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_{n+1}\nTask Output: Print n+1 lines.\nThe k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.\nTask Samples: input: 3\n1 2 1 3 output: 3\n5\n4\n1\n\nThere are three subsequences with length 1: 1 and 2 and 3.\nThere are five subsequences with length 2: 1,1 and 1,2 and 1,3 and 2,1 and 2,3.\nThere are four subsequences with length 3: 1,1,3 and 1,2,1 and 1,2,3 and 2,1,3.\nThere is one subsequence with length 4: 1,2,1,3.\ninput: 1\n1 1 output: 1\n1\n\nThere is one subsequence with length 1: 1.\nThere is one subsequence with length 2: 1,1.\ninput: 32\n29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9 output: 32\n525\n5453\n40919\n237336\n1107568\n4272048\n13884156\n38567100\n92561040\n193536720\n354817320\n573166440\n818809200\n37158313\n166803103\n166803103\n37158313\n818809200\n573166440\n354817320\n193536720\n92561040\n38567100\n13884156\n4272048\n1107568\n237336\n40920\n5456\n528\n33\n1\n\nBe sure to print the numbers modulo 10^9+7.\n\n" }, { "title": "", "content": "Problem Statement Snuke is buying a lamp.\nThe light of the lamp can be adjusted to m levels of brightness, represented by integers from 1 through m, by the two buttons on the remote control.\nThe first button is a \"forward\" button. When this button is pressed, the brightness level is increased by 1, except when the brightness level is m, in which case the brightness level becomes 1.\nThe second button is a \"favorite\" button. When this button is pressed, the brightness level becomes the favorite brightness level x, which is set when the lamp is purchased.\nSnuke is thinking of setting the favorite brightness level x so that he can efficiently adjust the brightness.\nHe is planning to change the brightness n-1 times. In the i-th change, the brightness level is changed from a_i to a_{i+1}. The initial brightness level is a_1.\nFind the number of times Snuke needs to press the buttons when x is set to minimize this number.", "constraint": "2 <= n,m <= 10^5\n1 <= a_i<= m\na_i \\neq a_{i+1}\nn, m and a_i are integers.", "input": "Input is given from Standard Input in the following format:\nn m\na_1 a_2 … a_n", "output": "Print the minimum number of times Snuke needs to press the buttons.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n1 5 1 4 output: 5\n\nWhen the favorite brightness level is set to 1,2,3,4,5 and 6, Snuke needs to press the buttons 8,9,7,5,6 and 9 times, respectively.\nThus, Snuke should set the favorite brightness level to 4.\nIn this case, the brightness is adjusted as follows:\n\nIn the first change, press the favorite button once, then press the forward button once.\nIn the second change, press the forward button twice.\nIn the third change, press the favorite button once.", "input: 10 10\n10 9 8 7 6 5 4 3 2 1 output: 45"], "Pid": "p03677", "ProblemText": "Task Description: Problem Statement Snuke is buying a lamp.\nThe light of the lamp can be adjusted to m levels of brightness, represented by integers from 1 through m, by the two buttons on the remote control.\nThe first button is a \"forward\" button. When this button is pressed, the brightness level is increased by 1, except when the brightness level is m, in which case the brightness level becomes 1.\nThe second button is a \"favorite\" button. When this button is pressed, the brightness level becomes the favorite brightness level x, which is set when the lamp is purchased.\nSnuke is thinking of setting the favorite brightness level x so that he can efficiently adjust the brightness.\nHe is planning to change the brightness n-1 times. In the i-th change, the brightness level is changed from a_i to a_{i+1}. The initial brightness level is a_1.\nFind the number of times Snuke needs to press the buttons when x is set to minimize this number.\nTask Constraint: 2 <= n,m <= 10^5\n1 <= a_i<= m\na_i \\neq a_{i+1}\nn, m and a_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nn m\na_1 a_2 … a_n\nTask Output: Print the minimum number of times Snuke needs to press the buttons.\nTask Samples: input: 4 6\n1 5 1 4 output: 5\n\nWhen the favorite brightness level is set to 1,2,3,4,5 and 6, Snuke needs to press the buttons 8,9,7,5,6 and 9 times, respectively.\nThus, Snuke should set the favorite brightness level to 4.\nIn this case, the brightness is adjusted as follows:\n\nIn the first change, press the favorite button once, then press the forward button once.\nIn the second change, press the forward button twice.\nIn the third change, press the favorite button once.\ninput: 10 10\n10 9 8 7 6 5 4 3 2 1 output: 45\n\n" }, { "title": "", "content": "Problem Statement We will call a string that can be obtained by concatenating two equal strings an even string.\nFor example, xyzxyz and aaaaaa are even, while ababab and xyzxy are not.\nFor a non-empty string S, we will define f(S) as the shortest even string that can be obtained by appending one or more characters to the end of S.\nFor example, f(abaaba)=abaababaab.\nIt can be shown that f(S) is uniquely determined for a non-empty string S.\nYou are given an even string S consisting of lowercase English letters.\nFor each letter in the lowercase English alphabet, find the number of its occurrences from the l-th character through the r-th character of f^{10^{100}} (S).\nHere, f^{10^{100}} (S) is the string f(f(f( . . . f(S) . . . ))) obtained by applying f to S 10^{100} times.", "constraint": "2 <= |S| <= 2* 10^5\n1 <= l <= r <= 10^{18}\nS is an even string consisting of lowercase English letters.\nl and r are integers.", "input": "Input is given from Standard Input in the following format:\nS\nl r", "output": "Print 26 integers in a line with spaces in between.\nThe i-th integer should be the number of the occurrences of the i-th letter in the lowercase English alphabet from the l-th character through the r-th character of f^{10^{100}} (S).", "content_img": false, "lang": "en", "error": false, "samples": ["input: abaaba\n6 10 output: 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n\nSince f(abaaba)=abaababaab, the first ten characters in f^{10^{100}}(S) is also abaababaab. Thus, the sixth through the tenth characters are abaab. In this string, a appears three times, b appears twice and no other letters appear, and thus the output should be 3 and 2 followed by twenty-four 0s.", "input: xx\n1 1000000000000000000 output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000000000000000 0 0", "input: vgxgpuamkvgxgvgxgpuamkvgxg\n1 1000000000000000000 output: 87167725689669676 0 0 0 0 0 282080685775825810 0 0 0 87167725689669676 0 87167725689669676 0 0 87167725689669676 0 0 0 0 87167725689669676 141040342887912905 0 141040342887912905 0 0"], "Pid": "p03678", "ProblemText": "Task Description: Problem Statement We will call a string that can be obtained by concatenating two equal strings an even string.\nFor example, xyzxyz and aaaaaa are even, while ababab and xyzxy are not.\nFor a non-empty string S, we will define f(S) as the shortest even string that can be obtained by appending one or more characters to the end of S.\nFor example, f(abaaba)=abaababaab.\nIt can be shown that f(S) is uniquely determined for a non-empty string S.\nYou are given an even string S consisting of lowercase English letters.\nFor each letter in the lowercase English alphabet, find the number of its occurrences from the l-th character through the r-th character of f^{10^{100}} (S).\nHere, f^{10^{100}} (S) is the string f(f(f( . . . f(S) . . . ))) obtained by applying f to S 10^{100} times.\nTask Constraint: 2 <= |S| <= 2* 10^5\n1 <= l <= r <= 10^{18}\nS is an even string consisting of lowercase English letters.\nl and r are integers.\nTask Input: Input is given from Standard Input in the following format:\nS\nl r\nTask Output: Print 26 integers in a line with spaces in between.\nThe i-th integer should be the number of the occurrences of the i-th letter in the lowercase English alphabet from the l-th character through the r-th character of f^{10^{100}} (S).\nTask Samples: input: abaaba\n6 10 output: 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n\nSince f(abaaba)=abaababaab, the first ten characters in f^{10^{100}}(S) is also abaababaab. Thus, the sixth through the tenth characters are abaab. In this string, a appears three times, b appears twice and no other letters appear, and thus the output should be 3 and 2 followed by twenty-four 0s.\ninput: xx\n1 1000000000000000000 output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000000000000000 0 0\ninput: vgxgpuamkvgxgvgxgpuamkvgxg\n1 1000000000000000000 output: 87167725689669676 0 0 0 0 0 282080685775825810 0 0 0 87167725689669676 0 87167725689669676 0 0 87167725689669676 0 0 0 0 87167725689669676 141040342887912905 0 141040342887912905 0 0\n\n" }, { "title": "", "content": "Problem Statement Takahashi has a strong stomach. He never gets a stomachache from eating something whose \"best-by\" date is at most X days earlier.\nHe gets a stomachache if the \"best-by\" date of the food is X+1 or more days earlier, though.\nOther than that, he finds the food delicious if he eats it not later than the \"best-by\" date. Otherwise, he does not find it delicious.\nTakahashi bought some food A days before the \"best-by\" date, and ate it B days after he bought it.\nWrite a program that outputs delicious if he found it delicious, safe if he did not found it delicious but did not get a stomachache either, and dangerous if he got a stomachache.", "constraint": "1 <= X,A,B <= 10^9", "input": "Input is given from Standard Input in the following format:\nX A B", "output": "Print delicious if Takahashi found the food delicious; print safe if he neither found it delicious nor got a stomachache; print dangerous if he got a stomachache.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 6 output: safe\n\nHe ate the food three days after the \"best-by\" date. It was not delicious or harmful for him.", "input: 6 5 1 output: delicious\n\nHe ate the food by the \"best-by\" date. It was delicious for him.", "input: 3 7 12 output: dangerous\n\nHe ate the food five days after the \"best-by\" date. It was harmful for him."], "Pid": "p03679", "ProblemText": "Task Description: Problem Statement Takahashi has a strong stomach. He never gets a stomachache from eating something whose \"best-by\" date is at most X days earlier.\nHe gets a stomachache if the \"best-by\" date of the food is X+1 or more days earlier, though.\nOther than that, he finds the food delicious if he eats it not later than the \"best-by\" date. Otherwise, he does not find it delicious.\nTakahashi bought some food A days before the \"best-by\" date, and ate it B days after he bought it.\nWrite a program that outputs delicious if he found it delicious, safe if he did not found it delicious but did not get a stomachache either, and dangerous if he got a stomachache.\nTask Constraint: 1 <= X,A,B <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nX A B\nTask Output: Print delicious if Takahashi found the food delicious; print safe if he neither found it delicious nor got a stomachache; print dangerous if he got a stomachache.\nTask Samples: input: 4 3 6 output: safe\n\nHe ate the food three days after the \"best-by\" date. It was not delicious or harmful for him.\ninput: 6 5 1 output: delicious\n\nHe ate the food by the \"best-by\" date. It was delicious for him.\ninput: 3 7 12 output: dangerous\n\nHe ate the food five days after the \"best-by\" date. It was harmful for him.\n\n" }, { "title": "", "content": "Problem Statement Takahashi wants to gain muscle, and decides to work out at At Coder Gym.\nThe exercise machine at the gym has N buttons, and exactly one of the buttons is lighten up.\nThese buttons are numbered 1 through N.\nWhen Button i is lighten up and you press it, the light is turned off, and then Button a_i will be lighten up. It is possible that i=a_i.\nWhen Button i is not lighten up, nothing will happen by pressing it.\nInitially, Button 1 is lighten up. Takahashi wants to quit pressing buttons when Button 2 is lighten up.\nDetermine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons.", "constraint": "2 <= N <= 10^5\n1 <= a_i <= N", "input": "Input is given from Standard Input in the following format:\nN\na_1\na_2\n:\na_N", "output": "Print -1 if it is impossible to lighten up Button 2.\nOtherwise, print the minimum number of times we need to press buttons in order to lighten up Button 2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3\n1\n2 output: 2\n\nPress Button 1, then Button 3.", "input: 4\n3\n4\n1\n2 output: -1\n\nPressing Button 1 lightens up Button 3, and vice versa, so Button 2 will never be lighten up.", "input: 5\n3\n3\n4\n2\n4 output: 3"], "Pid": "p03680", "ProblemText": "Task Description: Problem Statement Takahashi wants to gain muscle, and decides to work out at At Coder Gym.\nThe exercise machine at the gym has N buttons, and exactly one of the buttons is lighten up.\nThese buttons are numbered 1 through N.\nWhen Button i is lighten up and you press it, the light is turned off, and then Button a_i will be lighten up. It is possible that i=a_i.\nWhen Button i is not lighten up, nothing will happen by pressing it.\nInitially, Button 1 is lighten up. Takahashi wants to quit pressing buttons when Button 2 is lighten up.\nDetermine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons.\nTask Constraint: 2 <= N <= 10^5\n1 <= a_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN\na_1\na_2\n:\na_N\nTask Output: Print -1 if it is impossible to lighten up Button 2.\nOtherwise, print the minimum number of times we need to press buttons in order to lighten up Button 2.\nTask Samples: input: 3\n3\n1\n2 output: 2\n\nPress Button 1, then Button 3.\ninput: 4\n3\n4\n1\n2 output: -1\n\nPressing Button 1 lightens up Button 3, and vice versa, so Button 2 will never be lighten up.\ninput: 5\n3\n3\n4\n2\n4 output: 3\n\n" }, { "title": "", "content": "Problem Statement Snuke has N dogs and M monkeys. He wants them to line up in a row.\nAs a Japanese saying goes, these dogs and monkeys are on bad terms. (\"ken'en no naka\", literally \"the relationship of dogs and monkeys\", means a relationship of mutual hatred. ) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.\nHow many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that).\nHere, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.", "constraint": "1 <= N,M <= 10^5", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of possible arrangements, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 8\n\nWe will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.", "input: 3 2 output: 12", "input: 1 8 output: 0", "input: 100000 100000 output: 530123477"], "Pid": "p03681", "ProblemText": "Task Description: Problem Statement Snuke has N dogs and M monkeys. He wants them to line up in a row.\nAs a Japanese saying goes, these dogs and monkeys are on bad terms. (\"ken'en no naka\", literally \"the relationship of dogs and monkeys\", means a relationship of mutual hatred. ) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.\nHow many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that).\nHere, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.\nTask Constraint: 1 <= N,M <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of possible arrangements, modulo 10^9+7.\nTask Samples: input: 2 2 output: 8\n\nWe will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.\ninput: 3 2 output: 12\ninput: 1 8 output: 0\ninput: 100000 100000 output: 530123477\n\n" }, { "title": "", "content": "Problem Statement There are N towns on a plane. The i-th town is located at the coordinates (x_i, y_i). There may be more than one town at the same coordinates.\nYou can build a road between two towns at coordinates (a, b) and (c, d) for a cost of min(|a-c|, |b-d|) yen (the currency of Japan). It is not possible to build other types of roads.\nYour objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?", "constraint": "2 <= N <= 10^5\n0 <= x_i,y_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N", "output": "Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 5\n3 9\n7 8 output: 3\n\nBuild a road between Towns 1 and 2, and another between Towns 2 and 3. The total cost is 2+1=3 yen.", "input: 6\n8 3\n4 9\n12 19\n18 1\n13 5\n7 6 output: 8"], "Pid": "p03682", "ProblemText": "Task Description: Problem Statement There are N towns on a plane. The i-th town is located at the coordinates (x_i, y_i). There may be more than one town at the same coordinates.\nYou can build a road between two towns at coordinates (a, b) and (c, d) for a cost of min(|a-c|, |b-d|) yen (the currency of Japan). It is not possible to build other types of roads.\nYour objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?\nTask Constraint: 2 <= N <= 10^5\n0 <= x_i,y_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\nTask Output: Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.\nTask Samples: input: 3\n1 5\n3 9\n7 8 output: 3\n\nBuild a road between Towns 1 and 2, and another between Towns 2 and 3. The total cost is 2+1=3 yen.\ninput: 6\n8 3\n4 9\n12 19\n18 1\n13 5\n7 6 output: 8\n\n" }, { "title": "", "content": "Problem Statement Snuke has N dogs and M monkeys. He wants them to line up in a row.\nAs a Japanese saying goes, these dogs and monkeys are on bad terms. (\"ken'en no naka\", literally \"the relationship of dogs and monkeys\", means a relationship of mutual hatred. ) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.\nHow many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that).\nHere, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.", "constraint": "1 <= N,M <= 10^5", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the number of possible arrangements, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 8\n\nWe will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.", "input: 3 2 output: 12", "input: 1 8 output: 0", "input: 100000 100000 output: 530123477"], "Pid": "p03683", "ProblemText": "Task Description: Problem Statement Snuke has N dogs and M monkeys. He wants them to line up in a row.\nAs a Japanese saying goes, these dogs and monkeys are on bad terms. (\"ken'en no naka\", literally \"the relationship of dogs and monkeys\", means a relationship of mutual hatred. ) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.\nHow many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that).\nHere, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.\nTask Constraint: 1 <= N,M <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of possible arrangements, modulo 10^9+7.\nTask Samples: input: 2 2 output: 8\n\nWe will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.\ninput: 3 2 output: 12\ninput: 1 8 output: 0\ninput: 100000 100000 output: 530123477\n\n" }, { "title": "", "content": "Problem Statement There are N towns on a plane. The i-th town is located at the coordinates (x_i, y_i). There may be more than one town at the same coordinates.\nYou can build a road between two towns at coordinates (a, b) and (c, d) for a cost of min(|a-c|, |b-d|) yen (the currency of Japan). It is not possible to build other types of roads.\nYour objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?", "constraint": "2 <= N <= 10^5\n0 <= x_i,y_i <= 10^9\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N", "output": "Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 5\n3 9\n7 8 output: 3\n\nBuild a road between Towns 1 and 2, and another between Towns 2 and 3. The total cost is 2+1=3 yen.", "input: 6\n8 3\n4 9\n12 19\n18 1\n13 5\n7 6 output: 8"], "Pid": "p03684", "ProblemText": "Task Description: Problem Statement There are N towns on a plane. The i-th town is located at the coordinates (x_i, y_i). There may be more than one town at the same coordinates.\nYou can build a road between two towns at coordinates (a, b) and (c, d) for a cost of min(|a-c|, |b-d|) yen (the currency of Japan). It is not possible to build other types of roads.\nYour objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?\nTask Constraint: 2 <= N <= 10^5\n0 <= x_i,y_i <= 10^9\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\nTask Output: Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.\nTask Samples: input: 3\n1 5\n3 9\n7 8 output: 3\n\nBuild a road between Towns 1 and 2, and another between Towns 2 and 3. The total cost is 2+1=3 yen.\ninput: 6\n8 3\n4 9\n12 19\n18 1\n13 5\n7 6 output: 8\n\n" }, { "title": "", "content": "Problem Statement Snuke is playing a puzzle game.\nIn this game, you are given a rectangular board of dimensions R * C, filled with numbers. Each integer i from 1 through N is written twice, at the coordinates (x_{i, 1}, y_{i, 1}) and (x_{i, 2}, y_{i, 2}).\nThe objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from 1 through N.\nHere, the curves may not go outside the board or cross each other.\nDetermine whether this is possible.", "constraint": "1 <= R,C <= 10^8\n1 <= N <= 10^5\n0 <= x_{i,1},x_{i,2} <= R(1 <= i <= N)\n0 <= y_{i,1},y_{i,2} <= C(1 <= i <= N)\nAll given points are distinct.\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nR C N\nx_{1,1} y_{1,1} x_{1,2} y_{1,2}\n:\nx_{N, 1} y_{N, 1} x_{N, 2} y_{N, 2}", "output": "Print YES if the objective is achievable; print NO otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 3\n0 1 3 1\n1 1 4 1\n2 0 2 2 output: YES\nThe above figure shows a possible solution.", "input: 2 2 4\n0 0 2 2\n2 0 0 1\n0 2 1 2\n1 1 2 1 output: NO", "input: 5 5 7\n0 0 2 4\n2 3 4 5\n3 5 5 2\n5 5 5 4\n0 3 5 1\n2 2 4 4\n0 5 4 1 output: YES", "input: 1 1 2\n0 0 1 1\n1 0 0 1 output: NO"], "Pid": "p03685", "ProblemText": "Task Description: Problem Statement Snuke is playing a puzzle game.\nIn this game, you are given a rectangular board of dimensions R * C, filled with numbers. Each integer i from 1 through N is written twice, at the coordinates (x_{i, 1}, y_{i, 1}) and (x_{i, 2}, y_{i, 2}).\nThe objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from 1 through N.\nHere, the curves may not go outside the board or cross each other.\nDetermine whether this is possible.\nTask Constraint: 1 <= R,C <= 10^8\n1 <= N <= 10^5\n0 <= x_{i,1},x_{i,2} <= R(1 <= i <= N)\n0 <= y_{i,1},y_{i,2} <= C(1 <= i <= N)\nAll given points are distinct.\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nR C N\nx_{1,1} y_{1,1} x_{1,2} y_{1,2}\n:\nx_{N, 1} y_{N, 1} x_{N, 2} y_{N, 2}\nTask Output: Print YES if the objective is achievable; print NO otherwise.\nTask Samples: input: 4 2 3\n0 1 3 1\n1 1 4 1\n2 0 2 2 output: YES\nThe above figure shows a possible solution.\ninput: 2 2 4\n0 0 2 2\n2 0 0 1\n0 2 1 2\n1 1 2 1 output: NO\ninput: 5 5 7\n0 0 2 4\n2 3 4 5\n3 5 5 2\n5 5 5 4\n0 3 5 1\n2 2 4 4\n0 5 4 1 output: YES\ninput: 1 1 2\n0 0 1 1\n1 0 0 1 output: NO\n\n" }, { "title": "", "content": "Problem Statement There are M chairs arranged in a line. The coordinate of the i-th chair (1 <= i <= M) is i.\nN people of the Takahashi clan played too much games, and they are all suffering from backaches. They need to sit in chairs and rest, but they are particular about which chairs they sit in. Specifically, the i-th person wishes to sit in a chair whose coordinate is not greater than L_i, or not less than R_i. Naturally, only one person can sit in the same chair.\nIt may not be possible for all of them to sit in their favorite chairs, if nothing is done.\nAoki, who cares for the health of the people of the Takahashi clan, decides to provide additional chairs so that all of them can sit in chairs at their favorite positions.\nAdditional chairs can be placed at arbitrary real coordinates. Find the minimum required number of additional chairs.", "constraint": "1 <= N,M <= 2 * 10^5\n0 <= L_i < R_i <= M + 1(1 <= i <= N)\nAll input values are integers.", "input": "Input is given from Standard Input in the following format:\nN M\nL_1 R_1\n:\nL_N R_N", "output": "Print the minimum required number of additional chairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4\n0 3\n2 3\n1 3\n3 4 output: 0\n\nThe four people can sit in chairs at the coordinates 3,2,1 and 4, respectively, and no more chair is needed.", "input: 7 6\n0 7\n1 5\n3 6\n2 7\n1 6\n2 6\n3 7 output: 2\n\nIf we place additional chairs at the coordinates 0 and 2.5, the seven people can sit at coordinates 0,5,3,2,6,1 and 2.5, respectively.", "input: 3 1\n1 2\n1 2\n1 2 output: 2", "input: 6 6\n1 6\n1 6\n1 5\n1 5\n2 6\n2 6 output: 2"], "Pid": "p03686", "ProblemText": "Task Description: Problem Statement There are M chairs arranged in a line. The coordinate of the i-th chair (1 <= i <= M) is i.\nN people of the Takahashi clan played too much games, and they are all suffering from backaches. They need to sit in chairs and rest, but they are particular about which chairs they sit in. Specifically, the i-th person wishes to sit in a chair whose coordinate is not greater than L_i, or not less than R_i. Naturally, only one person can sit in the same chair.\nIt may not be possible for all of them to sit in their favorite chairs, if nothing is done.\nAoki, who cares for the health of the people of the Takahashi clan, decides to provide additional chairs so that all of them can sit in chairs at their favorite positions.\nAdditional chairs can be placed at arbitrary real coordinates. Find the minimum required number of additional chairs.\nTask Constraint: 1 <= N,M <= 2 * 10^5\n0 <= L_i < R_i <= M + 1(1 <= i <= N)\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format:\nN M\nL_1 R_1\n:\nL_N R_N\nTask Output: Print the minimum required number of additional chairs.\nTask Samples: input: 4 4\n0 3\n2 3\n1 3\n3 4 output: 0\n\nThe four people can sit in chairs at the coordinates 3,2,1 and 4, respectively, and no more chair is needed.\ninput: 7 6\n0 7\n1 5\n3 6\n2 7\n1 6\n2 6\n3 7 output: 2\n\nIf we place additional chairs at the coordinates 0 and 2.5, the seven people can sit at coordinates 0,5,3,2,6,1 and 2.5, respectively.\ninput: 3 1\n1 2\n1 2\n1 2 output: 2\ninput: 6 6\n1 6\n1 6\n1 5\n1 5\n2 6\n2 6 output: 2\n\n" }, { "title": "", "content": "Problem Statement Snuke can change a string t of length N into a string t' of length N - 1 under the following rule:\n\nFor each i (1 <= i <= N - 1), the i-th character of t' must be either the i-th or (i + 1)-th character of t.\n\nThere is a string s consisting of lowercase English letters.\nSnuke's objective is to apply the above operation to s repeatedly so that all the characters in s are the same.\nFind the minimum necessary number of operations.", "constraint": "1 <= |s| <= 100\ns consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\ns", "output": "Print the minimum necessary number of operations to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: serval output: 3\n\nOne solution is: serval → srvvl → svvv → vvv.", "input: jackal output: 2\n\nOne solution is: jackal → aacaa → aaaa.", "input: zzz output: 0\n\nAll the characters in s are the same from the beginning.", "input: whbrjpjyhsrywlqjxdbrbaomnw output: 8\n\nIn 8 operations, he can change s to rrrrrrrrrrrrrrrrrr."], "Pid": "p03687", "ProblemText": "Task Description: Problem Statement Snuke can change a string t of length N into a string t' of length N - 1 under the following rule:\n\nFor each i (1 <= i <= N - 1), the i-th character of t' must be either the i-th or (i + 1)-th character of t.\n\nThere is a string s consisting of lowercase English letters.\nSnuke's objective is to apply the above operation to s repeatedly so that all the characters in s are the same.\nFind the minimum necessary number of operations.\nTask Constraint: 1 <= |s| <= 100\ns consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\ns\nTask Output: Print the minimum necessary number of operations to achieve the objective.\nTask Samples: input: serval output: 3\n\nOne solution is: serval → srvvl → svvv → vvv.\ninput: jackal output: 2\n\nOne solution is: jackal → aacaa → aaaa.\ninput: zzz output: 0\n\nAll the characters in s are the same from the beginning.\ninput: whbrjpjyhsrywlqjxdbrbaomnw output: 8\n\nIn 8 operations, he can change s to rrrrrrrrrrrrrrrrrr.\n\n" }, { "title": "", "content": "Problem Statement There are N cats.\nWe number them from 1 through N.\nEach of the cats wears a hat.\nCat i says: \"there are exactly a_i different colors among the N - 1 hats worn by the cats except me. \"\nDetermine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.", "constraint": "2 <= N <= 10^5\n1 <= a_i <= N-1", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 2 output: Yes\n\nFor example, if cat 1,2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.", "input: 3\n1 1 2 output: No\n\nFrom the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.\nAlso, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.\nTherefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.", "input: 5\n4 3 4 3 4 output: No", "input: 3\n2 2 2 output: Yes", "input: 4\n2 2 2 2 output: Yes", "input: 5\n3 3 3 3 3 output: No"], "Pid": "p03688", "ProblemText": "Task Description: Problem Statement There are N cats.\nWe number them from 1 through N.\nEach of the cats wears a hat.\nCat i says: \"there are exactly a_i different colors among the N - 1 hats worn by the cats except me. \"\nDetermine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.\nTask Constraint: 2 <= N <= 10^5\n1 <= a_i <= N-1\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.\nTask Samples: input: 3\n1 2 2 output: Yes\n\nFor example, if cat 1,2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.\ninput: 3\n1 1 2 output: No\n\nFrom the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.\nAlso, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.\nTherefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.\ninput: 5\n4 3 4 3 4 output: No\ninput: 3\n2 2 2 output: Yes\ninput: 4\n2 2 2 2 output: Yes\ninput: 5\n3 3 3 3 3 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given four integers: H, W, h and w (1 <= h <= H, 1 <= w <= W).\nDetermine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix if the answer is positive:\n\nThe matrix has H rows and W columns.\nEach element of the matrix is an integer between -10^9 and 10^9 (inclusive).\nThe sum of all the elements of the matrix is positive.\nThe sum of all the elements within every subrectangle with h rows and w columns in the matrix is negative.", "constraint": "1 <= h <= H <= 500\n1 <= w <= W <= 500", "input": "Input is given from Standard Input in the following format:\nH W h w", "output": "If there does not exist a matrix that satisfies all of the conditions, print No.\nOtherwise, print Yes in the first line, and print a matrix in the subsequent lines in the following format:\na_{11} . . . a_{1W}\n:\na_{H1} . . . a_{HW}\n\nHere, a_{ij} represents the (i, \\ j) element of the matrix.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 2 2 output: Yes\n1 1 1\n1 -4 1\n1 1 1\n\nThe sum of all the elements of this matrix is 4, which is positive.\nAlso, in this matrix, there are four subrectangles with 2 rows and 2 columns as shown below. For each of them, the sum of all the elements inside is -1, which is negative.", "input: 2 4 1 2 output: No", "input: 3 4 2 3 output: Yes\n2 -5 8 7\n3 -5 -4 -5\n2 1 -1 7"], "Pid": "p03689", "ProblemText": "Task Description: Problem Statement You are given four integers: H, W, h and w (1 <= h <= H, 1 <= w <= W).\nDetermine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix if the answer is positive:\n\nThe matrix has H rows and W columns.\nEach element of the matrix is an integer between -10^9 and 10^9 (inclusive).\nThe sum of all the elements of the matrix is positive.\nThe sum of all the elements within every subrectangle with h rows and w columns in the matrix is negative.\nTask Constraint: 1 <= h <= H <= 500\n1 <= w <= W <= 500\nTask Input: Input is given from Standard Input in the following format:\nH W h w\nTask Output: If there does not exist a matrix that satisfies all of the conditions, print No.\nOtherwise, print Yes in the first line, and print a matrix in the subsequent lines in the following format:\na_{11} . . . a_{1W}\n:\na_{H1} . . . a_{HW}\n\nHere, a_{ij} represents the (i, \\ j) element of the matrix.\nTask Samples: input: 3 3 2 2 output: Yes\n1 1 1\n1 -4 1\n1 1 1\n\nThe sum of all the elements of this matrix is 4, which is positive.\nAlso, in this matrix, there are four subrectangles with 2 rows and 2 columns as shown below. For each of them, the sum of all the elements inside is -1, which is negative.\ninput: 2 4 1 2 output: No\ninput: 3 4 2 3 output: Yes\n2 -5 8 7\n3 -5 -4 -5\n2 1 -1 7\n\n" }, { "title": "", "content": "Problem Statement There is a sequence of length N: a = (a_1, a_2, . . . , a_N).\nHere, each a_i is a non-negative integer.\nSnuke can repeatedly perform the following operation:\n\nLet the XOR of all the elements in a be x. Select an integer i (1 <= i <= N) and replace a_i with x.\n\nSnuke's objective is to match a with another sequence b = (b_1, b_2, . . . , b_N).\nHere, each b_i is a non-negative integer.\nDetermine whether the objective is achievable, and find the minimum necessary number of operations if the answer is positive.", "constraint": "2 <= N <= 10^5\na_i and b_i are integers.\n0 <= a_i, b_i < 2^{30}", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nb_1 b_2 . . . b_N", "output": "If the objective is achievable, print the minimum necessary number of operations.\nOtherwise, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 1 2\n3 1 0 output: 2\n\nAt first, the XOR of all the elements of a is 3.\nIf we replace a_1 with 3, a becomes (3,1,2).\nNow, the XOR of all the elements of a is 0.\nIf we replace a_3 with 0, a becomes (3,1,0), which matches b.", "input: 3\n0 1 2\n0 1 2 output: 0", "input: 2\n1 1\n0 0 output: -1", "input: 4\n0 1 2 3\n1 0 3 2 output: 5"], "Pid": "p03690", "ProblemText": "Task Description: Problem Statement There is a sequence of length N: a = (a_1, a_2, . . . , a_N).\nHere, each a_i is a non-negative integer.\nSnuke can repeatedly perform the following operation:\n\nLet the XOR of all the elements in a be x. Select an integer i (1 <= i <= N) and replace a_i with x.\n\nSnuke's objective is to match a with another sequence b = (b_1, b_2, . . . , b_N).\nHere, each b_i is a non-negative integer.\nDetermine whether the objective is achievable, and find the minimum necessary number of operations if the answer is positive.\nTask Constraint: 2 <= N <= 10^5\na_i and b_i are integers.\n0 <= a_i, b_i < 2^{30}\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nb_1 b_2 . . . b_N\nTask Output: If the objective is achievable, print the minimum necessary number of operations.\nOtherwise, print -1 instead.\nTask Samples: input: 3\n0 1 2\n3 1 0 output: 2\n\nAt first, the XOR of all the elements of a is 3.\nIf we replace a_1 with 3, a becomes (3,1,2).\nNow, the XOR of all the elements of a is 0.\nIf we replace a_3 with 0, a becomes (3,1,0), which matches b.\ninput: 3\n0 1 2\n0 1 2 output: 0\ninput: 2\n1 1\n0 0 output: -1\ninput: 4\n0 1 2 3\n1 0 3 2 output: 5\n\n" }, { "title": "", "content": "Problem Statement There are N turkeys.\nWe number them from 1 through N.\nM men will visit here one by one.\nThe i-th man to visit will take the following action:\n\nIf both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.\nIf either turkey x_i or y_i is alive (but not both): eats the alive one.\nIf neither turkey x_i nor y_i is alive: does nothing.\n\nFind the number of pairs (i, \\ j) (1 <= i < j <= N) such that the following condition is held:\n\nThe probability of both turkeys i and j being alive after all the men took actions, is greater than 0.", "constraint": "2 <= N <= 400\n1 <= M <= 10^5\n1 <= x_i < y_i <= N", "input": "Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_M y_M", "output": "Print the number of pairs (i, \\ j) (1 <= i < j <= N) such that the condition is held.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1 2 output: 2\n\n(i,\\ j) = (1,\\ 3), (2,\\ 3) satisfy the condition.", "input: 4 3\n1 2\n3 4\n2 3 output: 1\n\n(i,\\ j) = (1,\\ 4) satisfies the condition.\nBoth turkeys 1 and 4 are alive if:\n\nThe first man eats turkey 2.\nThe second man eats turkey 3.\nThe third man does nothing.", "input: 3 2\n1 2\n1 2 output: 0", "input: 10 10\n8 9\n2 8\n4 6\n4 9\n7 8\n2 8\n1 8\n3 4\n3 4\n2 7 output: 5"], "Pid": "p03691", "ProblemText": "Task Description: Problem Statement There are N turkeys.\nWe number them from 1 through N.\nM men will visit here one by one.\nThe i-th man to visit will take the following action:\n\nIf both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.\nIf either turkey x_i or y_i is alive (but not both): eats the alive one.\nIf neither turkey x_i nor y_i is alive: does nothing.\n\nFind the number of pairs (i, \\ j) (1 <= i < j <= N) such that the following condition is held:\n\nThe probability of both turkeys i and j being alive after all the men took actions, is greater than 0.\nTask Constraint: 2 <= N <= 400\n1 <= M <= 10^5\n1 <= x_i < y_i <= N\nTask Input: Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_M y_M\nTask Output: Print the number of pairs (i, \\ j) (1 <= i < j <= N) such that the condition is held.\nTask Samples: input: 3 1\n1 2 output: 2\n\n(i,\\ j) = (1,\\ 3), (2,\\ 3) satisfy the condition.\ninput: 4 3\n1 2\n3 4\n2 3 output: 1\n\n(i,\\ j) = (1,\\ 4) satisfies the condition.\nBoth turkeys 1 and 4 are alive if:\n\nThe first man eats turkey 2.\nThe second man eats turkey 3.\nThe third man does nothing.\ninput: 3 2\n1 2\n1 2 output: 0\ninput: 10 10\n8 9\n2 8\n4 6\n4 9\n7 8\n2 8\n1 8\n3 4\n3 4\n2 7 output: 5\n\n" }, { "title": "", "content": "Problem Statement There is a directed graph G with N vertices and M edges.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i is directed from x_i to y_i.\nHere, x_i < y_i holds.\nAlso, there are no multiple edges in G.\nConsider selecting a subset of the set of the M edges in G, and removing these edges from G to obtain another graph G'.\nThere are 2^M different possible graphs as G'.\nAlice and Bob play against each other in the following game played on G'.\nFirst, place two pieces on vertices 1 and 2, one on each.\nThen, starting from Alice, Alice and Bob alternately perform the following operation:\n\nSelect an edge i such that there is a piece placed on vertex x_i, and move the piece to vertex y_i (if there are two pieces on vertex x_i, only move one). The two pieces are allowed to be placed on the same vertex.\n\nThe player loses when he/she becomes unable to perform the operation.\nWe assume that both players play optimally.\nAmong the 2^M different possible graphs as G', how many lead to Alice's victory?\nFind the count modulo 10^9+7.", "constraint": "2 <= N <= 15\n1 <= M <= N(N-1)/2\n1 <= x_i < y_i <= N\nAll (x_i,\\ y_i) are distinct.", "input": "Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_M y_M", "output": "Print the number of G' that lead to Alice's victory, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1\n1 2 output: 1\n\nThe figure below shows the two possible graphs as G'.\nA graph marked with ○ leads to Alice's victory, and a graph marked with * leads to Bob's victory.", "input: 3 3\n1 2\n1 3\n2 3 output: 6\n\nThe figure below shows the eight possible graphs as G'.", "input: 4 2\n1 3\n2 4 output: 2", "input: 5 10\n2 4\n3 4\n2 5\n2 3\n1 2\n3 5\n1 3\n1 5\n4 5\n1 4 output: 816"], "Pid": "p03692", "ProblemText": "Task Description: Problem Statement There is a directed graph G with N vertices and M edges.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i is directed from x_i to y_i.\nHere, x_i < y_i holds.\nAlso, there are no multiple edges in G.\nConsider selecting a subset of the set of the M edges in G, and removing these edges from G to obtain another graph G'.\nThere are 2^M different possible graphs as G'.\nAlice and Bob play against each other in the following game played on G'.\nFirst, place two pieces on vertices 1 and 2, one on each.\nThen, starting from Alice, Alice and Bob alternately perform the following operation:\n\nSelect an edge i such that there is a piece placed on vertex x_i, and move the piece to vertex y_i (if there are two pieces on vertex x_i, only move one). The two pieces are allowed to be placed on the same vertex.\n\nThe player loses when he/she becomes unable to perform the operation.\nWe assume that both players play optimally.\nAmong the 2^M different possible graphs as G', how many lead to Alice's victory?\nFind the count modulo 10^9+7.\nTask Constraint: 2 <= N <= 15\n1 <= M <= N(N-1)/2\n1 <= x_i < y_i <= N\nAll (x_i,\\ y_i) are distinct.\nTask Input: Input is given from Standard Input in the following format:\nN M\nx_1 y_1\nx_2 y_2\n:\nx_M y_M\nTask Output: Print the number of G' that lead to Alice's victory, modulo 10^9+7.\nTask Samples: input: 2 1\n1 2 output: 1\n\nThe figure below shows the two possible graphs as G'.\nA graph marked with ○ leads to Alice's victory, and a graph marked with * leads to Bob's victory.\ninput: 3 3\n1 2\n1 3\n2 3 output: 6\n\nThe figure below shows the eight possible graphs as G'.\ninput: 4 2\n1 3\n2 4 output: 2\ninput: 5 10\n2 4\n3 4\n2 5\n2 3\n1 2\n3 5\n1 3\n1 5\n4 5\n1 4 output: 816\n\n" }, { "title": "", "content": "Problem Statement At Co Deer has three cards, one red, one green and one blue.\nAn integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.\nWe will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.\nIs this integer a multiple of 4?", "constraint": "1 <= r, g, b <= 9", "input": "Input is given from Standard Input in the following format:\nr g b", "output": "If the three-digit integer is a multiple of 4, print YES (case-sensitive); otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 2 output: YES\n\n432 is a multiple of 4, and thus YES should be printed.", "input: 2 3 4 output: NO\n\n234 is not a multiple of 4, and thus NO should be printed."], "Pid": "p03693", "ProblemText": "Task Description: Problem Statement At Co Deer has three cards, one red, one green and one blue.\nAn integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.\nWe will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.\nIs this integer a multiple of 4?\nTask Constraint: 1 <= r, g, b <= 9\nTask Input: Input is given from Standard Input in the following format:\nr g b\nTask Output: If the three-digit integer is a multiple of 4, print YES (case-sensitive); otherwise, print NO.\nTask Samples: input: 4 3 2 output: YES\n\n432 is a multiple of 4, and thus YES should be printed.\ninput: 2 3 4 output: NO\n\n234 is not a multiple of 4, and thus NO should be printed.\n\n" }, { "title": "", "content": "Problem Statement It is only six months until Christmas, and At Co Deer the reindeer is now planning his travel to deliver gifts.\nThere are N houses along Top Co Deer street. The i-th house is located at coordinate a_i. He has decided to deliver gifts to all these houses.\nFind the minimum distance to be traveled when At Co Deer can start and end his travel at any positions.", "constraint": "1 <= N <= 100\n0 <= a_i <= 1000\na_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum distance to be traveled.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 3 7 9 output: 7\n\nThe travel distance of 7 can be achieved by starting at coordinate 9 and traveling straight to coordinate 2.\nIt is not possible to do with a travel distance of less than 7, and thus 7 is the minimum distance to be traveled.", "input: 8\n3 1 4 1 5 9 2 6 output: 8\n\nThere may be more than one house at a position."], "Pid": "p03694", "ProblemText": "Task Description: Problem Statement It is only six months until Christmas, and At Co Deer the reindeer is now planning his travel to deliver gifts.\nThere are N houses along Top Co Deer street. The i-th house is located at coordinate a_i. He has decided to deliver gifts to all these houses.\nFind the minimum distance to be traveled when At Co Deer can start and end his travel at any positions.\nTask Constraint: 1 <= N <= 100\n0 <= a_i <= 1000\na_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum distance to be traveled.\nTask Samples: input: 4\n2 3 7 9 output: 7\n\nThe travel distance of 7 can be achieved by starting at coordinate 9 and traveling straight to coordinate 2.\nIt is not possible to do with a travel distance of less than 7, and thus 7 is the minimum distance to be traveled.\ninput: 8\n3 1 4 1 5 9 2 6 output: 8\n\nThere may be more than one house at a position.\n\n" }, { "title": "", "content": "Problem Statement In At Coder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows: \n\nRating 1-399 : gray\nRating 400-799 : brown\nRating 800-1199 : green\nRating 1200-1599 : cyan\nRating 1600-1999 : blue\nRating 2000-2399 : yellow\nRating 2400-2799 : orange\nRating 2800-3199 : red\n\nOther than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.\nCurrently, there are N users who have participated in a contest in At Coder, and the i-th user has a rating of a_i.\nFind the minimum and maximum possible numbers of different colors of the users.", "constraint": "1 <= N <= 100\n1 <= a_i <= 4800\na_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2100 2500 2700 2700 output: 2 2\n\nThe user with rating 2100 is \"yellow\", and the others are \"orange\". There are two different colors.", "input: 5\n1100 1900 2800 3200 3200 output: 3 5\n\nThe user with rating 1100 is \"green\", the user with rating 1900 is blue and the user with rating 2800 is \"red\".\nIf the fourth user picks \"red\", and the fifth user picks \"blue\", there are three different colors. This is one possible scenario for the minimum number of colors.\nIf the fourth user picks \"purple\", and the fifth user picks \"black\", there are five different colors. This is one possible scenario for the maximum number of colors.", "input: 20\n800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 output: 1 1\n\nAll the users are \"green\", and thus there is one color."], "Pid": "p03695", "ProblemText": "Task Description: Problem Statement In At Coder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows: \n\nRating 1-399 : gray\nRating 400-799 : brown\nRating 800-1199 : green\nRating 1200-1599 : cyan\nRating 1600-1999 : blue\nRating 2000-2399 : yellow\nRating 2400-2799 : orange\nRating 2800-3199 : red\n\nOther than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.\nCurrently, there are N users who have participated in a contest in At Coder, and the i-th user has a rating of a_i.\nFind the minimum and maximum possible numbers of different colors of the users.\nTask Constraint: 1 <= N <= 100\n1 <= a_i <= 4800\na_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.\nTask Samples: input: 4\n2100 2500 2700 2700 output: 2 2\n\nThe user with rating 2100 is \"yellow\", and the others are \"orange\". There are two different colors.\ninput: 5\n1100 1900 2800 3200 3200 output: 3 5\n\nThe user with rating 1100 is \"green\", the user with rating 1900 is blue and the user with rating 2800 is \"red\".\nIf the fourth user picks \"red\", and the fifth user picks \"blue\", there are three different colors. This is one possible scenario for the minimum number of colors.\nIf the fourth user picks \"purple\", and the fifth user picks \"black\", there are five different colors. This is one possible scenario for the maximum number of colors.\ninput: 20\n800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 output: 1 1\n\nAll the users are \"green\", and thus there is one color.\n\n" }, { "title": "", "content": "Problem Statement You are given a string S of length N consisting of ( and ). Your task is to insert some number of ( and ) into S to obtain a correct bracket sequence.\nHere, a correct bracket sequence is defined as follows: \n\n() is a correct bracket sequence.\nIf X is a correct bracket sequence, the concatenation of (, X and ) in this order is also a correct bracket sequence.\nIf X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.\nEvery correct bracket sequence can be derived from the rules above.\n\nFind the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.", "constraint": "The length of S is N.\n1 <= N <= 100\nS consists of ( and ).", "input": "Input is given from Standard Input in the following format:\nN\nS", "output": "Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of ( and ) into S.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n()) output: (())", "input: 6\n)))()) output: (((()))())", "input: 8\n))))(((( output: (((())))(((())))"], "Pid": "p03696", "ProblemText": "Task Description: Problem Statement You are given a string S of length N consisting of ( and ). Your task is to insert some number of ( and ) into S to obtain a correct bracket sequence.\nHere, a correct bracket sequence is defined as follows: \n\n() is a correct bracket sequence.\nIf X is a correct bracket sequence, the concatenation of (, X and ) in this order is also a correct bracket sequence.\nIf X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.\nEvery correct bracket sequence can be derived from the rules above.\n\nFind the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.\nTask Constraint: The length of S is N.\n1 <= N <= 100\nS consists of ( and ).\nTask Input: Input is given from Standard Input in the following format:\nN\nS\nTask Output: Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of ( and ) into S.\nTask Samples: input: 3\n()) output: (())\ninput: 6\n)))()) output: (((()))())\ninput: 8\n))))(((( output: (((())))(((())))\n\n" }, { "title": "", "content": "Problem Statement You are given two integers A and B as the input. Output the value of A + B.\nHowever, if A + B is 10 or greater, output error instead.", "constraint": "A and B are integers.\n1 <= A, B <= 9", "input": "Input is given from Standard Input in the following format:\nA B", "output": "If A + B is 10 or greater, print the string error (case-sensitive); otherwise, print the value of A + B.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 3 output: 9", "input: 6 4 output: error"], "Pid": "p03697", "ProblemText": "Task Description: Problem Statement You are given two integers A and B as the input. Output the value of A + B.\nHowever, if A + B is 10 or greater, output error instead.\nTask Constraint: A and B are integers.\n1 <= A, B <= 9\nTask Input: Input is given from Standard Input in the following format:\nA B\nTask Output: If A + B is 10 or greater, print the string error (case-sensitive); otherwise, print the value of A + B.\nTask Samples: input: 6 3 output: 9\ninput: 6 4 output: error\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of lowercase English letters. Determine whether all the characters in S are different.", "constraint": "2 <= |S| <= 26, where |S| denotes the length of S.\nS consists of lowercase English letters.", "input": "Input is given from Standard Input in the following format:\nS", "output": "If all the characters in S are different, print yes (case-sensitive); otherwise, print no.", "content_img": false, "lang": "en", "error": false, "samples": ["input: uncopyrightable output: yes", "input: different output: no", "input: no output: yes"], "Pid": "p03698", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of lowercase English letters. Determine whether all the characters in S are different.\nTask Constraint: 2 <= |S| <= 26, where |S| denotes the length of S.\nS consists of lowercase English letters.\nTask Input: Input is given from Standard Input in the following format:\nS\nTask Output: If all the characters in S are different, print yes (case-sensitive); otherwise, print no.\nTask Samples: input: uncopyrightable output: yes\ninput: different output: no\ninput: no output: yes\n\n" }, { "title": "", "content": "Problem Statement You are taking a computer-based examination. The examination consists of N questions, and the score allocated to the i-th question is s_i. Your answer to each question will be judged as either \"correct\" or \"incorrect\", and your grade will be the sum of the points allocated to questions that are answered correctly. When you finish answering the questions, your answers will be immediately judged and your grade will be displayed. . . if everything goes well.\nHowever, the examination system is actually flawed, and if your grade is a multiple of 10, the system displays 0 as your grade. Otherwise, your grade is displayed correctly. In this situation, what is the maximum value that can be displayed as your grade?", "constraint": "All input values are integers.\n1 <= N <= 100\n1 <= s_i <= 100", "input": "Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N", "output": "Print the maximum value that can be displayed as your grade.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n5\n10\n15 output: 25\n\nYour grade will be 25 if the 10-point and 15-point questions are answered correctly and the 5-point question is not, and this grade will be displayed correctly. Your grade will become 30 if the 5-point question is also answered correctly, but this grade will be incorrectly displayed as 0.", "input: 3\n10\n10\n15 output: 35\n\nYour grade will be 35 if all the questions are answered correctly, and this grade will be displayed correctly.", "input: 3\n10\n20\n30 output: 0\n\nRegardless of whether each question is answered correctly or not, your grade will be a multiple of 10 and displayed as 0."], "Pid": "p03699", "ProblemText": "Task Description: Problem Statement You are taking a computer-based examination. The examination consists of N questions, and the score allocated to the i-th question is s_i. Your answer to each question will be judged as either \"correct\" or \"incorrect\", and your grade will be the sum of the points allocated to questions that are answered correctly. When you finish answering the questions, your answers will be immediately judged and your grade will be displayed. . . if everything goes well.\nHowever, the examination system is actually flawed, and if your grade is a multiple of 10, the system displays 0 as your grade. Otherwise, your grade is displayed correctly. In this situation, what is the maximum value that can be displayed as your grade?\nTask Constraint: All input values are integers.\n1 <= N <= 100\n1 <= s_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N\nTask Output: Print the maximum value that can be displayed as your grade.\nTask Samples: input: 3\n5\n10\n15 output: 25\n\nYour grade will be 25 if the 10-point and 15-point questions are answered correctly and the 5-point question is not, and this grade will be displayed correctly. Your grade will become 30 if the 5-point question is also answered correctly, but this grade will be incorrectly displayed as 0.\ninput: 3\n10\n10\n15 output: 35\n\nYour grade will be 35 if all the questions are answered correctly, and this grade will be displayed correctly.\ninput: 3\n10\n20\n30 output: 0\n\nRegardless of whether each question is answered correctly or not, your grade will be a multiple of 10 and displayed as 0.\n\n" }, { "title": "", "content": "Problem Statement You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is h_i at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.\nFortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:\n\nSelect an alive monster, and cause an explosion centered at that monster. The health of the monster at the center of the explosion will decrease by A, and the health of each of the other monsters will decrease by B. Here, A and B are predetermined parameters, and A > B holds.\n\nAt least how many explosions do you need to cause in order to vanish all the monsters?", "constraint": "All input values are integers.\n1 <= N <= 10^5\n1 <= B < A <= 10^9\n1 <= h_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN A B\nh_1\nh_2\n:\nh_N", "output": "Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 3\n8\n7\n4\n2 output: 2\n\nYou can vanish all the monsters in two explosion, as follows:\n\nFirst, cause an explosion centered at the monster with 8 health. The healths of the four monsters become 3,4,1 and -1, respectively, and the last monster vanishes.\nSecond, cause an explosion centered at the monster with 4 health remaining. The healths of the three remaining monsters become 0, -1 and -2, respectively, and all the monsters are now vanished.", "input: 2 10 4\n20\n20 output: 4\n\nYou need to cause two explosions centered at each monster, for a total of four.", "input: 5 2 1\n900000000\n900000000\n1000000000\n1000000000\n1000000000 output: 800000000"], "Pid": "p03700", "ProblemText": "Task Description: Problem Statement You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is h_i at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.\nFortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:\n\nSelect an alive monster, and cause an explosion centered at that monster. The health of the monster at the center of the explosion will decrease by A, and the health of each of the other monsters will decrease by B. Here, A and B are predetermined parameters, and A > B holds.\n\nAt least how many explosions do you need to cause in order to vanish all the monsters?\nTask Constraint: All input values are integers.\n1 <= N <= 10^5\n1 <= B < A <= 10^9\n1 <= h_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN A B\nh_1\nh_2\n:\nh_N\nTask Output: Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.\nTask Samples: input: 4 5 3\n8\n7\n4\n2 output: 2\n\nYou can vanish all the monsters in two explosion, as follows:\n\nFirst, cause an explosion centered at the monster with 8 health. The healths of the four monsters become 3,4,1 and -1, respectively, and the last monster vanishes.\nSecond, cause an explosion centered at the monster with 4 health remaining. The healths of the three remaining monsters become 0, -1 and -2, respectively, and all the monsters are now vanished.\ninput: 2 10 4\n20\n20 output: 4\n\nYou need to cause two explosions centered at each monster, for a total of four.\ninput: 5 2 1\n900000000\n900000000\n1000000000\n1000000000\n1000000000 output: 800000000\n\n" }, { "title": "", "content": "Problem Statement You are taking a computer-based examination. The examination consists of N questions, and the score allocated to the i-th question is s_i. Your answer to each question will be judged as either \"correct\" or \"incorrect\", and your grade will be the sum of the points allocated to questions that are answered correctly. When you finish answering the questions, your answers will be immediately judged and your grade will be displayed. . . if everything goes well.\nHowever, the examination system is actually flawed, and if your grade is a multiple of 10, the system displays 0 as your grade. Otherwise, your grade is displayed correctly. In this situation, what is the maximum value that can be displayed as your grade?", "constraint": "All input values are integers.\n1 <= N <= 100\n1 <= s_i <= 100", "input": "Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N", "output": "Print the maximum value that can be displayed as your grade.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n5\n10\n15 output: 25\n\nYour grade will be 25 if the 10-point and 15-point questions are answered correctly and the 5-point question is not, and this grade will be displayed correctly. Your grade will become 30 if the 5-point question is also answered correctly, but this grade will be incorrectly displayed as 0.", "input: 3\n10\n10\n15 output: 35\n\nYour grade will be 35 if all the questions are answered correctly, and this grade will be displayed correctly.", "input: 3\n10\n20\n30 output: 0\n\nRegardless of whether each question is answered correctly or not, your grade will be a multiple of 10 and displayed as 0."], "Pid": "p03701", "ProblemText": "Task Description: Problem Statement You are taking a computer-based examination. The examination consists of N questions, and the score allocated to the i-th question is s_i. Your answer to each question will be judged as either \"correct\" or \"incorrect\", and your grade will be the sum of the points allocated to questions that are answered correctly. When you finish answering the questions, your answers will be immediately judged and your grade will be displayed. . . if everything goes well.\nHowever, the examination system is actually flawed, and if your grade is a multiple of 10, the system displays 0 as your grade. Otherwise, your grade is displayed correctly. In this situation, what is the maximum value that can be displayed as your grade?\nTask Constraint: All input values are integers.\n1 <= N <= 100\n1 <= s_i <= 100\nTask Input: Input is given from Standard Input in the following format:\nN\ns_1\ns_2\n:\ns_N\nTask Output: Print the maximum value that can be displayed as your grade.\nTask Samples: input: 3\n5\n10\n15 output: 25\n\nYour grade will be 25 if the 10-point and 15-point questions are answered correctly and the 5-point question is not, and this grade will be displayed correctly. Your grade will become 30 if the 5-point question is also answered correctly, but this grade will be incorrectly displayed as 0.\ninput: 3\n10\n10\n15 output: 35\n\nYour grade will be 35 if all the questions are answered correctly, and this grade will be displayed correctly.\ninput: 3\n10\n20\n30 output: 0\n\nRegardless of whether each question is answered correctly or not, your grade will be a multiple of 10 and displayed as 0.\n\n" }, { "title": "", "content": "Problem Statement You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is h_i at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.\nFortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:\n\nSelect an alive monster, and cause an explosion centered at that monster. The health of the monster at the center of the explosion will decrease by A, and the health of each of the other monsters will decrease by B. Here, A and B are predetermined parameters, and A > B holds.\n\nAt least how many explosions do you need to cause in order to vanish all the monsters?", "constraint": "All input values are integers.\n1 <= N <= 10^5\n1 <= B < A <= 10^9\n1 <= h_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN A B\nh_1\nh_2\n:\nh_N", "output": "Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 3\n8\n7\n4\n2 output: 2\n\nYou can vanish all the monsters in two explosion, as follows:\n\nFirst, cause an explosion centered at the monster with 8 health. The healths of the four monsters become 3,4,1 and -1, respectively, and the last monster vanishes.\nSecond, cause an explosion centered at the monster with 4 health remaining. The healths of the three remaining monsters become 0, -1 and -2, respectively, and all the monsters are now vanished.", "input: 2 10 4\n20\n20 output: 4\n\nYou need to cause two explosions centered at each monster, for a total of four.", "input: 5 2 1\n900000000\n900000000\n1000000000\n1000000000\n1000000000 output: 800000000"], "Pid": "p03702", "ProblemText": "Task Description: Problem Statement You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is h_i at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.\nFortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:\n\nSelect an alive monster, and cause an explosion centered at that monster. The health of the monster at the center of the explosion will decrease by A, and the health of each of the other monsters will decrease by B. Here, A and B are predetermined parameters, and A > B holds.\n\nAt least how many explosions do you need to cause in order to vanish all the monsters?\nTask Constraint: All input values are integers.\n1 <= N <= 10^5\n1 <= B < A <= 10^9\n1 <= h_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN A B\nh_1\nh_2\n:\nh_N\nTask Output: Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.\nTask Samples: input: 4 5 3\n8\n7\n4\n2 output: 2\n\nYou can vanish all the monsters in two explosion, as follows:\n\nFirst, cause an explosion centered at the monster with 8 health. The healths of the four monsters become 3,4,1 and -1, respectively, and the last monster vanishes.\nSecond, cause an explosion centered at the monster with 4 health remaining. The healths of the three remaining monsters become 0, -1 and -2, respectively, and all the monsters are now vanished.\ninput: 2 10 4\n20\n20 output: 4\n\nYou need to cause two explosions centered at each monster, for a total of four.\ninput: 5 2 1\n900000000\n900000000\n1000000000\n1000000000\n1000000000 output: 800000000\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length N, a = {a_1, a_2, …, a_N}, and an integer K.\na has N(N+1)/2 non-empty contiguous subsequences, {a_l, a_{l+1}, …, a_r} (1 <= l <= r <= N). Among them, how many have an arithmetic mean that is greater than or equal to K?", "constraint": "All input values are integers.\n1 <= N <= 2 * 10^5\n1 <= K <= 10^9\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN K\na_1\na_2\n:\na_N", "output": "Print the number of the non-empty contiguous subsequences with an arithmetic mean that is greater than or equal to K.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 6\n7\n5\n7 output: 5\n\nAll the non-empty contiguous subsequences of a are listed below:\n\n{a_1} = {7}\n{a_1, a_2} = {7,5}\n{a_1, a_2, a_3} = {7,5,7}\n{a_2} = {5}\n{a_2, a_3} = {5,7}\n{a_3} = {7}\n\nTheir means are 7,6,19/3,5,6 and 7, respectively, and five among them are 6 or greater. Note that {a_1} and {a_3} are indistinguishable by the values of their elements, but we count them individually.", "input: 1 2\n1 output: 0", "input: 7 26\n10\n20\n30\n40\n30\n20\n10 output: 13"], "Pid": "p03703", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length N, a = {a_1, a_2, …, a_N}, and an integer K.\na has N(N+1)/2 non-empty contiguous subsequences, {a_l, a_{l+1}, …, a_r} (1 <= l <= r <= N). Among them, how many have an arithmetic mean that is greater than or equal to K?\nTask Constraint: All input values are integers.\n1 <= N <= 2 * 10^5\n1 <= K <= 10^9\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN K\na_1\na_2\n:\na_N\nTask Output: Print the number of the non-empty contiguous subsequences with an arithmetic mean that is greater than or equal to K.\nTask Samples: input: 3 6\n7\n5\n7 output: 5\n\nAll the non-empty contiguous subsequences of a are listed below:\n\n{a_1} = {7}\n{a_1, a_2} = {7,5}\n{a_1, a_2, a_3} = {7,5,7}\n{a_2} = {5}\n{a_2, a_3} = {5,7}\n{a_3} = {7}\n\nTheir means are 7,6,19/3,5,6 and 7, respectively, and five among them are 6 or greater. Note that {a_1} and {a_3} are indistinguishable by the values of their elements, but we count them individually.\ninput: 1 2\n1 output: 0\ninput: 7 26\n10\n20\n30\n40\n30\n20\n10 output: 13\n\n" }, { "title": "", "content": "Problem Statement For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4.\nYou are given a positive integer D. How many positive integers N satisfy rev(N) = N + D?", "constraint": "D is an integer.\n1 <= D < 10^9", "input": "Input is given from Standard Input in the following format:\nD", "output": "Print the number of the positive integers N such that rev(N) = N + D.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 63 output: 2\n\nThere are two positive integers N such that rev(N) = N + 63: N = 18 and 29.", "input: 75 output: 0\n\nThere are no positive integers N such that rev(N) = N + 75.", "input: 864197532 output: 1920"], "Pid": "p03704", "ProblemText": "Task Description: Problem Statement For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4.\nYou are given a positive integer D. How many positive integers N satisfy rev(N) = N + D?\nTask Constraint: D is an integer.\n1 <= D < 10^9\nTask Input: Input is given from Standard Input in the following format:\nD\nTask Output: Print the number of the positive integers N such that rev(N) = N + D.\nTask Samples: input: 63 output: 2\n\nThere are two positive integers N such that rev(N) = N + 63: N = 18 and 29.\ninput: 75 output: 0\n\nThere are no positive integers N such that rev(N) = N + 75.\ninput: 864197532 output: 1920\n\n" }, { "title": "", "content": "Problem Statement Snuke has N integers. Among them, the smallest is A, and the largest is B.\nWe are interested in the sum of those N integers. How many different possible sums there are?", "constraint": "1 <= N,A,B <= 10^9\nA and B are integers.", "input": "Input is given from Standard Input in the following format:\nN A B", "output": "Print the number of the different possible sums.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4 6 output: 5\n\nThere are five possible sums: 18=4+4+4+6,19=4+4+5+6,20=4+5+5+6,21=4+5+6+6 and 22=4+6+6+6.", "input: 5 4 3 output: 0", "input: 1 7 10 output: 0", "input: 1 3 3 output: 1"], "Pid": "p03705", "ProblemText": "Task Description: Problem Statement Snuke has N integers. Among them, the smallest is A, and the largest is B.\nWe are interested in the sum of those N integers. How many different possible sums there are?\nTask Constraint: 1 <= N,A,B <= 10^9\nA and B are integers.\nTask Input: Input is given from Standard Input in the following format:\nN A B\nTask Output: Print the number of the different possible sums.\nTask Samples: input: 4 4 6 output: 5\n\nThere are five possible sums: 18=4+4+4+6,19=4+4+5+6,20=4+5+5+6,21=4+5+6+6 and 22=4+6+6+6.\ninput: 5 4 3 output: 0\ninput: 1 7 10 output: 0\ninput: 1 3 3 output: 1\n\n" }, { "title": "", "content": "Problem Statement Skenu constructed a building that has N floors. The building has an elevator that stops at every floor.\nThere are buttons to control the elevator, but Skenu thoughtlessly installed only one button on each floor - up or down.\nThis means that, from each floor, one can only go in one direction.\nIf S_i is U, only \"up\" button is installed on the i-th floor and one can only go up; if S_i is D, only \"down\" button is installed on the i-th floor and one can only go down.\nThe residents have no choice but to go to their destination floors via other floors if necessary.\nFind the sum of the following numbers over all ordered pairs of two floors (i, j): the minimum number of times one needs to take the elevator to get to the j-th floor from the i-th floor.", "constraint": "2 <= |S| <= 10^5\nS_i is either U or D.\nS_1 is U.\nS_{|S|} is D.", "input": "Input The input is given from Standard Input in the following format:\nS_1S_2. . . S_{|S|}", "output": "Print the sum of the following numbers over all ordered pairs of two floors (i, j): the minimum number of times one needs to take the elevator to get to the j-th floor from the i-th floor.", "content_img": false, "lang": "en", "error": false, "samples": ["input: UUD output: 7\n\nFrom the 1-st floor, one can get to the 2-nd floor by taking the elevator once.\nFrom the 1-st floor, one can get to the 3-rd floor by taking the elevator once.\nFrom the 2-nd floor, one can get to the 1-st floor by taking the elevator twice.\nFrom the 2-nd floor, one can get to the 3-rd floor by taking the elevator once.\nFrom the 3-rd floor, one can get to the 1-st floor by taking the elevator once.\nFrom the 3-rd floor, one can get to the 2-nd floor by taking the elevator once.\nThe sum of these numbers of times, 7, should be printed.", "input: UUDUUDUD output: 77"], "Pid": "p03706", "ProblemText": "Task Description: Problem Statement Skenu constructed a building that has N floors. The building has an elevator that stops at every floor.\nThere are buttons to control the elevator, but Skenu thoughtlessly installed only one button on each floor - up or down.\nThis means that, from each floor, one can only go in one direction.\nIf S_i is U, only \"up\" button is installed on the i-th floor and one can only go up; if S_i is D, only \"down\" button is installed on the i-th floor and one can only go down.\nThe residents have no choice but to go to their destination floors via other floors if necessary.\nFind the sum of the following numbers over all ordered pairs of two floors (i, j): the minimum number of times one needs to take the elevator to get to the j-th floor from the i-th floor.\nTask Constraint: 2 <= |S| <= 10^5\nS_i is either U or D.\nS_1 is U.\nS_{|S|} is D.\nTask Input: Input The input is given from Standard Input in the following format:\nS_1S_2. . . S_{|S|}\nTask Output: Print the sum of the following numbers over all ordered pairs of two floors (i, j): the minimum number of times one needs to take the elevator to get to the j-th floor from the i-th floor.\nTask Samples: input: UUD output: 7\n\nFrom the 1-st floor, one can get to the 2-nd floor by taking the elevator once.\nFrom the 1-st floor, one can get to the 3-rd floor by taking the elevator once.\nFrom the 2-nd floor, one can get to the 1-st floor by taking the elevator twice.\nFrom the 2-nd floor, one can get to the 3-rd floor by taking the elevator once.\nFrom the 3-rd floor, one can get to the 1-st floor by taking the elevator once.\nFrom the 3-rd floor, one can get to the 2-nd floor by taking the elevator once.\nThe sum of these numbers of times, 7, should be printed.\ninput: UUDUUDUD output: 77\n\n" }, { "title": "", "content": "Problem Statement Nuske has a grid with N rows and M columns of squares. The rows are numbered 1 through N from top to bottom, and the columns are numbered 1 through M from left to right.\nEach square in the grid is painted in either blue or white. If S_{i, j} is 1, the square at the i-th row and j-th column is blue; if S_{i, j} is 0, the square is white.\nFor every pair of two blue square a and b, there is at most one path that starts from a, repeatedly proceeds to an adjacent (side by side) blue square and finally reaches b, without traversing the same square more than once.\nPhantom Thnook, Nuske's eternal rival, gives Q queries to Nuske. The i-th query consists of four integers x_{i, 1}, y_{i, 1}, x_{i, 2} and y_{i, 2} and asks him the following: when the rectangular region of the grid bounded by (and including) the x_{i, 1}-th row, x_{i, 2}-th row, y_{i, 1}-th column and y_{i, 2}-th column is cut out, how many connected components consisting of blue squares there are in the region?\nProcess all the queries.", "constraint": "1 <= N,M <= 2000\n1 <= Q <= 200000\nS_{i,j} is either 0 or 1.\nS_{i,j} satisfies the condition explained in the statement.\n1 <= x_{i,1} <= x_{i,2} <= N(1 <= i <= Q)\n1 <= y_{i,1} <= y_{i,2} <= M(1 <= i <= Q)", "input": "Input The input is given from Standard Input in the following format:\nN M Q\nS_{1,1}. . S_{1, M}\n:\nS_{N, 1}. . S_{N, M}\nx_{1,1} y_{i, 1} x_{i, 2} y_{i, 2}\n:\nx_{Q, 1} y_{Q, 1} x_{Q, 2} y_{Q, 2}", "output": "For each query, print the number of the connected components consisting of blue squares in the region.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4 4\n1101\n0110\n1101\n1 1 3 4\n1 1 3 1\n2 2 3 4\n1 2 2 4 output: 3\n2\n2\n2\nIn the first query, the whole grid is specified. There are three components consisting of blue squares, and thus 3 should be printed.\nIn the second query, the region within the red frame is specified. There are two components consisting of blue squares, and thus 2 should be printed.\nNote that squares that belong to the same component in the original grid may belong to different components.", "input: 5 5 6\n11010\n01110\n10101\n11101\n01010\n1 1 5 5\n1 2 4 5\n2 3 3 4\n3 3 3 3\n3 1 3 5\n1 1 3 4 output: 3\n2\n1\n1\n3\n2"], "Pid": "p03707", "ProblemText": "Task Description: Problem Statement Nuske has a grid with N rows and M columns of squares. The rows are numbered 1 through N from top to bottom, and the columns are numbered 1 through M from left to right.\nEach square in the grid is painted in either blue or white. If S_{i, j} is 1, the square at the i-th row and j-th column is blue; if S_{i, j} is 0, the square is white.\nFor every pair of two blue square a and b, there is at most one path that starts from a, repeatedly proceeds to an adjacent (side by side) blue square and finally reaches b, without traversing the same square more than once.\nPhantom Thnook, Nuske's eternal rival, gives Q queries to Nuske. The i-th query consists of four integers x_{i, 1}, y_{i, 1}, x_{i, 2} and y_{i, 2} and asks him the following: when the rectangular region of the grid bounded by (and including) the x_{i, 1}-th row, x_{i, 2}-th row, y_{i, 1}-th column and y_{i, 2}-th column is cut out, how many connected components consisting of blue squares there are in the region?\nProcess all the queries.\nTask Constraint: 1 <= N,M <= 2000\n1 <= Q <= 200000\nS_{i,j} is either 0 or 1.\nS_{i,j} satisfies the condition explained in the statement.\n1 <= x_{i,1} <= x_{i,2} <= N(1 <= i <= Q)\n1 <= y_{i,1} <= y_{i,2} <= M(1 <= i <= Q)\nTask Input: Input The input is given from Standard Input in the following format:\nN M Q\nS_{1,1}. . S_{1, M}\n:\nS_{N, 1}. . S_{N, M}\nx_{1,1} y_{i, 1} x_{i, 2} y_{i, 2}\n:\nx_{Q, 1} y_{Q, 1} x_{Q, 2} y_{Q, 2}\nTask Output: For each query, print the number of the connected components consisting of blue squares in the region.\nTask Samples: input: 3 4 4\n1101\n0110\n1101\n1 1 3 4\n1 1 3 1\n2 2 3 4\n1 2 2 4 output: 3\n2\n2\n2\nIn the first query, the whole grid is specified. There are three components consisting of blue squares, and thus 3 should be printed.\nIn the second query, the region within the red frame is specified. There are two components consisting of blue squares, and thus 2 should be printed.\nNote that squares that belong to the same component in the original grid may belong to different components.\ninput: 5 5 6\n11010\n01110\n10101\n11101\n01010\n1 1 5 5\n1 2 4 5\n2 3 3 4\n3 3 3 3\n3 1 3 5\n1 1 3 4 output: 3\n2\n1\n1\n3\n2\n\n" }, { "title": "", "content": "Problem Statement Nukes has an integer that can be represented as the bitwise OR of one or more integers between A and B (inclusive).\nHow many possible candidates of the value of Nukes's integer there are?", "constraint": "1 <= A <= B < 2^{60}\nA and B are integers.", "input": "Input The input is given from Standard Input in the following format:\nA\nB", "output": "Print the number of possible candidates of the value of Nukes's integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n9 output: 4\n\nIn this case, A=7 and B=9. There are four integers that can be represented as the bitwise OR of a non-empty subset of {7,8,9}: 7,8,9 and 15.", "input: 65\n98 output: 63", "input: 271828182845904523\n314159265358979323 output: 68833183630578410"], "Pid": "p03708", "ProblemText": "Task Description: Problem Statement Nukes has an integer that can be represented as the bitwise OR of one or more integers between A and B (inclusive).\nHow many possible candidates of the value of Nukes's integer there are?\nTask Constraint: 1 <= A <= B < 2^{60}\nA and B are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nA\nB\nTask Output: Print the number of possible candidates of the value of Nukes's integer.\nTask Samples: input: 7\n9 output: 4\n\nIn this case, A=7 and B=9. There are four integers that can be represented as the bitwise OR of a non-empty subset of {7,8,9}: 7,8,9 and 15.\ninput: 65\n98 output: 63\ninput: 271828182845904523\n314159265358979323 output: 68833183630578410\n\n" }, { "title": "", "content": "Problem Statement Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body.\nOn a number line, there are N copies of Takahashi, numbered 1 through N.\nThe i-th copy is located at position X_i and starts walking with velocity V_i in the positive direction at time 0.\nKenus is a master of Transformation Jutsu, and not only can he change into a person other than himself, but he can also transform another person into someone else.\nKenus can select some of the copies of Takahashi at time 0, and transform them into copies of Aoki, another Ninja.\nThe walking velocity of a copy does not change when it transforms.\nFrom then on, whenever a copy of Takahashi and a copy of Aoki are at the same coordinate, that copy of Takahashi transforms into a copy of Aoki.\nAmong the 2^N ways to transform some copies of Takahashi into copies of Aoki at time 0, in how many ways will all the copies of Takahashi become copies of Aoki after a sufficiently long time?\nFind the count modulo 10^9+7.", "constraint": "1 <= N <= 200000\n1 <= X_i,V_i <= 10^9(1 <= i <= N)\nX_i and V_i are integers.\nAll X_i are distinct.\nAll V_i are distinct.", "input": "Input The input is given from Standard Input in the following format:\nN\nX_1 V_1\n:\nX_N V_N", "output": "Print the number of the ways that cause all the copies of Takahashi to turn into copies of Aoki after a sufficiently long time, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 5\n6 1\n3 7 output: 6\n\nAll copies of Takahashi will turn into copies of Aoki after a sufficiently long time if Kenus transforms one of the following sets of copies of Takahashi into copies of Aoki: (2), (3), (1,2), (1,3), (2,3) and (1,2,3).", "input: 4\n3 7\n2 9\n8 16\n10 8 output: 9"], "Pid": "p03709", "ProblemText": "Task Description: Problem Statement Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body.\nOn a number line, there are N copies of Takahashi, numbered 1 through N.\nThe i-th copy is located at position X_i and starts walking with velocity V_i in the positive direction at time 0.\nKenus is a master of Transformation Jutsu, and not only can he change into a person other than himself, but he can also transform another person into someone else.\nKenus can select some of the copies of Takahashi at time 0, and transform them into copies of Aoki, another Ninja.\nThe walking velocity of a copy does not change when it transforms.\nFrom then on, whenever a copy of Takahashi and a copy of Aoki are at the same coordinate, that copy of Takahashi transforms into a copy of Aoki.\nAmong the 2^N ways to transform some copies of Takahashi into copies of Aoki at time 0, in how many ways will all the copies of Takahashi become copies of Aoki after a sufficiently long time?\nFind the count modulo 10^9+7.\nTask Constraint: 1 <= N <= 200000\n1 <= X_i,V_i <= 10^9(1 <= i <= N)\nX_i and V_i are integers.\nAll X_i are distinct.\nAll V_i are distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nX_1 V_1\n:\nX_N V_N\nTask Output: Print the number of the ways that cause all the copies of Takahashi to turn into copies of Aoki after a sufficiently long time, modulo 10^9+7.\nTask Samples: input: 3\n2 5\n6 1\n3 7 output: 6\n\nAll copies of Takahashi will turn into copies of Aoki after a sufficiently long time if Kenus transforms one of the following sets of copies of Takahashi into copies of Aoki: (2), (3), (1,2), (1,3), (2,3) and (1,2,3).\ninput: 4\n3 7\n2 9\n8 16\n10 8 output: 9\n\n" }, { "title": "", "content": "Problem Statement Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.\nYou are given Q queries. The i-th query is represented as a pair of two integers X_i and Y_i, and asks you the following: among all pairs of two integers (x, y) such that 1 <= x <= X_i and 1 <= y <= Y_i, find the maximum Euclidean step count (defined below), and how many pairs have the maximum step count, modulo 10^9+7.\nProcess all the queries. Here, the Euclidean step count of a pair of two non-negative integers (a, b) is defined as follows:\n\n(a, b) and (b, a) have the same Euclidean step count.\n(0, a) has a Euclidean step count of 0.\nIf a > 0 and a <= b, let p and q be a unique pair of integers such that b=pa+q and 0 <= q < a. Then, the Euclidean step count of (a, b) is the Euclidean step count of (q, a) plus 1.", "constraint": "1 <= Q <= 3 * 10^5\n1 <= X_i,Y_i <= 10^{18}(1 <= i <= Q)", "input": "Input The input is given from Standard Input in the following format:\nQ\nX_1 Y_1\n:\nX_Q Y_Q", "output": "For each query, print the maximum Euclidean step count, and the number of the pairs that have the maximum step count, modulo 10^9+7, with a space in between.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n4 4\n6 10\n12 11 output: 2 4\n4 1\n4 7\n\nIn the first query, (2,3), (3,2), (3,4) and (4,3) have a Euclidean step count of 2. No pairs have a step count of more than 2.\nIn the second query, (5,8) has a Euclidean step count of 4.\nIn the third query, (5,8), (8,5), (7,11), (8,11), (11,7), (11,8), (12,7) have a Euclidean step count of 4.", "input: 10\n1 1\n2 2\n5 1000000000000000000\n7 3\n1 334334334334334334\n23847657 23458792534\n111111111 111111111\n7 7\n4 19\n9 10 output: 1 1\n1 4\n4 600000013\n3 1\n1 993994017\n35 37447\n38 2\n3 6\n3 9\n4 2"], "Pid": "p03710", "ProblemText": "Task Description: Problem Statement Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.\nYou are given Q queries. The i-th query is represented as a pair of two integers X_i and Y_i, and asks you the following: among all pairs of two integers (x, y) such that 1 <= x <= X_i and 1 <= y <= Y_i, find the maximum Euclidean step count (defined below), and how many pairs have the maximum step count, modulo 10^9+7.\nProcess all the queries. Here, the Euclidean step count of a pair of two non-negative integers (a, b) is defined as follows:\n\n(a, b) and (b, a) have the same Euclidean step count.\n(0, a) has a Euclidean step count of 0.\nIf a > 0 and a <= b, let p and q be a unique pair of integers such that b=pa+q and 0 <= q < a. Then, the Euclidean step count of (a, b) is the Euclidean step count of (q, a) plus 1.\nTask Constraint: 1 <= Q <= 3 * 10^5\n1 <= X_i,Y_i <= 10^{18}(1 <= i <= Q)\nTask Input: Input The input is given from Standard Input in the following format:\nQ\nX_1 Y_1\n:\nX_Q Y_Q\nTask Output: For each query, print the maximum Euclidean step count, and the number of the pairs that have the maximum step count, modulo 10^9+7, with a space in between.\nTask Samples: input: 3\n4 4\n6 10\n12 11 output: 2 4\n4 1\n4 7\n\nIn the first query, (2,3), (3,2), (3,4) and (4,3) have a Euclidean step count of 2. No pairs have a step count of more than 2.\nIn the second query, (5,8) has a Euclidean step count of 4.\nIn the third query, (5,8), (8,5), (7,11), (8,11), (11,7), (11,8), (12,7) have a Euclidean step count of 4.\ninput: 10\n1 1\n2 2\n5 1000000000000000000\n7 3\n1 334334334334334334\n23847657 23458792534\n111111111 111111111\n7 7\n4 19\n9 10 output: 1 1\n1 4\n4 600000013\n3 1\n1 993994017\n35 37447\n38 2\n3 6\n3 9\n4 2\n\n" }, { "title": "", "content": "Problem Statement Based on some criterion, Snuke divided the integers from 1 through 12 into three groups as shown in the figure below.\nGiven two integers x and y (1 <= x < y <= 12), determine whether they belong to the same group.", "constraint": "x and y are integers.\n1 <= x < y <= 12", "input": "Input is given from Standard Input in the following format:\nx y", "output": "If x and y belong to the same group, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 output: Yes", "input: 2 4 output: No"], "Pid": "p03711", "ProblemText": "Task Description: Problem Statement Based on some criterion, Snuke divided the integers from 1 through 12 into three groups as shown in the figure below.\nGiven two integers x and y (1 <= x < y <= 12), determine whether they belong to the same group.\nTask Constraint: x and y are integers.\n1 <= x < y <= 12\nTask Input: Input is given from Standard Input in the following format:\nx y\nTask Output: If x and y belong to the same group, print Yes; otherwise, print No.\nTask Samples: input: 1 3 output: Yes\ninput: 2 4 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given a image with a height of H pixels and a width of W pixels.\nEach pixel is represented by a lowercase English letter.\nThe pixel at the i-th row from the top and j-th column from the left is a_{ij}.\nPut a box around this image and output the result. The box should consist of # and have a thickness of 1.", "constraint": "1 <= H, W <= 100\na_{ij} is a lowercase English letter.", "input": "Input is given from Standard Input in the following format:\nH W\na_{11} . . . a_{1W}\n:\na_{H1} . . . a_{HW}", "output": "Print the image surrounded by a box that consists of # and has a thickness of 1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\nabc\narc output: #####\n#abc#\n#arc#\n#####", "input: 1 1\nz output: ###\n#z#\n###"], "Pid": "p03712", "ProblemText": "Task Description: Problem Statement You are given a image with a height of H pixels and a width of W pixels.\nEach pixel is represented by a lowercase English letter.\nThe pixel at the i-th row from the top and j-th column from the left is a_{ij}.\nPut a box around this image and output the result. The box should consist of # and have a thickness of 1.\nTask Constraint: 1 <= H, W <= 100\na_{ij} is a lowercase English letter.\nTask Input: Input is given from Standard Input in the following format:\nH W\na_{11} . . . a_{1W}\n:\na_{H1} . . . a_{HW}\nTask Output: Print the image surrounded by a box that consists of # and has a thickness of 1.\nTask Samples: input: 2 3\nabc\narc output: #####\n#abc#\n#arc#\n#####\ninput: 1 1\nz output: ###\n#z#\n###\n\n" }, { "title": "", "content": "Problem Statement There is a bar of chocolate with a height of H blocks and a width of W blocks.\nSnuke is dividing this bar into exactly three pieces.\nHe can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.\nSnuke is trying to divide the bar as evenly as possible.\nMore specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.\nFind the minimum possible value of S_{max} - S_{min}.", "constraint": "2 <= H, W <= 10^5", "input": "Input is given from Standard Input in the following format:\nH W", "output": "Print the minimum possible value of S_{max} - S_{min}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 output: 0\n\nIn the division below, S_{max} - S_{min} = 5 - 5 = 0.", "input: 4 5 output: 2\n\nIn the division below, S_{max} - S_{min} = 8 - 6 = 2.", "input: 5 5 output: 4\n\nIn the division below, S_{max} - S_{min} = 10 - 6 = 4.", "input: 100000 2 output: 1", "input: 100000 100000 output: 50000"], "Pid": "p03713", "ProblemText": "Task Description: Problem Statement There is a bar of chocolate with a height of H blocks and a width of W blocks.\nSnuke is dividing this bar into exactly three pieces.\nHe can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.\nSnuke is trying to divide the bar as evenly as possible.\nMore specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.\nFind the minimum possible value of S_{max} - S_{min}.\nTask Constraint: 2 <= H, W <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nH W\nTask Output: Print the minimum possible value of S_{max} - S_{min}.\nTask Samples: input: 3 5 output: 0\n\nIn the division below, S_{max} - S_{min} = 5 - 5 = 0.\ninput: 4 5 output: 2\n\nIn the division below, S_{max} - S_{min} = 8 - 6 = 2.\ninput: 5 5 output: 4\n\nIn the division below, S_{max} - S_{min} = 10 - 6 = 4.\ninput: 100000 2 output: 1\ninput: 100000 100000 output: 50000\n\n" }, { "title": "", "content": "Problem Statement Let N be a positive integer.\nThere is a numerical sequence of length 3N, a = (a_1, a_2, . . . , a_{3N}).\nSnuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.\nHere, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').\nFind the maximum possible score of a'. partial score: Partial Score\nIn the test set worth 300 points, N <= 1000.", "constraint": "1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{3N}", "output": "Print the maximum possible score of a'.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 1 4 1 5 9 output: 1\n\nWhen a_2 and a_6 are removed, a' will be (3,4,1,5), which has a score of (3 + 4) - (1 + 5) = 1.", "input: 1\n1 2 3 output: -1\n\nFor example, when a_1 are removed, a' will be (2,3), which has a score of 2 - 3 = -1.", "input: 3\n8 2 2 7 4 6 5 3 8 output: 5\n\nFor example, when a_2, a_3 and a_9 are removed, a' will be (8,7,4,6,5,3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5."], "Pid": "p03714", "ProblemText": "Task Description: Problem Statement Let N be a positive integer.\nThere is a numerical sequence of length 3N, a = (a_1, a_2, . . . , a_{3N}).\nSnuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.\nHere, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').\nFind the maximum possible score of a'. partial score: Partial Score\nIn the test set worth 300 points, N <= 1000.\nTask Constraint: 1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{3N}\nTask Output: Print the maximum possible score of a'.\nTask Samples: input: 2\n3 1 4 1 5 9 output: 1\n\nWhen a_2 and a_6 are removed, a' will be (3,4,1,5), which has a score of (3 + 4) - (1 + 5) = 1.\ninput: 1\n1 2 3 output: -1\n\nFor example, when a_1 are removed, a' will be (2,3), which has a score of 2 - 3 = -1.\ninput: 3\n8 2 2 7 4 6 5 3 8 output: 5\n\nFor example, when a_2, a_3 and a_9 are removed, a' will be (8,7,4,6,5,3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.\n\n" }, { "title": "", "content": "Problem Statement There is a bar of chocolate with a height of H blocks and a width of W blocks.\nSnuke is dividing this bar into exactly three pieces.\nHe can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.\nSnuke is trying to divide the bar as evenly as possible.\nMore specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.\nFind the minimum possible value of S_{max} - S_{min}.", "constraint": "2 <= H, W <= 10^5", "input": "Input is given from Standard Input in the following format:\nH W", "output": "Print the minimum possible value of S_{max} - S_{min}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 5 output: 0\n\nIn the division below, S_{max} - S_{min} = 5 - 5 = 0.", "input: 4 5 output: 2\n\nIn the division below, S_{max} - S_{min} = 8 - 6 = 2.", "input: 5 5 output: 4\n\nIn the division below, S_{max} - S_{min} = 10 - 6 = 4.", "input: 100000 2 output: 1", "input: 100000 100000 output: 50000"], "Pid": "p03715", "ProblemText": "Task Description: Problem Statement There is a bar of chocolate with a height of H blocks and a width of W blocks.\nSnuke is dividing this bar into exactly three pieces.\nHe can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.\nSnuke is trying to divide the bar as evenly as possible.\nMore specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.\nFind the minimum possible value of S_{max} - S_{min}.\nTask Constraint: 2 <= H, W <= 10^5\nTask Input: Input is given from Standard Input in the following format:\nH W\nTask Output: Print the minimum possible value of S_{max} - S_{min}.\nTask Samples: input: 3 5 output: 0\n\nIn the division below, S_{max} - S_{min} = 5 - 5 = 0.\ninput: 4 5 output: 2\n\nIn the division below, S_{max} - S_{min} = 8 - 6 = 2.\ninput: 5 5 output: 4\n\nIn the division below, S_{max} - S_{min} = 10 - 6 = 4.\ninput: 100000 2 output: 1\ninput: 100000 100000 output: 50000\n\n" }, { "title": "", "content": "Problem Statement Let N be a positive integer.\nThere is a numerical sequence of length 3N, a = (a_1, a_2, . . . , a_{3N}).\nSnuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.\nHere, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').\nFind the maximum possible score of a'. partial score: Partial Score\nIn the test set worth 300 points, N <= 1000.", "constraint": "1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{3N}", "output": "Print the maximum possible score of a'.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n3 1 4 1 5 9 output: 1\n\nWhen a_2 and a_6 are removed, a' will be (3,4,1,5), which has a score of (3 + 4) - (1 + 5) = 1.", "input: 1\n1 2 3 output: -1\n\nFor example, when a_1 are removed, a' will be (2,3), which has a score of 2 - 3 = -1.", "input: 3\n8 2 2 7 4 6 5 3 8 output: 5\n\nFor example, when a_2, a_3 and a_9 are removed, a' will be (8,7,4,6,5,3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5."], "Pid": "p03716", "ProblemText": "Task Description: Problem Statement Let N be a positive integer.\nThere is a numerical sequence of length 3N, a = (a_1, a_2, . . . , a_{3N}).\nSnuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.\nHere, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').\nFind the maximum possible score of a'. partial score: Partial Score\nIn the test set worth 300 points, N <= 1000.\nTask Constraint: 1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{3N}\nTask Output: Print the maximum possible score of a'.\nTask Samples: input: 2\n3 1 4 1 5 9 output: 1\n\nWhen a_2 and a_6 are removed, a' will be (3,4,1,5), which has a score of (3 + 4) - (1 + 5) = 1.\ninput: 1\n1 2 3 output: -1\n\nFor example, when a_1 are removed, a' will be (2,3), which has a score of 2 - 3 = -1.\ninput: 3\n8 2 2 7 4 6 5 3 8 output: 5\n\nFor example, when a_2, a_3 and a_9 are removed, a' will be (8,7,4,6,5,3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.\n\n" }, { "title": "", "content": "Problem Statement There are N squares arranged in a row.\nThe squares are numbered 1,2, . . . , N, from left to right.\nSnuke is painting each square in red, green or blue.\nAccording to his aesthetic sense, the following M conditions must all be satisfied.\nThe i-th condition is:\n\nThere are exactly x_i different colors among squares l_i, l_i + 1, . . . , r_i.\n\nIn how many ways can the squares be painted to satisfy all the conditions?\nFind the count modulo 10^9+7.", "constraint": "1 <= N <= 300\n1 <= M <= 300\n1 <= l_i <= r_i <= N\n1 <= x_i <= 3", "input": "Input is given from Standard Input in the following format:\nN M\nl_1 r_1 x_1\nl_2 r_2 x_2\n:\nl_M r_M x_M", "output": "Print the number of ways to paint the squares to satisfy all the conditions, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1 3 3 output: 6\n\nThe six ways are:\n\nRGB\nRBG\nGRB\nGBR\nBRG\nBGR\n\nwhere R, G and B correspond to red, green and blue squares, respectively.", "input: 4 2\n1 3 1\n2 4 2 output: 6\n\nThe six ways are:\n\nRRRG\nRRRB\nGGGR\nGGGB\nBBBR\nBBBG", "input: 1 3\n1 1 1\n1 1 2\n1 1 3 output: 0\n\nThere are zero ways.", "input: 8 10\n2 6 2\n5 5 1\n3 5 2\n4 7 3\n4 4 1\n2 3 1\n7 7 1\n1 5 2\n1 7 3\n3 4 2 output: 108"], "Pid": "p03717", "ProblemText": "Task Description: Problem Statement There are N squares arranged in a row.\nThe squares are numbered 1,2, . . . , N, from left to right.\nSnuke is painting each square in red, green or blue.\nAccording to his aesthetic sense, the following M conditions must all be satisfied.\nThe i-th condition is:\n\nThere are exactly x_i different colors among squares l_i, l_i + 1, . . . , r_i.\n\nIn how many ways can the squares be painted to satisfy all the conditions?\nFind the count modulo 10^9+7.\nTask Constraint: 1 <= N <= 300\n1 <= M <= 300\n1 <= l_i <= r_i <= N\n1 <= x_i <= 3\nTask Input: Input is given from Standard Input in the following format:\nN M\nl_1 r_1 x_1\nl_2 r_2 x_2\n:\nl_M r_M x_M\nTask Output: Print the number of ways to paint the squares to satisfy all the conditions, modulo 10^9+7.\nTask Samples: input: 3 1\n1 3 3 output: 6\n\nThe six ways are:\n\nRGB\nRBG\nGRB\nGBR\nBRG\nBGR\n\nwhere R, G and B correspond to red, green and blue squares, respectively.\ninput: 4 2\n1 3 1\n2 4 2 output: 6\n\nThe six ways are:\n\nRRRG\nRRRB\nGGGR\nGGGB\nBBBR\nBBBG\ninput: 1 3\n1 1 1\n1 1 2\n1 1 3 output: 0\n\nThere are zero ways.\ninput: 8 10\n2 6 2\n5 5 1\n3 5 2\n4 7 3\n4 4 1\n2 3 1\n7 7 1\n1 5 2\n1 7 3\n3 4 2 output: 108\n\n" }, { "title": "", "content": "Problem Statement There is a pond with a rectangular shape.\nThe pond is divided into a grid with H rows and W columns of squares.\nWe will denote the square at the i-th row from the top and j-th column from the left by (i, \\ j).\nSome of the squares in the pond contains a lotus leaf floating on the water.\nOn one of those leaves, S, there is a frog trying to get to another leaf T.\nThe state of square (i, \\ j) is given to you by a character a_{ij}, as follows:\n\n. : A square without a leaf.\no : A square with a leaf floating on the water.\nS : A square with the leaf S.\nT : A square with the leaf T.\n\nThe frog will repeatedly perform the following action to get to the leaf T: \"jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located. \"\nSnuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T.\nDetermine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.", "constraint": "2 <= H, W <= 100\na_{ij} is ., o, S or T.\nThere is exactly one S among a_{ij}.\nThere is exactly one T among a_{ij}.", "input": "Input is given from Standard Input in the following format:\nH W\na_{11} . . . a_{1W}\n:\na_{H1} . . . a_{HW}", "output": "If the objective is achievable, print the minimum necessary number of leaves to remove.\nOtherwise, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\nS.o\n.o.\no.T output: 2\n\nRemove the upper-right and lower-left leaves.", "input: 3 4\nS...\n.oo.\n...T output: 0", "input: 4 3\n.S.\n.o.\n.o.\n.T. output: -1", "input: 10 10\n.o...o..o.\n....o.....\n....oo.oo.\n..oooo..o.\n....oo....\n..o..o....\no..o....So\no....T....\n....o.....\n........oo output: 5"], "Pid": "p03718", "ProblemText": "Task Description: Problem Statement There is a pond with a rectangular shape.\nThe pond is divided into a grid with H rows and W columns of squares.\nWe will denote the square at the i-th row from the top and j-th column from the left by (i, \\ j).\nSome of the squares in the pond contains a lotus leaf floating on the water.\nOn one of those leaves, S, there is a frog trying to get to another leaf T.\nThe state of square (i, \\ j) is given to you by a character a_{ij}, as follows:\n\n. : A square without a leaf.\no : A square with a leaf floating on the water.\nS : A square with the leaf S.\nT : A square with the leaf T.\n\nThe frog will repeatedly perform the following action to get to the leaf T: \"jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located. \"\nSnuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T.\nDetermine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.\nTask Constraint: 2 <= H, W <= 100\na_{ij} is ., o, S or T.\nThere is exactly one S among a_{ij}.\nThere is exactly one T among a_{ij}.\nTask Input: Input is given from Standard Input in the following format:\nH W\na_{11} . . . a_{1W}\n:\na_{H1} . . . a_{HW}\nTask Output: If the objective is achievable, print the minimum necessary number of leaves to remove.\nOtherwise, print -1 instead.\nTask Samples: input: 3 3\nS.o\n.o.\no.T output: 2\n\nRemove the upper-right and lower-left leaves.\ninput: 3 4\nS...\n.oo.\n...T output: 0\ninput: 4 3\n.S.\n.o.\n.o.\n.T. output: -1\ninput: 10 10\n.o...o..o.\n....o.....\n....oo.oo.\n..oooo..o.\n....oo....\n..o..o....\no..o....So\no....T....\n....o.....\n........oo output: 5\n\n" }, { "title": "", "content": "Problem Statement You are given three integers A, B and C.\nDetermine whether C is not less than A and not greater than B.", "constraint": "-100<=A,B,C<=100 \nA, B and C are all integers.", "input": "Input is given from Standard Input in the following format: \nA B C", "output": "If the condition is satisfied, print Yes; otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 2 output: Yes\n\nC=2 is not less than A=1 and not greater than B=3, and thus the output should be Yes.", "input: 6 5 4 output: No\n\nC=4 is less than A=6, and thus the output should be No.", "input: 2 2 2 output: Yes"], "Pid": "p03719", "ProblemText": "Task Description: Problem Statement You are given three integers A, B and C.\nDetermine whether C is not less than A and not greater than B.\nTask Constraint: -100<=A,B,C<=100 \nA, B and C are all integers.\nTask Input: Input is given from Standard Input in the following format: \nA B C\nTask Output: If the condition is satisfied, print Yes; otherwise, print No.\nTask Samples: input: 1 3 2 output: Yes\n\nC=2 is not less than A=1 and not greater than B=3, and thus the output should be Yes.\ninput: 6 5 4 output: No\n\nC=4 is less than A=6, and thus the output should be No.\ninput: 2 2 2 output: Yes\n\n" }, { "title": "", "content": "Problem Statement There are N cities and M roads.\nThe i-th road (1<=i<=M) connects two cities a_i and b_i (1<=a_i, b_i<=N) bidirectionally.\nThere may be more than one road that connects the same pair of two cities.\nFor each city, how many roads are connected to the city?", "constraint": "2<=N,M<=50\n1<=a_i,b_i<=N\na_i != b_i\nAll input values are integers.", "input": "Input is given from Standard Input in the following format: \nN M\na_1 b_1\n: \na_M b_M", "output": "Print the answer in N lines.\nIn the i-th line (1<=i<=N), print the number of roads connected to city i.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n1 2\n2 3\n1 4 output: 2\n2\n1\n1\nCity 1 is connected to the 1-st and 3-rd roads.\nCity 2 is connected to the 1-st and 2-nd roads.\nCity 3 is connected to the 2-nd road.\nCity 4 is connected to the 3-rd road.", "input: 2 5\n1 2\n2 1\n1 2\n2 1\n1 2 output: 5\n5", "input: 8 8\n1 2\n3 4\n1 5\n2 8\n3 7\n5 2\n4 1\n6 8 output: 3\n3\n2\n2\n2\n1\n1\n2"], "Pid": "p03720", "ProblemText": "Task Description: Problem Statement There are N cities and M roads.\nThe i-th road (1<=i<=M) connects two cities a_i and b_i (1<=a_i, b_i<=N) bidirectionally.\nThere may be more than one road that connects the same pair of two cities.\nFor each city, how many roads are connected to the city?\nTask Constraint: 2<=N,M<=50\n1<=a_i,b_i<=N\na_i != b_i\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format: \nN M\na_1 b_1\n: \na_M b_M\nTask Output: Print the answer in N lines.\nIn the i-th line (1<=i<=N), print the number of roads connected to city i.\nTask Samples: input: 4 3\n1 2\n2 3\n1 4 output: 2\n2\n1\n1\nCity 1 is connected to the 1-st and 3-rd roads.\nCity 2 is connected to the 1-st and 2-nd roads.\nCity 3 is connected to the 2-nd road.\nCity 4 is connected to the 3-rd road.\ninput: 2 5\n1 2\n2 1\n1 2\n2 1\n1 2 output: 5\n5\ninput: 8 8\n1 2\n3 4\n1 5\n2 8\n3 7\n5 2\n4 1\n6 8 output: 3\n3\n2\n2\n2\n1\n1\n2\n\n" }, { "title": "", "content": "Problem Statement There is an empty array.\nThe following N operations will be performed to insert integers into the array.\nIn the i-th operation (1<=i<=N), b_i copies of an integer a_i are inserted into the array.\nFind the K-th smallest integer in the array after the N operations.\nFor example, the 4-th smallest integer in the array \\{1,2,2,3,3,3\\} is 3.", "constraint": "1<=N<=10^5 \n1<=a_i,b_i<=10^5 \n1<=K<=b_1…+…b_n\nAll input values are integers.", "input": "Input is given from Standard Input in the following format: \nN K\na_1 b_1\n: \na_N b_N", "output": "Print the K-th smallest integer in the array after the N operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 4\n1 1\n2 2\n3 3 output: 3\n\nThe resulting array is the same as the one in the problem statement.", "input: 10 500000\n1 100000\n1 100000\n1 100000\n1 100000\n1 100000\n100000 100000\n100000 100000\n100000 100000\n100000 100000\n100000 100000 output: 1"], "Pid": "p03721", "ProblemText": "Task Description: Problem Statement There is an empty array.\nThe following N operations will be performed to insert integers into the array.\nIn the i-th operation (1<=i<=N), b_i copies of an integer a_i are inserted into the array.\nFind the K-th smallest integer in the array after the N operations.\nFor example, the 4-th smallest integer in the array \\{1,2,2,3,3,3\\} is 3.\nTask Constraint: 1<=N<=10^5 \n1<=a_i,b_i<=10^5 \n1<=K<=b_1…+…b_n\nAll input values are integers.\nTask Input: Input is given from Standard Input in the following format: \nN K\na_1 b_1\n: \na_N b_N\nTask Output: Print the K-th smallest integer in the array after the N operations.\nTask Samples: input: 3 4\n1 1\n2 2\n3 3 output: 3\n\nThe resulting array is the same as the one in the problem statement.\ninput: 10 500000\n1 100000\n1 100000\n1 100000\n1 100000\n1 100000\n100000 100000\n100000 100000\n100000 100000\n100000 100000\n100000 100000 output: 1\n\n" }, { "title": "", "content": "Problem Statement There is a directed graph with N vertices and M edges.\nThe i-th edge (1<=i<=M) points from vertex a_i to vertex b_i, and has a weight c_i.\nWe will play the following single-player game using this graph and a piece.\nInitially, the piece is placed at vertex 1, and the score of the player is set to 0.\nThe player can move the piece as follows:\n\nWhen the piece is placed at vertex a_i, move the piece along the i-th edge to vertex b_i. After this move, the score of the player is increased by c_i.\n\nThe player can end the game only when the piece is placed at vertex N.\nThe given graph guarantees that it is possible to traverse from vertex 1 to vertex N.\nWhen the player acts optimally to maximize the score at the end of the game, what will the score be?\nIf it is possible to increase the score indefinitely, print inf.", "constraint": "2<=N<=1000 \n1<=M<=min(N(N-1),2000) \n1<=a_i,b_i<=N (1<=i<=M) \na_i!=b_i (1<=i<=M) \na_i!=a_j or b_i!=b_j (1<=iB, LESS if A24, print GREATER.", "input: 850\n3777 output: LESS", "input: 9720246\n22516266 output: LESS", "input: 123456789012345678901234567890\n234567890123456789012345678901 output: LESS"], "Pid": "p03738", "ProblemText": "Task Description: Problem Statement You are given two positive integers A and B. Compare the magnitudes of these numbers.\nTask Constraint: 1 <= A, B <= 10^{100}\nNeither A nor B begins with a 0.\nTask Input: Input is given from Standard Input in the following format:\nA\nB\nTask Output: Print GREATER if A>B, LESS if A24, print GREATER.\ninput: 850\n3777 output: LESS\ninput: 9720246\n22516266 output: LESS\ninput: 123456789012345678901234567890\n234567890123456789012345678901 output: LESS\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length N. The i-th term in the sequence is a_i.\nIn one operation, you can select a term and either increment or decrement it by one.\nAt least how many operations are necessary to satisfy the following conditions?\n\nFor every i (1<=i<=n), the sum of the terms from the 1-st through i-th term is not zero.\nFor every i (1<=i<=n-1), the sign of the sum of the terms from the 1-st through i-th term, is different from the sign of the sum of the terms from the 1-st through (i+1)-th term.", "constraint": "2 <= n <= 10^5\n|a_i| <= 10^9\nEach a_i is an integer.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n", "output": "Print the minimum necessary count of operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 -3 1 0 output: 4\n\nFor example, the given sequence can be transformed into 1, -2,2, -2 by four operations. The sums of the first one, two, three and four terms are 1, -1,1 and -1, respectively, which satisfy the conditions.", "input: 5\n3 -6 4 -5 7 output: 0\n\nThe given sequence already satisfies the conditions.", "input: 6\n-1 4 3 2 -5 4 output: 8"], "Pid": "p03739", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length N. The i-th term in the sequence is a_i.\nIn one operation, you can select a term and either increment or decrement it by one.\nAt least how many operations are necessary to satisfy the following conditions?\n\nFor every i (1<=i<=n), the sum of the terms from the 1-st through i-th term is not zero.\nFor every i (1<=i<=n-1), the sign of the sum of the terms from the 1-st through i-th term, is different from the sign of the sum of the terms from the 1-st through (i+1)-th term.\nTask Constraint: 2 <= n <= 10^5\n|a_i| <= 10^9\nEach a_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n\nTask Output: Print the minimum necessary count of operations.\nTask Samples: input: 4\n1 -3 1 0 output: 4\n\nFor example, the given sequence can be transformed into 1, -2,2, -2 by four operations. The sums of the first one, two, three and four terms are 1, -1,1 and -1, respectively, which satisfy the conditions.\ninput: 5\n3 -6 4 -5 7 output: 0\n\nThe given sequence already satisfies the conditions.\ninput: 6\n-1 4 3 2 -5 4 output: 8\n\n" }, { "title": "", "content": "Problem Statement Alice and Brown loves games. Today, they will play the following game.\nIn this game, there are two piles initially consisting of X and Y stones, respectively.\nAlice and Bob alternately perform the following operation, starting from Alice:\n\nTake 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1<=i) can be freely chosen as long as there is a sufficient number of stones in the pile.\n\nThe player who becomes unable to perform the operation, loses the game.\nGiven X and Y, determine the winner of the game, assuming that both players play optimally.", "constraint": "0 <= X, Y <= 10^{18}", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "Print the winner: either Alice or Brown.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 output: Brown\n\nAlice can do nothing but taking two stones from the pile containing two stones. As a result, the piles consist of zero and two stones, respectively. Then, Brown will take the two stones, and the piles will consist of one and zero stones, respectively. Alice will be unable to perform the operation anymore, which means Brown's victory.", "input: 5 0 output: Alice", "input: 0 0 output: Brown", "input: 4 8 output: Alice"], "Pid": "p03740", "ProblemText": "Task Description: Problem Statement Alice and Brown loves games. Today, they will play the following game.\nIn this game, there are two piles initially consisting of X and Y stones, respectively.\nAlice and Bob alternately perform the following operation, starting from Alice:\n\nTake 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1<=i) can be freely chosen as long as there is a sufficient number of stones in the pile.\n\nThe player who becomes unable to perform the operation, loses the game.\nGiven X and Y, determine the winner of the game, assuming that both players play optimally.\nTask Constraint: 0 <= X, Y <= 10^{18}\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: Print the winner: either Alice or Brown.\nTask Samples: input: 2 1 output: Brown\n\nAlice can do nothing but taking two stones from the pile containing two stones. As a result, the piles consist of zero and two stones, respectively. Then, Brown will take the two stones, and the piles will consist of one and zero stones, respectively. Alice will be unable to perform the operation anymore, which means Brown's victory.\ninput: 5 0 output: Alice\ninput: 0 0 output: Brown\ninput: 4 8 output: Alice\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence of length N. The i-th term in the sequence is a_i.\nIn one operation, you can select a term and either increment or decrement it by one.\nAt least how many operations are necessary to satisfy the following conditions?\n\nFor every i (1<=i<=n), the sum of the terms from the 1-st through i-th term is not zero.\nFor every i (1<=i<=n-1), the sign of the sum of the terms from the 1-st through i-th term, is different from the sign of the sum of the terms from the 1-st through (i+1)-th term.", "constraint": "2 <= n <= 10^5\n|a_i| <= 10^9\nEach a_i is an integer.", "input": "Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n", "output": "Print the minimum necessary count of operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 -3 1 0 output: 4\n\nFor example, the given sequence can be transformed into 1, -2,2, -2 by four operations. The sums of the first one, two, three and four terms are 1, -1,1 and -1, respectively, which satisfy the conditions.", "input: 5\n3 -6 4 -5 7 output: 0\n\nThe given sequence already satisfies the conditions.", "input: 6\n-1 4 3 2 -5 4 output: 8"], "Pid": "p03741", "ProblemText": "Task Description: Problem Statement You are given an integer sequence of length N. The i-th term in the sequence is a_i.\nIn one operation, you can select a term and either increment or decrement it by one.\nAt least how many operations are necessary to satisfy the following conditions?\n\nFor every i (1<=i<=n), the sum of the terms from the 1-st through i-th term is not zero.\nFor every i (1<=i<=n-1), the sign of the sum of the terms from the 1-st through i-th term, is different from the sign of the sum of the terms from the 1-st through (i+1)-th term.\nTask Constraint: 2 <= n <= 10^5\n|a_i| <= 10^9\nEach a_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nn\na_1 a_2 . . . a_n\nTask Output: Print the minimum necessary count of operations.\nTask Samples: input: 4\n1 -3 1 0 output: 4\n\nFor example, the given sequence can be transformed into 1, -2,2, -2 by four operations. The sums of the first one, two, three and four terms are 1, -1,1 and -1, respectively, which satisfy the conditions.\ninput: 5\n3 -6 4 -5 7 output: 0\n\nThe given sequence already satisfies the conditions.\ninput: 6\n-1 4 3 2 -5 4 output: 8\n\n" }, { "title": "", "content": "Problem Statement Alice and Brown loves games. Today, they will play the following game.\nIn this game, there are two piles initially consisting of X and Y stones, respectively.\nAlice and Bob alternately perform the following operation, starting from Alice:\n\nTake 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1<=i) can be freely chosen as long as there is a sufficient number of stones in the pile.\n\nThe player who becomes unable to perform the operation, loses the game.\nGiven X and Y, determine the winner of the game, assuming that both players play optimally.", "constraint": "0 <= X, Y <= 10^{18}", "input": "Input is given from Standard Input in the following format:\nX Y", "output": "Print the winner: either Alice or Brown.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 output: Brown\n\nAlice can do nothing but taking two stones from the pile containing two stones. As a result, the piles consist of zero and two stones, respectively. Then, Brown will take the two stones, and the piles will consist of one and zero stones, respectively. Alice will be unable to perform the operation anymore, which means Brown's victory.", "input: 5 0 output: Alice", "input: 0 0 output: Brown", "input: 4 8 output: Alice"], "Pid": "p03742", "ProblemText": "Task Description: Problem Statement Alice and Brown loves games. Today, they will play the following game.\nIn this game, there are two piles initially consisting of X and Y stones, respectively.\nAlice and Bob alternately perform the following operation, starting from Alice:\n\nTake 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1<=i) can be freely chosen as long as there is a sufficient number of stones in the pile.\n\nThe player who becomes unable to perform the operation, loses the game.\nGiven X and Y, determine the winner of the game, assuming that both players play optimally.\nTask Constraint: 0 <= X, Y <= 10^{18}\nTask Input: Input is given from Standard Input in the following format:\nX Y\nTask Output: Print the winner: either Alice or Brown.\nTask Samples: input: 2 1 output: Brown\n\nAlice can do nothing but taking two stones from the pile containing two stones. As a result, the piles consist of zero and two stones, respectively. Then, Brown will take the two stones, and the piles will consist of one and zero stones, respectively. Alice will be unable to perform the operation anymore, which means Brown's victory.\ninput: 5 0 output: Alice\ninput: 0 0 output: Brown\ninput: 4 8 output: Alice\n\n" }, { "title": "", "content": "Problem Statement Alice lives on a line. Today, she will travel to some place in a mysterious vehicle.\nInitially, the distance between Alice and her destination is D. When she input a number x to the vehicle, it will travel in the direction of the destination by a distance of x if this move would shorten the distance between the vehicle and the destination, and it will stay at its position otherwise. Note that the vehicle may go past the destination when the distance between the vehicle and the destination is less than x.\nAlice made a list of N numbers. The i-th number in this list is d_i. She will insert these numbers to the vehicle one by one.\nHowever, a mischievous witch appeared. She is thinking of rewriting one number in the list so that Alice will not reach the destination after N moves.\nShe has Q plans to do this, as follows:\n\nRewrite only the q_i-th number in the list with some integer so that Alice will not reach the destination.\n\nWrite a program to determine whether each plan is feasible.", "constraint": "1<= N <= 5*10^5\n1<= Q <= 5*10^5\n1<= D <= 10^9\n1<= d_i <= 10^9(1<=i<=N)\n1<= q_i <= N(1<=i<=Q)\nD and each d_i are integers.", "input": "Input is given from Standard Input in the following format:\nN D\nd_1 d_2 . . . d_N\nQ\nq_1 q_2 . . . q_Q", "output": "Print Q lines. The i-th line should contain YES if the i-th plan is feasible, and NO otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 10\n3 4 3 3\n2\n4 3 output: NO\nYES\n\nFor the first plan, Alice will already arrive at the destination by the first three moves, and therefore the answer is NO.\nFor the second plan, rewriting the third number in the list with 5 will prevent Alice from reaching the destination as shown in the following figure, and thus the answer is YES.", "input: 5 9\n4 4 2 3 2\n5\n1 4 2 3 5 output: YES\nYES\nYES\nYES\nYES\n\nAlice will not reach the destination as it is, and therefore all the plans are feasible.", "input: 6 15\n4 3 5 4 2 1\n6\n1 2 3 4 5 6 output: NO\nNO\nYES\nNO\nNO\nYES"], "Pid": "p03743", "ProblemText": "Task Description: Problem Statement Alice lives on a line. Today, she will travel to some place in a mysterious vehicle.\nInitially, the distance between Alice and her destination is D. When she input a number x to the vehicle, it will travel in the direction of the destination by a distance of x if this move would shorten the distance between the vehicle and the destination, and it will stay at its position otherwise. Note that the vehicle may go past the destination when the distance between the vehicle and the destination is less than x.\nAlice made a list of N numbers. The i-th number in this list is d_i. She will insert these numbers to the vehicle one by one.\nHowever, a mischievous witch appeared. She is thinking of rewriting one number in the list so that Alice will not reach the destination after N moves.\nShe has Q plans to do this, as follows:\n\nRewrite only the q_i-th number in the list with some integer so that Alice will not reach the destination.\n\nWrite a program to determine whether each plan is feasible.\nTask Constraint: 1<= N <= 5*10^5\n1<= Q <= 5*10^5\n1<= D <= 10^9\n1<= d_i <= 10^9(1<=i<=N)\n1<= q_i <= N(1<=i<=Q)\nD and each d_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN D\nd_1 d_2 . . . d_N\nQ\nq_1 q_2 . . . q_Q\nTask Output: Print Q lines. The i-th line should contain YES if the i-th plan is feasible, and NO otherwise.\nTask Samples: input: 4 10\n3 4 3 3\n2\n4 3 output: NO\nYES\n\nFor the first plan, Alice will already arrive at the destination by the first three moves, and therefore the answer is NO.\nFor the second plan, rewriting the third number in the list with 5 will prevent Alice from reaching the destination as shown in the following figure, and thus the answer is YES.\ninput: 5 9\n4 4 2 3 2\n5\n1 4 2 3 5 output: YES\nYES\nYES\nYES\nYES\n\nAlice will not reach the destination as it is, and therefore all the plans are feasible.\ninput: 6 15\n4 3 5 4 2 1\n6\n1 2 3 4 5 6 output: NO\nNO\nYES\nNO\nNO\nYES\n\n" }, { "title": "", "content": "Problem Statement You are in charge of controlling a dam. The dam can store at most L liters of water. Initially, the dam is empty. Some amount of water flows into the dam every morning, and any amount of water may be discharged every night, but this amount needs to be set so that no water overflows the dam the next morning.\nIt is known that v_i liters of water at t_i degrees Celsius will flow into the dam on the morning of the i-th day.\nYou are wondering about the maximum possible temperature of water in the dam at noon of each day, under the condition that there needs to be exactly L liters of water in the dam at that time. For each i, find the maximum possible temperature of water in the dam at noon of the i-th day. Here, consider each maximization separately, that is, the amount of water discharged for the maximization of the temperature on the i-th day, may be different from the amount of water discharged for the maximization of the temperature on the j-th day (j! =i).\nAlso, assume that the temperature of water is not affected by anything but new water that flows into the dam. That is, when V_1 liters of water at T_1 degrees Celsius and V_2 liters of water at T_2 degrees Celsius are mixed together, they will become V_1+V_2 liters of water at \\frac{T_1*V_1+T_2*V_2}{V_1+V_2} degrees Celsius, and the volume and temperature of water are not affected by any other factors.", "constraint": "1<= N <= 5*10^5\n1<= L <= 10^9\n0<= t_i <= 10^9(1<=i<=N)\n1<= v_i <= L(1<=i<=N)\nv_1 = L\nL, each t_i and v_i are integers.", "input": "Input is given from Standard Input in the following format:\nN L\nt_1 v_1\nt_2 v_2\n:\nt_N v_N", "output": "Print N lines. The i-th line should contain the maximum temperature such that it is possible to store L liters of water at that temperature in the dam at noon of the i-th day.\nEach of these values is accepted if the absolute or relative error is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 10\n10 10\n20 5\n4 3 output: 10.0000000\n15.0000000\n13.2000000\n\nOn the first day, the temperature of water in the dam is always 10 degrees: the temperature of the only water that flows into the dam on the first day.\n10 liters of water at 15 degrees of Celsius can be stored on the second day, by discharging 5 liters of water on the night of the first day, and mix the remaining water with the water that flows into the dam on the second day.\n10 liters of water at 13.2 degrees of Celsius can be stored on the third day, by discharging 8 liters of water on the night of the first day, and mix the remaining water with the water that flows into the dam on the second and third days.", "input: 4 15\n0 15\n2 5\n3 6\n4 4 output: 0.0000000\n0.6666667\n1.8666667\n2.9333333", "input: 4 15\n1000000000 15\n9 5\n8 6\n7 4 output: 1000000000.0000000\n666666669.6666666\n400000005.0000000\n293333338.8666667\n\nAlthough the temperature of water may exceed 100 degrees Celsius, we assume that water does not vaporize."], "Pid": "p03744", "ProblemText": "Task Description: Problem Statement You are in charge of controlling a dam. The dam can store at most L liters of water. Initially, the dam is empty. Some amount of water flows into the dam every morning, and any amount of water may be discharged every night, but this amount needs to be set so that no water overflows the dam the next morning.\nIt is known that v_i liters of water at t_i degrees Celsius will flow into the dam on the morning of the i-th day.\nYou are wondering about the maximum possible temperature of water in the dam at noon of each day, under the condition that there needs to be exactly L liters of water in the dam at that time. For each i, find the maximum possible temperature of water in the dam at noon of the i-th day. Here, consider each maximization separately, that is, the amount of water discharged for the maximization of the temperature on the i-th day, may be different from the amount of water discharged for the maximization of the temperature on the j-th day (j! =i).\nAlso, assume that the temperature of water is not affected by anything but new water that flows into the dam. That is, when V_1 liters of water at T_1 degrees Celsius and V_2 liters of water at T_2 degrees Celsius are mixed together, they will become V_1+V_2 liters of water at \\frac{T_1*V_1+T_2*V_2}{V_1+V_2} degrees Celsius, and the volume and temperature of water are not affected by any other factors.\nTask Constraint: 1<= N <= 5*10^5\n1<= L <= 10^9\n0<= t_i <= 10^9(1<=i<=N)\n1<= v_i <= L(1<=i<=N)\nv_1 = L\nL, each t_i and v_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN L\nt_1 v_1\nt_2 v_2\n:\nt_N v_N\nTask Output: Print N lines. The i-th line should contain the maximum temperature such that it is possible to store L liters of water at that temperature in the dam at noon of the i-th day.\nEach of these values is accepted if the absolute or relative error is at most 10^{-6}.\nTask Samples: input: 3 10\n10 10\n20 5\n4 3 output: 10.0000000\n15.0000000\n13.2000000\n\nOn the first day, the temperature of water in the dam is always 10 degrees: the temperature of the only water that flows into the dam on the first day.\n10 liters of water at 15 degrees of Celsius can be stored on the second day, by discharging 5 liters of water on the night of the first day, and mix the remaining water with the water that flows into the dam on the second day.\n10 liters of water at 13.2 degrees of Celsius can be stored on the third day, by discharging 8 liters of water on the night of the first day, and mix the remaining water with the water that flows into the dam on the second and third days.\ninput: 4 15\n0 15\n2 5\n3 6\n4 4 output: 0.0000000\n0.6666667\n1.8666667\n2.9333333\ninput: 4 15\n1000000000 15\n9 5\n8 6\n7 4 output: 1000000000.0000000\n666666669.6666666\n400000005.0000000\n293333338.8666667\n\nAlthough the temperature of water may exceed 100 degrees Celsius, we assume that water does not vaporize.\n\n" }, { "title": "", "content": "Problem Statement You are given an array A of length N.\nYour task is to divide it into several contiguous subarrays.\nHere, all subarrays obtained must be sorted in either non-decreasing or non-increasing order.\nAt least how many subarrays do you need to divide A into?", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9\nEach A_i is an integer.", "input": "Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the minimum possible number of subarrays after division of A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n1 2 3 2 2 1 output: 2\n\nOne optimal solution is to divide the array into [1,2,3] and [2,2,1].", "input: 9\n1 2 1 2 1 2 1 2 1 output: 5", "input: 7\n1 2 3 2 1 999999999 1000000000 output: 3"], "Pid": "p03745", "ProblemText": "Task Description: Problem Statement You are given an array A of length N.\nYour task is to divide it into several contiguous subarrays.\nHere, all subarrays obtained must be sorted in either non-decreasing or non-increasing order.\nAt least how many subarrays do you need to divide A into?\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9\nEach A_i is an integer.\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the minimum possible number of subarrays after division of A.\nTask Samples: input: 6\n1 2 3 2 2 1 output: 2\n\nOne optimal solution is to divide the array into [1,2,3] and [2,2,1].\ninput: 9\n1 2 1 2 1 2 1 2 1 output: 5\ninput: 7\n1 2 3 2 1 999999999 1000000000 output: 3\n\n" }, { "title": "", "content": "Problem Statement You are given a connected undirected simple graph, which has N vertices and M edges.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i connects vertices A_i and B_i.\nYour task is to find a path that satisfies the following conditions:\n\nThe path traverses two or more vertices.\nThe path does not traverse the same vertex more than once.\nA vertex directly connected to at least one of the endpoints of the path, is always contained in the path.\n\nIt can be proved that such a path always exists.\nAlso, if there are more than one solution, any of them will be accepted.", "constraint": "2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i < B_i <= N\nThe given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them).", "input": "Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n:\nA_M B_M", "output": "Find one path that satisfies the conditions, and print it in the following format.\nIn the first line, print the count of the vertices contained in the path.\nIn the second line, print a space-separated list of the indices of the vertices, in order of appearance in the path.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 6\n1 3\n1 4\n2 3\n1 5\n3 5\n2 4 output: 4\n2 3 1 4\n\nThere are two vertices directly connected to vertex 2: vertices 3 and 4.\nThere are also two vertices directly connected to vertex 4: vertices 1 and 2.\nHence, the path 2 → 3 → 1 → 4 satisfies the conditions.", "input: 7 8\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n3 5\n2 6 output: 7\n1 2 3 4 5 6 7"], "Pid": "p03746", "ProblemText": "Task Description: Problem Statement You are given a connected undirected simple graph, which has N vertices and M edges.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i connects vertices A_i and B_i.\nYour task is to find a path that satisfies the following conditions:\n\nThe path traverses two or more vertices.\nThe path does not traverse the same vertex more than once.\nA vertex directly connected to at least one of the endpoints of the path, is always contained in the path.\n\nIt can be proved that such a path always exists.\nAlso, if there are more than one solution, any of them will be accepted.\nTask Constraint: 2 <= N <= 10^5\n1 <= M <= 10^5\n1 <= A_i < B_i <= N\nThe given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them).\nTask Input: Input is given from Standard Input in the following format:\nN M\nA_1 B_1\nA_2 B_2\n:\nA_M B_M\nTask Output: Find one path that satisfies the conditions, and print it in the following format.\nIn the first line, print the count of the vertices contained in the path.\nIn the second line, print a space-separated list of the indices of the vertices, in order of appearance in the path.\nTask Samples: input: 5 6\n1 3\n1 4\n2 3\n1 5\n3 5\n2 4 output: 4\n2 3 1 4\n\nThere are two vertices directly connected to vertex 2: vertices 3 and 4.\nThere are also two vertices directly connected to vertex 4: vertices 1 and 2.\nHence, the path 2 → 3 → 1 → 4 satisfies the conditions.\ninput: 7 8\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n3 5\n2 6 output: 7\n1 2 3 4 5 6 7\n\n" }, { "title": "", "content": "Problem Statement There is a circle with a circumference of L.\nEach point on the circumference has a coordinate value, which represents the arc length from a certain reference point clockwise to the point.\nOn this circumference, there are N ants.\nThese ants are numbered 1 through N in order of increasing coordinate, and ant i is at coordinate X_i.\nThe N ants have just started walking.\nFor each ant i, you are given the initial direction W_i. Ant i is initially walking clockwise if W_i is 1; counterclockwise if W_i is 2.\nEvery ant walks at a constant speed of 1 per second.\nSometimes, two ants bump into each other.\nEach of these two ants will then turn around and start walking in the opposite direction.\nFor each ant, find its position after T seconds.", "constraint": "All input values are integers.\n1 <= N <= 10^5\n1 <= L <= 10^9\n1 <= T <= 10^9\n0 <= X_1 < X_2 < ... < X_N <= L - 1\n1 <= W_i <= 2", "input": "Input The input is given from Standard Input in the following format:\nN L T\nX_1 W_1\nX_2 W_2\n:\nX_N W_N", "output": "Print N lines.\nThe i-th line should contain the coordinate of ant i after T seconds. Here, each coordinate must be between 0 and L-1, inclusive.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 8 3\n0 1\n3 2\n6 1 output: 1\n3\n0\n\n1.5 seconds after the ants start walking, ant 1 and 2 bump into each other at coordinate 1.5.\n1 second after that, ant 1 and 3 bump into each other at coordinate 0.5.\n0.5 seconds after that, that is, 3 seconds after the ants start walking, ants 1,2 and 3 are at coordinates 1,3 and 0, respectively.", "input: 4 20 9\n7 2\n9 1\n12 1\n18 1 output: 7\n18\n18\n1"], "Pid": "p03747", "ProblemText": "Task Description: Problem Statement There is a circle with a circumference of L.\nEach point on the circumference has a coordinate value, which represents the arc length from a certain reference point clockwise to the point.\nOn this circumference, there are N ants.\nThese ants are numbered 1 through N in order of increasing coordinate, and ant i is at coordinate X_i.\nThe N ants have just started walking.\nFor each ant i, you are given the initial direction W_i. Ant i is initially walking clockwise if W_i is 1; counterclockwise if W_i is 2.\nEvery ant walks at a constant speed of 1 per second.\nSometimes, two ants bump into each other.\nEach of these two ants will then turn around and start walking in the opposite direction.\nFor each ant, find its position after T seconds.\nTask Constraint: All input values are integers.\n1 <= N <= 10^5\n1 <= L <= 10^9\n1 <= T <= 10^9\n0 <= X_1 < X_2 < ... < X_N <= L - 1\n1 <= W_i <= 2\nTask Input: Input The input is given from Standard Input in the following format:\nN L T\nX_1 W_1\nX_2 W_2\n:\nX_N W_N\nTask Output: Print N lines.\nThe i-th line should contain the coordinate of ant i after T seconds. Here, each coordinate must be between 0 and L-1, inclusive.\nTask Samples: input: 3 8 3\n0 1\n3 2\n6 1 output: 1\n3\n0\n\n1.5 seconds after the ants start walking, ant 1 and 2 bump into each other at coordinate 1.5.\n1 second after that, ant 1 and 3 bump into each other at coordinate 0.5.\n0.5 seconds after that, that is, 3 seconds after the ants start walking, ants 1,2 and 3 are at coordinates 1,3 and 0, respectively.\ninput: 4 20 9\n7 2\n9 1\n12 1\n18 1 output: 7\n18\n18\n1\n\n" }, { "title": "", "content": "Problem Statement Joisino has a lot of red and blue bricks and a large box.\nShe will build a tower of these bricks in the following manner.\nFirst, she will pick a total of N bricks and put them into the box.\nHere, there may be any number of bricks of each color in the box, as long as there are N bricks in total.\nParticularly, there may be zero red bricks or zero blue bricks.\nThen, she will repeat an operation M times, which consists of the following three steps:\n\nTake out an arbitrary brick from the box.\nPut one red brick and one blue brick into the box.\nTake out another arbitrary brick from the box.\n\nAfter the M operations, Joisino will build a tower by stacking the 2 * M bricks removed from the box, in the order they are taken out.\nShe is interested in the following question: how many different sequences of colors of these 2 * M bricks are possible?\nWrite a program to find the answer.\nSince it can be extremely large, print the count modulo 10^9+7.", "constraint": "1 <= N <= 3000\n1 <= M <= 3000", "input": "Input is given from Standard Input in the following format:\nN M", "output": "Print the count of the different possible sequences of colors of 2 * M bricks that will be stacked, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 output: 56\n\nA total of six bricks will be removed from the box. The only impossible sequences of colors of these bricks are the ones where the colors of the second, third, fourth and fifth bricks are all the same. Therefore, there are 2^6 - 2 * 2 * 2 = 56 possible sequences of colors.", "input: 1000 10 output: 1048576", "input: 1000 3000 output: 693347555"], "Pid": "p03748", "ProblemText": "Task Description: Problem Statement Joisino has a lot of red and blue bricks and a large box.\nShe will build a tower of these bricks in the following manner.\nFirst, she will pick a total of N bricks and put them into the box.\nHere, there may be any number of bricks of each color in the box, as long as there are N bricks in total.\nParticularly, there may be zero red bricks or zero blue bricks.\nThen, she will repeat an operation M times, which consists of the following three steps:\n\nTake out an arbitrary brick from the box.\nPut one red brick and one blue brick into the box.\nTake out another arbitrary brick from the box.\n\nAfter the M operations, Joisino will build a tower by stacking the 2 * M bricks removed from the box, in the order they are taken out.\nShe is interested in the following question: how many different sequences of colors of these 2 * M bricks are possible?\nWrite a program to find the answer.\nSince it can be extremely large, print the count modulo 10^9+7.\nTask Constraint: 1 <= N <= 3000\n1 <= M <= 3000\nTask Input: Input is given from Standard Input in the following format:\nN M\nTask Output: Print the count of the different possible sequences of colors of 2 * M bricks that will be stacked, modulo 10^9+7.\nTask Samples: input: 2 3 output: 56\n\nA total of six bricks will be removed from the box. The only impossible sequences of colors of these bricks are the ones where the colors of the second, third, fourth and fifth bricks are all the same. Therefore, there are 2^6 - 2 * 2 * 2 = 56 possible sequences of colors.\ninput: 1000 10 output: 1048576\ninput: 1000 3000 output: 693347555\n\n" }, { "title": "", "content": "Problem Statement Joisino has a bar of length N, which has M marks on it.\nThe distance from the left end of the bar to the i-th mark is X_i.\nShe will place several squares on this bar.\nHere, the following conditions must be met:\n\nOnly squares with integral length sides can be placed.\nEach square must be placed so that its bottom side touches the bar.\nThe bar must be completely covered by squares.\nThat is, no square may stick out of the bar, and no part of the bar may be left uncovered.\nThe boundary line of two squares may not be directly above a mark.\n\nExamples of arrangements that satisfy/violate the conditions\n\nThe beauty of an arrangement of squares is defined as the product of the areas of all the squares placed.\nJoisino is interested in the sum of the beauty over all possible arrangements that satisfy the conditions.\nWrite a program to find it.\nSince it can be extremely large, print the sum modulo 10^9+7.", "constraint": "All input values are integers.\n1 <= N <= 10^9\n0 <= M <= 10^5\n1 <= X_1 < X_2 < ... < X_{M-1} < X_M <= N-1", "input": "Input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_{M-1} X_M", "output": "Print the sum of the beauty over all possible arrangements that satisfy the conditions, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n2 output: 13\n\nThere are two possible arrangements:\n\nPlace a square of side length 1 to the left, and place another square of side length 2 to the right\nPlace a square of side length 3\n\nThe sum of the beauty of these arrangements is (1 * 1 * 2 * 2) + (3 * 3) = 13.", "input: 5 2\n2 3 output: 66", "input: 10 9\n1 2 3 4 5 6 7 8 9 output: 100", "input: 1000000000 0 output: 693316425"], "Pid": "p03749", "ProblemText": "Task Description: Problem Statement Joisino has a bar of length N, which has M marks on it.\nThe distance from the left end of the bar to the i-th mark is X_i.\nShe will place several squares on this bar.\nHere, the following conditions must be met:\n\nOnly squares with integral length sides can be placed.\nEach square must be placed so that its bottom side touches the bar.\nThe bar must be completely covered by squares.\nThat is, no square may stick out of the bar, and no part of the bar may be left uncovered.\nThe boundary line of two squares may not be directly above a mark.\n\nExamples of arrangements that satisfy/violate the conditions\n\nThe beauty of an arrangement of squares is defined as the product of the areas of all the squares placed.\nJoisino is interested in the sum of the beauty over all possible arrangements that satisfy the conditions.\nWrite a program to find it.\nSince it can be extremely large, print the sum modulo 10^9+7.\nTask Constraint: All input values are integers.\n1 <= N <= 10^9\n0 <= M <= 10^5\n1 <= X_1 < X_2 < ... < X_{M-1} < X_M <= N-1\nTask Input: Input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_{M-1} X_M\nTask Output: Print the sum of the beauty over all possible arrangements that satisfy the conditions, modulo 10^9+7.\nTask Samples: input: 3 1\n2 output: 13\n\nThere are two possible arrangements:\n\nPlace a square of side length 1 to the left, and place another square of side length 2 to the right\nPlace a square of side length 3\n\nThe sum of the beauty of these arrangements is (1 * 1 * 2 * 2) + (3 * 3) = 13.\ninput: 5 2\n2 3 output: 66\ninput: 10 9\n1 2 3 4 5 6 7 8 9 output: 100\ninput: 1000000000 0 output: 693316425\n\n" }, { "title": "", "content": "Problem Statement There are N cards. The two sides of each of these cards are distinguishable.\nThe i-th of these cards has an integer A_i printed on the front side, and another integer B_i printed on the back side.\nWe will call the deck of these cards X.\nThere are also N+1 cards of another kind.\nThe i-th of these cards has an integer C_i printed on the front side, and nothing is printed on the back side.\nWe will call this another deck of cards Y.\nYou will play Q rounds of a game.\nEach of these rounds is played independently.\nIn the i-th round, you are given a new card. The two sides of this card are distinguishable.\nIt has an integer D_i printed on the front side, and another integer E_i printed on the back side.\nA new deck of cards Z is created by adding this card to X.\nThen, you are asked to form N+1 pairs of cards, each consisting of one card from Z and one card from Y.\nEach card must belong to exactly one of the pairs.\nAdditionally, for each card from Z, you need to specify which side to use.\nFor each pair, the following condition must be met:\n\n(The integer printed on the used side of the card from Z) <= (The integer printed on the card from Y)\n\nIf it is not possible to satisfy this condition regardless of how the pairs are formed and which sides are used, the score for the round will be -1.\nOtherwise, the score for the round will be the count of the cards from Z whose front side is used.\nFind the maximum possible score for each round.", "constraint": "All input values are integers.\n1 <= N <= 10^5\n1 <= Q <= 10^5\n1 <= A_i ,B_i ,C_i ,D_i ,E_i <= 10^9", "input": "Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nC_1 C_2 . . C_{N+1}\nQ\nD_1 E_1\nD_2 E_2\n:\nD_Q E_Q", "output": "For each round, print the maximum possible score in its own line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n4 1\n5 3\n3 1\n1 2 3 4\n3\n5 4\n4 3\n2 3 output: 0\n1\n2\n\nFor example, in the third round, the cards in Z are (4,1),(5,3),(3,1),(2,3).\nThe score of 2 can be obtained by using front, back, back and front sides of them, and pair them with the fourth, third, first and second cards in Y, respectively.\nIt is not possible to obtain a score of 3 or greater, and thus the answer is 2.", "input: 5\n7 1\n9 7\n13 13\n11 8\n12 9\n16 7 8 6 9 11\n7\n6 11\n7 10\n9 3\n12 9\n18 16\n8 9\n10 15 output: 4\n3\n3\n1\n-1\n3\n2", "input: 9\n89 67\n37 14\n6 1\n42 25\n61 22\n23 1\n63 60\n93 62\n14 2\n67 96 26 17 1 62 56 92 13 38\n11\n93 97\n17 93\n61 57\n88 62\n98 29\n49 1\n5 1\n1 77\n34 1\n63 27\n22 66 output: 7\n9\n8\n7\n7\n9\n9\n10\n9\n7\n9"], "Pid": "p03750", "ProblemText": "Task Description: Problem Statement There are N cards. The two sides of each of these cards are distinguishable.\nThe i-th of these cards has an integer A_i printed on the front side, and another integer B_i printed on the back side.\nWe will call the deck of these cards X.\nThere are also N+1 cards of another kind.\nThe i-th of these cards has an integer C_i printed on the front side, and nothing is printed on the back side.\nWe will call this another deck of cards Y.\nYou will play Q rounds of a game.\nEach of these rounds is played independently.\nIn the i-th round, you are given a new card. The two sides of this card are distinguishable.\nIt has an integer D_i printed on the front side, and another integer E_i printed on the back side.\nA new deck of cards Z is created by adding this card to X.\nThen, you are asked to form N+1 pairs of cards, each consisting of one card from Z and one card from Y.\nEach card must belong to exactly one of the pairs.\nAdditionally, for each card from Z, you need to specify which side to use.\nFor each pair, the following condition must be met:\n\n(The integer printed on the used side of the card from Z) <= (The integer printed on the card from Y)\n\nIf it is not possible to satisfy this condition regardless of how the pairs are formed and which sides are used, the score for the round will be -1.\nOtherwise, the score for the round will be the count of the cards from Z whose front side is used.\nFind the maximum possible score for each round.\nTask Constraint: All input values are integers.\n1 <= N <= 10^5\n1 <= Q <= 10^5\n1 <= A_i ,B_i ,C_i ,D_i ,E_i <= 10^9\nTask Input: Input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nC_1 C_2 . . C_{N+1}\nQ\nD_1 E_1\nD_2 E_2\n:\nD_Q E_Q\nTask Output: For each round, print the maximum possible score in its own line.\nTask Samples: input: 3\n4 1\n5 3\n3 1\n1 2 3 4\n3\n5 4\n4 3\n2 3 output: 0\n1\n2\n\nFor example, in the third round, the cards in Z are (4,1),(5,3),(3,1),(2,3).\nThe score of 2 can be obtained by using front, back, back and front sides of them, and pair them with the fourth, third, first and second cards in Y, respectively.\nIt is not possible to obtain a score of 3 or greater, and thus the answer is 2.\ninput: 5\n7 1\n9 7\n13 13\n11 8\n12 9\n16 7 8 6 9 11\n7\n6 11\n7 10\n9 3\n12 9\n18 16\n8 9\n10 15 output: 4\n3\n3\n1\n-1\n3\n2\ninput: 9\n89 67\n37 14\n6 1\n42 25\n61 22\n23 1\n63 60\n93 62\n14 2\n67 96 26 17 1 62 56 92 13 38\n11\n93 97\n17 93\n61 57\n88 62\n98 29\n49 1\n5 1\n1 77\n34 1\n63 27\n22 66 output: 7\n9\n8\n7\n7\n9\n9\n10\n9\n7\n9\n\n" }, { "title": "", "content": "Problem Statement\n\tMr. X, who the handle name is T, looked at the list which written N handle names, S_1, S_2, . . . , S_N. \n\tBut he couldn't see some parts of the list. Invisible part is denoted ? . \n\n\tPlease calculate all possible index of the handle name of Mr. X when you sort N+1 handle names (S_1, S_2, . . . , S_N and T) in lexicographical order. \n\tNote: If there are pair of people with same handle name, either one may come first. scoring: Scoring\nSubtask 1 [ 130 points ]\n\nThere are no ? 's.\n\nSubtask 2 [ 120 points ]\n\nThere are no additional constraints.", "constraint": "1 <= N <= 10000\n1 <= |S_i|, |T| <= 20 (|A| is the length of A.)\nS_i consists from lower-case alphabet and ?.\nT consists from lower-case alphabet.", "input": "The input is given from standard input in the following format.\n\nN\nS_1\nS_2\n :\nS_N\nT", "output": "Calculate the possible index and print in sorted order. The output should be separated with a space. Don't print a space after last number.\nPut a line break in the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\ntourist\npetr\ne output: \n1\n\tThere are no invisible part, so there are only one possibility.\n\tThe sorted handle names are e, petr, tourist, so e comes first."], "Pid": "p03751", "ProblemText": "Task Description: Problem Statement\n\tMr. X, who the handle name is T, looked at the list which written N handle names, S_1, S_2, . . . , S_N. \n\tBut he couldn't see some parts of the list. Invisible part is denoted ? . \n\n\tPlease calculate all possible index of the handle name of Mr. X when you sort N+1 handle names (S_1, S_2, . . . , S_N and T) in lexicographical order. \n\tNote: If there are pair of people with same handle name, either one may come first. scoring: Scoring\nSubtask 1 [ 130 points ]\n\nThere are no ? 's.\n\nSubtask 2 [ 120 points ]\n\nThere are no additional constraints.\nTask Constraint: 1 <= N <= 10000\n1 <= |S_i|, |T| <= 20 (|A| is the length of A.)\nS_i consists from lower-case alphabet and ?.\nT consists from lower-case alphabet.\nTask Input: The input is given from standard input in the following format.\n\nN\nS_1\nS_2\n :\nS_N\nT\nTask Output: Calculate the possible index and print in sorted order. The output should be separated with a space. Don't print a space after last number.\nPut a line break in the end.\nTask Samples: input: 2\ntourist\npetr\ne output: \n1\n\tThere are no invisible part, so there are only one possibility.\n\tThe sorted handle names are e, petr, tourist, so e comes first.\n\n" }, { "title": "", "content": "Problem Statement\n\tThere are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters. \n\tChokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left. \n\n\tYou can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer. \n\tYou cannot decrease height of buildings. \n\tCalculate the minimum cost of satisfying Chokudai's objective. \n\tNote: \"Building i can see from the left\" means there are no j exists that (height of building j) >= (height of building i) and j < i. scoring: Scoring\n\tSubtask 1 [120 points] \n\nN = K\n\n\tSubtask 2 [90 points] \n\nN <= 5\na_i <= 7\n\n\tSubtask 3 [140 points] \n\nThere are no additional constraints.", "constraint": "1 <= K <= N <= 15\n1 <= a_i <= 10^9", "input": "Input Format\n\nN K\\na_1 a_2 a_3 . . . a_N", "output": "Format\n\tPrint the minimum cost in one line. In the end put a line break.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n3949 3774 3598 3469 3424 output: \n1541\n\n\tThe optimal solution is (height of buildings from the left) = [3949,3950,3951,3952,3953].", "input: 5 3\n7 4 2 6 4 output: \n7\n\n\tThe optimal solution is (height of buildings from the left) = [7,8,2,9,4]."], "Pid": "p03752", "ProblemText": "Task Description: Problem Statement\n\tThere are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters. \n\tChokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left. \n\n\tYou can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer. \n\tYou cannot decrease height of buildings. \n\tCalculate the minimum cost of satisfying Chokudai's objective. \n\tNote: \"Building i can see from the left\" means there are no j exists that (height of building j) >= (height of building i) and j < i. scoring: Scoring\n\tSubtask 1 [120 points] \n\nN = K\n\n\tSubtask 2 [90 points] \n\nN <= 5\na_i <= 7\n\n\tSubtask 3 [140 points] \n\nThere are no additional constraints.\nTask Constraint: 1 <= K <= N <= 15\n1 <= a_i <= 10^9\nTask Input: Input Format\n\nN K\\na_1 a_2 a_3 . . . a_N\nTask Output: Format\n\tPrint the minimum cost in one line. In the end put a line break.\nTask Samples: input: 5 5\n3949 3774 3598 3469 3424 output: \n1541\n\n\tThe optimal solution is (height of buildings from the left) = [3949,3950,3951,3952,3953].\ninput: 5 3\n7 4 2 6 4 output: \n7\n\n\tThe optimal solution is (height of buildings from the left) = [7,8,2,9,4].\n\n" }, { "title": "", "content": "Problem Statement\n\tWe have a grid with n rows and 7 columns. We call it a calendar. The cell at i-th row and j-th column is denoted (i, j). \n\n\tInitially, each cell at (i, j) contains the integer 7i + j - 8, and each cell is white. \n\n\tSnuke likes painting, so he decided integer m, and did q operations with a calendar. \n\t・In i-th operation, he paint black on the cell in which an integer is written such remainder of dividing by m is a_i. \n\n\tPlease count the number of connected white parts. \n\tNote that if two adjacent cells are white, the cells belong to the same connected part. scoring: Scoring\n\tSubtask 1 [100 points] \n\nn <= 100000.\n\n\tSubtask 2 [90 points] \n\nm is divisible by 7.\na_{i + 1} - a_i = 1.\n\n\tSubtask 3 [200 points] \n\nm is divisible by 7.\n\n\tSubtask 4 [110 points] \n\nThere are no additional constraints.", "constraint": "n <= 10^{12}\n7n is divisible by m.\n1 <= q <= m <= 10^5\n0 <= a_1 < a_2 < ... < a_q < m", "input": "Input Format\n\tThe input format is following: \\nn m q\\na_1 a_2 . . . a_q", "output": "Format\n\tPrint the number of connected part in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 7 3\n1 3 5 output: \n4\n\n\tThe calendar looks like this:", "input: 10 14 8\n5 6 7 8 9 10 11 12 output: \n10\n\n\tThe calendar looks like this:"], "Pid": "p03753", "ProblemText": "Task Description: Problem Statement\n\tWe have a grid with n rows and 7 columns. We call it a calendar. The cell at i-th row and j-th column is denoted (i, j). \n\n\tInitially, each cell at (i, j) contains the integer 7i + j - 8, and each cell is white. \n\n\tSnuke likes painting, so he decided integer m, and did q operations with a calendar. \n\t・In i-th operation, he paint black on the cell in which an integer is written such remainder of dividing by m is a_i. \n\n\tPlease count the number of connected white parts. \n\tNote that if two adjacent cells are white, the cells belong to the same connected part. scoring: Scoring\n\tSubtask 1 [100 points] \n\nn <= 100000.\n\n\tSubtask 2 [90 points] \n\nm is divisible by 7.\na_{i + 1} - a_i = 1.\n\n\tSubtask 3 [200 points] \n\nm is divisible by 7.\n\n\tSubtask 4 [110 points] \n\nThere are no additional constraints.\nTask Constraint: n <= 10^{12}\n7n is divisible by m.\n1 <= q <= m <= 10^5\n0 <= a_1 < a_2 < ... < a_q < m\nTask Input: Input Format\n\tThe input format is following: \\nn m q\\na_1 a_2 . . . a_q\nTask Output: Format\n\tPrint the number of connected part in one line.\nTask Samples: input: 7 7 3\n1 3 5 output: \n4\n\n\tThe calendar looks like this:\ninput: 10 14 8\n5 6 7 8 9 10 11 12 output: \n10\n\n\tThe calendar looks like this:\n\n" }, { "title": "", "content": "Problem Statement\n\tThere is an undirected connected graph with $N$ vertices and $N-1$ edges. The i-th edge connects u_i and v_i.\n\n\tE869120 the coder moves in the graph as follows:\n\nHe move to adjacent vertex, but he can't a visit vertex two or more times.\nHe ends move when there is no way to move.\nOtherwise, he moves randomly. (equal probability) If he has $p$ way to move this turn, he choose each vertex with $1/p$ probability.\n\n\tCalculate the expected value of the number of turns, when E869120 starts from vertex i, for all i (1 <= i <= N). tasks: Subtasks\nSubtask 1 [ $190$ points ]\n\nThere is no vertex which degree is more than 2.\nThis means the graph looks like a list.\nSubtask 2 [ $220$ points ]\n\n1 <= N <= 1000.\nSubtask 3 [ $390$ points ]\n\nThere are no additional constraints.", "constraint": "$1 <= N <= 150,000$\nThe graph is connected.", "input": "The input is given from standard input in the following format. \nN\nu_1 v_1\nu_2 v_2\n :\nu_{N-1} v_{N-1}", "output": "In i-th (1 <= i <= N) line, print the expected vaule of the number of turns E869120 moves.\n\tThe relative error or absolute error of output should be within 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2\n2 3\n2 4 output: \n2.0\n1.0\n2.0\n2.0"], "Pid": "p03754", "ProblemText": "Task Description: Problem Statement\n\tThere is an undirected connected graph with $N$ vertices and $N-1$ edges. The i-th edge connects u_i and v_i.\n\n\tE869120 the coder moves in the graph as follows:\n\nHe move to adjacent vertex, but he can't a visit vertex two or more times.\nHe ends move when there is no way to move.\nOtherwise, he moves randomly. (equal probability) If he has $p$ way to move this turn, he choose each vertex with $1/p$ probability.\n\n\tCalculate the expected value of the number of turns, when E869120 starts from vertex i, for all i (1 <= i <= N). tasks: Subtasks\nSubtask 1 [ $190$ points ]\n\nThere is no vertex which degree is more than 2.\nThis means the graph looks like a list.\nSubtask 2 [ $220$ points ]\n\n1 <= N <= 1000.\nSubtask 3 [ $390$ points ]\n\nThere are no additional constraints.\nTask Constraint: $1 <= N <= 150,000$\nThe graph is connected.\nTask Input: The input is given from standard input in the following format. \nN\nu_1 v_1\nu_2 v_2\n :\nu_{N-1} v_{N-1}\nTask Output: In i-th (1 <= i <= N) line, print the expected vaule of the number of turns E869120 moves.\n\tThe relative error or absolute error of output should be within 10^{-6}.\nTask Samples: input: 4\n1 2\n2 3\n2 4 output: \n2.0\n1.0\n2.0\n2.0\n\n" }, { "title": "", "content": "Problem Statement\n\tThere is a railroad company in Atcoder Kingdom, \"Atcoder Railroad\". \n\tThere are N + 1 stations numbered 0,1,2, . . . , N along a railway. \n\tCurrently, two kinds of train are operated, local and express. \n\tA local train stops at every station, and it takes one minute from station i to i + 1, and vice versa. \n\tAn express train only stops at station S_0, S_1, S_2, . . . , S_{K-1} (0 = S_0 < S_1 < S_2 < . . . < S_{K-1} = N). It takes one minute from station S_i to S_{i + 1}, and vice versa. \n\tBut the president of Atcoder Railroad, Semiexp said it is not very convenient so he planned to operate one more kind of train, \"semi-express\". \n\tThe stations where the semi-express stops (This is T_0, T_1, T_2, . . . , T_{L-1}, 0 = T_0 < T_1 < T_2 < . . . < T_{L-1} = N) have to follow following conditions: \n\tFrom station T_i to T_{i+1} takes 1 minutes, and vice versa. \n\nThe center of Atcoder Kingdom is station 0, and you have to be able to go to station i atmost X minutes.\nIf the express stops at the station, semi-express should stops at the station.\n\n\tPrint the number of ways of the set of the station where semi-express stops (sequence T). \n\tSince the answer can be large, print the number modulo 10^9 + 7. scoring: Scoring\n\tSubtask 1 [120 points] \n\nN, K, X <= 15.\n\n\tSubtask 2 [90 points] \n\nK, X <= 15.\nS_{i + 1} - S_i <= 15.\n\n\tSubtask 3 [260 points] \n\nK, X <= 40.\nS_{i + 1} - S_i <= 40.\n\n\tSubtask 4 [160 points] \n\nK, X <= 300.\nS_{i + 1} - S_i <= 300.\n\n\tSubtask 5 [370 points] \n\nThere are no additional constraints.", "constraint": "2 <= K <= 2500.\n1 <= X <= 2500.\nS_0 = 0, S_{K-1} = N.\n1 <= S_{i + 1} - S_i <= 10000.", "input": "Input Format\n\nN K X\\n S_0 S_1 S_2 . . . S_{K-1}", "output": "Format\n\tPrint the number of ways of the set of the station where semi-express stops, mod 10^9 + 7 in one line. Print \\n (line break) in the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 2 3\n0 7 output: \n55\n\n\tThe set of trains that stops station 0 and 7, and can't satisfy the condition is: \n[0,7], [0,1,7], [0,1,2,7], [0,1,6,7], [0,1,2,6,7], [0,1,2,3,6,7], [0,1,2,5,6,7], [0,1,2,3,5,6,7], [0,1,2,3,4,5,6,7], 9 ways.\n\tTherefore, the number of ways is 2^6 - 9 = 55."], "Pid": "p03755", "ProblemText": "Task Description: Problem Statement\n\tThere is a railroad company in Atcoder Kingdom, \"Atcoder Railroad\". \n\tThere are N + 1 stations numbered 0,1,2, . . . , N along a railway. \n\tCurrently, two kinds of train are operated, local and express. \n\tA local train stops at every station, and it takes one minute from station i to i + 1, and vice versa. \n\tAn express train only stops at station S_0, S_1, S_2, . . . , S_{K-1} (0 = S_0 < S_1 < S_2 < . . . < S_{K-1} = N). It takes one minute from station S_i to S_{i + 1}, and vice versa. \n\tBut the president of Atcoder Railroad, Semiexp said it is not very convenient so he planned to operate one more kind of train, \"semi-express\". \n\tThe stations where the semi-express stops (This is T_0, T_1, T_2, . . . , T_{L-1}, 0 = T_0 < T_1 < T_2 < . . . < T_{L-1} = N) have to follow following conditions: \n\tFrom station T_i to T_{i+1} takes 1 minutes, and vice versa. \n\nThe center of Atcoder Kingdom is station 0, and you have to be able to go to station i atmost X minutes.\nIf the express stops at the station, semi-express should stops at the station.\n\n\tPrint the number of ways of the set of the station where semi-express stops (sequence T). \n\tSince the answer can be large, print the number modulo 10^9 + 7. scoring: Scoring\n\tSubtask 1 [120 points] \n\nN, K, X <= 15.\n\n\tSubtask 2 [90 points] \n\nK, X <= 15.\nS_{i + 1} - S_i <= 15.\n\n\tSubtask 3 [260 points] \n\nK, X <= 40.\nS_{i + 1} - S_i <= 40.\n\n\tSubtask 4 [160 points] \n\nK, X <= 300.\nS_{i + 1} - S_i <= 300.\n\n\tSubtask 5 [370 points] \n\nThere are no additional constraints.\nTask Constraint: 2 <= K <= 2500.\n1 <= X <= 2500.\nS_0 = 0, S_{K-1} = N.\n1 <= S_{i + 1} - S_i <= 10000.\nTask Input: Input Format\n\nN K X\\n S_0 S_1 S_2 . . . S_{K-1}\nTask Output: Format\n\tPrint the number of ways of the set of the station where semi-express stops, mod 10^9 + 7 in one line. Print \\n (line break) in the end.\nTask Samples: input: 7 2 3\n0 7 output: \n55\n\n\tThe set of trains that stops station 0 and 7, and can't satisfy the condition is: \n[0,7], [0,1,7], [0,1,2,7], [0,1,6,7], [0,1,2,6,7], [0,1,2,3,6,7], [0,1,2,5,6,7], [0,1,2,3,5,6,7], [0,1,2,3,4,5,6,7], 9 ways.\n\tTherefore, the number of ways is 2^6 - 9 = 55.\n\n" }, { "title": "", "content": "Problem Statement\n\tThere is a grid which size is $H * W$. the upper-left cell is $(1,1)$ and the lower-right cell is $(H, W)$.\n\tThere is $N$ arrows. Arrow which start point is $(a_i, b_i)$ of direction is $c_i$, and size is $d_i$. ($d_i$ may be negative)\n\tIt is guaranteed that there are no two arrow which start point is same.\n\n\tSothe want to move from cell $(sx, sy)$ to cell $(gx, gy)$ with arrows.\n\tBut it may not possible to move to goal in initial grid.\n\tSo, Snuke decided to change some arrows.\n\tSothe can change each arrow as follows:\n\nHe can't change the start point of this arrow.\nIt costs $e_i$ if he change the direction of this arrow.\nIt costs $f * |d_i-G|$ if he change d_i to $G$.\n\tHe can't add or erase arrows.\n\n\tPlease calculate the minimum cost that he can move to $(gx, gy)$. If he can't move to goal, please output '-1'.\n\tNote: Arrows are directed, and he can't turn in the middle of the arrow. tasks: Subtasks\nSubtask 1 [ 190 points ]\n\n$H=1$\n$W <= 600$\n\nSubtask 2 [ 170 points ]\n\n$H, W <= 80$\n\nSubtask 3 [ 360 points ]\n\n$H, W <= 600$\n\nSubtask 4 [ 430 points ]\n\nThere is no additional constraints.", "constraint": "$1 <= H,W <= 100000$\n$1 <= N <= 70000$\n$1 <= f,e_i <= 1000000$\n$1 <= d_i <= 100000$\n$1 <= a_i,sx,tx <= H$\n$1 <= b_i,sy,ty <= W$\n$c_i$ is N, E, S, or W, which means North, East, South, West.", "input": "The input is given from standard input in the following format. \nH W N f\nsx sy gx gy\na_1 b_1 c_1 d_1 e_1\na_2 b_2 c_2 d_2 e_2\n : : :\na_N b_N c_N d_N e_N", "output": "Please output a single integer: The minimum cost to clear this puzzle.\nIf you can't achieve the objective, print -1.\nPrint \\n (line break) in the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4 2 2\n1 1 2 2\n1 1 E 1 1\n1 2 E 2 2 output: \n4", "input: 1 4 2 10\n1 1 1 4\n1 1 E 1 4\n1 3 W 1 4 output: \n14", "input: 1 8 4 9\n1 3 1 6\n1 1 E 7 2\n1 8 W 7 5\n1 3 W 2 5\n1 6 E 2 8 output: \n14"], "Pid": "p03756", "ProblemText": "Task Description: Problem Statement\n\tThere is a grid which size is $H * W$. the upper-left cell is $(1,1)$ and the lower-right cell is $(H, W)$.\n\tThere is $N$ arrows. Arrow which start point is $(a_i, b_i)$ of direction is $c_i$, and size is $d_i$. ($d_i$ may be negative)\n\tIt is guaranteed that there are no two arrow which start point is same.\n\n\tSothe want to move from cell $(sx, sy)$ to cell $(gx, gy)$ with arrows.\n\tBut it may not possible to move to goal in initial grid.\n\tSo, Snuke decided to change some arrows.\n\tSothe can change each arrow as follows:\n\nHe can't change the start point of this arrow.\nIt costs $e_i$ if he change the direction of this arrow.\nIt costs $f * |d_i-G|$ if he change d_i to $G$.\n\tHe can't add or erase arrows.\n\n\tPlease calculate the minimum cost that he can move to $(gx, gy)$. If he can't move to goal, please output '-1'.\n\tNote: Arrows are directed, and he can't turn in the middle of the arrow. tasks: Subtasks\nSubtask 1 [ 190 points ]\n\n$H=1$\n$W <= 600$\n\nSubtask 2 [ 170 points ]\n\n$H, W <= 80$\n\nSubtask 3 [ 360 points ]\n\n$H, W <= 600$\n\nSubtask 4 [ 430 points ]\n\nThere is no additional constraints.\nTask Constraint: $1 <= H,W <= 100000$\n$1 <= N <= 70000$\n$1 <= f,e_i <= 1000000$\n$1 <= d_i <= 100000$\n$1 <= a_i,sx,tx <= H$\n$1 <= b_i,sy,ty <= W$\n$c_i$ is N, E, S, or W, which means North, East, South, West.\nTask Input: The input is given from standard input in the following format. \nH W N f\nsx sy gx gy\na_1 b_1 c_1 d_1 e_1\na_2 b_2 c_2 d_2 e_2\n : : :\na_N b_N c_N d_N e_N\nTask Output: Please output a single integer: The minimum cost to clear this puzzle.\nIf you can't achieve the objective, print -1.\nPrint \\n (line break) in the end.\nTask Samples: input: 4 4 2 2\n1 1 2 2\n1 1 E 1 1\n1 2 E 2 2 output: \n4\ninput: 1 4 2 10\n1 1 1 4\n1 1 E 1 4\n1 3 W 1 4 output: \n14\ninput: 1 8 4 9\n1 3 1 6\n1 1 E 7 2\n1 8 W 7 5\n1 3 W 2 5\n1 6 E 2 8 output: \n14\n\n" }, { "title": "", "content": "Problem Statement\n\tThere are N workers in Atcoder company. Each worker is numbered 0 through N - 1, and the boss for worker i is p_i like a tree structure and the salary is currently a_i. (p_i < i, especially p_0 = -1 because worker 0 is a president) \n\tIn atcoder, the boss of boss of boss of . . . (repeated k times) worker i called \"k-th upper boss\", and \"k-th lower subordinate\" called for vice versa. \n\n\tYou have to process Q queries for Atcoder: \n\nQuery 1: You are given v_i, d_i, x_i. Increase the salary of worker v_i, and all j-th (1 <= j <= d_i) lower subordinates by x_i.\nQuery 2: You are given v_i, d_i. Calculate the sum of salary of worker v_i and all j-th (1 <= j <= d_i) lower subordinates.\nQuery 3: You are given pr_i, ar_i. Now Atcoder has a new worker c! (c is the current number of workers) The boss is pr_i, and the first salary is ar_i.\n\n\tProcess all queries! ! ! scoring: Scoring\n\tSubtask 1 [170 points] \n\nN, Q <= 5000\n\n\tSubtask 2 [310 points] \n\np_i + 1 = i for all valid i.\n\n\tSubtask 3 [380 points] \n\nThere are no query 3.\n\n\tSubtask 4 [590 points] \n\nThere are no additional constraints.", "constraint": "N <= 400000\nQ <= 50000\np_i < i for all valid i.\nIn each question 1 or 2, worker v_i exists.\nd_i <= 400000\n0 <= a_i, x_i <= 1000", "input": "Input Format\n\tLet the i-th query query_i, the input format is following: \\n N Q\\np_0 a_0\\np_1 a_1\\n : : \\np_{N - 1} a_{N - 1}\\nquery_0\\nquery_1\\n : : \\nquery_{Q - 1}\\n THe format of query_i is one of the three format: \\n1 v_i d_i x_i\\n2 v_i d_i\\n3 pr_i ar_i\\n", "output": "Format\n\tPrint the result in one line for each query 2.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 7\n-1 6\n0 5\n0 4\n2 3\n2 2\n1 1\n2 0 1\n1 0 2 1\n2 2 1\n3 3 3\n2 0 3\n3 3 4\n2 1 1 output: \n15\n12\n30\n8", "input: 7 9\n-1 1\n0 5\n0 7\n0 8\n1 3\n4 1\n5 1\n2 1 1\n2 1 2\n1 1 2 3\n1 4 1 1\n2 3 1\n2 0 2\n3 6 1\n3 7 11\n2 0 15 output: \n8\n9\n8\n31\n49"], "Pid": "p03757", "ProblemText": "Task Description: Problem Statement\n\tThere are N workers in Atcoder company. Each worker is numbered 0 through N - 1, and the boss for worker i is p_i like a tree structure and the salary is currently a_i. (p_i < i, especially p_0 = -1 because worker 0 is a president) \n\tIn atcoder, the boss of boss of boss of . . . (repeated k times) worker i called \"k-th upper boss\", and \"k-th lower subordinate\" called for vice versa. \n\n\tYou have to process Q queries for Atcoder: \n\nQuery 1: You are given v_i, d_i, x_i. Increase the salary of worker v_i, and all j-th (1 <= j <= d_i) lower subordinates by x_i.\nQuery 2: You are given v_i, d_i. Calculate the sum of salary of worker v_i and all j-th (1 <= j <= d_i) lower subordinates.\nQuery 3: You are given pr_i, ar_i. Now Atcoder has a new worker c! (c is the current number of workers) The boss is pr_i, and the first salary is ar_i.\n\n\tProcess all queries! ! ! scoring: Scoring\n\tSubtask 1 [170 points] \n\nN, Q <= 5000\n\n\tSubtask 2 [310 points] \n\np_i + 1 = i for all valid i.\n\n\tSubtask 3 [380 points] \n\nThere are no query 3.\n\n\tSubtask 4 [590 points] \n\nThere are no additional constraints.\nTask Constraint: N <= 400000\nQ <= 50000\np_i < i for all valid i.\nIn each question 1 or 2, worker v_i exists.\nd_i <= 400000\n0 <= a_i, x_i <= 1000\nTask Input: Input Format\n\tLet the i-th query query_i, the input format is following: \\n N Q\\np_0 a_0\\np_1 a_1\\n : : \\np_{N - 1} a_{N - 1}\\nquery_0\\nquery_1\\n : : \\nquery_{Q - 1}\\n THe format of query_i is one of the three format: \\n1 v_i d_i x_i\\n2 v_i d_i\\n3 pr_i ar_i\\n\nTask Output: Format\n\tPrint the result in one line for each query 2.\nTask Samples: input: 6 7\n-1 6\n0 5\n0 4\n2 3\n2 2\n1 1\n2 0 1\n1 0 2 1\n2 2 1\n3 3 3\n2 0 3\n3 3 4\n2 1 1 output: \n15\n12\n30\n8\ninput: 7 9\n-1 1\n0 5\n0 7\n0 8\n1 3\n4 1\n5 1\n2 1 1\n2 1 2\n1 1 2 3\n1 4 1 1\n2 3 1\n2 0 2\n3 6 1\n3 7 11\n2 0 15 output: \n8\n9\n8\n31\n49\n\n" }, { "title": "", "content": "Problem Statement\n\tHuge kingdom: $Atcoder$ contains $N$ towns and $N-1$ roads. This kingdom is connected.\n\n\tYou have to detect the kingdom's road.\n\tIn order to detect, You can ask this form of questions.\n\nYou can output a string $S$. Length of $S$ must be $N$ and The character of string $S$ must be represented by '$0$' or '$1$'.\nComputer paint the towns with white or black according to the character string you output.\nIf $i$-th character of $S$ is '0', computer paint town $i$ white.\nIf $i$-th character of $S$ is '1', computer paint town $i$ black.\nPlease consider an undirected graph $G$.\nFor each edge, computer do the following processing: If both ends painted black, computer adds this edge to $G$.\nComputer returns value $x$: sum of \"diameter of tree\"$^2$ about each connected components.\n\n\tFor example, when $S$=\"11001111\" and the kingdom's structure is this, computer returns 10.\n\n\tPlease detect the structure of $Atcoder$ as few questions as possible. scoring: Scoring\n\tLet the number of questions be $L$.\nIf $L > 20000$, $score$ = $0$ points\nIf $18000 < L <= 20000$, $score$ = $200$ points\nIf $5000 < L <= 18000$, $score$ = $650-L/40$ points\nIf $4000 < L <= 5000$, $score$ = $800-L/20$ points\nIf $2000 < L <= 4000$, $score$ = $1400-L/5$ points\nIf $1200 < L <= 2000$, $score$ = $1500-L/4$ points\nIf $700 < L <= 1200$, $score$ = $1850-L/2$ points\nIf $L <= 700$, $score$ = $1500$ points\n\tThere is $5$ cases, so points of each case is $score/5$. Input, Output\nThis is a reactive problem. \\n The first input is as follows: \\n$N$\\n$N$ is number of towns in $Atcoder$. \\n Next, you can ask questions. \\n The question must be in the form as follows: \\n? $S$\\n$S$ is a string. The mean of $S$ written in the problem statement. Length of $S$ must be $N$. \\n The answer of question is as follows: \\n$x$\\n The mean of $x$ written in the problem statement. \\n Finally, your program must output as follows: \\n! $(a_1, b_1)$ $(a_2, b_2)$ $(a_3, b_3)$ … $(a_{N-1}, b_{N-1})$\\n This output means your program detects all roads of $Atcoder$. \\n$(a_i, b_i)$ means there is a road between $a_i$ and $b_i$. \\n You can output roads any order, but you must output the answer on a single line.", "constraint": "$N$=200\n$Atcoder$ contains $N-1$ roads and this kingdom is connected.\nAll cases were made randomly.", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": ["input: Sample Input\n\tThis case is $N=4$. This case is not include because this is not $N=200$.\n\nN=4\n0 1\n1 2\n1 3 output: Sample Output\n\tSample interaction is as follows:\nInput from computer\nOutput\n4\n \n \n? 1111\n4\n \n \n? 1101\n4\n \n \n? 1001\n0\n \n \n? 1100\n1\n \n \n? 1011\n0\n \n \n! (0,1) (1,2) (1,3)\n\n\tIn this sample, structure of $Atcoder$ is as follows:\n\tThis question is not always meaningful."], "Pid": "p03758", "ProblemText": "Task Description: Problem Statement\n\tHuge kingdom: $Atcoder$ contains $N$ towns and $N-1$ roads. This kingdom is connected.\n\n\tYou have to detect the kingdom's road.\n\tIn order to detect, You can ask this form of questions.\n\nYou can output a string $S$. Length of $S$ must be $N$ and The character of string $S$ must be represented by '$0$' or '$1$'.\nComputer paint the towns with white or black according to the character string you output.\nIf $i$-th character of $S$ is '0', computer paint town $i$ white.\nIf $i$-th character of $S$ is '1', computer paint town $i$ black.\nPlease consider an undirected graph $G$.\nFor each edge, computer do the following processing: If both ends painted black, computer adds this edge to $G$.\nComputer returns value $x$: sum of \"diameter of tree\"$^2$ about each connected components.\n\n\tFor example, when $S$=\"11001111\" and the kingdom's structure is this, computer returns 10.\n\n\tPlease detect the structure of $Atcoder$ as few questions as possible. scoring: Scoring\n\tLet the number of questions be $L$.\nIf $L > 20000$, $score$ = $0$ points\nIf $18000 < L <= 20000$, $score$ = $200$ points\nIf $5000 < L <= 18000$, $score$ = $650-L/40$ points\nIf $4000 < L <= 5000$, $score$ = $800-L/20$ points\nIf $2000 < L <= 4000$, $score$ = $1400-L/5$ points\nIf $1200 < L <= 2000$, $score$ = $1500-L/4$ points\nIf $700 < L <= 1200$, $score$ = $1850-L/2$ points\nIf $L <= 700$, $score$ = $1500$ points\n\tThere is $5$ cases, so points of each case is $score/5$. Input, Output\nThis is a reactive problem. \\n The first input is as follows: \\n$N$\\n$N$ is number of towns in $Atcoder$. \\n Next, you can ask questions. \\n The question must be in the form as follows: \\n? $S$\\n$S$ is a string. The mean of $S$ written in the problem statement. Length of $S$ must be $N$. \\n The answer of question is as follows: \\n$x$\\n The mean of $x$ written in the problem statement. \\n Finally, your program must output as follows: \\n! $(a_1, b_1)$ $(a_2, b_2)$ $(a_3, b_3)$ … $(a_{N-1}, b_{N-1})$\\n This output means your program detects all roads of $Atcoder$. \\n$(a_i, b_i)$ means there is a road between $a_i$ and $b_i$. \\n You can output roads any order, but you must output the answer on a single line.\nTask Constraint: $N$=200\n$Atcoder$ contains $N-1$ roads and this kingdom is connected.\nAll cases were made randomly.\nTask Input: \nTask Output: \nTask Samples: input: Sample Input\n\tThis case is $N=4$. This case is not include because this is not $N=200$.\n\nN=4\n0 1\n1 2\n1 3 output: Sample Output\n\tSample interaction is as follows:\nInput from computer\nOutput\n4\n \n \n? 1111\n4\n \n \n? 1101\n4\n \n \n? 1001\n0\n \n \n? 1100\n1\n \n \n? 1011\n0\n \n \n! (0,1) (1,2) (1,3)\n\n\tIn this sample, structure of $Atcoder$ is as follows:\n\tThis question is not always meaningful.\n\n" }, { "title": "", "content": "Problem Statement Three poles stand evenly spaced along a line. Their heights are a, b and c meters, from left to right.\nWe will call the arrangement of the poles beautiful if the tops of the poles lie on the same line, that is, b-a = c-b.\nDetermine whether the arrangement of the poles is beautiful.", "constraint": "1 <= a,b,c <= 100\na, b and c are integers.", "input": "Input is given from Standard Input in the following format:\na b c", "output": "Print YES if the arrangement of the poles is beautiful; print NO otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 4 6 output: YES\n\nSince 4-2 = 6-4, this arrangement of poles is beautiful.", "input: 2 5 6 output: NO\n\nSince 5-2 \\neq 6-5, this arrangement of poles is not beautiful.", "input: 3 2 1 output: YES\n\nSince 1-2 = 2-3, this arrangement of poles is beautiful."], "Pid": "p03759", "ProblemText": "Task Description: Problem Statement Three poles stand evenly spaced along a line. Their heights are a, b and c meters, from left to right.\nWe will call the arrangement of the poles beautiful if the tops of the poles lie on the same line, that is, b-a = c-b.\nDetermine whether the arrangement of the poles is beautiful.\nTask Constraint: 1 <= a,b,c <= 100\na, b and c are integers.\nTask Input: Input is given from Standard Input in the following format:\na b c\nTask Output: Print YES if the arrangement of the poles is beautiful; print NO otherwise.\nTask Samples: input: 2 4 6 output: YES\n\nSince 4-2 = 6-4, this arrangement of poles is beautiful.\ninput: 2 5 6 output: NO\n\nSince 5-2 \\neq 6-5, this arrangement of poles is not beautiful.\ninput: 3 2 1 output: YES\n\nSince 1-2 = 2-3, this arrangement of poles is beautiful.\n\n" }, { "title": "", "content": "Problem Statement Snuke signed up for a new website which holds programming competitions.\nHe worried that he might forget his password, and he took notes of it.\nSince directly recording his password would cause him trouble if stolen,\nhe took two notes: one contains the characters at the odd-numbered positions, and the other contains the characters at the even-numbered positions.\nYou are given two strings O and E. O contains the characters at the odd-numbered positions retaining their relative order, and E contains the characters at the even-numbered positions retaining their relative order.\nRestore the original password.", "constraint": "O and E consists of lowercase English letters (a - z).\n1 <= |O|,|E| <= 50\n|O| - |E| is either 0 or 1.", "input": "Input is given from Standard Input in the following format:\nO\nE", "output": "Print the original password.", "content_img": false, "lang": "en", "error": false, "samples": ["input: xyz\nabc output: xaybzc\n\nThe original password is xaybzc. Extracting the characters at the odd-numbered positions results in xyz, and extracting the characters at the even-numbered positions results in abc.", "input: atcoderbeginnercontest\natcoderregularcontest output: aattccooddeerrbreeggiunlnaerrccoonntteesstt"], "Pid": "p03760", "ProblemText": "Task Description: Problem Statement Snuke signed up for a new website which holds programming competitions.\nHe worried that he might forget his password, and he took notes of it.\nSince directly recording his password would cause him trouble if stolen,\nhe took two notes: one contains the characters at the odd-numbered positions, and the other contains the characters at the even-numbered positions.\nYou are given two strings O and E. O contains the characters at the odd-numbered positions retaining their relative order, and E contains the characters at the even-numbered positions retaining their relative order.\nRestore the original password.\nTask Constraint: O and E consists of lowercase English letters (a - z).\n1 <= |O|,|E| <= 50\n|O| - |E| is either 0 or 1.\nTask Input: Input is given from Standard Input in the following format:\nO\nE\nTask Output: Print the original password.\nTask Samples: input: xyz\nabc output: xaybzc\n\nThe original password is xaybzc. Extracting the characters at the odd-numbered positions results in xyz, and extracting the characters at the even-numbered positions results in abc.\ninput: atcoderbeginnercontest\natcoderregularcontest output: aattccooddeerrbreeggiunlnaerrccoonntteesstt\n\n" }, { "title": "", "content": "Problem Statement Snuke loves \"paper cutting\": he cuts out characters from a newspaper headline and rearranges them to form another string.\nHe will receive a headline which contains one of the strings S_1, . . . , S_n tomorrow.\nHe is excited and already thinking of what string he will create.\nSince he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.\nFind the longest string that can be created regardless of which string among S_1, . . . , S_n the headline contains.\nIf there are multiple such strings, find the lexicographically smallest one among them.", "constraint": "1 <= n <= 50\n1 <= |S_i| <= 50 for every i = 1, ..., n.\nS_i consists of lowercase English letters (a - z) for every i = 1, ..., n.", "input": "Input is given from Standard Input in the following format:\nn\nS_1\n. . .\nS_n", "output": "Print the lexicographically smallest string among the longest strings that satisfy the condition.\nIf the answer is an empty string, print an empty line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\ncbaa\ndaacc\nacacac output: aac\n\nThe strings that can be created from each of cbaa, daacc and acacac, are aa, aac, aca, caa and so forth.\nAmong them, aac, aca and caa are the longest, and the lexicographically smallest of these three is aac.", "input: 3\na\naa\nb output: \nThe answer is an empty string."], "Pid": "p03761", "ProblemText": "Task Description: Problem Statement Snuke loves \"paper cutting\": he cuts out characters from a newspaper headline and rearranges them to form another string.\nHe will receive a headline which contains one of the strings S_1, . . . , S_n tomorrow.\nHe is excited and already thinking of what string he will create.\nSince he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.\nFind the longest string that can be created regardless of which string among S_1, . . . , S_n the headline contains.\nIf there are multiple such strings, find the lexicographically smallest one among them.\nTask Constraint: 1 <= n <= 50\n1 <= |S_i| <= 50 for every i = 1, ..., n.\nS_i consists of lowercase English letters (a - z) for every i = 1, ..., n.\nTask Input: Input is given from Standard Input in the following format:\nn\nS_1\n. . .\nS_n\nTask Output: Print the lexicographically smallest string among the longest strings that satisfy the condition.\nIf the answer is an empty string, print an empty line.\nTask Samples: input: 3\ncbaa\ndaacc\nacacac output: aac\n\nThe strings that can be created from each of cbaa, daacc and acacac, are aa, aac, aca, caa and so forth.\nAmong them, aac, aca and caa are the longest, and the lexicographically smallest of these three is aac.\ninput: 3\na\naa\nb output: \nThe answer is an empty string.\n\n" }, { "title": "", "content": "Problem Statement On a two-dimensional plane, there are m lines drawn parallel to the x axis, and n lines drawn parallel to the y axis.\nAmong the lines parallel to the x axis, the i-th from the bottom is represented by y = y_i.\nSimilarly, among the lines parallel to the y axis, the i-th from the left is represented by x = x_i.\nFor every rectangle that is formed by these lines, find its area, and print the total area modulo 10^9+7.\nThat is, for every quadruple (i, j, k, l) satisfying 1<= i < j<= n and 1<= k < l<= m, find the area of the rectangle formed by the lines x=x_i, x=x_j, y=y_k and y=y_l, and print the sum of these areas modulo 10^9+7.", "constraint": "2 <= n,m <= 10^5\n-10^9 <= x_1 < ... < x_n <= 10^9\n-10^9 <= y_1 < ... < y_m <= 10^9\nx_i and y_i are integers.", "input": "Input is given from Standard Input in the following format:\nn m\nx_1 x_2 . . . x_n\ny_1 y_2 . . . y_m", "output": "Print the total area of the rectangles, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 3 4\n1 3 6 output: 60\n\nThe following figure illustrates this input:\n\nThe total area of the nine rectangles A, B, ..., I shown in the following figure, is 60.", "input: 6 5\n-790013317 -192321079 95834122 418379342 586260100 802780784\n-253230108 193944314 363756450 712662868 735867677 output: 835067060"], "Pid": "p03762", "ProblemText": "Task Description: Problem Statement On a two-dimensional plane, there are m lines drawn parallel to the x axis, and n lines drawn parallel to the y axis.\nAmong the lines parallel to the x axis, the i-th from the bottom is represented by y = y_i.\nSimilarly, among the lines parallel to the y axis, the i-th from the left is represented by x = x_i.\nFor every rectangle that is formed by these lines, find its area, and print the total area modulo 10^9+7.\nThat is, for every quadruple (i, j, k, l) satisfying 1<= i < j<= n and 1<= k < l<= m, find the area of the rectangle formed by the lines x=x_i, x=x_j, y=y_k and y=y_l, and print the sum of these areas modulo 10^9+7.\nTask Constraint: 2 <= n,m <= 10^5\n-10^9 <= x_1 < ... < x_n <= 10^9\n-10^9 <= y_1 < ... < y_m <= 10^9\nx_i and y_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nn m\nx_1 x_2 . . . x_n\ny_1 y_2 . . . y_m\nTask Output: Print the total area of the rectangles, modulo 10^9+7.\nTask Samples: input: 3 3\n1 3 4\n1 3 6 output: 60\n\nThe following figure illustrates this input:\n\nThe total area of the nine rectangles A, B, ..., I shown in the following figure, is 60.\ninput: 6 5\n-790013317 -192321079 95834122 418379342 586260100 802780784\n-253230108 193944314 363756450 712662868 735867677 output: 835067060\n\n" }, { "title": "", "content": "Problem Statement Snuke loves \"paper cutting\": he cuts out characters from a newspaper headline and rearranges them to form another string.\nHe will receive a headline which contains one of the strings S_1, . . . , S_n tomorrow.\nHe is excited and already thinking of what string he will create.\nSince he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.\nFind the longest string that can be created regardless of which string among S_1, . . . , S_n the headline contains.\nIf there are multiple such strings, find the lexicographically smallest one among them.", "constraint": "1 <= n <= 50\n1 <= |S_i| <= 50 for every i = 1, ..., n.\nS_i consists of lowercase English letters (a - z) for every i = 1, ..., n.", "input": "Input is given from Standard Input in the following format:\nn\nS_1\n. . .\nS_n", "output": "Print the lexicographically smallest string among the longest strings that satisfy the condition.\nIf the answer is an empty string, print an empty line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\ncbaa\ndaacc\nacacac output: aac\n\nThe strings that can be created from each of cbaa, daacc and acacac, are aa, aac, aca, caa and so forth.\nAmong them, aac, aca and caa are the longest, and the lexicographically smallest of these three is aac.", "input: 3\na\naa\nb output: \nThe answer is an empty string."], "Pid": "p03763", "ProblemText": "Task Description: Problem Statement Snuke loves \"paper cutting\": he cuts out characters from a newspaper headline and rearranges them to form another string.\nHe will receive a headline which contains one of the strings S_1, . . . , S_n tomorrow.\nHe is excited and already thinking of what string he will create.\nSince he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.\nFind the longest string that can be created regardless of which string among S_1, . . . , S_n the headline contains.\nIf there are multiple such strings, find the lexicographically smallest one among them.\nTask Constraint: 1 <= n <= 50\n1 <= |S_i| <= 50 for every i = 1, ..., n.\nS_i consists of lowercase English letters (a - z) for every i = 1, ..., n.\nTask Input: Input is given from Standard Input in the following format:\nn\nS_1\n. . .\nS_n\nTask Output: Print the lexicographically smallest string among the longest strings that satisfy the condition.\nIf the answer is an empty string, print an empty line.\nTask Samples: input: 3\ncbaa\ndaacc\nacacac output: aac\n\nThe strings that can be created from each of cbaa, daacc and acacac, are aa, aac, aca, caa and so forth.\nAmong them, aac, aca and caa are the longest, and the lexicographically smallest of these three is aac.\ninput: 3\na\naa\nb output: \nThe answer is an empty string.\n\n" }, { "title": "", "content": "Problem Statement On a two-dimensional plane, there are m lines drawn parallel to the x axis, and n lines drawn parallel to the y axis.\nAmong the lines parallel to the x axis, the i-th from the bottom is represented by y = y_i.\nSimilarly, among the lines parallel to the y axis, the i-th from the left is represented by x = x_i.\nFor every rectangle that is formed by these lines, find its area, and print the total area modulo 10^9+7.\nThat is, for every quadruple (i, j, k, l) satisfying 1<= i < j<= n and 1<= k < l<= m, find the area of the rectangle formed by the lines x=x_i, x=x_j, y=y_k and y=y_l, and print the sum of these areas modulo 10^9+7.", "constraint": "2 <= n,m <= 10^5\n-10^9 <= x_1 < ... < x_n <= 10^9\n-10^9 <= y_1 < ... < y_m <= 10^9\nx_i and y_i are integers.", "input": "Input is given from Standard Input in the following format:\nn m\nx_1 x_2 . . . x_n\ny_1 y_2 . . . y_m", "output": "Print the total area of the rectangles, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 3 4\n1 3 6 output: 60\n\nThe following figure illustrates this input:\n\nThe total area of the nine rectangles A, B, ..., I shown in the following figure, is 60.", "input: 6 5\n-790013317 -192321079 95834122 418379342 586260100 802780784\n-253230108 193944314 363756450 712662868 735867677 output: 835067060"], "Pid": "p03764", "ProblemText": "Task Description: Problem Statement On a two-dimensional plane, there are m lines drawn parallel to the x axis, and n lines drawn parallel to the y axis.\nAmong the lines parallel to the x axis, the i-th from the bottom is represented by y = y_i.\nSimilarly, among the lines parallel to the y axis, the i-th from the left is represented by x = x_i.\nFor every rectangle that is formed by these lines, find its area, and print the total area modulo 10^9+7.\nThat is, for every quadruple (i, j, k, l) satisfying 1<= i < j<= n and 1<= k < l<= m, find the area of the rectangle formed by the lines x=x_i, x=x_j, y=y_k and y=y_l, and print the sum of these areas modulo 10^9+7.\nTask Constraint: 2 <= n,m <= 10^5\n-10^9 <= x_1 < ... < x_n <= 10^9\n-10^9 <= y_1 < ... < y_m <= 10^9\nx_i and y_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nn m\nx_1 x_2 . . . x_n\ny_1 y_2 . . . y_m\nTask Output: Print the total area of the rectangles, modulo 10^9+7.\nTask Samples: input: 3 3\n1 3 4\n1 3 6 output: 60\n\nThe following figure illustrates this input:\n\nThe total area of the nine rectangles A, B, ..., I shown in the following figure, is 60.\ninput: 6 5\n-790013317 -192321079 95834122 418379342 586260100 802780784\n-253230108 193944314 363756450 712662868 735867677 output: 835067060\n\n" }, { "title": "", "content": "Problem Statement Let us consider the following operations on a string consisting of A and B:\n\nSelect a character in a string. If it is A, replace it with BB. If it is B, replace with AA.\nSelect a substring that is equal to either AAA or BBB, and delete it from the string.\n\nFor example, if the first operation is performed on ABA and the first character is selected, the string becomes BBBA.\nIf the second operation is performed on BBBAAAA and the fourth through sixth characters are selected, the string becomes BBBA.\nThese operations can be performed any number of times, in any order.\nYou are given two string S and T, and q queries a_i, b_i, c_i, d_i.\nFor each query, determine whether S_{a_i} S_{{a_i}+1} . . . S_{b_i}, a substring of S, can be made into T_{c_i} T_{{c_i}+1} . . . T_{d_i}, a substring of T.", "constraint": "1 <= |S|, |T| <= 10^5\nS and T consist of letters A and B.\n1 <= q <= 10^5\n1 <= a_i <= b_i <= |S|\n1 <= c_i <= d_i <= |T|", "input": "Input is given from Standard Input in the following format:\nS\nT\nq\na_1 b_1 c_1 d_1\n. . .\na_q b_q c_q d_q", "output": "Print q lines. The i-th line should contain the response to the i-th query. If S_{a_i} S_{{a_i}+1} . . . S_{b_i} can be made into T_{c_i} T_{{c_i}+1} . . . T_{d_i}, print YES. Otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: BBBAAAABA\nBBBBA\n4\n7 9 2 5\n7 9 1 4\n1 7 2 5\n1 7 2 4 output: YES\nNO\nYES\nNO\n\nThe first query asks whether the string ABA can be made into BBBA.\nAs explained in the problem statement, it can be done by the first operation.\nThe second query asks whether ABA can be made into BBBB, and the fourth query asks whether BBBAAAA can be made into BBB.\nNeither is possible.\nThe third query asks whether the string BBBAAAA can be made into BBBA.\nAs explained in the problem statement, it can be done by the second operation.", "input: AAAAABBBBAAABBBBAAAA\nBBBBAAABBBBBBAAAAABB\n10\n2 15 2 13\n2 13 6 16\n1 13 2 20\n4 20 3 20\n1 18 9 19\n2 14 1 11\n3 20 3 15\n6 16 1 17\n4 18 8 20\n7 20 3 14 output: YES\nYES\nYES\nYES\nYES\nYES\nNO\nNO\nNO\nNO"], "Pid": "p03765", "ProblemText": "Task Description: Problem Statement Let us consider the following operations on a string consisting of A and B:\n\nSelect a character in a string. If it is A, replace it with BB. If it is B, replace with AA.\nSelect a substring that is equal to either AAA or BBB, and delete it from the string.\n\nFor example, if the first operation is performed on ABA and the first character is selected, the string becomes BBBA.\nIf the second operation is performed on BBBAAAA and the fourth through sixth characters are selected, the string becomes BBBA.\nThese operations can be performed any number of times, in any order.\nYou are given two string S and T, and q queries a_i, b_i, c_i, d_i.\nFor each query, determine whether S_{a_i} S_{{a_i}+1} . . . S_{b_i}, a substring of S, can be made into T_{c_i} T_{{c_i}+1} . . . T_{d_i}, a substring of T.\nTask Constraint: 1 <= |S|, |T| <= 10^5\nS and T consist of letters A and B.\n1 <= q <= 10^5\n1 <= a_i <= b_i <= |S|\n1 <= c_i <= d_i <= |T|\nTask Input: Input is given from Standard Input in the following format:\nS\nT\nq\na_1 b_1 c_1 d_1\n. . .\na_q b_q c_q d_q\nTask Output: Print q lines. The i-th line should contain the response to the i-th query. If S_{a_i} S_{{a_i}+1} . . . S_{b_i} can be made into T_{c_i} T_{{c_i}+1} . . . T_{d_i}, print YES. Otherwise, print NO.\nTask Samples: input: BBBAAAABA\nBBBBA\n4\n7 9 2 5\n7 9 1 4\n1 7 2 5\n1 7 2 4 output: YES\nNO\nYES\nNO\n\nThe first query asks whether the string ABA can be made into BBBA.\nAs explained in the problem statement, it can be done by the first operation.\nThe second query asks whether ABA can be made into BBBB, and the fourth query asks whether BBBAAAA can be made into BBB.\nNeither is possible.\nThe third query asks whether the string BBBAAAA can be made into BBBA.\nAs explained in the problem statement, it can be done by the second operation.\ninput: AAAAABBBBAAABBBBAAAA\nBBBBAAABBBBBBAAAAABB\n10\n2 15 2 13\n2 13 6 16\n1 13 2 20\n4 20 3 20\n1 18 9 19\n2 14 1 11\n3 20 3 15\n6 16 1 17\n4 18 8 20\n7 20 3 14 output: YES\nYES\nYES\nYES\nYES\nYES\nNO\nNO\nNO\nNO\n\n" }, { "title": "", "content": "Problem Statement How many infinite sequences a_1, a_2, . . . consisting of {{1, . . . , n}} satisfy the following conditions?\n\nThe n-th and subsequent elements are all equal. That is, if n <= i, j, a_i = a_j.\nFor every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k<= i+a_i, a_j = a_k.\n\nFind the count modulo 10^9+7.", "constraint": "1 <= n <= 10^6", "input": "Input is given from Standard Input in the following format:\nn", "output": "Print how many sequences satisfy the conditions, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 4\n\nThe four sequences that satisfy the conditions are:\n\n1,1,1, ...\n1,2,2, ...\n2,1,1, ...\n2,2,2, ...", "input: 654321 output: 968545283"], "Pid": "p03766", "ProblemText": "Task Description: Problem Statement How many infinite sequences a_1, a_2, . . . consisting of {{1, . . . , n}} satisfy the following conditions?\n\nThe n-th and subsequent elements are all equal. That is, if n <= i, j, a_i = a_j.\nFor every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k<= i+a_i, a_j = a_k.\n\nFind the count modulo 10^9+7.\nTask Constraint: 1 <= n <= 10^6\nTask Input: Input is given from Standard Input in the following format:\nn\nTask Output: Print how many sequences satisfy the conditions, modulo 10^9+7.\nTask Samples: input: 2 output: 4\n\nThe four sequences that satisfy the conditions are:\n\n1,1,1, ...\n1,2,2, ...\n2,1,1, ...\n2,2,2, ...\ninput: 654321 output: 968545283\n\n" }, { "title": "", "content": "Problem Statement There are 3N participants in At Coder Group Contest.\nThe strength of the i-th participant is represented by an integer a_i.\nThey will form N teams, each consisting of three participants.\nNo participant may belong to multiple teams.\nThe strength of a team is defined as the second largest strength among its members.\nFor example, a team of participants of strength 1,5,2 has a strength 2, and a team of three participants of strength 3,2,3 has a strength 3.\nFind the maximum possible sum of the strengths of N teams.", "constraint": "1 <= N <= 10^5\n1 <= a_i <= 10^{9}\na_i are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{3N}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n5 2 8 5 1 5 output: 10\n\nThe following is one formation of teams that maximizes the sum of the strengths of teams:\n\nTeam 1: consists of the first, fourth and fifth participants.\nTeam 2: consists of the second, third and sixth participants.", "input: 10\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 10000000000\n\nThe sum of the strengths can be quite large."], "Pid": "p03767", "ProblemText": "Task Description: Problem Statement There are 3N participants in At Coder Group Contest.\nThe strength of the i-th participant is represented by an integer a_i.\nThey will form N teams, each consisting of three participants.\nNo participant may belong to multiple teams.\nThe strength of a team is defined as the second largest strength among its members.\nFor example, a team of participants of strength 1,5,2 has a strength 2, and a team of three participants of strength 3,2,3 has a strength 3.\nFind the maximum possible sum of the strengths of N teams.\nTask Constraint: 1 <= N <= 10^5\n1 <= a_i <= 10^{9}\na_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{3N}\nTask Output: Print the answer.\nTask Samples: input: 2\n5 2 8 5 1 5 output: 10\n\nThe following is one formation of teams that maximizes the sum of the strengths of teams:\n\nTeam 1: consists of the first, fourth and fifth participants.\nTeam 2: consists of the second, third and sixth participants.\ninput: 10\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 output: 10000000000\n\nThe sum of the strengths can be quite large.\n\n" }, { "title": "", "content": "Problem Statement Squid loves painting vertices in graphs.\nThere is a simple undirected graph consisting of N vertices numbered 1 through N, and M edges.\nInitially, all the vertices are painted in color 0. The i-th edge bidirectionally connects two vertices a_i and b_i. The length of every edge is 1.\nSquid performed Q operations on this graph. In the i-th operation, he repaints all the vertices within a distance of d_i from vertex v_i, in color c_i.\nFind the color of each vertex after the Q operations. partial score: Partial Score\n200 points will be awarded for passing the testset satisfying 1 <= N, M, Q <= 2{, }000.", "constraint": "1 <= N,M,Q <= 10^5\n1 <= a_i,b_i,v_i <= N\na_i != b_i\n0 <= d_i <= 10\n1 <= c_i <=10^5\nd_i and c_i are all integers.\nThere are no self-loops or multiple edges in the given graph.", "input": "Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_{M} b_{M}\nQ\nv_1 d_1 c_1\n:\nv_{Q} d_{Q} c_{Q}", "output": "Print the answer in N lines.\nIn the i-th line, print the color of vertex i after the Q operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 7\n1 2\n1 3\n1 4\n4 5\n5 6\n5 7\n2 3\n2\n6 1 1\n1 2 2 output: 2\n2\n2\n2\n2\n1\n0\n\nInitially, each vertex is painted in color 0.\nIn the first operation, vertices 5 and 6 are repainted in color 1.\nIn the second operation, vertices 1,2,3,4 and 5 are repainted in color 2.", "input: 14 10\n1 4\n5 7\n7 11\n4 10\n14 7\n14 3\n6 14\n8 11\n5 13\n8 3\n8\n8 6 2\n9 7 85\n6 9 3\n6 7 5\n10 3 1\n12 9 4\n9 6 6\n8 2 3 output: 1\n0\n3\n1\n5\n5\n3\n3\n6\n1\n3\n4\n5\n3\n\nThe given graph may not be connected."], "Pid": "p03768", "ProblemText": "Task Description: Problem Statement Squid loves painting vertices in graphs.\nThere is a simple undirected graph consisting of N vertices numbered 1 through N, and M edges.\nInitially, all the vertices are painted in color 0. The i-th edge bidirectionally connects two vertices a_i and b_i. The length of every edge is 1.\nSquid performed Q operations on this graph. In the i-th operation, he repaints all the vertices within a distance of d_i from vertex v_i, in color c_i.\nFind the color of each vertex after the Q operations. partial score: Partial Score\n200 points will be awarded for passing the testset satisfying 1 <= N, M, Q <= 2{, }000.\nTask Constraint: 1 <= N,M,Q <= 10^5\n1 <= a_i,b_i,v_i <= N\na_i != b_i\n0 <= d_i <= 10\n1 <= c_i <=10^5\nd_i and c_i are all integers.\nThere are no self-loops or multiple edges in the given graph.\nTask Input: Input is given from Standard Input in the following format:\nN M\na_1 b_1\n:\na_{M} b_{M}\nQ\nv_1 d_1 c_1\n:\nv_{Q} d_{Q} c_{Q}\nTask Output: Print the answer in N lines.\nIn the i-th line, print the color of vertex i after the Q operations.\nTask Samples: input: 7 7\n1 2\n1 3\n1 4\n4 5\n5 6\n5 7\n2 3\n2\n6 1 1\n1 2 2 output: 2\n2\n2\n2\n2\n1\n0\n\nInitially, each vertex is painted in color 0.\nIn the first operation, vertices 5 and 6 are repainted in color 1.\nIn the second operation, vertices 1,2,3,4 and 5 are repainted in color 2.\ninput: 14 10\n1 4\n5 7\n7 11\n4 10\n14 7\n14 3\n6 14\n8 11\n5 13\n8 3\n8\n8 6 2\n9 7 85\n6 9 3\n6 7 5\n10 3 1\n12 9 4\n9 6 6\n8 2 3 output: 1\n0\n3\n1\n5\n5\n3\n3\n6\n1\n3\n4\n5\n3\n\nThe given graph may not be connected.\n\n" }, { "title": "", "content": "Problem Statement We will call a string x good if it satisfies the following condition:\n\nCondition: x can be represented as a concatenation of two copies of another string y of length at least 1.\n\nFor example, aa and bubobubo are good; an empty string, a, abcabcabc and abba are not good.\nEagle and Owl created a puzzle on good strings.\nFind one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.\n\n1 <= |s| <= 200\nEach character of s is one of the 100 characters represented by the integers 1 through 100.\nAmong the 2^{|s|} subsequences of s, exactly N are good strings.", "constraint": "1 <= N <= 10^{12}", "input": "Input is given from Standard Input in the following format:\nN", "output": "In the first line, print |s|, the length of s.\nIn the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 output: 4\n1 1 1 1\n\nThere are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.", "input: 299 output: 23\n32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10"], "Pid": "p03769", "ProblemText": "Task Description: Problem Statement We will call a string x good if it satisfies the following condition:\n\nCondition: x can be represented as a concatenation of two copies of another string y of length at least 1.\n\nFor example, aa and bubobubo are good; an empty string, a, abcabcabc and abba are not good.\nEagle and Owl created a puzzle on good strings.\nFind one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.\n\n1 <= |s| <= 200\nEach character of s is one of the 100 characters represented by the integers 1 through 100.\nAmong the 2^{|s|} subsequences of s, exactly N are good strings.\nTask Constraint: 1 <= N <= 10^{12}\nTask Input: Input is given from Standard Input in the following format:\nN\nTask Output: In the first line, print |s|, the length of s.\nIn the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.\nTask Samples: input: 7 output: 4\n1 1 1 1\n\nThere are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.\ninput: 299 output: 23\n32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10\n\n" }, { "title": "", "content": "Problem Statement Snuke arranged N colorful balls in a row.\nThe i-th ball from the left has color c_i and weight w_i.\nHe can rearrange the balls by performing the following two operations any number of times, in any order:\n\nOperation 1: Select two balls with the same color. If the total weight of these balls is at most X, swap the positions of these balls.\nOperation 2: Select two balls with different colors. If the total weight of these balls is at most Y, swap the positions of these balls.\n\nHow many different sequences of colors of balls can be obtained? Find the count modulo 10^9 + 7.", "constraint": "1 <= N <= 2 * 10^5\n1 <= X, Y <= 10^9\n1 <= c_i <= N\n1 <= w_i <= 10^9\nX, Y, c_i, w_i are all integers.", "input": "Input is given from Standard Input in the following format:\nN X Y\nc_1 w_1\n:\nc_N w_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 7 3\n3 2\n4 3\n2 1\n4 4 output: 2\nThe sequence of colors (2,4,3,4) can be obtained by swapping the positions of the first and third balls by operation 2.\nIt is also possible to swap the positions of the second and fourth balls by operation 1, but it does not affect the sequence of colors.", "input: 1 1 1\n1 1 output: 1", "input: 21 77 68\n16 73\n16 99\n19 66\n2 87\n2 16\n7 17\n10 36\n10 68\n2 38\n10 74\n13 55\n21 21\n3 7\n12 41\n13 88\n18 6\n2 12\n13 87\n1 9\n2 27\n13 15 output: 129729600"], "Pid": "p03770", "ProblemText": "Task Description: Problem Statement Snuke arranged N colorful balls in a row.\nThe i-th ball from the left has color c_i and weight w_i.\nHe can rearrange the balls by performing the following two operations any number of times, in any order:\n\nOperation 1: Select two balls with the same color. If the total weight of these balls is at most X, swap the positions of these balls.\nOperation 2: Select two balls with different colors. If the total weight of these balls is at most Y, swap the positions of these balls.\n\nHow many different sequences of colors of balls can be obtained? Find the count modulo 10^9 + 7.\nTask Constraint: 1 <= N <= 2 * 10^5\n1 <= X, Y <= 10^9\n1 <= c_i <= N\n1 <= w_i <= 10^9\nX, Y, c_i, w_i are all integers.\nTask Input: Input is given from Standard Input in the following format:\nN X Y\nc_1 w_1\n:\nc_N w_N\nTask Output: Print the answer.\nTask Samples: input: 4 7 3\n3 2\n4 3\n2 1\n4 4 output: 2\nThe sequence of colors (2,4,3,4) can be obtained by swapping the positions of the first and third balls by operation 2.\nIt is also possible to swap the positions of the second and fourth balls by operation 1, but it does not affect the sequence of colors.\ninput: 1 1 1\n1 1 output: 1\ninput: 21 77 68\n16 73\n16 99\n19 66\n2 87\n2 16\n7 17\n10 36\n10 68\n2 38\n10 74\n13 55\n21 21\n3 7\n12 41\n13 88\n18 6\n2 12\n13 87\n1 9\n2 27\n13 15 output: 129729600\n\n" }, { "title": "", "content": "Problem Statement There are N oases on a number line. The coordinate of the i-th oases from the left is x_i.\nCamel hopes to visit all these oases.\nInitially, the volume of the hump on his back is V. When the volume of the hump is v, water of volume at most v can be stored. Water is only supplied at oases. He can get as much water as he can store at a oasis, and the same oasis can be used any number of times.\nCamel can travel on the line by either walking or jumping:\n\nWalking over a distance of d costs water of volume d from the hump. A walk that leads to a negative amount of stored water cannot be done.\nLet v be the amount of water stored at the moment. When v>0, Camel can jump to any point on the line of his choice. After this move, the volume of the hump becomes v/2 (rounded down to the nearest integer), and the amount of stored water becomes 0.\n\nFor each of the oases, determine whether it is possible to start from that oasis and visit all the oases.", "constraint": "2 <= N,V <= 2 * 10^5\n-10^9 <= x_1 < x_2 < ... < x_N <= 10^9\nV and x_i are all integers.", "input": "Input is given from Standard Input in the following format:\nN V\nx_1 x_2 . . . x_{N}", "output": "Print N lines. The i-th line should contain Possible if it is possible to start from the i-th oasis and visit all the oases, and Impossible otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 3 6 output: Possible\nPossible\nPossible\n\nIt is possible to start from the first oasis and visit all the oases, as follows:\n\nWalk from the first oasis to the second oasis. The amount of stored water becomes 0.\nGet water at the second oasis. The amount of stored water becomes 2.\nJump from the second oasis to the third oasis. The amount of stored water becomes 0, and the volume of the hump becomes 1.", "input: 7 2\n-10 -4 -2 0 2 4 10 output: Impossible\nPossible\nPossible\nPossible\nPossible\nPossible\nImpossible\n\nA oasis may be visited any number of times.", "input: 16 19\n-49 -48 -33 -30 -21 -14 0 15 19 23 44 52 80 81 82 84 output: Possible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nImpossible\nImpossible\nImpossible\nImpossible"], "Pid": "p03771", "ProblemText": "Task Description: Problem Statement There are N oases on a number line. The coordinate of the i-th oases from the left is x_i.\nCamel hopes to visit all these oases.\nInitially, the volume of the hump on his back is V. When the volume of the hump is v, water of volume at most v can be stored. Water is only supplied at oases. He can get as much water as he can store at a oasis, and the same oasis can be used any number of times.\nCamel can travel on the line by either walking or jumping:\n\nWalking over a distance of d costs water of volume d from the hump. A walk that leads to a negative amount of stored water cannot be done.\nLet v be the amount of water stored at the moment. When v>0, Camel can jump to any point on the line of his choice. After this move, the volume of the hump becomes v/2 (rounded down to the nearest integer), and the amount of stored water becomes 0.\n\nFor each of the oases, determine whether it is possible to start from that oasis and visit all the oases.\nTask Constraint: 2 <= N,V <= 2 * 10^5\n-10^9 <= x_1 < x_2 < ... < x_N <= 10^9\nV and x_i are all integers.\nTask Input: Input is given from Standard Input in the following format:\nN V\nx_1 x_2 . . . x_{N}\nTask Output: Print N lines. The i-th line should contain Possible if it is possible to start from the i-th oasis and visit all the oases, and Impossible otherwise.\nTask Samples: input: 3 2\n1 3 6 output: Possible\nPossible\nPossible\n\nIt is possible to start from the first oasis and visit all the oases, as follows:\n\nWalk from the first oasis to the second oasis. The amount of stored water becomes 0.\nGet water at the second oasis. The amount of stored water becomes 2.\nJump from the second oasis to the third oasis. The amount of stored water becomes 0, and the volume of the hump becomes 1.\ninput: 7 2\n-10 -4 -2 0 2 4 10 output: Impossible\nPossible\nPossible\nPossible\nPossible\nPossible\nImpossible\n\nA oasis may be visited any number of times.\ninput: 16 19\n-49 -48 -33 -30 -21 -14 0 15 19 23 44 52 80 81 82 84 output: Possible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nImpossible\nImpossible\nImpossible\nImpossible\n\n" }, { "title": "", "content": "Problem Statement Snuke received an integer sequence a of length 2N-1.\nHe arbitrarily permuted the elements in a, then used it to construct a new integer sequence b of length N, as follows:\n\nb_1 = the median of (a_1)\nb_2 = the median of (a_1, a_2, a_3)\nb_3 = the median of (a_1, a_2, a_3, a_4, a_5)\n:\nb_N = the median of (a_1, a_2, a_3, . . . , a_{2N-1})\n\nHow many different sequences can be obtained as b? Find the count modulo 10^{9} + 7.", "constraint": "1 <= N <= 50\n1 <= a_i <= 2N-1\na_i are integers.", "input": "Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{2N-1}", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 3 2 output: 3\n\nThere are three sequences that can be obtained as b: (1,2), (2,2) and (3,2). Each of these can be constructed from (1,2,3), (2,1,3) and (3,1,2), respectively.", "input: 4\n1 3 2 3 2 4 3 output: 16", "input: 15\n1 5 9 11 1 19 17 18 20 1 14 3 3 8 19 15 16 29 10 2 4 13 6 12 7 15 16 1 1 output: 911828634\n\nPrint the count modulo 10^{9} + 7."], "Pid": "p03772", "ProblemText": "Task Description: Problem Statement Snuke received an integer sequence a of length 2N-1.\nHe arbitrarily permuted the elements in a, then used it to construct a new integer sequence b of length N, as follows:\n\nb_1 = the median of (a_1)\nb_2 = the median of (a_1, a_2, a_3)\nb_3 = the median of (a_1, a_2, a_3, a_4, a_5)\n:\nb_N = the median of (a_1, a_2, a_3, . . . , a_{2N-1})\n\nHow many different sequences can be obtained as b? Find the count modulo 10^{9} + 7.\nTask Constraint: 1 <= N <= 50\n1 <= a_i <= 2N-1\na_i are integers.\nTask Input: Input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{2N-1}\nTask Output: Print the answer.\nTask Samples: input: 2\n1 3 2 output: 3\n\nThere are three sequences that can be obtained as b: (1,2), (2,2) and (3,2). Each of these can be constructed from (1,2,3), (2,1,3) and (3,1,2), respectively.\ninput: 4\n1 3 2 3 2 4 3 output: 16\ninput: 15\n1 5 9 11 1 19 17 18 20 1 14 3 3 8 19 15 16 29 10 2 4 13 6 12 7 15 16 1 1 output: 911828634\n\nPrint the count modulo 10^{9} + 7.\n\n" }, { "title": "", "content": "Problem Statement Dolphin loves programming contests. Today, he will take part in a contest in At Coder.\nIn this country, 24-hour clock is used. For example, 9: 00 p. m. is referred to as \"21 o'clock\".\nThe current time is A o'clock, and a contest will begin in exactly B hours.\nWhen will the contest begin? Answer in 24-hour time.", "constraint": "0 <= A,B <= 23\nA and B are integers.", "input": "Input The input is given from Standard Input in the following format:\nA B", "output": "Print the hour of the starting time of the contest in 24-hour time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9 12 output: 21\n\nIn this input, the current time is 9 o'clock, and 12 hours later it will be 21 o'clock in 24-hour time.", "input: 19 0 output: 19\n\nThe contest has just started.", "input: 23 2 output: 1\n\nThe contest will begin at 1 o'clock the next day."], "Pid": "p03773", "ProblemText": "Task Description: Problem Statement Dolphin loves programming contests. Today, he will take part in a contest in At Coder.\nIn this country, 24-hour clock is used. For example, 9: 00 p. m. is referred to as \"21 o'clock\".\nThe current time is A o'clock, and a contest will begin in exactly B hours.\nWhen will the contest begin? Answer in 24-hour time.\nTask Constraint: 0 <= A,B <= 23\nA and B are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nA B\nTask Output: Print the hour of the starting time of the contest in 24-hour time.\nTask Samples: input: 9 12 output: 21\n\nIn this input, the current time is 9 o'clock, and 12 hours later it will be 21 o'clock in 24-hour time.\ninput: 19 0 output: 19\n\nThe contest has just started.\ninput: 23 2 output: 1\n\nThe contest will begin at 1 o'clock the next day.\n\n" }, { "title": "", "content": "Problem Statement There are N students and M checkpoints on the xy-plane.\nThe coordinates of the i-th student (1 <= i <= N) is (a_i, b_i), and the coordinates of the checkpoint numbered j (1 <= j <= M) is (c_j, d_j).\nWhen the teacher gives a signal, each student has to go to the nearest checkpoint measured in Manhattan distance. \nThe Manhattan distance between two points (x_1, y_1) and (x_2, y_2) is |x_1-x_2|+|y_1-y_2|.\nHere, |x| denotes the absolute value of x.\nIf there are multiple nearest checkpoints for a student, he/she will select the checkpoint with the smallest index.\nWhich checkpoint will each student go to?", "constraint": "1 <= N,M <= 50\n-10^8 <= a_i,b_i,c_j,d_j <= 10^8\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN M\na_1 b_1\n: \na_N b_N\nc_1 d_1\n: \nc_M d_M", "output": "Print N lines.\nThe i-th line (1 <= i <= N) should contain the index of the checkpoint for the i-th student to go.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n2 0\n0 0\n-1 0\n1 0 output: 2\n1\n\nThe Manhattan distance between the first student and each checkpoint is:\n\nFor checkpoint 1: |2-(-1)|+|0-0|=3\nFor checkpoint 2: |2-1|+|0-0|=1\n\nThe nearest checkpoint is checkpoint 2. Thus, the first line in the output should contain 2.\nThe Manhattan distance between the second student and each checkpoint is:\n\nFor checkpoint 1: |0-(-1)|+|0-0|=1\nFor checkpoint 2: |0-1|+|0-0|=1\n\nWhen there are multiple nearest checkpoints, the student will go to the checkpoint with the smallest index. Thus, the second line in the output should contain 1.", "input: 3 4\n10 10\n-10 -10\n3 3\n1 2\n2 3\n3 5\n3 5 output: 3\n1\n2\n\nThere can be multiple checkpoints at the same coordinates.", "input: 5 5\n-100000000 -100000000\n-100000000 100000000\n100000000 -100000000\n100000000 100000000\n0 0\n0 0\n100000000 100000000\n100000000 -100000000\n-100000000 100000000\n-100000000 -100000000 output: 5\n4\n3\n2\n1"], "Pid": "p03774", "ProblemText": "Task Description: Problem Statement There are N students and M checkpoints on the xy-plane.\nThe coordinates of the i-th student (1 <= i <= N) is (a_i, b_i), and the coordinates of the checkpoint numbered j (1 <= j <= M) is (c_j, d_j).\nWhen the teacher gives a signal, each student has to go to the nearest checkpoint measured in Manhattan distance. \nThe Manhattan distance between two points (x_1, y_1) and (x_2, y_2) is |x_1-x_2|+|y_1-y_2|.\nHere, |x| denotes the absolute value of x.\nIf there are multiple nearest checkpoints for a student, he/she will select the checkpoint with the smallest index.\nWhich checkpoint will each student go to?\nTask Constraint: 1 <= N,M <= 50\n-10^8 <= a_i,b_i,c_j,d_j <= 10^8\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\na_1 b_1\n: \na_N b_N\nc_1 d_1\n: \nc_M d_M\nTask Output: Print N lines.\nThe i-th line (1 <= i <= N) should contain the index of the checkpoint for the i-th student to go.\nTask Samples: input: 2 2\n2 0\n0 0\n-1 0\n1 0 output: 2\n1\n\nThe Manhattan distance between the first student and each checkpoint is:\n\nFor checkpoint 1: |2-(-1)|+|0-0|=3\nFor checkpoint 2: |2-1|+|0-0|=1\n\nThe nearest checkpoint is checkpoint 2. Thus, the first line in the output should contain 2.\nThe Manhattan distance between the second student and each checkpoint is:\n\nFor checkpoint 1: |0-(-1)|+|0-0|=1\nFor checkpoint 2: |0-1|+|0-0|=1\n\nWhen there are multiple nearest checkpoints, the student will go to the checkpoint with the smallest index. Thus, the second line in the output should contain 1.\ninput: 3 4\n10 10\n-10 -10\n3 3\n1 2\n2 3\n3 5\n3 5 output: 3\n1\n2\n\nThere can be multiple checkpoints at the same coordinates.\ninput: 5 5\n-100000000 -100000000\n-100000000 100000000\n100000000 -100000000\n100000000 100000000\n0 0\n0 0\n100000000 100000000\n100000000 -100000000\n-100000000 100000000\n-100000000 -100000000 output: 5\n4\n3\n2\n1\n\n" }, { "title": "", "content": "Problem Statement You are given an integer N.\nFor two positive integers A and B, we will define F(A, B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.\nFor example, F(3,11) = 2 since 3 has one digit and 11 has two digits.\nFind the minimum value of F(A, B) as (A, B) ranges over all pairs of positive integers such that N = A * B.", "constraint": "1 <= N <= 10^{10}\nN is an integer.", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "Print the minimum value of F(A, B) as (A, B) ranges over all pairs of positive integers such that N = A * B.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10000 output: 3\n\nF(A,B) has a minimum value of 3 at (A,B)=(100,100).", "input: 1000003 output: 7\n\nThere are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.", "input: 9876543210 output: 6"], "Pid": "p03775", "ProblemText": "Task Description: Problem Statement You are given an integer N.\nFor two positive integers A and B, we will define F(A, B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.\nFor example, F(3,11) = 2 since 3 has one digit and 11 has two digits.\nFind the minimum value of F(A, B) as (A, B) ranges over all pairs of positive integers such that N = A * B.\nTask Constraint: 1 <= N <= 10^{10}\nN is an integer.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: Print the minimum value of F(A, B) as (A, B) ranges over all pairs of positive integers such that N = A * B.\nTask Samples: input: 10000 output: 3\n\nF(A,B) has a minimum value of 3 at (A,B)=(100,100).\ninput: 1000003 output: 7\n\nThere are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.\ninput: 9876543210 output: 6\n\n" }, { "title": "", "content": "Problem Statement You are given N items.\nThe value of the i-th item (1 <= i <= N) is v_i.\nYour have to select at least A and at most B of these items.\nUnder this condition, find the maximum possible arithmetic mean of the values of selected items.\nAdditionally, find the number of ways to select items so that the mean of the values of selected items is maximized.", "constraint": "1 <= N <= 50\n1 <= A,B <= N\n1 <= v_i <= 10^{15}\nEach v_i is an integer.", "input": "Input The input is given from Standard Input in the following format:\nN A B\nv_1\nv_2\n. . .\nv_N", "output": "Print two lines.\nThe first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.\nThe second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 2\n1 2 3 4 5 output: 4.500000\n1\n\nThe mean of the values of selected items will be maximized when selecting the fourth and fifth items. Hence, the first line of the output should contain 4.5.\nThere is no other way to select items so that the mean of the values will be 4.5, and thus the second line of the output should contain 1.", "input: 4 2 3\n10 20 10 10 output: 15.000000\n3\n\nThere can be multiple ways to select items so that the mean of the values will be maximized.", "input: 5 1 5\n1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996 output: 1000000000000000.000000\n1"], "Pid": "p03776", "ProblemText": "Task Description: Problem Statement You are given N items.\nThe value of the i-th item (1 <= i <= N) is v_i.\nYour have to select at least A and at most B of these items.\nUnder this condition, find the maximum possible arithmetic mean of the values of selected items.\nAdditionally, find the number of ways to select items so that the mean of the values of selected items is maximized.\nTask Constraint: 1 <= N <= 50\n1 <= A,B <= N\n1 <= v_i <= 10^{15}\nEach v_i is an integer.\nTask Input: Input The input is given from Standard Input in the following format:\nN A B\nv_1\nv_2\n. . .\nv_N\nTask Output: Print two lines.\nThe first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.\nThe second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.\nTask Samples: input: 5 2 2\n1 2 3 4 5 output: 4.500000\n1\n\nThe mean of the values of selected items will be maximized when selecting the fourth and fifth items. Hence, the first line of the output should contain 4.5.\nThere is no other way to select items so that the mean of the values will be 4.5, and thus the second line of the output should contain 1.\ninput: 4 2 3\n10 20 10 10 output: 15.000000\n3\n\nThere can be multiple ways to select items so that the mean of the values will be maximized.\ninput: 5 1 5\n1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996 output: 1000000000000000.000000\n1\n\n" }, { "title": "", "content": "Problem Statement Two deer, At Co Deer and Top Co Deer, are playing a game called Honest or Dishonest.\nIn this game, an honest player always tells the truth, and an dishonest player always tell lies.\nYou are given two characters a and b as the input. Each of them is either H or D, and carries the following information:\nIf a=H, At Co Deer is honest; if a=D, At Co Deer is dishonest.\nIf b=H, At Co Deer is saying that Top Co Deer is honest; if b=D, At Co Deer is saying that Top Co Deer is dishonest.\nGiven this information, determine whether Top Co Deer is honest.", "constraint": "a=H or a=D.\nb=H or b=D.", "input": "Input The input is given from Standard Input in the following format:\na b", "output": "If Top Co Deer is honest, print H. If he is dishonest, print D.", "content_img": false, "lang": "en", "error": false, "samples": ["input: H H output: H\n\nIn this input, AtCoDeer is honest. Hence, as he says, TopCoDeer is honest.", "input: D H output: D\n\nIn this input, AtCoDeer is dishonest. Hence, contrary to what he says, TopCoDeer is dishonest.", "input: D D output: H"], "Pid": "p03777", "ProblemText": "Task Description: Problem Statement Two deer, At Co Deer and Top Co Deer, are playing a game called Honest or Dishonest.\nIn this game, an honest player always tells the truth, and an dishonest player always tell lies.\nYou are given two characters a and b as the input. Each of them is either H or D, and carries the following information:\nIf a=H, At Co Deer is honest; if a=D, At Co Deer is dishonest.\nIf b=H, At Co Deer is saying that Top Co Deer is honest; if b=D, At Co Deer is saying that Top Co Deer is dishonest.\nGiven this information, determine whether Top Co Deer is honest.\nTask Constraint: a=H or a=D.\nb=H or b=D.\nTask Input: Input The input is given from Standard Input in the following format:\na b\nTask Output: If Top Co Deer is honest, print H. If he is dishonest, print D.\nTask Samples: input: H H output: H\n\nIn this input, AtCoDeer is honest. Hence, as he says, TopCoDeer is honest.\ninput: D H output: D\n\nIn this input, AtCoDeer is dishonest. Hence, contrary to what he says, TopCoDeer is dishonest.\ninput: D D output: H\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer found two rectangles lying on the table, each with height 1 and width W.\nIf we consider the surface of the desk as a two-dimensional plane, the first rectangle covers the vertical range of [0,1] and the horizontal range of [a, a+W], and the second rectangle covers the vertical range of [1,2] and the horizontal range of [b, b+W], as shown in the following figure:\n\nAt Co Deer will move the second rectangle horizontally so that it connects with the first rectangle.\nFind the minimum distance it needs to be moved.", "constraint": "All input values are integers.\n1<=W<=10^5\n1<=a,b<=10^5", "input": "Input The input is given from Standard Input in the following format:\nW a b", "output": "Print the minimum distance the second rectangle needs to be moved.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2 6 output: 1\n\nThis input corresponds to the figure in the statement. In this case, the second rectangle should be moved to the left by a distance of 1.", "input: 3 1 3 output: 0\n\nThe rectangles are already connected, and thus no move is needed.", "input: 5 10 1 output: 4"], "Pid": "p03778", "ProblemText": "Task Description: Problem Statement At Co Deer the deer found two rectangles lying on the table, each with height 1 and width W.\nIf we consider the surface of the desk as a two-dimensional plane, the first rectangle covers the vertical range of [0,1] and the horizontal range of [a, a+W], and the second rectangle covers the vertical range of [1,2] and the horizontal range of [b, b+W], as shown in the following figure:\n\nAt Co Deer will move the second rectangle horizontally so that it connects with the first rectangle.\nFind the minimum distance it needs to be moved.\nTask Constraint: All input values are integers.\n1<=W<=10^5\n1<=a,b<=10^5\nTask Input: Input The input is given from Standard Input in the following format:\nW a b\nTask Output: Print the minimum distance the second rectangle needs to be moved.\nTask Samples: input: 3 2 6 output: 1\n\nThis input corresponds to the figure in the statement. In this case, the second rectangle should be moved to the left by a distance of 1.\ninput: 3 1 3 output: 0\n\nThe rectangles are already connected, and thus no move is needed.\ninput: 5 10 1 output: 4\n\n" }, { "title": "", "content": "Problem Statement There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.\nDuring the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.\nThat is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.\nThe kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.\nFind the earliest possible time to reach coordinate X.", "constraint": "X is an integer.\n1<=X<=10^9", "input": "Input The input is given from Standard Input in the following format:\nX", "output": "Print the earliest possible time for the kangaroo to reach coordinate X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 output: 3\n\nThe kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.", "input: 2 output: 2\n\nHe can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.", "input: 11 output: 5"], "Pid": "p03779", "ProblemText": "Task Description: Problem Statement There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.\nDuring the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.\nThat is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.\nThe kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.\nFind the earliest possible time to reach coordinate X.\nTask Constraint: X is an integer.\n1<=X<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nX\nTask Output: Print the earliest possible time for the kangaroo to reach coordinate X.\nTask Samples: input: 6 output: 3\n\nThe kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.\ninput: 2 output: 2\n\nHe can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.\ninput: 11 output: 5\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer has N cards with positive integers written on them. The number on the i-th card (1<=i<=N) is a_i.\nBecause he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.\nThen, for each card i, he judges whether it is unnecessary or not, as follows:\n\nIf, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.\nOtherwise, card i is NOT unnecessary.\n\nFind the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary. partial score: Partial Score\n300 points will be awarded for passing the test set satisfying N, K<=400.", "constraint": "All input values are integers.\n1<=N<=5000\n1<=K<=5000\n1<=a_i<=10^9 (1<=i<=N)", "input": "Input The input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N", "output": "Print the number of the unnecessary cards.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 6\n1 4 3 output: 1\n\nThere are two good sets: {2,3} and {1,2,3}.\nCard 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.\nFor card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.\nNeither is card 3 for a similar reason, hence the answer is 1.", "input: 5 400\n3 1 4 1 5 output: 5\n\nIn this case, there is no good set. Therefore, all the cards are unnecessary.", "input: 6 20\n10 4 3 10 25 2 output: 3"], "Pid": "p03780", "ProblemText": "Task Description: Problem Statement At Co Deer the deer has N cards with positive integers written on them. The number on the i-th card (1<=i<=N) is a_i.\nBecause he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.\nThen, for each card i, he judges whether it is unnecessary or not, as follows:\n\nIf, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.\nOtherwise, card i is NOT unnecessary.\n\nFind the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary. partial score: Partial Score\n300 points will be awarded for passing the test set satisfying N, K<=400.\nTask Constraint: All input values are integers.\n1<=N<=5000\n1<=K<=5000\n1<=a_i<=10^9 (1<=i<=N)\nTask Input: Input The input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N\nTask Output: Print the number of the unnecessary cards.\nTask Samples: input: 3 6\n1 4 3 output: 1\n\nThere are two good sets: {2,3} and {1,2,3}.\nCard 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.\nFor card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.\nNeither is card 3 for a similar reason, hence the answer is 1.\ninput: 5 400\n3 1 4 1 5 output: 5\n\nIn this case, there is no good set. Therefore, all the cards are unnecessary.\ninput: 6 20\n10 4 3 10 25 2 output: 3\n\n" }, { "title": "", "content": "Problem Statement There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.\nDuring the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.\nThat is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.\nThe kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.\nFind the earliest possible time to reach coordinate X.", "constraint": "X is an integer.\n1<=X<=10^9", "input": "Input The input is given from Standard Input in the following format:\nX", "output": "Print the earliest possible time for the kangaroo to reach coordinate X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 output: 3\n\nThe kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.", "input: 2 output: 2\n\nHe can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.", "input: 11 output: 5"], "Pid": "p03781", "ProblemText": "Task Description: Problem Statement There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.\nDuring the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.\nThat is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.\nThe kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.\nFind the earliest possible time to reach coordinate X.\nTask Constraint: X is an integer.\n1<=X<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nX\nTask Output: Print the earliest possible time for the kangaroo to reach coordinate X.\nTask Samples: input: 6 output: 3\n\nThe kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.\ninput: 2 output: 2\n\nHe can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.\ninput: 11 output: 5\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer has N cards with positive integers written on them. The number on the i-th card (1<=i<=N) is a_i.\nBecause he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.\nThen, for each card i, he judges whether it is unnecessary or not, as follows:\n\nIf, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.\nOtherwise, card i is NOT unnecessary.\n\nFind the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary. partial score: Partial Score\n300 points will be awarded for passing the test set satisfying N, K<=400.", "constraint": "All input values are integers.\n1<=N<=5000\n1<=K<=5000\n1<=a_i<=10^9 (1<=i<=N)", "input": "Input The input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N", "output": "Print the number of the unnecessary cards.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 6\n1 4 3 output: 1\n\nThere are two good sets: {2,3} and {1,2,3}.\nCard 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.\nFor card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.\nNeither is card 3 for a similar reason, hence the answer is 1.", "input: 5 400\n3 1 4 1 5 output: 5\n\nIn this case, there is no good set. Therefore, all the cards are unnecessary.", "input: 6 20\n10 4 3 10 25 2 output: 3"], "Pid": "p03782", "ProblemText": "Task Description: Problem Statement At Co Deer the deer has N cards with positive integers written on them. The number on the i-th card (1<=i<=N) is a_i.\nBecause he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.\nThen, for each card i, he judges whether it is unnecessary or not, as follows:\n\nIf, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.\nOtherwise, card i is NOT unnecessary.\n\nFind the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary. partial score: Partial Score\n300 points will be awarded for passing the test set satisfying N, K<=400.\nTask Constraint: All input values are integers.\n1<=N<=5000\n1<=K<=5000\n1<=a_i<=10^9 (1<=i<=N)\nTask Input: Input The input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N\nTask Output: Print the number of the unnecessary cards.\nTask Samples: input: 3 6\n1 4 3 output: 1\n\nThere are two good sets: {2,3} and {1,2,3}.\nCard 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.\nFor card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.\nNeither is card 3 for a similar reason, hence the answer is 1.\ninput: 5 400\n3 1 4 1 5 output: 5\n\nIn this case, there is no good set. Therefore, all the cards are unnecessary.\ninput: 6 20\n10 4 3 10 25 2 output: 3\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer found N rectangle lying on the table, each with height 1.\nIf we consider the surface of the desk as a two-dimensional plane, the i-th rectangle i(1<=i<=N) covers the vertical range of [i-1, i] and the horizontal range of [l_i, r_i], as shown in the following figure:\n\nAt Co Deer will move these rectangles horizontally so that all the rectangles are connected.\nFor each rectangle, the cost to move it horizontally by a distance of x, is x.\nFind the minimum cost to achieve connectivity.\nIt can be proved that this value is always an integer under the constraints of the problem. partial score: Partial Score\n300 points will be awarded for passing the test set satisfying 1<=N<=400 and 1<=l_i=1", "input": "Input The input is given from Standard Input in the following format:\na_I a_O a_T a_J a_L a_S a_Z", "output": "Print the maximum possible value of K. If no rectangle can be formed, print 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 1 1 0 0 0 0 output: 3\n\nOne possible way to form the largest rectangle is shown in the following figure:", "input: 0 0 10 0 0 0 0 output: 0\n\nNo rectangle can be formed."], "Pid": "p03840", "ProblemText": "Task Description: Problem Statement A tetromino is a figure formed by joining four squares edge to edge.\nWe will refer to the following seven kinds of tetromino as I-, O-, T-, J-, L-, S- and Z-tetrominos, respectively:\n\nSnuke has many tetrominos. The number of I-, O-, T-, J-, L-, S- and Z-tetrominos in his possession are a_I, a_O, a_T, a_J, a_L, a_S and a_Z, respectively.\nSnuke will join K of his tetrominos to form a rectangle that is two squares tall and 2K squares wide.\nHere, the following rules must be followed:\n\nWhen placing each tetromino, rotation is allowed, but reflection is not.\nEach square in the rectangle must be covered by exactly one tetromino.\nNo part of each tetromino may be outside the rectangle.\n\nSnuke wants to form as large a rectangle as possible.\nFind the maximum possible value of K.\nTask Constraint: 0<=a_I,a_O,a_T,a_J,a_L,a_S,a_Z<=10^9\na_I+a_O+a_T+a_J+a_L+a_S+a_Z>=1\nTask Input: Input The input is given from Standard Input in the following format:\na_I a_O a_T a_J a_L a_S a_Z\nTask Output: Print the maximum possible value of K. If no rectangle can be formed, print 0.\nTask Samples: input: 2 1 1 0 0 0 0 output: 3\n\nOne possible way to form the largest rectangle is shown in the following figure:\ninput: 0 0 10 0 0 0 0 output: 0\n\nNo rectangle can be formed.\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence x of length N.\nDetermine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.\n\na is N^2 in length, containing N copies of each of the integers 1,2, . . . , N.\nFor each 1 <= i <= N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.", "constraint": "1 <= N <= 500\n1 <= x_i <= N^2\nAll x_i are distinct.", "input": "Input The input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N", "output": "If there does not exist an integer sequence a that satisfies all the conditions, print No.\nIf there does exist such an sequence a, print Yes in the first line, then print an instance of a in the second line, with spaces inbetween.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 5 9 output: Yes\n1 1 1 2 2 2 3 3 3\n\nFor example, the second occurrence of the integer 2 from the left in a in the output is the fifth element of a from the left.\nSimilarly, the condition is satisfied for the integers 1 and 3.", "input: 2\n4 1 output: No"], "Pid": "p03841", "ProblemText": "Task Description: Problem Statement You are given an integer sequence x of length N.\nDetermine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.\n\na is N^2 in length, containing N copies of each of the integers 1,2, . . . , N.\nFor each 1 <= i <= N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.\nTask Constraint: 1 <= N <= 500\n1 <= x_i <= N^2\nAll x_i are distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N\nTask Output: If there does not exist an integer sequence a that satisfies all the conditions, print No.\nIf there does exist such an sequence a, print Yes in the first line, then print an instance of a in the second line, with spaces inbetween.\nTask Samples: input: 3\n1 5 9 output: Yes\n1 1 1 2 2 2 3 3 3\n\nFor example, the second occurrence of the integer 2 from the left in a in the output is the fifth element of a from the left.\nSimilarly, the condition is satisfied for the integers 1 and 3.\ninput: 2\n4 1 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given an integer sequence a of length N.\nHow many permutations p of the integers 1 through N satisfy the following condition?\n\nFor each 1 <= i <= N, at least one of the following holds: p_i = a_i and p_{p_i} = a_i.\n\nFind the count modulo 10^9 + 7.", "constraint": "1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= N", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the number of the permutations p that satisfy the condition, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2 3 output: 4\n\nThe following four permutations satisfy the condition:\n\n(1,2,3)\n(1,3,2)\n(3,2,1)\n(2,1,3)\n\nFor example, (1,3,2) satisfies the condition because p_1 = 1, p_{p_2} = 2 and p_{p_3} = 3.", "input: 2\n1 1 output: 1\n\nThe following one permutation satisfies the condition:\n\n(2,1)", "input: 3\n2 1 1 output: 2\n\nThe following two permutations satisfy the condition:\n\n(2,3,1)\n(3,1,2)", "input: 3\n1 1 1 output: 0", "input: 13\n2 1 4 3 6 7 5 9 10 8 8 9 11 output: 6"], "Pid": "p03842", "ProblemText": "Task Description: Problem Statement You are given an integer sequence a of length N.\nHow many permutations p of the integers 1 through N satisfy the following condition?\n\nFor each 1 <= i <= N, at least one of the following holds: p_i = a_i and p_{p_i} = a_i.\n\nFind the count modulo 10^9 + 7.\nTask Constraint: 1 <= N <= 10^5\na_i is an integer.\n1 <= a_i <= N\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the number of the permutations p that satisfy the condition, modulo 10^9 + 7.\nTask Samples: input: 3\n1 2 3 output: 4\n\nThe following four permutations satisfy the condition:\n\n(1,2,3)\n(1,3,2)\n(3,2,1)\n(2,1,3)\n\nFor example, (1,3,2) satisfies the condition because p_1 = 1, p_{p_2} = 2 and p_{p_3} = 3.\ninput: 2\n1 1 output: 1\n\nThe following one permutation satisfies the condition:\n\n(2,1)\ninput: 3\n2 1 1 output: 2\n\nThe following two permutations satisfy the condition:\n\n(2,3,1)\n(3,1,2)\ninput: 3\n1 1 1 output: 0\ninput: 13\n2 1 4 3 6 7 5 9 10 8 8 9 11 output: 6\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices.\nThe vertices are numbered 1 through N.\nFor each 1 <= i <= N - 1, the i-th edge connects vertices a_i and b_i.\nThe lengths of all the edges are 1.\nSnuke likes some of the vertices.\nThe information on his favorite vertices are given to you as a string s of length N.\nFor each 1 <= i <= N, s_i is 1 if Snuke likes vertex i, and 0 if he does not like vertex i.\nInitially, all the vertices are white.\nSnuke will perform the following operation exactly once:\n\nSelect a vertex v that he likes, and a non-negative integer d. Then, paint all the vertices black whose distances from v are at most d.\n\nFind the number of the possible combinations of colors of the vertices after the operation. partial score: Partial Score\nIn the test set worth 1300 points, s consists only of 1.", "constraint": "2 <= N <= 2*10^5\n1 <= a_i, b_i <= N\nThe given graph is a tree.\n|s| = N\ns consists of 0 and 1.\ns contains at least one occurrence of 1.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_{N - 1} b_{N - 1}\ns", "output": "Print the number of the possible combinations of colors of the vertices after the operation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2\n1 3\n1 4\n1100 output: 4\n\nThe following four combinations of colors of the vertices are possible:", "input: 5\n1 2\n1 3\n1 4\n4 5\n11111 output: 11\n\nThis case satisfies the additional constraint for the partial score.", "input: 6\n1 2\n1 3\n1 4\n2 5\n2 6\n100011 output: 8"], "Pid": "p03843", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices.\nThe vertices are numbered 1 through N.\nFor each 1 <= i <= N - 1, the i-th edge connects vertices a_i and b_i.\nThe lengths of all the edges are 1.\nSnuke likes some of the vertices.\nThe information on his favorite vertices are given to you as a string s of length N.\nFor each 1 <= i <= N, s_i is 1 if Snuke likes vertex i, and 0 if he does not like vertex i.\nInitially, all the vertices are white.\nSnuke will perform the following operation exactly once:\n\nSelect a vertex v that he likes, and a non-negative integer d. Then, paint all the vertices black whose distances from v are at most d.\n\nFind the number of the possible combinations of colors of the vertices after the operation. partial score: Partial Score\nIn the test set worth 1300 points, s consists only of 1.\nTask Constraint: 2 <= N <= 2*10^5\n1 <= a_i, b_i <= N\nThe given graph is a tree.\n|s| = N\ns consists of 0 and 1.\ns contains at least one occurrence of 1.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_{N - 1} b_{N - 1}\ns\nTask Output: Print the number of the possible combinations of colors of the vertices after the operation.\nTask Samples: input: 4\n1 2\n1 3\n1 4\n1100 output: 4\n\nThe following four combinations of colors of the vertices are possible:\ninput: 5\n1 2\n1 3\n1 4\n4 5\n11111 output: 11\n\nThis case satisfies the additional constraint for the partial score.\ninput: 6\n1 2\n1 3\n1 4\n2 5\n2 6\n100011 output: 8\n\n" }, { "title": "", "content": "Problem Statement Joisino wants to evaluate the formula \"A op B\".\nHere, A and B are integers, and the binary operator op is either + or -.\nYour task is to evaluate the formula instead of her.", "constraint": "1<=A,B<=10^9\nop is either + or -.", "input": "Input The input is given from Standard Input in the following format:\nA op B", "output": "Output Evaluate the formula and print the result.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 + 2 output: 3\n\nSince 1 + 2 = 3, the output should be 3.", "input: 5 - 7 output: -2"], "Pid": "p03844", "ProblemText": "Task Description: Problem Statement Joisino wants to evaluate the formula \"A op B\".\nHere, A and B are integers, and the binary operator op is either + or -.\nYour task is to evaluate the formula instead of her.\nTask Constraint: 1<=A,B<=10^9\nop is either + or -.\nTask Input: Input The input is given from Standard Input in the following format:\nA op B\nTask Output: Output Evaluate the formula and print the result.\nTask Samples: input: 1 + 2 output: 3\n\nSince 1 + 2 = 3, the output should be 3.\ninput: 5 - 7 output: -2\n\n" }, { "title": "", "content": "Problem Statement Joisino is about to compete in the final round of a certain programming competition.\nIn this contest, there are N problems, numbered 1 through N.\nJoisino knows that it takes her T_i seconds to solve problem i(1<=i<=N).\nAlso, there are M kinds of drinks offered to the contestants, numbered 1 through M.\nIf Joisino takes drink i(1<=i<=M), her brain will be stimulated and the time it takes for her to solve problem P_i will become X_i seconds.\nIt does not affect the time to solve the other problems.\nA contestant is allowed to take exactly one of the drinks before the start of the contest.\nFor each drink, Joisino wants to know how many seconds it takes her to solve all the problems if she takes that drink.\nHere, assume that the time it takes her to solve all the problems is equal to the sum of the time it takes for her to solve individual problems.\nYour task is to write a program to calculate it instead of her.", "constraint": "All input values are integers.\n1<=N<=100\n1<=T_i<=10^5\n1<=M<=100\n1<=P_i<=N\n1<=X_i<=10^5", "input": "Input The input is given from Standard Input in the following format:\nN\nT_1 T_2 . . . T_N\nM\nP_1 X_1\nP_2 X_2\n:\nP_M X_M", "output": "For each drink, calculate how many seconds it takes Joisino to solve all the problems if she takes that drink, and print the results, one per line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 1 4\n2\n1 1\n2 3 output: 6\n9\n\nIf Joisino takes drink 1, the time it takes her to solve each problem will be 1,1 and 4 seconds, respectively, totaling 6 seconds.\nIf Joisino takes drink 2, the time it takes her to solve each problem will be 2,3 and 4 seconds, respectively, totaling 9 seconds.", "input: 5\n7 2 3 8 5\n3\n4 2\n1 7\n4 13 output: 19\n25\n30"], "Pid": "p03845", "ProblemText": "Task Description: Problem Statement Joisino is about to compete in the final round of a certain programming competition.\nIn this contest, there are N problems, numbered 1 through N.\nJoisino knows that it takes her T_i seconds to solve problem i(1<=i<=N).\nAlso, there are M kinds of drinks offered to the contestants, numbered 1 through M.\nIf Joisino takes drink i(1<=i<=M), her brain will be stimulated and the time it takes for her to solve problem P_i will become X_i seconds.\nIt does not affect the time to solve the other problems.\nA contestant is allowed to take exactly one of the drinks before the start of the contest.\nFor each drink, Joisino wants to know how many seconds it takes her to solve all the problems if she takes that drink.\nHere, assume that the time it takes her to solve all the problems is equal to the sum of the time it takes for her to solve individual problems.\nYour task is to write a program to calculate it instead of her.\nTask Constraint: All input values are integers.\n1<=N<=100\n1<=T_i<=10^5\n1<=M<=100\n1<=P_i<=N\n1<=X_i<=10^5\nTask Input: Input The input is given from Standard Input in the following format:\nN\nT_1 T_2 . . . T_N\nM\nP_1 X_1\nP_2 X_2\n:\nP_M X_M\nTask Output: For each drink, calculate how many seconds it takes Joisino to solve all the problems if she takes that drink, and print the results, one per line.\nTask Samples: input: 3\n2 1 4\n2\n1 1\n2 3 output: 6\n9\n\nIf Joisino takes drink 1, the time it takes her to solve each problem will be 1,1 and 4 seconds, respectively, totaling 6 seconds.\nIf Joisino takes drink 2, the time it takes her to solve each problem will be 2,3 and 4 seconds, respectively, totaling 9 seconds.\ninput: 5\n7 2 3 8 5\n3\n4 2\n1 7\n4 13 output: 19\n25\n30\n\n" }, { "title": "", "content": "Problem Statement There are N people, conveniently numbered 1 through N.\nThey were standing in a row yesterday, but now they are unsure of the order in which they were standing.\nHowever, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.\nAccording to their reports, the difference above for person i is A_i.\nBased on these reports, find the number of the possible orders in which they were standing.\nSince it can be extremely large, print the answer modulo 10^9+7.\nNote that the reports may be incorrect and thus there may be no consistent order.\nIn such a case, print 0.", "constraint": "1<=N<=10^5\n0<=A_i<=N-1", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the number of the possible orders in which they were standing, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 4 4 0 2 output: 4\n\nThere are four possible orders, as follows:\n\n2,1,4,5,3\n2,5,4,1,3\n3,1,4,5,2\n3,5,4,1,2", "input: 7\n6 4 0 2 4 0 2 output: 0\n\nAny order would be inconsistent with the reports, thus the answer is 0.", "input: 8\n7 5 1 1 7 3 5 3 output: 16"], "Pid": "p03846", "ProblemText": "Task Description: Problem Statement There are N people, conveniently numbered 1 through N.\nThey were standing in a row yesterday, but now they are unsure of the order in which they were standing.\nHowever, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.\nAccording to their reports, the difference above for person i is A_i.\nBased on these reports, find the number of the possible orders in which they were standing.\nSince it can be extremely large, print the answer modulo 10^9+7.\nNote that the reports may be incorrect and thus there may be no consistent order.\nIn such a case, print 0.\nTask Constraint: 1<=N<=10^5\n0<=A_i<=N-1\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the number of the possible orders in which they were standing, modulo 10^9+7.\nTask Samples: input: 5\n2 4 4 0 2 output: 4\n\nThere are four possible orders, as follows:\n\n2,1,4,5,3\n2,5,4,1,3\n3,1,4,5,2\n3,5,4,1,2\ninput: 7\n6 4 0 2 4 0 2 output: 0\n\nAny order would be inconsistent with the reports, thus the answer is 0.\ninput: 8\n7 5 1 1 7 3 5 3 output: 16\n\n" }, { "title": "", "content": "Problem Statement You are given a positive integer N.\nFind the number of the pairs of integers u and v (0<=u, v<=N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v.\nHere, xor denotes the bitwise exclusive OR.\nSince it can be extremely large, compute the answer modulo 10^9+7.", "constraint": "1<=N<=10^{18}", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "Print the number of the possible pairs of integers u and v, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 5\n\nThe five possible pairs of u and v are:\nu=0,v=0 (Let a=0,b=0, then 0 xor 0=0,0+0=0.)\nu=0,v=2 (Let a=1,b=1, then 1 xor 1=0,1+1=2.）\nu=1,v=1 (Let a=1,b=0, then 1 xor 0=1,1+0=1.）\nu=2,v=2 (Let a=2,b=0, then 2 xor 0=2,2+0=2.）\nu=3,v=3 (Let a=3,b=0, then 3 xor 0=3,3+0=3.）", "input: 1422 output: 52277", "input: 1000000000000000000 output: 787014179"], "Pid": "p03847", "ProblemText": "Task Description: Problem Statement You are given a positive integer N.\nFind the number of the pairs of integers u and v (0<=u, v<=N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v.\nHere, xor denotes the bitwise exclusive OR.\nSince it can be extremely large, compute the answer modulo 10^9+7.\nTask Constraint: 1<=N<=10^{18}\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: Print the number of the possible pairs of integers u and v, modulo 10^9+7.\nTask Samples: input: 3 output: 5\n\nThe five possible pairs of u and v are:\nu=0,v=0 (Let a=0,b=0, then 0 xor 0=0,0+0=0.)\nu=0,v=2 (Let a=1,b=1, then 1 xor 1=0,1+1=2.）\nu=1,v=1 (Let a=1,b=0, then 1 xor 0=1,1+0=1.）\nu=2,v=2 (Let a=2,b=0, then 2 xor 0=2,2+0=2.）\nu=3,v=3 (Let a=3,b=0, then 3 xor 0=3,3+0=3.）\ninput: 1422 output: 52277\ninput: 1000000000000000000 output: 787014179\n\n" }, { "title": "", "content": "Problem Statement There are N people, conveniently numbered 1 through N.\nThey were standing in a row yesterday, but now they are unsure of the order in which they were standing.\nHowever, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.\nAccording to their reports, the difference above for person i is A_i.\nBased on these reports, find the number of the possible orders in which they were standing.\nSince it can be extremely large, print the answer modulo 10^9+7.\nNote that the reports may be incorrect and thus there may be no consistent order.\nIn such a case, print 0.", "constraint": "1<=N<=10^5\n0<=A_i<=N-1", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the number of the possible orders in which they were standing, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 4 4 0 2 output: 4\n\nThere are four possible orders, as follows:\n\n2,1,4,5,3\n2,5,4,1,3\n3,1,4,5,2\n3,5,4,1,2", "input: 7\n6 4 0 2 4 0 2 output: 0\n\nAny order would be inconsistent with the reports, thus the answer is 0.", "input: 8\n7 5 1 1 7 3 5 3 output: 16"], "Pid": "p03848", "ProblemText": "Task Description: Problem Statement There are N people, conveniently numbered 1 through N.\nThey were standing in a row yesterday, but now they are unsure of the order in which they were standing.\nHowever, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.\nAccording to their reports, the difference above for person i is A_i.\nBased on these reports, find the number of the possible orders in which they were standing.\nSince it can be extremely large, print the answer modulo 10^9+7.\nNote that the reports may be incorrect and thus there may be no consistent order.\nIn such a case, print 0.\nTask Constraint: 1<=N<=10^5\n0<=A_i<=N-1\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the number of the possible orders in which they were standing, modulo 10^9+7.\nTask Samples: input: 5\n2 4 4 0 2 output: 4\n\nThere are four possible orders, as follows:\n\n2,1,4,5,3\n2,5,4,1,3\n3,1,4,5,2\n3,5,4,1,2\ninput: 7\n6 4 0 2 4 0 2 output: 0\n\nAny order would be inconsistent with the reports, thus the answer is 0.\ninput: 8\n7 5 1 1 7 3 5 3 output: 16\n\n" }, { "title": "", "content": "Problem Statement You are given a positive integer N.\nFind the number of the pairs of integers u and v (0<=u, v<=N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v.\nHere, xor denotes the bitwise exclusive OR.\nSince it can be extremely large, compute the answer modulo 10^9+7.", "constraint": "1<=N<=10^{18}", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "Print the number of the possible pairs of integers u and v, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 5\n\nThe five possible pairs of u and v are:\nu=0,v=0 (Let a=0,b=0, then 0 xor 0=0,0+0=0.)\nu=0,v=2 (Let a=1,b=1, then 1 xor 1=0,1+1=2.）\nu=1,v=1 (Let a=1,b=0, then 1 xor 0=1,1+0=1.）\nu=2,v=2 (Let a=2,b=0, then 2 xor 0=2,2+0=2.）\nu=3,v=3 (Let a=3,b=0, then 3 xor 0=3,3+0=3.）", "input: 1422 output: 52277", "input: 1000000000000000000 output: 787014179"], "Pid": "p03849", "ProblemText": "Task Description: Problem Statement You are given a positive integer N.\nFind the number of the pairs of integers u and v (0<=u, v<=N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v.\nHere, xor denotes the bitwise exclusive OR.\nSince it can be extremely large, compute the answer modulo 10^9+7.\nTask Constraint: 1<=N<=10^{18}\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: Print the number of the possible pairs of integers u and v, modulo 10^9+7.\nTask Samples: input: 3 output: 5\n\nThe five possible pairs of u and v are:\nu=0,v=0 (Let a=0,b=0, then 0 xor 0=0,0+0=0.)\nu=0,v=2 (Let a=1,b=1, then 1 xor 1=0,1+1=2.）\nu=1,v=1 (Let a=1,b=0, then 1 xor 0=1,1+0=1.）\nu=2,v=2 (Let a=2,b=0, then 2 xor 0=2,2+0=2.）\nu=3,v=3 (Let a=3,b=0, then 3 xor 0=3,3+0=3.）\ninput: 1422 output: 52277\ninput: 1000000000000000000 output: 787014179\n\n" }, { "title": "", "content": "Problem Statement Joisino has a formula consisting of N terms: A_1 op_1 A_2 . . . op_{N-1} A_N.\nHere, A_i is an integer, and op_i is an binary operator either + or -.\nBecause Joisino loves large numbers, she wants to maximize the evaluated value of the formula by inserting an arbitrary number of pairs of parentheses (possibly zero) into the formula.\nOpening parentheses can only be inserted immediately before an integer, and closing parentheses can only be inserted immediately after an integer.\nIt is allowed to insert any number of parentheses at a position.\nYour task is to write a program to find the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.", "constraint": "1<=N<=10^5\n1<=A_i<=10^9\nop_i is either + or -.", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 op_1 A_2 . . . op_{N-1} A_N", "output": "Print the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n5 - 1 - 3 output: 7\n\nThe maximum possible value is: 5 - (1 - 3) = 7.", "input: 5\n1 - 2 + 3 - 4 + 5 output: 5\n\nThe maximum possible value is: 1 - (2 + 3 - 4) + 5 = 5.", "input: 5\n1 - 20 - 13 + 14 - 5 output: 13\n\nThe maximum possible value is: 1 - (20 - (13 + 14) - 5) = 13."], "Pid": "p03850", "ProblemText": "Task Description: Problem Statement Joisino has a formula consisting of N terms: A_1 op_1 A_2 . . . op_{N-1} A_N.\nHere, A_i is an integer, and op_i is an binary operator either + or -.\nBecause Joisino loves large numbers, she wants to maximize the evaluated value of the formula by inserting an arbitrary number of pairs of parentheses (possibly zero) into the formula.\nOpening parentheses can only be inserted immediately before an integer, and closing parentheses can only be inserted immediately after an integer.\nIt is allowed to insert any number of parentheses at a position.\nYour task is to write a program to find the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.\nTask Constraint: 1<=N<=10^5\n1<=A_i<=10^9\nop_i is either + or -.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 op_1 A_2 . . . op_{N-1} A_N\nTask Output: Print the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.\nTask Samples: input: 3\n5 - 1 - 3 output: 7\n\nThe maximum possible value is: 5 - (1 - 3) = 7.\ninput: 5\n1 - 2 + 3 - 4 + 5 output: 5\n\nThe maximum possible value is: 1 - (2 + 3 - 4) + 5 = 5.\ninput: 5\n1 - 20 - 13 + 14 - 5 output: 13\n\nThe maximum possible value is: 1 - (20 - (13 + 14) - 5) = 13.\n\n" }, { "title": "", "content": "Problem Statement Joisino is about to compete in the final round of a certain programming competition.\nIn this contest, there are N problems, numbered 1 through N.\nJoisino knows that it takes her T_i seconds to solve problem i(1<=i<=N).\nIn this contest, a contestant will first select some number of problems to solve.\nThen, the contestant will solve the selected problems.\nAfter that, the score of the contestant will be calculated as follows:\n\n(The score) = (The number of the pairs of integers L and R (1<=L<=R<=N) such that for every i satisfying L<=i<=R, problem i is solved) - (The total number of seconds it takes for the contestant to solve the selected problems)\n\nNote that a contestant is allowed to choose to solve zero problems, in which case the score will be 0.\nAlso, there are M kinds of drinks offered to the contestants, numbered 1 through M.\nIf Joisino takes drink i(1<=i<=M), her brain will be stimulated and the time it takes for her to solve problem P_i will become X_i seconds.\nHere, X_i may be greater than the length of time originally required to solve problem P_i.\nTaking drink i does not affect the time required to solve the other problems.\nA contestant is allowed to take exactly one of the drinks before the start of the contest.\nFor each drink, Joisino wants to know the maximum score that can be obtained in the contest if she takes that drink.\nYour task is to write a program to calculate it instead of her.", "constraint": "All input values are integers.\n1<=N<=3*10^5\n1<=T_i<=10^9\n(The sum of T_i) <=10^{12}\n1<=M<=3*10^5\n1<=P_i<=N\n1<=X_i<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN\nT_1 T_2 . . . T_N\nM\nP_1 X_1\nP_2 X_2\n:\nP_M X_M", "output": "For each drink, print the maximum score that can be obtained if Joisino takes that drink, in order, one per line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 1 4 1 1\n2\n3 2\n3 10 output: 9\n2\n\nIf she takes drink 1, the maximum score can be obtained by solving all the problems.\nIf she takes drink 2, the maximum score can be obtained by solving the problems 1,2,4 and 5.", "input: 12\n1 2 1 3 4 1 2 1 12 3 12 12\n10\n9 3\n11 1\n5 35\n6 15\n12 1\n1 9\n4 3\n10 2\n5 1\n7 6 output: 34\n35\n5\n11\n35\n17\n25\n26\n28\n21"], "Pid": "p03851", "ProblemText": "Task Description: Problem Statement Joisino is about to compete in the final round of a certain programming competition.\nIn this contest, there are N problems, numbered 1 through N.\nJoisino knows that it takes her T_i seconds to solve problem i(1<=i<=N).\nIn this contest, a contestant will first select some number of problems to solve.\nThen, the contestant will solve the selected problems.\nAfter that, the score of the contestant will be calculated as follows:\n\n(The score) = (The number of the pairs of integers L and R (1<=L<=R<=N) such that for every i satisfying L<=i<=R, problem i is solved) - (The total number of seconds it takes for the contestant to solve the selected problems)\n\nNote that a contestant is allowed to choose to solve zero problems, in which case the score will be 0.\nAlso, there are M kinds of drinks offered to the contestants, numbered 1 through M.\nIf Joisino takes drink i(1<=i<=M), her brain will be stimulated and the time it takes for her to solve problem P_i will become X_i seconds.\nHere, X_i may be greater than the length of time originally required to solve problem P_i.\nTaking drink i does not affect the time required to solve the other problems.\nA contestant is allowed to take exactly one of the drinks before the start of the contest.\nFor each drink, Joisino wants to know the maximum score that can be obtained in the contest if she takes that drink.\nYour task is to write a program to calculate it instead of her.\nTask Constraint: All input values are integers.\n1<=N<=3*10^5\n1<=T_i<=10^9\n(The sum of T_i) <=10^{12}\n1<=M<=3*10^5\n1<=P_i<=N\n1<=X_i<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN\nT_1 T_2 . . . T_N\nM\nP_1 X_1\nP_2 X_2\n:\nP_M X_M\nTask Output: For each drink, print the maximum score that can be obtained if Joisino takes that drink, in order, one per line.\nTask Samples: input: 5\n1 1 4 1 1\n2\n3 2\n3 10 output: 9\n2\n\nIf she takes drink 1, the maximum score can be obtained by solving all the problems.\nIf she takes drink 2, the maximum score can be obtained by solving the problems 1,2,4 and 5.\ninput: 12\n1 2 1 3 4 1 2 1 12 3 12 12\n10\n9 3\n11 1\n5 35\n6 15\n12 1\n1 9\n4 3\n10 2\n5 1\n7 6 output: 34\n35\n5\n11\n35\n17\n25\n26\n28\n21\n\n" }, { "title": "", "content": "Problem Statement Given a lowercase English letter c, determine whether it is a vowel. Here, there are five vowels in the English alphabet: a, e, i, o and u.", "constraint": "c is a lowercase English letter.", "input": "Input The input is given from Standard Input in the following format:\nc", "output": "If c is a vowel, print vowel. Otherwise, print consonant.", "content_img": false, "lang": "en", "error": false, "samples": ["input: a output: vowel\n\nSince a is a vowel, print vowel.", "input: z output: consonant", "input: s output: consonant"], "Pid": "p03852", "ProblemText": "Task Description: Problem Statement Given a lowercase English letter c, determine whether it is a vowel. Here, there are five vowels in the English alphabet: a, e, i, o and u.\nTask Constraint: c is a lowercase English letter.\nTask Input: Input The input is given from Standard Input in the following format:\nc\nTask Output: If c is a vowel, print vowel. Otherwise, print consonant.\nTask Samples: input: a output: vowel\n\nSince a is a vowel, print vowel.\ninput: z output: consonant\ninput: s output: consonant\n\n" }, { "title": "", "content": "Problem Statement There is an image with a height of H pixels and a width of W pixels. Each of the pixels is represented by either . or *. The character representing the pixel at the i-th row from the top and the j-th column from the left, is denoted by C_{i, j}.\nExtend this image vertically so that its height is doubled. That is, print a image with a height of 2H pixels and a width of W pixels where the pixel at the i-th row and j-th column is equal to C_{(i+1)/2, j} (the result of division is rounded down).", "constraint": "1<=H, W<=100\nC_{i,j} is either . or *.", "input": "Input The input is given from Standard Input in the following format:\nH W\nC_{1,1}. . . C_{1, W}\n:\nC_{H, 1}. . . C_{H, W}", "output": "Print the extended image.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n*.\n.* output: *.\n*.\n.*\n.*", "input: 1 4\n***. output: ***.\n***.", "input: 9 20\n.....***....***.....\n....*...*..*...*....\n...*.....**.....*...\n...*.....*......*...\n....*.....*....*....\n.....**..*...**.....\n.......*..*.*.......\n........**.*........\n.........**......... output: .....***....***.....\n.....***....***.....\n....*...*..*...*....\n....*...*..*...*....\n...*.....**.....*...\n...*.....**.....*...\n...*.....*......*...\n...*.....*......*...\n....*.....*....*....\n....*.....*....*....\n.....**..*...**.....\n.....**..*...**.....\n.......*..*.*.......\n.......*..*.*.......\n........**.*........\n........**.*........\n.........**.........\n.........**........."], "Pid": "p03853", "ProblemText": "Task Description: Problem Statement There is an image with a height of H pixels and a width of W pixels. Each of the pixels is represented by either . or *. The character representing the pixel at the i-th row from the top and the j-th column from the left, is denoted by C_{i, j}.\nExtend this image vertically so that its height is doubled. That is, print a image with a height of 2H pixels and a width of W pixels where the pixel at the i-th row and j-th column is equal to C_{(i+1)/2, j} (the result of division is rounded down).\nTask Constraint: 1<=H, W<=100\nC_{i,j} is either . or *.\nTask Input: Input The input is given from Standard Input in the following format:\nH W\nC_{1,1}. . . C_{1, W}\n:\nC_{H, 1}. . . C_{H, W}\nTask Output: Print the extended image.\nTask Samples: input: 2 2\n*.\n.* output: *.\n*.\n.*\n.*\ninput: 1 4\n***. output: ***.\n***.\ninput: 9 20\n.....***....***.....\n....*...*..*...*....\n...*.....**.....*...\n...*.....*......*...\n....*.....*....*....\n.....**..*...**.....\n.......*..*.*.......\n........**.*........\n.........**......... output: .....***....***.....\n.....***....***.....\n....*...*..*...*....\n....*...*..*...*....\n...*.....**.....*...\n...*.....**.....*...\n...*.....*......*...\n...*.....*......*...\n....*.....*....*....\n....*.....*....*....\n.....**..*...**.....\n.....**..*...**.....\n.......*..*.*.......\n.......*..*.*.......\n........**.*........\n........**.*........\n.........**.........\n.........**.........\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of lowercase English letters.\nAnother string T is initially empty.\nDetermine whether it is possible to obtain S = T by performing the following operation an arbitrary number of times:\n\nAppend one of the following at the end of T: dream, dreamer, erase and eraser.", "constraint": "1<=|S|<=10^5\nS consists of lowercase English letters.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "If it is possible to obtain S = T, print YES. Otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: erasedream output: YES\n\nAppend erase and dream at the end of T in this order, to obtain S = T.", "input: dreameraser output: YES\n\nAppend dream and eraser at the end of T in this order, to obtain S = T.", "input: dreamerer output: NO"], "Pid": "p03854", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of lowercase English letters.\nAnother string T is initially empty.\nDetermine whether it is possible to obtain S = T by performing the following operation an arbitrary number of times:\n\nAppend one of the following at the end of T: dream, dreamer, erase and eraser.\nTask Constraint: 1<=|S|<=10^5\nS consists of lowercase English letters.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: If it is possible to obtain S = T, print YES. Otherwise, print NO.\nTask Samples: input: erasedream output: YES\n\nAppend erase and dream at the end of T in this order, to obtain S = T.\ninput: dreameraser output: YES\n\nAppend dream and eraser at the end of T in this order, to obtain S = T.\ninput: dreamerer output: NO\n\n" }, { "title": "", "content": "Problem Statement There are N cities. There are also K roads and L railways, extending between the cities.\nThe i-th road bidirectionally connects the p_i-th and q_i-th cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th cities.\nNo two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.\nWe will say city A and B are connected by roads if city B is reachable from city A by traversing some number of roads. Here, any city is considered to be connected to itself by roads.\nWe will also define connectivity by railways similarly.\nFor each city, find the number of the cities connected to that city by both roads and railways.", "constraint": "2 <= N <= 2*10^5\n1 <= K, L<= 10^5\n1 <= p_i, q_i, r_i, s_i <= N\np_i < q_i\nr_i < s_i\nWhen i != j, (p_i, q_i) != (p_j, q_j)\nWhen i != j, (r_i, s_i) != (r_j, s_j)", "input": "Input The input is given from Standard Input in the following format:\nN K L\np_1 q_1\n:\np_K q_K\nr_1 s_1\n:\nr_L s_L", "output": "Print N integers. The i-th of them should represent the number of the cities connected to the i-th city by both roads and railways.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 1\n1 2\n2 3\n3 4\n2 3 output: 1 2 2 1\n\nAll the four cities are connected to each other by roads.\nBy railways, only the second and third cities are connected. Thus, the answers for the cities are 1,2,2 and 1, respectively.", "input: 4 2 2\n1 2\n2 3\n1 4\n2 3 output: 1 2 2 1", "input: 7 4 4\n1 2\n2 3\n2 5\n6 7\n3 5\n4 5\n3 4\n6 7 output: 1 1 2 1 2 2 2"], "Pid": "p03855", "ProblemText": "Task Description: Problem Statement There are N cities. There are also K roads and L railways, extending between the cities.\nThe i-th road bidirectionally connects the p_i-th and q_i-th cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th cities.\nNo two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.\nWe will say city A and B are connected by roads if city B is reachable from city A by traversing some number of roads. Here, any city is considered to be connected to itself by roads.\nWe will also define connectivity by railways similarly.\nFor each city, find the number of the cities connected to that city by both roads and railways.\nTask Constraint: 2 <= N <= 2*10^5\n1 <= K, L<= 10^5\n1 <= p_i, q_i, r_i, s_i <= N\np_i < q_i\nr_i < s_i\nWhen i != j, (p_i, q_i) != (p_j, q_j)\nWhen i != j, (r_i, s_i) != (r_j, s_j)\nTask Input: Input The input is given from Standard Input in the following format:\nN K L\np_1 q_1\n:\np_K q_K\nr_1 s_1\n:\nr_L s_L\nTask Output: Print N integers. The i-th of them should represent the number of the cities connected to the i-th city by both roads and railways.\nTask Samples: input: 4 3 1\n1 2\n2 3\n3 4\n2 3 output: 1 2 2 1\n\nAll the four cities are connected to each other by roads.\nBy railways, only the second and third cities are connected. Thus, the answers for the cities are 1,2,2 and 1, respectively.\ninput: 4 2 2\n1 2\n2 3\n1 4\n2 3 output: 1 2 2 1\ninput: 7 4 4\n1 2\n2 3\n2 5\n6 7\n3 5\n4 5\n3 4\n6 7 output: 1 1 2 1 2 2 2\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of lowercase English letters.\nAnother string T is initially empty.\nDetermine whether it is possible to obtain S = T by performing the following operation an arbitrary number of times:\n\nAppend one of the following at the end of T: dream, dreamer, erase and eraser.", "constraint": "1<=|S|<=10^5\nS consists of lowercase English letters.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "If it is possible to obtain S = T, print YES. Otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: erasedream output: YES\n\nAppend erase and dream at the end of T in this order, to obtain S = T.", "input: dreameraser output: YES\n\nAppend dream and eraser at the end of T in this order, to obtain S = T.", "input: dreamerer output: NO"], "Pid": "p03856", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of lowercase English letters.\nAnother string T is initially empty.\nDetermine whether it is possible to obtain S = T by performing the following operation an arbitrary number of times:\n\nAppend one of the following at the end of T: dream, dreamer, erase and eraser.\nTask Constraint: 1<=|S|<=10^5\nS consists of lowercase English letters.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: If it is possible to obtain S = T, print YES. Otherwise, print NO.\nTask Samples: input: erasedream output: YES\n\nAppend erase and dream at the end of T in this order, to obtain S = T.\ninput: dreameraser output: YES\n\nAppend dream and eraser at the end of T in this order, to obtain S = T.\ninput: dreamerer output: NO\n\n" }, { "title": "", "content": "Problem Statement There are N cities. There are also K roads and L railways, extending between the cities.\nThe i-th road bidirectionally connects the p_i-th and q_i-th cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th cities.\nNo two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.\nWe will say city A and B are connected by roads if city B is reachable from city A by traversing some number of roads. Here, any city is considered to be connected to itself by roads.\nWe will also define connectivity by railways similarly.\nFor each city, find the number of the cities connected to that city by both roads and railways.", "constraint": "2 <= N <= 2*10^5\n1 <= K, L<= 10^5\n1 <= p_i, q_i, r_i, s_i <= N\np_i < q_i\nr_i < s_i\nWhen i != j, (p_i, q_i) != (p_j, q_j)\nWhen i != j, (r_i, s_i) != (r_j, s_j)", "input": "Input The input is given from Standard Input in the following format:\nN K L\np_1 q_1\n:\np_K q_K\nr_1 s_1\n:\nr_L s_L", "output": "Print N integers. The i-th of them should represent the number of the cities connected to the i-th city by both roads and railways.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3 1\n1 2\n2 3\n3 4\n2 3 output: 1 2 2 1\n\nAll the four cities are connected to each other by roads.\nBy railways, only the second and third cities are connected. Thus, the answers for the cities are 1,2,2 and 1, respectively.", "input: 4 2 2\n1 2\n2 3\n1 4\n2 3 output: 1 2 2 1", "input: 7 4 4\n1 2\n2 3\n2 5\n6 7\n3 5\n4 5\n3 4\n6 7 output: 1 1 2 1 2 2 2"], "Pid": "p03857", "ProblemText": "Task Description: Problem Statement There are N cities. There are also K roads and L railways, extending between the cities.\nThe i-th road bidirectionally connects the p_i-th and q_i-th cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th cities.\nNo two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.\nWe will say city A and B are connected by roads if city B is reachable from city A by traversing some number of roads. Here, any city is considered to be connected to itself by roads.\nWe will also define connectivity by railways similarly.\nFor each city, find the number of the cities connected to that city by both roads and railways.\nTask Constraint: 2 <= N <= 2*10^5\n1 <= K, L<= 10^5\n1 <= p_i, q_i, r_i, s_i <= N\np_i < q_i\nr_i < s_i\nWhen i != j, (p_i, q_i) != (p_j, q_j)\nWhen i != j, (r_i, s_i) != (r_j, s_j)\nTask Input: Input The input is given from Standard Input in the following format:\nN K L\np_1 q_1\n:\np_K q_K\nr_1 s_1\n:\nr_L s_L\nTask Output: Print N integers. The i-th of them should represent the number of the cities connected to the i-th city by both roads and railways.\nTask Samples: input: 4 3 1\n1 2\n2 3\n3 4\n2 3 output: 1 2 2 1\n\nAll the four cities are connected to each other by roads.\nBy railways, only the second and third cities are connected. Thus, the answers for the cities are 1,2,2 and 1, respectively.\ninput: 4 2 2\n1 2\n2 3\n1 4\n2 3 output: 1 2 2 1\ninput: 7 4 4\n1 2\n2 3\n2 5\n6 7\n3 5\n4 5\n3 4\n6 7 output: 1 1 2 1 2 2 2\n\n" }, { "title": "", "content": "Problem Statement There are N pinholes on the xy-plane. The i-th pinhole is located at (x_i, y_i).\nWe will denote the Manhattan distance between the i-th and j-th pinholes as d(i, j)(=|x_i-x_j|+|y_i-y_j|).\nYou have a peculiar pair of compasses, called Manhattan Compass.\nThis instrument always points at two of the pinholes.\nThe two legs of the compass are indistinguishable, thus we do not distinguish the following two states: the state where the compass points at the p-th and q-th pinholes, and the state where it points at the q-th and p-th pinholes.\nWhen the compass points at the p-th and q-th pinholes and d(p, q)=d(p, r), one of the legs can be moved so that the compass will point at the p-th and r-th pinholes.\nInitially, the compass points at the a-th and b-th pinholes.\nFind the number of the pairs of pinholes that can be pointed by the compass.", "constraint": "2<=N<=10^5\n1<=x_i, y_i<=10^9\n1<=a < b<=N\nWhen i != j, (x_i, y_i) != (x_j, y_j)\nx_i and y_i are integers.", "input": "Input The input is given from Standard Input in the following format:\nN a b\nx_1 y_1\n:\nx_N y_N", "output": "Print the number of the pairs of pinholes that can be pointed by the compass.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 1 2\n1 1\n4 3\n6 1\n5 5\n4 8 output: 4\n\nInitially, the compass points at the first and second pinholes.\nSince d(1,2) = d(1,3), the compass can be moved so that it will point at the first and third pinholes.\nSince d(1,3) = d(3,4), the compass can also point at the third and fourth pinholes.\nSince d(1,2) = d(2,5), the compass can also point at the second and fifth pinholes.\nNo other pairs of pinholes can be pointed by the compass, thus the answer is 4.", "input: 6 2 3\n1 3\n5 3\n3 5\n8 4\n4 7\n2 5 output: 4", "input: 8 1 2\n1 5\n4 3\n8 2\n4 7\n8 8\n3 3\n6 6\n4 8 output: 7"], "Pid": "p03858", "ProblemText": "Task Description: Problem Statement There are N pinholes on the xy-plane. The i-th pinhole is located at (x_i, y_i).\nWe will denote the Manhattan distance between the i-th and j-th pinholes as d(i, j)(=|x_i-x_j|+|y_i-y_j|).\nYou have a peculiar pair of compasses, called Manhattan Compass.\nThis instrument always points at two of the pinholes.\nThe two legs of the compass are indistinguishable, thus we do not distinguish the following two states: the state where the compass points at the p-th and q-th pinholes, and the state where it points at the q-th and p-th pinholes.\nWhen the compass points at the p-th and q-th pinholes and d(p, q)=d(p, r), one of the legs can be moved so that the compass will point at the p-th and r-th pinholes.\nInitially, the compass points at the a-th and b-th pinholes.\nFind the number of the pairs of pinholes that can be pointed by the compass.\nTask Constraint: 2<=N<=10^5\n1<=x_i, y_i<=10^9\n1<=a < b<=N\nWhen i != j, (x_i, y_i) != (x_j, y_j)\nx_i and y_i are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN a b\nx_1 y_1\n:\nx_N y_N\nTask Output: Print the number of the pairs of pinholes that can be pointed by the compass.\nTask Samples: input: 5 1 2\n1 1\n4 3\n6 1\n5 5\n4 8 output: 4\n\nInitially, the compass points at the first and second pinholes.\nSince d(1,2) = d(1,3), the compass can be moved so that it will point at the first and third pinholes.\nSince d(1,3) = d(3,4), the compass can also point at the third and fourth pinholes.\nSince d(1,2) = d(2,5), the compass can also point at the second and fifth pinholes.\nNo other pairs of pinholes can be pointed by the compass, thus the answer is 4.\ninput: 6 2 3\n1 3\n5 3\n3 5\n8 4\n4 7\n2 5 output: 4\ninput: 8 1 2\n1 5\n4 3\n8 2\n4 7\n8 8\n3 3\n6 6\n4 8 output: 7\n\n" }, { "title": "", "content": "Problem Statement There is a string S of length N consisting of characters 0 and 1. You will perform the following operation for each i = 1,2, . . . , m:\n\nArbitrarily permute the characters within the substring of S starting at the l_i-th character from the left and extending through the r_i-th character.\n\nHere, the sequence l_i is non-decreasing.\nHow many values are possible for S after the M operations, modulo 1000000007(= 10^9+7)?", "constraint": "2<=N<=3000\n1<=M<=3000\nS consists of characters 0 and 1.\nThe length of S equals N.\n1<=l_i < r_i<=N\nl_i <= l_{i+1}", "input": "Input The input is given from Standard Input in the following format:\nN M\nS\nl_1 r_1\n:\nl_M r_M", "output": "Print the number of the possible values for S after the M operations, modulo 1000000007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2\n01001\n2 4\n3 5 output: 6\n\nAfter the first operation, S can be one of the following three: 01001,00101 and 00011.\nAfter the second operation, S can be one of the following six: 01100,01010,01001,00011,00101 and 00110.", "input: 9 3\n110111110\n1 4\n4 6\n6 9 output: 26", "input: 11 6\n00101000110\n2 4\n2 3\n4 7\n5 6\n6 10\n10 11 output: 143"], "Pid": "p03859", "ProblemText": "Task Description: Problem Statement There is a string S of length N consisting of characters 0 and 1. You will perform the following operation for each i = 1,2, . . . , m:\n\nArbitrarily permute the characters within the substring of S starting at the l_i-th character from the left and extending through the r_i-th character.\n\nHere, the sequence l_i is non-decreasing.\nHow many values are possible for S after the M operations, modulo 1000000007(= 10^9+7)?\nTask Constraint: 2<=N<=3000\n1<=M<=3000\nS consists of characters 0 and 1.\nThe length of S equals N.\n1<=l_i < r_i<=N\nl_i <= l_{i+1}\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nS\nl_1 r_1\n:\nl_M r_M\nTask Output: Print the number of the possible values for S after the M operations, modulo 1000000007.\nTask Samples: input: 5 2\n01001\n2 4\n3 5 output: 6\n\nAfter the first operation, S can be one of the following three: 01001,00101 and 00011.\nAfter the second operation, S can be one of the following six: 01100,01010,01001,00011,00101 and 00110.\ninput: 9 3\n110111110\n1 4\n4 6\n6 9 output: 26\ninput: 11 6\n00101000110\n2 4\n2 3\n4 7\n5 6\n6 10\n10 11 output: 143\n\n" }, { "title": "", "content": "Problem Statement Snuke is going to open a contest named \"At Coder s Contest\".\nHere, s is a string of length 1 or greater, where the first character is an uppercase English letter, and the second and subsequent characters are lowercase English letters.\nSnuke has decided to abbreviate the name of the contest as \"Ax C\".\nHere, x is the uppercase English letter at the beginning of s.\nGiven the name of the contest, print the abbreviation of the name.", "constraint": "The length of s is between 1 and 100, inclusive.\nThe first character in s is an uppercase English letter.\nThe second and subsequent characters in s are lowercase English letters.", "input": "Input The input is given from Standard Input in the following format:\nAt Coder s Contest", "output": "Print the abbreviation of the name of the contest.", "content_img": false, "lang": "en", "error": false, "samples": ["input: AtCoder Beginner Contest output: ABC\n\nThe contest in which you are participating now.", "input: AtCoder Snuke Contest output: ASC\n\nThis contest does not actually exist.", "input: AtCoder X Contest output: AXC"], "Pid": "p03860", "ProblemText": "Task Description: Problem Statement Snuke is going to open a contest named \"At Coder s Contest\".\nHere, s is a string of length 1 or greater, where the first character is an uppercase English letter, and the second and subsequent characters are lowercase English letters.\nSnuke has decided to abbreviate the name of the contest as \"Ax C\".\nHere, x is the uppercase English letter at the beginning of s.\nGiven the name of the contest, print the abbreviation of the name.\nTask Constraint: The length of s is between 1 and 100, inclusive.\nThe first character in s is an uppercase English letter.\nThe second and subsequent characters in s are lowercase English letters.\nTask Input: Input The input is given from Standard Input in the following format:\nAt Coder s Contest\nTask Output: Print the abbreviation of the name of the contest.\nTask Samples: input: AtCoder Beginner Contest output: ABC\n\nThe contest in which you are participating now.\ninput: AtCoder Snuke Contest output: ASC\n\nThis contest does not actually exist.\ninput: AtCoder X Contest output: AXC\n\n" }, { "title": "", "content": "Problem Statement You are given nonnegative integers a and b (a <= b), and a positive integer x.\nAmong the integers between a and b, inclusive, how many are divisible by x?", "constraint": "0 <= a <= b <= 10^{18}\n1 <= x <= 10^{18}", "input": "Input The input is given from Standard Input in the following format:\na b x", "output": "Print the number of the integers between a and b, inclusive, that are divisible by x.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 8 2 output: 3\n\nThere are three integers between 4 and 8, inclusive, that are divisible by 2: 4,6 and 8.", "input: 0 5 1 output: 6\n\nThere are six integers between 0 and 5, inclusive, that are divisible by 1: 0,1,2,3,4 and 5.", "input: 9 9 2 output: 0\n\nThere are no integer between 9 and 9, inclusive, that is divisible by 2.", "input: 1 1000000000000000000 3 output: 333333333333333333\n\nWatch out for integer overflows."], "Pid": "p03861", "ProblemText": "Task Description: Problem Statement You are given nonnegative integers a and b (a <= b), and a positive integer x.\nAmong the integers between a and b, inclusive, how many are divisible by x?\nTask Constraint: 0 <= a <= b <= 10^{18}\n1 <= x <= 10^{18}\nTask Input: Input The input is given from Standard Input in the following format:\na b x\nTask Output: Print the number of the integers between a and b, inclusive, that are divisible by x.\nTask Samples: input: 4 8 2 output: 3\n\nThere are three integers between 4 and 8, inclusive, that are divisible by 2: 4,6 and 8.\ninput: 0 5 1 output: 6\n\nThere are six integers between 0 and 5, inclusive, that are divisible by 1: 0,1,2,3,4 and 5.\ninput: 9 9 2 output: 0\n\nThere are no integer between 9 and 9, inclusive, that is divisible by 2.\ninput: 1 1000000000000000000 3 output: 333333333333333333\n\nWatch out for integer overflows.\n\n" }, { "title": "", "content": "Problem Statement There are N boxes arranged in a row.\nInitially, the i-th box from the left contains a_i candies.\nSnuke can perform the following operation any number of times:\n\nChoose a box containing at least one candy, and eat one of the candies in the chosen box.\n\nHis objective is as follows:\n\nAny two neighboring boxes contain at most x candies in total.\n\nFind the minimum number of operations required to achieve the objective.", "constraint": "2 <= N <= 10^5\n0 <= a_i <= 10^9\n0 <= x <= 10^9", "input": "Input The input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N", "output": "Print the minimum number of operations required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n2 2 2 output: 1\n\nEat one candy in the second box.\nThen, the number of candies in each box becomes (2,1,2).", "input: 6 1\n1 6 1 2 0 4 output: 11\n\nFor example, eat six candies in the second box, two in the fourth box, and three in the sixth box.\nThen, the number of candies in each box becomes (1,0,1,0,0,1).", "input: 5 9\n3 1 4 1 5 output: 0\n\nThe objective is already achieved without performing operations.", "input: 2 0\n5 5 output: 10\n\nAll the candies need to be eaten."], "Pid": "p03862", "ProblemText": "Task Description: Problem Statement There are N boxes arranged in a row.\nInitially, the i-th box from the left contains a_i candies.\nSnuke can perform the following operation any number of times:\n\nChoose a box containing at least one candy, and eat one of the candies in the chosen box.\n\nHis objective is as follows:\n\nAny two neighboring boxes contain at most x candies in total.\n\nFind the minimum number of operations required to achieve the objective.\nTask Constraint: 2 <= N <= 10^5\n0 <= a_i <= 10^9\n0 <= x <= 10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N\nTask Output: Print the minimum number of operations required to achieve the objective.\nTask Samples: input: 3 3\n2 2 2 output: 1\n\nEat one candy in the second box.\nThen, the number of candies in each box becomes (2,1,2).\ninput: 6 1\n1 6 1 2 0 4 output: 11\n\nFor example, eat six candies in the second box, two in the fourth box, and three in the sixth box.\nThen, the number of candies in each box becomes (1,0,1,0,0,1).\ninput: 5 9\n3 1 4 1 5 output: 0\n\nThe objective is already achieved without performing operations.\ninput: 2 0\n5 5 output: 10\n\nAll the candies need to be eaten.\n\n" }, { "title": "", "content": "Problem Statement There is a string s of length 3 or greater.\nNo two neighboring characters in s are equal.\nTakahashi and Aoki will play a game against each other.\nThe two players alternately performs the following operation, Takahashi going first:\n\nRemove one of the characters in s, excluding both ends. However, a character cannot be removed if removal of the character would result in two neighboring equal characters in s.\n\nThe player who becomes unable to perform the operation, loses the game. Determine which player will win when the two play optimally.", "constraint": "3 <= |s| <= 10^5\ns consists of lowercase English letters.\nNo two neighboring characters in s are equal.", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "If Takahashi will win, print First. If Aoki will win, print Second.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aba output: Second\n\nTakahashi, who goes first, cannot perform the operation, since removal of the b, which is the only character not at either ends of s, would result in s becoming aa, with two as neighboring.", "input: abc output: First\n\nWhen Takahashi removes b from s, it becomes ac.\nThen, Aoki cannot perform the operation, since there is no character in s, excluding both ends.", "input: abcab output: First"], "Pid": "p03863", "ProblemText": "Task Description: Problem Statement There is a string s of length 3 or greater.\nNo two neighboring characters in s are equal.\nTakahashi and Aoki will play a game against each other.\nThe two players alternately performs the following operation, Takahashi going first:\n\nRemove one of the characters in s, excluding both ends. However, a character cannot be removed if removal of the character would result in two neighboring equal characters in s.\n\nThe player who becomes unable to perform the operation, loses the game. Determine which player will win when the two play optimally.\nTask Constraint: 3 <= |s| <= 10^5\ns consists of lowercase English letters.\nNo two neighboring characters in s are equal.\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: If Takahashi will win, print First. If Aoki will win, print Second.\nTask Samples: input: aba output: Second\n\nTakahashi, who goes first, cannot perform the operation, since removal of the b, which is the only character not at either ends of s, would result in s becoming aa, with two as neighboring.\ninput: abc output: First\n\nWhen Takahashi removes b from s, it becomes ac.\nThen, Aoki cannot perform the operation, since there is no character in s, excluding both ends.\ninput: abcab output: First\n\n" }, { "title": "", "content": "Problem Statement There are N boxes arranged in a row.\nInitially, the i-th box from the left contains a_i candies.\nSnuke can perform the following operation any number of times:\n\nChoose a box containing at least one candy, and eat one of the candies in the chosen box.\n\nHis objective is as follows:\n\nAny two neighboring boxes contain at most x candies in total.\n\nFind the minimum number of operations required to achieve the objective.", "constraint": "2 <= N <= 10^5\n0 <= a_i <= 10^9\n0 <= x <= 10^9", "input": "Input The input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N", "output": "Print the minimum number of operations required to achieve the objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n2 2 2 output: 1\n\nEat one candy in the second box.\nThen, the number of candies in each box becomes (2,1,2).", "input: 6 1\n1 6 1 2 0 4 output: 11\n\nFor example, eat six candies in the second box, two in the fourth box, and three in the sixth box.\nThen, the number of candies in each box becomes (1,0,1,0,0,1).", "input: 5 9\n3 1 4 1 5 output: 0\n\nThe objective is already achieved without performing operations.", "input: 2 0\n5 5 output: 10\n\nAll the candies need to be eaten."], "Pid": "p03864", "ProblemText": "Task Description: Problem Statement There are N boxes arranged in a row.\nInitially, the i-th box from the left contains a_i candies.\nSnuke can perform the following operation any number of times:\n\nChoose a box containing at least one candy, and eat one of the candies in the chosen box.\n\nHis objective is as follows:\n\nAny two neighboring boxes contain at most x candies in total.\n\nFind the minimum number of operations required to achieve the objective.\nTask Constraint: 2 <= N <= 10^5\n0 <= a_i <= 10^9\n0 <= x <= 10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N\nTask Output: Print the minimum number of operations required to achieve the objective.\nTask Samples: input: 3 3\n2 2 2 output: 1\n\nEat one candy in the second box.\nThen, the number of candies in each box becomes (2,1,2).\ninput: 6 1\n1 6 1 2 0 4 output: 11\n\nFor example, eat six candies in the second box, two in the fourth box, and three in the sixth box.\nThen, the number of candies in each box becomes (1,0,1,0,0,1).\ninput: 5 9\n3 1 4 1 5 output: 0\n\nThe objective is already achieved without performing operations.\ninput: 2 0\n5 5 output: 10\n\nAll the candies need to be eaten.\n\n" }, { "title": "", "content": "Problem Statement There is a string s of length 3 or greater.\nNo two neighboring characters in s are equal.\nTakahashi and Aoki will play a game against each other.\nThe two players alternately performs the following operation, Takahashi going first:\n\nRemove one of the characters in s, excluding both ends. However, a character cannot be removed if removal of the character would result in two neighboring equal characters in s.\n\nThe player who becomes unable to perform the operation, loses the game. Determine which player will win when the two play optimally.", "constraint": "3 <= |s| <= 10^5\ns consists of lowercase English letters.\nNo two neighboring characters in s are equal.", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "If Takahashi will win, print First. If Aoki will win, print Second.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aba output: Second\n\nTakahashi, who goes first, cannot perform the operation, since removal of the b, which is the only character not at either ends of s, would result in s becoming aa, with two as neighboring.", "input: abc output: First\n\nWhen Takahashi removes b from s, it becomes ac.\nThen, Aoki cannot perform the operation, since there is no character in s, excluding both ends.", "input: abcab output: First"], "Pid": "p03865", "ProblemText": "Task Description: Problem Statement There is a string s of length 3 or greater.\nNo two neighboring characters in s are equal.\nTakahashi and Aoki will play a game against each other.\nThe two players alternately performs the following operation, Takahashi going first:\n\nRemove one of the characters in s, excluding both ends. However, a character cannot be removed if removal of the character would result in two neighboring equal characters in s.\n\nThe player who becomes unable to perform the operation, loses the game. Determine which player will win when the two play optimally.\nTask Constraint: 3 <= |s| <= 10^5\ns consists of lowercase English letters.\nNo two neighboring characters in s are equal.\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: If Takahashi will win, print First. If Aoki will win, print Second.\nTask Samples: input: aba output: Second\n\nTakahashi, who goes first, cannot perform the operation, since removal of the b, which is the only character not at either ends of s, would result in s becoming aa, with two as neighboring.\ninput: abc output: First\n\nWhen Takahashi removes b from s, it becomes ac.\nThen, Aoki cannot perform the operation, since there is no character in s, excluding both ends.\ninput: abcab output: First\n\n" }, { "title": "", "content": "Problem Statement On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t).\nHe can move in arbitrary directions with speed 1.\nHere, we will consider him as a point without size.\nThere are N circular barriers deployed on the plane.\nThe center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively.\nThe barriers may overlap or contain each other.\nA point on the plane is exposed to cosmic rays if the point is not within any of the barriers.\nSnuke wants to avoid exposure to cosmic rays as much as possible during the travel.\nFind the minimum possible duration of time he is exposed to cosmic rays during the travel.", "constraint": "All input values are integers.\n-10^9 <= x_s, y_s, x_t, y_t <= 10^9\n(x_s, y_s) != (x_t, y_t)\n1<=N<=1,000\n-10^9 <= x_i, y_i <= 10^9\n1 <= r_i <= 10^9", "input": "Input The input is given from Standard Input in the following format:\nx_s y_s x_t y_t\nN\nx_1 y_1 r_1\nx_2 y_2 r_2\n:\nx_N y_N r_N", "output": "Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel.\nThe output is considered correct if the absolute or relative error is at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: -2 -2 2 2\n1\n0 0 1 output: 3.6568542495\n\nAn optimal route is as follows:", "input: -2 0 2 0\n2\n-1 0 2\n1 0 2 output: 0.0000000000\n\nAn optimal route is as follows:", "input: 4 -2 -2 4\n3\n0 0 2\n4 0 1\n0 4 1 output: 4.0000000000\n\nAn optimal route is as follows:"], "Pid": "p03866", "ProblemText": "Task Description: Problem Statement On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t).\nHe can move in arbitrary directions with speed 1.\nHere, we will consider him as a point without size.\nThere are N circular barriers deployed on the plane.\nThe center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively.\nThe barriers may overlap or contain each other.\nA point on the plane is exposed to cosmic rays if the point is not within any of the barriers.\nSnuke wants to avoid exposure to cosmic rays as much as possible during the travel.\nFind the minimum possible duration of time he is exposed to cosmic rays during the travel.\nTask Constraint: All input values are integers.\n-10^9 <= x_s, y_s, x_t, y_t <= 10^9\n(x_s, y_s) != (x_t, y_t)\n1<=N<=1,000\n-10^9 <= x_i, y_i <= 10^9\n1 <= r_i <= 10^9\nTask Input: Input The input is given from Standard Input in the following format:\nx_s y_s x_t y_t\nN\nx_1 y_1 r_1\nx_2 y_2 r_2\n:\nx_N y_N r_N\nTask Output: Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel.\nThe output is considered correct if the absolute or relative error is at most 10^{-9}.\nTask Samples: input: -2 -2 2 2\n1\n0 0 1 output: 3.6568542495\n\nAn optimal route is as follows:\ninput: -2 0 2 0\n2\n-1 0 2\n1 0 2 output: 0.0000000000\n\nAn optimal route is as follows:\ninput: 4 -2 -2 4\n3\n0 0 2\n4 0 1\n0 4 1 output: 4.0000000000\n\nAn optimal route is as follows:\n\n" }, { "title": "", "content": "Problem Statement Takahashi and Aoki are going to together construct a sequence of integers.\nFirst, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:\n\nThe length of a is N.\nEach element in a is an integer between 1 and K, inclusive.\na is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.\n\nThen, Aoki will perform the following operation an arbitrary number of times:\n\nMove the first element in a to the end of a.\n\nHow many sequences a can be obtained after this procedure, modulo 10^9+7?", "constraint": "1<=N<=10^9\n1<=K<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN K", "output": "Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2 output: 6\n\nThe following six sequences can be obtained:\n\n(1,1,1,1)\n(1,1,2,2)\n(1,2,2,1)\n(2,2,1,1)\n(2,1,1,2)\n(2,2,2,2)", "input: 1 10 output: 10", "input: 6 3 output: 75", "input: 1000000000 1000000000 output: 875699961"], "Pid": "p03867", "ProblemText": "Task Description: Problem Statement Takahashi and Aoki are going to together construct a sequence of integers.\nFirst, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:\n\nThe length of a is N.\nEach element in a is an integer between 1 and K, inclusive.\na is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.\n\nThen, Aoki will perform the following operation an arbitrary number of times:\n\nMove the first element in a to the end of a.\n\nHow many sequences a can be obtained after this procedure, modulo 10^9+7?\nTask Constraint: 1<=N<=10^9\n1<=K<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.\nTask Samples: input: 4 2 output: 6\n\nThe following six sequences can be obtained:\n\n(1,1,1,1)\n(1,1,2,2)\n(1,2,2,1)\n(2,2,1,1)\n(2,1,1,2)\n(2,2,2,2)\ninput: 1 10 output: 10\ninput: 6 3 output: 75\ninput: 1000000000 1000000000 output: 875699961\n\n" }, { "title": "", "content": "Problem Statement\nThere are N computers and N sockets in a one-dimensional world.\nThe coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i.\nIt is guaranteed that these 2N coordinates are pairwise distinct.\nSnuke wants to connect each computer to a socket using a cable.\nEach socket can be connected to only one computer.\nIn how many ways can he minimize the total length of the cables?\nCompute the answer modulo 10^9+7.", "constraint": "1 <= N <= 10^5\n0 <= a_i, b_i <= 10^9\nThe coordinates are integers.\nThe coordinates are pairwise distinct.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nb_1\n:\nb_N", "output": "Print the number of ways to minimize the total length of the cables, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0\n10\n20\n30 output: 2\n\nThere are two optimal connections: 0-20,10-30 and 0-30,10-20.\nIn both connections the total length of the cables is 40.", "input: 3\n3\n10\n8\n7\n12\n5 output: 1"], "Pid": "p03868", "ProblemText": "Task Description: Problem Statement\nThere are N computers and N sockets in a one-dimensional world.\nThe coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i.\nIt is guaranteed that these 2N coordinates are pairwise distinct.\nSnuke wants to connect each computer to a socket using a cable.\nEach socket can be connected to only one computer.\nIn how many ways can he minimize the total length of the cables?\nCompute the answer modulo 10^9+7.\nTask Constraint: 1 <= N <= 10^5\n0 <= a_i, b_i <= 10^9\nThe coordinates are integers.\nThe coordinates are pairwise distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nb_1\n:\nb_N\nTask Output: Print the number of ways to minimize the total length of the cables, modulo 10^9+7.\nTask Samples: input: 2\n0\n10\n20\n30 output: 2\n\nThere are two optimal connections: 0-20,10-30 and 0-30,10-20.\nIn both connections the total length of the cables is 40.\ninput: 3\n3\n10\n8\n7\n12\n5 output: 1\n\n" }, { "title": "", "content": "Problem Statement\nSnuke received a triangle as a birthday present.\nThe coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).\nHe wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch).\nCompute the maximum possible radius of the circles.", "constraint": "0 <= x_i, y_i <= 1000\nThe coordinates are integers.\nThe three points are not on the same line.", "input": "Input The input is given from Standard Input in the following format:\nx_1 y_1\nx_2 y_2\nx_3 y_3", "output": "Print the maximum possible radius of the circles.\nThe absolute error or the relative error must be at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0\n1 1\n2 0 output: 0.292893218813", "input: 3 1\n1 5\n4 9 output: 0.889055514217"], "Pid": "p03869", "ProblemText": "Task Description: Problem Statement\nSnuke received a triangle as a birthday present.\nThe coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).\nHe wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch).\nCompute the maximum possible radius of the circles.\nTask Constraint: 0 <= x_i, y_i <= 1000\nThe coordinates are integers.\nThe three points are not on the same line.\nTask Input: Input The input is given from Standard Input in the following format:\nx_1 y_1\nx_2 y_2\nx_3 y_3\nTask Output: Print the maximum possible radius of the circles.\nThe absolute error or the relative error must be at most 10^{-9}.\nTask Samples: input: 0 0\n1 1\n2 0 output: 0.292893218813\ninput: 3 1\n1 5\n4 9 output: 0.889055514217\n\n" }, { "title": "", "content": "Problem Statement\nA cheetah and a cheater are going to play the game of Nim.\nIn this game they use N piles of stones.\nInitially the i-th pile contains a_i stones.\nThe players take turns alternately, and the cheetah plays first.\nIn each turn, the player chooses one of the piles, and takes one or more stones from the pile.\nThe player who can't make a move loses.\nHowever, before the game starts, the cheater wants to cheat a bit to make sure that he can win regardless of the moves by the cheetah.\nFrom each pile, the cheater takes zero or one stone and eats it before the game.\nIn case there are multiple ways to guarantee his winning, he wants to minimize the number of stones he eats.\nCompute the number of stones the cheater will eat.\nIn case there is no way for the cheater to win the game even with the cheating, print -1 instead.", "constraint": "1 <= N <= 10^5\n2 <= a_i <= 10^9", "input": "Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2\n3\n4 output: 3\n\nThe only way for the cheater to win the game is to take stones from all piles and eat them.", "input: 3\n100\n100\n100 output: -1"], "Pid": "p03870", "ProblemText": "Task Description: Problem Statement\nA cheetah and a cheater are going to play the game of Nim.\nIn this game they use N piles of stones.\nInitially the i-th pile contains a_i stones.\nThe players take turns alternately, and the cheetah plays first.\nIn each turn, the player chooses one of the piles, and takes one or more stones from the pile.\nThe player who can't make a move loses.\nHowever, before the game starts, the cheater wants to cheat a bit to make sure that he can win regardless of the moves by the cheetah.\nFrom each pile, the cheater takes zero or one stone and eats it before the game.\nIn case there are multiple ways to guarantee his winning, he wants to minimize the number of stones he eats.\nCompute the number of stones the cheater will eat.\nIn case there is no way for the cheater to win the game even with the cheating, print -1 instead.\nTask Constraint: 1 <= N <= 10^5\n2 <= a_i <= 10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nTask Output: Print the answer.\nTask Samples: input: 3\n2\n3\n4 output: 3\n\nThe only way for the cheater to win the game is to take stones from all piles and eat them.\ninput: 3\n100\n100\n100 output: -1\n\n" }, { "title": "", "content": "Problem Statement\nThere are two (6-sided) dice: a red die and a blue die.\nWhen a red die is rolled, it shows i with probability p_i percents, and when a blue die is rolled, it shows j with probability q_j percents.\nPetr and tourist are playing the following game.\nBoth players know the probabilistic distributions of the two dice.\nFirst, Petr chooses a die in his will (without showing it to tourist), rolls it, and tells tourist the number it shows.\nThen, tourist guesses the color of the chosen die.\nIf he guesses the color correctly, tourist wins. Otherwise Petr wins.\nIf both players play optimally, what is the probability that tourist wins the game?", "constraint": "0 <= p_i, q_i <= 100\np_1 + ... + p_6 = q_1 + ... + q_6 = 100\nAll values in the input are integers.", "input": "Input The input is given from Standard Input in the following format:\np_1 p_2 p_3 p_4 p_5 p_6\nq_1 q_2 q_3 q_4 q_5 q_6", "output": "Print the probability that tourist wins.\nThe absolute error or the relative error must be at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 25 25 25 25 0 0\n0 0 0 0 50 50 output: 1.000000000000\n\ntourist can always win the game: If the number is at most 4, the color is definitely red. Otherwise the color is definitely blue.", "input: 10 20 20 10 20 20\n20 20 20 10 10 20 output: 0.550000000000"], "Pid": "p03871", "ProblemText": "Task Description: Problem Statement\nThere are two (6-sided) dice: a red die and a blue die.\nWhen a red die is rolled, it shows i with probability p_i percents, and when a blue die is rolled, it shows j with probability q_j percents.\nPetr and tourist are playing the following game.\nBoth players know the probabilistic distributions of the two dice.\nFirst, Petr chooses a die in his will (without showing it to tourist), rolls it, and tells tourist the number it shows.\nThen, tourist guesses the color of the chosen die.\nIf he guesses the color correctly, tourist wins. Otherwise Petr wins.\nIf both players play optimally, what is the probability that tourist wins the game?\nTask Constraint: 0 <= p_i, q_i <= 100\np_1 + ... + p_6 = q_1 + ... + q_6 = 100\nAll values in the input are integers.\nTask Input: Input The input is given from Standard Input in the following format:\np_1 p_2 p_3 p_4 p_5 p_6\nq_1 q_2 q_3 q_4 q_5 q_6\nTask Output: Print the probability that tourist wins.\nThe absolute error or the relative error must be at most 10^{-9}.\nTask Samples: input: 25 25 25 25 0 0\n0 0 0 0 50 50 output: 1.000000000000\n\ntourist can always win the game: If the number is at most 4, the color is definitely red. Otherwise the color is definitely blue.\ninput: 10 20 20 10 20 20\n20 20 20 10 10 20 output: 0.550000000000\n\n" }, { "title": "", "content": "Problem Statement\nThere are N cities in a two-dimensional plane.\nThe coordinates of the i-th city is (x_i, y_i).\nInitially, the amount of water stored in the i-th city is a_i liters.\nSnuke can carry any amount of water from a city to another city.\nHowever, water leaks out a bit while he carries it.\nIf he carries l liters of water from the s-th city to the t-th city, only max(l-d_{s, t}, 0) liters of water remains when he arrives at the destination.\nHere d_{s, t} denotes the (Euclidean) distance between the s-th city and the t-th city.\nHe can perform arbitrary number of operations of this type.\nSnuke wants to maximize the minimum amount of water among the N cities.\nFind the maximum X such that he can distribute at least X liters of water to each city.", "constraint": "1 <= N <= 15\n0 <= x_i, y_i, a_i <= 10^9\nAll values in the input are integers.\nNo two cities are at the same position.", "input": "Input The input is given from Standard Input in the following format:\nN\nx_1 y_1 a_1\n:\nx_N y_N a_N", "output": "Print the maximum of the minimum amount of water among the N cities.\nThe absolute error or the relative error must be at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 10\n2 0 5\n0 5 8 output: 6.500000000000\n\nThe optimal solution is to carry 3.5 liters of water from the 1st city to the 2nd city.\nAfter the operation, both the 1st and the 2nd cities will have 6.5 liters of water, and the 3rd city will have 8 liters of water.", "input: 15\n335279264 849598327 822889311\n446755913 526239859 548830120\n181424399 715477619 342858071\n625711486 448565595 480845266\n647639160 467825612 449656269\n160714711 336869678 545923679\n61020590 573085537 816372580\n626006012 389312924 135599877\n547865075 511429216 605997004\n561330066 539239436 921749002\n650693494 63219754 786119025\n849028504 632532642 655702582\n285323416 611583586 211428413\n990607689 590857173 393671555\n560686330 679513171 501983447 output: 434666178.237122833729"], "Pid": "p03872", "ProblemText": "Task Description: Problem Statement\nThere are N cities in a two-dimensional plane.\nThe coordinates of the i-th city is (x_i, y_i).\nInitially, the amount of water stored in the i-th city is a_i liters.\nSnuke can carry any amount of water from a city to another city.\nHowever, water leaks out a bit while he carries it.\nIf he carries l liters of water from the s-th city to the t-th city, only max(l-d_{s, t}, 0) liters of water remains when he arrives at the destination.\nHere d_{s, t} denotes the (Euclidean) distance between the s-th city and the t-th city.\nHe can perform arbitrary number of operations of this type.\nSnuke wants to maximize the minimum amount of water among the N cities.\nFind the maximum X such that he can distribute at least X liters of water to each city.\nTask Constraint: 1 <= N <= 15\n0 <= x_i, y_i, a_i <= 10^9\nAll values in the input are integers.\nNo two cities are at the same position.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nx_1 y_1 a_1\n:\nx_N y_N a_N\nTask Output: Print the maximum of the minimum amount of water among the N cities.\nThe absolute error or the relative error must be at most 10^{-9}.\nTask Samples: input: 3\n0 0 10\n2 0 5\n0 5 8 output: 6.500000000000\n\nThe optimal solution is to carry 3.5 liters of water from the 1st city to the 2nd city.\nAfter the operation, both the 1st and the 2nd cities will have 6.5 liters of water, and the 3rd city will have 8 liters of water.\ninput: 15\n335279264 849598327 822889311\n446755913 526239859 548830120\n181424399 715477619 342858071\n625711486 448565595 480845266\n647639160 467825612 449656269\n160714711 336869678 545923679\n61020590 573085537 816372580\n626006012 389312924 135599877\n547865075 511429216 605997004\n561330066 539239436 921749002\n650693494 63219754 786119025\n849028504 632532642 655702582\n285323416 611583586 211428413\n990607689 590857173 393671555\n560686330 679513171 501983447 output: 434666178.237122833729\n\n" }, { "title": "", "content": "Problem Statement\nSnuke received N intervals as a birthday present.\nThe i-th interval was [-L_i, R_i].\nIt is guaranteed that both L_i and R_i are positive.\nIn other words, the origin is strictly inside each interval.\nSnuke doesn't like overlapping intervals, so he decided to move some intervals.\nFor any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d.\nThat is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].\nHe can repeat this type of operation arbitrary number of times.\nAfter the operations, the intervals must be pairwise disjoint (however, they may touch at a point).\nFormally, for any two intervals, the length of the intersection must be zero.\nCompute the minimum cost required to achieve his goal.", "constraint": "1 <= N <= 5000\n1 <= L_i, R_i <= 10^9\nAll values in the input are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\nL_1 R_1\n:\nL_N R_N", "output": "Print the minimum cost required to achieve his goal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 7\n2 5\n4 1\n7 5 output: 22\n\nOne optimal solution is as follows:\n\nMove the interval [-2,7] to [6,15] with 8 dollars\nMove the interval [-2,5] to [-1,6] with 1 dollars\nMove the interval [-4,1] to [-6, -1] with 2 dollars\nMove the interval [-7,5] to [-18, -6] with 11 dollars\n\nThe total cost is 8 + 1 + 2 + 11 = 22 dollars.", "input: 20\n97 2\n75 25\n82 84\n17 56\n32 2\n28 37\n57 39\n18 11\n79 6\n40 68\n68 16\n40 63\n93 49\n91 10\n55 68\n31 80\n57 18\n34 28\n76 55\n21 80 output: 7337"], "Pid": "p03873", "ProblemText": "Task Description: Problem Statement\nSnuke received N intervals as a birthday present.\nThe i-th interval was [-L_i, R_i].\nIt is guaranteed that both L_i and R_i are positive.\nIn other words, the origin is strictly inside each interval.\nSnuke doesn't like overlapping intervals, so he decided to move some intervals.\nFor any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d.\nThat is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].\nHe can repeat this type of operation arbitrary number of times.\nAfter the operations, the intervals must be pairwise disjoint (however, they may touch at a point).\nFormally, for any two intervals, the length of the intersection must be zero.\nCompute the minimum cost required to achieve his goal.\nTask Constraint: 1 <= N <= 5000\n1 <= L_i, R_i <= 10^9\nAll values in the input are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nL_1 R_1\n:\nL_N R_N\nTask Output: Print the minimum cost required to achieve his goal.\nTask Samples: input: 4\n2 7\n2 5\n4 1\n7 5 output: 22\n\nOne optimal solution is as follows:\n\nMove the interval [-2,7] to [6,15] with 8 dollars\nMove the interval [-2,5] to [-1,6] with 1 dollars\nMove the interval [-4,1] to [-6, -1] with 2 dollars\nMove the interval [-7,5] to [-18, -6] with 11 dollars\n\nThe total cost is 8 + 1 + 2 + 11 = 22 dollars.\ninput: 20\n97 2\n75 25\n82 84\n17 56\n32 2\n28 37\n57 39\n18 11\n79 6\n40 68\n68 16\n40 63\n93 49\n91 10\n55 68\n31 80\n57 18\n34 28\n76 55\n21 80 output: 7337\n\n" }, { "title": "", "content": "Problem Statement\nWelcome to CODE FESTIVAL 2016!\nIn order to celebrate this contest, find a string s that satisfies the following conditions:\n\nThe length of s is between 1 and 5000, inclusive.\ns consists of uppercase letters.\ns contains exactly K occurrences of the string \"FESTIVAL\" as a subsequence.\nIn other words, there are exactly K tuples of integers (i_0, i_1, . . . , i_7) such that 0 <= i_0 < i_1 < . . . < i_7 <= |s|-1 and s[i_0]='F', s[i_1]='E', . . . , s[i_7]='L'.\n\nIt can be proved that under the given constraints, the solution always exists.\nIn case there are multiple possible solutions, you can output any.", "constraint": "1 <= K <= 10^{18}", "input": "Input The input is given from Standard Input in the following format:\nK", "output": "Print a string that satisfies the conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 output: FESSSSSSSTIVAL", "input: 256 output: FFEESSTTIIVVAALL"], "Pid": "p03874", "ProblemText": "Task Description: Problem Statement\nWelcome to CODE FESTIVAL 2016!\nIn order to celebrate this contest, find a string s that satisfies the following conditions:\n\nThe length of s is between 1 and 5000, inclusive.\ns consists of uppercase letters.\ns contains exactly K occurrences of the string \"FESTIVAL\" as a subsequence.\nIn other words, there are exactly K tuples of integers (i_0, i_1, . . . , i_7) such that 0 <= i_0 < i_1 < . . . < i_7 <= |s|-1 and s[i_0]='F', s[i_1]='E', . . . , s[i_7]='L'.\n\nIt can be proved that under the given constraints, the solution always exists.\nIn case there are multiple possible solutions, you can output any.\nTask Constraint: 1 <= K <= 10^{18}\nTask Input: Input The input is given from Standard Input in the following format:\nK\nTask Output: Print a string that satisfies the conditions.\nTask Samples: input: 7 output: FESSSSSSSTIVAL\ninput: 256 output: FFEESSTTIIVVAALL\n\n" }, { "title": "", "content": "Problem Statement\nSnuke received two matrices A and B as birthday presents.\nEach of the matrices is an N by N matrix that consists of only 0 and 1.\nThen he computed the product of the two matrices, C = AB.\nSince he performed all computations in modulo two, C was also an N by N matrix that consists of only 0 and 1.\nFor each 1 <= i, j <= N, you are given c_{i, j}, the (i, j)-element of the matrix C.\nHowever, Snuke accidentally ate the two matrices A and B, and now he only knows C.\nCompute the number of possible (ordered) pairs of the two matrices A and B, modulo 10^9+7.", "constraint": "1 <= N <= 300\nc_{i, j} is either 0 or 1.", "input": "Input The input is given from Standard Input in the following format:\nN\nc_{1,1} . . . c_{1, N}\n:\nc_{N, 1} . . . c_{N, N}", "output": "Print the number of possible (ordered) pairs of two matrices A and B (modulo 10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 1\n1 0 output: 6", "input: 10\n1 0 0 1 1 1 0 0 1 0\n0 0 0 1 1 0 0 0 1 0\n0 0 1 1 1 1 1 1 1 1\n0 1 0 1 0 0 0 1 1 0\n0 0 1 0 1 1 1 1 1 1\n1 0 0 0 0 1 0 0 0 0\n1 1 1 0 1 0 0 0 0 1\n0 0 0 1 0 0 1 0 1 0\n0 0 0 1 1 1 0 0 0 0\n1 0 1 0 0 1 1 1 1 1 output: 741992411"], "Pid": "p03875", "ProblemText": "Task Description: Problem Statement\nSnuke received two matrices A and B as birthday presents.\nEach of the matrices is an N by N matrix that consists of only 0 and 1.\nThen he computed the product of the two matrices, C = AB.\nSince he performed all computations in modulo two, C was also an N by N matrix that consists of only 0 and 1.\nFor each 1 <= i, j <= N, you are given c_{i, j}, the (i, j)-element of the matrix C.\nHowever, Snuke accidentally ate the two matrices A and B, and now he only knows C.\nCompute the number of possible (ordered) pairs of the two matrices A and B, modulo 10^9+7.\nTask Constraint: 1 <= N <= 300\nc_{i, j} is either 0 or 1.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nc_{1,1} . . . c_{1, N}\n:\nc_{N, 1} . . . c_{N, N}\nTask Output: Print the number of possible (ordered) pairs of two matrices A and B (modulo 10^9+7).\nTask Samples: input: 2\n0 1\n1 0 output: 6\ninput: 10\n1 0 0 1 1 1 0 0 1 0\n0 0 0 1 1 0 0 0 1 0\n0 0 1 1 1 1 1 1 1 1\n0 1 0 1 0 0 0 1 1 0\n0 0 1 0 1 1 1 1 1 1\n1 0 0 0 0 1 0 0 0 0\n1 1 1 0 1 0 0 0 0 1\n0 0 0 1 0 0 1 0 1 0\n0 0 0 1 1 1 0 0 0 0\n1 0 1 0 0 1 1 1 1 1 output: 741992411\n\n" }, { "title": "", "content": "Problem Statement\nConstruct an N-gon that satisfies the following conditions:\n\nThe polygon is simple (see notes for the definition).\nEach edge of the polygon is parallel to one of the coordinate axes.\nEach coordinate is an integer between 0 and 10^9, inclusive.\nThe vertices are numbered 1 through N in counter-clockwise order.\nThe internal angle at the i-th vertex is exactly a_i degrees.\n\nIn case there are multiple possible answers, you can output any. note: Notes A polygon is called simple if each edge has a positive length, and no two edges have a common point (except for adjacent edges touching at a vertex).", "constraint": "3 <= N <= 1000\na_i is either 90 or 270.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N", "output": "In case the answer exists, print the answer in the following format:\nx_1 y_1\n:\nx_N y_N\n\nHere (x_i, y_i) are the coordinates of the i-th vertex.\nIn case the answer doesn't exist, print a single -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n90\n90\n270\n90\n90\n90\n270\n90 output: 0 0\n2 0\n2 1\n3 1\n3 2\n1 2\n1 1\n0 1", "input: 3\n90\n90\n90 output: -1"], "Pid": "p03876", "ProblemText": "Task Description: Problem Statement\nConstruct an N-gon that satisfies the following conditions:\n\nThe polygon is simple (see notes for the definition).\nEach edge of the polygon is parallel to one of the coordinate axes.\nEach coordinate is an integer between 0 and 10^9, inclusive.\nThe vertices are numbered 1 through N in counter-clockwise order.\nThe internal angle at the i-th vertex is exactly a_i degrees.\n\nIn case there are multiple possible answers, you can output any. note: Notes A polygon is called simple if each edge has a positive length, and no two edges have a common point (except for adjacent edges touching at a vertex).\nTask Constraint: 3 <= N <= 1000\na_i is either 90 or 270.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nTask Output: In case the answer exists, print the answer in the following format:\nx_1 y_1\n:\nx_N y_N\n\nHere (x_i, y_i) are the coordinates of the i-th vertex.\nIn case the answer doesn't exist, print a single -1.\nTask Samples: input: 8\n90\n90\n270\n90\n90\n90\n270\n90 output: 0 0\n2 0\n2 1\n3 1\n3 2\n1 2\n1 1\n0 1\ninput: 3\n90\n90\n90 output: -1\n\n" }, { "title": "", "content": "Problem Statement\nConsider all integers between 1 and 2N, inclusive.\nSnuke wants to divide these integers into N pairs such that:\n\nEach integer between 1 and 2N is contained in exactly one of the pairs.\nIn exactly A pairs, the difference between the two integers is 1.\nIn exactly B pairs, the difference between the two integers is 2.\nIn exactly C pairs, the difference between the two integers is 3.\n\nNote that the constraints guarantee that N = A + B + C, thus no pair can have the difference of 4 or more.\nCompute the number of ways to do this, modulo 10^9+7.", "constraint": "1 <= N <= 5000\n0 <= A, B, C\nA + B + C = N", "input": "Input The input is given from Standard Input in the following format:\nN A B C", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 2 0 output: 2\n\nThere are two possibilities: 1-2,3-5,4-6 or 1-3,2-4,5-6.", "input: 600 100 200 300 output: 522158867"], "Pid": "p03877", "ProblemText": "Task Description: Problem Statement\nConsider all integers between 1 and 2N, inclusive.\nSnuke wants to divide these integers into N pairs such that:\n\nEach integer between 1 and 2N is contained in exactly one of the pairs.\nIn exactly A pairs, the difference between the two integers is 1.\nIn exactly B pairs, the difference between the two integers is 2.\nIn exactly C pairs, the difference between the two integers is 3.\n\nNote that the constraints guarantee that N = A + B + C, thus no pair can have the difference of 4 or more.\nCompute the number of ways to do this, modulo 10^9+7.\nTask Constraint: 1 <= N <= 5000\n0 <= A, B, C\nA + B + C = N\nTask Input: Input The input is given from Standard Input in the following format:\nN A B C\nTask Output: Print the answer.\nTask Samples: input: 3 1 2 0 output: 2\n\nThere are two possibilities: 1-2,3-5,4-6 or 1-3,2-4,5-6.\ninput: 600 100 200 300 output: 522158867\n\n" }, { "title": "", "content": "Problem Statement\nThere are N computers and N sockets in a one-dimensional world.\nThe coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i.\nIt is guaranteed that these 2N coordinates are pairwise distinct.\nSnuke wants to connect each computer to a socket using a cable.\nEach socket can be connected to only one computer.\nIn how many ways can he minimize the total length of the cables?\nCompute the answer modulo 10^9+7.", "constraint": "1 <= N <= 10^5\n0 <= a_i, b_i <= 10^9\nThe coordinates are integers.\nThe coordinates are pairwise distinct.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nb_1\n:\nb_N", "output": "Print the number of ways to minimize the total length of the cables, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0\n10\n20\n30 output: 2\n\nThere are two optimal connections: 0-20,10-30 and 0-30,10-20.\nIn both connections the total length of the cables is 40.", "input: 3\n3\n10\n8\n7\n12\n5 output: 1"], "Pid": "p03878", "ProblemText": "Task Description: Problem Statement\nThere are N computers and N sockets in a one-dimensional world.\nThe coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i.\nIt is guaranteed that these 2N coordinates are pairwise distinct.\nSnuke wants to connect each computer to a socket using a cable.\nEach socket can be connected to only one computer.\nIn how many ways can he minimize the total length of the cables?\nCompute the answer modulo 10^9+7.\nTask Constraint: 1 <= N <= 10^5\n0 <= a_i, b_i <= 10^9\nThe coordinates are integers.\nThe coordinates are pairwise distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nb_1\n:\nb_N\nTask Output: Print the number of ways to minimize the total length of the cables, modulo 10^9+7.\nTask Samples: input: 2\n0\n10\n20\n30 output: 2\n\nThere are two optimal connections: 0-20,10-30 and 0-30,10-20.\nIn both connections the total length of the cables is 40.\ninput: 3\n3\n10\n8\n7\n12\n5 output: 1\n\n" }, { "title": "", "content": "Problem Statement\nSnuke received a triangle as a birthday present.\nThe coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).\nHe wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch).\nCompute the maximum possible radius of the circles.", "constraint": "0 <= x_i, y_i <= 1000\nThe coordinates are integers.\nThe three points are not on the same line.", "input": "Input The input is given from Standard Input in the following format:\nx_1 y_1\nx_2 y_2\nx_3 y_3", "output": "Print the maximum possible radius of the circles.\nThe absolute error or the relative error must be at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 0 0\n1 1\n2 0 output: 0.292893218813", "input: 3 1\n1 5\n4 9 output: 0.889055514217"], "Pid": "p03879", "ProblemText": "Task Description: Problem Statement\nSnuke received a triangle as a birthday present.\nThe coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).\nHe wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch).\nCompute the maximum possible radius of the circles.\nTask Constraint: 0 <= x_i, y_i <= 1000\nThe coordinates are integers.\nThe three points are not on the same line.\nTask Input: Input The input is given from Standard Input in the following format:\nx_1 y_1\nx_2 y_2\nx_3 y_3\nTask Output: Print the maximum possible radius of the circles.\nThe absolute error or the relative error must be at most 10^{-9}.\nTask Samples: input: 0 0\n1 1\n2 0 output: 0.292893218813\ninput: 3 1\n1 5\n4 9 output: 0.889055514217\n\n" }, { "title": "", "content": "Problem Statement\nA cheetah and a cheater are going to play the game of Nim.\nIn this game they use N piles of stones.\nInitially the i-th pile contains a_i stones.\nThe players take turns alternately, and the cheetah plays first.\nIn each turn, the player chooses one of the piles, and takes one or more stones from the pile.\nThe player who can't make a move loses.\nHowever, before the game starts, the cheater wants to cheat a bit to make sure that he can win regardless of the moves by the cheetah.\nFrom each pile, the cheater takes zero or one stone and eats it before the game.\nIn case there are multiple ways to guarantee his winning, he wants to minimize the number of stones he eats.\nCompute the number of stones the cheater will eat.\nIn case there is no way for the cheater to win the game even with the cheating, print -1 instead.", "constraint": "1 <= N <= 10^5\n2 <= a_i <= 10^9", "input": "Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2\n3\n4 output: 3\n\nThe only way for the cheater to win the game is to take stones from all piles and eat them.", "input: 3\n100\n100\n100 output: -1"], "Pid": "p03880", "ProblemText": "Task Description: Problem Statement\nA cheetah and a cheater are going to play the game of Nim.\nIn this game they use N piles of stones.\nInitially the i-th pile contains a_i stones.\nThe players take turns alternately, and the cheetah plays first.\nIn each turn, the player chooses one of the piles, and takes one or more stones from the pile.\nThe player who can't make a move loses.\nHowever, before the game starts, the cheater wants to cheat a bit to make sure that he can win regardless of the moves by the cheetah.\nFrom each pile, the cheater takes zero or one stone and eats it before the game.\nIn case there are multiple ways to guarantee his winning, he wants to minimize the number of stones he eats.\nCompute the number of stones the cheater will eat.\nIn case there is no way for the cheater to win the game even with the cheating, print -1 instead.\nTask Constraint: 1 <= N <= 10^5\n2 <= a_i <= 10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nTask Output: Print the answer.\nTask Samples: input: 3\n2\n3\n4 output: 3\n\nThe only way for the cheater to win the game is to take stones from all piles and eat them.\ninput: 3\n100\n100\n100 output: -1\n\n" }, { "title": "", "content": "Problem Statement\nThere are two (6-sided) dice: a red die and a blue die.\nWhen a red die is rolled, it shows i with probability p_i percents, and when a blue die is rolled, it shows j with probability q_j percents.\nPetr and tourist are playing the following game.\nBoth players know the probabilistic distributions of the two dice.\nFirst, Petr chooses a die in his will (without showing it to tourist), rolls it, and tells tourist the number it shows.\nThen, tourist guesses the color of the chosen die.\nIf he guesses the color correctly, tourist wins. Otherwise Petr wins.\nIf both players play optimally, what is the probability that tourist wins the game?", "constraint": "0 <= p_i, q_i <= 100\np_1 + ... + p_6 = q_1 + ... + q_6 = 100\nAll values in the input are integers.", "input": "Input The input is given from Standard Input in the following format:\np_1 p_2 p_3 p_4 p_5 p_6\nq_1 q_2 q_3 q_4 q_5 q_6", "output": "Print the probability that tourist wins.\nThe absolute error or the relative error must be at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 25 25 25 25 0 0\n0 0 0 0 50 50 output: 1.000000000000\n\ntourist can always win the game: If the number is at most 4, the color is definitely red. Otherwise the color is definitely blue.", "input: 10 20 20 10 20 20\n20 20 20 10 10 20 output: 0.550000000000"], "Pid": "p03881", "ProblemText": "Task Description: Problem Statement\nThere are two (6-sided) dice: a red die and a blue die.\nWhen a red die is rolled, it shows i with probability p_i percents, and when a blue die is rolled, it shows j with probability q_j percents.\nPetr and tourist are playing the following game.\nBoth players know the probabilistic distributions of the two dice.\nFirst, Petr chooses a die in his will (without showing it to tourist), rolls it, and tells tourist the number it shows.\nThen, tourist guesses the color of the chosen die.\nIf he guesses the color correctly, tourist wins. Otherwise Petr wins.\nIf both players play optimally, what is the probability that tourist wins the game?\nTask Constraint: 0 <= p_i, q_i <= 100\np_1 + ... + p_6 = q_1 + ... + q_6 = 100\nAll values in the input are integers.\nTask Input: Input The input is given from Standard Input in the following format:\np_1 p_2 p_3 p_4 p_5 p_6\nq_1 q_2 q_3 q_4 q_5 q_6\nTask Output: Print the probability that tourist wins.\nThe absolute error or the relative error must be at most 10^{-9}.\nTask Samples: input: 25 25 25 25 0 0\n0 0 0 0 50 50 output: 1.000000000000\n\ntourist can always win the game: If the number is at most 4, the color is definitely red. Otherwise the color is definitely blue.\ninput: 10 20 20 10 20 20\n20 20 20 10 10 20 output: 0.550000000000\n\n" }, { "title": "", "content": "Problem Statement\nThere are N cities in a two-dimensional plane.\nThe coordinates of the i-th city is (x_i, y_i).\nInitially, the amount of water stored in the i-th city is a_i liters.\nSnuke can carry any amount of water from a city to another city.\nHowever, water leaks out a bit while he carries it.\nIf he carries l liters of water from the s-th city to the t-th city, only max(l-d_{s, t}, 0) liters of water remains when he arrives at the destination.\nHere d_{s, t} denotes the (Euclidean) distance between the s-th city and the t-th city.\nHe can perform arbitrary number of operations of this type.\nSnuke wants to maximize the minimum amount of water among the N cities.\nFind the maximum X such that he can distribute at least X liters of water to each city.", "constraint": "1 <= N <= 15\n0 <= x_i, y_i, a_i <= 10^9\nAll values in the input are integers.\nNo two cities are at the same position.", "input": "Input The input is given from Standard Input in the following format:\nN\nx_1 y_1 a_1\n:\nx_N y_N a_N", "output": "Print the maximum of the minimum amount of water among the N cities.\nThe absolute error or the relative error must be at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 10\n2 0 5\n0 5 8 output: 6.500000000000\n\nThe optimal solution is to carry 3.5 liters of water from the 1st city to the 2nd city.\nAfter the operation, both the 1st and the 2nd cities will have 6.5 liters of water, and the 3rd city will have 8 liters of water.", "input: 15\n335279264 849598327 822889311\n446755913 526239859 548830120\n181424399 715477619 342858071\n625711486 448565595 480845266\n647639160 467825612 449656269\n160714711 336869678 545923679\n61020590 573085537 816372580\n626006012 389312924 135599877\n547865075 511429216 605997004\n561330066 539239436 921749002\n650693494 63219754 786119025\n849028504 632532642 655702582\n285323416 611583586 211428413\n990607689 590857173 393671555\n560686330 679513171 501983447 output: 434666178.237122833729"], "Pid": "p03882", "ProblemText": "Task Description: Problem Statement\nThere are N cities in a two-dimensional plane.\nThe coordinates of the i-th city is (x_i, y_i).\nInitially, the amount of water stored in the i-th city is a_i liters.\nSnuke can carry any amount of water from a city to another city.\nHowever, water leaks out a bit while he carries it.\nIf he carries l liters of water from the s-th city to the t-th city, only max(l-d_{s, t}, 0) liters of water remains when he arrives at the destination.\nHere d_{s, t} denotes the (Euclidean) distance between the s-th city and the t-th city.\nHe can perform arbitrary number of operations of this type.\nSnuke wants to maximize the minimum amount of water among the N cities.\nFind the maximum X such that he can distribute at least X liters of water to each city.\nTask Constraint: 1 <= N <= 15\n0 <= x_i, y_i, a_i <= 10^9\nAll values in the input are integers.\nNo two cities are at the same position.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nx_1 y_1 a_1\n:\nx_N y_N a_N\nTask Output: Print the maximum of the minimum amount of water among the N cities.\nThe absolute error or the relative error must be at most 10^{-9}.\nTask Samples: input: 3\n0 0 10\n2 0 5\n0 5 8 output: 6.500000000000\n\nThe optimal solution is to carry 3.5 liters of water from the 1st city to the 2nd city.\nAfter the operation, both the 1st and the 2nd cities will have 6.5 liters of water, and the 3rd city will have 8 liters of water.\ninput: 15\n335279264 849598327 822889311\n446755913 526239859 548830120\n181424399 715477619 342858071\n625711486 448565595 480845266\n647639160 467825612 449656269\n160714711 336869678 545923679\n61020590 573085537 816372580\n626006012 389312924 135599877\n547865075 511429216 605997004\n561330066 539239436 921749002\n650693494 63219754 786119025\n849028504 632532642 655702582\n285323416 611583586 211428413\n990607689 590857173 393671555\n560686330 679513171 501983447 output: 434666178.237122833729\n\n" }, { "title": "", "content": "Problem Statement\nSnuke received N intervals as a birthday present.\nThe i-th interval was [-L_i, R_i].\nIt is guaranteed that both L_i and R_i are positive.\nIn other words, the origin is strictly inside each interval.\nSnuke doesn't like overlapping intervals, so he decided to move some intervals.\nFor any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d.\nThat is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].\nHe can repeat this type of operation arbitrary number of times.\nAfter the operations, the intervals must be pairwise disjoint (however, they may touch at a point).\nFormally, for any two intervals, the length of the intersection must be zero.\nCompute the minimum cost required to achieve his goal.", "constraint": "1 <= N <= 5000\n1 <= L_i, R_i <= 10^9\nAll values in the input are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\nL_1 R_1\n:\nL_N R_N", "output": "Print the minimum cost required to achieve his goal.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 7\n2 5\n4 1\n7 5 output: 22\n\nOne optimal solution is as follows:\n\nMove the interval [-2,7] to [6,15] with 8 dollars\nMove the interval [-2,5] to [-1,6] with 1 dollars\nMove the interval [-4,1] to [-6, -1] with 2 dollars\nMove the interval [-7,5] to [-18, -6] with 11 dollars\n\nThe total cost is 8 + 1 + 2 + 11 = 22 dollars.", "input: 20\n97 2\n75 25\n82 84\n17 56\n32 2\n28 37\n57 39\n18 11\n79 6\n40 68\n68 16\n40 63\n93 49\n91 10\n55 68\n31 80\n57 18\n34 28\n76 55\n21 80 output: 7337"], "Pid": "p03883", "ProblemText": "Task Description: Problem Statement\nSnuke received N intervals as a birthday present.\nThe i-th interval was [-L_i, R_i].\nIt is guaranteed that both L_i and R_i are positive.\nIn other words, the origin is strictly inside each interval.\nSnuke doesn't like overlapping intervals, so he decided to move some intervals.\nFor any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d.\nThat is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].\nHe can repeat this type of operation arbitrary number of times.\nAfter the operations, the intervals must be pairwise disjoint (however, they may touch at a point).\nFormally, for any two intervals, the length of the intersection must be zero.\nCompute the minimum cost required to achieve his goal.\nTask Constraint: 1 <= N <= 5000\n1 <= L_i, R_i <= 10^9\nAll values in the input are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nL_1 R_1\n:\nL_N R_N\nTask Output: Print the minimum cost required to achieve his goal.\nTask Samples: input: 4\n2 7\n2 5\n4 1\n7 5 output: 22\n\nOne optimal solution is as follows:\n\nMove the interval [-2,7] to [6,15] with 8 dollars\nMove the interval [-2,5] to [-1,6] with 1 dollars\nMove the interval [-4,1] to [-6, -1] with 2 dollars\nMove the interval [-7,5] to [-18, -6] with 11 dollars\n\nThe total cost is 8 + 1 + 2 + 11 = 22 dollars.\ninput: 20\n97 2\n75 25\n82 84\n17 56\n32 2\n28 37\n57 39\n18 11\n79 6\n40 68\n68 16\n40 63\n93 49\n91 10\n55 68\n31 80\n57 18\n34 28\n76 55\n21 80 output: 7337\n\n" }, { "title": "", "content": "Problem Statement\nWelcome to CODE FESTIVAL 2016!\nIn order to celebrate this contest, find a string s that satisfies the following conditions:\n\nThe length of s is between 1 and 5000, inclusive.\ns consists of uppercase letters.\ns contains exactly K occurrences of the string \"FESTIVAL\" as a subsequence.\nIn other words, there are exactly K tuples of integers (i_0, i_1, . . . , i_7) such that 0 <= i_0 < i_1 < . . . < i_7 <= |s|-1 and s[i_0]='F', s[i_1]='E', . . . , s[i_7]='L'.\n\nIt can be proved that under the given constraints, the solution always exists.\nIn case there are multiple possible solutions, you can output any.", "constraint": "1 <= K <= 10^{18}", "input": "Input The input is given from Standard Input in the following format: \\n K", "output": "Print a string that satisfies the conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 output: FESSSSSSSTIVAL", "input: 256 output: FFEESSTTIIVVAALL"], "Pid": "p03884", "ProblemText": "Task Description: Problem Statement\nWelcome to CODE FESTIVAL 2016!\nIn order to celebrate this contest, find a string s that satisfies the following conditions:\n\nThe length of s is between 1 and 5000, inclusive.\ns consists of uppercase letters.\ns contains exactly K occurrences of the string \"FESTIVAL\" as a subsequence.\nIn other words, there are exactly K tuples of integers (i_0, i_1, . . . , i_7) such that 0 <= i_0 < i_1 < . . . < i_7 <= |s|-1 and s[i_0]='F', s[i_1]='E', . . . , s[i_7]='L'.\n\nIt can be proved that under the given constraints, the solution always exists.\nIn case there are multiple possible solutions, you can output any.\nTask Constraint: 1 <= K <= 10^{18}\nTask Input: Input The input is given from Standard Input in the following format: \\n K\nTask Output: Print a string that satisfies the conditions.\nTask Samples: input: 7 output: FESSSSSSSTIVAL\ninput: 256 output: FFEESSTTIIVVAALL\n\n" }, { "title": "", "content": "Problem Statement\nSnuke received two matrices A and B as birthday presents.\nEach of the matrices is an N by N matrix that consists of only 0 and 1.\nThen he computed the product of the two matrices, C = AB.\nSince he performed all computations in modulo two, C was also an N by N matrix that consists of only 0 and 1.\nFor each 1 <= i, j <= N, you are given c_{i, j}, the (i, j)-element of the matrix C.\nHowever, Snuke accidentally ate the two matrices A and B, and now he only knows C.\nCompute the number of possible (ordered) pairs of the two matrices A and B, modulo 10^9+7.", "constraint": "1 <= N <= 300\nc_{i, j} is either 0 or 1.", "input": "Input The input is given from Standard Input in the following format:\nN\nc_{1,1} . . . c_{1, N}\n:\nc_{N, 1} . . . c_{N, N}", "output": "Print the number of possible (ordered) pairs of two matrices A and B (modulo 10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n0 1\n1 0 output: 6", "input: 10\n1 0 0 1 1 1 0 0 1 0\n0 0 0 1 1 0 0 0 1 0\n0 0 1 1 1 1 1 1 1 1\n0 1 0 1 0 0 0 1 1 0\n0 0 1 0 1 1 1 1 1 1\n1 0 0 0 0 1 0 0 0 0\n1 1 1 0 1 0 0 0 0 1\n0 0 0 1 0 0 1 0 1 0\n0 0 0 1 1 1 0 0 0 0\n1 0 1 0 0 1 1 1 1 1 output: 741992411"], "Pid": "p03885", "ProblemText": "Task Description: Problem Statement\nSnuke received two matrices A and B as birthday presents.\nEach of the matrices is an N by N matrix that consists of only 0 and 1.\nThen he computed the product of the two matrices, C = AB.\nSince he performed all computations in modulo two, C was also an N by N matrix that consists of only 0 and 1.\nFor each 1 <= i, j <= N, you are given c_{i, j}, the (i, j)-element of the matrix C.\nHowever, Snuke accidentally ate the two matrices A and B, and now he only knows C.\nCompute the number of possible (ordered) pairs of the two matrices A and B, modulo 10^9+7.\nTask Constraint: 1 <= N <= 300\nc_{i, j} is either 0 or 1.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nc_{1,1} . . . c_{1, N}\n:\nc_{N, 1} . . . c_{N, N}\nTask Output: Print the number of possible (ordered) pairs of two matrices A and B (modulo 10^9+7).\nTask Samples: input: 2\n0 1\n1 0 output: 6\ninput: 10\n1 0 0 1 1 1 0 0 1 0\n0 0 0 1 1 0 0 0 1 0\n0 0 1 1 1 1 1 1 1 1\n0 1 0 1 0 0 0 1 1 0\n0 0 1 0 1 1 1 1 1 1\n1 0 0 0 0 1 0 0 0 0\n1 1 1 0 1 0 0 0 0 1\n0 0 0 1 0 0 1 0 1 0\n0 0 0 1 1 1 0 0 0 0\n1 0 1 0 0 1 1 1 1 1 output: 741992411\n\n" }, { "title": "", "content": "Problem Statement\nConstruct an N-gon that satisfies the following conditions:\n\nThe polygon is simple (see notes for the definition).\nEach edge of the polygon is parallel to one of the coordinate axes.\nEach coordinate is an integer between 0 and 10^9, inclusive.\nThe vertices are numbered 1 through N in counter-clockwise order.\nThe internal angle at the i-th vertex is exactly a_i degrees.\n\nIn case there are multiple possible answers, you can output any. note: Notes A polygon is called simple if each edge has a positive length, and no two edges have a common point (except for adjacent edges touching at a vertex).", "constraint": "3 <= N <= 1000\na_i is either 90 or 270.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N", "output": "In case the answer exists, print the answer in the following format:\nx_1 y_1\n:\nx_N y_N\n\nHere (x_i, y_i) are the coordinates of the i-th vertex.\nIn case the answer doesn't exist, print a single -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n90\n90\n270\n90\n90\n90\n270\n90 output: 0 0\n2 0\n2 1\n3 1\n3 2\n1 2\n1 1\n0 1", "input: 3\n90\n90\n90 output: -1"], "Pid": "p03886", "ProblemText": "Task Description: Problem Statement\nConstruct an N-gon that satisfies the following conditions:\n\nThe polygon is simple (see notes for the definition).\nEach edge of the polygon is parallel to one of the coordinate axes.\nEach coordinate is an integer between 0 and 10^9, inclusive.\nThe vertices are numbered 1 through N in counter-clockwise order.\nThe internal angle at the i-th vertex is exactly a_i degrees.\n\nIn case there are multiple possible answers, you can output any. note: Notes A polygon is called simple if each edge has a positive length, and no two edges have a common point (except for adjacent edges touching at a vertex).\nTask Constraint: 3 <= N <= 1000\na_i is either 90 or 270.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1\n:\na_N\nTask Output: In case the answer exists, print the answer in the following format:\nx_1 y_1\n:\nx_N y_N\n\nHere (x_i, y_i) are the coordinates of the i-th vertex.\nIn case the answer doesn't exist, print a single -1.\nTask Samples: input: 8\n90\n90\n270\n90\n90\n90\n270\n90 output: 0 0\n2 0\n2 1\n3 1\n3 2\n1 2\n1 1\n0 1\ninput: 3\n90\n90\n90 output: -1\n\n" }, { "title": "", "content": "Problem Statement\nConsider all integers between 1 and 2N, inclusive.\nSnuke wants to divide these integers into N pairs such that:\n\nEach integer between 1 and 2N is contained in exactly one of the pairs.\nIn exactly A pairs, the difference between the two integers is 1.\nIn exactly B pairs, the difference between the two integers is 2.\nIn exactly C pairs, the difference between the two integers is 3.\n\nNote that the constraints guarantee that N = A + B + C, thus no pair can have the difference of 4 or more.\nCompute the number of ways to do this, modulo 10^9+7.", "constraint": "1 <= N <= 5000\n0 <= A, B, C\nA + B + C = N", "input": "Input The input is given from Standard Input in the following format:\nN A B C", "output": "Print the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 2 0 output: 2\n\nThere are two possibilities: 1-2,3-5,4-6 or 1-3,2-4,5-6.", "input: 600 100 200 300 output: 522158867"], "Pid": "p03887", "ProblemText": "Task Description: Problem Statement\nConsider all integers between 1 and 2N, inclusive.\nSnuke wants to divide these integers into N pairs such that:\n\nEach integer between 1 and 2N is contained in exactly one of the pairs.\nIn exactly A pairs, the difference between the two integers is 1.\nIn exactly B pairs, the difference between the two integers is 2.\nIn exactly C pairs, the difference between the two integers is 3.\n\nNote that the constraints guarantee that N = A + B + C, thus no pair can have the difference of 4 or more.\nCompute the number of ways to do this, modulo 10^9+7.\nTask Constraint: 1 <= N <= 5000\n0 <= A, B, C\nA + B + C = N\nTask Input: Input The input is given from Standard Input in the following format:\nN A B C\nTask Output: Print the answer.\nTask Samples: input: 3 1 2 0 output: 2\n\nThere are two possibilities: 1-2,3-5,4-6 or 1-3,2-4,5-6.\ninput: 600 100 200 300 output: 522158867\n\n" }, { "title": "", "content": "Problem Statement In an electric circuit, when two resistors R_1 and R_2 are connected in parallel, the equivalent resistance R_3 can be derived from the following formula:\n\n\\frac{1}{R_1} + \\frac{1}{R_2} = \\frac{1}{R_3}\n\nGiven R_1 and R_2, find R_3.", "constraint": "1 <= R_1, R_2 <= 100\nR_1 and R_2 are integers.", "input": "Input The input is given from Standard Input in the following format:\nR_1 R_2", "output": "Print the value of R_3.\nThe output is considered correct if the absolute or relative error is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3 output: 1.2000000000", "input: 100 99 output: 49.7487437186"], "Pid": "p03888", "ProblemText": "Task Description: Problem Statement In an electric circuit, when two resistors R_1 and R_2 are connected in parallel, the equivalent resistance R_3 can be derived from the following formula:\n\n\\frac{1}{R_1} + \\frac{1}{R_2} = \\frac{1}{R_3}\n\nGiven R_1 and R_2, find R_3.\nTask Constraint: 1 <= R_1, R_2 <= 100\nR_1 and R_2 are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nR_1 R_2\nTask Output: Print the value of R_3.\nThe output is considered correct if the absolute or relative error is at most 10^{-6}.\nTask Samples: input: 2 3 output: 1.2000000000\ninput: 100 99 output: 49.7487437186\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of letters b, d, p and q.\nDetermine whether S is a mirror string.\nHere, a mirror string is a string S such that the following sequence of operations on S results in the same string S:\nReverse the order of the characters in S.\nReplace each occurrence of b by d, d by b, p by q, and q by p, simultaneously.", "constraint": "1 <= |S| <= 10^5\nS consists of letters b, d, p, and q.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "If S is a mirror string, print Yes. Otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: pdbq output: Yes", "input: ppqb output: No"], "Pid": "p03889", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of letters b, d, p and q.\nDetermine whether S is a mirror string.\nHere, a mirror string is a string S such that the following sequence of operations on S results in the same string S:\nReverse the order of the characters in S.\nReplace each occurrence of b by d, d by b, p by q, and q by p, simultaneously.\nTask Constraint: 1 <= |S| <= 10^5\nS consists of letters b, d, p, and q.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: If S is a mirror string, print Yes. Otherwise, print No.\nTask Samples: input: pdbq output: Yes\ninput: ppqb output: No\n\n" }, { "title": "", "content": "Problem Statement Kode Festival is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for \"hardness\". )\nThis year, 2^N stones participated. The hardness of the i-th stone is A_i.\nIn the contest, stones are thrown at each other in a knockout tournament.\nWhen two stones with hardness X and Y are thrown at each other, the following will happen:\nWhen X > Y:\n The stone with hardness Y will be destroyed and eliminated.\n The hardness of the stone with hardness X will become X-Y.\nWhen X = Y:\n One of the stones will be destroyed and eliminated.\n The hardness of the other stone will remain the same.\nWhen X < Y:\n The stone with hardness X will be destroyed and eliminated.\n The hardness of the stone with hardness Y will become Y-X.\nThe 2^N stones will fight in a knockout tournament as follows:\nThe following pairs will fight: (the 1-st stone versus the 2-nd stone), (the 3-rd stone versus the 4-th stone), . . .\nThe following pairs will fight: (the winner of (1-st versus 2-nd) versus the winner of (3-rd versus 4-th)), (the winner of (5-th versus 6-th) versus the winner of (7-th versus 8-th)), . . .\nAnd so forth, until there is only one stone remaining.\nDetermine the eventual hardness of the last stone remaining.", "constraint": "1 <= N <= 18\n1 <= A_i <= 10^9\nA_i is an integer.", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1\nA_2\n:\nA_{2^N}", "output": "Print the eventual hardness of the last stone remaining.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1\n3\n10\n19 output: 7", "input: 3\n1\n3\n2\n4\n6\n8\n100\n104 output: 2"], "Pid": "p03890", "ProblemText": "Task Description: Problem Statement Kode Festival is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for \"hardness\". )\nThis year, 2^N stones participated. The hardness of the i-th stone is A_i.\nIn the contest, stones are thrown at each other in a knockout tournament.\nWhen two stones with hardness X and Y are thrown at each other, the following will happen:\nWhen X > Y:\n The stone with hardness Y will be destroyed and eliminated.\n The hardness of the stone with hardness X will become X-Y.\nWhen X = Y:\n One of the stones will be destroyed and eliminated.\n The hardness of the other stone will remain the same.\nWhen X < Y:\n The stone with hardness X will be destroyed and eliminated.\n The hardness of the stone with hardness Y will become Y-X.\nThe 2^N stones will fight in a knockout tournament as follows:\nThe following pairs will fight: (the 1-st stone versus the 2-nd stone), (the 3-rd stone versus the 4-th stone), . . .\nThe following pairs will fight: (the winner of (1-st versus 2-nd) versus the winner of (3-rd versus 4-th)), (the winner of (5-th versus 6-th) versus the winner of (7-th versus 8-th)), . . .\nAnd so forth, until there is only one stone remaining.\nDetermine the eventual hardness of the last stone remaining.\nTask Constraint: 1 <= N <= 18\n1 <= A_i <= 10^9\nA_i is an integer.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1\nA_2\n:\nA_{2^N}\nTask Output: Print the eventual hardness of the last stone remaining.\nTask Samples: input: 2\n1\n3\n10\n19 output: 7\ninput: 3\n1\n3\n2\n4\n6\n8\n100\n104 output: 2\n\n" }, { "title": "", "content": "Problem Statement A 3*3 grid with a integer written in each square, is called a magic square if and only if the integers in each row, the integers in each column, and the integers in each diagonal (from the top left corner to the bottom right corner, and from the top right corner to the bottom left corner), all add up to the same sum.\nYou are given the integers written in the following three squares in a magic square:\n\nThe integer A at the upper row and left column\nThe integer B at the upper row and middle column\nThe integer C at the middle row and middle column\n\nDetermine the integers written in the remaining squares in the magic square.\nIt can be shown that there exists a unique magic square consistent with the given information.", "constraint": "0 <= A, B, C <= 100", "input": "Input The input is given from Standard Input in the following format:\nA\nB\nC", "output": "Output the integers written in the magic square, in the following format:\nX_{1,1} X_{1,2} X_{1,3}\nX_{2,1} X_{2,2} X_{2,3}\nX_{3,1} X_{3,2} X_{3,3}\n\nwhere X_{i, j} is the integer written in the square at the i-th row and j-th column.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n3\n5 output: 8 3 4\n1 5 9\n6 7 2", "input: 1\n1\n1 output: 1 1 1\n1 1 1\n1 1 1"], "Pid": "p03891", "ProblemText": "Task Description: Problem Statement A 3*3 grid with a integer written in each square, is called a magic square if and only if the integers in each row, the integers in each column, and the integers in each diagonal (from the top left corner to the bottom right corner, and from the top right corner to the bottom left corner), all add up to the same sum.\nYou are given the integers written in the following three squares in a magic square:\n\nThe integer A at the upper row and left column\nThe integer B at the upper row and middle column\nThe integer C at the middle row and middle column\n\nDetermine the integers written in the remaining squares in the magic square.\nIt can be shown that there exists a unique magic square consistent with the given information.\nTask Constraint: 0 <= A, B, C <= 100\nTask Input: Input The input is given from Standard Input in the following format:\nA\nB\nC\nTask Output: Output the integers written in the magic square, in the following format:\nX_{1,1} X_{1,2} X_{1,3}\nX_{2,1} X_{2,2} X_{2,3}\nX_{3,1} X_{3,2} X_{3,3}\n\nwhere X_{i, j} is the integer written in the square at the i-th row and j-th column.\nTask Samples: input: 8\n3\n5 output: 8 3 4\n1 5 9\n6 7 2\ninput: 1\n1\n1 output: 1 1 1\n1 1 1\n1 1 1\n\n" }, { "title": "", "content": "Problem Statement Takahashi is drawing a segment on grid paper.\nFrom a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).\nWhen Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.\nHere, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.", "constraint": "1 <= A, B, C, D <= 10^9\nAt least one of A \\neq C and B \\neq D holds.", "input": "Input The input is given from Standard Input in the following format:\nA B C D", "output": "Print the number of the squares crossed by the segment.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 3 4 output: 4", "input: 2 3 10 7 output: 8"], "Pid": "p03892", "ProblemText": "Task Description: Problem Statement Takahashi is drawing a segment on grid paper.\nFrom a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).\nWhen Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.\nHere, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.\nTask Constraint: 1 <= A, B, C, D <= 10^9\nAt least one of A \\neq C and B \\neq D holds.\nTask Input: Input The input is given from Standard Input in the following format:\nA B C D\nTask Output: Print the number of the squares crossed by the segment.\nTask Samples: input: 1 1 3 4 output: 4\ninput: 2 3 10 7 output: 8\n\n" }, { "title": "", "content": "Problem Statement We have a cord whose length is a positive integer. We will perform the following condition until the length of the cord becomes at most 2:\n\nOperation:\n Cut the rope at two positions to obtain three cords, each with a length of a positive integer.\n Among these, discard one with the longest length and one with the shortest length, and keep the remaining one.\n\nLet f(N) be the maximum possible number of times to perform this operation, starting with a cord with the length N.\nYou are given a positive integer X. Find the maximum integer N such that f(N)=X.", "constraint": "1 <= X <= 40", "input": "Input The input is given from Standard Input in the following format:\nX", "output": "Print the value of the maximum integer N such that f(N)=X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 14"], "Pid": "p03893", "ProblemText": "Task Description: Problem Statement We have a cord whose length is a positive integer. We will perform the following condition until the length of the cord becomes at most 2:\n\nOperation:\n Cut the rope at two positions to obtain three cords, each with a length of a positive integer.\n Among these, discard one with the longest length and one with the shortest length, and keep the remaining one.\n\nLet f(N) be the maximum possible number of times to perform this operation, starting with a cord with the length N.\nYou are given a positive integer X. Find the maximum integer N such that f(N)=X.\nTask Constraint: 1 <= X <= 40\nTask Input: Input The input is given from Standard Input in the following format:\nX\nTask Output: Print the value of the maximum integer N such that f(N)=X.\nTask Samples: input: 2 output: 14\n\n" }, { "title": "", "content": "Problem Statement You have N cups and 1 ball.\nThe cups are arranged in a row, from left to right.\nYou turned down all the cups, then inserted the ball into the leftmost cup.\nThen, you will perform the following Q operations:\n\nThe i-th operation: swap the positions of the A_i-th and B_i-th cups from the left. If one of these cups contains the ball, the ball will also move.\n\nSince you are a magician, you can cast a magic described below:\n\nMagic: When the ball is contained in the i-th cup from the left, teleport the ball into the adjacent cup (that is, the (i-1)-th or (i+1)-th cup, if they exist).\n\nThe magic can be cast before the first operation, between two operations, or after the last operation, but you are allowed to cast it at most once during the whole process.\nFind the number of cups with a possibility of containing the ball after all the operations and possibly casting the magic.", "constraint": "2 <= N <= 10^5\n1 <= Q <= 10^5\n1 <= A_i < B_i <= N", "input": "Input The input is given from Standard Input in the following format:\nN Q\nA_1 B_1\nA_2 B_2\n: \nA_Q B_Q", "output": "Print the number of cups with a possibility of eventually containing the ball.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 3\n1 3\n2 4\n4 5 output: 4", "input: 20 3\n1 7\n8 20\n1 19 output: 5"], "Pid": "p03894", "ProblemText": "Task Description: Problem Statement You have N cups and 1 ball.\nThe cups are arranged in a row, from left to right.\nYou turned down all the cups, then inserted the ball into the leftmost cup.\nThen, you will perform the following Q operations:\n\nThe i-th operation: swap the positions of the A_i-th and B_i-th cups from the left. If one of these cups contains the ball, the ball will also move.\n\nSince you are a magician, you can cast a magic described below:\n\nMagic: When the ball is contained in the i-th cup from the left, teleport the ball into the adjacent cup (that is, the (i-1)-th or (i+1)-th cup, if they exist).\n\nThe magic can be cast before the first operation, between two operations, or after the last operation, but you are allowed to cast it at most once during the whole process.\nFind the number of cups with a possibility of containing the ball after all the operations and possibly casting the magic.\nTask Constraint: 2 <= N <= 10^5\n1 <= Q <= 10^5\n1 <= A_i < B_i <= N\nTask Input: Input The input is given from Standard Input in the following format:\nN Q\nA_1 B_1\nA_2 B_2\n: \nA_Q B_Q\nTask Output: Print the number of cups with a possibility of eventually containing the ball.\nTask Samples: input: 10 3\n1 3\n2 4\n4 5 output: 4\ninput: 20 3\n1 7\n8 20\n1 19 output: 5\n\n" }, { "title": "", "content": "Problem Statement Takahashi recorded his daily life for the last few days as a integer sequence of length 2N, as follows:\n\na_1, b_1, a_2, b_2, . . . , a_N, b_N\n\nThis means that, starting from a certain time T, he was:\n\nsleeping for exactly a_1 seconds\nthen awake for exactly b_1 seconds\nthen sleeping for exactly a_2 seconds\n:\nthen sleeping for exactly a_N seconds\nthen awake for exactly b_N seconds\n\nIn this record, he waked up N times.\nTakahashi is wondering how many times he waked up early during the recorded period.\nHere, he is said to wake up early if he wakes up between 4: 00 AM and 7: 00 AM, inclusive.\nIf he wakes up more than once during this period, each of these awakenings is counted as waking up early.\nUnfortunately, he forgot the time T.\nFind the maximum possible number of times he waked up early during the recorded period.\nFor your information, a day consists of 86400 seconds, and the length of the period between 4: 00 AM and 7: 00 AM is 10800 seconds.", "constraint": "1 <= N <= 10^5\n1 <= a_i, b_i <= 10^5\na_i and b_i are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_N b_N", "output": "Print the maximum possible number of times he waked up early during the recorded period.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n28800 57600\n28800 57600\n57600 28800 output: 2", "input: 10\n28800 57600\n4800 9600\n6000 1200\n600 600\n300 600\n5400 600\n6000 5760\n6760 2880\n6000 12000\n9000 600 output: 5"], "Pid": "p03895", "ProblemText": "Task Description: Problem Statement Takahashi recorded his daily life for the last few days as a integer sequence of length 2N, as follows:\n\na_1, b_1, a_2, b_2, . . . , a_N, b_N\n\nThis means that, starting from a certain time T, he was:\n\nsleeping for exactly a_1 seconds\nthen awake for exactly b_1 seconds\nthen sleeping for exactly a_2 seconds\n:\nthen sleeping for exactly a_N seconds\nthen awake for exactly b_N seconds\n\nIn this record, he waked up N times.\nTakahashi is wondering how many times he waked up early during the recorded period.\nHere, he is said to wake up early if he wakes up between 4: 00 AM and 7: 00 AM, inclusive.\nIf he wakes up more than once during this period, each of these awakenings is counted as waking up early.\nUnfortunately, he forgot the time T.\nFind the maximum possible number of times he waked up early during the recorded period.\nFor your information, a day consists of 86400 seconds, and the length of the period between 4: 00 AM and 7: 00 AM is 10800 seconds.\nTask Constraint: 1 <= N <= 10^5\n1 <= a_i, b_i <= 10^5\na_i and b_i are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_N b_N\nTask Output: Print the maximum possible number of times he waked up early during the recorded period.\nTask Samples: input: 3\n28800 57600\n28800 57600\n57600 28800 output: 2\ninput: 10\n28800 57600\n4800 9600\n6000 1200\n600 600\n300 600\n5400 600\n6000 5760\n6760 2880\n6000 12000\n9000 600 output: 5\n\n" }, { "title": "", "content": "Problem Statement There are N persons, conveniently numbered 1 through N. They will take 3y3s Challenge for N-1 seconds.\nDuring the challenge, each person must look at each of the N-1 other persons for 1 seconds, in some order.\nIf any two persons look at each other during the challenge, the challenge ends in failure.\nFind the order in which each person looks at each of the N-1 other persons, to be successful in the challenge. judging: Judging The output is considered correct only if all of the following conditions are satisfied:\n\n1 <= A_{i, j} <= N\nFor each i, A_{i, 1}, A_{i, 2}, . . . , A_{i, N-1} are pairwise distinct.\nLet X = A_{i, j}, then A_{X, j} \\neq i always holds.", "constraint": "2 <= N <= 100", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "If there exists no way to be successful in the challenge, print -1.\nIf there exists a way to be successful in the challenge, print any such way in the following format:\nA_{1,1} A_{1,2} . . . A_{1, N-1}\nA_{2,1} A_{2,2} . . . A_{2, N-1}\n:\nA_{N, 1} A_{N, 2} . . . A_{N, N-1}\n\nwhere A_{i, j} is the index of the person that the person numbered i looks at during the j-th second.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 output: 2 3 4 5 6 7\n5 3 1 6 4 7\n2 7 4 1 5 6\n2 1 7 5 3 6\n1 4 3 7 6 2\n2 5 7 3 4 1\n2 6 1 4 5 3", "input: 2 output: -1"], "Pid": "p03896", "ProblemText": "Task Description: Problem Statement There are N persons, conveniently numbered 1 through N. They will take 3y3s Challenge for N-1 seconds.\nDuring the challenge, each person must look at each of the N-1 other persons for 1 seconds, in some order.\nIf any two persons look at each other during the challenge, the challenge ends in failure.\nFind the order in which each person looks at each of the N-1 other persons, to be successful in the challenge. judging: Judging The output is considered correct only if all of the following conditions are satisfied:\n\n1 <= A_{i, j} <= N\nFor each i, A_{i, 1}, A_{i, 2}, . . . , A_{i, N-1} are pairwise distinct.\nLet X = A_{i, j}, then A_{X, j} \\neq i always holds.\nTask Constraint: 2 <= N <= 100\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: If there exists no way to be successful in the challenge, print -1.\nIf there exists a way to be successful in the challenge, print any such way in the following format:\nA_{1,1} A_{1,2} . . . A_{1, N-1}\nA_{2,1} A_{2,2} . . . A_{2, N-1}\n:\nA_{N, 1} A_{N, 2} . . . A_{N, N-1}\n\nwhere A_{i, j} is the index of the person that the person numbered i looks at during the j-th second.\nTask Samples: input: 7 output: 2 3 4 5 6 7\n5 3 1 6 4 7\n2 7 4 1 5 6\n2 1 7 5 3 6\n1 4 3 7 6 2\n2 5 7 3 4 1\n2 6 1 4 5 3\ninput: 2 output: -1\n\n" }, { "title": "", "content": "Problem Statement We have an N*N checkerboard.\nFrom the square at the upper left corner, a square that is i squares to the right and j squares below is denoted as (i, j). Particularly, the square at the upper left corner is denoted as (0,0).\nEach square (i, j) such that i+j is even, is colored black, and the other squares are colored white.\nWe will satisfy the following condition by painting some of the white squares:\n\nAny black square can be reached from square (0,0) by repeatedly moving to a black square that shares a side with the current square.\n\nAchieve the objective by painting at most 170000 squares black. judging: Judging The output is considered correct only if all of the following conditions are satisfied:\n\n0 <= K <= 170000\n0 <= x_i, y_i <= N-1\nFor each i, x_i + y_i is odd.\nIf i \\neq j, then (x_i, y_i) \\neq (x_j, y_j).\nThe condition in the statement is satisfied by painting all specified squares.", "constraint": "1 <= N <= 1,000", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "Print the squares to paint in the following format:\nK\nx_1 y_1\nx_2 y_2\n:\nx_K y_K\n\nThis means that a total of K squares are painted black, the i-th of which is (x_i, y_i).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 output: 1\n1 0", "input: 4 output: 3\n0 1\n2 1\n2 3"], "Pid": "p03897", "ProblemText": "Task Description: Problem Statement We have an N*N checkerboard.\nFrom the square at the upper left corner, a square that is i squares to the right and j squares below is denoted as (i, j). Particularly, the square at the upper left corner is denoted as (0,0).\nEach square (i, j) such that i+j is even, is colored black, and the other squares are colored white.\nWe will satisfy the following condition by painting some of the white squares:\n\nAny black square can be reached from square (0,0) by repeatedly moving to a black square that shares a side with the current square.\n\nAchieve the objective by painting at most 170000 squares black. judging: Judging The output is considered correct only if all of the following conditions are satisfied:\n\n0 <= K <= 170000\n0 <= x_i, y_i <= N-1\nFor each i, x_i + y_i is odd.\nIf i \\neq j, then (x_i, y_i) \\neq (x_j, y_j).\nThe condition in the statement is satisfied by painting all specified squares.\nTask Constraint: 1 <= N <= 1,000\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: Print the squares to paint in the following format:\nK\nx_1 y_1\nx_2 y_2\n:\nx_K y_K\n\nThis means that a total of K squares are painted black, the i-th of which is (x_i, y_i).\nTask Samples: input: 2 output: 1\n1 0\ninput: 4 output: 3\n0 1\n2 1\n2 3\n\n" }, { "title": "", "content": "Problem Statement There is a tree with N vertices, numbered 1 through N.\nThe i-th of the N-1 edges connects the vertices p_i and q_i.\nAmong the sequences of distinct vertices v_1, v_2, . . . , v_M that satisfy the following condition, find the maximum value of M.\n\nFor every 1 <= i < M, the path connecting the vertices v_i and v_{i+1} do not contain any vertex in v, except for v_i and v_{i+1}.", "constraint": "2 <= N <= 10^5\n1 <= p_i, q_i <= N\nThe given graph is a tree.", "input": "Input The input is given from Standard Input in the following format:\nN\np_1 q_1\np_2 q_2\n:\np_{N-1} q_{N-1}", "output": "Print the maximum value of M, the number of elements, among the sequences of vertices that satisfy the condition.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2\n2 3\n2 4 output: 3", "input: 10\n7 9\n1 2\n6 4\n8 1\n3 7\n6 5\n2 10\n9 6\n2 6 output: 8"], "Pid": "p03898", "ProblemText": "Task Description: Problem Statement There is a tree with N vertices, numbered 1 through N.\nThe i-th of the N-1 edges connects the vertices p_i and q_i.\nAmong the sequences of distinct vertices v_1, v_2, . . . , v_M that satisfy the following condition, find the maximum value of M.\n\nFor every 1 <= i < M, the path connecting the vertices v_i and v_{i+1} do not contain any vertex in v, except for v_i and v_{i+1}.\nTask Constraint: 2 <= N <= 10^5\n1 <= p_i, q_i <= N\nThe given graph is a tree.\nTask Input: Input The input is given from Standard Input in the following format:\nN\np_1 q_1\np_2 q_2\n:\np_{N-1} q_{N-1}\nTask Output: Print the maximum value of M, the number of elements, among the sequences of vertices that satisfy the condition.\nTask Samples: input: 4\n1 2\n2 3\n2 4 output: 3\ninput: 10\n7 9\n1 2\n6 4\n8 1\n3 7\n6 5\n2 10\n9 6\n2 6 output: 8\n\n" }, { "title": "", "content": "Problem Statement There are N panels arranged in a row in Takahashi's house, numbered 1 through N. The i-th panel has a number A_i written on it. Takahashi is playing by throwing balls at these panels.\nTakahashi threw a ball K times. Let the panel hit by a boll in the i-th throw be panel p_i. He set the score for the i-th throw as i * A_{p_i}.\nHe was about to calculate the total score for his throws, when he realized that he forgot the panels hit by balls, p_1, p_2, . . . , p_K. The only fact he remembers is that for every i (1 <= i <= K-1), 1 <= p_{i+1}-p_i <= M holds. Based on this fact, find the maximum possible total score for his throws. partial scores: Partial Scores\nIn the test set worth 100 points, M = N.\nIn the test set worth another 200 points, N <= 300 and K <= 30.\nIn the test set worth another 300 points, K <= 30.", "constraint": "1 <= M <= N <= 100,000\n1 <= K <= min(300,N)\n1 <= A_i <= 10^{9}", "input": "Input The input is given from Standard Input in the following format:\nN M K\nA_1 A_2 … A_N", "output": "Print the maximum possible total score for Takahashi's throws.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 2 3\n10 2 8 10 2 output: 56\n\nThe total score is maximized when panels 1,3 and 4 are hit, in this order.", "input: 5 5 2\n5 2 10 5 9 output: 28\n\nThis case satisfies the additional constraint M = N for a partial score.", "input: 10 3 5\n3 7 2 6 9 4 8 5 1 1000000000 output: 5000000078"], "Pid": "p03899", "ProblemText": "Task Description: Problem Statement There are N panels arranged in a row in Takahashi's house, numbered 1 through N. The i-th panel has a number A_i written on it. Takahashi is playing by throwing balls at these panels.\nTakahashi threw a ball K times. Let the panel hit by a boll in the i-th throw be panel p_i. He set the score for the i-th throw as i * A_{p_i}.\nHe was about to calculate the total score for his throws, when he realized that he forgot the panels hit by balls, p_1, p_2, . . . , p_K. The only fact he remembers is that for every i (1 <= i <= K-1), 1 <= p_{i+1}-p_i <= M holds. Based on this fact, find the maximum possible total score for his throws. partial scores: Partial Scores\nIn the test set worth 100 points, M = N.\nIn the test set worth another 200 points, N <= 300 and K <= 30.\nIn the test set worth another 300 points, K <= 30.\nTask Constraint: 1 <= M <= N <= 100,000\n1 <= K <= min(300,N)\n1 <= A_i <= 10^{9}\nTask Input: Input The input is given from Standard Input in the following format:\nN M K\nA_1 A_2 … A_N\nTask Output: Print the maximum possible total score for Takahashi's throws.\nTask Samples: input: 5 2 3\n10 2 8 10 2 output: 56\n\nThe total score is maximized when panels 1,3 and 4 are hit, in this order.\ninput: 5 5 2\n5 2 10 5 9 output: 28\n\nThis case satisfies the additional constraint M = N for a partial score.\ninput: 10 3 5\n3 7 2 6 9 4 8 5 1 1000000000 output: 5000000078\n\n" }, { "title": "", "content": "Problem Statement Takahashi found an integer sequence (A_1, A_2, . . . , A_N) with N terms. Since it was too heavy to carry, he decided to compress it into a single integer.\nThe compression takes place in N-1 steps, each of which shorten the length of the sequence by 1. Let S be a string describing the steps, and the sequence on which the i-th step is performed be (a_1, a_2, . . . , a_K), then the i-th step will be as follows:\n\nWhen the i-th character in S is M, let b_i = max(a_i, a_{i+1}) (1 <= i <= K-1), and replace the current sequence by (b_1, b_2, . . . , b_{K-1}).\nWhen the i-th character in S is m, let b_i = min(a_i, a_{i+1}) (1 <= i <= K-1), and replace the current sequence by (b_1, b_2, . . . , b_{K-1}).\n\nTakahashi decided the steps S, but he is too tired to carry out the compression. On behalf of him, find the single integer obtained from the compression. partial scores: Partial Scores\nIn the test set worth 400 points, there exists i (1 <= i < N-1) such that the first i characters in S are M, and the remaining characters are m, that is, S is in the form M. . . Mm. . . m.\nIn the test set worth 800 points, the odd-number-th characters in S are M, and the even-number-th characters are m, that is, S is in the form Mm Mm Mm. . . .", "constraint": "2 <= N <= 10^5\n1 <= A_i <= N\nS consists of N-1 characters.\nEach character in S is either M or m.", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 … A_N\nS", "output": "Print the single integer obtained from the compression.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 2 3 4\nMmM output: 3\n\nThe initial sequence ( 1 , 2 , 3 , 4 ) is compressed as follows:\n\nAfter the first step, the sequence is ( 2 , 3 , 4 ).\nAfter the second step, the sequence is ( 2 , 3 ).\nAfter the third step, the sequence is ( 3 ).\n\nThus, the single integer obtained from the compression is 3.", "input: 5\n3 4 2 2 1\nMMmm output: 2", "input: 10\n1 8 7 6 8 5 2 2 6 1\nMmmmmMMMm output: 5", "input: 20\n12 7 16 8 7 19 8 19 20 11 7 13 20 3 4 11 19 11 15 5\nmMMmmmMMMMMMmMmmmMM output: 11"], "Pid": "p03900", "ProblemText": "Task Description: Problem Statement Takahashi found an integer sequence (A_1, A_2, . . . , A_N) with N terms. Since it was too heavy to carry, he decided to compress it into a single integer.\nThe compression takes place in N-1 steps, each of which shorten the length of the sequence by 1. Let S be a string describing the steps, and the sequence on which the i-th step is performed be (a_1, a_2, . . . , a_K), then the i-th step will be as follows:\n\nWhen the i-th character in S is M, let b_i = max(a_i, a_{i+1}) (1 <= i <= K-1), and replace the current sequence by (b_1, b_2, . . . , b_{K-1}).\nWhen the i-th character in S is m, let b_i = min(a_i, a_{i+1}) (1 <= i <= K-1), and replace the current sequence by (b_1, b_2, . . . , b_{K-1}).\n\nTakahashi decided the steps S, but he is too tired to carry out the compression. On behalf of him, find the single integer obtained from the compression. partial scores: Partial Scores\nIn the test set worth 400 points, there exists i (1 <= i < N-1) such that the first i characters in S are M, and the remaining characters are m, that is, S is in the form M. . . Mm. . . m.\nIn the test set worth 800 points, the odd-number-th characters in S are M, and the even-number-th characters are m, that is, S is in the form Mm Mm Mm. . . .\nTask Constraint: 2 <= N <= 10^5\n1 <= A_i <= N\nS consists of N-1 characters.\nEach character in S is either M or m.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 … A_N\nS\nTask Output: Print the single integer obtained from the compression.\nTask Samples: input: 4\n1 2 3 4\nMmM output: 3\n\nThe initial sequence ( 1 , 2 , 3 , 4 ) is compressed as follows:\n\nAfter the first step, the sequence is ( 2 , 3 , 4 ).\nAfter the second step, the sequence is ( 2 , 3 ).\nAfter the third step, the sequence is ( 3 ).\n\nThus, the single integer obtained from the compression is 3.\ninput: 5\n3 4 2 2 1\nMMmm output: 2\ninput: 10\n1 8 7 6 8 5 2 2 6 1\nMmmmmMMMm output: 5\ninput: 20\n12 7 16 8 7 19 8 19 20 11 7 13 20 3 4 11 19 11 15 5\nmMMmmmMMMMMMmMmmmMM output: 11\n\n" }, { "title": "", "content": "Problem Statement Aoki is in search of Takahashi, who is missing in a one-dimentional world.\nInitially, the coordinate of Aoki is 0, and the coordinate of Takahashi is known to be x, but his coordinate afterwards cannot be known to Aoki.\nTime is divided into turns. In each turn, Aoki and Takahashi take the following actions simultaneously:\nLet the current coordinate of Aoki be a, then Aoki moves to a coordinate he selects from a-1, a and a+1.\nLet the current coordinate of Takahashi be b, then Takahashi moves to the coordinate b-1 with probability of p percent, and moves to the coordinate b+1 with probability of 100-p percent.\nWhen the coordinates of Aoki and Takahashi coincide, Aoki can find Takahashi.\nWhen they pass by each other, Aoki cannot find Takahashi.\nAoki wants to minimize the expected number of turns taken until he finds Takahashi. Find the minimum possible expected number of turns. partial scores: Partial Scores\nIn the test set worth 200 points, p=100.\nIn the test set worth 300 points, x <= 10.", "constraint": "1 <= x <= 1,000,000,000\n1 <= p <= 100\nx and p are integers.", "input": "Input The input is given from Standard Input in the following format:\nx\np", "output": "Print the minimum possible expected number of turns.\nThe output is considered correct if the absolute or relative error is at most 10^{-6}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n100 output: 2.0000000\n\nTakahashi always moves by -1.\nThus, by moving to the coordinate 1 in the 1-st turn and staying at that position in the 2-nd turn, Aoki can find Takahashi in 2 turns.", "input: 6\n40 output: 7.5000000", "input: 101\n80 output: 63.7500000"], "Pid": "p03901", "ProblemText": "Task Description: Problem Statement Aoki is in search of Takahashi, who is missing in a one-dimentional world.\nInitially, the coordinate of Aoki is 0, and the coordinate of Takahashi is known to be x, but his coordinate afterwards cannot be known to Aoki.\nTime is divided into turns. In each turn, Aoki and Takahashi take the following actions simultaneously:\nLet the current coordinate of Aoki be a, then Aoki moves to a coordinate he selects from a-1, a and a+1.\nLet the current coordinate of Takahashi be b, then Takahashi moves to the coordinate b-1 with probability of p percent, and moves to the coordinate b+1 with probability of 100-p percent.\nWhen the coordinates of Aoki and Takahashi coincide, Aoki can find Takahashi.\nWhen they pass by each other, Aoki cannot find Takahashi.\nAoki wants to minimize the expected number of turns taken until he finds Takahashi. Find the minimum possible expected number of turns. partial scores: Partial Scores\nIn the test set worth 200 points, p=100.\nIn the test set worth 300 points, x <= 10.\nTask Constraint: 1 <= x <= 1,000,000,000\n1 <= p <= 100\nx and p are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nx\np\nTask Output: Print the minimum possible expected number of turns.\nThe output is considered correct if the absolute or relative error is at most 10^{-6}.\nTask Samples: input: 3\n100 output: 2.0000000\n\nTakahashi always moves by -1.\nThus, by moving to the coordinate 1 in the 1-st turn and staying at that position in the 2-nd turn, Aoki can find Takahashi in 2 turns.\ninput: 6\n40 output: 7.5000000\ninput: 101\n80 output: 63.7500000\n\n" }, { "title": "", "content": "Problem Statement Takahashi is a magician. He can cast a spell on an integer sequence (a_1, a_2, . . . , a_M) with M terms, to turn it into another sequence (s_1, s_2, . . . , s_M), where s_i is the sum of the first i terms in the original sequence.\nOne day, he received N integer sequences, each with M terms, and named those sequences A_1, A_2, . . . , A_N. He will try to cast the spell on those sequences so that A_1 < A_2 < . . . < A_N will hold, where sequences are compared lexicographically.\nLet the action of casting the spell on a selected sequence be one cast of the spell. Find the minimum number of casts of the spell he needs to perform in order to achieve his objective.\nHere, for two sequences a = (a_1, a_2, . . . , a_M), b = (b_1, b_2, . . . , b_M) with M terms each, a < b holds lexicographically if and only if there exists i (1 <= i <= M) such that a_j = b_j (1 <= j < i) and a_i < b_i. partial scores: Partial Scores\nIn the test set worth 200 points, Takahashi can achieve his objective by at most 10^4 casts of the spell, while keeping the values of all terms at most 10^9.\nIn the test set worth another 800 points, A_{(i, j)} <= 80.", "constraint": "1 <= N <= 10^3\n1 <= M <= 10^3\nLet the j-th term in A_i be A_{(i,j)}, then 1 <= A_{(i,j)} <= 10^9.", "input": "Input The input is given from Standard Input in the following format:\nN M\nA_{(1,1)} A_{(1,2)} … A_{(1, M)}\nA_{(2,1)} A_{(2,2)} … A_{(2, M)}\n:\nA_{(N, 1)} A_{(N, 2)} … A_{(N, M)}", "output": "Print the minimum number of casts of the spell Takahashi needs to perform. If he cannot achieve his objective, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n2 3 1\n2 1 2\n2 6 3 output: 1\n\nTakahashi can achieve his objective by casting the spell on A_2 once to turn it into (2 , 3 , 5).", "input: 3 3\n3 2 10\n10 5 4\n9 1 9 output: -1\n\nIn this case, Takahashi cannot achieve his objective by casting the spell any number of times.", "input: 5 5\n2 6 5 6 9\n2 6 4 9 10\n2 6 8 6 7\n2 1 7 3 8\n2 1 4 8 3 output: 11"], "Pid": "p03902", "ProblemText": "Task Description: Problem Statement Takahashi is a magician. He can cast a spell on an integer sequence (a_1, a_2, . . . , a_M) with M terms, to turn it into another sequence (s_1, s_2, . . . , s_M), where s_i is the sum of the first i terms in the original sequence.\nOne day, he received N integer sequences, each with M terms, and named those sequences A_1, A_2, . . . , A_N. He will try to cast the spell on those sequences so that A_1 < A_2 < . . . < A_N will hold, where sequences are compared lexicographically.\nLet the action of casting the spell on a selected sequence be one cast of the spell. Find the minimum number of casts of the spell he needs to perform in order to achieve his objective.\nHere, for two sequences a = (a_1, a_2, . . . , a_M), b = (b_1, b_2, . . . , b_M) with M terms each, a < b holds lexicographically if and only if there exists i (1 <= i <= M) such that a_j = b_j (1 <= j < i) and a_i < b_i. partial scores: Partial Scores\nIn the test set worth 200 points, Takahashi can achieve his objective by at most 10^4 casts of the spell, while keeping the values of all terms at most 10^9.\nIn the test set worth another 800 points, A_{(i, j)} <= 80.\nTask Constraint: 1 <= N <= 10^3\n1 <= M <= 10^3\nLet the j-th term in A_i be A_{(i,j)}, then 1 <= A_{(i,j)} <= 10^9.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nA_{(1,1)} A_{(1,2)} … A_{(1, M)}\nA_{(2,1)} A_{(2,2)} … A_{(2, M)}\n:\nA_{(N, 1)} A_{(N, 2)} … A_{(N, M)}\nTask Output: Print the minimum number of casts of the spell Takahashi needs to perform. If he cannot achieve his objective, print -1 instead.\nTask Samples: input: 3 3\n2 3 1\n2 1 2\n2 6 3 output: 1\n\nTakahashi can achieve his objective by casting the spell on A_2 once to turn it into (2 , 3 , 5).\ninput: 3 3\n3 2 10\n10 5 4\n9 1 9 output: -1\n\nIn this case, Takahashi cannot achieve his objective by casting the spell any number of times.\ninput: 5 5\n2 6 5 6 9\n2 6 4 9 10\n2 6 8 6 7\n2 1 7 3 8\n2 1 4 8 3 output: 11\n\n" }, { "title": "", "content": "Problem Statement Takahashi found an undirected connected graph with N vertices and M edges. The vertices are numbered 1 through N. The i-th edge connects vertices a_i and b_i, and has a weight of c_i.\nHe will play Q rounds of a game using this graph. In the i-th round, two vertices S_i and T_i are specified, and he will choose a subset of the edges such that any vertex can be reached from at least one of the vertices S_i or T_i by traversing chosen edges.\nFor each round, find the minimum possible total weight of the edges chosen by Takahashi. partial scores: Partial Scores\nIn the test set worth 200 points, Q = 1.\nIn the test set worth another 300 points, Q <= 3000.", "constraint": "1 <= N <= 4,000\n1 <= M <= 400,000\n1 <= Q <= 100,000\n1 <= a_i,b_i,S_i,T_i <= N\n1 <= c_i <= 10^{9}\na_i \\neq b_i\nS_i \\neq T_i\nThe given graph is connected.", "input": "Input The input is given from Standard Input in the following format:\nN M\na_1 b_1 c_1\na_2 b_2 c_2\n:\na_M b_M c_M\nQ\nS_1 T_1\nS_2 T_2\n:\nS_Q T_Q", "output": "Print Q lines. The i-th line should contain the minimum possible total weight of the edges chosen by Takahashi.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 3\n1 2 3\n2 3 4\n3 4 5\n2\n2 3\n1 4 output: 8\n7\n\nWe will examine each round:\n\nIn the 1-st round, choosing edges 1 and 3 achieves the minimum total weight of 8.\nIn the 2-nd round, choosing edges 1 and 2 achieves the minimum total weight of 7.", "input: 4 6\n1 3 5\n4 1 10\n2 4 6\n3 2 2\n3 4 5\n2 1 3\n1\n2 3 output: 8\n\nThis input satisfies the additional constraints for both partial scores."], "Pid": "p03903", "ProblemText": "Task Description: Problem Statement Takahashi found an undirected connected graph with N vertices and M edges. The vertices are numbered 1 through N. The i-th edge connects vertices a_i and b_i, and has a weight of c_i.\nHe will play Q rounds of a game using this graph. In the i-th round, two vertices S_i and T_i are specified, and he will choose a subset of the edges such that any vertex can be reached from at least one of the vertices S_i or T_i by traversing chosen edges.\nFor each round, find the minimum possible total weight of the edges chosen by Takahashi. partial scores: Partial Scores\nIn the test set worth 200 points, Q = 1.\nIn the test set worth another 300 points, Q <= 3000.\nTask Constraint: 1 <= N <= 4,000\n1 <= M <= 400,000\n1 <= Q <= 100,000\n1 <= a_i,b_i,S_i,T_i <= N\n1 <= c_i <= 10^{9}\na_i \\neq b_i\nS_i \\neq T_i\nThe given graph is connected.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\na_1 b_1 c_1\na_2 b_2 c_2\n:\na_M b_M c_M\nQ\nS_1 T_1\nS_2 T_2\n:\nS_Q T_Q\nTask Output: Print Q lines. The i-th line should contain the minimum possible total weight of the edges chosen by Takahashi.\nTask Samples: input: 4 3\n1 2 3\n2 3 4\n3 4 5\n2\n2 3\n1 4 output: 8\n7\n\nWe will examine each round:\n\nIn the 1-st round, choosing edges 1 and 3 achieves the minimum total weight of 8.\nIn the 2-nd round, choosing edges 1 and 2 achieves the minimum total weight of 7.\ninput: 4 6\n1 3 5\n4 1 10\n2 4 6\n3 2 2\n3 4 5\n2 1 3\n1\n2 3 output: 8\n\nThis input satisfies the additional constraints for both partial scores.\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of digits between 1 and 9, inclusive.\nYou will insert at most K commas (, ) into this string to separate it into multiple numbers.\nYour task is to minimize the maximum number among those produced by inserting commas. Find minimum possible such value. partial scores: Partial Scores\nIn the test set worth 100 points, |S| <= 2.\nIn the test set worth another 100 points, |S| <= 16.\nIn the test set worth another 200 points, |S| <= 100.\nIn the test set worth another 200 points, |S| <= 2,000.", "constraint": "0 <= K < |S| <= 100,000\nS consists of digits between 1 and 9, inclusive.", "input": "Input The input is given from Standard Input in the following format:\nK\nS", "output": "Print the minimum possible value.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n15267315 output: 315\n\nWhen the string is separated into 152,67 and 315, the maximum among these is 315, which is the minimum possible value.", "input: 0\n12456174517653111 output: 12456174517653111\n\n12456174517653111 itself is the answer.", "input: 8\n127356176351764127645176543176531763517635176531278461856198765816581726586715987216581 output: 5317635176"], "Pid": "p03904", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of digits between 1 and 9, inclusive.\nYou will insert at most K commas (, ) into this string to separate it into multiple numbers.\nYour task is to minimize the maximum number among those produced by inserting commas. Find minimum possible such value. partial scores: Partial Scores\nIn the test set worth 100 points, |S| <= 2.\nIn the test set worth another 100 points, |S| <= 16.\nIn the test set worth another 200 points, |S| <= 100.\nIn the test set worth another 200 points, |S| <= 2,000.\nTask Constraint: 0 <= K < |S| <= 100,000\nS consists of digits between 1 and 9, inclusive.\nTask Input: Input The input is given from Standard Input in the following format:\nK\nS\nTask Output: Print the minimum possible value.\nTask Samples: input: 2\n15267315 output: 315\n\nWhen the string is separated into 152,67 and 315, the maximum among these is 315, which is the minimum possible value.\ninput: 0\n12456174517653111 output: 12456174517653111\n\n12456174517653111 itself is the answer.\ninput: 8\n127356176351764127645176543176531763517635176531278461856198765816581726586715987216581 output: 5317635176\n\n" }, { "title": "", "content": "Problem Statement There is an undirected connected graph with N vertices numbered 1 through N.\nThe lengths of all edges in this graph are 1.\nIt is known that for each i (1<=i<=N), the distance between vertex 1 and vertex i is A_i, and the distance between vertex 2 and vertex i is B_i.\nDetermine whether there exists such a graph.\nIf it exists, find the minimum possible number of edges in it.", "constraint": "2<=N<=10^5\n0<=A_i,B_i<=N-1", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N", "output": "If there exists a graph satisfying the conditions, print the minimum possible number of edges in such a graph. Otherwise, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 1\n1 0\n1 1\n2 1 output: 4\n\nThe figure below shows two possible graphs. The graph on the right has fewer edges.", "input: 3\n0 1\n1 0\n2 2 output: -1\n\nSuch a graph does not exist."], "Pid": "p03905", "ProblemText": "Task Description: Problem Statement There is an undirected connected graph with N vertices numbered 1 through N.\nThe lengths of all edges in this graph are 1.\nIt is known that for each i (1<=i<=N), the distance between vertex 1 and vertex i is A_i, and the distance between vertex 2 and vertex i is B_i.\nDetermine whether there exists such a graph.\nIf it exists, find the minimum possible number of edges in it.\nTask Constraint: 2<=N<=10^5\n0<=A_i,B_i<=N-1\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nTask Output: If there exists a graph satisfying the conditions, print the minimum possible number of edges in such a graph. Otherwise, print -1.\nTask Samples: input: 4\n0 1\n1 0\n1 1\n2 1 output: 4\n\nThe figure below shows two possible graphs. The graph on the right has fewer edges.\ninput: 3\n0 1\n1 0\n2 2 output: -1\n\nSuch a graph does not exist.\n\n" }, { "title": "", "content": "Problem Statement The currency used in Takahashi Kingdom is Myon.\nThere are 1-, 10-, 100-, 1000- and 10000-Myon coins, and so forth. Formally, there are 10^n-Myon coins for any non-negative integer n.\nThere are N items being sold at Ex Store.\nThe price of the i-th (1<=i<=N) item is A_i Myon.\nTakahashi is going to buy some, at least one, possibly all, of these N items.\nHe hates receiving change, so he wants to bring coins to the store so that he can pay the total price without receiving change, no matter what items he chooses to buy.\nAlso, since coins are heavy, he wants to bring as few coins as possible.\nFind the minimum number of coins he must bring to the store. It can be assumed that he has an infinite supply of coins.", "constraint": "1<=N<=20,000\n1<=A_i<=10^{12}", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the minimum number of coins Takahashi must bring to the store, so that he can pay the total price without receiving change, no matter what items he chooses to buy.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n43 24 37 output: 16\n\nThere are seven possible total prices: 24,37,43,61,67,80, and 104.\nWith seven 1-Myon coins, eight 10-Myon coins and one 100-Myon coin, Takahashi can pay any of these without receiving change.", "input: 5\n49735011221 970534221705 411566391637 760836201000 563515091165 output: 105"], "Pid": "p03906", "ProblemText": "Task Description: Problem Statement The currency used in Takahashi Kingdom is Myon.\nThere are 1-, 10-, 100-, 1000- and 10000-Myon coins, and so forth. Formally, there are 10^n-Myon coins for any non-negative integer n.\nThere are N items being sold at Ex Store.\nThe price of the i-th (1<=i<=N) item is A_i Myon.\nTakahashi is going to buy some, at least one, possibly all, of these N items.\nHe hates receiving change, so he wants to bring coins to the store so that he can pay the total price without receiving change, no matter what items he chooses to buy.\nAlso, since coins are heavy, he wants to bring as few coins as possible.\nFind the minimum number of coins he must bring to the store. It can be assumed that he has an infinite supply of coins.\nTask Constraint: 1<=N<=20,000\n1<=A_i<=10^{12}\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the minimum number of coins Takahashi must bring to the store, so that he can pay the total price without receiving change, no matter what items he chooses to buy.\nTask Samples: input: 3\n43 24 37 output: 16\n\nThere are seven possible total prices: 24,37,43,61,67,80, and 104.\nWith seven 1-Myon coins, eight 10-Myon coins and one 100-Myon coin, Takahashi can pay any of these without receiving change.\ninput: 5\n49735011221 970534221705 411566391637 760836201000 563515091165 output: 105\n\n" }, { "title": "", "content": "Problem Statement There is an undirected connected graph with N vertices numbered 1 through N.\nThe lengths of all edges in this graph are 1.\nIt is known that for each i (1<=i<=N), the distance between vertex 1 and vertex i is A_i, and the distance between vertex 2 and vertex i is B_i.\nDetermine whether there exists such a graph.\nIf it exists, find the minimum possible number of edges in it.", "constraint": "2<=N<=10^5\n0<=A_i,B_i<=N-1", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N", "output": "If there exists a graph satisfying the conditions, print the minimum possible number of edges in such a graph. Otherwise, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 1\n1 0\n1 1\n2 1 output: 4\n\nThe figure below shows two possible graphs. The graph on the right has fewer edges.", "input: 3\n0 1\n1 0\n2 2 output: -1\n\nSuch a graph does not exist."], "Pid": "p03907", "ProblemText": "Task Description: Problem Statement There is an undirected connected graph with N vertices numbered 1 through N.\nThe lengths of all edges in this graph are 1.\nIt is known that for each i (1<=i<=N), the distance between vertex 1 and vertex i is A_i, and the distance between vertex 2 and vertex i is B_i.\nDetermine whether there exists such a graph.\nIf it exists, find the minimum possible number of edges in it.\nTask Constraint: 2<=N<=10^5\n0<=A_i,B_i<=N-1\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_N B_N\nTask Output: If there exists a graph satisfying the conditions, print the minimum possible number of edges in such a graph. Otherwise, print -1.\nTask Samples: input: 4\n0 1\n1 0\n1 1\n2 1 output: 4\n\nThe figure below shows two possible graphs. The graph on the right has fewer edges.\ninput: 3\n0 1\n1 0\n2 2 output: -1\n\nSuch a graph does not exist.\n\n" }, { "title": "", "content": "Problem Statement The currency used in Takahashi Kingdom is Myon.\nThere are 1-, 10-, 100-, 1000- and 10000-Myon coins, and so forth. Formally, there are 10^n-Myon coins for any non-negative integer n.\nThere are N items being sold at Ex Store.\nThe price of the i-th (1<=i<=N) item is A_i Myon.\nTakahashi is going to buy some, at least one, possibly all, of these N items.\nHe hates receiving change, so he wants to bring coins to the store so that he can pay the total price without receiving change, no matter what items he chooses to buy.\nAlso, since coins are heavy, he wants to bring as few coins as possible.\nFind the minimum number of coins he must bring to the store. It can be assumed that he has an infinite supply of coins.", "constraint": "1<=N<=20,000\n1<=A_i<=10^{12}", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N", "output": "Print the minimum number of coins Takahashi must bring to the store, so that he can pay the total price without receiving change, no matter what items he chooses to buy.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n43 24 37 output: 16\n\nThere are seven possible total prices: 24,37,43,61,67,80, and 104.\nWith seven 1-Myon coins, eight 10-Myon coins and one 100-Myon coin, Takahashi can pay any of these without receiving change.", "input: 5\n49735011221 970534221705 411566391637 760836201000 563515091165 output: 105"], "Pid": "p03908", "ProblemText": "Task Description: Problem Statement The currency used in Takahashi Kingdom is Myon.\nThere are 1-, 10-, 100-, 1000- and 10000-Myon coins, and so forth. Formally, there are 10^n-Myon coins for any non-negative integer n.\nThere are N items being sold at Ex Store.\nThe price of the i-th (1<=i<=N) item is A_i Myon.\nTakahashi is going to buy some, at least one, possibly all, of these N items.\nHe hates receiving change, so he wants to bring coins to the store so that he can pay the total price without receiving change, no matter what items he chooses to buy.\nAlso, since coins are heavy, he wants to bring as few coins as possible.\nFind the minimum number of coins he must bring to the store. It can be assumed that he has an infinite supply of coins.\nTask Constraint: 1<=N<=20,000\n1<=A_i<=10^{12}\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_N\nTask Output: Print the minimum number of coins Takahashi must bring to the store, so that he can pay the total price without receiving change, no matter what items he chooses to buy.\nTask Samples: input: 3\n43 24 37 output: 16\n\nThere are seven possible total prices: 24,37,43,61,67,80, and 104.\nWith seven 1-Myon coins, eight 10-Myon coins and one 100-Myon coin, Takahashi can pay any of these without receiving change.\ninput: 5\n49735011221 970534221705 411566391637 760836201000 563515091165 output: 105\n\n" }, { "title": "", "content": "Problem Statement There is a grid with H rows and W columns.\nThe square at the i-th row and j-th column contains a string S_{i, j} of length 5.\nThe rows are labeled with the numbers from 1 through H, and the columns are labeled with the uppercase English letters from A through the W-th letter of the alphabet.\n\nExactly one of the squares in the grid contains the string snuke. Find this square and report its location.\nFor example, the square at the 6-th row and 8-th column should be reported as H6.", "constraint": "1<=H, W<=26\nThe length of S_{i,j} is 5.\nS_{i,j} consists of lowercase English letters (a-z).\nExactly one of the given strings is equal to snuke.", "input": "Input The input is given from Standard Input in the following format:\nH W\nS_{1,1} S_{1,2} . . . S_{1, W}\nS_{2,1} S_{2,2} . . . S_{2, W}\n:\nS_{H, 1} S_{H, 2} . . . S_{H, W}", "output": "Print the labels of the row and the column of the square containing the string snuke, with no space inbetween.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15 10\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snuke snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake output: H6", "input: 1 1\nsnuke output: A1"], "Pid": "p03909", "ProblemText": "Task Description: Problem Statement There is a grid with H rows and W columns.\nThe square at the i-th row and j-th column contains a string S_{i, j} of length 5.\nThe rows are labeled with the numbers from 1 through H, and the columns are labeled with the uppercase English letters from A through the W-th letter of the alphabet.\n\nExactly one of the squares in the grid contains the string snuke. Find this square and report its location.\nFor example, the square at the 6-th row and 8-th column should be reported as H6.\nTask Constraint: 1<=H, W<=26\nThe length of S_{i,j} is 5.\nS_{i,j} consists of lowercase English letters (a-z).\nExactly one of the given strings is equal to snuke.\nTask Input: Input The input is given from Standard Input in the following format:\nH W\nS_{1,1} S_{1,2} . . . S_{1, W}\nS_{2,1} S_{2,2} . . . S_{2, W}\n:\nS_{H, 1} S_{H, 2} . . . S_{H, W}\nTask Output: Print the labels of the row and the column of the square containing the string snuke, with no space inbetween.\nTask Samples: input: 15 10\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snuke snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake output: H6\ninput: 1 1\nsnuke output: A1\n\n" }, { "title": "", "content": "Problem Statement The problem set at CODE FESTIVAL 20XX Finals consists of N problems.\nThe score allocated to the i-th (1<=i<=N) problem is i points.\nTakahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.\nAs problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.\nDetermine the set of problems that should be solved. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1<=N<=1000.\nAdditional 100 points will be awarded for passing the test set without additional constraints.", "constraint": "1<=N<=10^7", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "Output Among the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.\nIf there exists more than one such set, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 1\n3\n\nSolving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.", "input: 7 output: 1\n2\n4\n\nThe set \\{3,4\\} will also be accepted.", "input: 1 output: 1"], "Pid": "p03910", "ProblemText": "Task Description: Problem Statement The problem set at CODE FESTIVAL 20XX Finals consists of N problems.\nThe score allocated to the i-th (1<=i<=N) problem is i points.\nTakahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.\nAs problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.\nDetermine the set of problems that should be solved. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1<=N<=1000.\nAdditional 100 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 1<=N<=10^7\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: Output Among the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.\nIf there exists more than one such set, any of them will be accepted.\nTask Samples: input: 4 output: 1\n3\n\nSolving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.\ninput: 7 output: 1\n2\n4\n\nThe set \\{3,4\\} will also be accepted.\ninput: 1 output: 1\n\n" }, { "title": "", "content": "Problem Statement On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.\nFor CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.\nThe i-th (1<=i<=N) participant can speak K_i languages numbered L_{i, 1}, L_{i, 2}, . . . , L_{i, {}K_i}.\nTwo participants A and B can communicate with each other if and only if one of the following conditions is satisfied:\n\nThere exists a language that both A and B can speak.\nThere exists a participant X that both A and B can communicate with.\n\nDetermine whether all N participants can communicate with all other participants. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying the following: N<=1000, M<=1000 and (The sum of all K_i)<=1000.\nAdditional 200 points will be awarded for passing the test set without additional constraints.", "constraint": "2<=N<=10^5\n1<=M<=10^5\n1<=K_i<=M\n(The sum of all K_i)<=10^5\n1<=L_{i,j}<=M\nL_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.", "input": "Input The input is given from Standard Input in the following format:\nN M\nK_1 L_{1,1} L_{1,2} . . . L_{1, {}K_1}\nK_2 L_{2,1} L_{2,2} . . . L_{2, {}K_2}\n:\nK_N L_{N, 1} L_{N, 2} . . . L_{N, {}K_N}", "output": "If all N participants can communicate with all other participants, print YES. Otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n3 1 2 3\n2 4 2\n2 4 6\n1 6 output: YES\n\nAny two participants can communicate with each other, as follows:\n\nParticipants 1 and 2: both can speak language 2.\nParticipants 2 and 3: both can speak language 4.\nParticipants 1 and 3: both can communicate with participant 2.\nParticipants 3 and 4: both can speak language 6.\nParticipants 2 and 4: both can communicate with participant 3.\nParticipants 1 and 4: both can communicate with participant 2.\n\nNote that there can be languages spoken by no participant.", "input: 4 4\n2 1 2\n2 1 2\n1 3\n2 4 3 output: NO\n\nFor example, participants 1 and 3 cannot communicate with each other."], "Pid": "p03911", "ProblemText": "Task Description: Problem Statement On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.\nFor CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.\nThe i-th (1<=i<=N) participant can speak K_i languages numbered L_{i, 1}, L_{i, 2}, . . . , L_{i, {}K_i}.\nTwo participants A and B can communicate with each other if and only if one of the following conditions is satisfied:\n\nThere exists a language that both A and B can speak.\nThere exists a participant X that both A and B can communicate with.\n\nDetermine whether all N participants can communicate with all other participants. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying the following: N<=1000, M<=1000 and (The sum of all K_i)<=1000.\nAdditional 200 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 2<=N<=10^5\n1<=M<=10^5\n1<=K_i<=M\n(The sum of all K_i)<=10^5\n1<=L_{i,j}<=M\nL_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nK_1 L_{1,1} L_{1,2} . . . L_{1, {}K_1}\nK_2 L_{2,1} L_{2,2} . . . L_{2, {}K_2}\n:\nK_N L_{N, 1} L_{N, 2} . . . L_{N, {}K_N}\nTask Output: If all N participants can communicate with all other participants, print YES. Otherwise, print NO.\nTask Samples: input: 4 6\n3 1 2 3\n2 4 2\n2 4 6\n1 6 output: YES\n\nAny two participants can communicate with each other, as follows:\n\nParticipants 1 and 2: both can speak language 2.\nParticipants 2 and 3: both can speak language 4.\nParticipants 1 and 3: both can communicate with participant 2.\nParticipants 3 and 4: both can speak language 6.\nParticipants 2 and 4: both can communicate with participant 3.\nParticipants 1 and 4: both can communicate with participant 2.\n\nNote that there can be languages spoken by no participant.\ninput: 4 4\n2 1 2\n2 1 2\n1 3\n2 4 3 output: NO\n\nFor example, participants 1 and 3 cannot communicate with each other.\n\n" }, { "title": "", "content": "Problem Statement Takahashi is playing with N cards.\nThe i-th card has an integer X_i on it.\nTakahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:\n\nThe integers on the two cards are the same.\nThe sum of the integers on the two cards is a multiple of M.\n\nFind the maximum number of pairs that can be created.\nNote that a card cannot be used in more than one pair.", "constraint": "2<=N<=10^5\n1<=M<=10^5\n1<=X_i<=10^5", "input": "Input The input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_N", "output": "Print the maximum number of pairs that can be created.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 5\n3 1 4 1 5 9 2 output: 3\n\nThree pairs (3,2), (1,4) and (1,9) can be created.\nIt is possible to create pairs (3,2) and (1,1), but the number of pairs is not maximized with this.", "input: 15 10\n1 5 6 10 11 11 11 20 21 25 25 26 99 99 99 output: 6"], "Pid": "p03912", "ProblemText": "Task Description: Problem Statement Takahashi is playing with N cards.\nThe i-th card has an integer X_i on it.\nTakahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:\n\nThe integers on the two cards are the same.\nThe sum of the integers on the two cards is a multiple of M.\n\nFind the maximum number of pairs that can be created.\nNote that a card cannot be used in more than one pair.\nTask Constraint: 2<=N<=10^5\n1<=M<=10^5\n1<=X_i<=10^5\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_N\nTask Output: Print the maximum number of pairs that can be created.\nTask Samples: input: 7 5\n3 1 4 1 5 9 2 output: 3\n\nThree pairs (3,2), (1,4) and (1,9) can be created.\nIt is possible to create pairs (3,2) and (1,1), but the number of pairs is not maximized with this.\ninput: 15 10\n1 5 6 10 11 11 11 20 21 25 25 26 99 99 99 output: 6\n\n" }, { "title": "", "content": "Problem Statement Rng is baking cookies.\nInitially, he can bake one cookie per second.\nHe can also eat the cookies baked by himself.\nWhen there are x cookies not yet eaten, he can choose to eat all those cookies. After he finishes eating those cookies, the number of cookies he can bake per second becomes x. Note that a cookie always needs to be baked for 1 second, that is, he cannot bake a cookie in 1/x seconds when x > 1.\nWhen he choose to eat the cookies, he must eat all of them; he cannot choose to eat only part of them.\nIt takes him A seconds to eat the cookies regardless of how many, during which no cookies can be baked.\nHe wants to give N cookies to Grandma.\nFind the shortest time needed to produce at least N cookies not yet eaten. partial score: Partial Score\n500 points will be awarded for passing the test set satisfying N<=10^6 and A<=10^6.\nAdditional 500 points will be awarded for passing the test set without additional constraints.", "constraint": "1<=N<=10^{12}\n0<=A<=10^{12}\nA is an integer.", "input": "Input The input is given from Standard Input in the following format:\nN A", "output": "Print the shortest time needed to produce at least N cookies not yet eaten.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 1 output: 7\n\nIt is possible to produce 8 cookies in 7 seconds, as follows:\n\nAfter 1 second: 1 cookie is done.\nAfter 2 seconds: 1 more cookie is done, totaling 2. Now, Rng starts eating those 2 cookies.\nAfter 3 seconds: He finishes eating the cookies, and he can now bake 2 cookies per second.\nAfter 4 seconds: 2 cookies are done.\nAfter 5 seconds: 2 more cookies are done, totaling 4.\nAfter 6 seconds: 2 more cookies are done, totaling 6.\nAfter 7 seconds: 2 more cookies are done, totaling 8.", "input: 1000000000000 1000000000000 output: 1000000000000"], "Pid": "p03913", "ProblemText": "Task Description: Problem Statement Rng is baking cookies.\nInitially, he can bake one cookie per second.\nHe can also eat the cookies baked by himself.\nWhen there are x cookies not yet eaten, he can choose to eat all those cookies. After he finishes eating those cookies, the number of cookies he can bake per second becomes x. Note that a cookie always needs to be baked for 1 second, that is, he cannot bake a cookie in 1/x seconds when x > 1.\nWhen he choose to eat the cookies, he must eat all of them; he cannot choose to eat only part of them.\nIt takes him A seconds to eat the cookies regardless of how many, during which no cookies can be baked.\nHe wants to give N cookies to Grandma.\nFind the shortest time needed to produce at least N cookies not yet eaten. partial score: Partial Score\n500 points will be awarded for passing the test set satisfying N<=10^6 and A<=10^6.\nAdditional 500 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 1<=N<=10^{12}\n0<=A<=10^{12}\nA is an integer.\nTask Input: Input The input is given from Standard Input in the following format:\nN A\nTask Output: Print the shortest time needed to produce at least N cookies not yet eaten.\nTask Samples: input: 8 1 output: 7\n\nIt is possible to produce 8 cookies in 7 seconds, as follows:\n\nAfter 1 second: 1 cookie is done.\nAfter 2 seconds: 1 more cookie is done, totaling 2. Now, Rng starts eating those 2 cookies.\nAfter 3 seconds: He finishes eating the cookies, and he can now bake 2 cookies per second.\nAfter 4 seconds: 2 cookies are done.\nAfter 5 seconds: 2 more cookies are done, totaling 4.\nAfter 6 seconds: 2 more cookies are done, totaling 6.\nAfter 7 seconds: 2 more cookies are done, totaling 8.\ninput: 1000000000000 1000000000000 output: 1000000000000\n\n" }, { "title": "", "content": "Problem Statement There are N towns in Takahashi Kingdom. They are conveniently numbered 1 through N.\nTakahashi the king is planning to go on a tour of inspection for M days. He will determine a sequence of towns c, and visit town c_i on the i-th day. That is, on the i-th day, he will travel from his current location to town c_i. If he is already at town c_i, he will stay at that town. His location just before the beginning of the tour is town 1, the capital. The tour ends at town c_M, without getting back to the capital. \nThe problem is that there is no paved road in this kingdom. He decided to resolve this issue by paving the road himself while traveling. When he travels from town a to town b, there will be a newly paved one-way road from town a to town b.\nSince he cares for his people, he wants the following condition to be satisfied after his tour is over: \"it is possible to travel from any town to any other town by traversing roads paved by him\". How many sequences of towns c satisfy this condition?", "constraint": "2<=N<=300\n1<=M<=300", "input": "Input The input is given from Standard Input in the following format:\nN M", "output": "Print the number of sequences of towns satisfying the condition, modulo 1000000007 (=10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 output: 2\n\nAs shown below, the condition is satisfied only when c = (2,3,1) or c = (3,2,1). Sequences such as c = (2,3,2), c = (2,1,3), c = (1,2,2) do not satisfy the condition.", "input: 150 300 output: 734286322", "input: 300 150 output: 0"], "Pid": "p03914", "ProblemText": "Task Description: Problem Statement There are N towns in Takahashi Kingdom. They are conveniently numbered 1 through N.\nTakahashi the king is planning to go on a tour of inspection for M days. He will determine a sequence of towns c, and visit town c_i on the i-th day. That is, on the i-th day, he will travel from his current location to town c_i. If he is already at town c_i, he will stay at that town. His location just before the beginning of the tour is town 1, the capital. The tour ends at town c_M, without getting back to the capital. \nThe problem is that there is no paved road in this kingdom. He decided to resolve this issue by paving the road himself while traveling. When he travels from town a to town b, there will be a newly paved one-way road from town a to town b.\nSince he cares for his people, he wants the following condition to be satisfied after his tour is over: \"it is possible to travel from any town to any other town by traversing roads paved by him\". How many sequences of towns c satisfy this condition?\nTask Constraint: 2<=N<=300\n1<=M<=300\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of sequences of towns satisfying the condition, modulo 1000000007 (=10^9+7).\nTask Samples: input: 3 3 output: 2\n\nAs shown below, the condition is satisfied only when c = (2,3,1) or c = (3,2,1). Sequences such as c = (2,3,2), c = (2,1,3), c = (1,2,2) do not satisfy the condition.\ninput: 150 300 output: 734286322\ninput: 300 150 output: 0\n\n" }, { "title": "", "content": "Problem Statement We have a graph with N vertices, numbered 0 through N-1. Edges are yet to be added.\nWe will process Q queries to add edges.\nIn the i-th (1<=i<=Q) query, three integers A_i, B_i and C_i will be given, and we will add infinitely many edges to the graph as follows:\n\nThe two vertices numbered A_i and B_i will be connected by an edge with a weight of C_i.\nThe two vertices numbered B_i and A_i+1 will be connected by an edge with a weight of C_i+1.\nThe two vertices numbered A_i+1 and B_i+1 will be connected by an edge with a weight of C_i+2.\nThe two vertices numbered B_i+1 and A_i+2 will be connected by an edge with a weight of C_i+3.\nThe two vertices numbered A_i+2 and B_i+2 will be connected by an edge with a weight of C_i+4.\nThe two vertices numbered B_i+2 and A_i+3 will be connected by an edge with a weight of C_i+5.\nThe two vertices numbered A_i+3 and B_i+3 will be connected by an edge with a weight of C_i+6.\n. . .\n\nHere, consider the indices of the vertices modulo N.\nFor example, the vertice numbered N is the one numbered 0, and the vertice numbered 2N-1 is the one numbered N-1.\nThe figure below shows the first seven edges added when N=16, A_i=7, B_i=14, C_i=1:\n\nAfter processing all the queries, find the total weight of the edges contained in a minimum spanning tree of the graph.", "constraint": "2<=N<=200,000\n1<=Q<=200,000\n0<=A_i,B_i<=N-1\n1<=C_i<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN Q\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_Q B_Q C_Q", "output": "Print the total weight of the edges contained in a minimum spanning tree of the graph.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 1\n5 2 1 output: 21\n\nThe figure below shows the minimum spanning tree of the graph:\n\nNote that there can be multiple edges connecting the same pair of vertices.", "input: 2 1\n0 0 1000000000 output: 1000000001\n\nAlso note that there can be self-loops.", "input: 5 3\n0 1 10\n0 2 10\n0 4 10 output: 42"], "Pid": "p03915", "ProblemText": "Task Description: Problem Statement We have a graph with N vertices, numbered 0 through N-1. Edges are yet to be added.\nWe will process Q queries to add edges.\nIn the i-th (1<=i<=Q) query, three integers A_i, B_i and C_i will be given, and we will add infinitely many edges to the graph as follows:\n\nThe two vertices numbered A_i and B_i will be connected by an edge with a weight of C_i.\nThe two vertices numbered B_i and A_i+1 will be connected by an edge with a weight of C_i+1.\nThe two vertices numbered A_i+1 and B_i+1 will be connected by an edge with a weight of C_i+2.\nThe two vertices numbered B_i+1 and A_i+2 will be connected by an edge with a weight of C_i+3.\nThe two vertices numbered A_i+2 and B_i+2 will be connected by an edge with a weight of C_i+4.\nThe two vertices numbered B_i+2 and A_i+3 will be connected by an edge with a weight of C_i+5.\nThe two vertices numbered A_i+3 and B_i+3 will be connected by an edge with a weight of C_i+6.\n. . .\n\nHere, consider the indices of the vertices modulo N.\nFor example, the vertice numbered N is the one numbered 0, and the vertice numbered 2N-1 is the one numbered N-1.\nThe figure below shows the first seven edges added when N=16, A_i=7, B_i=14, C_i=1:\n\nAfter processing all the queries, find the total weight of the edges contained in a minimum spanning tree of the graph.\nTask Constraint: 2<=N<=200,000\n1<=Q<=200,000\n0<=A_i,B_i<=N-1\n1<=C_i<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN Q\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_Q B_Q C_Q\nTask Output: Print the total weight of the edges contained in a minimum spanning tree of the graph.\nTask Samples: input: 7 1\n5 2 1 output: 21\n\nThe figure below shows the minimum spanning tree of the graph:\n\nNote that there can be multiple edges connecting the same pair of vertices.\ninput: 2 1\n0 0 1000000000 output: 1000000001\n\nAlso note that there can be self-loops.\ninput: 5 3\n0 1 10\n0 2 10\n0 4 10 output: 42\n\n" }, { "title": "", "content": "Problem Statement There are N squares in a row, numbered 1 through N from left to right.\nSnuke and Rng are playing a board game using these squares, described below:\n\nFirst, Snuke writes an integer into each square.\nEach of the two players possesses one piece. Snuke places his piece onto square 1, and Rng places his onto square 2.\nThe player whose piece is to the left of the opponent's, moves his piece. The destination must be a square to the right of the square where the piece is currently placed, and must not be a square where the opponent's piece is placed.\nRepeat step 3. When the pieces cannot be moved any more, the game ends.\nThe score of each player is calculated as the sum of the integers written in the squares where the player has placed his piece before the end of the game.\n\nSnuke has already written an integer A_i into square i (1<=i<=N-1), but not into square N yet.\nHe has decided to calculate for each of M integers X_1, X_2, . . . , X_M, if he writes it into square N and the game is played, what the value \"(Snuke's score) - (Rng's score)\" will be.\nHere, it is assumed that each player moves his piece to maximize the value \"(the player's score) - (the opponent's score)\". partial scores: Partial Scores\n700 points will be awarded for passing the test set satisfying M=1.\nAdditional 900 points will be awarded for passing the test set without additional constraints.", "constraint": "3<=N<=200,000\n0<=A_i<=10^6\nThe sum of all A_i is at most 10^6.\n1<=M<=200,000\n0<=X_i<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N-1}\nM\nX_1\nX_2\n:\nX_M", "output": "For each of the M integers X_1, . . . , X_M, print the value \"(Snuke's score) - (Rng's score)\" if it is written into square N, one per line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 7 1 8\n1\n2 output: 0\n\nThe game proceeds as follows, where S represents Snuke's piece, and R represents Rng's.\n\nBoth player scores 10, thus \"(Snuke's score) - (Rng's score)\" is 0.", "input: 9\n2 0 1 6 1 1 2 6\n5\n2016\n1\n1\n2\n6 output: 2001\n6\n6\n7\n7"], "Pid": "p03916", "ProblemText": "Task Description: Problem Statement There are N squares in a row, numbered 1 through N from left to right.\nSnuke and Rng are playing a board game using these squares, described below:\n\nFirst, Snuke writes an integer into each square.\nEach of the two players possesses one piece. Snuke places his piece onto square 1, and Rng places his onto square 2.\nThe player whose piece is to the left of the opponent's, moves his piece. The destination must be a square to the right of the square where the piece is currently placed, and must not be a square where the opponent's piece is placed.\nRepeat step 3. When the pieces cannot be moved any more, the game ends.\nThe score of each player is calculated as the sum of the integers written in the squares where the player has placed his piece before the end of the game.\n\nSnuke has already written an integer A_i into square i (1<=i<=N-1), but not into square N yet.\nHe has decided to calculate for each of M integers X_1, X_2, . . . , X_M, if he writes it into square N and the game is played, what the value \"(Snuke's score) - (Rng's score)\" will be.\nHere, it is assumed that each player moves his piece to maximize the value \"(the player's score) - (the opponent's score)\". partial scores: Partial Scores\n700 points will be awarded for passing the test set satisfying M=1.\nAdditional 900 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 3<=N<=200,000\n0<=A_i<=10^6\nThe sum of all A_i is at most 10^6.\n1<=M<=200,000\n0<=X_i<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N-1}\nM\nX_1\nX_2\n:\nX_M\nTask Output: For each of the M integers X_1, . . . , X_M, print the value \"(Snuke's score) - (Rng's score)\" if it is written into square N, one per line.\nTask Samples: input: 5\n2 7 1 8\n1\n2 output: 0\n\nThe game proceeds as follows, where S represents Snuke's piece, and R represents Rng's.\n\nBoth player scores 10, thus \"(Snuke's score) - (Rng's score)\" is 0.\ninput: 9\n2 0 1 6 1 1 2 6\n5\n2016\n1\n1\n2\n6 output: 2001\n6\n6\n7\n7\n\n" }, { "title": "", "content": "Problem Statement Snuke has a grid with H rows and W columns. The square at the i-th row and j-th column contains a character S_{i, j}.\nHe can perform the following two kinds of operation on the grid:\n\nRow-reverse: Reverse the order of the squares in a selected row.\nColumn-reverse: Reverse the order of the squares in a selected column.\n\nFor example, reversing the 2-nd row followed by reversing the 4-th column will result as follows:\n\nBy performing these operations any number of times in any order, how many placements of characters on the grid can be obtained?", "constraint": "1<=H,W<=200\nS_{i,j} is a lowercase English letter (a-z).", "input": "Input The input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}", "output": "Print the number of placements of characters on the grid that can be obtained, modulo 1000000007 (=10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\ncf\ncf output: 6\n\nThe following 6 placements of characters can be obtained:", "input: 1 12\ncodefestival output: 2"], "Pid": "p03917", "ProblemText": "Task Description: Problem Statement Snuke has a grid with H rows and W columns. The square at the i-th row and j-th column contains a character S_{i, j}.\nHe can perform the following two kinds of operation on the grid:\n\nRow-reverse: Reverse the order of the squares in a selected row.\nColumn-reverse: Reverse the order of the squares in a selected column.\n\nFor example, reversing the 2-nd row followed by reversing the 4-th column will result as follows:\n\nBy performing these operations any number of times in any order, how many placements of characters on the grid can be obtained?\nTask Constraint: 1<=H,W<=200\nS_{i,j} is a lowercase English letter (a-z).\nTask Input: Input The input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}\nTask Output: Print the number of placements of characters on the grid that can be obtained, modulo 1000000007 (=10^9+7).\nTask Samples: input: 2 2\ncf\ncf output: 6\n\nThe following 6 placements of characters can be obtained:\ninput: 1 12\ncodefestival output: 2\n\n" }, { "title": "", "content": "Problem Statement Snuke has a board with an N * N grid, and N * N tiles.\nEach side of a square that is part of the perimeter of the grid is attached with a socket.\nThat is, each side of the grid is attached with N sockets, for the total of 4 * N sockets.\nThese sockets are labeled as follows:\n\nThe sockets on the top side of the grid: U1, U2, . . . , UN from left to right\nThe sockets on the bottom side of the grid: D1, D2, . . . , DN from left to right\nThe sockets on the left side of the grid: L1, L2, . . . , LN from top to bottom\nThe sockets on the right side of the grid: R1, R2, . . . , RN from top to bottom\n\nFigure: The labels of the sockets\n\nSnuke can insert a tile from each socket into the square on which the socket is attached.\nWhen the square is already occupied by a tile, the occupying tile will be pushed into the next square, and when the next square is also occupied by another tile, that another occupying tile will be pushed as well, and so forth.\nSnuke cannot insert a tile if it would result in a tile pushed out of the grid.\nThe behavior of tiles when a tile is inserted is demonstrated in detail at Sample Input/Output 1.\nSnuke is trying to insert the N * N tiles one by one from the sockets, to reach the state where every square contains a tile.\nHere, he must insert exactly U_i tiles from socket Ui, D_i tiles from socket Di, L_i tiles from socket Li and R_i tiles from socket Ri.\nDetermine whether it is possible to insert the tiles under the restriction. If it is possible, in what order the tiles should be inserted from the sockets? partial scores: Partial Scores\n2000 points will be awarded for passing the test set satisfying N<=40.\nAdditional 100 points will be awarded for passing the test set without additional constraints.", "constraint": "1<=N<=300\nU_i,D_i,L_i and R_i are non-negative integers.\nThe sum of all values U_i,D_i,L_i and R_i is equal to N * N.", "input": "Input The input is given from Standard Input in the following format:\nN\nU_1 U_2 . . . U_N\nD_1 D_2 . . . D_N\nL_1 L_2 . . . L_N\nR_1 R_2 . . . R_N", "output": "If it is possible to insert the tiles so that every square will contain a tile, print the labels of the sockets in the order the tiles should be inserted from them, one per line. If it is impossible, print NO instead. If there exists more than one solution, print any of those.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 1\n1 1 0\n3 0 1\n0 1 1 output: L1\nL1\nL1\nL3\nD1\nR2\nU3\nR3\nD2\n\nSnuke can insert the tiles as shown in the figure below. An arrow indicates where a tile is inserted from, a circle represents a tile, and a number written in a circle indicates how many tiles are inserted before and including the tile.", "input: 2\n2 0\n2 0\n0 0\n0 0 output: NO"], "Pid": "p03918", "ProblemText": "Task Description: Problem Statement Snuke has a board with an N * N grid, and N * N tiles.\nEach side of a square that is part of the perimeter of the grid is attached with a socket.\nThat is, each side of the grid is attached with N sockets, for the total of 4 * N sockets.\nThese sockets are labeled as follows:\n\nThe sockets on the top side of the grid: U1, U2, . . . , UN from left to right\nThe sockets on the bottom side of the grid: D1, D2, . . . , DN from left to right\nThe sockets on the left side of the grid: L1, L2, . . . , LN from top to bottom\nThe sockets on the right side of the grid: R1, R2, . . . , RN from top to bottom\n\nFigure: The labels of the sockets\n\nSnuke can insert a tile from each socket into the square on which the socket is attached.\nWhen the square is already occupied by a tile, the occupying tile will be pushed into the next square, and when the next square is also occupied by another tile, that another occupying tile will be pushed as well, and so forth.\nSnuke cannot insert a tile if it would result in a tile pushed out of the grid.\nThe behavior of tiles when a tile is inserted is demonstrated in detail at Sample Input/Output 1.\nSnuke is trying to insert the N * N tiles one by one from the sockets, to reach the state where every square contains a tile.\nHere, he must insert exactly U_i tiles from socket Ui, D_i tiles from socket Di, L_i tiles from socket Li and R_i tiles from socket Ri.\nDetermine whether it is possible to insert the tiles under the restriction. If it is possible, in what order the tiles should be inserted from the sockets? partial scores: Partial Scores\n2000 points will be awarded for passing the test set satisfying N<=40.\nAdditional 100 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 1<=N<=300\nU_i,D_i,L_i and R_i are non-negative integers.\nThe sum of all values U_i,D_i,L_i and R_i is equal to N * N.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nU_1 U_2 . . . U_N\nD_1 D_2 . . . D_N\nL_1 L_2 . . . L_N\nR_1 R_2 . . . R_N\nTask Output: If it is possible to insert the tiles so that every square will contain a tile, print the labels of the sockets in the order the tiles should be inserted from them, one per line. If it is impossible, print NO instead. If there exists more than one solution, print any of those.\nTask Samples: input: 3\n0 0 1\n1 1 0\n3 0 1\n0 1 1 output: L1\nL1\nL1\nL3\nD1\nR2\nU3\nR3\nD2\n\nSnuke can insert the tiles as shown in the figure below. An arrow indicates where a tile is inserted from, a circle represents a tile, and a number written in a circle indicates how many tiles are inserted before and including the tile.\ninput: 2\n2 0\n2 0\n0 0\n0 0 output: NO\n\n" }, { "title": "", "content": "Problem Statement There is a grid with H rows and W columns.\nThe square at the i-th row and j-th column contains a string S_{i, j} of length 5.\nThe rows are labeled with the numbers from 1 through H, and the columns are labeled with the uppercase English letters from A through the W-th letter of the alphabet.\n\nExactly one of the squares in the grid contains the string snuke. Find this square and report its location.\nFor example, the square at the 6-th row and 8-th column should be reported as H6.", "constraint": "1<=H, W<=26\nThe length of S_{i,j} is 5.\nS_{i,j} consists of lowercase English letters (a-z).\nExactly one of the given strings is equal to snuke.", "input": "Input The input is given from Standard Input in the following format:\nH W\nS_{1,1} S_{1,2} . . . S_{1, W}\nS_{2,1} S_{2,2} . . . S_{2, W}\n:\nS_{H, 1} S_{H, 2} . . . S_{H, W}", "output": "Print the labels of the row and the column of the square containing the string snuke, with no space inbetween.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 15 10\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snuke snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake output: H6", "input: 1 1\nsnuke output: A1"], "Pid": "p03919", "ProblemText": "Task Description: Problem Statement There is a grid with H rows and W columns.\nThe square at the i-th row and j-th column contains a string S_{i, j} of length 5.\nThe rows are labeled with the numbers from 1 through H, and the columns are labeled with the uppercase English letters from A through the W-th letter of the alphabet.\n\nExactly one of the squares in the grid contains the string snuke. Find this square and report its location.\nFor example, the square at the 6-th row and 8-th column should be reported as H6.\nTask Constraint: 1<=H, W<=26\nThe length of S_{i,j} is 5.\nS_{i,j} consists of lowercase English letters (a-z).\nExactly one of the given strings is equal to snuke.\nTask Input: Input The input is given from Standard Input in the following format:\nH W\nS_{1,1} S_{1,2} . . . S_{1, W}\nS_{2,1} S_{2,2} . . . S_{2, W}\n:\nS_{H, 1} S_{H, 2} . . . S_{H, W}\nTask Output: Print the labels of the row and the column of the square containing the string snuke, with no space inbetween.\nTask Samples: input: 15 10\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snuke snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake\nsnake snake snake snake snake snake snake snake snake snake output: H6\ninput: 1 1\nsnuke output: A1\n\n" }, { "title": "", "content": "Problem Statement The problem set at CODE FESTIVAL 20XX Finals consists of N problems.\nThe score allocated to the i-th (1<=i<=N) problem is i points.\nTakahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.\nAs problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.\nDetermine the set of problems that should be solved. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1<=N<=1000.\nAdditional 100 points will be awarded for passing the test set without additional constraints.", "constraint": "1<=N<=10^7", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "Output Among the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.\nIf there exists more than one such set, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 output: 1\n3\n\nSolving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.", "input: 7 output: 1\n2\n4\n\nThe set \\{3,4\\} will also be accepted.", "input: 1 output: 1"], "Pid": "p03920", "ProblemText": "Task Description: Problem Statement The problem set at CODE FESTIVAL 20XX Finals consists of N problems.\nThe score allocated to the i-th (1<=i<=N) problem is i points.\nTakahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.\nAs problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.\nDetermine the set of problems that should be solved. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1<=N<=1000.\nAdditional 100 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 1<=N<=10^7\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: Output Among the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.\nIf there exists more than one such set, any of them will be accepted.\nTask Samples: input: 4 output: 1\n3\n\nSolving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.\ninput: 7 output: 1\n2\n4\n\nThe set \\{3,4\\} will also be accepted.\ninput: 1 output: 1\n\n" }, { "title": "", "content": "Problem Statement On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.\nFor CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.\nThe i-th (1<=i<=N) participant can speak K_i languages numbered L_{i, 1}, L_{i, 2}, . . . , L_{i, {}K_i}.\nTwo participants A and B can communicate with each other if and only if one of the following conditions is satisfied:\n\nThere exists a language that both A and B can speak.\nThere exists a participant X that both A and B can communicate with.\n\nDetermine whether all N participants can communicate with all other participants. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying the following: N<=1000, M<=1000 and (The sum of all K_i)<=1000.\nAdditional 200 points will be awarded for passing the test set without additional constraints.", "constraint": "2<=N<=10^5\n1<=M<=10^5\n1<=K_i<=M\n(The sum of all K_i)<=10^5\n1<=L_{i,j}<=M\nL_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.", "input": "Input The input is given from Standard Input in the following format:\nN M\nK_1 L_{1,1} L_{1,2} . . . L_{1, {}K_1}\nK_2 L_{2,1} L_{2,2} . . . L_{2, {}K_2}\n:\nK_N L_{N, 1} L_{N, 2} . . . L_{N, {}K_N}", "output": "If all N participants can communicate with all other participants, print YES. Otherwise, print NO.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 6\n3 1 2 3\n2 4 2\n2 4 6\n1 6 output: YES\n\nAny two participants can communicate with each other, as follows:\n\nParticipants 1 and 2: both can speak language 2.\nParticipants 2 and 3: both can speak language 4.\nParticipants 1 and 3: both can communicate with participant 2.\nParticipants 3 and 4: both can speak language 6.\nParticipants 2 and 4: both can communicate with participant 3.\nParticipants 1 and 4: both can communicate with participant 2.\n\nNote that there can be languages spoken by no participant.", "input: 4 4\n2 1 2\n2 1 2\n1 3\n2 4 3 output: NO\n\nFor example, participants 1 and 3 cannot communicate with each other."], "Pid": "p03921", "ProblemText": "Task Description: Problem Statement On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.\nFor CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.\nThe i-th (1<=i<=N) participant can speak K_i languages numbered L_{i, 1}, L_{i, 2}, . . . , L_{i, {}K_i}.\nTwo participants A and B can communicate with each other if and only if one of the following conditions is satisfied:\n\nThere exists a language that both A and B can speak.\nThere exists a participant X that both A and B can communicate with.\n\nDetermine whether all N participants can communicate with all other participants. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying the following: N<=1000, M<=1000 and (The sum of all K_i)<=1000.\nAdditional 200 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 2<=N<=10^5\n1<=M<=10^5\n1<=K_i<=M\n(The sum of all K_i)<=10^5\n1<=L_{i,j}<=M\nL_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nK_1 L_{1,1} L_{1,2} . . . L_{1, {}K_1}\nK_2 L_{2,1} L_{2,2} . . . L_{2, {}K_2}\n:\nK_N L_{N, 1} L_{N, 2} . . . L_{N, {}K_N}\nTask Output: If all N participants can communicate with all other participants, print YES. Otherwise, print NO.\nTask Samples: input: 4 6\n3 1 2 3\n2 4 2\n2 4 6\n1 6 output: YES\n\nAny two participants can communicate with each other, as follows:\n\nParticipants 1 and 2: both can speak language 2.\nParticipants 2 and 3: both can speak language 4.\nParticipants 1 and 3: both can communicate with participant 2.\nParticipants 3 and 4: both can speak language 6.\nParticipants 2 and 4: both can communicate with participant 3.\nParticipants 1 and 4: both can communicate with participant 2.\n\nNote that there can be languages spoken by no participant.\ninput: 4 4\n2 1 2\n2 1 2\n1 3\n2 4 3 output: NO\n\nFor example, participants 1 and 3 cannot communicate with each other.\n\n" }, { "title": "", "content": "Problem Statement Takahashi is playing with N cards.\nThe i-th card has an integer X_i on it.\nTakahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:\n\nThe integers on the two cards are the same.\nThe sum of the integers on the two cards is a multiple of M.\n\nFind the maximum number of pairs that can be created.\nNote that a card cannot be used in more than one pair.", "constraint": "2<=N<=10^5\n1<=M<=10^5\n1<=X_i<=10^5", "input": "Input The input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_N", "output": "Print the maximum number of pairs that can be created.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 5\n3 1 4 1 5 9 2 output: 3\n\nThree pairs (3,2), (1,4) and (1,9) can be created.\nIt is possible to create pairs (3,2) and (1,1), but the number of pairs is not maximized with this.", "input: 15 10\n1 5 6 10 11 11 11 20 21 25 25 26 99 99 99 output: 6"], "Pid": "p03922", "ProblemText": "Task Description: Problem Statement Takahashi is playing with N cards.\nThe i-th card has an integer X_i on it.\nTakahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:\n\nThe integers on the two cards are the same.\nThe sum of the integers on the two cards is a multiple of M.\n\nFind the maximum number of pairs that can be created.\nNote that a card cannot be used in more than one pair.\nTask Constraint: 2<=N<=10^5\n1<=M<=10^5\n1<=X_i<=10^5\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nX_1 X_2 . . . X_N\nTask Output: Print the maximum number of pairs that can be created.\nTask Samples: input: 7 5\n3 1 4 1 5 9 2 output: 3\n\nThree pairs (3,2), (1,4) and (1,9) can be created.\nIt is possible to create pairs (3,2) and (1,1), but the number of pairs is not maximized with this.\ninput: 15 10\n1 5 6 10 11 11 11 20 21 25 25 26 99 99 99 output: 6\n\n" }, { "title": "", "content": "Problem Statement Rng is baking cookies.\nInitially, he can bake one cookie per second.\nHe can also eat the cookies baked by himself.\nWhen there are x cookies not yet eaten, he can choose to eat all those cookies. After he finishes eating those cookies, the number of cookies he can bake per second becomes x. Note that a cookie always needs to be baked for 1 second, that is, he cannot bake a cookie in 1/x seconds when x > 1.\nWhen he choose to eat the cookies, he must eat all of them; he cannot choose to eat only part of them.\nIt takes him A seconds to eat the cookies regardless of how many, during which no cookies can be baked.\nHe wants to give N cookies to Grandma.\nFind the shortest time needed to produce at least N cookies not yet eaten. partial score: Partial Score\n500 points will be awarded for passing the test set satisfying N<=10^6 and A<=10^6.\nAdditional 500 points will be awarded for passing the test set without additional constraints.", "constraint": "1<=N<=10^{12}\n0<=A<=10^{12}\nA is an integer.", "input": "Input The input is given from Standard Input in the following format:\nN A", "output": "Print the shortest time needed to produce at least N cookies not yet eaten.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8 1 output: 7\n\nIt is possible to produce 8 cookies in 7 seconds, as follows:\n\nAfter 1 second: 1 cookie is done.\nAfter 2 seconds: 1 more cookie is done, totaling 2. Now, Rng starts eating those 2 cookies.\nAfter 3 seconds: He finishes eating the cookies, and he can now bake 2 cookies per second.\nAfter 4 seconds: 2 cookies are done.\nAfter 5 seconds: 2 more cookies are done, totaling 4.\nAfter 6 seconds: 2 more cookies are done, totaling 6.\nAfter 7 seconds: 2 more cookies are done, totaling 8.", "input: 1000000000000 1000000000000 output: 1000000000000"], "Pid": "p03923", "ProblemText": "Task Description: Problem Statement Rng is baking cookies.\nInitially, he can bake one cookie per second.\nHe can also eat the cookies baked by himself.\nWhen there are x cookies not yet eaten, he can choose to eat all those cookies. After he finishes eating those cookies, the number of cookies he can bake per second becomes x. Note that a cookie always needs to be baked for 1 second, that is, he cannot bake a cookie in 1/x seconds when x > 1.\nWhen he choose to eat the cookies, he must eat all of them; he cannot choose to eat only part of them.\nIt takes him A seconds to eat the cookies regardless of how many, during which no cookies can be baked.\nHe wants to give N cookies to Grandma.\nFind the shortest time needed to produce at least N cookies not yet eaten. partial score: Partial Score\n500 points will be awarded for passing the test set satisfying N<=10^6 and A<=10^6.\nAdditional 500 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 1<=N<=10^{12}\n0<=A<=10^{12}\nA is an integer.\nTask Input: Input The input is given from Standard Input in the following format:\nN A\nTask Output: Print the shortest time needed to produce at least N cookies not yet eaten.\nTask Samples: input: 8 1 output: 7\n\nIt is possible to produce 8 cookies in 7 seconds, as follows:\n\nAfter 1 second: 1 cookie is done.\nAfter 2 seconds: 1 more cookie is done, totaling 2. Now, Rng starts eating those 2 cookies.\nAfter 3 seconds: He finishes eating the cookies, and he can now bake 2 cookies per second.\nAfter 4 seconds: 2 cookies are done.\nAfter 5 seconds: 2 more cookies are done, totaling 4.\nAfter 6 seconds: 2 more cookies are done, totaling 6.\nAfter 7 seconds: 2 more cookies are done, totaling 8.\ninput: 1000000000000 1000000000000 output: 1000000000000\n\n" }, { "title": "", "content": "Problem Statement There are N towns in Takahashi Kingdom. They are conveniently numbered 1 through N.\nTakahashi the king is planning to go on a tour of inspection for M days. He will determine a sequence of towns c, and visit town c_i on the i-th day. That is, on the i-th day, he will travel from his current location to town c_i. If he is already at town c_i, he will stay at that town. His location just before the beginning of the tour is town 1, the capital. The tour ends at town c_M, without getting back to the capital. \nThe problem is that there is no paved road in this kingdom. He decided to resolve this issue by paving the road himself while traveling. When he travels from town a to town b, there will be a newly paved one-way road from town a to town b.\nSince he cares for his people, he wants the following condition to be satisfied after his tour is over: \"it is possible to travel from any town to any other town by traversing roads paved by him\". How many sequences of towns c satisfy this condition?", "constraint": "2<=N<=300\n1<=M<=300", "input": "Input The input is given from Standard Input in the following format:\nN M", "output": "Print the number of sequences of towns satisfying the condition, modulo 1000000007 (=10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 output: 2\n\nAs shown below, the condition is satisfied only when c = (2,3,1) or c = (3,2,1). Sequences such as c = (2,3,2), c = (2,1,3), c = (1,2,2) do not satisfy the condition.", "input: 150 300 output: 734286322", "input: 300 150 output: 0"], "Pid": "p03924", "ProblemText": "Task Description: Problem Statement There are N towns in Takahashi Kingdom. They are conveniently numbered 1 through N.\nTakahashi the king is planning to go on a tour of inspection for M days. He will determine a sequence of towns c, and visit town c_i on the i-th day. That is, on the i-th day, he will travel from his current location to town c_i. If he is already at town c_i, he will stay at that town. His location just before the beginning of the tour is town 1, the capital. The tour ends at town c_M, without getting back to the capital. \nThe problem is that there is no paved road in this kingdom. He decided to resolve this issue by paving the road himself while traveling. When he travels from town a to town b, there will be a newly paved one-way road from town a to town b.\nSince he cares for his people, he wants the following condition to be satisfied after his tour is over: \"it is possible to travel from any town to any other town by traversing roads paved by him\". How many sequences of towns c satisfy this condition?\nTask Constraint: 2<=N<=300\n1<=M<=300\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nTask Output: Print the number of sequences of towns satisfying the condition, modulo 1000000007 (=10^9+7).\nTask Samples: input: 3 3 output: 2\n\nAs shown below, the condition is satisfied only when c = (2,3,1) or c = (3,2,1). Sequences such as c = (2,3,2), c = (2,1,3), c = (1,2,2) do not satisfy the condition.\ninput: 150 300 output: 734286322\ninput: 300 150 output: 0\n\n" }, { "title": "", "content": "Problem Statement We have a graph with N vertices, numbered 0 through N-1. Edges are yet to be added.\nWe will process Q queries to add edges.\nIn the i-th (1<=i<=Q) query, three integers A_i, B_i and C_i will be given, and we will add infinitely many edges to the graph as follows:\n\nThe two vertices numbered A_i and B_i will be connected by an edge with a weight of C_i.\nThe two vertices numbered B_i and A_i+1 will be connected by an edge with a weight of C_i+1.\nThe two vertices numbered A_i+1 and B_i+1 will be connected by an edge with a weight of C_i+2.\nThe two vertices numbered B_i+1 and A_i+2 will be connected by an edge with a weight of C_i+3.\nThe two vertices numbered A_i+2 and B_i+2 will be connected by an edge with a weight of C_i+4.\nThe two vertices numbered B_i+2 and A_i+3 will be connected by an edge with a weight of C_i+5.\nThe two vertices numbered A_i+3 and B_i+3 will be connected by an edge with a weight of C_i+6.\n. . .\n\nHere, consider the indices of the vertices modulo N.\nFor example, the vertice numbered N is the one numbered 0, and the vertice numbered 2N-1 is the one numbered N-1.\nThe figure below shows the first seven edges added when N=16, A_i=7, B_i=14, C_i=1:\n\nAfter processing all the queries, find the total weight of the edges contained in a minimum spanning tree of the graph.", "constraint": "2<=N<=200,000\n1<=Q<=200,000\n0<=A_i,B_i<=N-1\n1<=C_i<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN Q\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_Q B_Q C_Q", "output": "Print the total weight of the edges contained in a minimum spanning tree of the graph.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 1\n5 2 1 output: 21\n\nThe figure below shows the minimum spanning tree of the graph:\n\nNote that there can be multiple edges connecting the same pair of vertices.", "input: 2 1\n0 0 1000000000 output: 1000000001\n\nAlso note that there can be self-loops.", "input: 5 3\n0 1 10\n0 2 10\n0 4 10 output: 42"], "Pid": "p03925", "ProblemText": "Task Description: Problem Statement We have a graph with N vertices, numbered 0 through N-1. Edges are yet to be added.\nWe will process Q queries to add edges.\nIn the i-th (1<=i<=Q) query, three integers A_i, B_i and C_i will be given, and we will add infinitely many edges to the graph as follows:\n\nThe two vertices numbered A_i and B_i will be connected by an edge with a weight of C_i.\nThe two vertices numbered B_i and A_i+1 will be connected by an edge with a weight of C_i+1.\nThe two vertices numbered A_i+1 and B_i+1 will be connected by an edge with a weight of C_i+2.\nThe two vertices numbered B_i+1 and A_i+2 will be connected by an edge with a weight of C_i+3.\nThe two vertices numbered A_i+2 and B_i+2 will be connected by an edge with a weight of C_i+4.\nThe two vertices numbered B_i+2 and A_i+3 will be connected by an edge with a weight of C_i+5.\nThe two vertices numbered A_i+3 and B_i+3 will be connected by an edge with a weight of C_i+6.\n. . .\n\nHere, consider the indices of the vertices modulo N.\nFor example, the vertice numbered N is the one numbered 0, and the vertice numbered 2N-1 is the one numbered N-1.\nThe figure below shows the first seven edges added when N=16, A_i=7, B_i=14, C_i=1:\n\nAfter processing all the queries, find the total weight of the edges contained in a minimum spanning tree of the graph.\nTask Constraint: 2<=N<=200,000\n1<=Q<=200,000\n0<=A_i,B_i<=N-1\n1<=C_i<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN Q\nA_1 B_1 C_1\nA_2 B_2 C_2\n:\nA_Q B_Q C_Q\nTask Output: Print the total weight of the edges contained in a minimum spanning tree of the graph.\nTask Samples: input: 7 1\n5 2 1 output: 21\n\nThe figure below shows the minimum spanning tree of the graph:\n\nNote that there can be multiple edges connecting the same pair of vertices.\ninput: 2 1\n0 0 1000000000 output: 1000000001\n\nAlso note that there can be self-loops.\ninput: 5 3\n0 1 10\n0 2 10\n0 4 10 output: 42\n\n" }, { "title": "", "content": "Problem Statement There are N squares in a row, numbered 1 through N from left to right.\nSnuke and Rng are playing a board game using these squares, described below:\n\nFirst, Snuke writes an integer into each square.\nEach of the two players possesses one piece. Snuke places his piece onto square 1, and Rng places his onto square 2.\nThe player whose piece is to the left of the opponent's, moves his piece. The destination must be a square to the right of the square where the piece is currently placed, and must not be a square where the opponent's piece is placed.\nRepeat step 3. When the pieces cannot be moved any more, the game ends.\nThe score of each player is calculated as the sum of the integers written in the squares where the player has placed his piece before the end of the game.\n\nSnuke has already written an integer A_i into square i (1<=i<=N-1), but not into square N yet.\nHe has decided to calculate for each of M integers X_1, X_2, . . . , X_M, if he writes it into square N and the game is played, what the value \"(Snuke's score) - (Rng's score)\" will be.\nHere, it is assumed that each player moves his piece to maximize the value \"(the player's score) - (the opponent's score)\". partial scores: Partial Scores\n700 points will be awarded for passing the test set satisfying M=1.\nAdditional 900 points will be awarded for passing the test set without additional constraints.", "constraint": "3<=N<=200,000\n0<=A_i<=10^6\nThe sum of all A_i is at most 10^6.\n1<=M<=200,000\n0<=X_i<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N-1}\nM\nX_1\nX_2\n:\nX_M", "output": "For each of the M integers X_1, . . . , X_M, print the value \"(Snuke's score) - (Rng's score)\" if it is written into square N, one per line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n2 7 1 8\n1\n2 output: 0\n\nThe game proceeds as follows, where S represents Snuke's piece, and R represents Rng's.\n\nBoth player scores 10, thus \"(Snuke's score) - (Rng's score)\" is 0.", "input: 9\n2 0 1 6 1 1 2 6\n5\n2016\n1\n1\n2\n6 output: 2001\n6\n6\n7\n7"], "Pid": "p03926", "ProblemText": "Task Description: Problem Statement There are N squares in a row, numbered 1 through N from left to right.\nSnuke and Rng are playing a board game using these squares, described below:\n\nFirst, Snuke writes an integer into each square.\nEach of the two players possesses one piece. Snuke places his piece onto square 1, and Rng places his onto square 2.\nThe player whose piece is to the left of the opponent's, moves his piece. The destination must be a square to the right of the square where the piece is currently placed, and must not be a square where the opponent's piece is placed.\nRepeat step 3. When the pieces cannot be moved any more, the game ends.\nThe score of each player is calculated as the sum of the integers written in the squares where the player has placed his piece before the end of the game.\n\nSnuke has already written an integer A_i into square i (1<=i<=N-1), but not into square N yet.\nHe has decided to calculate for each of M integers X_1, X_2, . . . , X_M, if he writes it into square N and the game is played, what the value \"(Snuke's score) - (Rng's score)\" will be.\nHere, it is assumed that each player moves his piece to maximize the value \"(the player's score) - (the opponent's score)\". partial scores: Partial Scores\n700 points will be awarded for passing the test set satisfying M=1.\nAdditional 900 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 3<=N<=200,000\n0<=A_i<=10^6\nThe sum of all A_i is at most 10^6.\n1<=M<=200,000\n0<=X_i<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 A_2 . . . A_{N-1}\nM\nX_1\nX_2\n:\nX_M\nTask Output: For each of the M integers X_1, . . . , X_M, print the value \"(Snuke's score) - (Rng's score)\" if it is written into square N, one per line.\nTask Samples: input: 5\n2 7 1 8\n1\n2 output: 0\n\nThe game proceeds as follows, where S represents Snuke's piece, and R represents Rng's.\n\nBoth player scores 10, thus \"(Snuke's score) - (Rng's score)\" is 0.\ninput: 9\n2 0 1 6 1 1 2 6\n5\n2016\n1\n1\n2\n6 output: 2001\n6\n6\n7\n7\n\n" }, { "title": "", "content": "Problem Statement Snuke has a grid with H rows and W columns. The square at the i-th row and j-th column contains a character S_{i, j}.\nHe can perform the following two kinds of operation on the grid:\n\nRow-reverse: Reverse the order of the squares in a selected row.\nColumn-reverse: Reverse the order of the squares in a selected column.\n\nFor example, reversing the 2-nd row followed by reversing the 4-th column will result as follows:\n\nBy performing these operations any number of times in any order, how many placements of characters on the grid can be obtained?", "constraint": "1<=H,W<=200\nS_{i,j} is a lowercase English letter (a-z).", "input": "Input The input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}", "output": "Print the number of placements of characters on the grid that can be obtained, modulo 1000000007 (=10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\ncf\ncf output: 6\n\nThe following 6 placements of characters can be obtained:", "input: 1 12\ncodefestival output: 2"], "Pid": "p03927", "ProblemText": "Task Description: Problem Statement Snuke has a grid with H rows and W columns. The square at the i-th row and j-th column contains a character S_{i, j}.\nHe can perform the following two kinds of operation on the grid:\n\nRow-reverse: Reverse the order of the squares in a selected row.\nColumn-reverse: Reverse the order of the squares in a selected column.\n\nFor example, reversing the 2-nd row followed by reversing the 4-th column will result as follows:\n\nBy performing these operations any number of times in any order, how many placements of characters on the grid can be obtained?\nTask Constraint: 1<=H,W<=200\nS_{i,j} is a lowercase English letter (a-z).\nTask Input: Input The input is given from Standard Input in the following format:\nH W\nS_{1,1}S_{1,2}. . . S_{1, W}\nS_{2,1}S_{2,2}. . . S_{2, W}\n:\nS_{H, 1}S_{H, 2}. . . S_{H, W}\nTask Output: Print the number of placements of characters on the grid that can be obtained, modulo 1000000007 (=10^9+7).\nTask Samples: input: 2 2\ncf\ncf output: 6\n\nThe following 6 placements of characters can be obtained:\ninput: 1 12\ncodefestival output: 2\n\n" }, { "title": "", "content": "Problem Statement Snuke has a board with an N * N grid, and N * N tiles.\nEach side of a square that is part of the perimeter of the grid is attached with a socket.\nThat is, each side of the grid is attached with N sockets, for the total of 4 * N sockets.\nThese sockets are labeled as follows:\n\nThe sockets on the top side of the grid: U1, U2, . . . , UN from left to right\nThe sockets on the bottom side of the grid: D1, D2, . . . , DN from left to right\nThe sockets on the left side of the grid: L1, L2, . . . , LN from top to bottom\nThe sockets on the right side of the grid: R1, R2, . . . , RN from top to bottom\n\nFigure: The labels of the sockets\n\nSnuke can insert a tile from each socket into the square on which the socket is attached.\nWhen the square is already occupied by a tile, the occupying tile will be pushed into the next square, and when the next square is also occupied by another tile, that another occupying tile will be pushed as well, and so forth.\nSnuke cannot insert a tile if it would result in a tile pushed out of the grid.\nThe behavior of tiles when a tile is inserted is demonstrated in detail at Sample Input/Output 1.\nSnuke is trying to insert the N * N tiles one by one from the sockets, to reach the state where every square contains a tile.\nHere, he must insert exactly U_i tiles from socket Ui, D_i tiles from socket Di, L_i tiles from socket Li and R_i tiles from socket Ri.\nDetermine whether it is possible to insert the tiles under the restriction. If it is possible, in what order the tiles should be inserted from the sockets? partial scores: Partial Scores\n2000 points will be awarded for passing the test set satisfying N<=40.\nAdditional 100 points will be awarded for passing the test set without additional constraints.", "constraint": "1<=N<=300\nU_i,D_i,L_i and R_i are non-negative integers.\nThe sum of all values U_i,D_i,L_i and R_i is equal to N * N.", "input": "Input The input is given from Standard Input in the following format:\nN\nU_1 U_2 . . . U_N\nD_1 D_2 . . . D_N\nL_1 L_2 . . . L_N\nR_1 R_2 . . . R_N", "output": "If it is possible to insert the tiles so that every square will contain a tile, print the labels of the sockets in the order the tiles should be inserted from them, one per line. If it is impossible, print NO instead. If there exists more than one solution, print any of those.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 0 1\n1 1 0\n3 0 1\n0 1 1 output: L1\nL1\nL1\nL3\nD1\nR2\nU3\nR3\nD2\n\nSnuke can insert the tiles as shown in the figure below. An arrow indicates where a tile is inserted from, a circle represents a tile, and a number written in a circle indicates how many tiles are inserted before and including the tile.", "input: 2\n2 0\n2 0\n0 0\n0 0 output: NO"], "Pid": "p03928", "ProblemText": "Task Description: Problem Statement Snuke has a board with an N * N grid, and N * N tiles.\nEach side of a square that is part of the perimeter of the grid is attached with a socket.\nThat is, each side of the grid is attached with N sockets, for the total of 4 * N sockets.\nThese sockets are labeled as follows:\n\nThe sockets on the top side of the grid: U1, U2, . . . , UN from left to right\nThe sockets on the bottom side of the grid: D1, D2, . . . , DN from left to right\nThe sockets on the left side of the grid: L1, L2, . . . , LN from top to bottom\nThe sockets on the right side of the grid: R1, R2, . . . , RN from top to bottom\n\nFigure: The labels of the sockets\n\nSnuke can insert a tile from each socket into the square on which the socket is attached.\nWhen the square is already occupied by a tile, the occupying tile will be pushed into the next square, and when the next square is also occupied by another tile, that another occupying tile will be pushed as well, and so forth.\nSnuke cannot insert a tile if it would result in a tile pushed out of the grid.\nThe behavior of tiles when a tile is inserted is demonstrated in detail at Sample Input/Output 1.\nSnuke is trying to insert the N * N tiles one by one from the sockets, to reach the state where every square contains a tile.\nHere, he must insert exactly U_i tiles from socket Ui, D_i tiles from socket Di, L_i tiles from socket Li and R_i tiles from socket Ri.\nDetermine whether it is possible to insert the tiles under the restriction. If it is possible, in what order the tiles should be inserted from the sockets? partial scores: Partial Scores\n2000 points will be awarded for passing the test set satisfying N<=40.\nAdditional 100 points will be awarded for passing the test set without additional constraints.\nTask Constraint: 1<=N<=300\nU_i,D_i,L_i and R_i are non-negative integers.\nThe sum of all values U_i,D_i,L_i and R_i is equal to N * N.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nU_1 U_2 . . . U_N\nD_1 D_2 . . . D_N\nL_1 L_2 . . . L_N\nR_1 R_2 . . . R_N\nTask Output: If it is possible to insert the tiles so that every square will contain a tile, print the labels of the sockets in the order the tiles should be inserted from them, one per line. If it is impossible, print NO instead. If there exists more than one solution, print any of those.\nTask Samples: input: 3\n0 0 1\n1 1 0\n3 0 1\n0 1 1 output: L1\nL1\nL1\nL3\nD1\nR2\nU3\nR3\nD2\n\nSnuke can insert the tiles as shown in the figure below. An arrow indicates where a tile is inserted from, a circle represents a tile, and a number written in a circle indicates how many tiles are inserted before and including the tile.\ninput: 2\n2 0\n2 0\n0 0\n0 0 output: NO\n\n" }, { "title": "", "content": "Problem Statement\n\tSnuke has a very long calendar. It has a grid with $n$ rows and $7$ columns. One day, he noticed that calendar has a following regularity. \n\nThe cell at the $i$-th row and $j$-th column contains the integer $7i+j-7$.\n\n\tA good sub-grid is a $3 * 3$ sub-grid and the sum of integers in this sub-grid mod $11$ is $k$. \n\tHow many good sub-grid are there? Write a program and help him. tasks: Subtasks\nSubtask 1 [ $150$ points ]\n\nThe testcase in the subtask satisfies $1 <= n <= 100$.\nSubtask 2 [ $100$ points ]\n\nThere are no additional constraints.", "constraint": "$1 <= n <= 10^9$\n$0 <= k <= 10$", "input": "The input is given from standard input in the following format. \n\n$n \\quad k$", "output": "Print the number of good sub-grid. If there are no solution exists, print 0.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 7 output: \n2\n\tIn this case, the calendar likes this matrix.\n\nSun.\nMon.\nTue.\nWed.\nThu.\nFri.\nSat.\nWeek 1\n1\n2\n3\n4\n5\n6\n7\nWeek 2\n8\n9\n10\n11\n12\n13\n14\nWeek 3\n15\n16\n17\n18\n19\n20\n21\nWeek 4\n22\n23\n24\n25\n26\n27\n28\nWeek 5\n29\n30\n31\n32\n33\n34\n35\nWeek 6\n36\n37\n38\n39\n40\n41\n42\nWeek 7\n43\n44\n45\n46\n47\n48\n49\n\n\tThe cell at $i$-th row and $j$-th column is denoted $(i, j)$. \n\nIf upper-left is $(1,5)$, the sum of integers is $5+6+7+12+13+14+19+20+21=117$.\nIf upper-left is $(3,2)$, the sum of integers is $16+17+18+23+24+25+30+31+32=216$.\n\n\tTherefore, there are 2 good sub-grids.", "input: 6 0 output: \n2\n\n\tIf upper-left is $(1,3)$ or $(4,4)$, it is a good sub-grid."], "Pid": "p03929", "ProblemText": "Task Description: Problem Statement\n\tSnuke has a very long calendar. It has a grid with $n$ rows and $7$ columns. One day, he noticed that calendar has a following regularity. \n\nThe cell at the $i$-th row and $j$-th column contains the integer $7i+j-7$.\n\n\tA good sub-grid is a $3 * 3$ sub-grid and the sum of integers in this sub-grid mod $11$ is $k$. \n\tHow many good sub-grid are there? Write a program and help him. tasks: Subtasks\nSubtask 1 [ $150$ points ]\n\nThe testcase in the subtask satisfies $1 <= n <= 100$.\nSubtask 2 [ $100$ points ]\n\nThere are no additional constraints.\nTask Constraint: $1 <= n <= 10^9$\n$0 <= k <= 10$\nTask Input: The input is given from standard input in the following format. \n\n$n \\quad k$\nTask Output: Print the number of good sub-grid. If there are no solution exists, print 0.\nTask Samples: input: 7 7 output: \n2\n\tIn this case, the calendar likes this matrix.\n\nSun.\nMon.\nTue.\nWed.\nThu.\nFri.\nSat.\nWeek 1\n1\n2\n3\n4\n5\n6\n7\nWeek 2\n8\n9\n10\n11\n12\n13\n14\nWeek 3\n15\n16\n17\n18\n19\n20\n21\nWeek 4\n22\n23\n24\n25\n26\n27\n28\nWeek 5\n29\n30\n31\n32\n33\n34\n35\nWeek 6\n36\n37\n38\n39\n40\n41\n42\nWeek 7\n43\n44\n45\n46\n47\n48\n49\n\n\tThe cell at $i$-th row and $j$-th column is denoted $(i, j)$. \n\nIf upper-left is $(1,5)$, the sum of integers is $5+6+7+12+13+14+19+20+21=117$.\nIf upper-left is $(3,2)$, the sum of integers is $16+17+18+23+24+25+30+31+32=216$.\n\n\tTherefore, there are 2 good sub-grids.\ninput: 6 0 output: \n2\n\n\tIf upper-left is $(1,3)$ or $(4,4)$, it is a good sub-grid.\n\n" }, { "title": "", "content": "Problem Statement\n\tWe are playing a puzzle. An upright board with $H$ rows by $W$ columns of cells, is used in this puzzle. \n\tA stone in $i$-th row and $j$-th column engraved with a digit, one of 1 through 9, is placed in each of the cells. \n\tYou can erase 1 cell in the board. \n\n\tThe game process is following: \n\nWhen $K$ or more stones in horizontally adjacent cells are engraved with the same digit, the stones will disappear. Disappearances of all such groups of stones take place simultaneously.\nWhen stones are in the cells above the emptied cells, these stones drop down so that the emptied cells are filled.\nAfter the completion of all stone drops, if one or more groups of stones satisfy the disappearance condition, repeat by returning to the step 1.\nScore is $\\sum_i 2^i * <=ft(\\text{Sum of numbers in the stones which disappeared in the $i$-th chain (0-indexed)}\\right)$.\n\n\tPlease answer the points if he erased the optimal place.", "constraint": "", "input": "The input is given from standard input in the following format.", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03930", "ProblemText": "Task Description: Problem Statement\n\tWe are playing a puzzle. An upright board with $H$ rows by $W$ columns of cells, is used in this puzzle. \n\tA stone in $i$-th row and $j$-th column engraved with a digit, one of 1 through 9, is placed in each of the cells. \n\tYou can erase 1 cell in the board. \n\n\tThe game process is following: \n\nWhen $K$ or more stones in horizontally adjacent cells are engraved with the same digit, the stones will disappear. Disappearances of all such groups of stones take place simultaneously.\nWhen stones are in the cells above the emptied cells, these stones drop down so that the emptied cells are filled.\nAfter the completion of all stone drops, if one or more groups of stones satisfy the disappearance condition, repeat by returning to the step 1.\nScore is $\\sum_i 2^i * <=ft(\\text{Sum of numbers in the stones which disappeared in the $i$-th chain (0-indexed)}\\right)$.\n\n\tPlease answer the points if he erased the optimal place.\nTask Input: The input is given from standard input in the following format.\nTask Output: \n\n" }, { "title": "", "content": "Problem Statement\nSample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21: 01)\n\tSnuke got a sequence $a$ of length $n$ from At Coder company. All elements in $a$ are distinct.\n\tHe made a sequence $b$, but actually, he is not remembered it. \n\tHowever, he is remembered a few things about sequence $b$. \n\nAll elements in $b$ are distinct. \nAll elements in $b$ is in $a$.\n$b_1 \\oplus b_2 \\oplus \\cdots \\oplus b_r = k$. ($r$ is length of sequence $b$) [$\\oplus$ means XOR]\n\tFor example, if $a = { 1,2,3 }$ and $k = 1$, he can make $b = { 1 }, { 2,3 }, { 3,2 }$. \n\tHe wants to restore sequence $b$, but he says that there are too many ways and he can't restore it.\n\tPlease calculate the ways to make $b$ and help him. \n\tSince the answer can be large, print the answer modulo $1,000,000,007$. tasks: Subtasks\n\tSubtask 1 [ $50$ points ] \n\n$1 <= n <= 4$\n\n\tSubtask 2 [ $170$ points ] \n\n$1 <= n <= 20$\n\n\tSubtask 3 [ $180$ points ] \n\nThere are no additional constraints.", "constraint": "$1 <= n <= 100$\n$1 <= a_i, k <= 255$\n$i \\neq j \\Rightarrow a_i \\neq a_j$", "input": "The input is given from Standard Input in the following format:\n$n \\ k$\n$a_1 \\ a_2 \\ \\cdots \\ a_n$", "output": "Print the number of ways to make sequence $b$. \nPrint the answer modulo $1,000,000,007$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n1 2 3 output: \n3\n\n\tYou can make 3 patterns: $b = \\{ 1 \\}, \\{ 2,3 \\}, \\{ 3,2 \\}$", "input: 3 10\n8 7 5 output: \n6\n\n\tYou can make 6 patterns: $b = \\{ 5,7,8 \\}, \\{ 5,8,7 \\}, \\{ 7,5,8 \\}, \\{ 7,8,5 \\}, \\{ 8,5,7 \\}, \\{ 8,7,5 \\}$.", "input: 25 127\n5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 output: \n235924722\n\nPlease output answer mod $1,000,000,007$."], "Pid": "p03931", "ProblemText": "Task Description: Problem Statement\nSample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21: 01)\n\tSnuke got a sequence $a$ of length $n$ from At Coder company. All elements in $a$ are distinct.\n\tHe made a sequence $b$, but actually, he is not remembered it. \n\tHowever, he is remembered a few things about sequence $b$. \n\nAll elements in $b$ are distinct. \nAll elements in $b$ is in $a$.\n$b_1 \\oplus b_2 \\oplus \\cdots \\oplus b_r = k$. ($r$ is length of sequence $b$) [$\\oplus$ means XOR]\n\tFor example, if $a = { 1,2,3 }$ and $k = 1$, he can make $b = { 1 }, { 2,3 }, { 3,2 }$. \n\tHe wants to restore sequence $b$, but he says that there are too many ways and he can't restore it.\n\tPlease calculate the ways to make $b$ and help him. \n\tSince the answer can be large, print the answer modulo $1,000,000,007$. tasks: Subtasks\n\tSubtask 1 [ $50$ points ] \n\n$1 <= n <= 4$\n\n\tSubtask 2 [ $170$ points ] \n\n$1 <= n <= 20$\n\n\tSubtask 3 [ $180$ points ] \n\nThere are no additional constraints.\nTask Constraint: $1 <= n <= 100$\n$1 <= a_i, k <= 255$\n$i \\neq j \\Rightarrow a_i \\neq a_j$\nTask Input: The input is given from Standard Input in the following format:\n$n \\ k$\n$a_1 \\ a_2 \\ \\cdots \\ a_n$\nTask Output: Print the number of ways to make sequence $b$. \nPrint the answer modulo $1,000,000,007$.\nTask Samples: input: 3 1\n1 2 3 output: \n3\n\n\tYou can make 3 patterns: $b = \\{ 1 \\}, \\{ 2,3 \\}, \\{ 3,2 \\}$\ninput: 3 10\n8 7 5 output: \n6\n\n\tYou can make 6 patterns: $b = \\{ 5,7,8 \\}, \\{ 5,8,7 \\}, \\{ 7,5,8 \\}, \\{ 7,8,5 \\}, \\{ 8,5,7 \\}, \\{ 8,7,5 \\}$.\ninput: 25 127\n5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 output: \n235924722\n\nPlease output answer mod $1,000,000,007$.\n\n" }, { "title": "", "content": "Problem Statement\n\tSigma and his brother Sugim are in the $H * W$ grid. They wants to buy some souvenirs. \n\tTheir start position is upper-left cell, and the goal position is lower-right cell. \n\tSome cells has a souvenir shop. At $i$-th row and $j$-th column, there is $a_{i, j}$ souvenirs. \n\tIn one move, they can go left, right, down, and up cell. \n\tBut they have little time, so they can move only $H+W-2$ times. \n\tThey wanted to buy souvenirs as many as possible, but they had no computer, so they couldn't get the maximal numbers of souvenirs. \n\tWrite a program and calculate the maximum souvenirs they can get, and help them. tasks: Subtasks\n\tSubtask 1 [ 50 points ] \n\nThe testcase in the subtask satisfies $1 <= H <= 2$.\n\n\tSubtask 2 [ 80 points ] \n\nThe testcase in the subtask satisfies $1 <= H <= 3$.\n\n\tSubtask 3 [ 120 points ] \n\nThe testcase in the subtask satisfies $1 <= H, W <= 7$.\n\n\tSubtask 4 [ 150 points ] \n\nThe testcase in the subtask satisfies $1 <= H, W <= 30$.\n\n\tSubtask 5 [ 200 points ] \n\nThere are no additional constraints.", "constraint": "$1 <= H, W <= 200$\n$0 <= a_{i, j} <= 10^5$", "input": "The input is given from standard input in the following format. \n$H \\ W$\n$a_{1,1} \\ a_{1,2} \\ \\cdots \\ a_{1, W}$\n$a_{2,1} \\ a_{2,2} \\ \\cdots \\ a_{2, W}$\n$\\vdots \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\vdots \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\vdots$\n$a_{H, 1} \\ a_{H, 2} \\ \\cdots \\ a_{H, W}$", "output": "Print the maximum number of souvenirs they can get.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 0 5\n2 2 3\n4 2 4 output: \n21\n\n\tThe cell at $i$-th row and $j$-th column is denoted $(i, j)$. \n\tIn this case, one of the optimal solution is this:\n\nSigma moves $(1,1) -> (1,2) -> (1,3) -> (2,3) -> (3,3)$.\nSugim moves $(1,1) -> (2,1) -> (3,1) -> (3,2) -> (3,3)$.\n\n\tThen, they can get $21$ souvernirs.", "input: 6 6\n1 2 3 4 5 6\n8 6 9 1 2 0\n3 1 4 1 5 9\n2 6 5 3 5 8\n1 4 1 4 2 1\n2 7 1 8 2 8 output: \n97"], "Pid": "p03932", "ProblemText": "Task Description: Problem Statement\n\tSigma and his brother Sugim are in the $H * W$ grid. They wants to buy some souvenirs. \n\tTheir start position is upper-left cell, and the goal position is lower-right cell. \n\tSome cells has a souvenir shop. At $i$-th row and $j$-th column, there is $a_{i, j}$ souvenirs. \n\tIn one move, they can go left, right, down, and up cell. \n\tBut they have little time, so they can move only $H+W-2$ times. \n\tThey wanted to buy souvenirs as many as possible, but they had no computer, so they couldn't get the maximal numbers of souvenirs. \n\tWrite a program and calculate the maximum souvenirs they can get, and help them. tasks: Subtasks\n\tSubtask 1 [ 50 points ] \n\nThe testcase in the subtask satisfies $1 <= H <= 2$.\n\n\tSubtask 2 [ 80 points ] \n\nThe testcase in the subtask satisfies $1 <= H <= 3$.\n\n\tSubtask 3 [ 120 points ] \n\nThe testcase in the subtask satisfies $1 <= H, W <= 7$.\n\n\tSubtask 4 [ 150 points ] \n\nThe testcase in the subtask satisfies $1 <= H, W <= 30$.\n\n\tSubtask 5 [ 200 points ] \n\nThere are no additional constraints.\nTask Constraint: $1 <= H, W <= 200$\n$0 <= a_{i, j} <= 10^5$\nTask Input: The input is given from standard input in the following format. \n$H \\ W$\n$a_{1,1} \\ a_{1,2} \\ \\cdots \\ a_{1, W}$\n$a_{2,1} \\ a_{2,2} \\ \\cdots \\ a_{2, W}$\n$\\vdots \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\vdots \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\vdots$\n$a_{H, 1} \\ a_{H, 2} \\ \\cdots \\ a_{H, W}$\nTask Output: Print the maximum number of souvenirs they can get.\nTask Samples: input: 3 3\n1 0 5\n2 2 3\n4 2 4 output: \n21\n\n\tThe cell at $i$-th row and $j$-th column is denoted $(i, j)$. \n\tIn this case, one of the optimal solution is this:\n\nSigma moves $(1,1) -> (1,2) -> (1,3) -> (2,3) -> (3,3)$.\nSugim moves $(1,1) -> (2,1) -> (3,1) -> (3,2) -> (3,3)$.\n\n\tThen, they can get $21$ souvernirs.\ninput: 6 6\n1 2 3 4 5 6\n8 6 9 1 2 0\n3 1 4 1 5 9\n2 6 5 3 5 8\n1 4 1 4 2 1\n2 7 1 8 2 8 output: \n97\n\n" }, { "title": "", "content": "Problem statement\n\tThere is a circle which radius is 1. \n\tThere are $N$ vertices on the circle's circumference. \n\tThe vertices divides into $N$ equal parts over the circumference. \n\tYou can choose $3$ distinct vertices, and you can make a triangle. \n\tThere are $\\frac{N(N - 1)(N - 2)}{6}$ ways choosing vertices.\n\tThe question is: Calculate the area of $K$-th smallest triangle in $\\frac{N(N-1)(N-2)}{6}$ triangles. \n\tIf the area is same, you can order in any order. \n\n\tIf $N = 4, K = 3$, the result is following:\n\nIf you select vertices $1$, $2$, and $3$, the area of triangle $= 1$.\nIf you select vertices $1$, $2$, and $4$, the area of triangle $= 1$.\nIf you select vertices $1$, $3$, and $4$, the area of triangle $= 1$.\nIf you select vertices $2$, $3$, and $4$, the area of triangle $= 1$.\n\n\tAs a result, the 3rd smallest triangle's area $= 1$. tasks: Subtasks\n\t\tSubtask 1 [ $160$ points ] \n\n$N <= 100$\n\n\t\tSubtask 2 [ $240$ points ] \n\n$N <= 1000$\n\n\t\tSubtask 3 [ $450$ points ] \n\n$N <= 200,000$", "constraint": "$3 <= N <= 200,000$\n$1 <= K <= \\frac{N(N-1)(N-2)}{6}$", "input": "The input is given from Standard Input in the following format: \n$N \\ K$", "output": "Please output the $K$-th triangle area.\nPrint a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{-9}$.", "content_img": false, "lang": "", "error": false, "samples": ["input: 4 3 output: \n1.0000000000000\n\n\tThis example is already explained in the problem statement.", "input: 6 9 output: \n0.86602540378\n\n\tThere are $6$ ways to choose a triangle which area is $\\frac{\\sqrt{3}}{4}$. \n\tThere are $10$ ways to choose a triangle which area is $\\frac{\\sqrt{3}}{2}$. \n\tThere are $2$ ways to choose a triangle which area is $\\frac{3 \\sqrt{3}}{4}$. \n\tTherefore, the 9th smallest triangle's area is $\\frac{\\sqrt{3}}{2}$.", "input: 12 220 output: \n1.29903810568"], "Pid": "p03933", "ProblemText": "Task Description: Problem statement\n\tThere is a circle which radius is 1. \n\tThere are $N$ vertices on the circle's circumference. \n\tThe vertices divides into $N$ equal parts over the circumference. \n\tYou can choose $3$ distinct vertices, and you can make a triangle. \n\tThere are $\\frac{N(N - 1)(N - 2)}{6}$ ways choosing vertices.\n\tThe question is: Calculate the area of $K$-th smallest triangle in $\\frac{N(N-1)(N-2)}{6}$ triangles. \n\tIf the area is same, you can order in any order. \n\n\tIf $N = 4, K = 3$, the result is following:\n\nIf you select vertices $1$, $2$, and $3$, the area of triangle $= 1$.\nIf you select vertices $1$, $2$, and $4$, the area of triangle $= 1$.\nIf you select vertices $1$, $3$, and $4$, the area of triangle $= 1$.\nIf you select vertices $2$, $3$, and $4$, the area of triangle $= 1$.\n\n\tAs a result, the 3rd smallest triangle's area $= 1$. tasks: Subtasks\n\t\tSubtask 1 [ $160$ points ] \n\n$N <= 100$\n\n\t\tSubtask 2 [ $240$ points ] \n\n$N <= 1000$\n\n\t\tSubtask 3 [ $450$ points ] \n\n$N <= 200,000$\nTask Constraint: $3 <= N <= 200,000$\n$1 <= K <= \\frac{N(N-1)(N-2)}{6}$\nTask Input: The input is given from Standard Input in the following format: \n$N \\ K$\nTask Output: Please output the $K$-th triangle area.\nPrint a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{-9}$.\nTask Samples: input: 4 3 output: \n1.0000000000000\n\n\tThis example is already explained in the problem statement.\ninput: 6 9 output: \n0.86602540378\n\n\tThere are $6$ ways to choose a triangle which area is $\\frac{\\sqrt{3}}{4}$. \n\tThere are $10$ ways to choose a triangle which area is $\\frac{\\sqrt{3}}{2}$. \n\tThere are $2$ ways to choose a triangle which area is $\\frac{3 \\sqrt{3}}{4}$. \n\tTherefore, the 9th smallest triangle's area is $\\frac{\\sqrt{3}}{2}$.\ninput: 12 220 output: \n1.29903810568\n\n" }, { "title": "", "content": "Problem statement\n\tThere are $N$ customers in a restaurant. Each customer is numbered $1$ through $N$. \n\tA sushi chef carried out $Q$ operations for customers. \n\n\tThe $i$-th operation is follows: \n\nThe sushi chef chooses a customer whose number of dishes of sushi eaten is minimum, in customer $1,2,3, \\dots, a_i$. If there are multiple customers who are minimum numbers of dishes, he selects the minimum-numbered customers. \nHe puts a dish of sushi on the selected seats.\nA customer who have selected for professional eats this sushi.\nRepeat 1-3, $b_i$ times.\n\tPlease calculate the number of dishes of sushi that have been eaten by each customer. tasks: Subtasks\n\t\tSubtask 1 [ $60$ points ] \n\n$N, Q <= 100$\n$b_i = 1$\n\n\t\tSubtask 2 [ $400$ points ] \n\n$N, Q <= 100$\n$b_i <= 10^{12}$\n\n\t\tSubtask 3 [ $240$ points ] \n\n$N, Q <= 100,000$\n$b_i = 1$\n\n\t\tSubtask 4 [ $500$ points ] \n\nThere are no additional constraints.", "constraint": "$3 <= N, Q <= 100,000$\n$1 <= a_i <= N$\n$1 <= b_i <= 10^{12}$\nAny final results do not exceed $2 * 10^{13}$.", "input": "The input is given from Standard Input in the following format: \n$N \\ Q$\n$a_1 \\ b_1$\n$a_2 \\ b_2$\n$ ： \\ ： $\n$a_Q \\ b_Q$", "output": "You have to print $N$ lines.\nThe $i$-th line should contain the number of dishes of sushi had eaten for customer $i (1 <= i <= N)$.", "content_img": false, "lang": "", "error": false, "samples": ["input: 9 3\n5 11\n8 4\n4 7 output: \n4\n4\n4\n4\n2\n2\n1\n1\n0\n\n\tThe change of the number of dishes of sushi have eaten is following: \nCustomer 1\nCustomer 2\nCustomer 3\nCustomer 4\nCustomer 5\nCustomer 6\nCustomer 7\nCustomer 8\nCustomer 9\n1st Operation\n3 2 2 2 2 0 0 0 0\n2nd Operation\n3 2 2 2 2 2 1 1 0\n3rd Operation\n4 4 4 4 2 2 1 1 0", "input: 6 6\n3 5\n6 11\n1 6\n4 7\n5 2\n2 5 output: \n10\n10\n5\n5\n4\n2", "input: 5 6\n1 1\n2 1\n3 1\n1 1\n5 1\n3 1 output: \n2\n2\n1\n1\n0", "input: 10 10\n10 10\n9 20\n8 30\n7 40\n6 50\n5 60\n4 70\n3 80\n2 90\n1 100 output: \n223\n123\n77\n50\n33\n21\n12\n7\n3\n1"], "Pid": "p03934", "ProblemText": "Task Description: Problem statement\n\tThere are $N$ customers in a restaurant. Each customer is numbered $1$ through $N$. \n\tA sushi chef carried out $Q$ operations for customers. \n\n\tThe $i$-th operation is follows: \n\nThe sushi chef chooses a customer whose number of dishes of sushi eaten is minimum, in customer $1,2,3, \\dots, a_i$. If there are multiple customers who are minimum numbers of dishes, he selects the minimum-numbered customers. \nHe puts a dish of sushi on the selected seats.\nA customer who have selected for professional eats this sushi.\nRepeat 1-3, $b_i$ times.\n\tPlease calculate the number of dishes of sushi that have been eaten by each customer. tasks: Subtasks\n\t\tSubtask 1 [ $60$ points ] \n\n$N, Q <= 100$\n$b_i = 1$\n\n\t\tSubtask 2 [ $400$ points ] \n\n$N, Q <= 100$\n$b_i <= 10^{12}$\n\n\t\tSubtask 3 [ $240$ points ] \n\n$N, Q <= 100,000$\n$b_i = 1$\n\n\t\tSubtask 4 [ $500$ points ] \n\nThere are no additional constraints.\nTask Constraint: $3 <= N, Q <= 100,000$\n$1 <= a_i <= N$\n$1 <= b_i <= 10^{12}$\nAny final results do not exceed $2 * 10^{13}$.\nTask Input: The input is given from Standard Input in the following format: \n$N \\ Q$\n$a_1 \\ b_1$\n$a_2 \\ b_2$\n$ ： \\ ： $\n$a_Q \\ b_Q$\nTask Output: You have to print $N$ lines.\nThe $i$-th line should contain the number of dishes of sushi had eaten for customer $i (1 <= i <= N)$.\nTask Samples: input: 9 3\n5 11\n8 4\n4 7 output: \n4\n4\n4\n4\n2\n2\n1\n1\n0\n\n\tThe change of the number of dishes of sushi have eaten is following: \nCustomer 1\nCustomer 2\nCustomer 3\nCustomer 4\nCustomer 5\nCustomer 6\nCustomer 7\nCustomer 8\nCustomer 9\n1st Operation\n3 2 2 2 2 0 0 0 0\n2nd Operation\n3 2 2 2 2 2 1 1 0\n3rd Operation\n4 4 4 4 2 2 1 1 0\ninput: 6 6\n3 5\n6 11\n1 6\n4 7\n5 2\n2 5 output: \n10\n10\n5\n5\n4\n2\ninput: 5 6\n1 1\n2 1\n3 1\n1 1\n5 1\n3 1 output: \n2\n2\n1\n1\n0\ninput: 10 10\n10 10\n9 20\n8 30\n7 40\n6 50\n5 60\n4 70\n3 80\n2 90\n1 100 output: \n223\n123\n77\n50\n33\n21\n12\n7\n3\n1\n\n" }, { "title": "", "content": "Problem Statement\n\tE869120 defined a sequence $a$ like this: \n\n$a_1=a_2=1$, $a_{k+2}=a_{k+1}+a_k \\ (k >= 1)$\n\tHe also defined sequences $d_1, d_2, d_3, \\dots , d_n$, as the following recurrence relation : \n\n$d_{1, j} = a_j$\n$d_{i, j} = \\sum_{k = 1}^j d_{i - 1, k} \\ (i >= 2)$\n\tYou are given integers $n$ and $m$. Please calculate the value of $d_{n, m}$. \n\tSince the answer can be large number, print the answer modulo $998,244,353$. \n\tCan you solve this problem? ? ? tasks: Subtasks\n\tSubtask 1 [ $100$ points ] \n\nThe testcase in this subtask satisfies $1 <= n, m <= 3,000$.\n\n\tSubtask 2 [ $170$ points ] \n\nThe testcase in this subtask satisfies $1 <= m <= 200,000$.\n\n\tSubtask 3 [ $230$ points ] \n\nThe testcase in this subtask satisfies $1 <= n <= 3$.\n\n\tSubtask 4 [ $420$ points ] \n\nThe testcase in this subtask satisfies $1 <= n <= 1000$.\n\n\tSubtask 5 [ $480$ points ] \n\nThere are no additional constraints.", "constraint": "$1 <= n <= 200,000$\n$1 <= m <= 10^{18}$", "input": "The input is given from standard input in the following format. \n\n$n \\quad m$", "output": "Print $d_{n, m}$ modulo $998,244,353$.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 7 output: \n176\n\n\tThe sequence is following:\n\n$d_{i, 1}$\n$d_{i, 2}$\n$d_{i, 3}$\n$d_{i, 4}$\n$d_{i, 5}$\n$d_{i, 6}$\n$d_{i, 7}$\n$d_1$\n1\n1\n2\n3\n5\n8\n13\n$d_2$\n1\n2\n4\n7\n12\n20\n33\n$d_3$\n1\n3\n7\n14\n26\n46\n79\n$d_4$\n1\n4\n11\n25\n51\n97\n176\n\n\tAs a result, the answer is $d_{4,7} = 176$.", "input: 12 20 output: \n174174144", "input: 16 30 output: \n102292850\n\n\tYou can calculate that $d_{16,30} = 1,193,004,294,685$.\n\tPlease don't forget printing the answer mod $998,244,353$."], "Pid": "p03935", "ProblemText": "Task Description: Problem Statement\n\tE869120 defined a sequence $a$ like this: \n\n$a_1=a_2=1$, $a_{k+2}=a_{k+1}+a_k \\ (k >= 1)$\n\tHe also defined sequences $d_1, d_2, d_3, \\dots , d_n$, as the following recurrence relation : \n\n$d_{1, j} = a_j$\n$d_{i, j} = \\sum_{k = 1}^j d_{i - 1, k} \\ (i >= 2)$\n\tYou are given integers $n$ and $m$. Please calculate the value of $d_{n, m}$. \n\tSince the answer can be large number, print the answer modulo $998,244,353$. \n\tCan you solve this problem? ? ? tasks: Subtasks\n\tSubtask 1 [ $100$ points ] \n\nThe testcase in this subtask satisfies $1 <= n, m <= 3,000$.\n\n\tSubtask 2 [ $170$ points ] \n\nThe testcase in this subtask satisfies $1 <= m <= 200,000$.\n\n\tSubtask 3 [ $230$ points ] \n\nThe testcase in this subtask satisfies $1 <= n <= 3$.\n\n\tSubtask 4 [ $420$ points ] \n\nThe testcase in this subtask satisfies $1 <= n <= 1000$.\n\n\tSubtask 5 [ $480$ points ] \n\nThere are no additional constraints.\nTask Constraint: $1 <= n <= 200,000$\n$1 <= m <= 10^{18}$\nTask Input: The input is given from standard input in the following format. \n\n$n \\quad m$\nTask Output: Print $d_{n, m}$ modulo $998,244,353$.\nTask Samples: input: 4 7 output: \n176\n\n\tThe sequence is following:\n\n$d_{i, 1}$\n$d_{i, 2}$\n$d_{i, 3}$\n$d_{i, 4}$\n$d_{i, 5}$\n$d_{i, 6}$\n$d_{i, 7}$\n$d_1$\n1\n1\n2\n3\n5\n8\n13\n$d_2$\n1\n2\n4\n7\n12\n20\n33\n$d_3$\n1\n3\n7\n14\n26\n46\n79\n$d_4$\n1\n4\n11\n25\n51\n97\n176\n\n\tAs a result, the answer is $d_{4,7} = 176$.\ninput: 12 20 output: \n174174144\ninput: 16 30 output: \n102292850\n\n\tYou can calculate that $d_{16,30} = 1,193,004,294,685$.\n\tPlease don't forget printing the answer mod $998,244,353$.\n\n" }, { "title": "", "content": "Problem Statement\n\tThere is a $50 * 50$ field. The cell at $i$-th row and $j$-th column is denoted $(i, j)$ (0-indexed). \n\tOne day, square1001 puts $250$ bombs in this field. In each cell, there is 1 or 0 bomb. \n\tYou want to know where the bombs are by asking some questions. \n\tYou can ask this question many times. \n\nYou can ask the number of bombs in the rectangular area in which upper-left cell is $(a, b)$ and lower-right cell is $(c, d)$.\n\tPlease find all bombs' positions asking as few questions as possible. \n\n\tNote: This problem Input/Output type is special. Please read Input/Output. If you want to use scanf/printf, you have to write fflush(stdout). score: Score\n\t\tThere are 5 testcases in the judge. \n\t\tThe $score$ in each testcase is defined by following formula: \n\n$Q$ is the number of questions.\nIf $Q > 2500$, $score = 0$ (Wrong Answer).\nIf $930 <= Q <= 2500$, $score = max(\\lfloor 125 - 3.2\\sqrt{Q - 920} \\rfloor, 40)$.\nIf $880 <= Q < 930$, $score = \\lfloor 288 - 22\\sqrt{Q - 870} \\rfloor$.\nIf $Q < 880$, $score = min(2860 - 3Q, 300)$. Sample Input・Output\n\tIn the case of the following arrangement, this input / output is conceivable.\n\tThis case is $H, W=4$, so this example is not include in testcases.\n\nH=4, W=4, N=4\n1001\n0000\n0010\n0100\n\n\tExample of Input・Output\nInput from program\nOutput\n4 4 4 1000000007\n \n \n? 0 0 0 1\n1\n \n \n? 0 1 0 2\n0\n \n \n? 0 3 1 3\n1\n \n \n? 2 1 3 2\n2\n \n \n? 2 2 2 2\n1\n \n \n! 9225\n\tThese question is not always meaningful.", "constraint": "$H, W = 50$\n$N = 250$\n$1,000,000,000 <= K <= 1,000,010,000$ ($K$ is random)", "input": "", "output": "", "content_img": false, "lang": "en", "error": true, "samples": [], "Pid": "p03936", "ProblemText": "Task Description: Problem Statement\n\tThere is a $50 * 50$ field. The cell at $i$-th row and $j$-th column is denoted $(i, j)$ (0-indexed). \n\tOne day, square1001 puts $250$ bombs in this field. In each cell, there is 1 or 0 bomb. \n\tYou want to know where the bombs are by asking some questions. \n\tYou can ask this question many times. \n\nYou can ask the number of bombs in the rectangular area in which upper-left cell is $(a, b)$ and lower-right cell is $(c, d)$.\n\tPlease find all bombs' positions asking as few questions as possible. \n\n\tNote: This problem Input/Output type is special. Please read Input/Output. If you want to use scanf/printf, you have to write fflush(stdout). score: Score\n\t\tThere are 5 testcases in the judge. \n\t\tThe $score$ in each testcase is defined by following formula: \n\n$Q$ is the number of questions.\nIf $Q > 2500$, $score = 0$ (Wrong Answer).\nIf $930 <= Q <= 2500$, $score = max(\\lfloor 125 - 3.2\\sqrt{Q - 920} \\rfloor, 40)$.\nIf $880 <= Q < 930$, $score = \\lfloor 288 - 22\\sqrt{Q - 870} \\rfloor$.\nIf $Q < 880$, $score = min(2860 - 3Q, 300)$. Sample Input・Output\n\tIn the case of the following arrangement, this input / output is conceivable.\n\tThis case is $H, W=4$, so this example is not include in testcases.\n\nH=4, W=4, N=4\n1001\n0000\n0010\n0100\n\n\tExample of Input・Output\nInput from program\nOutput\n4 4 4 1000000007\n \n \n? 0 0 0 1\n1\n \n \n? 0 1 0 2\n0\n \n \n? 0 3 1 3\n1\n \n \n? 2 1 3 2\n2\n \n \n? 2 2 2 2\n1\n \n \n! 9225\n\tThese question is not always meaningful.\nTask Constraint: $H, W = 50$\n$N = 250$\n$1,000,000,000 <= K <= 1,000,010,000$ ($K$ is random)\nTask Input: \nTask Output: \n\n" }, { "title": "", "content": "Problem Statement\nWe have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).\nYou are given a matrix of characters a_{ij} (1 <= i <= H, 1 <= j <= W). After Shik completes all moving actions, a_{ij} is # if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is . . Please determine whether it is possible that Shik only uses right and down moves in all steps.", "constraint": "2 <= H, W <= 8\na_{i,j} is either # or ..\nThere exists a valid sequence of moves for Shik to generate the map a.", "input": "Input The input is given from Standard Input in the following format:\nH W\na_{11}a_{12}. . . a_{1W}\n:\na_{H1}a_{H2}. . . a_{HW}", "output": "If it is possible that Shik only uses right and down moves, print Possible. Otherwise, print Impossible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5\n##...\n.##..\n..##.\n...## output: Possible\n\nThe matrix can be generated by a 7-move sequence: right, down, right, down, right, down, and right.", "input: 5 3\n###\n..#\n###\n#..\n### output: Impossible", "input: 4 5\n##...\n.###.\n.###.\n...## output: Impossible"], "Pid": "p03937", "ProblemText": "Task Description: Problem Statement\nWe have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).\nYou are given a matrix of characters a_{ij} (1 <= i <= H, 1 <= j <= W). After Shik completes all moving actions, a_{ij} is # if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is . . Please determine whether it is possible that Shik only uses right and down moves in all steps.\nTask Constraint: 2 <= H, W <= 8\na_{i,j} is either # or ..\nThere exists a valid sequence of moves for Shik to generate the map a.\nTask Input: Input The input is given from Standard Input in the following format:\nH W\na_{11}a_{12}. . . a_{1W}\n:\na_{H1}a_{H2}. . . a_{HW}\nTask Output: If it is possible that Shik only uses right and down moves, print Possible. Otherwise, print Impossible.\nTask Samples: input: 4 5\n##...\n.##..\n..##.\n...## output: Possible\n\nThe matrix can be generated by a 7-move sequence: right, down, right, down, right, down, and right.\ninput: 5 3\n###\n..#\n###\n#..\n### output: Impossible\ninput: 4 5\n##...\n.###.\n.###.\n...## output: Impossible\n\n" }, { "title": "", "content": "Problem Statement\nYou are given a permutation p of the set {1,2, . . . , N}. Please construct two sequences of positive integers a_1, a_2, . . . , a_N and b_1, b_2, . . . , b_N satisfying the following conditions:\n\n1 <= a_i, b_i <= 10^9 for all i\na_1 < a_2 < . . . < a_N\nb_1 > b_2 > . . . > b_N\na_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < . . . < a_{p_N}+b_{p_N}", "constraint": "2 <= N <= 20,000\np is a permutation of the set {1,2, ..., N}", "input": "Input The input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N", "output": "Output The output consists of two lines. The first line contains a_1, a_2, . . . , a_N seperated by a space. The second line contains b_1, b_2, . . . , b_N seperated by a space. \nIt can be shown that there always exists a solution for any input satisfying the constraints.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 2 output: 1 4\n5 4\n\na_1 + b_1 = 6 and a_2 + b_2 = 8. So this output satisfies all conditions.", "input: 3\n3 2 1 output: 1 2 3\n5 3 1", "input: 3\n2 3 1 output: 5 10 100\n100 10 1"], "Pid": "p03938", "ProblemText": "Task Description: Problem Statement\nYou are given a permutation p of the set {1,2, . . . , N}. Please construct two sequences of positive integers a_1, a_2, . . . , a_N and b_1, b_2, . . . , b_N satisfying the following conditions:\n\n1 <= a_i, b_i <= 10^9 for all i\na_1 < a_2 < . . . < a_N\nb_1 > b_2 > . . . > b_N\na_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < . . . < a_{p_N}+b_{p_N}\nTask Constraint: 2 <= N <= 20,000\np is a permutation of the set {1,2, ..., N}\nTask Input: Input The input is given from Standard Input in the following format:\nN\np_1 p_2 . . . p_N\nTask Output: Output The output consists of two lines. The first line contains a_1, a_2, . . . , a_N seperated by a space. The second line contains b_1, b_2, . . . , b_N seperated by a space. \nIt can be shown that there always exists a solution for any input satisfying the constraints.\nTask Samples: input: 2\n1 2 output: 1 4\n5 4\n\na_1 + b_1 = 6 and a_2 + b_2 = 8. So this output satisfies all conditions.\ninput: 3\n3 2 1 output: 1 2 3\n5 3 1\ninput: 3\n2 3 1 output: 5 10 100\n100 10 1\n\n" }, { "title": "", "content": "Problem Statement\nThere are N balls and N+1 holes in a line. Balls are numbered 1 through N from left to right. Holes are numbered 1 through N+1 from left to right. The i-th ball is located between the i-th hole and (i+1)-th hole. We denote the distance between neighboring items (one ball and one hole) from left to right as d_i (1 <= i <= 2 * N). You are given two parameters d_1 and x. d_i - d_{i-1} is equal to x for all i (2 <= i <= 2 * N).\nWe want to push all N balls into holes one by one. When a ball rolls over a hole, the ball will drop into the hole if there is no ball in the hole yet. Otherwise, the ball will pass this hole and continue to roll. (In any scenario considered in this problem, balls will never collide. )\nIn each step, we will choose one of the remaining balls uniformly at random and then choose a direction (either left or right) uniformly at random and push the ball in this direction. Please calculate the expected total distance rolled by all balls during this process.\nFor example, when N = 3, d_1 = 1, and x = 1, the following is one possible scenario:\nfirst step: push the ball numbered 2 to its left, it will drop into the hole numbered 2. The distance rolled is 3.\nsecond step: push the ball numbered 1 to its right, it will pass the hole numbered 2 and drop into the hole numbered 3. The distance rolled is 9.\nthird step: push the ball numbered 3 to its right, it will drop into the hole numbered 4. The distance rolled is 6.\n\nSo the total distance in this scenario is 18.\nNote that in all scenarios every ball will drop into some hole and there will be a hole containing no ball in the end.", "constraint": "1 <= N <= 200,000\n1 <= d_1 <= 100\n0 <= x <= 100\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN d_1 x", "output": "Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 3 output: 4.500000000000000\n\nThe distance between the only ball and the left hole is 3 and distance between the only ball and the right hole is 6. There are only two scenarios (i.e. push left and push right). The only ball will roll 3 and 6 unit distance, respectively. So the answer for this example is (3+6)/2 = 4.5.", "input: 2 1 0 output: 2.500000000000000", "input: 1000 100 100 output: 649620280.957660079002380"], "Pid": "p03939", "ProblemText": "Task Description: Problem Statement\nThere are N balls and N+1 holes in a line. Balls are numbered 1 through N from left to right. Holes are numbered 1 through N+1 from left to right. The i-th ball is located between the i-th hole and (i+1)-th hole. We denote the distance between neighboring items (one ball and one hole) from left to right as d_i (1 <= i <= 2 * N). You are given two parameters d_1 and x. d_i - d_{i-1} is equal to x for all i (2 <= i <= 2 * N).\nWe want to push all N balls into holes one by one. When a ball rolls over a hole, the ball will drop into the hole if there is no ball in the hole yet. Otherwise, the ball will pass this hole and continue to roll. (In any scenario considered in this problem, balls will never collide. )\nIn each step, we will choose one of the remaining balls uniformly at random and then choose a direction (either left or right) uniformly at random and push the ball in this direction. Please calculate the expected total distance rolled by all balls during this process.\nFor example, when N = 3, d_1 = 1, and x = 1, the following is one possible scenario:\nfirst step: push the ball numbered 2 to its left, it will drop into the hole numbered 2. The distance rolled is 3.\nsecond step: push the ball numbered 1 to its right, it will pass the hole numbered 2 and drop into the hole numbered 3. The distance rolled is 9.\nthird step: push the ball numbered 3 to its right, it will drop into the hole numbered 4. The distance rolled is 6.\n\nSo the total distance in this scenario is 18.\nNote that in all scenarios every ball will drop into some hole and there will be a hole containing no ball in the end.\nTask Constraint: 1 <= N <= 200,000\n1 <= d_1 <= 100\n0 <= x <= 100\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN d_1 x\nTask Output: Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than 10^{-9}.\nTask Samples: input: 1 3 3 output: 4.500000000000000\n\nThe distance between the only ball and the left hole is 3 and distance between the only ball and the right hole is 6. There are only two scenarios (i.e. push left and push right). The only ball will roll 3 and 6 unit distance, respectively. So the answer for this example is (3+6)/2 = 4.5.\ninput: 2 1 0 output: 2.500000000000000\ninput: 1000 100 100 output: 649620280.957660079002380\n\n" }, { "title": "", "content": "Problem Statement\nImagine a game played on a line. Initially, the player is located at position 0 with N candies in his possession, and the exit is at position E. There are also N bears in the game. The i-th bear is located at x_i. The maximum moving speed of the player is 1 while the bears do not move at all.\nWhen the player gives a candy to a bear, it will provide a coin after T units of time. More specifically, if the i-th bear is given a candy at time t, it will put a coin at its position at time t+T. The purpose of this game is to give candies to all the bears, pick up all the coins, and go to the exit. Note that the player can only give a candy to a bear if the player is at the exact same position of the bear. Also, each bear will only produce a coin once. If the player visits the position of a coin after or at the exact same time that the coin is put down, the player can pick up the coin. Coins do not disappear until collected by the player.\nShik is an expert of this game. He can give candies to bears and pick up coins instantly. You are given the configuration of the game. Please calculate the minimum time Shik needs to collect all the coins and go to the exit. partial scores: Partial Scores\nIn test cases worth 600 points, N <= 2,000.", "constraint": "1 <= N <= 100,000\n1 <= T, E <= 10^9\n0 < x_i < E\nx_i < x_{i+1} for 1 <= i < N\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN E T\nx_1 x_2 . . . x_N", "output": "Print an integer denoting the answer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 9 1\n1 3 8 output: 12\n\nThe optimal strategy is to wait for the coin after treating each bear. The total time spent on waiting is 3 and moving is 9. So the answer is 3 + 9 = 12.", "input: 3 9 3\n1 3 8 output: 16", "input: 2 1000000000 1000000000\n1 999999999 output: 2999999996"], "Pid": "p03940", "ProblemText": "Task Description: Problem Statement\nImagine a game played on a line. Initially, the player is located at position 0 with N candies in his possession, and the exit is at position E. There are also N bears in the game. The i-th bear is located at x_i. The maximum moving speed of the player is 1 while the bears do not move at all.\nWhen the player gives a candy to a bear, it will provide a coin after T units of time. More specifically, if the i-th bear is given a candy at time t, it will put a coin at its position at time t+T. The purpose of this game is to give candies to all the bears, pick up all the coins, and go to the exit. Note that the player can only give a candy to a bear if the player is at the exact same position of the bear. Also, each bear will only produce a coin once. If the player visits the position of a coin after or at the exact same time that the coin is put down, the player can pick up the coin. Coins do not disappear until collected by the player.\nShik is an expert of this game. He can give candies to bears and pick up coins instantly. You are given the configuration of the game. Please calculate the minimum time Shik needs to collect all the coins and go to the exit. partial scores: Partial Scores\nIn test cases worth 600 points, N <= 2,000.\nTask Constraint: 1 <= N <= 100,000\n1 <= T, E <= 10^9\n0 < x_i < E\nx_i < x_{i+1} for 1 <= i < N\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN E T\nx_1 x_2 . . . x_N\nTask Output: Print an integer denoting the answer.\nTask Samples: input: 3 9 1\n1 3 8 output: 12\n\nThe optimal strategy is to wait for the coin after treating each bear. The total time spent on waiting is 3 and moving is 9. So the answer is 3 + 9 = 12.\ninput: 3 9 3\n1 3 8 output: 16\ninput: 2 1000000000 1000000000\n1 999999999 output: 2999999996\n\n" }, { "title": "", "content": "Problem Statement\nIn the country there are N cities numbered 1 through N, which are connected by N-1 bidirectional roads. In terms of graph theory, there is a unique simple path connecting every pair of cities. That is, the N cities form a tree. Besides, if we view city 1 as the root of this tree, the tree will be a full binary tree (a tree is a full binary tree if and only if every non-leaf vertex in the tree has exactly two children). Roads are numbered 1 through N-1. The i-th road connects city i+1 and city a_i. When you pass through road i, the toll you should pay is v_i (if v_i is 0, it indicates the road does not require a toll).\nA company in city 1 will give each employee a family travel and cover a large part of the tolls incurred. Each employee can design the travel by themselves. That is, which cities he/she wants to visit in each day and which city to stay at each night. However, there are some constraints. More details are as follows:\nThe travel must start and end at city 1. If there are m leaves in the tree formed by the cities, then the number of days in the travel must be m+1. At the end of each day, except for the last day, the employee must stay at some hotel in a leaf city. During the whole travel, the employee must stay at all leaf cities exactly once.\nDuring the whole travel, all roads of the country must be passed through exactly twice.\nThe amount that the employee must pay for tolls by him/herself is the maximum total toll incurred in a single day during the travel, except the first day and the last day. The remaining tolls will be covered by the company.\nShik, as an employee of this company, has only one hope for his travel. He hopes that the amount he must pay for tolls by himself will be as small as possible. Please help Shik to design the travel which satisfies his hope.", "constraint": "2 < N < 131,072\n1 <= a_i <= i for all i\n0 <= v_i <= 131,072\nv_i is an integer\nThe given tree is a full binary tree", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 v_1\na_2 v_2\n:\na_{N-1} v_{N-1}", "output": "Print an integer denoting the minimum amount Shik must pay by himself for tolls incurred during the travel.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7\n1 1\n1 1\n2 1\n2 1\n3 1\n3 1 output: 4\n\nThere are 4 leaves in the tree formed by the cities (cities 4,5,6, and 7), so the travel must be 5 days long. There are 4! = 24 possible arrangements of the leaf cities to stay during the travel, but some of them are invalid. For example, (4,5,6,7) and (6,7,5,4) are valid orders, but (5,6,7,4) is invalid because the route passes 4 times through the road connecting city 1 and city 2. The figure below shows the routes of the travel for these arrangements.\n\nFor all valid orders, day 3 is the day with the maximum total incurred toll of 4, passing through 4 roads.", "input: 9\n1 2\n1 2\n3 2\n3 2\n5 2\n5 2\n7 2\n7 2 output: 6\n\nThe following figure shows the route of the travel for one possible arrangement of the stayed cities for the solution. Note that the tolls incurred in the first day and the last day are always covered by the company.", "input: 15\n1 2\n1 5\n3 3\n4 3\n4 3\n6 5\n5 4\n5 3\n6 3\n3 2\n11 5\n11 3\n13 2\n13 1 output: 15", "input: 3\n1 0\n1 0 output: 0"], "Pid": "p03941", "ProblemText": "Task Description: Problem Statement\nIn the country there are N cities numbered 1 through N, which are connected by N-1 bidirectional roads. In terms of graph theory, there is a unique simple path connecting every pair of cities. That is, the N cities form a tree. Besides, if we view city 1 as the root of this tree, the tree will be a full binary tree (a tree is a full binary tree if and only if every non-leaf vertex in the tree has exactly two children). Roads are numbered 1 through N-1. The i-th road connects city i+1 and city a_i. When you pass through road i, the toll you should pay is v_i (if v_i is 0, it indicates the road does not require a toll).\nA company in city 1 will give each employee a family travel and cover a large part of the tolls incurred. Each employee can design the travel by themselves. That is, which cities he/she wants to visit in each day and which city to stay at each night. However, there are some constraints. More details are as follows:\nThe travel must start and end at city 1. If there are m leaves in the tree formed by the cities, then the number of days in the travel must be m+1. At the end of each day, except for the last day, the employee must stay at some hotel in a leaf city. During the whole travel, the employee must stay at all leaf cities exactly once.\nDuring the whole travel, all roads of the country must be passed through exactly twice.\nThe amount that the employee must pay for tolls by him/herself is the maximum total toll incurred in a single day during the travel, except the first day and the last day. The remaining tolls will be covered by the company.\nShik, as an employee of this company, has only one hope for his travel. He hopes that the amount he must pay for tolls by himself will be as small as possible. Please help Shik to design the travel which satisfies his hope.\nTask Constraint: 2 < N < 131,072\n1 <= a_i <= i for all i\n0 <= v_i <= 131,072\nv_i is an integer\nThe given tree is a full binary tree\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 v_1\na_2 v_2\n:\na_{N-1} v_{N-1}\nTask Output: Print an integer denoting the minimum amount Shik must pay by himself for tolls incurred during the travel.\nTask Samples: input: 7\n1 1\n1 1\n2 1\n2 1\n3 1\n3 1 output: 4\n\nThere are 4 leaves in the tree formed by the cities (cities 4,5,6, and 7), so the travel must be 5 days long. There are 4! = 24 possible arrangements of the leaf cities to stay during the travel, but some of them are invalid. For example, (4,5,6,7) and (6,7,5,4) are valid orders, but (5,6,7,4) is invalid because the route passes 4 times through the road connecting city 1 and city 2. The figure below shows the routes of the travel for these arrangements.\n\nFor all valid orders, day 3 is the day with the maximum total incurred toll of 4, passing through 4 roads.\ninput: 9\n1 2\n1 2\n3 2\n3 2\n5 2\n5 2\n7 2\n7 2 output: 6\n\nThe following figure shows the route of the travel for one possible arrangement of the stayed cities for the solution. Note that the tolls incurred in the first day and the last day are always covered by the company.\ninput: 15\n1 2\n1 5\n3 3\n4 3\n4 3\n6 5\n5 4\n5 3\n6 3\n3 2\n11 5\n11 3\n13 2\n13 1 output: 15\ninput: 3\n1 0\n1 0 output: 0\n\n" }, { "title": "", "content": "Problem Statement\nShik's job is very boring. At day 0, his boss gives him a string S_0 of length N which consists of only lowercase English letters. In the i-th day after day 0, Shik's job is to copy the string S_{i-1} to a string S_i. We denote the j-th letter of S_i as S_i[j].\nShik is inexperienced in this job. In each day, when he is copying letters one by one from the first letter to the last letter, he would make mistakes. That is, he sometimes accidentally writes down the same letter that he wrote previously instead of the correct one. More specifically, S_i[j] is equal to either S_{i-1}[j] or S_{i}[j-1]. (Note that S_i[1] always equals to S_{i-1}[1]. )\nYou are given the string S_0 and another string T.\nPlease determine the smallest integer i such that S_i could be equal to T. If no such i exists, please print -1.", "constraint": "1 <= N <= 1,000,000\nThe lengths of S_0 and T are both N.\nBoth S_0 and T consist of lowercase English letters.", "input": "Input The input is given from Standard Input in the following format:\nN\nS_0\nT", "output": "Print the smallest integer i such that S_i could be equal to T. If no such i exists, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\nabcde\naaacc output: 2\n\nS_0 = abcde, S_1 = aaccc and S_2 = aaacc is a possible sequence such that S_2 = T.", "input: 5\nabcde\nabcde output: 0", "input: 4\nacaa\naaca output: 2", "input: 5\nabcde\nbbbbb output: -1"], "Pid": "p03942", "ProblemText": "Task Description: Problem Statement\nShik's job is very boring. At day 0, his boss gives him a string S_0 of length N which consists of only lowercase English letters. In the i-th day after day 0, Shik's job is to copy the string S_{i-1} to a string S_i. We denote the j-th letter of S_i as S_i[j].\nShik is inexperienced in this job. In each day, when he is copying letters one by one from the first letter to the last letter, he would make mistakes. That is, he sometimes accidentally writes down the same letter that he wrote previously instead of the correct one. More specifically, S_i[j] is equal to either S_{i-1}[j] or S_{i}[j-1]. (Note that S_i[1] always equals to S_{i-1}[1]. )\nYou are given the string S_0 and another string T.\nPlease determine the smallest integer i such that S_i could be equal to T. If no such i exists, please print -1.\nTask Constraint: 1 <= N <= 1,000,000\nThe lengths of S_0 and T are both N.\nBoth S_0 and T consist of lowercase English letters.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nS_0\nT\nTask Output: Print the smallest integer i such that S_i could be equal to T. If no such i exists, print -1 instead.\nTask Samples: input: 5\nabcde\naaacc output: 2\n\nS_0 = abcde, S_1 = aaccc and S_2 = aaacc is a possible sequence such that S_2 = T.\ninput: 5\nabcde\nabcde output: 0\ninput: 4\nacaa\naaca output: 2\ninput: 5\nabcde\nbbbbb output: -1\n\n" }, { "title": "", "content": "Problem Statement Two students of At Coder Kindergarten are fighting over candy packs.\nThere are three candy packs, each of which contains a, b, and c candies, respectively.\nTeacher Evi is trying to distribute the packs between the two students so that each student gets the same number of candies. Determine whether it is possible.\nNote that Evi cannot take candies out of the packs, and the whole contents of each pack must be given to one of the students.", "constraint": "1 <= a, b, c <= 100", "input": "Input The input is given from Standard Input in the following format:\na b c", "output": "If it is possible to distribute the packs so that each student gets the same number of candies, print Yes. Otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 30 20 output: Yes\n\nGive the pack with 30 candies to one student, and give the two packs with 10 and 20 candies to the other. Then, each gets 30 candies.", "input: 30 30 100 output: No\n\nIn this case, the student who gets the pack with 100 candies always has more candies than the other.\nNote that every pack must be given to one of them.", "input: 56 25 31 output: Yes"], "Pid": "p03943", "ProblemText": "Task Description: Problem Statement Two students of At Coder Kindergarten are fighting over candy packs.\nThere are three candy packs, each of which contains a, b, and c candies, respectively.\nTeacher Evi is trying to distribute the packs between the two students so that each student gets the same number of candies. Determine whether it is possible.\nNote that Evi cannot take candies out of the packs, and the whole contents of each pack must be given to one of the students.\nTask Constraint: 1 <= a, b, c <= 100\nTask Input: Input The input is given from Standard Input in the following format:\na b c\nTask Output: If it is possible to distribute the packs so that each student gets the same number of candies, print Yes. Otherwise, print No.\nTask Samples: input: 10 30 20 output: Yes\n\nGive the pack with 30 candies to one student, and give the two packs with 10 and 20 candies to the other. Then, each gets 30 candies.\ninput: 30 30 100 output: No\n\nIn this case, the student who gets the pack with 100 candies always has more candies than the other.\nNote that every pack must be given to one of them.\ninput: 56 25 31 output: Yes\n\n" }, { "title": "", "content": "Problem Statement There is a rectangle in the xy-plane, with its lower left corner at (0,0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.\nSnuke plotted N points into the rectangle. The coordinate of the i-th (1 <= i <= N) point was (x_i, y_i).\nThen, he created an integer sequence a of length N, and for each 1 <= i <= N, he painted some region within the rectangle black, as follows:\n\nIf a_i = 1, he painted the region satisfying x < x_i within the rectangle.\nIf a_i = 2, he painted the region satisfying x > x_i within the rectangle.\nIf a_i = 3, he painted the region satisfying y < y_i within the rectangle.\nIf a_i = 4, he painted the region satisfying y > y_i within the rectangle.\n\nFind the area of the white region within the rectangle after he finished painting.", "constraint": "1 <= W, H <= 100\n1 <= N <= 100\n0 <= x_i <= W (1 <= i <= N)\n0 <= y_i <= H (1 <= i <= N)\nW, H (21:32, added), x_i and y_i are integers.\na_i (1 <= i <= N) is 1,2,3 or 4.", "input": "Input The input is given from Standard Input in the following format:\nW H N\nx_1 y_1 a_1\nx_2 y_2 a_2\n:\nx_N y_N a_N", "output": "Print the area of the white region within the rectangle after Snuke finished painting.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 4 2\n2 1 1\n3 3 4 output: 9\n\nThe figure below shows the rectangle before Snuke starts painting.\n\nFirst, as (x_1, y_1) = (2,1) and a_1 = 1, he paints the region satisfying x < 2 within the rectangle:\n\nThen, as (x_2, y_2) = (3,3) and a_2 = 4, he paints the region satisfying y > 3 within the rectangle:\n\nNow, the area of the white region within the rectangle is 9.", "input: 5 4 3\n2 1 1\n3 3 4\n1 4 2 output: 0\n\nIt is possible that the whole region within the rectangle is painted black.", "input: 10 10 5\n1 6 1\n4 1 3\n6 9 4\n9 4 2\n3 1 3 output: 64"], "Pid": "p03944", "ProblemText": "Task Description: Problem Statement There is a rectangle in the xy-plane, with its lower left corner at (0,0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.\nSnuke plotted N points into the rectangle. The coordinate of the i-th (1 <= i <= N) point was (x_i, y_i).\nThen, he created an integer sequence a of length N, and for each 1 <= i <= N, he painted some region within the rectangle black, as follows:\n\nIf a_i = 1, he painted the region satisfying x < x_i within the rectangle.\nIf a_i = 2, he painted the region satisfying x > x_i within the rectangle.\nIf a_i = 3, he painted the region satisfying y < y_i within the rectangle.\nIf a_i = 4, he painted the region satisfying y > y_i within the rectangle.\n\nFind the area of the white region within the rectangle after he finished painting.\nTask Constraint: 1 <= W, H <= 100\n1 <= N <= 100\n0 <= x_i <= W (1 <= i <= N)\n0 <= y_i <= H (1 <= i <= N)\nW, H (21:32, added), x_i and y_i are integers.\na_i (1 <= i <= N) is 1,2,3 or 4.\nTask Input: Input The input is given from Standard Input in the following format:\nW H N\nx_1 y_1 a_1\nx_2 y_2 a_2\n:\nx_N y_N a_N\nTask Output: Print the area of the white region within the rectangle after Snuke finished painting.\nTask Samples: input: 5 4 2\n2 1 1\n3 3 4 output: 9\n\nThe figure below shows the rectangle before Snuke starts painting.\n\nFirst, as (x_1, y_1) = (2,1) and a_1 = 1, he paints the region satisfying x < 2 within the rectangle:\n\nThen, as (x_2, y_2) = (3,3) and a_2 = 4, he paints the region satisfying y > 3 within the rectangle:\n\nNow, the area of the white region within the rectangle is 9.\ninput: 5 4 3\n2 1 1\n3 3 4\n1 4 2 output: 0\n\nIt is possible that the whole region within the rectangle is painted black.\ninput: 10 10 5\n1 6 1\n4 1 3\n6 9 4\n9 4 2\n3 1 3 output: 64\n\n" }, { "title": "", "content": "Problem Statement Two foxes Jiro and Saburo are playing a game called 1D Reversi. This game is played on a board, using black and white stones. On the board, stones are placed in a row, and each player places a new stone to either end of the row. Similarly to the original game of Reversi, when a white stone is placed, all black stones between the new white stone and another white stone, turn into white stones, and vice versa.\nIn the middle of a game, something came up and Saburo has to leave the game. The state of the board at this point is described by a string S. There are |S| (the length of S) stones on the board, and each character in S represents the color of the i-th (1 <= i <= |S|) stone from the left. If the i-th character in S is B, it means that the color of the corresponding stone on the board is black. Similarly, if the i-th character in S is W, it means that the color of the corresponding stone is white.\nJiro wants all stones on the board to be of the same color. For this purpose, he will place new stones on the board according to the rules. Find the minimum number of new stones that he needs to place.", "constraint": "1 <= |S| <= 10^5\nEach character in S is B or W.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "Print the minimum number of new stones that Jiro needs to place for his purpose.", "content_img": false, "lang": "en", "error": false, "samples": ["input: BBBWW output: 1\n\nBy placing a new black stone to the right end of the row of stones, all white stones will become black. Also, by placing a new white stone to the left end of the row of stones, all black stones will become white.\nIn either way, Jiro's purpose can be achieved by placing one stone.", "input: WWWWWW output: 0\n\nIf all stones are already of the same color, no new stone is necessary.", "input: WBWBWBWBWB output: 9"], "Pid": "p03945", "ProblemText": "Task Description: Problem Statement Two foxes Jiro and Saburo are playing a game called 1D Reversi. This game is played on a board, using black and white stones. On the board, stones are placed in a row, and each player places a new stone to either end of the row. Similarly to the original game of Reversi, when a white stone is placed, all black stones between the new white stone and another white stone, turn into white stones, and vice versa.\nIn the middle of a game, something came up and Saburo has to leave the game. The state of the board at this point is described by a string S. There are |S| (the length of S) stones on the board, and each character in S represents the color of the i-th (1 <= i <= |S|) stone from the left. If the i-th character in S is B, it means that the color of the corresponding stone on the board is black. Similarly, if the i-th character in S is W, it means that the color of the corresponding stone is white.\nJiro wants all stones on the board to be of the same color. For this purpose, he will place new stones on the board according to the rules. Find the minimum number of new stones that he needs to place.\nTask Constraint: 1 <= |S| <= 10^5\nEach character in S is B or W.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: Print the minimum number of new stones that Jiro needs to place for his purpose.\nTask Samples: input: BBBWW output: 1\n\nBy placing a new black stone to the right end of the row of stones, all white stones will become black. Also, by placing a new white stone to the left end of the row of stones, all black stones will become white.\nIn either way, Jiro's purpose can be achieved by placing one stone.\ninput: WWWWWW output: 0\n\nIf all stones are already of the same color, no new stone is necessary.\ninput: WBWBWBWBWB output: 9\n\n" }, { "title": "", "content": "Problem Statement There are N towns located in a line, conveniently numbered 1 through N. Takahashi the merchant is going on a travel from town 1 to town N, buying and selling apples.\nTakahashi will begin the travel at town 1, with no apple in his possession. The actions that can be performed during the travel are as follows:\n\nMove: When at town i (i < N), move to town i + 1.\nMerchandise: Buy or sell an arbitrary number of apples at the current town. Here, it is assumed that one apple can always be bought and sold for A_i yen (the currency of Japan) at town i (1 <= i <= N), where A_i are distinct integers. Also, you can assume that he has an infinite supply of money.\n\nFor some reason, there is a constraint on merchandising apple during the travel: the sum of the number of apples bought and the number of apples sold during the whole travel, must be at most T. (Note that a single apple can be counted in both. )\nDuring the travel, Takahashi will perform actions so that the profit of the travel is maximized. Here, the profit of the travel is the amount of money that is gained by selling apples, minus the amount of money that is spent on buying apples. Note that we are not interested in apples in his possession at the end of the travel.\nAoki, a business rival of Takahashi, wants to trouble Takahashi by manipulating the market price of apples. Prior to the beginning of Takahashi's travel, Aoki can change A_i into another arbitrary non-negative integer A_i' for any town i, any number of times. The cost of performing this operation is |A_i - A_i'|. After performing this operation, different towns may have equal values of A_i.\nAoki's objective is to decrease Takahashi's expected profit by at least 1 yen. Find the minimum total cost to achieve it. You may assume that Takahashi's expected profit is initially at least 1 yen.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9 (1 <= i <= N)\nA_i are distinct.\n2 <= T <= 10^9\nIn the initial state, Takahashi's expected profit is at least 1 yen.", "input": "Input The input is given from Standard Input in the following format:\nN T\nA_1 A_2 . . . A_N", "output": "Print the minimum total cost to decrease Takahashi's expected profit by at least 1 yen.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n100 50 200 output: 1\n\nIn the initial state, Takahashi can achieve the maximum profit of 150 yen as follows:\n\nMove from town 1 to town 2.\nBuy one apple for 50 yen at town 2.\nMove from town 2 to town 3.\nSell one apple for 200 yen at town 3.\n\nIf, for example, Aoki changes the price of an apple at town 2 from 50 yen to 51 yen, Takahashi will not be able to achieve the profit of 150 yen. The cost of performing this operation is 1, thus the answer is 1.\nThere are other ways to decrease Takahashi's expected profit, such as changing the price of an apple at town 3 from 200 yen to 199 yen.", "input: 5 8\n50 30 40 10 20 output: 2", "input: 10 100\n7 10 4 5 9 3 6 8 2 1 output: 2"], "Pid": "p03946", "ProblemText": "Task Description: Problem Statement There are N towns located in a line, conveniently numbered 1 through N. Takahashi the merchant is going on a travel from town 1 to town N, buying and selling apples.\nTakahashi will begin the travel at town 1, with no apple in his possession. The actions that can be performed during the travel are as follows:\n\nMove: When at town i (i < N), move to town i + 1.\nMerchandise: Buy or sell an arbitrary number of apples at the current town. Here, it is assumed that one apple can always be bought and sold for A_i yen (the currency of Japan) at town i (1 <= i <= N), where A_i are distinct integers. Also, you can assume that he has an infinite supply of money.\n\nFor some reason, there is a constraint on merchandising apple during the travel: the sum of the number of apples bought and the number of apples sold during the whole travel, must be at most T. (Note that a single apple can be counted in both. )\nDuring the travel, Takahashi will perform actions so that the profit of the travel is maximized. Here, the profit of the travel is the amount of money that is gained by selling apples, minus the amount of money that is spent on buying apples. Note that we are not interested in apples in his possession at the end of the travel.\nAoki, a business rival of Takahashi, wants to trouble Takahashi by manipulating the market price of apples. Prior to the beginning of Takahashi's travel, Aoki can change A_i into another arbitrary non-negative integer A_i' for any town i, any number of times. The cost of performing this operation is |A_i - A_i'|. After performing this operation, different towns may have equal values of A_i.\nAoki's objective is to decrease Takahashi's expected profit by at least 1 yen. Find the minimum total cost to achieve it. You may assume that Takahashi's expected profit is initially at least 1 yen.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9 (1 <= i <= N)\nA_i are distinct.\n2 <= T <= 10^9\nIn the initial state, Takahashi's expected profit is at least 1 yen.\nTask Input: Input The input is given from Standard Input in the following format:\nN T\nA_1 A_2 . . . A_N\nTask Output: Print the minimum total cost to decrease Takahashi's expected profit by at least 1 yen.\nTask Samples: input: 3 2\n100 50 200 output: 1\n\nIn the initial state, Takahashi can achieve the maximum profit of 150 yen as follows:\n\nMove from town 1 to town 2.\nBuy one apple for 50 yen at town 2.\nMove from town 2 to town 3.\nSell one apple for 200 yen at town 3.\n\nIf, for example, Aoki changes the price of an apple at town 2 from 50 yen to 51 yen, Takahashi will not be able to achieve the profit of 150 yen. The cost of performing this operation is 1, thus the answer is 1.\nThere are other ways to decrease Takahashi's expected profit, such as changing the price of an apple at town 3 from 200 yen to 199 yen.\ninput: 5 8\n50 30 40 10 20 output: 2\ninput: 10 100\n7 10 4 5 9 3 6 8 2 1 output: 2\n\n" }, { "title": "", "content": "Problem Statement Two foxes Jiro and Saburo are playing a game called 1D Reversi. This game is played on a board, using black and white stones. On the board, stones are placed in a row, and each player places a new stone to either end of the row. Similarly to the original game of Reversi, when a white stone is placed, all black stones between the new white stone and another white stone, turn into white stones, and vice versa.\nIn the middle of a game, something came up and Saburo has to leave the game. The state of the board at this point is described by a string S. There are |S| (the length of S) stones on the board, and each character in S represents the color of the i-th (1 <= i <= |S|) stone from the left. If the i-th character in S is B, it means that the color of the corresponding stone on the board is black. Similarly, if the i-th character in S is W, it means that the color of the corresponding stone is white.\nJiro wants all stones on the board to be of the same color. For this purpose, he will place new stones on the board according to the rules. Find the minimum number of new stones that he needs to place.", "constraint": "1 <= |S| <= 10^5\nEach character in S is B or W.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "Print the minimum number of new stones that Jiro needs to place for his purpose.", "content_img": false, "lang": "en", "error": false, "samples": ["input: BBBWW output: 1\n\nBy placing a new black stone to the right end of the row of stones, all white stones will become black. Also, by placing a new white stone to the left end of the row of stones, all black stones will become white.\nIn either way, Jiro's purpose can be achieved by placing one stone.", "input: WWWWWW output: 0\n\nIf all stones are already of the same color, no new stone is necessary.", "input: WBWBWBWBWB output: 9"], "Pid": "p03947", "ProblemText": "Task Description: Problem Statement Two foxes Jiro and Saburo are playing a game called 1D Reversi. This game is played on a board, using black and white stones. On the board, stones are placed in a row, and each player places a new stone to either end of the row. Similarly to the original game of Reversi, when a white stone is placed, all black stones between the new white stone and another white stone, turn into white stones, and vice versa.\nIn the middle of a game, something came up and Saburo has to leave the game. The state of the board at this point is described by a string S. There are |S| (the length of S) stones on the board, and each character in S represents the color of the i-th (1 <= i <= |S|) stone from the left. If the i-th character in S is B, it means that the color of the corresponding stone on the board is black. Similarly, if the i-th character in S is W, it means that the color of the corresponding stone is white.\nJiro wants all stones on the board to be of the same color. For this purpose, he will place new stones on the board according to the rules. Find the minimum number of new stones that he needs to place.\nTask Constraint: 1 <= |S| <= 10^5\nEach character in S is B or W.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: Print the minimum number of new stones that Jiro needs to place for his purpose.\nTask Samples: input: BBBWW output: 1\n\nBy placing a new black stone to the right end of the row of stones, all white stones will become black. Also, by placing a new white stone to the left end of the row of stones, all black stones will become white.\nIn either way, Jiro's purpose can be achieved by placing one stone.\ninput: WWWWWW output: 0\n\nIf all stones are already of the same color, no new stone is necessary.\ninput: WBWBWBWBWB output: 9\n\n" }, { "title": "", "content": "Problem Statement There are N towns located in a line, conveniently numbered 1 through N. Takahashi the merchant is going on a travel from town 1 to town N, buying and selling apples.\nTakahashi will begin the travel at town 1, with no apple in his possession. The actions that can be performed during the travel are as follows:\n\nMove: When at town i (i < N), move to town i + 1.\nMerchandise: Buy or sell an arbitrary number of apples at the current town. Here, it is assumed that one apple can always be bought and sold for A_i yen (the currency of Japan) at town i (1 <= i <= N), where A_i are distinct integers. Also, you can assume that he has an infinite supply of money.\n\nFor some reason, there is a constraint on merchandising apple during the travel: the sum of the number of apples bought and the number of apples sold during the whole travel, must be at most T. (Note that a single apple can be counted in both. )\nDuring the travel, Takahashi will perform actions so that the profit of the travel is maximized. Here, the profit of the travel is the amount of money that is gained by selling apples, minus the amount of money that is spent on buying apples. Note that we are not interested in apples in his possession at the end of the travel.\nAoki, a business rival of Takahashi, wants to trouble Takahashi by manipulating the market price of apples. Prior to the beginning of Takahashi's travel, Aoki can change A_i into another arbitrary non-negative integer A_i' for any town i, any number of times. The cost of performing this operation is |A_i - A_i'|. After performing this operation, different towns may have equal values of A_i.\nAoki's objective is to decrease Takahashi's expected profit by at least 1 yen. Find the minimum total cost to achieve it. You may assume that Takahashi's expected profit is initially at least 1 yen.", "constraint": "1 <= N <= 10^5\n1 <= A_i <= 10^9 (1 <= i <= N)\nA_i are distinct.\n2 <= T <= 10^9\nIn the initial state, Takahashi's expected profit is at least 1 yen.", "input": "Input The input is given from Standard Input in the following format:\nN T\nA_1 A_2 . . . A_N", "output": "Print the minimum total cost to decrease Takahashi's expected profit by at least 1 yen.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n100 50 200 output: 1\n\nIn the initial state, Takahashi can achieve the maximum profit of 150 yen as follows:\n\nMove from town 1 to town 2.\nBuy one apple for 50 yen at town 2.\nMove from town 2 to town 3.\nSell one apple for 200 yen at town 3.\n\nIf, for example, Aoki changes the price of an apple at town 2 from 50 yen to 51 yen, Takahashi will not be able to achieve the profit of 150 yen. The cost of performing this operation is 1, thus the answer is 1.\nThere are other ways to decrease Takahashi's expected profit, such as changing the price of an apple at town 3 from 200 yen to 199 yen.", "input: 5 8\n50 30 40 10 20 output: 2", "input: 10 100\n7 10 4 5 9 3 6 8 2 1 output: 2"], "Pid": "p03948", "ProblemText": "Task Description: Problem Statement There are N towns located in a line, conveniently numbered 1 through N. Takahashi the merchant is going on a travel from town 1 to town N, buying and selling apples.\nTakahashi will begin the travel at town 1, with no apple in his possession. The actions that can be performed during the travel are as follows:\n\nMove: When at town i (i < N), move to town i + 1.\nMerchandise: Buy or sell an arbitrary number of apples at the current town. Here, it is assumed that one apple can always be bought and sold for A_i yen (the currency of Japan) at town i (1 <= i <= N), where A_i are distinct integers. Also, you can assume that he has an infinite supply of money.\n\nFor some reason, there is a constraint on merchandising apple during the travel: the sum of the number of apples bought and the number of apples sold during the whole travel, must be at most T. (Note that a single apple can be counted in both. )\nDuring the travel, Takahashi will perform actions so that the profit of the travel is maximized. Here, the profit of the travel is the amount of money that is gained by selling apples, minus the amount of money that is spent on buying apples. Note that we are not interested in apples in his possession at the end of the travel.\nAoki, a business rival of Takahashi, wants to trouble Takahashi by manipulating the market price of apples. Prior to the beginning of Takahashi's travel, Aoki can change A_i into another arbitrary non-negative integer A_i' for any town i, any number of times. The cost of performing this operation is |A_i - A_i'|. After performing this operation, different towns may have equal values of A_i.\nAoki's objective is to decrease Takahashi's expected profit by at least 1 yen. Find the minimum total cost to achieve it. You may assume that Takahashi's expected profit is initially at least 1 yen.\nTask Constraint: 1 <= N <= 10^5\n1 <= A_i <= 10^9 (1 <= i <= N)\nA_i are distinct.\n2 <= T <= 10^9\nIn the initial state, Takahashi's expected profit is at least 1 yen.\nTask Input: Input The input is given from Standard Input in the following format:\nN T\nA_1 A_2 . . . A_N\nTask Output: Print the minimum total cost to decrease Takahashi's expected profit by at least 1 yen.\nTask Samples: input: 3 2\n100 50 200 output: 1\n\nIn the initial state, Takahashi can achieve the maximum profit of 150 yen as follows:\n\nMove from town 1 to town 2.\nBuy one apple for 50 yen at town 2.\nMove from town 2 to town 3.\nSell one apple for 200 yen at town 3.\n\nIf, for example, Aoki changes the price of an apple at town 2 from 50 yen to 51 yen, Takahashi will not be able to achieve the profit of 150 yen. The cost of performing this operation is 1, thus the answer is 1.\nThere are other ways to decrease Takahashi's expected profit, such as changing the price of an apple at town 3 from 200 yen to 199 yen.\ninput: 5 8\n50 30 40 10 20 output: 2\ninput: 10 100\n7 10 4 5 9 3 6 8 2 1 output: 2\n\n" }, { "title": "", "content": "Problem Statement We have a tree with N vertices. The vertices are numbered 1,2, . . . , N. The i-th (1 <= i <= N - 1) edge connects the two vertices A_i and B_i.\nTakahashi wrote integers into K of the vertices. Specifically, for each 1 <= j <= K, he wrote the integer P_j into vertex V_j. The remaining vertices are left empty. After that, he got tired and fell asleep.\nThen, Aoki appeared. He is trying to surprise Takahashi by writing integers into all empty vertices so that the following condition is satisfied:\n\nCondition: For any two vertices directly connected by an edge, the integers written into these vertices differ by exactly 1.\n\nDetermine if it is possible to write integers into all empty vertices so that the condition is satisfied. If the answer is positive, find one specific way to satisfy the condition.", "constraint": "1 <= N <= 10^5\n1 <= K <= N\n1 <= A_i, B_i <= N (1 <= i <= N - 1)\n1 <= V_j <= N (1 <= j <= K) (21:18, a mistake in this constraint was corrected)\n0 <= P_j <= 10^5 (1 <= j <= K)\nThe given graph is a tree.\nAll v_j are distinct.", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_{N-1} B_{N-1}\nK\nV_1 P_1\nV_2 P_2\n:\nV_K P_K", "output": "If it is possible to write integers into all empty vertices so that the condition is satisfied, print Yes. Otherwise, print No.\nIf it is possible to satisfy the condition, print N lines in addition. The v-th (1 <= v <= N) of these N lines should contain the integer that should be written into vertex v. If there are multiple ways to satisfy the condition, any of those is accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 2\n3 1\n4 3\n3 5\n2\n2 6\n5 7 output: Yes\n5\n6\n6\n5\n7\n\nThe figure below shows the tree when Takahashi fell asleep. For each vertex, the integer written beside it represents the index of the vertex, and the integer written into the vertex is the integer written by Takahashi.\n\nAoki can, for example, satisfy the condition by writing integers into the remaining vertices as follows:\n\nThis corresponds to Sample Output 1. Note that other outputs that satisfy the condition will also be accepted, such as:\nYes\n7\n6\n8\n7\n7", "input: 5\n1 2\n3 1\n4 3\n3 5\n3\n2 6\n4 3\n5 7 output: No", "input: 4\n1 2\n2 3\n3 4\n1\n1 0 output: Yes\n0\n-1\n-2\n-3\n\nThe integers written by Aoki may be negative or exceed 10^6."], "Pid": "p03949", "ProblemText": "Task Description: Problem Statement We have a tree with N vertices. The vertices are numbered 1,2, . . . , N. The i-th (1 <= i <= N - 1) edge connects the two vertices A_i and B_i.\nTakahashi wrote integers into K of the vertices. Specifically, for each 1 <= j <= K, he wrote the integer P_j into vertex V_j. The remaining vertices are left empty. After that, he got tired and fell asleep.\nThen, Aoki appeared. He is trying to surprise Takahashi by writing integers into all empty vertices so that the following condition is satisfied:\n\nCondition: For any two vertices directly connected by an edge, the integers written into these vertices differ by exactly 1.\n\nDetermine if it is possible to write integers into all empty vertices so that the condition is satisfied. If the answer is positive, find one specific way to satisfy the condition.\nTask Constraint: 1 <= N <= 10^5\n1 <= K <= N\n1 <= A_i, B_i <= N (1 <= i <= N - 1)\n1 <= V_j <= N (1 <= j <= K) (21:18, a mistake in this constraint was corrected)\n0 <= P_j <= 10^5 (1 <= j <= K)\nThe given graph is a tree.\nAll v_j are distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1 B_1\nA_2 B_2\n:\nA_{N-1} B_{N-1}\nK\nV_1 P_1\nV_2 P_2\n:\nV_K P_K\nTask Output: If it is possible to write integers into all empty vertices so that the condition is satisfied, print Yes. Otherwise, print No.\nIf it is possible to satisfy the condition, print N lines in addition. The v-th (1 <= v <= N) of these N lines should contain the integer that should be written into vertex v. If there are multiple ways to satisfy the condition, any of those is accepted.\nTask Samples: input: 5\n1 2\n3 1\n4 3\n3 5\n2\n2 6\n5 7 output: Yes\n5\n6\n6\n5\n7\n\nThe figure below shows the tree when Takahashi fell asleep. For each vertex, the integer written beside it represents the index of the vertex, and the integer written into the vertex is the integer written by Takahashi.\n\nAoki can, for example, satisfy the condition by writing integers into the remaining vertices as follows:\n\nThis corresponds to Sample Output 1. Note that other outputs that satisfy the condition will also be accepted, such as:\nYes\n7\n6\n8\n7\n7\ninput: 5\n1 2\n3 1\n4 3\n3 5\n3\n2 6\n4 3\n5 7 output: No\ninput: 4\n1 2\n2 3\n3 4\n1\n1 0 output: Yes\n0\n-1\n-2\n-3\n\nThe integers written by Aoki may be negative or exceed 10^6.\n\n" }, { "title": "", "content": "Problem Statement There is a rectangle in the xy-plane, with its lower left corner at (0,0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.\nSnuke plotted N points into the rectangle. The coordinate of the i-th (1 <= i <= N) point was (x_i, y_i).\nThen, for each 1 <= i <= N, he will paint one of the following four regions black:\n\nthe region satisfying x < x_i within the rectangle\nthe region satisfying x > x_i within the rectangle\nthe region satisfying y < y_i within the rectangle\nthe region satisfying y > y_i within the rectangle\n\nFind the longest possible perimeter of the white region of a rectangular shape within the rectangle after he finishes painting.", "constraint": "1 <= W, H <= 10^8\n1 <= N <= 3 * 10^5\n0 <= x_i <= W (1 <= i <= N)\n0 <= y_i <= H (1 <= i <= N)\nW, H (21:32, added), x_i and y_i are integers.\nIf i != j, then x_i != x_j and y_i != y_j.", "input": "Input The input is given from Standard Input in the following format:\nW H N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N", "output": "Print the longest possible perimeter of the white region of a rectangular shape within the rectangle after Snuke finishes painting.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 10 4\n1 6\n4 1\n6 9\n9 4 output: 32\n\nIn this case, the maximum perimeter of 32 can be obtained by painting the rectangle as follows:", "input: 5 4 5\n0 0\n1 1\n2 2\n4 3\n5 4 output: 12", "input: 100 100 8\n19 33\n8 10\n52 18\n94 2\n81 36\n88 95\n67 83\n20 71 output: 270", "input: 100000000 100000000 1\n3 4 output: 399999994"], "Pid": "p03950", "ProblemText": "Task Description: Problem Statement There is a rectangle in the xy-plane, with its lower left corner at (0,0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.\nSnuke plotted N points into the rectangle. The coordinate of the i-th (1 <= i <= N) point was (x_i, y_i).\nThen, for each 1 <= i <= N, he will paint one of the following four regions black:\n\nthe region satisfying x < x_i within the rectangle\nthe region satisfying x > x_i within the rectangle\nthe region satisfying y < y_i within the rectangle\nthe region satisfying y > y_i within the rectangle\n\nFind the longest possible perimeter of the white region of a rectangular shape within the rectangle after he finishes painting.\nTask Constraint: 1 <= W, H <= 10^8\n1 <= N <= 3 * 10^5\n0 <= x_i <= W (1 <= i <= N)\n0 <= y_i <= H (1 <= i <= N)\nW, H (21:32, added), x_i and y_i are integers.\nIf i != j, then x_i != x_j and y_i != y_j.\nTask Input: Input The input is given from Standard Input in the following format:\nW H N\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\nTask Output: Print the longest possible perimeter of the white region of a rectangular shape within the rectangle after Snuke finishes painting.\nTask Samples: input: 10 10 4\n1 6\n4 1\n6 9\n9 4 output: 32\n\nIn this case, the maximum perimeter of 32 can be obtained by painting the rectangle as follows:\ninput: 5 4 5\n0 0\n1 1\n2 2\n4 3\n5 4 output: 12\ninput: 100 100 8\n19 33\n8 10\n52 18\n94 2\n81 36\n88 95\n67 83\n20 71 output: 270\ninput: 100000000 100000000 1\n3 4 output: 399999994\n\n" }, { "title": "", "content": "Problem Statement Snuke is interested in strings that satisfy the following conditions:\n\nThe length of the string is at least N.\nThe first N characters equal to the string s.\nThe last N characters equal to the string t.\n\nFind the length of the shortest string that satisfies the conditions.", "constraint": "1<=N<=100\nThe lengths of s and t are both N.\ns and t consist of lowercase English letters.", "input": "Input The input is given from Standard Input in the following format:\nN\ns\nt", "output": "Print the length of the shortest string that satisfies the conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\nabc\ncde output: 5\n\nThe shortest string is abcde.", "input: 1\na\nz output: 2\n\nThe shortest string is az.", "input: 4\nexpr\nexpr output: 4\n\nThe shortest string is expr."], "Pid": "p03951", "ProblemText": "Task Description: Problem Statement Snuke is interested in strings that satisfy the following conditions:\n\nThe length of the string is at least N.\nThe first N characters equal to the string s.\nThe last N characters equal to the string t.\n\nFind the length of the shortest string that satisfies the conditions.\nTask Constraint: 1<=N<=100\nThe lengths of s and t are both N.\ns and t consist of lowercase English letters.\nTask Input: Input The input is given from Standard Input in the following format:\nN\ns\nt\nTask Output: Print the length of the shortest string that satisfies the conditions.\nTask Samples: input: 3\nabc\ncde output: 5\n\nThe shortest string is abcde.\ninput: 1\na\nz output: 2\n\nThe shortest string is az.\ninput: 4\nexpr\nexpr output: 4\n\nThe shortest string is expr.\n\n" }, { "title": "", "content": "Problem Statement We have a pyramid with N steps, built with blocks.\nThe steps are numbered 1 through N from top to bottom.\nFor each 1<=i<=N, step i consists of 2i-1 blocks aligned horizontally.\nThe pyramid is built so that the blocks at the centers of the steps are aligned vertically.\nA pyramid with N=4 steps\n\nSnuke wrote a permutation of (1,2, . . . , 2N-1) into the blocks of step N.\nThen, he wrote integers into all remaining blocks, under the following rule:\n\nThe integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.\n\nWriting integers into the blocks\n\nAfterwards, he erased all integers written into the blocks.\nNow, he only remembers that the integer written into the block of step 1 was x.\nConstruct a permutation of (1,2, . . . , 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.", "constraint": "2<=N<=10^5\n1<=x<=2N-1", "input": "Input The input is given from Standard Input in the following format:\nN x", "output": "If no permutation of (1,2, . . . , 2N-1) could have been written into the blocks of step N, print No.\nOtherwise, print Yes in the first line, then print 2N-1 lines in addition.\nThe i-th of these 2N-1 lines should contain the i-th element of a possible permutation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4 output: Yes\n1\n6\n3\n7\n4\n5\n2\n\nThis case corresponds to the figure in the problem statement.", "input: 2 1 output: No\n\nNo matter what permutation was written into the blocks of step N, the integer written into the block of step 1 would be 2."], "Pid": "p03952", "ProblemText": "Task Description: Problem Statement We have a pyramid with N steps, built with blocks.\nThe steps are numbered 1 through N from top to bottom.\nFor each 1<=i<=N, step i consists of 2i-1 blocks aligned horizontally.\nThe pyramid is built so that the blocks at the centers of the steps are aligned vertically.\nA pyramid with N=4 steps\n\nSnuke wrote a permutation of (1,2, . . . , 2N-1) into the blocks of step N.\nThen, he wrote integers into all remaining blocks, under the following rule:\n\nThe integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.\n\nWriting integers into the blocks\n\nAfterwards, he erased all integers written into the blocks.\nNow, he only remembers that the integer written into the block of step 1 was x.\nConstruct a permutation of (1,2, . . . , 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.\nTask Constraint: 2<=N<=10^5\n1<=x<=2N-1\nTask Input: Input The input is given from Standard Input in the following format:\nN x\nTask Output: If no permutation of (1,2, . . . , 2N-1) could have been written into the blocks of step N, print No.\nOtherwise, print Yes in the first line, then print 2N-1 lines in addition.\nThe i-th of these 2N-1 lines should contain the i-th element of a possible permutation.\nTask Samples: input: 4 4 output: Yes\n1\n6\n3\n7\n4\n5\n2\n\nThis case corresponds to the figure in the problem statement.\ninput: 2 1 output: No\n\nNo matter what permutation was written into the blocks of step N, the integer written into the block of step 1 would be 2.\n\n" }, { "title": "", "content": "Problem Statement There are N rabbits on a number line.\nThe rabbits are conveniently numbered 1 through N.\nThe coordinate of the initial position of rabbit i is x_i.\nThe rabbits will now take exercise on the number line, by performing sets described below.\nA set consists of M jumps. The j-th jump of a set is performed by rabbit a_j (2<=a_j<=N-1).\nFor this jump, either rabbit a_j-1 or rabbit a_j+1 is chosen with equal probability (let the chosen rabbit be rabbit x), then rabbit a_j will jump to the symmetric point of its current position with respect to rabbit x.\nThe rabbits will perform K sets in succession.\nFor each rabbit, find the expected value of the coordinate of its eventual position after K sets are performed.", "constraint": "3<=N<=10^5\nx_i is an integer.\n|x_i|<=10^9\n1<=M<=10^5\n2<=a_j<=N-1\n1<=K<=10^{18}", "input": "Input The input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N\nM K\na_1 a_2 . . . a_M", "output": "Print N lines.\nThe i-th line should contain the expected value of the coordinate of the eventual position of rabbit i after K sets are performed.\nThe output is considered correct if the absolute or relative error is at most 10^{-9}.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n-1 0 2\n1 1\n2 output: -1.0\n1.0\n2.0\n\nRabbit 2 will perform the jump.\nIf rabbit 1 is chosen, the coordinate of the destination will be -2.\nIf rabbit 3 is chosen, the coordinate of the destination will be 4.\nThus, the expected value of the coordinate of the eventual position of rabbit 2 is 0.5*(-2)+0.5*4=1.0.", "input: 3\n1 -1 1\n2 2\n2 2 output: 1.0\n-1.0\n1.0\n\nx_i may not be distinct.", "input: 5\n0 1 3 6 10\n3 10\n2 3 4 output: 0.0\n3.0\n7.0\n8.0\n10.0"], "Pid": "p03953", "ProblemText": "Task Description: Problem Statement There are N rabbits on a number line.\nThe rabbits are conveniently numbered 1 through N.\nThe coordinate of the initial position of rabbit i is x_i.\nThe rabbits will now take exercise on the number line, by performing sets described below.\nA set consists of M jumps. The j-th jump of a set is performed by rabbit a_j (2<=a_j<=N-1).\nFor this jump, either rabbit a_j-1 or rabbit a_j+1 is chosen with equal probability (let the chosen rabbit be rabbit x), then rabbit a_j will jump to the symmetric point of its current position with respect to rabbit x.\nThe rabbits will perform K sets in succession.\nFor each rabbit, find the expected value of the coordinate of its eventual position after K sets are performed.\nTask Constraint: 3<=N<=10^5\nx_i is an integer.\n|x_i|<=10^9\n1<=M<=10^5\n2<=a_j<=N-1\n1<=K<=10^{18}\nTask Input: Input The input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N\nM K\na_1 a_2 . . . a_M\nTask Output: Print N lines.\nThe i-th line should contain the expected value of the coordinate of the eventual position of rabbit i after K sets are performed.\nThe output is considered correct if the absolute or relative error is at most 10^{-9}.\nTask Samples: input: 3\n-1 0 2\n1 1\n2 output: -1.0\n1.0\n2.0\n\nRabbit 2 will perform the jump.\nIf rabbit 1 is chosen, the coordinate of the destination will be -2.\nIf rabbit 3 is chosen, the coordinate of the destination will be 4.\nThus, the expected value of the coordinate of the eventual position of rabbit 2 is 0.5*(-2)+0.5*4=1.0.\ninput: 3\n1 -1 1\n2 2\n2 2 output: 1.0\n-1.0\n1.0\n\nx_i may not be distinct.\ninput: 5\n0 1 3 6 10\n3 10\n2 3 4 output: 0.0\n3.0\n7.0\n8.0\n10.0\n\n" }, { "title": "", "content": "Problem Statement We have a pyramid with N steps, built with blocks.\nThe steps are numbered 1 through N from top to bottom.\nFor each 1<=i<=N, step i consists of 2i-1 blocks aligned horizontally.\nThe pyramid is built so that the blocks at the centers of the steps are aligned vertically.\nA pyramid with N=4 steps\n\nSnuke wrote a permutation of (1,2, . . . , 2N-1) into the blocks of step N.\nThen, he wrote integers into all remaining blocks, under the following rule:\n\nThe integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.\n\nWriting integers into the blocks\n\nAfterwards, he erased all integers written into the blocks.\nNow, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, . . . , a_{2N-1}).\nFind the integer written into the block of step 1.", "constraint": "2<=N<=10^5\n(a_1, a_2, ..., a_{2N-1}) is a permutation of (1,2, ..., 2N-1).", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{2N-1}", "output": "Print the integer written into the block of step 1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n1 6 3 7 4 5 2 output: 4\n\nThis case corresponds to the figure in the problem statement.", "input: 2\n1 2 3 output: 2"], "Pid": "p03954", "ProblemText": "Task Description: Problem Statement We have a pyramid with N steps, built with blocks.\nThe steps are numbered 1 through N from top to bottom.\nFor each 1<=i<=N, step i consists of 2i-1 blocks aligned horizontally.\nThe pyramid is built so that the blocks at the centers of the steps are aligned vertically.\nA pyramid with N=4 steps\n\nSnuke wrote a permutation of (1,2, . . . , 2N-1) into the blocks of step N.\nThen, he wrote integers into all remaining blocks, under the following rule:\n\nThe integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.\n\nWriting integers into the blocks\n\nAfterwards, he erased all integers written into the blocks.\nNow, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, . . . , a_{2N-1}).\nFind the integer written into the block of step 1.\nTask Constraint: 2<=N<=10^5\n(a_1, a_2, ..., a_{2N-1}) is a permutation of (1,2, ..., 2N-1).\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_{2N-1}\nTask Output: Print the integer written into the block of step 1.\nTask Samples: input: 4\n1 6 3 7 4 5 2 output: 4\n\nThis case corresponds to the figure in the problem statement.\ninput: 2\n1 2 3 output: 2\n\n" }, { "title": "", "content": "Problem Statement We have a grid with 3 rows and N columns.\nThe cell at the i-th row and j-th column is denoted (i, j).\nInitially, each cell (i, j) contains the integer i+3j-3.\nA grid with N=5 columns\n\nSnuke can perform the following operation any number of times:\n\nChoose a 3*3 subrectangle of the grid. The placement of integers within the subrectangle is now rotated by 180°.\n\nAn example sequence of operations (each chosen subrectangle is colored blue)\n\nSnuke's objective is to manipulate the grid so that each cell (i, j) contains the integer a_{i, j}.\nDetermine whether it is achievable.", "constraint": "5<=N<=10^5\n1<=a_{i,j}<=3N\nAll a_{i,j} are distinct.", "input": "Input The input is given from Standard Input in the following format:\nN\na_{1,1} a_{1,2} . . . a_{1, N}\na_{2,1} a_{2,2} . . . a_{2, N}\na_{3,1} a_{3,2} . . . a_{3, N}", "output": "If Snuke's objective is achievable, print Yes. Otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n9 6 15 12 1\n8 5 14 11 2\n7 4 13 10 3 output: Yes\n\nThis case corresponds to the figure in the problem statement.", "input: 5\n1 2 3 4 5\n6 7 8 9 10\n11 12 13 14 15 output: No", "input: 5\n1 4 7 10 13\n2 5 8 11 14\n3 6 9 12 15 output: Yes\n\nThe objective is already achieved with the initial placement of the integers.", "input: 6\n15 10 3 4 9 16\n14 11 2 5 8 17\n13 12 1 6 7 18 output: Yes", "input: 7\n21 12 1 16 13 6 7\n20 11 2 17 14 5 8\n19 10 3 18 15 4 9 output: No"], "Pid": "p03955", "ProblemText": "Task Description: Problem Statement We have a grid with 3 rows and N columns.\nThe cell at the i-th row and j-th column is denoted (i, j).\nInitially, each cell (i, j) contains the integer i+3j-3.\nA grid with N=5 columns\n\nSnuke can perform the following operation any number of times:\n\nChoose a 3*3 subrectangle of the grid. The placement of integers within the subrectangle is now rotated by 180°.\n\nAn example sequence of operations (each chosen subrectangle is colored blue)\n\nSnuke's objective is to manipulate the grid so that each cell (i, j) contains the integer a_{i, j}.\nDetermine whether it is achievable.\nTask Constraint: 5<=N<=10^5\n1<=a_{i,j}<=3N\nAll a_{i,j} are distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_{1,1} a_{1,2} . . . a_{1, N}\na_{2,1} a_{2,2} . . . a_{2, N}\na_{3,1} a_{3,2} . . . a_{3, N}\nTask Output: If Snuke's objective is achievable, print Yes. Otherwise, print No.\nTask Samples: input: 5\n9 6 15 12 1\n8 5 14 11 2\n7 4 13 10 3 output: Yes\n\nThis case corresponds to the figure in the problem statement.\ninput: 5\n1 2 3 4 5\n6 7 8 9 10\n11 12 13 14 15 output: No\ninput: 5\n1 4 7 10 13\n2 5 8 11 14\n3 6 9 12 15 output: Yes\n\nThe objective is already achieved with the initial placement of the integers.\ninput: 6\n15 10 3 4 9 16\n14 11 2 5 8 17\n13 12 1 6 7 18 output: Yes\ninput: 7\n21 12 1 16 13 6 7\n20 11 2 17 14 5 8\n19 10 3 18 15 4 9 output: No\n\n" }, { "title": "", "content": "Problem Statement We have a grid with N rows and N columns.\nThe cell at the i-th row and j-th column is denoted (i, j).\nInitially, M of the cells are painted black, and all other cells are white.\nSpecifically, the cells (a_1, b_1), (a_2, b_2), . . . , (a_M, b_M) are painted black.\nSnuke will try to paint as many white cells black as possible, according to the following rule:\n\nIf two cells (x, y) and (y, z) are both black and a cell (z, x) is white for integers 1<=x, y, z<=N, paint the cell (z, x) black.\n\nFind the number of black cells when no more white cells can be painted black.", "constraint": "1<=N<=10^5\n1<=M<=10^5\n1<=a_i,b_i<=N\nAll pairs (a_i, b_i) are distinct.", "input": "Input The input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M", "output": "Print the number of black cells when no more white cells can be painted black.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n2 3 output: 3\n\nIt is possible to paint one white cell black, as follows:\n\nSince cells (1,2) and (2,3) are both black and a cell (3,1) is white, paint the cell (3,1) black.", "input: 2 2\n1 1\n1 2 output: 4\n\nIt is possible to paint two white cells black, as follows:\n\nSince cells (1,1) and (1,2) are both black and a cell (2,1) is white, paint the cell (2,1) black.\nSince cells (2,1) and (1,2) are both black and a cell (2,2) is white, paint the cell (2,2) black.", "input: 4 3\n1 2\n1 3\n4 4 output: 3\n\nNo white cells can be painted black."], "Pid": "p03956", "ProblemText": "Task Description: Problem Statement We have a grid with N rows and N columns.\nThe cell at the i-th row and j-th column is denoted (i, j).\nInitially, M of the cells are painted black, and all other cells are white.\nSpecifically, the cells (a_1, b_1), (a_2, b_2), . . . , (a_M, b_M) are painted black.\nSnuke will try to paint as many white cells black as possible, according to the following rule:\n\nIf two cells (x, y) and (y, z) are both black and a cell (z, x) is white for integers 1<=x, y, z<=N, paint the cell (z, x) black.\n\nFind the number of black cells when no more white cells can be painted black.\nTask Constraint: 1<=N<=10^5\n1<=M<=10^5\n1<=a_i,b_i<=N\nAll pairs (a_i, b_i) are distinct.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Output: Print the number of black cells when no more white cells can be painted black.\nTask Samples: input: 3 2\n1 2\n2 3 output: 3\n\nIt is possible to paint one white cell black, as follows:\n\nSince cells (1,2) and (2,3) are both black and a cell (3,1) is white, paint the cell (3,1) black.\ninput: 2 2\n1 1\n1 2 output: 4\n\nIt is possible to paint two white cells black, as follows:\n\nSince cells (1,1) and (1,2) are both black and a cell (2,1) is white, paint the cell (2,1) black.\nSince cells (2,1) and (1,2) are both black and a cell (2,2) is white, paint the cell (2,2) black.\ninput: 4 3\n1 2\n1 3\n4 4 output: 3\n\nNo white cells can be painted black.\n\n" }, { "title": "", "content": "Problem Statement This contest is CODEFESTIVAL, which can be shortened to the string CF by deleting some characters. \nMr. Takahashi, full of curiosity, wondered if he could obtain CF from other strings in the same way. \nYou are given a string s consisting of uppercase English letters.\nDetermine whether the string CF can be obtained from the string s by deleting some characters.", "constraint": "2 <= |s| <= 100\nAll characters in s are uppercase English letters (A-Z).", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "Print Yes if the string CF can be obtained from the string s by deleting some characters.\nOtherwise print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: CODEFESTIVAL output: Yes\n\nCF is obtained by deleting characters other than the first character C and the fifth character F.", "input: FESTIVALCODE output: No\n\nFC can be obtained but CF cannot be obtained because you cannot change the order of the characters.", "input: CF output: Yes\n\nIt is also possible not to delete any characters.", "input: FCF output: Yes\n\nCF is obtained by deleting the first character."], "Pid": "p03957", "ProblemText": "Task Description: Problem Statement This contest is CODEFESTIVAL, which can be shortened to the string CF by deleting some characters. \nMr. Takahashi, full of curiosity, wondered if he could obtain CF from other strings in the same way. \nYou are given a string s consisting of uppercase English letters.\nDetermine whether the string CF can be obtained from the string s by deleting some characters.\nTask Constraint: 2 <= |s| <= 100\nAll characters in s are uppercase English letters (A-Z).\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: Print Yes if the string CF can be obtained from the string s by deleting some characters.\nOtherwise print No.\nTask Samples: input: CODEFESTIVAL output: Yes\n\nCF is obtained by deleting characters other than the first character C and the fifth character F.\ninput: FESTIVALCODE output: No\n\nFC can be obtained but CF cannot be obtained because you cannot change the order of the characters.\ninput: CF output: Yes\n\nIt is also possible not to delete any characters.\ninput: FCF output: Yes\n\nCF is obtained by deleting the first character.\n\n" }, { "title": "", "content": "Problem Statement There are K pieces of cakes.\nMr. Takahashi would like to eat one cake per day, taking K days to eat them all.\nThere are T types of cake, and the number of the cakes of type i (1 <= i <= T) is a_i. \nEating the same type of cake two days in a row would be no fun,\nso Mr. Takahashi would like to decide the order for eating cakes that minimizes the number of days on which he has to eat the same type of cake as the day before. \nCompute the minimum number of days on which the same type of cake as the previous day will be eaten.", "constraint": "1 <= K <= 10000\n1 <= T <= 100\n1 <= a_i <= 100\na_1 + a_2 + ... + a_T = K", "input": "Input The input is given from Standard Input in the following format:\nK T\na_1 a_2 . . . a_T", "output": "Print the minimum number of days on which the same type of cake as the previous day will be eaten.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 7 3\n3 2 2 output: 0\n\nFor example, if Mr. Takahashi eats cakes in the order of 2,1,2,3,1,3,1, he can avoid eating the same type of cake as the previous day.", "input: 6 3\n1 4 1 output: 1\n\nThere are 6 cakes.\nFor example, if Mr. Takahashi eats cakes in the order of 2,3,2,2,1,2, he has to eat the same type of cake (i.e., type 2) as the previous day only on the fourth day.\nSince this is the minimum number, the answer is 1.", "input: 100 1\n100 output: 99\n\nSince Mr. Takahashi has only one type of cake, he has no choice but to eat the same type of cake as the previous day from the second day and after."], "Pid": "p03958", "ProblemText": "Task Description: Problem Statement There are K pieces of cakes.\nMr. Takahashi would like to eat one cake per day, taking K days to eat them all.\nThere are T types of cake, and the number of the cakes of type i (1 <= i <= T) is a_i. \nEating the same type of cake two days in a row would be no fun,\nso Mr. Takahashi would like to decide the order for eating cakes that minimizes the number of days on which he has to eat the same type of cake as the day before. \nCompute the minimum number of days on which the same type of cake as the previous day will be eaten.\nTask Constraint: 1 <= K <= 10000\n1 <= T <= 100\n1 <= a_i <= 100\na_1 + a_2 + ... + a_T = K\nTask Input: Input The input is given from Standard Input in the following format:\nK T\na_1 a_2 . . . a_T\nTask Output: Print the minimum number of days on which the same type of cake as the previous day will be eaten.\nTask Samples: input: 7 3\n3 2 2 output: 0\n\nFor example, if Mr. Takahashi eats cakes in the order of 2,1,2,3,1,3,1, he can avoid eating the same type of cake as the previous day.\ninput: 6 3\n1 4 1 output: 1\n\nThere are 6 cakes.\nFor example, if Mr. Takahashi eats cakes in the order of 2,3,2,2,1,2, he has to eat the same type of cake (i.e., type 2) as the previous day only on the fourth day.\nSince this is the minimum number, the answer is 1.\ninput: 100 1\n100 output: 99\n\nSince Mr. Takahashi has only one type of cake, he has no choice but to eat the same type of cake as the previous day from the second day and after.\n\n" }, { "title": "", "content": "Problem Statement Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range.\nThe mountain range consists of N mountains, extending from west to east in a straight line as Mt. 1, Mt. 2, . . . , Mt. N.\nMr. Takahashi traversed the range from the west and Mr. Aoki from the east. \nThe height of Mt. i is h_i, but they have forgotten the value of each h_i.\nInstead, for each i (1 <= i <= N), they recorded the maximum height of the mountains climbed up to the time they reached the peak of Mt. i (including Mt. i).\nMr. Takahashi's record is T_i and Mr. Aoki's record is A_i. \nWe know that the height of each mountain h_i is a positive integer.\nCompute the number of the possible sequences of the mountains' heights, modulo 10^9 + 7.\nNote that the records may be incorrect and thus there may be no possible sequence of the mountains' heights.\nIn such a case, output 0.", "constraint": "1 <= N <= 10^5\n1 <= T_i <= 10^9\n1 <= A_i <= 10^9\nT_i <= T_{i+1} (1 <= i <= N - 1)\nA_i >= A_{i+1} (1 <= i <= N - 1)", "input": "Input The input is given from Standard Input in the following format:\nN\nT_1 T_2 . . . T_N\nA_1 A_2 . . . A_N", "output": "Print the number of possible sequences of the mountains' heights, modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n1 3 3 3 3\n3 3 2 2 2 output: 4\n\nThe possible sequences of the mountains' heights are:\n\n1,3,2,2,2 \n1,3,2,1,2 \n1,3,1,2,2 \n1,3,1,1,2 \n\nfor a total of four sequences.", "input: 5\n1 1 1 2 2\n3 2 1 1 1 output: 0\n\nThe records are contradictory, since Mr. Takahashi recorded 2 as the highest peak after climbing all the mountains but Mr. Aoki recorded 3.", "input: 10\n1 3776 3776 8848 8848 8848 8848 8848 8848 8848\n8848 8848 8848 8848 8848 8848 8848 8848 3776 5 output: 884111967\n\nDon't forget to compute the number modulo 10^9 + 7.", "input: 1\n17\n17 output: 1\n\nSome mountain ranges consist of only one mountain."], "Pid": "p03959", "ProblemText": "Task Description: Problem Statement Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range.\nThe mountain range consists of N mountains, extending from west to east in a straight line as Mt. 1, Mt. 2, . . . , Mt. N.\nMr. Takahashi traversed the range from the west and Mr. Aoki from the east. \nThe height of Mt. i is h_i, but they have forgotten the value of each h_i.\nInstead, for each i (1 <= i <= N), they recorded the maximum height of the mountains climbed up to the time they reached the peak of Mt. i (including Mt. i).\nMr. Takahashi's record is T_i and Mr. Aoki's record is A_i. \nWe know that the height of each mountain h_i is a positive integer.\nCompute the number of the possible sequences of the mountains' heights, modulo 10^9 + 7.\nNote that the records may be incorrect and thus there may be no possible sequence of the mountains' heights.\nIn such a case, output 0.\nTask Constraint: 1 <= N <= 10^5\n1 <= T_i <= 10^9\n1 <= A_i <= 10^9\nT_i <= T_{i+1} (1 <= i <= N - 1)\nA_i >= A_{i+1} (1 <= i <= N - 1)\nTask Input: Input The input is given from Standard Input in the following format:\nN\nT_1 T_2 . . . T_N\nA_1 A_2 . . . A_N\nTask Output: Print the number of possible sequences of the mountains' heights, modulo 10^9 + 7.\nTask Samples: input: 5\n1 3 3 3 3\n3 3 2 2 2 output: 4\n\nThe possible sequences of the mountains' heights are:\n\n1,3,2,2,2 \n1,3,2,1,2 \n1,3,1,2,2 \n1,3,1,1,2 \n\nfor a total of four sequences.\ninput: 5\n1 1 1 2 2\n3 2 1 1 1 output: 0\n\nThe records are contradictory, since Mr. Takahashi recorded 2 as the highest peak after climbing all the mountains but Mr. Aoki recorded 3.\ninput: 10\n1 3776 3776 8848 8848 8848 8848 8848 8848 8848\n8848 8848 8848 8848 8848 8848 8848 8848 3776 5 output: 884111967\n\nDon't forget to compute the number modulo 10^9 + 7.\ninput: 1\n17\n17 output: 1\n\nSome mountain ranges consist of only one mountain.\n\n" }, { "title": "", "content": "Problem Statement Mr. Takahashi has in his room an art object with H rows and W columns, made up of H * W blocks.\nEach block has a color represented by a lowercase English letter (a-z).\nThe color of the block at the i-th row and j-th column is c_{i, j}. \nMr. Takahashi would like to dismantle the object, finding it a bit kitschy for his tastes.\nThe dismantling is processed by repeating the following operation: \n\nChoose one of the W columns and push down that column one row.\nThe block at the bottom of that column disappears.\n\nEach time the operation is performed, a cost is incurred.\nSince blocks of the same color have a property to draw each other together, the cost of the operation is the number of the pairs of blocks (p, q) such that:\n\nThe block p is in the selected column.\nThe two blocks p and q are horizontally adjacent (before pushing down the column).\nThe two blocks p and q have the same color.\n\nMr. Takahashi dismantles the object by repeating the operation H * W times to get rid of all the blocks.\nCompute the minimum total cost to dismantle the object. partial score: Partial Score\nIn test cases worth 300 points, W = 3.", "constraint": "1 <= H <= 300\n2 <= W <= 300\nAll characters c_{i,j} are lowercase English letters (a-z).", "input": "Input The input is given from Standard Input in the following format:\nH W\nc_{1,1}c_{1,2}. . c_{1, W}\nc_{2,1}c_{2,2}. . c_{2, W}\n:\nc_{H, 1}c_{H, 2}. . c_{H, W}", "output": "Print the minimum total cost to dismantle the object.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\nrrr\nbrg output: 2\n\nFor example, the total cost of 2 can be achieved by performing the operation as follows and this is the minimum value.", "input: 6 3\nxya\nxya\nayz\nayz\nxaz\nxaz output: 0\n\nThe total cost of 0 can be achieved by first pushing down all blocks of the middle column, then all of the left column, and all of the right column.", "input: 4 2\nay\nxa\nxy\nay output: 0\n\nThe total cost of 0 can be achieved by the following operations:\n\npushing down the right column one row;\npushing down the left column one row;\npushing down all of the right column;\nand pushing down all of the left column.", "input: 5 5\naaaaa\nabbba\nababa\nabbba\naaaaa output: 24", "input: 7 10\nxxxxxxxxxx\nccccxxffff\ncxxcxxfxxx\ncxxxxxffff\ncxxcxxfxxx\nccccxxfxxx\nxxxxxxxxxx output: 130"], "Pid": "p03960", "ProblemText": "Task Description: Problem Statement Mr. Takahashi has in his room an art object with H rows and W columns, made up of H * W blocks.\nEach block has a color represented by a lowercase English letter (a-z).\nThe color of the block at the i-th row and j-th column is c_{i, j}. \nMr. Takahashi would like to dismantle the object, finding it a bit kitschy for his tastes.\nThe dismantling is processed by repeating the following operation: \n\nChoose one of the W columns and push down that column one row.\nThe block at the bottom of that column disappears.\n\nEach time the operation is performed, a cost is incurred.\nSince blocks of the same color have a property to draw each other together, the cost of the operation is the number of the pairs of blocks (p, q) such that:\n\nThe block p is in the selected column.\nThe two blocks p and q are horizontally adjacent (before pushing down the column).\nThe two blocks p and q have the same color.\n\nMr. Takahashi dismantles the object by repeating the operation H * W times to get rid of all the blocks.\nCompute the minimum total cost to dismantle the object. partial score: Partial Score\nIn test cases worth 300 points, W = 3.\nTask Constraint: 1 <= H <= 300\n2 <= W <= 300\nAll characters c_{i,j} are lowercase English letters (a-z).\nTask Input: Input The input is given from Standard Input in the following format:\nH W\nc_{1,1}c_{1,2}. . c_{1, W}\nc_{2,1}c_{2,2}. . c_{2, W}\n:\nc_{H, 1}c_{H, 2}. . c_{H, W}\nTask Output: Print the minimum total cost to dismantle the object.\nTask Samples: input: 2 3\nrrr\nbrg output: 2\n\nFor example, the total cost of 2 can be achieved by performing the operation as follows and this is the minimum value.\ninput: 6 3\nxya\nxya\nayz\nayz\nxaz\nxaz output: 0\n\nThe total cost of 0 can be achieved by first pushing down all blocks of the middle column, then all of the left column, and all of the right column.\ninput: 4 2\nay\nxa\nxy\nay output: 0\n\nThe total cost of 0 can be achieved by the following operations:\n\npushing down the right column one row;\npushing down the left column one row;\npushing down all of the right column;\nand pushing down all of the left column.\ninput: 5 5\naaaaa\nabbba\nababa\nabbba\naaaaa output: 24\ninput: 7 10\nxxxxxxxxxx\nccccxxffff\ncxxcxxfxxx\ncxxxxxffff\ncxxcxxfxxx\nccccxxfxxx\nxxxxxxxxxx output: 130\n\n" }, { "title": "", "content": "Problem Statement One day Mr. Takahashi picked up a dictionary containing all of the N! permutations of integers 1 through N.\nThe dictionary has N! pages, and page i (1 <= i <= N! ) contains the i-th permutation in the lexicographical order.\nMr. Takahashi wanted to look up a certain permutation of length N in this dictionary, but he forgot some part of it.\nHis memory of the permutation is described by a sequence P_1, P_2, . . . , P_N.\nIf P_i = 0, it means that he forgot the i-th element of the permutation; otherwise, it means that he remembered the i-th element of the permutation and it is P_i.\nHe decided to look up all the possible permutations in the dictionary.\nCompute the sum of the page numbers of the pages he has to check, modulo 10^9 + 7. partial score: Partial Score\nIn test cases worth 500 points, 1 <= N <= 3000.", "constraint": "1 <= N <= 500000\n0 <= P_i <= N\nP_i != P_j if i != j (1 <= i, j <= N), P_i != 0 and P_j != 0.", "input": "Input The input is given from Standard Input in the following format:\nN\nP_1 P_2 . . . P_N", "output": "Print the sum of the page numbers of the pages he has to check, as modulo 10^9 + 7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n0 2 3 0 output: 23\n\nThe possible permutations are [1,2,3,4] and [4,2,3,1].\nSince the former is on page 1 and the latter is on page 22, the answer is 23.", "input: 3\n0 0 0 output: 21\n\nSince all permutations of length 3 are possible, the answer is 1 + 2 + 3 + 4 + 5 + 6 = 21.", "input: 5\n1 2 3 5 4 output: 2\n\nMr. Takahashi remembered all the elements of the permutation.", "input: 1\n0 output: 1\n\nThe dictionary consists of one page.", "input: 10\n0 3 0 0 1 0 4 0 0 0 output: 953330050"], "Pid": "p03961", "ProblemText": "Task Description: Problem Statement One day Mr. Takahashi picked up a dictionary containing all of the N! permutations of integers 1 through N.\nThe dictionary has N! pages, and page i (1 <= i <= N! ) contains the i-th permutation in the lexicographical order.\nMr. Takahashi wanted to look up a certain permutation of length N in this dictionary, but he forgot some part of it.\nHis memory of the permutation is described by a sequence P_1, P_2, . . . , P_N.\nIf P_i = 0, it means that he forgot the i-th element of the permutation; otherwise, it means that he remembered the i-th element of the permutation and it is P_i.\nHe decided to look up all the possible permutations in the dictionary.\nCompute the sum of the page numbers of the pages he has to check, modulo 10^9 + 7. partial score: Partial Score\nIn test cases worth 500 points, 1 <= N <= 3000.\nTask Constraint: 1 <= N <= 500000\n0 <= P_i <= N\nP_i != P_j if i != j (1 <= i, j <= N), P_i != 0 and P_j != 0.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nP_1 P_2 . . . P_N\nTask Output: Print the sum of the page numbers of the pages he has to check, as modulo 10^9 + 7.\nTask Samples: input: 4\n0 2 3 0 output: 23\n\nThe possible permutations are [1,2,3,4] and [4,2,3,1].\nSince the former is on page 1 and the latter is on page 22, the answer is 23.\ninput: 3\n0 0 0 output: 21\n\nSince all permutations of length 3 are possible, the answer is 1 + 2 + 3 + 4 + 5 + 6 = 21.\ninput: 5\n1 2 3 5 4 output: 2\n\nMr. Takahashi remembered all the elements of the permutation.\ninput: 1\n0 output: 1\n\nThe dictionary consists of one page.\ninput: 10\n0 3 0 0 1 0 4 0 0 0 output: 953330050\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer recently bought three paint cans.\nThe color of the one he bought two days ago is a, the color of the one he bought yesterday is b, and the color of the one he bought today is c.\nHere, the color of each paint can is represented by an integer between 1 and 100, inclusive.\nSince he is forgetful, he might have bought more than one paint can in the same color.\nCount the number of different kinds of colors of these paint cans and tell him.", "constraint": "1<=a,b,c<=100", "input": "Input The input is given from Standard Input in the following format:\na b c", "output": "Print the number of different kinds of colors of the paint cans.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 4 output: 3\n\nThree different colors: 1,3, and 4.", "input: 3 3 33 output: 2\n\nTwo different colors: 3 and 33."], "Pid": "p03962", "ProblemText": "Task Description: Problem Statement At Co Deer the deer recently bought three paint cans.\nThe color of the one he bought two days ago is a, the color of the one he bought yesterday is b, and the color of the one he bought today is c.\nHere, the color of each paint can is represented by an integer between 1 and 100, inclusive.\nSince he is forgetful, he might have bought more than one paint can in the same color.\nCount the number of different kinds of colors of these paint cans and tell him.\nTask Constraint: 1<=a,b,c<=100\nTask Input: Input The input is given from Standard Input in the following format:\na b c\nTask Output: Print the number of different kinds of colors of the paint cans.\nTask Samples: input: 3 1 4 output: 3\n\nThree different colors: 1,3, and 4.\ninput: 3 3 33 output: 2\n\nTwo different colors: 3 and 33.\n\n" }, { "title": "", "content": "Problem Statement There are N balls placed in a row.\nAt Co Deer the deer is painting each of these in one of the K colors of his paint cans.\nFor aesthetic reasons, any two adjacent balls must be painted in different colors.\nFind the number of the possible ways to paint the balls.", "constraint": "1<=N<=1000\n2<=K<=1000\nThe correct answer is at most 2^{31}-1.", "input": "Input The input is given from Standard Input in the following format:\nN K", "output": "Print the number of the possible ways to paint the balls.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2 output: 2\n\nWe will denote the colors by 0 and 1. There are two possible ways: we can either paint the left ball in color 0 and the right ball in color 1, or paint the left in color 1 and the right in color 0.", "input: 1 10 output: 10\n\nSince there is only one ball, we can use any of the ten colors to paint it. Thus, the answer is ten."], "Pid": "p03963", "ProblemText": "Task Description: Problem Statement There are N balls placed in a row.\nAt Co Deer the deer is painting each of these in one of the K colors of his paint cans.\nFor aesthetic reasons, any two adjacent balls must be painted in different colors.\nFind the number of the possible ways to paint the balls.\nTask Constraint: 1<=N<=1000\n2<=K<=1000\nThe correct answer is at most 2^{31}-1.\nTask Input: Input The input is given from Standard Input in the following format:\nN K\nTask Output: Print the number of the possible ways to paint the balls.\nTask Samples: input: 2 2 output: 2\n\nWe will denote the colors by 0 and 1. There are two possible ways: we can either paint the left ball in color 0 and the right ball in color 1, or paint the left in color 1 and the right in color 0.\ninput: 1 10 output: 10\n\nSince there is only one ball, we can use any of the ten colors to paint it. Thus, the answer is ten.\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer is seeing a quick report of election results on TV.\nTwo candidates are standing for the election: Takahashi and Aoki.\nThe report shows the ratio of the current numbers of votes the two candidates have obtained, but not the actual numbers of votes.\nAt Co Deer has checked the report N times, and when he checked it for the i-th (1<=i<=N) time, the ratio was T_i: A_i.\nIt is known that each candidate had at least one vote when he checked the report for the first time.\nFind the minimum possible total number of votes obtained by the two candidates when he checked the report for the N-th time.\nIt can be assumed that the number of votes obtained by each candidate never decreases.", "constraint": "1<=N<=1000\n1<=T_i,A_i<=1000 (1<=i<=N)\nT_i and A_i (1<=i<=N) are coprime.\nIt is guaranteed that the correct answer is at most 10^{18}.", "input": "Input The input is given from Standard Input in the following format:\nN\nT_1 A_1\nT_2 A_2\n:\nT_N A_N", "output": "Print the minimum possible total number of votes obtained by Takahashi and Aoki when At Co Deer checked the report for the N-th time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3\n1 1\n3 2 output: 10\n\nWhen the numbers of votes obtained by the two candidates change as 2,3 → 3,3 → 6,4, the total number of votes at the end is 10, which is the minimum possible number.", "input: 4\n1 1\n1 1\n1 5\n1 100 output: 101\n\nIt is possible that neither candidate obtained a vote between the moment when he checked the report, and the moment when he checked it for the next time.", "input: 5\n3 10\n48 17\n31 199\n231 23\n3 2 output: 6930"], "Pid": "p03964", "ProblemText": "Task Description: Problem Statement At Co Deer the deer is seeing a quick report of election results on TV.\nTwo candidates are standing for the election: Takahashi and Aoki.\nThe report shows the ratio of the current numbers of votes the two candidates have obtained, but not the actual numbers of votes.\nAt Co Deer has checked the report N times, and when he checked it for the i-th (1<=i<=N) time, the ratio was T_i: A_i.\nIt is known that each candidate had at least one vote when he checked the report for the first time.\nFind the minimum possible total number of votes obtained by the two candidates when he checked the report for the N-th time.\nIt can be assumed that the number of votes obtained by each candidate never decreases.\nTask Constraint: 1<=N<=1000\n1<=T_i,A_i<=1000 (1<=i<=N)\nT_i and A_i (1<=i<=N) are coprime.\nIt is guaranteed that the correct answer is at most 10^{18}.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nT_1 A_1\nT_2 A_2\n:\nT_N A_N\nTask Output: Print the minimum possible total number of votes obtained by Takahashi and Aoki when At Co Deer checked the report for the N-th time.\nTask Samples: input: 3\n2 3\n1 1\n3 2 output: 10\n\nWhen the numbers of votes obtained by the two candidates change as 2,3 → 3,3 → 6,4, the total number of votes at the end is 10, which is the minimum possible number.\ninput: 4\n1 1\n1 1\n1 5\n1 100 output: 101\n\nIt is possible that neither candidate obtained a vote between the moment when he checked the report, and the moment when he checked it for the next time.\ninput: 5\n3 10\n48 17\n31 199\n231 23\n3 2 output: 6930\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer and his friend Top Co Deer is playing a game.\nThe game consists of N turns.\nIn each turn, each player plays one of the two gestures, Rock and Paper, as in Rock-paper-scissors, under the following condition:\n(※) After each turn, (the number of times the player has played Paper)<=(the number of times the player has played Rock).\nEach player's score is calculated by (the number of turns where the player wins) - (the number of turns where the player loses), where the outcome of each turn is determined by the rules of Rock-paper-scissors.\n(For those who are not familiar with Rock-paper-scissors: If one player plays Rock and the other plays Paper, the latter player will win and the former player will lose. If both players play the same gesture, the round is a tie and neither player will win nor lose. )\nWith his supernatural power, At Co Deer was able to foresee the gesture that Top Co Deer will play in each of the N turns, before the game starts.\nPlan At Co Deer's gesture in each turn to maximize At Co Deer's score.\nThe gesture that Top Co Deer will play in each turn is given by a string s. If the i-th (1<=i<=N) character in s is g, Top Co Deer will play Rock in the i-th turn. Similarly, if the i-th (1<=i<=N) character of s in p, Top Co Deer will play Paper in the i-th turn.", "constraint": "1<=N<=10^5\nN=|s|\nEach character in s is g or p.\nThe gestures represented by s satisfy the condition (※).", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "Print the At Co Deer's maximum possible score.", "content_img": false, "lang": "en", "error": false, "samples": ["input: gpg output: 0\n\nPlaying the same gesture as the opponent in each turn results in the score of 0, which is the maximum possible score.", "input: ggppgggpgg output: 2\n\nFor example, consider playing gestures in the following order: Rock, Paper, Rock, Paper, Rock, Rock, Paper, Paper, Rock, Paper. This strategy earns three victories and suffers one defeat, resulting in the score of 2, which is the maximum possible score."], "Pid": "p03965", "ProblemText": "Task Description: Problem Statement At Co Deer the deer and his friend Top Co Deer is playing a game.\nThe game consists of N turns.\nIn each turn, each player plays one of the two gestures, Rock and Paper, as in Rock-paper-scissors, under the following condition:\n(※) After each turn, (the number of times the player has played Paper)<=(the number of times the player has played Rock).\nEach player's score is calculated by (the number of turns where the player wins) - (the number of turns where the player loses), where the outcome of each turn is determined by the rules of Rock-paper-scissors.\n(For those who are not familiar with Rock-paper-scissors: If one player plays Rock and the other plays Paper, the latter player will win and the former player will lose. If both players play the same gesture, the round is a tie and neither player will win nor lose. )\nWith his supernatural power, At Co Deer was able to foresee the gesture that Top Co Deer will play in each of the N turns, before the game starts.\nPlan At Co Deer's gesture in each turn to maximize At Co Deer's score.\nThe gesture that Top Co Deer will play in each turn is given by a string s. If the i-th (1<=i<=N) character in s is g, Top Co Deer will play Rock in the i-th turn. Similarly, if the i-th (1<=i<=N) character of s in p, Top Co Deer will play Paper in the i-th turn.\nTask Constraint: 1<=N<=10^5\nN=|s|\nEach character in s is g or p.\nThe gestures represented by s satisfy the condition (※).\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: Print the At Co Deer's maximum possible score.\nTask Samples: input: gpg output: 0\n\nPlaying the same gesture as the opponent in each turn results in the score of 0, which is the maximum possible score.\ninput: ggppgggpgg output: 2\n\nFor example, consider playing gestures in the following order: Rock, Paper, Rock, Paper, Rock, Rock, Paper, Paper, Rock, Paper. This strategy earns three victories and suffers one defeat, resulting in the score of 2, which is the maximum possible score.\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer is seeing a quick report of election results on TV.\nTwo candidates are standing for the election: Takahashi and Aoki.\nThe report shows the ratio of the current numbers of votes the two candidates have obtained, but not the actual numbers of votes.\nAt Co Deer has checked the report N times, and when he checked it for the i-th (1<=i<=N) time, the ratio was T_i: A_i.\nIt is known that each candidate had at least one vote when he checked the report for the first time.\nFind the minimum possible total number of votes obtained by the two candidates when he checked the report for the N-th time.\nIt can be assumed that the number of votes obtained by each candidate never decreases.", "constraint": "1<=N<=1000\n1<=T_i,A_i<=1000 (1<=i<=N)\nT_i and A_i (1<=i<=N) are coprime.\nIt is guaranteed that the correct answer is at most 10^{18}.", "input": "Input The input is given from Standard Input in the following format:\nN\nT_1 A_1\nT_2 A_2\n:\nT_N A_N", "output": "Print the minimum possible total number of votes obtained by Takahashi and Aoki when At Co Deer checked the report for the N-th time.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 3\n1 1\n3 2 output: 10\n\nWhen the numbers of votes obtained by the two candidates change as 2,3 → 3,3 → 6,4, the total number of votes at the end is 10, which is the minimum possible number.", "input: 4\n1 1\n1 1\n1 5\n1 100 output: 101\n\nIt is possible that neither candidate obtained a vote between the moment when he checked the report, and the moment when he checked it for the next time.", "input: 5\n3 10\n48 17\n31 199\n231 23\n3 2 output: 6930"], "Pid": "p03966", "ProblemText": "Task Description: Problem Statement At Co Deer the deer is seeing a quick report of election results on TV.\nTwo candidates are standing for the election: Takahashi and Aoki.\nThe report shows the ratio of the current numbers of votes the two candidates have obtained, but not the actual numbers of votes.\nAt Co Deer has checked the report N times, and when he checked it for the i-th (1<=i<=N) time, the ratio was T_i: A_i.\nIt is known that each candidate had at least one vote when he checked the report for the first time.\nFind the minimum possible total number of votes obtained by the two candidates when he checked the report for the N-th time.\nIt can be assumed that the number of votes obtained by each candidate never decreases.\nTask Constraint: 1<=N<=1000\n1<=T_i,A_i<=1000 (1<=i<=N)\nT_i and A_i (1<=i<=N) are coprime.\nIt is guaranteed that the correct answer is at most 10^{18}.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nT_1 A_1\nT_2 A_2\n:\nT_N A_N\nTask Output: Print the minimum possible total number of votes obtained by Takahashi and Aoki when At Co Deer checked the report for the N-th time.\nTask Samples: input: 3\n2 3\n1 1\n3 2 output: 10\n\nWhen the numbers of votes obtained by the two candidates change as 2,3 → 3,3 → 6,4, the total number of votes at the end is 10, which is the minimum possible number.\ninput: 4\n1 1\n1 1\n1 5\n1 100 output: 101\n\nIt is possible that neither candidate obtained a vote between the moment when he checked the report, and the moment when he checked it for the next time.\ninput: 5\n3 10\n48 17\n31 199\n231 23\n3 2 output: 6930\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer and his friend Top Co Deer is playing a game.\nThe game consists of N turns.\nIn each turn, each player plays one of the two gestures, Rock and Paper, as in Rock-paper-scissors, under the following condition:\n(※) After each turn, (the number of times the player has played Paper)<=(the number of times the player has played Rock).\nEach player's score is calculated by (the number of turns where the player wins) - (the number of turns where the player loses), where the outcome of each turn is determined by the rules of Rock-paper-scissors.\n(For those who are not familiar with Rock-paper-scissors: If one player plays Rock and the other plays Paper, the latter player will win and the former player will lose. If both players play the same gesture, the round is a tie and neither player will win nor lose. )\nWith his supernatural power, At Co Deer was able to foresee the gesture that Top Co Deer will play in each of the N turns, before the game starts.\nPlan At Co Deer's gesture in each turn to maximize At Co Deer's score.\nThe gesture that Top Co Deer will play in each turn is given by a string s. If the i-th (1<=i<=N) character in s is g, Top Co Deer will play Rock in the i-th turn. Similarly, if the i-th (1<=i<=N) character of s in p, Top Co Deer will play Paper in the i-th turn.", "constraint": "1<=N<=10^5\nN=|s|\nEach character in s is g or p.\nThe gestures represented by s satisfy the condition (※).", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "Print the At Co Deer's maximum possible score.", "content_img": false, "lang": "en", "error": false, "samples": ["input: gpg output: 0\n\nPlaying the same gesture as the opponent in each turn results in the score of 0, which is the maximum possible score.", "input: ggppgggpgg output: 2\n\nFor example, consider playing gestures in the following order: Rock, Paper, Rock, Paper, Rock, Rock, Paper, Paper, Rock, Paper. This strategy earns three victories and suffers one defeat, resulting in the score of 2, which is the maximum possible score."], "Pid": "p03967", "ProblemText": "Task Description: Problem Statement At Co Deer the deer and his friend Top Co Deer is playing a game.\nThe game consists of N turns.\nIn each turn, each player plays one of the two gestures, Rock and Paper, as in Rock-paper-scissors, under the following condition:\n(※) After each turn, (the number of times the player has played Paper)<=(the number of times the player has played Rock).\nEach player's score is calculated by (the number of turns where the player wins) - (the number of turns where the player loses), where the outcome of each turn is determined by the rules of Rock-paper-scissors.\n(For those who are not familiar with Rock-paper-scissors: If one player plays Rock and the other plays Paper, the latter player will win and the former player will lose. If both players play the same gesture, the round is a tie and neither player will win nor lose. )\nWith his supernatural power, At Co Deer was able to foresee the gesture that Top Co Deer will play in each of the N turns, before the game starts.\nPlan At Co Deer's gesture in each turn to maximize At Co Deer's score.\nThe gesture that Top Co Deer will play in each turn is given by a string s. If the i-th (1<=i<=N) character in s is g, Top Co Deer will play Rock in the i-th turn. Similarly, if the i-th (1<=i<=N) character of s in p, Top Co Deer will play Paper in the i-th turn.\nTask Constraint: 1<=N<=10^5\nN=|s|\nEach character in s is g or p.\nThe gestures represented by s satisfy the condition (※).\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: Print the At Co Deer's maximum possible score.\nTask Samples: input: gpg output: 0\n\nPlaying the same gesture as the opponent in each turn results in the score of 0, which is the maximum possible score.\ninput: ggppgggpgg output: 2\n\nFor example, consider playing gestures in the following order: Rock, Paper, Rock, Paper, Rock, Rock, Paper, Paper, Rock, Paper. This strategy earns three victories and suffers one defeat, resulting in the score of 2, which is the maximum possible score.\n\n" }, { "title": "", "content": "Problem Statement At Co Deer the deer has N square tiles. The tiles are numbered 1 through N, and the number given to each tile is written on one side of the tile. Also, each corner of each tile is painted in one of the 1000 colors, which are represented by the integers 0 between 999. The top-left, top-right, bottom-right and bottom-left corner of the tile with the number i are painted in color C_{i, 0}, C_{i, 1}, C_{i, 2} and C_{i, 3}, respectively, when seen in the direction of the number written on the tile (See Figure 1).\nFigure 1: The correspondence between the colors of a tile and the input\n\nAt Co Deer is constructing a cube using six of these tiles, under the following conditions:\n\nFor each tile, the side with the number must face outward.\nFor each vertex of the cube, the three corners of the tiles that forms it must all be painted in the same color.\n\nHelp him by finding the number of the different cubes that can be constructed under the conditions.\nSince each tile has a number written on it, two cubes are considered different if the set of the used tiles are different, or the tiles are used in different directions, even if the formation of the colors are the same. (Each tile can be used in one of the four directions, obtained by 90° rotations. ) Two cubes are considered the same only if rotating one in the three dimensional space can obtain an exact copy of the other, including the directions of the tiles.\nFigure 2: The four directions of a tile", "constraint": "6<=N<=400\n0<=C_{i,j}<=999 (1<=i<=N , 0<=j<=3)", "input": "Input The input is given from Standard Input in the following format:\nN\nC_{1,0} C_{1,1} C_{1,2} C_{1,3}\nC_{2,0} C_{2,1} C_{2,2} C_{2,3}\n:\nC_{N, 0} C_{N, 1} C_{N, 2} C_{N, 3}", "output": "Print the number of the different cubes that can be constructed under the conditions.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6\n0 1 2 3\n0 4 6 1\n1 6 7 2\n2 7 5 3\n6 4 5 7\n4 0 3 5 output: 1\n\nThe cube below can be constructed.", "input: 8\n0 0 0 0\n0 0 1 1\n0 1 0 1\n0 1 1 0\n1 0 0 1\n1 0 1 0\n1 1 0 0\n1 1 1 1 output: 144", "input: 6\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0 output: 122880"], "Pid": "p03968", "ProblemText": "Task Description: Problem Statement At Co Deer the deer has N square tiles. The tiles are numbered 1 through N, and the number given to each tile is written on one side of the tile. Also, each corner of each tile is painted in one of the 1000 colors, which are represented by the integers 0 between 999. The top-left, top-right, bottom-right and bottom-left corner of the tile with the number i are painted in color C_{i, 0}, C_{i, 1}, C_{i, 2} and C_{i, 3}, respectively, when seen in the direction of the number written on the tile (See Figure 1).\nFigure 1: The correspondence between the colors of a tile and the input\n\nAt Co Deer is constructing a cube using six of these tiles, under the following conditions:\n\nFor each tile, the side with the number must face outward.\nFor each vertex of the cube, the three corners of the tiles that forms it must all be painted in the same color.\n\nHelp him by finding the number of the different cubes that can be constructed under the conditions.\nSince each tile has a number written on it, two cubes are considered different if the set of the used tiles are different, or the tiles are used in different directions, even if the formation of the colors are the same. (Each tile can be used in one of the four directions, obtained by 90° rotations. ) Two cubes are considered the same only if rotating one in the three dimensional space can obtain an exact copy of the other, including the directions of the tiles.\nFigure 2: The four directions of a tile\nTask Constraint: 6<=N<=400\n0<=C_{i,j}<=999 (1<=i<=N , 0<=j<=3)\nTask Input: Input The input is given from Standard Input in the following format:\nN\nC_{1,0} C_{1,1} C_{1,2} C_{1,3}\nC_{2,0} C_{2,1} C_{2,2} C_{2,3}\n:\nC_{N, 0} C_{N, 1} C_{N, 2} C_{N, 3}\nTask Output: Print the number of the different cubes that can be constructed under the conditions.\nTask Samples: input: 6\n0 1 2 3\n0 4 6 1\n1 6 7 2\n2 7 5 3\n6 4 5 7\n4 0 3 5 output: 1\n\nThe cube below can be constructed.\ninput: 8\n0 0 0 0\n0 0 1 1\n0 1 0 1\n0 1 1 0\n1 0 0 1\n1 0 1 0\n1 1 0 0\n1 1 1 1 output: 144\ninput: 6\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0 output: 122880\n\n" }, { "title": "", "content": "Problem Statement One day, At Co Deer the deer found a simple graph (that is, a graph without self-loops and multiple edges) with N vertices and M edges, and brought it home.\nThe vertices are numbered 1 through N and mutually distinguishable, and the edges are represented by (a_i, b_i) (1<=i<=M).\nHe is painting each edge in the graph in one of the K colors of his paint cans. As he has enough supply of paint, the same color can be used to paint more than one edge.\nThe graph is made of a special material, and has a strange property. He can choose a simple cycle (that is, a cycle with no repeated vertex), and perform a circular shift of the colors along the chosen cycle. More formally, let e_1, e_2, . . . , e_a be the edges along a cycle in order, then he can perform the following simultaneously: paint e_2 in the current color of e_1, paint e_3 in the current color of e_2, . . . , paint e_a in the current color of e_{a-1}, and paint e_1 in the current color of e_{a}.\nFigure 1: An example of a circular shift\n\nTwo ways to paint the edges, A and B, are considered the same if A can be transformed into B by performing a finite number of circular shifts. Find the number of ways to paint the edges. Since this number can be extremely large, print the answer modulo 10^9+7.", "constraint": "1<=N<=50\n1<=M<=100\n1<=K<=100\n1<=a_i,b_i<=N (1<=i<=M)\nThe graph has neither self-loops nor multiple edges.", "input": "Input The input is given from Standard Input in the following format:\nN M K\na_1 b_1\na_2 b_2\n:\na_M b_M", "output": "Print the number of ways to paint the edges, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 4 2\n1 2\n2 3\n3 1\n3 4 output: 8", "input: 5 2 3\n1 2\n4 5 output: 9", "input: 11 12 48\n3 1\n8 2\n4 9\n5 4\n1 6\n2 9\n8 3\n10 8\n4 10\n8 6\n11 7\n1 8 output: 569519295"], "Pid": "p03969", "ProblemText": "Task Description: Problem Statement One day, At Co Deer the deer found a simple graph (that is, a graph without self-loops and multiple edges) with N vertices and M edges, and brought it home.\nThe vertices are numbered 1 through N and mutually distinguishable, and the edges are represented by (a_i, b_i) (1<=i<=M).\nHe is painting each edge in the graph in one of the K colors of his paint cans. As he has enough supply of paint, the same color can be used to paint more than one edge.\nThe graph is made of a special material, and has a strange property. He can choose a simple cycle (that is, a cycle with no repeated vertex), and perform a circular shift of the colors along the chosen cycle. More formally, let e_1, e_2, . . . , e_a be the edges along a cycle in order, then he can perform the following simultaneously: paint e_2 in the current color of e_1, paint e_3 in the current color of e_2, . . . , paint e_a in the current color of e_{a-1}, and paint e_1 in the current color of e_{a}.\nFigure 1: An example of a circular shift\n\nTwo ways to paint the edges, A and B, are considered the same if A can be transformed into B by performing a finite number of circular shifts. Find the number of ways to paint the edges. Since this number can be extremely large, print the answer modulo 10^9+7.\nTask Constraint: 1<=N<=50\n1<=M<=100\n1<=K<=100\n1<=a_i,b_i<=N (1<=i<=M)\nThe graph has neither self-loops nor multiple edges.\nTask Input: Input The input is given from Standard Input in the following format:\nN M K\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Output: Print the number of ways to paint the edges, modulo 10^9+7.\nTask Samples: input: 4 4 2\n1 2\n2 3\n3 1\n3 4 output: 8\ninput: 5 2 3\n1 2\n4 5 output: 9\ninput: 11 12 48\n3 1\n8 2\n4 9\n5 4\n1 6\n2 9\n8 3\n10 8\n4 10\n8 6\n11 7\n1 8 output: 569519295\n\n" }, { "title": "", "content": "Problem Statement CODE FESTIVAL 2016 is going to be held. For the occasion, Mr. Takahashi decided to make a signboard.\nHe intended to write CODEFESTIVAL2016 on it, but he mistakenly wrote a different string S. Fortunately, the string he wrote was the correct length.\nSo Mr. Takahashi decided to perform an operation that replaces a certain character with another in the minimum number of iterations, changing the string to CODEFESTIVAL2016.\nFind the minimum number of iterations for the rewrite operation.", "constraint": "S is 16 characters long.\nS consists of uppercase and lowercase alphabet letters and numerals.", "input": "Inputs are provided from Standard Input in the following form.\nS", "output": "Output an integer representing the minimum number of iterations needed for the rewrite operation.", "content_img": false, "lang": "en", "error": false, "samples": ["input: C0DEFESTIVAL2O16 output: 2\n\nThe second character 0 must be changed to O and the 14th character O changed to 0.", "input: FESTIVAL2016CODE output: 16"], "Pid": "p03970", "ProblemText": "Task Description: Problem Statement CODE FESTIVAL 2016 is going to be held. For the occasion, Mr. Takahashi decided to make a signboard.\nHe intended to write CODEFESTIVAL2016 on it, but he mistakenly wrote a different string S. Fortunately, the string he wrote was the correct length.\nSo Mr. Takahashi decided to perform an operation that replaces a certain character with another in the minimum number of iterations, changing the string to CODEFESTIVAL2016.\nFind the minimum number of iterations for the rewrite operation.\nTask Constraint: S is 16 characters long.\nS consists of uppercase and lowercase alphabet letters and numerals.\nTask Input: Inputs are provided from Standard Input in the following form.\nS\nTask Output: Output an integer representing the minimum number of iterations needed for the rewrite operation.\nTask Samples: input: C0DEFESTIVAL2O16 output: 2\n\nThe second character 0 must be changed to O and the 14th character O changed to 0.\ninput: FESTIVAL2016CODE output: 16\n\n" }, { "title": "", "content": "Problem Statement There are N participants in the CODE FESTIVAL 2016 Qualification contests. The participants are either students in Japan, students from overseas, or neither of these.\nOnly Japanese students or overseas students can pass the Qualification contests. The students pass when they satisfy the conditions listed below, from the top rank down. Participants who are not students cannot pass the Qualification contests.\n\nA Japanese student passes the Qualification contests if the number of the participants who have already definitively passed is currently fewer than A+B.\nAn overseas student passes the Qualification contests if the number of the participants who have already definitively passed is currently fewer than A+B and the student ranks B-th or above among all overseas students.\n\nA string S is assigned indicating attributes of all participants. If the i-th character of string S is a, this means the participant ranked i-th in the Qualification contests is a Japanese student; b means the participant ranked i-th is an overseas student; and c means the participant ranked i-th is neither of these.\nWrite a program that outputs for all the participants in descending rank either Yes if they passed the Qualification contests or No if they did not pass.", "constraint": "1<=N,A,B<=100000\nA+B<=N\nS is N characters long.\nS consists only of the letters a, b and c.", "input": "Inputs are provided from Standard Input in the following form.\nN A B\nS", "output": "Output N lines. On the i-th line, output Yes if the i-th participant passed the Qualification contests or No if that participant did not pass.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 10 2 3\nabccabaabb output: Yes\nYes\nNo\nNo\nYes\nYes\nYes\nNo\nNo\nNo\n\nThe first, second, fifth, sixth, and seventh participants pass the Qualification contests.", "input: 12 5 2\ncabbabaacaba output: No\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nNo\nYes\nNo\nNo\n\nThe sixth participant is third among overseas students and thus does not pass the Qualification contests.", "input: 5 2 2\nccccc output: No\nNo\nNo\nNo\nNo"], "Pid": "p03971", "ProblemText": "Task Description: Problem Statement There are N participants in the CODE FESTIVAL 2016 Qualification contests. The participants are either students in Japan, students from overseas, or neither of these.\nOnly Japanese students or overseas students can pass the Qualification contests. The students pass when they satisfy the conditions listed below, from the top rank down. Participants who are not students cannot pass the Qualification contests.\n\nA Japanese student passes the Qualification contests if the number of the participants who have already definitively passed is currently fewer than A+B.\nAn overseas student passes the Qualification contests if the number of the participants who have already definitively passed is currently fewer than A+B and the student ranks B-th or above among all overseas students.\n\nA string S is assigned indicating attributes of all participants. If the i-th character of string S is a, this means the participant ranked i-th in the Qualification contests is a Japanese student; b means the participant ranked i-th is an overseas student; and c means the participant ranked i-th is neither of these.\nWrite a program that outputs for all the participants in descending rank either Yes if they passed the Qualification contests or No if they did not pass.\nTask Constraint: 1<=N,A,B<=100000\nA+B<=N\nS is N characters long.\nS consists only of the letters a, b and c.\nTask Input: Inputs are provided from Standard Input in the following form.\nN A B\nS\nTask Output: Output N lines. On the i-th line, output Yes if the i-th participant passed the Qualification contests or No if that participant did not pass.\nTask Samples: input: 10 2 3\nabccabaabb output: Yes\nYes\nNo\nNo\nYes\nYes\nYes\nNo\nNo\nNo\n\nThe first, second, fifth, sixth, and seventh participants pass the Qualification contests.\ninput: 12 5 2\ncabbabaacaba output: No\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nNo\nYes\nNo\nNo\n\nThe sixth participant is third among overseas students and thus does not pass the Qualification contests.\ninput: 5 2 2\nccccc output: No\nNo\nNo\nNo\nNo\n\n" }, { "title": "", "content": "Problem Statement On an xy plane, in an area satisfying 0 <= x <= W, 0 <= y <= H, there is one house at each and every point where both x and y are integers.\nThere are unpaved roads between every pair of points for which either the x coordinates are equal and the difference between the y coordinates is 1, or the y coordinates are equal and the difference between the x coordinates is 1.\nThe cost of paving a road between houses on coordinates (i, j) and (i+1, j) is p_i for any value of j, while the cost of paving a road between houses on coordinates (i, j) and (i, j+1) is q_j for any value of i.\nMr. Takahashi wants to pave some of these roads and be able to travel between any two houses on paved roads only. Find the solution with the minimum total cost.", "constraint": "1 <= W,H <= 10^5\n1 <= p_i <= 10^8(0 <= i <= W-1)\n1 <= q_j <= 10^8(0 <= j <= H-1)\np_i (0 <= i <= W-1) is an integer.\nq_j (0 <= j <= H-1) is an integer.", "input": "Inputs are provided from Standard Input in the following form.\nW H\np_0\n:\np_{W-1}\nq_0\n:\nq_{H-1}", "output": "Output an integer representing the minimum total cost.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n3\n5\n2\n7 output: 29\n\nIt is enough to pave the following eight roads.\n\nRoad connecting houses at (0,0) and (0,1)\nRoad connecting houses at (0,1) and (1,1)\nRoad connecting houses at (0,2) and (1,2)\nRoad connecting houses at (1,0) and (1,1)\nRoad connecting houses at (1,0) and (2,0)\nRoad connecting houses at (1,1) and (1,2)\nRoad connecting houses at (1,2) and (2,2)\nRoad connecting houses at (2,0) and (2,1)", "input: 4 3\n2\n4\n8\n1\n2\n9\n3 output: 60"], "Pid": "p03972", "ProblemText": "Task Description: Problem Statement On an xy plane, in an area satisfying 0 <= x <= W, 0 <= y <= H, there is one house at each and every point where both x and y are integers.\nThere are unpaved roads between every pair of points for which either the x coordinates are equal and the difference between the y coordinates is 1, or the y coordinates are equal and the difference between the x coordinates is 1.\nThe cost of paving a road between houses on coordinates (i, j) and (i+1, j) is p_i for any value of j, while the cost of paving a road between houses on coordinates (i, j) and (i, j+1) is q_j for any value of i.\nMr. Takahashi wants to pave some of these roads and be able to travel between any two houses on paved roads only. Find the solution with the minimum total cost.\nTask Constraint: 1 <= W,H <= 10^5\n1 <= p_i <= 10^8(0 <= i <= W-1)\n1 <= q_j <= 10^8(0 <= j <= H-1)\np_i (0 <= i <= W-1) is an integer.\nq_j (0 <= j <= H-1) is an integer.\nTask Input: Inputs are provided from Standard Input in the following form.\nW H\np_0\n:\np_{W-1}\nq_0\n:\nq_{H-1}\nTask Output: Output an integer representing the minimum total cost.\nTask Samples: input: 2 2\n3\n5\n2\n7 output: 29\n\nIt is enough to pave the following eight roads.\n\nRoad connecting houses at (0,0) and (0,1)\nRoad connecting houses at (0,1) and (1,1)\nRoad connecting houses at (0,2) and (1,2)\nRoad connecting houses at (1,0) and (1,1)\nRoad connecting houses at (1,0) and (2,0)\nRoad connecting houses at (1,1) and (1,2)\nRoad connecting houses at (1,2) and (2,2)\nRoad connecting houses at (2,0) and (2,1)\ninput: 4 3\n2\n4\n8\n1\n2\n9\n3 output: 60\n\n" }, { "title": "", "content": "Problem Statement N people are waiting in a single line in front of the Takahashi Store. The cash on hand of the i-th person from the front of the line is a positive integer A_i.\nMr. Takahashi, the shop owner, has decided on the following scheme: He picks a product, sets a positive integer P indicating its price, and shows this product to customers in order, starting from the front of the line. This step is repeated as described below.\nAt each step, when a product is shown to a customer, if price P is equal to or less than the cash held by that customer at the time, the customer buys the product and Mr. Takahashi ends the current step. That is, the cash held by the first customer in line with cash equal to or greater than P decreases by P, and the next step begins.\nMr. Takahashi can set the value of positive integer P independently at each step.\nHe would like to sell as many products as possible. However, if a customer were to end up with 0 cash on hand after a purchase, that person would not have the fare to go home. Customers not being able to go home would be a problem for Mr. Takahashi, so he does not want anyone to end up with 0 cash.\nHelp out Mr. Takahashi by writing a program that determines the maximum number of products he can sell, when the initial cash in possession of each customer is given.", "constraint": "1 <= | N | <= 100000\n1 <= A_i <= 10^9(1 <= i <= N)\nAll inputs are integers.", "input": "Inputs are provided from Standard Inputs in the following form.\nN\nA_1\n:\nA_N", "output": "Output an integer representing the maximum number of products Mr. Takahashi can sell.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n3\n2\n5 output: 3\n\nAs values of P, select in order 1,4,1.", "input: 15\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3\n5\n8\n9\n7\n9 output: 18"], "Pid": "p03973", "ProblemText": "Task Description: Problem Statement N people are waiting in a single line in front of the Takahashi Store. The cash on hand of the i-th person from the front of the line is a positive integer A_i.\nMr. Takahashi, the shop owner, has decided on the following scheme: He picks a product, sets a positive integer P indicating its price, and shows this product to customers in order, starting from the front of the line. This step is repeated as described below.\nAt each step, when a product is shown to a customer, if price P is equal to or less than the cash held by that customer at the time, the customer buys the product and Mr. Takahashi ends the current step. That is, the cash held by the first customer in line with cash equal to or greater than P decreases by P, and the next step begins.\nMr. Takahashi can set the value of positive integer P independently at each step.\nHe would like to sell as many products as possible. However, if a customer were to end up with 0 cash on hand after a purchase, that person would not have the fare to go home. Customers not being able to go home would be a problem for Mr. Takahashi, so he does not want anyone to end up with 0 cash.\nHelp out Mr. Takahashi by writing a program that determines the maximum number of products he can sell, when the initial cash in possession of each customer is given.\nTask Constraint: 1 <= | N | <= 100000\n1 <= A_i <= 10^9(1 <= i <= N)\nAll inputs are integers.\nTask Input: Inputs are provided from Standard Inputs in the following form.\nN\nA_1\n:\nA_N\nTask Output: Output an integer representing the maximum number of products Mr. Takahashi can sell.\nTask Samples: input: 3\n3\n2\n5 output: 3\n\nAs values of P, select in order 1,4,1.\ninput: 15\n3\n1\n4\n1\n5\n9\n2\n6\n5\n3\n5\n8\n9\n7\n9 output: 18\n\n" }, { "title": "", "content": "Problem Statement There are N strings of lowercase alphabet only. The i-th string is S_i. Every string is unique.\nProvide answers for the Q queries below. The i-th query has the following format:\nQuery: An integer k_i and a string p_{i, 1}p_{i, 2}. . . p_{i, 26} that results from permuting {a, b, . . . , z} are given. Output the sequence of the string S_{k_i} among the N strings in lexicographical order when the literal sequence is p_{i, 1}= 1\nB_i >= 1\nA_1 + A_2 + ... + A_N <= 10^{12}\nB_1 + B_2 + ... + B_N <= A_1 + A_2 + ... + A_N\nThere is at least one way to satisfy the condition.", "input": "The input is given from Standard Input in the following format: \nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N", "output": "Print the minimum total cost required to satisfy the condition. \nPartial Scores\n\n30 points will be awarded for passing the test set satisfying the following:\n \nN <= 100\nA_1 + A_2 + . . . + A_N <= 400\n\n Another 30 points will be awarded for passing the test set satisfying the following:\n \nN <= 10^3\n\n Another 140 points will be awarded for passing the test set without addtional constraints and you can get 200 points in total.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n1 5\n3 1 output: 2\nIt costs least to move 2 materials from point 2 to point 1.", "input: 5\n1 2 3 4 5\n3 3 1 1 1 output: 6", "input: 27\n46 3 4 2 10 2 5 2 6 7 20 13 9 49 3 8 4 3 19 9 3 5 4 13 9 5 7\n10 2 5 6 2 6 3 2 2 5 3 11 13 2 2 7 7 3 9 5 13 4 17 2 2 2 4 output: 48\nThe input of this test case satisfies both the first and second additional constraints.", "input: 18\n3878348 423911 8031742 1035156 24256 10344593 19379 3867285 4481365 1475384 1959412 1383457 164869 4633165 6674637 9732852 10459147 2810788\n1236501 770807 4003004 131688 1965412 266841 3980782 565060 816313 192940 541896 250801 217586 3806049 1220252 1161079 31168 2008961 output: 6302172\nThe input of this test case satisfies the second additional constraint.", "input: 2\n1 99999999999\n1234567891 1 output: 1234567890\nThe input and output values may exceed the range of 32-bit integer."], "Pid": "p03982", "ProblemText": "Task Description: Problem Statement\n\n Kyoto University decided to build a straight wall on the west side of the university to protect against gorillas that attack the university from the west every night.\n Since it is difficult to protect the university at some points along the wall where gorillas attack violently, reinforcement materials are also built at those points.\n Although the number of the materials is limited, the state-of-the-art technology can make a prediction about the points where gorillas will attack next and the number of gorillas that will attack at each point.\n The materials are moved along the wall everyday according to the prediction.\n You, a smart student majoring in computer science, are called to find the way to move the materials more efficiently.\n \n\n Theare are N points where reinforcement materials can be build along the straight wall. They are numbered 1 through N.\n Because of the protection against the last attack of gorillas, A_i materials are build at point i (1 <= i <= N).\n For the next attack, the materials need to be rearranged such that at least B_i materials are built at point i (1 <= i <= N).\n It costs |i - j| to move 1 material from point i to point j.\n Find the minimum total cost required to satisfy the condition by moving materials.\n You do not need to consider the attack after the next.\nTask Constraint: 1 <= N <= 10^5\nA_i >= 1\nB_i >= 1\nA_1 + A_2 + ... + A_N <= 10^{12}\nB_1 + B_2 + ... + B_N <= A_1 + A_2 + ... + A_N\nThere is at least one way to satisfy the condition.\nTask Input: The input is given from Standard Input in the following format: \nN\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N\nTask Output: Print the minimum total cost required to satisfy the condition. \nPartial Scores\n\n30 points will be awarded for passing the test set satisfying the following:\n \nN <= 100\nA_1 + A_2 + . . . + A_N <= 400\n\n Another 30 points will be awarded for passing the test set satisfying the following:\n \nN <= 10^3\n\n Another 140 points will be awarded for passing the test set without addtional constraints and you can get 200 points in total.\nTask Samples: input: 2\n1 5\n3 1 output: 2\nIt costs least to move 2 materials from point 2 to point 1.\ninput: 5\n1 2 3 4 5\n3 3 1 1 1 output: 6\ninput: 27\n46 3 4 2 10 2 5 2 6 7 20 13 9 49 3 8 4 3 19 9 3 5 4 13 9 5 7\n10 2 5 6 2 6 3 2 2 5 3 11 13 2 2 7 7 3 9 5 13 4 17 2 2 2 4 output: 48\nThe input of this test case satisfies both the first and second additional constraints.\ninput: 18\n3878348 423911 8031742 1035156 24256 10344593 19379 3867285 4481365 1475384 1959412 1383457 164869 4633165 6674637 9732852 10459147 2810788\n1236501 770807 4003004 131688 1965412 266841 3980782 565060 816313 192940 541896 250801 217586 3806049 1220252 1161079 31168 2008961 output: 6302172\nThe input of this test case satisfies the second additional constraint.\ninput: 2\n1 99999999999\n1234567891 1 output: 1234567890\nThe input and output values may exceed the range of 32-bit integer.\n\n" }, { "title": "", "content": "Problem Statement\n\n Eli- 1 started a part-time job handing out leaflets for N seconds. \n Eli- 1 wants to hand out as many leaflets as possible with her special ability, Cloning. \n Eli- gen can perform two kinds of actions below. \n\t\n\n Clone herself and generate Eli- (gen + 1) . (one Eli- gen (cloning) and one Eli- (gen + 1) (cloned) exist as a result of Eli-gen 's cloning. )\n This action takes gen * C ( C is a coefficient related to cloning. ) seconds. \n Hand out one leaflet. This action takes one second regardress of the generation ( =gen ). \n They can not hand out leaflets while cloning. \n Given N and C , find the maximum number of leaflets Eli- 1 and her clones can hand out in total modulo 1000000007 (= 10^9 + 7). partial scores: Partial Scores\n 30 points will be awarded for passing the test set satisfying the condition: Q = 1 . \nAnother 270 points will be awarded for passing the test set without addtional constraints and you can get 300 points in total.", "constraint": "1 <= Q <= 100000 = 10^5 \n 1 <= N_q <= 100000 = 10^5 \n 1 <= C_q <= 20000 = 2 * 10^4", "input": "The input is given from Standard Input in the following format: \n\nQ\nN_1 C_1\n:\nN_Q C_Q\n\nThe input consists of multiple test cases. On line 1 , Q that represents the number of test cases is given. \n Each test case is given on the next Q lines.\n For the test case q ( 1 <= q <= Q ) , N_q and \n C_q are given separated by a single space. \n N_q and C_q represent the working time and the coefficient related to cloning for test case q respectively.", "output": "For each test case, Print the maximum number of leaflets Eli- 1 and her clones can hand out modulo 1000000007 ( = 10^9 + 7 ).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n20 8\n20 12 output: \n24\n20\n\n For the first test case, while only 20 leaflets can be handed out without cloning,\n\t 24 leaflets can be handed out by cloning first and two people handing out12 leaflets each. \n For the second test case, since two people can only hand out 8 leaflets each if Eli- 1 clones, she should hand out 20 leaflets without cloning.", "input: 1\n20 3 output: \n67\n\nOne way of handing out 67 leaflets is like the following image. Each black line means cloning, and each red line means handing out. \n\n This case satisfies the constraint of the partial score.", "input: 1\n200 1 output: \n148322100\n\n Note that the value modulo 1000000007 ( 10^9 + 7 ) must be printed. \n This case satisfies the constraint of the partial score."], "Pid": "p03983", "ProblemText": "Task Description: Problem Statement\n\n Eli- 1 started a part-time job handing out leaflets for N seconds. \n Eli- 1 wants to hand out as many leaflets as possible with her special ability, Cloning. \n Eli- gen can perform two kinds of actions below. \n\t\n\n Clone herself and generate Eli- (gen + 1) . (one Eli- gen (cloning) and one Eli- (gen + 1) (cloned) exist as a result of Eli-gen 's cloning. )\n This action takes gen * C ( C is a coefficient related to cloning. ) seconds. \n Hand out one leaflet. This action takes one second regardress of the generation ( =gen ). \n They can not hand out leaflets while cloning. \n Given N and C , find the maximum number of leaflets Eli- 1 and her clones can hand out in total modulo 1000000007 (= 10^9 + 7). partial scores: Partial Scores\n 30 points will be awarded for passing the test set satisfying the condition: Q = 1 . \nAnother 270 points will be awarded for passing the test set without addtional constraints and you can get 300 points in total.\nTask Constraint: 1 <= Q <= 100000 = 10^5 \n 1 <= N_q <= 100000 = 10^5 \n 1 <= C_q <= 20000 = 2 * 10^4\nTask Input: The input is given from Standard Input in the following format: \n\nQ\nN_1 C_1\n:\nN_Q C_Q\n\nThe input consists of multiple test cases. On line 1 , Q that represents the number of test cases is given. \n Each test case is given on the next Q lines.\n For the test case q ( 1 <= q <= Q ) , N_q and \n C_q are given separated by a single space. \n N_q and C_q represent the working time and the coefficient related to cloning for test case q respectively.\nTask Output: For each test case, Print the maximum number of leaflets Eli- 1 and her clones can hand out modulo 1000000007 ( = 10^9 + 7 ).\nTask Samples: input: 2\n20 8\n20 12 output: \n24\n20\n\n For the first test case, while only 20 leaflets can be handed out without cloning,\n\t 24 leaflets can be handed out by cloning first and two people handing out12 leaflets each. \n For the second test case, since two people can only hand out 8 leaflets each if Eli- 1 clones, she should hand out 20 leaflets without cloning.\ninput: 1\n20 3 output: \n67\n\nOne way of handing out 67 leaflets is like the following image. Each black line means cloning, and each red line means handing out. \n\n This case satisfies the constraint of the partial score.\ninput: 1\n200 1 output: \n148322100\n\n Note that the value modulo 1000000007 ( 10^9 + 7 ) must be printed. \n This case satisfies the constraint of the partial score.\n\n" }, { "title": "", "content": "Problem Statement\n\nMikan's birthday is coming soon. Since Mikan likes graphs very much, Aroma decided to give her a undirected graph this year too. \nAroma bought a connected undirected graph, which consists of n vertices and n edges. \nThe vertices are numbered from 1 to n and for each i(1 <= i <= n), vertex i and vartex a_i are connected with an undirected edge. \nAroma thinks it is not interesting only to give the ready-made graph and decided to paint it. \nCount the number of ways to paint the vertices of the purchased graph in k colors modulo 10^9 + 7. \nTwo ways are considered to be the same if the graph painted in one way can be identical to the graph painted in the other way by permutating the numbers of the vertices.", "constraint": "1 <= n <= 10^5 \n 1 <= k <= 10^5 \n 1 <= a_i <= n (1 <= i <= n) \n The given graph is connected\n The given graph contains no self-loops or multiple edges.", "input": "Each data set is given in the following format from the standard input.\n\nn k\na_1\n:\na_n", "output": "Output the number of ways to paint the vertices of the given graph in k colors modulo 10^9 + 7 in one line.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 2\n2\n3\n1\n1 output: \n12", "input: 4 4\n2\n3\n4\n1 output: \n55", "input: 10 5\n2\n3\n4\n1\n1\n1\n2\n3\n3\n4 output: \n926250"], "Pid": "p03984", "ProblemText": "Task Description: Problem Statement\n\nMikan's birthday is coming soon. Since Mikan likes graphs very much, Aroma decided to give her a undirected graph this year too. \nAroma bought a connected undirected graph, which consists of n vertices and n edges. \nThe vertices are numbered from 1 to n and for each i(1 <= i <= n), vertex i and vartex a_i are connected with an undirected edge. \nAroma thinks it is not interesting only to give the ready-made graph and decided to paint it. \nCount the number of ways to paint the vertices of the purchased graph in k colors modulo 10^9 + 7. \nTwo ways are considered to be the same if the graph painted in one way can be identical to the graph painted in the other way by permutating the numbers of the vertices.\nTask Constraint: 1 <= n <= 10^5 \n 1 <= k <= 10^5 \n 1 <= a_i <= n (1 <= i <= n) \n The given graph is connected\n The given graph contains no self-loops or multiple edges.\nTask Input: Each data set is given in the following format from the standard input.\n\nn k\na_1\n:\na_n\nTask Output: Output the number of ways to paint the vertices of the given graph in k colors modulo 10^9 + 7 in one line.\nTask Samples: input: 4 2\n2\n3\n1\n1 output: \n12\ninput: 4 4\n2\n3\n4\n1 output: \n55\ninput: 10 5\n2\n3\n4\n1\n1\n1\n2\n3\n3\n4 output: \n926250\n\n" }, { "title": "", "content": "story: Story\nI am a Summoner who can invoke monsters. I can embody the pictures of monsters drawn on sketchbooks. \nI recently have received a request from Primate Research Institute of Kyoto University to invoke \"Hundred Eyes Monster\". \nWhat an great honor it is to contribute to the prosperity of the primate research of Kyoto University!\nI decided to paint an extremely high-quarity monster to the best of my ability. \nI have already painted the forehead and mouth and this time I am going to paint as many eyes as possible between the forehead and mouth. \nWell. . . I cannot wait to see the complete painting. \n\nProblem Statement\n\nTwo circles A, B are given on a two-dimensional plane. \nThe coordinate of the center and radius of circle A is (x_A, y_A) and r_A respectively. \nThe coordinate of the center and radius of circle B is (x_B, y_B) and r_B respectively. \nThese two circles have no intersection inside. \nHere, we consider a set of circles S that satisfies the following conditions. \nEach circle in S touches both A and B, and does not have common points with them inside the circle. \nAny two different circles in S have no common points inside them.\nWrite a program that finds the maximum number of elements in S.", "constraint": "1 <= T <= 50000\n-10^5 <= x_A <= 10^5\n-10^5 <= y_A <= 10^5\n-10^5 <= x_B <= 10^5\n-10^5 <= y_B <= 10^5\n1 <= r_A <= 10^5\n1 <= r_B <= 10^5\n{r_A}^2 + {r_B}^2 < (x_A - x_B)^2 + (y_A - y_B)^2\nAll values given as input are integers.\nIt is guaranteed that, when the radiuses of A and B change by 0.0005, the answer does not change.", "input": "The input consists of multiple test cases and is given from Standard Input in the following format:\n\nT\ntestcase_1\n:\ntestcase_T\n\nEach test case is given with the following format. \n\nx_A y_A r_A x_B y_B r_B", "output": "The output consists of T lines. \nOn line i (1 <= i <= T), putput the maximum number of elements in S in i-th test case.", "content_img": false, "lang": "", "error": false, "samples": ["input: 4\n0 -3 2 0 3 2\n0 0 9 8 8 2\n0 0 9 10 10 5\n0 0 707 1000 1000 707 output: \n3\n10\n21\n180\n\nYou can arrange circles ,for example, like the following images in Sample 1,2."], "Pid": "p03985", "ProblemText": "Task Description: story: Story\nI am a Summoner who can invoke monsters. I can embody the pictures of monsters drawn on sketchbooks. \nI recently have received a request from Primate Research Institute of Kyoto University to invoke \"Hundred Eyes Monster\". \nWhat an great honor it is to contribute to the prosperity of the primate research of Kyoto University!\nI decided to paint an extremely high-quarity monster to the best of my ability. \nI have already painted the forehead and mouth and this time I am going to paint as many eyes as possible between the forehead and mouth. \nWell. . . I cannot wait to see the complete painting. \n\nProblem Statement\n\nTwo circles A, B are given on a two-dimensional plane. \nThe coordinate of the center and radius of circle A is (x_A, y_A) and r_A respectively. \nThe coordinate of the center and radius of circle B is (x_B, y_B) and r_B respectively. \nThese two circles have no intersection inside. \nHere, we consider a set of circles S that satisfies the following conditions. \nEach circle in S touches both A and B, and does not have common points with them inside the circle. \nAny two different circles in S have no common points inside them.\nWrite a program that finds the maximum number of elements in S.\nTask Constraint: 1 <= T <= 50000\n-10^5 <= x_A <= 10^5\n-10^5 <= y_A <= 10^5\n-10^5 <= x_B <= 10^5\n-10^5 <= y_B <= 10^5\n1 <= r_A <= 10^5\n1 <= r_B <= 10^5\n{r_A}^2 + {r_B}^2 < (x_A - x_B)^2 + (y_A - y_B)^2\nAll values given as input are integers.\nIt is guaranteed that, when the radiuses of A and B change by 0.0005, the answer does not change.\nTask Input: The input consists of multiple test cases and is given from Standard Input in the following format:\n\nT\ntestcase_1\n:\ntestcase_T\n\nEach test case is given with the following format. \n\nx_A y_A r_A x_B y_B r_B\nTask Output: The output consists of T lines. \nOn line i (1 <= i <= T), putput the maximum number of elements in S in i-th test case.\nTask Samples: input: 4\n0 -3 2 0 3 2\n0 0 9 8 8 2\n0 0 9 10 10 5\n0 0 707 1000 1000 707 output: \n3\n10\n21\n180\n\nYou can arrange circles ,for example, like the following images in Sample 1,2.\n\n" }, { "title": "", "content": "Problem Statement We have a string X, which has an even number of characters. Half the characters are S, and the other half are T.\nTakahashi, who hates the string ST, will perform the following operation 10^{10000} times:\n\nAmong the occurrences of ST in X as (contiguous) substrings, remove the leftmost one. If there is no occurrence, do nothing.\n\nFind the eventual length of X. partial scores: Partial Scores\nIn test cases worth 200 points, |X| <= 200.", "constraint": "2 <= |X| <= 200,000\nThe length of X is even.\nHalf the characters in X are S, and the other half are T.", "input": "Input The input is given from Standard Input in the following format:\nX", "output": "Print the eventual length of X.", "content_img": false, "lang": "en", "error": false, "samples": ["input: TSTTSS output: 4\n\nIn the 1-st operation, the 2-nd and 3-rd characters of TSTTSS are removed.\nX becomes TTSS, and since it does not contain ST anymore, nothing is done in the remaining 10^{10000}-1 operations.\nThus, the answer is 4.", "input: SSTTST output: 0\n\nX will eventually become an empty string: SSTTST ⇒ STST ⇒ ST ⇒ ``.", "input: TSSTTTSS output: 4\n\nX will become: TSSTTTSS ⇒ TSTTSS ⇒ TTSS."], "Pid": "p03986", "ProblemText": "Task Description: Problem Statement We have a string X, which has an even number of characters. Half the characters are S, and the other half are T.\nTakahashi, who hates the string ST, will perform the following operation 10^{10000} times:\n\nAmong the occurrences of ST in X as (contiguous) substrings, remove the leftmost one. If there is no occurrence, do nothing.\n\nFind the eventual length of X. partial scores: Partial Scores\nIn test cases worth 200 points, |X| <= 200.\nTask Constraint: 2 <= |X| <= 200,000\nThe length of X is even.\nHalf the characters in X are S, and the other half are T.\nTask Input: Input The input is given from Standard Input in the following format:\nX\nTask Output: Print the eventual length of X.\nTask Samples: input: TSTTSS output: 4\n\nIn the 1-st operation, the 2-nd and 3-rd characters of TSTTSS are removed.\nX becomes TTSS, and since it does not contain ST anymore, nothing is done in the remaining 10^{10000}-1 operations.\nThus, the answer is 4.\ninput: SSTTST output: 0\n\nX will eventually become an empty string: SSTTST ⇒ STST ⇒ ST ⇒ ``.\ninput: TSSTTTSS output: 4\n\nX will become: TSSTTTSS ⇒ TSTTSS ⇒ TTSS.\n\n" }, { "title": "", "content": "Problem Statement One day, Snuke was given a permutation of length N, a_1, a_2, . . . , a_N, from his friend.\nFind the following:", "constraint": "1 <= N <= 200,000\n(a_1, a_2, ..., a_N) is a permutation of (1,2, ..., N).", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the answer.\nNote that the answer may not fit into a 32-bit integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n2 1 3 output: 9", "input: 4\n1 3 2 4 output: 19", "input: 8\n5 4 8 1 2 6 7 3 output: 85"], "Pid": "p03987", "ProblemText": "Task Description: Problem Statement One day, Snuke was given a permutation of length N, a_1, a_2, . . . , a_N, from his friend.\nFind the following:\nTask Constraint: 1 <= N <= 200,000\n(a_1, a_2, ..., a_N) is a permutation of (1,2, ..., N).\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the answer.\nNote that the answer may not fit into a 32-bit integer.\nTask Samples: input: 3\n2 1 3 output: 9\ninput: 4\n1 3 2 4 output: 19\ninput: 8\n5 4 8 1 2 6 7 3 output: 85\n\n" }, { "title": "", "content": "Problem Statement Aoki loves numerical sequences and trees.\nOne day, Takahashi gave him an integer sequence of length N, a_1, a_2, . . . , a_N, which made him want to construct a tree.\nAoki wants to construct a tree with N vertices numbered 1 through N, such that for each i = 1,2, . . . , N, the distance between vertex i and the farthest vertex from it is a_i, assuming that the length of each edge is 1.\nDetermine whether such a tree exists.", "constraint": "2 <= N <= 100\n1 <= a_i <= N-1", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "If there exists a tree that satisfies the condition, print Possible. Otherwise, print Impossible.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3 2 2 3 3 output: Possible\nThe diagram above shows an example of a tree that satisfies the conditions. The red arrows show paths from each vertex to the farthest vertex from it.", "input: 3\n1 1 2 output: Impossible", "input: 10\n1 2 2 2 2 2 2 2 2 2 output: Possible", "input: 10\n1 1 2 2 2 2 2 2 2 2 output: Impossible", "input: 6\n1 1 1 1 1 5 output: Impossible", "input: 5\n4 3 2 3 4 output: Possible"], "Pid": "p03988", "ProblemText": "Task Description: Problem Statement Aoki loves numerical sequences and trees.\nOne day, Takahashi gave him an integer sequence of length N, a_1, a_2, . . . , a_N, which made him want to construct a tree.\nAoki wants to construct a tree with N vertices numbered 1 through N, such that for each i = 1,2, . . . , N, the distance between vertex i and the farthest vertex from it is a_i, assuming that the length of each edge is 1.\nDetermine whether such a tree exists.\nTask Constraint: 2 <= N <= 100\n1 <= a_i <= N-1\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: If there exists a tree that satisfies the condition, print Possible. Otherwise, print Impossible.\nTask Samples: input: 5\n3 2 2 3 3 output: Possible\nThe diagram above shows an example of a tree that satisfies the conditions. The red arrows show paths from each vertex to the farthest vertex from it.\ninput: 3\n1 1 2 output: Impossible\ninput: 10\n1 2 2 2 2 2 2 2 2 2 output: Possible\ninput: 10\n1 1 2 2 2 2 2 2 2 2 output: Impossible\ninput: 6\n1 1 1 1 1 5 output: Impossible\ninput: 5\n4 3 2 3 4 output: Possible\n\n" }, { "title": "", "content": "Problem Statement Snuke loves permutations. He is making a permutation of length N.\nSince he hates the integer K, his permutation will satisfy the following:\n\nLet the permutation be a_1, a_2, . . . , a_N. For each i = 1,2, . . . , N, |a_i - i| \\neq K.\n\nAmong the N! permutations of length N, how many satisfies this condition?\nSince the answer may be extremely large, find the answer modulo 924844033(prime).", "constraint": "2 <= N <= 2000\n1 <= K <= N-1", "input": "Input The input is given from Standard Input in the following format:\nN K", "output": "Print the answer modulo 924844033.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1 output: 2\n\n2 permutations (1,2,3), (3,2,1) satisfy the condition.", "input: 4 1 output: 5\n\n5 permutations (1,2,3,4), (1,4,3,2), (3,2,1,4), (3,4,1,2), (4,2,3,1) satisfy the condition.", "input: 4 2 output: 9", "input: 4 3 output: 14", "input: 425 48 output: 756765083"], "Pid": "p03989", "ProblemText": "Task Description: Problem Statement Snuke loves permutations. He is making a permutation of length N.\nSince he hates the integer K, his permutation will satisfy the following:\n\nLet the permutation be a_1, a_2, . . . , a_N. For each i = 1,2, . . . , N, |a_i - i| \\neq K.\n\nAmong the N! permutations of length N, how many satisfies this condition?\nSince the answer may be extremely large, find the answer modulo 924844033(prime).\nTask Constraint: 2 <= N <= 2000\n1 <= K <= N-1\nTask Input: Input The input is given from Standard Input in the following format:\nN K\nTask Output: Print the answer modulo 924844033.\nTask Samples: input: 3 1 output: 2\n\n2 permutations (1,2,3), (3,2,1) satisfy the condition.\ninput: 4 1 output: 5\n\n5 permutations (1,2,3,4), (1,4,3,2), (3,2,1,4), (3,4,1,2), (4,2,3,1) satisfy the condition.\ninput: 4 2 output: 9\ninput: 4 3 output: 14\ninput: 425 48 output: 756765083\n\n" }, { "title": "", "content": "Problem Statement Sigma and Sugim are playing a game.\nThe game is played on a graph with N vertices numbered 1 through N. The graph has N-1 red edges and N-1 blue edges, and the N-1 edges in each color forms a tree. The red edges are represented by pairs of integers (a_i, b_i), and the blue edges are represented by pairs of integers (c_i, d_i).\nEach player has his own piece. Initially, Sigma's piece is at vertex X, and Sugim's piece is at vertex Y.\nThe game is played in turns, where turns are numbered starting from turn 1. Sigma takes turns 1,3,5, . . . , and Sugim takes turns 2,4,6, . . . .\nIn each turn, the current player either moves his piece, or does nothing. Here, Sigma can only move his piece to a vertex that is directly connected to the current vertex by a red edge. Similarly, Sugim can only move his piece to a vertex that is directly connected to the current vertex by a blue edge.\nWhen the two pieces come to the same vertex, the game ends immediately. If the game ends just after the operation in turn i, let i be the total number of turns in the game.\nSigma's objective is to make the total number of turns as large as possible, while Sugim's objective is to make it as small as possible.\nDetermine whether the game will end in a finite number of turns, assuming both players plays optimally to achieve their respective objectives. If the answer is positive, find the number of turns in the game.", "constraint": "2 <= N <= 200,000\n1 <= X, Y <= N\nX \\neq Y\n1 <= a_i, b_i, c_i, d_i <= N\nThe N-1 edges in each color (red and blue) forms a tree.", "input": "Input The input is given from Standard Input in the following format:\nN X Y\na_1 b_1\na_2 b_2\n:\na_{N-1} b_{N-1}\nc_1 d_1\nc_2 d_2\n:\nc_{N-1} d_{N-1}", "output": "If the game will end in a finite number of turns, print the number of turns.\nOtherwise, print -1.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 1 2\n1 2\n1 3\n1 4\n2 1\n2 3\n1 4 output: 4", "input: 3 3 1\n1 2\n2 3\n1 2\n2 3 output: 4", "input: 4 1 2\n1 2\n3 4\n2 4\n1 2\n3 4\n1 3 output: 2", "input: 4 2 1\n1 2\n3 4\n2 4\n1 2\n3 4\n1 3 output: -1", "input: 5 1 2\n1 2\n1 3\n1 4\n4 5\n2 1\n1 3\n1 5\n5 4 output: 6"], "Pid": "p03990", "ProblemText": "Task Description: Problem Statement Sigma and Sugim are playing a game.\nThe game is played on a graph with N vertices numbered 1 through N. The graph has N-1 red edges and N-1 blue edges, and the N-1 edges in each color forms a tree. The red edges are represented by pairs of integers (a_i, b_i), and the blue edges are represented by pairs of integers (c_i, d_i).\nEach player has his own piece. Initially, Sigma's piece is at vertex X, and Sugim's piece is at vertex Y.\nThe game is played in turns, where turns are numbered starting from turn 1. Sigma takes turns 1,3,5, . . . , and Sugim takes turns 2,4,6, . . . .\nIn each turn, the current player either moves his piece, or does nothing. Here, Sigma can only move his piece to a vertex that is directly connected to the current vertex by a red edge. Similarly, Sugim can only move his piece to a vertex that is directly connected to the current vertex by a blue edge.\nWhen the two pieces come to the same vertex, the game ends immediately. If the game ends just after the operation in turn i, let i be the total number of turns in the game.\nSigma's objective is to make the total number of turns as large as possible, while Sugim's objective is to make it as small as possible.\nDetermine whether the game will end in a finite number of turns, assuming both players plays optimally to achieve their respective objectives. If the answer is positive, find the number of turns in the game.\nTask Constraint: 2 <= N <= 200,000\n1 <= X, Y <= N\nX \\neq Y\n1 <= a_i, b_i, c_i, d_i <= N\nThe N-1 edges in each color (red and blue) forms a tree.\nTask Input: Input The input is given from Standard Input in the following format:\nN X Y\na_1 b_1\na_2 b_2\n:\na_{N-1} b_{N-1}\nc_1 d_1\nc_2 d_2\n:\nc_{N-1} d_{N-1}\nTask Output: If the game will end in a finite number of turns, print the number of turns.\nOtherwise, print -1.\nTask Samples: input: 4 1 2\n1 2\n1 3\n1 4\n2 1\n2 3\n1 4 output: 4\ninput: 3 3 1\n1 2\n2 3\n1 2\n2 3 output: 4\ninput: 4 1 2\n1 2\n3 4\n2 4\n1 2\n3 4\n1 3 output: 2\ninput: 4 2 1\n1 2\n3 4\n2 4\n1 2\n3 4\n1 3 output: -1\ninput: 5 1 2\n1 2\n1 3\n1 4\n4 5\n2 1\n1 3\n1 5\n5 4 output: 6\n\n" }, { "title": "", "content": "Problem Statement\nOne day, Takahashi was given the following problem from Aoki:\n\nYou are given a tree with N vertices and an integer K. The vertices are numbered 1 through N. The edges are represented by pairs of integers (a_i, b_i).\nFor a set S of vertices in the tree, let f(S) be the minimum number of the vertices in a subtree of the given tree that contains all vertices in S.\nThere are ways to choose K vertices from the trees. For each of them, let S be the set of the chosen vertices, and find the sum of f(S) over all ways.\nSince the answer may be extremely large, print it modulo 924844033(prime).\n\nSince it was too easy for him, he decided to solve this problem for all K = 1,2, . . . , N.", "constraint": "2 <= N <= 200,000\n1 <= a_i, b_i <= N\nThe given graph is a tree.", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_{N-1} b_{N-1}", "output": "Print N lines. The i-th line should contain the answer to the problem where K=i, modulo 924844033.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n1 2\n2 3 output: 3\n7\n3\nThe diagram above illustrates the case where K=2. The chosen vertices are colored pink, and the subtrees with the minimum number of vertices are enclosed by red lines.", "input: 4\n1 2\n1 3\n1 4 output: 4\n15\n13\n4", "input: 7\n1 2\n2 3\n2 4\n4 5\n4 6\n6 7 output: 7\n67\n150\n179\n122\n45\n7"], "Pid": "p03991", "ProblemText": "Task Description: Problem Statement\nOne day, Takahashi was given the following problem from Aoki:\n\nYou are given a tree with N vertices and an integer K. The vertices are numbered 1 through N. The edges are represented by pairs of integers (a_i, b_i).\nFor a set S of vertices in the tree, let f(S) be the minimum number of the vertices in a subtree of the given tree that contains all vertices in S.\nThere are ways to choose K vertices from the trees. For each of them, let S be the set of the chosen vertices, and find the sum of f(S) over all ways.\nSince the answer may be extremely large, print it modulo 924844033(prime).\n\nSince it was too easy for him, he decided to solve this problem for all K = 1,2, . . . , N.\nTask Constraint: 2 <= N <= 200,000\n1 <= a_i, b_i <= N\nThe given graph is a tree.\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 b_1\na_2 b_2\n:\na_{N-1} b_{N-1}\nTask Output: Print N lines. The i-th line should contain the answer to the problem where K=i, modulo 924844033.\nTask Samples: input: 3\n1 2\n2 3 output: 3\n7\n3\nThe diagram above illustrates the case where K=2. The chosen vertices are colored pink, and the subtrees with the minimum number of vertices are enclosed by red lines.\ninput: 4\n1 2\n1 3\n1 4 output: 4\n15\n13\n4\ninput: 7\n1 2\n2 3\n2 4\n4 5\n4 6\n6 7 output: 7\n67\n150\n179\n122\n45\n7\n\n" }, { "title": "", "content": "Problem Statement This contest is CODE FESTIVAL.\nHowever, Mr. Takahashi always writes it CODEFESTIVAL, omitting the single space between CODE and FESTIVAL.\nSo he has decided to make a program that puts the single space he omitted.\nYou are given a string s with 12 letters.\nOutput the string putting a single space between the first 4 letters and last 8 letters in the string s.", "constraint": "s contains exactly 12 letters.\nAll letters in s are uppercase English letters.", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "Print the string putting a single space between the first 4 letters and last 8 letters in the string s.\nPut a line break at the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: CODEFESTIVAL output: CODE FESTIVAL\n\nPutting a single space between the first 4 letters and last 8 letters in CODEFESTIVAL makes it CODE FESTIVAL.", "input: POSTGRADUATE output: POST GRADUATE", "input: ABCDEFGHIJKL output: ABCD EFGHIJKL"], "Pid": "p03992", "ProblemText": "Task Description: Problem Statement This contest is CODE FESTIVAL.\nHowever, Mr. Takahashi always writes it CODEFESTIVAL, omitting the single space between CODE and FESTIVAL.\nSo he has decided to make a program that puts the single space he omitted.\nYou are given a string s with 12 letters.\nOutput the string putting a single space between the first 4 letters and last 8 letters in the string s.\nTask Constraint: s contains exactly 12 letters.\nAll letters in s are uppercase English letters.\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: Print the string putting a single space between the first 4 letters and last 8 letters in the string s.\nPut a line break at the end.\nTask Samples: input: CODEFESTIVAL output: CODE FESTIVAL\n\nPutting a single space between the first 4 letters and last 8 letters in CODEFESTIVAL makes it CODE FESTIVAL.\ninput: POSTGRADUATE output: POST GRADUATE\ninput: ABCDEFGHIJKL output: ABCD EFGHIJKL\n\n" }, { "title": "", "content": "Problem Statement There are N rabbits, numbered 1 through N.\nThe i-th (1<=i<=N) rabbit likes rabbit a_i.\nNote that no rabbit can like itself, that is, a_i! =i.\nFor a pair of rabbits i and j (i＜j), we call the pair (i，j) a friendly pair if the following condition is met.\n\nRabbit i likes rabbit j and rabbit j likes rabbit i.\n\nCalculate the number of the friendly pairs.", "constraint": "2<=N<=10^5\n1<=a_i<=N\na_i!=i", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the number of the friendly pairs.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2 1 4 3 output: 2\n\nThere are two friendly pairs: (1，2) and (3，4).", "input: 3\n2 3 1 output: 0\n\nThere are no friendly pairs.", "input: 5\n5 5 5 5 1 output: 1\n\nThere is one friendly pair: (1，5)."], "Pid": "p03993", "ProblemText": "Task Description: Problem Statement There are N rabbits, numbered 1 through N.\nThe i-th (1<=i<=N) rabbit likes rabbit a_i.\nNote that no rabbit can like itself, that is, a_i! =i.\nFor a pair of rabbits i and j (i＜j), we call the pair (i，j) a friendly pair if the following condition is met.\n\nRabbit i likes rabbit j and rabbit j likes rabbit i.\n\nCalculate the number of the friendly pairs.\nTask Constraint: 2<=N<=10^5\n1<=a_i<=N\na_i!=i\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the number of the friendly pairs.\nTask Samples: input: 4\n2 1 4 3 output: 2\n\nThere are two friendly pairs: (1，2) and (3，4).\ninput: 3\n2 3 1 output: 0\n\nThere are no friendly pairs.\ninput: 5\n5 5 5 5 1 output: 1\n\nThere is one friendly pair: (1，5).\n\n" }, { "title": "", "content": "Problem Statement Mr. Takahashi has a string s consisting of lowercase English letters.\nHe repeats the following operation on s exactly K times.\n\nChoose an arbitrary letter on s and change that letter to the next alphabet. Note that the next letter of z is a.\n\nFor example, if you perform an operation for the second letter on aaz, aaz becomes abz.\nIf you then perform an operation for the third letter on abz, abz becomes aba.\nMr. Takahashi wants to have the lexicographically smallest string after performing exactly K operations on s.\nFind the such string.", "constraint": "1<=|s|<=10^5\nAll letters in s are lowercase English letters.\n1<=K<=10^9", "input": "Input The input is given from Standard Input in the following format:\ns\nK", "output": "Print the lexicographically smallest string after performing exactly K operations on s.", "content_img": false, "lang": "en", "error": false, "samples": ["input: xyz\n4 output: aya\n\nFor example, you can perform the following operations: xyz, yyz, zyz, ayz, aya.", "input: a\n25 output: z\n\nYou have to perform exactly K operations.", "input: codefestival\n100 output: aaaafeaaivap"], "Pid": "p03994", "ProblemText": "Task Description: Problem Statement Mr. Takahashi has a string s consisting of lowercase English letters.\nHe repeats the following operation on s exactly K times.\n\nChoose an arbitrary letter on s and change that letter to the next alphabet. Note that the next letter of z is a.\n\nFor example, if you perform an operation for the second letter on aaz, aaz becomes abz.\nIf you then perform an operation for the third letter on abz, abz becomes aba.\nMr. Takahashi wants to have the lexicographically smallest string after performing exactly K operations on s.\nFind the such string.\nTask Constraint: 1<=|s|<=10^5\nAll letters in s are lowercase English letters.\n1<=K<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\ns\nK\nTask Output: Print the lexicographically smallest string after performing exactly K operations on s.\nTask Samples: input: xyz\n4 output: aya\n\nFor example, you can perform the following operations: xyz, yyz, zyz, ayz, aya.\ninput: a\n25 output: z\n\nYou have to perform exactly K operations.\ninput: codefestival\n100 output: aaaafeaaivap\n\n" }, { "title": "", "content": "Problem Statement There is a grid with R rows and C columns.\nWe call the cell in the r-th row and c-th column (r，c).\nMr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1<=i<=N).\nAfter that he fell asleep.\nMr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells.\nThe grid must meet the following conditions to really surprise Mr. Takahashi.\n\nCondition 1: Each cell contains a non-negative integer.\nCondition 2: For any 2*2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.\n\nDetermine whether it is possible to meet those conditions by properly writing integers into all remaining cells.", "constraint": "2<=R，C<=10^5\n1<=N<=10^5\n1<=r_i<=R\n1<=c_i<=C\n(r_i，c_i) != (r_j，c_j) (i!=j)\na_i is an integer.\n0<=a_i<=10^9", "input": "Input The input is given from Standard Input in the following format:\nR C\nN\nr_1 c_1 a_1\nr_2 c_2 a_2\n:\nr_N c_N a_N", "output": "Print Yes if it is possible to meet the conditions by properly writing integers into all remaining cells.\nOtherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n3\n1 1 0\n1 2 10\n2 1 20 output: Yes\n\nYou can write integers as follows.", "input: 2 3\n5\n1 1 0\n1 2 10\n1 3 20\n2 1 30\n2 3 40 output: No\n\nThere are two 2*2 squares on the grid, formed by the following cells:\n\nCells (1，1), (1，2), (2，1) and (2，2)\nCells (1，2), (1，3), (2，2) and (2，3)\n\nYou have to write 40 into the empty cell to meet the condition on the left square, but then it does not satisfy the condition on the right square.", "input: 2 2\n3\n1 1 20\n1 2 10\n2 1 0 output: No\n\nYou have to write -10 into the empty cell to meet condition 2, but then it does not satisfy condition 1.", "input: 3 3\n4\n1 1 0\n1 3 10\n3 1 10\n3 3 20 output: Yes\n\nYou can write integers as follows.", "input: 2 2\n4\n1 1 0\n1 2 10\n2 1 30\n2 2 20 output: No\n\nAll cells already contain a integer and condition 2 is not satisfied."], "Pid": "p03995", "ProblemText": "Task Description: Problem Statement There is a grid with R rows and C columns.\nWe call the cell in the r-th row and c-th column (r，c).\nMr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1<=i<=N).\nAfter that he fell asleep.\nMr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells.\nThe grid must meet the following conditions to really surprise Mr. Takahashi.\n\nCondition 1: Each cell contains a non-negative integer.\nCondition 2: For any 2*2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.\n\nDetermine whether it is possible to meet those conditions by properly writing integers into all remaining cells.\nTask Constraint: 2<=R，C<=10^5\n1<=N<=10^5\n1<=r_i<=R\n1<=c_i<=C\n(r_i，c_i) != (r_j，c_j) (i!=j)\na_i is an integer.\n0<=a_i<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nR C\nN\nr_1 c_1 a_1\nr_2 c_2 a_2\n:\nr_N c_N a_N\nTask Output: Print Yes if it is possible to meet the conditions by properly writing integers into all remaining cells.\nOtherwise, print No.\nTask Samples: input: 2 2\n3\n1 1 0\n1 2 10\n2 1 20 output: Yes\n\nYou can write integers as follows.\ninput: 2 3\n5\n1 1 0\n1 2 10\n1 3 20\n2 1 30\n2 3 40 output: No\n\nThere are two 2*2 squares on the grid, formed by the following cells:\n\nCells (1，1), (1，2), (2，1) and (2，2)\nCells (1，2), (1，3), (2，2) and (2，3)\n\nYou have to write 40 into the empty cell to meet the condition on the left square, but then it does not satisfy the condition on the right square.\ninput: 2 2\n3\n1 1 20\n1 2 10\n2 1 0 output: No\n\nYou have to write -10 into the empty cell to meet condition 2, but then it does not satisfy condition 1.\ninput: 3 3\n4\n1 1 0\n1 3 10\n3 1 10\n3 3 20 output: Yes\n\nYou can write integers as follows.\ninput: 2 2\n4\n1 1 0\n1 2 10\n2 1 30\n2 2 20 output: No\n\nAll cells already contain a integer and condition 2 is not satisfied.\n\n" }, { "title": "", "content": "Problem Statement There are N arrays.\nThe length of each array is M and initially each array contains integers (1，2，. . . ，M) in this order.\nMr. Takahashi has decided to perform Q operations on those N arrays.\nFor the i-th (1<=i<=Q) time, he performs the following operation.\n\nChoose an arbitrary array from the N arrays and move the integer a_i (1<=a_i<=M) to the front of that array. For example, after performing the operation on a_i=2 and the array (5，4，3，2，1), this array becomes (2，5，4，3，1).\n\nMr. Takahashi wants to make N arrays exactly the same after performing the Q operations.\nDetermine if it is possible or not.", "constraint": "2<=N<=10^5\n2<=M<=10^5\n1<=Q<=10^5\n1<=a_i<=M", "input": "Input The input is given from Standard Input in the following format:\nN M\nQ\na_1 a_2 . . . a_Q", "output": "Print Yes if it is possible to make N arrays exactly the same after performing the Q operations.\nOtherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 2\n3\n2 1 2 output: Yes\n\nYou can perform the operations as follows.", "input: 3 2\n3\n2 1 2 output: No", "input: 2 3\n3\n3 2 1 output: Yes\n\nYou can perform the operations as follows.", "input: 3 3\n6\n1 2 2 3 3 3 output: No"], "Pid": "p03996", "ProblemText": "Task Description: Problem Statement There are N arrays.\nThe length of each array is M and initially each array contains integers (1，2，. . . ，M) in this order.\nMr. Takahashi has decided to perform Q operations on those N arrays.\nFor the i-th (1<=i<=Q) time, he performs the following operation.\n\nChoose an arbitrary array from the N arrays and move the integer a_i (1<=a_i<=M) to the front of that array. For example, after performing the operation on a_i=2 and the array (5，4，3，2，1), this array becomes (2，5，4，3，1).\n\nMr. Takahashi wants to make N arrays exactly the same after performing the Q operations.\nDetermine if it is possible or not.\nTask Constraint: 2<=N<=10^5\n2<=M<=10^5\n1<=Q<=10^5\n1<=a_i<=M\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nQ\na_1 a_2 . . . a_Q\nTask Output: Print Yes if it is possible to make N arrays exactly the same after performing the Q operations.\nOtherwise, print No.\nTask Samples: input: 2 2\n3\n2 1 2 output: Yes\n\nYou can perform the operations as follows.\ninput: 3 2\n3\n2 1 2 output: No\ninput: 2 3\n3\n3 2 1 output: Yes\n\nYou can perform the operations as follows.\ninput: 3 3\n6\n1 2 2 3 3 3 output: No\n\n" }, { "title": "", "content": "Problem Statement You are given a trapezoid. The lengths of its upper base, lower base, and height are a, b, and h, respectively.\nAn example of a trapezoid\n\nFind the area of this trapezoid.", "constraint": "1<=a<=100\n1<=b<=100\n1<=h<=100\nAll input values are integers.\nh is even.", "input": "Input The input is given from Standard Input in the following format:\na\nb\nh", "output": "Print the area of the given trapezoid. It is guaranteed that the area is an integer.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n4\n2 output: 7\n\nWhen the lengths of the upper base, lower base, and height are 3,4, and 2, respectively, the area of the trapezoid is (3+4)*2/2 = 7.", "input: 4\n4\n4 output: 16\n\nIn this case, a parallelogram is given, which is also a trapezoid."], "Pid": "p03997", "ProblemText": "Task Description: Problem Statement You are given a trapezoid. The lengths of its upper base, lower base, and height are a, b, and h, respectively.\nAn example of a trapezoid\n\nFind the area of this trapezoid.\nTask Constraint: 1<=a<=100\n1<=b<=100\n1<=h<=100\nAll input values are integers.\nh is even.\nTask Input: Input The input is given from Standard Input in the following format:\na\nb\nh\nTask Output: Print the area of the given trapezoid. It is guaranteed that the area is an integer.\nTask Samples: input: 3\n4\n2 output: 7\n\nWhen the lengths of the upper base, lower base, and height are 3,4, and 2, respectively, the area of the trapezoid is (3+4)*2/2 = 7.\ninput: 4\n4\n4 output: 16\n\nIn this case, a parallelogram is given, which is also a trapezoid.\n\n" }, { "title": "", "content": "Problem Statement Alice, Bob and Charlie are playing Card Game for Three, as below:\n\nAt first, each of the three players has a deck consisting of some number of cards. Each card has a letter a, b or c written on it. The orders of the cards in the decks cannot be rearranged.\nThe players take turns. Alice goes first.\nIf the current player's deck contains at least one card, discard the top card in the deck. Then, the player whose name begins with the letter on the discarded card, takes the next turn. (For example, if the card says a, Alice takes the next turn. )\nIf the current player's deck is empty, the game ends and the current player wins the game.\n\nYou are given the initial decks of the players.\nMore specifically, you are given three strings S_A, S_B and S_C. The i-th (1<=i<=|S_A|) letter in S_A is the letter on the i-th card in Alice's initial deck. S_B and S_C describes Bob's and Charlie's initial decks in the same way.\nDetermine the winner of the game.", "constraint": "1<=|S_A|<=100\n1<=|S_B|<=100\n1<=|S_C|<=100\nEach letter in S_A, S_B, S_C is a, b or c.", "input": "Input The input is given from Standard Input in the following format:\nS_A\nS_B\nS_C", "output": "If Alice will win, print A. If Bob will win, print B. If Charlie will win, print C.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aca\naccc\nca output: A\n\nThe game will progress as below:\n\nAlice discards the top card in her deck, a. Alice takes the next turn.\nAlice discards the top card in her deck, c. Charlie takes the next turn.\nCharlie discards the top card in his deck, c. Charlie takes the next turn.\nCharlie discards the top card in his deck, a. Alice takes the next turn.\nAlice discards the top card in her deck, a. Alice takes the next turn.\nAlice's deck is empty. The game ends and Alice wins the game.", "input: abcb\naacb\nbccc output: C"], "Pid": "p03998", "ProblemText": "Task Description: Problem Statement Alice, Bob and Charlie are playing Card Game for Three, as below:\n\nAt first, each of the three players has a deck consisting of some number of cards. Each card has a letter a, b or c written on it. The orders of the cards in the decks cannot be rearranged.\nThe players take turns. Alice goes first.\nIf the current player's deck contains at least one card, discard the top card in the deck. Then, the player whose name begins with the letter on the discarded card, takes the next turn. (For example, if the card says a, Alice takes the next turn. )\nIf the current player's deck is empty, the game ends and the current player wins the game.\n\nYou are given the initial decks of the players.\nMore specifically, you are given three strings S_A, S_B and S_C. The i-th (1<=i<=|S_A|) letter in S_A is the letter on the i-th card in Alice's initial deck. S_B and S_C describes Bob's and Charlie's initial decks in the same way.\nDetermine the winner of the game.\nTask Constraint: 1<=|S_A|<=100\n1<=|S_B|<=100\n1<=|S_C|<=100\nEach letter in S_A, S_B, S_C is a, b or c.\nTask Input: Input The input is given from Standard Input in the following format:\nS_A\nS_B\nS_C\nTask Output: If Alice will win, print A. If Bob will win, print B. If Charlie will win, print C.\nTask Samples: input: aca\naccc\nca output: A\n\nThe game will progress as below:\n\nAlice discards the top card in her deck, a. Alice takes the next turn.\nAlice discards the top card in her deck, c. Charlie takes the next turn.\nCharlie discards the top card in his deck, c. Charlie takes the next turn.\nCharlie discards the top card in his deck, a. Alice takes the next turn.\nAlice discards the top card in her deck, a. Alice takes the next turn.\nAlice's deck is empty. The game ends and Alice wins the game.\ninput: abcb\naacb\nbccc output: C\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of digits between 1 and 9, inclusive.\nYou can insert the letter + into some of the positions (possibly none) between two letters in this string.\nHere, + must not occur consecutively after insertion.\nAll strings that can be obtained in this way can be evaluated as formulas.\nEvaluate all possible formulas, and print the sum of the results.", "constraint": "1 <= |S| <= 10\nAll letters in S are digits between 1 and 9, inclusive.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "Print the sum of the evaluated value over all possible formulas.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 125 output: 176\n\nThere are 4 formulas that can be obtained: 125,1+25,12+5 and 1+2+5. When each formula is evaluated,\n\n125\n1+25=26\n12+5=17\n1+2+5=8\n\nThus, the sum is 125+26+17+8=176.", "input: 9999999999 output: 12656242944"], "Pid": "p03999", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of digits between 1 and 9, inclusive.\nYou can insert the letter + into some of the positions (possibly none) between two letters in this string.\nHere, + must not occur consecutively after insertion.\nAll strings that can be obtained in this way can be evaluated as formulas.\nEvaluate all possible formulas, and print the sum of the results.\nTask Constraint: 1 <= |S| <= 10\nAll letters in S are digits between 1 and 9, inclusive.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: Print the sum of the evaluated value over all possible formulas.\nTask Samples: input: 125 output: 176\n\nThere are 4 formulas that can be obtained: 125,1+25,12+5 and 1+2+5. When each formula is evaluated,\n\n125\n1+25=26\n12+5=17\n1+2+5=8\n\nThus, the sum is 125+26+17+8=176.\ninput: 9999999999 output: 12656242944\n\n" }, { "title": "", "content": "Problem Statement We have a grid with H rows and W columns. At first, all cells were painted white.\nSnuke painted N of these cells. The i-th ( 1 <= i <= N ) cell he painted is the cell at the a_i-th row and b_i-th column.\nCompute the following:\n\nFor each integer j ( 0 <= j <= 9 ), how many subrectangles of size 3*3 of the grid contains exactly j black cells, after Snuke painted N cells?", "constraint": "3 <= H <= 10^9\n3 <= W <= 10^9\n0 <= N <= min(10^5,H*W)\n1 <= a_i <= H (1 <= i <= N)\n1 <= b_i <= W (1 <= i <= N)\n(a_i, b_i) \\neq (a_j, b_j) (i \\neq j)", "input": "Input The input is given from Standard Input in the following format:\nH W N\na_1 b_1\n:\na_N b_N", "output": "Print 10 lines.\nThe (j+1)-th ( 0 <= j <= 9 ) line should contain the number of the subrectangles of size 3*3 of the grid that contains exactly j black cells.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 8\n1 1\n1 4\n1 5\n2 3\n3 1\n3 2\n3 4\n4 4 output: 0\n0\n0\n2\n4\n0\n0\n0\n0\n0\nThere are six subrectangles of size 3*3. Two of them contain three black cells each, and the remaining four contain four black cells each.", "input: 10 10 20\n1 1\n1 4\n1 9\n2 5\n3 10\n4 2\n4 7\n5 9\n6 4\n6 6\n6 7\n7 1\n7 3\n7 7\n8 1\n8 5\n8 10\n9 2\n10 4\n10 9 output: 4\n26\n22\n10\n2\n0\n0\n0\n0\n0", "input: 1000000000 1000000000 0 output: 999999996000000004\n0\n0\n0\n0\n0\n0\n0\n0\n0"], "Pid": "p04000", "ProblemText": "Task Description: Problem Statement We have a grid with H rows and W columns. At first, all cells were painted white.\nSnuke painted N of these cells. The i-th ( 1 <= i <= N ) cell he painted is the cell at the a_i-th row and b_i-th column.\nCompute the following:\n\nFor each integer j ( 0 <= j <= 9 ), how many subrectangles of size 3*3 of the grid contains exactly j black cells, after Snuke painted N cells?\nTask Constraint: 3 <= H <= 10^9\n3 <= W <= 10^9\n0 <= N <= min(10^5,H*W)\n1 <= a_i <= H (1 <= i <= N)\n1 <= b_i <= W (1 <= i <= N)\n(a_i, b_i) \\neq (a_j, b_j) (i \\neq j)\nTask Input: Input The input is given from Standard Input in the following format:\nH W N\na_1 b_1\n:\na_N b_N\nTask Output: Print 10 lines.\nThe (j+1)-th ( 0 <= j <= 9 ) line should contain the number of the subrectangles of size 3*3 of the grid that contains exactly j black cells.\nTask Samples: input: 4 5 8\n1 1\n1 4\n1 5\n2 3\n3 1\n3 2\n3 4\n4 4 output: 0\n0\n0\n2\n4\n0\n0\n0\n0\n0\nThere are six subrectangles of size 3*3. Two of them contain three black cells each, and the remaining four contain four black cells each.\ninput: 10 10 20\n1 1\n1 4\n1 9\n2 5\n3 10\n4 2\n4 7\n5 9\n6 4\n6 6\n6 7\n7 1\n7 3\n7 7\n8 1\n8 5\n8 10\n9 2\n10 4\n10 9 output: 4\n26\n22\n10\n2\n0\n0\n0\n0\n0\ninput: 1000000000 1000000000 0 output: 999999996000000004\n0\n0\n0\n0\n0\n0\n0\n0\n0\n\n" }, { "title": "", "content": "Problem Statement You are given a string S consisting of digits between 1 and 9, inclusive.\nYou can insert the letter + into some of the positions (possibly none) between two letters in this string.\nHere, + must not occur consecutively after insertion.\nAll strings that can be obtained in this way can be evaluated as formulas.\nEvaluate all possible formulas, and print the sum of the results.", "constraint": "1 <= |S| <= 10\nAll letters in S are digits between 1 and 9, inclusive.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "Print the sum of the evaluated value over all possible formulas.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 125 output: 176\n\nThere are 4 formulas that can be obtained: 125,1+25,12+5 and 1+2+5. When each formula is evaluated,\n\n125\n1+25=26\n12+5=17\n1+2+5=8\n\nThus, the sum is 125+26+17+8=176.", "input: 9999999999 output: 12656242944"], "Pid": "p04001", "ProblemText": "Task Description: Problem Statement You are given a string S consisting of digits between 1 and 9, inclusive.\nYou can insert the letter + into some of the positions (possibly none) between two letters in this string.\nHere, + must not occur consecutively after insertion.\nAll strings that can be obtained in this way can be evaluated as formulas.\nEvaluate all possible formulas, and print the sum of the results.\nTask Constraint: 1 <= |S| <= 10\nAll letters in S are digits between 1 and 9, inclusive.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: Print the sum of the evaluated value over all possible formulas.\nTask Samples: input: 125 output: 176\n\nThere are 4 formulas that can be obtained: 125,1+25,12+5 and 1+2+5. When each formula is evaluated,\n\n125\n1+25=26\n12+5=17\n1+2+5=8\n\nThus, the sum is 125+26+17+8=176.\ninput: 9999999999 output: 12656242944\n\n" }, { "title": "", "content": "Problem Statement We have a grid with H rows and W columns. At first, all cells were painted white.\nSnuke painted N of these cells. The i-th ( 1 <= i <= N ) cell he painted is the cell at the a_i-th row and b_i-th column.\nCompute the following:\n\nFor each integer j ( 0 <= j <= 9 ), how many subrectangles of size 3*3 of the grid contains exactly j black cells, after Snuke painted N cells?", "constraint": "3 <= H <= 10^9\n3 <= W <= 10^9\n0 <= N <= min(10^5,H*W)\n1 <= a_i <= H (1 <= i <= N)\n1 <= b_i <= W (1 <= i <= N)\n(a_i, b_i) \\neq (a_j, b_j) (i \\neq j)", "input": "Input The input is given from Standard Input in the following format:\nH W N\na_1 b_1\n:\na_N b_N", "output": "Print 10 lines.\nThe (j+1)-th ( 0 <= j <= 9 ) line should contain the number of the subrectangles of size 3*3 of the grid that contains exactly j black cells.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 5 8\n1 1\n1 4\n1 5\n2 3\n3 1\n3 2\n3 4\n4 4 output: 0\n0\n0\n2\n4\n0\n0\n0\n0\n0\nThere are six subrectangles of size 3*3. Two of them contain three black cells each, and the remaining four contain four black cells each.", "input: 10 10 20\n1 1\n1 4\n1 9\n2 5\n3 10\n4 2\n4 7\n5 9\n6 4\n6 6\n6 7\n7 1\n7 3\n7 7\n8 1\n8 5\n8 10\n9 2\n10 4\n10 9 output: 4\n26\n22\n10\n2\n0\n0\n0\n0\n0", "input: 1000000000 1000000000 0 output: 999999996000000004\n0\n0\n0\n0\n0\n0\n0\n0\n0"], "Pid": "p04002", "ProblemText": "Task Description: Problem Statement We have a grid with H rows and W columns. At first, all cells were painted white.\nSnuke painted N of these cells. The i-th ( 1 <= i <= N ) cell he painted is the cell at the a_i-th row and b_i-th column.\nCompute the following:\n\nFor each integer j ( 0 <= j <= 9 ), how many subrectangles of size 3*3 of the grid contains exactly j black cells, after Snuke painted N cells?\nTask Constraint: 3 <= H <= 10^9\n3 <= W <= 10^9\n0 <= N <= min(10^5,H*W)\n1 <= a_i <= H (1 <= i <= N)\n1 <= b_i <= W (1 <= i <= N)\n(a_i, b_i) \\neq (a_j, b_j) (i \\neq j)\nTask Input: Input The input is given from Standard Input in the following format:\nH W N\na_1 b_1\n:\na_N b_N\nTask Output: Print 10 lines.\nThe (j+1)-th ( 0 <= j <= 9 ) line should contain the number of the subrectangles of size 3*3 of the grid that contains exactly j black cells.\nTask Samples: input: 4 5 8\n1 1\n1 4\n1 5\n2 3\n3 1\n3 2\n3 4\n4 4 output: 0\n0\n0\n2\n4\n0\n0\n0\n0\n0\nThere are six subrectangles of size 3*3. Two of them contain three black cells each, and the remaining four contain four black cells each.\ninput: 10 10 20\n1 1\n1 4\n1 9\n2 5\n3 10\n4 2\n4 7\n5 9\n6 4\n6 6\n6 7\n7 1\n7 3\n7 7\n8 1\n8 5\n8 10\n9 2\n10 4\n10 9 output: 4\n26\n22\n10\n2\n0\n0\n0\n0\n0\ninput: 1000000000 1000000000 0 output: 999999996000000004\n0\n0\n0\n0\n0\n0\n0\n0\n0\n\n" }, { "title": "", "content": "Problem Statement Snuke's town has a subway system, consisting of N stations and M railway lines. The stations are numbered 1 through N. Each line is operated by a company. Each company has an identification number.\nThe i-th ( 1 <= i <= M ) line connects station p_i and q_i bidirectionally. There is no intermediate station. This line is operated by company c_i.\nYou can change trains at a station where multiple lines are available.\nThe fare system used in this subway system is a bit strange. When a passenger only uses lines that are operated by the same company, the fare is 1 yen (the currency of Japan). Whenever a passenger changes to a line that is operated by a different company from the current line, the passenger is charged an additional fare of 1 yen. In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.\nSnuke is now at station 1 and wants to travel to station N by subway. Find the minimum required fare.", "constraint": "2 <= N <= 10^5\n0 <= M <= 2*10^5\n1 <= p_i <= N (1 <= i <= M)\n1 <= q_i <= N (1 <= i <= M)\n1 <= c_i <= 10^6 (1 <= i <= M)\np_i \\neq q_i (1 <= i <= M)", "input": "Input The input is given from Standard Input in the following format:\nN M\np_1 q_1 c_1\n:\np_M q_M c_M", "output": "Print the minimum required fare. If it is impossible to get to station N by subway, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\n1 2 1\n2 3 1\n3 1 2 output: 1\n\nUse company 1's lines: 1 → 2 → 3. The fare is 1 yen.", "input: 8 11\n1 3 1\n1 4 2\n2 3 1\n2 5 1\n3 4 3\n3 6 3\n3 7 3\n4 8 4\n5 6 1\n6 7 5\n7 8 5 output: 2\n\nFirst, use company 1's lines: 1 → 3 → 2 → 5 → 6. Then, use company 5's lines: 6 → 7 → 8. The fare is 2 yen.", "input: 2 0 output: -1"], "Pid": "p04003", "ProblemText": "Task Description: Problem Statement Snuke's town has a subway system, consisting of N stations and M railway lines. The stations are numbered 1 through N. Each line is operated by a company. Each company has an identification number.\nThe i-th ( 1 <= i <= M ) line connects station p_i and q_i bidirectionally. There is no intermediate station. This line is operated by company c_i.\nYou can change trains at a station where multiple lines are available.\nThe fare system used in this subway system is a bit strange. When a passenger only uses lines that are operated by the same company, the fare is 1 yen (the currency of Japan). Whenever a passenger changes to a line that is operated by a different company from the current line, the passenger is charged an additional fare of 1 yen. In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.\nSnuke is now at station 1 and wants to travel to station N by subway. Find the minimum required fare.\nTask Constraint: 2 <= N <= 10^5\n0 <= M <= 2*10^5\n1 <= p_i <= N (1 <= i <= M)\n1 <= q_i <= N (1 <= i <= M)\n1 <= c_i <= 10^6 (1 <= i <= M)\np_i \\neq q_i (1 <= i <= M)\nTask Input: Input The input is given from Standard Input in the following format:\nN M\np_1 q_1 c_1\n:\np_M q_M c_M\nTask Output: Print the minimum required fare. If it is impossible to get to station N by subway, print -1 instead.\nTask Samples: input: 3 3\n1 2 1\n2 3 1\n3 1 2 output: 1\n\nUse company 1's lines: 1 → 2 → 3. The fare is 1 yen.\ninput: 8 11\n1 3 1\n1 4 2\n2 3 1\n2 5 1\n3 4 3\n3 6 3\n3 7 3\n4 8 4\n5 6 1\n6 7 5\n7 8 5 output: 2\n\nFirst, use company 1's lines: 1 → 3 → 2 → 5 → 6. Then, use company 5's lines: 6 → 7 → 8. The fare is 2 yen.\ninput: 2 0 output: -1\n\n" }, { "title": "", "content": "Problem Statement Alice, Bob and Charlie are playing Card Game for Three, as below:\n\nAt first, each of the three players has a deck consisting of some number of cards. Alice's deck has N cards, Bob's deck has M cards, and Charlie's deck has K cards. Each card has a letter a, b or c written on it. The orders of the cards in the decks cannot be rearranged.\nThe players take turns. Alice goes first.\nIf the current player's deck contains at least one card, discard the top card in the deck. Then, the player whose name begins with the letter on the discarded card, takes the next turn. (For example, if the card says a, Alice takes the next turn. )\nIf the current player's deck is empty, the game ends and the current player wins the game.\n\nThere are 3^{N+M+K} possible patters of the three player's initial decks. Among these patterns, how many will lead to Alice's victory?\nSince the answer can be large, print the count modulo 1\\, 000\\, 000\\, 007 (=10^9+7). partial scores: Partial Scores\n500 points will be awarded for passing the test set satisfying the following: 1 <= N <= 1000,1 <= M <= 1000,1 <= K <= 1000.", "constraint": "1 <= N <= 3*10^5\n1 <= M <= 3*10^5\n1 <= K <= 3*10^5", "input": "Input The input is given from Standard Input in the following format:\nN M K", "output": "Print the answer modulo 1\\, 000\\, 000\\, 007 (=10^9+7).", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 1 1 output: 17\nIf Alice's card is a, then Alice will win regardless of Bob's and Charlie's card. There are 3*3=9 such patterns.\nIf Alice's card is b, Alice will only win when Bob's card is a, or when Bob's card is c and Charlie's card is a. There are 3+1=4 such patterns.\nIf Alice's card is c, Alice will only win when Charlie's card is a, or when Charlie's card is b and Bob's card is a. There are 3+1=4 such patterns.\n\nThus, there are total of 9+4+4=17 patterns that will lead to Alice's victory.", "input: 4 2 2 output: 1227", "input: 1000 1000 1000 output: 261790852"], "Pid": "p04004", "ProblemText": "Task Description: Problem Statement Alice, Bob and Charlie are playing Card Game for Three, as below:\n\nAt first, each of the three players has a deck consisting of some number of cards. Alice's deck has N cards, Bob's deck has M cards, and Charlie's deck has K cards. Each card has a letter a, b or c written on it. The orders of the cards in the decks cannot be rearranged.\nThe players take turns. Alice goes first.\nIf the current player's deck contains at least one card, discard the top card in the deck. Then, the player whose name begins with the letter on the discarded card, takes the next turn. (For example, if the card says a, Alice takes the next turn. )\nIf the current player's deck is empty, the game ends and the current player wins the game.\n\nThere are 3^{N+M+K} possible patters of the three player's initial decks. Among these patterns, how many will lead to Alice's victory?\nSince the answer can be large, print the count modulo 1\\, 000\\, 000\\, 007 (=10^9+7). partial scores: Partial Scores\n500 points will be awarded for passing the test set satisfying the following: 1 <= N <= 1000,1 <= M <= 1000,1 <= K <= 1000.\nTask Constraint: 1 <= N <= 3*10^5\n1 <= M <= 3*10^5\n1 <= K <= 3*10^5\nTask Input: Input The input is given from Standard Input in the following format:\nN M K\nTask Output: Print the answer modulo 1\\, 000\\, 000\\, 007 (=10^9+7).\nTask Samples: input: 1 1 1 output: 17\nIf Alice's card is a, then Alice will win regardless of Bob's and Charlie's card. There are 3*3=9 such patterns.\nIf Alice's card is b, Alice will only win when Bob's card is a, or when Bob's card is c and Charlie's card is a. There are 3+1=4 such patterns.\nIf Alice's card is c, Alice will only win when Charlie's card is a, or when Charlie's card is b and Bob's card is a. There are 3+1=4 such patterns.\n\nThus, there are total of 9+4+4=17 patterns that will lead to Alice's victory.\ninput: 4 2 2 output: 1227\ninput: 1000 1000 1000 output: 261790852\n\n" }, { "title": "", "content": "Problem Statement We have a rectangular parallelepiped of size A*B*C, built with blocks of size 1*1*1. Snuke will paint each of the A*B*C blocks either red or blue, so that:\n\nThere is at least one red block and at least one blue block.\nThe union of all red blocks forms a rectangular parallelepiped.\nThe union of all blue blocks forms a rectangular parallelepiped.\n\nSnuke wants to minimize the difference between the number of red blocks and the number of blue blocks. Find the minimum possible difference.", "constraint": "2<=A,B,C<=10^9", "input": "Input The input is given from Standard Input in the following format:\nA B C", "output": "Print the minimum possible difference between the number of red blocks and the number of blue blocks.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 3 output: 9\n\nFor example, Snuke can paint the blocks as shown in the diagram below.\nThere are 9 red blocks and 18 blue blocks, thus the difference is 9.", "input: 2 2 4 output: 0\n\nFor example, Snuke can paint the blocks as shown in the diagram below.\nThere are 8 red blocks and 8 blue blocks, thus the difference is 0.", "input: 5 3 5 output: 15\n\nFor example, Snuke can paint the blocks as shown in the diagram below.\nThere are 45 red blocks and 30 blue blocks, thus the difference is 9."], "Pid": "p04005", "ProblemText": "Task Description: Problem Statement We have a rectangular parallelepiped of size A*B*C, built with blocks of size 1*1*1. Snuke will paint each of the A*B*C blocks either red or blue, so that:\n\nThere is at least one red block and at least one blue block.\nThe union of all red blocks forms a rectangular parallelepiped.\nThe union of all blue blocks forms a rectangular parallelepiped.\n\nSnuke wants to minimize the difference between the number of red blocks and the number of blue blocks. Find the minimum possible difference.\nTask Constraint: 2<=A,B,C<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nA B C\nTask Output: Print the minimum possible difference between the number of red blocks and the number of blue blocks.\nTask Samples: input: 3 3 3 output: 9\n\nFor example, Snuke can paint the blocks as shown in the diagram below.\nThere are 9 red blocks and 18 blue blocks, thus the difference is 9.\ninput: 2 2 4 output: 0\n\nFor example, Snuke can paint the blocks as shown in the diagram below.\nThere are 8 red blocks and 8 blue blocks, thus the difference is 0.\ninput: 5 3 5 output: 15\n\nFor example, Snuke can paint the blocks as shown in the diagram below.\nThere are 45 red blocks and 30 blue blocks, thus the difference is 9.\n\n" }, { "title": "", "content": "Problem Statement Snuke lives in another world, where slimes are real creatures and kept by some people.\nSlimes come in N colors. Those colors are conveniently numbered 1 through N.\nSnuke currently has no slime. His objective is to have slimes of all the colors together.\nSnuke can perform the following two actions:\nSelect a color i (1<=i<=N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.\nCast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1<=i<=N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.\nFind the minimum time that Snuke needs to have slimes in all N colors.", "constraint": "2<=N<=2,000\na_i are integers.\n1<=a_i<=10^9\nx is an integer.\n1<=x<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N", "output": "Find the minimum time that Snuke needs to have slimes in all N colors.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 10\n1 100 output: 12\n\nSnuke can act as follows:\n\nCatch a slime in color 1. This takes 1 second.\nCast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.\nCatch a slime in color 1. This takes 1 second.", "input: 3 10\n100 1 100 output: 23\n\nSnuke can act as follows:\n\nCatch a slime in color 2. This takes 1 second.\nCast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.\nCatch a slime in color 2. This takes 1 second.\nCast the soell. The color of each slime changes: 3 → 1,2 → 3. This takes 10 seconds.\nCatch a slime in color 2. This takes 1 second.", "input: 4 10\n1 2 3 4 output: 10\n\nSnuke can act as follows:\n\nCatch a slime in color 1. This takes 1 second.\nCatch a slime in color 2. This takes 2 seconds.\nCatch a slime in color 3. This takes 3 seconds.\nCatch a slime in color 4. This takes 4 seconds."], "Pid": "p04006", "ProblemText": "Task Description: Problem Statement Snuke lives in another world, where slimes are real creatures and kept by some people.\nSlimes come in N colors. Those colors are conveniently numbered 1 through N.\nSnuke currently has no slime. His objective is to have slimes of all the colors together.\nSnuke can perform the following two actions:\nSelect a color i (1<=i<=N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.\nCast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1<=i<=N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.\nFind the minimum time that Snuke needs to have slimes in all N colors.\nTask Constraint: 2<=N<=2,000\na_i are integers.\n1<=a_i<=10^9\nx is an integer.\n1<=x<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN x\na_1 a_2 . . . a_N\nTask Output: Find the minimum time that Snuke needs to have slimes in all N colors.\nTask Samples: input: 2 10\n1 100 output: 12\n\nSnuke can act as follows:\n\nCatch a slime in color 1. This takes 1 second.\nCast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.\nCatch a slime in color 1. This takes 1 second.\ninput: 3 10\n100 1 100 output: 23\n\nSnuke can act as follows:\n\nCatch a slime in color 2. This takes 1 second.\nCast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.\nCatch a slime in color 2. This takes 1 second.\nCast the soell. The color of each slime changes: 3 → 1,2 → 3. This takes 10 seconds.\nCatch a slime in color 2. This takes 1 second.\ninput: 4 10\n1 2 3 4 output: 10\n\nSnuke can act as follows:\n\nCatch a slime in color 1. This takes 1 second.\nCatch a slime in color 2. This takes 2 seconds.\nCatch a slime in color 3. This takes 3 seconds.\nCatch a slime in color 4. This takes 4 seconds.\n\n" }, { "title": "", "content": "Problem Statement Snuke and Ciel went to a strange stationery store. Each of them got a transparent graph paper with H rows and W columns.\nSnuke painted some of the cells red in his paper. Here, the cells painted red were 4-connected, that is, it was possible to traverse from any red cell to any other red cell, by moving to vertically or horizontally adjacent red cells only.\nCiel painted some of the cells blue in her paper. Here, the cells painted blue were 4-connected.\nAfterwards, they precisely overlaid the two sheets in the same direction. Then, the intersection of the red cells and the blue cells appeared purple.\nYou are given a matrix of letters a_{ij} (1<=i<=H, 1<=j<=W) that describes the positions of the purple cells. If the cell at the i-th row and j-th column is purple, then a_{ij} is #, otherwise a_{ij} is . . Here, it is guaranteed that no outermost cell is purple. That is, if i=1, H or j = 1, W, then a_{ij} is . .\nFind a pair of the set of the positions of the red cells and the blue cells that is consistent with the situation described. It can be shown that a solution always exists.", "constraint": "3<=H,W<=500\na_{ij} is # or ..\nIf i=1,H or j=1,W, then a_{ij} is ..\nAt least one of a_{ij} is #.", "input": "Input The input is given from Standard Input in the following format:\nH W\na_{11}. . . a_{1W}\n:\na_{H1}. . . a_{HW}", "output": "Print a pair of the set of the positions of the red cells and the blue cells that is consistent with the situation, as follows:\n\nThe first H lines should describe the positions of the red cells.\nThe following 1 line should be empty.\nThe following H lines should describe the positions of the blue cells.\n\nThe description of the positions of the red or blue cells should follow the format of the description of the positions of the purple cells.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 5\n.....\n.#.#.\n.....\n.#.#.\n..... output: .....\n#####\n#....\n#####\n.....\n\n.###.\n.#.#.\n.#.#.\n.#.#.\n.....\n\nOne possible pair of the set of the positions of the red cells and the blue cells is as follows:", "input: 7 13\n.............\n.###.###.###.\n.#.#.#...#...\n.###.#...#...\n.#.#.#.#.#...\n.#.#.###.###.\n............. output: .............\n.###########.\n.###.###.###.\n.###.###.###.\n.###.###.###.\n.###.###.###.\n.............\n\n.............\n.###.###.###.\n.#.#.#...#...\n.###.#...#...\n.#.#.#.#.#...\n.#.#########.\n.............\n\nOne possible pair of the set of the positions of the red cells and the blue cells is as follows:"], "Pid": "p04007", "ProblemText": "Task Description: Problem Statement Snuke and Ciel went to a strange stationery store. Each of them got a transparent graph paper with H rows and W columns.\nSnuke painted some of the cells red in his paper. Here, the cells painted red were 4-connected, that is, it was possible to traverse from any red cell to any other red cell, by moving to vertically or horizontally adjacent red cells only.\nCiel painted some of the cells blue in her paper. Here, the cells painted blue were 4-connected.\nAfterwards, they precisely overlaid the two sheets in the same direction. Then, the intersection of the red cells and the blue cells appeared purple.\nYou are given a matrix of letters a_{ij} (1<=i<=H, 1<=j<=W) that describes the positions of the purple cells. If the cell at the i-th row and j-th column is purple, then a_{ij} is #, otherwise a_{ij} is . . Here, it is guaranteed that no outermost cell is purple. That is, if i=1, H or j = 1, W, then a_{ij} is . .\nFind a pair of the set of the positions of the red cells and the blue cells that is consistent with the situation described. It can be shown that a solution always exists.\nTask Constraint: 3<=H,W<=500\na_{ij} is # or ..\nIf i=1,H or j=1,W, then a_{ij} is ..\nAt least one of a_{ij} is #.\nTask Input: Input The input is given from Standard Input in the following format:\nH W\na_{11}. . . a_{1W}\n:\na_{H1}. . . a_{HW}\nTask Output: Print a pair of the set of the positions of the red cells and the blue cells that is consistent with the situation, as follows:\n\nThe first H lines should describe the positions of the red cells.\nThe following 1 line should be empty.\nThe following H lines should describe the positions of the blue cells.\n\nThe description of the positions of the red or blue cells should follow the format of the description of the positions of the purple cells.\nTask Samples: input: 5 5\n.....\n.#.#.\n.....\n.#.#.\n..... output: .....\n#####\n#....\n#####\n.....\n\n.###.\n.#.#.\n.#.#.\n.#.#.\n.....\n\nOne possible pair of the set of the positions of the red cells and the blue cells is as follows:\ninput: 7 13\n.............\n.###.###.###.\n.#.#.#...#...\n.###.#...#...\n.#.#.#.#.#...\n.#.#.###.###.\n............. output: .............\n.###########.\n.###.###.###.\n.###.###.###.\n.###.###.###.\n.###.###.###.\n.............\n\n.............\n.###.###.###.\n.#.#.#...#...\n.###.#...#...\n.#.#.#.#.#...\n.#.#########.\n.............\n\nOne possible pair of the set of the positions of the red cells and the blue cells is as follows:\n\n" }, { "title": "", "content": "Problem Statement There are N towns in Snuke Kingdom, conveniently numbered 1 through N.\nTown 1 is the capital.\nEach town in the kingdom has a Teleporter, a facility that instantly transports a person to another place.\nThe destination of the Teleporter of town i is town a_i (1<=a_i<=N).\nIt is guaranteed that one can get to the capital from any town by using the Teleporters some number of times.\nKing Snuke loves the integer K.\nThe selfish king wants to change the destination of the Teleporters so that the following holds:\n\nStarting from any town, one will be at the capital after using the Teleporters exactly K times in total.\n\nFind the minimum number of the Teleporters whose destinations need to be changed in order to satisfy the king's desire.", "constraint": "2<=N<=10^5\n1<=a_i<=N\nOne can get to the capital from any town by using the Teleporters some number of times.\n1<=K<=10^9", "input": "Input The input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N", "output": "Print the minimum number of the Teleporters whose destinations need to be changed in order to satisfy King Snuke's desire.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 1\n2 3 1 output: 2\n\nChange the destinations of the Teleporters to a = (1,1,1).", "input: 4 2\n1 1 2 2 output: 0\n\nThere is no need to change the destinations of the Teleporters, since the king's desire is already satisfied.", "input: 8 2\n4 1 2 3 1 2 3 4 output: 3\n\nFor example, change the destinations of the Teleporters to a = (1,1,2,1,1,2,2,4)."], "Pid": "p04008", "ProblemText": "Task Description: Problem Statement There are N towns in Snuke Kingdom, conveniently numbered 1 through N.\nTown 1 is the capital.\nEach town in the kingdom has a Teleporter, a facility that instantly transports a person to another place.\nThe destination of the Teleporter of town i is town a_i (1<=a_i<=N).\nIt is guaranteed that one can get to the capital from any town by using the Teleporters some number of times.\nKing Snuke loves the integer K.\nThe selfish king wants to change the destination of the Teleporters so that the following holds:\n\nStarting from any town, one will be at the capital after using the Teleporters exactly K times in total.\n\nFind the minimum number of the Teleporters whose destinations need to be changed in order to satisfy the king's desire.\nTask Constraint: 2<=N<=10^5\n1<=a_i<=N\nOne can get to the capital from any town by using the Teleporters some number of times.\n1<=K<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\nN K\na_1 a_2 . . . a_N\nTask Output: Print the minimum number of the Teleporters whose destinations need to be changed in order to satisfy King Snuke's desire.\nTask Samples: input: 3 1\n2 3 1 output: 2\n\nChange the destinations of the Teleporters to a = (1,1,1).\ninput: 4 2\n1 1 2 2 output: 0\n\nThere is no need to change the destinations of the Teleporters, since the king's desire is already satisfied.\ninput: 8 2\n4 1 2 3 1 2 3 4 output: 3\n\nFor example, change the destinations of the Teleporters to a = (1,1,2,1,1,2,2,4).\n\n" }, { "title": "", "content": "Problem Statement We have a grid with H rows and W columns.\nThe state of the cell at the i-th (1<=i<=H) row and j-th (1<=j<=W) column is represented by a letter a_{ij}, as follows:\n\n. : This cell is empty.\no : This cell contains a robot.\nE : This cell contains the exit. E occurs exactly once in the whole grid.\n\nSnuke is trying to salvage as many robots as possible, by performing the following operation some number of times:\n\nSelect one of the following directions: up, down, left, right. All remaining robots will move one cell in the selected direction, except when a robot would step outside the grid, in which case the robot will explode and immediately disappear from the grid. If a robot moves to the cell that contains the exit, the robot will be salvaged and immediately removed from the grid.\n\nFind the maximum number of robots that can be salvaged.", "constraint": "2<=H,W<=100\na_{ij} is ., o or E.\nE occurs exactly once in the whole grid.", "input": "Input The input is given from Standard Input in the following format:\nH W\na_{11}. . . a_{1W}\n:\na_{H1}. . . a_{HW}", "output": "Print the maximum number of robots that can be salvaged.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3\no.o\n.Eo\nooo output: 3\n\nFor example, select left, up, right.", "input: 2 2\nE.\n.. output: 0", "input: 3 4\no...\no...\noooE output: 5\n\nSelect right, right, right, down, down.", "input: 5 11\nooo.ooo.ooo\no.o.o...o..\nooo.oE..o..\no.o.o.o.o..\no.o.ooo.ooo output: 12"], "Pid": "p04009", "ProblemText": "Task Description: Problem Statement We have a grid with H rows and W columns.\nThe state of the cell at the i-th (1<=i<=H) row and j-th (1<=j<=W) column is represented by a letter a_{ij}, as follows:\n\n. : This cell is empty.\no : This cell contains a robot.\nE : This cell contains the exit. E occurs exactly once in the whole grid.\n\nSnuke is trying to salvage as many robots as possible, by performing the following operation some number of times:\n\nSelect one of the following directions: up, down, left, right. All remaining robots will move one cell in the selected direction, except when a robot would step outside the grid, in which case the robot will explode and immediately disappear from the grid. If a robot moves to the cell that contains the exit, the robot will be salvaged and immediately removed from the grid.\n\nFind the maximum number of robots that can be salvaged.\nTask Constraint: 2<=H,W<=100\na_{ij} is ., o or E.\nE occurs exactly once in the whole grid.\nTask Input: Input The input is given from Standard Input in the following format:\nH W\na_{11}. . . a_{1W}\n:\na_{H1}. . . a_{HW}\nTask Output: Print the maximum number of robots that can be salvaged.\nTask Samples: input: 3 3\no.o\n.Eo\nooo output: 3\n\nFor example, select left, up, right.\ninput: 2 2\nE.\n.. output: 0\ninput: 3 4\no...\no...\noooE output: 5\n\nSelect right, right, right, down, down.\ninput: 5 11\nooo.ooo.ooo\no.o.o...o..\nooo.oE..o..\no.o.o.o.o..\no.o.ooo.ooo output: 12\n\n" }, { "title": "", "content": "Problem Statement You are given an undirected graph with N vertices and M edges.\nHere, N-1<=M<=N holds and the graph is connected.\nThere are no self-loops or multiple edges in this graph.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i connects vertices a_i and b_i.\nThe color of each vertex can be either white or black.\nInitially, all the vertices are white.\nSnuke is trying to turn all the vertices black by performing the following operation some number of times:\n\nSelect a pair of adjacent vertices with the same color, and invert the colors of those vertices. That is, if the vertices are both white, then turn them black, and vice versa.\n\nDetermine if it is possible to turn all the vertices black. If the answer is positive, find the minimum number of times the operation needs to be performed in order to achieve the objective. partial score: Partial Score\nIn the test set worth 1500 points, M=N-1.", "constraint": "2<=N<=10^5\nN-1<=M<=N\n1<=a_i,b_i<=N\nThere are no self-loops or multiple edges in the given graph.\nThe given graph is connected.", "input": "Input The input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M", "output": "If it is possible to turn all the vertices black, print the minimum number of times the operation needs to be performed in order to achieve the objective.\nOtherwise, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 6 5\n1 2\n1 3\n1 4\n2 5\n2 6 output: 5\n\nFor example, it is possible to perform the operations as shown in the following diagram:", "input: 3 2\n1 2\n2 3 output: -1\n\nIt is not possible to turn all the vertices black.", "input: 4 4\n1 2\n2 3\n3 4\n4 1 output: 2\n\nThis case is not included in the test set for the partial score.", "input: 6 6\n1 2\n2 3\n3 1\n1 4\n1 5\n1 6 output: 7\n\nThis case is not included in the test set for the partial score."], "Pid": "p04010", "ProblemText": "Task Description: Problem Statement You are given an undirected graph with N vertices and M edges.\nHere, N-1<=M<=N holds and the graph is connected.\nThere are no self-loops or multiple edges in this graph.\nThe vertices are numbered 1 through N, and the edges are numbered 1 through M.\nEdge i connects vertices a_i and b_i.\nThe color of each vertex can be either white or black.\nInitially, all the vertices are white.\nSnuke is trying to turn all the vertices black by performing the following operation some number of times:\n\nSelect a pair of adjacent vertices with the same color, and invert the colors of those vertices. That is, if the vertices are both white, then turn them black, and vice versa.\n\nDetermine if it is possible to turn all the vertices black. If the answer is positive, find the minimum number of times the operation needs to be performed in order to achieve the objective. partial score: Partial Score\nIn the test set worth 1500 points, M=N-1.\nTask Constraint: 2<=N<=10^5\nN-1<=M<=N\n1<=a_i,b_i<=N\nThere are no self-loops or multiple edges in the given graph.\nThe given graph is connected.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\nTask Output: If it is possible to turn all the vertices black, print the minimum number of times the operation needs to be performed in order to achieve the objective.\nOtherwise, print -1 instead.\nTask Samples: input: 6 5\n1 2\n1 3\n1 4\n2 5\n2 6 output: 5\n\nFor example, it is possible to perform the operations as shown in the following diagram:\ninput: 3 2\n1 2\n2 3 output: -1\n\nIt is not possible to turn all the vertices black.\ninput: 4 4\n1 2\n2 3\n3 4\n4 1 output: 2\n\nThis case is not included in the test set for the partial score.\ninput: 6 6\n1 2\n2 3\n3 1\n1 4\n1 5\n1 6 output: 7\n\nThis case is not included in the test set for the partial score.\n\n" }, { "title": "", "content": "Problem Statement There is a hotel with the following accommodation fee:\n\nX yen (the currency of Japan) per night, for the first K nights\nY yen per night, for the (K+1)-th and subsequent nights\n\nTak is staying at this hotel for N consecutive nights.\nFind his total accommodation fee.", "constraint": "1 <= N, K <= 10000\n1 <= Y < X <= 10000\nN,\\,K,\\,X,\\,Y are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\nK\nX\nY", "output": "Print Tak's total accommodation fee.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5\n3\n10000\n9000 output: 48000\n\nThe accommodation fee is as follows:\n\n10000 yen for the 1-st night\n10000 yen for the 2-nd night\n10000 yen for the 3-rd night\n9000 yen for the 4-th night\n9000 yen for the 5-th night\n\nThus, the total is 48000 yen.", "input: 2\n3\n10000\n9000 output: 20000"], "Pid": "p04011", "ProblemText": "Task Description: Problem Statement There is a hotel with the following accommodation fee:\n\nX yen (the currency of Japan) per night, for the first K nights\nY yen per night, for the (K+1)-th and subsequent nights\n\nTak is staying at this hotel for N consecutive nights.\nFind his total accommodation fee.\nTask Constraint: 1 <= N, K <= 10000\n1 <= Y < X <= 10000\nN,\\,K,\\,X,\\,Y are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nK\nX\nY\nTask Output: Print Tak's total accommodation fee.\nTask Samples: input: 5\n3\n10000\n9000 output: 48000\n\nThe accommodation fee is as follows:\n\n10000 yen for the 1-st night\n10000 yen for the 2-nd night\n10000 yen for the 3-rd night\n9000 yen for the 4-th night\n9000 yen for the 5-th night\n\nThus, the total is 48000 yen.\ninput: 2\n3\n10000\n9000 output: 20000\n\n" }, { "title": "", "content": "Problem Statement Let w be a string consisting of lowercase letters.\nWe will call w beautiful if the following condition is satisfied:\n\nEach lowercase letter of the English alphabet occurs even number of times in w.\n\nYou are given the string w. Determine if w is beautiful.", "constraint": "1 <= |w| <= 100\nw consists of lowercase letters (a-z).", "input": "Input The input is given from Standard Input in the following format:\nw", "output": "Print Yes if w is beautiful. Print No otherwise.", "content_img": false, "lang": "en", "error": false, "samples": ["input: abaccaba output: Yes\n\na occurs four times, b occurs twice, c occurs twice and the other letters occur zero times.", "input: hthth output: No"], "Pid": "p04012", "ProblemText": "Task Description: Problem Statement Let w be a string consisting of lowercase letters.\nWe will call w beautiful if the following condition is satisfied:\n\nEach lowercase letter of the English alphabet occurs even number of times in w.\n\nYou are given the string w. Determine if w is beautiful.\nTask Constraint: 1 <= |w| <= 100\nw consists of lowercase letters (a-z).\nTask Input: Input The input is given from Standard Input in the following format:\nw\nTask Output: Print Yes if w is beautiful. Print No otherwise.\nTask Samples: input: abaccaba output: Yes\n\na occurs four times, b occurs twice, c occurs twice and the other letters occur zero times.\ninput: hthth output: No\n\n" }, { "title": "", "content": "Problem Statement Tak has N cards. On the i-th (1 <= i <= N) card is written an integer x_i.\nHe is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.\nIn how many ways can he make his selection? partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1 <= N <= 16.", "constraint": "1 <= N <= 50\n1 <= A <= 50\n1 <= x_i <= 50\nN,\\,A,\\,x_i are integers.", "input": "Input The input is given from Standard Input in the following format:\nN A\nx_1 x_2 . . . x_N", "output": "Print the number of ways to select cards such that the average of the written integers is exactly A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 8\n7 9 8 9 output: 5\nThe following are the 5 ways to select cards such that the average is 8:\nSelect the 3-rd card.\nSelect the 1-st and 2-nd cards.\nSelect the 1-st and 4-th cards.\nSelect the 1-st, 2-nd and 3-rd cards.\nSelect the 1-st, 3-rd and 4-th cards.", "input: 3 8\n6 6 9 output: 0", "input: 8 5\n3 6 2 8 7 6 5 9 output: 19", "input: 33 3\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 output: 8589934591\nThe answer may not fit into a 32-bit integer."], "Pid": "p04013", "ProblemText": "Task Description: Problem Statement Tak has N cards. On the i-th (1 <= i <= N) card is written an integer x_i.\nHe is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.\nIn how many ways can he make his selection? partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1 <= N <= 16.\nTask Constraint: 1 <= N <= 50\n1 <= A <= 50\n1 <= x_i <= 50\nN,\\,A,\\,x_i are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN A\nx_1 x_2 . . . x_N\nTask Output: Print the number of ways to select cards such that the average of the written integers is exactly A.\nTask Samples: input: 4 8\n7 9 8 9 output: 5\nThe following are the 5 ways to select cards such that the average is 8:\nSelect the 3-rd card.\nSelect the 1-st and 2-nd cards.\nSelect the 1-st and 4-th cards.\nSelect the 1-st, 2-nd and 3-rd cards.\nSelect the 1-st, 3-rd and 4-th cards.\ninput: 3 8\n6 6 9 output: 0\ninput: 8 5\n3 6 2 8 7 6 5 9 output: 19\ninput: 33 3\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 output: 8589934591\nThe answer may not fit into a 32-bit integer.\n\n" }, { "title": "", "content": "Problem Statement For integers b (b >= 2) and n (n >= 1), let the function f(b, n) be defined as follows:\n\nf(b, n) = n, when n < b\nf(b, n) = f(b, \\, {\\rm floor}(n / b)) + (n \\ {\\rm mod} \\ b), when n >= b\n\nHere, {\\rm floor}(n / b) denotes the largest integer not exceeding n / b,\nand n \\ {\\rm mod} \\ b denotes the remainder of n divided by b.\nLess formally, f(b, n) is equal to the sum of the digits of n written in base b.\nFor example, the following hold:\n\nf(10, \\, 87654)=8+7+6+5+4=30\nf(100, \\, 87654)=8+76+54=138\n\nYou are given integers n and s.\nDetermine if there exists an integer b (b >= 2) such that f(b, n)=s.\nIf the answer is positive, also find the smallest such b.", "constraint": "1 <= n <= 10^{11}\n1 <= s <= 10^{11}\nn,\\,s are integers.", "input": "Input The input is given from Standard Input in the following format:\nn\ns", "output": "If there exists an integer b (b >= 2) such that f(b, n)=s, print the smallest such b.\nIf such b does not exist, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 87654\n30 output: 10", "input: 87654\n138 output: 100", "input: 87654\n45678 output: -1", "input: 31415926535\n1 output: 31415926535", "input: 1\n31415926535 output: -1"], "Pid": "p04014", "ProblemText": "Task Description: Problem Statement For integers b (b >= 2) and n (n >= 1), let the function f(b, n) be defined as follows:\n\nf(b, n) = n, when n < b\nf(b, n) = f(b, \\, {\\rm floor}(n / b)) + (n \\ {\\rm mod} \\ b), when n >= b\n\nHere, {\\rm floor}(n / b) denotes the largest integer not exceeding n / b,\nand n \\ {\\rm mod} \\ b denotes the remainder of n divided by b.\nLess formally, f(b, n) is equal to the sum of the digits of n written in base b.\nFor example, the following hold:\n\nf(10, \\, 87654)=8+7+6+5+4=30\nf(100, \\, 87654)=8+76+54=138\n\nYou are given integers n and s.\nDetermine if there exists an integer b (b >= 2) such that f(b, n)=s.\nIf the answer is positive, also find the smallest such b.\nTask Constraint: 1 <= n <= 10^{11}\n1 <= s <= 10^{11}\nn,\\,s are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nn\ns\nTask Output: If there exists an integer b (b >= 2) such that f(b, n)=s, print the smallest such b.\nIf such b does not exist, print -1 instead.\nTask Samples: input: 87654\n30 output: 10\ninput: 87654\n138 output: 100\ninput: 87654\n45678 output: -1\ninput: 31415926535\n1 output: 31415926535\ninput: 1\n31415926535 output: -1\n\n" }, { "title": "", "content": "Problem Statement Tak has N cards. On the i-th (1 <= i <= N) card is written an integer x_i.\nHe is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.\nIn how many ways can he make his selection? partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1 <= N <= 16.", "constraint": "1 <= N <= 50\n1 <= A <= 50\n1 <= x_i <= 50\nN,\\,A,\\,x_i are integers.", "input": "Input The input is given from Standard Input in the following format:\nN A\nx_1 x_2 . . . x_N", "output": "Print the number of ways to select cards such that the average of the written integers is exactly A.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4 8\n7 9 8 9 output: 5\nThe following are the 5 ways to select cards such that the average is 8:\nSelect the 3-rd card.\nSelect the 1-st and 2-nd cards.\nSelect the 1-st and 4-th cards.\nSelect the 1-st, 2-nd and 3-rd cards.\nSelect the 1-st, 3-rd and 4-th cards.", "input: 3 8\n6 6 9 output: 0", "input: 8 5\n3 6 2 8 7 6 5 9 output: 19", "input: 33 3\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 output: 8589934591\nThe answer may not fit into a 32-bit integer."], "Pid": "p04015", "ProblemText": "Task Description: Problem Statement Tak has N cards. On the i-th (1 <= i <= N) card is written an integer x_i.\nHe is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.\nIn how many ways can he make his selection? partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 1 <= N <= 16.\nTask Constraint: 1 <= N <= 50\n1 <= A <= 50\n1 <= x_i <= 50\nN,\\,A,\\,x_i are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN A\nx_1 x_2 . . . x_N\nTask Output: Print the number of ways to select cards such that the average of the written integers is exactly A.\nTask Samples: input: 4 8\n7 9 8 9 output: 5\nThe following are the 5 ways to select cards such that the average is 8:\nSelect the 3-rd card.\nSelect the 1-st and 2-nd cards.\nSelect the 1-st and 4-th cards.\nSelect the 1-st, 2-nd and 3-rd cards.\nSelect the 1-st, 3-rd and 4-th cards.\ninput: 3 8\n6 6 9 output: 0\ninput: 8 5\n3 6 2 8 7 6 5 9 output: 19\ninput: 33 3\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 output: 8589934591\nThe answer may not fit into a 32-bit integer.\n\n" }, { "title": "", "content": "Problem Statement For integers b (b >= 2) and n (n >= 1), let the function f(b, n) be defined as follows:\n\nf(b, n) = n, when n < b\nf(b, n) = f(b, \\, {\\rm floor}(n / b)) + (n \\ {\\rm mod} \\ b), when n >= b\n\nHere, {\\rm floor}(n / b) denotes the largest integer not exceeding n / b,\nand n \\ {\\rm mod} \\ b denotes the remainder of n divided by b.\nLess formally, f(b, n) is equal to the sum of the digits of n written in base b.\nFor example, the following hold:\n\nf(10, \\, 87654)=8+7+6+5+4=30\nf(100, \\, 87654)=8+76+54=138\n\nYou are given integers n and s.\nDetermine if there exists an integer b (b >= 2) such that f(b, n)=s.\nIf the answer is positive, also find the smallest such b.", "constraint": "1 <= n <= 10^{11}\n1 <= s <= 10^{11}\nn,\\,s are integers.", "input": "Input The input is given from Standard Input in the following format:\nn\ns", "output": "If there exists an integer b (b >= 2) such that f(b, n)=s, print the smallest such b.\nIf such b does not exist, print -1 instead.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 87654\n30 output: 10", "input: 87654\n138 output: 100", "input: 87654\n45678 output: -1", "input: 31415926535\n1 output: 31415926535", "input: 1\n31415926535 output: -1"], "Pid": "p04016", "ProblemText": "Task Description: Problem Statement For integers b (b >= 2) and n (n >= 1), let the function f(b, n) be defined as follows:\n\nf(b, n) = n, when n < b\nf(b, n) = f(b, \\, {\\rm floor}(n / b)) + (n \\ {\\rm mod} \\ b), when n >= b\n\nHere, {\\rm floor}(n / b) denotes the largest integer not exceeding n / b,\nand n \\ {\\rm mod} \\ b denotes the remainder of n divided by b.\nLess formally, f(b, n) is equal to the sum of the digits of n written in base b.\nFor example, the following hold:\n\nf(10, \\, 87654)=8+7+6+5+4=30\nf(100, \\, 87654)=8+76+54=138\n\nYou are given integers n and s.\nDetermine if there exists an integer b (b >= 2) such that f(b, n)=s.\nIf the answer is positive, also find the smallest such b.\nTask Constraint: 1 <= n <= 10^{11}\n1 <= s <= 10^{11}\nn,\\,s are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nn\ns\nTask Output: If there exists an integer b (b >= 2) such that f(b, n)=s, print the smallest such b.\nIf such b does not exist, print -1 instead.\nTask Samples: input: 87654\n30 output: 10\ninput: 87654\n138 output: 100\ninput: 87654\n45678 output: -1\ninput: 31415926535\n1 output: 31415926535\ninput: 1\n31415926535 output: -1\n\n" }, { "title": "", "content": "Problem Statement N hotels are located on a straight line. The coordinate of the i-th hotel (1 <= i <= N) is x_i.\nTak the traveler has the following two personal principles:\n\nHe never travels a distance of more than L in a single day.\nHe never sleeps in the open. That is, he must stay at a hotel at the end of a day.\n\nYou are given Q queries. The j-th (1 <= j <= Q) query is described by two distinct integers a_j and b_j.\nFor each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles.\nIt is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying N <= 10^3 and Q <= 10^3.", "constraint": "2 <= N <= 10^5\n1 <= L <= 10^9\n1 <= Q <= 10^5\n1 <= x_i < x_2 < ... < x_N <= 10^9\nx_{i+1} - x_i <= L\n1 <= a_j,b_j <= N\na_j \\neq b_j\nN,\\,L,\\,Q,\\,x_i,\\,a_j,\\,b_j are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N\nL\nQ\na_1 b_1\na_2 b_2\n:\na_Q b_Q", "output": "Print Q lines.\nThe j-th line (1 <= j <= Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 9\n1 3 6 13 15 18 19 29 31\n10\n4\n1 8\n7 3\n6 7\n8 5 output: 4\n2\n1\n2\n\nFor the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:\n\nDay 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.\nDay 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.\nDay 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.\nDay 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10."], "Pid": "p04017", "ProblemText": "Task Description: Problem Statement N hotels are located on a straight line. The coordinate of the i-th hotel (1 <= i <= N) is x_i.\nTak the traveler has the following two personal principles:\n\nHe never travels a distance of more than L in a single day.\nHe never sleeps in the open. That is, he must stay at a hotel at the end of a day.\n\nYou are given Q queries. The j-th (1 <= j <= Q) query is described by two distinct integers a_j and b_j.\nFor each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles.\nIt is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying N <= 10^3 and Q <= 10^3.\nTask Constraint: 2 <= N <= 10^5\n1 <= L <= 10^9\n1 <= Q <= 10^5\n1 <= x_i < x_2 < ... < x_N <= 10^9\nx_{i+1} - x_i <= L\n1 <= a_j,b_j <= N\na_j \\neq b_j\nN,\\,L,\\,Q,\\,x_i,\\,a_j,\\,b_j are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nx_1 x_2 . . . x_N\nL\nQ\na_1 b_1\na_2 b_2\n:\na_Q b_Q\nTask Output: Print Q lines.\nThe j-th line (1 <= j <= Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.\nTask Samples: input: 9\n1 3 6 13 15 18 19 29 31\n10\n4\n1 8\n7 3\n6 7\n8 5 output: 4\n2\n1\n2\n\nFor the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:\n\nDay 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.\nDay 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.\nDay 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.\nDay 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10.\n\n" }, { "title": "", "content": "Problem Statement Let x be a string of length at least 1.\nWe will call x a good string, if for any string y and any integer k (k >= 2), the string obtained by concatenating k copies of y is different from x.\nFor example, a, bbc and cdcdc are good strings, while aa, bbbb and cdcdcd are not.\nLet w be a string of length at least 1.\nFor a sequence F=(\\, f_1, \\, f_2, \\, . . . , \\, f_m) consisting of m elements,\nwe will call F a good representation of w, if the following conditions are both satisfied:\n\nFor any i \\, (1 <= i <= m), f_i is a good string.\nThe string obtained by concatenating f_1, \\, f_2, \\, . . . , \\, f_m in this order, is w.\n\nFor example, when w=aabb, there are five good representations of w:\n\n(aabb)\n(a, abb)\n(aab, b)\n(a, ab, b)\n(a, a, b, b)\n\nAmong the good representations of w, the ones with the smallest number of elements are called the best representations of w.\nFor example, there are only one best representation of w=aabb: (aabb).\nYou are given a string w. Find the following:\n\nthe number of elements of a best representation of w\nthe number of the best representations of w, modulo 1000000007 \\, (=10^9+7)\n\n(It is guaranteed that a good representation of w always exists. ) partial score: Partial Score\n400 points will be awarded for passing the test set satisfying 1 <= |w| <= 4000.", "constraint": "1 <= |w| <= 500000 \\, (=5 * 10^5)\nw consists of lowercase letters (a-z).", "input": "Input The input is given from Standard Input in the following format:\nw", "output": "Print 2 lines.\n\nIn the first line, print the number of elements of a best representation of w.\nIn the second line, print the number of the best representations of w, modulo 1000000007.", "content_img": false, "lang": "en", "error": false, "samples": ["input: aab output: 1\n1", "input: bcbc output: 2\n3\nIn this case, there are 3 best representations of 2 elements:\n(b,cbc)\n(bc,bc)\n(bcb,c)", "input: ddd output: 3\n1"], "Pid": "p04018", "ProblemText": "Task Description: Problem Statement Let x be a string of length at least 1.\nWe will call x a good string, if for any string y and any integer k (k >= 2), the string obtained by concatenating k copies of y is different from x.\nFor example, a, bbc and cdcdc are good strings, while aa, bbbb and cdcdcd are not.\nLet w be a string of length at least 1.\nFor a sequence F=(\\, f_1, \\, f_2, \\, . . . , \\, f_m) consisting of m elements,\nwe will call F a good representation of w, if the following conditions are both satisfied:\n\nFor any i \\, (1 <= i <= m), f_i is a good string.\nThe string obtained by concatenating f_1, \\, f_2, \\, . . . , \\, f_m in this order, is w.\n\nFor example, when w=aabb, there are five good representations of w:\n\n(aabb)\n(a, abb)\n(aab, b)\n(a, ab, b)\n(a, a, b, b)\n\nAmong the good representations of w, the ones with the smallest number of elements are called the best representations of w.\nFor example, there are only one best representation of w=aabb: (aabb).\nYou are given a string w. Find the following:\n\nthe number of elements of a best representation of w\nthe number of the best representations of w, modulo 1000000007 \\, (=10^9+7)\n\n(It is guaranteed that a good representation of w always exists. ) partial score: Partial Score\n400 points will be awarded for passing the test set satisfying 1 <= |w| <= 4000.\nTask Constraint: 1 <= |w| <= 500000 \\, (=5 * 10^5)\nw consists of lowercase letters (a-z).\nTask Input: Input The input is given from Standard Input in the following format:\nw\nTask Output: Print 2 lines.\n\nIn the first line, print the number of elements of a best representation of w.\nIn the second line, print the number of the best representations of w, modulo 1000000007.\nTask Samples: input: aab output: 1\n1\ninput: bcbc output: 2\n3\nIn this case, there are 3 best representations of 2 elements:\n(b,cbc)\n(bc,bc)\n(bcb,c)\ninput: ddd output: 3\n1\n\n" }, { "title": "", "content": "Problem Statement Snuke lives on an infinite two-dimensional plane. He is going on an N-day trip.\nAt the beginning of Day 1, he is at home. His plan is described in a string S of length N.\nOn Day i(1 <= i <= N), he will travel a positive distance in the following direction:\n\nNorth if the i-th letter of S is N\nWest if the i-th letter of S is W\nSouth if the i-th letter of S is S\nEast if the i-th letter of S is E\n\nHe has not decided each day's travel distance. Determine whether it is possible to set each day's travel distance so that he will be back at home at the end of Day N.", "constraint": "1 <= | S | <= 1000\nS consists of the letters N, W, S, E.", "input": "Input The input is given from Standard Input in the following format:\nS", "output": "Print Yes if it is possible to set each day's travel distance so that he will be back at home at the end of Day N. Otherwise, print No.", "content_img": false, "lang": "en", "error": false, "samples": ["input: SENW output: Yes\n\nIf Snuke travels a distance of 1 on each day, he will be back at home at the end of day 4.", "input: NSNNSNSN output: Yes", "input: NNEW output: No", "input: W output: No"], "Pid": "p04019", "ProblemText": "Task Description: Problem Statement Snuke lives on an infinite two-dimensional plane. He is going on an N-day trip.\nAt the beginning of Day 1, he is at home. His plan is described in a string S of length N.\nOn Day i(1 <= i <= N), he will travel a positive distance in the following direction:\n\nNorth if the i-th letter of S is N\nWest if the i-th letter of S is W\nSouth if the i-th letter of S is S\nEast if the i-th letter of S is E\n\nHe has not decided each day's travel distance. Determine whether it is possible to set each day's travel distance so that he will be back at home at the end of Day N.\nTask Constraint: 1 <= | S | <= 1000\nS consists of the letters N, W, S, E.\nTask Input: Input The input is given from Standard Input in the following format:\nS\nTask Output: Print Yes if it is possible to set each day's travel distance so that he will be back at home at the end of Day N. Otherwise, print No.\nTask Samples: input: SENW output: Yes\n\nIf Snuke travels a distance of 1 on each day, he will be back at home at the end of day 4.\ninput: NSNNSNSN output: Yes\ninput: NNEW output: No\ninput: W output: No\n\n" }, { "title": "", "content": "Problem Statement Snuke has a large collection of cards. Each card has an integer between 1 and N, inclusive, written on it.\nHe has A_i cards with an integer i.\nTwo cards can form a pair if the absolute value of the difference of the integers written on them is at most 1.\nSnuke wants to create the maximum number of pairs from his cards, on the condition that no card should be used in multiple pairs. Find the maximum number of pairs that he can create.", "constraint": "1 <= N <= 10^5\n0 <= A_i <= 10^9 (1 <= i <= N)\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print the maximum number of pairs that Snuke can create.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n4\n0\n3\n2 output: 4\n\nFor example, Snuke can create the following four pairs: (1,1),(1,1),(3,4),(3,4).", "input: 8\n2\n0\n1\n6\n0\n8\n2\n1 output: 9"], "Pid": "p04020", "ProblemText": "Task Description: Problem Statement Snuke has a large collection of cards. Each card has an integer between 1 and N, inclusive, written on it.\nHe has A_i cards with an integer i.\nTwo cards can form a pair if the absolute value of the difference of the integers written on them is at most 1.\nSnuke wants to create the maximum number of pairs from his cards, on the condition that no card should be used in multiple pairs. Find the maximum number of pairs that he can create.\nTask Constraint: 1 <= N <= 10^5\n0 <= A_i <= 10^9 (1 <= i <= N)\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print the maximum number of pairs that Snuke can create.\nTask Samples: input: 4\n4\n0\n3\n2 output: 4\n\nFor example, Snuke can create the following four pairs: (1,1),(1,1),(3,4),(3,4).\ninput: 8\n2\n0\n1\n6\n0\n8\n2\n1 output: 9\n\n" }, { "title": "", "content": "Problem Statement Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 <= i <= N) element of the sequence is a_i. The elements are pairwise distinct.\nHe is sorting this sequence in increasing order.\nWith supernatural power, he can perform the following two operations on the sequence in any order:\n\nOperation 1: choose 2 consecutive elements, then reverse the order of those elements.\nOperation 2: choose 3 consecutive elements, then reverse the order of those elements.\n\nSnuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.", "constraint": "1 <= N <= 10^5\n0 <= A_i <= 10^9\nIf i != j, then A_i != A_j.\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N", "output": "Print the minimum number of times Operation 1 that Snuke has to perform.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 4\n2\n4\n3\n1 output: 1\n\nThe given sequence can be sorted as follows:\n\nFirst, reverse the order of the last three elements. The sequence is now: 2,1,3,4.\nThen, reverse the order of the first two elements. The sequence is now: 1,2,3,4.\n\nIn this sequence of operations, Operation 1 is performed once. It is not possible to sort the sequence with less number of Operation 1, thus the answer is 1.", "input: 5\n10\n8\n5\n3\n2 output: 0"], "Pid": "p04021", "ProblemText": "Task Description: Problem Statement Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 <= i <= N) element of the sequence is a_i. The elements are pairwise distinct.\nHe is sorting this sequence in increasing order.\nWith supernatural power, he can perform the following two operations on the sequence in any order:\n\nOperation 1: choose 2 consecutive elements, then reverse the order of those elements.\nOperation 2: choose 3 consecutive elements, then reverse the order of those elements.\n\nSnuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.\nTask Constraint: 1 <= N <= 10^5\n0 <= A_i <= 10^9\nIf i != j, then A_i != A_j.\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\nA_1\n:\nA_N\nTask Output: Print the minimum number of times Operation 1 that Snuke has to perform.\nTask Samples: input: 4\n2\n4\n3\n1 output: 1\n\nThe given sequence can be sorted as follows:\n\nFirst, reverse the order of the last three elements. The sequence is now: 2,1,3,4.\nThen, reverse the order of the first two elements. The sequence is now: 1,2,3,4.\n\nIn this sequence of operations, Operation 1 is performed once. It is not possible to sort the sequence with less number of Operation 1, thus the answer is 1.\ninput: 5\n10\n8\n5\n3\n2 output: 0\n\n" }, { "title": "", "content": "Problem Statement Snuke got positive integers s_1, . . . , s_N from his mother, as a birthday present. There may be duplicate elements.\nHe will circle some of these N integers. Since he dislikes cubic numbers, he wants to ensure that if both s_i and s_j (i ! = j) are circled, the product s_is_j is not cubic. For example, when s_1=1, s_2=1, s_3=2, s_4=4, it is not possible to circle both s_1 and s_2 at the same time. It is not possible to circle both s_3 and s_4 at the same time, either.\nFind the maximum number of integers that Snuke can circle.", "constraint": "1 <= N <= 10^5\n1 <= s_i <= 10^{10}\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN\ns_1\n:\ns_N", "output": "Print the maximum number of integers that Snuke can circle.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 8\n1\n2\n3\n4\n5\n6\n7\n8 output: 6\n\nSnuke can circle 1,2,3,5,6,7.", "input: 6\n2\n4\n8\n16\n32\n64 output: 3", "input: 10\n1\n10\n100\n1000000007\n10000000000\n1000000009\n999999999\n999\n999\n999 output: 9"], "Pid": "p04022", "ProblemText": "Task Description: Problem Statement Snuke got positive integers s_1, . . . , s_N from his mother, as a birthday present. There may be duplicate elements.\nHe will circle some of these N integers. Since he dislikes cubic numbers, he wants to ensure that if both s_i and s_j (i ! = j) are circled, the product s_is_j is not cubic. For example, when s_1=1, s_2=1, s_3=2, s_4=4, it is not possible to circle both s_1 and s_2 at the same time. It is not possible to circle both s_3 and s_4 at the same time, either.\nFind the maximum number of integers that Snuke can circle.\nTask Constraint: 1 <= N <= 10^5\n1 <= s_i <= 10^{10}\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN\ns_1\n:\ns_N\nTask Output: Print the maximum number of integers that Snuke can circle.\nTask Samples: input: 8\n1\n2\n3\n4\n5\n6\n7\n8 output: 6\n\nSnuke can circle 1,2,3,5,6,7.\ninput: 6\n2\n4\n8\n16\n32\n64 output: 3\ninput: 10\n1\n10\n100\n1000000007\n10000000000\n1000000009\n999999999\n999\n999\n999 output: 9\n\n" }, { "title": "", "content": "Problem Statement Snuke got an integer sequence from his mother, as a birthday present. The sequence has N elements, and the i-th of them is i.\nSnuke performs the following Q operations on this sequence. The i-th operation, described by a parameter q_i, is as follows:\n\nTake the first q_i elements from the sequence obtained by concatenating infinitely many copy of the current sequence, then replace the current sequence with those q_i elements.\n\nAfter these Q operations, find how many times each of the integers 1 through N appears in the final sequence.", "constraint": "1 <= N <= 10^5\n0 <= Q <= 10^5\n1 <= q_i <= 10^{18}\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN Q\nq_1\n:\nq_Q", "output": "Print N lines. The i-th line (1 <= i <= N) should contain the number of times integer i appears in the final sequence after the Q operations.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 5 3\n6\n4\n11 output: 3\n3\n3\n2\n0\n\nAfter the first operation, the sequence becomes: 1,2,3,4,5,1.\nAfter the second operation, the sequence becomes: 1,2,3,4.\nAfter the third operation, the sequence becomes: 1,2,3,4,1,2,3,4,1,2,3.\nIn this sequence, integers 1,2,3,4,5 appear 3,3,3,2,0 times, respectively.", "input: 10 10\n9\n13\n18\n8\n10\n10\n9\n19\n22\n27 output: 7\n4\n4\n3\n3\n2\n2\n2\n0\n0"], "Pid": "p04023", "ProblemText": "Task Description: Problem Statement Snuke got an integer sequence from his mother, as a birthday present. The sequence has N elements, and the i-th of them is i.\nSnuke performs the following Q operations on this sequence. The i-th operation, described by a parameter q_i, is as follows:\n\nTake the first q_i elements from the sequence obtained by concatenating infinitely many copy of the current sequence, then replace the current sequence with those q_i elements.\n\nAfter these Q operations, find how many times each of the integers 1 through N appears in the final sequence.\nTask Constraint: 1 <= N <= 10^5\n0 <= Q <= 10^5\n1 <= q_i <= 10^{18}\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN Q\nq_1\n:\nq_Q\nTask Output: Print N lines. The i-th line (1 <= i <= N) should contain the number of times integer i appears in the final sequence after the Q operations.\nTask Samples: input: 5 3\n6\n4\n11 output: 3\n3\n3\n2\n0\n\nAfter the first operation, the sequence becomes: 1,2,3,4,5,1.\nAfter the second operation, the sequence becomes: 1,2,3,4.\nAfter the third operation, the sequence becomes: 1,2,3,4,1,2,3,4,1,2,3.\nIn this sequence, integers 1,2,3,4,5 appear 3,3,3,2,0 times, respectively.\ninput: 10 10\n9\n13\n18\n8\n10\n10\n9\n19\n22\n27 output: 7\n4\n4\n3\n3\n2\n2\n2\n0\n0\n\n" }, { "title": "", "content": "Problem Statement Snuke got a grid from his mother, as a birthday present. The grid has H rows and W columns. Each cell is painted black or white. All black cells are 4-connected, that is, it is possible to traverse from any black cell to any other black cell by just visiting black cells, where it is only allowed to move horizontally or vertically.\nThe color of the cell at the i-th row and j-th column (1 <= i <= H, 1 <= j <= W) is represented by a character s_{ij}. If s_{ij} is #, the cell is painted black. If s_{ij} is . , the cell is painted white. At least one cell is painted black.\nWe will define fractals as follows.\nThe fractal of level 0 is a 1 * 1 grid with a black cell.\nThe fractal of level k+1 is obtained by arranging smaller grids in H rows and W columns, following the pattern of the Snuke's grid.\nAt a position that corresponds to a black cell in the Snuke's grid, a copy of the fractal of level k is placed.\nAt a position that corresponds to a white cell in the Snuke's grid, a grid whose cells are all white, with the same dimensions as the fractal of level k, is placed.\nYou are given the description of the Snuke's grid, and an integer K. Find the number of connected components of black cells in the fractal of level K, modulo 10^9+7.", "constraint": "1 <= H,W <= 1000\n0 <= K <= 10^{18}\nEach s_{ij} is either # or ..\nAll black cells in the given grid are 4-connected.\nThere is at least one black cell in the given grid.", "input": "Input The input is given from Standard Input in the following format:\nH W K\ns_{11} . . s_{1W}\n:\ns_{H1} . . s_{HW}", "output": "Print the number of connected components of black cells in the fractal of level K, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 3 3\n.#.\n###\n#.# output: 20\n\nThe fractal of level K=3 in this case is shown below. There are 20 connected components of black cells.\n\n.............#.............\n............###............\n............#.#............\n..........#..#..#..........\n.........#########.........\n.........#.##.##.#.........\n..........#.....#..........\n.........###...###.........\n.........#.#...#.#.........\n....#........#........#....\n...###......###......###...\n...#.#......#.#......#.#...\n.#..#..#..#..#..#..#..#..#.\n###########################\n#.##.##.##.##.##.##.##.##.#\n.#.....#..#.....#..#.....#.\n###...######...######...###\n#.#...#.##.#...#.##.#...#.#\n....#.................#....\n...###...............###...\n...#.#...............#.#...\n.#..#..#...........#..#..#.\n#########.........#########\n#.##.##.#.........#.##.##.#\n.#.....#...........#.....#.\n###...###.........###...###\n#.#...#.#.........#.#...#.#", "input: 3 3 3\n###\n#.#\n### output: 1", "input: 11 15 1000000000000000000\n.....#.........\n....###........\n....####.......\n...######......\n...#######.....\n..##.###.##....\n..##########...\n.###.....####..\n.####...######.\n###############\n#.##..##..##..# output: 301811921"], "Pid": "p04024", "ProblemText": "Task Description: Problem Statement Snuke got a grid from his mother, as a birthday present. The grid has H rows and W columns. Each cell is painted black or white. All black cells are 4-connected, that is, it is possible to traverse from any black cell to any other black cell by just visiting black cells, where it is only allowed to move horizontally or vertically.\nThe color of the cell at the i-th row and j-th column (1 <= i <= H, 1 <= j <= W) is represented by a character s_{ij}. If s_{ij} is #, the cell is painted black. If s_{ij} is . , the cell is painted white. At least one cell is painted black.\nWe will define fractals as follows.\nThe fractal of level 0 is a 1 * 1 grid with a black cell.\nThe fractal of level k+1 is obtained by arranging smaller grids in H rows and W columns, following the pattern of the Snuke's grid.\nAt a position that corresponds to a black cell in the Snuke's grid, a copy of the fractal of level k is placed.\nAt a position that corresponds to a white cell in the Snuke's grid, a grid whose cells are all white, with the same dimensions as the fractal of level k, is placed.\nYou are given the description of the Snuke's grid, and an integer K. Find the number of connected components of black cells in the fractal of level K, modulo 10^9+7.\nTask Constraint: 1 <= H,W <= 1000\n0 <= K <= 10^{18}\nEach s_{ij} is either # or ..\nAll black cells in the given grid are 4-connected.\nThere is at least one black cell in the given grid.\nTask Input: Input The input is given from Standard Input in the following format:\nH W K\ns_{11} . . s_{1W}\n:\ns_{H1} . . s_{HW}\nTask Output: Print the number of connected components of black cells in the fractal of level K, modulo 10^9+7.\nTask Samples: input: 3 3 3\n.#.\n###\n#.# output: 20\n\nThe fractal of level K=3 in this case is shown below. There are 20 connected components of black cells.\n\n.............#.............\n............###............\n............#.#............\n..........#..#..#..........\n.........#########.........\n.........#.##.##.#.........\n..........#.....#..........\n.........###...###.........\n.........#.#...#.#.........\n....#........#........#....\n...###......###......###...\n...#.#......#.#......#.#...\n.#..#..#..#..#..#..#..#..#.\n###########################\n#.##.##.##.##.##.##.##.##.#\n.#.....#..#.....#..#.....#.\n###...######...######...###\n#.#...#.##.#...#.##.#...#.#\n....#.................#....\n...###...............###...\n...#.#...............#.#...\n.#..#..#...........#..#..#.\n#########.........#########\n#.##.##.#.........#.##.##.#\n.#.....#...........#.....#.\n###...###.........###...###\n#.#...#.#.........#.#...#.#\ninput: 3 3 3\n###\n#.#\n### output: 1\ninput: 11 15 1000000000000000000\n.....#.........\n....###........\n....####.......\n...######......\n...#######.....\n..##.###.##....\n..##########...\n.###.....####..\n.####...######.\n###############\n#.##..##..##..# output: 301811921\n\n" }, { "title": "", "content": "Problem Statement Evi has N integers a_1, a_2, . . , a_N. His objective is to have N equal integers by transforming some of them.\nHe may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i! =j), he has to pay the cost separately for transforming each of them (See Sample 2).\nFind the minimum total cost to achieve his objective.", "constraint": "1<=N<=100\n-100<=a_i<=100", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum total cost to achieve Evi's objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4 8 output: 8\n\nTransforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.", "input: 3\n1 1 3 output: 3\n\nTransforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.", "input: 3\n4 2 5 output: 5\n\nLeaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.", "input: 4\n-100 -100 -100 -100 output: 0\n\nWithout transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0."], "Pid": "p04025", "ProblemText": "Task Description: Problem Statement Evi has N integers a_1, a_2, . . , a_N. His objective is to have N equal integers by transforming some of them.\nHe may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i! =j), he has to pay the cost separately for transforming each of them (See Sample 2).\nFind the minimum total cost to achieve his objective.\nTask Constraint: 1<=N<=100\n-100<=a_i<=100\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum total cost to achieve Evi's objective.\nTask Samples: input: 2\n4 8 output: 8\n\nTransforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.\ninput: 3\n1 1 3 output: 3\n\nTransforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.\ninput: 3\n4 2 5 output: 5\n\nLeaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.\ninput: 4\n-100 -100 -100 -100 output: 0\n\nWithout transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.\n\n" }, { "title": "", "content": "Problem Statement Given a string t, we will call it unbalanced if and only if the length of t is at least 2, and more than half of the letters in t are the same. For example, both voodoo and melee are unbalanced, while neither noon nor a is.\nYou are given a string s consisting of lowercase letters. Determine if there exists a (contiguous) substring of s that is unbalanced. If the answer is positive, show a position where such a substring occurs in s. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 2 <= N <= 100.", "constraint": "2 <= |s| <= 10^5\ns consists of lowercase letters.", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "If there exists no unbalanced substring of s, print -1 -1.\nIf there exists an unbalanced substring of s, let one such substring be s_a s_{a+1} . . . s_{b} (1 <= a < b <= |s|), and print a b. If there exists more than one such substring, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: needed output: 2 5\n\nThe string s_2 s_3 s_4 s_5 = eede is unbalanced. There are also other unbalanced substrings. For example, the output 2 6 will also be accepted.", "input: atcoder output: -1 -1\n\nThe string atcoder contains no unbalanced substring."], "Pid": "p04026", "ProblemText": "Task Description: Problem Statement Given a string t, we will call it unbalanced if and only if the length of t is at least 2, and more than half of the letters in t are the same. For example, both voodoo and melee are unbalanced, while neither noon nor a is.\nYou are given a string s consisting of lowercase letters. Determine if there exists a (contiguous) substring of s that is unbalanced. If the answer is positive, show a position where such a substring occurs in s. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 2 <= N <= 100.\nTask Constraint: 2 <= |s| <= 10^5\ns consists of lowercase letters.\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: If there exists no unbalanced substring of s, print -1 -1.\nIf there exists an unbalanced substring of s, let one such substring be s_a s_{a+1} . . . s_{b} (1 <= a < b <= |s|), and print a b. If there exists more than one such substring, any of them will be accepted.\nTask Samples: input: needed output: 2 5\n\nThe string s_2 s_3 s_4 s_5 = eede is unbalanced. There are also other unbalanced substrings. For example, the output 2 6 will also be accepted.\ninput: atcoder output: -1 -1\n\nThe string atcoder contains no unbalanced substring.\n\n" }, { "title": "", "content": "Problem Statement12: 17 (UTC): The sample input 1 and 2 were swapped. The error is now fixed. We are very sorry for your inconvenience.\nThere are N children in At Coder Kindergarten, conveniently numbered 1 through N. Mr. Evi will distribute C indistinguishable candies to the children.\nIf child i is given a candies, the child's happiness will become x_i^a, where x_i is the child's excitement level. The activity level of the kindergarten is the product of the happiness of all the N children.\nFor each possible way to distribute C candies to the children by giving zero or more candies to each child, calculate the activity level of the kindergarten. Then, calculate the sum over all possible way to distribute C candies. This sum can be seen as a function of the children's excitement levels x_1, . . , x_N, thus we call it f(x_1, . . , x_N).\nYou are given integers A_i, B_i (1<=i<=N). Find modulo 10^9+7. partial score: Partial Score\n400 points will be awarded for passing the test set satisfying A_i=B_i (1<=i<=N).", "constraint": "1<=N<=400\n1<=C<=400\n1<=A_i<=B_i<=400 (1<=i<=N)", "input": "Input The input is given from Standard Input in the following format:\nN C\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N", "output": "Print the value of modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2 3\n1 1\n1 1 output: 4\n\nThis case is included in the test set for the partial score, since A_i=B_i.\nWe only have to consider the sum of the activity level of the kindergarten where the excitement level of both child 1 and child 2 are 1 (f(1,1)).\n\nIf child 1 is given 0 candy, and child 2 is given 3 candies, the activity level of the kindergarten is 1^0*1^3=1.\nIf child 1 is given 1 candy, and child 2 is given 2 candies, the activity level of the kindergarten is 1^1*1^2=1.\nIf child 1 is given 2 candies, and child 2 is given 1 candy, the activity level of the kindergarten is 1^2*1^1=1.\nIf child 1 is given 3 candies, and child 2 is given 0 candy, the activity level of the kindergarten is 1^3*1^0=1.\n\nThus, f(1,1)=1+1+1+1=4, and the sum over all f is also 4.", "input: 1 2\n1\n3 output: 14\n\nSince there is only one child, child 1's happiness itself will be the activity level of the kindergarten. Since the only possible way to distribute 2 candies is to give both candies to child 1, the activity level in this case will become the value of f.\n\nWhen the excitement level of child 1 is 1, f(1)=1^2=1.\nWhen the excitement level of child 1 is 2, f(2)=2^2=4.\nWhen the excitement level of child 1 is 3, f(3)=3^2=9.\n\nThus, the answer is 1+4+9=14.", "input: 2 3\n1 1\n2 2 output: 66\n\nSince it can be seen that f(1,1)=4 , f(1,2)=15 , f(2,1)=15 , f(2,2)=32, the answer is 4+15+15+32=66.", "input: 4 8\n3 1 4 1\n3 1 4 1 output: 421749\n\nThis case is included in the test set for the partial score.", "input: 3 100\n7 6 5\n9 9 9 output: 139123417"], "Pid": "p04027", "ProblemText": "Task Description: Problem Statement12: 17 (UTC): The sample input 1 and 2 were swapped. The error is now fixed. We are very sorry for your inconvenience.\nThere are N children in At Coder Kindergarten, conveniently numbered 1 through N. Mr. Evi will distribute C indistinguishable candies to the children.\nIf child i is given a candies, the child's happiness will become x_i^a, where x_i is the child's excitement level. The activity level of the kindergarten is the product of the happiness of all the N children.\nFor each possible way to distribute C candies to the children by giving zero or more candies to each child, calculate the activity level of the kindergarten. Then, calculate the sum over all possible way to distribute C candies. This sum can be seen as a function of the children's excitement levels x_1, . . , x_N, thus we call it f(x_1, . . , x_N).\nYou are given integers A_i, B_i (1<=i<=N). Find modulo 10^9+7. partial score: Partial Score\n400 points will be awarded for passing the test set satisfying A_i=B_i (1<=i<=N).\nTask Constraint: 1<=N<=400\n1<=C<=400\n1<=A_i<=B_i<=400 (1<=i<=N)\nTask Input: Input The input is given from Standard Input in the following format:\nN C\nA_1 A_2 . . . A_N\nB_1 B_2 . . . B_N\nTask Output: Print the value of modulo 10^9+7.\nTask Samples: input: 2 3\n1 1\n1 1 output: 4\n\nThis case is included in the test set for the partial score, since A_i=B_i.\nWe only have to consider the sum of the activity level of the kindergarten where the excitement level of both child 1 and child 2 are 1 (f(1,1)).\n\nIf child 1 is given 0 candy, and child 2 is given 3 candies, the activity level of the kindergarten is 1^0*1^3=1.\nIf child 1 is given 1 candy, and child 2 is given 2 candies, the activity level of the kindergarten is 1^1*1^2=1.\nIf child 1 is given 2 candies, and child 2 is given 1 candy, the activity level of the kindergarten is 1^2*1^1=1.\nIf child 1 is given 3 candies, and child 2 is given 0 candy, the activity level of the kindergarten is 1^3*1^0=1.\n\nThus, f(1,1)=1+1+1+1=4, and the sum over all f is also 4.\ninput: 1 2\n1\n3 output: 14\n\nSince there is only one child, child 1's happiness itself will be the activity level of the kindergarten. Since the only possible way to distribute 2 candies is to give both candies to child 1, the activity level in this case will become the value of f.\n\nWhen the excitement level of child 1 is 1, f(1)=1^2=1.\nWhen the excitement level of child 1 is 2, f(2)=2^2=4.\nWhen the excitement level of child 1 is 3, f(3)=3^2=9.\n\nThus, the answer is 1+4+9=14.\ninput: 2 3\n1 1\n2 2 output: 66\n\nSince it can be seen that f(1,1)=4 , f(1,2)=15 , f(2,1)=15 , f(2,2)=32, the answer is 4+15+15+32=66.\ninput: 4 8\n3 1 4 1\n3 1 4 1 output: 421749\n\nThis case is included in the test set for the partial score.\ninput: 3 100\n7 6 5\n9 9 9 output: 139123417\n\n" }, { "title": "", "content": "Problem Statement Sig has built his own keyboard. Designed for ultimate simplicity, this keyboard only has 3 keys on it: the 0 key, the 1 key and the backspace key.\nTo begin with, he is using a plain text editor with this keyboard. This editor always displays one string (possibly empty). Just after the editor is launched, this string is empty. When each key on the keyboard is pressed, the following changes occur to the string:\n\nThe 0 key: a letter 0 will be inserted to the right of the string.\nThe 1 key: a letter 1 will be inserted to the right of the string.\nThe backspace key: if the string is empty, nothing happens. Otherwise, the rightmost letter of the string is deleted.\n\nSig has launched the editor, and pressed these keys N times in total. As a result, the editor displays a string s. Find the number of such ways to press the keys, modulo 10^9 + 7. partial score: Partial Score\n400 points will be awarded for passing the test set satisfying 1 <= N <= 300.", "constraint": "1 <= N <= 5000\n1 <= |s| <= N\ns consists of the letters 0 and 1.", "input": "Input The input is given from Standard Input in the following format:\nN\ns", "output": "Print the number of the ways to press the keys N times in total such that the editor displays the string s in the end, modulo 10^9+7.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3\n0 output: 5\n\nWe will denote the backspace key by B. The following 5 ways to press the keys will cause the editor to display the string 0 in the end: 00B, 01B, 0B0,1B0, BB0. In the last way, nothing will happen when the backspace key is pressed.", "input: 300\n1100100 output: 519054663", "input: 5000\n01000001011101000100001101101111011001000110010101110010000 output: 500886057"], "Pid": "p04028", "ProblemText": "Task Description: Problem Statement Sig has built his own keyboard. Designed for ultimate simplicity, this keyboard only has 3 keys on it: the 0 key, the 1 key and the backspace key.\nTo begin with, he is using a plain text editor with this keyboard. This editor always displays one string (possibly empty). Just after the editor is launched, this string is empty. When each key on the keyboard is pressed, the following changes occur to the string:\n\nThe 0 key: a letter 0 will be inserted to the right of the string.\nThe 1 key: a letter 1 will be inserted to the right of the string.\nThe backspace key: if the string is empty, nothing happens. Otherwise, the rightmost letter of the string is deleted.\n\nSig has launched the editor, and pressed these keys N times in total. As a result, the editor displays a string s. Find the number of such ways to press the keys, modulo 10^9 + 7. partial score: Partial Score\n400 points will be awarded for passing the test set satisfying 1 <= N <= 300.\nTask Constraint: 1 <= N <= 5000\n1 <= |s| <= N\ns consists of the letters 0 and 1.\nTask Input: Input The input is given from Standard Input in the following format:\nN\ns\nTask Output: Print the number of the ways to press the keys N times in total such that the editor displays the string s in the end, modulo 10^9+7.\nTask Samples: input: 3\n0 output: 5\n\nWe will denote the backspace key by B. The following 5 ways to press the keys will cause the editor to display the string 0 in the end: 00B, 01B, 0B0,1B0, BB0. In the last way, nothing will happen when the backspace key is pressed.\ninput: 300\n1100100 output: 519054663\ninput: 5000\n01000001011101000100001101101111011001000110010101110010000 output: 500886057\n\n" }, { "title": "", "content": "Problem Statement There are N children in At Coder Kindergarten. Mr. Evi will arrange the children in a line, then give 1 candy to the first child in the line, 2 candies to the second child, . . . , N candies to the N-th child. How many candies will be necessary in total?", "constraint": "1<=N<=100", "input": "Input The input is given from Standard Input in the following format:\nN", "output": "Print the necessary number of candies in total.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 output: 6\n\nThe answer is 1+2+3=6.", "input: 10 output: 55\n\nThe sum of the integers from 1 to 10 is 55.", "input: 1 output: 1\n\nOnly one child. The answer is 1 in this case."], "Pid": "p04029", "ProblemText": "Task Description: Problem Statement There are N children in At Coder Kindergarten. Mr. Evi will arrange the children in a line, then give 1 candy to the first child in the line, 2 candies to the second child, . . . , N candies to the N-th child. How many candies will be necessary in total?\nTask Constraint: 1<=N<=100\nTask Input: Input The input is given from Standard Input in the following format:\nN\nTask Output: Print the necessary number of candies in total.\nTask Samples: input: 3 output: 6\n\nThe answer is 1+2+3=6.\ninput: 10 output: 55\n\nThe sum of the integers from 1 to 10 is 55.\ninput: 1 output: 1\n\nOnly one child. The answer is 1 in this case.\n\n" }, { "title": "", "content": "Problem Statement Sig has built his own keyboard. Designed for ultimate simplicity, this keyboard only has 3 keys on it: the 0 key, the 1 key and the backspace key.\nTo begin with, he is using a plain text editor with this keyboard. This editor always displays one string (possibly empty). Just after the editor is launched, this string is empty. When each key on the keyboard is pressed, the following changes occur to the string:\n\nThe 0 key: a letter 0 will be inserted to the right of the string.\nThe 1 key: a letter 1 will be inserted to the right of the string.\nThe backspace key: if the string is empty, nothing happens. Otherwise, the rightmost letter of the string is deleted.\n\nSig has launched the editor, and pressed these keys several times. You are given a string s, which is a record of his keystrokes in order. In this string, the letter 0 stands for the 0 key, the letter 1 stands for the 1 key and the letter B stands for the backspace key. What string is displayed in the editor now?", "constraint": "1 <= |s| <= 10 (|s| denotes the length of s)\ns consists of the letters 0,1 and B.\nThe correct answer is not an empty string.", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "Print the string displayed in the editor in the end.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 01B0 output: 00\n\nEach time the key is pressed, the string in the editor will change as follows: 0,01,0,00.", "input: 0BB1 output: 1\n\nEach time the key is pressed, the string in the editor will change as follows: 0, (empty), (empty), 1."], "Pid": "p04030", "ProblemText": "Task Description: Problem Statement Sig has built his own keyboard. Designed for ultimate simplicity, this keyboard only has 3 keys on it: the 0 key, the 1 key and the backspace key.\nTo begin with, he is using a plain text editor with this keyboard. This editor always displays one string (possibly empty). Just after the editor is launched, this string is empty. When each key on the keyboard is pressed, the following changes occur to the string:\n\nThe 0 key: a letter 0 will be inserted to the right of the string.\nThe 1 key: a letter 1 will be inserted to the right of the string.\nThe backspace key: if the string is empty, nothing happens. Otherwise, the rightmost letter of the string is deleted.\n\nSig has launched the editor, and pressed these keys several times. You are given a string s, which is a record of his keystrokes in order. In this string, the letter 0 stands for the 0 key, the letter 1 stands for the 1 key and the letter B stands for the backspace key. What string is displayed in the editor now?\nTask Constraint: 1 <= |s| <= 10 (|s| denotes the length of s)\ns consists of the letters 0,1 and B.\nThe correct answer is not an empty string.\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: Print the string displayed in the editor in the end.\nTask Samples: input: 01B0 output: 00\n\nEach time the key is pressed, the string in the editor will change as follows: 0,01,0,00.\ninput: 0BB1 output: 1\n\nEach time the key is pressed, the string in the editor will change as follows: 0, (empty), (empty), 1.\n\n" }, { "title": "", "content": "Problem Statement Evi has N integers a_1, a_2, . . , a_N. His objective is to have N equal integers by transforming some of them.\nHe may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i! =j), he has to pay the cost separately for transforming each of them (See Sample 2).\nFind the minimum total cost to achieve his objective.", "constraint": "1<=N<=100\n-100<=a_i<=100", "input": "Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N", "output": "Print the minimum total cost to achieve Evi's objective.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 2\n4 8 output: 8\n\nTransforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.", "input: 3\n1 1 3 output: 3\n\nTransforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.", "input: 3\n4 2 5 output: 5\n\nLeaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.", "input: 4\n-100 -100 -100 -100 output: 0\n\nWithout transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0."], "Pid": "p04031", "ProblemText": "Task Description: Problem Statement Evi has N integers a_1, a_2, . . , a_N. His objective is to have N equal integers by transforming some of them.\nHe may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i! =j), he has to pay the cost separately for transforming each of them (See Sample 2).\nFind the minimum total cost to achieve his objective.\nTask Constraint: 1<=N<=100\n-100<=a_i<=100\nTask Input: Input The input is given from Standard Input in the following format:\nN\na_1 a_2 . . . a_N\nTask Output: Print the minimum total cost to achieve Evi's objective.\nTask Samples: input: 2\n4 8 output: 8\n\nTransforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.\ninput: 3\n1 1 3 output: 3\n\nTransforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.\ninput: 3\n4 2 5 output: 5\n\nLeaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.\ninput: 4\n-100 -100 -100 -100 output: 0\n\nWithout transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.\n\n" }, { "title": "", "content": "Problem Statement Given a string t, we will call it unbalanced if and only if the length of t is at least 2, and more than half of the letters in t are the same. For example, both voodoo and melee are unbalanced, while neither noon nor a is.\nYou are given a string s consisting of lowercase letters. Determine if there exists a (contiguous) substring of s that is unbalanced. If the answer is positive, show a position where such a substring occurs in s. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 2 <= N <= 100.", "constraint": "2 <= |s| <= 10^5\ns consists of lowercase letters.", "input": "Input The input is given from Standard Input in the following format:\ns", "output": "If there exists no unbalanced substring of s, print -1 -1.\nIf there exists an unbalanced substring of s, let one such substring be s_a s_{a+1} . . . s_{b} (1 <= a < b <= |s|), and print a b. If there exists more than one such substring, any of them will be accepted.", "content_img": false, "lang": "en", "error": false, "samples": ["input: needed output: 2 5\n\nThe string s_2 s_3 s_4 s_5 = eede is unbalanced. There are also other unbalanced substrings. For example, the output 2 6 will also be accepted.", "input: atcoder output: -1 -1\n\nThe string atcoder contains no unbalanced substring."], "Pid": "p04032", "ProblemText": "Task Description: Problem Statement Given a string t, we will call it unbalanced if and only if the length of t is at least 2, and more than half of the letters in t are the same. For example, both voodoo and melee are unbalanced, while neither noon nor a is.\nYou are given a string s consisting of lowercase letters. Determine if there exists a (contiguous) substring of s that is unbalanced. If the answer is positive, show a position where such a substring occurs in s. partial score: Partial Score\n200 points will be awarded for passing the test set satisfying 2 <= N <= 100.\nTask Constraint: 2 <= |s| <= 10^5\ns consists of lowercase letters.\nTask Input: Input The input is given from Standard Input in the following format:\ns\nTask Output: If there exists no unbalanced substring of s, print -1 -1.\nIf there exists an unbalanced substring of s, let one such substring be s_a s_{a+1} . . . s_{b} (1 <= a < b <= |s|), and print a b. If there exists more than one such substring, any of them will be accepted.\nTask Samples: input: needed output: 2 5\n\nThe string s_2 s_3 s_4 s_5 = eede is unbalanced. There are also other unbalanced substrings. For example, the output 2 6 will also be accepted.\ninput: atcoder output: -1 -1\n\nThe string atcoder contains no unbalanced substring.\n\n" }, { "title": "", "content": "Problem Statement You are given two integers a and b (a<=b). Determine if the product of the integers a, a+1, …, b is positive, negative or zero. partial score: Partial Score\nIn test cases worth 100 points, -10<=a<=b<=10.", "constraint": "a and b are integers.\n-10^9<=a<=b<=10^9", "input": "Input The input is given from Standard Input in the following format:\na b", "output": "If the product is positive, print Positive. If it is negative, print Negative. If it is zero, print Zero.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 1 3 output: Positive\n\n1*2*3=6 is positive.", "input: -3 -1 output: Negative\n\n(-3)*(-2)*(-1)=-6 is negative.", "input: -1 1 output: Zero\n\n(-1)*0*1=0."], "Pid": "p04033", "ProblemText": "Task Description: Problem Statement You are given two integers a and b (a<=b). Determine if the product of the integers a, a+1, …, b is positive, negative or zero. partial score: Partial Score\nIn test cases worth 100 points, -10<=a<=b<=10.\nTask Constraint: a and b are integers.\n-10^9<=a<=b<=10^9\nTask Input: Input The input is given from Standard Input in the following format:\na b\nTask Output: If the product is positive, print Positive. If it is negative, print Negative. If it is zero, print Zero.\nTask Samples: input: 1 3 output: Positive\n\n1*2*3=6 is positive.\ninput: -3 -1 output: Negative\n\n(-3)*(-2)*(-1)=-6 is negative.\ninput: -1 1 output: Zero\n\n(-1)*0*1=0.\n\n" }, { "title": "", "content": "Problem Statement We have N boxes, numbered 1 through N. At first, box 1 contains one red ball, and each of the other boxes contains one white ball.\nSnuke will perform the following M operations, one by one. In the i-th operation, he randomly picks one ball from box x_i, then he puts it into box y_i.\nFind the number of boxes that may contain the red ball after all operations are performed.", "constraint": "2<=N<=10^5\n1<=M<=10^5\n1<=x_i,y_i<=N\nx_i!=y_i\nJust before the i-th operation is performed, box x_i contains at least 1 ball.", "input": "Input The input is given from Standard Input in the following format:\nN M\nx_1 y_1\n:\nx_M y_M", "output": "Print the number of boxes that may contain the red ball after all operations are performed.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 2\n1 2\n2 3 output: 2\n\nJust after the first operation, box 1 is empty, box 2 contains one red ball and one white ball, and box 3 contains one white ball.\nNow, consider the second operation. If Snuke picks the red ball from box 2, the red ball will go into box 3. If he picks the white ball instead, the red ball will stay in box 2.\nThus, the number of boxes that may contain the red ball after all operations, is 2.", "input: 3 3\n1 2\n2 3\n2 3 output: 1\n\nAll balls will go into box 3.", "input: 4 4\n1 2\n2 3\n4 1\n3 4 output: 3"], "Pid": "p04034", "ProblemText": "Task Description: Problem Statement We have N boxes, numbered 1 through N. At first, box 1 contains one red ball, and each of the other boxes contains one white ball.\nSnuke will perform the following M operations, one by one. In the i-th operation, he randomly picks one ball from box x_i, then he puts it into box y_i.\nFind the number of boxes that may contain the red ball after all operations are performed.\nTask Constraint: 2<=N<=10^5\n1<=M<=10^5\n1<=x_i,y_i<=N\nx_i!=y_i\nJust before the i-th operation is performed, box x_i contains at least 1 ball.\nTask Input: Input The input is given from Standard Input in the following format:\nN M\nx_1 y_1\n:\nx_M y_M\nTask Output: Print the number of boxes that may contain the red ball after all operations are performed.\nTask Samples: input: 3 2\n1 2\n2 3 output: 2\n\nJust after the first operation, box 1 is empty, box 2 contains one red ball and one white ball, and box 3 contains one white ball.\nNow, consider the second operation. If Snuke picks the red ball from box 2, the red ball will go into box 3. If he picks the white ball instead, the red ball will stay in box 2.\nThus, the number of boxes that may contain the red ball after all operations, is 2.\ninput: 3 3\n1 2\n2 3\n2 3 output: 1\n\nAll balls will go into box 3.\ninput: 4 4\n1 2\n2 3\n4 1\n3 4 output: 3\n\n" }, { "title": "", "content": "Problem Statement We have N pieces of ropes, numbered 1 through N. The length of piece i is a_i.\nAt first, for each i (1<=i<=N-1), piece i and piece i+1 are tied at the ends, forming one long rope with N-1 knots. Snuke will try to untie all of the knots by performing the following operation repeatedly:\n\nChoose a (connected) rope with a total length of at least L, then untie one of its knots.\n\nIs it possible to untie all of the N-1 knots by properly applying this operation? If the answer is positive, find one possible order to untie the knots.", "constraint": "2<=N<=10^5\n1<=L<=10^9\n1<=a_i<=10^9\nAll input values are integers.", "input": "Input The input is given from Standard Input in the following format:\nN L\na_1 a_2 . . . a_n", "output": "If it is not possible to untie all of the N-1 knots, print Impossible.\nIf it is possible to untie all of the knots, print Possible, then print another N-1 lines that describe a possible order to untie the knots. The j-th of those N-1 lines should contain the index of the knot that is untied in the j-th operation. Here, the index of the knot connecting piece i and piece i+1 is i.\nIf there is more than one solution, output any.", "content_img": false, "lang": "en", "error": false, "samples": ["input: 3 50\n30 20 10 output: Possible\n2\n1\n\nIf the knot 1 is untied first, the knot 2 will become impossible to untie.", "input: 2 21\n10 10 output: Impossible", "input: 5 50\n10 20 30 40 50 output: Possible\n1\n2\n3\n4\n\nAnother example of a possible solution is 3,4,1,2."], "Pid": "p04035", "ProblemText": "Task Description: Problem Statement We have N pieces of ropes, numbered 1 through N. The length of piece i is a_i.\nAt first, for each i (1<=i<=N-1), piece i and piece i+1 are tied at the ends, forming one long rope with N-1 knots. Snuke will try to untie all of the knots by performing the following operation repeatedly:\n\nChoose a (connected) rope with a total length of at least L, then untie one of its knots.\n\nIs it possible to untie all of the N-1 knots by properly applying this operation? If the answer is positive, find one possible order to untie the knots.\nTask Constraint: 2<=N<=10^5\n1<=L<=10^9\n1<=a_i<=10^9\nAll input values are integers.\nTask Input: Input The input is given from Standard Input in the following format:\nN L\na_1 a_2 . . . a_n\nTask Output: If it is not possible to untie all of the N-1 knots, print Impossible.\nIf it is possible to untie all of the knots, print Possible, then print another N-1 lines that describe a possible order to untie the knots. The j-th of those N-1 lines should contain the index of the knot that is untied in the j-th operation. Here, the index of the knot connecting piece i and piece i+1 is i.\nIf there is more than one solution, output any.\nTask Samples: input: 3 50\n30 20 10 output: Possible\n2\n1\n\nIf the knot 1 is untied first, the knot 2 will become impossible to untie.\ninput: 2 21\n10 10 output: Impossible\ninput: 5 50\n10 20 30 40 50 output: Possible\n1\n2\n3\n4\n\nAnother example of a possible solution is 3,4,1,2.\n\n" }, { "title": "", "content": "Problem Statement We have an undirected graph with N vertices and M edges. The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i connects vertices a_i and b_i. The graph is connected.\nOn this graph, Q pairs of brothers are participating in an activity called Stamp Rally. The Stamp Rally for the i-th pair will be as follows:\n\nOne brother starts from vertex x_i, and the other starts from vertex y_i.\nThe two explore the graph along the edges to visit z_i vertices in total, including the starting vertices. Here, a vertex is counted only once, even if it is visited multiple times, or visited by both brothers.\nThe score is defined as the largest index of the edges traversed by either of them. Their objective is to minimize this value.\n\nFind the minimum possible score for each pair.", "constraint": "3<=N<=10^5\nN-1<=M<=10^5\n1<=a_i